LMFDB - Embedded newform 1368.2.s.k.505.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1368,2,Mod(505,1368)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1368.505"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1368, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1368 = 2^{3} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1368.s (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,0,1,0,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$10.9235349965$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.2696112.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 5x^{4} + 18x^{2} - 8x + 4 $ x^6 - x^5 + 5x^4 + 18x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.3
Root			$1.17146 - 2.02903i$ of defining polynomial
Character	$\chi$	$=$	1368.505
Dual form			1368.2.s.k.577.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.17146 - 2.02903i) q^{5} +3.83221 q^{7} -3.34292 q^{11} +(-3.08757 - 5.34782i) q^{13} +(2.59828 - 4.50035i) q^{17} +(-3.01438 - 3.14857i) q^{19} +(1.17146 + 2.02903i) q^{23} +(-0.244644 - 0.423736i) q^{25} +(0.0250961 + 0.0434676i) q^{29} -3.43910 q^{31} +(4.48929 - 7.77568i) q^{35} -5.43910 q^{37} +(-3.64637 + 6.31569i) q^{41} +(4.43049 - 7.67383i) q^{43} +(5.36802 + 9.29768i) q^{47} +7.68585 q^{49} +(-1.59828 - 2.76830i) q^{53} +(-3.91611 + 6.78289i) q^{55} +(1.92682 - 3.33735i) q^{59} +(-1.46419 - 2.53606i) q^{61} -14.4679 q^{65} +(5.75903 + 9.97493i) q^{67} +(0.744644 - 1.28976i) q^{71} +(3.84292 - 6.65614i) q^{73} -12.8108 q^{77} +(-0.0875674 + 0.151671i) q^{79} +7.00735 q^{83} +(-6.08757 - 10.5440i) q^{85} +(-6.77341 - 11.7319i) q^{89} +(-11.8322 - 20.4940i) q^{91} +(-9.91978 + 2.42785i) q^{95} +(1.84292 - 3.19204i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{5} - 4 q^{7} - 8 q^{11} + q^{13} + 11 q^{17} + q^{23} + 6 q^{25} - 3 q^{29} - 12 q^{31} + 12 q^{35} - 24 q^{37} - 19 q^{41} - 5 q^{43} + 17 q^{47} + 22 q^{49} - 5 q^{53} - 10 q^{55} + 13 q^{59}+ \cdots - q^{97}+O(q^{100}) $ 6 * q + q^5 - 4 * q^7 - 8 * q^11 + q^13 + 11 * q^17 + q^23 + 6 * q^25 - 3 * q^29 - 12 * q^31 + 12 * q^35 - 24 * q^37 - 19 * q^41 - 5 * q^43 + 17 * q^47 + 22 * q^49 - 5 * q^53 - 10 * q^55 + 13 * q^59 + 3 * q^61 - 42 * q^65 + 9 * q^67 - 3 * q^71 + 11 * q^73 - 20 * q^77 + 19 * q^79 - 24 * q^83 - 17 * q^85 + 3 * q^89 - 44 * q^91 - 13 * q^95 - q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1368\mathbb{Z}\right)^\times$.

$n$	$343$	$685$	$1009$	$1217$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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
$5$	1.17146	−	2.02903i	0.523894	−	0.907410i	−0.475720	−	0.879597i	$-0.657812\pi$
$5$	1.17146	−	2.02903i	0.523894	−	0.907410i	0.999613	−	0.0278132i	$-0.00885437\pi$
$6$		0			0
$7$	3.83221			1.44844			0.724220	−	0.689569i	$-0.242200\pi$
$7$	3.83221			1.44844			0.724220	+	0.689569i	$0.242200\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−3.34292			−1.00793			−0.503965	−	0.863724i	$-0.668126\pi$
$11$	−3.34292			−1.00793			−0.503965	+	0.863724i	$0.668126\pi$
$12$		0			0
$13$	−3.08757	−	5.34782i	−0.856337	−	1.48322i	−0.875399	−	0.483401i	$-0.839401\pi$
$13$	−3.08757	−	5.34782i	−0.856337	−	1.48322i	0.0190619	−	0.999818i	$-0.493932\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	2.59828	−	4.50035i	0.630175	−	1.09150i	−0.357340	−	0.933974i	$-0.616316\pi$
$17$	2.59828	−	4.50035i	0.630175	−	1.09150i	0.987516	−	0.157521i	$-0.0503503\pi$
$18$		0			0
$19$	−3.01438	−	3.14857i	−0.691547	−	0.722331i
$19$	−3.01438	−	3.14857i	−0.691547	−	0.722331i
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.17146	+	2.02903i	0.244267	+	0.423082i	0.961925	−	0.273313i	$-0.0881195\pi$
$23$	1.17146	+	2.02903i	0.244267	+	0.423082i	−0.717659	+	0.696395i	$0.754786\pi$
$24$		0			0
$25$	−0.244644	−	0.423736i	−0.0489289	−	0.0847473i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.0250961	+	0.0434676i	0.00466022	+	0.00807174i	0.868346	−	0.495959i	$-0.165183\pi$
$29$	0.0250961	+	0.0434676i	0.00466022	+	0.00807174i	−0.863686	+	0.504030i	$0.831850\pi$
$30$		0			0
$31$	−3.43910			−0.617680			−0.308840	−	0.951114i	$-0.599941\pi$
$31$	−3.43910			−0.617680			−0.308840	+	0.951114i	$0.599941\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.48929	−	7.77568i	0.758828	−	1.31433i
$36$		0			0
$37$	−5.43910			−0.894182			−0.447091	−	0.894488i	$-0.647540\pi$
$37$	−5.43910			−0.894182			−0.447091	+	0.894488i	$0.647540\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.64637	+	6.31569i	−0.569467	+	0.986345i	0.427152	+	0.904180i	$0.359517\pi$
$41$	−3.64637	+	6.31569i	−0.569467	+	0.986345i	−0.996619	+	0.0821653i	$0.973816\pi$
$42$		0			0
$43$	4.43049	−	7.67383i	0.675643	−	1.17025i	−0.300637	−	0.953739i	$-0.597199\pi$
$43$	4.43049	−	7.67383i	0.675643	−	1.17025i	0.976280	−	0.216510i	$-0.0694674\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.36802	+	9.29768i	0.783006	+	1.35621i	0.930183	+	0.367096i	$0.119648\pi$
$47$	5.36802	+	9.29768i	0.783006	+	1.35621i	−0.147177	+	0.989110i	$0.547019\pi$
$48$		0			0
$49$	7.68585			1.09798
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−1.59828	−	2.76830i	−0.219540	−	0.380255i	0.735127	−	0.677929i	$-0.237122\pi$
$53$	−1.59828	−	2.76830i	−0.219540	−	0.380255i	−0.954668	+	0.297674i	$0.903789\pi$
$54$		0			0
$55$	−3.91611	+	6.78289i	−0.528048	+	0.914605i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.92682	−	3.33735i	0.250850	−	0.434485i	−0.712910	−	0.701256i	$-0.752623\pi$
$59$	1.92682	−	3.33735i	0.250850	−	0.434485i	0.963760	+	0.266770i	$0.0859565\pi$
$60$		0			0
$61$	−1.46419	−	2.53606i	−0.187471	−	0.324709i	0.756936	−	0.653489i	$-0.226696\pi$
$61$	−1.46419	−	2.53606i	−0.187471	−	0.324709i	−0.944406	+	0.328781i	$0.893362\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−14.4679			−1.79452
$66$		0			0
$67$	5.75903	+	9.97493i	0.703577	+	1.21863i	0.967203	+	0.254007i	$0.0817485\pi$
