LMFDB - Embedded newform 1872.2.by.g.1297.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1872,2,Mod(433,1872)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1872, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1872.433"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1872 = 2^{4} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1872.by (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,-6,0,0,0,-6,0,0,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$14.9479952584$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 312)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1297.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1872.1297
Dual form			1872.2.by.g.433.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q-1.73205i q^{5} +(-2.36603 - 1.36603i) q^{7} +(-2.36603 + 1.36603i) q^{11} +(-2.59808 - 2.50000i) q^{13} +(0.133975 - 0.232051i) q^{17} +(-4.09808 - 2.36603i) q^{19} +(4.09808 + 7.09808i) q^{23} +2.00000 q^{25} +(3.96410 + 6.86603i) q^{29} +1.46410i q^{31} +(-2.36603 + 4.09808i) q^{35} +(-1.33013 + 0.767949i) q^{37} +(-4.33013 + 2.50000i) q^{41} +(-6.09808 + 10.5622i) q^{43} +3.26795i q^{47} +(0.232051 + 0.401924i) q^{49} +7.92820 q^{53} +(2.36603 + 4.09808i) q^{55} +(3.13397 - 5.42820i) q^{61} +(-4.33013 + 4.50000i) q^{65} +(-7.56218 + 4.36603i) q^{67} +(-1.90192 - 1.09808i) q^{71} -9.19615i q^{73} +7.46410 q^{77} +8.39230 q^{79} -1.66025i q^{83} +(-0.401924 - 0.232051i) q^{85} +(-8.19615 + 4.73205i) q^{89} +(2.73205 + 9.46410i) q^{91} +(-4.09808 + 7.09808i) q^{95} +(8.66025 + 5.00000i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{7} - 6 q^{11} + 4 q^{17} - 6 q^{19} + 6 q^{23} + 8 q^{25} + 2 q^{29} - 6 q^{35} + 12 q^{37} - 14 q^{43} - 6 q^{49} + 4 q^{53} + 6 q^{55} + 16 q^{61} - 6 q^{67} - 18 q^{71} + 16 q^{77} - 8 q^{79}+ \cdots - 6 q^{95}+O(q^{100}) $ 4 * q - 6 * q^7 - 6 * q^11 + 4 * q^17 - 6 * q^19 + 6 * q^23 + 8 * q^25 + 2 * q^29 - 6 * q^35 + 12 * q^37 - 14 * q^43 - 6 * q^49 + 4 * q^53 + 6 * q^55 + 16 * q^61 - 6 * q^67 - 18 * q^71 + 16 * q^77 - 8 * q^79 - 12 * q^85 - 12 * q^89 + 4 * q^91 - 6 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1872\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$	$1$

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
$3$		0			0
$3$		0			0
$4$		0			0
$5$		−	1.73205i		−	0.774597i	−0.921954	−	0.387298i	$-0.873408\pi$
$5$		−	1.73205i		−	0.774597i	0.921954	−	0.387298i	$-0.126592\pi$
$6$		0			0
$7$	−2.36603	−	1.36603i	−0.894274	−	0.516309i	−0.0189356	−	0.999821i	$-0.506028\pi$
$7$	−2.36603	−	1.36603i	−0.894274	−	0.516309i	−0.875338	+	0.483512i	$0.839361\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−2.36603	+	1.36603i	−0.713384	+	0.411872i	−0.812313	−	0.583222i	$-0.801792\pi$
$11$	−2.36603	+	1.36603i	−0.713384	+	0.411872i	0.0989291	+	0.995094i	$0.468458\pi$
$12$		0			0
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$13$	−2.59808	−	2.50000i	−0.720577	−	0.693375i
$14$		0			0
$15$		0			0
$16$		0			0
$17$	0.133975	−	0.232051i	0.0324936	−	0.0562806i	−0.849321	−	0.527876i	$-0.822988\pi$
$17$	0.133975	−	0.232051i	0.0324936	−	0.0562806i	0.881815	+	0.471596i	$0.156322\pi$
$18$		0			0
$19$	−4.09808	−	2.36603i	−0.940163	−	0.542803i	−0.0501517	−	0.998742i	$-0.515970\pi$
$19$	−4.09808	−	2.36603i	−0.940163	−	0.542803i	−0.890011	+	0.455938i	$0.849304\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	0.877101	+	0.480306i	$0.159475\pi$
$23$	4.09808	+	7.09808i	0.854508	+	1.48005i	−0.0225928	+	0.999745i	$0.507192\pi$
$24$		0			0
$25$	2.00000			0.400000
$26$		0			0
$27$		0			0
$28$		0			0
$29$	3.96410	+	6.86603i	0.736115	+	1.27499i	0.954232	+	0.299066i	$0.0966752\pi$
$29$	3.96410	+	6.86603i	0.736115	+	1.27499i	−0.218117	+	0.975923i	$0.569991\pi$
$30$		0			0
$31$			1.46410i			0.262960i	0.991319	+	0.131480i	$0.0419730\pi$
$31$			1.46410i			0.262960i	−0.991319	+	0.131480i	$0.958027\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.36603	+	4.09808i	−0.399931	+	0.692701i
$36$		0			0
$37$	−1.33013	+	0.767949i	−0.218672	+	0.126250i	−0.605335	−	0.795971i	$-0.706961\pi$
$37$	−1.33013	+	0.767949i	−0.218672	+	0.126250i	0.386663	+	0.922221i	$0.373628\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−4.33013	+	2.50000i	−0.676252	+	0.390434i	−0.798441	−	0.602072i	$-0.794342\pi$
$41$	−4.33013	+	2.50000i	−0.676252	+	0.390434i	0.122189	+	0.992507i	$0.461009\pi$
$42$		0			0
$43$	−6.09808	+	10.5622i	−0.929948	+	1.61072i	−0.146544	+	0.989204i	$0.546815\pi$
$43$	−6.09808	+	10.5622i	−0.929948	+	1.61072i	−0.783404	+	0.621513i	$0.786518\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$			3.26795i			0.476679i	0.971182	+	0.238340i	$0.0766032\pi$
$47$			3.26795i			0.476679i	−0.971182	+	0.238340i	$0.923397\pi$
$48$		0			0
$49$	0.232051	+	0.401924i	0.0331501	+	0.0574177i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	7.92820			1.08902			0.544511	−	0.838754i	$-0.316715\pi$
$53$	7.92820			1.08902			0.544511	+	0.838754i	$0.316715\pi$
$54$		0			0
$55$	2.36603	+	4.09808i	0.319035	+	0.552584i
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$59$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$60$		0			0
$61$	3.13397	−	5.42820i	0.401264	−	0.695010i	−0.592614	−	0.805486i	$-0.701904\pi$
$61$	3.13397	−	5.42820i	0.401264	−	0.695010i	0.993879	+	0.110476i	$0.0352375\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−4.33013	+	4.50000i	−0.537086	+	0.558156i
$66$		0			0
$67$	−7.56218	+	4.36603i	−0.923867	+	0.533395i	−0.884867	−	0.465844i	$-0.845751\pi$
$67$	−7.56218	+	4.36603i	−0.923867	+	0.533395i	−0.0390004	+	0.999239i	$0.512417\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.90192	−	1.09808i	−0.225717	−	0.130318i	0.382878	−	0.923799i	$-0.374933\pi$
$71$	−1.90192	−	1.09808i	−0.225717	−	0.130318i	−0.608595	+	0.793481i	$0.708266\pi$
$72$		0			0
$73$		−	9.19615i		−	1.07633i	−0.842840	−	0.538164i	$-0.819118\pi$
