LMFDB - Embedded newform 1512.2.s.m.865.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1512,2,Mod(865,1512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1512, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1512.865");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1512 = 2^{3} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1512.s (of order $3$, degree $2$, 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:	$12.0733807856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.9391935744.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 12x^{5} - 76x^{4} + 84x^{3} + 245x^{2} - 1372x + 2401 $ x^8 - 4x^7 + 5x^6 + 12x^5 - 76x^4 + 84x^3 + 245x^2 - 1372*x + 2401
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			865.3
Root			$1.57052 + 2.12920i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.m.1297.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.366025 + 0.633975i) q^{5} +(-2.62920 + 0.295509i) q^{7} +O(q^{10})$	$q+(0.366025 + 0.633975i) q^{5} +(-2.62920 + 0.295509i) q^{7} +(-1.55868 + 2.69971i) q^{11} -2.32307 q^{13} +(3.09808 - 5.36603i) q^{17} +(3.36125 + 5.82185i) q^{19} +(-2.33369 - 4.04207i) q^{23} +(2.23205 - 3.86603i) q^{25} -9.24884 q^{29} +(-0.326629 + 0.565738i) q^{31} +(-1.14970 - 1.55868i) q^{35} +(-5.41993 - 9.38759i) q^{37} -12.4309 q^{41} +1.77062 q^{43} +(-5.50706 - 9.53850i) q^{47} +(6.82535 - 1.55390i) q^{49} +(-0.398363 + 0.689985i) q^{53} -2.28207 q^{55} +(-0.290731 + 0.503561i) q^{59} +(0.264389 + 0.457934i) q^{61} +(-0.850302 - 1.47277i) q^{65} +(-5.59330 + 9.68788i) q^{67} +6.34674 q^{71} +(-1.48816 + 2.57757i) q^{73} +(3.30029 - 7.55868i) q^{77} +(4.68788 + 8.11964i) q^{79} -11.0527 q^{83} +4.53590 q^{85} +(-5.89237 - 10.2059i) q^{89} +(6.10780 - 0.686487i) q^{91} +(-2.46060 + 4.26189i) q^{95} -1.77062 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 2 q^{7}+O(q^{10}) $ 8 * q - 4 * q^5 - 2 * q^7	$ 8 q - 4 q^{5} - 2 q^{7} - 2 q^{11} - 8 q^{13} + 4 q^{17} - 6 q^{19} + 2 q^{23} + 4 q^{25} + 16 q^{29} - 6 q^{31} - 2 q^{35} - 16 q^{41} - 20 q^{47} - 6 q^{49} - 10 q^{53} + 16 q^{55} + 22 q^{59} + 2 q^{61} - 14 q^{65} + 2 q^{67} + 44 q^{71} - 10 q^{73} + 54 q^{77} + 8 q^{79} - 40 q^{83} + 64 q^{85} - 16 q^{89} - 24 q^{91} - 30 q^{95}+O(q^{100}) $ 8 * q - 4 * q^5 - 2 * q^7 - 2 * q^11 - 8 * q^13 + 4 * q^17 - 6 * q^19 + 2 * q^23 + 4 * q^25 + 16 * q^29 - 6 * q^31 - 2 * q^35 - 16 * q^41 - 20 * q^47 - 6 * q^49 - 10 * q^53 + 16 * q^55 + 22 * q^59 + 2 * q^61 - 14 * q^65 + 2 * q^67 + 44 * q^71 - 10 * q^73 + 54 * q^77 + 8 * q^79 - 40 * q^83 + 64 * q^85 - 16 * q^89 - 24 * q^91 - 30 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1081$	$1135$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	0.366025	+	0.633975i	0.163692	+	0.283522i	0.936190	−	0.351495i	$-0.114326\pi$
$5$	0.366025	+	0.633975i	0.163692	+	0.283522i	−0.772498	+	0.635017i	$0.780993\pi$
$6$		0			0
$7$	−2.62920	+	0.295509i	−0.993743	+	0.111692i
$7$	−2.62920	+	0.295509i	−0.993743	+	0.111692i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.55868	+	2.69971i	−0.469960	+	0.813994i	−0.999410	−	0.0343469i	$-0.989065\pi$
$11$	−1.55868	+	2.69971i	−0.469960	+	0.813994i	0.529450	+	0.848341i	$0.322398\pi$
$12$		0			0
$13$	−2.32307			−0.644303			−0.322152	−	0.946688i	$-0.604406\pi$
$13$	−2.32307			−0.644303			−0.322152	+	0.946688i	$0.604406\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.09808	−	5.36603i	0.751394	−	1.30145i	−0.195753	−	0.980653i	$-0.562715\pi$
$17$	3.09808	−	5.36603i	0.751394	−	1.30145i	0.947147	−	0.320799i	$-0.103951\pi$
$18$		0			0
$19$	3.36125	+	5.82185i	0.771123	+	1.33562i	0.936948	+	0.349469i	$0.113638\pi$
$19$	3.36125	+	5.82185i	0.771123	+	1.33562i	−0.165825	+	0.986155i	$0.553029\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2.33369	−	4.04207i	−0.486608	−	0.842829i	0.513274	−	0.858225i	$-0.328432\pi$
$23$	−2.33369	−	4.04207i	−0.486608	−	0.842829i	−0.999881	+	0.0153959i	$0.995099\pi$
$24$		0			0
$25$	2.23205	−	3.86603i	0.446410	−	0.773205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−9.24884			−1.71747			−0.858733	−	0.512423i	$-0.828748\pi$
$29$	−9.24884			−1.71747			−0.858733	+	0.512423i	$0.828748\pi$
$30$		0			0
$31$	−0.326629	+	0.565738i	−0.0586643	+	0.101610i	−0.893866	−	0.448334i	$-0.852018\pi$
$31$	−0.326629	+	0.565738i	−0.0586643	+	0.101610i	0.835202	+	0.549944i	$0.185351\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.14970	−	1.55868i	−0.194334	−	0.263465i
$36$		0			0
$37$	−5.41993	−	9.38759i	−0.891031	−	1.54331i	−0.838642	−	0.544683i	$-0.816650\pi$
$37$	−5.41993	−	9.38759i	−0.891031	−	1.54331i	−0.0523889	−	0.998627i	$-0.516684\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−12.4309			−1.94138			−0.970688	−	0.240343i	$-0.922740\pi$
$41$	−12.4309			−1.94138			−0.970688	+	0.240343i	$0.922740\pi$
$42$		0			0
$43$	1.77062			0.270017			0.135008	−	0.990844i	$-0.456894\pi$
$43$	1.77062			0.270017			0.135008	+	0.990844i	$0.456894\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.50706	−	9.53850i	−0.803287	−	1.39133i	−0.917441	−	0.397871i	$-0.869749\pi$
$47$	−5.50706	−	9.53850i	−0.803287	−	1.39133i	0.114154	−	0.993463i	$-0.463584\pi$
$48$		0			0
$49$	6.82535	−	1.55390i	0.975050	−	0.221986i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−0.398363	+	0.689985i	−0.0547194	+	0.0947768i	−0.892088	−	0.451863i	$-0.850760\pi$
$53$	−0.398363	+	0.689985i	−0.0547194	+	0.0947768i	0.837368	+	0.546639i	$0.184093\pi$
$54$		0			0
$55$	−2.28207			−0.307714
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.290731	+	0.503561i	−0.0378499	+	0.0655580i	−0.884330	−	0.466863i	$-0.845384\pi$
$59$	−0.290731	+	0.503561i	−0.0378499	+	0.0655580i	0.846480	+	0.532421i	$0.178718\pi$
$60$		0			0
$61$	0.264389	+	0.457934i	0.0338515	+	0.0586325i	0.882455	−	0.470397i	$-0.155889\pi$
$61$	0.264389	+	0.457934i	0.0338515	+	0.0586325i	−0.848603	+	0.529030i	$0.822556\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.850302	−	1.47277i	−0.105467	−	0.182674i
