LMFDB - Embedded newform 1512.2.s.m.865.1

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			865.1
Root			$2.61033 - 0.431486i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.m.1297.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.36603 - 2.36603i) q^{5} +(-0.931486 + 2.47635i) q^{7} +O(q^{10})$	$q+(-1.36603 - 2.36603i) q^{5} +(-0.931486 + 2.47635i) q^{7} +(1.17884 - 2.04182i) q^{11} +6.68476 q^{13} +(-2.09808 + 3.63397i) q^{17} +(-1.80056 - 3.11867i) q^{19} +(-3.40784 - 5.90255i) q^{23} +(-1.23205 + 2.13397i) q^{25} +1.00610 q^{29} +(-1.05321 + 1.82421i) q^{31} +(7.13155 - 1.17884i) q^{35} +(2.47941 + 4.29446i) q^{37} +8.91152 q^{41} -2.25127 q^{43} +(-5.85463 - 10.1405i) q^{47} +(-5.26467 - 4.61338i) q^{49} +(4.13989 - 7.17050i) q^{53} -6.44132 q^{55} +(5.91089 - 10.2380i) q^{59} +(-6.00592 - 10.4026i) q^{61} +(-9.13155 - 15.8163i) q^{65} +(3.03262 - 5.25264i) q^{67} +4.89358 q^{71} +(2.28917 - 3.96496i) q^{73} +(3.95818 + 4.82116i) q^{77} +(0.252644 + 0.437591i) q^{79} -11.1900 q^{83} +11.4641 q^{85} +(-4.22900 - 7.32484i) q^{89} +(-6.22676 + 16.5538i) q^{91} +(-4.91923 + 8.52036i) q^{95} +2.25127 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.957472\pi$
$5$	−1.36603	−	2.36603i	−0.610905	−	1.05812i	0.380183	−	0.924911i	$-0.375861\pi$
$6$		0			0
$7$	−0.931486	+	2.47635i	−0.352069	+	0.935974i
$7$	−0.931486	+	2.47635i	−0.352069	+	0.935974i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.17884	−	2.04182i	0.355435	−	0.615631i	−0.631758	−	0.775166i	$-0.717666\pi$
$11$	1.17884	−	2.04182i	0.355435	−	0.615631i	0.987192	+	0.159535i	$0.0509996\pi$
$12$		0			0
$13$	6.68476			1.85402			0.927009	−	0.375038i	$-0.122370\pi$
$13$	6.68476			1.85402			0.927009	+	0.375038i	$0.122370\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.09808	+	3.63397i	−0.508858	+	0.881368i	0.491089	+	0.871109i	$0.336599\pi$
$17$	−2.09808	+	3.63397i	−0.508858	+	0.881368i	−0.999947	+	0.0102590i	$0.996734\pi$
$18$		0			0
$19$	−1.80056	−	3.11867i	−0.413078	−	0.715472i	0.582147	−	0.813084i	$-0.302213\pi$
$19$	−1.80056	−	3.11867i	−0.413078	−	0.715472i	−0.995225	+	0.0976120i	$0.968880\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.40784	−	5.90255i	−0.710584	−	1.23077i	−0.964638	−	0.263578i	$-0.915097\pi$
$23$	−3.40784	−	5.90255i	−0.710584	−	1.23077i	0.254054	−	0.967190i	$-0.418236\pi$
$24$		0			0
$25$	−1.23205	+	2.13397i	−0.246410	+	0.426795i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	1.00610			0.186829			0.0934145	−	0.995627i	$-0.470222\pi$
$29$	1.00610			0.186829			0.0934145	+	0.995627i	$0.470222\pi$
$30$		0			0
$31$	−1.05321	+	1.82421i	−0.189162	+	0.327638i	−0.944971	−	0.327154i	$-0.893910\pi$
$31$	−1.05321	+	1.82421i	−0.189162	+	0.327638i	0.755809	+	0.654792i	$0.227244\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	7.13155	−	1.17884i	1.20545	−	0.199261i
$36$		0			0
$37$	2.47941	+	4.29446i	0.407612	+	0.706005i	0.994622	−	0.103575i	$-0.0330282\pi$
$37$	2.47941	+	4.29446i	0.407612	+	0.706005i	−0.587010	+	0.809580i	$0.699695\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	8.91152			1.39175			0.695873	−	0.718165i	$-0.255018\pi$
$41$	8.91152			1.39175			0.695873	+	0.718165i	$0.255018\pi$
$42$		0			0
$43$	−2.25127			−0.343315			−0.171658	−	0.985157i	$-0.554912\pi$
$43$	−2.25127			−0.343315			−0.171658	+	0.985157i	$0.554912\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.85463	−	10.1405i	−0.853986	−	1.47915i	−0.877583	−	0.479426i	$-0.840845\pi$
$47$	−5.85463	−	10.1405i	−0.853986	−	1.47915i	0.0235965	−	0.999722i	$-0.492488\pi$
$48$		0			0
$49$	−5.26467	−	4.61338i	−0.752095	−	0.659055i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	4.13989	−	7.17050i	0.568658	−	0.984944i	−0.428041	−	0.903759i	$-0.640796\pi$
$53$	4.13989	−	7.17050i	0.568658	−	0.984944i	0.996699	−	0.0811851i	$-0.0258705\pi$
$54$		0			0
$55$	−6.44132			−0.868547
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.91089	−	10.2380i	0.769533	−	1.33287i	−0.168284	−	0.985739i	$-0.553822\pi$
$59$	5.91089	−	10.2380i	0.769533	−	1.33287i	0.937817	−	0.347131i	$-0.112844\pi$
$60$		0			0
$61$	−6.00592	−	10.4026i	−0.768979	−	1.33191i	−0.938117	−	0.346318i	$-0.887432\pi$
$61$	−6.00592	−	10.4026i	−0.768979	−	1.33191i	0.169138	−	0.985592i	$-0.445902\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−9.13155	−	15.8163i	−1.13263	−	1.96177i
$66$		0			0
$67$	3.03262	−	5.25264i	0.370493	−	0.641713i	−0.619149	−	0.785274i	$-0.712522\pi$
$67$	3.03262	−	5.25264i	0.370493	−	0.641713i	0.989641	+	0.143561i	$0.0458554\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	4.89358			0.580762			0.290381	−	0.956911i	$-0.406218\pi$
$71$	4.89358			0.580762			0.290381	+	0.956911i	$0.406218\pi$
$72$		0			0
$73$	2.28917	−	3.96496i	0.267927	−	0.464064i	−0.700399	−	0.713751i	$-0.746995\pi$
$73$	2.28917	−	3.96496i	0.267927	−	0.464064i	0.968326	+	0.249688i	$0.0803279\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.95818	+	4.82116i	0.451077	+	0.549422i
$78$		0			0
$79$	0.252644	+	0.437591i	0.0284246	+	0.0492329i	0.879888	−	0.475182i	$-0.157618\pi$
$79$	0.252644	+	0.437591i	0.0284246	+	0.0492329i	−0.851463	+	0.524414i	$0.824284\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−11.1900			−1.22827			−0.614134	−	0.789202i	$-0.710494\pi$
$83$	−11.1900			−1.22827			−0.614134	+	0.789202i	$0.710494\pi$
$84$		0			0
$85$	11.4641			1.24346
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−4.22900	−	7.32484i	−0.448273	−	0.776431i	0.550001	−	0.835164i	$-0.314627\pi$
$89$	−4.22900	−	7.32484i	−0.448273	−	0.776431i	−0.998274	+	0.0587326i	$0.981294\pi$
$90$		0			0
