LMFDB - Embedded newform 432.2.l.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(107,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 2]))

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.l (of order $4$, 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:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.2
Character	$\chi$	$=$	432.107
Dual form			432.2.l.a.323.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38130 - 0.303332i) q^{2} +(1.81598 + 0.837984i) q^{4} +(1.39178 - 1.39178i) q^{5} -1.33599 q^{7} +(-2.25423 - 1.70835i) q^{8} +O(q^{10})$	\(q+(-1.38130 - 0.303332i) q^{2} +(1.81598 + 0.837984i) q^{4} +(1.39178 - 1.39178i) q^{5} -1.33599 q^{7} +(-2.25423 - 1.70835i) q^{8} +(-2.34464 + 1.50029i) q^{10} +(-4.37602 - 4.37602i) q^{11} +(1.20314 - 1.20314i) q^{13} +(1.84541 + 0.405249i) q^{14} +(2.59557 + 3.04352i) q^{16} -1.84799i q^{17} +(-1.19463 - 1.19463i) q^{19} +(3.69373 - 1.36115i) q^{20} +(4.71721 + 7.37198i) q^{22} +2.84298i q^{23} +1.12590i q^{25} +(-2.02686 + 1.29695i) q^{26} +(-2.42614 - 1.11954i) q^{28} +(0.485646 + 0.485646i) q^{29} -9.61300i q^{31} +(-2.66206 - 4.99134i) q^{32} +(-0.560554 + 2.55263i) q^{34} +(-1.85941 + 1.85941i) q^{35} +(-6.99709 - 6.99709i) q^{37} +(1.28778 + 2.01251i) q^{38} +(-5.51503 + 0.759737i) q^{40} +9.58349 q^{41} +(5.79108 - 5.79108i) q^{43} +(-4.27973 - 11.6138i) q^{44} +(0.862366 - 3.92701i) q^{46} -8.06957 q^{47} -5.21512 q^{49} +(0.341521 - 1.55520i) q^{50} +(3.19310 - 1.17667i) q^{52} +(-3.25428 + 3.25428i) q^{53} -12.1809 q^{55} +(3.01163 + 2.28235i) q^{56} +(-0.523511 - 0.818135i) q^{58} +(-0.730119 - 0.730119i) q^{59} +(7.32974 - 7.32974i) q^{61} +(-2.91593 + 13.2784i) q^{62} +(2.16307 + 7.70202i) q^{64} -3.34902i q^{65} +(7.38696 + 7.38696i) q^{67} +(1.54859 - 3.35591i) q^{68} +(3.13242 - 2.00438i) q^{70} -4.40733i q^{71} +0.385877i q^{73} +(7.54264 + 11.7875i) q^{74} +(-1.16834 - 3.17051i) q^{76} +(5.84633 + 5.84633i) q^{77} +8.84274i q^{79} +(7.84837 + 0.623460i) q^{80} +(-13.2377 - 2.90698i) q^{82} +(-6.75487 + 6.75487i) q^{83} +(-2.57200 - 2.57200i) q^{85} +(-9.75584 + 6.24260i) q^{86} +(2.38876 + 17.3403i) q^{88} +13.3980 q^{89} +(-1.60739 + 1.60739i) q^{91} +(-2.38237 + 5.16279i) q^{92} +(11.1465 + 2.44776i) q^{94} -3.32533 q^{95} -2.81458 q^{97} +(7.20365 + 1.58191i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) $ 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−1.38130	−	0.303332i	−0.976727	−	0.214488i
$2$	−1.38130	−	0.303332i	−0.976727	−	0.214488i
$3$		0			0
$3$		0			0
$4$	1.81598	+	0.837984i	0.907990	+	0.418992i
$5$	1.39178	−	1.39178i	0.622423	−	0.622423i	−0.323728	−	0.946150i	$-0.604936\pi$
$5$	1.39178	−	1.39178i	0.622423	−	0.622423i	0.946150	+	0.323728i	$0.104936\pi$
$6$		0			0
$7$	−1.33599			−0.504958			−0.252479	−	0.967602i	$-0.581246\pi$
$7$	−1.33599			−0.504958			−0.252479	+	0.967602i	$0.581246\pi$
$8$	−2.25423	−	1.70835i	−0.796989	−	0.603993i
$9$		0			0
$10$	−2.34464	+	1.50029i	−0.741439	+	0.474435i
$11$	−4.37602	−	4.37602i	−1.31942	−	1.31942i	−0.914236	−	0.405183i	$-0.867208\pi$
