LMFDB - Embedded newform 3024.2.bf.i.2287.15

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(1711,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 2, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.1711"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 3024 = 2^{4} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3024.bf (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2287.15
Character	$\chi$	$=$	3024.2287
Dual form			3024.2.bf.i.1711.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+4.29566i q^{5} +(0.334043 + 2.62458i) q^{7} -3.60507i q^{11} +(-4.45873 + 2.57425i) q^{13} +(0.886675 - 0.511922i) q^{17} +(0.662930 - 1.14823i) q^{19} -3.14466i q^{23} -13.4527 q^{25} +(0.373020 - 0.646090i) q^{29} +(-4.64826 + 8.05102i) q^{31} +(-11.2743 + 1.43494i) q^{35} +(-0.761414 + 1.31881i) q^{37} +(-4.22328 + 2.43831i) q^{41} +(6.14560 + 3.54817i) q^{43} +(3.70487 + 6.41703i) q^{47} +(-6.77683 + 1.75345i) q^{49} +(0.0746200 + 0.129246i) q^{53} +15.4862 q^{55} +(-0.996973 + 1.72681i) q^{59} +(5.05446 - 2.91820i) q^{61} +(-11.0581 - 19.1532i) q^{65} +(-7.86136 - 4.53876i) q^{67} -11.3710i q^{71} +(4.04560 - 2.33573i) q^{73} +(9.46180 - 1.20425i) q^{77} +(-9.68102 + 5.58934i) q^{79} +(6.90574 - 11.9611i) q^{83} +(2.19904 + 3.80885i) q^{85} +(-14.0722 - 8.12459i) q^{89} +(-8.24573 - 10.8424i) q^{91} +(4.93240 + 2.84772i) q^{95} +(-6.25228 - 3.60975i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 6 q^{13} + 18 q^{17} - 32 q^{25} + 12 q^{29} + 2 q^{37} - 36 q^{41} + 2 q^{49} + 12 q^{53} + 42 q^{61} - 18 q^{65} + 66 q^{77} - 12 q^{85} + 18 q^{89} - 6 q^{97}+O(q^{100}) $ 32 * q - 6 * q^13 + 18 * q^17 - 32 * q^25 + 12 * q^29 + 2 * q^37 - 36 * q^41 + 2 * q^49 + 12 * q^53 + 42 * q^61 - 18 * q^65 + 66 * q^77 - 12 * q^85 + 18 * q^89 - 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times$.

$n$	$757$	$785$	$1135$	$2593$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{5}{6}\right)$

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
$5$			4.29566i			1.92108i	0.278147	+	0.960539i	$0.410280\pi$
$5$			4.29566i			1.92108i	−0.278147	+	0.960539i	$0.589720\pi$
$6$		0			0
$7$	0.334043	+	2.62458i	0.126256	+	0.991998i
$7$	0.334043	+	2.62458i	0.126256	+	0.991998i
$8$		0			0
$9$		0			0
$10$		0			0
$11$		−	3.60507i		−	1.08697i	−0.839419	−	0.543485i	$-0.817104\pi$
$11$		−	3.60507i		−	1.08697i	0.839419	−	0.543485i	$-0.182896\pi$
$12$		0			0
$13$	−4.45873	+	2.57425i	−1.23663	+	0.713968i	−0.968404	−	0.249388i	$-0.919770\pi$
$13$	−4.45873	+	2.57425i	−1.23663	+	0.713968i	−0.268225	+	0.963356i	$0.586437\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.886675	−	0.511922i	0.215050	−	0.124159i	−0.388606	−	0.921404i	$-0.627043\pi$
$17$	0.886675	−	0.511922i	0.215050	−	0.124159i	0.603656	+	0.797245i	$0.293710\pi$
$18$		0			0
$19$	0.662930	−	1.14823i	0.152087	−	0.263422i	−0.779908	−	0.625894i	$-0.784734\pi$
$19$	0.662930	−	1.14823i	0.152087	−	0.263422i	0.931994	+	0.362473i	$0.118067\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$		−	3.14466i		−	0.655706i	−0.944729	−	0.327853i	$-0.893675\pi$
$23$		−	3.14466i		−	0.655706i	0.944729	−	0.327853i	$-0.106325\pi$
$24$		0			0
$25$	−13.4527			−2.69054
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.373020	−	0.646090i	0.0692681	−	0.119976i	−0.829311	−	0.558787i	$-0.811267\pi$
$29$	0.373020	−	0.646090i	0.0692681	−	0.119976i	0.898579	+	0.438811i	$0.144600\pi$
$30$		0			0
$31$	−4.64826	+	8.05102i	−0.834851	+	1.44601i	0.0592999	+	0.998240i	$0.481113\pi$
$31$	−4.64826	+	8.05102i	−0.834851	+	1.44601i	−0.894151	+	0.447765i	$0.852220\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−11.2743	+	1.43494i	−1.90570	+	0.242548i
$36$		0			0
$37$	−0.761414	+	1.31881i	−0.125176	+	0.216811i	−0.921802	−	0.387662i	$-0.873283\pi$
$37$	−0.761414	+	1.31881i	−0.125176	+	0.216811i	0.796626	+	0.604473i	$0.206616\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.22328	+	2.43831i	−0.659565	+	0.380800i	−0.792111	−	0.610377i	$-0.791018\pi$
$41$	−4.22328	+	2.43831i	−0.659565	+	0.380800i	0.132546	+	0.991177i	$0.457685\pi$
$42$		0			0
$43$	6.14560	+	3.54817i	0.937196	+	0.541090i	0.889080	−	0.457752i	$-0.151345\pi$
$43$	6.14560	+	3.54817i	0.937196	+	0.541090i	0.0481156	+	0.998842i	$0.484678\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	3.70487	+	6.41703i	0.540411	+	0.936020i	0.998880	+	0.0473095i	$0.0150647\pi$
$47$	3.70487	+	6.41703i	0.540411	+	0.936020i	−0.458469	+	0.888710i	$0.651602\pi$
$48$		0			0
$49$	−6.77683	+	1.75345i	−0.968119	+	0.250492i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	0.0746200	+	0.129246i	0.0102499	+	0.0177533i	0.871105	−	0.491097i	$-0.163404\pi$
$53$	0.0746200	+	0.129246i	0.0102499	+	0.0177533i	−0.860855	+	0.508850i	$0.830071\pi$
$54$		0			0
$55$	15.4862			2.08815
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−0.996973	+	1.72681i	−0.129795	+	0.224811i	−0.923597	−	0.383365i	$-0.874765\pi$
$59$	−0.996973	+	1.72681i	−0.129795	+	0.224811i	0.793802	+	0.608176i	$0.208099\pi$
$60$		0			0
$61$	5.05446	−	2.91820i	0.647158	−	0.373637i	−0.140209	−	0.990122i	$-0.544777\pi$
$61$	5.05446	−	2.91820i	0.647158	−	0.373637i	0.787366	+	0.616485i	$0.211444\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−11.0581	−	19.1532i	−1.37159	−	2.37566i
$66$		0			0
$67$	−7.86136	−	4.53876i	−0.960418	−	0.554498i	−0.0641164	−	0.997942i	$-0.520423\pi$
$67$	−7.86136	−	4.53876i	−0.960418	−	0.554498i	−0.896302	+	0.443445i	$0.853756\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	11.3710i		−	1.34949i	−0.738052	−	0.674743i	$-0.764254\pi$
$71$		−	11.3710i		−	1.34949i	0.738052	−	0.674743i	$-0.235746\pi$
$72$		0			0
$73$	4.04560	−	2.33573i	0.473502	−	0.273377i	−0.244202	−	0.969724i	$-0.578526\pi$
$73$	4.04560	−	2.33573i	0.473502	−	0.273377i	0.717705	+	0.696348i	$0.245193\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	9.46180	−	1.20425i	1.07827	−	0.137237i
$78$		0			0