$91$	−6.22676	+	16.5538i	−0.652742	+	1.73531i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.91923	+	8.52036i	−0.504703	+	0.874171i
$96$		0			0
$97$	2.25127			0.228582			0.114291	−	0.993447i	$-0.463540\pi$
$97$	2.25127			0.228582			0.114291	+	0.993447i	$0.463540\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.53653	−	6.12545i	0.351898	−	0.609505i	−0.634684	−	0.772772i	$-0.718870\pi$
$101$	3.53653	−	6.12545i	0.351898	−	0.609505i	0.986582	+	0.163267i	$0.0522031\pi$
$102$		0			0
$103$	−2.87828	−	4.98532i	−0.283605	−	0.491219i	0.688665	−	0.725080i	$-0.258197\pi$
$103$	−2.87828	−	4.98532i	−0.283605	−	0.491219i	−0.972270	+	0.233861i	$0.924864\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	9.04245	+	15.6620i	0.874166	+	1.51410i	0.857648	+	0.514237i	$0.171925\pi$
$107$	9.04245	+	15.6620i	0.874166	+	1.51410i	0.0165180	+	0.999864i	$0.494742\pi$
$108$		0			0
$109$	8.00592	−	13.8667i	0.766828	−	1.32818i	−0.172447	−	0.985019i	$-0.555167\pi$
$109$	8.00592	−	13.8667i	0.766828	−	1.32818i	0.939275	−	0.343166i	$-0.111499\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−2.84457			−0.267595			−0.133797	−	0.991009i	$-0.542717\pi$
$113$	−2.84457			−0.267595			−0.133797	+	0.991009i	$0.542717\pi$
$114$		0			0
$115$	−9.31040	+	16.1261i	−0.868199	+	1.50376i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7.04468	−	8.58058i	−0.645785	−	0.786580i
$120$		0			0
$121$	2.72066	+	4.71232i	0.247333	+	0.428393i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.92820			−0.619677
$126$		0			0
$127$	−4.64231			−0.411939			−0.205969	−	0.978558i	$-0.566035\pi$
$127$	−4.64231			−0.411939			−0.205969	+	0.978558i	$0.566035\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	3.27692	+	5.67579i	0.286306	+	0.495896i	0.972925	−	0.231121i	$-0.0742394\pi$
$131$	3.27692	+	5.67579i	0.286306	+	0.495896i	−0.686619	+	0.727017i	$0.740906\pi$
$132$		0			0
$133$	9.40013	−	1.55384i	0.815095	−	0.134735i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.78221	+	10.0151i	−0.494007	+	0.855646i	−0.999976	−	0.00690610i	$-0.997802\pi$
$137$	−5.78221	+	10.0151i	−0.494007	+	0.855646i	0.505969	+	0.862552i	$0.331135\pi$
$138$		0			0
$139$	−12.5065			−1.06079			−0.530396	−	0.847750i	$-0.677957\pi$
$139$	−12.5065			−1.06079			−0.530396	+	0.847750i	$0.677957\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	7.88028	−	13.6490i	0.658982	−	1.14139i
$144$		0			0
$145$	−1.37436	−	2.38047i	−0.114135	−	0.197687i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−3.36603	−	5.83013i	−0.275756	−	0.477623i	0.694570	−	0.719425i	$-0.255595\pi$
$149$	−3.36603	−	5.83013i	−0.275756	−	0.477623i	−0.970325	+	0.241803i	$0.922261\pi$
$150$		0			0
$151$	2.41089	−	4.17579i	0.196196	−	0.339821i	−0.751096	−	0.660193i	$-0.770475\pi$
$151$	2.41089	−	4.17579i	0.196196	−	0.339821i	0.947292	+	0.320372i	$0.103808\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	5.75483			0.462239
$156$		0			0
$157$	−10.5538	+	18.2798i	−0.842288	+	1.45889i	0.0456678	+	0.998957i	$0.485458\pi$
$157$	−10.5538	+	18.2798i	−0.842288	+	1.45889i	−0.887956	+	0.459929i	$0.847875\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	17.7912	−	2.94087i	1.40214	−	0.231773i
$162$		0			0
$163$	6.36297	+	11.0210i	0.498387	+	0.863231i	0.999998	−	0.00186211i	$-0.000592727\pi$
$163$	6.36297	+	11.0210i	0.498387	+	0.863231i	−0.501612	+	0.865093i	$0.667259\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−12.4535			−0.963683			−0.481841	−	0.876258i	$-0.660032\pi$
$167$	−12.4535			−0.963683			−0.481841	+	0.876258i	$0.660032\pi$
$168$		0			0
$169$	31.6860			2.43739
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−9.81282	−	16.9963i	−0.746055	−	1.29220i	−0.949700	−	0.313160i	$-0.898612\pi$
$173$	−9.81282	−	16.9963i	−0.746055	−	1.29220i	0.203646	−	0.979045i	$-0.434721\pi$
$174$		0			0
$175$	−4.13684	−	5.03876i	−0.312716	−	0.380895i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−6.50305	+	11.2636i	−0.486061	+	0.841882i	−0.999872	−	0.0160213i	$-0.994900\pi$
$179$	−6.50305	+	11.2636i	−0.486061	+	0.841882i	0.513811	+	0.857904i	$0.328233\pi$
$180$		0			0
$181$	15.7684			1.17206			0.586028	−	0.810291i	$-0.300691\pi$
$181$	15.7684			1.17206			0.586028	+	0.810291i	$0.300691\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	6.77387	−	11.7327i	0.498025	−	0.862604i
$186$		0			0
$187$	4.94660	+	8.56777i	0.361732	+	0.626537i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	2.47244	+	4.28239i	0.178900	+	0.309863i	0.941504	−	0.337002i	$-0.109413\pi$
$191$	2.47244	+	4.28239i	0.178900	+	0.309863i	−0.762604	+	0.646865i	$0.776080\pi$
$192$		0			0
$193$	−4.92620	+	8.53243i	−0.354596	+	0.614178i	−0.987049	−	0.160421i	$-0.948715\pi$
$193$	−4.92620	+	8.53243i	−0.354596	+	0.614178i	0.632453	+	0.774599i	$0.282048\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	27.0955			1.93047			0.965236	−	0.261380i	$-0.0841775\pi$
$197$	27.0955			1.93047			0.965236	+	0.261380i	$0.0841775\pi$
$198$		0			0
$199$	13.7441	−	23.8054i	0.974292	−	1.68752i	0.292038	−	0.956407i	$-0.405667\pi$
$199$	13.7441	−	23.8054i	0.974292	−	1.68752i	0.682253	−	0.731116i	$-0.261000\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−0.937173	+	2.49147i	−0.0657767	+	0.174867i
$204$		0			0
$205$	−12.1734	−	21.0849i	−0.850225	−	1.47263i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−8.49033			−0.587288
$210$		0			0
$211$	1.66636			0.114717			0.0573584	−	0.998354i	$-0.481732\pi$
$211$	1.66636			0.114717			0.0573584	+	0.998354i	$0.481732\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.07529	+	5.32656i	0.209733	+	0.363269i
$216$		0			0
