LMFDB - Embedded newform 840.2.f.a.41.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(41,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 1, 0, 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("840.41"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,-16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + x^{14} - 4 x^{13} + 10 x^{12} - 32 x^{11} + 71 x^{10} - 70 x^{9} + 74 x^{8} + \cdots + 6561 $ x^16 - 2x^15 + x^14 - 4x^13 + 10x^12 - 32x^11 + 71x^10 - 70x^9 + 74x^8 - 210x^7 + 639x^6 - 864x^5 + 810x^4 - 972x^3 + 729x^2 - 4374x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{16} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			41.13
Root			$-1.12510 - 1.31688i$ of defining polynomial
Character	$\chi$	$=$	840.41
Dual form			840.2.f.a.41.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.31688 - 1.12510i) q^{3} -1.00000 q^{5} +(2.64497 + 0.0644212i) q^{7} +(0.468322 - 2.96322i) q^{9} -2.69896i q^{11} +6.61014i q^{13} +(-1.31688 + 1.12510i) q^{15} +7.03420 q^{17} -3.22748i q^{19} +(3.55557 - 2.89100i) q^{21} -2.56574i q^{23} +1.00000 q^{25} +(-2.71718 - 4.42910i) q^{27} -8.21890i q^{29} +2.87007i q^{31} +(-3.03659 - 3.55419i) q^{33} +(-2.64497 - 0.0644212i) q^{35} -6.79684 q^{37} +(7.43703 + 8.70473i) q^{39} -10.0478 q^{41} +11.6680 q^{43} +(-0.468322 + 2.96322i) q^{45} +2.56626 q^{47} +(6.99170 + 0.340784i) q^{49} +(9.26316 - 7.91414i) q^{51} -2.70121i q^{53} +2.69896i q^{55} +(-3.63122 - 4.25019i) q^{57} +3.03797 q^{59} +7.83481i q^{61} +(1.42959 - 7.80745i) q^{63} -6.61014i q^{65} -12.5077 q^{67} +(-2.88670 - 3.37875i) q^{69} +14.0203i q^{71} -1.81228i q^{73} +(1.31688 - 1.12510i) q^{75} +(0.173870 - 7.13866i) q^{77} +13.4166 q^{79} +(-8.56135 - 2.77548i) q^{81} -3.01554 q^{83} -7.03420 q^{85} +(-9.24705 - 10.8233i) q^{87} -4.17450 q^{89} +(-0.425833 + 17.4836i) q^{91} +(3.22911 + 3.77953i) q^{93} +3.22748i q^{95} -9.55176i q^{97} +(-7.99761 - 1.26398i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{5} + 2 q^{7} - 2 q^{9} + 2 q^{21} + 16 q^{25} - 6 q^{27} - 6 q^{33} - 2 q^{35} + 12 q^{37} + 6 q^{39} - 32 q^{41} + 32 q^{43} + 2 q^{45} - 4 q^{47} - 4 q^{49} + 6 q^{51} + 24 q^{59} - 4 q^{63}+ \cdots - 58 q^{99}+O(q^{100}) $ 16 * q - 16 * q^5 + 2 * q^7 - 2 * q^9 + 2 * q^21 + 16 * q^25 - 6 * q^27 - 6 * q^33 - 2 * q^35 + 12 * q^37 + 6 * q^39 - 32 * q^41 + 32 * q^43 + 2 * q^45 - 4 * q^47 - 4 * q^49 + 6 * q^51 + 24 * q^59 - 4 * q^63 - 8 * q^69 + 32 * q^77 - 4 * q^79 - 6 * q^81 - 20 * q^83 - 6 * q^87 + 24 * q^89 + 20 * q^91 - 32 * q^93 - 58 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$-1$	$1$	$1$	$1$

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
$3$	1.31688	−	1.12510i	0.760298	−	0.649574i
$3$	1.31688	−	1.12510i	0.760298	−	0.649574i
$4$		0			0
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$		0			0
$7$	2.64497	+	0.0644212i	0.999704	+	0.0243489i
$7$	2.64497	+	0.0644212i	0.999704	+	0.0243489i
$8$		0			0
$9$	0.468322	−	2.96322i	0.156107	−	0.987740i
$10$		0			0
$11$		−	2.69896i		−	0.813767i	−0.913480	−	0.406884i	$-0.866615\pi$
$11$		−	2.69896i		−	0.813767i	0.913480	−	0.406884i	$-0.133385\pi$
$12$		0			0
$13$			6.61014i			1.83332i	0.399665	+	0.916661i	$0.369127\pi$
$13$			6.61014i			1.83332i	−0.399665	+	0.916661i	$0.630873\pi$
$14$		0			0
$15$	−1.31688	+	1.12510i	−0.340016	+	0.290498i
$16$		0			0
$17$	7.03420			1.70604			0.853022	−	0.521875i	$-0.174767\pi$
$17$	7.03420			1.70604			0.853022	+	0.521875i	$0.174767\pi$
$18$		0			0
$19$		−	3.22748i		−	0.740435i	−0.928945	−	0.370217i	$-0.879283\pi$
$19$		−	3.22748i		−	0.740435i	0.928945	−	0.370217i	$-0.120717\pi$
$20$		0			0
$21$	3.55557	−	2.89100i	0.775889	−	0.630869i
$22$		0			0
$23$		−	2.56574i		−	0.534993i	−0.963559	−	0.267496i	$-0.913804\pi$
$23$		−	2.56574i		−	0.534993i	0.963559	−	0.267496i	$-0.0861964\pi$
$24$		0			0
$25$	1.00000			0.200000
$26$		0			0
$27$	−2.71718	−	4.42910i	−0.522922	−	0.852381i
$28$		0			0
$29$		−	8.21890i		−	1.52621i	−0.646273	−	0.763106i	$-0.723673\pi$
$29$		−	8.21890i		−	1.52621i	0.646273	−	0.763106i	$-0.276327\pi$
$30$		0			0
$31$			2.87007i			0.515481i	0.966214	+	0.257740i	$0.0829779\pi$
$31$			2.87007i			0.515481i	−0.966214	+	0.257740i	$0.917022\pi$
$32$		0			0
$33$	−3.03659	−	3.55419i	−0.528602	−	0.618706i
$34$		0			0
$35$	−2.64497	−	0.0644212i	−0.447081	−	0.0108892i
$36$		0			0
$37$	−6.79684			−1.11739			−0.558697	−	0.829372i	$-0.688699\pi$
$37$	−6.79684			−1.11739			−0.558697	+	0.829372i	$0.688699\pi$
$38$		0			0
$39$	7.43703	+	8.70473i	1.19088	+	1.39387i
$40$		0			0
$41$	−10.0478			−1.56920			−0.784600	−	0.620002i	$-0.787132\pi$
$41$	−10.0478			−1.56920			−0.784600	+	0.620002i	$0.787132\pi$
$42$		0			0
$43$	11.6680			1.77935			0.889673	−	0.456599i	$-0.150932\pi$
$43$	11.6680			1.77935			0.889673	+	0.456599i	$0.150932\pi$
$44$		0			0
$45$	−0.468322	+	2.96322i	−0.0698133	+	0.441731i
$46$		0			0
$47$	2.56626			0.374328			0.187164	−	0.982329i	$-0.440070\pi$
$47$	2.56626			0.374328			0.187164	+	0.982329i	$0.440070\pi$
$48$		0			0
$49$	6.99170	+	0.340784i	0.998814	+	0.0486834i
$50$		0			0
$51$	9.26316	−	7.91414i	1.29710	−	1.10820i
$52$		0			0
$53$		−	2.70121i		−	0.371040i	−0.982641	−	0.185520i	$-0.940603\pi$
$53$		−	2.70121i		−	0.371040i	0.982641	−	0.185520i	$-0.0593969\pi$
$54$		0			0
$55$			2.69896i			0.363928i
$56$		0			0
$57$	−3.63122	−	4.25019i	−0.480967	−	0.562951i
$58$		0			0
$59$	3.03797			0.395510			0.197755	−	0.980251i	$-0.436635\pi$
$59$	3.03797			0.395510			0.197755	+	0.980251i	$0.436635\pi$
$60$		0			0
$61$			7.83481i			1.00315i	0.865116	+	0.501573i	$0.167245\pi$
$61$			7.83481i			1.00315i	−0.865116	+	0.501573i	$0.832755\pi$
$62$		0			0
$63$	1.42959	−	7.80745i	0.180111	−	0.983646i
$64$		0			0
$65$		−	6.61014i		−	0.819887i
$66$		0			0
$67$	−12.5077			−1.52805			−0.764027	−	0.645184i	$-0.776781\pi$
$67$	−12.5077			−1.52805			−0.764027	+	0.645184i	$0.776781\pi$
