LMFDB - Embedded newform 2112.2.b.u.65.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2112,2,Mod(65,2112)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2112, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2112.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2112 = 2^{6} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2112.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$16.8644049069$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1544804416.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 39x^{4} + 46x^{2} + 4 $ x^8 + 11x^6 + 39x^4 + 46*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 1056)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			65.4
Root			$-1.58495i$ of defining polynomial
Character	$\chi$	$=$	2112.65
Dual form			2112.2.b.u.65.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26870 + 1.17915i) q^{3} +3.83206i q^{5} +3.02045i q^{7} +(0.219224 - 2.99198i) q^{9} +O(q^{10})$	\(q+(-1.26870 + 1.17915i) q^{3} +3.83206i q^{5} +3.02045i q^{7} +(0.219224 - 2.99198i) q^{9} +(3.24985 + 0.662153i) q^{11} +2.15190i q^{13} +(-4.51856 - 4.86175i) q^{15} -7.12311 q^{17} +4.71659i q^{19} +(-3.56155 - 3.83206i) q^{21} +4.05444i q^{23} -9.68466 q^{25} +(3.24985 + 4.05444i) q^{27} -5.12311 q^{29} +9.03712 q^{31} +(-4.90388 + 2.99198i) q^{33} -11.5745 q^{35} +6.68466 q^{37} +(-2.53741 - 2.73013i) q^{39} +6.00000 q^{41} +8.68951i q^{43} +(11.4654 + 0.840077i) q^{45} -0.371834i q^{47} -2.12311 q^{49} +(9.03712 - 8.39919i) q^{51} +5.51221i q^{53} +(-2.53741 + 12.4536i) q^{55} +(-5.56155 - 5.98396i) q^{57} -8.39919i q^{59} -5.51221i q^{61} +(9.03712 + 0.662153i) q^{63} -8.24621 q^{65} -3.96230 q^{67} +(-4.78078 - 5.14388i) q^{69} +5.37874i q^{71} -11.9679i q^{73} +(12.2870 - 11.4196i) q^{75} +(-2.00000 + 9.81602i) q^{77} -6.99337i q^{79} +(-8.90388 - 1.31182i) q^{81} +10.1496 q^{83} -27.2961i q^{85} +(6.49971 - 6.04090i) q^{87} -5.98396i q^{89} -6.49971 q^{91} +(-11.4654 + 10.6561i) q^{93} -18.0742 q^{95} -1.56155 q^{97} +(2.69359 - 9.57834i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{9}+O(q^{10}) $ 8 * q + 10 * q^9	$ 8 q + 10 q^{9} - 24 q^{17} - 12 q^{21} - 28 q^{25} - 8 q^{29} + 2 q^{33} + 4 q^{37} + 48 q^{41} + 34 q^{45} + 16 q^{49} - 28 q^{57} - 30 q^{69} - 16 q^{77} - 30 q^{81} - 34 q^{93} + 4 q^{97}+O(q^{100}) $ 8 * q + 10 * q^9 - 24 * q^17 - 12 * q^21 - 28 * q^25 - 8 * q^29 + 2 * q^33 + 4 * q^37 + 48 * q^41 + 34 * q^45 + 16 * q^49 - 28 * q^57 - 30 * q^69 - 16 * q^77 - 30 * q^81 - 34 * q^93 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2112\mathbb{Z}\right)^\times$.

$n$	$133$	$1409$	$1729$	$2047$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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
$3$	−1.26870	+	1.17915i	−0.732487	+	0.680781i
$3$	−1.26870	+	1.17915i	−0.732487	+	0.680781i
$4$		0			0
$5$			3.83206i			1.71375i	0.515526	+	0.856874i	$0.327597\pi$
$5$			3.83206i			1.71375i	−0.515526	+	0.856874i	$0.672403\pi$
$6$		0			0
$7$			3.02045i			1.14162i	0.821081	+	0.570811i	$0.193371\pi$
$7$			3.02045i			1.14162i	−0.821081	+	0.570811i	$0.806629\pi$
$8$		0			0
$9$	0.219224	−	2.99198i	0.0730745	−	0.997326i
$10$		0			0
$11$	3.24985	+	0.662153i	0.979868	+	0.199647i
$11$	3.24985	+	0.662153i	0.979868	+	0.199647i
$12$		0			0
$13$			2.15190i			0.596830i	0.954436	+	0.298415i	$0.0964580\pi$
$13$			2.15190i			0.596830i	−0.954436	+	0.298415i	$0.903542\pi$
$14$		0			0
$15$	−4.51856	−	4.86175i	−1.16669	−	1.25530i
$16$		0			0
$17$	−7.12311			−1.72761			−0.863803	−	0.503829i	$-0.831924\pi$
$17$	−7.12311			−1.72761			−0.863803	+	0.503829i	$0.831924\pi$
$18$		0			0
$19$			4.71659i			1.08206i	0.841003	+	0.541030i	$0.181965\pi$
$19$			4.71659i			1.08206i	−0.841003	+	0.541030i	$0.818035\pi$
$20$		0			0
$21$	−3.56155	−	3.83206i	−0.777195	−	0.836223i
$22$		0			0
$23$			4.05444i			0.845408i	0.906268	+	0.422704i	$0.138919\pi$
$23$			4.05444i			0.845408i	−0.906268	+	0.422704i	$0.861081\pi$
$24$		0			0
$25$	−9.68466			−1.93693
$26$		0			0
$27$	3.24985	+	4.05444i	0.625435	+	0.780276i
$28$		0			0
$29$	−5.12311			−0.951337			−0.475668	−	0.879625i	$-0.657794\pi$
$29$	−5.12311			−0.951337			−0.475668	+	0.879625i	$0.657794\pi$
$30$		0			0
$31$	9.03712			1.62311			0.811557	−	0.584273i	$-0.198620\pi$
$31$	9.03712			1.62311			0.811557	+	0.584273i	$0.198620\pi$
$32$		0			0
$33$	−4.90388	+	2.99198i	−0.853656	+	0.520837i
$34$		0			0
$35$	−11.5745			−1.95645
$36$		0			0
$37$	6.68466			1.09895			0.549476	−	0.835510i	$-0.314828\pi$
$37$	6.68466			1.09895			0.549476	+	0.835510i	$0.314828\pi$
$38$		0			0
$39$	−2.53741	−	2.73013i	−0.406311	−	0.437170i
$40$		0			0
$41$	6.00000			0.937043			0.468521	−	0.883452i	$-0.344787\pi$
$41$	6.00000			0.937043			0.468521	+	0.883452i	$0.344787\pi$
$42$		0			0
$43$			8.68951i			1.32514i	0.749001	+	0.662569i	$0.230534\pi$
$43$			8.68951i			1.32514i	−0.749001	+	0.662569i	$0.769466\pi$
$44$		0			0
$45$	11.4654	+	0.840077i	1.70917	+	0.125231i
$46$		0			0
$47$		−	0.371834i		−	0.0542376i	−0.999632	−	0.0271188i	$-0.991367\pi$
$47$		−	0.371834i		−	0.0542376i	0.999632	−	0.0271188i	$-0.00863324\pi$
$48$		0			0
$49$	−2.12311			−0.303301
$50$		0			0
$51$	9.03712	−	8.39919i	1.26545	−	1.17612i
$52$		0			0
$53$			5.51221i			0.757160i	0.925568	+	0.378580i	$0.123588\pi$
$53$			5.51221i			0.757160i	−0.925568	+	0.378580i	$0.876412\pi$
$54$		0			0
$55$	−2.53741	+	12.4536i	−0.342144	+	1.67925i
$56$		0			0
$57$	−5.56155	−	5.98396i	−0.736646	−	0.792595i
$58$		0			0
$59$		−	8.39919i		−	1.09348i	−0.837302	−	0.546741i	$-0.815868\pi$
$59$		−	8.39919i		−	1.09348i	0.837302	−	0.546741i	$-0.184132\pi$
$60$		0			0
$61$		−	5.51221i		−	0.705766i	−0.935667	−	0.352883i	$-0.885201\pi$
$61$		−	5.51221i		−	0.705766i	0.935667	−	0.352883i	$-0.114799\pi$
$62$		0			0
$63$	9.03712	+	0.662153i	1.13857	+	0.0834235i
$64$		0			0
$65$	−8.24621			−1.02282
$66$		0			0
$67$	−3.96230			−0.484072			−0.242036	−	0.970267i	$-0.577815\pi$
