LMFDB - Embedded newform 1638.2.cm.a.341.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(269,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("1638.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.cm (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			341.13
Character	$\chi$	$=$	1638.341
Dual form			1638.2.cm.a.269.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -1.00000 q^{4} +(0.831839 - 1.44079i) q^{5} +(-0.654454 - 2.56353i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.831839 - 1.44079i) q^{5} +(-0.654454 - 2.56353i) q^{7} +1.00000i q^{8} +(-1.44079 - 0.831839i) q^{10} +(0.423264 + 0.244372i) q^{11} +(2.73254 + 2.35228i) q^{13} +(-2.56353 + 0.654454i) q^{14} +1.00000 q^{16} +3.32788 q^{17} +(5.15480 - 2.97613i) q^{19} +(-0.831839 + 1.44079i) q^{20} +(0.244372 - 0.423264i) q^{22} -7.51620i q^{23} +(1.11609 + 1.93312i) q^{25} +(2.35228 - 2.73254i) q^{26} +(0.654454 + 2.56353i) q^{28} +(1.89125 - 1.09191i) q^{29} +(-3.79697 + 2.19218i) q^{31} -1.00000i q^{32} -3.32788i q^{34} +(-4.23790 - 1.18952i) q^{35} -7.02383 q^{37} +(-2.97613 - 5.15480i) q^{38} +(1.44079 + 0.831839i) q^{40} +(-2.04384 - 3.54003i) q^{41} +(1.67491 - 2.90102i) q^{43} +(-0.423264 - 0.244372i) q^{44} -7.51620 q^{46} +(4.89698 - 8.48183i) q^{47} +(-6.14338 + 3.35543i) q^{49} +(1.93312 - 1.11609i) q^{50} +(-2.73254 - 2.35228i) q^{52} +(-0.998216 + 0.576320i) q^{53} +(0.704175 - 0.406556i) q^{55} +(2.56353 - 0.654454i) q^{56} +(-1.09191 - 1.89125i) q^{58} +0.693648 q^{59} +(-5.82533 + 3.36326i) q^{61} +(2.19218 + 3.79697i) q^{62} -1.00000 q^{64} +(5.66217 - 1.98028i) q^{65} +(-2.57698 + 4.46346i) q^{67} -3.32788 q^{68} +(-1.18952 + 4.23790i) q^{70} +(-4.02154 - 2.32184i) q^{71} +(-5.99414 + 3.46072i) q^{73} +7.02383i q^{74} +(-5.15480 + 2.97613i) q^{76} +(0.349448 - 1.24498i) q^{77} +(2.22800 - 3.85901i) q^{79} +(0.831839 - 1.44079i) q^{80} +(-3.54003 + 2.04384i) q^{82} +1.84311 q^{83} +(2.76826 - 4.79477i) q^{85} +(-2.90102 - 1.67491i) q^{86} +(-0.244372 + 0.423264i) q^{88} -5.05718 q^{89} +(4.24183 - 8.54441i) q^{91} +7.51620i q^{92} +(-8.48183 - 4.89698i) q^{94} -9.90263i q^{95} +(-5.21500 - 3.01088i) q^{97} +(3.35543 + 6.14338i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) $ 72 * q - 72 * q^4 - 4 * q^7	$ 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) $ 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$		0			0
$3$		0			0
$4$	−1.00000			−0.500000
$5$	0.831839	−	1.44079i	0.372010	−	0.644340i	−0.617865	−	0.786284i	$-0.712002\pi$
$5$	0.831839	−	1.44079i	0.372010	−	0.644340i	0.989875	+	0.141945i	$0.0453355\pi$
$6$		0			0
$7$	−0.654454	−	2.56353i	−0.247360	−	0.968924i
$7$	−0.654454	−	2.56353i	−0.247360	−	0.968924i
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.44079	−	0.831839i	−0.455617	−	0.263051i
$11$	0.423264	+	0.244372i	0.127619	+	0.0736808i	0.562450	−	0.826831i	$-0.309859\pi$
$11$	0.423264	+	0.244372i	0.127619	+	0.0736808i	−0.434831	+	0.900512i	$0.643192\pi$
$12$		0			0
$13$	2.73254	+	2.35228i	0.757870	+	0.652406i
$13$	2.73254	+	2.35228i	0.757870	+	0.652406i
$14$	−2.56353	+	0.654454i	−0.685132	+	0.174910i
$15$		0			0
$16$	1.00000			0.250000
$17$	3.32788			0.807129			0.403565	−	0.914951i	$-0.367771\pi$
$17$	3.32788			0.807129			0.403565	+	0.914951i	$0.367771\pi$
$18$		0			0
$19$	5.15480	−	2.97613i	1.18259	−	0.682770i	0.225980	−	0.974132i	$-0.427442\pi$
$19$	5.15480	−	2.97613i	1.18259	−	0.682770i	0.956613	+	0.291362i	$0.0941084\pi$
$20$	−0.831839	+	1.44079i	−0.186005	+	0.322170i
$21$		0			0
$22$	0.244372	−	0.423264i	0.0521002	−	0.0902402i
$23$		−	7.51620i		−	1.56724i	−0.621243	−	0.783618i	$-0.713372\pi$
$23$		−	7.51620i		−	1.56724i	0.621243	−	0.783618i	$-0.286628\pi$
$24$		0			0
$25$	1.11609	+	1.93312i	0.223218	+	0.386624i
$26$	2.35228	−	2.73254i	0.461321	−	0.535895i
$27$		0			0
$28$	0.654454	+	2.56353i	0.123680	+	0.484462i
$29$	1.89125	−	1.09191i	0.351196	−	0.202763i	−0.314016	−	0.949418i	$-0.601675\pi$
$29$	1.89125	−	1.09191i	0.351196	−	0.202763i	0.665212	+	0.746655i	$0.268341\pi$
$30$		0			0
$31$	−3.79697	+	2.19218i	−0.681956	+	0.393727i	−0.800591	−	0.599211i	$-0.795481\pi$
$31$	−3.79697	+	2.19218i	−0.681956	+	0.393727i	0.118636	+	0.992938i	$0.462148\pi$
$32$		−	1.00000i		−	0.176777i
$33$		0			0
$34$		−	3.32788i		−	0.570727i
$35$	−4.23790	−	1.18952i	−0.716336	−	0.201065i
$36$		0			0
$37$	−7.02383			−1.15471			−0.577355	−	0.816493i	$-0.695915\pi$
$37$	−7.02383			−1.15471			−0.577355	+	0.816493i	$0.695915\pi$
$38$	−2.97613	−	5.15480i	−0.482791	−	0.836219i
$39$		0			0
$40$	1.44079	+	0.831839i	0.227808	+	0.131525i
$41$	−2.04384	−	3.54003i	−0.319193	−	0.552859i	0.661127	−	0.750274i	$-0.270079\pi$
$41$	−2.04384	−	3.54003i	−0.319193	−	0.552859i	−0.980320	+	0.197415i	$0.936745\pi$
$42$		0			0
$43$	1.67491	−	2.90102i	0.255421	−	0.442402i	−0.709589	−	0.704616i	$-0.751119\pi$
$43$	1.67491	−	2.90102i	0.255421	−	0.442402i	0.965010	+	0.262214i	$0.0844526\pi$
$44$	−0.423264	−	0.244372i	−0.0638095	−	0.0368404i
$45$		0			0
$46$	−7.51620			−1.10820
$47$	4.89698	−	8.48183i	0.714299	−	1.23720i	−0.248931	−	0.968521i	$-0.580079\pi$
$47$	4.89698	−	8.48183i	0.714299	−	1.23720i	0.963229	−	0.268680i	$-0.0865875\pi$
$48$		0			0
$49$	−6.14338	+	3.35543i	−0.877626	+	0.479346i
$50$	1.93312	−	1.11609i	0.273385	−	0.157839i
$51$		0			0
$52$	−2.73254	−	2.35228i	−0.378935	−	0.326203i
$53$	−0.998216	+	0.576320i	−0.137115	+	0.0791637i	−0.566989	−	0.823726i	$-0.691892\pi$
$53$	−0.998216	+	0.576320i	−0.137115	+	0.0791637i	0.429873	+	0.902889i	$0.358558\pi$
$54$		0			0
$55$	0.704175	−	0.406556i	0.0949510	−	0.0548200i
$56$	2.56353	−	0.654454i	0.342566	−	0.0874551i
$57$		0			0
$58$	−1.09191	−	1.89125i	−0.143375	−	0.248333i
$59$	0.693648			0.0903053			0.0451526	−	0.998980i	$-0.485623\pi$
$59$	0.693648			0.0903053			0.0451526	+	0.998980i	$0.485623\pi$
$60$		0			0
$61$	−5.82533	+	3.36326i	−0.745858	+	0.430621i	−0.824195	−	0.566306i	$-0.808372\pi$
$61$	−5.82533	+	3.36326i	−0.745858	+	0.430621i	0.0783376	+	0.996927i	$0.475039\pi$
$62$	2.19218	+	3.79697i	0.278407	+	0.482215i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	5.66217	−	1.98028i	0.702306	−	0.245624i
$66$		0			0
$67$	−2.57698	+	4.46346i	−0.314828	+	0.545298i	−0.979401	−	0.201925i	$-0.935280\pi$
$67$	−2.57698	+	4.46346i	−0.314828	+	0.545298i	0.664573	+	0.747223i	$0.268614\pi$
$68$	−3.32788			−0.403565
$69$		0			0
$70$	−1.18952	+	4.23790i	−0.142174	+	0.506526i
$71$	−4.02154	−	2.32184i	−0.477269	−	0.275551i	0.242009	−	0.970274i	$-0.422194\pi$
$71$	−4.02154	−	2.32184i	−0.477269	−	0.275551i	−0.719278	+	0.694723i	$0.755527\pi$
$72$		0			0
$73$	−5.99414	+	3.46072i	−0.701561	+	0.405046i	−0.807928	−	0.589281i	$-0.799411\pi$
$73$	−5.99414	+	3.46072i	−0.701561	+	0.405046i	0.106368	+	0.994327i	$0.466078\pi$
$74$			7.02383i			0.816504i
$75$		0			0
$76$	−5.15480	+	2.97613i	−0.591296	+	0.341385i
$77$	0.349448	−	1.24498i	0.0398232	−	0.141879i
$78$		0			0
$79$	2.22800	−	3.85901i	0.250670	−	0.434173i	−0.713041	−	0.701123i	$-0.752683\pi$
$79$	2.22800	−	3.85901i	0.250670	−	0.434173i	0.963710	+	0.266950i	$0.0860159\pi$
$80$	0.831839	−	1.44079i	0.0930024	−	0.161085i
$81$		0			0
$82$	−3.54003	+	2.04384i	−0.390931	+	0.225704i