$73$		−	9.19615i		−	1.07633i	0.842840	−	0.538164i	$-0.180882\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	7.46410			0.850613
$78$		0			0
$79$	8.39230			0.944208			0.472104	−	0.881543i	$-0.343495\pi$
$79$	8.39230			0.944208			0.472104	+	0.881543i	$0.343495\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$		−	1.66025i		−	0.182237i	−0.995840	−	0.0911183i	$-0.970956\pi$
$83$		−	1.66025i		−	0.182237i	0.995840	−	0.0911183i	$-0.0290441\pi$
$84$		0			0
$85$	−0.401924	−	0.232051i	−0.0435948	−	0.0251694i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−8.19615	+	4.73205i	−0.868790	+	0.501596i	−0.866946	−	0.498402i	$-0.833920\pi$
$89$	−8.19615	+	4.73205i	−0.868790	+	0.501596i	−0.00184433	+	0.999998i	$0.500587\pi$
$90$		0			0
$91$	2.73205	+	9.46410i	0.286397	+	0.992107i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.09808	+	7.09808i	−0.420454	+	0.728247i
$96$		0			0
$97$	8.66025	+	5.00000i	0.879316	+	0.507673i	0.870433	−	0.492287i	$-0.163839\pi$
$97$	8.66025	+	5.00000i	0.879316	+	0.507673i	0.00888289	+	0.999961i	$0.497172\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	3.76795	+	6.52628i	0.374925	+	0.649389i	0.990316	−	0.138833i	$-0.0443351\pi$
$101$	3.76795	+	6.52628i	0.374925	+	0.649389i	−0.615391	+	0.788222i	$0.711002\pi$
$102$		0			0
$103$	0.732051			0.0721311			0.0360656	−	0.999349i	$-0.488517\pi$
$103$	0.732051			0.0721311			0.0360656	+	0.999349i	$0.488517\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−4.56218	−	7.90192i	−0.441042	−	0.763908i	0.556725	−	0.830697i	$-0.312058\pi$
$107$	−4.56218	−	7.90192i	−0.441042	−	0.763908i	−0.997767	+	0.0667892i	$0.978724\pi$
$108$		0			0
$109$			20.3923i			1.95323i	0.214999	+	0.976614i	$0.431025\pi$
$109$			20.3923i			1.95323i	−0.214999	+	0.976614i	$0.568975\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.33013	+	10.9641i	−0.595488	+	1.03142i	0.397990	+	0.917390i	$0.369708\pi$
$113$	−6.33013	+	10.9641i	−0.595488	+	1.03142i	−0.993478	+	0.114026i	$0.963625\pi$
$114$		0			0
$115$	12.2942	−	7.09808i	1.14644	−	0.661899i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.633975	+	0.366025i	−0.0581164	+	0.0335535i
$120$		0			0
$121$	−1.76795	+	3.06218i	−0.160723	+	0.278380i
$122$		0			0
$123$		0			0
$124$		0			0
$125$		−	12.1244i		−	1.08444i
$126$		0			0
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	0.763542	−	0.645758i	$-0.223458\pi$
$127$	−2.00000	−	3.46410i	−0.177471	−	0.307389i	−0.941014	+	0.338368i	$0.890125\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−15.3205			−1.33856			−0.669280	−	0.743011i	$-0.733397\pi$
$131$	−15.3205			−1.33856			−0.669280	+	0.743011i	$0.733397\pi$
$132$		0			0
$133$	6.46410	+	11.1962i	0.560509	+	0.970830i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−4.79423	−	2.76795i	−0.409599	−	0.236482i	0.281019	−	0.959702i	$-0.409328\pi$
$137$	−4.79423	−	2.76795i	−0.409599	−	0.236482i	−0.690617	+	0.723220i	$0.742661\pi$
$138$		0			0
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	−0.0346338	−	0.999400i	$-0.511026\pi$
$139$	10.0000	−	17.3205i	0.848189	−	1.46911i	0.882823	−	0.469706i	$-0.155640\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	9.56218	+	2.36603i	0.799629	+	0.197857i
$144$		0			0
$145$	11.8923	−	6.86603i	0.987602	−	0.570192i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−18.6962	−	10.7942i	−1.53165	−	0.884298i	−0.999286	−	0.0377811i	$-0.987971\pi$
$149$	−18.6962	−	10.7942i	−1.53165	−	0.884298i	−0.532362	−	0.846517i	$-0.678696\pi$
$150$		0			0
$151$			17.2679i			1.40525i	0.711562	+	0.702623i	$0.247988\pi$
$151$			17.2679i			1.40525i	−0.711562	+	0.702623i	$0.752012\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.53590			0.203688
$156$		0			0
$157$	−23.0526			−1.83979			−0.919897	−	0.392159i	$-0.871728\pi$
$157$	−23.0526			−1.83979			−0.919897	+	0.392159i	$0.871728\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$		−	22.3923i		−	1.76476i
$162$		0			0
$163$	−11.6603	−	6.73205i	−0.913302	−	0.527295i	−0.0318096	−	0.999494i	$-0.510127\pi$
$163$	−11.6603	−	6.73205i	−0.913302	−	0.527295i	−0.881492	+	0.472199i	$0.843460\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1.26795	+	0.732051i	−0.0981169	+	0.0566478i	−0.548256	−	0.836311i	$-0.684708\pi$
$167$	−1.26795	+	0.732051i	−0.0981169	+	0.0566478i	0.450139	+	0.892959i	$0.351375\pi$
$168$		0			0
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−8.73205	+	15.1244i	−0.663886	+	1.14988i	0.315701	+	0.948859i	$0.397760\pi$
$173$	−8.73205	+	15.1244i	−0.663886	+	1.14988i	−0.979586	+	0.201025i	$0.935573\pi$
$174$		0			0
$175$	−4.73205	−	2.73205i	−0.357709	−	0.206524i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	10.3660	+	17.9545i	0.774793	+	1.34198i	0.934911	+	0.354883i	$0.115479\pi$
$179$	10.3660	+	17.9545i	0.774793	+	1.34198i	−0.160118	+	0.987098i	$0.551187\pi$
$180$		0			0
$181$	−19.1962			−1.42684			−0.713419	−	0.700737i	$-0.752855\pi$
$181$	−19.1962			−1.42684			−0.713419	+	0.700737i	$0.752855\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.33013	+	2.30385i	0.0977929	+	0.169382i
$186$		0			0
$187$			0.732051i			0.0535329i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.46410	−	12.9282i	0.540083	−	0.935452i	−0.458815	−	0.888532i	$-0.651726\pi$
$191$	7.46410	−	12.9282i	0.540083	−	0.935452i	0.998899	−	0.0469202i	$-0.0149407\pi$
$192$		0			0
$193$	−10.1603	+	5.86603i	−0.731351	+	0.422246i	−0.818916	−	0.573913i	$-0.805425\pi$
$193$	−10.1603	+	5.86603i	−0.731351	+	0.422246i	0.0875652	+	0.996159i	$0.472091\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	0.928203	−	0.535898i	0.0661317	−	0.0381812i	−0.466570	−	0.884485i	$-0.654510\pi$
$197$	0.928203	−	0.535898i	0.0661317	−	0.0381812i	0.532701	+	0.846303i	$0.321177\pi$
$198$		0			0
$199$	0.169873	−	0.294229i	0.0120420	−	0.0208573i	−0.859942	−	0.510392i	$-0.829500\pi$
