LMFDB - Embedded newform 1512.2.s.p.865.4

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			865.4
Root			$-2.47635 + 0.931486i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.p.1297.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 + 2.36603i) q^{5} +(0.431486 - 2.61033i) q^{7} +O(q^{10})$	$q+(1.36603 + 2.36603i) q^{5} +(0.431486 - 2.61033i) q^{7} +(2.54487 - 4.40784i) q^{11} -3.48861 q^{13} +(2.09808 - 3.63397i) q^{17} +(-3.16354 - 5.47941i) q^{19} +(-3.04182 - 5.26858i) q^{23} +(-1.23205 + 2.13397i) q^{25} -6.45800 q^{29} +(-4.77692 + 8.27387i) q^{31} +(6.76553 - 2.54487i) q^{35} +(0.118669 + 0.205541i) q^{37} +5.98332 q^{41} +12.6436 q^{43} +(-4.31873 - 7.48027i) q^{47} +(-6.62764 - 2.25264i) q^{49} +(2.30977 - 4.00063i) q^{53} +13.9054 q^{55} +(-2.18718 + 3.78831i) q^{59} +(0.443740 + 0.768580i) q^{61} +(-4.76553 - 8.25414i) q^{65} +(4.39559 - 7.61338i) q^{67} +2.55384 q^{71} +(-6.52122 + 11.2951i) q^{73} +(-10.4078 - 8.54487i) q^{77} +(2.61338 + 4.52651i) q^{79} +5.73816 q^{83} +11.4641 q^{85} +(1.50305 + 2.60336i) q^{89} +(-1.50529 + 9.10642i) q^{91} +(8.64294 - 14.9700i) q^{95} -12.6436 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	1.36603	+	2.36603i	0.610905	+	1.05812i	0.991088	+	0.133207i	$0.0425277\pi$
$5$	1.36603	+	2.36603i	0.610905	+	1.05812i	−0.380183	+	0.924911i	$0.624139\pi$
$6$		0			0
$7$	0.431486	−	2.61033i	0.163087	−	0.986612i
$7$	0.431486	−	2.61033i	0.163087	−	0.986612i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.54487	−	4.40784i	0.767307	−	1.32901i	−0.171712	−	0.985147i	$-0.554930\pi$
$11$	2.54487	−	4.40784i	0.767307	−	1.32901i	0.939018	−	0.343867i	$-0.111737\pi$
$12$		0			0
$13$	−3.48861			−0.967566			−0.483783	−	0.875188i	$-0.660738\pi$
$13$	−3.48861			−0.967566			−0.483783	+	0.875188i	$0.660738\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.09808	−	3.63397i	0.508858	−	0.881368i	−0.491089	−	0.871109i	$-0.663401\pi$
$17$	2.09808	−	3.63397i	0.508858	−	0.881368i	0.999947	−	0.0102590i	$-0.00326559\pi$
$18$		0			0
$19$	−3.16354	−	5.47941i	−0.725765	−	1.25706i	−0.958658	−	0.284560i	$-0.908153\pi$
$19$	−3.16354	−	5.47941i	−0.725765	−	1.25706i	0.232893	−	0.972502i	$-0.425181\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.04182	−	5.26858i	−0.634262	−	1.09857i	−0.986671	−	0.162728i	$-0.947971\pi$
$23$	−3.04182	−	5.26858i	−0.634262	−	1.09857i	0.352408	−	0.935846i	$-0.385363\pi$
$24$		0			0
$25$	−1.23205	+	2.13397i	−0.246410	+	0.426795i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−6.45800			−1.19922			−0.599610	−	0.800292i	$-0.704678\pi$
$29$	−6.45800			−1.19922			−0.599610	+	0.800292i	$0.704678\pi$
$30$		0			0
$31$	−4.77692	+	8.27387i	−0.857960	+	1.48603i	0.0159115	+	0.999873i	$0.494935\pi$
$31$	−4.77692	+	8.27387i	−0.857960	+	1.48603i	−0.873872	+	0.486157i	$0.838398\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	6.76553	−	2.54487i	1.14358	−	0.430161i
$36$		0			0
$37$	0.118669	+	0.205541i	0.0195091	+	0.0337907i	0.875615	−	0.483010i	$-0.160456\pi$
$37$	0.118669	+	0.205541i	0.0195091	+	0.0337907i	−0.856106	+	0.516800i	$0.827123\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5.98332			0.934438			0.467219	−	0.884142i	$-0.345256\pi$
$41$	5.98332			0.934438			0.467219	+	0.884142i	$0.345256\pi$
$42$		0			0
$43$	12.6436			1.92813			0.964064	−	0.265672i	$-0.0855937\pi$
$43$	12.6436			1.92813			0.964064	+	0.265672i	$0.0855937\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−4.31873	−	7.48027i	−0.629952	−	1.09111i	−0.987561	−	0.157238i	$-0.949741\pi$
$47$	−4.31873	−	7.48027i	−0.629952	−	1.09111i	0.357609	−	0.933872i	$-0.383592\pi$
$48$		0			0
$49$	−6.62764	−	2.25264i	−0.946806	−	0.321806i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	2.30977	−	4.00063i	0.317271	−	0.549529i	−0.662647	−	0.748932i	$-0.730567\pi$
$53$	2.30977	−	4.00063i	0.317271	−	0.549529i	0.979918	+	0.199403i	$0.0639003\pi$
$54$		0			0
$55$	13.9054			1.87501
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−2.18718	+	3.78831i	−0.284747	+	0.493196i	−0.972548	−	0.232703i	$-0.925243\pi$
$59$	−2.18718	+	3.78831i	−0.284747	+	0.493196i	0.687801	+	0.725899i	$0.258576\pi$
$60$		0			0
$61$	0.443740	+	0.768580i	0.0568150	+	0.0984065i	0.893034	−	0.449989i	$-0.148572\pi$
$61$	0.443740	+	0.768580i	0.0568150	+	0.0984065i	−0.836219	+	0.548396i	$0.815239\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.76553	−	8.25414i	−0.591091	−	1.02380i
$66$		0			0
$67$	4.39559	−	7.61338i	0.537007	−	0.930123i	−0.462057	−	0.886850i	$-0.652888\pi$
$67$	4.39559	−	7.61338i	0.537007	−	0.930123i	0.999063	−	0.0432723i	$-0.0137783\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.55384			0.303085			0.151542	−	0.988451i	$-0.451576\pi$
$71$	2.55384			0.303085			0.151542	+	0.988451i	$0.451576\pi$
$72$		0			0
$73$	−6.52122	+	11.2951i	−0.763251	+	1.32199i	0.177915	+	0.984046i	$0.443065\pi$
$73$	−6.52122	+	11.2951i	−0.763251	+	1.32199i	−0.941166	+	0.337944i	$0.890268\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−10.4078	−	8.54487i	−1.18608	−	0.973778i
$78$		0			0
$79$	2.61338	+	4.52651i	0.294028	+	0.509272i	0.974758	−	0.223262i	$-0.0716706\pi$
$79$	2.61338	+	4.52651i	0.294028	+	0.509272i	−0.680730	+	0.732534i	$0.738337\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	5.73816			0.629844			0.314922	−	0.949117i	$-0.398022\pi$
$83$	5.73816			0.629844			0.314922	+	0.949117i	$0.398022\pi$
$84$		0			0
$85$	11.4641			1.24346
$86$		0			0
$87$		0			0
$88$		0			0
$89$	1.50305	+	2.60336i	0.159323	+	0.275956i	0.934625	−	0.355635i	$-0.115735\pi$
$89$	1.50305	+	2.60336i	0.159323	+	0.275956i	−0.775302	+	0.631591i	$0.782402\pi$
$90$		0			0