$66$		0			0
$67$	−5.59330	+	9.68788i	−0.683330	+	1.18356i	0.290628	+	0.956836i	$0.406136\pi$
$67$	−5.59330	+	9.68788i	−0.683330	+	1.18356i	−0.973958	+	0.226726i	$0.927198\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	6.34674			0.753220			0.376610	−	0.926372i	$-0.377090\pi$
$71$	6.34674			0.753220			0.376610	+	0.926372i	$0.377090\pi$
$72$		0			0
$73$	−1.48816	+	2.57757i	−0.174176	+	0.301682i	−0.939876	−	0.341516i	$-0.889060\pi$
$73$	−1.48816	+	2.57757i	−0.174176	+	0.301682i	0.765700	+	0.643198i	$0.222393\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.30029	−	7.55868i	0.376103	−	0.861392i
$78$		0			0
$79$	4.68788	+	8.11964i	0.527427	+	0.913531i	0.999489	+	0.0319654i	$0.0101766\pi$
$79$	4.68788	+	8.11964i	0.527427	+	0.913531i	−0.472062	+	0.881566i	$0.656490\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−11.0527			−1.21319			−0.606595	−	0.795011i	$-0.707465\pi$
$83$	−11.0527			−1.21319			−0.606595	+	0.795011i	$0.707465\pi$
$84$		0			0
$85$	4.53590			0.491987
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.89237	−	10.2059i	−0.624590	−	1.08182i	−0.988620	−	0.150434i	$-0.951933\pi$
$89$	−5.89237	−	10.2059i	−0.624590	−	1.08182i	0.364030	−	0.931387i	$-0.381400\pi$
$90$		0			0
$91$	6.10780	−	0.686487i	0.640272	−	0.0719634i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−2.46060	+	4.26189i	−0.252453	+	0.437261i
$96$		0			0
$97$	−1.77062			−0.179779			−0.0898895	−	0.995952i	$-0.528651\pi$
$97$	−1.77062			−0.179779			−0.0898895	+	0.995952i	$0.528651\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−4.67604	+	8.09914i	−0.465283	+	0.805894i	−0.999214	−	0.0396337i	$-0.987381\pi$
$101$	−4.67604	+	8.09914i	−0.465283	+	0.805894i	0.533931	+	0.845528i	$0.320714\pi$
$102$		0			0
$103$	−5.30257	−	9.18432i	−0.522477	−	0.904958i	−0.999658	−	0.0261522i	$-0.991675\pi$
$103$	−5.30257	−	9.18432i	−0.522477	−	0.904958i	0.477180	−	0.878805i	$-0.341659\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−5.44043	−	9.42310i	−0.525946	−	0.910965i	−0.999543	−	0.0302237i	$-0.990378\pi$
$107$	−5.44043	−	9.42310i	−0.525946	−	0.910965i	0.473597	−	0.880742i	$-0.342955\pi$
$108$		0			0
$109$	1.73561	−	3.00617i	0.166241	−	0.287939i	−0.770854	−	0.637012i	$-0.780170\pi$
$109$	1.73561	−	3.00617i	0.166241	−	0.287939i	0.937095	+	0.349073i	$0.113504\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.3276			1.15969			0.579843	−	0.814728i	$-0.303114\pi$
$113$	12.3276			1.15969			0.579843	+	0.814728i	$0.303114\pi$
$114$		0			0
$115$	1.70838	−	2.95900i	0.159307	−	0.275928i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.55974	+	15.0238i	−0.601331	+	1.37723i
$120$		0			0
$121$	0.641033	+	1.11030i	0.0582757	+	0.100937i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.92820			0.619677
$126$		0			0
$127$	−10.1174			−0.897771			−0.448885	−	0.893589i	$-0.648179\pi$
$127$	−10.1174			−0.897771			−0.448885	+	0.893589i	$0.648179\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.65676	−	8.06574i	−0.406863	−	0.704707i	0.587674	−	0.809098i	$-0.300044\pi$
$131$	−4.65676	−	8.06574i	−0.406863	−	0.704707i	−0.994536	+	0.104391i	$0.966711\pi$
$132$		0			0
$133$	−10.5578	−	14.3135i	−0.915476	−	1.24114i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.71900	+	11.6376i	−0.574043	+	0.994271i	0.422102	+	0.906548i	$0.361292\pi$
$137$	−6.71900	+	11.6376i	−0.574043	+	0.994271i	−0.996145	+	0.0877228i	$0.972041\pi$
$138$		0			0
$139$	8.90453			0.755272			0.377636	−	0.925954i	$-0.376737\pi$
$139$	8.90453			0.755272			0.377636	+	0.925954i	$0.376737\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	3.62092	−	6.27162i	0.302797	−	0.524459i
$144$		0			0
$145$	−3.38531	−	5.86353i	−0.281135	−	0.486939i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−1.63397	−	2.83013i	−0.133860	−	0.231853i	0.791301	−	0.611427i	$-0.209404\pi$
$149$	−1.63397	−	2.83013i	−0.133860	−	0.231853i	−0.925162	+	0.379574i	$0.876071\pi$
$150$		0			0
$151$	−3.79073	+	6.56574i	−0.308485	+	0.534312i	−0.978031	−	0.208458i	$-0.933155\pi$
$151$	−3.79073	+	6.56574i	−0.308485	+	0.534312i	0.669546	+	0.742771i	$0.266489\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.478218			−0.0384114
$156$		0			0
$157$	5.31351	−	9.20327i	0.424064	−	0.734501i	−0.572268	−	0.820067i	$-0.693936\pi$
$157$	5.31351	−	9.20327i	0.424064	−	0.734501i	0.996333	+	0.0855654i	$0.0272697\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	7.33019	+	9.93776i	0.577700	+	0.783205i
$162$		0			0
$163$	9.75839	+	16.9020i	0.764336	+	1.32387i	0.940597	+	0.339526i	$0.110267\pi$
$163$	9.75839	+	16.9020i	0.764336	+	1.32387i	−0.176260	+	0.984344i	$0.556400\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	12.2156			0.945272			0.472636	−	0.881258i	$-0.343303\pi$
$167$	12.2156			0.945272			0.472636	+	0.881258i	$0.343303\pi$
$168$		0			0
$169$	−7.60335			−0.584873
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.80735	−	15.2548i	−0.669610	−	1.15980i	−0.978013	−	0.208543i	$-0.933128\pi$
$173$	−8.80735	−	15.2548i	−0.669610	−	1.15980i	0.308403	−	0.951256i	$-0.400205\pi$
$174$		0			0
$175$	−4.72606	+	10.8241i	−0.357256	+	0.818227i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−1.37558	+	2.38258i	−0.102816	+	0.178082i	−0.912844	−	0.408309i	$-0.866119\pi$
$179$	−1.37558	+	2.38258i	−0.102816	+	0.178082i	0.810028	+	0.586391i	$0.199452\pi$
$180$		0			0
$181$	8.07636			0.600311			0.300155	−	0.953890i	$-0.402961\pi$
$181$	8.07636			0.600311			0.300155	+	0.953890i	$0.402961\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	3.96766	−	6.87219i	0.291708	−	0.505254i
$186$		0			0
$187$	9.65782	+	16.7278i	0.706250	+	1.22326i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−0.712767	−	1.23455i	−0.0515740	−	0.0893288i	0.839086	−	0.543999i	$-0.183090\pi$
$191$	−0.712767	−	1.23455i	−0.0515740	−	0.0893288i	−0.890660	+	0.454670i	$0.849757\pi$
$192$		0			0