$199$	0.169873	−	0.294229i	0.0120420	−	0.0208573i	0.871984	+	0.489535i	$0.162833\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$		−	21.6603i		−	1.52025i
$204$		0			0
$205$	4.33013	+	7.50000i	0.302429	+	0.523823i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	12.9282			0.894263
$210$		0			0
$211$	−5.66025	−	9.80385i	−0.389668	−	0.674925i	0.602737	−	0.797940i	$-0.294077\pi$
$211$	−5.66025	−	9.80385i	−0.389668	−	0.674925i	−0.992405	+	0.123015i	$0.960744\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	18.2942	+	10.5622i	1.24766	+	0.720335i
$216$		0			0
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−0.928203	+	0.267949i	−0.0624377	+	0.0180242i
$222$		0			0
$223$	14.5359	−	8.39230i	0.973396	−	0.561990i	0.0731260	−	0.997323i	$-0.476702\pi$
$223$	14.5359	−	8.39230i	0.973396	−	0.561990i	0.900270	+	0.435332i	$0.143369\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.0981	−	11.0263i	−1.26758	−	0.731840i	−0.293054	−	0.956096i	$-0.594671\pi$
$227$	−19.0981	−	11.0263i	−1.26758	−	0.731840i	−0.974530	+	0.224256i	$0.928005\pi$
$228$		0			0
$229$		−	0.143594i		−	0.00948893i	−0.999989	−	0.00474446i	$-0.998490\pi$
$229$		−	0.143594i		−	0.00948893i	0.999989	−	0.00474446i	$-0.00151022\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−2.00000			−0.131024			−0.0655122	−	0.997852i	$-0.520868\pi$
$233$	−2.00000			−0.131024			−0.0655122	+	0.997852i	$0.520868\pi$
$234$		0			0
$235$	5.66025			0.369234
$236$		0			0
$237$		0			0
$238$		0			0
$239$			23.2679i			1.50508i	0.658547	+	0.752539i	$0.271171\pi$
$239$			23.2679i			1.50508i	−0.658547	+	0.752539i	$0.728829\pi$
$240$		0			0
$241$	4.62436	+	2.66987i	0.297881	+	0.171982i	0.641491	−	0.767131i	$-0.278316\pi$
$241$	4.62436	+	2.66987i	0.297881	+	0.171982i	−0.343610	+	0.939113i	$0.611650\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	0.696152	−	0.401924i	0.0444755	−	0.0256780i
$246$		0			0
$247$	4.73205	+	16.3923i	0.301093	+	1.04302i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−1.26795	+	2.19615i	−0.0800322	+	0.138620i	−0.903264	−	0.429086i	$-0.858836\pi$
$251$	−1.26795	+	2.19615i	−0.0800322	+	0.138620i	0.823231	+	0.567706i	$0.192169\pi$
$252$		0			0
$253$	−19.3923	−	11.1962i	−1.21918	−	0.703896i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	7.13397	+	12.3564i	0.445005	+	0.770771i	0.998053	−	0.0623783i	$-0.0198685\pi$
$257$	7.13397	+	12.3564i	0.445005	+	0.770771i	−0.553047	+	0.833150i	$0.686535\pi$
$258$		0			0
$259$	4.19615			0.260736
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−14.8301	−	25.6865i	−0.914465	−	1.58390i	−0.807683	−	0.589617i	$-0.799279\pi$
$263$	−14.8301	−	25.6865i	−0.914465	−	1.58390i	−0.106782	−	0.994282i	$-0.534055\pi$
$264$		0			0
$265$		−	13.7321i		−	0.843553i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.26795	−	2.19615i	0.0773082	−	0.133902i	−0.824779	−	0.565455i	$-0.808701\pi$
$269$	1.26795	−	2.19615i	0.0773082	−	0.133902i	0.902088	+	0.431553i	$0.142034\pi$
$270$		0			0
$271$	13.8564	−	8.00000i	0.841717	−	0.485965i	−0.0161307	−	0.999870i	$-0.505135\pi$
$271$	13.8564	−	8.00000i	0.841717	−	0.485965i	0.857847	+	0.513905i	$0.171801\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−4.73205	+	2.73205i	−0.285353	+	0.164749i
$276$		0			0
$277$	8.06218	−	13.9641i	0.484409	−	0.839022i	−0.515430	−	0.856932i	$-0.672368\pi$
$277$	8.06218	−	13.9641i	0.484409	−	0.839022i	0.999840	+	0.0179100i	$0.00570122\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$			30.7128i			1.83217i	0.400981	+	0.916086i	$0.368669\pi$
$281$			30.7128i			1.83217i	−0.400981	+	0.916086i	$0.631331\pi$
$282$		0			0
$283$	−11.7583	−	20.3660i	−0.698960	−	1.21063i	−0.968827	−	0.247737i	$-0.920313\pi$
$283$	−11.7583	−	20.3660i	−0.698960	−	1.21063i	0.269867	−	0.962898i	$-0.413020\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	13.6603			0.806339
$288$		0			0
$289$	8.46410	+	14.6603i	0.497888	+	0.862368i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	19.1603	+	11.0622i	1.11935	+	0.646259i	0.941236	−	0.337750i	$-0.109666\pi$
$293$	19.1603	+	11.0622i	1.11935	+	0.646259i	0.178118	+	0.984009i	$0.442999\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	7.09808	−	28.6865i	0.410492	−	1.65899i
$300$		0			0
$301$	28.8564	−	16.6603i	1.66326	−	0.960281i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−9.40192	−	5.42820i	−0.538353	−	0.310818i
$306$		0			0
$307$		−	7.26795i		−	0.414804i	−0.978256	−	0.207402i	$-0.933499\pi$
$307$		−	7.26795i		−	0.414804i	0.978256	−	0.207402i	$-0.0665008\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	21.6603			1.22824			0.614120	−	0.789213i	$-0.289511\pi$
$311$	21.6603			1.22824			0.614120	+	0.789213i	$0.289511\pi$
$312$		0			0
$313$	−31.3205			−1.77034			−0.885170	−	0.465268i	$-0.845958\pi$
$313$	−31.3205			−1.77034			−0.885170	+	0.465268i	$0.845958\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$		−	0.803848i		−	0.0451486i	−0.999745	−	0.0225743i	$-0.992814\pi$
$317$		−	0.803848i		−	0.0451486i	0.999745	−	0.0225743i	$-0.00718623\pi$
$318$		0			0
$319$	−18.7583	−	10.8301i	−1.05026	−	0.606371i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−1.09808	+	0.633975i	−0.0610986	+	0.0352753i
$324$		0			0
$325$	−5.19615	−	5.00000i	−0.288231	−	0.277350i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	4.46410	−	7.73205i	0.246114	−	0.426282i
$330$		0			0
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	0.757634	−	0.652680i	$-0.226355\pi$
$331$	10.3923	+	6.00000i	0.571213	+	0.329790i	−0.186421	+	0.982470i	$0.559689\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.56218	+	13.0981i	0.413166	+	0.715624i
$336$		0			0
$337$	4.07180			0.221805			0.110902	−	0.993831i	$-0.464626\pi$
$337$	4.07180			0.221805			0.110902	+	0.993831i	$0.464626\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$		0			0
$343$			17.8564i			0.964155i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	8.75833	−	15.1699i	0.470172	−	0.814361i	−0.529246	−	0.848468i	$-0.677525\pi$