$91$	−1.50529	+	9.10642i	−0.157797	+	0.954612i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	8.64294	−	14.9700i	0.886747	−	1.53589i
$96$		0			0
$97$	−12.6436			−1.28376			−0.641880	−	0.766805i	$-0.721845\pi$
$97$	−12.6436			−1.28376			−0.641880	+	0.766805i	$0.721845\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	7.63460	−	13.2235i	0.759672	−	1.31579i	−0.183347	−	0.983048i	$-0.558693\pi$
$101$	7.63460	−	13.2235i	0.759672	−	1.31579i	0.943018	−	0.332741i	$-0.107974\pi$
$102$		0			0
$103$	2.20841	+	3.82507i	0.217601	+	0.376895i	0.954074	−	0.299571i	$-0.0968436\pi$
$103$	2.20841	+	3.82507i	0.217601	+	0.376895i	−0.736473	+	0.676467i	$0.763510\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	8.57834	+	14.8581i	0.829300	+	1.43639i	0.898588	+	0.438793i	$0.144594\pi$
$107$	8.57834	+	14.8581i	0.829300	+	1.43639i	−0.0692884	+	0.997597i	$0.522073\pi$
$108$		0			0
$109$	1.55626	−	2.69552i	0.149063	−	0.258184i	−0.781819	−	0.623506i	$-0.785708\pi$
$109$	1.55626	−	2.69552i	0.149063	−	0.258184i	0.930881	+	0.365322i	$0.119041\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	15.7439			1.48106			0.740530	−	0.672023i	$-0.234574\pi$
$113$	15.7439			1.48106			0.740530	+	0.672023i	$0.234574\pi$
$114$		0			0
$115$	8.31040	−	14.3940i	0.774948	−	1.34225i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−8.58058	−	7.04468i	−0.786580	−	0.645785i
$120$		0			0
$121$	−7.45271	−	12.9085i	−0.677519	−	1.17350i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	6.92820			0.619677
$126$		0			0
$127$	−12.0897			−1.07279			−0.536395	−	0.843967i	$-0.680214\pi$
$127$	−12.0897			−1.07279			−0.536395	+	0.843967i	$0.680214\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	0.446792	+	0.773867i	0.0390364	+	0.0676130i	0.884884	−	0.465812i	$-0.154238\pi$
$131$	0.446792	+	0.773867i	0.0390364	+	0.0676130i	−0.845847	+	0.533425i	$0.820905\pi$
$132$		0			0
$133$	−15.6681	+	5.89358i	−1.35859	+	0.511039i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	6.77997	−	11.7433i	0.579252	−	1.00329i	−0.416313	−	0.909221i	$-0.636678\pi$
$137$	6.77997	−	11.7433i	0.579252	−	1.00329i	0.995565	−	0.0940728i	$-0.0299886\pi$
$138$		0			0
$139$	5.11424			0.433784			0.216892	−	0.976196i	$-0.430408\pi$
$139$	5.11424			0.433784			0.216892	+	0.976196i	$0.430408\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−8.87805	+	15.3772i	−0.742420	+	1.28591i
$144$		0			0
$145$	−8.82179	−	15.2798i	−0.732610	−	1.26892i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.36603	+	5.83013i	0.275756	+	0.477623i	0.970325	−	0.241803i	$-0.0777386\pi$
$149$	3.36603	+	5.83013i	0.275756	+	0.477623i	−0.694570	+	0.719425i	$0.744405\pi$
$150$		0			0
$151$	−1.31282	+	2.27387i	−0.106836	+	0.185045i	−0.914487	−	0.404616i	$-0.867405\pi$
$151$	−1.31282	+	2.27387i	−0.106836	+	0.185045i	0.807651	+	0.589661i	$0.200739\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−26.1016			−2.09653
$156$		0			0
$157$	−3.10642	+	5.38047i	−0.247919	+	0.429408i	−0.962948	−	0.269686i	$-0.913080\pi$
$157$	−3.10642	+	5.38047i	−0.247919	+	0.429408i	0.715029	+	0.699095i	$0.246413\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−15.0652	+	5.66682i	−1.18731	+	0.446608i
$162$		0			0
$163$	3.63703	+	6.29952i	0.284874	+	0.493416i	0.972579	−	0.232574i	$-0.0747149\pi$
$163$	3.63703	+	6.29952i	0.284874	+	0.493416i	−0.687705	+	0.725991i	$0.741382\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.01057			0.232965			0.116483	−	0.993193i	$-0.462838\pi$
$167$	3.01057			0.232965			0.116483	+	0.993193i	$0.462838\pi$
$168$		0			0
$169$	−0.829615			−0.0638165
$170$		0			0
$171$		0			0
$172$		0			0
$173$	6.08911	+	10.5466i	0.462946	+	0.801846i	0.999106	−	0.0422700i	$-0.0134590\pi$
$173$	6.08911	+	10.5466i	0.462946	+	0.801846i	−0.536160	+	0.844116i	$0.680126\pi$
$174$		0			0
$175$	5.03876	+	4.13684i	0.380895	+	0.312716i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.22900	−	15.9851i	0.689808	−	1.19478i	−0.282092	−	0.959387i	$-0.591028\pi$
$179$	9.22900	−	15.9851i	0.689808	−	1.19478i	0.971900	−	0.235395i	$-0.0756383\pi$
$180$		0			0
$181$	−7.30429			−0.542924			−0.271462	−	0.962449i	$-0.587507\pi$
$181$	−7.30429			−0.542924			−0.271462	+	0.962449i	$0.587507\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−0.324210	+	0.561547i	−0.0238364	+	0.0412858i
$186$		0			0
$187$	−10.6787	−	18.4960i	−0.780901	−	1.35256i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.91986	−	17.1817i	−0.717776	−	1.24322i	−0.961879	−	0.273475i	$-0.911827\pi$
$191$	−9.91986	−	17.1817i	−0.717776	−	1.24322i	0.244103	−	0.969749i	$-0.421507\pi$
$192$		0			0
$193$	1.15825	−	2.00615i	0.0833727	−	0.144406i	−0.821324	−	0.570462i	$-0.806764\pi$
$193$	1.15825	−	2.00615i	0.0833727	−	0.144406i	0.904697	+	0.426056i	$0.140097\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−1.29684			−0.0923959			−0.0461980	−	0.998932i	$-0.514711\pi$
$197$	−1.29684			−0.0923959			−0.0461980	+	0.998932i	$0.514711\pi$
$198$		0			0
$199$	12.7463	−	22.0773i	0.903562	−	1.56501i	0.0807256	−	0.996736i	$-0.474276\pi$
$199$	12.7463	−	22.0773i	0.903562	−	1.56501i	0.822836	−	0.568279i	$-0.192390\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−2.78654	+	16.8575i	−0.195577	+	1.18316i
$204$		0			0
$205$	8.17337	+	14.1567i	0.570853	+	0.988746i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−32.2031			−2.22754
$210$		0			0
$211$	7.11825			0.490041			0.245020	−	0.969518i	$-0.421205\pi$
$211$	7.11825			0.490041			0.245020	+	0.969518i	$0.421205\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	17.2714	+	29.9150i	1.17790	+	2.04019i
$216$		0			0
