LMFDB - Embedded newform 1512.2.s.p.865.2

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			865.2
Root			$0.295509 - 2.62920i$ of defining polynomial
Character	$\chi$	$=$	1512.865
Dual form			1512.2.s.p.1297.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.366025 - 0.633975i) q^{5} +(2.12920 + 1.57052i) q^{7} +O(q^{10})$	$q+(-0.366025 - 0.633975i) q^{5} +(2.12920 + 1.57052i) q^{7} +(-1.92471 + 3.33369i) q^{11} -4.87308 q^{13} +(-3.09808 + 5.36603i) q^{17} +(-1.39715 - 2.41993i) q^{19} +(-3.69971 - 6.40809i) q^{23} +(2.23205 - 3.86603i) q^{25} -9.78474 q^{29} +(3.15676 - 5.46766i) q^{31} +(0.216328 - 1.92471i) q^{35} +(2.82185 + 4.88759i) q^{37} -1.50267 q^{41} -12.1629 q^{43} +(2.95704 + 5.12175i) q^{47} +(2.06696 + 6.68788i) q^{49} +(6.43176 - 11.1401i) q^{53} +2.81796 q^{55} +(-3.19265 + 5.52984i) q^{59} +(6.29779 + 10.9081i) q^{61} +(1.78367 + 3.08941i) q^{65} +(-0.834905 + 1.44610i) q^{67} -13.3135 q^{71} +(0.720214 - 1.24745i) q^{73} +(-9.33369 + 4.07529i) q^{77} +(-3.55390 - 6.15554i) q^{79} -7.98089 q^{83} +4.53590 q^{85} +(-3.62442 - 6.27768i) q^{89} +(-10.3758 - 7.65326i) q^{91} +(-1.02278 + 1.77151i) q^{95} +12.1629 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5} - 2 q^{7}+O(q^{10}) $ 8 * q + 4 * q^5 - 2 * q^7	$ 8 q + 4 q^{5} - 2 q^{7} + 2 q^{11} - 8 q^{13} - 4 q^{17} - 6 q^{19} - 2 q^{23} + 4 q^{25} - 16 q^{29} - 6 q^{31} + 2 q^{35} + 16 q^{41} + 20 q^{47} - 6 q^{49} + 10 q^{53} + 16 q^{55} - 22 q^{59} + 2 q^{61} + 14 q^{65} + 2 q^{67} - 44 q^{71} - 10 q^{73} - 54 q^{77} + 8 q^{79} + 40 q^{83} + 64 q^{85} + 16 q^{89} - 24 q^{91} + 30 q^{95}+O(q^{100}) $ 8 * q + 4 * q^5 - 2 * q^7 + 2 * q^11 - 8 * q^13 - 4 * q^17 - 6 * q^19 - 2 * q^23 + 4 * q^25 - 16 * q^29 - 6 * q^31 + 2 * q^35 + 16 * q^41 + 20 * q^47 - 6 * q^49 + 10 * q^53 + 16 * q^55 - 22 * q^59 + 2 * q^61 + 14 * q^65 + 2 * q^67 - 44 * q^71 - 10 * q^73 - 54 * q^77 + 8 * q^79 + 40 * q^83 + 64 * q^85 + 16 * q^89 - 24 * q^91 + 30 * q^95

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.366025	−	0.633975i	−0.163692	−	0.283522i	0.772498	−	0.635017i	$-0.219007\pi$
$5$	−0.366025	−	0.633975i	−0.163692	−	0.283522i	−0.936190	+	0.351495i	$0.885674\pi$
$6$		0			0
$7$	2.12920	+	1.57052i	0.804761	+	0.593599i
$7$	2.12920	+	1.57052i	0.804761	+	0.593599i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.92471	+	3.33369i	−0.580321	+	1.00514i	0.415121	+	0.909766i	$0.363739\pi$
$11$	−1.92471	+	3.33369i	−0.580321	+	1.00514i	−0.995441	+	0.0953782i	$0.969594\pi$
$12$		0			0
$13$	−4.87308			−1.35155			−0.675775	−	0.737108i	$-0.736191\pi$
$13$	−4.87308			−1.35155			−0.675775	+	0.737108i	$0.736191\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.09808	+	5.36603i	−0.751394	+	1.30145i	0.195753	+	0.980653i	$0.437285\pi$
$17$	−3.09808	+	5.36603i	−0.751394	+	1.30145i	−0.947147	+	0.320799i	$0.896049\pi$
$18$		0			0
$19$	−1.39715	−	2.41993i	−0.320527	−	0.555169i	0.660070	−	0.751204i	$-0.270527\pi$
$19$	−1.39715	−	2.41993i	−0.320527	−	0.555169i	−0.980597	+	0.196035i	$0.937193\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.69971	−	6.40809i	−0.771443	−	1.33618i	−0.936772	−	0.349941i	$-0.886202\pi$
$23$	−3.69971	−	6.40809i	−0.771443	−	1.33618i	0.165328	−	0.986239i	$-0.447132\pi$
$24$		0			0
$25$	2.23205	−	3.86603i	0.446410	−	0.773205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−9.78474			−1.81698			−0.908490	−	0.417907i	$-0.862764\pi$
$29$	−9.78474			−1.81698			−0.908490	+	0.417907i	$0.862764\pi$
$30$		0			0
$31$	3.15676	−	5.46766i	0.566970	−	0.982021i	−0.429893	−	0.902880i	$-0.641449\pi$
$31$	3.15676	−	5.46766i	0.566970	−	0.982021i	0.996863	−	0.0791414i	$-0.0252179\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	0.216328	−	1.92471i	0.0365660	−	0.325335i
$36$		0			0
$37$	2.82185	+	4.88759i	0.463909	+	0.803515i	0.999152	−	0.0411839i	$-0.0131130\pi$
$37$	2.82185	+	4.88759i	0.463909	+	0.803515i	−0.535242	+	0.844699i	$0.679780\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.50267			−0.234678			−0.117339	−	0.993092i	$-0.537436\pi$
$41$	−1.50267			−0.234678			−0.117339	+	0.993092i	$0.537436\pi$
$42$		0			0
$43$	−12.1629			−1.85483			−0.927414	−	0.374036i	$-0.877974\pi$
$43$	−12.1629			−1.85483			−0.927414	+	0.374036i	$0.877974\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.95704	+	5.12175i	0.431329	+	0.747084i	0.996988	−	0.0775554i	$-0.0247115\pi$
$47$	2.95704	+	5.12175i	0.431329	+	0.747084i	−0.565659	+	0.824639i	$0.691378\pi$
$48$		0			0
$49$	2.06696	+	6.68788i	0.295279	+	0.955411i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.43176	−	11.1401i	0.883471	−	1.53022i	0.0360142	−	0.999351i	$-0.488534\pi$
$53$	6.43176	−	11.1401i	0.883471	−	1.53022i	0.847456	−	0.530865i	$-0.178133\pi$
$54$		0			0
$55$	2.81796			0.379974
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.19265	+	5.52984i	−0.415648	+	0.719924i	−0.995496	−	0.0948008i	$-0.969779\pi$
$59$	−3.19265	+	5.52984i	−0.415648	+	0.719924i	0.579848	+	0.814725i	$0.303112\pi$
$60$		0			0
$61$	6.29779	+	10.9081i	0.806349	+	1.39664i	0.915376	+	0.402599i	$0.131893\pi$
$61$	6.29779	+	10.9081i	0.806349	+	1.39664i	−0.109027	+	0.994039i	$0.534774\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	1.78367	+	3.08941i	0.221237	+	0.383194i
$66$		0			0
$67$	−0.834905	+	1.44610i	−0.102000	+	0.176669i	−0.912509	−	0.409058i	$-0.865857\pi$
$67$	−0.834905	+	1.44610i	−0.102000	+	0.176669i	0.810509	+	0.585727i	$0.199191\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−13.3135			−1.58002			−0.790012	−	0.613092i	$-0.789926\pi$
$71$	−13.3135			−1.58002			−0.790012	+	0.613092i	$0.789926\pi$
$72$		0			0
$73$	0.720214	−	1.24745i	0.0842947	−	0.146003i	−0.820796	−	0.571222i	$-0.806470\pi$