$67$	−3.96230			−0.484072			−0.242036	+	0.970267i	$0.577815\pi$
$68$		0			0
$69$	−4.78078	−	5.14388i	−0.575538	−	0.619251i
$70$		0			0
$71$			5.37874i			0.638339i	0.947698	+	0.319170i	$0.103404\pi$
$71$			5.37874i			0.638339i	−0.947698	+	0.319170i	$0.896596\pi$
$72$		0			0
$73$		−	11.9679i		−	1.40074i	−0.713781	−	0.700369i	$-0.753019\pi$
$73$		−	11.9679i		−	1.40074i	0.713781	−	0.700369i	$-0.246981\pi$
$74$		0			0
$75$	12.2870	−	11.4196i	1.41878	−	1.31863i
$76$		0			0
$77$	−2.00000	+	9.81602i	−0.227921	+	1.11864i
$78$		0			0
$79$		−	6.99337i		−	0.786815i	−0.919364	−	0.393408i	$-0.871296\pi$
$79$		−	6.99337i		−	0.786815i	0.919364	−	0.393408i	$-0.128704\pi$
$80$		0			0
$81$	−8.90388	−	1.31182i	−0.989320	−	0.145758i
$82$		0			0
$83$	10.1496			1.11407			0.557034	−	0.830490i	$-0.311939\pi$
$83$	10.1496			1.11407			0.557034	+	0.830490i	$0.311939\pi$
$84$		0			0
$85$		−	27.2961i		−	2.96068i
$86$		0			0
$87$	6.49971	−	6.04090i	0.696842	−	0.647652i
$88$		0			0
$89$		−	5.98396i		−	0.634298i	−0.948376	−	0.317149i	$-0.897274\pi$
$89$		−	5.98396i		−	0.634298i	0.948376	−	0.317149i	$-0.102726\pi$
$90$		0			0
$91$	−6.49971			−0.681355
$92$		0			0
$93$	−11.4654	+	10.6561i	−1.18891	+	1.10499i
$94$		0			0
$95$	−18.0742			−1.85438
$96$		0			0
$97$	−1.56155			−0.158552			−0.0792758	−	0.996853i	$-0.525261\pi$
$97$	−1.56155			−0.158552			−0.0792758	+	0.996853i	$0.525261\pi$
$98$		0			0
$99$	2.69359	−	9.57834i	0.270716	−	0.962659i
$100$		0			0
$101$	−0.246211			−0.0244989			−0.0122495	−	0.999925i	$-0.503899\pi$
$101$	−0.246211			−0.0244989			−0.0122495	+	0.999925i	$0.503899\pi$
$102$		0			0
$103$	12.9994			1.28087			0.640435	−	0.768012i	$-0.278754\pi$
$103$	12.9994			1.28087			0.640435	+	0.768012i	$0.278754\pi$
$104$		0			0
$105$	14.6847	−	13.6481i	1.43308	−	1.33192i
$106$		0			0
$107$	−11.5745			−1.11895			−0.559476	−	0.828847i	$-0.688998\pi$
$107$	−11.5745			−1.11895			−0.559476	+	0.828847i	$0.688998\pi$
$108$		0			0
$109$			5.51221i			0.527974i	0.964526	+	0.263987i	$0.0850376\pi$
$109$			5.51221i			0.527974i	−0.964526	+	0.263987i	$0.914962\pi$
$110$		0			0
$111$	−8.48086	+	7.88220i	−0.804967	+	0.748145i
$112$		0			0
$113$		−	2.62365i		−	0.246812i	−0.992356	−	0.123406i	$-0.960618\pi$
$113$		−	2.62365i		−	0.246812i	0.992356	−	0.123406i	$-0.0393818\pi$
$114$		0			0
$115$	−15.5368			−1.44882
$116$		0			0
$117$	6.43845	+	0.471748i	0.595235	+	0.0436131i
$118$		0			0
$119$		−	21.5150i		−	1.97227i
$120$		0			0
$121$	10.1231	+	4.30380i	0.920282	+	0.391255i
$122$		0			0
$123$	−7.61223	+	7.07488i	−0.686372	+	0.637921i
$124$		0			0
$125$		−	17.9519i		−	1.60566i
$126$		0			0
$127$		−	6.41273i		−	0.569038i	−0.958670	−	0.284519i	$-0.908166\pi$
$127$		−	6.41273i		−	0.569038i	0.958670	−	0.284519i	$-0.0918338\pi$
$128$		0			0
$129$	−10.2462	−	11.0244i	−0.902129	−	0.970646i
$130$		0			0
$131$	−7.92460			−0.692375			−0.346188	−	0.938165i	$-0.612524\pi$
$131$	−7.92460			−0.692375			−0.346188	+	0.938165i	$0.612524\pi$
$132$		0			0
$133$	−14.2462			−1.23530
$134$		0			0
$135$	−15.5368	+	12.4536i	−1.33720	+	1.07184i
$136$		0			0
$137$		−	1.68015i		−	0.143545i	−0.997421	−	0.0717726i	$-0.977134\pi$
$137$		−	1.68015i		−	0.143545i	0.997421	−	0.0717726i	$-0.0228656\pi$
$138$		0			0
$139$		−	7.36520i		−	0.624708i	−0.949966	−	0.312354i	$-0.898882\pi$
$139$		−	7.36520i		−	0.624708i	0.949966	−	0.312354i	$-0.101118\pi$
$140$		0			0
$141$	0.438447	+	0.471748i	0.0369239	+	0.0397283i
$142$		0			0
$143$	−1.42489	+	6.99337i	−0.119155	+	0.584815i
$144$		0			0
$145$		−	19.6320i		−	1.63035i
$146$		0			0
$147$	2.69359	−	2.50345i	0.222164	−	0.206481i
$148$		0			0
$149$	−4.24621			−0.347863			−0.173932	−	0.984758i	$-0.555647\pi$
$149$	−4.24621			−0.347863			−0.173932	+	0.984758i	$0.555647\pi$
$150$		0			0
$151$			5.08842i			0.414090i	0.978331	+	0.207045i	$0.0663847\pi$
$151$			5.08842i			0.414090i	−0.978331	+	0.207045i	$0.933615\pi$
$152$		0			0
$153$	−1.56155	+	21.3122i	−0.126244	+	1.72299i
$154$		0			0
$155$			34.6307i			2.78161i
$156$		0			0
$157$	3.56155			0.284243			0.142121	−	0.989849i	$-0.454608\pi$
$157$	3.56155			0.284243			0.142121	+	0.989849i	$0.454608\pi$
$158$		0			0
$159$	−6.49971	−	6.99337i	−0.515460	−	0.554610i
$160$		0			0
$161$	−12.2462			−0.965137
$162$		0			0
$163$	16.6493			1.30408			0.652039	−	0.758186i	$-0.273914\pi$
$163$	16.6493			1.30408			0.652039	+	0.758186i	$0.273914\pi$
$164$		0			0
$165$	−11.4654	−	18.7920i	−0.892583	−	1.46295i
$166$		0			0
$167$	15.2245			1.17810			0.589052	−	0.808095i	$-0.299501\pi$
$167$	15.2245			1.17810			0.589052	+	0.808095i	$0.299501\pi$
$168$		0			0
$169$	8.36932			0.643794
$170$		0			0
$171$	14.1119	+	1.03399i	1.07917	+	0.0790710i
$172$		0			0
$173$	7.36932			0.560279			0.280139	−	0.959959i	$-0.409619\pi$
$173$	7.36932			0.560279			0.280139	+	0.959959i	$0.409619\pi$
$174$		0			0
$175$		−	29.2520i		−	2.21124i
$176$		0			0
$177$	9.90388	+	10.6561i	0.744421	+	0.800961i
$178$		0			0
$179$			16.3450i			1.22169i	0.791752	+	0.610843i	$0.209169\pi$
$179$			16.3450i			1.22169i	−0.791752	+	0.610843i	$0.790831\pi$
$180$		0			0
$181$	5.31534			0.395086			0.197543	−	0.980294i	$-0.436704\pi$
$181$	5.31534			0.395086			0.197543	+	0.980294i	$0.436704\pi$
$182$		0			0
$183$	6.49971	+	6.99337i	0.480472	+	0.516965i
$184$		0			0
$185$			25.6160i			1.88333i
$186$		0			0
$187$	−23.1491	−	4.71659i	−1.69283	−	0.344911i
$188$		0			0
$189$	−12.2462	+	9.81602i	−0.890781	+	0.714010i
$190$		0			0
$191$		−	4.05444i		−	0.293369i	−0.989183	−	0.146684i	$-0.953140\pi$
$191$		−	4.05444i		−	0.293369i	0.989183	−	0.146684i	$-0.0468602\pi$
$192$		0			0
$193$			4.30380i			0.309795i	0.987931	+	0.154897i	$0.0495047\pi$
$193$			4.30380i			0.309795i	−0.987931	+	0.154897i	$0.950495\pi$
$194$		0			0
$195$	10.4620	−	9.72350i	0.749200	−	0.696314i
$196$		0			0
$197$	−23.3693			−1.66499			−0.832497	−	0.554029i	$-0.813090\pi$
$197$	−23.3693			−1.66499			−0.832497	+	0.554029i	$0.813090\pi$