$347$	8.75833	−	15.1699i	0.470172	−	0.814361i	0.999418	+	0.0341067i	$0.0108586\pi$
$348$		0			0
$349$	−10.7321	+	6.19615i	−0.574474	+	0.331672i	−0.758934	−	0.651167i	$-0.774280\pi$
$349$	−10.7321	+	6.19615i	−0.574474	+	0.331672i	0.184461	+	0.982840i	$0.440946\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	15.1865	−	8.76795i	0.808298	−	0.466671i	−0.0380667	−	0.999275i	$-0.512120\pi$
$353$	15.1865	−	8.76795i	0.808298	−	0.466671i	0.846364	+	0.532604i	$0.178787\pi$
$354$		0			0
$355$	−1.90192	+	3.29423i	−0.100944	+	0.174840i
$356$		0			0
$357$		0			0
$358$		0			0
$359$			25.5167i			1.34672i	0.739316	+	0.673359i	$0.235149\pi$
$359$			25.5167i			1.34672i	−0.739316	+	0.673359i	$0.764851\pi$
$360$		0			0
$361$	1.69615	+	2.93782i	0.0892712	+	0.154622i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−15.9282			−0.833720
$366$		0			0
$367$	−0.562178	−	0.973721i	−0.0293454	−	0.0508278i	0.850980	−	0.525199i	$-0.176009\pi$
$367$	−0.562178	−	0.973721i	−0.0293454	−	0.0508278i	−0.880325	+	0.474371i	$0.842676\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−18.7583	−	10.8301i	−0.973884	−	0.562272i
$372$		0			0
$373$	16.3301	−	28.2846i	0.845542	−	1.46452i	−0.0396078	−	0.999215i	$-0.512611\pi$
$373$	16.3301	−	28.2846i	0.845542	−	1.46452i	0.885150	−	0.465306i	$-0.154056\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.86603	−	27.7487i	0.353618	−	1.42913i
$378$		0			0
$379$	−13.5167	+	7.80385i	−0.694304	+	0.400857i	−0.805222	−	0.592973i	$-0.797954\pi$
$379$	−13.5167	+	7.80385i	−0.694304	+	0.400857i	0.110918	+	0.993830i	$0.464621\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	0.588457	+	0.339746i	0.0300688	+	0.0173602i	0.514959	−	0.857215i	$-0.327807\pi$
$383$	0.588457	+	0.339746i	0.0300688	+	0.0173602i	−0.484890	+	0.874575i	$0.661140\pi$
$384$		0			0
$385$		−	12.9282i		−	0.658882i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	17.5359			0.889105			0.444553	−	0.895753i	$-0.353363\pi$
$389$	17.5359			0.889105			0.444553	+	0.895753i	$0.353363\pi$
$390$		0			0
$391$	2.19615			0.111064
$392$		0			0
$393$		0			0
$394$		0			0
$395$		−	14.5359i		−	0.731380i
$396$		0			0
$397$	15.1244	+	8.73205i	0.759070	+	0.438249i	0.828962	−	0.559305i	$-0.188932\pi$
$397$	15.1244	+	8.73205i	0.759070	+	0.438249i	−0.0698920	+	0.997555i	$0.522265\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.4545	−	11.2321i	0.971511	−	0.560902i	0.0718141	−	0.997418i	$-0.477121\pi$
$401$	19.4545	−	11.2321i	0.971511	−	0.560902i	0.899696	+	0.436516i	$0.143788\pi$
$402$		0			0
$403$	3.66025	−	3.80385i	0.182330	−	0.189483i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	2.09808	−	3.63397i	0.103998	−	0.180129i
$408$		0			0
$409$	−28.7487	−	16.5981i	−1.42153	−	0.820722i	−0.425102	−	0.905145i	$-0.639762\pi$
$409$	−28.7487	−	16.5981i	−1.42153	−	0.820722i	−0.996430	+	0.0844233i	$0.973095\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.87564			−0.141160
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.80385	+	10.0526i	0.283537	+	0.491100i	0.972253	−	0.233931i	$-0.0751590\pi$
$419$	5.80385	+	10.0526i	0.283537	+	0.491100i	−0.688717	+	0.725031i	$0.741826\pi$
$420$		0			0
$421$		−	5.00000i		−	0.243685i	−0.992549	−	0.121843i	$-0.961120\pi$
$421$		−	5.00000i		−	0.243685i	0.992549	−	0.121843i	$-0.0388803\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.267949	−	0.464102i	0.0129974	−	0.0225122i
$426$		0			0
$427$	−14.8301	+	8.56218i	−0.717680	+	0.414353i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−24.2942	+	14.0263i	−1.17021	+	0.675622i	−0.953730	−	0.300665i	$-0.902792\pi$
$431$	−24.2942	+	14.0263i	−1.17021	+	0.675622i	−0.216482	+	0.976287i	$0.569458\pi$
$432$		0			0
$433$	−1.57180	+	2.72243i	−0.0755357	+	0.130832i	−0.901319	−	0.433156i	$-0.857400\pi$
$433$	−1.57180	+	2.72243i	−0.0755357	+	0.130832i	0.825783	+	0.563987i	$0.190733\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$		−	38.7846i		−	1.85532i
$438$		0			0
$439$	−4.90192	−	8.49038i	−0.233956	−	0.405224i	0.725013	−	0.688735i	$-0.241834\pi$
$439$	−4.90192	−	8.49038i	−0.233956	−	0.405224i	−0.958969	+	0.283512i	$0.908501\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	19.3205			0.917945			0.458973	−	0.888450i	$-0.348218\pi$
$443$	19.3205			0.917945			0.458973	+	0.888450i	$0.348218\pi$
$444$		0			0
$445$	8.19615	+	14.1962i	0.388535	+	0.672962i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.87564	−	1.66025i	−0.135710	−	0.0783522i	0.430608	−	0.902539i	$-0.358299\pi$
$449$	−2.87564	−	1.66025i	−0.135710	−	0.0783522i	−0.566318	+	0.824187i	$0.691633\pi$
$450$		0			0
$451$	6.83013	−	11.8301i	0.321618	−	0.557059i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	16.3923	−	4.73205i	0.768483	−	0.221842i
$456$		0			0
$457$	34.1603	−	19.7224i	1.59795	−	0.922576i	0.606067	−	0.795413i	$-0.292746\pi$
$457$	34.1603	−	19.7224i	1.59795	−	0.922576i	0.991882	−	0.127163i	$-0.0405872\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−29.0885	−	16.7942i	−1.35478	−	0.782185i	−0.365869	−	0.930666i	$-0.619228\pi$
$461$	−29.0885	−	16.7942i	−1.35478	−	0.782185i	−0.988915	+	0.148481i	$0.952562\pi$
$462$		0			0
$463$		−	6.33975i		−	0.294633i	−0.989089	−	0.147316i	$-0.952936\pi$
$463$		−	6.33975i		−	0.294633i	0.989089	−	0.147316i	$-0.0470636\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−11.6603			−0.539572			−0.269786	−	0.962920i	$-0.586953\pi$
$467$	−11.6603			−0.539572			−0.269786	+	0.962920i	$0.586953\pi$
$468$		0			0
$469$	23.8564			1.10159
$470$		0			0
$471$		0			0
$472$		0			0
$473$		−	33.3205i		−	1.53208i
$474$		0			0
$475$	−8.19615	−	4.73205i	−0.376065	−	0.217121i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	1.26795	−	0.732051i	0.0579341	−	0.0334483i	−0.470753	−	0.882265i	$-0.656018\pi$
$479$	1.26795	−	0.732051i	0.0579341	−	0.0334483i	0.528687	+	0.848817i	$0.322684\pi$
$480$		0			0