$79$	−9.68102	+	5.58934i	−1.08920	+	0.628850i	−0.933363	−	0.358933i	$-0.883141\pi$
$79$	−9.68102	+	5.58934i	−1.08920	+	0.628850i	−0.155836	+	0.987783i	$0.549807\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	6.90574	−	11.9611i	0.758003	−	1.31290i	−0.185864	−	0.982575i	$-0.559508\pi$
$83$	6.90574	−	11.9611i	0.758003	−	1.31290i	0.943867	−	0.330324i	$-0.107158\pi$
$84$		0			0
$85$	2.19904	+	3.80885i	0.238520	+	0.413128i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−14.0722	−	8.12459i	−1.49165	−	0.861205i	−0.491697	−	0.870767i	$-0.663623\pi$
$89$	−14.0722	−	8.12459i	−1.49165	−	0.861205i	−0.999954	+	0.00956141i	$0.996956\pi$
$90$		0			0
$91$	−8.24573	−	10.8424i	−0.864387	−	1.13659i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.93240	+	2.84772i	0.506053	+	0.292170i
$96$		0			0
$97$	−6.25228	−	3.60975i	−0.634822	−	0.366515i	0.147795	−	0.989018i	$-0.452782\pi$
$97$	−6.25228	−	3.60975i	−0.634822	−	0.366515i	−0.782617	+	0.622503i	$0.786116\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$			9.00333i			0.895865i	0.894067	+	0.447932i	$0.147839\pi$
$101$			9.00333i			0.895865i	−0.894067	+	0.447932i	$0.852161\pi$
$102$		0			0
$103$	−9.29530			−0.915893			−0.457947	−	0.888980i	$-0.651415\pi$
$103$	−9.29530			−0.915893			−0.457947	+	0.888980i	$0.651415\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	4.62335	+	2.66929i	0.446956	+	0.258050i	0.706544	−	0.707669i	$-0.250253\pi$
$107$	4.62335	+	2.66929i	0.446956	+	0.258050i	−0.259588	+	0.965720i	$0.583587\pi$
$108$		0			0
$109$	−2.66385	−	4.61393i	−0.255151	−	0.441934i	0.709786	−	0.704418i	$-0.248792\pi$
$109$	−2.66385	−	4.61393i	−0.255151	−	0.441934i	−0.964936	+	0.262484i	$0.915458\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.83794	−	10.1116i	−0.549187	−	0.951221i	−0.998330	−	0.0577607i	$-0.981604\pi$
$113$	−5.83794	−	10.1116i	−0.549187	−	0.951221i	0.449143	−	0.893460i	$-0.351729\pi$
$114$		0			0
$115$	13.5084			1.25966
$116$		0			0
$117$		0			0
$118$		0			0
$119$	1.63977	+	2.15614i	0.150317	+	0.197653i
$120$		0			0
$121$	−1.99655			−0.181504
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	36.3099i		−	3.24765i
$126$		0			0
$127$		−	13.4887i		−	1.19693i	−0.801150	−	0.598463i	$-0.795778\pi$
$127$		−	13.4887i		−	1.19693i	0.801150	−	0.598463i	$-0.204222\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	16.5823			1.44880			0.724399	−	0.689381i	$-0.242117\pi$
$131$	16.5823			1.44880			0.724399	+	0.689381i	$0.242117\pi$
$132$		0			0
$133$	3.23506	+	1.35635i	0.280516	+	0.117611i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−5.97903			−0.510823			−0.255411	−	0.966832i	$-0.582211\pi$
$137$	−5.97903			−0.510823			−0.255411	+	0.966832i	$0.582211\pi$
$138$		0			0
$139$	8.75126	+	15.1576i	0.742272	+	1.28565i	0.951459	+	0.307777i	$0.0995850\pi$
$139$	8.75126	+	15.1576i	0.742272	+	1.28565i	−0.209187	+	0.977876i	$0.567082\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.28035	+	16.0740i	0.776062	+	1.34418i
$144$		0			0
$145$	2.77538	+	1.60237i	0.230483	+	0.133069i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	15.1776			1.24339			0.621697	−	0.783258i	$-0.286444\pi$
$149$	15.1776			1.24339			0.621697	+	0.783258i	$0.286444\pi$
$150$		0			0
$151$			7.04117i			0.573003i	0.958080	+	0.286501i	$0.0924923\pi$
$151$			7.04117i			0.573003i	−0.958080	+	0.286501i	$0.907508\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−34.5844	−	19.9673i	−2.77789	−	1.60381i
$156$		0			0
$157$	−13.7064	−	7.91337i	−1.09389	−	0.631556i	−0.159278	−	0.987234i	$-0.550917\pi$
$157$	−13.7064	−	7.91337i	−1.09389	−	0.631556i	−0.934609	+	0.355678i	$0.884250\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	8.25340	−	1.05045i	0.650459	−	0.0827871i
$162$		0			0
$163$	9.98202	+	5.76312i	0.781852	+	0.451403i	0.837086	−	0.547071i	$-0.184257\pi$
$163$	9.98202	+	5.76312i	0.781852	+	0.451403i	−0.0552341	+	0.998473i	$0.517591\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.14269	+	5.44330i	0.243189	+	0.421215i	0.961621	−	0.274382i	$-0.0884732\pi$
$167$	3.14269	+	5.44330i	0.243189	+	0.421215i	−0.718432	+	0.695597i	$0.755140\pi$
$168$		0			0
$169$	6.75351	−	11.6974i	0.519500	−	0.899801i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−6.21442	+	3.58789i	−0.472473	+	0.272783i	−0.717274	−	0.696791i	$-0.754611\pi$
$173$	−6.21442	+	3.58789i	−0.472473	+	0.272783i	0.244801	+	0.969573i	$0.421277\pi$
$174$		0			0
$175$	−4.49378	−	35.3076i	−0.339698	−	2.66901i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−17.9847	+	10.3835i	−1.34424	+	0.776098i	−0.987427	−	0.158077i	$-0.949471\pi$
$179$	−17.9847	+	10.3835i	−1.34424	+	0.776098i	−0.356815	+	0.934175i	$0.616137\pi$
$180$		0			0
$181$			13.7498i			1.02201i	0.859577	+	0.511005i	$0.170727\pi$
$181$			13.7498i			1.02201i	−0.859577	+	0.511005i	$0.829273\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−5.66515	−	3.27077i	−0.416510	−	0.240472i
$186$		0			0
$187$	−1.84552	−	3.19653i	−0.134957	−	0.233753i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−5.06422	+	2.92383i	−0.366434	+	0.211561i	−0.671899	−	0.740642i	$-0.734521\pi$
$191$	−5.06422	+	2.92383i	−0.366434	+	0.211561i	0.305466	+	0.952203i	$0.401188\pi$
$192$		0			0
$193$	1.13564	−	1.96698i	0.0817448	−	0.141586i	−0.822255	−	0.569120i	$-0.807284\pi$
$193$	1.13564	−	1.96698i	0.0817448	−	0.141586i	0.903999	+	0.427534i	$0.140617\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.34192			0.665584			0.332792	−	0.943000i	$-0.392009\pi$
$197$	9.34192			0.665584			0.332792	+	0.943000i	$0.392009\pi$
$198$		0			0
$199$	−1.05079	−	1.82002i	−0.0744883	−	0.129017i	0.826375	−	0.563120i	$-0.190399\pi$
$199$	−1.05079	−	1.82002i	−0.0744883	−	0.129017i	−0.900864	+	0.434102i	$0.857066\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	1.82032	+	0.763199i	0.127761	+	0.0535660i
$204$		0			0
$205$	−10.4741	−	18.1418i	−0.731546	−	1.26707i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.13945	−	2.38991i	−0.286332	−	0.165314i
