LMFDB - Embedded newform 936.2.cl.a.155.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(155,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.155"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.cl (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{6}]$

Embedding invariants

Embedding label			155.5
Character	$\chi$	$=$	936.155
Dual form			936.2.cl.a.779.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.19661 + 1.25225i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.62973 - 0.940923i) q^{5} +(-0.580075 - 2.37981i) q^{6} +(-2.40917 + 4.17280i) q^{7} -2.82843i q^{8} +(-0.136235 + 2.99691i) q^{9} -2.66133 q^{10} +(-0.972339 + 3.32484i) q^{12} +(-1.80278 - 3.12250i) q^{13} +(5.90124 - 3.40708i) q^{14} +(3.12842 + 0.914896i) q^{15} +(-2.00000 + 3.46410i) q^{16} +3.88874i q^{17} +(2.28599 - 3.57411i) q^{18} +(3.25945 + 1.88185i) q^{20} +(-8.10822 + 1.97636i) q^{21} +(3.54188 - 3.38453i) q^{24} +(-0.729330 + 1.26324i) q^{25} +5.09902i q^{26} +(-3.91588 + 3.41554i) q^{27} -9.63668 q^{28} +(-3.18458 - 3.33264i) q^{30} +(5.47701 + 9.48646i) q^{31} +(4.89898 - 2.82843i) q^{32} +(2.74975 - 4.76271i) q^{34} +9.06737i q^{35} +(-5.32703 + 2.76094i) q^{36} -11.1407 q^{37} +(1.75291 - 5.99394i) q^{39} +(-2.66133 - 4.60956i) q^{40} +(11.3280 + 3.31284i) q^{42} +(4.84086 - 8.38461i) q^{43} +(2.59783 + 5.01232i) q^{45} +(0.284956 + 0.164519i) q^{47} +(-6.73113 + 1.64070i) q^{48} +(-8.10819 - 14.0438i) q^{49} +(1.78649 - 1.03143i) q^{50} +(-4.86966 + 4.65332i) q^{51} +(3.60555 - 6.24500i) q^{52} +(7.21110 - 1.41421i) q^{54} +(11.8025 + 6.81416i) q^{56} +(1.54377 + 6.33347i) q^{60} -15.4913i q^{62} +(-12.1773 - 7.78853i) q^{63} -8.00000 q^{64} +(-5.87606 - 3.39254i) q^{65} +(-6.73550 + 3.88874i) q^{68} +(6.41160 - 11.1052i) q^{70} +16.8514i q^{71} +(8.47653 + 0.385332i) q^{72} +(13.6445 + 7.87766i) q^{74} +(-2.45461 + 0.598305i) q^{75} +(-6.38522 + 6.10155i) q^{78} +7.52738i q^{80} +(-8.96288 - 0.816569i) q^{81} +(-11.5314 - 12.0675i) q^{84} +(3.65900 + 6.33758i) q^{85} +(-11.8576 + 6.84601i) q^{86} +(0.362567 - 7.97576i) q^{90} +17.3728 q^{91} +(-5.32551 + 18.2102i) q^{93} +(-0.232666 - 0.402989i) q^{94} +(9.40407 + 2.75019i) q^{96} +22.9334i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4} - 48 q^{16} + 60 q^{25} + 12 q^{27} + 48 q^{30} + 48 q^{42} - 84 q^{49} - 60 q^{51} - 192 q^{64} - 168 q^{75} - 96 q^{90}+O(q^{100}) $ 24 * q + 24 * q^4 - 48 * q^16 + 60 * q^25 + 12 * q^27 + 48 * q^30 + 48 * q^42 - 84 * q^49 - 60 * q^51 - 192 * q^64 - 168 * q^75 - 96 * q^90

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i
$2$	−1.22474	−	0.707107i	−0.866025	−	0.500000i
$3$	1.19661	+	1.25225i	0.690865	+	0.722984i
$3$	1.19661	+	1.25225i	0.690865	+	0.722984i
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$	1.62973	−	0.940923i	0.728835	−	0.420793i	−0.0891605	−	0.996017i	$-0.528418\pi$
$5$	1.62973	−	0.940923i	0.728835	−	0.420793i	0.817996	+	0.575224i	$0.195085\pi$
$6$	−0.580075	−	2.37981i	−0.236814	−	0.971555i
$7$	−2.40917	+	4.17280i	−0.910580	+	1.57717i	−0.0973341	+	0.995252i	$0.531032\pi$
$7$	−2.40917	+	4.17280i	−0.910580	+	1.57717i	−0.813246	+	0.581920i	$0.802302\pi$
$8$		−	2.82843i		−	1.00000i
$9$	−0.136235	+	2.99691i	−0.0454118	+	0.998968i
$10$	−2.66133			−0.841587
$11$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$11$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$12$	−0.972339	+	3.32484i	−0.280690	+	0.959798i
$13$	−1.80278	−	3.12250i	−0.500000	−	0.866025i
$13$	−1.80278	−	3.12250i	−0.500000	−	0.866025i
$14$	5.90124	−	3.40708i	1.57717	−	0.910580i
$15$	3.12842	+	0.914896i	0.807754	+	0.236225i
$16$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$17$			3.88874i			0.943158i	0.881824	+	0.471579i	$0.156316\pi$
$17$			3.88874i			0.943158i	−0.881824	+	0.471579i	$0.843684\pi$
$18$	2.28599	−	3.57411i	0.538812	−	0.842426i
$19$		0			0		1.00000			$0$
$19$		0			0		−1.00000			$\pi$
$20$	3.25945	+	1.88185i	0.728835	+	0.420793i
$21$	−8.10822	+	1.97636i	−1.76936	+	0.431277i
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	3.54188	−	3.38453i	0.722984	−	0.690865i
$25$	−0.729330	+	1.26324i	−0.145866	+	0.252647i
$26$			5.09902i			1.00000i
$27$	−3.91588	+	3.41554i	−0.753612	+	0.657320i
$28$	−9.63668			−1.82116
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$	−3.18458	−	3.33264i	−0.581423	−	0.608454i
$31$	5.47701	+	9.48646i	0.983700	+	1.70382i	0.647576	+	0.762001i	$0.275783\pi$
$31$	5.47701	+	9.48646i	0.983700	+	1.70382i	0.336124	+	0.941818i	$0.390884\pi$
$32$	4.89898	−	2.82843i	0.866025	−	0.500000i
$33$		0			0
$34$	2.74975	−	4.76271i	0.471579	−	0.816799i
$35$			9.06737i			1.53266i
$36$	−5.32703	+	2.76094i	−0.887838	+	0.460156i
$37$	−11.1407			−1.83152			−0.915759	−	0.401727i	$-0.868410\pi$
$37$	−11.1407			−1.83152			−0.915759	+	0.401727i	$0.868410\pi$
$38$		0			0
$39$	1.75291	−	5.99394i	0.280690	−	0.959798i
$40$	−2.66133	−	4.60956i	−0.420793	−	0.728835i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	11.3280	+	3.31284i	1.74795	+	0.511182i
$43$	4.84086	−	8.38461i	0.738224	−	1.27864i	−0.215071	−	0.976599i	$-0.568998\pi$
$43$	4.84086	−	8.38461i	0.738224	−	1.27864i	0.953294	−	0.302043i	$-0.0976685\pi$
$44$		0			0
$45$	2.59783	+	5.01232i	0.387262	+	0.747193i
$46$		0			0
$47$	0.284956	+	0.164519i	0.0415651	+	0.0239976i	0.520639	−	0.853777i	$-0.325694\pi$
$47$	0.284956	+	0.164519i	0.0415651	+	0.0239976i	−0.479073	+	0.877775i	$0.659027\pi$
$48$	−6.73113	+	1.64070i	−0.971555	+	0.236814i
$49$	−8.10819	−	14.0438i	−1.15831	−	2.00626i
$50$	1.78649	−	1.03143i	0.252647	−	0.145866i
$51$	−4.86966	+	4.65332i	−0.681888	+	0.651595i
$52$	3.60555	−	6.24500i	0.500000	−	0.866025i
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	7.21110	−	1.41421i	0.981307	−	0.192450i
$55$		0			0
$56$	11.8025	+	6.81416i	1.57717	+	0.910580i
$57$		0			0
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$	1.54377	+	6.33347i	0.199300	+	0.817648i
$61$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$61$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$62$		−	15.4913i		−	1.96740i
$63$	−12.1773	−	7.78853i	−1.53419	−	0.981263i