$481$	5.37564	+	1.33013i	0.245108	+	0.0606486i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	8.66025	−	15.0000i	0.393242	−	0.681115i
$486$		0			0
$487$	−0.509619	−	0.294229i	−0.0230930	−	0.0133328i	0.488409	−	0.872615i	$-0.337577\pi$
$487$	−0.509619	−	0.294229i	−0.0230930	−	0.0133328i	−0.511502	+	0.859282i	$0.670911\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−12.9545	−	22.4378i	−0.584628	−	1.01260i	−0.994922	−	0.100651i	$-0.967907\pi$
$491$	−12.9545	−	22.4378i	−0.584628	−	1.01260i	0.410294	−	0.911953i	$-0.365426\pi$
$492$		0			0
$493$	2.12436			0.0956762
$494$		0			0
$495$		0			0
$496$		0			0
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$		0			0
$499$		−	13.8564i		−	0.620298i	−0.950688	−	0.310149i	$-0.899621\pi$
$499$		−	13.8564i		−	0.620298i	0.950688	−	0.310149i	$-0.100379\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−4.63397	+	8.02628i	−0.206619	+	0.357874i	−0.950647	−	0.310274i	$-0.899579\pi$
$503$	−4.63397	+	8.02628i	−0.206619	+	0.357874i	0.744029	+	0.668148i	$0.232913\pi$
$504$		0			0
$505$	11.3038	−	6.52628i	0.503015	−	0.290416i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−25.6244	+	14.7942i	−1.13578	+	0.655743i	−0.945382	−	0.325964i	$-0.894311\pi$
$509$	−25.6244	+	14.7942i	−1.13578	+	0.655743i	−0.190398	+	0.981707i	$0.560978\pi$
$510$		0			0
$511$	−12.5622	+	21.7583i	−0.555718	+	0.962532i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		−	1.26795i		−	0.0558725i
$516$		0			0
$517$	−4.46410	−	7.73205i	−0.196331	−	0.340055i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−19.9808			−0.875373			−0.437687	−	0.899128i	$-0.644202\pi$
$521$	−19.9808			−0.875373			−0.437687	+	0.899128i	$0.644202\pi$
$522$		0			0
$523$	−4.29423	−	7.43782i	−0.187774	−	0.325233i	0.756734	−	0.653723i	$-0.226794\pi$
$523$	−4.29423	−	7.43782i	−0.187774	−	0.325233i	−0.944508	+	0.328490i	$0.893460\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	0.339746	+	0.196152i	0.0147996	+	0.00854453i
$528$		0			0
$529$	−22.0885	+	38.2583i	−0.960368	+	1.66341i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	17.5000	+	4.33013i	0.758009	+	0.187559i
$534$		0			0
$535$	−13.6865	+	7.90192i	−0.591720	+	0.341630i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.09808	−	0.633975i	−0.0472975	−	0.0273072i
$540$		0			0
$541$			17.3923i			0.747754i	0.927478	+	0.373877i	$0.121972\pi$
$541$			17.3923i			0.747754i	−0.927478	+	0.373877i	$0.878028\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	35.3205			1.51296
$546$		0			0
$547$	2.05256			0.0877611			0.0438805	−	0.999037i	$-0.486028\pi$
$547$	2.05256			0.0877611			0.0438805	+	0.999037i	$0.486028\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		−	37.5167i		−	1.59826i
$552$		0			0
$553$	−19.8564	−	11.4641i	−0.844380	−	0.487503i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−0.356406	+	0.205771i	−0.0151014	+	0.00871881i	−0.507532	−	0.861633i	$-0.669442\pi$
$557$	−0.356406	+	0.205771i	−0.0151014	+	0.00871881i	0.492430	+	0.870352i	$0.336109\pi$
$558$		0			0
$559$	42.2487	−	12.1962i	1.78693	−	0.515842i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−9.46410	+	16.3923i	−0.398864	+	0.690853i	−0.993586	−	0.113078i	$-0.963929\pi$
$563$	−9.46410	+	16.3923i	−0.398864	+	0.690853i	0.594722	+	0.803932i	$0.297262\pi$
$564$		0			0
$565$	18.9904	+	10.9641i	0.798931	+	0.461263i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	8.00000	+	13.8564i	0.335377	+	0.580891i	0.983557	−	0.180597i	$-0.0578028\pi$
$569$	8.00000	+	13.8564i	0.335377	+	0.580891i	−0.648180	+	0.761487i	$0.724469\pi$
$570$		0			0
$571$	−13.6603			−0.571664			−0.285832	−	0.958280i	$-0.592270\pi$
$571$	−13.6603			−0.571664			−0.285832	+	0.958280i	$0.592270\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	8.19615	+	14.1962i	0.341803	+	0.592020i
$576$		0			0
$577$		−	25.5885i		−	1.06526i	−0.846348	−	0.532631i	$-0.821203\pi$
$577$		−	25.5885i		−	1.06526i	0.846348	−	0.532631i	$-0.178797\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−2.26795	+	3.92820i	−0.0940904	+	0.162969i
$582$		0			0
$583$	−18.7583	+	10.8301i	−0.776891	+	0.448538i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−25.8564	+	14.9282i	−1.06721	+	0.616153i	−0.927417	−	0.374028i	$-0.877976\pi$
$587$	−25.8564	+	14.9282i	−1.06721	+	0.616153i	−0.139791	+	0.990181i	$0.544643\pi$
$588$		0			0
$589$	3.46410	−	6.00000i	0.142736	−	0.247226i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			28.1769i			1.15709i	0.815651	+	0.578544i	$0.196379\pi$
$593$			28.1769i			1.15709i	−0.815651	+	0.578544i	$0.803621\pi$
$594$		0			0
$595$	0.633975	+	1.09808i	0.0259904	+	0.0450167i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−26.5359			−1.08423			−0.542114	−	0.840305i	$-0.682376\pi$
$599$	−26.5359			−1.08423			−0.542114	+	0.840305i	$0.682376\pi$
$600$		0			0
$601$	20.8205	+	36.0622i	0.849286	+	1.47101i	0.881846	+	0.471537i	$0.156301\pi$
$601$	20.8205	+	36.0622i	0.849286	+	1.47101i	−0.0325600	+	0.999470i	$0.510366\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	5.30385	+	3.06218i	0.215632	+	0.124495i
$606$		0			0
$607$	0.392305	−	0.679492i	0.0159232	−	0.0275797i	−0.857954	−	0.513726i	$-0.828265\pi$
$607$	0.392305	−	0.679492i	0.0159232	−	0.0275797i	0.873877	+	0.486147i	$0.161598\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.16987	−	8.49038i	0.330518	−	0.343484i
$612$		0			0
$613$	31.4545	−	18.1603i	1.27043	−	0.733486i	0.295365	−	0.955385i	$-0.404559\pi$
$613$	31.4545	−	18.1603i	1.27043	−	0.733486i	0.975070	+	0.221899i	$0.0712255\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−32.7224	−	18.8923i	−1.31736	−	0.760576i	−0.334053	−	0.942554i	$-0.608416\pi$
$617$	−32.7224	−	18.8923i	−1.31736	−	0.760576i	−0.983302	+	0.181979i	$0.941750\pi$
$618$		0			0
$619$			44.3923i			1.78428i	0.451762	+	0.892139i	$0.350796\pi$
$619$			44.3923i			1.78428i	−0.451762	+	0.892139i	$0.649204\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	25.8564			1.03592
