LMFDB - Embedded newform 912.2.f.h.113.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(113,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, 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("912.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.f (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:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	10.0.20322144469993472.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} - x^{8} - 2x^{7} - 2x^{6} + 22x^{5} - 6x^{4} - 18x^{3} - 27x^{2} - 81x + 243 $ x^10 - x^9 - x^8 - 2x^7 - 2x^6 + 22x^5 - 6x^4 - 18x^3 - 27x^2 - 81*x + 243
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 456)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			113.3
Root			$1.39399 + 1.02801i$ of defining polynomial
Character	$\chi$	$=$	912.113
Dual form			912.2.f.h.113.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39399 - 1.02801i) q^{3} -1.12291i q^{5} -3.21832 q^{7} +(0.886389 + 2.86606i) q^{9} +O(q^{10})$	\(q+(-1.39399 - 1.02801i) q^{3} -1.12291i q^{5} -3.21832 q^{7} +(0.886389 + 2.86606i) q^{9} +3.06841i q^{11} -0.110515i q^{13} +(-1.15436 + 1.56532i) q^{15} +1.89721i q^{17} +(2.66196 - 3.45166i) q^{19} +(4.48630 + 3.30847i) q^{21} +7.89866i q^{23} +3.73908 q^{25} +(1.71073 - 4.90647i) q^{27} +1.77278 q^{29} -5.07614i q^{31} +(3.15436 - 4.27732i) q^{33} +3.61388i q^{35} +3.59682i q^{37} +(-0.113611 + 0.154057i) q^{39} -1.01519 q^{41} +8.31502 q^{43} +(3.21832 - 0.995334i) q^{45} -5.68383i q^{47} +3.35762 q^{49} +(1.95035 - 2.64468i) q^{51} -0.535944 q^{53} +3.44555 q^{55} +(-7.25908 + 2.07505i) q^{57} +12.5182 q^{59} +7.02149 q^{61} +(-2.85269 - 9.22392i) q^{63} -0.124099 q^{65} +12.5389i q^{67} +(8.11991 - 11.0106i) q^{69} +2.76317 q^{71} -5.47035 q^{73} +(-5.21222 - 3.84381i) q^{75} -9.87515i q^{77} +17.5218i q^{79} +(-7.42863 + 5.08089i) q^{81} +8.67296i q^{83} +2.13039 q^{85} +(-2.47123 - 1.82243i) q^{87} +2.12793 q^{89} +0.355674i q^{91} +(-5.21832 + 7.07606i) q^{93} +(-3.87590 - 2.98913i) q^{95} +12.8252i q^{97} +(-8.79427 + 2.71981i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) $ 10 * q - q^3 + 2 * q^7 + 3 * q^9	$ 10 q - q^{3} + 2 q^{7} + 3 q^{9} + 10 q^{15} - 2 q^{19} - 5 q^{21} - 14 q^{25} - 10 q^{27} + 6 q^{29} + 10 q^{33} - 7 q^{39} + 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} + q^{51} + 26 q^{53} + 12 q^{55} - 11 q^{57} + 2 q^{59} - 4 q^{61} + 17 q^{63} - 32 q^{65} + 27 q^{69} + 8 q^{71} - 26 q^{73} + 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} - 4 q^{89} - 18 q^{93} - 8 q^{95} - 2 q^{99}+O(q^{100}) $ 10 * q - q^3 + 2 * q^7 + 3 * q^9 + 10 * q^15 - 2 * q^19 - 5 * q^21 - 14 * q^25 - 10 * q^27 + 6 * q^29 + 10 * q^33 - 7 * q^39 + 4 * q^41 - 20 * q^43 - 2 * q^45 + 16 * q^49 + q^51 + 26 * q^53 + 12 * q^55 - 11 * q^57 + 2 * q^59 - 4 * q^61 + 17 * q^63 - 32 * q^65 + 27 * q^69 + 8 * q^71 - 26 * q^73 + 39 * q^75 + 23 * q^81 - 8 * q^85 - 13 * q^87 - 4 * q^89 - 18 * q^93 - 8 * q^95 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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
$3$	−1.39399	−	1.02801i	−0.804818	−	0.593522i
$3$	−1.39399	−	1.02801i	−0.804818	−	0.593522i
$4$		0			0
$5$		−	1.12291i		−	0.502180i	−0.967964	−	0.251090i	$-0.919211\pi$
$5$		−	1.12291i		−	0.502180i	0.967964	−	0.251090i	$-0.0807890\pi$
$6$		0			0
$7$	−3.21832			−1.21641			−0.608206	−	0.793779i	$-0.708111\pi$
$7$	−3.21832			−1.21641			−0.608206	+	0.793779i	$0.708111\pi$
$8$		0			0
$9$	0.886389	+	2.86606i	0.295463	+	0.955354i
$10$		0			0
$11$			3.06841i			0.925162i	0.886577	+	0.462581i	$0.153076\pi$
$11$			3.06841i			0.925162i	−0.886577	+	0.462581i	$0.846924\pi$
$12$		0			0
$13$		−	0.110515i		−	0.0306514i	−0.999883	−	0.0153257i	$-0.995121\pi$
$13$		−	0.110515i		−	0.0306514i	0.999883	−	0.0153257i	$-0.00487852\pi$
$14$		0			0
$15$	−1.15436	+	1.56532i	−0.298055	+	0.404163i
$16$		0			0
$17$			1.89721i			0.460141i	0.973174	+	0.230071i	$0.0738957\pi$
$17$			1.89721i			0.460141i	−0.973174	+	0.230071i	$0.926104\pi$
$18$		0			0
$19$	2.66196	−	3.45166i	0.610695	−	0.791866i
$19$	2.66196	−	3.45166i	0.610695	−	0.791866i
$20$		0			0
$21$	4.48630	+	3.30847i	0.978990	+	0.721968i
$22$		0			0
$23$			7.89866i			1.64698i	0.567327	+	0.823492i	$0.307977\pi$
$23$			7.89866i			1.64698i	−0.567327	+	0.823492i	$0.692023\pi$
$24$		0			0
$25$	3.73908			0.747815
$26$		0			0
$27$	1.71073	−	4.90647i	0.329230	−	0.944250i
$28$		0			0
$29$	1.77278			0.329197			0.164598	−	0.986361i	$-0.447367\pi$
$29$	1.77278			0.329197			0.164598	+	0.986361i	$0.447367\pi$
$30$		0			0
$31$		−	5.07614i		−	0.911702i	−0.890056	−	0.455851i	$-0.849335\pi$
$31$		−	5.07614i		−	0.911702i	0.890056	−	0.455851i	$-0.150665\pi$
$32$		0			0
$33$	3.15436	−	4.27732i	0.549104	−	0.744586i
$34$		0			0
$35$			3.61388i			0.610858i
$36$		0			0
$37$			3.59682i			0.591314i	0.955294	+	0.295657i	$0.0955386\pi$
$37$			3.59682i			0.591314i	−0.955294	+	0.295657i	$0.904461\pi$
$38$		0			0
$39$	−0.113611	+	0.154057i	−0.0181923	+	0.0246688i
$40$		0			0
$41$	−1.01519			−0.158546			−0.0792732	−	0.996853i	$-0.525260\pi$
$41$	−1.01519			−0.158546			−0.0792732	+	0.996853i	$0.525260\pi$
$42$		0			0
$43$	8.31502			1.26803			0.634014	−	0.773321i	$-0.281406\pi$
$43$	8.31502			1.26803			0.634014	+	0.773321i	$0.281406\pi$
$44$		0			0
$45$	3.21832	−	0.995334i	0.479760	−	0.148376i
$46$		0			0
$47$		−	5.68383i		−	0.829072i	−0.910033	−	0.414536i	$-0.863944\pi$
$47$		−	5.68383i		−	0.829072i	0.910033	−	0.414536i	$-0.136056\pi$
$48$		0			0
$49$	3.35762			0.479659
$50$		0			0
$51$	1.95035	−	2.64468i	0.273104	−	0.370330i
$52$		0			0
$53$	−0.535944			−0.0736176			−0.0368088	−	0.999322i	$-0.511719\pi$
$53$	−0.535944			−0.0736176			−0.0368088	+	0.999322i	$0.511719\pi$
$54$		0			0
$55$	3.44555			0.464597
$56$		0			0
$57$	−7.25908	+	2.07505i	−0.961488	+	0.274847i
$58$		0			0
$59$	12.5182			1.62972			0.814862	−	0.579655i	$-0.196813\pi$
$59$	12.5182			1.62972			0.814862	+	0.579655i	$0.196813\pi$