$83$	1.84311			0.202308			0.101154	−	0.994871i	$-0.467747\pi$
$83$	1.84311			0.202308			0.101154	+	0.994871i	$0.467747\pi$
$84$		0			0
$85$	2.76826	−	4.79477i	0.300260	−	0.520065i
$86$	−2.90102	−	1.67491i	−0.312825	−	0.180610i
$87$		0			0
$88$	−0.244372	+	0.423264i	−0.0260501	+	0.0451201i
$89$	−5.05718			−0.536060			−0.268030	−	0.963411i	$-0.586373\pi$
$89$	−5.05718			−0.536060			−0.268030	+	0.963411i	$0.586373\pi$
$90$		0			0
$91$	4.24183	−	8.54441i	0.444665	−	0.895697i
$92$			7.51620i			0.783618i
$93$		0			0
$94$	−8.48183	−	4.89698i	−0.874833	−	0.505085i
$95$		−	9.90263i		−	1.01599i
$96$		0			0
$97$	−5.21500	−	3.01088i	−0.529503	−	0.305709i	0.211311	−	0.977419i	$-0.432227\pi$
$97$	−5.21500	−	3.01088i	−0.529503	−	0.305709i	−0.740814	+	0.671710i	$0.765560\pi$
$98$	3.35543	+	6.14338i	0.338949	+	0.620575i
$99$		0			0
$100$	−1.11609	−	1.93312i	−0.111609	−	0.193312i
$101$	5.73328	−	9.93033i	0.570483	−	0.988105i	−0.426034	−	0.904707i	$-0.640090\pi$
$101$	5.73328	−	9.93033i	0.570483	−	0.988105i	0.996516	−	0.0833976i	$-0.0265771\pi$
$102$		0			0
$103$	13.9216	+	8.03762i	1.37173	+	0.791970i	0.991146	−	0.132776i	$-0.0423889\pi$
$103$	13.9216	+	8.03762i	1.37173	+	0.791970i	0.380586	+	0.924745i	$0.375722\pi$
$104$	−2.35228	+	2.73254i	−0.230660	+	0.267947i
$105$		0			0
$106$	0.576320	+	0.998216i	0.0559772	+	0.0969553i
$107$		−	4.77327i		−	0.461449i	−0.973019	−	0.230725i	$-0.925890\pi$
$107$		−	4.77327i		−	0.461449i	0.973019	−	0.230725i	$-0.0741097\pi$
$108$		0			0
$109$	−0.0971207	−	0.168218i	−0.00930248	−	0.0161124i	0.861337	−	0.508035i	$-0.169628\pi$
$109$	−0.0971207	−	0.168218i	−0.00930248	−	0.0161124i	−0.870639	+	0.491922i	$0.836294\pi$
$110$	−0.406556	−	0.704175i	−0.0387636	−	0.0671405i
$111$		0			0
$112$	−0.654454	−	2.56353i	−0.0618401	−	0.242231i
$113$	4.41465	+	2.54880i	0.415296	+	0.239771i	0.693063	−	0.720877i	$-0.256261\pi$
$113$	4.41465	+	2.54880i	0.415296	+	0.239771i	−0.277767	+	0.960649i	$0.589594\pi$
$114$		0			0
$115$	−10.8292	−	6.25227i	−1.00983	−	0.583027i
$116$	−1.89125	+	1.09191i	−0.175598	+	0.101381i
$117$		0			0
$118$		−	0.693648i		−	0.0638555i
$119$	−2.17794	−	8.53112i	−0.199652	−	0.782047i
$120$		0			0
$121$	−5.38056	−	9.31941i	−0.489142	−	0.847219i
$122$	3.36326	+	5.82533i	0.304495	+	0.527401i
$123$		0			0
$124$	3.79697	−	2.19218i	0.340978	−	0.196864i
$125$	12.0320			1.07618
$126$		0			0
$127$	2.55827	+	4.43106i	0.227010	+	0.393193i	0.956921	−	0.290350i	$-0.0937717\pi$
$127$	2.55827	+	4.43106i	0.227010	+	0.393193i	−0.729911	+	0.683543i	$0.760438\pi$
$128$			1.00000i			0.0883883i
$129$		0			0
$130$	−1.98028	−	5.66217i	−0.173682	−	0.496605i
$131$	−3.82765	+	6.62968i	−0.334423	+	0.579238i	−0.983374	−	0.181593i	$-0.941875\pi$
$131$	−3.82765	+	6.62968i	−0.334423	+	0.579238i	0.648951	+	0.760830i	$0.275208\pi$
$132$		0			0
$133$	−11.0030	−	11.2668i	−0.954079	−	0.976952i
$134$	4.46346	+	2.57698i	0.385584	+	0.222617i
$135$		0			0
$136$			3.32788i			0.285363i
$137$		−	8.46617i		−	0.723314i	−0.932311	−	0.361657i	$-0.882211\pi$
$137$		−	8.46617i		−	0.723314i	0.932311	−	0.361657i	$-0.117789\pi$
$138$		0			0
$139$	2.11086	+	1.21871i	0.179041	+	0.103369i	0.586842	−	0.809701i	$-0.300371\pi$
$139$	2.11086	+	1.21871i	0.179041	+	0.103369i	−0.407801	+	0.913071i	$0.633704\pi$
$140$	4.23790	+	1.18952i	0.358168	+	0.100532i
$141$		0			0
$142$	−2.32184	+	4.02154i	−0.194844	+	0.337480i
$143$	0.581754	+	1.66339i	0.0486487	+	0.139100i
$144$		0			0
$145$		−	3.63318i		−	0.301719i
$146$	3.46072	+	5.99414i	0.286411	+	0.496078i
$147$		0			0
$148$	7.02383			0.577355
$149$	−5.38866	+	3.11115i	−0.441456	+	0.254875i	−0.704215	−	0.709987i	$-0.748701\pi$
$149$	−5.38866	+	3.11115i	−0.441456	+	0.254875i	0.262759	+	0.964862i	$0.415368\pi$
$150$		0			0
$151$	−10.3105	−	17.8583i	−0.839058	−	1.45329i	−0.890683	−	0.454625i	$-0.849773\pi$
$151$	−10.3105	−	17.8583i	−0.839058	−	1.45329i	0.0516245	−	0.998667i	$-0.483560\pi$
$152$	2.97613	+	5.15480i	0.241396	+	0.418110i
$153$		0			0
$154$	−1.24498	−	0.349448i	−0.100323	−	0.0281593i
$155$			7.29416i			0.585881i
$156$		0			0
$157$	−7.37520	+	4.25807i	−0.588605	+	0.339831i	−0.764546	−	0.644569i	$-0.777037\pi$
$157$	−7.37520	+	4.25807i	−0.588605	+	0.339831i	0.175941	+	0.984401i	$0.443703\pi$
$158$	−3.85901	−	2.22800i	−0.307006	−	0.177250i
$159$		0			0
$160$	−1.44079	−	0.831839i	−0.113904	−	0.0657626i
$161$	−19.2680	+	4.91900i	−1.51853	+	0.387672i
$162$		0			0
$163$	10.2983	+	17.8372i	0.806628	+	1.39712i	0.915186	+	0.403031i	$0.132043\pi$
$163$	10.2983	+	17.8372i	0.806628	+	1.39712i	−0.108558	+	0.994090i	$0.534623\pi$
$164$	2.04384	+	3.54003i	0.159597	+	0.276430i
$165$		0			0
$166$		−	1.84311i		−	0.143053i
$167$	−10.2340	−	17.7259i	−0.791934	−	1.37167i	−0.924768	−	0.380532i	$-0.875741\pi$
$167$	−10.2340	−	17.7259i	−0.791934	−	1.37167i	0.132834	−	0.991138i	$-0.457592\pi$
$168$		0			0
$169$	1.93353	+	12.8554i	0.148733	+	0.988877i
$170$	−4.79477	−	2.76826i	−0.367742	−	0.212316i
$171$		0			0
$172$	−1.67491	+	2.90102i	−0.127710	+	0.221201i
$173$	−8.21015	−	14.2204i	−0.624206	−	1.08116i	−0.988694	−	0.149949i	$-0.952089\pi$
$173$	−8.21015	−	14.2204i	−0.624206	−	1.08116i	0.364488	−	0.931208i	$-0.381244\pi$
$174$		0			0
$175$	4.22519	−	4.12626i	0.319394	−	0.311916i
$176$	0.423264	+	0.244372i	0.0319047	+	0.0184202i
$177$		0			0
$178$			5.05718i			0.379052i
$179$	14.8243	+	8.55881i	1.10802	+	0.639716i	0.938316	−	0.345779i	$-0.112385\pi$
$179$	14.8243	+	8.55881i	1.10802	+	0.639716i	0.169704	+	0.985495i	$0.445719\pi$
$180$		0			0
$181$			11.0003i			0.817649i	0.912613	+	0.408824i	$0.134061\pi$
$181$			11.0003i			0.817649i	−0.912613	+	0.408824i	$0.865939\pi$
$182$	−8.54441	−	4.24183i	−0.633353	−	0.314425i
$183$		0			0
$184$	7.51620			0.554101
$185$	−5.84270	+	10.1198i	−0.429564	+	0.744026i
$186$		0			0
$187$	1.40857	+	0.813240i	0.103005	+	0.0594700i
$188$	−4.89698	+	8.48183i	−0.357149	+	0.618601i
$189$		0			0
$190$	−9.90263			−0.718412
$191$	14.2205	−	8.21023i	1.02896	−	0.594072i	0.112275	−	0.993677i	$-0.464186\pi$
$191$	14.2205	−	8.21023i	1.02896	−	0.594072i	0.916687	+	0.399606i	$0.130853\pi$
$192$		0			0
$193$	9.64252	−	16.7013i	0.694084	−	1.20219i	−0.276405	−	0.961041i	$-0.589143\pi$
$193$	9.64252	−	16.7013i	0.694084	−	1.20219i	0.970489	−	0.241147i	$-0.0775235\pi$
$194$	−3.01088	+	5.21500i	−0.216169	+	0.374415i
$195$		0			0
$196$	6.14338	−	3.35543i	0.438813	−	0.239673i
$197$	−2.93579	+	1.69498i	−0.209167	+	0.120762i	−0.600924	−	0.799306i	$-0.705201\pi$
$197$	−2.93579	+	1.69498i	−0.209167	+	0.120762i	0.391757	+	0.920069i	$0.371867\pi$
$198$		0			0
$199$			20.9952i			1.48831i	0.668006	+	0.744156i	$0.267148\pi$
$199$			20.9952i			1.48831i	−0.668006	+	0.744156i	$0.732852\pi$
$200$	−1.93312	+	1.11609i	−0.136692	+	0.0789193i
$201$		0			0
$202$	−9.93033	−	5.73328i	−0.698696	−	0.403392i
$203$	−4.03688	−	4.13366i	−0.283334	−	0.290126i
$204$		0			0
$205$	−6.80057			−0.474972
$206$	8.03762	−	13.9216i	0.560007	−	0.969961i
$207$		0			0
$208$	2.73254	+	2.35228i	0.189467	+	0.163102i
$209$	2.90912			0.201228
$210$		0			0
$211$	9.99131	+	17.3055i	0.687830	+	1.19136i	0.972538	+	0.232742i	$0.0747699\pi$
$211$	9.99131	+	17.3055i	0.687830	+	1.19136i	−0.284708	+	0.958614i	$0.591897\pi$
$212$	0.998216	−	0.576320i	0.0685577	−	0.0395818i