$624$		0			0
$625$	−11.0000			−0.440000
$626$		0			0
$627$		0			0
$628$		0			0
$629$			0.411543i			0.0164093i
$630$		0			0
$631$	29.3205	+	16.9282i	1.16723	+	0.673901i	0.953026	−	0.302888i	$-0.0979507\pi$
$631$	29.3205	+	16.9282i	1.16723	+	0.673901i	0.214205	+	0.976789i	$0.431284\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−6.00000	+	3.46410i	−0.238103	+	0.137469i
$636$		0			0
$637$	0.401924	−	1.62436i	0.0159248	−	0.0643593i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	6.25833	−	10.8397i	0.247189	−	0.428144i	−0.715556	−	0.698556i	$-0.753826\pi$
$641$	6.25833	−	10.8397i	0.247189	−	0.428144i	0.962745	+	0.270412i	$0.0871598\pi$
$642$		0			0
$643$	24.0000	+	13.8564i	0.946468	+	0.546443i	0.891982	−	0.452071i	$-0.149315\pi$
$643$	24.0000	+	13.8564i	0.946468	+	0.546443i	0.0544858	+	0.998515i	$0.482648\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.12436	−	12.3397i	−0.280087	−	0.485125i	0.691319	−	0.722550i	$-0.257030\pi$
$647$	−7.12436	−	12.3397i	−0.280087	−	0.485125i	−0.971406	+	0.237425i	$0.923697\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	16.7321	+	28.9808i	0.654776	+	1.13410i	0.981950	+	0.189141i	$0.0605703\pi$
$653$	16.7321	+	28.9808i	0.654776	+	1.13410i	−0.327174	+	0.944964i	$0.606096\pi$
$654$		0			0
$655$			26.5359i			1.03684i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	4.33975	−	7.51666i	0.169053	−	0.292808i	−0.769034	−	0.639207i	$-0.779263\pi$
$659$	4.33975	−	7.51666i	0.169053	−	0.292808i	0.938087	+	0.346400i	$0.112596\pi$
$660$		0			0
$661$	−4.66987	+	2.69615i	−0.181637	+	0.104868i	−0.588062	−	0.808816i	$-0.700109\pi$
$661$	−4.66987	+	2.69615i	−0.181637	+	0.104868i	0.406425	+	0.913684i	$0.366775\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	19.3923	−	11.1962i	0.752001	−	0.434168i
$666$		0			0
$667$	−32.4904	+	56.2750i	−1.25803	+	2.17898i
$668$		0			0
$669$		0			0
$670$		0			0
$671$			17.1244i			0.661078i
$672$		0			0
$673$	−23.8923	−	41.3827i	−0.920981	−	1.59519i	−0.797901	−	0.602789i	$-0.794056\pi$
$673$	−23.8923	−	41.3827i	−0.920981	−	1.59519i	−0.123080	−	0.992397i	$-0.539277\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−21.4641			−0.824932			−0.412466	−	0.910973i	$-0.635333\pi$
$677$	−21.4641			−0.824932			−0.412466	+	0.910973i	$0.635333\pi$
$678$		0			0
$679$	−13.6603	−	23.6603i	−0.524232	−	0.907997i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−32.7846	−	18.9282i	−1.25447	−	0.724268i	−0.282475	−	0.959275i	$-0.591155\pi$
$683$	−32.7846	−	18.9282i	−1.25447	−	0.724268i	−0.971994	+	0.235007i	$0.924489\pi$
$684$		0			0
$685$	−4.79423	+	8.30385i	−0.183178	+	0.317274i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−20.5981	−	19.8205i	−0.784724	−	0.755101i
$690$		0			0
$691$	23.9545	−	13.8301i	0.911271	−	0.526123i	0.0304314	−	0.999537i	$-0.490312\pi$
$691$	23.9545	−	13.8301i	0.911271	−	0.526123i	0.880840	+	0.473414i	$0.156979\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−30.0000	−	17.3205i	−1.13796	−	0.657004i
$696$		0			0
$697$			1.33975i			0.0507465i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−44.1051			−1.66583			−0.832914	−	0.553403i	$-0.813329\pi$
$701$	−44.1051			−1.66583			−0.832914	+	0.553403i	$0.813329\pi$
$702$		0			0
$703$	7.26795			0.274116
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	20.5885i		−	0.774309i
$708$		0			0
$709$	6.18653	+	3.57180i	0.232340	+	0.134142i	0.611651	−	0.791128i	$-0.290506\pi$
$709$	6.18653	+	3.57180i	0.232340	+	0.134142i	−0.379311	+	0.925269i	$0.623839\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−10.3923	+	6.00000i	−0.389195	+	0.224702i
$714$		0			0
$715$	4.09808	−	16.5622i	0.153259	−	0.619390i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−12.5885	+	21.8038i	−0.469470	+	0.813146i	−0.999391	−	0.0349010i	$-0.988888\pi$
$719$	−12.5885	+	21.8038i	−0.469470	+	0.813146i	0.529921	+	0.848047i	$0.322222\pi$
$720$		0			0
$721$	−1.73205	−	1.00000i	−0.0645049	−	0.0372419i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	7.92820	+	13.7321i	0.294446	+	0.509996i
$726$		0			0
$727$	4.73205			0.175502			0.0877510	−	0.996142i	$-0.472032\pi$
$727$	4.73205			0.175502			0.0877510	+	0.996142i	$0.472032\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	1.63397	+	2.83013i	0.0604347	+	0.104676i
$732$		0			0
$733$		−	35.0000i		−	1.29275i	−0.763018	−	0.646377i	$-0.776283\pi$
$733$		−	35.0000i		−	1.29275i	0.763018	−	0.646377i	$-0.223717\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	11.9282	−	20.6603i	0.439381	−	0.761030i
$738$		0			0
$739$	14.5359	−	8.39230i	0.534712	−	0.308716i	−0.208221	−	0.978082i	$-0.566767\pi$
$739$	14.5359	−	8.39230i	0.534712	−	0.308716i	0.742933	+	0.669366i	$0.233434\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	38.1962	−	22.0526i	1.40128	−	0.809030i	0.406757	−	0.913537i	$-0.366660\pi$
$743$	38.1962	−	22.0526i	1.40128	−	0.809030i	0.994524	+	0.104507i	$0.0333263\pi$
$744$		0			0
$745$	−18.6962	+	32.3827i	−0.684974	+	1.18641i
$746$		0			0
$747$		0			0
$748$		0			0
$749$			24.9282i			0.910857i
$750$		0			0
$751$	−7.83013	−	13.5622i	−0.285725	−	0.494891i	0.687059	−	0.726601i	$-0.258901\pi$
$751$	−7.83013	−	13.5622i	−0.285725	−	0.494891i	−0.972785	+	0.231710i	$0.925568\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	29.9090			1.08850
$756$		0			0
$757$	3.39230	+	5.87564i	0.123295	+	0.213554i	0.921065	−	0.389408i	$-0.127320\pi$
$757$	3.39230	+	5.87564i	0.123295	+	0.213554i	−0.797770	+	0.602962i	$0.793987\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	2.19615	+	1.26795i	0.0796105	+	0.0459631i	0.539277	−	0.842129i	$-0.318698\pi$
$761$	2.19615	+	1.26795i	0.0796105	+	0.0459631i	−0.459666	+	0.888092i	$0.652031\pi$
$762$		0			0
$763$	27.8564	−	48.2487i	1.00847	−	1.74672i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−37.7321	+	21.7846i	−1.36065	+	0.785573i	−0.989711	−	0.143083i	$-0.954298\pi$