$60$		0			0
$61$	7.02149			0.899009			0.449505	−	0.893278i	$-0.351601\pi$
$61$	7.02149			0.899009			0.449505	+	0.893278i	$0.351601\pi$
$62$		0			0
$63$	−2.85269	−	9.22392i	−0.359405	−	1.16210i
$64$		0			0
$65$	−0.124099			−0.0153925
$66$		0			0
$67$			12.5389i			1.53187i	0.642920	+	0.765933i	$0.277723\pi$
$67$			12.5389i			1.53187i	−0.642920	+	0.765933i	$0.722277\pi$
$68$		0			0
$69$	8.11991	−	11.0106i	0.977522	−	1.32552i
$70$		0			0
$71$	2.76317			0.327927			0.163964	−	0.986466i	$-0.447572\pi$
$71$	2.76317			0.327927			0.163964	+	0.986466i	$0.447572\pi$
$72$		0			0
$73$	−5.47035			−0.640256			−0.320128	−	0.947374i	$-0.603726\pi$
$73$	−5.47035			−0.640256			−0.320128	+	0.947374i	$0.603726\pi$
$74$		0			0
$75$	−5.21222	−	3.84381i	−0.601855	−	0.443845i
$76$		0			0
$77$		−	9.87515i		−	1.12538i
$78$		0			0
$79$			17.5218i			1.97136i	0.168638	+	0.985678i	$0.446063\pi$
$79$			17.5218i			1.97136i	−0.168638	+	0.985678i	$0.553937\pi$
$80$		0			0
$81$	−7.42863	+	5.08089i	−0.825403	+	0.564544i
$82$		0			0
$83$			8.67296i			0.951981i	0.879450	+	0.475991i	$0.157910\pi$
$83$			8.67296i			0.951981i	−0.879450	+	0.475991i	$0.842090\pi$
$84$		0			0
$85$	2.13039			0.231074
$86$		0			0
$87$	−2.47123	−	1.82243i	−0.264943	−	0.195385i
$88$		0			0
$89$	2.12793			0.225560			0.112780	−	0.993620i	$-0.464024\pi$
$89$	2.12793			0.225560			0.112780	+	0.993620i	$0.464024\pi$
$90$		0			0
$91$			0.355674i			0.0372848i
$92$		0			0
$93$	−5.21832	+	7.07606i	−0.541115	+	0.733754i
$94$		0			0
$95$	−3.87590	−	2.98913i	−0.397659	−	0.306679i
$96$		0			0
$97$			12.8252i			1.30221i	0.758989	+	0.651103i	$0.225694\pi$
$97$			12.8252i			1.30221i	−0.758989	+	0.651103i	$0.774306\pi$
$98$		0			0
$99$	−8.79427	+	2.71981i	−0.883857	+	0.273351i
$100$		0			0
$101$			7.75789i			0.771939i	0.922511	+	0.385970i	$0.126133\pi$
$101$			7.75789i			0.771939i	−0.922511	+	0.385970i	$0.873867\pi$
$102$		0			0
$103$		−	1.13610i		−	0.111943i	−0.998432	−	0.0559717i	$-0.982174\pi$
$103$		−	1.13610i		−	0.111943i	0.998432	−	0.0559717i	$-0.0178257\pi$
$104$		0			0
$105$	3.71511	−	5.03770i	0.362558	−	0.491629i
$106$		0			0
$107$	16.2398			1.56996			0.784981	−	0.619520i	$-0.212673\pi$
$107$	16.2398			1.56996			0.784981	+	0.619520i	$0.212673\pi$
$108$		0			0
$109$		−	14.2633i		−	1.36618i	−0.730334	−	0.683090i	$-0.760636\pi$
$109$		−	14.2633i		−	1.36618i	0.730334	−	0.683090i	$-0.239364\pi$
$110$		0			0
$111$	3.69757	−	5.01392i	0.350958	−	0.475900i
$112$		0			0
$113$	−15.7428			−1.48096			−0.740478	−	0.672081i	$-0.765401\pi$
$113$	−15.7428			−1.48096			−0.740478	+	0.672081i	$0.765401\pi$
$114$		0			0
$115$	8.86947			0.827082
$116$		0			0
$117$	0.316744	−	0.0979596i	0.0292830	−	0.00905637i
$118$		0			0
$119$		−	6.10584i		−	0.559722i
$120$		0			0
$121$	1.58484			0.144076
$122$		0			0
$123$	1.41516	+	1.04363i	0.127601	+	0.0941008i
$124$		0			0
$125$		−	9.81318i		−	0.877718i
$126$		0			0
$127$		−	3.71514i		−	0.329666i	−0.986322	−	0.164833i	$-0.947292\pi$
$127$		−	3.71514i		−	0.329666i	0.986322	−	0.164833i	$-0.0527084\pi$
$128$		0			0
$129$	−11.5910	−	8.54793i	−1.02053	−	0.752603i
$130$		0			0
$131$			0.822597i			0.0718707i	0.999354	+	0.0359353i	$0.0114410\pi$
$131$			0.822597i			0.0718707i	−0.999354	+	0.0359353i	$0.988559\pi$
$132$		0			0
$133$	−8.56704	+	11.1086i	−0.742857	+	0.963236i
$134$		0			0
$135$	−5.50951	−	1.92099i	−0.474183	−	0.165333i
$136$		0			0
$137$			1.34296i			0.114736i	0.998353	+	0.0573682i	$0.0182709\pi$
$137$			1.34296i			0.114736i	−0.998353	+	0.0573682i	$0.981729\pi$
$138$		0			0
$139$	18.1430			1.53887			0.769434	−	0.638726i	$-0.220538\pi$
$139$	18.1430			1.53887			0.769434	+	0.638726i	$0.220538\pi$
$140$		0			0
$141$	−5.84304	+	7.92318i	−0.492072	+	0.667252i
$142$		0			0
$143$	0.339107			0.0283575
$144$		0			0
$145$		−	1.99067i		−	0.165316i
$146$		0			0
$147$	−4.68047	−	3.45166i	−0.386038	−	0.284688i
$148$		0			0
$149$			20.8112i			1.70492i	0.522790	+	0.852462i	$0.324891\pi$
$149$			20.8112i			1.70492i	−0.522790	+	0.852462i	$0.675109\pi$
$150$		0			0
$151$			7.63958i			0.621700i	0.950459	+	0.310850i	$0.100614\pi$
$151$			7.63958i			0.621700i	−0.950459	+	0.310850i	$0.899386\pi$
$152$		0			0
$153$	−5.43753	+	1.68167i	−0.439598	+	0.135955i
$154$		0			0
$155$	−5.70004			−0.457838
$156$		0			0
$157$	−6.71523			−0.535934			−0.267967	−	0.963428i	$-0.586352\pi$
$157$	−6.71523			−0.535934			−0.267967	+	0.963428i	$0.586352\pi$
$158$		0			0
$159$	0.747098	+	0.550956i	0.0592488	+	0.0436937i
$160$		0			0
$161$		−	25.4205i		−	2.00341i
$162$		0			0
$163$	−13.5885			−1.06434			−0.532168	−	0.846639i	$-0.678623\pi$
$163$	−13.5885			−1.06434			−0.532168	+	0.846639i	$0.678623\pi$
$164$		0			0
$165$	−4.80304	−	3.54206i	−0.373916	−	0.275749i
$166$		0			0
$167$	−25.4907			−1.97253			−0.986267	−	0.165161i	$-0.947185\pi$
$167$	−25.4907			−1.97253			−0.986267	+	0.165161i	$0.947185\pi$
$168$		0			0
$169$	12.9878			0.999060
$170$		0			0
$171$	12.2522	+	4.56982i	0.936950	+	0.349463i
$172$		0			0
$173$	−7.36476			−0.559932			−0.279966	−	0.960010i	$-0.590323\pi$
$173$	−7.36476			−0.559932			−0.279966	+	0.960010i	$0.590323\pi$
$174$		0			0
$175$	−12.0336			−0.909652
$176$		0			0
$177$	−17.4501	−	12.8688i	−1.31163	−	0.967277i
$178$		0			0
$179$	−4.71906			−0.352719			−0.176360	−	0.984326i	$-0.556432\pi$
$179$	−4.71906			−0.352719			−0.176360	+	0.984326i	$0.556432\pi$
$180$		0			0
$181$		−	5.17885i		−	0.384941i	−0.981303	−	0.192471i	$-0.938350\pi$
$181$		−	5.17885i		−	0.384941i	0.981303	−	0.192471i	$-0.0616500\pi$
$182$		0			0
$183$	−9.78785	−	7.21816i	−0.723539	−	0.533582i
$184$		0			0
$185$	4.03890			0.296946
$186$		0			0
$187$	−5.82143			−0.425705
$188$		0			0
$189$	−5.50568	+	15.7906i	−0.400479	+	1.14860i
$190$		0			0
$191$		−	23.6896i		−	1.71412i	−0.515217	−	0.857060i	$-0.672289\pi$
$191$		−	23.6896i		−	1.71412i	0.515217	−	0.857060i	$-0.327711\pi$
$192$		0			0