$67$	5.75903	+	9.97493i	0.703577	+	1.21863i	−0.263625	+	0.964625i	$0.584918\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	0.744644	−	1.28976i	0.0883730	−	0.153067i	−0.818451	−	0.574577i	$-0.805167\pi$
$71$	0.744644	−	1.28976i	0.0883730	−	0.153067i	0.906824	+	0.421510i	$0.138500\pi$
$72$		0			0
$73$	3.84292	−	6.65614i	0.449780	−	0.779042i	−0.548591	−	0.836091i	$-0.684836\pi$
$73$	3.84292	−	6.65614i	0.449780	−	0.779042i	0.998371	+	0.0570486i	$0.0181690\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−12.8108			−1.45992
$78$		0			0
$79$	−0.0875674	+	0.151671i	−0.00985210	+	0.0170643i	−0.870909	−	0.491444i	$-0.836469\pi$
$79$	−0.0875674	+	0.151671i	−0.00985210	+	0.0170643i	0.861057	+	0.508508i	$0.169803\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	7.00735			0.769156			0.384578	−	0.923092i	$-0.374347\pi$
$83$	7.00735			0.769156			0.384578	+	0.923092i	$0.374347\pi$
$84$		0			0
$85$	−6.08757	−	10.5440i	−0.660289	−	1.14365i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−6.77341	−	11.7319i	−0.717980	−	1.24358i	−0.961799	−	0.273758i	$-0.911733\pi$
$89$	−6.77341	−	11.7319i	−0.717980	−	1.24358i	0.243818	−	0.969821i	$-0.421600\pi$
$90$		0			0
$91$	−11.8322	−	20.4940i	−1.24035	−	2.14835i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−9.91978	+	2.42785i	−1.01775	+	0.249092i
$96$		0			0
$97$	1.84292	−	3.19204i	0.187120	−	0.324102i	−0.757169	−	0.653220i	$-0.773418\pi$
$97$	1.84292	−	3.19204i	0.187120	−	0.324102i	0.944289	+	0.329117i	$0.106751\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−3.80712	−	6.59412i	−0.378822	−	0.656139i	0.612069	−	0.790804i	$-0.290337\pi$
$101$	−3.80712	−	6.59412i	−0.378822	−	0.656139i	−0.990891	+	0.134665i	$0.957004\pi$
$102$		0			0
$103$	16.6430			1.63988			0.819942	−	0.572447i	$-0.194006\pi$
$103$	16.6430			1.63988			0.819942	+	0.572447i	$0.194006\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	6.29273			0.608341			0.304171	−	0.952618i	$-0.401621\pi$
$107$	6.29273			0.608341			0.304171	+	0.952618i	$0.401621\pi$
$108$		0			0
$109$	−5.57686	+	9.65940i	−0.534166	+	0.925203i	0.465037	+	0.885291i	$0.346041\pi$
$109$	−5.57686	+	9.65940i	−0.534166	+	0.925203i	−0.999203	+	0.0399114i	$0.987292\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	17.7606			1.67078			0.835388	−	0.549660i	$-0.185243\pi$
$113$	17.7606			1.67078			0.835388	+	0.549660i	$0.185243\pi$
$114$		0			0
$115$	5.48929			0.511879
$116$		0			0
$117$		0			0
$118$		0			0
$119$	9.95715	−	17.2463i	0.912771	−	1.58097i
$120$		0			0
$121$	0.175135			0.0159213
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.5682			0.945253
$126$		0			0
$127$	−9.21251	−	15.9565i	−0.817478	−	1.41591i	−0.907535	−	0.419977i	$-0.862038\pi$
$127$	−9.21251	−	15.9565i	−0.817478	−	1.41591i	0.0900567	−	0.995937i	$-0.471295\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−1.61266	+	2.79321i	−0.140899	+	0.244044i	−0.927835	−	0.372990i	$-0.878333\pi$
$131$	−1.61266	+	2.79321i	−0.140899	+	0.244044i	0.786936	+	0.617034i	$0.211666\pi$
$132$		0			0
$133$	−11.5518	−	12.0660i	−1.00166	−	1.04625i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−2.98929	−	5.17760i	−0.255392	−	0.442352i	0.709610	−	0.704595i	$-0.248871\pi$
$137$	−2.98929	−	5.17760i	−0.255392	−	0.442352i	−0.965002	+	0.262243i	$0.915538\pi$
$138$		0			0
$139$	4.58389	+	7.93954i	0.388801	+	0.673423i	0.992289	−	0.123950i	$-0.0395561\pi$
$139$	4.58389	+	7.93954i	0.388801	+	0.673423i	−0.603488	+	0.797372i	$0.706223\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	10.3215	+	17.8774i	0.863127	+	1.49498i
$144$		0			0
$145$	0.117596			0.00976584
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.07529	−	5.32656i	0.251937	−	0.436368i	−0.712122	−	0.702056i	$-0.752266\pi$
$149$	3.07529	−	5.32656i	0.251937	−	0.436368i	0.964059	+	0.265688i	$0.0855990\pi$
$150$		0			0
$151$	5.14637			0.418805			0.209403	−	0.977830i	$-0.432848\pi$
$151$	5.14637			0.418805			0.209403	+	0.977830i	$0.432848\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−4.02877	+	6.97803i	−0.323599	+	0.560489i
$156$		0			0
$157$	−2.20516	+	3.81946i	−0.175991	+	0.304826i	−0.940504	−	0.339783i	$-0.889646\pi$
$157$	−2.20516	+	3.81946i	−0.175991	+	0.304826i	0.764513	+	0.644609i	$0.222980\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	4.48929	+	7.77568i	0.353806	+	0.612809i
$162$		0			0
$163$	12.3215			0.965094			0.482547	−	0.875870i	$-0.339712\pi$
$163$	12.3215			0.965094			0.482547	+	0.875870i	$0.339712\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	2.89101	+	5.00738i	0.223713	+	0.387482i	0.955933	−	0.293586i	$-0.0948488\pi$
$167$	2.89101	+	5.00738i	0.223713	+	0.387482i	−0.732220	+	0.681069i	$0.761515\pi$
$168$		0			0
$169$	−12.5661	+	21.7652i	−0.966627	+	1.67425i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−0.912433	+	1.58038i	−0.0693710	+	0.120154i	−0.898625	−	0.438718i	$-0.855433\pi$
$173$	−0.912433	+	1.58038i	−0.0693710	+	0.120154i	0.829254	+	0.558872i	$0.188766\pi$
$174$		0			0
$175$	−0.937529	−	1.62385i	−0.0708705	−	0.122751i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.26396			−0.617678			−0.308839	−	0.951114i	$-0.599940\pi$
$179$	−8.26396			−0.617678			−0.308839	+	0.951114i	$0.599940\pi$
$180$		0			0
$181$	10.8573	+	18.8054i	0.807017	+	1.39780i	0.914921	+	0.403634i	$0.132253\pi$
$181$	10.8573	+	18.8054i	0.807017	+	1.39780i	−0.107903	+	0.994161i	$0.534414\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−6.37169	+	11.0361i	−0.468456	+	0.811390i
$186$		0			0
$187$	−8.68585	+	15.0443i	−0.635172	+	1.10015i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	4.58546			0.331792			0.165896	−	0.986143i	$-0.446948\pi$
$191$	4.58546			0.331792			0.165896	+	0.986143i	$0.446948\pi$
$192$		0			0
$193$	6.08757	−	10.5440i	0.438193	−	0.758972i	−0.559357	−	0.828927i	$-0.688952\pi$
$193$	6.08757	−	10.5440i	0.438193	−	0.758972i	0.997550	+	0.0699545i	$0.0222854\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.26817			0.304095			0.152047	−	0.988373i	$-0.451413\pi$
$197$	4.26817			0.304095			0.152047	+	0.988373i	$0.451413\pi$