$210$		0			0
$211$	8.07179	−	4.66025i	0.555685	−	0.320825i	−0.195727	−	0.980658i	$-0.562707\pi$
$211$	8.07179	−	4.66025i	0.555685	−	0.320825i	0.751412	+	0.659834i	$0.229373\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−15.2417	+	26.3994i	−1.03948	+	1.80043i
$216$		0			0
$217$	−22.6832	−	9.51033i	−1.53984	−	0.645603i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−2.63563	+	4.56504i	−0.177292	+	0.307078i
$222$		0			0
$223$	3.87550	−	6.71256i	0.259523	−	0.449506i	−0.706591	−	0.707622i	$-0.749768\pi$
$223$	3.87550	−	6.71256i	0.259523	−	0.449506i	0.966114	+	0.258115i	$0.0831014\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.3087			1.21519			0.607595	−	0.794247i	$-0.292134\pi$
$227$	18.3087			1.21519			0.607595	+	0.794247i	$0.292134\pi$
$228$		0			0
$229$			22.2784i			1.47220i	0.676874	+	0.736099i	$0.263334\pi$
$229$			22.2784i			1.47220i	−0.676874	+	0.736099i	$0.736666\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.35026	+	4.07076i	−0.153970	+	0.266684i	−0.932684	−	0.360696i	$-0.882539\pi$
$233$	−2.35026	+	4.07076i	−0.153970	+	0.266684i	0.778713	+	0.627380i	$0.215873\pi$
$234$		0			0
$235$	−27.5654	+	15.9149i	−1.79817	+	1.03817i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	9.76287	−	5.63659i	0.631507	−	0.364601i	−0.149828	−	0.988712i	$-0.547872\pi$
$239$	9.76287	−	5.63659i	0.631507	−	0.364601i	0.781336	+	0.624111i	$0.214539\pi$
$240$		0			0
$241$			3.72908i			0.240211i	0.992761	+	0.120106i	$0.0383233\pi$
$241$			3.72908i			0.240211i	−0.992761	+	0.120106i	$0.961677\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−7.53220	−	29.1110i	−0.481215	−	1.85983i
$246$		0			0
$247$			6.82619i			0.434340i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	12.5374			0.791354			0.395677	−	0.918390i	$-0.370510\pi$
$251$	12.5374			0.791354			0.395677	+	0.918390i	$0.370510\pi$
$252$		0			0
$253$	−11.3367			−0.712733
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	15.4524i		−	0.963894i	−0.876200	−	0.481947i	$-0.839930\pi$
$257$		−	15.4524i		−	0.963894i	0.876200	−	0.481947i	$-0.160070\pi$
$258$		0			0
$259$	−3.71566	−	1.55785i	−0.230880	−	0.0968002i
$260$		0			0
$261$		0			0
$262$		0			0
$263$		−	17.2727i		−	1.06508i	−0.846404	−	0.532541i	$-0.821237\pi$
$263$		−	17.2727i		−	1.06508i	0.846404	−	0.532541i	$-0.178763\pi$
$264$		0			0
$265$	−0.555196	+	0.320542i	−0.0341054	+	0.0196908i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−8.06706	+	4.65752i	−0.491857	+	0.283974i	−0.725345	−	0.688386i	$-0.758320\pi$
$269$	−8.06706	+	4.65752i	−0.491857	+	0.283974i	0.233487	+	0.972360i	$0.424986\pi$
$270$		0			0
$271$	−10.1759	+	17.6251i	−0.618140	+	1.07065i	0.371685	+	0.928359i	$0.378780\pi$
$271$	−10.1759	+	17.6251i	−0.618140	+	1.07065i	−0.989825	+	0.142291i	$0.954553\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$			48.4979i			2.92453i
$276$		0			0
$277$	−32.6761			−1.96331			−0.981657	−	0.190654i	$-0.938939\pi$
$277$	−32.6761			−1.96331			−0.981657	+	0.190654i	$0.938939\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−10.8916	+	18.8647i	−0.649736	+	1.12538i	0.333449	+	0.942768i	$0.391787\pi$
$281$	−10.8916	+	18.8647i	−0.649736	+	1.12538i	−0.983186	+	0.182609i	$0.941546\pi$
$282$		0			0
$283$	−1.72157	+	2.98184i	−0.102336	+	0.177252i	−0.912647	−	0.408749i	$-0.865965\pi$
$283$	−1.72157	+	2.98184i	−0.102336	+	0.177252i	0.810310	+	0.586001i	$0.199298\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−7.81029	−	10.2698i	−0.461027	−	0.606208i
$288$		0			0
$289$	−7.97587	+	13.8146i	−0.469169	+	0.812624i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−17.0502	+	9.84397i	−0.996086	+	0.575091i	−0.907088	−	0.420941i	$-0.861700\pi$
$293$	−17.0502	+	9.84397i	−0.996086	+	0.575091i	−0.0889983	+	0.996032i	$0.528367\pi$
$294$		0			0
$295$	−7.41778	−	4.28266i	−0.431880	−	0.249346i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	8.09513	+	14.0212i	0.468153	+	0.810865i
$300$		0			0
$301$	−7.25954	+	17.3149i	−0.418433	+	0.998012i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	12.5356	+	21.7123i	0.717785	+	1.24324i
$306$		0			0
$307$	−12.5054			−0.713719			−0.356859	−	0.934158i	$-0.616152\pi$
$307$	−12.5054			−0.713719			−0.356859	+	0.934158i	$0.616152\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−5.35524	+	9.27554i	−0.303668	+	0.525968i	−0.976964	−	0.213405i	$-0.931545\pi$
$311$	−5.35524	+	9.27554i	−0.303668	+	0.525968i	0.673296	+	0.739373i	$0.264878\pi$
$312$		0			0
$313$	−9.95819	+	5.74936i	−0.562870	+	0.324973i	−0.754297	−	0.656534i	$-0.772022\pi$
$313$	−9.95819	+	5.74936i	−0.562870	+	0.324973i	0.191427	+	0.981507i	$0.438689\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.70784	+	15.0824i	0.489081	+	0.847113i	0.999921	−	0.0125628i	$-0.00399896\pi$
$317$	8.70784	+	15.0824i	0.489081	+	0.847113i	−0.510840	+	0.859676i	$0.670666\pi$
$318$		0			0
$319$	−2.32920	−	1.34476i	−0.130410	−	0.0752923i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	1.35747i		−	0.0755319i
$324$		0			0
$325$	59.9819	−	34.6306i	3.32720	−	1.92096i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−15.6044	+	11.8673i	−0.860299	+	0.654265i
$330$		0			0
$331$	10.1816	−	5.87837i	0.559634	−	0.323105i	−0.193365	−	0.981127i	$-0.561940\pi$
$331$	10.1816	−	5.87837i	0.559634	−	0.323105i	0.752998	+	0.658022i	$0.228607\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	19.4970	−	33.7697i	1.06523	−	1.84504i
$336$		0			0
$337$	9.72282	+	16.8404i	0.529636	+	0.917356i	0.999402	+	0.0345655i	$0.0110047\pi$
$337$	9.72282	+	16.8404i	0.529636	+	0.917356i	−0.469767	+	0.882791i	$0.655662\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	29.0245	+	16.7573i	1.57176	+	0.907459i
$342$		0			0
$343$	−6.86581	−	17.2006i	−0.370719	−	0.928745i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−8.58776	−	4.95814i	−0.461015	−	0.266167i	0.251456	−	0.967869i	$-0.419091\pi$