$213$		0			0
$214$	−4.77327			−0.326294
$215$	−2.78651	−	4.82637i	−0.190038	−	0.329156i
$216$		0			0
$217$	8.10466	+	8.29896i	0.550180	+	0.563370i
$218$	−0.168218	+	0.0971207i	−0.0113932	+	0.00657785i
$219$		0			0
$220$	−0.704175	+	0.406556i	−0.0474755	+	0.0274100i
$221$	9.09356	+	7.82812i	0.611699	+	0.526576i
$222$		0			0
$223$	5.30183	−	3.06101i	0.355037	−	0.204981i	−0.311865	−	0.950127i	$-0.600954\pi$
$223$	5.30183	−	3.06101i	0.355037	−	0.204981i	0.666902	+	0.745146i	$0.267620\pi$
$224$	−2.56353	+	0.654454i	−0.171283	+	0.0437275i
$225$		0			0
$226$	2.54880	−	4.41465i	0.169544	−	0.293658i
$227$	−10.1922			−0.676482			−0.338241	−	0.941059i	$-0.609832\pi$
$227$	−10.1922			−0.676482			−0.338241	+	0.941059i	$0.609832\pi$
$228$		0			0
$229$	14.1465	+	8.16747i	0.934826	+	0.539722i	0.888335	−	0.459197i	$-0.151863\pi$
$229$	14.1465	+	8.16747i	0.934826	+	0.539722i	0.0464912	+	0.998919i	$0.485196\pi$
$230$	−6.25227	+	10.8292i	−0.412262	+	0.714059i
$231$		0			0
$232$	1.09191	+	1.89125i	0.0716875	+	0.124166i
$233$	23.7859	+	13.7328i	1.55826	+	0.899664i	0.997423	+	0.0717401i	$0.0228552\pi$
$233$	23.7859	+	13.7328i	1.55826	+	0.899664i	0.560840	+	0.827924i	$0.310478\pi$
$234$		0			0
$235$	−8.14700	−	14.1110i	−0.531452	−	0.920502i
$236$	−0.693648			−0.0451526
$237$		0			0
$238$	−8.53112	+	2.17794i	−0.552990	+	0.141175i
$239$			25.9617i			1.67932i	0.543109	+	0.839662i	$0.317247\pi$
$239$			25.9617i			1.67932i	−0.543109	+	0.839662i	$0.682753\pi$
$240$		0			0
$241$		−	5.70637i		−	0.367580i	−0.982966	−	0.183790i	$-0.941163\pi$
$241$		−	5.70637i		−	0.367580i	0.982966	−	0.183790i	$-0.0588366\pi$
$242$	−9.31941	+	5.38056i	−0.599074	+	0.345876i
$243$		0			0
$244$	5.82533	−	3.36326i	0.372929	−	0.215311i
$245$	−0.275849	+	11.6425i	−0.0176233	+	0.743811i
$246$		0			0
$247$	21.0864	+	3.99318i	1.34169	+	0.254080i
$248$	−2.19218	−	3.79697i	−0.139204	−	0.241108i
$249$		0			0
$250$		−	12.0320i		−	0.760971i
$251$	6.73431	−	11.6642i	0.425066	−	0.736236i	−0.571361	−	0.820699i	$-0.693584\pi$
$251$	6.73431	−	11.6642i	0.425066	−	0.736236i	0.996427	+	0.0844633i	$0.0269176\pi$
$252$		0			0
$253$	1.83675	−	3.18134i	0.115475	−	0.200009i
$254$	4.43106	−	2.55827i	0.278029	−	0.160520i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−19.4021			−1.21027			−0.605133	−	0.796124i	$-0.706880\pi$
$257$	−19.4021			−1.21027			−0.605133	+	0.796124i	$0.706880\pi$
$258$		0			0
$259$	4.59677	+	18.0058i	0.285630	+	1.11883i
$260$	−5.66217	+	1.98028i	−0.351153	+	0.122812i
$261$		0			0
$262$	6.62968	+	3.82765i	0.409583	+	0.236473i
$263$	22.0862	+	12.7515i	1.36190	+	0.786291i	0.989876	−	0.141934i	$-0.0453320\pi$
$263$	22.0862	+	12.7515i	1.36190	+	0.786291i	0.372020	+	0.928225i	$0.378665\pi$
$264$		0			0
$265$			1.91762i			0.117799i
$266$	−11.2668	+	11.0030i	−0.690809	+	0.674635i
$267$		0			0
$268$	2.57698	−	4.46346i	0.157414	−	0.272649i
$269$	−19.2863			−1.17590			−0.587952	−	0.808896i	$-0.700066\pi$
$269$	−19.2863			−1.17590			−0.587952	+	0.808896i	$0.700066\pi$
$270$		0			0
$271$		−	22.6343i		−	1.37494i	−0.726213	−	0.687469i	$-0.758722\pi$
$271$		−	22.6343i		−	1.37494i	0.726213	−	0.687469i	$-0.241278\pi$
$272$	3.32788			0.201782
$273$		0			0
$274$	−8.46617			−0.511460
$275$			1.09096i			0.0657874i
$276$		0			0
$277$	−13.9103			−0.835790			−0.417895	−	0.908495i	$-0.637232\pi$
$277$	−13.9103			−0.835790			−0.417895	+	0.908495i	$0.637232\pi$
$278$	1.21871	−	2.11086i	0.0730932	−	0.126601i
$279$		0			0
$280$	1.18952	−	4.23790i	0.0710872	−	0.253263i
$281$			4.84774i			0.289192i	0.989491	+	0.144596i	$0.0461882\pi$
$281$			4.84774i			0.289192i	−0.989491	+	0.144596i	$0.953812\pi$
$282$		0			0
$283$	4.29064	+	2.47720i	0.255052	+	0.147254i	0.622075	−	0.782957i	$-0.286290\pi$
$283$	4.29064	+	2.47720i	0.255052	+	0.147254i	−0.367023	+	0.930212i	$0.619623\pi$
$284$	4.02154	+	2.32184i	0.238634	+	0.137776i
$285$		0			0
$286$	1.66339	−	0.581754i	0.0983584	−	0.0343998i
$287$	−7.73737	+	7.55622i	−0.456723	+	0.446029i
$288$		0			0
$289$	−5.92522			−0.348542
$290$	−3.63318			−0.213348
$291$		0			0
$292$	5.99414	−	3.46072i	0.350780	−	0.202523i
$293$	−7.44051	+	12.8873i	−0.434679	+	0.752886i	−0.997269	−	0.0738496i	$-0.976472\pi$
$293$	−7.44051	+	12.8873i	−0.434679	+	0.752886i	0.562590	+	0.826736i	$0.309805\pi$
$294$		0			0
$295$	0.577003	−	0.999399i	0.0335944	−	0.0581873i
$296$		−	7.02383i		−	0.408252i
$297$		0			0
$298$	3.11115	+	5.38866i	0.180224	+	0.312157i
$299$	17.6802	−	20.5383i	1.02247	−	1.18776i
$300$		0			0
$301$	−8.53301	−	2.39509i	−0.491835	−	0.138051i
$302$	−17.8583	+	10.3105i	−1.02763	+	0.593304i
$303$		0			0
$304$	5.15480	−	2.97613i	0.295648	−	0.170693i
$305$			11.1908i			0.640781i
$306$		0			0
$307$		−	16.4307i		−	0.937748i	−0.883265	−	0.468874i	$-0.844660\pi$
$307$		−	16.4307i		−	0.937748i	0.883265	−	0.468874i	$-0.155340\pi$
$308$	−0.349448	+	1.24498i	−0.0199116	+	0.0709394i
$309$		0			0
$310$	7.29416			0.414281
$311$	1.16501	+	2.01786i	0.0660619	+	0.114423i	0.897165	−	0.441697i	$-0.145623\pi$
$311$	1.16501	+	2.01786i	0.0660619	+	0.114423i	−0.831103	+	0.556119i	$0.812290\pi$
$312$		0			0
$313$	26.3888	+	15.2356i	1.49158	+	0.861167i	0.999954	−	0.00963660i	$-0.00306747\pi$
$313$	26.3888	+	15.2356i	1.49158	+	0.861167i	0.491631	+	0.870803i	$0.336401\pi$
$314$	4.25807	+	7.37520i	0.240297	+	0.416207i
$315$		0			0
$316$	−2.22800	+	3.85901i	−0.125335	+	0.217086i
$317$	21.7969	+	12.5845i	1.22424	+	0.706814i	0.965819	−	0.259219i	$-0.0834652\pi$
$317$	21.7969	+	12.5845i	1.22424	+	0.706814i	0.258419	+	0.966033i	$0.416799\pi$
$318$		0			0
$319$	1.06733			0.0597590
$320$	−0.831839	+	1.44079i	−0.0465012	+	0.0805425i
$321$		0			0
$322$	4.91900	+	19.2680i	0.274125	+	1.07376i
$323$	17.1546	−	9.90419i	0.954505	−	0.551084i
$324$		0			0
$325$	−1.49750	+	7.90768i	−0.0830662	+	0.438639i
$326$	17.8372	−	10.2983i	0.987914	−	0.570372i
$327$		0			0
$328$	3.54003	−	2.04384i	0.195465	−	0.112852i
$329$	−24.9483	−	7.00261i	−1.37544	−	0.386066i
$330$		0			0
$331$	−1.80777	−	3.13114i	−0.0993638	−	0.172103i	0.812058	−	0.583577i	$-0.198347\pi$
$331$	−1.80777	−	3.13114i	−0.0993638	−	0.172103i	−0.911422	+	0.411474i	$0.865014\pi$
$332$	−1.84311			−0.101154
$333$		0			0
$334$	−17.7259	+	10.2340i	−0.969917	+	0.559982i
$335$	4.28726	+	7.42575i	0.234238	+	0.405712i
$336$		0			0
$337$	18.6613			1.01654			0.508272	−	0.861197i	$-0.330284\pi$
$337$	18.6613			1.01654			0.508272	+	0.861197i	$0.330284\pi$
$338$	12.8554	−	1.93353i	0.699242	−	0.105170i
$339$		0			0
$340$	−2.76826	+	4.79477i	−0.150130	+	0.260033i
$341$	−2.14283			−0.116041
$342$		0			0
$343$	12.6223	+	13.5528i	0.681540	+	0.731781i
$344$	2.90102	+	1.67491i	0.156413	+	0.0903049i
$345$		0			0
$346$	−14.2204	+	8.21015i	−0.764493	+	0.441380i
$347$			10.7211i			0.575539i	0.957700	+	0.287770i	$0.0929137\pi$
$347$			10.7211i			0.575539i	−0.957700	+	0.287770i	$0.907086\pi$
$348$		0			0
$349$	27.4296	−	15.8365i	1.46827	−	0.847708i	0.468906	−	0.883248i	$-0.344648\pi$
$349$	27.4296	−	15.8365i	1.46827	−	0.847708i	0.999368	+	0.0355401i	$0.0113151\pi$
$350$	−4.12626	−	4.22519i	−0.220558	−	0.225846i
$351$		0			0
$352$	0.244372	−	0.423264i	0.0130251	−	0.0225601i
$353$	3.84712	−	6.66340i	0.204761	−	0.354657i	−0.745295	−	0.666735i	$-0.767691\pi$