$198$		0			0
$199$	1.43049	+	2.47768i	0.101405	+	0.175638i	0.912264	−	0.409604i	$-0.134333\pi$
$199$	1.43049	+	2.47768i	0.101405	+	0.175638i	−0.810859	+	0.585242i	$0.801000\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	0.0961734	+	0.166577i	0.00675005	+	0.0116914i
$204$		0			0
$205$	8.54315	+	14.7972i	0.596680	+	1.03348i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	10.0769	+	10.5254i	0.697031	+	0.728059i
$210$		0			0
$211$	−9.13776	+	15.8271i	−0.629069	+	1.08958i	0.358670	+	0.933465i	$0.383231\pi$
$211$	−9.13776	+	15.8271i	−0.629069	+	1.08958i	−0.987739	+	0.156115i	$0.950103\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−10.3803	−	17.9792i	−0.707930	−	1.22617i
$216$		0			0
$217$	−13.1793			−0.894672
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−32.0894			−2.15857
$222$		0			0
$223$	6.02510	−	10.4358i	0.403470	−	0.698831i	−0.590672	−	0.806912i	$-0.701137\pi$
$223$	6.02510	−	10.4358i	0.403470	−	0.698831i	0.994142	+	0.108081i	$0.0344705\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	8.71462			0.578409			0.289205	−	0.957267i	$-0.406609\pi$
$227$	8.71462			0.578409			0.289205	+	0.957267i	$0.406609\pi$
$228$		0			0
$229$	15.5640			1.02850			0.514250	−	0.857640i	$-0.328070\pi$
$229$	15.5640			1.02850			0.514250	+	0.857640i	$0.328070\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−11.2146	+	19.4243i	−0.734694	+	1.27253i	0.220164	+	0.975463i	$0.429341\pi$
$233$	−11.2146	+	19.4243i	−0.734694	+	1.27253i	−0.954858	+	0.297064i	$0.903992\pi$
$234$		0			0
$235$	25.1537			1.64085
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−30.7434			−1.98862			−0.994312	−	0.106505i	$-0.966034\pi$
$239$	−30.7434			−1.98862			−0.994312	+	0.106505i	$0.966034\pi$
$240$		0			0
$241$	−2.47858	−	4.29302i	−0.159659	−	0.276538i	0.775087	−	0.631855i	$-0.217706\pi$
$241$	−2.47858	−	4.29302i	−0.159659	−	0.276538i	−0.934746	+	0.355317i	$0.884373\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	9.00367	−	15.5948i	0.575224	−	0.996316i
$246$		0			0
$247$	−7.53087	+	25.8418i	−0.479178	+	1.64428i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.7664	+	23.8441i	0.868926	+	1.50502i	0.863095	+	0.505041i	$0.168523\pi$
$251$	13.7664	+	23.8441i	0.868926	+	1.50502i	0.00583044	+	0.999983i	$0.498144\pi$
$252$		0			0
$253$	−3.91611	−	6.78289i	−0.246203	−	0.426437i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−5.94331	−	10.2941i	−0.370733	−	0.642129i	0.618945	−	0.785434i	$-0.287560\pi$
$257$	−5.94331	−	10.2941i	−0.370733	−	0.642129i	−0.989679	+	0.143305i	$0.954227\pi$
$258$		0			0
$259$	−20.8438			−1.29517
$260$		0			0
$261$		0			0
$262$		0			0
$263$	9.71094	−	16.8198i	0.598802	−	1.03716i	−0.394196	−	0.919026i	$-0.628977\pi$
$263$	9.71094	−	16.8198i	0.598802	−	1.03716i	0.992998	−	0.118130i	$-0.0376898\pi$
$264$		0			0
$265$	−7.48929			−0.460063
$266$		0			0
$267$		0			0
$268$		0			0
$269$	9.24128	−	16.0064i	0.563451	−	0.975925i	−0.433741	−	0.901037i	$-0.642807\pi$
$269$	9.24128	−	16.0064i	0.563451	−	0.975925i	0.997192	−	0.0748878i	$-0.0238599\pi$
$270$		0			0
$271$	−8.17146	+	14.1534i	−0.496381	+	0.859757i	−0.999991	−	0.00417390i	$-0.998671\pi$
$271$	−8.17146	+	14.1534i	−0.496381	+	0.859757i	0.503610	+	0.863931i	$0.332005\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.817827	+	1.41652i	0.0493168	+	0.0854192i
$276$		0			0
$277$	15.7894			0.948691			0.474346	−	0.880339i	$-0.342685\pi$
$277$	15.7894			0.948691			0.474346	+	0.880339i	$0.342685\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	4.21462	+	7.29993i	0.251423	+	0.435477i	0.963918	−	0.266200i	$-0.0857682\pi$
$281$	4.21462	+	7.29993i	0.251423	+	0.435477i	−0.712495	+	0.701677i	$0.752435\pi$
$282$		0			0
$283$	−0.905394	+	1.56819i	−0.0538201	+	0.0932192i	−0.891680	−	0.452666i	$-0.850473\pi$
$283$	−0.905394	+	1.56819i	−0.0538201	+	0.0932192i	0.837860	+	0.545885i	$0.183806\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−13.9736	+	24.2031i	−0.824838	+	1.42866i
$288$		0			0
$289$	−5.00211	−	8.66390i	−0.294241	−	0.509641i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−24.2400			−1.41612			−0.708059	−	0.706154i	$-0.750429\pi$
$293$	−24.2400			−1.41612			−0.708059	+	0.706154i	$0.750429\pi$
$294$		0			0
$295$	−4.51438	−	7.81914i	−0.262838	−	0.455248i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	7.23393	−	12.5295i	0.418349	−	0.724602i
$300$		0			0
$301$	16.9786	−	29.4078i	0.978629	−	1.69504i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.86098			−0.392859
$306$		0			0
$307$	−11.0016	+	19.0553i	−0.627893	+	1.08754i	0.360081	+	0.932921i	$0.382749\pi$
$307$	−11.0016	+	19.0553i	−0.627893	+	1.08754i	−0.987974	+	0.154621i	$0.950584\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	32.4752			1.84150			0.920750	−	0.390153i	$-0.127578\pi$
$311$	32.4752			1.84150			0.920750	+	0.390153i	$0.127578\pi$
$312$		0			0
$313$	4.62494	+	8.01064i	0.261417	+	0.452788i	0.966619	−	0.256219i	$-0.0824768\pi$
$313$	4.62494	+	8.01064i	0.261417	+	0.452788i	−0.705202	+	0.709007i	$0.749143\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3.08757	+	5.34782i	0.173415	+	0.300364i	0.939612	−	0.342243i	$-0.111186\pi$
$317$	3.08757	+	5.34782i	0.173415	+	0.300364i	−0.766197	+	0.642606i	$0.777853\pi$
$318$		0			0
$319$	−0.0838942	−	0.145309i	−0.00469717	−	0.00813574i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−22.0019	+	5.38493i	−1.22422	+	0.299625i
$324$		0			0
$325$	−1.51071	+	2.61663i	−0.0837992	+	0.145144i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	20.5714	+	35.6307i	1.13414	+	1.96438i
$330$		0			0
$331$	−10.3643			−0.569676			−0.284838	−	0.958576i	$-0.591940\pi$
$331$	−10.3643			−0.569676			−0.284838	+	0.958576i	$0.591940\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	26.9859			1.47440
$336$		0			0
$337$	−10.3108	+	17.8588i	−0.561664	+	0.972831i	0.435687	+	0.900098i	$0.356505\pi$
$337$	−10.3108	+	17.8588i	−0.561664	+	0.972831i	−0.997351	+	0.0727331i	$0.976828\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	11.4966			0.622578