$347$	−8.58776	−	4.95814i	−0.461015	−	0.266167i	−0.712471	+	0.701702i	$0.752424\pi$
$348$		0			0
$349$	8.22452	+	4.74843i	0.440248	+	0.254178i	0.703703	−	0.710494i	$-0.251529\pi$
$349$	8.22452	+	4.74843i	0.440248	+	0.254178i	−0.263455	+	0.964672i	$0.584862\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$			7.38308i			0.392962i	0.980508	+	0.196481i	$0.0629514\pi$
$353$			7.38308i			0.392962i	−0.980508	+	0.196481i	$0.937049\pi$
$354$		0			0
$355$	48.8458			2.59247
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−9.92939	−	5.73274i	−0.524053	−	0.302562i	0.214538	−	0.976716i	$-0.431175\pi$
$359$	−9.92939	−	5.73274i	−0.524053	−	0.302562i	−0.738591	+	0.674153i	$0.764509\pi$
$360$		0			0
$361$	8.62105	+	14.9321i	0.453739	+	0.785900i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	10.0335	+	17.3785i	0.525178	+	0.909634i
$366$		0			0
$367$	−26.7766			−1.39773			−0.698864	−	0.715254i	$-0.746311\pi$
$367$	−26.7766			−1.39773			−0.698864	+	0.715254i	$0.746311\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−0.314289	+	0.239020i	−0.0163171	+	0.0124093i
$372$		0			0
$373$	−13.6607			−0.707323			−0.353662	−	0.935373i	$-0.615064\pi$
$373$	−13.6607			−0.707323			−0.353662	+	0.935373i	$0.615064\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			3.84098i			0.197821i
$378$		0			0
$379$		−	1.70006i		−	0.0873261i	−0.999046	−	0.0436630i	$-0.986097\pi$
$379$		−	1.70006i		−	0.0873261i	0.999046	−	0.0436630i	$-0.0139028\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	20.6059			1.05291			0.526455	−	0.850203i	$-0.323521\pi$
$383$	20.6059			1.05291			0.526455	+	0.850203i	$0.323521\pi$
$384$		0			0
$385$	5.17305	+	40.6447i	0.263643	+	2.07144i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	13.4475			0.681814			0.340907	−	0.940097i	$-0.389266\pi$
$389$	13.4475			0.681814			0.340907	+	0.940097i	$0.389266\pi$
$390$		0			0
$391$	−1.60982	−	2.78829i	−0.0814120	−	0.141010i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−24.0099	−	41.5863i	−1.20807	−	2.09244i
$396$		0			0
$397$	−10.9040	−	6.29540i	−0.547254	−	0.315957i	0.200760	−	0.979641i	$-0.435659\pi$
$397$	−10.9040	−	6.29540i	−0.547254	−	0.315957i	−0.748014	+	0.663683i	$0.768992\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−4.60899			−0.230162			−0.115081	−	0.993356i	$-0.536713\pi$
$401$	−4.60899			−0.230162			−0.115081	+	0.993356i	$0.536713\pi$
$402$		0			0
$403$		−	47.8631i		−	2.38423i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.75439	+	2.74495i	0.235667	+	0.136062i
$408$		0			0
$409$	−17.8209	−	10.2889i	−0.881187	−	0.508754i	−0.0101377	−	0.999949i	$-0.503227\pi$
$409$	−17.8209	−	10.2889i	−0.881187	−	0.508754i	−0.871050	+	0.491195i	$0.836560\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.86518	−	2.03981i	−0.239400	−	0.100372i
$414$		0			0
$415$	51.3808	+	29.6647i	2.52218	+	1.45618i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	3.93303	+	6.81221i	0.192141	+	0.332798i	0.945960	−	0.324284i	$-0.105123\pi$
$419$	3.93303	+	6.81221i	0.192141	+	0.332798i	−0.753818	+	0.657083i	$0.771790\pi$
$420$		0			0
$421$	10.8367	−	18.7697i	0.528149	−	0.914781i	−0.471312	−	0.881966i	$-0.656220\pi$
$421$	10.8367	−	18.7697i	0.528149	−	0.914781i	0.999461	−	0.0328148i	$-0.0104471\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−11.9282	+	6.88672i	−0.578601	+	0.334055i
$426$		0			0
$427$	9.34745	+	12.2910i	0.452355	+	0.594805i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	0.640472	−	0.369776i	0.0308504	−	0.0178115i	−0.484495	−	0.874794i	$-0.660997\pi$
$431$	0.640472	−	0.369776i	0.0308504	−	0.0178115i	0.515346	+	0.856982i	$0.327663\pi$
$432$		0			0
$433$			26.1089i			1.25471i	0.778732	+	0.627357i	$0.215863\pi$
$433$			26.1089i			1.25471i	−0.778732	+	0.627357i	$0.784137\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−3.61078	−	2.08469i	−0.172727	−	0.0997241i
$438$		0			0
$439$	−7.41381	−	12.8411i	−0.353842	−	0.612872i	0.633077	−	0.774089i	$-0.281792\pi$
$439$	−7.41381	−	12.8411i	−0.353842	−	0.612872i	−0.986919	+	0.161216i	$0.948458\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	8.78723	−	5.07331i	0.417494	−	0.241040i	−0.276511	−	0.961011i	$-0.589178\pi$
$443$	8.78723	−	5.07331i	0.417494	−	0.241040i	0.694005	+	0.719971i	$0.255845\pi$
$444$		0			0
$445$	34.9005	−	60.4494i	1.65444	−	2.86558i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−25.0880			−1.18397			−0.591987	−	0.805948i	$-0.701656\pi$
$449$	−25.0880			−1.18397			−0.591987	+	0.805948i	$0.701656\pi$
$450$		0			0
$451$	8.79028	+	15.2252i	0.413918	+	0.716927i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	46.5751	−	35.4208i	2.18348	−	1.66055i
$456$		0			0
$457$	11.9988	+	20.7825i	0.561279	+	0.972163i	0.997385	+	0.0722682i	$0.0230237\pi$
$457$	11.9988	+	20.7825i	0.561279	+	0.972163i	−0.436107	+	0.899895i	$0.643643\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	12.2178	+	7.05393i	0.569038	+	0.328534i	0.756765	−	0.653687i	$-0.226779\pi$
$461$	12.2178	+	7.05393i	0.569038	+	0.328534i	−0.187727	+	0.982221i	$0.560112\pi$
$462$		0			0
$463$	12.0911	−	6.98080i	0.561921	−	0.324425i	−0.191995	−	0.981396i	$-0.561496\pi$
$463$	12.0911	−	6.98080i	0.561921	−	0.324425i	0.753916	+	0.656971i	$0.228163\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.2526	+	22.9542i	−0.613258	+	1.06219i	0.377429	+	0.926038i	$0.376808\pi$
$467$	−13.2526	+	22.9542i	−0.613258	+	1.06219i	−0.990687	+	0.136156i	$0.956525\pi$
$468$		0			0
$469$	9.28630	−	22.1489i	0.428801	−	1.02274i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.7914	−	22.1553i	0.588149	−	1.01870i
$474$		0			0
$475$	−8.91819	+	15.4468i	−0.409195	+	0.708746i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−39.0894			−1.78604			−0.893019	−	0.450018i	$-0.851418\pi$
$479$	−39.0894			−1.78604			−0.893019	+	0.450018i	$0.851418\pi$
$480$		0			0
$481$		−	7.84027i		−	0.357486i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	15.5063	−	26.8576i	0.704103	−	1.21954i