$73$	0.720214	−	1.24745i	0.0842947	−	0.146003i	0.905090	+	0.425219i	$0.139803\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−9.33369	+	4.07529i	−1.06367	+	0.464423i
$78$		0			0
$79$	−3.55390	−	6.15554i	−0.399845	−	0.692552i	0.593861	−	0.804567i	$-0.297603\pi$
$79$	−3.55390	−	6.15554i	−0.399845	−	0.692552i	−0.993706	+	0.112015i	$0.964269\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−7.98089			−0.876016			−0.438008	−	0.898971i	$-0.644316\pi$
$83$	−7.98089			−0.876016			−0.438008	+	0.898971i	$0.644316\pi$
$84$		0			0
$85$	4.53590			0.491987
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.62442	−	6.27768i	−0.384188	−	0.665432i	0.607469	−	0.794344i	$-0.292185\pi$
$89$	−3.62442	−	6.27768i	−0.384188	−	0.665432i	−0.991656	+	0.128911i	$0.958852\pi$
$90$		0			0
$91$	−10.3758	−	7.65326i	−1.08767	−	0.802279i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.02278	+	1.77151i	−0.104935	+	0.181753i
$96$		0			0
$97$	12.1629			1.23496			0.617479	−	0.786587i	$-0.288154\pi$
$97$	12.1629			1.23496			0.617479	+	0.786587i	$0.288154\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.77412	+	10.0011i	−0.574546	+	0.995143i	0.421545	+	0.906808i	$0.361488\pi$
$101$	−5.77412	+	10.0011i	−0.574546	+	0.995143i	−0.996091	+	0.0883353i	$0.971845\pi$
$102$		0			0
$103$	−4.02756	−	6.97594i	−0.396847	−	0.687360i	0.596488	−	0.802622i	$-0.296562\pi$
$103$	−4.02756	−	6.97594i	−0.396847	−	0.687360i	−0.993335	+	0.115263i	$0.963229\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	1.02367	+	1.77305i	0.0989622	+	0.171408i	0.911255	−	0.411842i	$-0.135114\pi$
$107$	1.02367	+	1.77305i	0.0989622	+	0.171408i	−0.812293	+	0.583249i	$0.801781\pi$
$108$		0			0
$109$	−4.29779	+	7.44399i	−0.411654	+	0.713005i	−0.995071	−	0.0991678i	$-0.968382\pi$
$109$	−4.29779	+	7.44399i	−0.411654	+	0.713005i	0.583417	+	0.812173i	$0.301715\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−0.260828			−0.0245366			−0.0122683	−	0.999925i	$-0.503905\pi$
$113$	−0.260828			−0.0245366			−0.0122683	+	0.999925i	$0.503905\pi$
$114$		0			0
$115$	−2.70838	+	4.69105i	−0.252558	+	0.437442i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−15.0238	+	6.55974i	−1.37723	+	0.601331i
$120$		0			0
$121$	−1.90898	−	3.30645i	−0.173544	−	0.300587i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.92820			−0.619677
$126$		0			0
$127$	−3.15059			−0.279570			−0.139785	−	0.990182i	$-0.544641\pi$
$127$	−3.15059			−0.279570			−0.139785	+	0.990182i	$0.544641\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	1.17337	+	2.03234i	0.102518	+	0.177566i	0.912721	−	0.408582i	$-0.133977\pi$
$131$	1.17337	+	2.03234i	0.102518	+	0.177566i	−0.810204	+	0.586149i	$0.800643\pi$
$132$		0			0
$133$	0.825738	−	7.34674i	0.0716006	−	0.637043i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.28117	+	10.8793i	−0.536637	+	0.929483i	0.462445	+	0.886648i	$0.346972\pi$
$137$	−6.28117	+	10.8793i	−0.536637	+	0.929483i	−0.999082	+	0.0428346i	$0.986361\pi$
$138$		0			0
$139$	4.48777			0.380648			0.190324	−	0.981721i	$-0.439046\pi$
$139$	4.48777			0.380648			0.190324	+	0.981721i	$0.439046\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.37925	−	16.2453i	0.784332	−	1.35850i
$144$		0			0
$145$	3.58146	+	6.20327i	0.297424	+	0.515154i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	1.63397	+	2.83013i	0.133860	+	0.231853i	0.925162	−	0.379574i	$-0.123929\pi$
$149$	1.63397	+	2.83013i	0.133860	+	0.231853i	−0.791301	+	0.611427i	$0.790596\pi$
$150$		0			0
$151$	−0.307345	+	0.532338i	−0.0250114	+	0.0433210i	−0.878260	−	0.478183i	$-0.841296\pi$
$151$	−0.307345	+	0.532338i	−0.0250114	+	0.0433210i	0.853249	+	0.521504i	$0.174629\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.62181			−0.371233
$156$		0			0
$157$	−1.65326	+	2.86353i	−0.131944	+	0.228534i	−0.924426	−	0.381361i	$-0.875455\pi$
$157$	−1.65326	+	2.86353i	−0.131944	+	0.228534i	0.792482	+	0.609896i	$0.208789\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	2.18660	−	19.4545i	0.172328	−	1.53323i
$162$		0			0
$163$	0.241607	+	0.418475i	0.0189241	+	0.0327775i	0.875332	−	0.483522i	$-0.160643\pi$
$163$	0.241607	+	0.418475i	0.0189241	+	0.0327775i	−0.856408	+	0.516299i	$0.827309\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	20.7515			1.60580			0.802900	−	0.596114i	$-0.203289\pi$
$167$	20.7515			1.60580			0.802900	+	0.596114i	$0.203289\pi$
$168$		0			0
$169$	10.7469			0.826688
$170$		0			0
$171$		0			0
$172$		0			0
$173$	12.2907	+	21.2882i	0.934447	+	1.61851i	0.775617	+	0.631204i	$0.217439\pi$
$173$	12.2907	+	21.2882i	0.934447	+	1.61851i	0.158830	+	0.987306i	$0.449228\pi$
$174$		0			0
$175$	10.8241	−	4.72606i	0.818227	−	0.357256i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.8924	−	18.8661i	0.814134	−	1.41012i	−0.0958144	−	0.995399i	$-0.530546\pi$
$179$	10.8924	−	18.8661i	0.814134	−	1.41012i	0.909948	−	0.414722i	$-0.136121\pi$
$180$		0			0
$181$	−6.54046			−0.486148			−0.243074	−	0.970008i	$-0.578156\pi$
$181$	−6.54046			−0.486148			−0.243074	+	0.970008i	$0.578156\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.06574	−	3.57796i	0.151876	−	0.263057i
$186$		0			0
$187$	−11.9258	−	20.6560i	−0.872099	−	1.51052i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.67954	+	13.3013i	0.555672	+	0.962452i	0.997851	+	0.0655251i	$0.0208722\pi$
$191$	7.67954	+	13.3013i	0.555672	+	0.962452i	−0.442179	+	0.896927i	$0.645794\pi$
$192$		0			0
$193$	−9.47861	+	16.4174i	−0.682285	+	1.18175i	0.291997	+	0.956419i	$0.405680\pi$
$193$	−9.47861	+	16.4174i	−0.682285	+	1.18175i	−0.974282	+	0.225333i	$0.927653\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	8.26295			0.588711			0.294356	−	0.955696i	$-0.404895\pi$
$197$	8.26295			0.588711			0.294356	+	0.955696i	$0.404895\pi$
$198$		0			0