$769$	−37.7321	+	21.7846i	−1.36065	+	0.785573i	−0.370942	+	0.928656i	$0.620965\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	4.51666	+	2.60770i	0.162453	+	0.0937923i	0.579022	−	0.815312i	$-0.303434\pi$
$773$	4.51666	+	2.60770i	0.162453	+	0.0937923i	−0.416569	+	0.909104i	$0.636768\pi$
$774$		0			0
$775$			2.92820i			0.105184i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	23.6603			0.847717
$780$		0			0
$781$	6.00000			0.214697
$782$		0			0
$783$		0			0
$784$		0			0
$785$			39.9282i			1.42510i
$786$		0			0
$787$	−37.5167	−	21.6603i	−1.33732	−	0.772105i	−0.350915	−	0.936407i	$-0.614129\pi$
$787$	−37.5167	−	21.6603i	−1.33732	−	0.772105i	−0.986410	+	0.164303i	$0.947463\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	29.9545	−	17.2942i	1.06506	−	0.614912i
$792$		0			0
$793$	−21.7128	+	6.26795i	−0.771045	+	0.222581i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	−0.914255	−	0.405140i	$-0.867223\pi$
$797$	−3.00000	+	5.19615i	−0.106265	+	0.184057i	0.807989	+	0.589197i	$0.200556\pi$
$798$		0			0
$799$	0.758330	+	0.437822i	0.0268278	+	0.0154890i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	12.5622	+	21.7583i	0.443310	+	0.767835i
$804$		0			0
$805$	−38.7846			−1.36698
$806$		0			0
$807$		0			0
$808$		0			0
$809$	2.86603	+	4.96410i	0.100764	+	0.174529i	0.912000	−	0.410191i	$-0.134538\pi$
$809$	2.86603	+	4.96410i	0.100764	+	0.174529i	−0.811236	+	0.584719i	$0.801205\pi$
$810$		0			0
$811$			1.75129i			0.0614961i	0.999527	+	0.0307480i	$0.00978895\pi$
$811$			1.75129i			0.0614961i	−0.999527	+	0.0307480i	$0.990211\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−11.6603	+	20.1962i	−0.408441	+	0.707440i
$816$		0			0
$817$	49.9808	−	28.8564i	1.74861	−	1.00956i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	13.0526	−	7.53590i	0.455537	−	0.263005i	−0.254629	−	0.967039i	$-0.581953\pi$
$821$	13.0526	−	7.53590i	0.455537	−	0.263005i	0.710166	+	0.704034i	$0.248620\pi$
$822$		0			0
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	−0.577474	−	0.816409i	$-0.695962\pi$
$823$	12.0000	−	20.7846i	0.418294	−	0.724506i	0.995768	+	0.0919029i	$0.0292950\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$			56.3923i			1.96095i	0.196637	+	0.980476i	$0.436998\pi$
$827$			56.3923i			1.96095i	−0.196637	+	0.980476i	$0.563002\pi$
$828$		0			0
$829$	12.8660	+	22.2846i	0.446856	+	0.773976i	0.998179	−	0.0603148i	$-0.0192105\pi$
$829$	12.8660	+	22.2846i	0.446856	+	0.773976i	−0.551324	+	0.834291i	$0.685877\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	0.124356			0.00430867
$834$		0			0
$835$	1.26795	+	2.19615i	0.0438792	+	0.0760010i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.4641	+	8.92820i	0.533880	+	0.308236i	0.742595	−	0.669741i	$-0.233595\pi$
$839$	15.4641	+	8.92820i	0.533880	+	0.308236i	−0.208715	+	0.977977i	$0.566928\pi$
$840$		0			0
$841$	−16.9282	+	29.3205i	−0.583731	+	1.01105i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	22.5000	−	0.866025i	0.774024	−	0.0297922i
$846$		0			0
$847$	8.36603	−	4.83013i	0.287460	−	0.165965i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−10.9019	−	6.29423i	−0.373713	−	0.215763i
$852$		0			0
$853$			34.0333i			1.16528i	0.812731	+	0.582639i	$0.197980\pi$
$853$			34.0333i			1.16528i	−0.812731	+	0.582639i	$0.802020\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−34.5167			−1.17907			−0.589533	−	0.807744i	$-0.700688\pi$
$857$	−34.5167			−1.17907			−0.589533	+	0.807744i	$0.700688\pi$
$858$		0			0
$859$	−34.4449			−1.17524			−0.587622	−	0.809136i	$-0.699936\pi$
$859$	−34.4449			−1.17524			−0.587622	+	0.809136i	$0.699936\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		−	27.6603i		−	0.941566i	−0.882249	−	0.470783i	$-0.843971\pi$
$863$		−	27.6603i		−	0.941566i	0.882249	−	0.470783i	$-0.156029\pi$
$864$		0			0
$865$	26.1962	+	15.1244i	0.890696	+	0.514244i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−19.8564	+	11.4641i	−0.673582	+	0.388893i
$870$		0			0
$871$	30.5622	+	7.56218i	1.03556	+	0.256235i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−16.5622	+	28.6865i	−0.559904	+	0.969782i
$876$		0			0
$877$	−16.4545	−	9.50000i	−0.555628	−	0.320792i	0.195761	−	0.980652i	$-0.437282\pi$
$877$	−16.4545	−	9.50000i	−0.555628	−	0.320792i	−0.751389	+	0.659860i	$0.770616\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	12.2583	+	21.2321i	0.412994	+	0.715326i	0.995216	−	0.0977040i	$-0.0311498\pi$
$881$	12.2583	+	21.2321i	0.412994	+	0.715326i	−0.582222	+	0.813030i	$0.697817\pi$
$882$		0			0
$883$	−8.78461			−0.295626			−0.147813	−	0.989015i	$-0.547223\pi$
$883$	−8.78461			−0.295626			−0.147813	+	0.989015i	$0.547223\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	14.9282	+	25.8564i	0.501240	+	0.868173i	0.999999	+	0.00143243i	$0.000455957\pi$
$887$	14.9282	+	25.8564i	0.501240	+	0.868173i	−0.498759	+	0.866741i	$0.666211\pi$
$888$		0			0
$889$			10.9282i			0.366520i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	7.73205	−	13.3923i	0.258743	−	0.448156i
$894$		0			0
$895$	31.0981	−	17.9545i	1.03949	−	0.600152i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−10.0526	+	5.80385i	−0.335272	+	0.193569i
$900$		0			0
$901$	1.06218	−	1.83975i	0.0353863	−	0.0612908i
$902$		0			0
$903$		0			0
$904$		0			0
$905$			33.2487i			1.10522i
$906$		0			0
$907$	25.5167	+	44.1962i	0.847267	+	1.46751i	0.883638	+	0.468171i	$0.155087\pi$
$907$	25.5167	+	44.1962i	0.847267	+	1.46751i	−0.0363712	+	0.999338i	$0.511580\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−2.53590			−0.0840181			−0.0420090	−	0.999117i	$-0.513376\pi$
$911$	−2.53590			−0.0840181			−0.0420090	+	0.999117i	$0.513376\pi$
$912$		0			0
$913$	2.26795	+	3.92820i	0.0750582	+	0.130005i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	36.2487	+	20.9282i	1.19704	+	0.691110i
$918$		0			0