$486$		0			0
$487$	−6.79167	+	3.92117i	−0.307760	+	0.177685i	−0.645924	−	0.763402i	$-0.723528\pi$
$487$	−6.79167	+	3.92117i	−0.307760	+	0.177685i	0.338164	+	0.941087i	$0.390194\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−17.8659	+	10.3149i	−0.806278	+	0.465505i	−0.845662	−	0.533720i	$-0.820794\pi$
$491$	−17.8659	+	10.3149i	−0.806278	+	0.465505i	0.0393839	+	0.999224i	$0.487460\pi$
$492$		0			0
$493$		−	0.763828i		−	0.0344011i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	29.8440	−	3.79840i	1.33869	−	0.170381i
$498$		0			0
$499$			34.4187i			1.54079i	0.637565	+	0.770397i	$0.279942\pi$
$499$			34.4187i			1.54079i	−0.637565	+	0.770397i	$0.720058\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−25.7268			−1.14710			−0.573552	−	0.819169i	$-0.694435\pi$
$503$	−25.7268			−1.14710			−0.573552	+	0.819169i	$0.694435\pi$
$504$		0			0
$505$	−38.6752			−1.72103
$506$		0			0
$507$		0			0
$508$		0			0
$509$		−	24.1729i		−	1.07144i	−0.844395	−	0.535722i	$-0.820040\pi$
$509$		−	24.1729i		−	1.07144i	0.844395	−	0.535722i	$-0.179960\pi$
$510$		0			0
$511$	7.48172	+	9.83777i	0.330972	+	0.435198i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	39.9294i		−	1.75950i
$516$		0			0
$517$	23.1339	−	13.3563i	1.01743	−	0.587411i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−31.1079	+	17.9602i	−1.36286	+	0.786849i	−0.990004	−	0.141040i	$-0.954955\pi$
$521$	−31.1079	+	17.9602i	−1.36286	+	0.786849i	−0.372858	+	0.927888i	$0.621622\pi$
$522$		0			0
$523$	7.02897	−	12.1745i	0.307355	−	0.532355i	−0.670428	−	0.741975i	$-0.733889\pi$
$523$	7.02897	−	12.1745i	0.307355	−	0.532355i	0.977783	+	0.209620i	$0.0672226\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$			9.51817i			0.414618i
$528$		0			0
$529$	13.1111			0.570049
$530$		0			0
$531$		0			0
$532$		0			0
$533$	12.5536	−	21.7435i	0.543758	−	0.941816i
$534$		0			0
$535$	−11.4664	+	19.8603i	−0.495735	+	0.858638i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	6.32130	+	24.4310i	0.272278	+	1.05232i
$540$		0			0
$541$	−2.60496	+	4.51193i	−0.111996	+	0.193983i	−0.916575	−	0.399863i	$-0.869058\pi$
$541$	−2.60496	+	4.51193i	−0.111996	+	0.193983i	0.804579	+	0.593846i	$0.202391\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	19.8199	−	11.4430i	0.848989	−	0.490164i
$546$		0			0
$547$	−11.1833	−	6.45666i	−0.478162	−	0.276067i	0.241488	−	0.970404i	$-0.422365\pi$
$547$	−11.1833	−	6.45666i	−0.478162	−	0.276067i	−0.719650	+	0.694337i	$0.755698\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−0.494572	−	0.856625i	−0.0210695	−	0.0364934i
$552$		0			0
$553$	−17.9035	−	23.5415i	−0.761336	−	1.00109i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	12.6086	+	21.8388i	0.534245	+	0.925339i	0.999199	+	0.0400045i	$0.0127372\pi$
$557$	12.6086	+	21.8388i	0.534245	+	0.925339i	−0.464955	+	0.885334i	$0.653929\pi$
$558$		0			0
$559$	−36.5354			−1.54528
$560$		0			0
$561$		0			0
$562$		0			0
$563$	16.9925	−	29.4318i	0.716148	−	1.24040i	−0.246367	−	0.969176i	$-0.579237\pi$
$563$	16.9925	−	29.4318i	0.716148	−	1.24040i	0.962515	−	0.271228i	$-0.0874297\pi$
$564$		0			0
$565$	43.4360	−	25.0778i	1.82737	−	1.05503i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	13.3518	+	23.1260i	0.559736	+	0.969490i	0.997518	+	0.0704095i	$0.0224306\pi$
$569$	13.3518	+	23.1260i	0.559736	+	0.969490i	−0.437783	+	0.899081i	$0.644236\pi$
$570$		0			0
$571$	−24.4861	−	14.1371i	−1.02471	−	0.591618i	−0.109247	−	0.994015i	$-0.534844\pi$
$571$	−24.4861	−	14.1371i	−1.02471	−	0.591618i	−0.915465	+	0.402397i	$0.868177\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			42.3041i			1.76420i
$576$		0			0
$577$	−8.61528	+	4.97403i	−0.358659	+	0.207072i	−0.668492	−	0.743719i	$-0.733060\pi$
$577$	−8.61528	+	4.97403i	−0.358659	+	0.207072i	0.309833	+	0.950791i	$0.399727\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	33.6996	+	14.1291i	1.39810	+	0.586175i
$582$		0			0
$583$	0.465940	−	0.269011i	0.0192973	−	0.0111413i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.00256306	+	0.00443935i	−0.000105789	+	0.000183231i	−0.866078	−	0.499908i	$-0.833367\pi$
$587$	−0.00256306	+	0.00443935i	−0.000105789	+	0.000183231i	0.865973	+	0.500092i	$0.166700\pi$
$588$		0			0
$589$	6.16294	+	10.6745i	0.253939	+	0.439836i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−9.34883	−	5.39755i	−0.383910	−	0.221651i	0.295608	−	0.955309i	$-0.404478\pi$
$593$	−9.34883	−	5.39755i	−0.383910	−	0.221651i	−0.679518	+	0.733659i	$0.737811\pi$
$594$		0			0
$595$	−9.26206	+	7.04388i	−0.379707	+	0.288771i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−16.2237	−	9.36674i	−0.662881	−	0.382714i	0.130493	−	0.991449i	$-0.458344\pi$
$599$	−16.2237	−	9.36674i	−0.662881	−	0.382714i	−0.793374	+	0.608735i	$0.791677\pi$
$600$		0			0
$601$	37.3269	+	21.5507i	1.52260	+	0.879072i	0.999643	+	0.0267107i	$0.00850329\pi$
$601$	37.3269	+	21.5507i	1.52260	+	0.879072i	0.522954	+	0.852361i	$0.324830\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$		−	8.57648i		−	0.348684i
$606$		0			0
$607$	30.9609			1.25666			0.628331	−	0.777946i	$-0.283738\pi$
$607$	30.9609			1.25666			0.628331	+	0.777946i	$0.283738\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−33.0380	−	19.0745i	−1.33658	−	0.771673i
$612$		0			0
$613$	15.9145	+	27.5646i	0.642779	+	1.11333i	0.984810	+	0.173637i	$0.0555519\pi$
$613$	15.9145	+	27.5646i	0.642779	+	1.11333i	−0.342031	+	0.939689i	$0.611115\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.34757	+	14.4584i	0.336060	+	0.582074i	0.983688	−	0.179883i	$-0.0575720\pi$
$617$	8.34757	+	14.4584i	0.336060	+	0.582074i	−0.647627	+	0.761957i	$0.724239\pi$
$618$		0			0
$619$	8.08787			0.325079			0.162539	−	0.986702i	$-0.448032\pi$
$619$	8.08787			0.325079			0.162539	+	0.986702i	$0.448032\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	16.6229	−	39.6476i	0.665983	−	1.58845i
$624$		0			0
$625$	88.7114			3.54846