$217$	19.5363	+	16.0394i	1.32621	+	1.08882i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−7.31937	+	12.6775i	−0.492354	+	0.852782i
$222$		0			0
$223$	−0.261844			−0.0175344			−0.00876719	−	0.999962i	$-0.502791\pi$
$223$	−0.261844			−0.0175344			−0.00876719	+	0.999962i	$0.502791\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2.04792	−	3.54710i	0.135925	−	0.235429i	−0.790025	−	0.613074i	$-0.789933\pi$
$227$	2.04792	−	3.54710i	0.135925	−	0.235429i	0.925951	+	0.377645i	$0.123266\pi$
$228$		0			0
$229$	−1.26553	−	2.19196i	−0.0836284	−	0.144849i	0.821178	−	0.570673i	$-0.193318\pi$
$229$	−1.26553	−	2.19196i	−0.0836284	−	0.144849i	−0.904806	+	0.425824i	$0.859984\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.0843	+	22.6626i	0.857179	+	1.48468i	0.874609	+	0.484829i	$0.161118\pi$
$233$	13.0843	+	22.6626i	0.857179	+	1.48468i	−0.0174307	+	0.999848i	$0.505549\pi$
$234$		0			0
$235$	11.7990	−	20.4365i	0.769682	−	1.33313i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.40898			−0.414563			−0.207281	−	0.978281i	$-0.566462\pi$
$239$	−6.40898			−0.414563			−0.207281	+	0.978281i	$0.566462\pi$
$240$		0			0
$241$	−9.44660	+	16.3620i	−0.608509	+	1.05397i	0.382977	+	0.923758i	$0.374899\pi$
$241$	−9.44660	+	16.3620i	−0.608509	+	1.05397i	−0.991486	+	0.130211i	$0.958434\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.72371	−	18.7583i	−0.237899	−	1.19843i
$246$		0			0
$247$	11.0363	+	19.1155i	0.702226	+	1.21629i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	11.5477			0.728886			0.364443	−	0.931226i	$-0.381259\pi$
$251$	11.5477			0.728886			0.364443	+	0.931226i	$0.381259\pi$
$252$		0			0
$253$	−30.9641			−1.94670
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−2.86908	−	4.96939i	−0.178968	−	0.309982i	0.762559	−	0.646918i	$-0.223943\pi$
$257$	−2.86908	−	4.96939i	−0.178968	−	0.309982i	−0.941527	+	0.336936i	$0.890609\pi$
$258$		0			0
$259$	0.587733	−	0.221077i	0.0365199	−	0.0137371i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.96168	+	12.0580i	−0.429276	+	0.743527i	−0.996809	−	0.0798233i	$-0.974564\pi$
$263$	−6.96168	+	12.0580i	−0.429276	+	0.743527i	0.567533	+	0.823350i	$0.307898\pi$
$264$		0			0
$265$	12.6208			0.775289
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.98332	+	3.43521i	−0.120925	+	0.209449i	−0.920133	−	0.391607i	$-0.871919\pi$
$269$	−1.98332	+	3.43521i	−0.120925	+	0.209449i	0.799208	+	0.601055i	$0.205253\pi$
$270$		0			0
$271$	7.25942	+	12.5737i	0.440978	+	0.763797i	0.997762	−	0.0668603i	$-0.0212982\pi$
$271$	7.25942	+	12.5737i	0.440978	+	0.763797i	−0.556784	+	0.830657i	$0.687965\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.27081	+	10.8614i	0.378144	+	0.654965i
$276$		0			0
$277$	−5.13460	+	8.89340i	−0.308509	+	0.534352i	−0.978036	−	0.208435i	$-0.933163\pi$
$277$	−5.13460	+	8.89340i	−0.308509	+	0.534352i	0.669528	+	0.742787i	$0.266496\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−17.1387			−1.02241			−0.511206	−	0.859458i	$-0.670801\pi$
$281$	−17.1387			−1.02241			−0.511206	+	0.859458i	$0.670801\pi$
$282$		0			0
$283$	−1.23205	+	2.13397i	−0.0732378	+	0.126852i	−0.900319	−	0.435231i	$-0.856667\pi$
$283$	−1.23205	+	2.13397i	−0.0732378	+	0.126852i	0.827081	+	0.562083i	$0.190000\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.58172	−	15.6184i	0.152394	−	0.921927i
$288$		0			0
$289$	−0.303848	−	0.526279i	−0.0178734	−	0.0309576i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	18.2798			1.06792			0.533958	−	0.845511i	$-0.320704\pi$
$293$	18.2798			1.06792			0.533958	+	0.845511i	$0.320704\pi$
$294$		0			0
$295$	−11.9510			−0.695813
$296$		0			0
$297$		0			0
$298$		0			0
$299$	10.6117	+	18.3800i	0.613691	+	1.06294i
$300$		0			0
$301$	5.45553	−	33.0039i	0.314452	−	1.90231i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−1.21232	+	2.09980i	−0.0694172	+	0.120234i
$306$		0			0
$307$	7.40451			0.422598			0.211299	−	0.977421i	$-0.432231\pi$
$307$	7.40451			0.422598			0.211299	+	0.977421i	$0.432231\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−10.1705	+	17.6158i	−0.576716	+	0.998902i	0.419136	+	0.907923i	$0.362333\pi$
$311$	−10.1705	+	17.6158i	−0.576716	+	0.998902i	−0.995853	+	0.0909788i	$0.971000\pi$
$312$		0			0
$313$	13.5803	+	23.5219i	0.767607	+	1.32953i	0.938857	+	0.344306i	$0.111886\pi$
$313$	13.5803	+	23.5219i	0.767607	+	1.32953i	−0.171251	+	0.985227i	$0.554781\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.3360	+	19.6346i	0.636696	+	1.10279i	0.986153	+	0.165837i	$0.0530326\pi$
$317$	11.3360	+	19.6346i	0.636696	+	1.10279i	−0.349457	+	0.936952i	$0.613634\pi$
$318$		0			0
$319$	−16.4348	+	28.4658i	−0.920169	+	1.59378i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−26.5494			−1.47725
$324$		0			0
$325$	4.29814	−	7.44460i	0.238418	−	0.412952i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−21.3894	+	8.04569i	−1.17924	+	0.443573i
$330$		0			0
$331$	−4.87280	−	8.43994i	−0.267834	−	0.463901i	0.700469	−	0.713683i	$-0.252974\pi$
$331$	−4.87280	−	8.43994i	−0.267834	−	0.463901i	−0.968302	+	0.249782i	$0.919641\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	24.0179			1.31224
$336$		0			0
$337$	11.1492			0.607338			0.303669	−	0.952778i	$-0.401788\pi$
$337$	11.1492			0.607338			0.303669	+	0.952778i	$0.401788\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	24.3133	+	42.1118i	1.31664	+	2.28048i
$342$		0			0
$343$	−8.73988	+	16.3283i	−0.471909	+	0.881647i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.53590	−	14.7846i	0.458231	−	0.793679i	−0.540637	−	0.841256i	$-0.681817\pi$
$347$	8.53590	−	14.7846i	0.458231	−	0.793679i	0.998868	+	0.0475768i	$0.0151499\pi$
$348$		0			0