$353$	3.84712	−	6.66340i	0.204761	−	0.354657i	0.950057	+	0.312077i	$0.101025\pi$
$354$		0			0
$355$	−6.69054	+	3.86279i	−0.355097	+	0.205015i
$356$	5.05718			0.268030
$357$		0			0
$358$	8.55881	−	14.8243i	0.452347	−	0.783489i
$359$	−24.7514	−	14.2902i	−1.30633	−	0.754209i	−0.324848	−	0.945766i	$-0.605313\pi$
$359$	−24.7514	−	14.2902i	−1.30633	−	0.754209i	−0.981482	+	0.191557i	$0.938646\pi$
$360$		0			0
$361$	8.21465	−	14.2282i	0.432350	−	0.748852i
$362$	11.0003			0.578165
$363$		0			0
$364$	−4.24183	+	8.54441i	−0.222332	+	0.447849i
$365$			11.5150i			0.602724i
$366$		0			0
$367$	−2.68074	−	1.54773i	−0.139934	−	0.0807908i	0.428399	−	0.903590i	$-0.359078\pi$
$367$	−2.68074	−	1.54773i	−0.139934	−	0.0807908i	−0.568332	+	0.822799i	$0.692411\pi$
$368$		−	7.51620i		−	0.391809i
$369$		0			0
$370$	10.1198	+	5.84270i	0.526106	+	0.303747i
$371$	2.13070	+	2.18178i	0.110620	+	0.113272i
$372$		0			0
$373$	−2.85791	−	4.95005i	−0.147977	−	0.256304i	0.782503	−	0.622647i	$-0.213943\pi$
$373$	−2.85791	−	4.95005i	−0.147977	−	0.256304i	−0.930480	+	0.366344i	$0.880609\pi$
$374$	0.813240	−	1.40857i	0.0420516	−	0.0728355i
$375$		0			0
$376$	8.48183	+	4.89698i	0.437417	+	0.252543i
$377$	7.73639	+	1.46506i	0.398444	+	0.0754543i
$378$		0			0
$379$	17.5041	+	30.3180i	0.899126	+	1.55733i	0.828614	+	0.559821i	$0.189130\pi$
$379$	17.5041	+	30.3180i	0.899126	+	1.55733i	0.0705125	+	0.997511i	$0.477537\pi$
$380$			9.90263i			0.507994i
$381$		0			0
$382$	−8.21023	−	14.2205i	−0.420072	−	0.727586i
$383$	2.58410	+	4.47579i	0.132041	+	0.228702i	0.924463	−	0.381271i	$-0.124514\pi$
$383$	2.58410	+	4.47579i	0.132041	+	0.228702i	−0.792422	+	0.609973i	$0.791180\pi$
$384$		0			0
$385$	−1.50307	−	1.53910i	−0.0766035	−	0.0784400i
$386$	−16.7013	−	9.64252i	−0.850075	−	0.490791i
$387$		0			0
$388$	5.21500	+	3.01088i	0.264752	+	0.152854i
$389$	25.6356	−	14.8007i	1.29978	−	0.750428i	0.319413	−	0.947616i	$-0.396514\pi$
$389$	25.6356	−	14.8007i	1.29978	−	0.750428i	0.980366	+	0.197188i	$0.0631809\pi$
$390$		0			0
$391$		−	25.0130i		−	1.26496i
$392$	−3.35543	−	6.14338i	−0.169475	−	0.310288i
$393$		0			0
$394$	1.69498	+	2.93579i	0.0853919	+	0.147903i
$395$	−3.70667	−	6.42015i	−0.186503	−	0.323033i
$396$		0			0
$397$	−3.90460	+	2.25432i	−0.195966	+	0.113141i	−0.594773	−	0.803894i	$-0.702758\pi$
$397$	−3.90460	+	2.25432i	−0.195966	+	0.113141i	0.398806	+	0.917035i	$0.369425\pi$
$398$	20.9952			1.05240
$399$		0			0
$400$	1.11609	+	1.93312i	0.0558044	+	0.0966561i
$401$			35.9824i			1.79688i	0.439100	+	0.898438i	$0.355298\pi$
$401$			35.9824i			1.79688i	−0.439100	+	0.898438i	$0.644702\pi$
$402$		0			0
$403$	−15.5320	−	2.94133i	−0.773704	−	0.146518i
$404$	−5.73328	+	9.93033i	−0.285241	+	0.494052i
$405$		0			0
$406$	−4.13366	+	4.03688i	−0.205150	+	0.200347i
$407$	−2.97294	−	1.71643i	−0.147363	−	0.0850801i
$408$		0			0
$409$			9.44105i			0.466830i	0.972377	+	0.233415i	$0.0749900\pi$
$409$			9.44105i			0.466830i	−0.972377	+	0.233415i	$0.925010\pi$
$410$			6.80057i			0.335856i
$411$		0			0
$412$	−13.9216	−	8.03762i	−0.685866	−	0.395985i
$413$	−0.453961	−	1.77819i	−0.0223379	−	0.0874989i
$414$		0			0
$415$	1.53317	−	2.65553i	0.0752604	−	0.130355i
$416$	2.35228	−	2.73254i	0.115330	−	0.133974i
$417$		0			0
$418$		−	2.90912i		−	0.142290i
$419$	−12.7942	−	22.1603i	−0.625039	−	1.08260i	−0.988533	−	0.151003i	$-0.951750\pi$
$419$	−12.7942	−	22.1603i	−0.625039	−	1.08260i	0.363494	−	0.931597i	$-0.381584\pi$
$420$		0			0
$421$	5.69249			0.277435			0.138718	−	0.990332i	$-0.455702\pi$
$421$	5.69249			0.277435			0.138718	+	0.990332i	$0.455702\pi$
$422$	17.3055	−	9.99131i	0.842416	−	0.486369i
$423$		0			0
$424$	−0.576320	−	0.998216i	−0.0279886	−	0.0484776i
$425$	3.71421	+	6.43319i	0.180165	+	0.312056i
$426$		0			0
$427$	12.4342	+	12.7323i	0.601735	+	0.616160i
$428$			4.77327i			0.230725i
$429$		0			0
$430$	−4.82637	+	2.78651i	−0.232748	+	0.134377i
$431$	−27.0630	−	15.6248i	−1.30358	−	0.752621i	−0.322563	−	0.946548i	$-0.604544\pi$
$431$	−27.0630	−	15.6248i	−1.30358	−	0.752621i	−0.981016	+	0.193927i	$0.937878\pi$
$432$		0			0
$433$	−9.67442	−	5.58553i	−0.464923	−	0.268423i	0.249189	−	0.968455i	$-0.419836\pi$
$433$	−9.67442	−	5.58553i	−0.464923	−	0.268423i	−0.714112	+	0.700031i	$0.753169\pi$
$434$	8.29896	−	8.10466i	0.398363	−	0.389036i
$435$		0			0
$436$	0.0971207	+	0.168218i	0.00465124	+	0.00805618i
$437$	−22.3692	−	38.7445i	−1.07006	−	1.85340i
$438$		0			0
$439$		−	13.4451i		−	0.641697i	−0.947130	−	0.320849i	$-0.896032\pi$
$439$		−	13.4451i		−	0.641697i	0.947130	−	0.320849i	$-0.103968\pi$
$440$	0.406556	+	0.704175i	0.0193818	+	0.0335702i
$441$		0			0
$442$	7.82812	−	9.09356i	0.372345	−	0.432536i
$443$	13.3641	+	7.71577i	0.634948	+	0.366587i	0.782666	−	0.622442i	$-0.213859\pi$
$443$	13.3641	+	7.71577i	0.634948	+	0.366587i	−0.147718	+	0.989030i	$0.547193\pi$
$444$		0			0
$445$	−4.20676	+	7.28632i	−0.199419	+	0.345405i
$446$	−3.06101	−	5.30183i	−0.144943	−	0.251049i
$447$		0			0
$448$	0.654454	+	2.56353i	0.0309200	+	0.121115i
$449$	−6.83240	−	3.94469i	−0.322441	−	0.186161i	0.330039	−	0.943967i	$-0.392938\pi$
$449$	−6.83240	−	3.94469i	−0.322441	−	0.186161i	−0.652480	+	0.757806i	$0.726271\pi$
$450$		0			0
$451$		−	1.99782i		−	0.0940738i
$452$	−4.41465	−	2.54880i	−0.207648	−	0.119886i
$453$		0			0
$454$			10.1922i			0.478345i
$455$	−8.78215	−	13.2191i	−0.411714	−	0.619723i
$456$		0			0
$457$	35.7129			1.67058			0.835289	−	0.549811i	$-0.185300\pi$
$457$	35.7129			1.67058			0.835289	+	0.549811i	$0.185300\pi$
$458$	8.16747	−	14.1465i	0.381641	−	0.661022i
$459$		0			0
$460$	10.8292	+	6.25227i	0.504916	+	0.291513i
$461$	−13.7643	+	23.8404i	−0.641066	+	1.11036i	0.344130	+	0.938922i	$0.388174\pi$
$461$	−13.7643	+	23.8404i	−0.641066	+	1.11036i	−0.985195	+	0.171436i	$0.945159\pi$
$462$		0			0
$463$	13.9941			0.650362			0.325181	−	0.945652i	$-0.394575\pi$
$463$	13.9941			0.650362			0.325181	+	0.945652i	$0.394575\pi$
$464$	1.89125	−	1.09191i	0.0877989	−	0.0506907i
$465$		0			0
$466$	13.7328	−	23.7859i	0.636159	−	1.10186i
$467$	−17.8982	+	31.0006i	−0.828230	+	1.43454i	0.0711959	+	0.997462i	$0.477318\pi$
$467$	−17.8982	+	31.0006i	−0.828230	+	1.43454i	−0.899426	+	0.437074i	$0.856015\pi$
$468$		0			0
$469$	13.1287	+	3.68504i	0.606228	+	0.170159i
$470$	−14.1110	+	8.14700i	−0.650893	+	0.375793i
$471$		0			0
$472$			0.693648i			0.0319277i
$473$	1.41786	−	0.818600i	0.0651931	−	0.0376393i
$474$		0			0
$475$	11.5064	+	6.64324i	0.527951	+	0.304813i
$476$	2.17794	+	8.53112i	0.0998259	+	0.391023i
$477$		0			0
$478$	25.9617			1.18746
$479$	4.87710	−	8.44739i	0.222840	−	0.385971i	−0.732829	−	0.680413i	$-0.761800\pi$
$479$	4.87710	−	8.44739i	0.222840	−	0.385971i	0.955669	+	0.294442i	$0.0951338\pi$
$480$		0			0
$481$	−19.1929	−	16.5220i	−0.875120	−	0.753340i
$482$	−5.70637			−0.259918
$483$		0			0
$484$	5.38056	+	9.31941i	0.244571	+	0.423610i
$485$	−8.67608	+	5.00914i	−0.393961	+	0.227453i
$486$		0			0
$487$	17.7515			0.804396			0.402198	−	0.915553i	$-0.368246\pi$
$487$	17.7515			0.804396			0.402198	+	0.915553i	$0.368246\pi$
$488$	−3.36326	−	5.82533i	−0.152248	−	0.263700i
$489$		0			0
$490$	11.6425	+	0.275849i	0.525954	+	0.0124616i
$491$	25.4777	−	14.7096i	1.14979	−	0.663834i	0.200957	−	0.979600i	$-0.435595\pi$