$199$	6.75490	−	11.6998i	0.478842	−	0.829378i	−0.520864	−	0.853640i	$-0.674390\pi$
$199$	6.75490	−	11.6998i	0.478842	−	0.829378i	0.999706	+	0.0242614i	$0.00772340\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−20.8336	−	15.3671i	−1.46223	−	1.07856i
$204$		0			0
$205$	0.550015	+	0.952654i	0.0384147	+	0.0665363i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.7564			0.744034
$210$		0			0
$211$	−6.87552			−0.473330			−0.236665	−	0.971591i	$-0.576054\pi$
$211$	−6.87552			−0.473330			−0.236665	+	0.971591i	$0.576054\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	4.45194	+	7.71098i	0.303620	+	0.525885i
$216$		0			0
$217$	15.3084	−	6.68399i	1.03920	−	0.453739i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	15.0972	−	26.1491i	1.01555	−	1.75898i
$222$		0			0
$223$	−13.9809			−0.936229			−0.468115	−	0.883668i	$-0.655067\pi$
$223$	−13.9809			−0.936229			−0.468115	+	0.883668i	$0.655067\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−7.54912	+	13.0755i	−0.501053	+	0.867849i	0.498946	+	0.866633i	$0.333720\pi$
$227$	−7.54912	+	13.0755i	−0.501053	+	0.867849i	−0.999999	+	0.00121627i	$0.999613\pi$
$228$		0			0
$229$	5.28367	+	9.15159i	0.349155	+	0.604754i	0.986100	−	0.166155i	$-0.0531354\pi$
$229$	5.28367	+	9.15159i	0.349155	+	0.604754i	−0.636945	+	0.770910i	$0.719802\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−0.740716	−	1.28296i	−0.0485259	−	0.0840493i	0.840742	−	0.541436i	$-0.182119\pi$
$233$	−0.740716	−	1.28296i	−0.0485259	−	0.0840493i	−0.889268	+	0.457386i	$0.848786\pi$
$234$		0			0
$235$	2.16471	−	3.74938i	0.141210	−	0.244583i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.88964			0.445653			0.222827	−	0.974858i	$-0.428472\pi$
$239$	6.88964			0.445653			0.222827	+	0.974858i	$0.428472\pi$
$240$		0			0
$241$	−14.1578	+	24.5221i	−0.911985	+	1.57960i	−0.100729	+	0.994914i	$0.532118\pi$
$241$	−14.1578	+	24.5221i	−0.911985	+	1.57960i	−0.811256	+	0.584691i	$0.801216\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	3.48339	−	3.75833i	0.222545	−	0.240111i
$246$		0			0
$247$	6.80841	+	11.7925i	0.433209	+	0.750339i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	5.93532			0.374634			0.187317	−	0.982299i	$-0.440021\pi$
$251$	5.93532			0.374634			0.187317	+	0.982299i	$0.440021\pi$
$252$		0			0
$253$	28.4834			1.79074
$254$		0			0
$255$		0			0
$256$		0			0
$257$	3.99044	+	6.91165i	0.248917	+	0.431137i	0.963226	−	0.268694i	$-0.0865920\pi$
$257$	3.99044	+	6.91165i	0.248917	+	0.431137i	−0.714309	+	0.699831i	$0.753259\pi$
$258$		0			0
$259$	−1.66776	+	14.8384i	−0.103630	+	0.922013i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.97982	−	17.2856i	0.615382	−	1.06587i	−0.374935	−	0.927051i	$-0.622335\pi$
$263$	9.97982	−	17.2856i	0.615382	−	1.06587i	0.990317	−	0.138822i	$-0.0443317\pi$
$264$		0			0
$265$	−9.41676			−0.578467
$266$		0			0
$267$		0			0
$268$		0			0
$269$	5.50267	−	9.53090i	0.335504	−	0.581109i	−0.648078	−	0.761574i	$-0.724427\pi$
$269$	5.50267	−	9.53090i	0.335504	−	0.581109i	0.983581	+	0.180465i	$0.0577602\pi$
$270$		0			0
$271$	10.9652	+	18.9922i	0.666086	+	1.15370i	0.978990	+	0.203910i	$0.0653651\pi$
$271$	10.9652	+	18.9922i	0.666086	+	1.15370i	−0.312903	+	0.949785i	$0.601302\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	8.59208	+	14.8819i	0.518122	+	0.897414i
$276$		0			0
$277$	8.27412	−	14.3312i	0.497143	−	0.861078i	−0.502851	−	0.864373i	$-0.667716\pi$
$277$	8.27412	−	14.3312i	0.497143	−	0.861078i	0.999995	+	0.00329530i	$0.00104893\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−24.8250			−1.48093			−0.740466	−	0.672093i	$-0.765395\pi$
$281$	−24.8250			−1.48093			−0.740466	+	0.672093i	$0.765395\pi$
$282$		0			0
$283$	2.23205	−	3.86603i	0.132682	−	0.229811i	−0.792028	−	0.610485i	$-0.790975\pi$
$283$	2.23205	−	3.86603i	0.132682	−	0.229811i	0.924709	+	0.380674i	$0.124308\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.19948	−	2.35997i	−0.188859	−	0.139304i
$288$		0			0
$289$	−10.6962	−	18.5263i	−0.629185	−	1.08978i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	9.20327			0.537661			0.268830	−	0.963188i	$-0.413363\pi$
$293$	9.20327			0.537661			0.268830	+	0.963188i	$0.413363\pi$
$294$		0			0
$295$	4.67437			0.272152
$296$		0			0
$297$		0			0
$298$		0			0
$299$	18.0290	+	31.2272i	1.04264	+	1.80591i
$300$		0			0
$301$	−25.8973	−	19.1021i	−1.49269	−	1.10103i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	4.61030	−	7.98528i	0.263985	−	0.457236i
$306$		0			0
$307$	−33.8900			−1.93420			−0.967102	−	0.254390i	$-0.918125\pi$
$307$	−33.8900			−1.93420			−0.967102	+	0.254390i	$0.918125\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.68999	+	6.39124i	−0.209240	+	0.362414i	−0.951475	−	0.307725i	$-0.900432\pi$
$311$	−3.68999	+	6.39124i	−0.209240	+	0.362414i	0.742235	+	0.670139i	$0.233766\pi$
$312$		0			0
$313$	−0.657974	−	1.13964i	−0.0371909	−	0.0644165i	0.846831	−	0.531862i	$-0.178508\pi$
$313$	−0.657974	−	1.13964i	−0.0371909	−	0.0644165i	−0.884022	+	0.467446i	$0.845174\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−3.59452	−	6.22588i	−0.201888	−	0.349680i	0.747249	−	0.664545i	$-0.231374\pi$
$317$	−3.59452	−	6.22588i	−0.201888	−	0.349680i	−0.949137	+	0.314864i	$0.898041\pi$
$318$		0			0
$319$	18.8327	−	32.6193i	1.05443	−	1.82633i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	17.3139			0.963369
$324$		0			0
$325$	−10.8770	+	18.8395i	−0.603346	+	1.04503i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.74767	+	15.5493i	−0.0963519	+	0.857260i
$330$		0			0
$331$	−2.41126	−	4.17643i	−0.132535	−	0.229557i	0.792118	−	0.610368i	$-0.208978\pi$
$331$	−2.41126	−	4.17643i	−0.132535	−	0.229557i	−0.924653	+	0.380811i	$0.875645\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	1.22239			0.0667861