$349$	12.7317			0.681511			0.340755	−	0.940152i	$-0.389317\pi$
$349$	12.7317			0.681511			0.340755	+	0.940152i	$0.389317\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−17.7272	+	30.7044i	−0.943524	+	1.63423i	−0.184844	+	0.982768i	$0.559178\pi$
$353$	−17.7272	+	30.7044i	−0.943524	+	1.63423i	−0.758680	+	0.651464i	$0.774155\pi$
$354$		0			0
$355$	3.48861	+	6.04245i	0.185156	+	0.320700i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.57834	−	14.8581i	−0.452748	−	0.784182i	0.545808	−	0.837910i	$-0.316223\pi$
$359$	−8.57834	−	14.8581i	−0.452748	−	0.784182i	−0.998556	+	0.0537283i	$0.982890\pi$
$360$		0			0
$361$	−10.5159	+	18.2141i	−0.553470	+	0.958639i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−35.6326			−1.86510
$366$		0			0
$367$	3.96738	−	6.87171i	0.207096	−	0.358700i	−0.743703	−	0.668511i	$-0.766932\pi$
$367$	3.96738	−	6.87171i	0.207096	−	0.358700i	0.950798	+	0.309810i	$0.100265\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−9.44633	−	7.75547i	−0.490429	−	0.402644i
$372$		0			0
$373$	−14.4188	−	24.9741i	−0.746578	−	1.29311i	−0.949454	−	0.313906i	$-0.898362\pi$
$373$	−14.4188	−	24.9741i	−0.746578	−	1.29311i	0.202876	−	0.979204i	$-0.434971\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	22.5294			1.16032
$378$		0			0
$379$	−21.2659			−1.09235			−0.546177	−	0.837670i	$-0.683917\pi$
$379$	−21.2659			−1.09235			−0.546177	+	0.837670i	$0.683917\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.50655	+	16.4658i	0.485762	+	0.841364i	0.999866	−	0.0163634i	$-0.00520888\pi$
$383$	9.50655	+	16.4658i	0.485762	+	0.841364i	−0.514104	+	0.857728i	$0.671876\pi$
$384$		0			0
$385$	6.00000	−	36.2977i	0.305788	−	1.84990i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.8942	−	24.0655i	0.704465	−	1.22017i	−0.262420	−	0.964954i	$-0.584521\pi$
$389$	13.8942	−	24.0655i	0.704465	−	1.22017i	0.966884	−	0.255215i	$-0.0821462\pi$
$390$		0			0
$391$	−25.5278			−1.29100
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−7.13989	+	12.3667i	−0.359247	+	0.622234i
$396$		0			0
$397$	9.64600	+	16.7074i	0.484119	+	0.838518i	0.999834	−	0.0182421i	$-0.00580695\pi$
$397$	9.64600	+	16.7074i	0.484119	+	0.838518i	−0.515715	+	0.856760i	$0.672474\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	13.6346	+	23.6158i	0.680880	+	1.17932i	0.974713	+	0.223461i	$0.0717357\pi$
$401$	13.6346	+	23.6158i	0.680880	+	1.17932i	−0.293833	+	0.955857i	$0.594931\pi$
$402$		0			0
$403$	16.6648	−	28.8643i	0.830133	−	1.43783i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	1.20799			0.0598777
$408$		0			0
$409$	6.72266	−	11.6440i	0.332414	−	0.575758i	−0.650570	−	0.759446i	$-0.725470\pi$
$409$	6.72266	−	11.6440i	0.332414	−	0.575758i	0.982985	+	0.183688i	$0.0588035\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	8.94500	+	7.34387i	0.440155	+	0.361368i
$414$		0			0
$415$	7.83847	+	13.5766i	0.384775	+	0.666450i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−1.38620			−0.0677203			−0.0338601	−	0.999427i	$-0.510780\pi$
$419$	−1.38620			−0.0677203			−0.0338601	+	0.999427i	$0.510780\pi$
$420$		0			0
$421$	20.0197			0.975699			0.487849	−	0.872928i	$-0.337782\pi$
$421$	20.0197			0.975699			0.487849	+	0.872928i	$0.337782\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	5.16987	+	8.95448i	0.250776	+	0.434356i
$426$		0			0
$427$	2.19771	−	0.826675i	0.106355	−	0.0400056i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3.85526	+	6.67751i	−0.185702	+	0.321644i	−0.943813	−	0.330481i	$-0.892789\pi$
$431$	−3.85526	+	6.67751i	−0.185702	+	0.321644i	0.758111	+	0.652125i	$0.226122\pi$
$432$		0			0
$433$	9.16726			0.440551			0.220275	−	0.975438i	$-0.429304\pi$
$433$	9.16726			0.440551			0.220275	+	0.975438i	$0.429304\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−19.2458	+	33.3347i	−0.920651	+	1.59461i
$438$		0			0
$439$	5.43349	+	9.41108i	0.259326	+	0.449166i	0.966062	−	0.258312i	$-0.0831661\pi$
$439$	5.43349	+	9.41108i	0.259326	+	0.449166i	−0.706735	+	0.707478i	$0.749833\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−17.8330	−	30.8876i	−0.847271	−	1.46752i	−0.883634	−	0.468178i	$-0.844911\pi$
$443$	−17.8330	−	30.8876i	−0.847271	−	1.46752i	0.0363633	−	0.999339i	$-0.488423\pi$
$444$		0			0
$445$	−4.10642	+	7.11252i	−0.194663	+	0.337166i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	3.39841			0.160381			0.0801904	−	0.996780i	$-0.474447\pi$
$449$	3.39841			0.160381			0.0801904	+	0.996780i	$0.474447\pi$
$450$		0			0
$451$	15.2268	−	26.3735i	0.717000	−	1.24188i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−23.6023	+	8.87805i	−1.10649	+	0.416209i
$456$		0			0
$457$	−18.4115	−	31.8897i	−0.861255	−	1.49174i	−0.870718	−	0.491782i	$-0.836346\pi$
$457$	−18.4115	−	31.8897i	−0.861255	−	1.49174i	0.00946370	−	0.999955i	$-0.496988\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−27.9356			−1.30109			−0.650545	−	0.759468i	$-0.725459\pi$
$461$	−27.9356			−1.30109			−0.650545	+	0.759468i	$0.725459\pi$
$462$		0			0
$463$	−24.5678			−1.14176			−0.570881	−	0.821033i	$-0.693398\pi$
$463$	−24.5678			−1.14176			−0.570881	+	0.821033i	$0.693398\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.6876	−	18.5115i	−0.494564	−	0.856611i	0.505416	−	0.862876i	$-0.331339\pi$
$467$	−10.6876	−	18.5115i	−0.494564	−	0.856611i	−0.999980	+	0.00626525i	$0.998006\pi$
$468$		0			0
$469$	−17.9768	−	14.7590i	−0.830091	−	0.681507i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	32.1762	−	55.7309i	1.47946	−	2.56251i
$474$		0			0
$475$	15.5906			0.715344
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.44966	+	9.43908i	−0.249001	+	0.431283i	−0.963249	−	0.268610i	$-0.913436\pi$