$193$			12.9367i			0.931207i	0.884993	+	0.465604i	$0.154163\pi$
$193$			12.9367i			0.931207i	−0.884993	+	0.465604i	$0.845837\pi$
$194$		0			0
$195$	0.172992	+	0.127575i	0.0123882	+	0.00913581i
$196$		0			0
$197$		−	5.76723i		−	0.410898i	−0.978668	−	0.205449i	$-0.934135\pi$
$197$		−	5.76723i		−	0.410898i	0.978668	−	0.205449i	$-0.0658655\pi$
$198$		0			0
$199$	−14.8246			−1.05089			−0.525446	−	0.850827i	$-0.676101\pi$
$199$	−14.8246			−1.05089			−0.525446	+	0.850827i	$0.676101\pi$
$200$		0			0
$201$	12.8901	−	17.4790i	0.909196	−	1.23287i
$202$		0			0
$203$	−5.70538			−0.400439
$204$		0			0
$205$			1.13997i			0.0796188i
$206$		0			0
$207$	−22.6381	+	7.00129i	−1.57345	+	0.486623i
$208$		0			0
$209$	10.5911	+	8.16799i	0.732604	+	0.564991i
$210$		0			0
$211$		−	13.5203i		−	0.930774i	−0.885107	−	0.465387i	$-0.845915\pi$
$211$		−	13.5203i		−	0.930774i	0.885107	−	0.465387i	$-0.154085\pi$
$212$		0			0
$213$	−3.85181	−	2.84056i	−0.263922	−	0.194632i
$214$		0			0
$215$		−	9.33700i		−	0.636778i
$216$		0			0
$217$			16.3367i			1.10901i
$218$		0			0
$219$	7.62559	+	5.62358i	0.515289	+	0.380006i
$220$		0			0
$221$	0.209671			0.0141040
$222$		0			0
$223$			19.3249i			1.29409i	0.762453	+	0.647044i	$0.223995\pi$
$223$			19.3249i			1.29409i	−0.762453	+	0.647044i	$0.776005\pi$
$224$		0			0
$225$	3.31428	+	10.7164i	0.220952	+	0.714429i
$226$		0			0
$227$	−21.4358			−1.42274			−0.711372	−	0.702816i	$-0.751926\pi$
$227$	−21.4358			−1.42274			−0.711372	+	0.702816i	$0.751926\pi$
$228$		0			0
$229$	2.96072			0.195650			0.0978249	−	0.995204i	$-0.468811\pi$
$229$	2.96072			0.195650			0.0978249	+	0.995204i	$0.468811\pi$
$230$		0			0
$231$	−10.1518	+	13.7658i	−0.667937	+	0.905724i
$232$		0			0
$233$			6.63499i			0.434672i	0.976097	+	0.217336i	$0.0697368\pi$
$233$			6.63499i			0.434672i	−0.976097	+	0.217336i	$0.930263\pi$
$234$		0			0
$235$	−6.38242			−0.416343
$236$		0			0
$237$	18.0126	−	24.4251i	1.17004	−	1.58658i
$238$		0			0
$239$			1.04461i			0.0675703i	0.999429	+	0.0337851i	$0.0107562\pi$
$239$			1.04461i			0.0675703i	−0.999429	+	0.0337851i	$0.989244\pi$
$240$		0			0
$241$			2.51441i			0.161967i	0.996715	+	0.0809836i	$0.0258061\pi$
$241$			2.51441i			0.161967i	−0.996715	+	0.0809836i	$0.974194\pi$
$242$		0			0
$243$	15.5786	+	0.554018i	0.999368	+	0.0355403i
$244$		0			0
$245$		−	3.77029i		−	0.240875i
$246$		0			0
$247$	−0.381462	−	0.294187i	−0.0242718	−	0.0187187i
$248$		0			0
$249$	8.91590	−	12.0900i	0.565022	−	0.766172i
$250$		0			0
$251$			9.74389i			0.615029i	0.951543	+	0.307514i	$0.0994973\pi$
$251$			9.74389i			0.615029i	−0.951543	+	0.307514i	$0.900503\pi$
$252$		0			0
$253$	−24.2364			−1.52373
$254$		0			0
$255$	−2.96974	−	2.19007i	−0.185972	−	0.137147i
$256$		0			0
$257$	20.9086			1.30424			0.652122	−	0.758114i	$-0.273879\pi$
$257$	20.9086			1.30424			0.652122	+	0.758114i	$0.273879\pi$
$258$		0			0
$259$		−	11.5757i		−	0.719282i
$260$		0			0
$261$	1.57137	+	5.08089i	0.0972654	+	0.314499i
$262$		0			0
$263$		−	5.87701i		−	0.362392i	−0.983447	−	0.181196i	$-0.942003\pi$
$263$		−	5.87701i		−	0.362392i	0.983447	−	0.181196i	$-0.0579968\pi$
$264$		0			0
$265$			0.601816i			0.0369693i
$266$		0			0
$267$	−2.96630	−	2.18753i	−0.181535	−	0.133875i
$268$		0			0
$269$	−17.8973			−1.09121			−0.545607	−	0.838041i	$-0.683701\pi$
$269$	−17.8973			−1.09121			−0.545607	+	0.838041i	$0.683701\pi$
$270$		0			0
$271$	4.33760			0.263490			0.131745	−	0.991284i	$-0.457942\pi$
$271$	4.33760			0.263490			0.131745	+	0.991284i	$0.457942\pi$
$272$		0			0
$273$	0.365637	−	0.495805i	0.0221293	−	0.0300075i
$274$		0			0
$275$			11.4730i			0.691850i
$276$		0			0
$277$	25.7189			1.54530			0.772650	−	0.634832i	$-0.218931\pi$
$277$	25.7189			1.54530			0.772650	+	0.634832i	$0.218931\pi$
$278$		0			0
$279$	14.5485	−	4.49944i	0.870998	−	0.269374i
$280$		0			0
$281$	9.74797			0.581515			0.290758	−	0.956797i	$-0.406093\pi$
$281$	9.74797			0.581515			0.290758	+	0.956797i	$0.406093\pi$
$282$		0			0
$283$	6.99110			0.415578			0.207789	−	0.978174i	$-0.433373\pi$
$283$	6.99110			0.415578			0.207789	+	0.978174i	$0.433373\pi$
$284$		0			0
$285$	2.33009	+	8.15127i	0.138023	+	0.482840i
$286$		0			0
$287$	3.26722			0.192858
$288$		0			0
$289$	13.4006			0.788270
$290$		0			0
$291$	13.1845	−	17.8782i	0.772888	−	1.04804i
$292$		0			0
$293$	−12.3072			−0.718995			−0.359498	−	0.933146i	$-0.617052\pi$
$293$	−12.3072			−0.718995			−0.359498	+	0.933146i	$0.617052\pi$
$294$		0			0
$295$		−	14.0567i		−	0.818415i
$296$		0			0
$297$	15.0551	+	5.24922i	0.873584	+	0.304591i
$298$		0			0
$299$	0.872923			0.0504824
$300$		0			0
$301$	−26.7604			−1.54245
$302$		0			0
$303$	7.97520	−	10.8144i	0.458163	−	0.621270i
$304$		0			0
$305$		−	7.88449i		−	0.451464i
$306$		0			0
$307$		−	16.1837i		−	0.923654i	−0.886970	−	0.461827i	$-0.847194\pi$
$307$		−	16.1837i		−	0.923654i	0.886970	−	0.461827i	$-0.152806\pi$
$308$		0			0
$309$	−1.16792	+	1.58371i	−0.0664408	+	0.0900940i
$310$		0			0
$311$		−	15.9076i		−	0.902037i	−0.892515	−	0.451018i	$-0.851061\pi$
$311$		−	15.9076i		−	0.902037i	0.892515	−	0.451018i	$-0.148939\pi$
$312$		0			0
$313$	20.6852			1.16920			0.584599	−	0.811322i	$-0.301252\pi$
$313$	20.6852			1.16920			0.584599	+	0.811322i	$0.301252\pi$
$314$		0			0
$315$	−10.3576	+	3.20331i	−0.583586	+	0.180486i
$316$		0			0
$317$	21.2638			1.19429			0.597146	−	0.802133i	$-0.296301\pi$
$317$	21.2638			1.19429			0.597146	+	0.802133i	$0.296301\pi$
$318$		0			0
$319$			5.43962i			0.304560i
$320$		0			0
$321$	−22.6381	−	16.6947i	−1.26353	−	0.931807i
$322$		0			0
$323$	6.54853	+	5.05029i	0.364370	+	0.281006i
$324$		0			0
$325$		−	0.413225i		−	0.0229216i
$326$		0			0
$327$	−14.6629	+	19.8829i	−0.810858	+	1.09953i
$328$		0			0
$329$			18.2924i			1.00849i
$330$		0			0
$331$			21.9164i			1.20463i	0.798258	+	0.602316i	$0.205755\pi$
$331$			21.9164i			1.20463i	−0.798258	+	0.602316i	$0.794245\pi$
$332$		0			0
$333$	−10.3087	+	3.18819i	−0.564915	+	0.174711i
$334$		0			0