$193$	2.24656	−	3.89115i	0.161711	−	0.280091i	−0.773772	−	0.633465i	$-0.781632\pi$
$193$	2.24656	−	3.89115i	0.161711	−	0.280091i	0.935482	+	0.353374i	$0.114966\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	15.8706			1.13074			0.565368	−	0.824838i	$-0.308734\pi$
$197$	15.8706			1.13074			0.565368	+	0.824838i	$0.308734\pi$
$198$		0			0
$199$	−6.24528	+	10.8171i	−0.442716	+	0.766806i	−0.997890	−	0.0649277i	$-0.979318\pi$
$199$	−6.24528	+	10.8171i	−0.442716	+	0.766806i	0.555174	+	0.831734i	$0.312652\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	24.3170	−	2.73311i	1.70672	−	0.191827i
$204$		0			0
$205$	−4.55002	−	7.88086i	−0.317787	−	0.550423i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−20.9564			−1.44959
$210$		0			0
$211$	−25.9091			−1.78366			−0.891828	−	0.452375i	$-0.850577\pi$
$211$	−25.9091			−1.78366			−0.891828	+	0.452375i	$0.850577\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	0.648091	+	1.12253i	0.0441995	+	0.0765557i
$216$		0			0
$217$	0.691592	−	1.58396i	0.0469483	−	0.107526i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.19704	+	12.4656i	−0.484126	+	0.838530i
$222$		0			0
$223$	5.05268			0.338353			0.169176	−	0.985586i	$-0.445889\pi$
$223$	5.05268			0.338353			0.169176	+	0.985586i	$0.445889\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.45105	+	9.44149i	−0.361799	+	0.626654i	−0.988257	−	0.152801i	$-0.951171\pi$
$227$	−5.45105	+	9.44149i	−0.361799	+	0.626654i	0.626458	+	0.779455i	$0.284504\pi$
$228$		0			0
$229$	4.35030	+	7.53494i	0.287476	+	0.497923i	0.973207	−	0.229932i	$-0.0738505\pi$
$229$	4.35030	+	7.53494i	0.287476	+	0.497923i	−0.685731	+	0.727855i	$0.740517\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	2.35736	+	4.08307i	0.154436	+	0.267491i	0.932853	−	0.360256i	$-0.117311\pi$
$233$	2.35736	+	4.08307i	0.154436	+	0.267491i	−0.778418	+	0.627747i	$0.783977\pi$
$234$		0			0
$235$	4.03145	−	6.98267i	0.262983	−	0.455499i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−20.8232			−1.34694			−0.673470	−	0.739215i	$-0.735197\pi$
$239$	−20.8232			−1.34694			−0.673470	+	0.739215i	$0.735197\pi$
$240$		0			0
$241$	7.42577	−	12.8618i	0.478336	−	0.828502i	−0.521356	−	0.853339i	$-0.674574\pi$
$241$	7.42577	−	12.8618i	0.478336	−	0.828502i	0.999692	+	0.0248376i	$0.00790685\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.48339	+	3.75833i	0.222545	+	0.240111i
$246$		0			0
$247$	−7.80841	−	13.5246i	−0.496837	−	0.860547i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	6.13148			0.387015			0.193508	−	0.981099i	$-0.438014\pi$
$251$	6.13148			0.387015			0.193508	+	0.981099i	$0.438014\pi$
$252$		0			0
$253$	14.5499			0.914744
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.52634	+	9.57191i	0.344724	+	0.597079i	0.985304	−	0.170813i	$-0.0546393\pi$
$257$	5.52634	+	9.57191i	0.344724	+	0.597079i	−0.640580	+	0.767892i	$0.721306\pi$
$258$		0			0
$259$	17.0242	+	23.0802i	1.05783	+	1.43413i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−9.04645	+	15.6689i	−0.557828	+	0.966187i	0.439849	+	0.898072i	$0.355032\pi$
$263$	−9.04645	+	15.6689i	−0.557828	+	0.966187i	−0.997677	+	0.0681153i	$0.978301\pi$
$264$		0			0
$265$	−0.583244			−0.0358284
$266$		0			0
$267$		0			0
$268$		0			0
$269$	8.43087	−	14.6027i	0.514039	−	0.890342i	−0.485828	−	0.874054i	$-0.661482\pi$
$269$	8.43087	−	14.6027i	0.514039	−	0.890342i	0.999867	−	0.0162879i	$-0.00518482\pi$
$270$		0			0
$271$	−7.13504	−	12.3582i	−0.433423	−	0.750710i	0.563743	−	0.825950i	$-0.309361\pi$
$271$	−7.13504	−	12.3582i	−0.433423	−	0.750710i	−0.997165	+	0.0752403i	$0.976028\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.95811	+	12.0518i	0.419590	+	0.726750i
$276$		0			0
$277$	−2.17604	+	3.76901i	−0.130746	+	0.226458i	−0.923964	−	0.382479i	$-0.875070\pi$
$277$	−2.17604	+	3.76901i	−0.130746	+	0.226458i	0.793219	+	0.608937i	$0.208404\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	26.6917			1.59229			0.796147	−	0.605104i	$-0.206868\pi$
$281$	26.6917			1.59229			0.796147	+	0.605104i	$0.206868\pi$
$282$		0			0
$283$	2.23205	−	3.86603i	0.132682	−	0.229811i	−0.792028	−	0.610485i	$-0.790975\pi$
$283$	2.23205	−	3.86603i	0.132682	−	0.229811i	0.924709	+	0.380674i	$0.124308\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	32.6832	−	3.67343i	1.92923	−	0.216836i
$288$		0			0
$289$	−10.6962	−	18.5263i	−0.629185	−	1.08978i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	2.86353			0.167289			0.0836445	−	0.996496i	$-0.473344\pi$
$293$	2.86353			0.167289			0.0836445	+	0.996496i	$0.473344\pi$
$294$		0			0
$295$	−0.425660			−0.0247829
$296$		0			0
$297$		0			0
$298$		0			0
$299$	5.42132	+	9.39000i	0.313523	+	0.543037i
$300$		0			0
$301$	−4.65530	+	0.523234i	−0.268327	+	0.0301587i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.193546	+	0.335231i	−0.0110824	+	0.0191953i
$306$		0			0
$307$	4.17717			0.238403			0.119202	−	0.992870i	$-0.461966\pi$
$307$	4.17717			0.238403			0.119202	+	0.992870i	$0.461966\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	14.1401	−	24.4914i	0.801814	−	1.38878i	−0.116607	−	0.993178i	$-0.537202\pi$
$311$	14.1401	−	24.4914i	0.801814	−	1.38878i	0.918421	−	0.395604i	$-0.129465\pi$
$312$		0			0
$313$	−7.96638	−	13.7982i	−0.450287	−	0.779919i	0.548117	−	0.836402i	$-0.315345\pi$
$313$	−7.96638	−	13.7982i	−0.450287	−	0.779919i	−0.998404	+	0.0564825i	$0.982011\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.62792	+	16.6760i	0.540758	+	0.936620i	0.998861	+	0.0477206i	$0.0151957\pi$
$317$	9.62792	+	16.6760i	0.540758	+	0.936620i	−0.458103	+	0.888899i	$0.651471\pi$
$318$		0			0
$319$	14.4160	−	24.9692i	0.807140	−	1.39801i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	41.6536			2.31767
$324$		0			0
$325$	−5.18521	+	8.98104i	−0.287624	+	0.498179i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	17.2979	+	23.4512i	0.953661	+	1.29291i
$330$		0			0
$331$	7.44716	+	12.8989i	0.409333	+	0.708986i	0.994815	−	0.101700i	$-0.0324281\pi$