$336$		0			0
$337$	−12.7561			−0.694867			−0.347434	−	0.937705i	$-0.612947\pi$
$337$	−12.7561			−0.694867			−0.347434	+	0.937705i	$0.612947\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	12.1517	+	21.0473i	0.658049	+	1.13977i
$342$		0			0
$343$	−6.10247	+	17.4860i	−0.329502	+	0.944155i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	15.4641	−	26.7846i	0.830156	−	1.43787i	−0.0677573	−	0.997702i	$-0.521584\pi$
$347$	15.4641	−	26.7846i	0.830156	−	1.43787i	0.897914	−	0.440171i	$-0.145082\pi$
$348$		0			0
$349$	17.2368			0.922667			0.461334	−	0.887227i	$-0.347371\pi$
$349$	17.2368			0.922667			0.461334	+	0.887227i	$0.347371\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.76350	−	9.98267i	0.306760	−	0.531324i	−0.670892	−	0.741555i	$-0.734088\pi$
$353$	5.76350	−	9.98267i	0.306760	−	0.531324i	0.977652	+	0.210231i	$0.0674218\pi$
$354$		0			0
$355$	4.87308	+	8.44043i	0.258636	+	0.447971i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−1.02367	−	1.77305i	−0.0540274	−	0.0935782i	0.837747	−	0.546059i	$-0.183872\pi$
$359$	−1.02367	−	1.77305i	−0.0540274	−	0.0935782i	−0.891774	+	0.452481i	$0.850539\pi$
$360$		0			0
$361$	5.59597	−	9.69250i	0.294525	−	0.510132i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−1.05447			−0.0551933
$366$		0			0
$367$	12.5933	−	21.8122i	0.657365	−	1.13859i	−0.323931	−	0.946081i	$-0.605004\pi$
$367$	12.5933	−	21.8122i	0.657365	−	1.13859i	0.981295	−	0.192508i	$-0.0616623\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	31.1903	−	13.6184i	1.61932	−	0.707030i
$372$		0			0
$373$	4.73677	+	8.20432i	0.245260	+	0.424804i	0.962205	−	0.272327i	$-0.0877932\pi$
$373$	4.73677	+	8.20432i	0.245260	+	0.424804i	−0.716944	+	0.697130i	$0.754460\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	47.6818			2.45574
$378$		0			0
$379$	−21.6176			−1.11042			−0.555211	−	0.831710i	$-0.687362\pi$
$379$	−21.6176			−1.11042			−0.555211	+	0.831710i	$0.687362\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−11.9045	−	20.6193i	−0.608293	−	1.05359i	−0.991522	−	0.129941i	$-0.958521\pi$
$383$	−11.9045	−	20.6193i	−0.608293	−	1.05359i	0.383229	−	0.923654i	$-0.374812\pi$
$384$		0			0
$385$	6.00000	+	4.42566i	0.305788	+	0.225552i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	0.206600	−	0.357841i	0.0104750	−	0.0181433i	−0.860740	−	0.509044i	$-0.829999\pi$
$389$	0.206600	−	0.357841i	0.0104750	−	0.0181433i	0.871215	+	0.490901i	$0.163332\pi$
$390$		0			0
$391$	45.8480			2.31863
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.60164	+	4.50617i	−0.130903	+	0.226730i
$396$		0			0
$397$	−5.14720	−	8.91521i	−0.258331	−	0.447442i	0.707464	−	0.706749i	$-0.249839\pi$
$397$	−5.14720	−	8.91521i	−0.258331	−	0.447442i	−0.965795	+	0.259307i	$0.916506\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	0.225884	+	0.391242i	0.0112801	+	0.0195377i	0.871610	−	0.490199i	$-0.163076\pi$
$401$	0.225884	+	0.391242i	0.0112801	+	0.0195377i	−0.860330	+	0.509737i	$0.829743\pi$
$402$		0			0
$403$	−15.3831	+	26.6444i	−0.766289	+	1.32725i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−21.7249			−1.07686
$408$		0			0
$409$	−2.04061	+	3.53445i	−0.100902	+	0.174767i	−0.912056	−	0.410065i	$-0.865506\pi$
$409$	−2.04061	+	3.53445i	−0.100902	+	0.174767i	0.811155	+	0.584832i	$0.198839\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−15.4825	+	6.76000i	−0.761844	+	0.332638i
$414$		0			0
$415$	2.92121	+	5.05968i	0.143396	+	0.248370i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	9.14347			0.446688			0.223344	−	0.974740i	$-0.428303\pi$
$419$	9.14347			0.446688			0.223344	+	0.974740i	$0.428303\pi$
$420$		0			0
$421$	8.30574			0.404797			0.202398	−	0.979303i	$-0.435126\pi$
$421$	8.30574			0.404797			0.202398	+	0.979303i	$0.435126\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	13.8301	+	23.9545i	0.670860	+	1.16196i
$426$		0			0
$427$	−3.72211	+	33.1163i	−0.180125	+	1.60261i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	11.6331	−	20.1491i	0.560346	−	0.970548i	−0.437120	−	0.899403i	$-0.644002\pi$
$431$	11.6331	−	20.1491i	0.560346	−	0.970548i	0.997466	−	0.0711444i	$-0.0226651\pi$
$432$		0			0
$433$	11.7989			0.567017			0.283508	−	0.958970i	$-0.408502\pi$
$433$	11.7989			0.567017			0.283508	+	0.958970i	$0.408502\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−10.3381	+	17.9061i	−0.494537	+	0.856564i
$438$		0			0
$439$	0.447550	+	0.775179i	0.0213604	+	0.0369973i	0.876508	−	0.481387i	$-0.159867\pi$
$439$	0.447550	+	0.775179i	0.0213604	+	0.0369973i	−0.855148	+	0.518385i	$0.826534\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−8.02990	−	13.9082i	−0.381512	−	0.660799i	0.609766	−	0.792581i	$-0.291263\pi$
$443$	−8.02990	−	13.9082i	−0.381512	−	0.660799i	−0.991279	+	0.131783i	$0.957930\pi$
$444$		0			0
$445$	−2.65326	+	4.59558i	−0.125777	+	0.217851i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−27.6411			−1.30447			−0.652233	−	0.758018i	$-0.726168\pi$
$449$	−27.6411			−1.30447			−0.652233	+	0.758018i	$0.726168\pi$
$450$		0			0
$451$	2.89220	−	5.00943i	0.136188	−	0.235885i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−1.05418	+	9.37925i	−0.0494208	+	0.439706i
$456$		0			0
$457$	2.93087	+	5.07642i	0.137100	+	0.237465i	0.926398	−	0.376546i	$-0.122888\pi$
$457$	2.93087	+	5.07642i	0.137100	+	0.237465i	−0.789297	+	0.614011i	$0.789555\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	26.4573			1.23224			0.616120	−	0.787652i	$-0.288704\pi$
$461$	26.4573			1.23224			0.616120	+	0.787652i	$0.288704\pi$
$462$		0			0
$463$	0.727834			0.0338253			0.0169126	−	0.999857i	$-0.494616\pi$
$463$	0.727834			0.0338253			0.0169126	+	0.999857i	$0.494616\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−0.536961	−	0.930044i	−0.0248476	−	0.0430373i	0.853334	−	0.521364i	$-0.174577\pi$