$11$	−4.37602	−	4.37602i	−1.31942	−	1.31942i	−0.405183	−	0.914236i	$-0.632792\pi$
$12$		0			0
$13$	1.20314	−	1.20314i	0.333692	−	0.333692i	−0.520295	−	0.853987i	$-0.674178\pi$
$13$	1.20314	−	1.20314i	0.333692	−	0.333692i	0.853987	+	0.520295i	$0.174178\pi$
$14$	1.84541	+	0.405249i	0.493206	+	0.108307i
$15$		0			0
$16$	2.59557	+	3.04352i	0.648891	+	0.760881i
$17$		−	1.84799i		−	0.448204i	−0.974566	−	0.224102i	$-0.928055\pi$
$17$		−	1.84799i		−	0.448204i	0.974566	−	0.224102i	$-0.0719448\pi$
$18$		0			0
$19$	−1.19463	−	1.19463i	−0.274067	−	0.274067i	0.556668	−	0.830735i	$-0.312080\pi$
$19$	−1.19463	−	1.19463i	−0.274067	−	0.274067i	−0.830735	+	0.556668i	$0.812080\pi$
$20$	3.69373	−	1.36115i	0.825944	−	0.304363i
$21$		0			0
$22$	4.71721	+	7.37198i	1.00571	+	1.57171i
$23$			2.84298i			0.592802i	0.955064	+	0.296401i	$0.0957865\pi$
$23$			2.84298i			0.592802i	−0.955064	+	0.296401i	$0.904213\pi$
$24$		0			0
$25$			1.12590i			0.225180i
$26$	−2.02686	+	1.29695i	−0.397499	+	0.254353i
$27$		0			0
$28$	−2.42614	−	1.11954i	−0.458497	−	0.211573i
$29$	0.485646	+	0.485646i	0.0901823	+	0.0901823i	0.750759	−	0.660576i	$-0.229688\pi$
$29$	0.485646	+	0.485646i	0.0901823	+	0.0901823i	−0.660576	+	0.750759i	$0.729688\pi$
$30$		0			0
$31$		−	9.61300i		−	1.72654i	−0.504738	−	0.863272i	$-0.668411\pi$
$31$		−	9.61300i		−	1.72654i	0.504738	−	0.863272i	$-0.331589\pi$
$32$	−2.66206	−	4.99134i	−0.470590	−	0.882352i
$33$		0			0
$34$	−0.560554	+	2.55263i	−0.0961342	+	0.437772i
$35$	−1.85941	+	1.85941i	−0.314298	+	0.314298i
$36$		0			0
$37$	−6.99709	−	6.99709i	−1.15031	−	1.15031i	−0.986489	−	0.163825i	$-0.947617\pi$
$37$	−6.99709	−	6.99709i	−1.15031	−	1.15031i	−0.163825	−	0.986489i	$-0.552383\pi$
$38$	1.28778	+	2.01251i	0.208905	+	0.326473i
$39$		0			0
$40$	−5.51503	+	0.759737i	−0.872004	+	0.120125i
$41$	9.58349			1.49669			0.748345	−	0.663310i	$-0.230849\pi$
$41$	9.58349			1.49669			0.748345	+	0.663310i	$0.230849\pi$
$42$		0			0
$43$	5.79108	−	5.79108i	0.883132	−	0.883132i	−0.110720	−	0.993852i	$-0.535316\pi$
$43$	5.79108	−	5.79108i	0.883132	−	0.883132i	0.993852	+	0.110720i	$0.0353156\pi$
$44$	−4.27973	−	11.6138i	−0.645193	−	1.75084i
$45$		0			0
$46$	0.862366	−	3.92701i	0.127149	−	0.579006i
$47$	−8.06957			−1.17707			−0.588534	−	0.808473i	$-0.700295\pi$
$47$	−8.06957			−1.17707			−0.588534	+	0.808473i	$0.700295\pi$
$48$		0			0
$49$	−5.21512			−0.745017
$50$	0.341521	−	1.55520i	0.0482983	−	0.219939i
$51$		0			0
$52$	3.19310	−	1.17667i	0.442804	−	0.163175i
$53$	−3.25428	+	3.25428i	−0.447010	+	0.447010i	−0.894359	−	0.447349i	$-0.852368\pi$
$53$	−3.25428	+	3.25428i	−0.447010	+	0.447010i	0.447349	+	0.894359i	$0.352368\pi$
$54$		0			0
$55$	−12.1809			−1.64247
$56$	3.01163	+	2.28235i	0.402446	+	0.304992i
$57$		0			0
$58$	−0.523511	−	0.818135i	−0.0687404	−	0.107426i
$59$	−0.730119	−	0.730119i	−0.0950534	−	0.0950534i	0.657981	−	0.753034i	$-0.271411\pi$
$59$	−0.730119	−	0.730119i	−0.0950534	−	0.0950534i	−0.753034	+	0.657981i	$0.771411\pi$
$60$		0			0
$61$	7.32974	−	7.32974i	0.938478	−	0.938478i	−0.0597365	−	0.998214i	$-0.519026\pi$