$919$	6.19615	−	10.7321i	0.204392	−	0.354018i	−0.745547	−	0.666453i	$-0.767812\pi$
$919$	6.19615	−	10.7321i	0.204392	−	0.354018i	0.949939	+	0.312436i	$0.101145\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	2.19615	+	7.60770i	0.0722872	+	0.250410i
$924$		0			0
$925$	−2.66025	+	1.53590i	−0.0874686	+	0.0505000i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	34.5788	+	19.9641i	1.13449	+	0.655001i	0.945061	−	0.326893i	$-0.106002\pi$
$929$	34.5788	+	19.9641i	1.13449	+	0.655001i	0.189433	+	0.981894i	$0.439335\pi$
$930$		0			0
$931$		−	2.19615i		−	0.0719760i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	1.26795			0.0414664
$936$		0			0
$937$	−19.6795			−0.642901			−0.321450	−	0.946926i	$-0.604170\pi$
$937$	−19.6795			−0.642901			−0.321450	+	0.946926i	$0.604170\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$		−	26.7846i		−	0.873153i	−0.899667	−	0.436577i	$-0.856191\pi$
$941$		−	26.7846i		−	0.873153i	0.899667	−	0.436577i	$-0.143809\pi$
$942$		0			0
$943$	−35.4904	−	20.4904i	−1.15573	−	0.667259i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	23.3205	−	13.4641i	0.757815	−	0.437525i	−0.0706959	−	0.997498i	$-0.522522\pi$
$947$	23.3205	−	13.4641i	0.757815	−	0.437525i	0.828511	+	0.559973i	$0.189189\pi$
$948$		0			0
$949$	−22.9904	+	23.8923i	−0.746299	+	0.775577i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−16.3923	+	28.3923i	−0.530999	+	0.919717i	0.468347	+	0.883545i	$0.344850\pi$
$953$	−16.3923	+	28.3923i	−0.530999	+	0.919717i	−0.999346	+	0.0361722i	$0.988484\pi$
$954$		0			0
$955$	−22.3923	−	12.9282i	−0.724598	−	0.418347i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.56218	+	13.0981i	0.244195	+	0.422959i
$960$		0			0
$961$	28.8564			0.930852
$962$		0			0
$963$		0			0
$964$		0			0
$965$	10.1603	+	17.5981i	0.327070	+	0.566502i
$966$		0			0
$967$			2.73205i			0.0878568i	0.999035	+	0.0439284i	$0.0139873\pi$
$967$			2.73205i			0.0878568i	−0.999035	+	0.0439284i	$0.986013\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.196152	+	0.339746i	−0.00629483	+	0.0109030i	−0.869156	−	0.494539i	$-0.835337\pi$
$971$	−0.196152	+	0.339746i	−0.00629483	+	0.0109030i	0.862861	+	0.505442i	$0.168670\pi$
$972$		0			0
$973$	−47.3205	+	27.3205i	−1.51703	+	0.875855i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	42.4019	−	24.4808i	1.35656	−	0.783209i	0.367400	−	0.930063i	$-0.380248\pi$
$977$	42.4019	−	24.4808i	1.35656	−	0.783209i	0.989158	+	0.146854i	$0.0469148\pi$
$978$		0			0
$979$	12.9282	−	22.3923i	0.413187	−	0.715661i
$980$		0			0
$981$		0			0
$982$		0			0
$983$			42.6410i			1.36004i	0.733195	+	0.680019i	$0.238028\pi$
$983$			42.6410i			1.36004i	−0.733195	+	0.680019i	$0.761972\pi$
$984$		0			0
$985$	−0.928203	−	1.60770i	−0.0295750	−	0.0512254i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−99.9615			−3.17859
$990$		0			0
$991$	−18.5622	−	32.1506i	−0.589647	−	1.02130i	−0.994279	−	0.106819i	$-0.965934\pi$
$991$	−18.5622	−	32.1506i	−0.589647	−	1.02130i	0.404631	−	0.914480i	$-0.367400\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−0.509619	−	0.294229i	−0.0161560	−	0.00932767i
$996$		0			0
$997$	−9.99038	+	17.3038i	−0.316399	+	0.548018i	−0.979734	−	0.200304i	$-0.935807\pi$
$997$	−9.99038	+	17.3038i	−0.316399	+	0.548018i	0.663335	+	0.748322i	$0.269140\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1872.2.by.g.1297.1		4
3.2	odd	2		624.2.bv.c.49.1		4
4.3	odd	2		936.2.bi.a.361.2		4
12.11	even	2		312.2.bf.a.49.2	✓	4
13.4	even	6	inner	1872.2.by.g.433.1		4
39.2	even	12		8112.2.a.br.1.2		2
39.11	even	12		8112.2.a.bw.1.1		2
39.17	odd	6		624.2.bv.c.433.1		4
52.43	odd	6		936.2.bi.a.433.2		4
156.11	odd	12		4056.2.a.t.1.1		2
156.23	even	6		4056.2.c.k.337.2		4
156.95	even	6		312.2.bf.a.121.2	yes	4
156.107	even	6		4056.2.c.k.337.3		4
156.119	odd	12		4056.2.a.u.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
312.2.bf.a.49.2	✓	4	12.11	even	2
312.2.bf.a.121.2	yes	4	156.95	even	6
624.2.bv.c.49.1		4	3.2	odd	2
624.2.bv.c.433.1		4	39.17	odd	6
936.2.bi.a.361.2		4	4.3	odd	2
936.2.bi.a.433.2		4	52.43	odd	6
1872.2.by.g.433.1		4	13.4	even	6	inner
1872.2.by.g.1297.1		4	1.1	even	1	trivial
4056.2.a.t.1.1		2	156.11	odd	12
4056.2.a.u.1.2		2	156.119	odd	12
4056.2.c.k.337.2		4	156.23	even	6
4056.2.c.k.337.3		4	156.107	even	6
8112.2.a.br.1.2		2	39.2	even	12
8112.2.a.bw.1.1		2	39.11	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1872 = 2^{4} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1872.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{5} +(-2.36603 - 1.36603i) q^{7} +(-2.36603 + 1.36603i) q^{11} +(-2.59808 - 2.50000i) q^{13} +(0.133975 - 0.232051i) q^{17} +(-4.09808 - 2.36603i) q^{19} +(4.09808 + 7.09808i) q^{23} +2.00000 q^{25} +(3.96410 + 6.86603i) q^{29} +1.46410i q^{31} +(-2.36603 + 4.09808i) q^{35} +(-1.33013 + 0.767949i) q^{37} +(-4.33013 + 2.50000i) q^{41} +(-6.09808 + 10.5622i) q^{43} +3.26795i q^{47} +(0.232051 + 0.401924i) q^{49} +7.92820 q^{53} +(2.36603 + 4.09808i) q^{55} +(3.13397 - 5.42820i) q^{61} +(-4.33013 + 4.50000i) q^{65} +(-7.56218 + 4.36603i) q^{67} +(-1.90192 - 1.09808i) q^{71} -9.19615i q^{73} +7.46410 q^{77} +8.39230 q^{79} -1.66025i q^{83} +(-0.401924 - 0.232051i) q^{85} +(-8.19615 + 4.73205i) q^{89} +(2.73205 + 9.46410i) q^{91} +(-4.09808 + 7.09808i) q^{95} +(8.66025 + 5.00000i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{7} - 6 q^{11} + 4 q^{17} - 6 q^{19} + 6 q^{23} + 8 q^{25} + 2 q^{29} - 6 q^{35} + 12 q^{37} - 14 q^{43} - 6 q^{49} + 4 q^{53} + 6 q^{55} + 16 q^{61} - 6 q^{67} - 18 q^{71} + 16 q^{77} - 8 q^{79}+ \cdots - 6 q^{95}+O(q^{100}) \) 4 * q - 6 * q^7 - 6 * q^11 + 4 * q^17 - 6 * q^19 + 6 * q^23 + 8 * q^25 + 2 * q^29 - 6 * q^35 + 12 * q^37 - 14 * q^43 - 6 * q^49 + 4 * q^53 + 6 * q^55 + 16 * q^61 - 6 * q^67 - 18 * q^71 + 16 * q^77 - 8 * q^79 - 12 * q^85 - 12 * q^89 + 4 * q^91 - 6 * q^95

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