$68$		0			0
$69$	−2.88670	−	3.37875i	−0.347517	−	0.406754i
$70$		0			0
$71$			14.0203i			1.66391i	0.554846	+	0.831953i	$0.312777\pi$
$71$			14.0203i			1.66391i	−0.554846	+	0.831953i	$0.687223\pi$
$72$		0			0
$73$		−	1.81228i		−	0.212111i	−0.994360	−	0.106056i	$-0.966178\pi$
$73$		−	1.81228i		−	0.212111i	0.994360	−	0.106056i	$-0.0338222\pi$
$74$		0			0
$75$	1.31688	−	1.12510i	0.152060	−	0.129915i
$76$		0			0
$77$	0.173870	−	7.13866i	0.0198143	−	0.813526i
$78$		0			0
$79$	13.4166			1.50949			0.754744	−	0.656020i	$-0.227761\pi$
$79$	13.4166			1.50949			0.754744	+	0.656020i	$0.227761\pi$
$80$		0			0
$81$	−8.56135	−	2.77548i	−0.951261	−	0.308387i
$82$		0			0
$83$	−3.01554			−0.330998			−0.165499	−	0.986210i	$-0.552924\pi$
$83$	−3.01554			−0.330998			−0.165499	+	0.986210i	$0.552924\pi$
$84$		0			0
$85$	−7.03420			−0.762966
$86$		0			0
$87$	−9.24705	−	10.8233i	−0.991388	−	1.16038i
$88$		0			0
$89$	−4.17450			−0.442496			−0.221248	−	0.975218i	$-0.571013\pi$
$89$	−4.17450			−0.442496			−0.221248	+	0.975218i	$0.571013\pi$
$90$		0			0
$91$	−0.425833	+	17.4836i	−0.0446394	+	1.83278i
$92$		0			0
$93$	3.22911	+	3.77953i	0.334843	+	0.391919i
$94$		0			0
$95$			3.22748i			0.331133i
$96$		0			0
$97$		−	9.55176i		−	0.969834i	−0.874560	−	0.484917i	$-0.838850\pi$
$97$		−	9.55176i		−	0.969834i	0.874560	−	0.484917i	$-0.161150\pi$
$98$		0			0
$99$	−7.99761	−	1.26398i	−0.803790	−	0.127035i
$100$		0			0
$101$	−10.5849			−1.05324			−0.526620	−	0.850101i	$-0.676541\pi$
$101$	−10.5849			−1.05324			−0.526620	+	0.850101i	$0.676541\pi$
$102$		0			0
$103$		−	1.89424i		−	0.186645i	−0.995636	−	0.0933226i	$-0.970251\pi$
$103$		−	1.89424i		−	0.186645i	0.995636	−	0.0933226i	$-0.0297488\pi$
$104$		0			0
$105$	−3.55557	+	2.89100i	−0.346988	+	0.282133i
$106$		0			0
$107$			5.25101i			0.507634i	0.967252	+	0.253817i	$0.0816861\pi$
$107$			5.25101i			0.507634i	−0.967252	+	0.253817i	$0.918314\pi$
$108$		0			0
$109$	−2.53893			−0.243185			−0.121593	−	0.992580i	$-0.538800\pi$
$109$	−2.53893			−0.243185			−0.121593	+	0.992580i	$0.538800\pi$
$110$		0			0
$111$	−8.95060	+	7.64709i	−0.849553	+	0.725830i
$112$		0			0
$113$			8.73583i			0.821798i	0.911681	+	0.410899i	$0.134785\pi$
$113$			8.73583i			0.821798i	−0.911681	+	0.410899i	$0.865215\pi$
$114$		0			0
$115$			2.56574i			0.239256i
$116$		0			0
$117$	19.5873	+	3.09567i	1.81085	+	0.286195i
$118$		0			0
$119$	18.6052	+	0.453151i	1.70554	+	0.0415403i
$120$		0			0
$121$	3.71562			0.337783
$122$		0			0
$123$	−13.2317	+	11.3047i	−1.19306	+	1.01931i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	7.71266			0.684388			0.342194	−	0.939629i	$-0.388830\pi$
$127$	7.71266			0.684388			0.342194	+	0.939629i	$0.388830\pi$
$128$		0			0
$129$	15.3652	−	13.1276i	1.35283	−	1.15582i
$130$		0			0
$131$	−2.91632			−0.254800			−0.127400	−	0.991851i	$-0.540663\pi$
$131$	−2.91632			−0.254800			−0.127400	+	0.991851i	$0.540663\pi$
$132$		0			0
$133$	0.207918	−	8.53658i	0.0180288	−	0.740215i
$134$		0			0
$135$	2.71718	+	4.42910i	0.233858	+	0.381196i
$136$		0			0
$137$			18.7142i			1.59886i	0.600759	+	0.799430i	$0.294865\pi$
$137$			18.7142i			1.59886i	−0.600759	+	0.799430i	$0.705135\pi$
$138$		0			0
$139$			19.5502i			1.65823i	0.559080	+	0.829114i	$0.311155\pi$
$139$			19.5502i			1.65823i	−0.559080	+	0.829114i	$0.688845\pi$
$140$		0			0
$141$	3.37945	−	2.88729i	0.284601	−	0.243154i
$142$		0			0
$143$	17.8405			1.49190
$144$		0			0
$145$			8.21890i			0.682543i
$146$		0			0
$147$	9.59061	−	7.41756i	0.791020	−	0.611790i
$148$		0			0
$149$		−	3.35377i		−	0.274751i	−0.990519	−	0.137376i	$-0.956133\pi$
$149$		−	3.35377i		−	0.274751i	0.990519	−	0.137376i	$-0.0438667\pi$
$150$		0			0
$151$	−6.20015			−0.504561			−0.252280	−	0.967654i	$-0.581181\pi$
$151$	−6.20015			−0.504561			−0.252280	+	0.967654i	$0.581181\pi$
$152$		0			0
$153$	3.29427	−	20.8439i	0.266326	−	1.68513i
$154$		0			0
$155$		−	2.87007i		−	0.230530i
$156$		0			0
$157$			9.90178i			0.790248i	0.918628	+	0.395124i	$0.129298\pi$
$157$			9.90178i			0.790248i	−0.918628	+	0.395124i	$0.870702\pi$
$158$		0			0
$159$	−3.03912	−	3.55716i	−0.241018	−	0.282101i
$160$		0			0
$161$	0.165288	−	6.78629i	0.0130265	−	0.534834i
$162$		0			0
$163$	−13.4953			−1.05703			−0.528515	−	0.848924i	$-0.677251\pi$
$163$	−13.4953			−1.05703			−0.528515	+	0.848924i	$0.677251\pi$
$164$		0			0
$165$	3.03659	+	3.55419i	0.236398	+	0.276694i
$166$		0			0
$167$	4.40548			0.340907			0.170453	−	0.985366i	$-0.445477\pi$
$167$	4.40548			0.340907			0.170453	+	0.985366i	$0.445477\pi$
$168$		0			0
$169$	−30.6939			−2.36107
$170$		0			0
$171$	−9.56374	−	1.51150i	−0.731357	−	0.115587i
$172$		0			0
$173$	−5.90091			−0.448638			−0.224319	−	0.974516i	$-0.572016\pi$
$173$	−5.90091			−0.448638			−0.224319	+	0.974516i	$0.572016\pi$
$174$		0			0
$175$	2.64497	+	0.0644212i	0.199941	+	0.00486978i
$176$		0			0
$177$	4.00063	−	3.41801i	0.300706	−	0.256913i
$178$		0			0
$179$			7.34159i			0.548736i	0.961625	+	0.274368i	$0.0884687\pi$
$179$			7.34159i			0.548736i	−0.961625	+	0.274368i	$0.911531\pi$
$180$		0			0
$181$			17.0168i			1.26485i	0.774623	+	0.632423i	$0.217940\pi$
$181$			17.0168i			1.26485i	−0.774623	+	0.632423i	$0.782060\pi$
$182$		0			0
$183$	8.81491	+	10.3175i	0.651617	+	0.762690i
$184$		0			0
$185$	6.79684			0.499714
$186$		0			0
$187$		−	18.9850i		−	1.38832i
$188$		0			0
$189$	−6.90153	−	11.8899i	−0.502012	−	0.864860i
$190$		0			0
$191$			1.75110i			0.126705i	0.997991	+	0.0633525i	$0.0201792\pi$
$191$			1.75110i			0.126705i	−0.997991	+	0.0633525i	$0.979821\pi$
$192$		0			0
$193$	−12.8740			−0.926694			−0.463347	−	0.886177i	$-0.653352\pi$
$193$	−12.8740			−0.926694			−0.463347	+	0.886177i	$0.653352\pi$
$194$		0			0
$195$	−7.43703	−	8.70473i	−0.532577	−	0.623359i
$196$		0			0
$197$			7.93648i			0.565451i	0.959201	+	0.282725i	$0.0912385\pi$
$197$			7.93648i			0.565451i	−0.959201	+	0.282725i	$0.908762\pi$