$479$	−5.44966	+	9.43908i	−0.249001	+	0.431283i	0.714248	+	0.699893i	$0.246769\pi$
$480$		0			0
$481$	−0.413989	−	0.717051i	−0.0188763	−	0.0326947i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−17.2714	−	29.9150i	−0.784256	−	1.35837i
$486$		0			0
$487$	−10.3675	+	17.9571i	−0.469797	+	0.813712i	−0.999404	−	0.0345311i	$-0.989006\pi$
$487$	−10.3675	+	17.9571i	−0.469797	+	0.813712i	0.529607	+	0.848243i	$0.322340\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	16.8670			0.761196			0.380598	−	0.924741i	$-0.375718\pi$
$491$	16.8670			0.761196			0.380598	+	0.924741i	$0.375718\pi$
$492$		0			0
$493$	−13.5494	+	23.4682i	−0.610233	+	1.05695i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	1.10195	−	6.66636i	0.0494291	−	0.299027i
$498$		0			0
$499$	−17.4054	−	30.1471i	−0.779174	−	1.34957i	−0.932419	−	0.361380i	$-0.882306\pi$
$499$	−17.4054	−	30.1471i	−0.779174	−	1.34957i	0.153245	−	0.988188i	$-0.451028\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−5.98561			−0.266885			−0.133442	−	0.991057i	$-0.542603\pi$
$503$	−5.98561			−0.266885			−0.133442	+	0.991057i	$0.542603\pi$
$504$		0			0
$505$	41.7163			1.85635
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.9299	−	24.1273i	−0.617433	−	1.06943i	−0.989952	−	0.141401i	$-0.954839\pi$
$509$	−13.9299	−	24.1273i	−0.617433	−	1.06943i	0.372519	−	0.928024i	$-0.378494\pi$
$510$		0			0
$511$	26.6701	+	21.8962i	1.17982	+	0.968632i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−6.03348	+	10.4503i	−0.265867	+	0.460495i
$516$		0			0
$517$	−43.9624			−1.93347
$518$		0			0
$519$		0			0
$520$		0			0
$521$	4.20398	−	7.28151i	0.184180	−	0.319009i	−0.759120	−	0.650951i	$-0.774370\pi$
$521$	4.20398	−	7.28151i	0.184180	−	0.319009i	0.943300	+	0.331942i	$0.107704\pi$
$522$		0			0
$523$	−9.50373	−	16.4609i	−0.415569	−	0.719786i	0.579919	−	0.814674i	$-0.303084\pi$
$523$	−9.50373	−	16.4609i	−0.415569	−	0.719786i	−0.995488	+	0.0948876i	$0.969751\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	20.0447	+	34.7184i	0.873160	+	1.51236i
$528$		0			0
$529$	−7.00529	+	12.1335i	−0.304578	+	0.527544i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−20.8735			−0.904130
$534$		0			0
$535$	−23.4365	+	40.5932i	−1.01325	+	1.75500i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−26.7958	+	23.4809i	−1.15418	+	1.01139i
$540$		0			0
$541$	−5.80585	−	10.0560i	−0.249613	−	0.432342i	0.713805	−	0.700344i	$-0.246970\pi$
$541$	−5.80585	−	10.0560i	−0.249613	−	0.432342i	−0.963418	+	0.268002i	$0.913637\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	8.50356			0.364253
$546$		0			0
$547$	−39.2855			−1.67973			−0.839864	−	0.542797i	$-0.817365\pi$
$547$	−39.2855			−1.67973			−0.839864	+	0.542797i	$0.817365\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	20.4301	+	35.3860i	0.870352	+	1.50749i
$552$		0			0
$553$	12.9433	−	4.86866i	0.550406	−	0.207036i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−1.93654	+	3.35419i	−0.0820540	+	0.142122i	−0.904132	−	0.427253i	$-0.859481\pi$
$557$	−1.93654	+	3.35419i	−0.0820540	+	0.142122i	0.822078	+	0.569375i	$0.192815\pi$
$558$		0			0
$559$	−44.1085			−1.86559
$560$		0			0
$561$		0			0
$562$		0			0
$563$	0.863603	−	1.49580i	0.0363965	−	0.0630407i	−0.847253	−	0.531189i	$-0.821745\pi$
$563$	0.863603	−	1.49580i	0.0363965	−	0.0630407i	0.883650	+	0.468148i	$0.155079\pi$
$564$		0			0
$565$	21.5065	+	37.2504i	0.904787	+	1.56714i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.05016	+	7.01507i	0.169791	+	0.294087i	0.938346	−	0.345696i	$-0.112357\pi$
$569$	4.05016	+	7.01507i	0.169791	+	0.294087i	−0.768555	+	0.639784i	$0.779024\pi$
$570$		0			0
$571$	−9.47393	+	16.4093i	−0.396472	+	0.686709i	−0.993288	−	0.115669i	$-0.963099\pi$
$571$	−9.47393	+	16.4093i	−0.396472	+	0.686709i	0.596816	+	0.802378i	$0.296432\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	14.9907			0.625155
$576$		0			0
$577$	2.32379	−	4.02492i	0.0967407	−	0.167560i	−0.813593	−	0.581435i	$-0.802492\pi$
$577$	2.32379	−	4.02492i	0.0967407	−	0.167560i	0.910334	+	0.413875i	$0.135825\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	2.47594	−	14.9785i	0.102719	−	0.621412i
$582$		0			0
$583$	−11.7561	−	20.3622i	−0.486888	−	0.843314i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	30.4939			1.25862			0.629308	−	0.777156i	$-0.283338\pi$
$587$	30.4939			1.25862			0.629308	+	0.777156i	$0.283338\pi$
$588$		0			0
$589$	60.4478			2.49071
$590$		0			0
$591$		0			0
$592$		0			0
$593$	1.85400	+	3.21123i	0.0761348	+	0.131869i	0.901579	−	0.432614i	$-0.142409\pi$
$593$	1.85400	+	3.21123i	0.0761348	+	0.131869i	−0.825444	+	0.564483i	$0.809075\pi$
$594$		0			0
$595$	4.94660	−	29.9251i	0.202791	−	1.22681i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	20.1070	−	34.8264i	0.821552	−	1.42297i	−0.0829748	−	0.996552i	$-0.526442\pi$
$599$	20.1070	−	34.8264i	0.821552	−	1.42297i	0.904526	−	0.426418i	$-0.140225\pi$
$600$		0			0
$601$	−14.4852			−0.590866			−0.295433	−	0.955364i	$-0.595464\pi$
$601$	−14.4852			−0.590866			−0.295433	+	0.955364i	$0.595464\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	20.3612	−	35.2666i	0.827800	−	1.43379i
$606$		0			0
$607$	8.93193	+	15.4706i	0.362536	+	0.627930i	0.988377	−	0.152020i	$-0.0485777\pi$
$607$	8.93193	+	15.4706i	0.362536	+	0.627930i	−0.625842	+	0.779950i	$0.715244\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	15.0664	+	26.0957i	0.609520	+	1.05572i
$612$		0			0
$613$	18.2243	−	31.5655i	0.736074	−	1.27492i	−0.218176	−	0.975909i	$-0.570011\pi$
$613$	18.2243	−	31.5655i	0.736074	−	1.27492i	0.954250	−	0.299009i	$-0.0966559\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	22.8769			0.920990			0.460495	−	0.887662i	$-0.347672\pi$