$342$		0			0
$343$	2.62831			0.141915
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.9054	+	24.0848i	−0.746481	+	1.29294i	0.203019	+	0.979175i	$0.434925\pi$
$347$	−13.9054	+	24.0848i	−0.746481	+	1.29294i	−0.949500	+	0.313768i	$0.898409\pi$
$348$		0			0
$349$	5.60688			0.300130			0.150065	−	0.988676i	$-0.452052\pi$
$349$	5.60688			0.300130			0.150065	+	0.988676i	$0.452052\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	30.0105			1.59730			0.798648	−	0.601798i	$-0.205549\pi$
$353$	30.0105			1.59730			0.798648	+	0.601798i	$0.205549\pi$
$354$		0			0
$355$	−1.74464	−	3.02181i	−0.0925961	−	0.160381i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.48562	+	7.76931i	−0.236742	+	0.410049i	−0.959777	−	0.280762i	$-0.909413\pi$
$359$	−4.48562	+	7.76931i	−0.236742	+	0.410049i	0.723036	+	0.690811i	$0.242746\pi$
$360$		0			0
$361$	−0.826971	+	18.9820i	−0.0435248	+	0.999052i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−9.00367	−	15.5948i	−0.471274	−	0.816270i
$366$		0			0
$367$	5.24621	+	9.08671i	0.273850	+	0.474322i	0.969844	−	0.243725i	$-0.0783695\pi$
$367$	5.24621	+	9.08671i	0.273850	+	0.474322i	−0.695994	+	0.718047i	$0.745036\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−6.12494	−	10.6087i	−0.317991	−	0.550777i
$372$		0			0
$373$	−18.3074			−0.947922			−0.473961	−	0.880546i	$-0.657176\pi$
$373$	−18.3074			−0.947922			−0.473961	+	0.880546i	$0.657176\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	0.154972	−	0.268419i	0.00798144	−	0.0138243i
$378$		0			0
$379$	24.8438			1.27614			0.638069	−	0.769979i	$-0.279733\pi$
$379$	24.8438			1.27614			0.638069	+	0.769979i	$0.279733\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.58600	−	2.74703i	0.0810408	−	0.140367i	−0.822656	−	0.568539i	$-0.807509\pi$
$383$	1.58600	−	2.74703i	0.0810408	−	0.140367i	0.903697	+	0.428172i	$0.140842\pi$
$384$		0			0
$385$	−15.0073	+	25.9935i	−0.764845	+	1.32475i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−5.69445	−	9.86308i	−0.288720	−	0.500078i	0.684784	−	0.728746i	$-0.259896\pi$
$389$	−5.69445	−	9.86308i	−0.288720	−	0.500078i	−0.973505	+	0.228668i	$0.926563\pi$
$390$		0			0
$391$	12.1751			0.615723
$392$		0			0
$393$		0			0
$394$		0			0
$395$	0.205164	+	0.355354i	0.0103229	+	0.0178798i
$396$		0			0
$397$	9.44277	−	16.3554i	0.473919	−	0.820852i	−0.525635	−	0.850710i	$-0.676172\pi$
$397$	9.44277	−	16.3554i	0.473919	−	0.820852i	0.999554	+	0.0298583i	$0.00950560\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−10.0107	+	17.3391i	−0.499911	+	0.865871i	−1.00000		0.000102681i	$-0.999967\pi$
$401$	−10.0107	+	17.3391i	−0.499911	+	0.865871i	0.500089	+	0.865974i	$0.333301\pi$
$402$		0			0
$403$	10.6184	+	18.3917i	0.528942	+	0.916155i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	18.1825			0.901272
$408$		0			0
$409$	−5.45715	−	9.45207i	−0.269839	−	0.467375i	0.698981	−	0.715140i	$-0.253637\pi$
$409$	−5.45715	−	9.45207i	−0.269839	−	0.467375i	−0.968820	+	0.247765i	$0.920304\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	7.38397	−	12.7894i	0.363341	−	0.629326i
$414$		0			0
$415$	8.20884	−	14.2181i	0.402956	−	0.697940i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	15.4145			0.753049			0.376525	−	0.926407i	$-0.377119\pi$
$419$	15.4145			0.753049			0.376525	+	0.926407i	$0.377119\pi$
$420$		0			0
$421$	2.98225	−	5.16541i	0.145346	−	0.251747i	−0.784156	−	0.620564i	$-0.786904\pi$
$421$	2.98225	−	5.16541i	0.145346	−	0.251747i	0.929502	+	0.368817i	$0.120237\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−2.54262			−0.123335
$426$		0			0
$427$	−5.61110	−	9.71870i	−0.271540	−	0.470321i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−14.5095	−	25.1311i	−0.698896	−	1.21052i	−0.968850	−	0.247650i	$-0.920342\pi$
$431$	−14.5095	−	25.1311i	−0.698896	−	1.21052i	0.269954	−	0.962873i	$-0.412992\pi$
$432$		0			0
$433$	9.19109	+	15.9194i	0.441695	+	0.765039i	0.997815	−	0.0660630i	$-0.0210438\pi$
$433$	9.19109	+	15.9194i	0.441695	+	0.765039i	−0.556120	+	0.831102i	$0.687711\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.85731	−	9.80471i	0.136684	−	0.469023i
$438$		0			0
$439$	−3.80712	+	6.59412i	−0.181704	+	0.314720i	−0.942461	−	0.334317i	$-0.891495\pi$
$439$	−3.80712	+	6.59412i	−0.181704	+	0.314720i	0.760757	+	0.649037i	$0.224828\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	3.75168	+	6.49810i	0.178248	+	0.308734i	0.941280	−	0.337626i	$-0.109624\pi$
$443$	3.75168	+	6.49810i	0.178248	+	0.308734i	−0.763033	+	0.646360i	$0.776290\pi$
$444$		0			0
$445$	−31.7392			−1.50458
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−9.31836			−0.439761			−0.219880	−	0.975527i	$-0.570567\pi$
$449$	−9.31836			−0.439761			−0.219880	+	0.975527i	$0.570567\pi$
$450$		0			0
$451$	12.1895	−	21.1129i	0.573982	−	0.994166i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−55.4439			−2.59925
$456$		0			0
$457$	22.4893			1.05200			0.526002	−	0.850483i	$-0.323690\pi$
$457$	22.4893			1.05200			0.526002	+	0.850483i	$0.323690\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.67303	−	2.89777i	0.0779207	−	0.134963i	−0.824432	−	0.565961i	$-0.808505\pi$
$461$	1.67303	−	2.89777i	0.0779207	−	0.134963i	0.902353	+	0.430998i	$0.141839\pi$
$462$		0			0
$463$	−26.0147			−1.20901			−0.604503	−	0.796603i	$-0.706628\pi$
$463$	−26.0147			−1.20901			−0.604503	+	0.796603i	$0.706628\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	11.3429			0.524888			0.262444	−	0.964947i	$-0.415472\pi$
$467$	11.3429			0.524888			0.262444	+	0.964947i	$0.415472\pi$
$468$		0			0
$469$	22.0698	+	38.2260i	1.01909	+	1.76511i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−14.8108	+	25.6530i	−0.681001	+	1.17953i
$474$		0			0
$475$	−0.596711	+	2.04758i	−0.0273790	+	0.0939496i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−5.75199	−	9.96274i	−0.262815	−	0.455209i	0.704174	−	0.710028i	$-0.251318\pi$