$198$		0			0
$199$		−	8.56247i		−	0.606977i	−0.952835	−	0.303489i	$-0.901849\pi$
$199$		−	8.56247i		−	0.606977i	0.952835	−	0.303489i	$-0.0981515\pi$
$200$		0			0
$201$	−16.4710	+	14.0723i	−1.16178	+	0.992585i
$202$		0			0
$203$	0.529471	−	21.7387i	0.0371616	−	1.52576i
$204$		0			0
$205$	10.0478			0.701768
$206$		0			0
$207$	−7.60284	−	1.20159i	−0.528434	−	0.0835163i
$208$		0			0
$209$	−8.71084			−0.602541
$210$		0			0
$211$	−9.30759			−0.640761			−0.320380	−	0.947289i	$-0.603811\pi$
$211$	−9.30759			−0.640761			−0.320380	+	0.947289i	$0.603811\pi$
$212$		0			0
$213$	15.7742	+	18.4630i	1.08083	+	1.26507i
$214$		0			0
$215$	−11.6680			−0.795748
$216$		0			0
$217$	−0.184894	+	7.59125i	−0.0125514	+	0.515328i
$218$		0			0
$219$	−2.03899	−	2.38655i	−0.137782	−	0.161268i
$220$		0			0
$221$			46.4970i			3.12773i
$222$		0			0
$223$			19.9132i			1.33349i	0.745287	+	0.666744i	$0.232313\pi$
$223$			19.9132i			1.33349i	−0.745287	+	0.666744i	$0.767687\pi$
$224$		0			0
$225$	0.468322	−	2.96322i	0.0312215	−	0.197548i
$226$		0			0
$227$	12.8987			0.856116			0.428058	−	0.903751i	$-0.359198\pi$
$227$	12.8987			0.856116			0.428058	+	0.903751i	$0.359198\pi$
$228$		0			0
$229$		−	6.88453i		−	0.454942i	−0.973785	−	0.227471i	$-0.926954\pi$
$229$		−	6.88453i		−	0.454942i	0.973785	−	0.227471i	$-0.0730458\pi$
$230$		0			0
$231$	−7.80271	−	9.59635i	−0.513380	−	0.631393i
$232$		0			0
$233$		−	15.3574i		−	1.00610i	−0.864258	−	0.503049i	$-0.832212\pi$
$233$		−	15.3574i		−	1.00610i	0.864258	−	0.503049i	$-0.167788\pi$
$234$		0			0
$235$	−2.56626			−0.167405
$236$		0			0
$237$	17.6680	−	15.0950i	1.14766	−	0.980524i
$238$		0			0
$239$			22.0305i			1.42504i	0.701654	+	0.712518i	$0.252445\pi$
$239$			22.0305i			1.42504i	−0.701654	+	0.712518i	$0.747555\pi$
$240$		0			0
$241$			7.25586i			0.467391i	0.972310	+	0.233695i	$0.0750819\pi$
$241$			7.25586i			0.467391i	−0.972310	+	0.233695i	$0.924918\pi$
$242$		0			0
$243$	−14.3969	+	5.97737i	−0.923562	+	0.383448i
$244$		0			0
$245$	−6.99170	−	0.340784i	−0.446683	−	0.0217719i
$246$		0			0
$247$	21.3341			1.35746
$248$		0			0
$249$	−3.97109	+	3.39277i	−0.251658	+	0.215008i
$250$		0			0
$251$	7.87952			0.497351			0.248676	−	0.968587i	$-0.420005\pi$
$251$	7.87952			0.497351			0.248676	+	0.968587i	$0.420005\pi$
$252$		0			0
$253$	−6.92482			−0.435360
$254$		0			0
$255$	−9.26316	+	7.91414i	−0.580082	+	0.495603i
$256$		0			0
$257$	5.11492			0.319060			0.159530	−	0.987193i	$-0.449002\pi$
$257$	5.11492			0.319060			0.159530	+	0.987193i	$0.449002\pi$
$258$		0			0
$259$	−17.9774	−	0.437861i	−1.11706	−	0.0272073i
$260$		0			0
$261$	−24.3544	−	3.84909i	−1.50750	−	0.238253i
$262$		0			0
$263$			4.14488i			0.255584i	0.991801	+	0.127792i	$0.0407890\pi$
$263$			4.14488i			0.255584i	−0.991801	+	0.127792i	$0.959211\pi$
$264$		0			0
$265$			2.70121i			0.165934i
$266$		0			0
$267$	−5.49730	+	4.69671i	−0.336429	+	0.287434i
$268$		0			0
$269$	−25.3797			−1.54743			−0.773714	−	0.633535i	$-0.781603\pi$
$269$	−25.3797			−1.54743			−0.773714	+	0.633535i	$0.781603\pi$
$270$		0			0
$271$			4.50193i			0.273473i	0.990607	+	0.136736i	$0.0436613\pi$
$271$			4.50193i			0.273473i	−0.990607	+	0.136736i	$0.956339\pi$
$272$		0			0
$273$	19.1099	+	23.5028i	1.15659	+	1.42246i
$274$		0			0
$275$		−	2.69896i		−	0.162753i
$276$		0			0
$277$	4.75704			0.285823			0.142911	−	0.989736i	$-0.454354\pi$
$277$	4.75704			0.285823			0.142911	+	0.989736i	$0.454354\pi$
$278$		0			0
$279$	8.50466	+	1.34412i	0.509161	+	0.0804703i
$280$		0			0
$281$		−	10.5156i		−	0.627310i	−0.949537	−	0.313655i	$-0.898447\pi$
$281$		−	10.5156i		−	0.627310i	0.949537	−	0.313655i	$-0.101553\pi$
$282$		0			0
$283$		−	2.59242i		−	0.154103i	−0.997027	−	0.0770517i	$-0.975449\pi$
$283$		−	2.59242i		−	0.154103i	0.997027	−	0.0770517i	$-0.0245506\pi$
$284$		0			0
$285$	3.63122	+	4.25019i	0.215095	+	0.251760i
$286$		0			0
$287$	−26.5761	−	0.647290i	−1.56874	−	0.0382083i
$288$		0			0
$289$	32.4800			1.91059
$290$		0			0
$291$	−10.7466	−	12.5785i	−0.629979	−	0.737364i
$292$		0			0
$293$	−11.7742			−0.687856			−0.343928	−	0.938996i	$-0.611758\pi$
$293$	−11.7742			−0.687856			−0.343928	+	0.938996i	$0.611758\pi$
$294$		0			0
$295$	−3.03797			−0.176878
$296$		0			0
$297$	−11.9540	+	7.33357i	−0.693639	+	0.425537i
$298$		0			0
$299$	16.9599			0.980815
$300$		0			0
$301$	30.8613	+	0.751663i	1.77882	+	0.0433251i
$302$		0			0
$303$	−13.9390	+	11.9090i	−0.800776	+	0.684157i
$304$		0			0
$305$		−	7.83481i		−	0.448620i
$306$		0			0
$307$		−	27.4395i		−	1.56606i	−0.621986	−	0.783028i	$-0.713674\pi$
$307$		−	27.4395i		−	1.56606i	0.621986	−	0.783028i	$-0.286326\pi$
$308$		0			0
$309$	−2.13120	−	2.49448i	−0.121240	−	0.141906i
$310$		0			0
$311$	−15.5480			−0.881645			−0.440822	−	0.897594i	$-0.645313\pi$
$311$	−15.5480			−0.881645			−0.440822	+	0.897594i	$0.645313\pi$
$312$		0			0
$313$		−	12.6650i		−	0.715869i	−0.933747	−	0.357935i	$-0.883481\pi$
$313$		−	12.6650i		−	0.715869i	0.933747	−	0.357935i	$-0.116519\pi$
$314$		0			0
$315$	−1.42959	+	7.80745i	−0.0805483	+	0.439900i
$316$		0			0
$317$		−	18.2682i		−	1.02604i	−0.858376	−	0.513021i	$-0.828526\pi$
$317$		−	18.2682i		−	1.02604i	0.858376	−	0.513021i	$-0.171474\pi$
$318$		0			0
$319$	−22.1825			−1.24198
$320$		0			0
$321$	5.90789	+	6.91493i	0.329746	+	0.385954i
$322$		0			0
$323$		−	22.7027i		−	1.26321i
$324$		0			0
$325$			6.61014i			0.366665i
$326$		0			0
$327$	−3.34345	+	2.85654i	−0.184893	+	0.157967i
$328$		0			0
$329$	6.78768	+	0.165322i	0.374217	+	0.00911448i
$330$		0			0
$331$	−15.7692			−0.866751			−0.433376	−	0.901213i	$-0.642678\pi$
$331$	−15.7692			−0.866751			−0.433376	+	0.901213i	$0.642678\pi$
$332$		0			0
$333$	−3.18311	+	20.1405i	−0.174433	+	1.10369i
$334$		0			0
$335$	12.5077			0.683367
$336$		0			0
$337$	3.90831			0.212899			0.106450	−	0.994318i	$-0.466052\pi$