$198$		0			0
$199$	10.1496			0.719489			0.359744	−	0.933051i	$-0.382864\pi$
$199$	10.1496			0.719489			0.359744	+	0.933051i	$0.382864\pi$
$200$		0			0
$201$	5.02699	−	4.67213i	0.354576	−	0.329547i
$202$		0			0
$203$		−	15.4741i		−	1.08607i
$204$		0			0
$205$			22.9923i			1.60585i
$206$		0			0
$207$	12.1308	+	0.888828i	0.843148	+	0.0617778i
$208$		0			0
$209$	−3.12311	+	15.3282i	−0.216030	+	1.06028i
$210$		0			0
$211$		−	22.2586i		−	1.53235i	−0.642633	−	0.766174i	$-0.722158\pi$
$211$		−	22.2586i		−	1.53235i	0.642633	−	0.766174i	$-0.277842\pi$
$212$		0			0
$213$	−6.34233	−	6.82404i	−0.434569	−	0.467575i
$214$		0			0
$215$	−33.2987			−2.27095
$216$		0			0
$217$			27.2961i			1.85298i
$218$		0			0
$219$	14.1119	+	15.1838i	0.953596	+	1.02602i
$220$		0			0
$221$		−	15.3282i		−	1.03109i
$222$		0			0
$223$	3.96230			0.265335			0.132668	−	0.991161i	$-0.457646\pi$
$223$	3.96230			0.265335			0.132668	+	0.991161i	$0.457646\pi$
$224$		0			0
$225$	−2.12311	+	28.9763i	−0.141540	+	1.93175i
$226$		0			0
$227$	−1.42489			−0.0945732			−0.0472866	−	0.998881i	$-0.515057\pi$
$227$	−1.42489			−0.0945732			−0.0472866	+	0.998881i	$0.515057\pi$
$228$		0			0
$229$	−9.80776			−0.648115			−0.324058	−	0.946037i	$-0.605047\pi$
$229$	−9.80776			−0.648115			−0.324058	+	0.946037i	$0.605047\pi$
$230$		0			0
$231$	−9.03712	−	14.8119i	−0.594599	−	0.974553i
$232$		0			0
$233$	3.36932			0.220731			0.110366	−	0.993891i	$-0.464798\pi$
$233$	3.36932			0.220731			0.110366	+	0.993891i	$0.464798\pi$
$234$		0			0
$235$	1.42489			0.0929495
$236$		0			0
$237$	8.24621	+	8.87252i	0.535649	+	0.576332i
$238$		0			0
$239$	−2.84978			−0.184337			−0.0921684	−	0.995743i	$-0.529380\pi$
$239$	−2.84978			−0.184337			−0.0921684	+	0.995743i	$0.529380\pi$
$240$		0			0
$241$		−	11.0244i		−	0.710145i	−0.934839	−	0.355073i	$-0.884456\pi$
$241$		−	11.0244i		−	0.710145i	0.934839	−	0.355073i	$-0.115544\pi$
$242$		0			0
$243$	12.8432	−	8.83467i	0.823894	−	0.566744i
$244$		0			0
$245$		−	8.13586i		−	0.519781i
$246$		0			0
$247$	−10.1496			−0.645806
$248$		0			0
$249$	−12.8769	+	11.9679i	−0.816040	+	0.758436i
$250$		0			0
$251$		−	13.1158i		−	0.827861i	−0.910309	−	0.413930i	$-0.864156\pi$
$251$		−	13.1158i		−	0.827861i	0.910309	−	0.413930i	$-0.135844\pi$
$252$		0			0
$253$	−2.68466	+	13.1763i	−0.168783	+	0.828388i
$254$		0			0
$255$	32.1862	+	34.6307i	2.01558	+	2.16866i
$256$		0			0
$257$		−	23.9358i		−	1.49308i	−0.665343	−	0.746538i	$-0.731715\pi$
$257$		−	23.9358i		−	1.49308i	0.665343	−	0.746538i	$-0.268285\pi$
$258$		0			0
$259$			20.1907i			1.25459i
$260$		0			0
$261$	−1.12311	+	15.3282i	−0.0695185	+	0.948793i
$262$		0			0
$263$	−15.2245			−0.938780			−0.469390	−	0.882991i	$-0.655526\pi$
$263$	−15.2245			−0.938780			−0.469390	+	0.882991i	$0.655526\pi$
$264$		0			0
$265$	−21.1231			−1.29758
$266$		0			0
$267$	7.05597	+	7.59188i	0.431818	+	0.464615i
$268$		0			0
$269$		−	16.5366i		−	1.00826i	−0.863629	−	0.504128i	$-0.831814\pi$
$269$		−	16.5366i		−	1.00826i	0.863629	−	0.504128i	$-0.168186\pi$
$270$		0			0
$271$		−	5.66906i		−	0.344371i	−0.985065	−	0.172185i	$-0.944917\pi$
$271$		−	5.66906i		−	0.344371i	0.985065	−	0.172185i	$-0.0550828\pi$
$272$		0			0
$273$	8.24621	−	7.66411i	0.499083	−	0.463853i
$274$		0			0
$275$	−31.4737	−	6.41273i	−1.89794	−	0.386702i
$276$		0			0
$277$			14.1198i			0.848378i	0.905574	+	0.424189i	$0.139441\pi$
$277$			14.1198i			0.848378i	−0.905574	+	0.424189i	$0.860559\pi$
$278$		0			0
$279$	1.98115	−	27.0389i	0.118608	−	1.61877i
$280$		0			0
$281$	−1.75379			−0.104622			−0.0523111	−	0.998631i	$-0.516659\pi$
$281$	−1.75379			−0.104622			−0.0523111	+	0.998631i	$0.516659\pi$
$282$		0			0
$283$		−	16.9614i		−	1.00825i	−0.863630	−	0.504126i	$-0.831815\pi$
$283$		−	16.9614i		−	1.00825i	0.863630	−	0.504126i	$-0.168185\pi$
$284$		0			0
$285$	22.9309	−	21.3122i	1.35831	−	1.26242i
$286$		0			0
$287$			18.1227i			1.06975i
$288$		0			0
$289$	33.7386			1.98463
$290$		0			0
$291$	1.98115	−	1.84130i	0.116137	−	0.107939i
$292$		0			0
$293$	−20.2462			−1.18280			−0.591398	−	0.806380i	$-0.701424\pi$
$293$	−20.2462			−1.18280			−0.591398	+	0.806380i	$0.701424\pi$
$294$		0			0
$295$	32.1862			1.87395
$296$		0			0
$297$	7.87689	+	15.3282i	0.457064	+	0.889434i
$298$		0			0
$299$	−8.72475			−0.504565
$300$		0			0
$301$	−26.2462			−1.51281
$302$		0			0
$303$	0.312369	−	0.290319i	0.0179452	−	0.0166784i
$304$		0			0
$305$	21.1231			1.20951
$306$		0			0
$307$			8.85254i			0.505241i	0.967565	+	0.252621i	$0.0812924\pi$
$307$			8.85254i			0.505241i	−0.967565	+	0.252621i	$0.918708\pi$
$308$		0			0
$309$	−16.4924	+	15.3282i	−0.938221	+	0.871992i
$310$		0			0
$311$			33.2249i			1.88401i	0.335595	+	0.942006i	$0.391063\pi$
$311$			33.2249i			1.88401i	−0.335595	+	0.942006i	$0.608937\pi$
$312$		0			0
$313$	25.8078			1.45874			0.729371	−	0.684119i	$-0.239813\pi$
$313$	25.8078			1.45874			0.729371	+	0.684119i	$0.239813\pi$
$314$		0			0
$315$	−2.53741	+	34.6307i	−0.142967	+	1.95122i
$316$		0			0
$317$			20.1038i			1.12914i	0.825385	+	0.564570i	$0.190958\pi$
$317$			20.1038i			1.12914i	−0.825385	+	0.564570i	$0.809042\pi$
$318$		0			0
$319$	−16.6493	−	3.39228i	−0.932184	−	0.189931i
$320$		0			0
$321$	14.6847	−	13.6481i	0.819618	−	0.761761i
$322$		0			0
$323$		−	33.5968i		−	1.86937i
$324$		0			0
$325$		−	20.8404i		−	1.15602i
$326$		0			0
$327$	−6.49971	−	6.99337i	−0.359435	−	0.386734i
$328$		0			0
$329$	1.12311			0.0619188
$330$		0			0
$331$	−0.312369			−0.0171694			−0.00858469	−	0.999963i	$-0.502733\pi$
$331$	−0.312369			−0.0171694			−0.00858469	+	0.999963i	$0.502733\pi$
$332$		0			0
$333$	1.46543	−	20.0004i	0.0803053	−	1.09601i
$334$		0			0
$335$		−	15.1838i		−	0.829577i
$336$		0			0
$337$		−	11.9679i		−	0.651934i	−0.945381	−	0.325967i	$-0.894310\pi$
$337$		−	11.9679i		−	0.651934i	0.945381	−	0.325967i	$-0.105690\pi$
$338$		0			0
$339$	3.09367	+	3.32864i	0.168025	+	0.180787i