$479$	−5.75199	−	9.96274i	−0.262815	−	0.455209i	−0.966989	+	0.254818i	$0.917984\pi$
$480$		0			0
$481$	16.7936	+	29.0873i	0.765721	+	1.32627i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.31783	−	7.47870i	−0.196062	−	0.339590i
$486$		0			0
$487$	22.3832			1.01428			0.507141	−	0.861863i	$-0.330702\pi$
$487$	22.3832			1.01428			0.507141	+	0.861863i	$0.330702\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−11.0160	+	19.0802i	−0.497143	+	0.861077i	−0.999995	−	0.00329588i	$-0.998951\pi$
$491$	−11.0160	+	19.0802i	−0.497143	+	0.861077i	0.502852	+	0.864373i	$0.332284\pi$
$492$		0			0
$493$	0.260826			0.0117470
$494$		0			0
$495$		0			0
$496$		0			0
$497$	2.85363	−	4.94264i	0.128003	−	0.221708i
$498$		0			0
$499$	0.605317	−	1.04844i	0.0270977	−	0.0469346i	−0.852159	−	0.523284i	$-0.824707\pi$
$499$	0.605317	−	1.04844i	0.0270977	−	0.0469346i	0.879256	+	0.476349i	$0.158040\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−15.2462	−	26.4072i	−0.679795	−	1.17744i	−0.975042	−	0.222019i	$-0.928735\pi$
$503$	−15.2462	−	26.4072i	−0.679795	−	1.17744i	0.295247	−	0.955421i	$-0.404598\pi$
$504$		0			0
$505$	−17.8396			−0.793850
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−0.423144	−	0.732907i	−0.0187555	−	0.0324855i	0.856495	−	0.516155i	$-0.172637\pi$
$509$	−0.423144	−	0.732907i	−0.0187555	−	0.0324855i	−0.875251	+	0.483669i	$0.839304\pi$
$510$		0			0
$511$	14.7269	−	25.5077i	0.651479	−	1.12840i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	19.4966	−	33.7692i	0.859124	−	1.48805i
$516$		0			0
$517$	−17.9449	−	31.0814i	−0.789215	−	1.36696i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	42.6044			1.86653			0.933266	−	0.359187i	$-0.116946\pi$
$521$	42.6044			1.86653			0.933266	+	0.359187i	$0.116946\pi$
$522$		0			0
$523$	5.86224	+	10.1537i	0.256338	+	0.443990i	0.965258	−	0.261299i	$-0.0841507\pi$
$523$	5.86224	+	10.1537i	0.256338	+	0.443990i	−0.708920	+	0.705289i	$0.750817\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8.93573	+	15.4771i	−0.389247	+	0.674195i
$528$		0			0
$529$	8.75536	−	15.1647i	0.380668	−	0.659336i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	45.0336			1.95062
$534$		0			0
$535$	7.37169	−	12.7681i	0.318706	−	0.552015i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−25.6932			−1.10668
$540$		0			0
$541$	9.06614	+	15.7030i	0.389784	+	0.675126i	0.992420	−	0.122890i	$-0.0392163\pi$
$541$	9.06614	+	15.7030i	0.389784	+	0.675126i	−0.602636	+	0.798016i	$0.705883\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	13.0661	+	22.6312i	0.559692	+	0.969415i
$546$		0			0
$547$	−21.7018	−	37.5886i	−0.927902	−	1.60717i	−0.786826	−	0.617174i	$-0.788277\pi$
$547$	−21.7018	−	37.5886i	−0.927902	−	1.60717i	−0.141076	−	0.989999i	$-0.545056\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	0.0612117	−	0.210045i	0.00260771	−	0.00894821i
$552$		0			0
$553$	−0.335577	+	0.581236i	−0.0142702	+	0.0247167i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.59828	+	7.96445i	0.194835	+	0.337465i	0.946847	−	0.321686i	$-0.104249\pi$
$557$	4.59828	+	7.96445i	0.194835	+	0.337465i	−0.752011	+	0.659150i	$0.770916\pi$
$558$		0			0
$559$	−54.7178			−2.31431
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−41.3576			−1.74302			−0.871508	−	0.490382i	$-0.836857\pi$
$563$	−41.3576			−1.74302			−0.871508	+	0.490382i	$0.836857\pi$
$564$		0			0
$565$	20.8059	−	36.0368i	0.875309	−	1.51608i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.22219			−0.0512369			−0.0256185	−	0.999672i	$-0.508156\pi$
$569$	−1.22219			−0.0512369			−0.0256185	+	0.999672i	$0.508156\pi$
$570$		0			0
$571$	−4.32150			−0.180849			−0.0904246	−	0.995903i	$-0.528822\pi$
$571$	−4.32150			−0.180849			−0.0904246	+	0.995903i	$0.528822\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.573183	−	0.992782i	0.0239034	−	0.0414019i
$576$		0			0
$577$	2.03863			0.0848695			0.0424347	−	0.999099i	$-0.486489\pi$
$577$	2.03863			0.0848695			0.0424347	+	0.999099i	$0.486489\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	26.8536			1.11408
$582$		0			0
$583$	5.34292	+	9.25421i	0.221281	+	0.383270i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−4.33011	+	7.49996i	−0.178723	+	0.309557i	−0.941443	−	0.337171i	$-0.890530\pi$
$587$	−4.33011	+	7.49996i	−0.178723	+	0.309557i	0.762721	+	0.646728i	$0.223863\pi$
$588$		0			0
$589$	10.3668	+	10.8282i	0.427155	+	0.446170i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	5.48592	+	9.50190i	0.225280	+	0.390196i	0.956403	−	0.292049i	$-0.0943370\pi$
$593$	5.48592	+	9.50190i	0.225280	+	0.390196i	−0.731123	+	0.682245i	$0.761004\pi$
$594$		0			0
$595$	−23.3288	−	40.4067i	−0.956389	−	1.65652i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	22.7109	+	39.3365i	0.927944	+	1.60725i	0.786757	+	0.617263i	$0.211759\pi$
$599$	22.7109	+	39.3365i	0.927944	+	1.60725i	0.141187	+	0.989983i	$0.454908\pi$
$600$		0			0
$601$	29.8757			1.21865			0.609327	−	0.792919i	$-0.291440\pi$
$601$	29.8757			1.21865			0.609327	+	0.792919i	$0.291440\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	0.205164	−	0.355354i	0.00834109	−	0.0144472i
$606$		0			0
$607$	−34.7764			−1.41153			−0.705765	−	0.708446i	$-0.749396\pi$
$607$	−34.7764			−1.41153			−0.705765	+	0.708446i	$0.749396\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	33.1482	−	57.4144i	1.34103	−	2.32274i
$612$		0			0
$613$	−7.38030	+	12.7831i	−0.298087	+	0.516303i	−0.975698	−	0.219118i	$-0.929682\pi$
$613$	−7.38030	+	12.7831i	−0.298087	+	0.516303i	0.677611	+	0.735421i	$0.263015\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−13.0181	−	22.5479i	−0.524087	−	0.907746i	−0.999607	−	0.0280406i	$-0.991073\pi$
$617$	−13.0181	−	22.5479i	−0.524087	−	0.907746i	0.475520	−	0.879705i	$-0.342260\pi$
$618$		0			0
$619$	−40.7497			−1.63787			−0.818933	−	0.573888i	$-0.805434\pi$
$619$	−40.7497			−1.63787			−0.818933	+	0.573888i	$0.805434\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−25.9572	−	44.9591i	−1.03995	−	1.80125i
$624$		0			0