$337$	3.90831			0.212899			0.106450	+	0.994318i	$0.466052\pi$
$338$		0			0
$339$	9.82864	+	11.5040i	0.533819	+	0.624812i
$340$		0			0
$341$	7.74622			0.419481
$342$		0			0
$343$	18.4709	+	1.35178i	0.997333	+	0.0729890i
$344$		0			0
$345$	2.88670	+	3.37875i	0.155415	+	0.181906i
$346$		0			0
$347$		−	18.5501i		−	0.995821i	−0.867228	−	0.497911i	$-0.834101\pi$
$347$		−	18.5501i		−	0.995821i	0.867228	−	0.497911i	$-0.165899\pi$
$348$		0			0
$349$		−	27.1665i		−	1.45419i	−0.686537	−	0.727095i	$-0.740870\pi$
$349$		−	27.1665i		−	1.45419i	0.686537	−	0.727095i	$-0.259130\pi$
$350$		0			0
$351$	29.2770	−	17.9610i	1.56269	−	0.958685i
$352$		0			0
$353$	−29.1433			−1.55114			−0.775569	−	0.631262i	$-0.782537\pi$
$353$	−29.1433			−1.55114			−0.775569	+	0.631262i	$0.782537\pi$
$354$		0			0
$355$		−	14.0203i		−	0.744121i
$356$		0			0
$357$	25.0106	−	20.3359i	1.32370	−	1.07629i
$358$		0			0
$359$		−	23.0333i		−	1.21565i	−0.794070	−	0.607827i	$-0.792042\pi$
$359$		−	23.0333i		−	1.21565i	0.794070	−	0.607827i	$-0.207958\pi$
$360$		0			0
$361$	8.58337			0.451756
$362$		0			0
$363$	4.89300	−	4.18042i	0.256816	−	0.219415i
$364$		0			0
$365$			1.81228i			0.0948591i
$366$		0			0
$367$		−	21.3177i		−	1.11277i	−0.830923	−	0.556387i	$-0.812187\pi$
$367$		−	21.3177i		−	1.11277i	0.830923	−	0.556387i	$-0.187813\pi$
$368$		0			0
$369$	−4.70560	+	29.7738i	−0.244964	+	1.54996i
$370$		0			0
$371$	0.174015	−	7.14461i	0.00903442	−	0.370930i
$372$		0			0
$373$	1.49852			0.0775906			0.0387953	−	0.999247i	$-0.487648\pi$
$373$	1.49852			0.0775906			0.0387953	+	0.999247i	$0.487648\pi$
$374$		0			0
$375$	−1.31688	+	1.12510i	−0.0680032	+	0.0580997i
$376$		0			0
$377$	54.3281			2.79804
$378$		0			0
$379$	9.44524			0.485170			0.242585	−	0.970130i	$-0.422005\pi$
$379$	9.44524			0.485170			0.242585	+	0.970130i	$0.422005\pi$
$380$		0			0
$381$	10.1566	−	8.67748i	0.520339	−	0.444561i
$382$		0			0
$383$	22.6101			1.15532			0.577662	−	0.816276i	$-0.303965\pi$
$383$	22.6101			1.15532			0.577662	+	0.816276i	$0.303965\pi$
$384$		0			0
$385$	−0.173870	+	7.13866i	−0.00886124	+	0.363820i
$386$		0			0
$387$	5.46436	−	34.5747i	0.277769	−	1.75753i
$388$		0			0
$389$			19.4779i			0.987569i	0.869584	+	0.493784i	$0.164387\pi$
$389$			19.4779i			0.987569i	−0.869584	+	0.493784i	$0.835613\pi$
$390$		0			0
$391$		−	18.0479i		−	0.912721i
$392$		0			0
$393$	−3.84043	+	3.28113i	−0.193724	+	0.165511i
$394$		0			0
$395$	−13.4166			−0.675063
$396$		0			0
$397$		−	4.10316i		−	0.205932i	−0.994685	−	0.102966i	$-0.967167\pi$
$397$		−	4.10316i		−	0.205932i	0.994685	−	0.102966i	$-0.0328333\pi$
$398$		0			0
$399$	−9.33066	−	11.4755i	−0.467117	−	0.574496i
$400$		0			0
$401$		−	2.69031i		−	0.134348i	−0.997741	−	0.0671738i	$-0.978602\pi$
$401$		−	2.69031i		−	0.134348i	0.997741	−	0.0671738i	$-0.0213982\pi$
$402$		0			0
$403$	−18.9716			−0.945042
$404$		0			0
$405$	8.56135	+	2.77548i	0.425417	+	0.137915i
$406$		0			0
$407$			18.3444i			0.909298i
$408$		0			0
$409$		−	22.9345i		−	1.13404i	−0.823705	−	0.567019i	$-0.808097\pi$
$409$		−	22.9345i		−	1.13404i	0.823705	−	0.567019i	$-0.191903\pi$
$410$		0			0
$411$	21.0552	+	24.6442i	1.03858	+	1.21561i
$412$		0			0
$413$	8.03533	+	0.195710i	0.395393	+	0.00963024i
$414$		0			0
$415$	3.01554			0.148027
$416$		0			0
$417$	21.9959	+	25.7452i	1.07714	+	1.26075i
$418$		0			0
$419$	7.76656			0.379421			0.189711	−	0.981840i	$-0.439245\pi$
$419$	7.76656			0.379421			0.189711	+	0.981840i	$0.439245\pi$
$420$		0			0
$421$	3.86035			0.188142			0.0940710	−	0.995565i	$-0.470012\pi$
$421$	3.86035			0.188142			0.0940710	+	0.995565i	$0.470012\pi$
$422$		0			0
$423$	1.20184	−	7.60441i	0.0584354	−	0.369739i
$424$		0			0
$425$	7.03420			0.341209
$426$		0			0
$427$	−0.504728	+	20.7228i	−0.0244255	+	1.00285i
$428$		0			0
$429$	23.4937	−	20.0723i	1.13429	−	0.969098i
$430$		0			0
$431$			5.05754i			0.243613i	0.992554	+	0.121807i	$0.0388688\pi$
$431$			5.05754i			0.243613i	−0.992554	+	0.121807i	$0.961131\pi$
$432$		0			0
$433$			37.7647i			1.81486i	0.420208	+	0.907428i	$0.361957\pi$
$433$			37.7647i			1.81486i	−0.420208	+	0.907428i	$0.638043\pi$
$434$		0			0
$435$	9.24705	+	10.8233i	0.443362	+	0.518936i
$436$		0			0
$437$	−8.28086			−0.396127
$438$		0			0
$439$		−	7.03026i		−	0.335536i	−0.985827	−	0.167768i	$-0.946344\pi$
$439$		−	7.03026i		−	0.335536i	0.985827	−	0.167768i	$-0.0536559\pi$
$440$		0			0
$441$	4.28419	−	20.5584i	0.204009	−	0.978969i
$442$		0			0
$443$		−	24.2815i		−	1.15365i	−0.816869	−	0.576824i	$-0.804292\pi$
$443$		−	24.2815i		−	1.15365i	0.816869	−	0.576824i	$-0.195708\pi$
$444$		0			0
$445$	4.17450			0.197890
$446$		0			0
$447$	−3.77330	−	4.41649i	−0.178471	−	0.208893i
$448$		0			0
$449$			19.0341i			0.898276i	0.893462	+	0.449138i	$0.148269\pi$
$449$			19.0341i			0.898276i	−0.893462	+	0.449138i	$0.851731\pi$
$450$		0			0
$451$			27.1186i			1.27696i
$452$		0			0
$453$	−8.16482	+	6.97575i	−0.383617	+	0.327750i
$454$		0			0
$455$	0.425833	−	17.4836i	0.0199634	−	0.819644i
$456$		0			0
$457$	7.29974			0.341467			0.170734	−	0.985317i	$-0.445386\pi$
$457$	7.29974			0.341467			0.170734	+	0.985317i	$0.445386\pi$
$458$		0			0
$459$	−19.1132	−	31.1552i	−0.892128	−	1.45420i
$460$		0			0
$461$	−22.3544			−1.04115			−0.520575	−	0.853816i	$-0.674282\pi$
$461$	−22.3544			−1.04115			−0.520575	+	0.853816i	$0.674282\pi$
$462$		0			0
$463$	8.45971			0.393156			0.196578	−	0.980488i	$-0.437017\pi$
$463$	8.45971			0.393156			0.196578	+	0.980488i	$0.437017\pi$
$464$		0			0
$465$	−3.22911	−	3.77953i	−0.149746	−	0.175272i
$466$		0			0
$467$	−11.9314			−0.552120			−0.276060	−	0.961140i	$-0.589029\pi$
$467$	−11.9314			−0.552120			−0.276060	+	0.961140i	$0.589029\pi$
$468$		0			0
$469$	−33.0824	−	0.805759i	−1.52760	−	0.0372065i
$470$		0			0
$471$	11.1404	+	13.0394i	0.513325	+	0.600824i
$472$		0			0
$473$		−	31.4913i		−	1.44797i
$474$		0			0
$475$		−	3.22748i		−	0.148087i
$476$		0			0