$491$	25.4777	−	14.7096i	1.14979	−	0.663834i	0.948837	+	0.315766i	$0.102262\pi$
$492$		0			0
$493$	6.29384	−	3.63375i	0.283460	−	0.163656i
$494$	3.99318	−	21.0864i	0.179662	−	0.948721i
$495$		0			0
$496$	−3.79697	+	2.19218i	−0.170489	+	0.0984318i
$497$	−3.32019	+	11.8289i	−0.148931	+	0.530597i
$498$		0			0
$499$	−5.32795	+	9.22827i	−0.238512	+	0.413114i	−0.960287	−	0.279013i	$-0.909993\pi$
$499$	−5.32795	+	9.22827i	−0.238512	+	0.413114i	0.721776	+	0.692127i	$0.243326\pi$
$500$	−12.0320			−0.538088
$501$		0			0
$502$	−11.6642	−	6.73431i	−0.520597	−	0.300567i
$503$	−2.47048	+	4.27900i	−0.110153	+	0.190791i	−0.915832	−	0.401562i	$-0.868468\pi$
$503$	−2.47048	+	4.27900i	−0.110153	+	0.190791i	0.805679	+	0.592353i	$0.201801\pi$
$504$		0			0
$505$	−9.53833	−	16.5209i	−0.424450	−	0.735169i
$506$	−3.18134	−	1.83675i	−0.141428	−	0.0816533i
$507$		0			0
$508$	−2.55827	−	4.43106i	−0.113505	−	0.196596i
$509$	−7.08191			−0.313900			−0.156950	−	0.987607i	$-0.550166\pi$
$509$	−7.08191			−0.313900			−0.156950	+	0.987607i	$0.550166\pi$
$510$		0			0
$511$	12.7945	+	13.1013i	0.565997	+	0.579566i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$			19.4021i			0.855788i
$515$	23.1610	−	13.3720i	1.02060	−	0.589241i
$516$		0			0
$517$	4.14544	−	2.39337i	0.182316	−	0.105260i
$518$	18.0058	−	4.59677i	0.791130	−	0.201971i
$519$		0			0
$520$	1.98028	+	5.66217i	0.0868412	+	0.248303i
$521$	−3.89162	−	6.74048i	−0.170495	−	0.295306i	0.768098	−	0.640332i	$-0.221203\pi$
$521$	−3.89162	−	6.74048i	−0.170495	−	0.295306i	−0.938593	+	0.345027i	$0.887870\pi$
$522$		0			0
$523$			26.7014i			1.16757i	0.811908	+	0.583786i	$0.198429\pi$
$523$			26.7014i			1.16757i	−0.811908	+	0.583786i	$0.801571\pi$
$524$	3.82765	−	6.62968i	0.167212	−	0.289619i
$525$		0			0
$526$	12.7515	−	22.0862i	0.555992	−	0.963006i
$527$	−12.6359	+	7.29531i	−0.550426	+	0.317789i
$528$		0			0
$529$	−33.4932			−1.45623
$530$	1.91762			0.0832962
$531$		0			0
$532$	11.0030	+	11.2668i	0.477039	+	0.488476i
$533$	2.74229	−	14.4809i	0.118782	−	0.627239i
$534$		0			0
$535$	−6.87727	−	3.97059i	−0.297330	−	0.171664i
$536$	−4.46346	−	2.57698i	−0.192792	−	0.111309i
$537$		0			0
$538$			19.2863i			0.831490i
$539$	−3.42024	−	0.0810370i	−0.147320	−	0.00349051i
$540$		0			0
$541$	−3.98266	+	6.89816i	−0.171228	+	0.296575i	−0.938849	−	0.344328i	$-0.888107\pi$
$541$	−3.98266	+	6.89816i	−0.171228	+	0.296575i	0.767622	+	0.640903i	$0.221440\pi$
$542$	−22.6343			−0.972228
$543$		0			0
$544$		−	3.32788i		−	0.142682i
$545$	−0.323155			−0.0138424
$546$		0			0
$547$	25.5726			1.09340			0.546702	−	0.837327i	$-0.315883\pi$
$547$	25.5726			1.09340			0.546702	+	0.837327i	$0.315883\pi$
$548$			8.46617i			0.361657i
$549$		0			0
$550$	1.09096			0.0465188
$551$	6.49933	−	11.2572i	0.276881	−	0.479572i
$552$		0			0
$553$	−11.3508	−	3.18600i	−0.482686	−	0.135483i
$554$			13.9103i			0.590993i
$555$		0			0
$556$	−2.11086	−	1.21871i	−0.0895205	−	0.0516847i
$557$	20.0948	+	11.6017i	0.851444	+	0.491581i	0.861138	−	0.508372i	$-0.169752\pi$
$557$	20.0948	+	11.6017i	0.851444	+	0.491581i	−0.00969404	+	0.999953i	$0.503086\pi$
$558$		0			0
$559$	11.4008	−	3.98730i	0.482201	−	0.168645i
$560$	−4.23790	−	1.18952i	−0.179084	−	0.0502662i
$561$		0			0
$562$	4.84774			0.204489
$563$	17.9126			0.754927			0.377463	−	0.926025i	$-0.376796\pi$
$563$	17.9126			0.754927			0.377463	+	0.926025i	$0.376796\pi$
$564$		0			0
$565$	7.34456	−	4.24038i	0.308988	−	0.178394i
$566$	2.47720	−	4.29064i	0.104125	−	0.180349i
$567$		0			0
$568$	2.32184	−	4.02154i	0.0974221	−	0.168740i
$569$			39.9166i			1.67339i	0.547669	+	0.836695i	$0.315515\pi$
$569$			39.9166i			1.67339i	−0.547669	+	0.836695i	$0.684485\pi$
$570$		0			0
$571$	−12.3269	−	21.3508i	−0.515864	−	0.893503i	−0.999830	−	0.0184165i	$-0.994138\pi$
$571$	−12.3269	−	21.3508i	−0.515864	−	0.893503i	0.483966	−	0.875087i	$-0.339196\pi$
$572$	−0.581754	−	1.66339i	−0.0243244	−	0.0695499i
$573$		0			0
$574$	7.55622	+	7.73737i	0.315390	+	0.322952i
$575$	14.5297	−	8.38874i	0.605931	−	0.349835i
$576$		0			0
$577$	−22.0411	+	12.7254i	−0.917584	+	0.529767i	−0.882863	−	0.469630i	$-0.844387\pi$
$577$	−22.0411	+	12.7254i	−0.917584	+	0.529767i	−0.0347205	+	0.999397i	$0.511054\pi$
$578$			5.92522i			0.246457i
$579$		0			0
$580$			3.63318i			0.150860i
$581$	−1.20623	−	4.72487i	−0.0500429	−	0.196021i
$582$		0			0
$583$	−0.563345			−0.0233314
$584$	−3.46072	−	5.99414i	−0.143205	−	0.248039i
$585$		0			0
$586$	12.8873	+	7.44051i	0.532371	+	0.307364i
$587$	−10.6068	−	18.3714i	−0.437788	−	0.758271i	0.559731	−	0.828675i	$-0.310905\pi$
$587$	−10.6068	−	18.3714i	−0.437788	−	0.758271i	−0.997519	+	0.0704038i	$0.977571\pi$
$588$		0			0
$589$	−13.0484	+	22.6005i	−0.537650	+	0.931238i
$590$	−0.999399	−	0.577003i	−0.0411446	−	0.0237549i
$591$		0			0
$592$	−7.02383			−0.288678
$593$	−18.1719	+	31.4746i	−0.746230	+	1.29251i	0.203387	+	0.979098i	$0.434805\pi$
$593$	−18.1719	+	31.4746i	−0.746230	+	1.29251i	−0.949618	+	0.313411i	$0.898528\pi$
$594$		0			0
$595$	−14.1032	−	3.95857i	−0.578176	−	0.162285i
$596$	5.38866	−	3.11115i	0.220728	−	0.127437i
$597$		0			0
$598$	−20.5383	−	17.6802i	−0.839873	−	0.722998i
$599$	−19.5316	+	11.2766i	−0.798042	+	0.460750i	−0.842786	−	0.538249i	$-0.819086\pi$
$599$	−19.5316	+	11.2766i	−0.798042	+	0.460750i	0.0447443	+	0.998998i	$0.485753\pi$
$600$		0			0
$601$	−32.3904	+	18.7006i	−1.32123	+	0.762814i	−0.983925	−	0.178580i	$-0.942850\pi$
$601$	−32.3904	+	18.7006i	−1.32123	+	0.762814i	−0.337308	+	0.941395i	$0.609516\pi$
$602$	−2.39509	+	8.53301i	−0.0976165	+	0.347780i
$603$		0			0
$604$	10.3105	+	17.8583i	0.419529	+	0.726646i
$605$	−17.9031			−0.727863
$606$		0			0
$607$	−26.5234	+	15.3133i	−1.07655	+	0.621548i	−0.929964	−	0.367650i	$-0.880163\pi$
$607$	−26.5234	+	15.3133i	−1.07655	+	0.621548i	−0.146588	+	0.989198i	$0.546829\pi$
$608$	−2.97613	−	5.15480i	−0.120698	−	0.209055i
$609$		0			0
$610$	11.1908			0.453100
$611$	33.3329	−	11.6578i	1.34850	−	0.471625i
$612$		0			0
$613$	−3.80835	+	6.59625i	−0.153818	+	0.266420i	−0.932628	−	0.360840i	$-0.882490\pi$
$613$	−3.80835	+	6.59625i	−0.153818	+	0.266420i	0.778810	+	0.627260i	$0.215824\pi$
$614$	−16.4307			−0.663088
$615$		0			0
$616$	1.24498	+	0.349448i	0.0501617	+	0.0140796i
$617$	36.3252	+	20.9723i	1.46240	+	0.844315i	0.999122	−	0.0419004i	$-0.0133412\pi$
$617$	36.3252	+	20.9723i	1.46240	+	0.844315i	0.463274	+	0.886215i	$0.346675\pi$
$618$		0			0
$619$	0.00234973	−	0.00135662i	9.44437e−5	−	5.45271e-5i	−0.499953	−	0.866053i	$-0.666649\pi$
$619$	0.00234973	−	0.00135662i	9.44437e−5	−	5.45271e-5i	0.500047	+	0.865998i	$0.333316\pi$
$620$		−	7.29416i		−	0.292941i
$621$		0			0
$622$	2.01786	−	1.16501i	0.0809089	−	0.0467128i
$623$	3.30969	+	12.9642i	0.132600	+	0.519401i
$624$		0			0
$625$	4.42825	−	7.66996i	0.177130	−	0.306798i
$626$	15.2356	−	26.3888i	0.608937	−	1.05471i
$627$		0			0
$628$	7.37520	−	4.25807i	0.294303	−	0.169916i
$629$	−23.3745			−0.932001
$630$		0			0
$631$	0.844792	−	1.46322i	0.0336306	−	0.0582499i	−0.848720	−	0.528842i	$-0.822626\pi$
$631$	0.844792	−	1.46322i	0.0336306	−	0.0582499i	0.882351	+	0.470592i	$0.155960\pi$
$632$	3.85901	+	2.22800i	0.153503	+	0.0886251i
$633$		0			0