$626$		0			0
$627$		0			0
$628$		0			0
$629$			1.55914i			0.0621669i
$630$		0			0
$631$			46.7312i			1.86034i	0.367130	+	0.930170i	$0.380340\pi$
$631$			46.7312i			1.86034i	−0.367130	+	0.930170i	$0.619660\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	57.9427			2.29939
$636$		0			0
$637$	25.7022	−	25.2634i	1.01836	−	1.00097i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	32.3555			1.27796			0.638982	−	0.769222i	$-0.279356\pi$
$641$	32.3555			1.27796			0.638982	+	0.769222i	$0.279356\pi$
$642$		0			0
$643$	−7.92549	−	13.7273i	−0.312551	−	0.541354i	0.666363	−	0.745627i	$-0.267850\pi$
$643$	−7.92549	−	13.7273i	−0.312551	−	0.541354i	−0.978914	+	0.204274i	$0.934517\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	22.9784	+	39.7997i	0.903373	+	1.56469i	0.823087	+	0.567916i	$0.192250\pi$
$647$	22.9784	+	39.7997i	0.903373	+	1.56469i	0.0802858	+	0.996772i	$0.474417\pi$
$648$		0			0
$649$	6.22527	+	3.59416i	0.244363	+	0.141083i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−28.4529			−1.11345			−0.556725	−	0.830697i	$-0.687942\pi$
$653$	−28.4529			−1.11345			−0.556725	+	0.830697i	$0.687942\pi$
$654$		0			0
$655$			71.2317i			2.78325i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	24.8634	+	14.3549i	0.968539	+	0.559186i	0.898791	−	0.438378i	$-0.144447\pi$
$659$	24.8634	+	14.3549i	0.968539	+	0.559186i	0.0697486	+	0.997565i	$0.477780\pi$
$660$		0			0
$661$	18.2524	+	10.5380i	0.709935	+	0.409881i	0.811037	−	0.584995i	$-0.198903\pi$
$661$	18.2524	+	10.5380i	0.709935	+	0.409881i	−0.101102	+	0.994876i	$0.532237\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−5.82644	+	13.8967i	−0.225940	+	0.538892i
$666$		0			0
$667$	−2.03173	−	1.17302i	−0.0786689	−	0.0454195i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−10.5203	−	18.2217i	−0.406132	−	0.703441i
$672$		0			0
$673$	−1.51490	+	2.62388i	−0.0583950	+	0.101143i	−0.893745	−	0.448575i	$-0.851932\pi$
$673$	−1.51490	+	2.62388i	−0.0583950	+	0.101143i	0.835350	+	0.549718i	$0.185265\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−30.8917	+	17.8353i	−1.18726	+	0.685468i	−0.957684	−	0.287822i	$-0.907069\pi$
$677$	−30.8917	+	17.8353i	−1.18726	+	0.685468i	−0.229581	+	0.973290i	$0.573736\pi$
$678$		0			0
$679$	7.38555	−	17.6154i	0.283431	−	0.676017i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−14.7745	+	8.53004i	−0.565329	+	0.326393i	−0.755282	−	0.655400i	$-0.772500\pi$
$683$	−14.7745	+	8.53004i	−0.565329	+	0.326393i	0.189952	+	0.981793i	$0.439167\pi$
$684$		0			0
$685$		−	25.6839i		−	0.981330i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−0.665421	−	0.384181i	−0.0253505	−	0.0146361i
$690$		0			0
$691$	2.03132	+	3.51835i	0.0772750	+	0.133844i	0.902073	−	0.431583i	$-0.142045\pi$
$691$	2.03132	+	3.51835i	0.0772750	+	0.133844i	−0.824798	+	0.565427i	$0.808711\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−65.1120	+	37.5924i	−2.46984	+	1.42596i
$696$		0			0
$697$	−2.49645	+	4.32397i	−0.0945597	+	0.163782i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−40.4912			−1.52933			−0.764666	−	0.644427i	$-0.777096\pi$
$701$	−40.4912			−1.52933			−0.764666	+	0.644427i	$0.777096\pi$
$702$		0			0
$703$	1.00953	+	1.74855i	0.0380751	+	0.0659480i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−23.6299	+	3.00750i	−0.888696	+	0.113109i
$708$		0			0
$709$	8.81206	+	15.2629i	0.330944	+	0.573212i	0.982697	−	0.185219i	$-0.0592996\pi$
$709$	8.81206	+	15.2629i	0.330944	+	0.573212i	−0.651753	+	0.758431i	$0.725966\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	25.3177	+	14.6172i	0.948155	+	0.547417i
$714$		0			0
$715$	−69.0486	+	39.8652i	−2.58227	+	1.49087i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	20.7748	−	35.9829i	0.774768	−	1.34194i	−0.160157	−	0.987092i	$-0.551200\pi$
$719$	20.7748	−	35.9829i	0.774768	−	1.34194i	0.934925	−	0.354846i	$-0.115467\pi$
$720$		0			0
$721$	−3.10503	−	24.3963i	−0.115637	−	0.908564i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−5.01812	+	8.69164i	−0.186368	+	0.322799i
$726$		0			0
$727$	19.2047	−	33.2636i	0.712264	−	1.23368i	−0.251741	−	0.967795i	$-0.581003\pi$
$727$	19.2047	−	33.2636i	0.712264	−	1.23368i	0.964005	−	0.265884i	$-0.0856637\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	7.26553			0.268726
$732$		0			0
$733$		−	35.1602i		−	1.29867i	−0.760501	−	0.649336i	$-0.775047\pi$
$733$		−	35.1602i		−	1.29867i	0.760501	−	0.649336i	$-0.224953\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−16.3626	+	28.3408i	−0.602722	+	1.04395i
$738$		0			0
$739$	14.6816	−	8.47640i	0.540070	−	0.311809i	−0.205037	−	0.978754i	$-0.565732\pi$
$739$	14.6816	−	8.47640i	0.540070	−	0.311809i	0.745107	+	0.666945i	$0.232398\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−23.2333	+	13.4138i	−0.852349	+	0.492104i	−0.861443	−	0.507855i	$-0.830439\pi$
$743$	−23.2333	+	13.4138i	−0.852349	+	0.492104i	0.00909404	+	0.999959i	$0.497105\pi$
$744$		0			0
$745$			65.1976i			2.38866i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−5.46137	+	13.0260i	−0.199554	+	0.475960i
$750$		0			0
$751$			22.4872i			0.820569i	0.911958	+	0.410285i	$0.134571\pi$
$751$			22.4872i			0.820569i	−0.911958	+	0.410285i	$0.865429\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−30.2465			−1.10078
$756$		0			0
$757$	27.2088			0.988921			0.494460	−	0.869200i	$-0.335366\pi$
$757$	27.2088			0.988921			0.494460	+	0.869200i	$0.335366\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$			2.76386i			0.100190i	0.998744	+	0.0500949i	$0.0159524\pi$
$761$			2.76386i			0.100190i	−0.998744	+	0.0500949i	$0.984048\pi$
$762$		0			0
$763$	11.2198	−	8.53274i	0.406183	−	0.308906i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		−	10.2658i		−	0.370678i
$768$		0			0
$769$	−13.4636	+	7.77321i	−0.485510	+	0.280309i	−0.722710	−	0.691152i	$-0.757104\pi$
$769$	−13.4636	+	7.77321i	−0.485510	+	0.280309i	0.237200	+	0.971461i	$0.423770\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.21399	−	1.27825i	0.0796317	−	0.0459754i	−0.459655	−	0.888097i	$-0.652027\pi$