$477$	−8.00428	−	1.26504i	−0.366491	−	0.0579221i
$478$		0			0
$479$	16.4398			0.751155			0.375578	−	0.926791i	$-0.377444\pi$
$479$	16.4398			0.751155			0.375578	+	0.926791i	$0.377444\pi$
$480$		0			0
$481$		−	44.9281i		−	2.04854i
$482$		0			0
$483$	−7.41755	−	9.12266i	−0.337510	−	0.415095i
$484$		0			0
$485$			9.55176i			0.433723i
$486$		0			0
$487$	4.41408			0.200021			0.100011	−	0.994986i	$-0.468112\pi$
$487$	4.41408			0.200021			0.100011	+	0.994986i	$0.468112\pi$
$488$		0			0
$489$	−17.7716	+	15.1835i	−0.803659	+	0.686620i
$490$		0			0
$491$			15.2188i			0.686817i	0.939186	+	0.343408i	$0.111581\pi$
$491$			15.2188i			0.686817i	−0.939186	+	0.343408i	$0.888419\pi$
$492$		0			0
$493$		−	57.8134i		−	2.60378i
$494$		0			0
$495$	7.99761	+	1.26398i	0.359466	+	0.0568118i
$496$		0			0
$497$	−0.903206	+	37.0833i	−0.0405143	+	1.66341i
$498$		0			0
$499$	33.3095			1.49114			0.745570	−	0.666427i	$-0.232177\pi$
$499$	33.3095			1.49114			0.745570	+	0.666427i	$0.232177\pi$
$500$		0			0
$501$	5.80147	−	4.95659i	0.259191	−	0.221444i
$502$		0			0
$503$	9.24941			0.412411			0.206205	−	0.978509i	$-0.433889\pi$
$503$	9.24941			0.412411			0.206205	+	0.978509i	$0.433889\pi$
$504$		0			0
$505$	10.5849			0.471023
$506$		0			0
$507$	−40.4201	+	34.5336i	−1.79512	+	1.53369i
$508$		0			0
$509$	13.0016			0.576286			0.288143	−	0.957587i	$-0.406962\pi$
$509$	13.0016			0.576286			0.288143	+	0.957587i	$0.406962\pi$
$510$		0			0
$511$	0.116749	−	4.79342i	0.00516468	−	0.212048i
$512$		0			0
$513$	−14.2948	+	8.76965i	−0.631132	+	0.387190i
$514$		0			0
$515$			1.89424i			0.0834702i
$516$		0			0
$517$		−	6.92624i		−	0.304616i
$518$		0			0
$519$	−7.77076	+	6.63908i	−0.341099	+	0.291423i
$520$		0			0
$521$	1.37469			0.0602262			0.0301131	−	0.999546i	$-0.490413\pi$
$521$	1.37469			0.0602262			0.0301131	+	0.999546i	$0.490413\pi$
$522$		0			0
$523$		−	4.30714i		−	0.188338i	−0.995556	−	0.0941690i	$-0.969981\pi$
$523$		−	4.30714i		−	0.188338i	0.995556	−	0.0941690i	$-0.0300194\pi$
$524$		0			0
$525$	3.55557	−	2.89100i	0.155178	−	0.126174i
$526$		0			0
$527$			20.1887i			0.879432i
$528$		0			0
$529$	16.4170			0.713783
$530$		0			0
$531$	1.42275	−	9.00218i	0.0617421	−	0.390661i
$532$		0			0
$533$		−	66.4173i		−	2.87685i
$534$		0			0
$535$		−	5.25101i		−	0.227021i
$536$		0			0
$537$	8.25999	+	9.66796i	0.356445	+	0.417203i
$538$		0			0
$539$	0.919762	−	18.8703i	0.0396169	−	0.812802i
$540$		0			0
$541$	−13.7698			−0.592011			−0.296006	−	0.955186i	$-0.595655\pi$
$541$	−13.7698			−0.592011			−0.296006	+	0.955186i	$0.595655\pi$
$542$		0			0
$543$	19.1455	+	22.4090i	0.821611	+	0.961660i
$544$		0			0
$545$	2.53893			0.108756
$546$		0			0
$547$	11.9601			0.511375			0.255688	−	0.966759i	$-0.417698\pi$
$547$	11.9601			0.511375			0.255688	+	0.966759i	$0.417698\pi$
$548$		0			0
$549$	23.2163	+	3.66922i	0.990847	+	0.156598i
$550$		0			0
$551$	−26.5263			−1.13006
$552$		0			0
$553$	35.4865	+	0.864314i	1.50904	+	0.0367544i
$554$		0			0
$555$	8.95060	−	7.64709i	0.379932	−	0.324601i
$556$		0			0
$557$		−	8.97976i		−	0.380485i	−0.981737	−	0.190242i	$-0.939073\pi$
$557$		−	8.97976i		−	0.380485i	0.981737	−	0.190242i	$-0.0609274\pi$
$558$		0			0
$559$			77.1268i			3.26211i
$560$		0			0
$561$	−21.3600	−	25.0009i	−0.901818	−	1.05554i
$562$		0			0
$563$	−6.48868			−0.273465			−0.136733	−	0.990608i	$-0.543660\pi$
$563$	−6.48868			−0.273465			−0.136733	+	0.990608i	$0.543660\pi$
$564$		0			0
$565$		−	8.73583i		−	0.367519i
$566$		0			0
$567$	−22.4657	−	7.89259i	−0.943470	−	0.331458i
$568$		0			0
$569$			22.1663i			0.929260i	0.885505	+	0.464630i	$0.153813\pi$
$569$			22.1663i			0.929260i	−0.885505	+	0.464630i	$0.846187\pi$
$570$		0			0
$571$	−23.6346			−0.989077			−0.494539	−	0.869156i	$-0.664663\pi$
$571$	−23.6346			−0.989077			−0.494539	+	0.869156i	$0.664663\pi$
$572$		0			0
$573$	1.97015	+	2.30598i	0.0823043	+	0.0963336i
$574$		0			0
$575$		−	2.56574i		−	0.106999i
$576$		0			0
$577$			35.1403i			1.46291i	0.681890	+	0.731455i	$0.261158\pi$
$577$			35.1403i			1.46291i	−0.681890	+	0.731455i	$0.738842\pi$
$578$		0			0
$579$	−16.9535	+	14.4845i	−0.704564	+	0.601956i
$580$		0			0
$581$	−7.97600	−	0.194265i	−0.330900	−	0.00805945i
$582$		0			0
$583$	−7.29046			−0.301940
$584$		0			0
$585$	−19.5873	−	3.09567i	−0.809835	−	0.127990i
$586$		0			0
$587$	6.59955			0.272393			0.136196	−	0.990682i	$-0.456512\pi$
$587$	6.59955			0.272393			0.136196	+	0.990682i	$0.456512\pi$
$588$		0			0
$589$	9.26311			0.381680
$590$		0			0
$591$	8.92929	+	10.4514i	0.367302	+	0.429911i
$592$		0			0
$593$	9.20187			0.377876			0.188938	−	0.981989i	$-0.439496\pi$
$593$	9.20187			0.377876			0.188938	+	0.981989i	$0.439496\pi$
$594$		0			0
$595$	−18.6052	−	0.453151i	−0.762740	−	0.0185774i
$596$		0			0
$597$	−9.63359	−	11.2757i	−0.394277	−	0.461484i
$598$		0			0
$599$		−	23.7274i		−	0.969476i	−0.874659	−	0.484738i	$-0.838915\pi$
$599$		−	23.7274i		−	0.969476i	0.874659	−	0.484738i	$-0.161085\pi$
$600$		0			0
$601$			6.04185i			0.246452i	0.992379	+	0.123226i	$0.0393240\pi$
$601$			6.04185i			0.246452i	−0.992379	+	0.123226i	$0.960676\pi$
$602$		0			0
$603$	−5.85762	+	37.0630i	−0.238541	+	1.50932i
$604$		0			0
$605$	−3.71562			−0.151061
$606$		0			0
$607$		−	42.3266i		−	1.71799i	−0.511988	−	0.858993i	$-0.671091\pi$
$607$		−	42.3266i		−	1.71799i	0.511988	−	0.858993i	$-0.328909\pi$
$608$		0			0
$609$	−23.7609	−	29.2229i	−0.962840	−	1.18417i
$610$		0			0
$611$			16.9634i			0.686264i
$612$		0			0
$613$	26.8987			1.08643			0.543215	−	0.839594i	$-0.317207\pi$
$613$	26.8987			1.08643			0.543215	+	0.839594i	$0.317207\pi$
$614$		0			0
$615$	13.2317	−	11.3047i	0.533553	−	0.455850i
$616$		0			0
$617$		−	40.3624i		−	1.62493i	−0.583010	−	0.812465i	$-0.698125\pi$
$617$		−	40.3624i		−	1.62493i	0.583010	−	0.812465i	$-0.301875\pi$
$618$		0			0
$619$		−	24.1095i		−	0.969042i	−0.874780	−	0.484521i	$-0.838994\pi$