$340$		0			0
$341$	29.3693	+	5.98396i	1.59044	+	0.324050i
$342$		0			0
$343$			14.7304i			0.795367i
$344$		0			0
$345$	19.7116	−	18.3202i	1.06124	−	0.986327i
$346$		0			0
$347$	2.22504			0.119446			0.0597232	−	0.998215i	$-0.480978\pi$
$347$	2.22504			0.119446			0.0597232	+	0.998215i	$0.480978\pi$
$348$		0			0
$349$		−	21.7839i		−	1.16607i	−0.812448	−	0.583034i	$-0.801866\pi$
$349$		−	21.7839i		−	1.16607i	0.812448	−	0.583034i	$-0.198134\pi$
$350$		0			0
$351$	−8.72475	+	6.99337i	−0.465693	+	0.373278i
$352$		0			0
$353$		−	9.34427i		−	0.497345i	−0.968588	−	0.248673i	$-0.920006\pi$
$353$		−	9.34427i		−	0.497345i	0.968588	−	0.248673i	$-0.0799943\pi$
$354$		0			0
$355$	−20.6116			−1.09395
$356$		0			0
$357$	25.3693	+	27.2961i	1.34269	+	1.44467i
$358$		0			0
$359$	18.0742			0.953922			0.476961	−	0.878925i	$-0.341738\pi$
$359$	18.0742			0.953922			0.476961	+	0.878925i	$0.341738\pi$
$360$		0			0
$361$	−3.24621			−0.170853
$362$		0			0
$363$	−17.9181	+	6.47637i	−0.940454	+	0.339922i
$364$		0			0
$365$	45.8617			2.40051
$366$		0			0
$367$	−29.3364			−1.53135			−0.765674	−	0.643229i	$-0.777594\pi$
$367$	−29.3364			−1.53135			−0.765674	+	0.643229i	$0.777594\pi$
$368$		0			0
$369$	1.31534	−	17.9519i	0.0684739	−	0.934537i
$370$		0			0
$371$	−16.6493			−0.864391
$372$		0			0
$373$			28.5046i			1.47591i	0.674850	+	0.737955i	$0.264208\pi$
$373$			28.5046i			1.47591i	−0.674850	+	0.737955i	$0.735792\pi$
$374$		0			0
$375$	21.1679	+	22.7756i	1.09311	+	1.17613i
$376$		0			0
$377$		−	11.0244i		−	0.567787i
$378$		0			0
$379$	18.3866			0.944456			0.472228	−	0.881476i	$-0.343450\pi$
$379$	18.3866			0.944456			0.472228	+	0.881476i	$0.343450\pi$
$380$		0			0
$381$	7.56155	+	8.13586i	0.387390	+	0.416813i
$382$		0			0
$383$			20.2722i			1.03586i	0.855423	+	0.517930i	$0.173297\pi$
$383$			20.2722i			1.03586i	−0.855423	+	0.517930i	$0.826703\pi$
$384$		0			0
$385$	−37.6155	−	7.66411i	−1.91706	−	0.390599i
$386$		0			0
$387$	25.9988	+	1.90495i	1.32160	+	0.0968338i
$388$		0			0
$389$		−	0.471748i		−	0.0239186i	−0.999928	−	0.0119593i	$-0.996193\pi$
$389$		−	0.471748i		−	0.0239186i	0.999928	−	0.0119593i	$-0.00380685\pi$
$390$		0			0
$391$		−	28.8802i		−	1.46053i
$392$		0			0
$393$	10.0540	−	9.34427i	0.507156	−	0.471356i
$394$		0			0
$395$	26.7990			1.34840
$396$		0			0
$397$	6.49242			0.325845			0.162923	−	0.986639i	$-0.447908\pi$
$397$	6.49242			0.325845			0.162923	+	0.986639i	$0.447908\pi$
$398$		0			0
$399$	18.0742	−	16.7984i	0.904844	−	0.840971i
$400$		0			0
$401$			12.9114i			0.644765i	0.946609	+	0.322383i	$0.104484\pi$
$401$			12.9114i			0.644765i	−0.946609	+	0.322383i	$0.895516\pi$
$402$		0			0
$403$			19.4470i			0.968724i
$404$		0			0
$405$	5.02699	−	34.1202i	0.249793	−	1.69545i
$406$		0			0
$407$	21.7242	+	4.42627i	1.07683	+	0.219402i
$408$		0			0
$409$			34.9603i			1.72867i	0.502913	+	0.864337i	$0.332261\pi$
$409$			34.9603i			1.72867i	−0.502913	+	0.864337i	$0.667739\pi$
$410$		0			0
$411$	1.98115	+	2.13162i	0.0977229	+	0.105145i
$412$		0			0
$413$	25.3693			1.24834
$414$		0			0
$415$			38.8940i			1.90923i
$416$		0			0
$417$	8.68466	+	9.34427i	0.425290	+	0.457591i
$418$		0			0
$419$			0.580639i			0.0283661i	0.999899	+	0.0141830i	$0.00451475\pi$
$419$			0.580639i			0.0283661i	−0.999899	+	0.0141830i	$0.995485\pi$
$420$		0			0
$421$	8.24621			0.401896			0.200948	−	0.979602i	$-0.435598\pi$
$421$	8.24621			0.401896			0.200948	+	0.979602i	$0.435598\pi$
$422$		0			0
$423$	−1.11252	−	0.0815148i	−0.0540926	−	0.00396339i
$424$		0			0
$425$	68.9848			3.34626
$426$		0			0
$427$	16.6493			0.805718
$428$		0			0
$429$	−6.43845	−	10.5527i	−0.310851	−	0.509488i
$430$		0			0
$431$	−10.7744			−0.518983			−0.259492	−	0.965745i	$-0.583555\pi$
$431$	−10.7744			−0.518983			−0.259492	+	0.965745i	$0.583555\pi$
$432$		0			0
$433$	−22.6847			−1.09016			−0.545078	−	0.838386i	$-0.683500\pi$
$433$	−22.6847			−1.09016			−0.545078	+	0.838386i	$0.683500\pi$
$434$		0			0
$435$	23.1491	+	24.9073i	1.10991	+	1.19421i
$436$		0			0
$437$	−19.1231			−0.914782
$438$		0			0
$439$			28.5083i			1.36063i	0.732920	+	0.680314i	$0.238157\pi$
$439$			28.5083i			1.36063i	−0.732920	+	0.680314i	$0.761843\pi$
$440$		0			0
$441$	−0.465435	+	6.35229i	−0.0221636	+	0.302490i
$442$		0			0
$443$			2.52132i			0.119792i	0.998205	+	0.0598959i	$0.0190769\pi$
$443$			2.52132i			0.119792i	−0.998205	+	0.0598959i	$0.980923\pi$
$444$		0			0
$445$	22.9309			1.08703
$446$		0			0
$447$	5.38719	−	5.00691i	0.254805	−	0.236819i
$448$		0			0
$449$			5.04046i			0.237874i	0.992902	+	0.118937i	$0.0379487\pi$
$449$			5.04046i			0.237874i	−0.992902	+	0.118937i	$0.962051\pi$
$450$		0			0
$451$	19.4991	+	3.97292i	0.918178	+	0.187078i
$452$		0			0
$453$	−6.00000	−	6.45571i	−0.281905	−	0.303316i
$454$		0			0
$455$		−	24.9073i		−	1.16767i
$456$		0			0
$457$			26.3526i			1.23272i	0.787463	+	0.616362i	$0.211394\pi$
$457$			26.3526i			1.23272i	−0.787463	+	0.616362i	$0.788606\pi$
$458$		0			0
$459$	−23.1491	−	28.8802i	−1.08051	−	1.34801i
$460$		0			0
$461$	17.6155			0.820437			0.410218	−	0.911987i	$-0.365452\pi$
$461$	17.6155			0.820437			0.410218	+	0.911987i	$0.365452\pi$
$462$		0			0
$463$	6.18734			0.287550			0.143775	−	0.989610i	$-0.454076\pi$
$463$	6.18734			0.287550			0.143775	+	0.989610i	$0.454076\pi$
$464$		0			0
$465$	−40.8348	−	43.9362i	−1.89367	−	2.03749i
$466$		0			0
$467$			21.8053i			1.00903i	0.863403	+	0.504514i	$0.168328\pi$
$467$			21.8053i			1.00903i	−0.863403	+	0.504514i	$0.831672\pi$
$468$		0			0
$469$		−	11.9679i		−	0.552627i
$470$		0			0
$471$	−4.51856	+	4.19960i	−0.208204	+	0.193507i
$472$		0			0
$473$	−5.75379	+	28.2396i	−0.264559	+	1.29846i
$474$		0			0
$475$		−	45.6786i		−	2.09588i
$476$		0			0
$477$	16.4924	+	1.20841i	0.755136	+	0.0553291i
$478$		0			0
$479$	−25.3741			−1.15937			−0.579686	−	0.814840i	$-0.696825\pi$
$479$	−25.3741			−1.15937			−0.579686	+	0.814840i	$0.696825\pi$
$480$		0			0
$481$			14.3847i			0.655887i