$217$	−3.53634	−	4.30734i	−0.240062	−	0.292401i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−14.0251	+	24.2922i	−0.943433	+	1.63407i
$222$		0			0
$223$	5.19005			0.347551			0.173776	−	0.984785i	$-0.444403\pi$
$223$	5.19005			0.347551			0.173776	+	0.984785i	$0.444403\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.05016	+	1.81892i	−0.0697013	+	0.120726i	−0.898770	−	0.438421i	$-0.855538\pi$
$227$	−1.05016	+	1.81892i	−0.0697013	+	0.120726i	0.829069	+	0.559147i	$0.188871\pi$
$228$		0			0
$229$	12.6316	+	21.8785i	0.834716	+	1.44577i	0.894261	+	0.447546i	$0.147702\pi$
$229$	12.6316	+	21.8785i	0.834716	+	1.44577i	−0.0595446	+	0.998226i	$0.518965\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	10.9862	+	19.0286i	0.719729	+	1.24661i	0.961107	+	0.276176i	$0.0890673\pi$
$233$	10.9862	+	19.0286i	0.719729	+	1.24661i	−0.241378	+	0.970431i	$0.577599\pi$
$234$		0			0
$235$	−15.9952	+	27.7044i	−1.04341	+	1.80724i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	21.3038			1.37803			0.689015	−	0.724747i	$-0.258043\pi$
$239$	21.3038			1.37803			0.689015	+	0.724747i	$0.258043\pi$
$240$		0			0
$241$	6.17866	−	10.7017i	0.398002	−	0.689360i	−0.595477	−	0.803372i	$-0.703037\pi$
$241$	6.17866	−	10.7017i	0.398002	−	0.689360i	0.993479	+	0.114012i	$0.0363703\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−3.72371	+	18.7583i	−0.237899	+	1.19843i
$246$		0			0
$247$	−12.0363	−	20.8476i	−0.765854	−	1.32650i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	1.35158			0.0853110			0.0426555	−	0.999090i	$-0.486418\pi$
$251$	1.35158			0.0853110			0.0426555	+	0.999090i	$0.486418\pi$
$252$		0			0
$253$	−16.0692			−1.01026
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.59502	+	9.69087i	0.349008	+	0.604500i	0.986074	−	0.166310i	$-0.0531853\pi$
$257$	5.59502	+	9.69087i	0.349008	+	0.604500i	−0.637066	+	0.770810i	$0.719852\pi$
$258$		0			0
$259$	−12.9441	+	2.13966i	−0.804310	+	0.132952i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−6.93540	+	12.0125i	−0.427655	+	0.740720i	−0.996664	−	0.0816108i	$-0.973994\pi$
$263$	−6.93540	+	12.0125i	−0.427655	+	0.740720i	0.569009	+	0.822331i	$0.307327\pi$
$264$		0			0
$265$	−22.6208			−1.38958
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.9115	+	22.3634i	−0.787230	+	1.36352i	0.140429	+	0.990091i	$0.455152\pi$
$269$	−12.9115	+	22.3634i	−0.787230	+	1.36352i	−0.927658	+	0.373431i	$0.878181\pi$
$270$		0			0
$271$	−12.0895	−	20.9397i	−0.734388	−	1.27200i	−0.954991	−	0.296633i	$-0.904136\pi$
$271$	−12.0895	−	20.9397i	−0.734388	−	1.27200i	0.220604	−	0.975364i	$-0.429197\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	2.90479	+	5.03124i	0.175165	+	0.303395i
$276$		0			0
$277$	6.03653	−	10.4556i	0.362700	−	0.628215i	−0.625704	−	0.780060i	$-0.715188\pi$
$277$	6.03653	−	10.4556i	0.362700	−	0.628215i	0.988404	+	0.151846i	$0.0485217\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.6554			−0.635648			−0.317824	−	0.948150i	$-0.602952\pi$
$281$	−10.6554			−0.635648			−0.317824	+	0.948150i	$0.602952\pi$
$282$		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
$287$	−8.30096	+	22.0681i	−0.489990	+	1.30264i
$288$		0			0
$289$	−0.303848	−	0.526279i	−0.0178734	−	0.0309576i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−5.38047			−0.314330			−0.157165	−	0.987572i	$-0.550236\pi$
$293$	−5.38047			−0.314330			−0.157165	+	0.987572i	$0.550236\pi$
$294$		0			0
$295$	−32.2977			−1.88045
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−22.7806	−	39.4572i	−1.31744	−	2.28187i
$300$		0			0
$301$	2.09703	−	5.57494i	0.120871	−	0.321334i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−16.4085	+	28.4203i	−0.939546	+	1.62734i
$306$		0			0
$307$	18.3083			1.04491			0.522455	−	0.852667i	$-0.325016\pi$
$307$	18.3083			1.04491			0.522455	+	0.852667i	$0.325016\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−1.00063	+	1.73314i	−0.0567405	+	0.0982775i	−0.893000	−	0.450056i	$-0.851404\pi$
$311$	−1.00063	+	1.73314i	−0.0567405	+	0.0982775i	0.836260	+	0.548333i	$0.184737\pi$
$312$		0			0
$313$	2.04401	+	3.54032i	0.115534	+	0.200111i	0.917993	−	0.396596i	$-0.129809\pi$
$313$	2.04401	+	3.54032i	0.115534	+	0.200111i	−0.802459	+	0.596707i	$0.796475\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−4.88639	−	8.46347i	−0.274447	−	0.475356i	0.695549	−	0.718479i	$-0.255161\pi$
$317$	−4.88639	−	8.46347i	−0.274447	−	0.475356i	−0.969995	+	0.243123i	$0.921828\pi$
$318$		0			0
$319$	1.18604	−	2.05428i	0.0664055	−	0.115018i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	15.1109			0.840792
$324$		0			0
$325$	−8.23596	+	14.2651i	−0.456849	+	0.791286i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	30.5650	−	5.05239i	1.68511	−	0.278547i
$330$		0			0
$331$	16.8369	+	29.1624i	0.925440	+	1.60291i	0.790852	+	0.612008i	$0.209638\pi$
$331$	16.8369	+	29.1624i	0.925440	+	1.60291i	0.134588	+	0.990902i	$0.457029\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−16.5705			−0.905344
$336$		0			0
$337$	24.7790			1.34980			0.674898	−	0.737911i	$-0.264188\pi$
$337$	24.7790			1.34980			0.674898	+	0.737911i	$0.264188\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	2.48313	+	4.30091i	0.134469	+	0.232908i
$342$		0			0
$343$	16.3283	−	8.73988i	0.881647	−	0.471909i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.53590	+	14.7846i	−0.458231	+	0.793679i	−0.998868	−	0.0475768i	$-0.984850\pi$
$347$	−8.53590	+	14.7846i	−0.458231	+	0.793679i	0.540637	+	0.841256i	$0.318183\pi$
$348$		0			0
$349$	−11.0714			−0.592640			−0.296320	−	0.955089i	$-0.595759\pi$