$619$		−	24.1095i		−	0.969042i	0.874780	−	0.484521i	$-0.161006\pi$
$620$		0			0
$621$	−11.3639	+	6.97157i	−0.456018	+	0.279760i
$622$		0			0
$623$	−11.0414	−	0.268926i	−0.442365	−	0.0107743i
$624$		0			0
$625$	1.00000			0.0400000
$626$		0			0
$627$	−11.4711	+	9.80052i	−0.458111	+	0.391395i
$628$		0			0
$629$	−47.8103			−1.90632
$630$		0			0
$631$	7.34458			0.292383			0.146191	−	0.989256i	$-0.453298\pi$
$631$	7.34458			0.292383			0.146191	+	0.989256i	$0.453298\pi$
$632$		0			0
$633$	−12.2569	+	10.4719i	−0.487170	+	0.416222i
$634$		0			0
$635$	−7.71266			−0.306068
$636$		0			0
$637$	−2.25263	+	46.2161i	−0.0892524	+	1.83115i
$638$		0			0
$639$	41.5453	+	6.56603i	1.64351	+	0.259748i
$640$		0			0
$641$			20.2949i			0.801601i	0.916165	+	0.400800i	$0.131268\pi$
$641$			20.2949i			0.801601i	−0.916165	+	0.400800i	$0.868732\pi$
$642$		0			0
$643$		−	43.6248i		−	1.72040i	−0.509961	−	0.860198i	$-0.670340\pi$
$643$		−	43.6248i		−	1.72040i	0.509961	−	0.860198i	$-0.329660\pi$
$644$		0			0
$645$	−15.3652	+	13.1276i	−0.605006	+	0.516897i
$646$		0			0
$647$	−17.1667			−0.674894			−0.337447	−	0.941345i	$-0.609563\pi$
$647$	−17.1667			−0.674894			−0.337447	+	0.941345i	$0.609563\pi$
$648$		0			0
$649$		−	8.19936i		−	0.321853i
$650$		0			0
$651$	8.29740	+	10.2048i	0.325201	+	0.399956i
$652$		0			0
$653$			19.3345i			0.756619i	0.925679	+	0.378309i	$0.123494\pi$
$653$			19.3345i			0.756619i	−0.925679	+	0.378309i	$0.876506\pi$
$654$		0			0
$655$	2.91632			0.113950
$656$		0			0
$657$	−5.37019	−	0.848731i	−0.209511	−	0.0331122i
$658$		0			0
$659$		−	1.43175i		−	0.0557731i	−0.999611	−	0.0278866i	$-0.991122\pi$
$659$		−	1.43175i		−	0.0557731i	0.999611	−	0.0278866i	$-0.00887772\pi$
$660$		0			0
$661$		−	33.9771i		−	1.32156i	−0.750582	−	0.660778i	$-0.770227\pi$
$661$		−	33.9771i		−	1.32156i	0.750582	−	0.660778i	$-0.229773\pi$
$662$		0			0
$663$	52.3136	+	61.2308i	2.03169	+	2.37801i
$664$		0			0
$665$	−0.207918	+	8.53658i	−0.00806272	+	0.331034i
$666$		0			0
$667$	−21.0875			−0.816513
$668$		0			0
$669$	22.4043	+	26.2232i	0.866199	+	1.01385i
$670$		0			0
$671$	21.1458			0.816326
$672$		0			0
$673$	−5.78793			−0.223108			−0.111554	−	0.993758i	$-0.535583\pi$
$673$	−5.78793			−0.223108			−0.111554	+	0.993758i	$0.535583\pi$
$674$		0			0
$675$	−2.71718	−	4.42910i	−0.104584	−	0.170476i
$676$		0			0
$677$	−21.3272			−0.819672			−0.409836	−	0.912159i	$-0.634414\pi$
$677$	−21.3272			−0.819672			−0.409836	+	0.912159i	$0.634414\pi$
$678$		0			0
$679$	0.615336	−	25.2641i	0.0236144	−	0.969547i
$680$		0			0
$681$	16.9860	−	14.5122i	0.650904	−	0.556111i
$682$		0			0
$683$			31.4723i			1.20425i	0.798401	+	0.602127i	$0.205680\pi$
$683$			31.4723i			1.20425i	−0.798401	+	0.602127i	$0.794320\pi$
$684$		0			0
$685$		−	18.7142i		−	0.715032i
$686$		0			0
$687$	−7.74575	−	9.06607i	−0.295519	−	0.345892i
$688$		0			0
$689$	17.8554			0.680236
$690$		0			0
$691$		−	35.8993i		−	1.36568i	−0.730570	−	0.682838i	$-0.760746\pi$
$691$		−	35.8993i		−	1.36568i	0.730570	−	0.682838i	$-0.239254\pi$
$692$		0			0
$693$	−21.0720	−	3.85841i	−0.800459	−	0.146569i
$694$		0			0
$695$		−	19.5502i		−	0.741582i
$696$		0			0
$697$	−70.6781			−2.67713
$698$		0			0
$699$	−17.2786	−	20.2238i	−0.653535	−	0.764934i
$700$		0			0
$701$			41.8942i			1.58232i	0.611609	+	0.791160i	$0.290523\pi$
$701$			41.8942i			1.58232i	−0.611609	+	0.791160i	$0.709477\pi$
$702$		0			0
$703$			21.9367i			0.827357i
$704$		0			0
$705$	−3.37945	+	2.88729i	−0.127277	+	0.108742i
$706$		0			0
$707$	−27.9968	−	0.681893i	−1.05293	−	0.0256452i
$708$		0			0
$709$	−28.6731			−1.07684			−0.538420	−	0.842676i	$-0.680979\pi$
$709$	−28.6731			−1.07684			−0.538420	+	0.842676i	$0.680979\pi$
$710$		0			0
$711$	6.28330	−	39.7564i	0.235642	−	1.49098i
$712$		0			0
$713$	7.36385			0.275778
$714$		0			0
$715$	−17.8405			−0.667197
$716$		0			0
$717$	24.7864	+	29.0114i	0.925666	+	1.08345i
$718$		0			0
$719$	−31.6353			−1.17980			−0.589899	−	0.807477i	$-0.700832\pi$
$719$	−31.6353			−1.17980			−0.589899	+	0.807477i	$0.700832\pi$
$720$		0			0
$721$	0.122029	−	5.01021i	0.00454461	−	0.186590i
$722$		0			0
$723$	8.16353	+	9.55506i	0.303605	+	0.355357i
$724$		0			0
$725$		−	8.21890i		−	0.305242i
$726$		0			0
$727$			3.14677i			0.116707i	0.998296	+	0.0583536i	$0.0185851\pi$
$727$			3.14677i			0.116707i	−0.998296	+	0.0583536i	$0.981415\pi$
$728$		0			0
$729$	−12.2338	+	24.0693i	−0.453105	+	0.891457i
$730$		0			0
$731$	82.0747			3.03564
$732$		0			0
$733$		−	12.4598i		−	0.460213i	−0.973165	−	0.230106i	$-0.926093\pi$
$733$		−	12.4598i		−	0.460213i	0.973165	−	0.230106i	$-0.0739074\pi$
$734$		0			0
$735$	−9.59061	+	7.41756i	−0.353755	+	0.273601i
$736$		0			0
$737$			33.7577i			1.24348i
$738$		0			0
$739$	23.1373			0.851118			0.425559	−	0.904931i	$-0.360077\pi$
$739$	23.1373			0.851118			0.425559	+	0.904931i	$0.360077\pi$
$740$		0			0
$741$	28.0943	−	24.0029i	1.03207	−	0.881768i
$742$		0			0
$743$			29.0418i			1.06544i	0.846292	+	0.532720i	$0.178830\pi$
$743$			29.0418i			1.06544i	−0.846292	+	0.532720i	$0.821170\pi$
$744$		0			0
$745$			3.35377i			0.122872i
$746$		0			0
$747$	−1.41224	+	8.93571i	−0.0516713	+	0.326940i
$748$		0			0
$749$	−0.338276	+	13.8887i	−0.0123603	+	0.507484i
$750$		0			0
$751$	−5.94574			−0.216963			−0.108482	−	0.994098i	$-0.534599\pi$
$751$	−5.94574			−0.216963			−0.108482	+	0.994098i	$0.534599\pi$
$752$		0			0
$753$	10.3764	−	8.86521i	0.378135	−	0.323066i
$754$		0			0
$755$	6.20015			0.225646
$756$		0			0
$757$	−43.8676			−1.59439			−0.797197	−	0.603719i	$-0.793685\pi$
$757$	−43.8676			−1.59439			−0.797197	+	0.603719i	$0.793685\pi$
$758$		0			0
$759$	−9.11912	+	7.79108i	−0.331003	+	0.282798i
$760$		0			0
$761$	26.6453			0.965893			0.482946	−	0.875650i	$-0.339567\pi$
$761$	26.6453			0.965893			0.482946	+	0.875650i	$0.339567\pi$
$762$		0			0
$763$	−6.71538	−	0.163561i	−0.243113	−	0.00592130i