$64$	−8.00000			−1.00000
$65$	−5.87606	−	3.39254i	−0.728835	−	0.420793i
$66$		0			0
$67$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$67$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$68$	−6.73550	+	3.88874i	−0.816799	+	0.471579i
$69$		0			0
$70$	6.41160	−	11.1052i	0.766332	−	1.32733i
$71$			16.8514i			1.99989i	0.0105471	+	0.999944i	$0.496643\pi$
$71$			16.8514i			1.99989i	−0.0105471	+	0.999944i	$0.503357\pi$
$72$	8.47653	+	0.385332i	0.998968	+	0.0454118i
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	13.6445	+	7.87766i	1.58614	+	0.915759i
$75$	−2.45461	+	0.598305i	−0.283433	+	0.0690863i
$76$		0			0
$77$		0			0
$78$	−6.38522	+	6.10155i	−0.722984	+	0.690865i
$79$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$79$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$80$			7.52738i			0.841587i
$81$	−8.96288	−	0.816569i	−0.995876	−	0.0907298i
$82$		0			0
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$	−11.5314	−	12.0675i	−1.25818	−	1.31667i
$85$	3.65900	+	6.33758i	0.396875	+	0.687407i
$86$	−11.8576	+	6.84601i	−1.27864	+	0.738224i
$87$		0			0
$88$		0			0
$89$		0			0			−	1.00000i	$-0.5\pi$
$89$		0			0				1.00000i	$0.5\pi$
$90$	0.362567	−	7.97576i	0.0382179	−	0.840718i
$91$	17.3728			1.82116
$92$		0			0
$93$	−5.32551	+	18.2102i	−0.552230	+	1.88831i
$94$	−0.232666	−	0.402989i	−0.0239976	−	0.0415651i
$95$		0			0
$96$	9.40407	+	2.75019i	0.959798	+	0.280690i
$97$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$97$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$98$			22.9334i			2.31663i
$99$		0			0
$100$	−2.91732			−0.291732
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$	9.25448	−	2.25576i	0.916330	−	0.223353i
$103$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$103$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$104$	−8.83176	+	5.09902i	−0.866025	+	0.500000i
$105$	−11.3546	+	10.8501i	−1.10809	+	1.05886i
$106$		0			0
$107$			10.1980i			0.985882i	0.870063	+	0.492941i	$0.164078\pi$
$107$			10.1980i			0.985882i	−0.870063	+	0.492941i	$0.835922\pi$
$108$	−9.83176	−	3.36697i	−0.946062	−	0.323987i
$109$	7.41038			0.709785			0.354893	−	0.934907i	$-0.384517\pi$
$109$	7.41038			0.709785			0.354893	+	0.934907i	$0.384517\pi$
$110$		0			0
$111$	−13.3311	−	13.9509i	−1.26533	−	1.32416i
$112$	−9.63668	−	16.6912i	−0.910580	−	1.57717i
$113$	13.3318	−	7.69710i	1.25415	−	0.724082i	0.282216	−	0.959351i	$-0.408930\pi$
$113$	13.3318	−	7.69710i	1.25415	−	0.724082i	0.971930	+	0.235269i	$0.0755971\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	9.60343	−	4.97735i	0.887838	−	0.460156i
$118$		0			0
$119$	−16.2269	−	9.36863i	−1.48752	−	0.858821i
$120$	2.58772	−	8.84850i	0.236225	−	0.807754i
$121$	5.50000	+	9.52628i	0.500000	+	0.866025i
$122$		0			0
$123$		0			0
$124$	−10.9540	+	18.9729i	−0.983700	+	1.70382i
$125$			12.1542i			1.08710i
$126$	9.40674	+	18.1496i	0.838019	+	1.61690i
$127$		0			0		1.00000			$0$
$127$		0			0		−1.00000			$\pi$
$128$	9.79796	+	5.65685i	0.866025	+	0.500000i
$129$	16.2922	−	3.97119i	1.43445	−	0.349644i
$130$	4.79778	+	8.31000i	0.420793	+	0.728835i
$131$	19.1791	−	11.0730i	1.67568	−	0.967456i	0.711321	−	0.702867i	$-0.248097\pi$
$131$	19.1791	−	11.0730i	1.67568	−	0.967456i	0.964361	−	0.264588i	$-0.0852361\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−3.16806	+	9.25093i	−0.272663	+	0.796193i
$136$	10.9990			0.943158
$137$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$137$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$138$		0			0
$139$	2.22772	+	3.85853i	0.188953	+	0.327276i	0.944901	−	0.327355i	$-0.106157\pi$
$139$	2.22772	+	3.85853i	0.188953	+	0.327276i	−0.755948	+	0.654631i	$0.772824\pi$
$140$	−15.7051	+	9.06737i	−1.32733	+	0.766332i
$141$	0.134963	+	0.553701i	0.0113660	+	0.0466300i
$142$	11.9157	−	20.6386i	0.999944	−	1.73195i
$143$		0			0
$144$	−10.1091	−	6.46574i	−0.842426	−	0.538812i
$145$		0			0
$146$		0			0
$147$	7.88391	−	26.9584i	0.650254	−	2.22349i
$148$	−11.1407	−	19.2962i	−0.915759	−	1.58614i
$149$	11.3260	−	6.53907i	0.927862	−	0.535701i	0.0417274	−	0.999129i	$-0.486714\pi$
$149$	11.3260	−	6.53907i	0.927862	−	0.535701i	0.886135	+	0.463428i	$0.153381\pi$
$150$	3.42933	+	1.00290i	0.280004	+	0.0818863i
$151$	−11.9133	+	20.6344i	−0.969487	+	1.67920i	−0.272445	+	0.962171i	$0.587832\pi$
$151$	−11.9133	+	20.6344i	−0.969487	+	1.67920i	−0.697042	+	0.717030i	$0.745501\pi$
$152$		0			0
$153$	−11.6542	−	0.529784i	−0.942185	−	0.0428305i
$154$		0			0
$155$	17.8520	+	10.3069i	1.43391	+	0.827869i
$156$	12.1347	−	2.95781i	0.971555	−	0.236814i
$157$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$157$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$158$		0			0
$159$		0			0
$160$	5.32266	−	9.21912i	0.420793	−	0.728835i
$161$		0			0
$162$	10.3998	+	7.33780i	0.817089	+	0.576512i
$163$		0			0		1.00000			$0$
$163$		0			0		−1.00000			$\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	22.3487	−	12.9030i	1.72939	−	0.998467i	0.837018	−	0.547176i	$-0.184297\pi$
$167$	22.3487	−	12.9030i	1.72939	−	0.998467i	0.892377	−	0.451291i	$-0.149036\pi$
$168$	5.58999	+	22.9335i	0.431277	+	1.76936i
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$		−	10.3492i		−	0.793749i
$171$		0			0
$172$	19.3634			1.47645
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	−3.51416	−	6.08670i	−0.265645	−	0.460111i
$176$		0			0
$177$		0			0
$178$		0			0
$179$			19.8735i			1.48541i	0.669616	+	0.742707i	$0.266459\pi$
$179$			19.8735i			1.48541i	−0.669616	+	0.742707i	$0.733541\pi$
$180$	−6.08376	+	9.51189i	−0.453457	+	0.708975i
$181$		0			0		1.00000			$0$
$181$		0			0		−1.00000			$\pi$
$182$	−21.2772	−	12.2844i	−1.57717	−	0.910580i
$183$		0			0
$184$		0			0
$185$	−18.1563	+	10.4825i	−1.33488	+	0.770691i
$186$	19.3989	−	18.5371i	1.42240	−	1.35921i
$187$		0			0
$188$			0.658078i			0.0479953i
$189$	−4.81834	−	24.5688i	−0.350483	−	1.78712i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	−9.57290	−	10.0180i	−0.690865	−	0.722984i
$193$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$193$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$194$		0			0
$195$	−2.78307	−	11.4178i	−0.199300	−	0.817648i