$331$	7.44716	+	12.8989i	0.409333	+	0.708986i	−0.585482	+	0.810685i	$0.699095\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.18916			−0.447421
$336$		0			0
$337$	34.8279			1.89719			0.948597	−	0.316486i	$-0.102503\pi$
$337$	34.8279			1.89719			0.948597	+	0.316486i	$0.102503\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−1.01822	−	1.76361i	−0.0551398	−	0.0955049i
$342$		0			0
$343$	−17.4860	+	6.10247i	−0.944155	+	0.329502i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−15.4641	+	26.7846i	−0.830156	+	1.43787i	0.0677573	+	0.997702i	$0.478416\pi$
$347$	−15.4641	+	26.7846i	−0.830156	+	1.43787i	−0.897914	+	0.440171i	$0.854918\pi$
$348$		0			0
$349$	−32.8971			−1.76094			−0.880471	−	0.474101i	$-0.842773\pi$
$349$	−32.8971			−1.76094			−0.880471	+	0.474101i	$0.842773\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−3.89676	+	6.74938i	−0.207403	+	0.359233i	−0.950896	−	0.309511i	$-0.899835\pi$
$353$	−3.89676	+	6.74938i	−0.207403	+	0.359233i	0.743492	+	0.668744i	$0.233168\pi$
$354$		0			0
$355$	2.32307	+	4.02367i	0.123296	+	0.213554i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	5.44043	+	9.42310i	0.287135	+	0.497332i	0.973125	−	0.230279i	$-0.0739639\pi$
$359$	5.44043	+	9.42310i	0.287135	+	0.497332i	−0.685990	+	0.727611i	$0.740631\pi$
$360$		0			0
$361$	−13.0960	+	22.6829i	−0.689261	+	1.19384i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.17882			−0.114045
$366$		0			0
$367$	7.83491	−	13.5705i	0.408979	−	0.708372i	−0.585797	−	0.810458i	$-0.699218\pi$
$367$	7.83491	−	13.5705i	0.408979	−	0.708372i	0.994776	+	0.102086i	$0.0325517\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	0.843478	−	1.93183i	0.0437912	−	0.100295i
$372$		0			0
$373$	19.0119	+	32.9297i	0.984401	+	1.70503i	0.644568	+	0.764547i	$0.277037\pi$
$373$	19.0119	+	32.9297i	0.984401	+	1.70503i	0.339834	+	0.940486i	$0.389629\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	21.4857			1.10657
$378$		0			0
$379$	20.8663			1.07183			0.535915	−	0.844272i	$-0.319967\pi$
$379$	20.8663			1.07183			0.535915	+	0.844272i	$0.319967\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	7.48777	+	12.9692i	0.382607	+	0.662695i	0.991434	−	0.130608i	$-0.0416929\pi$
$383$	7.48777	+	12.9692i	0.382607	+	0.662695i	−0.608827	+	0.793303i	$0.708360\pi$
$384$		0			0
$385$	6.00000	−	0.674371i	0.305788	−	0.0343691i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−17.6235	+	30.5248i	−0.893548	+	1.54767i	−0.0579573	+	0.998319i	$0.518459\pi$
$389$	−17.6235	+	30.5248i	−0.893548	+	1.54767i	−0.835591	+	0.549352i	$0.814875\pi$
$390$		0			0
$391$	−28.9198			−1.46254
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−3.43176	+	5.94399i	−0.172671	+	0.299075i
$396$		0			0
$397$	7.85297	+	13.6017i	0.394129	+	0.682652i	0.992990	−	0.118201i	$-0.0377129\pi$
$397$	7.85297	+	13.6017i	0.394129	+	0.682652i	−0.598860	+	0.800854i	$0.704380\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.6760	−	18.4914i	−0.533136	−	0.923419i	−0.999251	−	0.0386945i	$-0.987680\pi$
$401$	−10.6760	−	18.4914i	−0.533136	−	0.923419i	0.466115	−	0.884724i	$-0.345653\pi$
$402$		0			0
$403$	0.758782	−	1.31425i	0.0377976	−	0.0654674i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	33.7917			1.67499
$408$		0			0
$409$	−16.3158	+	28.2598i	−0.806764	+	1.39736i	0.108330	+	0.994115i	$0.465450\pi$
$409$	−16.3158	+	28.2598i	−0.806764	+	1.39736i	−0.915094	+	0.403241i	$0.867884\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	0.615582	−	1.40987i	0.0302908	−	0.0693753i
$414$		0			0
$415$	−4.04556	−	7.00712i	−0.198589	−	0.343966i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−28.1770			−1.37654			−0.688269	−	0.725455i	$-0.741629\pi$
$419$	−28.1770			−1.37654			−0.688269	+	0.725455i	$0.741629\pi$
$420$		0			0
$421$	7.62246			0.371496			0.185748	−	0.982597i	$-0.440529\pi$
$421$	7.62246			0.371496			0.185748	+	0.982597i	$0.440529\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−13.8301	−	23.9545i	−0.670860	−	1.16196i
$426$		0			0
$427$	−0.830453	−	1.12587i	−0.0401884	−	0.0544847i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3.73294	+	6.46565i	−0.179809	+	0.311439i	−0.941815	−	0.336131i	$-0.890881\pi$
$431$	−3.73294	+	6.46565i	−0.179809	+	0.311439i	0.762006	+	0.647570i	$0.224215\pi$
$432$		0			0
$433$	−12.3348			−0.592770			−0.296385	−	0.955069i	$-0.595781\pi$
$433$	−12.3348			−0.592770			−0.296385	+	0.955069i	$0.595781\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	15.6882	−	27.1728i	0.750469	−	1.29985i
$438$		0			0
$439$	−16.0360	−	27.7752i	−0.765357	−	1.32564i	−0.940058	−	0.341015i	$-0.889229\pi$
$439$	−16.0360	−	27.7752i	−0.765357	−	1.32564i	0.174701	−	0.984622i	$-0.444104\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−7.52028	−	13.0255i	−0.357299	−	0.618861i	0.630209	−	0.776425i	$-0.282969\pi$
$443$	−7.52028	−	13.0255i	−0.357299	−	0.618861i	−0.987509	+	0.157565i	$0.949636\pi$
$444$		0			0
$445$	4.31351	−	7.47122i	0.204480	−	0.354170i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	8.60757			0.406216			0.203108	−	0.979156i	$-0.434896\pi$
$449$	8.60757			0.406216			0.203108	+	0.979156i	$0.434896\pi$
$450$		0			0
$451$	19.3758	−	33.5598i	0.912369	−	1.58027i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	2.67083	+	3.62092i	0.125210	+	0.169751i
$456$		0			0
$457$	−11.0027	−	19.0572i	−0.514683	−	0.891457i	−0.999855	−	0.0170385i	$-0.994576\pi$
$457$	−11.0027	−	19.0572i	−0.514683	−	0.891457i	0.485172	−	0.874419i	$-0.338757\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	13.4766			0.627666			0.313833	−	0.949478i	$-0.398387\pi$
$461$	13.4766			0.627666			0.313833	+	0.949478i	$0.398387\pi$
$462$		0			0
$463$	−36.6560			−1.70355			−0.851775	−	0.523907i	$-0.824474\pi$
$463$	−36.6560			−1.70355			−0.851775	+	0.523907i	$0.824474\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−17.5632	−	30.4204i	−0.812730	−	1.40769i	−0.910947	−	0.412524i	$-0.864647\pi$