$349$	−11.0714			−0.592640			−0.296320	+	0.955089i	$0.595759\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−10.0670	+	17.4365i	−0.535810	+	0.928050i	0.463314	+	0.886194i	$0.346660\pi$
$353$	−10.0670	+	17.4365i	−0.535810	+	0.928050i	−0.999124	+	0.0418556i	$0.986673\pi$
$354$		0			0
$355$	−6.68476	−	11.5783i	−0.354790	−	0.614515i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.04245	−	15.6620i	−0.477242	−	0.826607i	0.522418	−	0.852690i	$-0.325030\pi$
$359$	−9.04245	−	15.6620i	−0.477242	−	0.826607i	−0.999660	+	0.0260822i	$0.991697\pi$
$360$		0			0
$361$	3.01594	−	5.22375i	0.158733	−	0.274934i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−12.5083			−0.654713
$366$		0			0
$367$	2.60441	−	4.51097i	0.135949	−	0.235471i	−0.790010	−	0.613093i	$-0.789925\pi$
$367$	2.60441	−	4.51097i	0.135949	−	0.235471i	0.925960	+	0.377622i	$0.123258\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.9005	+	16.9311i	0.721676	+	0.879017i
$372$		0			0
$373$	−10.3299	−	17.8919i	−0.534862	−	0.926408i	−0.999170	−	0.0407341i	$-0.987030\pi$
$373$	−10.3299	−	17.8919i	−0.534862	−	0.926408i	0.464308	−	0.885674i	$-0.346303\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.72557			0.346385
$378$		0			0
$379$	−27.9829			−1.43738			−0.718691	−	0.695329i	$-0.755259\pi$
$379$	−27.9829			−1.43738			−0.718691	+	0.695329i	$0.755259\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	8.11424	+	14.0543i	0.414618	+	0.718140i	0.995388	−	0.0959276i	$-0.0305817\pi$
$383$	8.11424	+	14.0543i	0.414618	+	0.718140i	−0.580770	+	0.814068i	$0.697248\pi$
$384$		0			0
$385$	6.00000	−	15.9510i	0.305788	−	0.812938i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	4.72434	−	8.18280i	0.239534	−	0.414884i	−0.721047	−	0.692886i	$-0.756339\pi$
$389$	4.72434	−	8.18280i	0.239534	−	0.414884i	0.960581	+	0.278002i	$0.0896721\pi$
$390$		0			0
$391$	28.5996			1.44635
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.690235	−	1.19552i	0.0347295	−	0.0601532i
$396$		0			0
$397$	8.64823	+	14.9792i	0.434042	+	0.751783i	0.997217	−	0.0745546i	$-0.0237535\pi$
$397$	8.64823	+	14.9792i	0.434042	+	0.751783i	−0.563175	+	0.826338i	$0.690420\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−2.46347	−	4.26686i	−0.123020	−	0.213077i	0.797937	−	0.602740i	$-0.205925\pi$
$401$	−2.46347	−	4.26686i	−0.123020	−	0.213077i	−0.920957	+	0.389664i	$0.872591\pi$
$402$		0			0
$403$	−7.04044	+	12.1944i	−0.350709	+	0.607447i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	11.6913			0.579518
$408$		0			0
$409$	2.63374	−	4.56178i	0.130230	−	0.225565i	−0.793535	−	0.608525i	$-0.791762\pi$
$409$	2.63374	−	4.56178i	0.130230	−	0.225565i	0.923765	+	0.382959i	$0.125095\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	19.8469	+	24.1740i	0.976603	+	1.18952i
$414$		0			0
$415$	15.2859	+	26.4759i	0.750355	+	1.29965i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−4.06569			−0.198622			−0.0993110	−	0.995056i	$-0.531664\pi$
$419$	−4.06569			−0.198622			−0.0993110	+	0.995056i	$0.531664\pi$
$420$		0			0
$421$	−17.9479			−0.874725			−0.437363	−	0.899285i	$-0.644087\pi$
$421$	−17.9479			−0.874725			−0.437363	+	0.899285i	$0.644087\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−5.16987	−	8.95448i	−0.250776	−	0.434356i
$426$		0			0
$427$	31.3548	−	5.18294i	1.51737	−	0.250820i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−17.4892	+	30.2922i	−0.842427	+	1.45913i	0.0454101	+	0.998968i	$0.485541\pi$
$431$	−17.4892	+	30.2922i	−0.842427	+	1.45913i	−0.887837	+	0.460158i	$0.847793\pi$
$432$		0			0
$433$	−16.6314			−0.799252			−0.399626	−	0.916678i	$-0.630860\pi$
$433$	−16.6314			−0.799252			−0.399626	+	0.916678i	$0.630860\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−12.2721	+	21.2559i	−0.587053	+	1.01681i
$438$		0			0
$439$	10.1550	+	17.5889i	0.484670	+	0.839473i	0.999845	−	0.0176119i	$-0.00560632\pi$
$439$	10.1550	+	17.5889i	0.484670	+	0.839473i	−0.515175	+	0.857085i	$0.672273\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.65739	+	14.9950i	0.411325	+	0.712436i	0.995035	−	0.0995265i	$-0.0317328\pi$
$443$	8.65739	+	14.9950i	0.411325	+	0.712436i	−0.583710	+	0.811962i	$0.698399\pi$
$444$		0			0
$445$	−11.5538	+	20.0118i	−0.547704	+	0.948652i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−8.85030			−0.417672			−0.208836	−	0.977951i	$-0.566967\pi$
$449$	−8.85030			−0.417672			−0.208836	+	0.977951i	$0.566967\pi$
$450$		0			0
$451$	10.5053	−	18.1957i	0.494675	−	0.856802i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	47.6727	−	7.88028i	2.23493	−	0.369433i
$456$		0			0
$457$	−3.51668	−	6.09107i	−0.164503	−	0.284928i	0.771975	−	0.635652i	$-0.219269\pi$
$457$	−3.51668	−	6.09107i	−0.164503	−	0.284928i	−0.936479	+	0.350724i	$0.885935\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.0452			0.514426			0.257213	−	0.966355i	$-0.417196\pi$
$461$	11.0452			0.514426			0.257213	+	0.966355i	$0.417196\pi$
$462$		0			0
$463$	2.49597			0.115998			0.0579989	−	0.998317i	$-0.481528\pi$
$463$	2.49597			0.115998			0.0579989	+	0.998317i	$0.481528\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−8.66135	−	15.0019i	−0.400799	−	0.694205i	0.593023	−	0.805185i	$-0.297934\pi$
$467$	−8.66135	−	15.0019i	−0.400799	−	0.694205i	−0.993823	+	0.110981i	$0.964601\pi$
$468$		0			0
$469$	10.1826	+	12.4026i	0.470187	+	0.572699i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−2.65389	+	4.59668i	−0.122026	+	0.211356i
$474$		0			0
$475$	8.87355			0.407146
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−7.44966	+	12.9032i	−0.340384	+	0.589562i	−0.984504	−	0.175363i	$-0.943890\pi$
$479$	−7.44966	+	12.9032i	−0.340384	+	0.589562i	0.644120	+	0.764924i	$0.277224\pi$