$196$	16.2164	−	28.0876i	1.15831	−	2.00626i
$197$		−	25.9853i		−	1.85137i	−0.378289	−	0.925687i	$-0.623488\pi$
$197$		−	25.9853i		−	1.85137i	0.378289	−	0.925687i	$-0.376512\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	3.57297	+	2.06286i	0.252647	+	0.145866i
$201$		0			0
$202$		0			0
$203$		0			0
$204$	−12.9294	−	3.78117i	−0.905242	−	0.264735i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	14.4222			1.00000
$209$		0			0
$210$	21.5786	−	5.25975i	1.48907	−	0.362957i
$211$	−13.4308	−	23.2629i	−0.924618	−	1.60148i	−0.792175	−	0.610294i	$-0.791051\pi$
$211$	−13.4308	−	23.2629i	−0.924618	−	1.60148i	−0.132443	−	0.991191i	$-0.542282\pi$
$212$		0			0
$213$	−21.1020	+	20.1646i	−1.44589	+	1.38165i
$214$	7.21110	−	12.4900i	0.492941	−	0.853799i
$215$		−	18.2195i		−	1.24256i
$216$	9.66059	+	11.0758i	0.657320	+	0.753612i
$217$	−52.7802			−3.58295
$218$	−9.07582	−	5.23993i	−0.614692	−	0.354893i
$219$		0			0
$220$		0			0
$221$	12.1426	−	7.01053i	0.816799	−	0.471579i
$222$	6.46243	+	26.5128i	0.433730	+	1.77942i
$223$	0.955433	−	1.65486i	0.0639805	−	0.110818i	−0.832261	−	0.554384i	$-0.812954\pi$
$223$	0.955433	−	1.65486i	0.0639805	−	0.110818i	0.896241	+	0.443567i	$0.146287\pi$
$224$			27.2566i			1.82116i
$225$	−3.68644	−	2.35783i	−0.245763	−	0.157189i
$226$	−21.7707			−1.44816
$227$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$227$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$228$		0			0
$229$	7.11548	+	12.3244i	0.470204	+	0.814417i	0.999419	−	0.0340703i	$-0.0108470\pi$
$229$	7.11548	+	12.3244i	0.470204	+	0.814417i	−0.529215	+	0.848487i	$0.677514\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$		−	26.6877i		−	1.74837i	−0.485596	−	0.874183i	$-0.661397\pi$
$233$		−	26.6877i		−	1.74837i	0.485596	−	0.874183i	$-0.338603\pi$
$234$	−15.2813	−	0.694666i	−0.998968	−	0.0454118i
$235$	0.619200			0.0403922
$236$		0			0
$237$		0			0
$238$	13.2492	+	22.9484i	0.858821	+	1.48752i
$239$	22.8604	−	13.1985i	1.47872	−	0.853737i	0.479006	−	0.877812i	$-0.340997\pi$
$239$	22.8604	−	13.1985i	1.47872	−	0.853737i	0.999710	+	0.0240747i	$0.00766395\pi$
$240$	−9.42612	+	9.00736i	−0.608454	+	0.581423i
$241$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$241$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$242$		−	15.5563i		−	1.00000i
$243$	−9.70255	−	12.2008i	−0.622419	−	0.782684i
$244$		0			0
$245$	−26.4283	−	15.2584i	−1.68844	−	0.974821i
$246$		0			0
$247$		0			0
$248$	26.8318	−	15.4913i	1.70382	−	0.983700i
$249$		0			0
$250$	8.59431	−	14.8858i	0.543552	−	0.941460i
$251$		−	31.0798i		−	1.96174i	−0.194668	−	0.980869i	$-0.562363\pi$
$251$		−	31.0798i		−	1.96174i	0.194668	−	0.980869i	$-0.437637\pi$
$252$	1.31286	−	28.8802i	0.0827021	−	1.81928i
$253$		0			0
$254$		0			0
$255$	−3.55779	+	12.1656i	−0.222798	+	0.761839i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	9.66084	−	5.57769i	0.602627	−	0.347927i	−0.167448	−	0.985881i	$-0.553552\pi$
$257$	9.66084	−	5.57769i	0.602627	−	0.347927i	0.770074	+	0.637954i	$0.220219\pi$
$258$	−22.7619	−	6.65664i	−1.41709	−	0.414424i
$259$	26.8398	−	46.4879i	1.66775	−	2.88862i
$260$		−	13.5702i		−	0.841587i
$261$		0			0
$262$	−31.3193			−1.93491
$263$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$263$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		0			0
$268$		0			0
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$	10.4215	−	9.08987i	0.634229	−	0.553192i
$271$	20.7363			1.25964			0.629819	−	0.776742i	$-0.283129\pi$
$271$	20.7363			1.25964			0.629819	+	0.776742i	$0.283129\pi$
$272$	−13.4710	−	7.77748i	−0.816799	−	0.471579i
$273$	20.7885	+	21.7550i	1.25818	+	1.31667i
$274$		0			0
$275$		0			0
$276$		0			0
$277$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$277$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$278$		−	6.30095i		−	0.377906i
$279$	−29.1762	+	15.1217i	−1.74673	+	0.905312i
$280$	25.6464			1.53266
$281$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$281$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$282$	0.226230	−	0.773576i	0.0134718	−	0.0460658i
$283$	16.7476	+	29.0078i	0.995544	+	1.72433i	0.579437	+	0.815017i	$0.303272\pi$
$283$	16.7476	+	29.0078i	0.995544	+	1.72433i	0.416107	+	0.909316i	$0.363394\pi$
$284$	−29.1874	+	16.8514i	−1.73195	+	0.999944i
$285$		0			0
$286$		0			0
$287$		0			0
$288$	7.80911	+	15.0671i	0.460156	+	0.887838i
$289$	1.87770			0.110453
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−9.13692	+	5.27520i	−0.533785	+	0.308181i	−0.742556	−	0.669784i	$-0.766387\pi$
$293$	−9.13692	+	5.27520i	−0.533785	+	0.308181i	0.208772	+	0.977964i	$0.433053\pi$
$294$	−28.7183	+	27.4424i	−1.67488	+	1.60048i
$295$		0			0
$296$			31.5106i			1.83152i
$297$		0			0
$298$	−18.4953			−1.07140
$299$		0			0
$300$	−3.49090	−	3.65320i	−0.201547	−	0.210917i
$301$	23.3249	+	40.3999i	1.34442	+	2.32861i
$302$	29.1814	−	16.8479i	1.67920	−	0.969487i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	13.8988	+	8.88960i	0.794541	+	0.508185i
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	−14.5761	−	25.2466i	−0.827869	−	1.43391i
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$	−16.9534	−	4.95798i	−0.959798	−	0.280690i
$313$	−17.4228	+	30.1772i	−0.984797	+	1.70572i	−0.341964	+	0.939713i	$0.611092\pi$
$313$	−17.4228	+	30.1772i	−0.984797	+	1.70572i	−0.642834	+	0.766006i	$0.722241\pi$
$314$		0			0
$315$	−27.1740	−	1.23530i	−1.53108	−	0.0696010i
$316$		0			0
$317$	−3.97753	−	2.29643i	−0.223400	−	0.128980i	0.384123	−	0.923282i	$-0.374504\pi$
$317$	−3.97753	−	2.29643i	−0.223400	−	0.128980i	−0.607524	+	0.794301i	$0.707837\pi$
$318$		0			0
$319$		0			0
$320$	−13.0378	+	7.52738i	−0.728835	+	0.420793i
$321$	−12.7704	+	12.2031i	−0.712777	+	0.681111i
$322$		0			0
$323$		0			0
$324$	−7.54854	−	16.3407i	−0.419363	−	0.907818i
$325$	5.25927			0.291732
$326$		0			0
$327$	8.86735	+	9.27961i	0.490366	+	0.513163i
$328$		0			0
$329$	−1.37301	+	0.792710i	−0.0756967	+	0.0437035i
$330$		0			0
$331$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$331$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$332$		0			0
$333$	1.51776	−	33.3876i	0.0831725	−	1.82963i