$467$	−17.5632	−	30.4204i	−0.812730	−	1.40769i	0.0982167	−	0.995165i	$-0.468686\pi$
$468$		0			0
$469$	11.8430	−	27.1242i	0.546860	−	1.25248i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.75983	+	4.78016i	−0.126897	+	0.219792i
$474$		0			0
$475$	30.0099			1.37695
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.03340	+	12.1822i	−0.321364	+	0.556619i	−0.980770	−	0.195168i	$-0.937475\pi$
$479$	−7.03340	+	12.1822i	−0.321364	+	0.556619i	0.659406	+	0.751787i	$0.270808\pi$
$480$		0			0
$481$	12.5909	+	21.8080i	0.574094	+	0.994360i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−0.648091	−	1.12253i	−0.0294283	−	0.0509713i
$486$		0			0
$487$	−5.66064	+	9.80452i	−0.256508	+	0.444285i	−0.965304	−	0.261128i	$-0.915905\pi$
$487$	−5.66064	+	9.80452i	−0.256508	+	0.444285i	0.708796	+	0.705414i	$0.249239\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	26.0720			1.17661			0.588307	−	0.808638i	$-0.299795\pi$
$491$	26.0720			1.17661			0.588307	+	0.808638i	$0.299795\pi$
$492$		0			0
$493$	−28.6536	+	49.6295i	−1.29049	+	2.23520i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−16.6868	+	1.87552i	−0.748507	+	0.0841285i
$498$		0			0
$499$	−1.21793	−	2.10952i	−0.0545222	−	0.0944352i	0.837476	−	0.546474i	$-0.184030\pi$
$499$	−1.21793	−	2.10952i	−0.0545222	−	0.0944352i	−0.891998	+	0.452039i	$0.850697\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−27.8161			−1.24026			−0.620128	−	0.784500i	$-0.712919\pi$
$503$	−27.8161			−1.24026			−0.620128	+	0.784500i	$0.712919\pi$
$504$		0			0
$505$	−6.84620			−0.304652
$506$		0			0
$507$		0			0
$508$		0			0
$509$	3.50510	+	6.07102i	0.155361	+	0.269093i	0.933190	−	0.359382i	$-0.117013\pi$
$509$	3.50510	+	6.07102i	0.155361	+	0.269093i	−0.777829	+	0.628475i	$0.783679\pi$
$510$		0			0
$511$	3.15098	−	7.21672i	0.139391	−	0.319249i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.88175	−	6.72339i	0.171050	−	0.296268i
$516$		0			0
$517$	34.3350			1.51005
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.02189	+	10.4302i	−0.263824	+	0.456956i	−0.967255	−	0.253807i	$-0.918317\pi$
$521$	−6.02189	+	10.4302i	−0.263824	+	0.456956i	0.703431	+	0.710764i	$0.251650\pi$
$522$		0			0
$523$	5.47350	+	9.48039i	0.239340	+	0.414548i	0.960525	−	0.278194i	$-0.0897357\pi$
$523$	5.47350	+	9.48039i	0.239340	+	0.414548i	−0.721185	+	0.692742i	$0.756402\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.02384	+	3.50540i	0.0881601	+	0.152698i
$528$		0			0
$529$	0.607804	−	1.05275i	0.0264263	−	0.0457716i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	28.8778			1.25084
$534$		0			0
$535$	3.98267	−	6.89819i	0.172186	−	0.298235i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.44345	+	20.8485i	−0.277539	+	0.898009i
$540$		0			0
$541$	2.21066	+	3.82897i	0.0950436	+	0.164620i	0.909627	−	0.415426i	$-0.136368\pi$
$541$	2.21066	+	3.82897i	0.0950436	+	0.164620i	−0.814583	+	0.580047i	$0.803034\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	2.54111			0.108849
$546$		0			0
$547$	15.2438			0.651780			0.325890	−	0.945408i	$-0.394336\pi$
$547$	15.2438			0.651780			0.325890	+	0.945408i	$0.394336\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−31.0876	−	53.8454i	−1.32438	−	2.29389i
$552$		0			0
$553$	−14.7248	−	19.9628i	−0.626161	−	0.848906i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−15.1436	+	26.2296i	−0.641657	+	1.11138i	0.343406	+	0.939187i	$0.388419\pi$
$557$	−15.1436	+	26.2296i	−0.641657	+	1.11138i	−0.985063	+	0.172195i	$0.944914\pi$
$558$		0			0
$559$	−4.11327			−0.173973
$560$		0			0
$561$		0			0
$562$		0			0
$563$	9.94838	−	17.2311i	0.419274	−	0.726204i	−0.576592	−	0.817032i	$-0.695618\pi$
$563$	9.94838	−	17.2311i	0.419274	−	0.726204i	0.995867	+	0.0908278i	$0.0289513\pi$
$564$		0			0
$565$	4.51223	+	7.81540i	0.189831	+	0.328797i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.54912	+	7.87931i	0.190709	+	0.330318i	0.945485	−	0.325664i	$-0.105588\pi$
$569$	4.54912	+	7.87931i	0.190709	+	0.330318i	−0.754776	+	0.655982i	$0.772255\pi$
$570$		0			0
$571$	3.65287	−	6.32696i	0.152868	−	0.264775i	−0.779413	−	0.626511i	$-0.784482\pi$
$571$	3.65287	−	6.32696i	0.152868	−	0.264775i	0.932281	+	0.361736i	$0.117816\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−20.8356			−0.868906
$576$		0			0
$577$	−21.5215	+	37.2763i	−0.895952	+	1.55183i	−0.0633297	+	0.997993i	$0.520172\pi$
$577$	−21.5215	+	37.2763i	−0.895952	+	1.55183i	−0.832622	+	0.553841i	$0.813161\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	29.0597	−	3.26617i	1.20560	−	0.135503i
$582$		0			0
$583$	−1.24184	−	2.15093i	−0.0514318	−	0.0890825i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	16.8705			0.696321			0.348161	−	0.937435i	$-0.386806\pi$
$587$	16.8705			0.696321			0.348161	+	0.937435i	$0.386806\pi$
$588$		0			0
$589$	−4.39153			−0.180950
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−3.64703	−	6.31684i	−0.149766	−	0.259401i	0.781375	−	0.624062i	$-0.214519\pi$
$593$	−3.64703	−	6.31684i	−0.149766	−	0.259401i	−0.931141	+	0.364660i	$0.881185\pi$
$594$		0			0
$595$	−11.9258	+	1.34040i	−0.488909	+	0.0549510i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−6.99650	+	12.1183i	−0.285869	+	0.495140i	−0.972820	−	0.231564i	$-0.925616\pi$
$599$	−6.99650	+	12.1183i	−0.285869	+	0.495140i	0.686950	+	0.726704i	$0.258949\pi$
$600$		0			0
$601$	22.8953			0.933919			0.466960	−	0.884279i	$-0.345349\pi$
$601$	22.8953			0.933919			0.466960	+	0.884279i	$0.345349\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.469269	+	0.812797i	−0.0190785	+	0.0330449i
$606$		0			0
$607$	−19.9017	−	34.4708i	−0.807785	−	1.39913i	−0.914395	−	0.404824i	$-0.867333\pi$
$607$	−19.9017	−	34.4708i	−0.807785	−	1.39913i	0.106609	−	0.994301i	$-0.466001\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	12.7933	+	22.1586i	0.517560	+	0.896441i
$612$		0			0
$613$	13.2934	−	23.0248i	0.536915	−	0.929965i	−0.462153	−	0.886800i	$-0.652923\pi$