$634$	12.5845	−	21.7969i	0.499793	−	0.865667i
$635$	8.51228			0.337800
$636$		0			0
$637$	−24.6799	−	5.28215i	−0.977854	−	0.209286i
$638$		−	1.06733i		−	0.0422560i
$639$		0			0
$640$	1.44079	+	0.831839i	0.0569521	+	0.0328813i
$641$			8.78996i			0.347183i	0.984818	+	0.173591i	$0.0555372\pi$
$641$			8.78996i			0.347183i	−0.984818	+	0.173591i	$0.944463\pi$
$642$		0			0
$643$	−13.7595	−	7.94403i	−0.542620	−	0.313282i	0.203520	−	0.979071i	$-0.434762\pi$
$643$	−13.7595	−	7.94403i	−0.542620	−	0.313282i	−0.746140	+	0.665789i	$0.768095\pi$
$644$	19.2680	−	4.91900i	0.759266	−	0.193836i
$645$		0			0
$646$	−9.90419	−	17.1546i	−0.389675	−	0.674937i
$647$	−8.96037	+	15.5198i	−0.352268	+	0.610147i	−0.986647	−	0.162876i	$-0.947923\pi$
$647$	−8.96037	+	15.5198i	−0.352268	+	0.610147i	0.634378	+	0.773023i	$0.281256\pi$
$648$		0			0
$649$	0.293596	+	0.169508i	0.0115247	+	0.00665377i
$650$	7.90768	+	1.49750i	0.310165	+	0.0587366i
$651$		0			0
$652$	−10.2983	−	17.8372i	−0.403314	−	0.698560i
$653$			15.3344i			0.600083i	0.953926	+	0.300041i	$0.0970005\pi$
$653$			15.3344i			0.600083i	−0.953926	+	0.300041i	$0.902999\pi$
$654$		0			0
$655$	6.36797	+	11.0297i	0.248817	+	0.430964i
$656$	−2.04384	−	3.54003i	−0.0797984	−	0.138215i
$657$		0			0
$658$	−7.00261	+	24.9483i	−0.272990	+	0.972585i
$659$	5.55642	+	3.20800i	0.216448	+	0.124966i	0.604304	−	0.796754i	$-0.293451\pi$
$659$	5.55642	+	3.20800i	0.216448	+	0.124966i	−0.387857	+	0.921720i	$0.626784\pi$
$660$		0			0
$661$	−35.0142	−	20.2155i	−1.36190	−	0.786291i	−0.372020	−	0.928225i	$-0.621335\pi$
$661$	−35.0142	−	20.2155i	−1.36190	−	0.786291i	−0.989876	+	0.141934i	$0.954668\pi$
$662$	−3.13114	+	1.80777i	−0.121695	+	0.0702608i
$663$		0			0
$664$			1.84311i			0.0715265i
$665$	−25.3857	+	6.48081i	−0.984415	+	0.251315i
$666$		0			0
$667$	−8.20702	−	14.2150i	−0.317777	−	0.550406i
$668$	10.2340	+	17.7259i	0.395967	+	0.685835i
$669$		0			0
$670$	7.42575	−	4.28726i	0.286882	−	0.165631i
$671$	−3.28754			−0.126914
$672$		0			0
$673$	−21.9648	−	38.0441i	−0.846680	−	1.46649i	−0.884155	−	0.467195i	$-0.845265\pi$
$673$	−21.9648	−	38.0441i	−0.846680	−	1.46649i	0.0374750	−	0.999298i	$-0.488069\pi$
$674$		−	18.6613i		−	0.718805i
$675$		0			0
$676$	−1.93353	−	12.8554i	−0.0743664	−	0.494439i
$677$	14.2642	−	24.7062i	0.548216	−	0.949538i	−0.450181	−	0.892937i	$-0.648641\pi$
$677$	14.2642	−	24.7062i	0.548216	−	0.949538i	0.998397	−	0.0566005i	$-0.0180261\pi$
$678$		0			0
$679$	−4.30551	+	15.3393i	−0.165230	+	0.588668i
$680$	4.79477	+	2.76826i	0.183871	+	0.106158i
$681$		0			0
$682$			2.14283i			0.0820531i
$683$		−	17.2828i		−	0.661309i	−0.943752	−	0.330655i	$-0.892730\pi$
$683$		−	17.2828i		−	0.661309i	0.943752	−	0.330655i	$-0.107270\pi$
$684$		0			0
$685$	−12.1979	−	7.04249i	−0.466060	−	0.269080i
$686$	13.5528	−	12.6223i	0.517447	−	0.481921i
$687$		0			0
$688$	1.67491	−	2.90102i	0.0638552	−	0.110600i
$689$	−4.08333	−	0.773270i	−0.155562	−	0.0294592i
$690$		0			0
$691$			0.505240i			0.0192202i	0.999954	+	0.00961012i	$0.00305904\pi$
$691$			0.505240i			0.0192202i	−0.999954	+	0.00961012i	$0.996941\pi$
$692$	8.21015	+	14.2204i	0.312103	+	0.540578i
$693$		0			0
$694$	10.7211			0.406968
$695$	3.51179	−	2.02754i	0.133210	−	0.0769088i
$696$		0			0
$697$	−6.80164	−	11.7808i	−0.257630	−	0.446229i
$698$	−15.8365	−	27.4296i	−0.599420	−	1.03823i
$699$		0			0
$700$	−4.22519	+	4.12626i	−0.159697	+	0.155958i
$701$			43.0138i			1.62461i	0.583233	+	0.812305i	$0.301787\pi$
$701$			43.0138i			1.62461i	−0.583233	+	0.812305i	$0.698213\pi$
$702$		0			0
$703$	−36.2065	+	20.9038i	−1.36555	+	0.788402i
$704$	−0.423264	−	0.244372i	−0.0159524	−	0.00921011i
$705$		0			0
$706$	−6.66340	−	3.84712i	−0.250780	−	0.144788i
$707$	−29.2089	−	8.19849i	−1.09851	−	0.308336i
$708$		0			0
$709$	−18.4716	−	31.9937i	−0.693714	−	1.20155i	−0.970612	−	0.240648i	$-0.922640\pi$
$709$	−18.4716	−	31.9937i	−0.693714	−	1.20155i	0.276899	−	0.960899i	$-0.410693\pi$
$710$	3.86279	+	6.69054i	0.144968	+	0.251092i
$711$		0			0
$712$		−	5.05718i		−	0.189526i
$713$	16.4769	+	28.5388i	0.617063	+	1.06879i
$714$		0			0
$715$	2.88052	+	0.545491i	0.107725	+	0.0204002i
$716$	−14.8243	−	8.55881i	−0.554010	−	0.319858i
$717$		0			0
$718$	−14.2902	+	24.7514i	−0.533307	+	0.923714i
$719$	1.39841	+	2.42211i	0.0521517	+	0.0903295i	0.890923	−	0.454155i	$-0.150059\pi$
$719$	1.39841	+	2.42211i	0.0521517	+	0.0903295i	−0.838771	+	0.544484i	$0.816725\pi$
$720$		0			0
$721$	11.4937	−	40.9486i	0.428046	−	1.52501i
$722$	−14.2282	−	8.21465i	−0.529519	−	0.305718i
$723$		0			0
$724$		−	11.0003i		−	0.408824i
$725$	4.22160	+	2.43734i	0.156786	+	0.0905205i
$726$		0			0
$727$			28.9334i			1.07308i	0.843875	+	0.536539i	$0.180269\pi$
$727$			28.9334i			1.07308i	−0.843875	+	0.536539i	$0.819731\pi$
$728$	8.54441	+	4.24183i	0.316677	+	0.157213i
$729$		0			0
$730$	11.5150			0.426191
$731$	5.57389	−	9.65426i	0.206158	−	0.357076i
$732$		0			0
$733$	40.2142	+	23.2177i	1.48535	+	0.857565i	0.999861	−	0.0166798i	$-0.00530958\pi$
$733$	40.2142	+	23.2177i	1.48535	+	0.857565i	0.485485	+	0.874245i	$0.338643\pi$
$734$	−1.54773	+	2.68074i	−0.0571277	+	0.0989481i
$735$		0			0
$736$	−7.51620			−0.277051
$737$	−2.18149	+	1.25948i	−0.0803560	+	0.0463936i
$738$		0			0
$739$	23.4731	−	40.6566i	0.863472	−	1.49558i	−0.00508384	−	0.999987i	$-0.501618\pi$
$739$	23.4731	−	40.6566i	0.863472	−	1.49558i	0.868556	−	0.495591i	$-0.165048\pi$
$740$	5.84270	−	10.1198i	0.214782	−	0.372013i
$741$		0			0
$742$	2.18178	−	2.13070i	0.0800957	−	0.0782205i
$743$	8.23934	−	4.75698i	0.302272	−	0.174517i	−0.341191	−	0.939994i	$-0.610830\pi$
$743$	8.23934	−	4.75698i	0.302272	−	0.174517i	0.643463	+	0.765477i	$0.277497\pi$
$744$		0			0
$745$			10.3519i			0.379264i
$746$	−4.95005	+	2.85791i	−0.181234	+	0.104636i
$747$		0			0
$748$	−1.40857	−	0.813240i	−0.0515025	−	0.0297350i
$749$	−12.2364	+	3.12388i	−0.447109	+	0.114144i
$750$		0			0
$751$	−4.04984			−0.147781			−0.0738904	−	0.997266i	$-0.523541\pi$
$751$	−4.04984			−0.147781			−0.0738904	+	0.997266i	$0.523541\pi$
$752$	4.89698	−	8.48183i	0.178575	−	0.309300i
$753$		0			0
$754$	1.46506	−	7.73639i	0.0533543	−	0.281743i
$755$	−34.3068			−1.24855
$756$		0			0
$757$	22.0493	+	38.1906i	0.801396	+	1.38806i	0.918697	+	0.394963i	$0.129243\pi$
$757$	22.0493	+	38.1906i	0.801396	+	1.38806i	−0.117301	+	0.993096i	$0.537424\pi$
$758$	30.3180	−	17.5041i	1.10120	−	0.635778i
$759$		0			0
$760$	9.90263			0.359206
$761$	24.7515	+	42.8709i	0.897242	+	1.55407i	0.831005	+	0.556265i	$0.187766\pi$
$761$	24.7515	+	42.8709i	0.897242	+	1.55407i	0.0662369	+	0.997804i	$0.478901\pi$
$762$		0			0
$763$	−0.367671	+	0.359063i	−0.0133106	+	0.0129989i
$764$	−14.2205	+	8.21023i	−0.514481	+	0.297036i
$765$		0			0
$766$	4.47579	−	2.58410i	0.161717	−	0.0933673i
$767$	1.89542	+	1.63166i	0.0684396	+	0.0589157i
$768$		0			0
$769$	−9.30365	+	5.37146i	−0.335498	+	0.193700i	−0.658279	−	0.752774i	$-0.728715\pi$
$769$	−9.30365	+	5.37146i	−0.335498	+	0.193700i	0.322781	+	0.946474i	$0.395382\pi$
$770$	−1.53910	+	1.50307i	−0.0554654	+	0.0541668i
$771$		0			0
$772$	−9.64252	+	16.7013i	−0.347042	+	0.601094i
$773$	−12.7851			−0.459849			−0.229925	−	0.973208i	$-0.573848\pi$
$773$	−12.7851			−0.459849			−0.229925	+	0.973208i	$0.573848\pi$