$467$	−0.536961	−	0.930044i	−0.0248476	−	0.0430373i	−0.878182	+	0.478327i	$0.841243\pi$
$468$		0			0
$469$	−4.04880	+	1.76779i	−0.186956	+	0.0816292i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	23.4100	−	40.5474i	1.07640	−	1.86437i
$474$		0			0
$475$	−12.4740			−0.572346
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.03340	+	8.71811i	−0.229982	+	0.398340i	−0.957802	−	0.287427i	$-0.907200\pi$
$479$	−5.03340	+	8.71811i	−0.229982	+	0.398340i	0.727821	+	0.685768i	$0.240533\pi$
$480$		0			0
$481$	−13.7511	−	23.8176i	−0.626997	−	1.08599i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.45194	−	7.71098i	−0.202152	−	0.350138i
$486$		0			0
$487$	0.964491	−	1.67055i	0.0437052	−	0.0756997i	−0.843345	−	0.537372i	$-0.819417\pi$
$487$	0.964491	−	1.67055i	0.0437052	−	0.0756997i	0.887051	+	0.461672i	$0.152750\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.89510			0.311172			0.155586	−	0.987822i	$-0.450274\pi$
$491$	6.89510			0.311172			0.155586	+	0.987822i	$0.450274\pi$
$492$		0			0
$493$	30.3139	−	52.5051i	1.36527	−	2.36471i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−28.3471	−	20.9091i	−1.27154	−	0.937901i
$498$		0			0
$499$	−6.31796	−	10.9430i	−0.282831	−	0.489878i	0.689250	−	0.724524i	$-0.257940\pi$
$499$	−6.31796	−	10.9430i	−0.282831	−	0.489878i	−0.972081	+	0.234646i	$0.924607\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	25.9493			1.15702			0.578511	−	0.815674i	$-0.303634\pi$
$503$	25.9493			1.15702			0.578511	+	0.815674i	$0.303634\pi$
$504$		0			0
$505$	8.45389			0.376193
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−11.1551	−	19.3213i	−0.494443	−	0.856401i	0.505536	−	0.862805i	$-0.331295\pi$
$509$	−11.1551	−	19.3213i	−0.494443	−	0.856401i	−0.999979	+	0.00640446i	$0.997961\pi$
$510$		0			0
$511$	3.49262	−	1.52495i	0.154504	−	0.0674600i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−2.94838	+	5.10674i	−0.129921	+	0.225030i
$516$		0			0
$517$	−22.7657			−1.00124
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−5.36164	+	9.28663i	−0.234898	+	0.406855i	−0.959243	−	0.282583i	$-0.908809\pi$
$521$	−5.36164	+	9.28663i	−0.234898	+	0.406855i	0.724345	+	0.689437i	$0.242142\pi$
$522$		0			0
$523$	−13.9017	−	24.0785i	−0.607879	−	1.05288i	−0.991589	−	0.129424i	$-0.958687\pi$
$523$	−13.9017	−	24.0785i	−0.607879	−	1.05288i	0.383710	−	0.923454i	$-0.374646\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	19.5597	+	33.8785i	0.852036	+	1.47577i
$528$		0			0
$529$	−15.8758	+	27.4976i	−0.690250	+	1.19555i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	7.32263			0.317178
$534$		0			0
$535$	0.749381	−	1.29797i	0.0323985	−	0.0561159i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−26.2736	−	5.98161i	−1.13168	−	0.257646i
$540$		0			0
$541$	−9.51451	−	16.4796i	−0.409061	−	0.708514i	0.585724	−	0.810510i	$-0.300810\pi$
$541$	−9.51451	−	16.4796i	−0.409061	−	0.708514i	−0.994785	+	0.101997i	$0.967477\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	6.29240			0.269537
$546$		0			0
$547$	−27.9233			−1.19392			−0.596958	−	0.802273i	$-0.703624\pi$
$547$	−27.9233			−1.19392			−0.596958	+	0.802273i	$0.703624\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	13.6707	+	23.6783i	0.582391	+	1.00873i
$552$		0			0
$553$	2.10042	−	18.6878i	0.0893189	−	0.794687i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	8.17687	−	14.1628i	0.346465	−	0.600095i	−0.639154	−	0.769079i	$-0.720715\pi$
$557$	8.17687	−	14.1628i	0.346465	−	0.600095i	0.985619	+	0.168984i	$0.0540486\pi$
$558$		0			0
$559$	59.2709			2.50689
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−10.8817	+	18.8477i	−0.458611	+	0.794338i	−0.998888	−	0.0471498i	$-0.984986\pi$
$563$	−10.8817	+	18.8477i	−0.458611	+	0.794338i	0.540277	+	0.841487i	$0.318320\pi$
$564$		0			0
$565$	0.0954697	+	0.165358i	0.00401644	+	0.00695668i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.45105	+	14.6376i	0.354286	+	0.613642i	0.986996	−	0.160748i	$-0.0513905\pi$
$569$	8.45105	+	14.6376i	0.354286	+	0.613642i	−0.632709	+	0.774389i	$0.718057\pi$
$570$		0			0
$571$	3.31123	−	5.73522i	0.138571	−	0.240012i	−0.788385	−	0.615182i	$-0.789082\pi$
$571$	3.31123	−	5.73522i	0.138571	−	0.240012i	0.926956	+	0.375170i	$0.122416\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−33.0318			−1.37752
$576$		0			0
$577$	−16.7631	+	29.0346i	−0.697857	+	1.20872i	0.271351	+	0.962481i	$0.412530\pi$
$577$	−16.7631	+	29.0346i	−0.697857	+	1.20872i	−0.969208	+	0.246244i	$0.920804\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−16.9929	−	12.5341i	−0.704983	−	0.520003i
$582$		0			0
$583$	24.7585	+	42.8830i	1.02539	+	1.77603i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−11.7705			−0.485820			−0.242910	−	0.970049i	$-0.578102\pi$
$587$	−11.7705			−0.485820			−0.242910	+	0.970049i	$0.578102\pi$
$588$		0			0
$589$	−17.6418			−0.726917
$590$		0			0
$591$		0			0
$592$		0			0
$593$	16.6472	+	28.8338i	0.683619	+	1.18406i	0.973869	+	0.227111i	$0.0729281\pi$
$593$	16.6472	+	28.8338i	0.683619	+	1.18406i	−0.290250	+	0.956951i	$0.593739\pi$
$594$		0			0
$595$	9.65782	+	7.12370i	0.395932	+	0.292043i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	3.51312	−	6.08490i	0.143542	−	0.248622i	−0.785286	−	0.619133i	$-0.787484\pi$
$599$	3.51312	−	6.08490i	0.143542	−	0.248622i	0.928828	+	0.370511i	$0.120817\pi$
$600$		0			0
$601$	−43.0389			−1.75559			−0.877797	−	0.479033i	$-0.840987\pi$
$601$	−43.0389			−1.75559			−0.877797	+	0.479033i	$0.840987\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.39747	+	2.42049i	−0.0568153	+	0.0984070i
$606$		0			0
$607$	−0.526497	−	0.911919i	−0.0213698	−	0.0370137i	0.855143	−	0.518393i	$-0.173469\pi$