$334$	−36.4953			−1.99693
$335$		0			0
$336$	9.37012	−	32.0404i	0.511182	−	1.74795i
$337$	−14.1434	−	24.4972i	−0.770442	−	1.33444i	−0.937321	−	0.348467i	$-0.886702\pi$
$337$	−14.1434	−	24.4972i	−0.770442	−	1.33444i	0.166879	−	0.985977i	$-0.446631\pi$
$338$	15.9217	−	9.19239i	0.866025	−	0.500000i
$339$	25.5916	+	7.48419i	1.38995	+	0.406485i
$340$	−7.31801	+	12.6752i	−0.396875	+	0.687407i
$341$		0			0
$342$		0			0
$343$	44.4077			2.39779
$344$	−23.7153	−	13.6920i	−1.27864	−	0.738224i
$345$		0			0
$346$		0			0
$347$	3.98367	−	2.29997i	0.213855	−	0.123469i	−0.389247	−	0.921133i	$-0.627265\pi$
$347$	3.98367	−	2.29997i	0.213855	−	0.123469i	0.603101	+	0.797664i	$0.293931\pi$
$348$		0			0
$349$	4.02522	−	6.97188i	0.215465	−	0.373196i	−0.737951	−	0.674854i	$-0.764207\pi$
$349$	4.02522	−	6.97188i	0.215465	−	0.373196i	0.953416	+	0.301658i	$0.0975400\pi$
$350$			9.93954i			0.531291i
$351$	17.7245	+	6.06989i	0.946062	+	0.323987i
$352$		0			0
$353$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$353$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$354$		0			0
$355$	15.8558	+	27.4631i	0.841540	+	1.45759i
$356$		0			0
$357$	−7.68555	−	31.5307i	−0.406762	−	1.66878i
$358$	14.0527	−	24.3400i	0.742707	−	1.28641i
$359$			34.2913i			1.80983i	0.425595	+	0.904914i	$0.360065\pi$
$359$			34.2913i			1.80983i	−0.425595	+	0.904914i	$0.639935\pi$
$360$	14.1770	−	7.34777i	0.747193	−	0.387262i
$361$	19.0000			1.00000
$362$		0			0
$363$	−5.34787	+	18.2866i	−0.280690	+	0.959798i
$364$	17.3728	+	30.0905i	0.910580	+	1.57717i
$365$		0			0
$366$		0			0
$367$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$367$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$368$		0			0
$369$		0			0
$370$	29.6491			1.54138
$371$		0			0
$372$	−36.8665	+	8.98612i	−1.91144	+	0.465909i
$373$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$373$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$374$		0			0
$375$	−15.2200	+	14.5439i	−0.785959	+	0.751042i
$376$	0.465331	−	0.805977i	0.0239976	−	0.0415651i
$377$		0			0
$378$	−11.4715	+	33.4976i	−0.590032	+	1.72293i
$379$		0			0		1.00000			$0$
$379$		0			0		−1.00000			$\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	27.9607	−	16.1431i	1.42873	−	0.824875i	0.431705	−	0.902015i	$-0.357912\pi$
$383$	27.9607	−	16.1431i	1.42873	−	0.824875i	0.997020	+	0.0771400i	$0.0245788\pi$
$384$	4.64060	+	19.0385i	0.236814	+	0.971555i
$385$		0			0
$386$		0			0
$387$	24.4684	+	15.6499i	1.24380	+	0.795528i
$388$		0			0
$389$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$389$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$390$	−4.66507	+	15.9519i	−0.236225	+	0.807754i
$391$		0			0
$392$	−39.7219	+	22.9334i	−2.00626	+	1.15831i
$393$	36.8161	+	10.7667i	1.85712	+	0.543111i
$394$	−18.3744	+	31.8253i	−0.925687	+	1.60334i
$395$		0			0
$396$		0			0
$397$	32.7247			1.64241			0.821203	−	0.570637i	$-0.193304\pi$
$397$	32.7247			1.64241			0.821203	+	0.570637i	$0.193304\pi$
$398$		0			0
$399$		0			0
$400$	−2.91732	−	5.05294i	−0.145866	−	0.252647i
$401$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$401$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$402$		0			0
$403$	19.7476	−	34.2039i	0.983700	−	1.70382i
$404$		0			0
$405$	−15.3754	+	7.10259i	−0.764008	+	0.352931i
$406$		0			0
$407$		0			0
$408$	13.1616	+	13.7735i	0.651595	+	0.681888i
$409$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$409$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	−17.6635	−	10.1980i	−0.866025	−	0.500000i
$417$	−2.16610	+	7.40682i	−0.106075	+	0.362714i
$418$		0			0
$419$	−35.0575	+	20.2404i	−1.71267	+	0.988810i	−0.781745	+	0.623598i	$0.785670\pi$
$419$	−35.0575	+	20.2404i	−1.71267	+	0.988810i	−0.930924	+	0.365212i	$0.880997\pi$
$420$	−30.1475	−	8.81656i	−1.47105	−	0.430204i
$421$	2.81150	−	4.86966i	0.137024	−	0.237333i	−0.789345	−	0.613950i	$-0.789580\pi$
$421$	2.81150	−	4.86966i	0.137024	−	0.237333i	0.926369	+	0.376617i	$0.122913\pi$
$422$			37.9882i			1.84924i
$423$	−0.531870	+	0.831573i	−0.0258604	+	0.0404325i
$424$		0			0
$425$	−4.91240	−	2.83617i	−0.238286	−	0.137575i
$426$	40.1031	−	9.77505i	1.94300	−	0.473603i
$427$		0			0
$428$	−17.6635	+	10.1980i	−0.853799	+	0.492941i
$429$		0			0
$430$	−12.8831	+	22.3142i	−0.621279	+	1.07609i
$431$		−	39.8700i		−	1.92047i	−0.279191	−	0.960236i	$-0.590066\pi$
$431$		−	39.8700i		−	1.92047i	0.279191	−	0.960236i	$-0.409934\pi$
$432$	−4.00000	−	20.3961i	−0.192450	−	0.981307i
$433$	−15.3696			−0.738614			−0.369307	−	0.929308i	$-0.620405\pi$
$433$	−15.3696			−0.738614			−0.369307	+	0.929308i	$0.620405\pi$
$434$	64.6423	+	37.3212i	3.10293	+	1.79148i
$435$		0			0
$436$	7.41038	+	12.8351i	0.354893	+	0.614692i
$437$		0			0
$438$		0			0
$439$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$439$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$440$		0			0
$441$	43.1926	−	22.3862i	2.05679	−	1.06601i
$442$	−19.8288			−0.943158
$443$	18.1965	+	10.5057i	0.864540	+	0.499142i	0.865530	−	0.500857i	$-0.166982\pi$
$443$	18.1965	+	10.5057i	0.864540	+	0.499142i	−0.000990059		1.00000i	$0.500315\pi$
$444$	10.8325	−	37.0410i	0.514089	−	1.75789i
$445$		0			0
$446$	−2.34032	+	1.35119i	−0.110818	+	0.0639805i
$447$	21.7414	+	6.35819i	1.02833	+	0.300732i
$448$	19.2734	−	33.3824i	0.910580	−	1.57717i
$449$		0			0			−	1.00000i	$-0.5\pi$
$449$		0			0				1.00000i	$0.5\pi$
$450$	2.84771	+	5.49444i	0.134242	+	0.259011i
$451$		0			0
$452$	26.6635	+	15.3942i	1.25415	+	0.724082i
$453$	−40.0949	+	9.77303i	−1.88382	+	0.459177i
$454$		0			0
$455$	28.3128	−	16.3464i	1.32733	−	0.766332i
$456$		0			0
$457$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$457$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$458$		−	20.1256i		−	0.940408i
$459$	−13.2821	−	15.2278i	−0.619957	−	0.710775i
$460$		0			0
$461$	35.8709	+	20.7101i	1.67068	+	0.964565i	0.967261	+	0.253784i	$0.0816754\pi$
$461$	35.8709	+	20.7101i	1.67068	+	0.964565i	0.703414	+	0.710780i	$0.251658\pi$
$462$		0			0
$463$	−16.5684	−	28.6973i	−0.769999	−	1.33368i	−0.937563	−	0.347816i	$-0.886923\pi$
$463$	−16.5684	−	28.6973i	−0.769999	−	1.33368i	0.167564	−	0.985861i	$-0.446410\pi$