$617$	22.8769			0.920990			0.460495	+	0.887662i	$0.347672\pi$
$618$		0			0
$619$	9.46082	−	16.3866i	0.380262	−	0.658634i	−0.610837	−	0.791756i	$-0.709167\pi$
$619$	9.46082	−	16.3866i	0.380262	−	0.658634i	0.991100	+	0.133122i	$0.0425003\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	7.44418	−	2.80015i	0.298245	−	0.112185i
$624$		0			0
$625$	15.6244	+	27.0622i	0.624974	+	1.08249i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.995906			0.0397094
$630$		0			0
$631$	−1.38657			−0.0551987			−0.0275993	−	0.999619i	$-0.508786\pi$
$631$	−1.38657			−0.0551987			−0.0275993	+	0.999619i	$0.508786\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−16.5149	−	28.6046i	−0.655373	−	1.13514i
$636$		0			0
$637$	23.1212	+	7.85859i	0.916097	+	0.311369i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	13.6625	−	23.6641i	0.539636	−	0.934677i	−0.459288	−	0.888288i	$-0.651895\pi$
$641$	13.6625	−	23.6641i	0.539636	−	0.934677i	0.998923	−	0.0463891i	$-0.0147714\pi$
$642$		0			0
$643$	29.1795			1.15073			0.575363	−	0.817898i	$-0.304861\pi$
$643$	29.1795			1.15073			0.575363	+	0.817898i	$0.304861\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.55384	−	14.8157i	0.336286	−	0.582465i	−0.647445	−	0.762112i	$-0.724162\pi$
$647$	8.55384	−	14.8157i	0.336286	−	0.582465i	0.983731	+	0.179648i	$0.0574958\pi$
$648$		0			0
$649$	11.1322	+	19.2815i	0.436976	+	0.756865i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−4.26075	−	7.37984i	−0.166736	−	0.288795i	0.770534	−	0.637398i	$-0.219989\pi$
$653$	−4.26075	−	7.37984i	−0.166736	−	0.288795i	−0.937270	+	0.348603i	$0.886656\pi$
$654$		0			0
$655$	−1.22066	+	2.11424i	−0.0476951	+	0.0826103i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−38.6253			−1.50463			−0.752313	−	0.658806i	$-0.771062\pi$
$659$	−38.6253			−1.50463			−0.752313	+	0.658806i	$0.771062\pi$
$660$		0			0
$661$	14.0584	−	24.3498i	0.546808	−	0.947099i	−0.451683	−	0.892178i	$-0.649176\pi$
$661$	14.0584	−	24.3498i	0.546808	−	0.947099i	0.998491	−	0.0549202i	$-0.0174905\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−35.3474	−	29.0203i	−1.37071	−	1.12536i
$666$		0			0
$667$	19.6440	+	34.0245i	0.760620	+	1.31743i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.51704			0.174378
$672$		0			0
$673$	5.10115			0.196635			0.0983174	−	0.995155i	$-0.468654\pi$
$673$	5.10115			0.196635			0.0983174	+	0.995155i	$0.468654\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	23.7561	+	41.1468i	0.913021	+	1.58140i	0.809773	+	0.586743i	$0.199590\pi$
$677$	23.7561	+	41.1468i	0.913021	+	1.58140i	0.103248	+	0.994656i	$0.467077\pi$
$678$		0			0
$679$	−5.45553	+	33.0039i	−0.209364	+	1.26657i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.1639	−	27.9968i	0.618496	−	1.07127i	−0.371264	−	0.928527i	$-0.621076\pi$
$683$	16.1639	−	27.9968i	0.618496	−	1.07127i	0.989760	−	0.142739i	$-0.0455910\pi$
$684$		0			0
$685$	37.0465			1.41547
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.05786	+	13.9566i	−0.306980	+	0.531705i
$690$		0			0
$691$	−3.99471	−	6.91905i	−0.151966	−	0.263213i	0.779984	−	0.625799i	$-0.215227\pi$
$691$	−3.99471	−	6.91905i	−0.151966	−	0.263213i	−0.931950	+	0.362586i	$0.881894\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	6.98619	+	12.1004i	0.265001	+	0.458995i
$696$		0			0
$697$	12.5535	−	21.7432i	0.475496	−	0.823584i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−31.9891			−1.20821			−0.604105	−	0.796905i	$-0.706469\pi$
$701$	−31.9891			−1.20821			−0.604105	+	0.796905i	$0.706469\pi$
$702$		0			0
$703$	0.750827	−	1.30047i	0.0283180	−	0.0490482i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−31.2235	−	25.6346i	−1.17428	−	0.964089i
$708$		0			0
$709$	12.9258	+	22.3881i	0.485438	+	0.840803i	0.999860	−	0.0167340i	$-0.00532685\pi$
$709$	12.9258	+	22.3881i	0.485438	+	0.840803i	−0.514422	+	0.857537i	$0.671994\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	58.1220			2.17669
$714$		0			0
$715$	−48.5106			−1.81419
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−11.7362	−	20.3277i	−0.437686	−	0.758094i	0.559825	−	0.828611i	$-0.310868\pi$
$719$	−11.7362	−	20.3277i	−0.437686	−	0.758094i	−0.997511	+	0.0705173i	$0.977535\pi$
$720$		0			0
$721$	10.9376	−	4.11420i	0.407337	−	0.153221i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.95658	−	13.7812i	0.295500	−	0.511821i
$726$		0			0
$727$	9.63621			0.357387			0.178694	−	0.983905i	$-0.442813\pi$
$727$	9.63621			0.357387			0.178694	+	0.983905i	$0.442813\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	26.5272	−	45.9464i	0.981143	−	1.69939i
$732$		0			0
$733$	14.5335	+	25.1727i	0.536806	+	0.929776i	0.999074	+	0.0430350i	$0.0137027\pi$
$733$	14.5335	+	25.1727i	0.536806	+	0.929776i	−0.462267	+	0.886741i	$0.652964\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−22.3724	−	38.7501i	−0.824097	−	1.42738i
$738$		0			0
$739$	−10.4527	+	18.1046i	−0.384509	+	0.665989i	−0.991701	−	0.128566i	$-0.958963\pi$
$739$	−10.4527	+	18.1046i	−0.384509	+	0.665989i	0.607192	+	0.794555i	$0.292296\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	22.6497			0.830936			0.415468	−	0.909608i	$-0.363618\pi$
$743$	22.6497			0.830936			0.415468	+	0.909608i	$0.363618\pi$
$744$		0			0
$745$	−9.19615	+	15.9282i	−0.336921	+	0.583564i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	42.4860	−	15.9812i	1.55241	−	0.583941i
$750$		0			0
$751$	3.80757	+	6.59491i	0.138940	+	0.240652i	0.927096	−	0.374825i	$-0.122297\pi$
$751$	3.80757	+	6.59491i	0.138940	+	0.240652i	−0.788155	+	0.615476i	$0.788964\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−7.17337			−0.261066