$335$	14.0800			0.769272
$336$		0			0
$337$			32.9088i			1.79266i	0.443392	+	0.896328i	$0.353775\pi$
$337$			32.9088i			1.79266i	−0.443392	+	0.896328i	$0.646225\pi$
$338$		0			0
$339$	21.9452	+	16.1837i	1.19190	+	0.878980i
$340$		0			0
$341$	15.5757			0.843471
$342$		0			0
$343$	11.7224			0.632949
$344$		0			0
$345$	−12.3639	−	9.11791i	−0.665651	−	0.490892i
$346$		0			0
$347$		−	29.3356i		−	1.57482i	−0.616430	−	0.787410i	$-0.711422\pi$
$347$		−	29.3356i		−	1.57482i	0.616430	−	0.787410i	$-0.288578\pi$
$348$		0			0
$349$	−12.7429			−0.682112			−0.341056	−	0.940043i	$-0.610785\pi$
$349$	−12.7429			−0.682112			−0.341056	+	0.940043i	$0.610785\pi$
$350$		0			0
$351$	−0.542240	−	0.189062i	−0.0289426	−	0.0100914i
$352$		0			0
$353$		−	1.79475i		−	0.0955248i	−0.998859	−	0.0477624i	$-0.984791\pi$
$353$		−	1.79475i		−	0.0955248i	0.998859	−	0.0477624i	$-0.0152090\pi$
$354$		0			0
$355$		−	3.10278i		−	0.164679i
$356$		0			0
$357$	−6.27687	+	8.51145i	−0.332207	+	0.450474i
$358$		0			0
$359$			22.2796i			1.17587i	0.808908	+	0.587936i	$0.200059\pi$
$359$			22.2796i			1.17587i	−0.808908	+	0.587936i	$0.799941\pi$
$360$		0			0
$361$	−4.82797	−	18.3764i	−0.254103	−	0.967177i
$362$		0			0
$363$	−2.20924	−	1.62923i	−0.115955	−	0.0855124i
$364$		0			0
$365$			6.14270i			0.321524i
$366$		0			0
$367$	27.7819			1.45020			0.725102	−	0.688641i	$-0.241793\pi$
$367$	27.7819			1.45020			0.725102	+	0.688641i	$0.241793\pi$
$368$		0			0
$369$	−0.899855	−	2.90960i	−0.0468446	−	0.151468i
$370$		0			0
$371$	1.72484			0.0895494
$372$		0			0
$373$		−	37.1660i		−	1.92438i	−0.272379	−	0.962190i	$-0.587810\pi$
$373$		−	37.1660i		−	1.92438i	0.272379	−	0.962190i	$-0.412190\pi$
$374$		0			0
$375$	−10.0881	+	13.6794i	−0.520945	+	0.706403i
$376$		0			0
$377$		−	0.195919i		−	0.0100903i
$378$		0			0
$379$			15.1179i			0.776555i	0.921543	+	0.388277i	$0.126930\pi$
$379$			15.1179i			0.776555i	−0.921543	+	0.388277i	$0.873070\pi$
$380$		0			0
$381$	−3.81920	+	5.17885i	−0.195664	+	0.265321i
$382$		0			0
$383$	−32.3643			−1.65374			−0.826869	−	0.562395i	$-0.809880\pi$
$383$	−32.3643			−1.65374			−0.826869	+	0.562395i	$0.809880\pi$
$384$		0			0
$385$	−11.0889			−0.565142
$386$		0			0
$387$	7.37034	+	23.8314i	0.374655	+	1.21142i
$388$		0			0
$389$			10.5965i			0.537263i	0.963243	+	0.268632i	$0.0865715\pi$
$389$			10.5965i			0.537263i	−0.963243	+	0.268632i	$0.913429\pi$
$390$		0			0
$391$	−14.9854			−0.757846
$392$		0			0
$393$	0.845639	−	1.14669i	0.0426568	−	0.0578428i
$394$		0			0
$395$	19.6754			0.989975
$396$		0			0
$397$	10.8103			0.542554			0.271277	−	0.962501i	$-0.412554\pi$
$397$	10.8103			0.542554			0.271277	+	0.962501i	$0.412554\pi$
$398$		0			0
$399$	23.3621	−	6.67818i	1.16957	−	0.334327i
$400$		0			0
$401$	0.786462			0.0392740			0.0196370	−	0.999807i	$-0.493749\pi$
$401$	0.786462			0.0392740			0.0196370	+	0.999807i	$0.493749\pi$
$402$		0			0
$403$	−0.560991			−0.0279450
$404$		0			0
$405$	5.70538	+	8.34167i	0.283502	+	0.414501i
$406$		0			0
$407$	−11.0365			−0.547061
$408$		0			0
$409$		−	25.5912i		−	1.26540i	−0.774396	−	0.632701i	$-0.781946\pi$
$409$		−	25.5912i		−	1.26540i	0.774396	−	0.632701i	$-0.218054\pi$
$410$		0			0
$411$	1.38057	−	1.87206i	0.0680986	−	0.0923419i
$412$		0			0
$413$	−40.2875			−1.98242
$414$		0			0
$415$	9.73894			0.478066
$416$		0			0
$417$	−25.2911	−	18.6512i	−1.23851	−	0.913352i
$418$		0			0
$419$		−	29.6591i		−	1.44894i	−0.689305	−	0.724472i	$-0.742084\pi$
$419$		−	29.6591i		−	1.44894i	0.689305	−	0.724472i	$-0.257916\pi$
$420$		0			0
$421$		−	9.61195i		−	0.468458i	−0.972181	−	0.234229i	$-0.924743\pi$
$421$		−	9.61195i		−	0.468458i	0.972181	−	0.234229i	$-0.0752565\pi$
$422$		0			0
$423$	16.2902	−	5.03809i	0.792057	−	0.244960i
$424$		0			0
$425$			7.09382i			0.344101i
$426$		0			0
$427$	−22.5974			−1.09357
$428$		0			0
$429$	−0.472710	−	0.348605i	−0.0228226	−	0.0168308i
$430$		0			0
$431$	26.5325			1.27803			0.639013	−	0.769196i	$-0.279343\pi$
$431$	26.5325			1.27803			0.639013	+	0.769196i	$0.279343\pi$
$432$		0			0
$433$			12.9367i			0.621700i	0.950459	+	0.310850i	$0.100614\pi$
$433$			12.9367i			0.621700i	−0.950459	+	0.310850i	$0.899386\pi$
$434$		0			0
$435$	−2.04643	+	2.77496i	−0.0981186	+	0.133049i
$436$		0			0
$437$	27.2635	+	21.0259i	1.30419	+	1.00581i
$438$		0			0
$439$			6.57572i			0.313842i	0.987611	+	0.156921i	$0.0501568\pi$
$439$			6.57572i			0.313842i	−0.987611	+	0.156921i	$0.949843\pi$
$440$		0			0
$441$	2.97615	+	9.62314i	0.141722	+	0.458245i
$442$		0			0
$443$		−	28.7194i		−	1.36450i	−0.731119	−	0.682250i	$-0.761002\pi$
$443$		−	28.7194i		−	1.36450i	0.731119	−	0.682250i	$-0.238998\pi$
$444$		0			0
$445$		−	2.38947i		−	0.113272i
$446$		0			0
$447$	21.3942	−	29.0106i	1.01191	−	1.37215i
$448$		0			0
$449$	−12.0178			−0.567155			−0.283577	−	0.958949i	$-0.591521\pi$
$449$	−12.0178			−0.567155			−0.283577	+	0.958949i	$0.591521\pi$
$450$		0			0
$451$		−	3.11503i		−	0.146681i
$452$		0			0
$453$	7.85356	−	10.6495i	0.368993	−	0.500355i
$454$		0			0
$455$	0.399389			0.0187237
$456$		0			0
$457$	4.96247			0.232135			0.116067	−	0.993241i	$-0.462971\pi$
$457$	4.96247			0.232135			0.116067	+	0.993241i	$0.462971\pi$
$458$		0			0
$459$	9.30860	+	3.24561i	0.434488	+	0.151492i
$460$		0			0
$461$			19.4495i			0.905856i	0.891547	+	0.452928i	$0.149620\pi$
$461$			19.4495i			0.905856i	−0.891547	+	0.452928i	$0.850380\pi$
$462$		0			0
$463$	−18.9667			−0.881456			−0.440728	−	0.897641i	$-0.645280\pi$
$463$	−18.9667			−0.881456			−0.440728	+	0.897641i	$0.645280\pi$
$464$		0			0
$465$	7.94577	+	5.85970i	0.368476	+	0.271737i
$466$		0			0
$467$			42.2099i			1.95324i	0.214969	+	0.976621i	$0.431035\pi$
$467$			42.2099i			1.95324i	−0.214969	+	0.976621i	$0.568965\pi$
$468$		0			0
$469$		−	40.3541i		−	1.86338i
$470$		0			0
$471$	9.36093	+	6.90333i	0.431329	+	0.318089i
$472$		0			0
$473$			25.5139i			1.17313i
$474$		0			0
$475$	9.95326	−	12.9060i	0.456687	−	0.592170i
