LMFDB - Embedded newform 3024.2.cx.i.559.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [3024,2,Mod(559,3024)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3024.559"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3024, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 0, 4, 3])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [24,0,0,0,0,0,-6,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$24.1467615712$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 1008)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			559.12
Character	$\chi$	$=$	3024.559
Dual form			3024.2.cx.i.2575.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.48918 - 2.01448i) q^{5} +(-2.54444 - 0.725126i) q^{7} +(-4.95331 - 2.85980i) q^{11} +(1.74224 - 1.00589i) q^{13} -4.18025i q^{17} +3.22849 q^{19} +(-3.63065 + 2.09616i) q^{23} +(5.61625 - 9.72763i) q^{25} +(-1.27096 + 2.20137i) q^{29} +(3.10138 + 5.37176i) q^{31} +(-10.3388 + 2.59563i) q^{35} +3.21605 q^{37} +(-5.51107 + 3.18181i) q^{41} +(-3.71365 - 2.14408i) q^{43} +(2.92547 - 5.06707i) q^{47} +(5.94838 + 3.69008i) q^{49} -13.9105 q^{53} -23.0440 q^{55} +(-4.26142 - 7.38100i) q^{59} +(-10.9025 - 6.29455i) q^{61} +(4.05267 - 7.01943i) q^{65} +(4.54387 - 2.62341i) q^{67} -12.5319i q^{71} +7.93971i q^{73} +(10.5297 + 10.8684i) q^{77} +(4.48851 + 2.59144i) q^{79} +(-2.68950 + 4.65836i) q^{83} +(-8.42103 - 14.5857i) q^{85} +3.51148i q^{89} +(-5.16244 + 1.29607i) q^{91} +(11.2648 - 6.50372i) q^{95} +(-9.29978 - 5.36923i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{7} - 18 q^{23} + 24 q^{25} + 6 q^{29} - 12 q^{37} + 42 q^{43} + 12 q^{49} - 96 q^{53} - 42 q^{65} + 36 q^{67} + 18 q^{77} - 60 q^{79} - 6 q^{85} + 126 q^{95}+O(q^{100}) $ 24 * q - 6 * q^7 - 18 * q^23 + 24 * q^25 + 6 * q^29 - 12 * q^37 + 42 * q^43 + 12 * q^49 - 96 * q^53 - 42 * q^65 + 36 * q^67 + 18 * q^77 - 60 * q^79 - 6 * q^85 + 126 * q^95

Character values

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

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

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
$5$	3.48918	−	2.01448i	1.56041	−	0.900902i	0.563193	−	0.826325i	$-0.309573\pi$
$5$	3.48918	−	2.01448i	1.56041	−	0.900902i	0.997215	−	0.0745770i	$-0.0237607\pi$
$6$		0			0
$7$	−2.54444	−	0.725126i	−0.961709	−	0.274072i
$7$	−2.54444	−	0.725126i	−0.961709	−	0.274072i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−4.95331	−	2.85980i	−1.49348	−	0.862261i	−0.493508	−	0.869741i	$-0.664286\pi$
$11$	−4.95331	−	2.85980i	−1.49348	−	0.862261i	−0.999972	+	0.00747985i	$0.997619\pi$
$12$		0			0
$13$	1.74224	−	1.00589i	0.483212	−	0.278982i	−0.238542	−	0.971132i	$-0.576670\pi$
$13$	1.74224	−	1.00589i	0.483212	−	0.278982i	0.721754	+	0.692150i	$0.243336\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	4.18025i		−	1.01386i	−0.861987	−	0.506930i	$-0.830780\pi$
$17$		−	4.18025i		−	1.01386i	0.861987	−	0.506930i	$-0.169220\pi$
$18$		0			0
$19$	3.22849			0.740666			0.370333	−	0.928899i	$-0.379244\pi$
$19$	3.22849			0.740666			0.370333	+	0.928899i	$0.379244\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−3.63065	+	2.09616i	−0.757044	+	0.437079i	−0.828233	−	0.560383i	$-0.810654\pi$
$23$	−3.63065	+	2.09616i	−0.757044	+	0.437079i	0.0711897	+	0.997463i	$0.477320\pi$
$24$		0			0
$25$	5.61625	−	9.72763i	1.12325	−	1.94553i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−1.27096	+	2.20137i	−0.236011	+	0.408784i	−0.959566	−	0.281483i	$-0.909174\pi$
$29$	−1.27096	+	2.20137i	−0.236011	+	0.408784i	0.723555	+	0.690267i	$0.242507\pi$
$30$		0			0
$31$	3.10138	+	5.37176i	0.557025	+	0.964796i	0.997743	+	0.0671502i	$0.0213907\pi$
$31$	3.10138	+	5.37176i	0.557025	+	0.964796i	−0.440718	+	0.897646i	$0.645276\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−10.3388	+	2.59563i	−1.74757	+	0.438742i
$36$		0			0
$37$	3.21605			0.528716			0.264358	−	0.964425i	$-0.414840\pi$
$37$	3.21605			0.528716			0.264358	+	0.964425i	$0.414840\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.51107	+	3.18181i	−0.860684	+	0.496916i	−0.864241	−	0.503078i	$-0.832201\pi$
$41$	−5.51107	+	3.18181i	−0.860684	+	0.496916i	0.00355743	+	0.999994i	$0.498868\pi$
$42$		0			0
$43$	−3.71365	−	2.14408i	−0.566327	−	0.326969i	0.189354	−	0.981909i	$-0.439361\pi$
$43$	−3.71365	−	2.14408i	−0.566327	−	0.326969i	−0.755681	+	0.654940i	$0.772694\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	2.92547	−	5.06707i	0.426724	−	0.739108i	−0.569855	−	0.821745i	$-0.693001\pi$
$47$	2.92547	−	5.06707i	0.426724	−	0.739108i	0.996580	+	0.0826368i	$0.0263342\pi$
$48$		0			0
$49$	5.94838	+	3.69008i	0.849769	+	0.527155i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−13.9105			−1.91076			−0.955379	−	0.295383i	$-0.904553\pi$
$53$	−13.9105			−1.91076			−0.955379	+	0.295383i	$0.904553\pi$
$54$		0			0
$55$	−23.0440			−3.10725
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−4.26142	−	7.38100i	−0.554790	−	0.960925i	−0.997920	−	0.0644671i	$-0.979465\pi$
$59$	−4.26142	−	7.38100i	−0.554790	−	0.960925i	0.443130	−	0.896457i	$-0.353868\pi$
$60$		0			0
$61$	−10.9025	−	6.29455i	−1.39592	−	0.805934i	−0.401957	−	0.915659i	$-0.631670\pi$
$61$	−10.9025	−	6.29455i	−1.39592	−	0.805934i	−0.993962	+	0.109724i	$0.965003\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.05267	−	7.01943i	0.502672	−	0.870653i
$66$		0			0
$67$	4.54387	−	2.62341i	0.555122	−	0.320500i	−0.196063	−	0.980591i	$-0.562816\pi$
$67$	4.54387	−	2.62341i	0.555122	−	0.320500i	0.751185	+	0.660091i	$0.229482\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		−	12.5319i		−	1.48727i	−0.668587	−	0.743634i	$-0.733101\pi$
$71$		−	12.5319i		−	1.48727i	0.668587	−	0.743634i	$-0.266899\pi$
$72$		0			0
$73$			7.93971i			0.929273i	0.885502	+	0.464636i	$0.153815\pi$
$73$			7.93971i			0.929273i	−0.885502	+	0.464636i	$0.846185\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	10.5297	+	10.8684i	1.19997	+	1.23857i