$756$		0			0
$757$	−2.38838			−0.0868073			−0.0434036	−	0.999058i	$-0.513820\pi$
$757$	−2.38838			−0.0868073			−0.0434036	+	0.999058i	$0.513820\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−5.02278	−	8.69972i	−0.182076	−	0.315365i	0.760511	−	0.649325i	$-0.224948\pi$
$761$	−5.02278	−	8.69972i	−0.182076	−	0.315365i	−0.942587	+	0.333960i	$0.891615\pi$
$762$		0			0
$763$	−6.36470	−	5.22543i	−0.230417	−	0.189173i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	7.63022	−	13.2159i	0.275511	−	0.477200i
$768$		0			0
$769$	−18.9120			−0.681984			−0.340992	−	0.940066i	$-0.610763\pi$
$769$	−18.9120			−0.681984			−0.340992	+	0.940066i	$0.610763\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	6.53042	−	11.3110i	0.234883	−	0.406829i	−0.724356	−	0.689426i	$-0.757863\pi$
$773$	6.53042	−	11.3110i	0.234883	−	0.406829i	0.959239	+	0.282597i	$0.0911960\pi$
$774$		0			0
$775$	−11.7708	−	20.3876i	−0.422820	−	0.732346i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−18.9285	−	32.7851i	−0.678182	−	1.17465i
$780$		0			0
$781$	6.49918	−	11.2569i	0.232559	−	0.402804i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−16.9738			−0.605820
$786$		0			0
$787$	16.4299	−	28.4575i	0.585664	−	1.01440i	−0.409129	−	0.912477i	$-0.634167\pi$
$787$	16.4299	−	28.4575i	0.585664	−	1.01440i	0.994792	−	0.101922i	$-0.0324994\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	6.79327	−	41.0967i	0.241541	−	1.46123i
$792$		0			0
$793$	−1.54803	−	2.68127i	−0.0549723	−	0.0952148i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.43559			0.227960			0.113980	−	0.993483i	$-0.463640\pi$
$797$	6.43559			0.227960			0.113980	+	0.993483i	$0.463640\pi$
$798$		0			0
$799$	−36.2441			−1.28223
$800$		0			0
$801$		0			0
$802$		0			0
$803$	33.1913	+	57.4890i	1.17130	+	2.02874i
$804$		0			0
$805$	−33.9873	−	27.9037i	−1.19790	−	0.983476i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	0.768767	−	1.33154i	0.0270284	−	0.0468146i	−0.852195	−	0.523225i	$-0.824729\pi$
$809$	0.768767	−	1.33154i	0.0270284	−	0.0468146i	0.879223	+	0.476410i	$0.158062\pi$
$810$		0			0
$811$	−36.3467			−1.27631			−0.638153	−	0.769909i	$-0.720301\pi$
$811$	−36.3467			−1.27631			−0.638153	+	0.769909i	$0.720301\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−9.93654	+	17.2106i	−0.348062	+	0.602861i
$816$		0			0
$817$	−39.9984	−	69.2793i	−1.39937	−	2.42378i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	8.10367	+	14.0360i	0.282820	+	0.489859i	0.972078	−	0.234657i	$-0.0753968\pi$
$821$	8.10367	+	14.0360i	0.282820	+	0.489859i	−0.689258	+	0.724516i	$0.742063\pi$
$822$		0			0
$823$	24.0628	−	41.6780i	0.838777	−	1.45280i	−0.0521412	−	0.998640i	$-0.516605\pi$
$823$	24.0628	−	41.6780i	0.838777	−	1.45280i	0.890918	−	0.454164i	$-0.150062\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−34.4493			−1.19792			−0.598960	−	0.800779i	$-0.704419\pi$
$827$	−34.4493			−1.19792			−0.598960	+	0.800779i	$0.704419\pi$
$828$		0			0
$829$	−21.5379	+	37.3047i	−0.748042	+	1.29565i	0.200718	+	0.979649i	$0.435673\pi$
$829$	−21.5379	+	37.3047i	−0.748042	+	1.29565i	−0.948760	+	0.315998i	$0.897661\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−22.0913	+	19.3585i	−0.765420	+	0.670731i
$834$		0			0
$835$	4.11252	+	7.12309i	0.142320	+	0.246505i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−40.4772			−1.39743			−0.698714	−	0.715401i	$-0.746244\pi$
$839$	−40.4772			−1.39743			−0.698714	+	0.715401i	$0.746244\pi$
$840$		0			0
$841$	12.7057			0.438128
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−1.13327	−	1.96289i	−0.0389858	−	0.0675254i
$846$		0			0
$847$	−36.9111	+	13.8842i	−1.26828	+	0.477067i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.721938	−	1.25043i	0.0247477	−	0.0428643i
$852$		0			0
$853$	10.7194			0.367025			0.183512	−	0.983017i	$-0.441253\pi$
$853$	10.7194			0.367025			0.183512	+	0.983017i	$0.441253\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−13.7059	+	23.7394i	−0.468186	+	0.810922i	−0.999339	−	0.0363540i	$-0.988426\pi$
$857$	−13.7059	+	23.7394i	−0.468186	+	0.810922i	0.531153	+	0.847276i	$0.321759\pi$
$858$		0			0
$859$	−13.9307	−	24.1288i	−0.475311	−	0.823263i	0.524289	−	0.851540i	$-0.324331\pi$
$859$	−13.9307	−	24.1288i	−0.475311	−	0.823263i	−0.999600	+	0.0282777i	$0.990998\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.8881	+	18.8588i	0.370636	+	0.641960i	0.989663	−	0.143409i	$-0.0458066\pi$
$863$	10.8881	+	18.8588i	0.370636	+	0.641960i	−0.619028	+	0.785369i	$0.712473\pi$
$864$		0			0
$865$	−16.6357	+	28.8140i	−0.565632	+	0.979704i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	26.6029			0.902440
$870$		0			0
$871$	−15.3345	+	26.5601i	−0.519589	+	0.899955i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.98943	−	18.0849i	0.101061	−	0.611381i
$876$		0			0
$877$	4.26380	+	7.38513i	0.143978	+	0.249378i	0.928991	−	0.370101i	$-0.120677\pi$
$877$	4.26380	+	7.38513i	0.143978	+	0.249378i	−0.785013	+	0.619479i	$0.787344\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−0.394489			−0.0132907			−0.00664533	−	0.999978i	$-0.502115\pi$
$881$	−0.394489			−0.0132907			−0.00664533	+	0.999978i	$0.502115\pi$
$882$		0			0
$883$	−8.60457			−0.289567			−0.144783	−	0.989463i	$-0.546249\pi$
$883$	−8.60457			−0.289567			−0.144783	+	0.989463i	$0.546249\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−23.1812	−	40.1510i	−0.778348	−	1.34814i	−0.932893	−	0.360153i	$-0.882724\pi$
$887$	−23.1812	−	40.1510i	−0.778348	−	1.34814i	0.154545	−	0.987986i	$-0.450609\pi$
$888$		0			0
$889$	−5.21656	+	31.5582i	−0.174958	+	1.05843i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−27.3250	+	47.3282i	−0.914395	+	1.58378i