$464$		0			0
$465$	8.45524	+	34.6885i	0.392103	+	1.60864i
$466$	−18.8710	+	32.6856i	−0.874183	+	1.51413i
$467$			31.2740i			1.44719i	0.690225	+	0.723595i	$0.257512\pi$
$467$			31.2740i			1.44719i	−0.690225	+	0.723595i	$0.742488\pi$
$468$	18.2245	+	11.6563i	0.842426	+	0.538812i
$469$		0			0
$470$	−0.758362	−	0.437841i	−0.0349806	−	0.0201961i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		−	37.4745i		−	1.71764i
$477$		0			0
$478$	−37.3309			−1.70747
$479$	−37.7879	−	21.8169i	−1.72657	−	0.996837i	−0.903020	−	0.429598i	$-0.858655\pi$
$479$	−37.7879	−	21.8169i	−1.72657	−	0.996837i	−0.823553	−	0.567240i	$-0.808011\pi$
$480$	17.9138	−	4.36644i	0.817648	−	0.199300i
$481$	20.0842	+	34.7868i	0.915759	+	1.58614i
$482$		0			0
$483$		0			0
$484$	−11.0000	+	19.0526i	−0.500000	+	0.866025i
$485$		0			0
$486$	3.25586	+	21.8037i	0.147689	+	0.989034i
$487$	−36.0555			−1.63383			−0.816916	−	0.576757i	$-0.804318\pi$
$487$	−36.0555			−1.63383			−0.816916	+	0.576757i	$0.804318\pi$
$488$		0			0
$489$		0			0
$490$	21.5786	+	37.3752i	0.974821	+	1.68844i
$491$	−32.6501	+	18.8505i	−1.47348	+	0.850712i	−0.999554	−	0.0298549i	$-0.990495\pi$
$491$	−32.6501	+	18.8505i	−1.47348	+	0.850712i	−0.473922	+	0.880567i	$0.657162\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−43.8161			−1.96740
$497$	−70.3174	−	40.5978i	−3.15417	−	1.82106i
$498$		0			0
$499$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$499$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$500$	−21.0517	+	12.1542i	−0.941460	+	0.543552i
$501$	42.9005	+	12.5461i	1.91665	+	0.560519i
$502$	−21.9767	+	38.0648i	−0.980869	+	1.69892i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$	−22.0293	+	34.4426i	−0.981263	+	1.53419i
$505$		0			0
$506$		0			0
$507$	−21.8762	+	5.33227i	−0.971555	+	0.236814i
$508$		0			0
$509$	33.3714	−	19.2670i	1.47916	−	0.853994i	0.479440	−	0.877575i	$-0.340840\pi$
$509$	33.3714	−	19.2670i	1.47916	−	0.853994i	0.999722	+	0.0235804i	$0.00750657\pi$
$510$	12.9598	−	12.3840i	0.573868	−	0.548373i
$511$		0			0
$512$			22.6274i			1.00000i
$513$		0			0
$514$	−15.7761			−0.695853
$515$		0			0
$516$	23.1705	+	24.2478i	1.02003	+	1.06745i
$517$		0			0
$518$	−65.7439	+	37.9572i	−2.88862	+	1.66775i
$519$		0			0
$520$	−9.59556	+	16.6200i	−0.420793	+	0.728835i
$521$		−	42.6660i		−	1.86923i	−0.355658	−	0.934616i	$-0.615743\pi$
$521$		−	42.6660i		−	1.86923i	0.355658	−	0.934616i	$-0.384257\pi$
$522$		0			0
$523$	−9.49528			−0.415200			−0.207600	−	0.978214i	$-0.566565\pi$
$523$	−9.49528			−0.415200			−0.207600	+	0.978214i	$0.566565\pi$
$524$	38.3581	+	22.1461i	1.67568	+	0.967456i
$525$	3.41695	−	11.6840i	0.149128	−	0.509932i
$526$		0			0
$527$	−36.8904	+	21.2987i	−1.60697	+	0.927785i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	9.59556	+	16.6200i	0.414852	+	0.718545i
$536$		0			0
$537$	−24.8865	+	23.7809i	−1.07393	+	1.02622i
$538$		0			0
$539$		0			0
$540$	−19.1911	+	3.76369i	−0.825855	+	0.161963i
$541$	−42.5604			−1.82981			−0.914907	−	0.403665i	$-0.867736\pi$
$541$	−42.5604			−1.82981			−0.914907	+	0.403665i	$0.867736\pi$
$542$	−25.3966	−	14.6627i	−1.09088	−	0.629819i
$543$		0			0
$544$	10.9990	+	19.0509i	0.471579	+	0.816799i
$545$	12.0769	−	6.97259i	0.517317	−	0.298673i
$546$	−10.0775	−	41.3439i	−0.431277	−	1.76936i
$547$	−5.44685	+	9.43423i	−0.232891	+	0.403378i	−0.958658	−	0.284562i	$-0.908152\pi$
$547$	−5.44685	+	9.43423i	−0.232891	+	0.403378i	0.725767	+	0.687941i	$0.241485\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−34.8527	−	10.1926i	−1.47942	−	0.432651i
$556$	−4.45545	+	7.71706i	−0.188953	+	0.327276i
$557$			40.7470i			1.72651i	0.504772	+	0.863253i	$0.331577\pi$
$557$			40.7470i			1.72651i	−0.504772	+	0.863253i	$0.668423\pi$
$558$	46.4260	+	2.11047i	1.96537	+	0.0893431i
$559$	−34.9079			−1.47645
$560$	−31.4103	−	18.1347i	−1.32733	−	0.766332i
$561$		0			0
$562$		0			0
$563$	−40.8159	+	23.5651i	−1.72018	+	0.993149i	−0.801665	+	0.597773i	$0.796052\pi$
$563$	−40.8159	+	23.5651i	−1.72018	+	0.993149i	−0.918519	+	0.395376i	$0.870614\pi$
$564$	−0.824075	+	0.787464i	−0.0346998	+	0.0331582i
$565$	14.4847	−	25.0883i	0.609378	−	1.05547i
$566$		−	47.3695i		−	1.99109i
$567$	25.0005	−	35.4331i	1.04992	−	1.48805i
$568$	47.6628			1.99989
$569$	33.1651	+	19.1479i	1.39035	+	0.802720i	0.993354	−	0.115099i	$-0.0367185\pi$
$569$	33.1651	+	19.1479i	1.39035	+	0.802720i	0.396998	+	0.917819i	$0.370052\pi$
$570$		0			0
$571$	23.7390	+	41.1171i	0.993444	+	1.72070i	0.595723	+	0.803190i	$0.296866\pi$
$571$	23.7390	+	41.1171i	0.993444	+	1.72070i	0.397721	+	0.917506i	$0.369801\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.08988	−	23.9752i	0.0454118	−	0.998968i
$577$		0			0		1.00000			$0$
$577$		0			0		−1.00000			$\pi$
$578$	−2.29970	−	1.32773i	−0.0956551	−	0.0552265i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$		0			0
$584$		0			0
$585$	10.9677	−	17.1478i	0.453457	−	0.708975i
$586$	14.9205			0.616361
$587$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$587$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$588$	54.5773	−	13.3031i	2.25073	−	0.548611i
$589$		0			0
$590$		0			0
$591$	32.5399	−	31.0943i	1.33851	−	1.27905i
$592$	22.2814	−	38.5925i	0.915759	−	1.58614i
$593$		0			0			−	1.00000i	$-0.5\pi$
$593$		0			0				1.00000i	$0.5\pi$
$594$		0			0
$595$	−35.2606			−1.44554
$596$	22.6520	+	13.0781i	0.927862	+	0.535701i
$597$		0			0
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$	1.69226	+	6.94267i	0.0690863	+	0.283433i
$601$	−23.5063	+	40.7141i	−0.958842	+	1.66076i	−0.233520	+	0.972352i	$0.575025\pi$
$601$	−23.5063	+	40.7141i	−0.958842	+	1.66076i	−0.725321	+	0.688410i	$0.758309\pi$
$602$		−	65.9727i		−	2.68885i
$603$		0			0
$604$	−47.6530			−1.93897
$605$	17.9270	+	10.3501i	0.728835	+	0.420793i
$606$		0			0
$607$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$607$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		−	1.18637i		−	0.0479953i
$612$	−10.7366	−	20.7154i	−0.434000	−	0.837371i
$613$	−11.3661			−0.459073			−0.229537	−	0.973300i	$-0.573721\pi$