$78$		0			0
$79$	4.48851	+	2.59144i	0.504997	+	0.291560i	0.730775	−	0.682619i	$-0.239159\pi$
$79$	4.48851	+	2.59144i	0.504997	+	0.291560i	−0.225778	+	0.974179i	$0.572492\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−2.68950	+	4.65836i	−0.295211	+	0.511321i	−0.975034	−	0.222055i	$-0.928723\pi$
$83$	−2.68950	+	4.65836i	−0.295211	+	0.511321i	0.679823	+	0.733377i	$0.262057\pi$
$84$		0			0
$85$	−8.42103	−	14.5857i	−0.913389	−	1.58204i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			3.51148i			0.372216i	0.982529	+	0.186108i	$0.0595874\pi$
$89$			3.51148i			0.372216i	−0.982529	+	0.186108i	$0.940413\pi$
$90$		0			0
$91$	−5.16244	+	1.29607i	−0.541170	+	0.135865i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	11.2648	−	6.50372i	1.15574	−	0.667268i
$96$		0			0
$97$	−9.29978	−	5.36923i	−0.944250	−	0.545163i	−0.0529598	−	0.998597i	$-0.516866\pi$
$97$	−9.29978	−	5.36923i	−0.944250	−	0.545163i	−0.891290	+	0.453434i	$0.850199\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−2.98052	−	1.72080i	−0.296573	−	0.171226i	0.344330	−	0.938849i	$-0.388106\pi$
$101$	−2.98052	−	1.72080i	−0.296573	−	0.171226i	−0.640902	+	0.767623i	$0.721440\pi$
$102$		0			0
$103$	0.562042	+	0.973484i	0.0553796	+	0.0959203i	0.892386	−	0.451273i	$-0.149030\pi$
$103$	0.562042	+	0.973484i	0.0553796	+	0.0959203i	−0.837007	+	0.547193i	$0.815696\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			2.50195i			0.241872i	0.992660	+	0.120936i	$0.0385897\pi$
$107$			2.50195i			0.241872i	−0.992660	+	0.120936i	$0.961410\pi$
$108$		0			0
$109$	−11.1266			−1.06573			−0.532867	−	0.846199i	$-0.678885\pi$
$109$	−11.1266			−1.06573			−0.532867	+	0.846199i	$0.678885\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	0.599354	+	1.03811i	0.0563825	+	0.0976574i	0.892839	−	0.450376i	$-0.148710\pi$
$113$	0.599354	+	1.03811i	0.0563825	+	0.0976574i	−0.836457	+	0.548033i	$0.815377\pi$
$114$		0			0
$115$	−8.44533	+	14.6277i	−0.787532	+	1.36404i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.03121	+	10.6364i	−0.277871	+	0.975039i
$120$		0			0
$121$	10.8569	+	18.8047i	0.986989	+	1.70951i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	25.1105i		−	2.24595i
$126$		0			0
$127$			3.48012i			0.308811i	0.988008	+	0.154405i	$0.0493462\pi$
$127$			3.48012i			0.308811i	−0.988008	+	0.154405i	$0.950654\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−2.73241	−	4.73267i	−0.238732	−	0.413495i	0.721619	−	0.692290i	$-0.243398\pi$
$131$	−2.73241	−	4.73267i	−0.238732	−	0.413495i	−0.960351	+	0.278795i	$0.910065\pi$
$132$		0			0
$133$	−8.21471	−	2.34106i	−0.712306	−	0.202996i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.49760	−	7.79007i	0.384256	−	0.665551i	−0.607410	−	0.794389i	$-0.707791\pi$
$137$	4.49760	−	7.79007i	0.384256	−	0.665551i	0.991666	+	0.128838i	$0.0411247\pi$
$138$		0			0
$139$	3.12779	+	5.41748i	0.265295	+	0.459505i	0.967641	−	0.252331i	$-0.0811972\pi$
$139$	3.12779	+	5.41748i	0.265295	+	0.459505i	−0.702346	+	0.711836i	$0.747864\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−11.5065			−0.962223
$144$		0			0
$145$			10.2413i			0.850493i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.32221	+	10.9504i	0.517936	+	0.897091i	0.999783	+	0.0208358i	$0.00663271\pi$
$149$	6.32221	+	10.9504i	0.517936	+	0.897091i	−0.481847	+	0.876255i	$0.660034\pi$
$150$		0			0
$151$	13.8107	+	7.97363i	1.12390	+	0.648884i	0.942394	−	0.334505i	$-0.108569\pi$
$151$	13.8107	+	7.97363i	1.12390	+	0.648884i	0.181507	+	0.983390i	$0.441903\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	21.6426	+	12.4953i	1.73837	+	1.00365i
$156$		0			0
$157$	15.3782	−	8.87858i	1.22731	−	0.708588i	0.260844	−	0.965381i	$-0.415999\pi$
$157$	15.3782	−	8.87858i	1.22731	−	0.708588i	0.966467	+	0.256793i	$0.0826658\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	10.7580	−	2.70088i	0.847847	−	0.212859i
$162$		0			0
$163$		−	10.1287i		−	0.793339i	−0.917962	−	0.396669i	$-0.870166\pi$
$163$		−	10.1287i		−	0.793339i	0.917962	−	0.396669i	$-0.129834\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−7.08298	−	12.2681i	−0.548098	−	0.949333i	−0.998405	−	0.0564595i	$-0.982019\pi$
$167$	−7.08298	−	12.2681i	−0.548098	−	0.949333i	0.450307	−	0.892874i	$-0.351315\pi$
$168$		0			0
$169$	−4.47639	+	7.75334i	−0.344338	+	0.596410i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	9.42612	+	5.44217i	0.716654	+	0.413761i	0.813520	−	0.581537i	$-0.197548\pi$
$173$	9.42612	+	5.44217i	0.716654	+	0.413761i	−0.0968656	+	0.995297i	$0.530882\pi$
$174$		0			0
$175$	−21.3440	+	20.6789i	−1.61345	+	1.56318i
$176$		0			0
$177$		0			0
$178$		0			0
$179$		−	11.7278i		−	0.876578i	−0.898834	−	0.438289i	$-0.855585\pi$
$179$		−	11.7278i		−	0.876578i	0.898834	−	0.438289i	$-0.144415\pi$
$180$		0			0
$181$		−	17.6522i		−	1.31208i	−0.754727	−	0.656039i	$-0.772231\pi$
$181$		−	17.6522i		−	1.31208i	0.754727	−	0.656039i	$-0.227769\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	11.2214	−	6.47867i	0.825012	−	0.476321i
$186$		0			0
$187$	−11.9547	+	20.7061i	−0.874213	+	1.51418i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.581366	+	0.335652i	0.0420662	+	0.0242869i	0.520886	−	0.853626i	$-0.325602\pi$
$191$	0.581366	+	0.335652i	0.0420662	+	0.0242869i	−0.478819	+	0.877913i	$0.658935\pi$
$192$		0			0
$193$	−7.45526	−	12.9129i	−0.536642	−	0.929491i	−0.999082	−	0.0428402i	$-0.986359\pi$
$193$	−7.45526	−	12.9129i	−0.536642	−	0.929491i	0.462440	−	0.886650i	$-0.346974\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−8.84703			−0.630325			−0.315163	−	0.949038i	$-0.602059\pi$
$197$	−8.84703			−0.630325			−0.315163	+	0.949038i	$0.602059\pi$
$198$		0			0
$199$	−4.99197			−0.353872			−0.176936	−	0.984222i	$-0.556619\pi$
$199$	−4.99197			−0.353872			−0.176936	+	0.984222i	$0.556619\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	4.83016	−	4.67965i	0.339010	−	0.328447i
$204$		0			0