$774$		0			0
$775$	−8.47550	−	4.89333i	−0.304449	−	0.175774i
$776$	3.01088	−	5.21500i	0.108084	−	0.187208i
$777$		0			0
$778$	−14.8007	−	25.6356i	−0.530633	−	0.919083i
$779$	−21.0711	−	12.1654i	−0.754952	−	0.435871i
$780$		0			0
$781$	−1.13478	−	1.96550i	−0.0406057	−	0.0703311i
$782$	−25.0130			−0.894463
$783$		0			0
$784$	−6.14338	+	3.35543i	−0.219406	+	0.119837i
$785$			14.1681i			0.505682i
$786$		0			0
$787$			24.9818i			0.890506i	0.895405	+	0.445253i	$0.146886\pi$
$787$			24.9818i			0.890506i	−0.895405	+	0.445253i	$0.853114\pi$
$788$	2.93579	−	1.69498i	0.104583	−	0.0603812i
$789$		0			0
$790$	−6.42015	+	3.70667i	−0.228419	+	0.131878i
$791$	3.64474	−	12.9852i	0.129592	−	0.461700i
$792$		0			0
$793$	−23.8293	−	4.51261i	−0.846203	−	0.160247i
$794$	2.25432	+	3.90460i	0.0800028	+	0.138569i
$795$		0			0
$796$		−	20.9952i		−	0.744156i
$797$	15.1313	−	26.2083i	0.535980	−	0.928344i	−0.463136	−	0.886287i	$-0.653276\pi$
$797$	15.1313	−	26.2083i	0.535980	−	0.928344i	0.999115	−	0.0420566i	$-0.0133910\pi$
$798$		0			0
$799$	16.2966	−	28.2265i	0.576531	−	0.998581i
$800$	1.93312	−	1.11609i	0.0683462	−	0.0394597i
$801$		0			0
$802$	35.9824			1.27058
$803$	−3.38280			−0.119377
$804$		0			0
$805$	−8.94064	+	31.8529i	−0.315116	+	1.12267i
$806$	−2.94133	+	15.5320i	−0.103604	+	0.547091i
$807$		0			0
$808$	9.93033	+	5.73328i	0.349348	+	0.201696i
$809$	32.9089	+	19.0000i	1.15702	+	0.668003i	0.950587	−	0.310459i	$-0.100483\pi$
$809$	32.9089	+	19.0000i	1.15702	+	0.668003i	0.206428	+	0.978462i	$0.433816\pi$
$810$		0			0
$811$		−	19.6791i		−	0.691027i	−0.938414	−	0.345514i	$-0.887705\pi$
$811$		−	19.6791i		−	0.691027i	0.938414	−	0.345514i	$-0.112295\pi$
$812$	4.03688	+	4.13366i	0.141667	+	0.145063i
$813$		0			0
$814$	−1.71643	+	2.97294i	−0.0601607	+	0.104201i
$815$	34.2662			1.20029
$816$		0			0
$817$		−	19.9389i		−	0.697575i
$818$	9.44105			0.330099
$819$		0			0
$820$	6.80057			0.237486
$821$		−	19.5488i		−	0.682258i	−0.940016	−	0.341129i	$-0.889191\pi$
$821$		−	19.5488i		−	0.682258i	0.940016	−	0.341129i	$-0.110809\pi$
$822$		0			0
$823$	−52.6491			−1.83523			−0.917617	−	0.397466i	$-0.869890\pi$
$823$	−52.6491			−1.83523			−0.917617	+	0.397466i	$0.869890\pi$
$824$	−8.03762	+	13.9216i	−0.280004	+	0.484981i
$825$		0			0
$826$	−1.77819	+	0.453961i	−0.0618711	+	0.0157953i
$827$		−	35.4763i		−	1.23363i	−0.787107	−	0.616817i	$-0.788422\pi$
$827$		−	35.4763i		−	1.23363i	0.787107	−	0.616817i	$-0.211578\pi$
$828$		0			0
$829$	−23.9711	−	13.8397i	−0.832551	−	0.480674i	0.0221743	−	0.999754i	$-0.492941\pi$
$829$	−23.9711	−	13.8397i	−0.832551	−	0.480674i	−0.854725	+	0.519081i	$0.826274\pi$
$830$	−2.65553	−	1.53317i	−0.0921747	−	0.0532171i
$831$		0			0
$832$	−2.73254	−	2.35228i	−0.0947337	−	0.0815508i
$833$	−20.4444	+	11.1665i	−0.708357	+	0.386895i
$834$		0			0
$835$	−34.0523			−1.17843
$836$	−2.90912			−0.100614
$837$		0			0
$838$	−22.1603	+	12.7942i	−0.765514	+	0.441970i
$839$	17.4306	−	30.1906i	0.601770	−	1.04230i	−0.390783	−	0.920483i	$-0.627796\pi$
$839$	17.4306	−	30.1906i	0.601770	−	1.04230i	0.992553	−	0.121813i	$-0.0388709\pi$
$840$		0			0
$841$	−12.1155	+	20.9846i	−0.417774	+	0.723606i
$842$		−	5.69249i		−	0.196176i
$843$		0			0
$844$	−9.99131	−	17.3055i	−0.343915	−	0.595678i
$845$	20.1303	+	7.90783i	0.692503	+	0.272038i
$846$		0			0
$847$	−20.3693	+	19.8924i	−0.699896	+	0.683510i
$848$	−0.998216	+	0.576320i	−0.0342789	+	0.0197909i
$849$		0			0
$850$	6.43319	−	3.71421i	0.220657	−	0.127396i
$851$			52.7925i			1.80970i
$852$		0			0
$853$		−	21.4601i		−	0.734780i	−0.930067	−	0.367390i	$-0.880251\pi$
$853$		−	21.4601i		−	0.734780i	0.930067	−	0.367390i	$-0.119749\pi$
$854$	12.7323	−	12.4342i	0.435691	−	0.425491i
$855$		0			0
$856$	4.77327			0.163147
$857$	26.0364	+	45.0963i	0.889385	+	1.54046i	0.840603	+	0.541651i	$0.182201\pi$
$857$	26.0364	+	45.0963i	0.889385	+	1.54046i	0.0487823	+	0.998809i	$0.484466\pi$
$858$		0			0
$859$	−23.0468	−	13.3061i	−0.786348	−	0.453998i	0.0523276	−	0.998630i	$-0.483336\pi$
$859$	−23.0468	−	13.3061i	−0.786348	−	0.453998i	−0.838675	+	0.544632i	$0.816669\pi$
$860$	2.78651	+	4.82637i	0.0950190	+	0.164578i
$861$		0			0
$862$	−15.6248	+	27.0630i	−0.532184	+	0.921769i
$863$	−8.20534	−	4.73736i	−0.279313	−	0.161261i	0.353799	−	0.935321i	$-0.384890\pi$
$863$	−8.20534	−	4.73736i	−0.279313	−	0.161261i	−0.633112	+	0.774060i	$0.718223\pi$
$864$		0			0
$865$	−27.3181			−0.928843
$866$	−5.58553	+	9.67442i	−0.189804	+	0.328750i
$867$		0			0
$868$	−8.10466	−	8.29896i	−0.275090	−	0.281685i
$869$	1.88607	−	1.08892i	0.0639804	−	0.0369391i
$870$		0			0
$871$	−17.5410	+	6.13478i	−0.594354	+	0.207869i
$872$	0.168218	−	0.0971207i	0.00569658	−	0.00328892i
$873$		0			0
$874$	−38.7445	+	22.3692i	−1.31055	+	0.756648i
$875$	−7.87440	−	30.8444i	−0.266203	−	1.04273i
$876$		0			0
$877$	5.85432	+	10.1400i	0.197686	+	0.342403i	0.947778	−	0.318931i	$-0.103324\pi$
$877$	5.85432	+	10.1400i	0.197686	+	0.342403i	−0.750092	+	0.661334i	$0.769991\pi$
$878$	−13.4451			−0.453748
$879$		0			0
$880$	0.704175	−	0.406556i	0.0237377	−	0.0137050i
$881$	−16.0806	−	27.8525i	−0.541770	−	0.938374i	−0.998803	−	0.0489238i	$-0.984421\pi$
$881$	−16.0806	−	27.8525i	−0.541770	−	0.938374i	0.457032	−	0.889450i	$-0.348912\pi$
$882$		0			0
$883$	−5.95402			−0.200369			−0.100184	−	0.994969i	$-0.531943\pi$
$883$	−5.95402			−0.200369			−0.100184	+	0.994969i	$0.531943\pi$
$884$	−9.09356	−	7.82812i	−0.305849	−	0.263288i
$885$		0			0
$886$	7.71577	−	13.3641i	0.259217	−	0.448976i
$887$	−26.3648			−0.885242			−0.442621	−	0.896709i	$-0.645951\pi$
$887$	−26.3648			−0.885242			−0.442621	+	0.896709i	$0.645951\pi$
$888$		0			0
$889$	9.68488	−	9.45813i	0.324820	−	0.317216i
$890$	7.28632	+	4.20676i	0.244238	+	0.141011i
$891$		0			0
$892$	−5.30183	+	3.06101i	−0.177519	+	0.102490i
$893$		−	58.2962i		−	1.95081i
$894$		0			0
$895$	24.6629	−	14.2391i	0.824388	−	0.475961i
$896$	2.56353	−	0.654454i	0.0856416	−	0.0218638i
$897$		0			0
$898$	−3.94469	+	6.83240i	−0.131636	+	0.228000i
$899$	−4.78734	+	8.29191i	−0.159667	+	0.276551i
$900$		0			0
$901$	−3.32194	+	1.91792i	−0.110670	+	0.0638953i
$902$	−1.99782			−0.0665202
$903$		0			0
$904$	−2.54880	+	4.41465i	−0.0847719	+	0.146829i
$905$	15.8491	+	9.15051i	0.526843	+	0.304173i
$906$		0			0
$907$	−11.1748	+	19.3554i	−0.371054	+	0.642685i	−0.989728	−	0.142963i	$-0.954337\pi$
$907$	−11.1748	+	19.3554i	−0.371054	+	0.642685i	0.618674	+	0.785648i	$0.287670\pi$
$908$	10.1922			0.338241
$909$		0			0
$910$	−13.2191	+	8.78215i	−0.438210	+	0.291125i
$911$		−	24.6855i		−	0.817866i	−0.912564	−	0.408933i	$-0.865901\pi$
$911$		−	24.6855i		−	0.817866i	0.912564	−	0.408933i	$-0.134099\pi$
$912$		0			0
$913$	0.780122	+	0.450404i	0.0258183	+	0.0149062i
$914$		−	35.7129i		−	1.18128i
$915$		0			0
$916$	−14.1465	−	8.16747i	−0.467413	−	0.269861i
$917$	19.5004	+	5.47347i	0.643960	+	0.180750i
$918$		0			0
$919$	−22.3177	−	38.6553i	−0.736191	−	1.27512i	−0.954199	−	0.299174i	$-0.903289\pi$
$919$	−22.3177	−	38.6553i	−0.736191	−	1.27512i	0.218007	−	0.975947i	$-0.430044\pi$
$920$	6.25227	−	10.8292i	0.206131	−	0.357030i
$921$		0			0
$922$	23.8404	+	13.7643i	0.785142	+	0.453302i
$923$	−5.52739	−	15.8043i	−0.181936	−	0.520205i
$924$		0			0