$482$		0			0
$483$	15.5368	−	14.4401i	0.706950	−	0.657047i
$484$		0			0
$485$		−	5.98396i		−	0.271718i
$486$		0			0
$487$	−42.9606			−1.94673			−0.973364	−	0.229264i	$-0.926368\pi$
$487$	−42.9606			−1.94673			−0.973364	+	0.229264i	$0.926368\pi$
$488$		0			0
$489$	−21.1231	+	19.6320i	−0.955220	+	0.887791i
$490$		0			0
$491$	−6.49971			−0.293328			−0.146664	−	0.989186i	$-0.546854\pi$
$491$	−6.49971			−0.293328			−0.146664	+	0.989186i	$0.546854\pi$
$492$		0			0
$493$	36.4924			1.64354
$494$		0			0
$495$	36.7047	+	10.3220i	1.64976	+	0.463940i
$496$		0			0
$497$	−16.2462			−0.728742
$498$		0			0
$499$	−36.9486			−1.65405			−0.827024	−	0.562167i	$-0.809968\pi$
$499$	−36.9486			−1.65405			−0.827024	+	0.562167i	$0.809968\pi$
$500$		0			0
$501$	−19.3153	+	17.9519i	−0.862946	+	0.802031i
$502$		0			0
$503$	10.1496			0.452550			0.226275	−	0.974063i	$-0.427345\pi$
$503$	10.1496			0.452550			0.226275	+	0.974063i	$0.427345\pi$
$504$		0			0
$505$		−	0.943495i		−	0.0419850i
$506$		0			0
$507$	−10.6182	+	9.86866i	−0.471570	+	0.438282i
$508$		0			0
$509$			19.1603i			0.849265i	0.905366	+	0.424632i	$0.139597\pi$
$509$			19.1603i			0.849265i	−0.905366	+	0.424632i	$0.860403\pi$
$510$		0			0
$511$	36.1485			1.59911
$512$		0			0
$513$	−19.1231	+	15.3282i	−0.844306	+	0.676758i
$514$		0			0
$515$			49.8145i			2.19509i
$516$		0			0
$517$	0.246211	−	1.20841i	0.0108284	−	0.0531457i
$518$		0			0
$519$	−9.34949	+	8.68951i	−0.410397	+	0.381427i
$520$		0			0
$521$		−	28.9763i		−	1.26947i	−0.772728	−	0.634737i	$-0.781108\pi$
$521$		−	28.9763i		−	1.26947i	0.772728	−	0.634737i	$-0.218892\pi$
$522$		0			0
$523$			43.1930i			1.88870i	0.328947	+	0.944348i	$0.393306\pi$
$523$			43.1930i			1.88870i	−0.328947	+	0.944348i	$0.606694\pi$
$524$		0			0
$525$	34.4924	+	37.1122i	1.50537	+	1.61971i
$526$		0			0
$527$	−64.3723			−2.80410
$528$		0			0
$529$	6.56155			0.285285
$530$		0			0
$531$	−25.1302	−	1.84130i	−1.09056	−	0.0799056i
$532$		0			0
$533$			12.9114i			0.559255i
$534$		0			0
$535$		−	44.3542i		−	1.91760i
$536$		0			0
$537$	−19.2732	−	20.7370i	−0.831700	−	0.894868i
$538$		0			0
$539$	−6.89978	−	1.40582i	−0.297195	−	0.0605530i
$540$		0			0
$541$		−	6.45571i		−	0.277553i	−0.990324	−	0.138776i	$-0.955683\pi$
$541$		−	6.45571i		−	0.277553i	0.990324	−	0.138776i	$-0.0443169\pi$
$542$		0			0
$543$	−6.74360	+	6.26757i	−0.289396	+	0.268967i
$544$		0			0
$545$	−21.1231			−0.904814
$546$		0			0
$547$			16.2177i			0.693421i	0.937972	+	0.346710i	$0.112701\pi$
$547$			16.2177i			0.693421i	−0.937972	+	0.346710i	$0.887299\pi$
$548$		0			0
$549$	−16.4924	−	1.20841i	−0.703879	−	0.0515735i
$550$		0			0
$551$		−	24.1636i		−	1.02940i
$552$		0			0
$553$	21.1231			0.898246
$554$		0			0
$555$	−30.2050	−	32.4991i	−1.28213	−	1.37951i
$556$		0			0
$557$	18.9848			0.804414			0.402207	−	0.915549i	$-0.368243\pi$
$557$	18.9848			0.804414			0.402207	+	0.915549i	$0.368243\pi$
$558$		0			0
$559$	−18.6990			−0.790882
$560$		0			0
$561$	34.9309	−	21.3122i	1.47478	−	0.899801i
$562$		0			0
$563$	−39.7984			−1.67730			−0.838651	−	0.544669i	$-0.816655\pi$
$563$	−39.7984			−1.67730			−0.838651	+	0.544669i	$0.816655\pi$
$564$		0			0
$565$	10.0540			0.422974
$566$		0			0
$567$	3.96230	−	26.8937i	0.166401	−	1.12943i
$568$		0			0
$569$	−18.2462			−0.764921			−0.382460	−	0.923972i	$-0.624923\pi$
$569$	−18.2462			−0.764921			−0.382460	+	0.923972i	$0.624923\pi$
$570$		0			0
$571$		−	7.94584i		−	0.332523i	−0.986082	−	0.166262i	$-0.946830\pi$
$571$		−	7.94584i		−	0.332523i	0.986082	−	0.166262i	$-0.0531696\pi$
$572$		0			0
$573$	4.78078	+	5.14388i	0.199720	+	0.214889i
$574$		0			0
$575$		−	39.2658i		−	1.63750i
$576$		0			0
$577$	−19.4233			−0.808602			−0.404301	−	0.914626i	$-0.632485\pi$
$577$	−19.4233			−0.808602			−0.404301	+	0.914626i	$0.632485\pi$
$578$		0			0
$579$	−5.07482	−	5.46026i	−0.210902	−	0.226921i
$580$		0			0
$581$			30.6565i			1.27184i
$582$		0			0
$583$	−3.64993	+	17.9139i	−0.151165	+	0.741917i
$584$		0			0
$585$	−1.80776	+	24.6725i	−0.0747418	+	1.02008i
$586$		0			0
$587$		−	6.20393i		−	0.256063i	−0.991770	−	0.128032i	$-0.959134\pi$
$587$		−	6.20393i		−	0.256063i	0.991770	−	0.128032i	$-0.0408659\pi$
$588$		0			0
$589$			42.6244i			1.75631i
$590$		0			0
$591$	29.6488	−	27.5559i	1.21959	−	1.13350i
$592$		0			0
$593$	28.4924			1.17004			0.585022	−	0.811018i	$-0.301086\pi$
$593$	28.4924			1.17004			0.585022	+	0.811018i	$0.301086\pi$
$594$		0			0
$595$	82.4466			3.37998
$596$		0			0
$597$	−12.8769	+	11.9679i	−0.527016	+	0.489814i
$598$		0			0
$599$		−	16.5896i		−	0.677832i	−0.940817	−	0.338916i	$-0.889940\pi$
$599$		−	16.5896i		−	0.677832i	0.940817	−	0.338916i	$-0.110060\pi$
$600$		0			0
$601$			11.9679i			0.488182i	0.969752	+	0.244091i	$0.0784895\pi$
$601$			11.9679i			0.488182i	−0.969752	+	0.244091i	$0.921511\pi$
$602$		0			0
$603$	−0.868629	+	11.8551i	−0.0353733	+	0.482778i
$604$		0			0
$605$	−16.4924	+	38.7923i	−0.670512	+	1.57713i
$606$		0			0
$607$			32.6443i			1.32499i	0.749066	+	0.662495i	$0.230503\pi$
$607$			32.6443i			1.32499i	−0.749066	+	0.662495i	$0.769497\pi$
$608$		0			0
$609$	18.2462	+	19.6320i	0.739374	+	0.795530i
$610$		0			0
$611$	0.800151			0.0323706
$612$		0			0
$613$			38.0557i			1.53705i	0.639818	+	0.768527i	$0.279010\pi$
$613$			38.0557i			1.53705i	−0.639818	+	0.768527i	$0.720990\pi$
$614$		0			0
$615$	−27.1114	−	29.1705i	−1.09324	−	1.17627i
$616$		0			0
$617$		−	45.9847i		−	1.85127i	−0.378413	−	0.925637i	$-0.623530\pi$
$617$		−	45.9847i		−	1.85127i	0.378413	−	0.925637i	$-0.376470\pi$
$618$		0			0
$619$	42.3358			1.70162			0.850810	−	0.525474i	$-0.176112\pi$
$619$	42.3358			1.70162			0.850810	+	0.525474i	$0.176112\pi$
$620$		0			0
$621$	−16.4384	+	13.1763i	−0.659652	+	0.528748i
$622$		0			0
$623$	18.0742			0.724129
$624$		0			0
$625$	20.3693			0.814773
$626$		0			0
$627$	−14.1119	−	23.1296i	−0.563576	−	0.923707i
$628$		0			0
$629$	−47.6155			−1.89856
$630$		0			0