$480$		0			0
$481$	16.5742	+	28.7074i	0.755720	+	1.30895i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−3.07529	−	5.32656i	−0.139642	−	0.241867i
$486$		0			0
$487$	16.0637	−	27.8231i	0.727914	−	1.26078i	−0.229849	−	0.973226i	$-0.573823\pi$
$487$	16.0637	−	27.8231i	0.727914	−	1.26078i	0.957763	−	0.287558i	$-0.0928435\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−26.3099			−1.18735			−0.593675	−	0.804705i	$-0.702324\pi$
$491$	−26.3099			−1.18735			−0.593675	+	0.804705i	$0.702324\pi$
$492$		0			0
$493$	−2.11088	+	3.65616i	−0.0950695	+	0.164665i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−4.55831	+	12.1183i	−0.204468	+	0.543578i
$498$		0			0
$499$	2.94132	+	5.09451i	0.131671	+	0.228062i	0.924321	−	0.381616i	$-0.124632\pi$
$499$	2.94132	+	5.09451i	0.131671	+	0.228062i	−0.792650	+	0.609678i	$0.791299\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	33.7798			1.50617			0.753083	−	0.657926i	$-0.228566\pi$
$503$	33.7798			1.50617			0.753083	+	0.657926i	$0.228566\pi$
$504$		0			0
$505$	−19.3240			−0.859905
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−16.5902	−	28.7350i	−0.735347	−	1.27366i	−0.954571	−	0.297983i	$-0.903686\pi$
$509$	−16.5902	−	28.7350i	−0.735347	−	1.27366i	0.219224	−	0.975674i	$-0.429647\pi$
$510$		0			0
$511$	7.68632	+	9.36211i	0.340023	+	0.414155i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−7.86360	+	13.6202i	−0.346512	+	0.600176i
$516$		0			0
$517$	−27.6068			−1.21414
$518$		0			0
$519$		0			0
$520$		0			0
$521$	20.8642	−	36.1379i	0.914079	−	1.58323i	0.105834	−	0.994384i	$-0.466249\pi$
$521$	20.8642	−	36.1379i	0.914079	−	1.58323i	0.808245	−	0.588847i	$-0.200418\pi$
$522$		0			0
$523$	14.9319	+	25.8629i	0.652928	+	1.13090i	0.982409	+	0.186742i	$0.0597928\pi$
$523$	14.9319	+	25.8629i	0.652928	+	1.13090i	−0.329481	+	0.944162i	$0.606874\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−4.41942	−	7.65466i	−0.192513	−	0.333442i
$528$		0			0
$529$	−11.7268	+	20.3114i	−0.509859	+	0.883102i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	59.5714			2.58032
$534$		0			0
$535$	24.7044	−	42.7893i	1.06807	−	1.84994i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−15.6259	+	5.31103i	−0.673055	+	0.228762i
$540$		0			0
$541$	−11.8903	−	20.5946i	−0.511204	−	0.885431i	−0.999916	−	0.0129859i	$-0.995866\pi$
$541$	−11.8903	−	20.5946i	−0.511204	−	0.885431i	0.488712	−	0.872445i	$-0.337467\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−43.7451			−1.87384
$546$		0			0
$547$	−8.03499			−0.343552			−0.171776	−	0.985136i	$-0.554950\pi$
$547$	−8.03499			−0.343552			−0.171776	+	0.985136i	$0.554950\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−1.81156	−	3.13771i	−0.0771749	−	0.133671i
$552$		0			0
$553$	−1.31897	+	0.218025i	−0.0560881	+	0.00927135i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	9.38397	−	16.2535i	0.397611	−	0.688683i	−0.595819	−	0.803119i	$-0.703173\pi$
$557$	9.38397	−	16.2535i	0.397611	−	0.688683i	0.993431	+	0.114435i	$0.0365059\pi$
$558$		0			0
$559$	−15.0492			−0.636513
$560$		0			0
$561$		0			0
$562$		0			0
$563$	13.0335	−	22.5746i	0.549296	−	0.951408i	−0.449027	−	0.893518i	$-0.648229\pi$
$563$	13.0335	−	22.5746i	0.549296	−	0.951408i	0.998323	−	0.0578898i	$-0.0184372\pi$
$564$		0			0
$565$	3.88576	+	6.73033i	0.163475	+	0.283147i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−5.04792	−	8.74326i	−0.211620	−	0.366536i	0.740602	−	0.671944i	$-0.234541\pi$
$569$	−5.04792	−	8.74326i	−0.211620	−	0.366536i	−0.952222	+	0.305408i	$0.901207\pi$
$570$		0			0
$571$	9.50983	−	16.4715i	0.397974	−	0.689311i	−0.595502	−	0.803354i	$-0.703047\pi$
$571$	9.50983	−	16.4715i	0.397974	−	0.689311i	0.993476	+	0.114043i	$0.0363801\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	16.7945			0.700380
$576$		0			0
$577$	0.960818	−	1.66419i	0.0399994	−	0.0692810i	−0.845333	−	0.534240i	$-0.820598\pi$
$577$	0.960818	−	1.66419i	0.0399994	−	0.0692810i	0.885332	+	0.464959i	$0.153931\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	10.4234	−	27.7105i	0.432435	−	1.14963i
$582$		0			0
$583$	−9.76056	−	16.9058i	−0.404241	−	0.700166i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−10.1471			−0.418817			−0.209409	−	0.977828i	$-0.567154\pi$
$587$	−10.1471			−0.418817			−0.209409	+	0.977828i	$0.567154\pi$
$588$		0			0
$589$	7.58547			0.312554
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−2.85177	−	4.93941i	−0.117108	−	0.202837i	0.801512	−	0.597978i	$-0.204029\pi$
$593$	−2.85177	−	4.93941i	−0.117108	−	0.202837i	−0.918620	+	0.395141i	$0.870696\pi$
$594$		0			0
$595$	−10.6787	+	28.3892i	−0.437782	+	1.16384i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.3833	+	28.3768i	−0.669405	+	1.15944i	0.308666	+	0.951171i	$0.400118\pi$
$599$	−16.3833	+	28.3768i	−0.669405	+	1.15944i	−0.978071	+	0.208273i	$0.933216\pi$
$600$		0			0
$601$	−33.3712			−1.36124			−0.680619	−	0.732638i	$-0.738289\pi$
$601$	−33.3712			−1.36124			−0.680619	+	0.732638i	$0.738289\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	7.43298	−	12.8743i	0.302194	−	0.523415i
$606$		0			0
$607$	−15.5037	−	26.8532i	−0.629277	−	1.08994i	−0.987697	−	0.156379i	$-0.950018\pi$
$607$	−15.5037	−	26.8532i	−0.629277	−	1.08994i	0.358420	−	0.933560i	$-0.383315\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−39.1368	−	67.7870i	−1.58331	−	2.74237i
$612$		0			0
$613$	−0.394215	+	0.682800i	−0.0159222	+	0.0275780i	−0.873877	−	0.486148i	$-0.838402\pi$
$613$	−0.394215	+	0.682800i	−0.0159222	+	0.0275780i	0.857955	+	0.513726i	$0.171735\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−0.534638			−0.0215237			−0.0107619	−	0.999942i	$-0.503426\pi$