$205$	−12.8194	+	22.2038i	−0.895345	+	1.55078i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−15.9917	−	9.23282i	−1.10617	−	0.638648i
$210$		0			0
$211$	1.47412	−	0.851085i	0.101483	−	0.0585911i	−0.448400	−	0.893833i	$-0.648006\pi$
$211$	1.47412	−	0.851085i	0.101483	−	0.0585911i	0.549882	+	0.835242i	$0.314673\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−17.2768			−1.17827
$216$		0			0
$217$	−3.99610	−	15.9170i	−0.271273	−	1.08052i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−4.20486	−	7.28302i	−0.282849	−	0.489909i
$222$		0			0
$223$	10.0164	−	17.3488i	0.670745	−	1.16176i	−0.306948	−	0.951726i	$-0.599308\pi$
$223$	10.0164	−	17.3488i	0.670745	−	1.16176i	0.977693	−	0.210038i	$-0.0673588\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−5.16212	+	8.94105i	−0.342622	+	0.593438i	−0.984919	−	0.173018i	$-0.944648\pi$
$227$	−5.16212	+	8.94105i	−0.342622	+	0.593438i	0.642297	+	0.766456i	$0.277982\pi$
$228$		0			0
$229$	2.90563	−	1.67756i	0.192009	−	0.110857i	−0.400914	−	0.916116i	$-0.631307\pi$
$229$	2.90563	−	1.67756i	0.192009	−	0.110857i	0.592923	+	0.805259i	$0.297974\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	20.1788			1.32196			0.660978	−	0.750405i	$-0.270142\pi$
$233$	20.1788			1.32196			0.660978	+	0.750405i	$0.270142\pi$
$234$		0			0
$235$		−	23.5732i		−	1.53775i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	2.94777	−	1.70189i	0.190675	−	0.110086i	−0.401623	−	0.915805i	$-0.631554\pi$
$239$	2.94777	−	1.70189i	0.190675	−	0.110086i	0.592299	+	0.805719i	$0.298221\pi$
$240$		0			0
$241$	1.83067	+	1.05694i	0.117924	+	0.0680832i	0.557802	−	0.829974i	$-0.311645\pi$
$241$	1.83067	+	1.05694i	0.117924	+	0.0680832i	−0.439878	+	0.898058i	$0.644978\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	28.1886	+	0.892469i	1.80090	+	0.0570177i
$246$		0			0
$247$	5.62482	−	3.24749i	0.357899	−	0.206633i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.31087			−0.0827413			−0.0413707	−	0.999144i	$-0.513172\pi$
$251$	−1.31087			−0.0827413			−0.0413707	+	0.999144i	$0.513172\pi$
$252$		0			0
$253$	23.9784			1.50751
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−9.71045	+	5.60633i	−0.605721	+	0.349713i	−0.771289	−	0.636485i	$-0.780388\pi$
$257$	−9.71045	+	5.60633i	−0.605721	+	0.349713i	0.165568	+	0.986198i	$0.447054\pi$
$258$		0			0
$259$	−8.18306	−	2.33204i	−0.508471	−	0.144906i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.54810	−	0.893798i	−0.0954601	−	0.0551139i	0.451510	−	0.892266i	$-0.350886\pi$
$263$	−1.54810	−	0.893798i	−0.0954601	−	0.0551139i	−0.546970	+	0.837152i	$0.684219\pi$
$264$		0			0
$265$	−48.5363	+	28.0225i	−2.98156	+	1.72141i
$266$		0			0
$267$		0			0
$268$		0			0
$269$			22.8546i			1.39347i	0.717330	+	0.696734i	$0.245364\pi$
$269$			22.8546i			1.39347i	−0.717330	+	0.696734i	$0.754636\pi$
$270$		0			0
$271$	13.4933			0.819657			0.409828	−	0.912163i	$-0.365589\pi$
$271$	13.4933			0.819657			0.409828	+	0.912163i	$0.365589\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−55.6381	+	32.1227i	−3.35510	+	1.93707i
$276$		0			0
$277$	10.0276	−	17.3684i	0.602503	−	1.04357i	−0.389938	−	0.920841i	$-0.627504\pi$
$277$	10.0276	−	17.3684i	0.602503	−	1.04357i	0.992441	−	0.122724i	$-0.0391630\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.99902	−	13.8547i	0.477181	−	0.826502i	−0.522477	−	0.852654i	$-0.674992\pi$
$281$	7.99902	−	13.8547i	0.477181	−	0.826502i	0.999658	+	0.0261512i	$0.00832512\pi$
$282$		0			0
$283$	−9.43384	−	16.3399i	−0.560783	−	0.971305i	−0.997428	−	0.0716713i	$-0.977167\pi$
$283$	−9.43384	−	16.3399i	−0.560783	−	0.971305i	0.436645	−	0.899634i	$-0.356167\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	16.3298	−	4.09973i	0.963918	−	0.242000i
$288$		0			0
$289$	−0.474525			−0.0279132
$290$		0			0
$291$		0			0
$292$		0			0
$293$	13.2893	−	7.67260i	0.776371	−	0.448238i	−0.0587718	−	0.998271i	$-0.518718\pi$
$293$	13.2893	−	7.67260i	0.776371	−	0.448238i	0.835143	+	0.550034i	$0.185385\pi$
$294$		0			0
$295$	−29.7377	−	17.1691i	−1.73140	−	0.999623i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−4.21699	+	7.30404i	−0.243875	+	0.422404i
$300$		0			0
$301$	7.89445	+	8.14835i	0.455029	+	0.469663i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−50.7209			−2.90427
$306$		0			0
$307$	12.8290			0.732192			0.366096	−	0.930577i	$-0.380694\pi$
$307$	12.8290			0.732192			0.366096	+	0.930577i	$0.380694\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	1.01728	+	1.76198i	0.0576846	+	0.0999127i	0.893426	−	0.449211i	$-0.148295\pi$
$311$	1.01728	+	1.76198i	0.0576846	+	0.0999127i	−0.835741	+	0.549124i	$0.814962\pi$
$312$		0			0
$313$	−8.42991	−	4.86701i	−0.476487	−	0.275100i	0.242465	−	0.970160i	$-0.422044\pi$
$313$	−8.42991	−	4.86701i	−0.476487	−	0.275100i	−0.718951	+	0.695061i	$0.755378\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	11.5075	−	19.9315i	0.646325	−	1.11947i	−0.337669	−	0.941265i	$-0.609639\pi$
$317$	11.5075	−	19.9315i	0.646325	−	1.11947i	0.983994	−	0.178202i	$-0.0570282\pi$
$318$		0			0
$319$	12.5909	−	7.26938i	0.704957	−	0.407007i
$320$		0			0
$321$		0			0
$322$		0			0
$323$		−	13.4959i		−	0.750932i
$324$		0			0
$325$		−	22.5972i		−	1.25347i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−11.1180	+	10.7715i	−0.612953	+	0.593854i
$330$		0			0
$331$	−18.3921	−	10.6187i	−1.01092	−	0.583656i	−0.0994598	−	0.995042i	$-0.531711\pi$
$331$	−18.3921	−	10.6187i	−1.01092	−	0.583656i	−0.911461	+	0.411386i	$0.865045\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	10.5696	−	18.3071i	0.577478	−	1.00022i
$336$		0			0
$337$	−13.0884	−	22.6698i	−0.712971	−	1.23490i	−0.963737	−	0.266854i	$-0.914016\pi$
$337$	−13.0884	−	22.6698i	−0.712971	−	1.23490i	0.250766	−	0.968048i	$-0.419318\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	35.4773i		−	1.92120i
$342$		0			0
$343$	−12.4596	−	13.7025i	−0.672753	−	0.739867i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.1001	+	7.56336i	−0.703251	+	0.406022i	−0.808557	−	0.588417i	$-0.799751\pi$