$631$	−27.1114			−1.07929			−0.539643	−	0.841894i	$-0.681441\pi$
$631$	−27.1114			−1.07929			−0.539643	+	0.841894i	$0.681441\pi$
$632$		0			0
$633$	26.2462	+	28.2396i	1.04319	+	1.12242i
$634$		0			0
$635$	24.5739			0.975187
$636$		0			0
$637$		−	4.56872i		−	0.181019i
$638$		0			0
$639$	16.0931	+	1.17915i	0.636633	+	0.0466463i
$640$		0			0
$641$			13.6481i			0.539066i	0.962991	+	0.269533i	$0.0868694\pi$
$641$			13.6481i			0.539066i	−0.962991	+	0.269533i	$0.913131\pi$
$642$		0			0
$643$	3.96230			0.156258			0.0781289	−	0.996943i	$-0.475105\pi$
$643$	3.96230			0.156258			0.0781289	+	0.996943i	$0.475105\pi$
$644$		0			0
$645$	42.2462	−	39.2641i	1.66344	−	1.54602i
$646$		0			0
$647$			46.3407i			1.82184i	0.412582	+	0.910921i	$0.364627\pi$
$647$			46.3407i			1.82184i	−0.412582	+	0.910921i	$0.635373\pi$
$648$		0			0
$649$	5.56155	−	27.2961i	0.218310	−	1.07147i
$650$		0			0
$651$	−32.1862	−	34.6307i	−1.26148	−	1.35729i
$652$		0			0
$653$		−	13.9130i		−	0.544457i	−0.962233	−	0.272229i	$-0.912239\pi$
$653$		−	13.9130i		−	0.544457i	0.962233	−	0.272229i	$-0.0877607\pi$
$654$		0			0
$655$		−	30.3675i		−	1.18656i
$656$		0			0
$657$	−35.8078	−	2.62365i	−1.39699	−	0.102358i
$658$		0			0
$659$	39.7984			1.55033			0.775163	−	0.631762i	$-0.217668\pi$
$659$	39.7984			1.55033			0.775163	+	0.631762i	$0.217668\pi$
$660$		0			0
$661$	32.0540			1.24676			0.623378	−	0.781921i	$-0.285760\pi$
$661$	32.0540			1.24676			0.623378	+	0.781921i	$0.285760\pi$
$662$		0			0
$663$	18.0742	+	19.4470i	0.701945	+	0.755259i
$664$		0			0
$665$		−	54.5923i		−	2.11700i
$666$		0			0
$667$		−	20.7713i		−	0.804268i
$668$		0			0
$669$	−5.02699	+	4.67213i	−0.194355	+	0.180635i
$670$		0			0
$671$	3.64993	−	17.9139i	0.140904	−	0.691558i
$672$		0			0
$673$			4.30380i			0.165899i	0.996554	+	0.0829497i	$0.0264341\pi$
$673$			4.30380i			0.165899i	−0.996554	+	0.0829497i	$0.973566\pi$
$674$		0			0
$675$	−31.4737	−	39.2658i	−1.21142	−	1.51134i
$676$		0			0
$677$	26.0000			0.999261			0.499631	−	0.866239i	$-0.333469\pi$
$677$	26.0000			0.999261			0.499631	+	0.866239i	$0.333469\pi$
$678$		0			0
$679$		−	4.71659i		−	0.181006i
$680$		0			0
$681$	1.80776	−	1.68015i	0.0692737	−	0.0643837i
$682$		0			0
$683$			20.9343i			0.801030i	0.916290	+	0.400515i	$0.131169\pi$
$683$			20.9343i			0.801030i	−0.916290	+	0.400515i	$0.868831\pi$
$684$		0			0
$685$	6.43845			0.246000
$686$		0			0
$687$	12.4432	−	11.5648i	0.474736	−	0.441225i
$688$		0			0
$689$	−11.8617			−0.451896
$690$		0			0
$691$	−1.73726			−0.0660884			−0.0330442	−	0.999454i	$-0.510520\pi$
$691$	−1.73726			−0.0660884			−0.0330442	+	0.999454i	$0.510520\pi$
$692$		0			0
$693$	28.9309	+	8.13586i	1.09899	+	0.309056i
$694$		0			0
$695$	28.2239			1.07059
$696$		0			0
$697$	−42.7386			−1.61884
$698$		0			0
$699$	−4.27467	+	3.97292i	−0.161683	+	0.150270i
$700$		0			0
$701$	−40.7386			−1.53868			−0.769338	−	0.638841i	$-0.779414\pi$
$701$	−40.7386			−1.53868			−0.769338	+	0.638841i	$0.779414\pi$
$702$		0			0
$703$			31.5288i			1.18913i
$704$		0			0
$705$	−1.80776	+	1.68015i	−0.0680843	+	0.0632783i
$706$		0			0
$707$		−	0.743668i		−	0.0279685i
$708$		0			0
$709$	−42.7926			−1.60711			−0.803555	−	0.595230i	$-0.797061\pi$
$709$	−42.7926			−1.60711			−0.803555	+	0.595230i	$0.797061\pi$
$710$		0			0
$711$	−20.9240	−	1.53311i	−0.784712	−	0.0574962i
$712$		0			0
$713$			36.6404i			1.37219i
$714$		0			0
$715$	−26.7990	−	5.46026i	−1.00223	−	0.204202i
$716$		0			0
$717$	3.61553	−	3.36031i	0.135024	−	0.125493i
$718$		0			0
$719$		−	8.93405i		−	0.333184i	−0.986026	−	0.166592i	$-0.946724\pi$
$719$		−	8.93405i		−	0.333184i	0.986026	−	0.166592i	$-0.0532763\pi$
$720$		0			0
$721$			39.2641i			1.46227i
$722$		0			0
$723$	12.9994	+	13.9867i	0.483454	+	0.520172i
$724$		0			0
$725$	49.6155			1.84267
$726$		0			0
$727$	39.4860			1.46446			0.732228	−	0.681060i	$-0.238481\pi$
$727$	39.4860			1.46446			0.732228	+	0.681060i	$0.238481\pi$
$728$		0			0
$729$	−5.87689	+	26.3526i	−0.217663	+	0.976024i
$730$		0			0
$731$		−	61.8963i		−	2.28932i
$732$		0			0
$733$		−	9.81602i		−	0.362563i	−0.983431	−	0.181281i	$-0.941976\pi$
$733$		−	9.81602i		−	0.362563i	0.983431	−	0.181281i	$-0.0580245\pi$
$734$		0			0
$735$	9.59338	+	10.3220i	0.353857	+	0.380733i
$736$		0			0
$737$	−12.8769	−	2.62365i	−0.474327	−	0.0966434i
$738$		0			0
$739$		−	32.8531i		−	1.20852i	−0.796787	−	0.604260i	$-0.793469\pi$
$739$		−	32.8531i		−	1.20852i	0.796787	−	0.604260i	$-0.206531\pi$
$740$		0			0
$741$	12.8769	−	11.9679i	0.473045	−	0.439652i
$742$		0			0
$743$	15.8492			0.581451			0.290725	−	0.956807i	$-0.406103\pi$
$743$	15.8492			0.581451			0.290725	+	0.956807i	$0.406103\pi$
$744$		0			0
$745$		−	16.2717i		−	0.596150i
$746$		0			0
$747$	2.22504	−	30.3675i	0.0814100	−	1.11109i
$748$		0			0
$749$		−	34.9603i		−	1.27742i
$750$		0			0
$751$	40.1108			1.46366			0.731831	−	0.681486i	$-0.238666\pi$
$751$	40.1108			1.46366			0.731831	+	0.681486i	$0.238666\pi$
$752$		0			0
$753$	15.4654	+	16.6401i	0.563592	+	0.606397i
$754$		0			0
$755$	−19.4991			−0.709646
$756$		0			0
$757$	−18.0000			−0.654221			−0.327111	−	0.944986i	$-0.606075\pi$
$757$	−18.0000			−0.654221			−0.327111	+	0.944986i	$0.606075\pi$
$758$		0			0
$759$	−12.1308	−	19.8825i	−0.440320	−	0.721688i
$760$		0			0
$761$	15.1231			0.548212			0.274106	−	0.961699i	$-0.411618\pi$
$761$	15.1231			0.548212			0.274106	+	0.961699i	$0.411618\pi$
$762$		0			0
$763$	−16.6493			−0.602747
$764$		0			0
$765$	−81.6695	−	5.98396i	−2.95277	−	0.216350i
$766$		0			0
$767$	18.0742			0.652623
$768$		0			0
$769$		−	53.6488i		−	1.93462i	−0.253587	−	0.967312i	$-0.581611\pi$
$769$		−	53.6488i		−	1.93462i	0.253587	−	0.967312i	$-0.418389\pi$
$770$		0			0
$771$	28.2239	+	30.3675i	1.01646	+	1.09366i
$772$		0			0
$773$		−	38.0557i		−	1.36877i	−0.729122	−	0.684383i	$-0.760071\pi$
$773$		−	38.0557i		−	1.36877i	0.729122	−	0.684383i	$-0.239929\pi$
$774$		0			0
$775$	−87.5214			−3.14386