$617$	−0.534638			−0.0215237			−0.0107619	+	0.999942i	$0.503426\pi$
$618$		0			0
$619$	10.8238	−	18.7474i	0.435045	−	0.753520i	−0.562254	−	0.826964i	$-0.690066\pi$
$619$	10.8238	−	18.7474i	0.435045	−	0.753520i	0.997299	+	0.0734444i	$0.0233992\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.0782	−	3.64951i	0.884543	−	0.146215i
$624$		0			0
$625$	15.6244	+	27.0622i	0.624974	+	1.08249i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−20.8079			−0.829667
$630$		0			0
$631$	−19.7378			−0.785749			−0.392874	−	0.919592i	$-0.628519\pi$
$631$	−19.7378			−0.785749			−0.392874	+	0.919592i	$0.628519\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	6.34152	+	10.9838i	0.251656	+	0.435880i
$636$		0			0
$637$	−35.1930	−	30.8394i	−1.39440	−	1.22190i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−15.6580	+	27.1205i	−0.618455	+	1.07119i	0.371313	+	0.928508i	$0.378908\pi$
$641$	−15.6580	+	27.1205i	−0.618455	+	1.07119i	−0.989768	+	0.142687i	$0.954426\pi$
$642$		0			0
$643$	14.2846			0.563331			0.281665	−	0.959513i	$-0.409113\pi$
$643$	14.2846			0.563331			0.281665	+	0.959513i	$0.409113\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−1.10642	+	1.91637i	−0.0434977	+	0.0753402i	−0.886955	−	0.461857i	$-0.847183\pi$
$647$	−1.10642	+	1.91637i	−0.0434977	+	0.0753402i	0.843457	+	0.537197i	$0.180517\pi$
$648$		0			0
$649$	−13.9360	−	24.1379i	−0.547037	−	0.947496i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.1578	+	31.4503i	0.710571	+	1.23074i	0.964643	+	0.263560i	$0.0848966\pi$
$653$	18.1578	+	31.4503i	0.710571	+	1.23074i	−0.254072	+	0.967185i	$0.581770\pi$
$654$		0			0
$655$	8.95271	−	15.5065i	0.349811	−	0.605891i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	7.37474			0.287279			0.143640	−	0.989630i	$-0.454119\pi$
$659$	7.37474			0.287279			0.143640	+	0.989630i	$0.454119\pi$
$660$		0			0
$661$	−17.0943	+	29.6082i	−0.664890	+	1.15162i	0.314425	+	0.949282i	$0.398188\pi$
$661$	−17.0943	+	29.6082i	−0.664890	+	1.15162i	−0.979315	+	0.202342i	$0.935145\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−16.5172	−	20.1184i	−0.640511	−	0.780157i
$666$		0			0
$667$	−3.42865	−	5.93859i	−0.132758	−	0.229943i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−28.3201			−1.09329
$672$		0			0
$673$	22.7219			0.875866			0.437933	−	0.899008i	$-0.355711\pi$
$673$	22.7219			0.875866			0.437933	+	0.899008i	$0.355711\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.7606	−	37.6904i	−0.836326	−	1.44856i	−0.892946	−	0.450164i	$-0.851365\pi$
$677$	−21.7606	−	37.6904i	−0.836326	−	1.44856i	0.0566194	−	0.998396i	$-0.481968\pi$
$678$		0			0
$679$	−2.09703	+	5.57494i	−0.0804765	+	0.213947i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.71875	+	13.3693i	−0.295350	+	0.511561i	−0.975066	−	0.221914i	$-0.928769\pi$
$683$	−7.71875	+	13.3693i	−0.295350	+	0.511561i	0.679716	+	0.733475i	$0.262103\pi$
$684$		0			0
$685$	31.5946			1.20717
$686$		0			0
$687$		0			0
$688$		0			0
$689$	27.6742	−	47.9331i	1.05430	−	1.82611i
$690$		0			0
$691$	0.726764	+	1.25879i	0.0276474	+	0.0478867i	0.879518	−	0.475866i	$-0.157865\pi$
$691$	0.726764	+	1.25879i	0.0276474	+	0.0478867i	−0.851871	+	0.523752i	$0.824532\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	17.0843	+	29.5908i	0.648043	+	1.12244i
$696$		0			0
$697$	−18.6971	+	32.3843i	−0.708202	+	1.22664i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−1.25700			−0.0474762			−0.0237381	−	0.999718i	$-0.507557\pi$
$701$	−1.25700			−0.0474762			−0.0237381	+	0.999718i	$0.507557\pi$
$702$		0			0
$703$	8.92866	−	15.4649i	0.336751	−	0.583270i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	11.8746	+	14.4635i	0.446589	+	0.543955i
$708$		0			0
$709$	−0.971298	−	1.68234i	−0.0364779	−	0.0631815i	0.847210	−	0.531258i	$-0.178281\pi$
$709$	−0.971298	−	1.68234i	−0.0364779	−	0.0631815i	−0.883688	+	0.468076i	$0.844947\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	14.3567			0.537661
$714$		0			0
$715$	−43.0587			−1.61030
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−19.7817	−	34.2629i	−0.737733	−	1.27779i	−0.953514	−	0.301349i	$-0.902563\pi$
$719$	−19.7817	−	34.2629i	−0.737733	−	1.27779i	0.215781	−	0.976442i	$-0.430770\pi$
$720$		0			0
$721$	15.0265	−	2.48388i	0.559616	−	0.0925044i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−1.23957	+	2.14700i	−0.0460366	+	0.0797377i
$726$		0			0
$727$	11.6317			0.431397			0.215699	−	0.976460i	$-0.430797\pi$
$727$	11.6317			0.431397			0.215699	+	0.976460i	$0.430797\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	4.72334	−	8.18106i	0.174699	−	0.302587i
$732$		0			0
$733$	0.636397	+	1.10227i	0.0235058	+	0.0407133i	0.877539	−	0.479505i	$-0.159184\pi$
$733$	0.636397	+	1.10227i	0.0235058	+	0.0407133i	−0.854033	+	0.520219i	$0.825850\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−7.14995	−	12.3841i	−0.263372	−	0.456174i
$738$		0			0
$739$	−0.279341	+	0.483833i	−0.0102757	+	0.0177981i	−0.871118	−	0.491075i	$-0.836604\pi$
$739$	−0.279341	+	0.483833i	−0.0102757	+	0.0177981i	0.860842	+	0.508873i	$0.169938\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−13.2067			−0.484508			−0.242254	−	0.970213i	$-0.577887\pi$
$743$	−13.2067			−0.484508			−0.242254	+	0.970213i	$0.577887\pi$
$744$		0			0
$745$	−9.19615	+	15.9282i	−0.336921	+	0.583564i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−47.2075	+	7.80339i	−1.72493	+	0.285130i
$750$		0			0
$751$	−20.6281	−	35.7289i	−0.752729	−	1.30377i	−0.946495	−	0.322718i	$-0.895404\pi$