$476$		0			0
$477$	−0.475055	−	1.53605i	−0.0217513	−	0.0703309i
$478$		0			0
$479$			38.2201i			1.74632i	0.487433	+	0.873160i	$0.337933\pi$
$479$			38.2201i			1.74632i	−0.487433	+	0.873160i	$0.662067\pi$
$480$		0			0
$481$	0.397504			0.0181246
$482$		0			0
$483$	−26.1325	+	35.4357i	−1.18907	+	1.61238i
$484$		0			0
$485$	14.4016			0.653942
$486$		0			0
$487$			0.549890i			0.0249179i	0.999922	+	0.0124589i	$0.00396591\pi$
$487$			0.549890i			0.0249179i	−0.999922	+	0.0124589i	$0.996034\pi$
$488$		0			0
$489$	18.9422	+	13.9692i	0.856596	+	0.631707i
$490$		0			0
$491$			19.5830i			0.883767i	0.897073	+	0.441883i	$0.145689\pi$
$491$			19.5830i			0.883767i	−0.897073	+	0.441883i	$0.854311\pi$
$492$		0			0
$493$			3.36333i			0.151477i
$494$		0			0
$495$	3.05410	+	9.87515i	0.137271	+	0.443855i
$496$		0			0
$497$	−8.89277			−0.398895
$498$		0			0
$499$	14.8013			0.662596			0.331298	−	0.943526i	$-0.392513\pi$
$499$	14.8013			0.662596			0.331298	+	0.943526i	$0.392513\pi$
$500$		0			0
$501$	35.5337	+	26.2048i	1.58753	+	1.17074i
$502$		0			0
$503$		−	1.38174i		−	0.0616089i	−0.999525	−	0.0308045i	$-0.990193\pi$
$503$		−	1.38174i		−	0.0616089i	0.999525	−	0.0308045i	$-0.00980691\pi$
$504$		0			0
$505$	8.71140			0.387652
$506$		0			0
$507$	−18.1048	−	13.3516i	−0.804062	−	0.592964i
$508$		0			0
$509$	37.6491			1.66877			0.834383	−	0.551186i	$-0.185824\pi$
$509$	37.6491			1.66877			0.834383	+	0.551186i	$0.185824\pi$
$510$		0			0
$511$	17.6054			0.778816
$512$		0			0
$513$	−12.3816	−	18.9657i	−0.546660	−	0.837355i
$514$		0			0
$515$	−1.27574			−0.0562157
$516$		0			0
$517$	17.4403			0.767025
$518$		0			0
$519$	10.2664	+	7.57105i	0.450644	+	0.332332i
$520$		0			0
$521$	−35.7627			−1.56679			−0.783396	−	0.621523i	$-0.786514\pi$
$521$	−35.7627			−1.56679			−0.783396	+	0.621523i	$0.786514\pi$
$522$		0			0
$523$		−	28.9246i		−	1.26478i	−0.774649	−	0.632391i	$-0.782073\pi$
$523$		−	28.9246i		−	1.26478i	0.774649	−	0.632391i	$-0.217927\pi$
$524$		0			0
$525$	16.7746	+	12.3706i	0.732104	+	0.539899i
$526$		0			0
$527$	9.63051			0.419512
$528$		0			0
$529$	−39.3888			−1.71256
$530$		0			0
$531$	11.0960	+	35.8778i	0.481523	+	1.55696i
$532$		0			0
$533$			0.112194i			0.00485967i
$534$		0			0
$535$		−	18.2358i		−	0.788403i
$536$		0			0
$537$	6.57830	+	4.85124i	0.283875	+	0.209347i
$538$		0			0
$539$			10.3026i			0.443762i
$540$		0			0
$541$	−24.9541			−1.07286			−0.536430	−	0.843945i	$-0.680227\pi$
$541$	−24.9541			−1.07286			−0.536430	+	0.843945i	$0.680227\pi$
$542$		0			0
$543$	−5.32391	+	7.21924i	−0.228471	+	0.309807i
$544$		0			0
$545$	−16.0164			−0.686068
$546$		0			0
$547$		−	18.3342i		−	0.783912i	−0.919984	−	0.391956i	$-0.871799\pi$
$547$		−	18.3342i		−	0.783912i	0.919984	−	0.391956i	$-0.128201\pi$
$548$		0			0
$549$	6.22377	+	20.1240i	0.265624	+	0.858872i
$550$		0			0
$551$	4.71906	−	6.11903i	0.201039	−	0.260680i
$552$		0			0
$553$		−	56.3908i		−	2.39798i
$554$		0			0
$555$	−5.63017	−	4.15203i	−0.238987	−	0.176244i
$556$		0			0
$557$		−	21.8056i		−	0.923933i	−0.886897	−	0.461966i	$-0.847144\pi$
$557$		−	21.8056i		−	0.923933i	0.886897	−	0.461966i	$-0.152856\pi$
$558$		0			0
$559$		−	0.918937i		−	0.0388669i
$560$		0			0
$561$	8.11498	+	5.98449i	0.342615	+	0.252665i
$562$		0			0
$563$	18.1632			0.765489			0.382745	−	0.923854i	$-0.374979\pi$
$563$	18.1632			0.765489			0.382745	+	0.923854i	$0.374979\pi$
$564$		0			0
$565$			17.6777i			0.743706i
$566$		0			0
$567$	23.9077	−	16.3520i	1.00403	−	0.686718i
$568$		0			0
$569$	26.8909			1.12732			0.563662	−	0.826006i	$-0.309392\pi$
$569$	26.8909			1.12732			0.563662	+	0.826006i	$0.309392\pi$
$570$		0			0
$571$	−5.32391			−0.222799			−0.111399	−	0.993776i	$-0.535533\pi$
$571$	−5.32391			−0.222799			−0.111399	+	0.993776i	$0.535533\pi$
$572$		0			0
$573$	−24.3532	+	33.0230i	−1.01737	+	1.37955i
$574$		0			0
$575$			29.5337i			1.23164i
$576$		0			0
$577$	29.1457			1.21335			0.606676	−	0.794949i	$-0.292503\pi$
$577$	29.1457			1.21335			0.606676	+	0.794949i	$0.292503\pi$
$578$		0			0
$579$	13.2991	−	18.0336i	0.552692	−	0.749452i
$580$		0			0
$581$		−	27.9124i		−	1.15800i
$582$		0			0
$583$		−	1.64450i		−	0.0681082i
$584$		0			0
$585$	−0.110000	−	0.355674i	−0.00454792	−	0.0147053i
$586$		0			0
$587$		−	27.7041i		−	1.14347i	−0.820438	−	0.571735i	$-0.806271\pi$
$587$		−	27.7041i		−	1.14347i	0.820438	−	0.571735i	$-0.193729\pi$
$588$		0			0
$589$	−17.5211	−	13.5125i	−0.721946	−	0.556772i
$590$		0			0
$591$	−5.92877	+	8.03943i	−0.243877	+	0.330698i
$592$		0			0
$593$		−	28.1676i		−	1.15670i	−0.815788	−	0.578352i	$-0.803696\pi$
$593$		−	28.1676i		−	1.15670i	0.815788	−	0.578352i	$-0.196304\pi$
$594$		0			0
$595$	−6.85630			−0.281081
$596$		0			0
$597$	20.6653	+	15.2399i	0.845776	+	0.623727i
$598$		0			0
$599$	42.0200			1.71689			0.858445	−	0.512906i	$-0.171431\pi$
$599$	42.0200			1.71689			0.858445	+	0.512906i	$0.171431\pi$
$600$		0			0
$601$			39.5141i			1.61181i	0.592044	+	0.805906i	$0.298321\pi$
$601$			39.5141i			1.61181i	−0.592044	+	0.805906i	$0.701679\pi$
$602$		0			0
$603$	−35.9372	+	11.1143i	−1.46347	+	0.452610i
$604$		0			0
$605$		−	1.77963i		−	0.0723521i
$606$		0			0
$607$		−	22.3596i		−	0.907548i	−0.891117	−	0.453774i	$-0.850077\pi$
$607$		−	22.3596i		−	0.907548i	0.891117	−	0.453774i	$-0.149923\pi$
$608$		0			0
$609$	7.95321	+	5.86519i	0.322280	+	0.237669i
$610$		0			0
$611$	−0.628150			−0.0254122
$612$		0			0
$613$	−28.7108			−1.15962			−0.579810	−	0.814752i	$-0.696873\pi$
$613$	−28.7108			−1.15962			−0.579810	+	0.814752i	$0.696873\pi$
$614$		0			0
$615$	1.17190	−	1.58910i	0.0472555	−	0.0640786i
$616$		0			0
$617$		−	3.09571i		−	0.124629i	−0.998057	−	0.0623144i	$-0.980152\pi$
$617$		−	3.09571i		−	0.124629i	0.998057	−	0.0623144i	$-0.0198481\pi$
$618$		0			0
$619$	9.06313			0.364278			0.182139	−	0.983273i	$-0.441698\pi$
$619$	9.06313			0.364278			0.182139	+	0.983273i	$0.441698\pi$
$620$		0			0
$621$	38.7545	+	13.5125i	1.55516	+	0.542237i