$764$		0			0
$765$	−3.29427	+	20.8439i	−0.119105	+	0.753612i
$766$		0			0
$767$			20.0814i			0.725098i
$768$		0			0
$769$			18.3596i			0.662065i	0.943619	+	0.331032i	$0.107397\pi$
$769$			18.3596i			0.662065i	−0.943619	+	0.331032i	$0.892603\pi$
$770$		0			0
$771$	6.73571	−	5.75477i	0.242581	−	0.207253i
$772$		0			0
$773$	−2.57902			−0.0927610			−0.0463805	−	0.998924i	$-0.514769\pi$
$773$	−2.57902			−0.0927610			−0.0463805	+	0.998924i	$0.514769\pi$
$774$		0			0
$775$			2.87007i			0.103096i
$776$		0			0
$777$	−24.1667	+	19.6497i	−0.866974	+	0.704929i
$778$		0			0
$779$			32.4290i			1.16189i
$780$		0			0
$781$	37.8403			1.35403
$782$		0			0
$783$	−36.4023	+	22.3323i	−1.30091	+	0.798090i
$784$		0			0
$785$		−	9.90178i		−	0.353410i
$786$		0			0
$787$			31.5892i			1.12603i	0.826446	+	0.563016i	$0.190359\pi$
$787$			31.5892i			1.12603i	−0.826446	+	0.563016i	$0.809641\pi$
$788$		0			0
$789$	4.66338	+	5.45829i	0.166021	+	0.194320i
$790$		0			0
$791$	−0.562773	+	23.1060i	−0.0200099	+	0.821555i
$792$		0			0
$793$	−51.7892			−1.83909
$794$		0			0
$795$	3.03912	+	3.55716i	0.107786	+	0.126159i
$796$		0			0
$797$	17.2603			0.611393			0.305696	−	0.952129i	$-0.401111\pi$
$797$	17.2603			0.611393			0.305696	+	0.952129i	$0.401111\pi$
$798$		0			0
$799$	18.0516			0.638620
$800$		0			0
$801$	−1.95501	+	12.3700i	−0.0690769	+	0.437071i
$802$		0			0
$803$	−4.89127			−0.172609
$804$		0			0
$805$	−0.165288	+	6.78629i	−0.00582563	+	0.239185i
$806$		0			0
$807$	−33.4219	+	28.5546i	−1.17651	+	1.00517i
$808$		0			0
$809$		−	20.6539i		−	0.726152i	−0.931760	−	0.363076i	$-0.881727\pi$
$809$		−	20.6539i		−	0.726152i	0.931760	−	0.363076i	$-0.118273\pi$
$810$		0			0
$811$			21.0641i			0.739660i	0.929099	+	0.369830i	$0.120584\pi$
$811$			21.0641i			0.739660i	−0.929099	+	0.369830i	$0.879416\pi$
$812$		0			0
$813$	5.06510	+	5.92848i	0.177641	+	0.207921i
$814$		0			0
$815$	13.4953			0.472718
$816$		0			0
$817$		−	37.6581i		−	1.31749i
$818$		0			0
$819$	51.6083	+	9.44979i	1.80334	+	0.330202i
$820$		0			0
$821$		−	40.7909i		−	1.42361i	−0.702376	−	0.711806i	$-0.747877\pi$
$821$		−	40.7909i		−	1.42361i	0.702376	−	0.711806i	$-0.252123\pi$
$822$		0			0
$823$	−12.5422			−0.437194			−0.218597	−	0.975815i	$-0.570148\pi$
$823$	−12.5422			−0.437194			−0.218597	+	0.975815i	$0.570148\pi$
$824$		0			0
$825$	−3.03659	−	3.55419i	−0.105720	−	0.123741i
$826$		0			0
$827$			10.0641i			0.349964i	0.984572	+	0.174982i	$0.0559867\pi$
$827$			10.0641i			0.349964i	−0.984572	+	0.174982i	$0.944013\pi$
$828$		0			0
$829$			26.1382i			0.907816i	0.891049	+	0.453908i	$0.149971\pi$
$829$			26.1382i			0.907816i	−0.891049	+	0.453908i	$0.850029\pi$
$830$		0			0
$831$	6.26442	−	5.35212i	0.217310	−	0.185663i
$832$		0			0
$833$	49.1810	+	2.39714i	1.70402	+	0.0830560i
$834$		0			0
$835$	−4.40548			−0.152458
$836$		0			0
$837$	12.7118	−	7.79852i	0.439386	−	0.269556i
$838$		0			0
$839$	−35.0785			−1.21105			−0.605523	−	0.795828i	$-0.707036\pi$
$839$	−35.0785			−1.21105			−0.605523	+	0.795828i	$0.707036\pi$
$840$		0			0
$841$	−38.5504			−1.32932
$842$		0			0
$843$	−11.8311	−	13.8478i	−0.407484	−	0.476943i
$844$		0			0
$845$	30.6939			1.05590
$846$		0			0
$847$	9.82768	+	0.239364i	0.337683	+	0.00822465i
$848$		0			0
$849$	−2.91672	−	3.41389i	−0.100101	−	0.117165i
$850$		0			0
$851$			17.4389i			0.597798i
$852$		0			0
$853$			11.2995i			0.386889i	0.981111	+	0.193444i	$0.0619659\pi$
$853$			11.2995i			0.386889i	−0.981111	+	0.193444i	$0.938034\pi$
$854$		0			0
$855$	9.56374	+	1.51150i	0.327073	+	0.0516922i
$856$		0			0
$857$	−45.4081			−1.55111			−0.775556	−	0.631279i	$-0.782530\pi$
$857$	−45.4081			−1.55111			−0.775556	+	0.631279i	$0.782530\pi$
$858$		0			0
$859$			5.83938i			0.199237i	0.995026	+	0.0996186i	$0.0317623\pi$
$859$			5.83938i			0.199237i	−0.995026	+	0.0996186i	$0.968238\pi$
$860$		0			0
$861$	−35.7256	+	29.0482i	−1.21753	+	0.989960i
$862$		0			0
$863$		−	40.2731i		−	1.37091i	−0.728113	−	0.685457i	$-0.759603\pi$
$863$		−	40.2731i		−	1.37091i	0.728113	−	0.685457i	$-0.240397\pi$
$864$		0			0
$865$	5.90091			0.200637
$866$		0			0
$867$	42.7721	−	36.5430i	1.45262	−	1.24107i
$868$		0			0
$869$		−	36.2109i		−	1.22837i
$870$		0			0
$871$		−	82.6774i		−	2.80142i
$872$		0			0
$873$	−28.3040	−	4.47330i	−0.957944	−	0.151398i
$874$		0			0
$875$	−2.64497	−	0.0644212i	−0.0894162	−	0.00217783i
$876$		0			0
$877$	−31.2384			−1.05484			−0.527422	−	0.849603i	$-0.676841\pi$
$877$	−31.2384			−1.05484			−0.527422	+	0.849603i	$0.676841\pi$
$878$		0			0
$879$	−15.5052	+	13.2471i	−0.522976	+	0.446813i
$880$		0			0
$881$	31.3074			1.05477			0.527387	−	0.849625i	$-0.323172\pi$
$881$	31.3074			1.05477			0.527387	+	0.849625i	$0.323172\pi$
$882$		0			0
$883$	43.3854			1.46003			0.730017	−	0.683429i	$-0.239512\pi$
$883$	43.3854			1.46003			0.730017	+	0.683429i	$0.239512\pi$
$884$		0			0
$885$	−4.00063	+	3.41801i	−0.134480	+	0.114895i
$886$		0			0
$887$	−18.2749			−0.613609			−0.306805	−	0.951772i	$-0.599260\pi$
$887$	−18.2749			−0.613609			−0.306805	+	0.951772i	$0.599260\pi$
$888$		0			0
$889$	20.3997	+	0.496859i	0.684185	+	0.0166641i
$890$		0			0
$891$	−7.49092	+	23.1067i	−0.250955	+	0.774105i
$892$		0			0
$893$		−	8.28257i		−	0.277166i
$894$		0			0
$895$		−	7.34159i		−	0.245402i
$896$		0			0
$897$	22.3340	−	19.0815i	0.745712	−	0.637112i
$898$		0			0
$899$	23.5889			0.786733
$900$		0			0
$901$		−	19.0009i		−	0.633010i
$902$		0			0
$903$	41.4862	−	33.7321i	1.38058	−	1.12253i
$904$		0			0
$905$		−	17.0168i		−	0.565656i
$906$		0			0
$907$	41.4276			1.37558			0.687790	−	0.725910i	$-0.258581\pi$
$907$	41.4276			1.37558			0.687790	+	0.725910i	$0.258581\pi$
$908$		0			0
$909$	−4.95715	+	31.3655i	−0.164418	+	1.04033i
$910$		0			0
$911$			3.58416i			0.118748i	0.998236	+	0.0593742i	$0.0189105\pi$
$911$			3.58416i			0.118748i	−0.998236	+	0.0593742i	$0.981089\pi$
$912$		0			0
$913$			8.13882i			0.269356i