$894$		0			0
$895$	50.4282			1.68563
$896$		0			0
$897$		0			0
$898$		0			0
$899$	30.8493	−	53.4326i	1.02888	−	1.78208i
$900$		0			0
$901$	−9.69213	−	16.7873i	−0.322892	−	0.559265i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−9.97785	−	17.2821i	−0.331675	−	0.574478i
$906$		0			0
$907$	−3.43021	+	5.94129i	−0.113898	+	0.197277i	−0.917339	−	0.398108i	$-0.869667\pi$
$907$	−3.43021	+	5.94129i	−0.113898	+	0.197277i	0.803441	+	0.595385i	$0.203000\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−12.4343			−0.411968			−0.205984	−	0.978555i	$-0.566039\pi$
$911$	−12.4343			−0.411968			−0.205984	+	0.978555i	$0.566039\pi$
$912$		0			0
$913$	14.6029	−	25.2929i	0.483284	−	0.837072i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	2.21283	−	0.832362i	0.0730741	−	0.0274870i
$918$		0			0
$919$	23.1447	+	40.0878i	0.763474	+	1.32238i	0.941050	+	0.338268i	$0.109841\pi$
$919$	23.1447	+	40.0878i	0.763474	+	1.32238i	−0.177576	+	0.984107i	$0.556826\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−8.90934			−0.293255
$924$		0			0
$925$	−0.584825			−0.0192289
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.8008	−	20.4395i	−0.387171	−	0.670600i	0.604897	−	0.796304i	$-0.293214\pi$
$929$	−11.8008	−	20.4395i	−0.387171	−	0.670600i	−0.992068	+	0.125704i	$0.959881\pi$
$930$		0			0
$931$	8.62363	+	43.4419i	0.282628	+	1.42375i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	29.1746	−	50.5319i	0.954112	−	1.65257i
$936$		0			0
$937$	5.22028			0.170539			0.0852696	−	0.996358i	$-0.472825\pi$
$937$	5.22028			0.170539			0.0852696	+	0.996358i	$0.472825\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.2966	−	24.7624i	0.466055	−	0.807231i	−0.533193	−	0.845993i	$-0.679008\pi$
$941$	14.2966	−	24.7624i	0.466055	−	0.807231i	0.999248	+	0.0387621i	$0.0123415\pi$
$942$		0			0
$943$	−18.2002	−	31.5236i	−0.592679	−	1.02655i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	19.8253	+	34.3384i	0.644235	+	1.11585i	0.984478	+	0.175510i	$0.0561575\pi$
$947$	19.8253	+	34.3384i	0.644235	+	1.11585i	−0.340242	+	0.940338i	$0.610509\pi$
$948$		0			0
$949$	22.7500	−	39.4041i	0.738496	−	1.27911i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−9.14322			−0.296178			−0.148089	−	0.988974i	$-0.547312\pi$
$953$	−9.14322			−0.296178			−0.148089	+	0.988974i	$0.547312\pi$
$954$		0			0
$955$	27.1016	−	46.9413i	0.876986	−	1.51898i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−27.7283	−	22.7650i	−0.895393	−	0.735121i
$960$		0			0
$961$	−30.1379	−	52.2004i	−0.972191	−	1.68388i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	6.32880			0.203731
$966$		0			0
$967$	−15.4184			−0.495824			−0.247912	−	0.968783i	$-0.579744\pi$
$967$	−15.4184			−0.495824			−0.247912	+	0.968783i	$0.579744\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	18.8102	+	32.5802i	0.603648	+	1.04555i	0.992264	+	0.124149i	$0.0396202\pi$
$971$	18.8102	+	32.5802i	0.603648	+	1.04555i	−0.388615	+	0.921400i	$0.627046\pi$
$972$		0			0
$973$	2.20673	−	13.3499i	0.0707444	−	0.427977i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−12.3222	+	21.3427i	−0.394223	+	0.682814i	−0.993002	−	0.118100i	$-0.962320\pi$
$977$	−12.3222	+	21.3427i	−0.394223	+	0.682814i	0.598779	+	0.800915i	$0.295653\pi$
$978$		0			0
$979$	15.3003			0.488999
$980$		0			0
$981$		0			0
$982$		0			0
$983$	29.2336	−	50.6341i	0.932408	−	1.61498i	0.153217	−	0.988193i	$-0.451037\pi$
$983$	29.2336	−	50.6341i	0.932408	−	1.61498i	0.779192	−	0.626786i	$-0.215630\pi$
$984$		0			0
$985$	−1.77151	−	3.06835i	−0.0564451	−	0.0977658i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−38.4594	−	66.6137i	−1.22294	−	2.11819i
$990$		0			0
$991$	−11.0731	+	19.1792i	−0.351749	+	0.609247i	−0.986556	−	0.163424i	$-0.947746\pi$
$991$	−11.0731	+	19.1792i	−0.351749	+	0.609247i	0.634807	+	0.772671i	$0.281079\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	69.6471			2.20796
$996$		0			0
$997$	−0.752874	+	1.30402i	−0.0238438	+	0.0412986i	−0.877701	−	0.479209i	$-0.840924\pi$
$997$	−0.752874	+	1.30402i	−0.0238438	+	0.0412986i	0.853857	+	0.520507i	$0.174257\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1512.2.s.p.865.4	yes	8
3.2	odd	2		1512.2.s.m.865.2	✓	8
7.2	even	3	inner	1512.2.s.p.1297.4	yes	8
21.2	odd	6		1512.2.s.m.1297.2	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1512.2.s.m.865.2	✓	8	3.2	odd	2
1512.2.s.m.1297.2	yes	8	21.2	odd	6
1512.2.s.p.865.4	yes	8	1.1	even	1	trivial
1512.2.s.p.1297.4	yes	8	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.36603 + 2.36603i) q^{5} +(0.431486 - 2.61033i) q^{7} +O(q^{10})\)	\(q+(1.36603 + 2.36603i) q^{5} +(0.431486 - 2.61033i) q^{7} +(2.54487 - 4.40784i) q^{11} -3.48861 q^{13} +(2.09808 - 3.63397i) q^{17} +(-3.16354 - 5.47941i) q^{19} +(-3.04182 - 5.26858i) q^{23} +(-1.23205 + 2.13397i) q^{25} -6.45800 q^{29} +(-4.77692 + 8.27387i) q^{31} +(6.76553 - 2.54487i) q^{35} +(0.118669 + 0.205541i) q^{37} +5.98332 q^{41} +12.6436 q^{43} +(-4.31873 - 7.48027i) q^{47} +(-6.62764 - 2.25264i) q^{49} +(2.30977 - 4.00063i) q^{53} +13.9054 q^{55} +(-2.18718 + 3.78831i) q^{59} +(0.443740 + 0.768580i) q^{61} +(-4.76553 - 8.25414i) q^{65} +(4.39559 - 7.61338i) q^{67} +2.55384 q^{71} +(-6.52122 + 11.2951i) q^{73} +(-10.4078 - 8.54487i) q^{77} +(2.61338 + 4.52651i) q^{79} +5.73816 q^{83} +11.4641 q^{85} +(1.50305 + 2.60336i) q^{89} +(-1.50529 + 9.10642i) q^{91} +(8.64294 - 14.9700i) q^{95} -12.6436 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 2 q^{7}+O(q^{10}) \) 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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