$607$	−0.526497	−	0.911919i	−0.0213698	−	0.0370137i	−0.876513	+	0.481379i	$0.840136\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−14.4099	−	24.9587i	−0.582963	−	1.00972i
$612$		0			0
$613$	−4.12353	+	7.14216i	−0.166548	+	0.288469i	−0.937204	−	0.348782i	$-0.886595\pi$
$613$	−4.12353	+	7.14216i	−0.166548	+	0.288469i	0.770656	+	0.637251i	$0.219929\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	16.8441			0.678117			0.339058	−	0.940765i	$-0.389892\pi$
$617$	16.8441			0.678117			0.339058	+	0.940765i	$0.389892\pi$
$618$		0			0
$619$	−13.0215	+	22.5539i	−0.523378	+	0.906518i	0.476251	+	0.879309i	$0.341995\pi$
$619$	−13.0215	+	22.5539i	−0.523378	+	0.906518i	−0.999630	+	0.0272087i	$0.991338\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.14210	−	19.0586i	0.0858213	−	0.763567i
$624$		0			0
$625$	−8.62436	−	14.9378i	−0.344974	−	0.597513i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−34.9692			−1.39431
$630$		0			0
$631$	17.1124			0.681232			0.340616	−	0.940202i	$-0.389364\pi$
$631$	17.1124			0.681232			0.340616	+	0.940202i	$0.389364\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	1.15320	+	1.99739i	0.0457632	+	0.0792641i
$636$		0			0
$637$	−10.0724	−	32.5906i	−0.399085	−	1.29129i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.3399	−	17.9093i	0.408402	−	0.707373i	−0.586309	−	0.810088i	$-0.699419\pi$
$641$	10.3399	−	17.9093i	0.408402	−	0.707373i	0.994711	+	0.102714i	$0.0327528\pi$
$642$		0			0
$643$	11.3012			0.445675			0.222837	−	0.974856i	$-0.428468\pi$
$643$	11.3012			0.445675			0.222837	+	0.974856i	$0.428468\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.31351	+	12.6674i	−0.287524	+	0.498006i	−0.973218	−	0.229884i	$-0.926165\pi$
$647$	−7.31351	+	12.6674i	−0.287524	+	0.498006i	0.685694	+	0.727890i	$0.259499\pi$
$648$		0			0
$649$	−12.2898	−	21.2866i	−0.482418	−	0.835573i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	8.24261	+	14.2766i	0.322558	+	0.558687i	0.981015	−	0.193931i	$-0.0621239\pi$
$653$	8.24261	+	14.2766i	0.322558	+	0.558687i	−0.658457	+	0.752618i	$0.728791\pi$
$654$		0			0
$655$	0.858967	−	1.48777i	0.0335626	−	0.0581322i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−44.5836			−1.73673			−0.868365	−	0.495926i	$-0.834829\pi$
$659$	−44.5836			−1.73673			−0.868365	+	0.495926i	$0.834829\pi$
$660$		0			0
$661$	−16.5364	+	28.6419i	−0.643191	+	1.11404i	0.341525	+	0.939873i	$0.389057\pi$
$661$	−16.5364	+	28.6419i	−0.643191	+	1.11404i	−0.984716	+	0.174167i	$0.944277\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.95989	+	2.16560i	−0.192336	+	0.0839783i
$666$		0			0
$667$	36.2007	+	62.7015i	1.40170	+	2.42781i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−48.4856			−1.87176
$672$		0			0
$673$	47.2968			1.82316			0.911580	−	0.411124i	$-0.134864\pi$
$673$	47.2968			1.82316			0.911580	+	0.411124i	$0.134864\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−12.7585	−	22.0984i	−0.490349	−	0.849309i	0.509589	−	0.860418i	$-0.329797\pi$
$677$	−12.7585	−	22.0984i	−0.490349	−	0.849309i	−0.999938	+	0.0111083i	$0.996464\pi$
$678$		0			0
$679$	25.8973	+	19.1021i	0.993845	+	0.733070i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−21.4248	+	37.1089i	−0.819798	+	1.41993i	0.0860333	+	0.996292i	$0.472581\pi$
$683$	−21.4248	+	37.1089i	−0.819798	+	1.41993i	−0.905831	+	0.423639i	$0.860752\pi$
$684$		0			0
$685$	9.19628			0.351372
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−31.3425	+	54.2868i	−1.19406	+	2.06816i
$690$		0			0
$691$	4.87575	+	8.44505i	0.185482	+	0.321265i	0.943739	−	0.330691i	$-0.107282\pi$
$691$	4.87575	+	8.44505i	0.185482	+	0.321265i	−0.758257	+	0.651956i	$0.773949\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.64264	−	2.84514i	−0.0623089	−	0.107922i
$696$		0			0
$697$	4.65538	−	8.06336i	0.176335	−	0.305422i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−22.2174			−0.839139			−0.419570	−	0.907723i	$-0.637819\pi$
$701$	−22.2174			−0.839139			−0.419570	+	0.907723i	$0.637819\pi$
$702$		0			0
$703$	7.88507	−	13.6574i	0.297391	−	0.515097i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−28.0011	+	12.2259i	−1.05309	+	0.459802i
$708$		0			0
$709$	−10.9439	−	18.9554i	−0.411008	−	0.711886i	0.583992	−	0.811759i	$-0.301490\pi$
$709$	−10.9439	−	18.9554i	−0.411008	−	0.711886i	−0.995000	+	0.0998727i	$0.968156\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−46.7164			−1.74954
$714$		0			0
$715$	−13.7322			−0.513554
$716$		0			0
$717$		0			0
$718$		0			0
$719$	23.1523	+	40.1010i	0.863435	+	1.49551i	0.868593	+	0.495527i	$0.165025\pi$
$719$	23.1523	+	40.1010i	0.863435	+	1.49551i	−0.00515726	+	0.999987i	$0.501642\pi$
$720$		0			0
$721$	2.38036	−	21.1785i	0.0886492	−	0.788728i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−21.8400	+	37.8280i	−0.811118	+	1.40490i
$726$		0			0
$727$	25.3662			0.940780			0.470390	−	0.882459i	$-0.344113\pi$
$727$	25.3662			0.940780			0.470390	+	0.882459i	$0.344113\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	37.6817	−	65.2666i	1.39371	−	2.41397i
$732$		0			0
$733$	11.4484	+	19.8292i	0.422856	+	0.732407i	0.996217	−	0.0868950i	$-0.0276944\pi$
$733$	11.4484	+	19.8292i	0.422856	+	0.732407i	−0.573362	+	0.819302i	$0.694361\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−3.21389	−	5.56663i	−0.118385	−	0.205049i
$738$		0			0
$739$	−4.90898	+	8.50261i	−0.180580	+	0.312773i	−0.942078	−	0.335393i	$-0.891131\pi$
$739$	−4.90898	+	8.50261i	−0.180580	+	0.312773i	0.761498	+	0.648167i	$0.224464\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−12.4118			−0.455343			−0.227672	−	0.973738i	$-0.573111\pi$
$743$	−12.4118			−0.455343			−0.227672	+	0.973738i	$0.573111\pi$
$744$		0			0