$613$	13.2934	−	23.0248i	0.536915	−	0.929965i	0.999068	−	0.0431643i	$-0.0137439\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−37.7444			−1.51953			−0.759766	−	0.650197i	$-0.774686\pi$
$617$	−37.7444			−1.51953			−0.759766	+	0.650197i	$0.774686\pi$
$618$		0			0
$619$	−8.26311	+	14.3121i	−0.332122	+	0.575253i	−0.982928	−	0.183992i	$-0.941098\pi$
$619$	−8.26311	+	14.3121i	−0.332122	+	0.575253i	0.650805	+	0.759245i	$0.274431\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	18.5081	+	25.0920i	0.741512	+	1.00529i
$624$		0			0
$625$	−8.62436	−	14.9378i	−0.344974	−	0.597513i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−67.1654			−2.67806
$630$		0			0
$631$	−13.9880			−0.556854			−0.278427	−	0.960457i	$-0.589813\pi$
$631$	−13.9880			−0.556854			−0.278427	+	0.960457i	$0.589813\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−3.70321	−	6.41415i	−0.146957	−	0.254538i
$636$		0			0
$637$	−15.8558	+	3.60982i	−0.628228	+	0.143026i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.6604	−	27.1247i	0.618550	−	1.07136i	−0.371201	−	0.928553i	$-0.621054\pi$
$641$	15.6604	−	27.1247i	0.618550	−	1.07136i	0.989751	−	0.142807i	$-0.0456128\pi$
$642$		0			0
$643$	25.2347			0.995160			0.497580	−	0.867418i	$-0.334222\pi$
$643$	25.2347			0.995160			0.497580	+	0.867418i	$0.334222\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.346742	−	0.600574i	0.0136318	−	0.0236110i	−0.859129	−	0.511759i	$-0.828994\pi$
$647$	0.346742	−	0.600574i	0.0136318	−	0.0236110i	0.872761	+	0.488148i	$0.162327\pi$
$648$		0			0
$649$	−0.906313	−	1.56978i	−0.0355759	−	0.0616192i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−9.17598	−	15.8933i	−0.359084	−	0.621951i	0.628724	−	0.777628i	$-0.283577\pi$
$653$	−9.17598	−	15.8933i	−0.359084	−	0.621951i	−0.987808	+	0.155677i	$0.950244\pi$
$654$		0			0
$655$	3.40898	−	5.90453i	0.133200	−	0.230709i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	1.41641			0.0551756			0.0275878	−	0.999619i	$-0.491217\pi$
$659$	1.41641			0.0551756			0.0275878	+	0.999619i	$0.491217\pi$
$660$		0			0
$661$	6.57229	−	11.3835i	0.255633	−	0.442769i	−0.709435	−	0.704771i	$-0.751050\pi$
$661$	6.57229	−	11.3835i	0.255633	−	0.442769i	0.965067	+	0.262003i	$0.0843829\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.20998	−	11.9325i	0.202035	−	0.462722i
$666$		0			0
$667$	21.5839	+	37.3844i	0.835732	+	1.44753i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−1.64839			−0.0636353
$672$		0			0
$673$	42.8801			1.65291			0.826453	−	0.563006i	$-0.190355\pi$
$673$	42.8801			1.65291			0.826453	+	0.563006i	$0.190355\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.2418	−	22.9355i	−0.508925	−	0.881484i	−0.999947	−	0.0103369i	$-0.996710\pi$
$677$	−13.2418	−	22.9355i	−0.508925	−	0.881484i	0.491021	−	0.871148i	$-0.336624\pi$
$678$		0			0
$679$	4.65530	−	0.523234i	0.178654	−	0.0200799i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	1.45787	−	2.52511i	0.0557839	−	0.0966206i	−0.836785	−	0.547532i	$-0.815568\pi$
$683$	1.45787	−	2.52511i	0.0557839	−	0.0966206i	0.892569	+	0.450911i	$0.148901\pi$
$684$		0			0
$685$	−9.83729			−0.375864
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.925425	−	1.60288i	0.0352559	−	0.0610650i
$690$		0			0
$691$	−11.6078	−	20.1053i	−0.441582	−	0.764842i	0.556225	−	0.831031i	$-0.312249\pi$
$691$	−11.6078	−	20.1053i	−0.441582	−	0.764842i	−0.997807	+	0.0661896i	$0.978916\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.25928	+	5.64525i	0.123632	+	0.214136i
$696$		0			0
$697$	−38.5118	+	66.7044i	−1.45874	+	2.52661i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	5.05056			0.190757			0.0953785	−	0.995441i	$-0.469594\pi$
$701$	5.05056			0.190757			0.0953785	+	0.995441i	$0.469594\pi$
$702$		0			0
$703$	36.4354	−	63.1080i	1.37419	−	2.38016i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	9.90086	−	22.6760i	0.372360	−	0.852820i
$708$		0			0
$709$	−10.0106	−	17.3388i	−0.375954	−	0.651172i	0.614515	−	0.788905i	$-0.289352\pi$
$709$	−10.0106	−	17.3388i	−0.375954	−	0.651172i	−0.990469	+	0.137733i	$0.956018\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	3.04900			0.114186
$714$		0			0
$715$	5.30140			0.198261
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−17.8022	−	30.8343i	−0.663909	−	1.14992i	−0.979580	−	0.201056i	$-0.935563\pi$
$719$	−17.8022	−	30.8343i	−0.663909	−	1.14992i	0.315671	−	0.948869i	$-0.397771\pi$
$720$		0			0
$721$	16.6555	+	22.5804i	0.620285	+	0.840939i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−20.6439	+	35.7562i	−0.766694	+	1.32795i
$726$		0			0
$727$	−0.634146			−0.0235192			−0.0117596	−	0.999931i	$-0.503743\pi$
$727$	−0.634146			−0.0235192			−0.0117596	+	0.999931i	$0.503743\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	5.48551	−	9.50118i	0.202889	−	0.351414i
$732$		0			0
$733$	12.3817	+	21.4458i	0.457330	+	0.792119i	0.998819	−	0.0485888i	$-0.0154724\pi$
$733$	12.3817	+	21.4458i	0.457330	+	0.792119i	−0.541489	+	0.840708i	$0.682139\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−17.4363	−	30.2006i	−0.642275	−	1.11245i
$738$		0			0
$739$	−2.35897	+	4.08585i	−0.0867760	+	0.150300i	−0.906147	−	0.422964i	$-0.860990\pi$
$739$	−2.35897	+	4.08585i	−0.0867760	+	0.150300i	0.819371	+	0.573264i	$0.194323\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−20.5554			−0.754103			−0.377051	−	0.926192i	$-0.623062\pi$
$743$	−20.5554			−0.754103			−0.377051	+	0.926192i	$0.623062\pi$
$744$		0			0
$745$	1.19615	−	2.07180i	0.0438236	−	0.0759048i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	17.0886	+	23.1675i	0.624403	+	0.846521i
$750$		0			0
$751$	−0.777351	−	1.34641i	−0.0283659	−	0.0491312i	0.851494	−	0.524364i	$-0.175697\pi$
$751$	−0.777351	−	1.34641i	−0.0283659	−	0.0491312i	−0.879860	+	0.475233i	$0.842364\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.55002			−0.201986
$756$		0			0
$757$	10.9305			0.397274			0.198637	−	0.980073i	$-0.436349\pi$