$347$	−13.1001	+	7.56336i	−0.703251	+	0.406022i	0.105306	+	0.994440i	$0.466418\pi$
$348$		0			0
$349$	18.8255	+	10.8689i	1.00771	+	0.581799i	0.910519	−	0.413467i	$-0.135682\pi$
$349$	18.8255	+	10.8689i	1.00771	+	0.581799i	0.0971868	+	0.995266i	$0.469016\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	17.9454	+	10.3608i	0.955136	+	0.551448i	0.894673	−	0.446722i	$-0.147409\pi$
$353$	17.9454	+	10.3608i	0.955136	+	0.551448i	0.0604636	+	0.998170i	$0.480742\pi$
$354$		0			0
$355$	−25.2453	−	43.7262i	−1.33988	−	2.32074i
$356$		0			0
$357$		0			0
$358$		0			0
$359$		−	8.70585i		−	0.459477i	−0.973252	−	0.229739i	$-0.926213\pi$
$359$		−	8.70585i		−	0.459477i	0.973252	−	0.229739i	$-0.0737871\pi$
$360$		0			0
$361$	−8.57686			−0.451414
$362$		0			0
$363$		0			0
$364$		0			0
$365$	15.9944	+	27.7031i	0.837184	+	1.45005i
$366$		0			0
$367$	−10.5062	+	18.1973i	−0.548419	+	0.949890i	0.449964	+	0.893047i	$0.351437\pi$
$367$	−10.5062	+	18.1973i	−0.548419	+	0.949890i	−0.998383	+	0.0568434i	$0.981896\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	35.3946	+	10.0869i	1.83759	+	0.523685i
$372$		0			0
$373$	6.05267	+	10.4835i	0.313395	+	0.542817i	0.979095	−	0.203403i	$-0.0652002\pi$
$373$	6.05267	+	10.4835i	0.313395	+	0.542817i	−0.665700	+	0.746220i	$0.731867\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			5.11376i			0.263372i
$378$		0			0
$379$			32.3259i			1.66047i	0.557414	+	0.830234i	$0.311794\pi$
$379$			32.3259i			1.66047i	−0.557414	+	0.830234i	$0.688206\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	2.70529	+	4.68571i	0.138234	+	0.239428i	0.926828	−	0.375486i	$-0.122524\pi$
$383$	2.70529	+	4.68571i	0.138234	+	0.239428i	−0.788594	+	0.614914i	$0.789191\pi$
$384$		0			0
$385$	58.6342	+	16.7098i	2.98827	+	0.851610i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	8.74076	−	15.1394i	0.443174	−	0.767600i	−0.554749	−	0.832018i	$-0.687186\pi$
$389$	8.74076	−	15.1394i	0.443174	−	0.767600i	0.997923	+	0.0644180i	$0.0205191\pi$
$390$		0			0
$391$	8.76248	+	15.1771i	0.443138	+	0.767537i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	20.8816			1.05067
$396$		0			0
$397$		−	12.6177i		−	0.633264i	−0.948549	−	0.316632i	$-0.897448\pi$
$397$		−	12.6177i		−	0.633264i	0.948549	−	0.316632i	$-0.102552\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−5.40011	−	9.35327i	−0.269669	−	0.467080i	0.699108	−	0.715017i	$-0.253581\pi$
$401$	−5.40011	−	9.35327i	−0.269669	−	0.467080i	−0.968776	+	0.247937i	$0.920248\pi$
$402$		0			0
$403$	10.8067	+	6.23927i	0.538322	+	0.310800i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−15.9301	−	9.19725i	−0.789626	−	0.455891i
$408$		0			0
$409$	9.66191	−	5.57831i	0.477751	−	0.275830i	−0.241728	−	0.970344i	$-0.577714\pi$
$409$	9.66191	−	5.57831i	0.477751	−	0.275830i	0.719479	+	0.694515i	$0.244381\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	5.49080	+	21.8706i	0.270184	+	1.07618i
$414$		0			0
$415$			21.6718i			1.06383i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−7.36007	−	12.7480i	−0.359563	−	0.622781i	0.628325	−	0.777951i	$-0.283741\pi$
$419$	−7.36007	−	12.7480i	−0.359563	−	0.622781i	−0.987888	+	0.155170i	$0.950408\pi$
$420$		0			0
$421$	7.90063	−	13.6843i	0.385053	−	0.666932i	−0.606723	−	0.794913i	$-0.707516\pi$
$421$	7.90063	−	13.6843i	0.385053	−	0.666932i	0.991777	+	0.127981i	$0.0408497\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−40.6640	−	23.4773i	−1.97249	−	1.13882i
$426$		0			0
$427$	23.1764	+	23.9218i	1.12158	+	1.15766i
$428$		0			0
$429$		0			0
$430$		0			0
$431$			0.798303i			0.0384529i	0.999815	+	0.0192265i	$0.00612035\pi$
$431$			0.798303i			0.0384529i	−0.999815	+	0.0192265i	$0.993880\pi$
$432$		0			0
$433$			31.2293i			1.50079i	0.660992	+	0.750393i	$0.270136\pi$
$433$			31.2293i			1.50079i	−0.660992	+	0.750393i	$0.729864\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−11.7215	+	6.76743i	−0.560717	+	0.323730i
$438$		0			0
$439$	−2.94795	+	5.10600i	−0.140698	+	0.243696i	−0.927760	−	0.373178i	$-0.878268\pi$
$439$	−2.94795	+	5.10600i	−0.140698	+	0.243696i	0.787062	+	0.616874i	$0.211601\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−2.02844	−	1.17112i	−0.0963742	−	0.0556417i	0.451038	−	0.892505i	$-0.351054\pi$
$443$	−2.02844	−	1.17112i	−0.0963742	−	0.0556417i	−0.547413	+	0.836863i	$0.684387\pi$
$444$		0			0
$445$	7.07379	+	12.2522i	0.335330	+	0.580809i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−23.9242			−1.12905			−0.564527	−	0.825415i	$-0.690941\pi$
$449$	−23.9242			−1.12905			−0.564527	+	0.825415i	$0.690941\pi$
$450$		0			0
$451$	36.3974			1.71389
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−15.4018	+	14.9218i	−0.722045	+	0.699547i
$456$		0			0
$457$	−7.24703	+	12.5522i	−0.339002	+	0.587168i	−0.984245	−	0.176809i	$-0.943423\pi$
$457$	−7.24703	+	12.5522i	−0.339002	+	0.587168i	0.645244	+	0.763977i	$0.276756\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−16.2137	−	9.36101i	−0.755149	−	0.435986i	0.0724022	−	0.997376i	$-0.476933\pi$
$461$	−16.2137	−	9.36101i	−0.755149	−	0.435986i	−0.827551	+	0.561390i	$0.810267\pi$
$462$		0			0
$463$	−1.88529	+	1.08847i	−0.0876166	+	0.0505855i	−0.543168	−	0.839624i	$-0.682775\pi$
$463$	−1.88529	+	1.08847i	−0.0876166	+	0.0505855i	0.455552	+	0.890209i	$0.349442\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	20.8089			0.962923			0.481461	−	0.876467i	$-0.340106\pi$
$467$	20.8089			0.962923			0.481461	+	0.876467i	$0.340106\pi$
$468$		0			0
$469$	−13.4639	+	3.38023i	−0.621706	+	0.156084i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.2633	+	21.2406i	0.563865	+	0.976643i
$474$		0			0
$475$	18.1320	−	31.4055i	0.831953	−	1.44099i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.5470	+	26.9281i	−0.710359	+	1.23038i	0.254364	+	0.967109i	$0.418134\pi$
$479$	−15.5470	+	26.9281i	−0.710359	+	1.23038i	−0.964723	+	0.263269i	$0.915199\pi$