$745$	1.19615	−	2.07180i	0.0438236	−	0.0759048i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−0.605009	+	5.38287i	−0.0221065	+	0.196686i
$750$		0			0
$751$	18.5979	+	32.2124i	0.678646	+	1.17545i	0.975389	+	0.220491i	$0.0707660\pi$
$751$	18.5979	+	32.2124i	0.678646	+	1.17545i	−0.296743	+	0.954957i	$0.595901\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	0.449985			0.0163766
$756$		0			0
$757$	−44.3035			−1.61024			−0.805119	−	0.593113i	$-0.797899\pi$
$757$	−44.3035			−1.61024			−0.805119	+	0.593113i	$0.797899\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−2.25383	−	3.90375i	−0.0817014	−	0.141511i	0.822279	−	0.569084i	$-0.192702\pi$
$761$	−2.25383	−	3.90375i	−0.0817014	−	0.141511i	−0.903981	+	0.427573i	$0.859369\pi$
$762$		0			0
$763$	−20.8417	+	9.09997i	−0.754522	+	0.329441i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	15.5581	−	26.9474i	0.561769	−	0.973013i
$768$		0			0
$769$	−38.9328			−1.40395			−0.701976	−	0.712201i	$-0.747698\pi$
$769$	−38.9328			−1.40395			−0.701976	+	0.712201i	$0.747698\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	8.57280	−	14.8485i	0.308342	−	0.534064i	−0.669658	−	0.742670i	$-0.733559\pi$
$773$	8.57280	−	14.8485i	0.308342	−	0.534064i	0.978000	+	0.208606i	$0.0668925\pi$
$774$		0			0
$775$	−14.0921	−	24.4082i	−0.506202	−	0.876768i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	2.09945	+	3.63635i	0.0752205	+	0.130286i
$780$		0			0
$781$	25.6246	−	44.3831i	0.916920	−	1.58815i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	2.42054			0.0863927
$786$		0			0
$787$	13.6551	−	23.6514i	0.486754	−	0.843082i	−0.513131	−	0.858311i	$-0.671514\pi$
$787$	13.6551	−	23.6514i	0.486754	−	0.843082i	0.999884	+	0.0152288i	$0.00484765\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.555354	−	0.409635i	−0.0197461	−	0.0145649i
$792$		0			0
$793$	−30.6897	−	53.1560i	−1.08982	−	1.88763i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	4.56201			0.161595			0.0807973	−	0.996731i	$-0.474253\pi$
$797$	4.56201			0.161595			0.0807973	+	0.996731i	$0.474253\pi$
$798$		0			0
$799$	−36.6446			−1.29639
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.77240	+	4.80194i	0.0978359	+	0.169457i
$804$		0			0
$805$	−13.1340	+	5.73461i	−0.462914	+	0.202118i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−14.8925	+	25.7946i	−0.523594	+	0.906891i	0.476029	+	0.879430i	$0.342076\pi$
$809$	−14.8925	+	25.7946i	−0.523594	+	0.906891i	−0.999623	+	0.0274615i	$0.991258\pi$
$810$		0			0
$811$	−21.1000			−0.740922			−0.370461	−	0.928848i	$-0.620800\pi$
$811$	−21.1000			−0.740922			−0.370461	+	0.928848i	$0.620800\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	0.176869	−	0.306345i	0.00619543	−	0.0107308i
$816$		0			0
$817$	16.9934	+	29.4334i	0.594523	+	1.02974i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−10.2637	−	17.7773i	−0.358207	−	0.620432i	0.629455	−	0.777037i	$-0.283278\pi$
$821$	−10.2637	−	17.7773i	−0.358207	−	0.620432i	−0.987661	+	0.156605i	$0.949945\pi$
$822$		0			0
$823$	−3.20232	+	5.54658i	−0.111626	+	0.193342i	−0.916426	−	0.400204i	$-0.868939\pi$
$823$	−3.20232	+	5.54658i	−0.111626	+	0.193342i	0.804800	+	0.593546i	$0.202272\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.55548			−0.123636			−0.0618181	−	0.998087i	$-0.519690\pi$
$827$	−3.55548			−0.123636			−0.0618181	+	0.998087i	$0.519690\pi$
$828$		0			0
$829$	−21.7825	+	37.7283i	−0.756536	+	1.31036i	0.188071	+	0.982155i	$0.439776\pi$
$829$	−21.7825	+	37.7283i	−0.756536	+	1.31036i	−0.944607	+	0.328203i	$0.893557\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−42.2909	−	9.62821i	−1.46529	−	0.333598i
$834$		0			0
$835$	−7.59558	−	13.1559i	−0.262856	−	0.455280i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	9.27316			0.320145			0.160073	−	0.987105i	$-0.448827\pi$
$839$	9.27316			0.320145			0.160073	+	0.987105i	$0.448827\pi$
$840$		0			0
$841$	66.7410			2.30142
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.93366	−	6.81329i	−0.135322	−	0.234384i
$846$		0			0
$847$	1.12824	−	10.0382i	0.0387669	−	0.344916i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	20.8801	−	36.1654i	0.715760	−	1.23973i
$852$		0			0
$853$	−13.5980			−0.465587			−0.232794	−	0.972526i	$-0.574787\pi$
$853$	−13.5980			−0.465587			−0.232794	+	0.972526i	$0.574787\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.2095	−	47.1283i	0.929461	−	1.60987i	0.145235	−	0.989397i	$-0.453606\pi$
$857$	27.2095	−	47.1283i	0.929461	−	1.60987i	0.784226	−	0.620476i	$-0.213060\pi$
$858$		0			0
$859$	7.96944	+	13.8035i	0.271914	+	0.470969i	0.969352	−	0.245677i	$-0.0790101\pi$
$859$	7.96944	+	13.8035i	0.271914	+	0.470969i	−0.697438	+	0.716645i	$0.745677\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.45544	+	12.9132i	0.253786	+	0.439570i	0.964565	−	0.263845i	$-0.0849908\pi$
$863$	7.45544	+	12.9132i	0.253786	+	0.439570i	−0.710779	+	0.703415i	$0.751657\pi$
$864$		0			0
$865$	8.99744	−	15.5840i	0.305922	−	0.529873i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	27.3609			0.928154
$870$		0			0
$871$	4.06856	−	7.04696i	0.137858	−	0.238777i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−14.7515	−	10.8809i	−0.498692	−	0.367840i
$876$		0			0
$877$	−13.3670	−	23.1524i	−0.451372	−	0.781800i	0.547099	−	0.837068i	$-0.315732\pi$
$877$	−13.3670	−	23.1524i	−0.451372	−	0.781800i	−0.998472	+	0.0552679i	$0.982399\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−32.0547			−1.07995			−0.539975	−	0.841681i	$-0.681566\pi$
$881$	−32.0547			−1.07995			−0.539975	+	0.841681i	$0.681566\pi$
$882$		0			0
$883$	−20.4442			−0.688002			−0.344001	−	0.938969i	$-0.611782\pi$
$883$	−20.4442			−0.688002			−0.344001	+	0.938969i	$0.611782\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−16.3845	−	28.3788i	−0.550139	−	0.952868i	−0.998264	−	0.0588975i	$-0.981242\pi$