$751$	−20.6281	−	35.7289i	−0.752729	−	1.30377i	0.193766	−	0.981048i	$-0.437930\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−13.1734			−0.479428
$756$		0			0
$757$	41.7615			1.51785			0.758923	−	0.651181i	$-0.225726\pi$
$757$	41.7615			1.51785			0.758923	+	0.651181i	$0.225726\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	25.3695	+	43.9413i	0.919644	+	1.59287i	0.799955	+	0.600059i	$0.204856\pi$
$761$	25.3695	+	43.9413i	0.919644	+	1.59287i	0.119689	+	0.992811i	$0.461810\pi$
$762$		0			0
$763$	26.8814	+	32.7421i	0.973170	+	1.18534i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	39.5129	−	68.4384i	1.42673	−	2.47117i
$768$		0			0
$769$	4.16070			0.150039			0.0750193	−	0.997182i	$-0.476098\pi$
$769$	4.16070			0.150039			0.0750193	+	0.997182i	$0.476098\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	10.0926	−	17.4809i	0.363006	−	0.628744i	−0.625448	−	0.780266i	$-0.715084\pi$
$773$	10.0926	−	17.4809i	0.363006	−	0.628744i	0.988454	+	0.151521i	$0.0484172\pi$
$774$		0			0
$775$	−2.59521	−	4.49504i	−0.0932227	−	0.161467i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−16.0458	−	27.7921i	−0.574899	−	0.995755i
$780$		0			0
$781$	5.76877	−	9.99180i	0.206423	−	0.357535i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	57.6672			2.05823
$786$		0			0
$787$	−14.0902	+	24.4049i	−0.502261	+	0.869941i	0.497736	+	0.867329i	$0.334165\pi$
$787$	−14.0902	+	24.4049i	−0.502261	+	0.869941i	−0.999997	+	0.00261235i	$0.999168\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	2.64968	−	7.04417i	0.0942118	−	0.250462i
$792$		0			0
$793$	−40.1481	−	69.5386i	−1.42570	−	2.46939i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−4.44006			−0.157275			−0.0786374	−	0.996903i	$-0.525057\pi$
$797$	−4.44006			−0.157275			−0.0786374	+	0.996903i	$0.525057\pi$
$798$		0			0
$799$	49.1339			1.73823
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−5.39715	−	9.34814i	−0.190461	−	0.329889i
$804$		0			0
$805$	−31.2614	−	38.0771i	−1.10182	−	1.34204i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−1.49918	+	2.59666i	−0.0527084	+	0.0912937i	−0.891176	−	0.453658i	$-0.850119\pi$
$809$	−1.49918	+	2.59666i	−0.0527084	+	0.0912937i	0.838467	+	0.544952i	$0.183452\pi$
$810$		0			0
$811$	4.34674			0.152635			0.0763173	−	0.997084i	$-0.475684\pi$
$811$	4.34674			0.152635			0.0763173	+	0.997084i	$0.475684\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	17.3840	−	30.1099i	0.608934	−	1.05470i
$816$		0			0
$817$	4.05356	+	7.02097i	0.141816	+	0.245633i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	18.9601	+	32.8398i	0.661711	+	1.14612i	0.980166	+	0.198179i	$0.0635028\pi$
$821$	18.9601	+	32.8398i	0.661711	+	1.14612i	−0.318455	+	0.947938i	$0.603164\pi$
$822$		0			0
$823$	12.8917	−	22.3290i	0.449376	−	0.778341i	−0.548970	−	0.835842i	$-0.684980\pi$
$823$	12.8917	−	22.3290i	0.449376	−	0.778341i	0.998345	+	0.0575009i	$0.0183132\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	38.4404			1.33670			0.668352	−	0.743845i	$-0.267000\pi$
$827$	38.4404			1.33670			0.668352	+	0.743845i	$0.267000\pi$
$828$		0			0
$829$	−27.6224	+	47.8433i	−0.959364	+	1.66167i	−0.235314	+	0.971919i	$0.575612\pi$
$829$	−27.6224	+	47.8433i	−0.959364	+	1.66167i	−0.724050	+	0.689748i	$0.757721\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	27.8106	−	9.45244i	0.963580	−	0.327507i
$834$		0			0
$835$	17.0118	+	29.4654i	0.588719	+	1.01969i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.23562			0.180754			0.0903768	−	0.995908i	$-0.471193\pi$
$839$	5.23562			0.180754			0.0903768	+	0.995908i	$0.471193\pi$
$840$		0			0
$841$	−27.9878			−0.965095
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−43.2839	−	74.9699i	−1.48901	−	2.57904i
$846$		0			0
$847$	−14.2036	+	2.34785i	−0.488043	+	0.0806732i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	16.8989	−	29.2697i	0.579285	−	1.00335i
$852$		0			0
$853$	7.99343			0.273690			0.136845	−	0.990592i	$-0.456304\pi$
$853$	7.99343			0.273690			0.136845	+	0.990592i	$0.456304\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.7126	−	18.5548i	0.365937	−	0.633821i	−0.622989	−	0.782231i	$-0.714082\pi$
$857$	10.7126	−	18.5548i	0.365937	−	0.633821i	0.988926	+	0.148409i	$0.0474152\pi$
$858$		0			0
$859$	15.8589	+	27.4685i	0.541100	+	0.937213i	0.998841	+	0.0481275i	$0.0153254\pi$
$859$	15.8589	+	27.4685i	0.541100	+	0.937213i	−0.457741	+	0.889086i	$0.651341\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	13.1823	+	22.8325i	0.448732	+	0.777227i	0.998304	−	0.0582199i	$-0.0185424\pi$
$863$	13.1823	+	22.8325i	0.448732	+	0.777227i	−0.549572	+	0.835447i	$0.685209\pi$
$864$		0			0
$865$	−26.8091	+	46.4348i	−0.911537	+	1.57883i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	1.19131			0.0404124
$870$		0			0
$871$	20.2723	−	35.1127i	0.686901	−	1.18975i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	6.45353	−	17.1567i	0.218169	−	0.580002i
$876$		0			0
$877$	20.8868	+	36.1771i	0.705298	+	1.22161i	0.966584	+	0.256351i	$0.0825202\pi$
$877$	20.8868	+	36.1771i	0.705298	+	1.22161i	−0.261286	+	0.965262i	$0.584146\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−38.3035			−1.29048			−0.645238	−	0.763982i	$-0.723242\pi$
$881$	−38.3035			−1.29048			−0.645238	+	0.763982i	$0.723242\pi$
$882$		0			0
$883$	49.7097			1.67286			0.836432	−	0.548070i	$-0.184637\pi$
$883$	49.7097			1.67286			0.836432	+	0.548070i	$0.184637\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−22.2338	−	38.5100i	−0.746536	−	1.29304i	−0.949473	−	0.313847i	$-0.898382\pi$
$887$	−22.2338	−	38.5100i	−0.746536	−	1.29304i	0.202937	−	0.979192i	$-0.434951\pi$
$888$		0			0