$625$	13.6035	−	23.5620i	0.544141	−	0.942479i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−14.1323	+	24.4778i	−0.563491	+	0.975996i
$630$		0			0
$631$	−15.9106	−	27.5580i	−0.633392	−	1.09707i	−0.986853	−	0.161619i	$-0.948329\pi$
$631$	−15.9106	−	27.5580i	−0.633392	−	1.09707i	0.353461	−	0.935449i	$-0.385005\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−43.1684			−1.71309
$636$		0			0
$637$	−23.7306	−	41.1025i	−0.940239	−	1.62854i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−4.08233	+	7.07080i	−0.161242	+	0.279280i	−0.935314	−	0.353818i	$-0.884883\pi$
$641$	−4.08233	+	7.07080i	−0.161242	+	0.279280i	0.774072	+	0.633097i	$0.218217\pi$
$642$		0			0
$643$	−3.29851	+	5.71319i	−0.130081	+	0.225306i	−0.923707	−	0.383099i	$-0.874857\pi$
$643$	−3.29851	+	5.71319i	−0.130081	+	0.225306i	0.793627	+	0.608405i	$0.208190\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−2.60015			−0.102223			−0.0511113	−	0.998693i	$-0.516276\pi$
$647$	−2.60015			−0.102223			−0.0511113	+	0.998693i	$0.516276\pi$
$648$		0			0
$649$	−6.44120	+	11.1565i	−0.252839	+	0.437930i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.39312			0.0936498			0.0468249	−	0.998903i	$-0.485090\pi$
$653$	2.39312			0.0936498			0.0468249	+	0.998903i	$0.485090\pi$
$654$		0			0
$655$	3.77835	+	6.54429i	0.147632	+	0.255706i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	11.3417	+	19.6443i	0.441808	+	0.765235i	0.997824	−	0.0659373i	$-0.0210037\pi$
$659$	11.3417	+	19.6443i	0.441808	+	0.765235i	−0.556015	+	0.831172i	$0.687670\pi$
$660$		0			0
$661$	−20.2750	−	35.1173i	−0.788605	−	1.36590i	−0.926821	−	0.375502i	$-0.877470\pi$
$661$	−20.2750	−	35.1173i	−0.788605	−	1.36590i	0.138216	−	0.990402i	$-0.455863\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−38.0147	+	9.30404i	−1.47415	+	0.360795i
$666$		0			0
$667$	−0.0587981	+	0.101841i	−0.00227667	+	0.00394331i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	4.89468	+	8.47784i	0.188957	+	0.327283i
$672$		0			0
$673$	−20.1004			−0.774813			−0.387406	−	0.921909i	$-0.626629\pi$
$673$	−20.1004			−0.774813			−0.387406	+	0.921909i	$0.626629\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	19.3717			0.744515			0.372257	−	0.928130i	$-0.378584\pi$
$677$	19.3717			0.744515			0.372257	+	0.928130i	$0.378584\pi$
$678$		0			0
$679$	7.06247	−	12.2326i	0.271033	−	0.469443i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	16.1151			0.616626			0.308313	−	0.951285i	$-0.400236\pi$
$683$	16.1151			0.616626			0.308313	+	0.951285i	$0.400236\pi$
$684$		0			0
$685$	−14.0073			−0.535193
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−9.86959	+	17.0946i	−0.376001	+	0.651253i
$690$		0			0
$691$	15.4145			0.586397			0.293198	−	0.956052i	$-0.405280\pi$
$691$	15.4145			0.586397			0.293198	+	0.956052i	$0.405280\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	21.4794			0.814761
$696$		0			0
$697$	18.9485	+	32.8198i	0.717727	+	1.24314i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	17.9148	−	31.0294i	0.676634	−	1.17197i	−0.299354	−	0.954142i	$-0.596771\pi$
$701$	17.9148	−	31.0294i	0.676634	−	1.17197i	0.975988	−	0.217823i	$-0.0698956\pi$
$702$		0			0
$703$	16.3955	+	17.1254i	0.618369	+	0.645896i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−14.5897	−	25.2701i	−0.548701	−	0.950378i
$708$		0			0
$709$	−4.41400	−	7.64527i	−0.165771	−	0.287124i	0.771158	−	0.636644i	$-0.219678\pi$
$709$	−4.41400	−	7.64527i	−0.165771	−	0.287124i	−0.936929	+	0.349520i	$0.886345\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−4.02877	−	6.97803i	−0.150879	−	0.261329i
$714$		0			0
$715$	48.3650			1.80875
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−8.13355	+	14.0877i	−0.303330	+	0.525383i	−0.976888	−	0.213751i	$-0.931432\pi$
$719$	−8.13355	+	14.0877i	−0.303330	+	0.525383i	0.673558	+	0.739134i	$0.264765\pi$
$720$		0			0
$721$	63.7795			2.37527
$722$		0			0
$723$		0			0
$724$		0			0
$725$	0.0122792	−	0.0212682i	0.000456038	−	0.000789882i
$726$		0			0
$727$	−20.3803	+	35.2997i	−0.755863	+	1.30919i	0.189081	+	0.981962i	$0.439449\pi$
$727$	−20.3803	+	35.2997i	−0.755863	+	1.30919i	−0.944944	+	0.327232i	$0.893884\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−23.0233	−	39.8775i	−0.851547	−	1.47492i
$732$		0			0
$733$	19.6827			0.726998			0.363499	−	0.931595i	$-0.381582\pi$
$733$	19.6827			0.726998			0.363499	+	0.931595i	$0.381582\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−19.2520	−	33.3454i	−0.709156	−	1.22829i
$738$		0			0
$739$	21.3775	−	37.0269i	0.786383	−	1.36206i	−0.141786	−	0.989897i	$-0.545285\pi$
$739$	21.3775	−	37.0269i	0.786383	−	1.36206i	0.928169	−	0.372158i	$-0.121382\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−8.34239	+	14.4494i	−0.306052	+	0.530098i	−0.977495	−	0.210958i	$-0.932342\pi$
$743$	−8.34239	+	14.4494i	−0.306052	+	0.530098i	0.671443	+	0.741057i	$0.265675\pi$
$744$		0			0
$745$	−7.20516	−	12.4797i	−0.263977	−	0.457221i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	24.1151			0.881146
$750$		0			0
$751$	15.4305	+	26.7264i	0.563067	+	0.975260i	0.997227	+	0.0744242i	$0.0237119\pi$
$751$	15.4305	+	26.7264i	0.563067	+	0.975260i	−0.434160	+	0.900836i	$0.642955\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.02877	−	10.4421i	0.219409	−	0.380028i
$756$		0			0
$757$	7.99139	−	13.8415i	0.290452	−	0.503078i	−0.683465	−	0.729984i	$-0.739528\pi$
$757$	7.99139	−	13.8415i	0.290452	−	0.503078i	0.973917	+	0.226906i	$0.0728610\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−22.9975			−0.833658			−0.416829	−	0.908985i	$-0.636859\pi$
$761$	−22.9975			−0.833658			−0.416829	+	0.908985i	$0.636859\pi$
$762$		0			0
$763$	−21.3717	+	37.0169i	−0.773707	+	1.34010i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−23.7967			−0.859249
$768$		0			0
$769$	−14.9731	−	25.9342i	−0.539944	−	0.935211i	−0.998906	−	0.0467548i	$-0.985112\pi$