$480$		0			0
$481$	5.60315	−	3.23498i	0.255481	−	0.147502i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−43.2648			−1.96455
$486$		0			0
$487$			19.1545i			0.867972i	0.900920	+	0.433986i	$0.142893\pi$
$487$			19.1545i			0.867972i	−0.900920	+	0.433986i	$0.857107\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	33.4660	−	19.3216i	1.51030	−	0.871972i	0.510371	−	0.859954i	$-0.329508\pi$
$491$	33.4660	−	19.3216i	1.51030	−	0.871972i	0.999928	−	0.0120176i	$-0.00382540\pi$
$492$		0			0
$493$	9.20228	+	5.31294i	0.414450	+	0.239283i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.08723	+	31.8868i	−0.407618	+	1.43032i
$498$		0			0
$499$	37.8146	−	21.8323i	1.69281	−	0.977346i	0.740584	−	0.671964i	$-0.234549\pi$
$499$	37.8146	−	21.8323i	1.69281	−	0.977346i	0.952230	−	0.305382i	$-0.0987843\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	34.6828			1.54643			0.773215	−	0.634144i	$-0.218647\pi$
$503$	34.6828			1.54643			0.773215	+	0.634144i	$0.218647\pi$
$504$		0			0
$505$	−13.8661			−0.617032
$506$		0			0
$507$		0			0
$508$		0			0
$509$	9.03205	−	5.21466i	0.400339	−	0.231136i	−0.286291	−	0.958143i	$-0.592423\pi$
$509$	9.03205	−	5.21466i	0.400339	−	0.231136i	0.686630	+	0.727007i	$0.259089\pi$
$510$		0			0
$511$	5.75729	−	20.2021i	0.254688	−	0.893690i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.92213	+	2.26444i	0.172830	+	0.0997832i
$516$		0			0
$517$	−28.9816	+	16.7325i	−1.27461	+	0.735896i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			8.72877i			0.382414i	0.981550	+	0.191207i	$0.0612402\pi$
$521$			8.72877i			0.382414i	−0.981550	+	0.191207i	$0.938760\pi$
$522$		0			0
$523$	10.6357			0.465068			0.232534	−	0.972588i	$-0.425298\pi$
$523$	10.6357			0.465068			0.232534	+	0.972588i	$0.425298\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	22.4553	−	12.9646i	0.978169	−	0.564746i
$528$		0			0
$529$	−2.71224	+	4.69773i	−0.117923	+	0.204249i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−6.40108	+	11.0870i	−0.277262	+	0.480231i
$534$		0			0
$535$	5.04012	+	8.72974i	0.217903	+	0.377420i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−18.9113	−	35.2893i	−0.814569	−	1.52002i
$540$		0			0
$541$	35.8565			1.54159			0.770797	−	0.637081i	$-0.219858\pi$
$541$	35.8565			1.54159			0.770797	+	0.637081i	$0.219858\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−38.8226	+	22.4143i	−1.66298	+	0.960121i
$546$		0			0
$547$	35.5209	+	20.5080i	1.51876	+	0.876859i	0.999756	+	0.0220901i	$0.00703206\pi$
$547$	35.5209	+	20.5080i	1.51876	+	0.876859i	0.519009	+	0.854769i	$0.326301\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−4.10328	+	7.10709i	−0.174806	+	0.302772i
$552$		0			0
$553$	−9.54165	−	9.84852i	−0.405752	−	0.418802i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	33.8693			1.43509			0.717545	−	0.696512i	$-0.245266\pi$
$557$	33.8693			1.43509			0.717545	+	0.696512i	$0.245266\pi$
$558$		0			0
$559$	−8.62679			−0.364874
$560$		0			0
$561$		0			0
$562$		0			0
$563$	14.7326	+	25.5176i	0.620904	+	1.07544i	0.989318	+	0.145775i	$0.0465676\pi$
$563$	14.7326	+	25.5176i	0.620904	+	1.07544i	−0.368414	+	0.929662i	$0.620099\pi$
$564$		0			0
$565$	4.18251	+	2.41477i	0.175960	+	0.101590i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.11670	+	15.7906i	−0.382192	+	0.661976i	−0.991375	−	0.131054i	$-0.958164\pi$
$569$	−9.11670	+	15.7906i	−0.382192	+	0.661976i	0.609183	+	0.793029i	$0.291497\pi$
$570$		0			0
$571$	−21.9710	+	12.6850i	−0.919459	+	0.530850i	−0.883462	−	0.468502i	$-0.844794\pi$
$571$	−21.9710	+	12.6850i	−0.919459	+	0.530850i	−0.0359963	+	0.999352i	$0.511460\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$			47.0902i			1.96380i
$576$		0			0
$577$		−	3.50461i		−	0.145899i	−0.997336	−	0.0729493i	$-0.976759\pi$
$577$		−	3.50461i		−	0.145899i	0.997336	−	0.0729493i	$-0.0232411\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	10.2212	−	9.90270i	0.424046	−	0.410833i
$582$		0			0
$583$	68.9032	+	39.7813i	2.85368	+	1.64757i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	20.1658	−	34.9282i	0.832332	−	1.44164i	−0.0638526	−	0.997959i	$-0.520339\pi$
$587$	20.1658	−	34.9282i	0.832332	−	1.44164i	0.896184	−	0.443682i	$-0.146328\pi$
$588$		0			0
$589$	10.0128	+	17.3427i	0.412570	+	0.714592i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			9.30611i			0.382156i	0.981575	+	0.191078i	$0.0611984\pi$
$593$			9.30611i			0.382156i	−0.981575	+	0.191078i	$0.938802\pi$
$594$		0			0
$595$	10.8504	+	43.2187i	0.444823	+	1.77179i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−0.0337880	+	0.0195075i	−0.00138054	+	0.000797056i	−0.500690	−	0.865627i	$-0.666920\pi$
$599$	−0.0337880	+	0.0195075i	−0.00138054	+	0.000797056i	0.499310	+	0.866424i	$0.333587\pi$
$600$		0			0
$601$	−34.4552	−	19.8927i	−1.40546	−	0.811441i	−0.410511	−	0.911856i	$-0.634650\pi$
$601$	−34.4552	−	19.8927i	−1.40546	−	0.811441i	−0.994946	+	0.100415i	$0.967983\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	75.7632	+	43.7419i	3.08021	+	1.77836i
$606$		0			0
$607$	−20.0081	−	34.6551i	−0.812104	−	1.40661i	−0.911389	−	0.411547i	$-0.864989\pi$
$607$	−20.0081	−	34.6551i	−0.812104	−	1.40661i	0.0992843	−	0.995059i	$-0.468345\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	11.7708i		−	0.476194i
$612$		0			0
$613$	5.49560			0.221965			0.110983	−	0.993822i	$-0.464600\pi$
$613$	5.49560			0.221965			0.110983	+	0.993822i	$0.464600\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	18.1436	+	31.4256i	0.730432	+	1.26515i	0.956699	+	0.291080i	$0.0940146\pi$
$617$	18.1436	+	31.4256i	0.730432	+	1.26515i	−0.226266	+	0.974065i	$0.572652\pi$
$618$		0			0
$619$	16.5285	−	28.6281i	0.664335	−	1.15066i	−0.315130	−	0.949048i	$-0.602048\pi$
$619$	16.5285	−	28.6281i	0.664335	−	1.15066i	0.979465	−	0.201613i	$-0.0646185\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	2.54626	−	8.93475i	0.102014	−	0.357963i
$624$		0			0