$622$		0			0
$623$	−6.84836			−0.274374
$624$		0			0
$625$	7.67609			0.307043
$626$		0			0
$627$	−6.36711	−	22.2738i	−0.254278	−	0.889532i
$628$		0			0
$629$	−6.82393			−0.272088
$630$		0			0
$631$	−29.1845			−1.16182			−0.580908	−	0.813969i	$-0.697302\pi$
$631$	−29.1845			−1.16182			−0.580908	+	0.813969i	$0.697302\pi$
$632$		0			0
$633$	−13.8990	+	18.8471i	−0.552435	+	0.749103i
$634$		0			0
$635$	−4.17176			−0.165551
$636$		0			0
$637$		−	0.371068i		−	0.0147022i
$638$		0			0
$639$	2.44924	+	7.91941i	0.0968905	+	0.313287i
$640$		0			0
$641$	−34.7454			−1.37236			−0.686180	−	0.727432i	$-0.740714\pi$
$641$	−34.7454			−1.37236			−0.686180	+	0.727432i	$0.740714\pi$
$642$		0			0
$643$	−38.6626			−1.52471			−0.762353	−	0.647162i	$-0.775956\pi$
$643$	−38.6626			−1.52471			−0.762353	+	0.647162i	$0.775956\pi$
$644$		0			0
$645$	−9.59853	+	13.0156i	−0.377942	+	0.512490i
$646$		0			0
$647$			37.4963i			1.47413i	0.675822	+	0.737065i	$0.263789\pi$
$647$			37.4963i			1.47413i	−0.675822	+	0.737065i	$0.736211\pi$
$648$		0			0
$649$			38.4109i			1.50776i
$650$		0			0
$651$	16.7943	−	22.7731i	0.658219	−	0.892547i
$652$		0			0
$653$		−	39.8643i		−	1.56001i	−0.625772	−	0.780006i	$-0.715216\pi$
$653$		−	39.8643i		−	1.56001i	0.625772	−	0.780006i	$-0.284784\pi$
$654$		0			0
$655$	0.923701			0.0360920
$656$		0			0
$657$	−4.84886	−	15.6784i	−0.189172	−	0.611671i
$658$		0			0
$659$	2.67263			0.104111			0.0520555	−	0.998644i	$-0.483423\pi$
$659$	2.67263			0.104111			0.0520555	+	0.998644i	$0.483423\pi$
$660$		0			0
$661$		−	15.9290i		−	0.619567i	−0.950807	−	0.309783i	$-0.899743\pi$
$661$		−	15.9290i		−	0.619567i	0.950807	−	0.309783i	$-0.100257\pi$
$662$		0			0
$663$	−0.292278	−	0.215544i	−0.0113511	−	0.00837103i
$664$		0			0
$665$	12.4739	+	9.62000i	0.483717	+	0.373048i
$666$		0			0
$667$			14.0026i			0.542182i
$668$		0			0
$669$	19.8662	−	26.9386i	0.768070	−	1.04151i
$670$		0			0
$671$			21.5448i			0.831729i
$672$		0			0
$673$			8.62485i			0.332464i	0.986087	+	0.166232i	$0.0531600\pi$
$673$			8.62485i			0.332464i	−0.986087	+	0.166232i	$0.946840\pi$
$674$		0			0
$675$	6.39655	−	18.3457i	0.246203	−	0.706125i
$676$		0			0
$677$	31.8459			1.22394			0.611968	−	0.790882i	$-0.290378\pi$
$677$	31.8459			1.22394			0.611968	+	0.790882i	$0.290378\pi$
$678$		0			0
$679$		−	41.2758i		−	1.58402i
$680$		0			0
$681$	29.8812	+	22.0362i	1.14505	+	0.844430i
$682$		0			0
$683$	−45.6721			−1.74759			−0.873797	−	0.486290i	$-0.838350\pi$
$683$	−45.6721			−1.74759			−0.873797	+	0.486290i	$0.838350\pi$
$684$		0			0
$685$	1.50802			0.0576183
$686$		0			0
$687$	−4.12720	−	3.04365i	−0.157462	−	0.116122i
$688$		0			0
$689$			0.0592301i			0.00225649i
$690$		0			0
$691$	−36.7339			−1.39742			−0.698711	−	0.715404i	$-0.746243\pi$
$691$	−36.7339			−1.39742			−0.698711	+	0.715404i	$0.746243\pi$
$692$		0			0
$693$	28.3028	−	8.75323i	1.07513	−	0.332508i
$694$		0			0
$695$		−	20.3729i		−	0.772788i
$696$		0			0
$697$		−	1.92603i		−	0.0729537i
$698$		0			0
$699$	6.82083	−	9.24907i	0.257988	−	0.349832i
$700$		0			0
$701$		−	33.3805i		−	1.26077i	−0.776284	−	0.630383i	$-0.782898\pi$
$701$		−	33.3805i		−	1.26077i	0.776284	−	0.630383i	$-0.217102\pi$
$702$		0			0
$703$	12.4150	+	9.57459i	0.468242	+	0.361113i
$704$		0			0
$705$	8.89700	+	6.56119i	0.335080	+	0.247109i
$706$		0			0
$707$		−	24.9674i		−	0.938997i
$708$		0			0
$709$	3.93260			0.147692			0.0738459	−	0.997270i	$-0.476473\pi$
$709$	3.93260			0.147692			0.0738459	+	0.997270i	$0.476473\pi$
$710$		0			0
$711$	−50.2186	+	15.5311i	−1.88334	+	0.582463i
$712$		0			0
$713$	40.0947			1.50156
$714$		0			0
$715$		−	0.380786i		−	0.0142406i
$716$		0			0
$717$	1.07387	−	1.45617i	0.0401045	−	0.0543818i
$718$		0			0
$719$		−	25.3129i		−	0.944013i	−0.881595	−	0.472007i	$-0.843530\pi$
$719$		−	25.3129i		−	0.944013i	0.881595	−	0.472007i	$-0.156470\pi$
$720$		0			0
$721$			3.65634i			0.136169i
$722$		0			0
$723$	2.58484	−	3.50505i	0.0961311	−	0.130354i
$724$		0			0
$725$	6.62855			0.246178
$726$		0			0
$727$	−9.67940			−0.358989			−0.179495	−	0.983759i	$-0.557446\pi$
$727$	−9.67940			−0.358989			−0.179495	+	0.983759i	$0.557446\pi$
$728$		0			0
$729$	−21.1468	−	16.7873i	−0.783215	−	0.621751i
$730$		0			0
$731$			15.7753i			0.583472i
$732$		0			0
$733$	15.1166			0.558343			0.279172	−	0.960241i	$-0.409940\pi$
$733$	15.1166			0.558343			0.279172	+	0.960241i	$0.409940\pi$
$734$		0			0
$735$	−3.87590	+	5.25573i	−0.142965	+	0.193861i
$736$		0			0
$737$	−38.4744			−1.41722
$738$		0			0
$739$	11.2840			0.415088			0.207544	−	0.978226i	$-0.433453\pi$
$739$	11.2840			0.415088			0.207544	+	0.978226i	$0.433453\pi$
$740$		0			0
$741$	0.229325	+	0.802239i	0.00842445	+	0.0294710i
$742$		0			0
$743$	−17.2922			−0.634388			−0.317194	−	0.948361i	$-0.602741\pi$
$743$	−17.2922			−0.634388			−0.317194	+	0.948361i	$0.602741\pi$
$744$		0			0
$745$	23.3691			0.856178
$746$		0			0
$747$	−24.8573	+	7.68762i	−0.909479	+	0.281275i
$748$		0			0
$749$	−52.2650			−1.90972
$750$		0			0
$751$		−	34.2993i		−	1.25160i	−0.779983	−	0.625800i	$-0.784773\pi$
$751$		−	34.2993i		−	1.25160i	0.779983	−	0.625800i	$-0.215227\pi$
$752$		0			0
$753$	10.0168	−	13.5828i	0.365033	−	0.494986i
$754$		0			0
$755$	8.57854			0.312205
$756$		0			0
$757$	19.2944			0.701266			0.350633	−	0.936513i	$-0.385966\pi$
$757$	19.2944			0.701266			0.350633	+	0.936513i	$0.385966\pi$
$758$		0			0
$759$	33.7851	+	24.9152i	1.22632	+	0.904366i
$760$		0			0
$761$		−	19.1046i		−	0.692540i	−0.938135	−	0.346270i	$-0.887448\pi$
$761$		−	19.1046i		−	0.692540i	0.938135	−	0.346270i	$-0.112552\pi$
$762$		0			0
$763$			45.9041i			1.66184i
$764$		0			0
$765$	1.88836	+	6.10584i	0.0682737	+	0.220757i
$766$		0			0
$767$		−	1.38345i		−	0.0499534i
$768$		0			0
$769$	−14.5296			−0.523953			−0.261976	−	0.965074i	$-0.584374\pi$
$769$	−14.5296			−0.523953			−0.261976	+	0.965074i	$0.584374\pi$
$770$		0			0
$771$	−29.1463	−	21.4943i	−1.04968	−	0.774097i