$914$		0			0
$915$	−8.81491	−	10.3175i	−0.291412	−	0.341085i
$916$		0			0
$917$	−7.71356	−	0.187873i	−0.254724	−	0.00620410i
$918$		0			0
$919$	−20.5460			−0.677749			−0.338874	−	0.940832i	$-0.610046\pi$
$919$	−20.5460			−0.677749			−0.338874	+	0.940832i	$0.610046\pi$
$920$		0			0
$921$	−30.8721	−	36.1344i	−1.01727	−	1.19067i
$922$		0			0
$923$	−92.6763			−3.05048
$924$		0			0
$925$	−6.79684			−0.223479
$926$		0			0
$927$	−5.61305	−	0.887115i	−0.184357	−	0.0291367i
$928$		0			0
$929$	20.6332			0.676953			0.338477	−	0.940975i	$-0.390088\pi$
$929$	20.6332			0.676953			0.338477	+	0.940975i	$0.390088\pi$
$930$		0			0
$931$	1.09987	−	22.5656i	0.0360469	−	0.739557i
$932$		0			0
$933$	−20.4747	+	17.4929i	−0.670313	+	0.572693i
$934$		0			0
$935$			18.9850i			0.620877i
$936$		0			0
$937$			18.9657i			0.619581i	0.950805	+	0.309791i	$0.100259\pi$
$937$			18.9657i			0.619581i	−0.950805	+	0.309791i	$0.899741\pi$
$938$		0			0
$939$	−14.2493	−	16.6782i	−0.465010	−	0.544274i
$940$		0			0
$941$	21.1459			0.689337			0.344668	−	0.938725i	$-0.387991\pi$
$941$	21.1459			0.689337			0.344668	+	0.938725i	$0.387991\pi$
$942$		0			0
$943$			25.7800i			0.839511i
$944$		0			0
$945$	6.90153	+	11.8899i	0.224507	+	0.386777i
$946$		0			0
$947$			43.7955i			1.42316i	0.702604	+	0.711581i	$0.252021\pi$
$947$			43.7955i			1.42316i	−0.702604	+	0.711581i	$0.747979\pi$
$948$		0			0
$949$	11.9794			0.388869
$950$		0			0
$951$	−20.5534	−	24.0569i	−0.666490	−	0.780098i
$952$		0			0
$953$		−	22.0324i		−	0.713701i	−0.934162	−	0.356850i	$-0.883851\pi$
$953$		−	22.0324i		−	0.713701i	0.934162	−	0.356850i	$-0.116149\pi$
$954$		0			0
$955$		−	1.75110i		−	0.0566642i
$956$		0			0
$957$	−29.2116	+	24.9574i	−0.944276	+	0.806758i
$958$		0			0
$959$	−1.20559	+	49.4984i	−0.0389305	+	1.59839i
$960$		0			0
$961$	22.7627			0.734280
$962$		0			0
$963$	15.5599	+	2.45916i	0.501411	+	0.0792455i
$964$		0			0
$965$	12.8740			0.414430
$966$		0			0
$967$	32.8422			1.05613			0.528066	−	0.849203i	$-0.322917\pi$
$967$	32.8422			1.05613			0.528066	+	0.849203i	$0.322917\pi$
$968$		0			0
$969$	−25.5427	−	29.8967i	−0.820551	−	0.960420i
$970$		0			0
$971$	37.7928			1.21283			0.606414	−	0.795149i	$-0.292607\pi$
$971$	37.7928			1.21283			0.606414	+	0.795149i	$0.292607\pi$
$972$		0			0
$973$	−1.25945	+	51.7097i	−0.0403761	+	1.65774i
$974$		0			0
$975$	7.43703	+	8.70473i	0.238176	+	0.278774i
$976$		0			0
$977$		−	15.8791i		−	0.508017i	−0.967202	−	0.254008i	$-0.918251\pi$
$977$		−	15.8791i		−	0.508017i	0.967202	−	0.254008i	$-0.0817491\pi$
$978$		0			0
$979$			11.2668i			0.360089i
$980$		0			0
$981$	−1.18904	+	7.52341i	−0.0379630	+	0.240204i
$982$		0			0
$983$	21.7320			0.693142			0.346571	−	0.938024i	$-0.387346\pi$
$983$	21.7320			0.693142			0.346571	+	0.938024i	$0.387346\pi$
$984$		0			0
$985$		−	7.93648i		−	0.252877i
$986$		0			0
$987$	9.12454	−	7.41908i	0.290437	−	0.236152i
$988$		0			0
$989$		−	29.9369i		−	0.951937i
$990$		0			0
$991$	−33.1739			−1.05380			−0.526902	−	0.849926i	$-0.676646\pi$
$991$	−33.1739			−1.05380			−0.526902	+	0.849926i	$0.676646\pi$
$992$		0			0
$993$	−20.7660	+	17.7418i	−0.658990	+	0.563019i
$994$		0			0
$995$			8.56247i			0.271449i
$996$		0			0
$997$			3.50680i			0.111061i	0.998457	+	0.0555307i	$0.0176851\pi$
$997$			3.50680i			0.111061i	−0.998457	+	0.0555307i	$0.982315\pi$
$998$		0			0
$999$	18.4683	+	30.1039i	0.584310	+	0.952445i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.f.a.41.13	✓	16
3.2	odd	2		840.2.f.b.41.3	yes	16
4.3	odd	2		1680.2.f.k.881.4		16
7.6	odd	2		840.2.f.b.41.4	yes	16
12.11	even	2		1680.2.f.l.881.14		16
21.20	even	2	inner	840.2.f.a.41.14	yes	16
28.27	even	2		1680.2.f.l.881.13		16
84.83	odd	2		1680.2.f.k.881.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.f.a.41.13	✓	16	1.1	even	1	trivial
840.2.f.a.41.14	yes	16	21.20	even	2	inner
840.2.f.b.41.3	yes	16	3.2	odd	2
840.2.f.b.41.4	yes	16	7.6	odd	2
1680.2.f.k.881.3		16	84.83	odd	2
1680.2.f.k.881.4		16	4.3	odd	2
1680.2.f.l.881.13		16	28.27	even	2
1680.2.f.l.881.14		16	12.11	even	2

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.31688 - 1.12510i) q^{3} -1.00000 q^{5} +(2.64497 + 0.0644212i) q^{7} +(0.468322 - 2.96322i) q^{9} -2.69896i q^{11} +6.61014i q^{13} +(-1.31688 + 1.12510i) q^{15} +7.03420 q^{17} -3.22748i q^{19} +(3.55557 - 2.89100i) q^{21} -2.56574i q^{23} +1.00000 q^{25} +(-2.71718 - 4.42910i) q^{27} -8.21890i q^{29} +2.87007i q^{31} +(-3.03659 - 3.55419i) q^{33} +(-2.64497 - 0.0644212i) q^{35} -6.79684 q^{37} +(7.43703 + 8.70473i) q^{39} -10.0478 q^{41} +11.6680 q^{43} +(-0.468322 + 2.96322i) q^{45} +2.56626 q^{47} +(6.99170 + 0.340784i) q^{49} +(9.26316 - 7.91414i) q^{51} -2.70121i q^{53} +2.69896i q^{55} +(-3.63122 - 4.25019i) q^{57} +3.03797 q^{59} +7.83481i q^{61} +(1.42959 - 7.80745i) q^{63} -6.61014i q^{65} -12.5077 q^{67} +(-2.88670 - 3.37875i) q^{69} +14.0203i q^{71} -1.81228i q^{73} +(1.31688 - 1.12510i) q^{75} +(0.173870 - 7.13866i) q^{77} +13.4166 q^{79} +(-8.56135 - 2.77548i) q^{81} -3.01554 q^{83} -7.03420 q^{85} +(-9.24705 - 10.8233i) q^{87} -4.17450 q^{89} +(-0.425833 + 17.4836i) q^{91} +(3.22911 + 3.77953i) q^{93} +3.22748i q^{95} -9.55176i q^{97} +(-7.99761 - 1.26398i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{5} + 2 q^{7} - 2 q^{9} + 2 q^{21} + 16 q^{25} - 6 q^{27} - 6 q^{33} - 2 q^{35} + 12 q^{37} + 6 q^{39} - 32 q^{41} + 32 q^{43} + 2 q^{45} - 4 q^{47} - 4 q^{49} + 6 q^{51} + 24 q^{59} - 4 q^{63}+ \cdots - 58 q^{99}+O(q^{100}) \) 16 * q - 16 * q^5 + 2 * q^7 - 2 * q^9 + 2 * q^21 + 16 * q^25 - 6 * q^27 - 6 * q^33 - 2 * q^35 + 12 * q^37 + 6 * q^39 - 32 * q^41 + 32 * q^43 + 2 * q^45 - 4 * q^47 - 4 * q^49 + 6 * q^51 + 24 * q^59 - 4 * q^63 - 8 * q^69 + 32 * q^77 - 4 * q^79 - 6 * q^81 - 20 * q^83 - 6 * q^87 + 24 * q^89 + 20 * q^91 - 32 * q^93 - 58 * q^99

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