$776$		0			0
$777$	−23.8078	−	25.6160i	−0.854099	−	0.918969i
$778$		0			0
$779$			28.2995i			1.01394i
$780$		0			0
$781$	−3.56155	+	17.4801i	−0.127442	+	0.625488i
$782$		0			0
$783$	−16.6493	−	20.7713i	−0.594999	−	0.742306i
$784$		0			0
$785$			13.6481i			0.487121i
$786$		0			0
$787$		−	24.9073i		−	0.887848i	−0.896065	−	0.443924i	$-0.853586\pi$
$787$		−	24.9073i		−	0.887848i	0.896065	−	0.443924i	$-0.146414\pi$
$788$		0			0
$789$	19.3153	−	17.9519i	0.687644	−	0.639104i
$790$		0			0
$791$	7.92460			0.281766
$792$		0			0
$793$	11.8617			0.421223
$794$		0			0
$795$	26.7990	−	24.9073i	0.950462	−	0.883369i
$796$		0			0
$797$		−	40.6793i		−	1.44093i	−0.693489	−	0.720467i	$-0.743927\pi$
$797$		−	40.6793i		−	1.44093i	0.693489	−	0.720467i	$-0.256073\pi$
$798$		0			0
$799$			2.64861i			0.0937012i
$800$		0			0
$801$	−17.9039	−	1.31182i	−0.632603	−	0.0463511i
$802$		0			0
$803$	7.92460	−	38.8940i	0.279653	−	1.37254i
$804$		0			0
$805$		−	46.9282i		−	1.65400i
$806$		0			0
$807$	19.4991	+	20.9801i	0.686402	+	0.738535i
$808$		0			0
$809$	−22.0000			−0.773479			−0.386739	−	0.922189i	$-0.626399\pi$
$809$	−22.0000			−0.773479			−0.386739	+	0.922189i	$0.626399\pi$
$810$		0			0
$811$			35.8278i			1.25808i	0.777372	+	0.629042i	$0.216552\pi$
$811$			35.8278i			1.25808i	−0.777372	+	0.629042i	$0.783448\pi$
$812$		0			0
$813$	6.68466	+	7.19237i	0.234441	+	0.252247i
$814$		0			0
$815$			63.8012i			2.23486i
$816$		0			0
$817$	−40.9848			−1.43388
$818$		0			0
$819$	−1.42489	+	19.4470i	−0.0497897	+	0.679533i
$820$		0			0
$821$	−20.6307			−0.720016			−0.360008	−	0.932949i	$-0.617226\pi$
$821$	−20.6307			−0.720016			−0.360008	+	0.932949i	$0.617226\pi$
$822$		0			0
$823$	−22.0365			−0.768145			−0.384073	−	0.923303i	$-0.625479\pi$
$823$	−22.0365			−0.768145			−0.384073	+	0.923303i	$0.625479\pi$
$824$		0			0
$825$	47.4924	−	28.9763i	1.65347	−	1.00883i
$826$		0			0
$827$	−2.22504			−0.0773722			−0.0386861	−	0.999251i	$-0.512317\pi$
$827$	−2.22504			−0.0773722			−0.0386861	+	0.999251i	$0.512317\pi$
$828$		0			0
$829$	0.438447			0.0152279			0.00761395	−	0.999971i	$-0.497576\pi$
$829$	0.438447			0.0152279			0.00761395	+	0.999971i	$0.497576\pi$
$830$		0			0
$831$	−16.6493	−	17.9139i	−0.577559	−	0.621426i
$832$		0			0
$833$	15.1231			0.523985
$834$		0			0
$835$			58.3410i			2.01897i
$836$		0			0
$837$	29.3693	+	36.6404i	1.01515	+	1.26648i
$838$		0			0
$839$			43.2745i			1.49400i	0.664823	+	0.747001i	$0.268507\pi$
$839$			43.2745i			1.49400i	−0.664823	+	0.747001i	$0.731493\pi$
$840$		0			0
$841$	−2.75379			−0.0949582
$842$		0			0
$843$	2.22504	−	2.06798i	0.0766345	−	0.0712248i
$844$		0			0
$845$			32.0717i			1.10330i
$846$		0			0
$847$	−12.9994	+	30.5763i	−0.446665	+	1.05061i
$848$		0			0
$849$	20.0000	+	21.5190i	0.686398	+	0.738531i
$850$		0			0
$851$			27.1025i			0.929062i
$852$		0			0
$853$		−	27.0312i		−	0.925532i	−0.886481	−	0.462766i	$-0.846857\pi$
$853$		−	27.0312i		−	0.925532i	0.886481	−	0.462766i	$-0.153143\pi$
$854$		0			0
$855$	−3.96230	+	54.0777i	−0.135508	+	1.84942i
$856$		0			0
$857$	−1.12311			−0.0383646			−0.0191823	−	0.999816i	$-0.506106\pi$
$857$	−1.12311			−0.0383646			−0.0191823	+	0.999816i	$0.506106\pi$
$858$		0			0
$859$	4.76245			0.162493			0.0812463	−	0.996694i	$-0.474110\pi$
$859$	4.76245			0.162493			0.0812463	+	0.996694i	$0.474110\pi$
$860$		0			0
$861$	−21.3693	−	22.9923i	−0.728264	−	0.783577i
$862$		0			0
$863$			10.5487i			0.359081i	0.983751	+	0.179541i	$0.0574611\pi$
$863$			10.5487i			0.359081i	−0.983751	+	0.179541i	$0.942539\pi$
$864$		0			0
$865$			28.2396i			0.960177i
$866$		0			0
$867$	−42.8044	+	39.7828i	−1.45371	+	1.35110i
$868$		0			0
$869$	4.63068	−	22.7274i	0.157085	−	0.770975i
$870$		0			0
$871$		−	8.52648i		−	0.288909i
$872$		0			0
$873$	−0.342329	+	4.67213i	−0.0115861	+	0.158128i
$874$		0			0
$875$	54.2227			1.83306
$876$		0			0
$877$			37.1122i			1.25319i	0.779346	+	0.626594i	$0.215552\pi$
$877$			37.1122i			1.25319i	−0.779346	+	0.626594i	$0.784448\pi$
$878$		0			0
$879$	25.6865	−	23.8733i	0.866383	−	0.805225i
$880$		0			0
$881$			48.6083i			1.63766i	0.574039	+	0.818828i	$0.305376\pi$
$881$			48.6083i			1.63766i	−0.574039	+	0.818828i	$0.694624\pi$
$882$		0			0
$883$	15.8492			0.533368			0.266684	−	0.963784i	$-0.414072\pi$
$883$	15.8492			0.533368			0.266684	+	0.963784i	$0.414072\pi$
$884$		0			0
$885$	−40.8348	+	37.9522i	−1.37265	+	1.27575i
$886$		0			0
$887$	−46.2981			−1.55454			−0.777269	−	0.629168i	$-0.783396\pi$
$887$	−46.2981			−1.55454			−0.777269	+	0.629168i	$0.783396\pi$
$888$		0			0
$889$	19.3693			0.649626
$890$		0			0
$891$	−28.0677	−	10.1590i	−0.940303	−	0.340339i
$892$		0			0
$893$	1.75379			0.0586883
$894$		0			0
$895$	−62.6351			−2.09366
$896$		0			0
$897$	11.0691	−	10.2878i	0.369588	−	0.343498i
$898$		0			0
$899$	−46.2981			−1.54413
$900$		0			0
$901$		−	39.2641i		−	1.30808i
$902$		0			0
$903$	33.2987	−	30.9481i	1.10811	−	1.02989i
$904$		0			0
$905$			20.3687i			0.677078i
$906$		0			0
$907$	−20.2993			−0.674026			−0.337013	−	0.941500i	$-0.609417\pi$
$907$	−20.2993			−0.674026			−0.337013	+	0.941500i	$0.609417\pi$
$908$		0			0
$909$	−0.0539753	+	0.736659i	−0.00179025	+	0.0244334i
$910$		0			0
$911$			37.3609i			1.23782i	0.785461	+	0.618911i	$0.212426\pi$
$911$			37.3609i			1.23782i	−0.785461	+	0.618911i	$0.787574\pi$
$912$		0			0
$913$	32.9848	+	6.72062i	1.09164	+	0.222420i
$914$		0			0
$915$	−26.7990	+	24.9073i	−0.885947	+	0.823408i
$916$		0			0
$917$		−	23.9358i		−	0.790431i
$918$		0			0
$919$		−	3.18348i		−	0.105013i	−0.998621	−	0.0525066i	$-0.983279\pi$
$919$		−	3.18348i		−	0.105013i	0.998621	−	0.0525066i	$-0.0167211\pi$
$920$		0			0
$921$	−10.4384	−	11.2313i	−0.343959	−	0.370083i
$922$		0			0
$923$	−11.5745			−0.380980
$924$		0			0
$925$	−64.7386			−2.12859
$926$		0			0
$927$	2.84978	−	38.8940i	0.0935990	−	1.27745i
$928$		0			0
$929$		−	4.30380i		−	0.141203i	−0.997505	−	0.0706016i	$-0.977508\pi$