$772$		0			0
$773$	5.31337			0.191109			0.0955544	−	0.995424i	$-0.469538\pi$
$773$	5.31337			0.191109			0.0955544	+	0.995424i	$0.469538\pi$
$774$		0			0
$775$		−	18.9801i		−	0.681785i
$776$		0			0
$777$	−11.9000	+	16.1364i	−0.426910	+	0.578891i
$778$		0			0
$779$	−2.70240	+	3.50410i	−0.0968235	+	0.125547i
$780$		0			0
$781$			8.47854i			0.303386i
$782$		0			0
$783$	3.03274	−	8.69808i	0.108381	−	0.310844i
$784$		0			0
$785$			7.54059i			0.269135i
$786$		0			0
$787$			30.6337i			1.09197i	0.837794	+	0.545987i	$0.183845\pi$
$787$			30.6337i			1.09197i	−0.837794	+	0.545987i	$0.816155\pi$
$788$		0			0
$789$	−6.04163	+	8.19246i	−0.215088	+	0.291659i
$790$		0			0
$791$	50.6654			1.80145
$792$		0			0
$793$		−	0.775982i		−	0.0275559i
$794$		0			0
$795$	0.618673	−	0.838923i	0.0219421	−	0.0297535i
$796$		0			0
$797$	9.97137			0.353204			0.176602	−	0.984282i	$-0.443489\pi$
$797$	9.97137			0.353204			0.176602	+	0.984282i	$0.443489\pi$
$798$		0			0
$799$	10.7834			0.381490
$800$		0			0
$801$	1.88617	+	6.09877i	0.0666446	+	0.215490i
$802$		0			0
$803$		−	16.7853i		−	0.592340i
$804$		0			0
$805$	−28.5448			−1.00607
$806$		0			0
$807$	24.9485	+	18.3986i	0.878229	+	0.647660i
$808$		0			0
$809$			22.4569i			0.789543i	0.918779	+	0.394772i	$0.129176\pi$
$809$			22.4569i			0.789543i	−0.918779	+	0.394772i	$0.870824\pi$
$810$		0			0
$811$		−	3.60463i		−	0.126576i	−0.997995	−	0.0632878i	$-0.979841\pi$
$811$		−	3.60463i		−	0.126576i	0.997995	−	0.0632878i	$-0.0201586\pi$
$812$		0			0
$813$	−6.04655	−	4.45910i	−0.212062	−	0.156387i
$814$		0			0
$815$			15.2587i			0.534488i
$816$		0			0
$817$	22.1342	−	28.7006i	0.774378	−	1.00411i
$818$		0			0
$819$	−1.01938	+	0.315266i	−0.0356202	+	0.0110163i
$820$		0			0
$821$			8.90493i			0.310784i	0.987853	+	0.155392i	$0.0496641\pi$
$821$			8.90493i			0.310784i	−0.987853	+	0.155392i	$0.950336\pi$
$822$		0			0
$823$	−8.08397			−0.281789			−0.140895	−	0.990025i	$-0.544998\pi$
$823$	−8.08397			−0.281789			−0.140895	+	0.990025i	$0.544998\pi$
$824$		0			0
$825$	11.7944	−	15.9932i	0.410628	−	0.556813i
$826$		0			0
$827$	−37.6610			−1.30960			−0.654801	−	0.755801i	$-0.727248\pi$
$827$	−37.6610			−1.30960			−0.654801	+	0.755801i	$0.727248\pi$
$828$		0			0
$829$		−	25.3065i		−	0.878931i	−0.898259	−	0.439466i	$-0.855168\pi$
$829$		−	25.3065i		−	0.878931i	0.898259	−	0.439466i	$-0.144832\pi$
$830$		0			0
$831$	−35.8518	−	26.4393i	−1.24369	−	0.917170i
$832$		0			0
$833$			6.37011i			0.220711i
$834$		0			0
$835$			28.6238i			0.990566i
$836$		0			0
$837$	−24.9059	−	8.68390i	−0.860874	−	0.300159i
$838$		0			0
$839$	−17.6367			−0.608887			−0.304443	−	0.952530i	$-0.598470\pi$
$839$	−17.6367			−0.608887			−0.304443	+	0.952530i	$0.598470\pi$
$840$		0			0
$841$	−25.8573			−0.891630
$842$		0			0
$843$	−13.5885	−	10.0210i	−0.468014	−	0.345142i
$844$		0			0
$845$		−	14.5841i		−	0.501708i
$846$		0			0
$847$	−5.10052			−0.175256
$848$		0			0
$849$	−9.74549	−	7.18693i	−0.334464	−	0.246655i
$850$		0			0
$851$	−28.4101			−0.973886
$852$		0			0
$853$	−6.26845			−0.214627			−0.107314	−	0.994225i	$-0.534225\pi$
$853$	−6.26845			−0.214627			−0.107314	+	0.994225i	$0.534225\pi$
$854$		0			0
$855$	5.13149	−	13.7581i	0.175493	−	0.470517i
$856$		0			0
$857$	23.7290			0.810569			0.405284	−	0.914191i	$-0.367172\pi$
$857$	23.7290			0.810569			0.405284	+	0.914191i	$0.367172\pi$
$858$		0			0
$859$	−2.13279			−0.0727699			−0.0363850	−	0.999338i	$-0.511584\pi$
$859$	−2.13279			−0.0727699			−0.0363850	+	0.999338i	$0.511584\pi$
$860$		0			0
$861$	−4.55445	−	3.35873i	−0.155215	−	0.114465i
$862$		0			0
$863$	17.1020			0.582160			0.291080	−	0.956699i	$-0.405985\pi$
$863$	17.1020			0.582160			0.291080	+	0.956699i	$0.405985\pi$
$864$		0			0
$865$			8.26995i			0.281187i
$866$		0			0
$867$	−18.6802	−	13.7759i	−0.634414	−	0.467856i
$868$		0			0
$869$	−53.7641			−1.82382
$870$		0			0
$871$	1.38574			0.0469539
$872$		0			0
$873$	−36.7580	+	11.3682i	−1.24407	+	0.384754i
$874$		0			0
$875$			31.5820i			1.06767i
$876$		0			0
$877$			36.5776i			1.23514i	0.786517	+	0.617569i	$0.211882\pi$
$877$			36.5776i			1.23514i	−0.786517	+	0.617569i	$0.788118\pi$
$878$		0			0
$879$	17.1561	+	12.6519i	0.578660	+	0.426739i
$880$		0			0
$881$		−	24.9469i		−	0.840483i	−0.907412	−	0.420241i	$-0.861945\pi$
$881$		−	24.9469i		−	0.840483i	0.907412	−	0.420241i	$-0.138055\pi$
$882$		0			0
$883$	−35.6173			−1.19862			−0.599309	−	0.800518i	$-0.704558\pi$
$883$	−35.6173			−1.19862			−0.599309	+	0.800518i	$0.704558\pi$
$884$		0			0
$885$	−14.4505	+	19.5949i	−0.485747	+	0.658675i
$886$		0			0
$887$	33.8871			1.13782			0.568909	−	0.822400i	$-0.307366\pi$
$887$	33.8871			1.13782			0.568909	+	0.822400i	$0.307366\pi$
$888$		0			0
$889$			11.9565i			0.401009i
$890$		0			0
$891$	−15.5903	−	22.7941i	−0.522294	−	0.763631i
$892$		0			0
$893$	−19.6187	−	15.1301i	−0.656514	−	0.506310i
$894$		0			0
$895$			5.29907i			0.177128i
$896$		0			0
$897$	−1.21684	−	0.897374i	−0.0406292	−	0.0299624i
$898$		0			0
$899$		−	8.99887i		−	0.300129i
$900$		0			0
$901$		−	1.01680i		−	0.0338745i
$902$		0			0
$903$	37.3036	+	27.5100i	1.24139	+	0.915475i
$904$		0			0
$905$	−5.81538			−0.193310
$906$		0			0
$907$			20.7685i			0.689607i	0.938675	+	0.344804i	$0.112055\pi$
$907$			20.7685i			0.689607i	−0.938675	+	0.344804i	$0.887945\pi$
$908$		0			0
$909$	−22.2346	+	6.87651i	−0.737475	+	0.228080i
$910$		0			0
$911$	−54.4137			−1.80280			−0.901402	−	0.432982i	$-0.857461\pi$
$911$	−54.4137			−1.80280			−0.901402	+	0.432982i	$0.857461\pi$
$912$		0			0
$913$	−26.6122			−0.880737
$914$		0			0
$915$	−8.10533	+	10.9909i	−0.267954	+	0.363346i
$916$		0			0
$917$		−	2.64739i		−	0.0874244i
$918$		0			0
$919$	52.5253			1.73265			0.866325	−	0.499481i	$-0.166476\pi$
$919$	52.5253			1.73265			0.866325	+	0.499481i	$0.166476\pi$
$920$		0			0
$921$	−16.6370	+	22.5599i	−0.548209	+	0.743373i
$922$		0			0
$923$		−	0.305372i		−	0.0100514i
$924$		0			0
$925$			13.4488i			0.442194i