$613$	−11.3661			−0.459073			−0.229537	+	0.973300i	$0.573721\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$617$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$618$		0			0
$619$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$619$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$620$			41.2275i			1.65574i
$621$		0			0
$622$		0			0
$623$		0			0
$624$	17.2578	+	18.0601i	0.690865	+	0.722984i
$625$	7.78951	+	13.4918i	0.311580	+	0.539673i
$626$	42.6771	−	24.6396i	1.70572	−	0.984797i
$627$		0			0
$628$		0			0
$629$		−	43.3233i		−	1.72741i
$630$	32.4078	+	20.7279i	1.29116	+	0.825818i
$631$	49.7287			1.97967			0.989834	−	0.142230i	$-0.0454274\pi$
$631$	49.7287			1.97967			0.989834	+	0.142230i	$0.0454274\pi$
$632$		0			0
$633$	13.0593	−	44.6554i	0.519062	−	1.77489i
$634$	3.24764	+	5.62508i	0.128980	+	0.223400i
$635$		0			0
$636$		0			0
$637$	−29.2345	+	50.6356i	−1.15831	+	2.00626i
$638$		0			0
$639$	−50.5019	−	2.29575i	−1.99783	−	0.0908185i
$640$	21.2906			0.841587
$641$	40.1635	+	23.1884i	1.58636	+	0.915888i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	40.1635	+	23.1884i	1.58636	+	0.915888i	0.592464	+	0.805597i	$0.298155\pi$
$642$	24.2694	−	5.91562i	0.957838	−	0.233471i
$643$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$643$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$644$		0			0
$645$	22.8153	−	21.8017i	0.898350	−	0.858440i
$646$		0			0
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−2.30960	+	25.3509i	−0.0907298	+	0.995876i
$649$		0			0
$650$	−6.44126	−	3.71887i	−0.252647	−	0.145866i
$651$	−63.1574	−	66.0937i	−2.47534	−	2.59042i
$652$		0			0
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$	−4.29857	−	17.6353i	−0.168087	−	0.689595i
$655$	20.8377	−	36.0920i	0.814198	−	1.41023i
$656$		0			0
$657$		0			0
$658$	2.24212			0.0874071
$659$	−26.5794	−	15.3456i	−1.03539	−	0.597781i	−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−26.5794	−	15.3456i	−1.03539	−	0.597781i	−0.918523	+	0.395367i	$0.870617\pi$
$660$		0			0
$661$	−3.60555	−	6.24500i	−0.140240	−	0.242902i	0.787347	−	0.616510i	$-0.211454\pi$
$661$	−3.60555	−	6.24500i	−0.140240	−	0.242902i	−0.927587	+	0.373608i	$0.878121\pi$
$662$		0			0
$663$	23.3089	+	6.81661i	0.905242	+	0.264735i
$664$		0			0
$665$		0			0
$666$	−25.4675	+	39.8181i	−0.986844	+	1.54292i
$667$		0			0
$668$	44.6974	+	25.8061i	1.72939	+	0.998467i
$669$	3.21557	−	0.783789i	0.124321	−	0.0303030i
$670$		0			0
$671$		0			0
$672$	−34.1320	+	32.6156i	−1.31667	+	1.25818i
$673$	4.11619	−	7.12945i	0.158667	−	0.274820i	−0.775721	−	0.631076i	$-0.782614\pi$
$673$	4.11619	−	7.12945i	0.158667	−	0.274820i	0.934388	+	0.356256i	$0.115947\pi$
$674$			40.0037i			1.54088i
$675$	−1.45866	−	7.43773i	−0.0561438	−	0.286278i
$676$	−26.0000			−1.00000
$677$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$677$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$678$	−26.0511	−	27.2622i	−1.00049	−	1.04700i
$679$		0			0
$680$	17.9254	−	10.3492i	0.687407	−	0.396875i
$681$		0			0
$682$		0			0
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$		0			0
$685$		0			0
$686$	−54.3880	−	31.4010i	−2.07655	−	1.19889i
$687$	−6.91866	+	23.6578i	−0.263963	+	0.902602i
$688$	19.3634	+	33.5384i	0.738224	+	1.27864i
$689$		0			0
$690$		0			0
$691$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$691$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$692$		0			0
$693$		0			0
$694$	−6.50530			−0.246938
$695$	7.26116	+	4.19223i	0.275431	+	0.159020i
$696$		0			0
$697$		0			0
$698$	−9.85973	+	5.69252i	−0.373196	+	0.215465i
$699$	33.4195	−	31.9348i	1.26404	−	1.20788i
$700$	7.02831	−	12.1734i	0.265645	−	0.460111i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$	−17.4159	−	19.9672i	−0.657320	−	0.753612i
$703$		0			0
$704$		0			0
$705$	0.740943	+	0.775390i	0.0279055	+	0.0292029i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	5.27096	−	9.12957i	0.197955	−	0.342868i	−0.749910	−	0.661540i	$-0.769903\pi$
$709$	5.27096	−	9.12957i	0.197955	−	0.342868i	0.947865	+	0.318671i	$0.103237\pi$
$710$		−	44.8470i		−	1.68308i
$711$		0			0
$712$		0			0
$713$		0			0
$714$	−12.8828	+	44.0516i	−0.482125	+	1.64859i
$715$		0			0
$716$	−34.4219	+	19.8735i	−1.28641	+	0.742707i
$717$	43.8827	+	12.8334i	1.63883	+	0.479271i
$718$	24.2476	−	41.9981i	0.904914	−	1.56736i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$	−22.5588	−	1.02549i	−0.840718	−	0.0382179i
$721$		0			0
$722$	−23.2702	−	13.4350i	−0.866025	−	0.500000i
$723$		0			0
$724$		0			0
$725$		0			0
$726$	19.4804	−	18.6149i	0.722984	−	0.690865i
$727$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$727$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$728$		−	49.1376i		−	1.82116i
$729$	3.66824	−	26.7497i	0.135861	−	0.990728i
$730$		0			0
$731$	32.6056	+	18.8248i	1.20596	+	0.696262i
$732$		0			0
$733$	−26.0985	−	45.2040i	−0.963971	−	1.66965i	−0.712354	−	0.701820i	$-0.752371\pi$
$733$	−26.0985	−	45.2040i	−0.963971	−	1.66965i	−0.251617	−	0.967827i	$-0.580962\pi$
$734$		0			0
$735$	−12.5172	−	51.3530i	−0.461703	−	1.89418i
$736$		0			0
$737$		0			0
$738$		0			0
$739$		0			0		1.00000			$0$
$739$		0			0		−1.00000			$\pi$
$740$	−36.3126	−	20.9651i	−1.33488	−	0.770691i
$741$		0			0
$742$		0			0
$743$	−46.5757	+	26.8905i	−1.70870	+	0.986516i	−0.772514	+	0.634998i	$0.781001\pi$
$743$	−46.5757	+	26.8905i	−1.70870	+	0.986516i	−0.936181	+	0.351518i	$0.885666\pi$
$744$	51.5062	+	15.0628i	1.88831	+	0.552230i
$745$	12.3055	−	21.3138i	0.450839	−	0.780876i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−42.5544	−	24.5688i	−1.55490	−	0.897724i
$750$	28.9247	−	7.05034i	1.05618	−	0.257442i
$751$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$751$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$752$	−1.13982	+	0.658078i	−0.0415651	+	0.0239976i
$753$	38.9195	−	37.1905i	1.41831	−	1.35530i
$754$		0			0
$755$			44.8378i			1.63182i
$756$	37.7361	−	32.9144i	1.37245	−	1.19709i
$757$		0			0		1.00000			$0$
$757$		0			0		−1.00000			$\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$	−17.8528	+	30.9220i	−0.646316	+	1.11945i
$764$		0			0
$765$	−19.4916	+	10.1023i	−0.704721	+	0.365249i
$766$	−45.6596			−1.64975
$767$		0			0