$625$	−22.5033	−	38.9768i	−0.900130	−	1.55907i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	13.4439i		−	0.536044i
$630$		0			0
$631$		−	27.6502i		−	1.10074i	−0.834921	−	0.550370i	$-0.814487\pi$
$631$		−	27.6502i		−	1.10074i	0.834921	−	0.550370i	$-0.185513\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	7.01063	+	12.1428i	0.278208	+	0.481871i
$636$		0			0
$637$	14.0753	+	0.445634i	0.557685	+	0.0176567i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.92939	−	12.0020i	0.273694	−	0.474052i	−0.696111	−	0.717935i	$-0.745088\pi$
$641$	6.92939	−	12.0020i	0.273694	−	0.474052i	0.969805	+	0.243882i	$0.0784210\pi$
$642$		0			0
$643$	−18.7853	−	32.5370i	−0.740819	−	1.28314i	−0.952123	−	0.305715i	$-0.901104\pi$
$643$	−18.7853	−	32.5370i	−0.740819	−	1.28314i	0.211304	−	0.977420i	$-0.432229\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−19.3733			−0.761641			−0.380821	−	0.924649i	$-0.624358\pi$
$647$	−19.3733			−0.761641			−0.380821	+	0.924649i	$0.624358\pi$
$648$		0			0
$649$			48.7472i			1.91350i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	4.26860	+	7.39344i	0.167043	+	0.289328i	0.937379	−	0.348311i	$-0.113245\pi$
$653$	4.26860	+	7.39344i	0.167043	+	0.289328i	−0.770336	+	0.637639i	$0.779911\pi$
$654$		0			0
$655$	−19.0677	−	11.0088i	−0.745038	−	0.430148i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.61026	−	2.66174i	−0.179590	−	0.103687i	0.407510	−	0.913201i	$-0.366397\pi$
$659$	−4.61026	−	2.66174i	−0.179590	−	0.103687i	−0.587100	+	0.809514i	$0.699731\pi$
$660$		0			0
$661$	12.3847	−	7.15033i	0.481710	−	0.278115i	−0.239419	−	0.970916i	$-0.576957\pi$
$661$	12.3847	−	7.15033i	0.481710	−	0.278115i	0.721129	+	0.692801i	$0.243624\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−33.3786	+	8.37997i	−1.29437	+	0.324961i
$666$		0			0
$667$		−	10.6565i		−	0.412623i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	36.0023	+	62.3577i	1.38985	+	2.40729i
$672$		0			0
$673$	−18.3816	+	31.8378i	−0.708558	+	1.22726i	0.256834	+	0.966456i	$0.417321\pi$
$673$	−18.3816	+	31.8378i	−0.708558	+	1.22726i	−0.965392	+	0.260803i	$0.916013\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	7.71366	+	4.45348i	0.296460	+	0.171161i	0.640852	−	0.767665i	$-0.278581\pi$
$677$	7.71366	+	4.45348i	0.296460	+	0.171161i	−0.344391	+	0.938826i	$0.611915\pi$
$678$		0			0
$679$	19.7694	+	20.4052i	0.758680	+	0.783080i
$680$		0			0
$681$		0			0
$682$		0			0
$683$			13.6622i			0.522768i	0.965235	+	0.261384i	$0.0841789\pi$
$683$			13.6622i			0.522768i	−0.965235	+	0.261384i	$0.915821\pi$
$684$		0			0
$685$		−	36.2413i		−	1.38471i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−24.2355	+	13.9924i	−0.923300	+	0.533068i
$690$		0			0
$691$	−17.2087	+	29.8063i	−0.654648	+	1.13388i	0.327334	+	0.944909i	$0.393850\pi$
$691$	−17.2087	+	29.8063i	−0.654648	+	1.13388i	−0.981982	+	0.188975i	$0.939483\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.8268	+	12.6017i	0.827938	+	0.478010i
$696$		0			0
$697$	13.3008	+	23.0377i	0.503804	+	0.872613i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−18.0060			−0.680078			−0.340039	−	0.940411i	$-0.610440\pi$
$701$	−18.0060			−0.680078			−0.340039	+	0.940411i	$0.610440\pi$
$702$		0			0
$703$	10.3830			0.391602
$704$		0			0
$705$		0			0
$706$		0			0
$707$	6.33596	+	6.53973i	0.238288	+	0.245952i
$708$		0			0
$709$	25.2917	−	43.8065i	0.949849	−	1.64519i	0.204111	−	0.978948i	$-0.434570\pi$
$709$	25.2917	−	43.8065i	0.949849	−	1.64519i	0.745738	−	0.666239i	$-0.232097\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−22.5201	−	13.0020i	−0.843385	−	0.486928i
$714$		0			0
$715$	−40.1483	+	23.1796i	−1.50146	+	0.866869i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	44.2317			1.64956			0.824782	−	0.565450i	$-0.191298\pi$
$719$	44.2317			1.64956			0.824782	+	0.565450i	$0.191298\pi$
$720$		0			0
$721$	−0.724184	−	2.88453i	−0.0269700	−	0.107425i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	14.2761	+	24.7269i	0.530200	+	0.918332i
$726$		0			0
$727$	23.3313	−	40.4110i	0.865310	−	1.49876i	−0.00142913	−	0.999999i	$-0.500455\pi$
$727$	23.3313	−	40.4110i	0.865310	−	1.49876i	0.866739	−	0.498762i	$-0.166212\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−8.96279	+	15.5240i	−0.331501	+	0.574176i
$732$		0			0
$733$	29.4459	−	17.0006i	1.08761	−	0.627932i	0.154671	−	0.987966i	$-0.450568\pi$
$733$	29.4459	−	17.0006i	1.08761	−	0.627932i	0.932939	+	0.360034i	$0.117235\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−30.0096			−1.10542
$738$		0			0
$739$			12.4853i			0.459279i	0.973276	+	0.229640i	$0.0737548\pi$
$739$			12.4853i			0.459279i	−0.973276	+	0.229640i	$0.926245\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−24.6313	+	14.2209i	−0.903636	+	0.521714i	−0.878378	−	0.477967i	$-0.841374\pi$
$743$	−24.6313	+	14.2209i	−0.903636	+	0.521714i	−0.0252578	+	0.999681i	$0.508041\pi$
$744$		0			0
$745$	44.1187	+	25.4719i	1.61638	+	0.933219i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	1.81423	−	6.36606i	0.0662904	−	0.232611i
$750$		0			0
$751$	−3.91640	+	2.26113i	−0.142911	+	0.0825100i	−0.569751	−	0.821817i	$-0.692960\pi$
$751$	−3.91640	+	2.26113i	−0.142911	+	0.0825100i	0.426839	+	0.904327i	$0.359627\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	64.2508			2.33833
$756$		0			0
$757$	−9.85242			−0.358092			−0.179046	−	0.983841i	$-0.557301\pi$
$757$	−9.85242			−0.358092			−0.179046	+	0.983841i	$0.557301\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−45.5417	+	26.2935i	−1.65089	+	0.953139i	−0.674176	+	0.738571i	$0.735501\pi$
$761$	−45.5417	+	26.2935i	−1.65089	+	0.953139i	−0.976709	+	0.214568i	$0.931166\pi$
$762$		0			0
$763$	28.3110	+	8.06817i	1.02493	+	0.292087i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−14.8489	−	8.57300i	−0.536162	−	0.309553i
$768$		0			0
$769$	9.80437	−	5.66055i	0.353555	−	0.204125i	−0.312695	−	0.949854i	$-0.601232\pi$