$887$	−16.3845	−	28.3788i	−0.550139	−	0.952868i	0.448125	−	0.893971i	$-0.352092\pi$
$888$		0			0
$889$	−6.70822	−	4.94805i	−0.224987	−	0.165952i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.26284	−	14.3117i	0.276505	−	0.478921i
$894$		0			0
$895$	−15.9475			−0.533067
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−30.8880	+	53.4996i	−1.03017	+	1.78431i
$900$		0			0
$901$	39.8522	+	69.0260i	1.32767	+	2.29959i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	2.39397	+	4.14648i	0.0795784	+	0.137834i
$906$		0			0
$907$	17.1098	−	29.6351i	0.568123	−	0.984018i	−0.428628	−	0.903481i	$-0.641003\pi$
$907$	17.1098	−	29.6351i	0.568123	−	0.984018i	0.996752	−	0.0805374i	$-0.0256636\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−40.8423			−1.35317			−0.676583	−	0.736367i	$-0.736540\pi$
$911$	−40.8423			−1.35317			−0.676583	+	0.736367i	$0.736540\pi$
$912$		0			0
$913$	15.3609	−	26.6058i	0.508370	−	0.880523i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.693483	+	6.17004i	−0.0229008	+	0.203753i
$918$		0			0
$919$	−13.8862	−	24.0517i	−0.458065	−	0.793392i	0.540794	−	0.841155i	$-0.318124\pi$
$919$	−13.8862	−	24.0517i	−0.458065	−	0.793392i	−0.998859	+	0.0477634i	$0.984791\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	64.8779			2.13548
$924$		0			0
$925$	25.1941			0.828376
$926$		0			0
$927$		0			0
$928$		0			0
$929$	25.1988	+	43.6455i	0.826744	+	1.43196i	0.900579	+	0.434693i	$0.143143\pi$
$929$	25.1988	+	43.6455i	0.826744	+	1.43196i	−0.0738343	+	0.997271i	$0.523524\pi$
$930$		0			0
$931$	13.2963	−	14.3458i	0.435770	−	0.470165i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.73027	+	15.1213i	−0.285510	+	0.494518i
$936$		0			0
$937$	11.1099			0.362946			0.181473	−	0.983396i	$-0.441914\pi$
$937$	11.1099			0.362946			0.181473	+	0.983396i	$0.441914\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−5.35102	+	9.26823i	−0.174438	+	0.302136i	−0.939967	−	0.341266i	$-0.889144\pi$
$941$	−5.35102	+	9.26823i	−0.174438	+	0.302136i	0.765529	+	0.643402i	$0.222478\pi$
$942$		0			0
$943$	5.55945	+	9.62924i	0.181040	+	0.313571i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−8.86157	−	15.3487i	−0.287962	−	0.498766i	0.685361	−	0.728204i	$-0.259645\pi$
$947$	−8.86157	−	15.3487i	−0.287962	−	0.498766i	−0.973323	+	0.229438i	$0.926311\pi$
$948$		0			0
$949$	−3.50966	+	6.07892i	−0.113929	+	0.197330i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−44.8253			−1.45203			−0.726017	−	0.687677i	$-0.758631\pi$
$953$	−44.8253			−1.45203			−0.726017	+	0.687677i	$0.758631\pi$
$954$		0			0
$955$	5.62181	−	9.73726i	0.181918	−	0.315090i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−30.4600	+	13.2995i	−0.983605	+	0.429464i
$960$		0			0
$961$	−4.43022	−	7.67337i	−0.142910	−	0.247528i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	13.8776			0.446737
$966$		0			0
$967$	35.3043			1.13531			0.567655	−	0.823267i	$-0.307851\pi$
$967$	35.3043			1.13531			0.567655	+	0.823267i	$0.307851\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	11.7761	+	20.3968i	0.377912	+	0.654563i	0.990758	−	0.135639i	$-0.0433088\pi$
$971$	11.7761	+	20.3968i	0.377912	+	0.654563i	−0.612846	+	0.790202i	$0.709975\pi$
$972$		0			0
$973$	9.55535	+	7.04812i	0.306331	+	0.225952i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	11.2372	−	19.4633i	0.359508	−	0.622687i	−0.628370	−	0.777914i	$-0.716278\pi$
$977$	11.2372	−	19.4633i	0.359508	−	0.622687i	0.987879	+	0.155227i	$0.0496111\pi$
$978$		0			0
$979$	27.9038			0.891808
$980$		0			0
$981$		0			0
$982$		0			0
$983$	2.38893	−	4.13775i	0.0761951	−	0.131974i	−0.825410	−	0.564533i	$-0.809056\pi$
$983$	2.38893	−	4.13775i	0.0761951	−	0.131974i	0.901605	+	0.432560i	$0.142389\pi$
$984$		0			0
$985$	−3.02445	−	5.23850i	−0.0963670	−	0.166913i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	44.9993	+	77.9411i	1.43090	+	2.47838i
$990$		0			0
$991$	−19.3142	+	33.4532i	−0.613535	+	1.06267i	0.377104	+	0.926171i	$0.376920\pi$
$991$	−19.3142	+	33.4532i	−0.613535	+	1.06267i	−0.990640	+	0.136504i	$0.956413\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−9.88985			−0.313529
$996$		0			0
$997$	−25.8697	+	44.8076i	−0.819301	+	1.41907i	0.0868962	+	0.996217i	$0.472305\pi$
$997$	−25.8697	+	44.8076i	−0.819301	+	1.41907i	−0.906198	+	0.422854i	$0.861028\pi$
$998$		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.865.2	yes	8
3.2	odd	2		1512.2.s.m.865.4	✓	8
7.2	even	3	inner	1512.2.s.p.1297.2	yes	8
21.2	odd	6		1512.2.s.m.1297.4	yes	8

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

\(f(q)\)	\(=\)	\(q+(-0.366025 - 0.633975i) q^{5} +(2.12920 + 1.57052i) q^{7} +O(q^{10})\)	\(q+(-0.366025 - 0.633975i) q^{5} +(2.12920 + 1.57052i) q^{7} +(-1.92471 + 3.33369i) q^{11} -4.87308 q^{13} +(-3.09808 + 5.36603i) q^{17} +(-1.39715 - 2.41993i) q^{19} +(-3.69971 - 6.40809i) q^{23} +(2.23205 - 3.86603i) q^{25} -9.78474 q^{29} +(3.15676 - 5.46766i) q^{31} +(0.216328 - 1.92471i) q^{35} +(2.82185 + 4.88759i) q^{37} -1.50267 q^{41} -12.1629 q^{43} +(2.95704 + 5.12175i) q^{47} +(2.06696 + 6.68788i) q^{49} +(6.43176 - 11.1401i) q^{53} +2.81796 q^{55} +(-3.19265 + 5.52984i) q^{59} +(6.29779 + 10.9081i) q^{61} +(1.78367 + 3.08941i) q^{65} +(-0.834905 + 1.44610i) q^{67} -13.3135 q^{71} +(0.720214 - 1.24745i) q^{73} +(-9.33369 + 4.07529i) q^{77} +(-3.55390 - 6.15554i) q^{79} -7.98089 q^{83} +4.53590 q^{85} +(-3.62442 - 6.27768i) q^{89} +(-10.3758 - 7.65326i) q^{91} +(-1.02278 + 1.77151i) q^{95} +12.1629 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5} - 2 q^{7}+O(q^{10}) \) 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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