$926$		0			0
$927$	3.25614	−	1.00703i	0.106946	−	0.0330751i
$928$		0			0
$929$		−	23.4235i		−	0.768501i	−0.923229	−	0.384250i	$-0.874460\pi$
$929$		−	23.4235i		−	0.768501i	0.923229	−	0.384250i	$-0.125540\pi$
$930$		0			0
$931$	8.93783	−	11.5894i	0.292926	−	0.379826i
$932$		0			0
$933$	−16.3532	+	22.1749i	−0.535379	+	0.725975i
$934$		0			0
$935$			6.53693i			0.213780i
$936$		0			0
$937$	−6.73733			−0.220099			−0.110049	−	0.993926i	$-0.535101\pi$
$937$	−6.73733			−0.220099			−0.110049	+	0.993926i	$0.535101\pi$
$938$		0			0
$939$	−28.8349	−	21.2646i	−0.940991	−	0.693945i
$940$		0			0
$941$	−43.9061			−1.43130			−0.715650	−	0.698459i	$-0.753869\pi$
$941$	−43.9061			−1.43130			−0.715650	+	0.698459i	$0.753869\pi$
$942$		0			0
$943$		−	8.01866i		−	0.261123i
$944$		0			0
$945$	17.7314	+	6.18237i	0.576802	+	0.201113i
$946$		0			0
$947$		−	40.1163i		−	1.30360i	−0.758389	−	0.651802i	$-0.774013\pi$
$947$		−	40.1163i		−	1.30360i	0.758389	−	0.651802i	$-0.225987\pi$
$948$		0			0
$949$			0.604558i			0.0196248i
$950$		0			0
$951$	−29.6414	−	21.8594i	−0.961187	−	0.708839i
$952$		0			0
$953$	−33.3795			−1.08127			−0.540634	−	0.841258i	$-0.681815\pi$
$953$	−33.3795			−1.08127			−0.540634	+	0.841258i	$0.681815\pi$
$954$		0			0
$955$	−26.6013			−0.860796
$956$		0			0
$957$	5.59198	−	7.58275i	0.180763	−	0.245115i
$958$		0			0
$959$		−	4.32207i		−	0.139567i
$960$		0			0
$961$	5.23280			0.168800
$962$		0			0
$963$	14.3948	+	46.5443i	0.463866	+	1.49987i
$964$		0			0
$965$	14.5268			0.467634
$966$		0			0
$967$	−5.50334			−0.176975			−0.0884877	−	0.996077i	$-0.528203\pi$
$967$	−5.50334			−0.176975			−0.0884877	+	0.996077i	$0.528203\pi$
$968$		0			0
$969$	−3.93680	−	13.7720i	−0.126468	−	0.442420i
$970$		0			0
$971$	22.4580			0.720712			0.360356	−	0.932815i	$-0.382655\pi$
$971$	22.4580			0.720712			0.360356	+	0.932815i	$0.382655\pi$
$972$		0			0
$973$	−58.3900			−1.87190
$974$		0			0
$975$	−0.424800	+	0.576030i	−0.0136045	+	0.0184477i
$976$		0			0
$977$	−36.5252			−1.16854			−0.584272	−	0.811558i	$-0.698620\pi$
$977$	−36.5252			−1.16854			−0.584272	+	0.811558i	$0.698620\pi$
$978$		0			0
$979$			6.52936i			0.208679i
$980$		0			0
$981$	40.8796	−	12.6429i	1.30519	−	0.403656i
$982$		0			0
$983$	19.3826			0.618207			0.309104	−	0.951028i	$-0.399971\pi$
$983$	19.3826			0.618207			0.309104	+	0.951028i	$0.399971\pi$
$984$		0			0
$985$	−6.47607			−0.206345
$986$		0			0
$987$	18.8048	−	25.4994i	0.598563	−	0.811653i
$988$		0			0
$989$			65.6775i			2.08842i
$990$		0			0
$991$			42.9880i			1.36556i	0.730624	+	0.682780i	$0.239229\pi$
$991$			42.9880i			1.36556i	−0.730624	+	0.682780i	$0.760771\pi$
$992$		0			0
$993$	22.5302	−	30.5511i	0.714976	−	0.969509i
$994$		0			0
$995$			16.6467i			0.527736i
$996$		0			0
$997$	−27.8836			−0.883083			−0.441542	−	0.897241i	$-0.645568\pi$
$997$	−27.8836			−0.883083			−0.441542	+	0.897241i	$0.645568\pi$
$998$		0			0
$999$	17.6477	+	6.15319i	0.558348	+	0.194678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.f.h.113.3		10
3.2	odd	2		912.2.f.i.113.7		10
4.3	odd	2		456.2.f.b.113.8	yes	10
12.11	even	2		456.2.f.a.113.4	yes	10
19.18	odd	2		912.2.f.i.113.8		10
57.56	even	2	inner	912.2.f.h.113.4		10
76.75	even	2		456.2.f.a.113.3	✓	10
228.227	odd	2		456.2.f.b.113.7	yes	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
456.2.f.a.113.3	✓	10	76.75	even	2
456.2.f.a.113.4	yes	10	12.11	even	2
456.2.f.b.113.7	yes	10	228.227	odd	2
456.2.f.b.113.8	yes	10	4.3	odd	2
912.2.f.h.113.3		10	1.1	even	1	trivial
912.2.f.h.113.4		10	57.56	even	2	inner
912.2.f.i.113.7		10	3.2	odd	2
912.2.f.i.113.8		10	19.18	odd	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:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.f (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.39399 - 1.02801i) q^{3} -1.12291i q^{5} -3.21832 q^{7} +(0.886389 + 2.86606i) q^{9} +O(q^{10})\)	\(q+(-1.39399 - 1.02801i) q^{3} -1.12291i q^{5} -3.21832 q^{7} +(0.886389 + 2.86606i) q^{9} +3.06841i q^{11} -0.110515i q^{13} +(-1.15436 + 1.56532i) q^{15} +1.89721i q^{17} +(2.66196 - 3.45166i) q^{19} +(4.48630 + 3.30847i) q^{21} +7.89866i q^{23} +3.73908 q^{25} +(1.71073 - 4.90647i) q^{27} +1.77278 q^{29} -5.07614i q^{31} +(3.15436 - 4.27732i) q^{33} +3.61388i q^{35} +3.59682i q^{37} +(-0.113611 + 0.154057i) q^{39} -1.01519 q^{41} +8.31502 q^{43} +(3.21832 - 0.995334i) q^{45} -5.68383i q^{47} +3.35762 q^{49} +(1.95035 - 2.64468i) q^{51} -0.535944 q^{53} +3.44555 q^{55} +(-7.25908 + 2.07505i) q^{57} +12.5182 q^{59} +7.02149 q^{61} +(-2.85269 - 9.22392i) q^{63} -0.124099 q^{65} +12.5389i q^{67} +(8.11991 - 11.0106i) q^{69} +2.76317 q^{71} -5.47035 q^{73} +(-5.21222 - 3.84381i) q^{75} -9.87515i q^{77} +17.5218i q^{79} +(-7.42863 + 5.08089i) q^{81} +8.67296i q^{83} +2.13039 q^{85} +(-2.47123 - 1.82243i) q^{87} +2.12793 q^{89} +0.355674i q^{91} +(-5.21832 + 7.07606i) q^{93} +(-3.87590 - 2.98913i) q^{95} +12.8252i q^{97} +(-8.79427 + 2.71981i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{3} + 2 q^{7} + 3 q^{9}+O(q^{10}) \) 10 * q - q^3 + 2 * q^7 + 3 * q^9	\( 10 q - q^{3} + 2 q^{7} + 3 q^{9} + 10 q^{15} - 2 q^{19} - 5 q^{21} - 14 q^{25} - 10 q^{27} + 6 q^{29} + 10 q^{33} - 7 q^{39} + 4 q^{41} - 20 q^{43} - 2 q^{45} + 16 q^{49} + q^{51} + 26 q^{53} + 12 q^{55} - 11 q^{57} + 2 q^{59} - 4 q^{61} + 17 q^{63} - 32 q^{65} + 27 q^{69} + 8 q^{71} - 26 q^{73} + 39 q^{75} + 23 q^{81} - 8 q^{85} - 13 q^{87} - 4 q^{89} - 18 q^{93} - 8 q^{95} - 2 q^{99}+O(q^{100}) \) 10 * q - q^3 + 2 * q^7 + 3 * q^9 + 10 * q^15 - 2 * q^19 - 5 * q^21 - 14 * q^25 - 10 * q^27 + 6 * q^29 + 10 * q^33 - 7 * q^39 + 4 * q^41 - 20 * q^43 - 2 * q^45 + 16 * q^49 + q^51 + 26 * q^53 + 12 * q^55 - 11 * q^57 + 2 * q^59 - 4 * q^61 + 17 * q^63 - 32 * q^65 + 27 * q^69 + 8 * q^71 - 26 * q^73 + 39 * q^75 + 23 * q^81 - 8 * q^85 - 13 * q^87 - 4 * q^89 - 18 * q^93 - 8 * q^95 - 2 * q^99

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