$768$	7.77871	−	26.5987i	0.280690	−	0.959798i
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$		0			0
$771$	18.5449	+	5.42341i	0.667879	+	0.195319i
$772$		0			0
$773$		−	14.6791i		−	0.527972i	−0.964527	−	0.263986i	$-0.914963\pi$
$773$		−	14.6791i		−	0.527972i	0.964527	−	0.263986i	$-0.0850372\pi$
$774$	−18.9014	−	36.4689i	−0.679397	−	1.31085i
$775$	−15.9782			−0.573953
$776$		0			0
$777$	90.3312	−	22.0180i	3.24061	−	0.789892i
$778$		0			0
$779$		0			0
$780$	16.9932	−	16.2382i	0.608454	−	0.581423i
$781$		0			0
$782$		0			0
$783$		0			0
$784$	64.8655			2.31663
$785$		0			0
$786$	−37.4771	−	39.2194i	−1.33676	−	1.39891i
$787$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$787$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$788$	45.0078	−	25.9853i	1.60334	−	0.925687i
$789$		0			0
$790$		0			0
$791$			74.1744i			2.63734i
$792$		0			0
$793$		0			0
$794$	−40.0794	−	23.1399i	−1.42236	−	0.821203i
$795$		0			0
$796$		0			0
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$		0			0
$799$	−0.639773	+	1.10812i	−0.0226336	+	0.0392025i
$800$			8.25142i			0.291732i
$801$		0			0
$802$		0			0
$803$		0			0
$804$		0			0
$805$		0			0
$806$	−48.3716	+	27.9274i	−1.70382	+	0.983700i
$807$		0			0
$808$		0			0
$809$		−	55.9584i		−	1.96739i	−0.179841	−	0.983696i	$-0.557558\pi$
$809$		−	55.9584i		−	1.96739i	0.179841	−	0.983696i	$-0.442442\pi$
$810$	23.8532	+	2.17316i	0.838116	+	0.0763570i
$811$		0			0		1.00000			$0$
$811$		0			0		−1.00000			$\pi$
$812$		0			0
$813$	24.8133	+	25.9669i	0.870240	+	0.910698i
$814$		0			0
$815$		0			0
$816$	−6.38025	−	26.1756i	−0.223353	−	0.916330i
$817$		0			0
$818$		0			0
$819$	−2.36678	+	52.0645i	−0.0827021	+	1.81928i
$820$		0			0
$821$	−10.4329	−	6.02341i	−0.364109	−	0.210218i	0.306773	−	0.951783i	$-0.400751\pi$
$821$	−10.4329	−	6.02341i	−0.364109	−	0.210218i	−0.670882	+	0.741564i	$0.734084\pi$
$822$		0			0
$823$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$823$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0			−	1.00000i	$-0.5\pi$
$827$		0			0				1.00000i	$0.5\pi$
$828$		0			0
$829$		0			0		1.00000			$0$
$829$		0			0		−1.00000			$\pi$
$830$		0			0
$831$		0			0
$832$	14.4222	+	24.9800i	0.500000	+	0.866025i
$833$	54.6127	−	31.5307i	1.89222	−	1.09247i
$834$	7.89034	−	7.53980i	0.273220	−	0.261082i
$835$	24.2815	−	42.0568i	0.840296	−	1.45544i
$836$		0			0
$837$	−53.8487	−	18.4409i	−1.86128	−	0.637412i
$838$	57.2486			1.97762
$839$	7.04517	+	4.06753i	0.243226	+	0.140427i	0.616659	−	0.787231i	$-0.288486\pi$
$839$	7.04517	+	4.06753i	0.243226	+	0.140427i	−0.373432	+	0.927657i	$0.621819\pi$
$840$	30.6888	+	32.1156i	1.05886	+	1.10809i
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−6.88674	+	3.97606i	−0.237333	+	0.137024i
$843$		0			0
$844$	26.8617	−	46.5258i	0.924618	−	1.60148i
$845$			24.4640i			0.841587i
$846$	1.23942	−	0.642376i	0.0426120	−	0.0220853i
$847$	−53.0017			−1.82116
$848$		0			0
$849$	−16.2844	+	55.6832i	−0.558879	+	1.91104i
$850$	4.01095	+	6.94718i	0.137575	+	0.238286i
$851$		0			0
$852$	−56.0281	−	16.3852i	−1.91949	−	0.561349i
$853$	−20.2037	+	34.9939i	−0.691762	+	1.19817i	0.279498	+	0.960146i	$0.409832\pi$
$853$	−20.2037	+	34.9939i	−0.691762	+	1.19817i	−0.971260	+	0.238021i	$0.923501\pi$
$854$		0			0
$855$		0			0
$856$	28.8444			0.985882
$857$	−13.8365	−	7.98849i	−0.472645	−	0.272882i	0.244701	−	0.969599i	$-0.421310\pi$
$857$	−13.8365	−	7.98849i	−0.472645	−	0.272882i	−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	25.7476	+	44.5962i	0.878498	+	1.52160i	0.852989	+	0.521929i	$0.174787\pi$
$859$	25.7476	+	44.5962i	0.878498	+	1.52160i	0.0255092	+	0.999675i	$0.491879\pi$
$860$	31.5571	−	18.2195i	1.07609	−	0.621279i
$861$		0			0
$862$	−28.1924	+	48.8306i	−0.960236	+	1.66318i
$863$			54.9248i			1.86966i	0.355094	+	0.934831i	$0.384449\pi$
$863$			54.9248i			1.86966i	−0.355094	+	0.934831i	$0.615551\pi$
$864$	−9.52323	+	27.8084i	−0.323987	+	0.946062i
$865$		0			0
$866$	18.8238	+	10.8679i	0.639658	+	0.369307i
$867$	2.24688	+	2.35134i	0.0763081	+	0.0798557i
$868$	−52.7802	−	91.4179i	−1.79148	−	3.10293i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		−	20.9597i		−	0.709785i
$873$		0			0
$874$		0			0
$875$	−50.7171	−	29.2815i	−1.71455	−	0.989896i
$876$		0			0
$877$	−29.3969	−	50.9169i	−0.992662	−	1.71934i	−0.601055	−	0.799208i	$-0.705253\pi$
$877$	−29.3969	−	50.9169i	−0.992662	−	1.71934i	−0.391607	−	0.920133i	$-0.628081\pi$
$878$		0			0
$879$	−17.5392	−	5.12929i	−0.591583	−	0.173007i
$880$		0			0
$881$			2.41480i			0.0813567i	0.999172	+	0.0406783i	$0.0129519\pi$
$881$			2.41480i			0.0813567i	−0.999172	+	0.0406783i	$0.987048\pi$
$882$	−68.7293	−	3.12434i	−2.31424	−	0.105202i
$883$	−48.1523			−1.62046			−0.810228	−	0.586115i	$-0.800657\pi$
$883$	−48.1523			−1.62046			−0.810228	+	0.586115i	$0.800657\pi$
$884$	24.2852	+	14.0211i	0.816799	+	0.471579i
$885$		0			0
$886$	−14.8573	−	25.7337i	−0.499142	−	0.864540i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	−39.4590	+	37.7060i	−1.32416	+	1.26533i
$889$		0			0
$890$		0			0
$891$		0			0
$892$	3.82173			0.127961
$893$		0			0
$894$	−22.1317	−	23.1606i	−0.740195	−	0.774607i
$895$	18.6994	+	32.3883i	0.625053	+	1.08262i
$896$	−47.2099	+	27.2566i	−1.57717	+	0.910580i
$897$		0			0
$898$		0			0
$899$		0			0
$900$	0.397442	−	8.74293i	0.0132481	−	0.291431i
$901$		0			0
$902$		0			0
$903$	−22.6797	+	77.5515i	−0.754733	+	2.58075i
$904$	−21.7707	−	37.7079i	−0.724082	−	1.25415i
$905$		0			0
$906$	56.0165	+	16.3819i	1.86102	+	0.544251i
$907$	13.1418	−	22.7623i	0.436367	−	0.755810i	−0.561039	−	0.827789i	$-0.689598\pi$
$907$	13.1418	−	22.7623i	0.436367	−	0.755810i	0.997406	+	0.0719791i	$0.0229315\pi$
$908$		0			0
$909$		0			0
$910$	−46.2347			−1.53266
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−14.2310	+	24.6487i	−0.470204	+	0.814417i
$917$			106.707i			3.52378i
$918$	5.49951	+	28.0421i	0.181511	+	0.925527i
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−29.2885	−	50.7291i	−0.964565	−	1.67068i
$923$	52.6184	−	30.3792i	1.73195	−	0.999944i
$924$		0			0
$925$	8.12524	−	14.0733i	0.267156	−	0.462728i
$926$			46.8625i			1.54000i
$927$		0			0
$928$		0			0