$757$	10.9305			0.397274			0.198637	+	0.980073i	$0.436349\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	7.35386	+	12.7373i	0.266577	+	0.461725i	0.967976	−	0.251044i	$-0.0807739\pi$
$761$	7.35386	+	12.7373i	0.266577	+	0.461725i	−0.701398	+	0.712769i	$0.747441\pi$
$762$		0			0
$763$	−3.67491	+	8.41669i	−0.133041	+	0.304705i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.675388	−	1.16981i	0.0243868	−	0.0422392i
$768$		0			0
$769$	−24.3159			−0.876855			−0.438428	−	0.898766i	$-0.644464\pi$
$769$	−24.3159			−0.876855			−0.438428	+	0.898766i	$0.644464\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	0.0106190	−	0.0183927i	0.000381939	−	0.000661538i	−0.865834	−	0.500331i	$-0.833212\pi$
$773$	0.0106190	−	0.0183927i	0.000381939	−	0.000661538i	0.866216	+	0.499669i	$0.166545\pi$
$774$		0			0
$775$	1.45811	+	2.52551i	0.0523767	+	0.0907191i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−41.7832	−	72.3707i	−1.49704	−	2.59295i
$780$		0			0
$781$	−9.89254	+	17.1344i	−0.353983	+	0.613116i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	7.77952			0.277663
$786$		0			0
$787$	6.00510	−	10.4011i	0.214059	−	0.370761i	−0.738922	−	0.673791i	$-0.764665\pi$
$787$	6.00510	−	10.4011i	0.214059	−	0.370761i	0.952981	+	0.303030i	$0.0979982\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−32.4118	+	3.64292i	−1.15243	+	0.129527i
$792$		0			0
$793$	−0.614193	−	1.06381i	−0.0218106	−	0.0377771i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−30.5623			−1.08257			−0.541287	−	0.840838i	$-0.682063\pi$
$797$	−30.5623			−1.08257			−0.541287	+	0.840838i	$0.682063\pi$
$798$		0			0
$799$	−68.2451			−2.41434
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−4.63914	−	8.03523i	−0.163712	−	0.283557i
$804$		0			0
$805$	−3.61725	+	8.28463i	−0.127491	+	0.291995i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−20.6246	+	35.7228i	−0.725122	+	1.25595i	0.233802	+	0.972284i	$0.424883\pi$
$809$	−20.6246	+	35.7228i	−0.725122	+	1.25595i	−0.958924	+	0.283664i	$0.908450\pi$
$810$		0			0
$811$	−10.9000			−0.382750			−0.191375	−	0.981517i	$-0.561295\pi$
$811$	−10.9000			−0.382750			−0.191375	+	0.981517i	$0.561295\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−7.14364	+	12.3731i	−0.250231	+	0.433412i
$816$		0			0
$817$	5.95149	+	10.3083i	0.208216	+	0.360641i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−27.1201	−	46.9735i	−0.946499	−	1.63938i	−0.752721	−	0.658340i	$-0.771259\pi$
$821$	−27.1201	−	46.9735i	−0.946499	−	1.63938i	−0.193778	−	0.981045i	$-0.562074\pi$
$822$		0			0
$823$	7.24784	−	12.5536i	0.252644	−	0.437592i	−0.711609	−	0.702576i	$-0.752033\pi$
$823$	7.24784	−	12.5536i	0.252644	−	0.437592i	0.964253	+	0.264984i	$0.0853666\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−48.4452			−1.68460			−0.842302	−	0.539005i	$-0.818800\pi$
$827$	−48.4452			−1.68460			−0.842302	+	0.539005i	$0.818800\pi$
$828$		0			0
$829$	−10.0573	+	17.4197i	−0.349304	+	0.605013i	−0.986126	−	0.165998i	$-0.946915\pi$
$829$	−10.0573	+	17.4197i	−0.349304	+	0.605013i	0.636822	+	0.771011i	$0.280249\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	12.8072	−	41.4391i	0.443742	−	1.43578i
$834$		0			0
$835$	4.47122	+	7.74439i	0.154733	+	0.268005i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−0.439651			−0.0151784			−0.00758921	−	0.999971i	$-0.502416\pi$
$839$	−0.439651			−0.0151784			−0.00758921	+	0.999971i	$0.502416\pi$
$840$		0			0
$841$	56.5410			1.94969
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−2.78302	−	4.82033i	−0.0957388	−	0.165824i
$846$		0			0
$847$	−2.01351	−	2.72977i	−0.0691849	−	0.0937960i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−25.2968	+	43.8154i	−0.867164	+	1.50197i
$852$		0			0
$853$	−23.1148			−0.791436			−0.395718	−	0.918372i	$-0.629504\pi$
$853$	−23.1148			−0.791436			−0.395718	+	0.918372i	$0.629504\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	11.7910	−	20.4226i	0.402772	−	0.697621i	−0.591288	−	0.806461i	$-0.701380\pi$
$857$	11.7910	−	20.4226i	0.402772	−	0.697621i	0.994059	+	0.108840i	$0.0347135\pi$
$858$		0			0
$859$	−19.8976	−	34.4637i	−0.678899	−	1.17589i	−0.975313	−	0.220828i	$-0.929124\pi$
$859$	−19.8976	−	34.4637i	−0.678899	−	1.17589i	0.296414	−	0.955060i	$-0.404209\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−5.83879	−	10.1131i	−0.198755	−	0.344253i	0.749370	−	0.662151i	$-0.230356\pi$
$863$	−5.83879	−	10.1131i	−0.198755	−	0.344253i	−0.948125	+	0.317898i	$0.897023\pi$
$864$		0			0
$865$	6.44742	−	11.1673i	0.219219	−	0.379698i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−29.2276			−0.991478
$870$		0			0
$871$	12.9936	−	22.5056i	0.440272	−	0.762573i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.2156	+	2.04735i	−0.615800	+	0.0692129i
$876$		0			0
$877$	−4.78361	−	8.28545i	−0.161531	−	0.279780i	0.773887	−	0.633324i	$-0.218310\pi$
$877$	−4.78361	−	8.28545i	−0.161531	−	0.279780i	−0.935418	+	0.353544i	$0.884977\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−4.14572			−0.139673			−0.0698364	−	0.997558i	$-0.522248\pi$
$881$	−4.14572			−0.139673			−0.0698364	+	0.997558i	$0.522248\pi$
$882$		0			0
$883$	−14.6609			−0.493379			−0.246689	−	0.969095i	$-0.579343\pi$
$883$	−14.6609			−0.493379			−0.246689	+	0.969095i	$0.579343\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	22.6680	+	39.2622i	0.761118	+	1.31829i	0.942275	+	0.334841i	$0.108682\pi$
$887$	22.6680	+	39.2622i	0.761118	+	1.31829i	−0.181157	+	0.983454i	$0.557984\pi$
$888$		0			0
$889$	26.6005	−	2.98977i	0.892153	−	0.100274i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	37.0212	−	64.1225i	1.23887	−	2.14578i
$894$		0			0
$895$	−2.01399			−0.0673203
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.02094	−	5.23242i	0.100754	−	0.174511i
$900$		0			0
$901$	2.46832	+	4.27525i	0.0822316	+	0.142429i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.95615	+	5.12021i	0.0982658	+	0.170201i
$906$		0			0
$907$	28.8350	−	49.9437i	0.957451	−	1.65835i	0.228794	−	0.973475i	$-0.426522\pi$