$925$	−7.83921	−	13.5779i	−0.257752	−	0.446439i
$926$		−	13.9941i		−	0.459875i
$927$		0			0
$928$	−1.09191	−	1.89125i	−0.0358438	−	0.0620832i
$929$	21.6219	+	37.4501i	0.709390	+	1.22870i	0.965084	+	0.261942i	$0.0843628\pi$
$929$	21.6219	+	37.4501i	0.709390	+	1.22870i	−0.255694	+	0.966758i	$0.582304\pi$
$930$		0			0
$931$	−21.6817	+	35.5800i	−0.710590	+	1.16609i
$932$	−23.7859	−	13.7328i	−0.779132	−	0.449832i
$933$		0			0
$934$	31.0006	+	17.8982i	1.01437	+	0.585647i
$935$	2.34341	−	1.35297i	0.0766377	−	0.0442468i
$936$		0			0
$937$			15.8134i			0.516601i	0.966065	+	0.258300i	$0.0831625\pi$
$937$			15.8134i			0.516601i	−0.966065	+	0.258300i	$0.916838\pi$
$938$	3.68504	−	13.1287i	0.120321	−	0.428668i
$939$		0			0
$940$	8.14700	+	14.1110i	0.265726	+	0.460251i
$941$	−24.3948	−	42.2531i	−0.795249	−	1.37741i	−0.922681	−	0.385565i	$-0.874007\pi$
$941$	−24.3948	−	42.2531i	−0.795249	−	1.37741i	0.127432	−	0.991847i	$-0.459327\pi$
$942$		0			0
$943$	−26.6075	+	15.3619i	−0.866461	+	0.500251i
$944$	0.693648			0.0225763
$945$		0			0
$946$	−0.818600	−	1.41786i	−0.0266150	−	0.0460985i
$947$			26.7389i			0.868899i	0.900696	+	0.434449i	$0.143057\pi$
$947$			26.7389i			0.868899i	−0.900696	+	0.434449i	$0.856943\pi$
$948$		0			0
$949$	−24.5198	−	4.64337i	−0.795946	−	0.150730i
$950$	6.64324	−	11.5064i	0.215535	−	0.373318i
$951$		0			0
$952$	8.53112	−	2.17794i	0.276495	−	0.0705876i
$953$	−32.8658	−	18.9751i	−1.06463	−	0.614662i	−0.137918	−	0.990444i	$-0.544041\pi$
$953$	−32.8658	−	18.9751i	−1.06463	−	0.614662i	−0.926708	+	0.375781i	$0.877374\pi$
$954$		0			0
$955$		−	27.3184i		−	0.884001i
$956$		−	25.9617i		−	0.839662i
$957$		0			0
$958$	−8.44739	−	4.87710i	−0.272923	−	0.157572i
$959$	−21.7033	+	5.54072i	−0.700836	+	0.178919i
$960$		0			0
$961$	−5.88869	+	10.1995i	−0.189958	+	0.329016i
$962$	−16.5220	+	19.1929i	−0.532692	+	0.618803i
$963$		0			0
$964$			5.70637i			0.183790i
$965$	−16.0420	−	27.7856i	−0.516412	−	0.894451i
$966$		0			0
$967$	52.2662			1.68077			0.840383	−	0.541992i	$-0.182330\pi$
$967$	52.2662			1.68077			0.840383	+	0.541992i	$0.182330\pi$
$968$	9.31941	−	5.38056i	0.299537	−	0.172938i
$969$		0			0
$970$	5.00914	+	8.67608i	0.160834	+	0.278572i
$971$	10.9696	+	18.9999i	0.352030	+	0.609735i	0.986605	−	0.163127i	$-0.0521580\pi$
$971$	10.9696	+	18.9999i	0.352030	+	0.609735i	−0.634575	+	0.772862i	$0.718825\pi$
$972$		0			0
$973$	1.74273	−	6.20885i	0.0558694	−	0.199047i
$974$		−	17.7515i		−	0.568794i
$975$		0			0
$976$	−5.82533	+	3.36326i	−0.186464	+	0.107655i
$977$	−11.4661	−	6.61996i	−0.366833	−	0.211791i	0.305241	−	0.952275i	$-0.401263\pi$
$977$	−11.4661	−	6.61996i	−0.366833	−	0.211791i	−0.672074	+	0.740484i	$0.734596\pi$
$978$		0			0
$979$	−2.14052	−	1.23583i	−0.0684114	−	0.0394973i
$980$	0.275849	−	11.6425i	0.00881167	−	0.371905i
$981$		0			0
$982$	−14.7096	−	25.4777i	−0.469401	−	0.813027i
$983$	−21.7269	−	37.6320i	−0.692979	−	1.20028i	−0.970857	−	0.239659i	$-0.922964\pi$
$983$	−21.7269	−	37.6320i	−0.692979	−	1.20028i	0.277878	−	0.960616i	$-0.410369\pi$
$984$		0			0
$985$			5.63980i			0.179699i
$986$	−3.63375	−	6.29384i	−0.115722	−	0.200437i
$987$		0			0
$988$	−21.0864	−	3.99318i	−0.670847	−	0.127040i
$989$	−21.8047	−	12.5889i	−0.693348	−	0.400305i
$990$		0			0
$991$	24.6534	−	42.7010i	0.783142	−	1.35644i	−0.146961	−	0.989142i	$-0.546949\pi$
$991$	24.6534	−	42.7010i	0.783142	−	1.35644i	0.930103	−	0.367299i	$-0.119717\pi$
$992$	2.19218	+	3.79697i	0.0696018	+	0.120554i
$993$		0			0
$994$	11.8289	+	3.32019i	0.375189	+	0.105310i
$995$	30.2496	+	17.4646i	0.958978	+	0.553666i
$996$		0			0
$997$			14.3884i			0.455686i	0.973698	+	0.227843i	$0.0731674\pi$
$997$			14.3884i			0.455686i	−0.973698	+	0.227843i	$0.926833\pi$
$998$	9.22827	+	5.32795i	0.292116	+	0.168653i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.cm.a.341.13	yes	72
3.2	odd	2	inner	1638.2.cm.a.341.24	yes	72
7.3	odd	6		1638.2.bq.a.1277.25	yes	72
13.9	even	3		1638.2.bq.a.971.12	✓	72
21.17	even	6		1638.2.bq.a.1277.12	yes	72
39.35	odd	6		1638.2.bq.a.971.25	yes	72
91.87	odd	6	inner	1638.2.cm.a.269.24	yes	72
273.269	even	6	inner	1638.2.cm.a.269.13	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1638.2.bq.a.971.12	✓	72	13.9	even	3
1638.2.bq.a.971.25	yes	72	39.35	odd	6
1638.2.bq.a.1277.12	yes	72	21.17	even	6
1638.2.bq.a.1277.25	yes	72	7.3	odd	6
1638.2.cm.a.269.13	yes	72	273.269	even	6	inner
1638.2.cm.a.269.24	yes	72	91.87	odd	6	inner
1638.2.cm.a.341.13	yes	72	1.1	even	1	trivial
1638.2.cm.a.341.24	yes	72	3.2	odd	2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.cm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.831839 - 1.44079i) q^{5} +(-0.654454 - 2.56353i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q-1.00000i q^{2} -1.00000 q^{4} +(0.831839 - 1.44079i) q^{5} +(-0.654454 - 2.56353i) q^{7} +1.00000i q^{8} +(-1.44079 - 0.831839i) q^{10} +(0.423264 + 0.244372i) q^{11} +(2.73254 + 2.35228i) q^{13} +(-2.56353 + 0.654454i) q^{14} +1.00000 q^{16} +3.32788 q^{17} +(5.15480 - 2.97613i) q^{19} +(-0.831839 + 1.44079i) q^{20} +(0.244372 - 0.423264i) q^{22} -7.51620i q^{23} +(1.11609 + 1.93312i) q^{25} +(2.35228 - 2.73254i) q^{26} +(0.654454 + 2.56353i) q^{28} +(1.89125 - 1.09191i) q^{29} +(-3.79697 + 2.19218i) q^{31} -1.00000i q^{32} -3.32788i q^{34} +(-4.23790 - 1.18952i) q^{35} -7.02383 q^{37} +(-2.97613 - 5.15480i) q^{38} +(1.44079 + 0.831839i) q^{40} +(-2.04384 - 3.54003i) q^{41} +(1.67491 - 2.90102i) q^{43} +(-0.423264 - 0.244372i) q^{44} -7.51620 q^{46} +(4.89698 - 8.48183i) q^{47} +(-6.14338 + 3.35543i) q^{49} +(1.93312 - 1.11609i) q^{50} +(-2.73254 - 2.35228i) q^{52} +(-0.998216 + 0.576320i) q^{53} +(0.704175 - 0.406556i) q^{55} +(2.56353 - 0.654454i) q^{56} +(-1.09191 - 1.89125i) q^{58} +0.693648 q^{59} +(-5.82533 + 3.36326i) q^{61} +(2.19218 + 3.79697i) q^{62} -1.00000 q^{64} +(5.66217 - 1.98028i) q^{65} +(-2.57698 + 4.46346i) q^{67} -3.32788 q^{68} +(-1.18952 + 4.23790i) q^{70} +(-4.02154 - 2.32184i) q^{71} +(-5.99414 + 3.46072i) q^{73} +7.02383i q^{74} +(-5.15480 + 2.97613i) q^{76} +(0.349448 - 1.24498i) q^{77} +(2.22800 - 3.85901i) q^{79} +(0.831839 - 1.44079i) q^{80} +(-3.54003 + 2.04384i) q^{82} +1.84311 q^{83} +(2.76826 - 4.79477i) q^{85} +(-2.90102 - 1.67491i) q^{86} +(-0.244372 + 0.423264i) q^{88} -5.05718 q^{89} +(4.24183 - 8.54441i) q^{91} +7.51620i q^{92} +(-8.48183 - 4.89698i) q^{94} -9.90263i q^{95} +(-5.21500 - 3.01088i) q^{97} +(3.35543 + 6.14338i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 72 q^{4} - 4 q^{7}+O(q^{10}) \) 72 * q - 72 * q^4 - 4 * q^7	\( 72 q - 72 q^{4} - 4 q^{7} + 4 q^{13} + 72 q^{16} - 36 q^{19} - 28 q^{25} + 4 q^{28} - 40 q^{37} + 12 q^{43} - 16 q^{46} + 4 q^{49} - 4 q^{52} + 48 q^{55} + 16 q^{58} - 60 q^{61} - 72 q^{64} + 64 q^{67} + 108 q^{73} + 36 q^{76} + 64 q^{79} + 48 q^{82} - 64 q^{85} + 16 q^{91} - 24 q^{94} - 108 q^{97}+O(q^{100}) \) 72 * q - 72 * q^4 - 4 * q^7 + 4 * q^13 + 72 * q^16 - 36 * q^19 - 28 * q^25 + 4 * q^28 - 40 * q^37 + 12 * q^43 - 16 * q^46 + 4 * q^49 - 4 * q^52 + 48 * q^55 + 16 * q^58 - 60 * q^61 - 72 * q^64 + 64 * q^67 + 108 * q^73 + 36 * q^76 + 64 * q^79 + 48 * q^82 - 64 * q^85 + 16 * q^91 - 24 * q^94 - 108 * q^97

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