$929$		−	4.30380i		−	0.141203i	0.997505	−	0.0706016i	$-0.0224919\pi$
$930$		0			0
$931$		−	10.0138i		−	0.328190i
$932$		0			0
$933$	−39.1771	−	42.1526i	−1.28260	−	1.38001i
$934$		0			0
$935$	18.0742	−	88.7085i	0.591091	−	2.90108i
$936$		0			0
$937$			5.24730i			0.171422i	0.996320	+	0.0857109i	$0.0273161\pi$
$937$			5.24730i			0.171422i	−0.996320	+	0.0857109i	$0.972684\pi$
$938$		0			0
$939$	−32.7424	+	30.4312i	−1.06851	+	0.993083i
$940$		0			0
$941$	17.1231			0.558197			0.279099	−	0.960262i	$-0.409964\pi$
$941$	17.1231			0.558197			0.279099	+	0.960262i	$0.409964\pi$
$942$		0			0
$943$			24.3266i			0.792184i
$944$		0			0
$945$	−37.6155	−	46.9282i	−1.22363	−	1.52657i
$946$		0			0
$947$		−	56.5633i		−	1.83806i	−0.394186	−	0.919031i	$-0.628974\pi$
$947$		−	56.5633i		−	1.83806i	0.394186	−	0.919031i	$-0.371026\pi$
$948$		0			0
$949$	25.7538			0.836003
$950$		0			0
$951$	−23.7053	−	25.5058i	−0.768698	−	0.827081i
$952$		0			0
$953$	19.7538			0.639888			0.319944	−	0.947436i	$-0.396336\pi$
$953$	19.7538			0.639888			0.319944	+	0.947436i	$0.396336\pi$
$954$		0			0
$955$	15.5368			0.502760
$956$		0			0
$957$	25.1231	−	15.3282i	0.812115	−	0.495491i
$958$		0			0
$959$	5.07482			0.163874
$960$		0			0
$961$	50.6695			1.63450
$962$		0			0
$963$	−2.53741	+	34.6307i	−0.0817669	+	1.11596i
$964$		0			0
$965$	−16.4924			−0.530910
$966$		0			0
$967$		−	45.4697i		−	1.46221i	−0.682266	−	0.731104i	$-0.739005\pi$
$967$		−	45.4697i		−	1.46221i	0.682266	−	0.731104i	$-0.260995\pi$
$968$		0			0
$969$	39.6155	+	42.6244i	1.27263	+	1.36929i
$970$		0			0
$971$		−	18.9936i		−	0.609535i	−0.952427	−	0.304768i	$-0.901421\pi$
$971$		−	18.9936i		−	0.609535i	0.952427	−	0.304768i	$-0.0985788\pi$
$972$		0			0
$973$	22.2462			0.713181
$974$		0			0
$975$	24.5739	+	26.4404i	0.786996	+	0.846769i
$976$		0			0
$977$		−	40.9442i		−	1.30992i	−0.755663	−	0.654961i	$-0.772685\pi$
$977$		−	40.9442i		−	1.30992i	0.755663	−	0.654961i	$-0.227315\pi$
$978$		0			0
$979$	3.96230	−	19.4470i	0.126636	−	0.621529i
$980$		0			0
$981$	16.4924	+	1.20841i	0.526563	+	0.0385815i
$982$		0			0
$983$		−	9.93230i		−	0.316791i	−0.987376	−	0.158396i	$-0.949368\pi$
$983$		−	9.93230i		−	0.316791i	0.987376	−	0.158396i	$-0.0506321\pi$
$984$		0			0
$985$		−	89.5525i		−	2.85338i
$986$		0			0
$987$	−1.42489	+	1.32431i	−0.0453547	+	0.0421532i
$988$		0			0
$989$	−35.2311			−1.12028
$990$		0			0
$991$	17.4495			0.554302			0.277151	−	0.960826i	$-0.410610\pi$
$991$	17.4495			0.554302			0.277151	+	0.960826i	$0.410610\pi$
$992$		0			0
$993$	0.396305	−	0.368330i	0.0125763	−	0.0116886i
$994$		0			0
$995$			38.8940i			1.23302i
$996$		0			0
$997$		−	43.8328i		−	1.38820i	−0.719880	−	0.694099i	$-0.755803\pi$
$997$		−	43.8328i		−	1.38820i	0.719880	−	0.694099i	$-0.244197\pi$
$998$		0			0
$999$	21.7242	+	27.1025i	0.687322	+	0.857486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2112.2.b.u.65.4		8
3.2	odd	2		2112.2.b.v.65.3		8
4.3	odd	2	inner	2112.2.b.u.65.5		8
8.3	odd	2		1056.2.b.i.65.4	yes	8
8.5	even	2		1056.2.b.i.65.5	yes	8
11.10	odd	2		2112.2.b.v.65.4		8
12.11	even	2		2112.2.b.v.65.6		8
24.5	odd	2		1056.2.b.j.65.6	yes	8
24.11	even	2		1056.2.b.j.65.3	yes	8
33.32	even	2	inner	2112.2.b.u.65.3		8
44.43	even	2		2112.2.b.v.65.5		8
88.21	odd	2		1056.2.b.j.65.5	yes	8
88.43	even	2		1056.2.b.j.65.4	yes	8
132.131	odd	2	inner	2112.2.b.u.65.6		8
264.131	odd	2		1056.2.b.i.65.3	✓	8
264.197	even	2		1056.2.b.i.65.6	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1056.2.b.i.65.3	✓	8	264.131	odd	2
1056.2.b.i.65.4	yes	8	8.3	odd	2
1056.2.b.i.65.5	yes	8	8.5	even	2
1056.2.b.i.65.6	yes	8	264.197	even	2
1056.2.b.j.65.3	yes	8	24.11	even	2
1056.2.b.j.65.4	yes	8	88.43	even	2
1056.2.b.j.65.5	yes	8	88.21	odd	2
1056.2.b.j.65.6	yes	8	24.5	odd	2
2112.2.b.u.65.3		8	33.32	even	2	inner
2112.2.b.u.65.4		8	1.1	even	1	trivial
2112.2.b.u.65.5		8	4.3	odd	2	inner
2112.2.b.u.65.6		8	132.131	odd	2	inner
2112.2.b.v.65.3		8	3.2	odd	2
2112.2.b.v.65.4		8	11.10	odd	2
2112.2.b.v.65.5		8	44.43	even	2
2112.2.b.v.65.6		8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 2112 = 2^{6} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2112.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.26870 + 1.17915i) q^{3} +3.83206i q^{5} +3.02045i q^{7} +(0.219224 - 2.99198i) q^{9} +O(q^{10})\)	\(q+(-1.26870 + 1.17915i) q^{3} +3.83206i q^{5} +3.02045i q^{7} +(0.219224 - 2.99198i) q^{9} +(3.24985 + 0.662153i) q^{11} +2.15190i q^{13} +(-4.51856 - 4.86175i) q^{15} -7.12311 q^{17} +4.71659i q^{19} +(-3.56155 - 3.83206i) q^{21} +4.05444i q^{23} -9.68466 q^{25} +(3.24985 + 4.05444i) q^{27} -5.12311 q^{29} +9.03712 q^{31} +(-4.90388 + 2.99198i) q^{33} -11.5745 q^{35} +6.68466 q^{37} +(-2.53741 - 2.73013i) q^{39} +6.00000 q^{41} +8.68951i q^{43} +(11.4654 + 0.840077i) q^{45} -0.371834i q^{47} -2.12311 q^{49} +(9.03712 - 8.39919i) q^{51} +5.51221i q^{53} +(-2.53741 + 12.4536i) q^{55} +(-5.56155 - 5.98396i) q^{57} -8.39919i q^{59} -5.51221i q^{61} +(9.03712 + 0.662153i) q^{63} -8.24621 q^{65} -3.96230 q^{67} +(-4.78078 - 5.14388i) q^{69} +5.37874i q^{71} -11.9679i q^{73} +(12.2870 - 11.4196i) q^{75} +(-2.00000 + 9.81602i) q^{77} -6.99337i q^{79} +(-8.90388 - 1.31182i) q^{81} +10.1496 q^{83} -27.2961i q^{85} +(6.49971 - 6.04090i) q^{87} -5.98396i q^{89} -6.49971 q^{91} +(-11.4654 + 10.6561i) q^{93} -18.0742 q^{95} -1.56155 q^{97} +(2.69359 - 9.57834i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{9}+O(q^{10}) \) 8 * q + 10 * q^9	\( 8 q + 10 q^{9} - 24 q^{17} - 12 q^{21} - 28 q^{25} - 8 q^{29} + 2 q^{33} + 4 q^{37} + 48 q^{41} + 34 q^{45} + 16 q^{49} - 28 q^{57} - 30 q^{69} - 16 q^{77} - 30 q^{81} - 34 q^{93} + 4 q^{97}+O(q^{100}) \) 8 * q + 10 * q^9 - 24 * q^17 - 12 * q^21 - 28 * q^25 - 8 * q^29 + 2 * q^33 + 4 * q^37 + 48 * q^41 + 34 * q^45 + 16 * q^49 - 28 * q^57 - 30 * q^69 - 16 * q^77 - 30 * q^81 - 34 * q^93 + 4 * q^97

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