$769$	9.80437	−	5.66055i	0.353555	−	0.204125i	0.666250	+	0.745729i	$0.267899\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	1.42526i		−	0.0512631i	−0.999671	−	0.0256316i	$-0.991840\pi$
$773$		−	1.42526i		−	0.0512631i	0.999671	−	0.0256316i	$-0.00815967\pi$
$774$		0			0
$775$	69.6726			2.50271
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−17.7924	+	10.2725i	−0.637479	+	0.368049i
$780$		0			0
$781$	−35.8388	+	62.0746i	−1.28241	+	2.22120i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	35.7714	−	61.9579i	1.27674	−	2.21137i
$786$		0			0
$787$	20.9215	+	36.2370i	0.745769	+	1.29171i	0.949834	+	0.312753i	$0.101251\pi$
$787$	20.9215	+	36.2370i	0.745769	+	1.29171i	−0.204065	+	0.978957i	$0.565415\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−0.772261	−	3.07603i	−0.0274585	−	0.109371i
$792$		0			0
$793$	−25.3264			−0.899366
$794$		0			0
$795$		0			0
$796$		0			0
$797$	7.85796	−	4.53679i	0.278343	−	0.160701i	−0.354330	−	0.935120i	$-0.615291\pi$
$797$	7.85796	−	4.53679i	0.278343	−	0.160701i	0.632673	+	0.774419i	$0.281958\pi$
$798$		0			0
$799$	−21.1816	−	12.2292i	−0.749353	−	0.432639i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	22.7060	−	39.3279i	0.801276	−	1.38785i
$804$		0			0
$805$	32.0956	−	31.0955i	1.13122	−	1.09597i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	18.6037			0.654071			0.327035	−	0.945012i	$-0.393950\pi$
$809$	18.6037			0.654071			0.327035	+	0.945012i	$0.393950\pi$
$810$		0			0
$811$	−43.7813			−1.53737			−0.768684	−	0.639628i	$-0.779088\pi$
$811$	−43.7813			−1.53737			−0.768684	+	0.639628i	$0.779088\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−20.4040	−	35.3407i	−0.714721	−	1.23793i
$816$		0			0
$817$	−11.9895	−	6.92213i	−0.419459	−	0.242175i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	11.8053	−	20.4474i	0.412009	−	0.713620i	−0.583101	−	0.812400i	$-0.698161\pi$
$821$	11.8053	−	20.4474i	0.412009	−	0.713620i	0.995109	+	0.0987801i	$0.0314940\pi$
$822$		0			0
$823$	0.653789	−	0.377465i	0.0227897	−	0.0131576i	−0.488562	−	0.872529i	$-0.662478\pi$
$823$	0.653789	−	0.377465i	0.0227897	−	0.0131576i	0.511352	+	0.859372i	$0.329145\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	5.64456i		−	0.196281i	−0.995173	−	0.0981404i	$-0.968711\pi$
$827$		−	5.64456i		−	0.196281i	0.995173	−	0.0981404i	$-0.0312894\pi$
$828$		0			0
$829$			26.2077i			0.910230i	0.890433	+	0.455115i	$0.150402\pi$
$829$			26.2077i			0.910230i	−0.890433	+	0.455115i	$0.849598\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	15.4255	−	24.8658i	0.534461	−	0.861548i
$834$		0			0
$835$	−49.4276	−	28.5370i	−1.71051	−	0.987565i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	10.5365	−	18.2498i	0.363761	−	0.630053i	−0.624815	−	0.780773i	$-0.714826\pi$
$839$	10.5365	−	18.2498i	0.363761	−	0.630053i	0.988577	+	0.150720i	$0.0481591\pi$
$840$		0			0
$841$	11.2693	+	19.5190i	0.388597	+	0.673070i
$842$		0			0
$843$		0			0
$844$		0			0
$845$			36.0704i			1.24086i
$846$		0			0
$847$	−13.9890	−	55.7200i	−0.480666	−	1.91456i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−11.6764	+	6.74135i	−0.400261	+	0.231091i
$852$		0			0
$853$	−30.6601	−	17.7016i	−1.04978	−	0.606092i	−0.127193	−	0.991878i	$-0.540597\pi$
$853$	−30.6601	−	17.7016i	−1.04978	−	0.606092i	−0.922588	+	0.385786i	$0.873930\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−19.1852	−	11.0766i	−0.655356	−	0.378370i	0.135149	−	0.990825i	$-0.456849\pi$
$857$	−19.1852	−	11.0766i	−0.655356	−	0.378370i	−0.790505	+	0.612455i	$0.790182\pi$
$858$		0			0
$859$	2.32382	+	4.02497i	0.0792876	+	0.137330i	0.902943	−	0.429761i	$-0.141402\pi$
$859$	2.32382	+	4.02497i	0.0792876	+	0.137330i	−0.823655	+	0.567091i	$0.808069\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	10.5090i		−	0.357732i	−0.983873	−	0.178866i	$-0.942757\pi$
$863$		−	10.5090i		−	0.357732i	0.983873	−	0.178866i	$-0.0572428\pi$
$864$		0			0
$865$	43.8526			1.49103
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−14.8220	−	25.6725i	−0.502802	−	0.870879i
$870$		0			0
$871$	5.27769	−	9.14122i	0.178828	−	0.309739i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−18.2082	+	63.8922i	−0.615551	+	2.15995i
$876$		0			0
$877$	−3.60317	−	6.24087i	−0.121670	−	0.210739i	0.798756	−	0.601655i	$-0.205492\pi$
$877$	−3.60317	−	6.24087i	−0.121670	−	0.210739i	−0.920427	+	0.390916i	$0.872158\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	47.4313i		−	1.59800i	−0.601331	−	0.799000i	$-0.705363\pi$
$881$		−	47.4313i		−	1.59800i	0.601331	−	0.799000i	$-0.294637\pi$
$882$		0			0
$883$		−	44.5341i		−	1.49869i	−0.662178	−	0.749346i	$-0.730368\pi$
$883$		−	44.5341i		−	1.49869i	0.662178	−	0.749346i	$-0.269632\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−6.55039	−	11.3456i	−0.219941	−	0.380948i	0.734849	−	0.678231i	$-0.237253\pi$
$887$	−6.55039	−	11.3456i	−0.219941	−	0.380948i	−0.954790	+	0.297283i	$0.903920\pi$
$888$		0			0
$889$	2.52352	−	8.85497i	0.0846363	−	0.296986i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	9.44486	−	16.3590i	0.316060	−	0.547432i
$894$		0			0
$895$	−23.6254	−	40.9205i	−0.789711	−	1.36782i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−15.7669			−0.525857
$900$		0			0
$901$			58.1495i			1.93724i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−35.5600	−	61.5917i	−1.18205	−	2.04738i
$906$		0			0
$907$	−16.1687	−	9.33500i	−0.536872	−	0.309963i	0.206938	−	0.978354i	$-0.433650\pi$
$907$	−16.1687	−	9.33500i	−0.536872	−	0.309963i	−0.743810	+	0.668391i	$0.766983\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−9.20898	−	5.31680i	−0.305107	−	0.176154i	0.339628	−	0.940560i	$-0.389699\pi$
$911$	−9.20898	−	5.31680i	−0.305107	−	0.176154i	−0.644735	+	0.764406i	$0.723032\pi$
$912$		0			0
$913$	26.6439	−	15.3829i	0.881785	−	0.509099i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	3.52068	+	14.0234i	0.116263	+	0.463092i
$918$		0			0
$919$		−	25.9144i		−	0.854836i	−0.904054	−	0.427418i	$-0.859423\pi$