$907$	28.8350	−	49.9437i	0.957451	−	1.65835i	0.728657	−	0.684879i	$-0.240145\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	45.9423			1.52214			0.761068	−	0.648672i	$-0.224675\pi$
$911$	45.9423			1.52214			0.761068	+	0.648672i	$0.224675\pi$
$912$		0			0
$913$	17.2276	−	29.8391i	0.570150	−	0.987529i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	14.6270	+	19.8303i	0.483027	+	0.654854i
$918$		0			0
$919$	−7.85285	−	13.6015i	−0.259041	−	0.448673i	0.706944	−	0.707270i	$-0.250073\pi$
$919$	−7.85285	−	13.6015i	−0.259041	−	0.448673i	−0.965985	+	0.258597i	$0.916740\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14.7439			−0.485302
$924$		0			0
$925$	−48.3902			−1.59106
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−20.7820	−	35.9955i	−0.681835	−	1.18097i	−0.974420	−	0.224734i	$-0.927849\pi$
$929$	−20.7820	−	35.9955i	−0.681835	−	1.18097i	0.292585	−	0.956240i	$-0.405485\pi$
$930$		0			0
$931$	31.9883	+	34.5131i	1.04837	+	1.13112i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−7.07001	+	12.2456i	−0.231214	+	0.400475i
$936$		0			0
$937$	−41.5740			−1.35816			−0.679082	−	0.734062i	$-0.737622\pi$
$937$	−41.5740			−1.35816			−0.679082	+	0.734062i	$0.737622\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	2.55091	−	4.41830i	0.0831572	−	0.144032i	−0.821447	−	0.570284i	$-0.806833\pi$
$941$	2.55091	−	4.41830i	0.0831572	−	0.144032i	0.904604	+	0.426252i	$0.140166\pi$
$942$		0			0
$943$	29.0098	+	50.2464i	0.944688	+	1.63625i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.99483	+	12.1154i	0.227302	+	0.393698i	0.957007	−	0.290063i	$-0.0936764\pi$
$947$	6.99483	+	12.1154i	0.227302	+	0.393698i	−0.729706	+	0.683761i	$0.760343\pi$
$948$		0			0
$949$	3.45711	−	5.98788i	0.112222	−	0.194375i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−5.30864			−0.171964			−0.0859819	−	0.996297i	$-0.527403\pi$
$953$	−5.30864			−0.171964			−0.0859819	+	0.996297i	$0.527403\pi$
$954$		0			0
$955$	0.521782	−	0.903752i	0.0168845	−	0.0292447i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	14.2265	−	32.5832i	0.459399	−	1.05217i
$960$		0			0
$961$	15.2866	+	26.4772i	0.493117	+	0.854104i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	3.28919			0.105883
$966$		0			0
$967$	−33.1799			−1.06700			−0.533498	−	0.845802i	$-0.679123\pi$
$967$	−33.1799			−1.06700			−0.533498	+	0.845802i	$0.679123\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	8.87415	+	15.3705i	0.284785	+	0.493262i	0.972557	−	0.232665i	$-0.0747445\pi$
$971$	8.87415	+	15.3705i	0.284785	+	0.493262i	−0.687772	+	0.725927i	$0.741411\pi$
$972$		0			0
$973$	−23.4118	+	2.63137i	−0.750547	+	0.0843578i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.8872	+	32.7136i	−0.604255	+	1.04660i	0.387914	+	0.921696i	$0.373196\pi$
$977$	−18.8872	+	32.7136i	−0.604255	+	1.04660i	−0.992169	+	0.124905i	$0.960137\pi$
$978$		0			0
$979$	36.7373			1.17413
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20.1280	−	34.8628i	0.641984	−	1.11195i	−0.343005	−	0.939334i	$-0.611445\pi$
$983$	20.1280	−	34.8628i	0.641984	−	1.11195i	0.984989	−	0.172616i	$-0.0552219\pi$
$984$		0			0
$985$	5.80906	+	10.0616i	0.185092	+	0.320589i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.13207	−	7.15696i	−0.131392	−	0.227578i
$990$		0			0
$991$	−0.872347	+	1.51095i	−0.0277110	+	0.0479969i	−0.879548	−	0.475810i	$-0.842155\pi$
$991$	−0.872347	+	1.51095i	−0.0277110	+	0.0479969i	0.851837	+	0.523806i	$0.175488\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.14372			−0.289875
$996$		0			0
$997$	−3.35274	+	5.80711i	−0.106182	+	0.183913i	−0.914221	−	0.405217i	$-0.867196\pi$
$997$	−3.35274	+	5.80711i	−0.106182	+	0.183913i	0.808038	+	0.589130i	$0.200529\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.s.m.865.3	✓	8
3.2	odd	2		1512.2.s.p.865.1	yes	8
7.2	even	3	inner	1512.2.s.m.1297.3	yes	8
21.2	odd	6		1512.2.s.p.1297.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.m.865.3	✓	8	1.1	even	1	trivial
1512.2.s.m.1297.3	yes	8	7.2	even	3	inner
1512.2.s.p.865.1	yes	8	3.2	odd	2
1512.2.s.p.1297.1	yes	8	21.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1512.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.366025 + 0.633975i) q^{5} +(-2.62920 + 0.295509i) q^{7} +O(q^{10})\)	\(q+(0.366025 + 0.633975i) q^{5} +(-2.62920 + 0.295509i) q^{7} +(-1.55868 + 2.69971i) q^{11} -2.32307 q^{13} +(3.09808 - 5.36603i) q^{17} +(3.36125 + 5.82185i) q^{19} +(-2.33369 - 4.04207i) q^{23} +(2.23205 - 3.86603i) q^{25} -9.24884 q^{29} +(-0.326629 + 0.565738i) q^{31} +(-1.14970 - 1.55868i) q^{35} +(-5.41993 - 9.38759i) q^{37} -12.4309 q^{41} +1.77062 q^{43} +(-5.50706 - 9.53850i) q^{47} +(6.82535 - 1.55390i) q^{49} +(-0.398363 + 0.689985i) q^{53} -2.28207 q^{55} +(-0.290731 + 0.503561i) q^{59} +(0.264389 + 0.457934i) q^{61} +(-0.850302 - 1.47277i) q^{65} +(-5.59330 + 9.68788i) q^{67} +6.34674 q^{71} +(-1.48816 + 2.57757i) q^{73} +(3.30029 - 7.55868i) q^{77} +(4.68788 + 8.11964i) q^{79} -11.0527 q^{83} +4.53590 q^{85} +(-5.89237 - 10.2059i) q^{89} +(6.10780 - 0.686487i) q^{91} +(-2.46060 + 4.26189i) q^{95} -1.77062 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 2 q^{7}+O(q^{10}) \) 8 * q - 4 * q^5 - 2 * q^7	\( 8 q - 4 q^{5} - 2 q^{7} - 2 q^{11} - 8 q^{13} + 4 q^{17} - 6 q^{19} + 2 q^{23} + 4 q^{25} + 16 q^{29} - 6 q^{31} - 2 q^{35} - 16 q^{41} - 20 q^{47} - 6 q^{49} - 10 q^{53} + 16 q^{55} + 22 q^{59} + 2 q^{61} - 14 q^{65} + 2 q^{67} + 44 q^{71} - 10 q^{73} + 54 q^{77} + 8 q^{79} - 40 q^{83} + 64 q^{85} - 16 q^{89} - 24 q^{91} - 30 q^{95}+O(q^{100}) \) 8 * q - 4 * q^5 - 2 * q^7 - 2 * q^11 - 8 * q^13 + 4 * q^17 - 6 * q^19 + 2 * q^23 + 4 * q^25 + 16 * q^29 - 6 * q^31 - 2 * q^35 - 16 * q^41 - 20 * q^47 - 6 * q^49 - 10 * q^53 + 16 * q^55 + 22 * q^59 + 2 * q^61 - 14 * q^65 + 2 * q^67 + 44 * q^71 - 10 * q^73 + 54 * q^77 + 8 * q^79 - 40 * q^83 + 64 * q^85 - 16 * q^89 - 24 * q^91 - 30 * q^95

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