$889$	4.32425	−	11.4960i	0.145031	−	0.385564i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−21.0833	+	36.5173i	−0.705525	+	1.22201i
$894$		0			0
$895$	35.5333			1.18775
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−1.05964	+	1.83535i	−0.0353409	+	0.0612122i
$900$		0			0
$901$	17.3716	+	30.0885i	0.578733	+	1.00239i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−21.5400	−	37.3084i	−0.716015	−	1.24017i
$906$		0			0
$907$	−9.51466	+	16.4799i	−0.315929	+	0.547205i	−0.979635	−	0.200789i	$-0.935649\pi$
$907$	−9.51466	+	16.4799i	−0.315929	+	0.547205i	0.663706	+	0.747994i	$0.268983\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	32.7811			1.08609			0.543043	−	0.839705i	$-0.317272\pi$
$911$	32.7811			1.08609			0.543043	+	0.839705i	$0.317272\pi$
$912$		0			0
$913$	−13.1913	+	22.8480i	−0.436569	+	0.756159i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−17.1077	+	2.82789i	−0.564945	+	0.0933852i
$918$		0			0
$919$	29.5944	+	51.2590i	0.976228	+	1.69088i	0.675821	+	0.737066i	$0.263789\pi$
$919$	29.5944	+	51.2590i	0.976228	+	1.69088i	0.300408	+	0.953811i	$0.402877\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	32.7124			1.07674
$924$		0			0
$925$	−12.2190			−0.401759
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−5.82001	−	10.0806i	−0.190948	−	0.330732i	0.754616	−	0.656166i	$-0.227823\pi$
$929$	−5.82001	−	10.0806i	−0.190948	−	0.330732i	−0.945565	+	0.325434i	$0.894490\pi$
$930$		0			0
$931$	−4.90824	+	24.7254i	−0.160861	+	0.810344i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	13.5144	−	23.4076i	0.441967	−	0.765510i
$936$		0			0
$937$	−28.7562			−0.939424			−0.469712	−	0.882820i	$-0.655642\pi$
$937$	−28.7562			−0.939424			−0.469712	+	0.882820i	$0.655642\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.3947	−	47.4489i	0.893040	−	1.54679i	0.0568289	−	0.998384i	$-0.481901\pi$
$941$	27.3947	−	47.4489i	0.893040	−	1.54679i	0.836211	−	0.548407i	$-0.184766\pi$
$942$		0			0
$943$	−30.3691	−	52.6008i	−0.988953	−	1.71292i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	7.96888	+	13.8025i	0.258954	+	0.448521i	0.965962	−	0.258684i	$-0.0832890\pi$
$947$	7.96888	+	13.8025i	0.258954	+	0.448521i	−0.707008	+	0.707205i	$0.749956\pi$
$948$		0			0
$949$	15.3026	−	26.5048i	0.496742	−	0.860383i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14.6599			−0.474880			−0.237440	−	0.971402i	$-0.576308\pi$
$953$	−14.6599			−0.474880			−0.237440	+	0.971402i	$0.576308\pi$
$954$		0			0
$955$	6.75483	−	11.6997i	0.218581	−	0.378594i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−19.4148	−	23.6477i	−0.626938	−	0.763624i
$960$		0			0
$961$	13.2815	+	23.0042i	0.428436	+	0.742072i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	26.9173			0.866497
$966$		0			0
$967$	−6.70591			−0.215647			−0.107824	−	0.994170i	$-0.534388\pi$
$967$	−6.70591			−0.215647			−0.107824	+	0.994170i	$0.534388\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	10.7121	+	18.5540i	0.343769	+	0.595425i	0.985129	−	0.171815i	$-0.0549631\pi$
$971$	10.7121	+	18.5540i	0.343769	+	0.595425i	−0.641361	+	0.767240i	$0.721630\pi$
$972$		0			0
$973$	11.6497	−	30.9706i	0.373472	−	0.992873i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−18.1979	+	31.5196i	−0.582202	+	1.00840i	0.413016	+	0.910724i	$0.364475\pi$
$977$	−18.1979	+	31.5196i	−0.582202	+	1.00840i	−0.995218	+	0.0976791i	$0.968858\pi$
$978$		0			0
$979$	−19.9413			−0.637327
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−27.5055	+	47.6408i	−0.877288	+	1.51951i	−0.0229823	+	0.999736i	$0.507316\pi$
$983$	−27.5055	+	47.6408i	−0.877288	+	1.51951i	−0.854306	+	0.519771i	$0.826017\pi$
$984$		0			0
$985$	−37.0131	−	64.1086i	−1.17934	−	2.04267i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.67197	+	13.2882i	0.243954	+	0.422542i
$990$		0			0
$991$	27.2596	−	47.2151i	0.865931	−	1.49984i	−0.000189141	−	1.00000i	$-0.500060\pi$
$991$	27.2596	−	47.2151i	0.865931	−	1.49984i	0.866120	−	0.499836i	$-0.166606\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−75.0990			−2.38080
$996$		0			0
$997$	0.975306	−	1.68928i	0.0308883	−	0.0535000i	−0.850168	−	0.526511i	$-0.823500\pi$
$997$	0.975306	−	1.68928i	0.0308883	−	0.0535000i	0.881056	+	0.473011i	$0.156833\pi$
$998$		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.865.1	✓	8
3.2	odd	2		1512.2.s.p.865.3	yes	8
7.2	even	3	inner	1512.2.s.m.1297.1	yes	8
21.2	odd	6		1512.2.s.p.1297.3	yes	8

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

\(f(q)\)	\(=\)	\(q+(-1.36603 - 2.36603i) q^{5} +(-0.931486 + 2.47635i) q^{7} +O(q^{10})\)	\(q+(-1.36603 - 2.36603i) q^{5} +(-0.931486 + 2.47635i) q^{7} +(1.17884 - 2.04182i) q^{11} +6.68476 q^{13} +(-2.09808 + 3.63397i) q^{17} +(-1.80056 - 3.11867i) q^{19} +(-3.40784 - 5.90255i) q^{23} +(-1.23205 + 2.13397i) q^{25} +1.00610 q^{29} +(-1.05321 + 1.82421i) q^{31} +(7.13155 - 1.17884i) q^{35} +(2.47941 + 4.29446i) q^{37} +8.91152 q^{41} -2.25127 q^{43} +(-5.85463 - 10.1405i) q^{47} +(-5.26467 - 4.61338i) q^{49} +(4.13989 - 7.17050i) q^{53} -6.44132 q^{55} +(5.91089 - 10.2380i) q^{59} +(-6.00592 - 10.4026i) q^{61} +(-9.13155 - 15.8163i) q^{65} +(3.03262 - 5.25264i) q^{67} +4.89358 q^{71} +(2.28917 - 3.96496i) q^{73} +(3.95818 + 4.82116i) q^{77} +(0.252644 + 0.437591i) q^{79} -11.1900 q^{83} +11.4641 q^{85} +(-4.22900 - 7.32484i) q^{89} +(-6.22676 + 16.5538i) q^{91} +(-4.91923 + 8.52036i) q^{95} +2.25127 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 2 q^{7}+O(q^{10}) \) 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

Introduction

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