$769$	−14.9731	−	25.9342i	−0.539944	−	0.935211i	0.458962	−	0.888456i	$-0.348221\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.75379	+	4.76970i	0.0990469	+	0.171554i	0.911290	−	0.411764i	$-0.135087\pi$
$773$	2.75379	+	4.76970i	0.0990469	+	0.171554i	−0.812244	+	0.583318i	$0.801754\pi$
$774$		0			0
$775$	0.841355	+	1.45727i	0.0302224	+	0.0523467i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	30.8769	−	7.55709i	1.10628	−	0.270761i
$780$		0			0
$781$	−2.48929	+	4.31157i	−0.0890737	+	0.154280i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.16653	+	8.94869i	0.184401	+	0.319392i
$786$		0			0
$787$	−8.40719			−0.299684			−0.149842	−	0.988710i	$-0.547877\pi$
$787$	−8.40719			−0.299684			−0.149842	+	0.988710i	$0.547877\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	68.0624			2.42002
$792$		0			0
$793$	−9.04159	+	15.6605i	−0.321076	+	0.556120i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−33.2186			−1.17666			−0.588332	−	0.808620i	$-0.700215\pi$
$797$	−33.2186			−1.17666			−0.588332	+	0.808620i	$0.700215\pi$
$798$		0			0
$799$	55.7904			1.97372
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−12.8466	+	22.2510i	−0.453347	+	0.785219i
$804$		0			0
$805$	21.0361			0.741426
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−12.8971			−0.453438			−0.226719	−	0.973960i	$-0.572800\pi$
$809$	−12.8971			−0.453438			−0.226719	+	0.973960i	$0.572800\pi$
$810$		0			0
$811$	1.33432	+	2.31110i	0.0468542	+	0.0811539i	0.888501	−	0.458874i	$-0.151747\pi$
$811$	1.33432	+	2.31110i	0.0468542	+	0.0811539i	−0.841647	+	0.540028i	$0.818414\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	14.4342	−	25.0007i	0.505607	−	0.875736i
$816$		0			0
$817$	−37.5168	+	9.18219i	−1.31255	+	0.321244i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−16.8267	−	29.1448i	−0.587257	−	1.01716i	−0.994590	−	0.103880i	$-0.966874\pi$
$821$	−16.8267	−	29.1448i	−0.587257	−	1.01716i	0.407333	−	0.913280i	$-0.366459\pi$
$822$		0			0
$823$	−8.91978	−	15.4495i	−0.310924	−	0.538536i	0.667639	−	0.744485i	$-0.267305\pi$
$823$	−8.91978	−	15.4495i	−0.310924	−	0.538536i	−0.978563	+	0.205949i	$0.933972\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	1.87663	+	3.25041i	0.0652567	+	0.113028i	0.896808	−	0.442420i	$-0.145880\pi$
$827$	1.87663	+	3.25041i	0.0652567	+	0.113028i	−0.831551	+	0.555448i	$0.812547\pi$
$828$		0			0
$829$	2.77781			0.0964773			0.0482386	−	0.998836i	$-0.484639\pi$
$829$	2.77781			0.0964773			0.0482386	+	0.998836i	$0.484639\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	19.9700	−	34.5890i	0.691918	−	1.19844i
$834$		0			0
$835$	13.5468			0.468807
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−28.1114	+	48.6904i	−0.970513	+	1.68098i	−0.276504	+	0.961013i	$0.589176\pi$
$839$	−28.1114	+	48.6904i	−0.970513	+	1.68098i	−0.694010	+	0.719966i	$0.744157\pi$
$840$		0			0
$841$	14.4987	−	25.1126i	0.499957	−	0.865950i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	29.4415	+	50.9942i	1.01282	+	1.75425i
$846$		0			0
$847$	0.671153			0.0230611
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.37169	−	11.0361i	−0.218419	−	0.378312i
$852$		0			0
$853$	5.16232	−	8.94140i	0.176754	−	0.306148i	−0.764013	−	0.645201i	$-0.776774\pi$
$853$	5.16232	−	8.94140i	0.176754	−	0.306148i	0.940767	+	0.339054i	$0.110107\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	26.5894	−	46.0543i	0.908278	−	1.57318i	0.0918226	−	0.995775i	$-0.470731\pi$
$857$	26.5894	−	46.0543i	0.908278	−	1.57318i	0.816455	−	0.577408i	$-0.195936\pi$
$858$		0			0
$859$	5.12651	+	8.87938i	0.174914	+	0.302960i	0.940132	−	0.340812i	$-0.110702\pi$
$859$	5.12651	+	8.87938i	0.174914	+	0.302960i	−0.765217	+	0.643772i	$0.777369\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	10.7679			0.366545			0.183273	−	0.983062i	$-0.441331\pi$
$863$	10.7679			0.366545			0.183273	+	0.983062i	$0.441331\pi$
$864$		0			0
$865$	2.13776	+	3.70271i	0.0726860	+	0.125896i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	0.292731	−	0.507025i	0.00993022	−	0.0171996i
$870$		0			0
$871$	35.5628	−	61.5965i	1.20500	−	2.08712i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	40.4998			1.36914
$876$		0			0
$877$	−11.3638	+	19.6827i	−0.383729	+	0.664637i	−0.991592	−	0.129404i	$-0.958693\pi$
$877$	−11.3638	+	19.6827i	−0.383729	+	0.664637i	0.607863	+	0.794042i	$0.292027\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	8.44644			0.284568			0.142284	−	0.989826i	$-0.454555\pi$
$881$	8.44644			0.284568			0.142284	+	0.989826i	$0.454555\pi$
$882$		0			0
$883$	−22.5196	−	39.0051i	−0.757846	−	1.31263i	−0.943947	−	0.330097i	$-0.892919\pi$
$883$	−22.5196	−	39.0051i	−0.757846	−	1.31263i	0.186101	−	0.982531i	$-0.440415\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−10.4231	−	18.0534i	−0.349975	−	0.606174i	0.636270	−	0.771467i	$-0.280477\pi$
$887$	−10.4231	−	18.0534i	−0.349975	−	0.606174i	−0.986245	+	0.165292i	$0.947143\pi$
$888$		0			0
$889$	−35.3043	−	61.1488i	−1.18407	−	2.05087i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	13.0931	−	44.9284i	0.438144	−	1.50347i
$894$		0			0
$895$	−9.68091	+	16.7678i	−0.323597	+	0.560487i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−0.0863077	−	0.149489i	−0.00287852	−	0.00498575i
$900$		0			0
$901$	−16.6111			−0.553396
$902$		0			0
$903$		0			0
$904$		0			0
$905$	50.8757			1.69116
$906$		0			0
$907$	−12.2055	+	21.1405i	−0.405276	+	0.701959i	−0.994354	−	0.106118i	$-0.966158\pi$
$907$	−12.2055	+	21.1405i	−0.405276	+	0.701959i	0.589078	+	0.808077i	$0.299491\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−24.2744			−0.804248			−0.402124	−	0.915585i	$-0.631728\pi$
$911$	−24.2744			−0.804248			−0.402124	+	0.915585i	$0.631728\pi$
$912$		0			0
$913$	−23.4250			−0.775255
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−6.18007	+	10.7042i	−0.204084	+	0.353484i
$918$		0			0
$919$	−31.8568			−1.05086			−0.525429	−	0.850837i	$-0.676095\pi$
$919$	−31.8568			−1.05086			−0.525429	+	0.850837i	$0.676095\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−9.19656			−0.302708