$929$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$	14.1729	−	48.4633i	0.464749	−	1.58917i
$931$		0			0
$932$	46.2244	−	26.6877i	1.51413	−	0.874183i
$933$		0			0
$934$	22.1141	−	38.3027i	0.723595	−	1.25330i
$935$		0			0
$936$	−14.0781	−	27.1626i	−0.460156	−	0.887838i
$937$	51.9906			1.69846			0.849229	−	0.528025i	$-0.177067\pi$
$937$	51.9906			1.69846			0.849229	+	0.528025i	$0.177067\pi$
$938$		0			0
$939$	−58.6377	+	14.2928i	−1.91357	+	0.466428i
$940$	0.619200	+	1.07249i	0.0201961	+	0.0349806i
$941$	24.9573	−	14.4091i	0.813586	−	0.469724i	−0.0346136	−	0.999401i	$-0.511020\pi$
$941$	24.9573	−	14.4091i	0.813586	−	0.469724i	0.848200	+	0.529677i	$0.177687\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−30.9699	−	35.5067i	−1.00745	−	1.15503i
$946$		0			0
$947$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$947$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	−1.88387	−	7.72878i	−0.0610888	−	0.250623i
$952$	−26.4985	+	45.8967i	−0.858821	+	1.48752i
$953$		−	41.4539i		−	1.34282i	−0.741084	−	0.671412i	$-0.765688\pi$
$953$		−	41.4539i		−	1.34282i	0.741084	−	0.671412i	$-0.234312\pi$
$954$		0			0
$955$		0			0
$956$	45.7208	+	26.3969i	1.47872	+	0.853737i
$957$		0			0
$958$	30.8537	+	53.4402i	0.996837	+	1.72657i
$959$		0			0
$960$	−25.0273	−	7.31917i	−0.807754	−	0.236225i
$961$	−44.4953	+	77.0681i	−1.43533	+	2.48607i
$962$		−	56.8066i		−	1.83152i
$963$	−30.5626	−	1.38933i	−0.984865	−	0.0447706i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	30.3638	+	52.5917i	0.976435	+	1.69124i	0.675114	+	0.737713i	$0.264094\pi$
$967$	30.3638	+	52.5917i	0.976435	+	1.69124i	0.301321	+	0.953523i	$0.402572\pi$
$968$	26.9444	−	15.5563i	0.866025	−	0.500000i
$969$		0			0
$970$		0			0
$971$		−	36.1106i		−	1.15884i	−0.815028	−	0.579422i	$-0.803278\pi$
$971$		−	36.1106i		−	1.15884i	0.815028	−	0.579422i	$-0.196722\pi$
$972$	11.4299	−	29.0062i	0.366615	−	0.930373i
$973$	−21.4679			−0.688228
$974$	44.1588	+	25.4951i	1.41494	+	0.816916i
$975$	6.29331	+	6.58590i	0.201547	+	0.210917i
$976$		0			0
$977$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$977$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$978$		0			0
$979$		0			0
$980$		−	61.0334i		−	1.94964i
$981$	−1.00955	+	22.2082i	−0.0322326	+	0.709053i
$982$	53.3173			1.70142
$983$	14.9717	+	8.64394i	0.477524	+	0.275699i	0.719384	−	0.694612i	$-0.244424\pi$
$983$	14.9717	+	8.64394i	0.477524	+	0.275699i	−0.241860	+	0.970311i	$0.577757\pi$
$984$		0			0
$985$	−24.4501	−	42.3489i	−0.779046	−	1.34935i
$986$		0			0
$987$	−2.63563	−	0.770783i	−0.0838932	−	0.0245343i
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		1.00000			$0$
$991$		0			0		−1.00000			$\pi$
$992$	53.6635	+	30.9826i	1.70382	+	0.983700i
$993$		0			0
$994$	57.4139	+	99.4439i	1.82106	+	3.15417i
$995$		0			0
$996$		0			0
$997$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$997$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$998$		0			0
$999$	43.6256	−	38.0514i	1.38025	−	1.20389i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.cl.a.155.5	✓	24
8.3	odd	2	inner	936.2.cl.a.155.11	yes	24
9.5	odd	6	inner	936.2.cl.a.779.5	yes	24
13.12	even	2	inner	936.2.cl.a.155.11	yes	24
72.59	even	6	inner	936.2.cl.a.779.11	yes	24
104.51	odd	2	CM	936.2.cl.a.155.5	✓	24
117.77	odd	6	inner	936.2.cl.a.779.11	yes	24
936.779	even	6	inner	936.2.cl.a.779.5	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cl.a.155.5	✓	24	1.1	even	1	trivial
936.2.cl.a.155.5	✓	24	104.51	odd	2	CM
936.2.cl.a.155.11	yes	24	8.3	odd	2	inner
936.2.cl.a.155.11	yes	24	13.12	even	2	inner
936.2.cl.a.779.5	yes	24	9.5	odd	6	inner
936.2.cl.a.779.5	yes	24	936.779	even	6	inner
936.2.cl.a.779.11	yes	24	72.59	even	6	inner
936.2.cl.a.779.11	yes	24	117.77	odd	6	inner

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:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.cl (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.19661 + 1.25225i) q^{3} +(1.00000 + 1.73205i) q^{4} +(1.62973 - 0.940923i) q^{5} +(-0.580075 - 2.37981i) q^{6} +(-2.40917 + 4.17280i) q^{7} -2.82843i q^{8} +(-0.136235 + 2.99691i) q^{9} -2.66133 q^{10} +(-0.972339 + 3.32484i) q^{12} +(-1.80278 - 3.12250i) q^{13} +(5.90124 - 3.40708i) q^{14} +(3.12842 + 0.914896i) q^{15} +(-2.00000 + 3.46410i) q^{16} +3.88874i q^{17} +(2.28599 - 3.57411i) q^{18} +(3.25945 + 1.88185i) q^{20} +(-8.10822 + 1.97636i) q^{21} +(3.54188 - 3.38453i) q^{24} +(-0.729330 + 1.26324i) q^{25} +5.09902i q^{26} +(-3.91588 + 3.41554i) q^{27} -9.63668 q^{28} +(-3.18458 - 3.33264i) q^{30} +(5.47701 + 9.48646i) q^{31} +(4.89898 - 2.82843i) q^{32} +(2.74975 - 4.76271i) q^{34} +9.06737i q^{35} +(-5.32703 + 2.76094i) q^{36} -11.1407 q^{37} +(1.75291 - 5.99394i) q^{39} +(-2.66133 - 4.60956i) q^{40} +(11.3280 + 3.31284i) q^{42} +(4.84086 - 8.38461i) q^{43} +(2.59783 + 5.01232i) q^{45} +(0.284956 + 0.164519i) q^{47} +(-6.73113 + 1.64070i) q^{48} +(-8.10819 - 14.0438i) q^{49} +(1.78649 - 1.03143i) q^{50} +(-4.86966 + 4.65332i) q^{51} +(3.60555 - 6.24500i) q^{52} +(7.21110 - 1.41421i) q^{54} +(11.8025 + 6.81416i) q^{56} +(1.54377 + 6.33347i) q^{60} -15.4913i q^{62} +(-12.1773 - 7.78853i) q^{63} -8.00000 q^{64} +(-5.87606 - 3.39254i) q^{65} +(-6.73550 + 3.88874i) q^{68} +(6.41160 - 11.1052i) q^{70} +16.8514i q^{71} +(8.47653 + 0.385332i) q^{72} +(13.6445 + 7.87766i) q^{74} +(-2.45461 + 0.598305i) q^{75} +(-6.38522 + 6.10155i) q^{78} +7.52738i q^{80} +(-8.96288 - 0.816569i) q^{81} +(-11.5314 - 12.0675i) q^{84} +(3.65900 + 6.33758i) q^{85} +(-11.8576 + 6.84601i) q^{86} +(0.362567 - 7.97576i) q^{90} +17.3728 q^{91} +(-5.32551 + 18.2102i) q^{93} +(-0.232666 - 0.402989i) q^{94} +(9.40407 + 2.75019i) q^{96} +22.9334i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4} - 48 q^{16} + 60 q^{25} + 12 q^{27} + 48 q^{30} + 48 q^{42} - 84 q^{49} - 60 q^{51} - 192 q^{64} - 168 q^{75} - 96 q^{90}+O(q^{100}) \) 24 * q + 24 * q^4 - 48 * q^16 + 60 * q^25 + 12 * q^27 + 48 * q^30 + 48 * q^42 - 84 * q^49 - 60 * q^51 - 192 * q^64 - 168 * q^75 - 96 * q^90

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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