$773$	2.21399	−	1.27825i	0.0796317	−	0.0459754i	0.539287	+	0.842122i	$0.318694\pi$
$774$		0			0
$775$	62.5315	−	108.308i	2.24620	−	3.89053i
$776$		0			0
$777$		0			0
$778$		0			0
$779$			6.46571i			0.231658i
$780$		0			0
$781$	−40.9932			−1.46685
$782$		0			0
$783$		0			0
$784$		0			0
$785$	33.9932	−	58.8779i	1.21327	−	2.10144i
$786$		0			0
$787$	25.4781	−	44.1294i	0.908196	−	1.57304i	0.0916280	−	0.995793i	$-0.470793\pi$
$787$	25.4781	−	44.1294i	0.908196	−	1.57304i	0.816568	−	0.577249i	$-0.195874\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	24.5886	−	18.6999i	0.874270	−	0.664890i
$792$		0			0
$793$	−15.0243	+	26.0229i	−0.533529	+	0.924100i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−12.2946	+	7.09827i	−0.435496	+	0.251434i	−0.701685	−	0.712487i	$-0.747569\pi$
$797$	−12.2946	+	7.09827i	−0.435496	+	0.251434i	0.266189	+	0.963921i	$0.414235\pi$
$798$		0			0
$799$	6.57003	+	3.79321i	0.232431	+	0.134194i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−8.42048	−	14.5847i	−0.297152	−	0.514683i
$804$		0			0
$805$	4.51238	+	35.4538i	0.159041	+	1.24958i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	8.76155	+	15.1755i	0.308040	+	0.533541i	0.977933	−	0.208916i	$-0.0669937\pi$
$809$	8.76155	+	15.1755i	0.308040	+	0.533541i	−0.669894	+	0.742457i	$0.733660\pi$
$810$		0			0
$811$	−21.5806			−0.757796			−0.378898	−	0.925438i	$-0.623697\pi$
$811$	−21.5806			−0.757796			−0.378898	+	0.925438i	$0.623697\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−24.7564	+	42.8794i	−0.867179	+	1.50200i
$816$		0			0
$817$	8.14821	−	4.70437i	0.285070	−	0.164585i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	3.69769	+	6.40458i	0.129050	+	0.223522i	0.923309	−	0.384058i	$-0.125474\pi$
$821$	3.69769	+	6.40458i	0.129050	+	0.223522i	−0.794259	+	0.607580i	$0.792140\pi$
$822$		0			0
$823$	7.58110	+	4.37695i	0.264261	+	0.152571i	0.626277	−	0.779601i	$-0.284578\pi$
$823$	7.58110	+	4.37695i	0.264261	+	0.152571i	−0.362016	+	0.932172i	$0.617911\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	10.9322i		−	0.380150i	−0.981770	−	0.190075i	$-0.939127\pi$
$827$		−	10.9322i		−	0.380150i	0.981770	−	0.190075i	$-0.0608732\pi$
$828$		0			0
$829$	2.09152	−	1.20754i	0.0726415	−	0.0419396i	−0.463239	−	0.886233i	$-0.653313\pi$
$829$	2.09152	−	1.20754i	0.0726415	−	0.0419396i	0.535881	+	0.844294i	$0.319980\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−5.11122	+	5.02394i	−0.177093	+	0.174069i
$834$		0			0
$835$	−23.3826	+	13.4999i	−0.809187	+	0.467185i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−17.1615	+	29.7246i	−0.592481	+	1.02621i	0.401416	+	0.915896i	$0.368518\pi$
$839$	−17.1615	+	29.7246i	−0.592481	+	1.02621i	−0.993897	+	0.110311i	$0.964815\pi$
$840$		0			0
$841$	14.2217	+	24.6327i	0.490404	+	0.849404i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	50.2481	+	29.0108i	1.72859	+	0.998001i
$846$		0			0
$847$	−0.666933	−	5.24009i	−0.0229161	−	0.180052i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	4.14720	+	2.39438i	0.142164	+	0.0820784i
$852$		0			0
$853$	−35.5925	−	20.5493i	−1.21866	−	0.703596i	−0.254032	−	0.967196i	$-0.581757\pi$
$853$	−35.5925	−	20.5493i	−1.21866	−	0.703596i	−0.964632	+	0.263600i	$0.915090\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			20.9248i			0.714779i	0.933955	+	0.357390i	$0.116333\pi$
$857$			20.9248i			0.714779i	−0.933955	+	0.357390i	$0.883667\pi$
$858$		0			0
$859$	16.5702			0.565366			0.282683	−	0.959213i	$-0.408775\pi$
$859$	16.5702			0.565366			0.282683	+	0.959213i	$0.408775\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	7.89280	+	4.55691i	0.268674	+	0.155119i	0.628285	−	0.777983i	$-0.283757\pi$
$863$	7.89280	+	4.55691i	0.268674	+	0.155119i	−0.359611	+	0.933102i	$0.617091\pi$
$864$		0			0
$865$	−15.4124	−	26.6950i	−0.524036	−	0.907658i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	20.1500	+	34.9008i	0.683541	+	1.18393i
$870$		0			0
$871$	46.7356			1.58357
$872$		0			0
$873$		0			0
$874$		0			0
$875$	95.2981	−	12.1291i	3.22166	−	0.410037i
$876$		0			0
$877$	−23.0860			−0.779558			−0.389779	−	0.920908i	$-0.627449\pi$
$877$	−23.0860			−0.779558			−0.389779	+	0.920908i	$0.627449\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$			17.9457i			0.604606i	0.953212	+	0.302303i	$0.0977554\pi$
$881$			17.9457i			0.604606i	−0.953212	+	0.302303i	$0.902245\pi$
$882$		0			0
$883$			12.6165i			0.424580i	0.977207	+	0.212290i	$0.0680922\pi$
$883$			12.6165i			0.424580i	−0.977207	+	0.212290i	$0.931908\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	28.5632			0.959059			0.479530	−	0.877526i	$-0.340807\pi$
$887$	28.5632			0.959059			0.479530	+	0.877526i	$0.340807\pi$
$888$		0			0
$889$	35.4021	−	4.50580i	1.18735	−	0.151120i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.82429			0.328757
$894$		0			0
$895$	−44.6039	−	77.2563i	−1.49094	−	2.58239i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.46778	+	6.00638i	0.115657	+	0.200324i
$900$		0			0
$901$	0.132327	+	0.0763993i	0.00440846	+	0.00254523i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−59.0642			−1.96336
$906$		0			0
$907$		−	14.8918i		−	0.494474i	−0.968955	−	0.247237i	$-0.920477\pi$
$907$		−	14.8918i		−	0.494474i	0.968955	−	0.247237i	$-0.0795226\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−16.3355	−	9.43130i	−0.541219	−	0.312473i	0.204354	−	0.978897i	$-0.434491\pi$
$911$	−16.3355	−	9.43130i	−0.541219	−	0.312473i	−0.745573	+	0.666424i	$0.767824\pi$
$912$		0			0
$913$	−43.1206	−	24.8957i	−1.42708	−	0.823927i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.53919	+	43.5214i	0.182920	+	1.43720i
$918$		0			0
$919$	−23.9314	−	13.8168i	−0.789424	−	0.455774i	0.0503355	−	0.998732i	$-0.483971\pi$
$919$	−23.9314	−	13.8168i	−0.789424	−	0.455774i	−0.839760	+	0.542958i	$0.817304\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	29.2717	+	50.7001i	0.963490	+	1.66881i