$924$		0			0
$925$	1.33064	+	2.30474i	0.0437513	+	0.0757795i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−25.1044	+	43.4820i	−0.823648	+	1.42660i	0.0793010	+	0.996851i	$0.474731\pi$
$929$	−25.1044	+	43.4820i	−0.823648	+	1.42660i	−0.902949	+	0.429749i	$0.858602\pi$
$930$		0			0
$931$	−23.1681	−	24.1994i	−0.759304	−	0.793104i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	20.3503	+	35.2477i	0.665525	+	1.15272i
$936$		0			0
$937$	2.32800	+	4.03222i	0.0760525	+	0.131727i	0.901543	−	0.432689i	$-0.142435\pi$
$937$	2.32800	+	4.03222i	0.0760525	+	0.131727i	−0.825491	+	0.564415i	$0.809102\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−11.6987	−	20.2627i	−0.381366	−	0.660544i	0.609892	−	0.792484i	$-0.291213\pi$
$941$	−11.6987	−	20.2627i	−0.381366	−	0.660544i	−0.991258	+	0.131940i	$0.957879\pi$
$942$		0			0
$943$	−17.0863			−0.556407
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−28.7134	+	49.7330i	−0.933059	+	1.61611i	−0.154999	+	0.987915i	$0.549537\pi$
$947$	−28.7134	+	49.7330i	−0.933059	+	1.61611i	−0.778060	+	0.628190i	$0.783796\pi$
$948$		0			0
$949$	−47.4611			−1.54065
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−19.9966	+	34.6352i	−0.647755	+	1.12194i	0.335903	+	0.941896i	$0.390958\pi$
$953$	−19.9966	+	34.6352i	−0.647755	+	1.12194i	−0.983658	+	0.180047i	$0.942375\pi$
$954$		0			0
$955$	5.37169	−	9.30404i	0.173824	−	0.301072i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−11.4556	−	19.8417i	−0.369920	−	0.640721i
$960$		0			0
$961$	−19.1726			−0.618471
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−14.2627	−	24.7037i	−0.459133	−	0.795241i
$966$		0			0
$967$	1.94120	−	3.36226i	0.0624248	−	0.108123i	−0.833124	−	0.553086i	$-0.813450\pi$
$967$	1.94120	−	3.36226i	0.0624248	−	0.108123i	0.895549	+	0.444963i	$0.146783\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−0.687414	+	1.19064i	−0.0220602	+	0.0382093i	−0.876845	−	0.480774i	$-0.840356\pi$
$971$	−0.687414	+	1.19064i	−0.0220602	+	0.0382093i	0.854785	+	0.518983i	$0.173689\pi$
$972$		0			0
$973$	17.5665	+	30.4260i	0.563155	+	0.975412i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−20.2541			−0.647986			−0.323993	−	0.946059i	$-0.605025\pi$
$977$	−20.2541			−0.647986			−0.323993	+	0.946059i	$0.605025\pi$
$978$		0			0
$979$	22.6430	+	39.2188i	0.723673	+	1.25344i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	6.38030	−	11.0510i	0.203500	−	0.352472i	−0.746154	−	0.665774i	$-0.768102\pi$
$983$	6.38030	−	11.0510i	0.203500	−	0.352472i	0.949654	+	0.313301i	$0.101435\pi$
$984$		0			0
$985$	5.00000	−	8.66025i	0.159313	−	0.275939i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	20.7606			0.660149
$990$		0			0
$991$	9.47647	−	16.4137i	0.301030	−	0.521399i	−0.675339	−	0.737507i	$-0.736003\pi$
$991$	9.47647	−	16.4137i	0.301030	−	0.521399i	0.976370	+	0.216108i	$0.0693362\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	6.70306			0.212501
$996$		0			0
$997$	6.03244	+	10.4485i	0.191049	+	0.330907i	0.945598	−	0.325337i	$-0.105478\pi$
$997$	6.03244	+	10.4485i	0.191049	+	0.330907i	−0.754549	+	0.656244i	$0.772144\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1368.2.s.k.505.3		6
3.2	odd	2		152.2.i.c.49.2	✓	6
4.3	odd	2		2736.2.s.y.1873.3		6
12.11	even	2		304.2.i.f.49.2		6
19.7	even	3	inner	1368.2.s.k.577.3		6
24.5	odd	2		1216.2.i.n.961.2		6
24.11	even	2		1216.2.i.m.961.2		6
57.8	even	6		2888.2.a.n.1.2		3
57.11	odd	6		2888.2.a.r.1.2		3
57.26	odd	6		152.2.i.c.121.2	yes	6
76.7	odd	6		2736.2.s.y.577.3		6
228.11	even	6		5776.2.a.bk.1.2		3
228.83	even	6		304.2.i.f.273.2		6
228.179	odd	6		5776.2.a.bq.1.2		3
456.83	even	6		1216.2.i.m.577.2		6
456.197	odd	6		1216.2.i.n.577.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.i.c.49.2	✓	6	3.2	odd	2
152.2.i.c.121.2	yes	6	57.26	odd	6
304.2.i.f.49.2		6	12.11	even	2
304.2.i.f.273.2		6	228.83	even	6
1216.2.i.m.577.2		6	456.83	even	6
1216.2.i.m.961.2		6	24.11	even	2
1216.2.i.n.577.2		6	456.197	odd	6
1216.2.i.n.961.2		6	24.5	odd	2
1368.2.s.k.505.3		6	1.1	even	1	trivial
1368.2.s.k.577.3		6	19.7	even	3	inner
2736.2.s.y.577.3		6	76.7	odd	6
2736.2.s.y.1873.3		6	4.3	odd	2
2888.2.a.n.1.2		3	57.8	even	6
2888.2.a.r.1.2		3	57.11	odd	6
5776.2.a.bk.1.2		3	228.11	even	6
5776.2.a.bq.1.2		3	228.179	odd	6

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:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1368.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.17146 - 2.02903i) q^{5} +3.83221 q^{7} -3.34292 q^{11} +(-3.08757 - 5.34782i) q^{13} +(2.59828 - 4.50035i) q^{17} +(-3.01438 - 3.14857i) q^{19} +(1.17146 + 2.02903i) q^{23} +(-0.244644 - 0.423736i) q^{25} +(0.0250961 + 0.0434676i) q^{29} -3.43910 q^{31} +(4.48929 - 7.77568i) q^{35} -5.43910 q^{37} +(-3.64637 + 6.31569i) q^{41} +(4.43049 - 7.67383i) q^{43} +(5.36802 + 9.29768i) q^{47} +7.68585 q^{49} +(-1.59828 - 2.76830i) q^{53} +(-3.91611 + 6.78289i) q^{55} +(1.92682 - 3.33735i) q^{59} +(-1.46419 - 2.53606i) q^{61} -14.4679 q^{65} +(5.75903 + 9.97493i) q^{67} +(0.744644 - 1.28976i) q^{71} +(3.84292 - 6.65614i) q^{73} -12.8108 q^{77} +(-0.0875674 + 0.151671i) q^{79} +7.00735 q^{83} +(-6.08757 - 10.5440i) q^{85} +(-6.77341 - 11.7319i) q^{89} +(-11.8322 - 20.4940i) q^{91} +(-9.91978 + 2.42785i) q^{95} +(1.84292 - 3.19204i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{5} - 4 q^{7} - 8 q^{11} + q^{13} + 11 q^{17} + q^{23} + 6 q^{25} - 3 q^{29} - 12 q^{31} + 12 q^{35} - 24 q^{37} - 19 q^{41} - 5 q^{43} + 17 q^{47} + 22 q^{49} - 5 q^{53} - 10 q^{55} + 13 q^{59}+ \cdots - q^{97}+O(q^{100}) \) 6 * q + q^5 - 4 * q^7 - 8 * q^11 + q^13 + 11 * q^17 + q^23 + 6 * q^25 - 3 * q^29 - 12 * q^31 + 12 * q^35 - 24 * q^37 - 19 * q^41 - 5 * q^43 + 17 * q^47 + 22 * q^49 - 5 * q^53 - 10 * q^55 + 13 * q^59 + 3 * q^61 - 42 * q^65 + 9 * q^67 - 3 * q^71 + 11 * q^73 - 20 * q^77 + 19 * q^79 - 24 * q^83 - 17 * q^85 + 3 * q^89 - 44 * q^91 - 13 * q^95 - q^97

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