$919$		−	25.9144i		−	0.854836i	0.904054	−	0.427418i	$-0.140577\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−12.6057	−	21.8337i	−0.414921	−	0.718665i
$924$		0			0
$925$	18.0621	−	31.2846i	0.593880	−	1.02863i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	44.4016	+	25.6353i	1.45677	+	0.841066i	0.998851	−	0.0479287i	$-0.0152620\pi$
$929$	44.4016	+	25.6353i	1.45677	+	0.841066i	0.457918	+	0.888994i	$0.348595\pi$
$930$		0			0
$931$	19.2043	+	11.9134i	0.629395	+	0.390446i
$932$		0			0
$933$		0			0
$934$		0			0
$935$			96.3298i			3.15032i
$936$		0			0
$937$			47.7056i			1.55847i	0.626729	+	0.779237i	$0.284393\pi$
$937$			47.7056i			1.55847i	−0.626729	+	0.779237i	$0.715607\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	49.3584	−	28.4971i	1.60904	−	0.928978i	0.619452	−	0.785035i	$-0.287355\pi$
$941$	49.3584	−	28.4971i	1.60904	−	0.928978i	0.989586	−	0.143944i	$-0.0459784\pi$
$942$		0			0
$943$	13.3392	−	23.1041i	0.434383	−	0.752374i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−4.86698	−	2.80995i	−0.158156	−	0.0913113i	0.418833	−	0.908063i	$-0.362439\pi$
$947$	−4.86698	−	2.80995i	−0.158156	−	0.0913113i	−0.576989	+	0.816752i	$0.695772\pi$
$948$		0			0
$949$	7.98644	+	13.8329i	0.259251	+	0.449035i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	39.6935			1.28580			0.642899	−	0.765951i	$-0.277731\pi$
$953$	39.6935			1.28580			0.642899	+	0.765951i	$0.277731\pi$
$954$		0			0
$955$	2.70465			0.0875205
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−17.0927	+	16.5601i	−0.551951	+	0.534753i
$960$		0			0
$961$	−3.73718	+	6.47298i	−0.120554	+	0.208806i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−52.0255	−	30.0369i	−1.67476	−	0.966923i
$966$		0			0
$967$	23.3249	−	13.4666i	0.750078	−	0.433058i	−0.0756442	−	0.997135i	$-0.524101\pi$
$967$	23.3249	−	13.4666i	0.750078	−	0.433058i	0.825722	+	0.564077i	$0.190768\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−9.63591			−0.309231			−0.154616	−	0.987975i	$-0.549414\pi$
$971$	−9.63591			−0.309231			−0.154616	+	0.987975i	$0.549414\pi$
$972$		0			0
$973$	−4.03012	−	16.0525i	−0.129200	−	0.514620i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	25.0233	+	43.3417i	0.800567	+	1.38662i	0.919243	+	0.393690i	$0.128802\pi$
$977$	25.0233	+	43.3417i	0.800567	+	1.38662i	−0.118676	+	0.992933i	$0.537865\pi$
$978$		0			0
$979$	10.0421	−	17.3934i	0.320947	−	0.555897i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	20.3246	−	35.2032i	0.648254	−	1.12281i	−0.335286	−	0.942116i	$-0.608833\pi$
$983$	20.3246	−	35.2032i	0.648254	−	1.12281i	0.983540	−	0.180692i	$-0.0578337\pi$
$984$		0			0
$985$	−30.8689	+	17.8222i	−0.983564	+	0.567861i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	17.9773			0.571645
$990$		0			0
$991$			7.45474i			0.236808i	0.992966	+	0.118404i	$0.0377777\pi$
$991$			7.45474i			0.236808i	−0.992966	+	0.118404i	$0.962222\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−17.4179	+	10.0562i	−0.552184	+	0.318804i
$996$		0			0
$997$	−10.3529	−	5.97727i	−0.327881	−	0.189302i	0.327019	−	0.945018i	$-0.393956\pi$
$997$	−10.3529	−	5.97727i	−0.327881	−	0.189302i	−0.654900	+	0.755716i	$0.727289\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3024.2.cx.i.559.12		24
3.2	odd	2		1008.2.cx.i.223.7	yes	24
4.3	odd	2		3024.2.cx.j.559.12		24
7.6	odd	2	inner	3024.2.cx.i.559.1		24
9.4	even	3		3024.2.cx.j.2575.1		24
9.5	odd	6		1008.2.cx.j.895.7	yes	24
12.11	even	2		1008.2.cx.j.223.6	yes	24
21.20	even	2		1008.2.cx.i.223.6	✓	24
28.27	even	2		3024.2.cx.j.559.1		24
36.23	even	6		1008.2.cx.i.895.6	yes	24
36.31	odd	6	inner	3024.2.cx.i.2575.1		24
63.13	odd	6		3024.2.cx.j.2575.12		24
63.41	even	6		1008.2.cx.j.895.6	yes	24
84.83	odd	2		1008.2.cx.j.223.7	yes	24
252.139	even	6	inner	3024.2.cx.i.2575.12		24
252.167	odd	6		1008.2.cx.i.895.7	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.cx.i.223.6	✓	24	21.20	even	2
1008.2.cx.i.223.7	yes	24	3.2	odd	2
1008.2.cx.i.895.6	yes	24	36.23	even	6
1008.2.cx.i.895.7	yes	24	252.167	odd	6
1008.2.cx.j.223.6	yes	24	12.11	even	2
1008.2.cx.j.223.7	yes	24	84.83	odd	2
1008.2.cx.j.895.6	yes	24	63.41	even	6
1008.2.cx.j.895.7	yes	24	9.5	odd	6
3024.2.cx.i.559.1		24	7.6	odd	2	inner
3024.2.cx.i.559.12		24	1.1	even	1	trivial
3024.2.cx.i.2575.1		24	36.31	odd	6	inner
3024.2.cx.i.2575.12		24	252.139	even	6	inner
3024.2.cx.j.559.1		24	28.27	even	2
3024.2.cx.j.559.12		24	4.3	odd	2
3024.2.cx.j.2575.1		24	9.4	even	3
3024.2.cx.j.2575.12		24	63.13	odd	6

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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.cx (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.48918 - 2.01448i) q^{5} +(-2.54444 - 0.725126i) q^{7} +(-4.95331 - 2.85980i) q^{11} +(1.74224 - 1.00589i) q^{13} -4.18025i q^{17} +3.22849 q^{19} +(-3.63065 + 2.09616i) q^{23} +(5.61625 - 9.72763i) q^{25} +(-1.27096 + 2.20137i) q^{29} +(3.10138 + 5.37176i) q^{31} +(-10.3388 + 2.59563i) q^{35} +3.21605 q^{37} +(-5.51107 + 3.18181i) q^{41} +(-3.71365 - 2.14408i) q^{43} +(2.92547 - 5.06707i) q^{47} +(5.94838 + 3.69008i) q^{49} -13.9105 q^{53} -23.0440 q^{55} +(-4.26142 - 7.38100i) q^{59} +(-10.9025 - 6.29455i) q^{61} +(4.05267 - 7.01943i) q^{65} +(4.54387 - 2.62341i) q^{67} -12.5319i q^{71} +7.93971i q^{73} +(10.5297 + 10.8684i) q^{77} +(4.48851 + 2.59144i) q^{79} +(-2.68950 + 4.65836i) q^{83} +(-8.42103 - 14.5857i) q^{85} +3.51148i q^{89} +(-5.16244 + 1.29607i) q^{91} +(11.2648 - 6.50372i) q^{95} +(-9.29978 - 5.36923i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{7} - 18 q^{23} + 24 q^{25} + 6 q^{29} - 12 q^{37} + 42 q^{43} + 12 q^{49} - 96 q^{53} - 42 q^{65} + 36 q^{67} + 18 q^{77} - 60 q^{79} - 6 q^{85} + 126 q^{95}+O(q^{100}) \) 24 * q - 6 * q^7 - 18 * q^23 + 24 * q^25 + 6 * q^29 - 12 * q^37 + 42 * q^43 + 12 * q^49 - 96 * q^53 - 42 * q^65 + 36 * q^67 + 18 * q^77 - 60 * q^79 - 6 * q^85 + 126 * q^95

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