$924$		0			0
$925$	10.2431	−	17.7415i	0.336790	−	0.583337i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	15.1178	−	8.72825i	0.495998	−	0.286365i	−0.231061	−	0.972939i	$-0.574220\pi$
$929$	15.1178	−	8.72825i	0.495998	−	0.286365i	0.727059	+	0.686575i	$0.240886\pi$
$930$		0			0
$931$	−2.47921	+	8.94376i	−0.0812528	+	0.293120i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	13.7312	−	7.92770i	0.449058	−	0.259264i
$936$		0			0
$937$			6.00080i			0.196038i	0.995185	+	0.0980189i	$0.0312505\pi$
$937$			6.00080i			0.196038i	−0.995185	+	0.0980189i	$0.968749\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	15.0847	+	8.70913i	0.491746	+	0.283909i	0.725298	−	0.688435i	$-0.241702\pi$
$941$	15.0847	+	8.70913i	0.491746	+	0.283909i	−0.233553	+	0.972344i	$0.575035\pi$
$942$		0			0
$943$	7.66764	+	13.2808i	0.249693	+	0.432481i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−11.7264	+	6.77021i	−0.381055	+	0.220002i	−0.678277	−	0.734806i	$-0.737273\pi$
$947$	−11.7264	+	6.77021i	−0.381055	+	0.220002i	0.297222	+	0.954808i	$0.403940\pi$
$948$		0			0
$949$	−12.0255	+	20.8288i	−0.390364	+	0.676131i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	4.27802			0.138579			0.0692893	−	0.997597i	$-0.477927\pi$
$953$	4.27802			0.138579			0.0692893	+	0.997597i	$0.477927\pi$
$954$		0			0
$955$	−12.5598	−	21.7541i	−0.406424	−	0.703948i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−1.99725	−	15.6924i	−0.0644947	−	0.506735i
$960$		0			0
$961$	−27.7126	−	47.9996i	−0.893954	−	1.54837i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	8.44947	+	4.87830i	0.271998	+	0.157038i
$966$		0			0
$967$	−40.6804	+	23.4868i	−1.30819	+	0.755285i	−0.981794	−	0.189947i	$-0.939168\pi$
$967$	−40.6804	+	23.4868i	−1.30819	+	0.755285i	−0.326398	+	0.945232i	$0.605835\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	28.9103	−	50.0741i	0.927776	−	1.60695i	0.140740	−	0.990047i	$-0.455052\pi$
$971$	28.9103	−	50.0741i	0.927776	−	1.60695i	0.787035	−	0.616908i	$-0.211615\pi$
$972$		0			0
$973$	−36.8591	+	28.0317i	−1.18165	+	0.898654i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−5.53978	+	9.59517i	−0.177233	+	0.306977i	−0.940932	−	0.338596i	$-0.890048\pi$
$977$	−5.53978	+	9.59517i	−0.177233	+	0.306977i	0.763699	+	0.645573i	$0.223381\pi$
$978$		0			0
$979$	−29.2897	+	50.7313i	−0.936104	+	1.62138i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−22.1053			−0.705050			−0.352525	−	0.935802i	$-0.614677\pi$
$983$	−22.1053			−0.705050			−0.352525	+	0.935802i	$0.614677\pi$
$984$		0			0
$985$			40.1297i			1.27864i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	11.1578	−	19.3258i	0.354796	−	0.614525i
$990$		0			0
$991$	−0.396571	+	0.228961i	−0.0125975	+	0.00727317i	−0.506286	−	0.862366i	$-0.668982\pi$
$991$	−0.396571	+	0.228961i	−0.0125975	+	0.00727317i	0.493688	+	0.869639i	$0.335648\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	7.81817	−	4.51382i	0.247853	−	0.143098i
$996$		0			0
$997$			34.3499i			1.08787i	0.839127	+	0.543936i	$0.183066\pi$
$997$			34.3499i			1.08787i	−0.839127	+	0.543936i	$0.816934\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.bf.i.2287.15		32
3.2	odd	2		1008.2.bf.i.943.4	yes	32
4.3	odd	2	inner	3024.2.bf.i.2287.16		32
7.3	odd	6		3024.2.cz.i.2719.16		32
9.4	even	3		3024.2.cz.i.1279.15		32
9.5	odd	6		1008.2.cz.i.607.7	yes	32
12.11	even	2		1008.2.bf.i.943.13	yes	32
21.17	even	6		1008.2.cz.i.367.10	yes	32
28.3	even	6		3024.2.cz.i.2719.15		32
36.23	even	6		1008.2.cz.i.607.10	yes	32
36.31	odd	6		3024.2.cz.i.1279.16		32
63.31	odd	6	inner	3024.2.bf.i.1711.1		32
63.59	even	6		1008.2.bf.i.31.13	yes	32
84.59	odd	6		1008.2.cz.i.367.7	yes	32
252.31	even	6	inner	3024.2.bf.i.1711.2		32
252.59	odd	6		1008.2.bf.i.31.4	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.bf.i.31.4	✓	32	252.59	odd	6
1008.2.bf.i.31.13	yes	32	63.59	even	6
1008.2.bf.i.943.4	yes	32	3.2	odd	2
1008.2.bf.i.943.13	yes	32	12.11	even	2
1008.2.cz.i.367.7	yes	32	84.59	odd	6
1008.2.cz.i.367.10	yes	32	21.17	even	6
1008.2.cz.i.607.7	yes	32	9.5	odd	6
1008.2.cz.i.607.10	yes	32	36.23	even	6
3024.2.bf.i.1711.1		32	63.31	odd	6	inner
3024.2.bf.i.1711.2		32	252.31	even	6	inner
3024.2.bf.i.2287.15		32	1.1	even	1	trivial
3024.2.bf.i.2287.16		32	4.3	odd	2	inner
3024.2.cz.i.1279.15		32	9.4	even	3
3024.2.cz.i.1279.16		32	36.31	odd	6
3024.2.cz.i.2719.15		32	28.3	even	6
3024.2.cz.i.2719.16		32	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3024.bf (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+4.29566i q^{5} +(0.334043 + 2.62458i) q^{7} -3.60507i q^{11} +(-4.45873 + 2.57425i) q^{13} +(0.886675 - 0.511922i) q^{17} +(0.662930 - 1.14823i) q^{19} -3.14466i q^{23} -13.4527 q^{25} +(0.373020 - 0.646090i) q^{29} +(-4.64826 + 8.05102i) q^{31} +(-11.2743 + 1.43494i) q^{35} +(-0.761414 + 1.31881i) q^{37} +(-4.22328 + 2.43831i) q^{41} +(6.14560 + 3.54817i) q^{43} +(3.70487 + 6.41703i) q^{47} +(-6.77683 + 1.75345i) q^{49} +(0.0746200 + 0.129246i) q^{53} +15.4862 q^{55} +(-0.996973 + 1.72681i) q^{59} +(5.05446 - 2.91820i) q^{61} +(-11.0581 - 19.1532i) q^{65} +(-7.86136 - 4.53876i) q^{67} -11.3710i q^{71} +(4.04560 - 2.33573i) q^{73} +(9.46180 - 1.20425i) q^{77} +(-9.68102 + 5.58934i) q^{79} +(6.90574 - 11.9611i) q^{83} +(2.19904 + 3.80885i) q^{85} +(-14.0722 - 8.12459i) q^{89} +(-8.24573 - 10.8424i) q^{91} +(4.93240 + 2.84772i) q^{95} +(-6.25228 - 3.60975i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 6 q^{13} + 18 q^{17} - 32 q^{25} + 12 q^{29} + 2 q^{37} - 36 q^{41} + 2 q^{49} + 12 q^{53} + 42 q^{61} - 18 q^{65} + 66 q^{77} - 12 q^{85} + 18 q^{89} - 6 q^{97}+O(q^{100}) \) 32 * q - 6 * q^13 + 18 * q^17 - 32 * q^25 + 12 * q^29 + 2 * q^37 - 36 * q^41 + 2 * q^49 + 12 * q^53 + 42 * q^61 - 18 * q^65 + 66 * q^77 - 12 * q^85 + 18 * q^89 - 6 * q^97

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