$61$	7.32974	−	7.32974i	0.938478	−	0.938478i	0.998214	+	0.0597365i	$0.0190261\pi$
$62$	−2.91593	+	13.2784i	−0.370323	+	1.68636i
$63$		0			0
$64$	2.16307	+	7.70202i	0.270384	+	0.962753i
$65$		−	3.34902i		−	0.415395i
$66$		0			0
$67$	7.38696	+	7.38696i	0.902461	+	0.902461i	0.995649	−	0.0931880i	$-0.0297057\pi$
$67$	7.38696	+	7.38696i	0.902461	+	0.902461i	−0.0931880	+	0.995649i	$0.529706\pi$
$68$	1.54859	−	3.35591i	0.187794	−	0.406964i
$69$		0			0
$70$	3.13242	−	2.00438i	0.374396	−	0.239570i
$71$		−	4.40733i		−	0.523054i	−0.965196	−	0.261527i	$-0.915774\pi$
$71$		−	4.40733i		−	0.523054i	0.965196	−	0.261527i	$-0.0842260\pi$
$72$		0			0
$73$			0.385877i			0.0451635i	0.999745	+	0.0225818i	$0.00718861\pi$
$73$			0.385877i			0.0451635i	−0.999745	+	0.0225818i	$0.992811\pi$
$74$	7.54264	+	11.7875i	0.876814	+	1.37027i
$75$		0			0
$76$	−1.16834	−	3.17051i	−0.134018	−	0.363682i
$77$	5.84633	+	5.84633i	0.666251	+	0.666251i
$78$		0			0
$79$			8.84274i			0.994886i	0.867497	+	0.497443i	$0.165728\pi$
$79$			8.84274i			0.994886i	−0.867497	+	0.497443i	$0.834272\pi$
$80$	7.84837	+	0.623460i	0.877474	+	0.0697049i
$81$		0			0
$82$	−13.2377	−	2.90698i	−1.46186	−	0.321022i
$83$	−6.75487	+	6.75487i	−0.741443	+	0.741443i	−0.972856	−	0.231412i	$-0.925665\pi$
$83$	−6.75487	+	6.75487i	−0.741443	+	0.741443i	0.231412	+	0.972856i	$0.425665\pi$
$84$		0			0
$85$	−2.57200	−	2.57200i	−0.278972	−	0.278972i
$86$	−9.75584	+	6.24260i	−1.05200	+	0.673157i
$87$		0			0
$88$	2.38876	+	17.3403i	0.254642	+	1.84848i
$89$	13.3980			1.42018			0.710091	−	0.704110i	$-0.248654\pi$
$89$	13.3980			1.42018			0.710091	+	0.704110i	$0.248654\pi$
$90$		0			0
$91$	−1.60739	+	1.60739i	−0.168501	+	0.168501i
$92$	−2.38237	+	5.16279i	−0.248379	+	0.538259i
$93$		0			0
$94$	11.1465	+	2.44776i	1.14967	+	0.252467i
$95$	−3.32533			−0.341171
$96$		0			0
$97$	−2.81458			−0.285777			−0.142889	−	0.989739i	$-0.545639\pi$
$97$	−2.81458			−0.285777			−0.142889	+	0.989739i	$0.545639\pi$
$98$	7.20365	+	1.58191i	0.727678	+	0.159797i
$99$		0			0
$100$	−0.943486	+	2.04461i	−0.0943486	+	0.204461i
$101$	9.18142	−	9.18142i	0.913585	−	0.913585i	−0.0829670	−	0.996552i	$-0.526440\pi$
$101$	9.18142	−	9.18142i	0.913585	−	0.913585i	0.996552	+	0.0829670i	$0.0264396\pi$
$102$		0			0
$103$	1.32705			0.130758			0.0653791	−	0.997860i	$-0.479174\pi$
$103$	1.32705			0.130758			0.0653791	+	0.997860i	$0.479174\pi$
$104$	−4.76755	+	0.656766i	−0.467497	+	0.0644012i
$105$		0			0
$106$	5.48227	−	3.50802i	0.532485	−	0.340729i
$107$	8.35676	+	8.35676i	0.807879	+	0.807879i	0.984313	−	0.176434i	$-0.0564562\pi$
$107$	8.35676	+	8.35676i	0.807879	+	0.807879i	−0.176434	+	0.984313i	$0.556456\pi$
$108$		0			0
$109$	9.82294	−	9.82294i	0.940867	−	0.940867i	−0.0574793	−	0.998347i	$-0.518306\pi$
$109$	9.82294	−	9.82294i	0.940867	−	0.940867i	0.998347	+	0.0574793i	$0.0183063\pi$
$110$	16.8255	+	3.69485i	1.60425	+	0.352290i
$111$		0			0
$112$	−3.46766	−	4.06613i	−0.327663	−	0.384213i
$113$			12.8196i			1.20596i	0.797755	+	0.602981i	$0.206021\pi$
$113$			12.8196i			1.20596i	−0.797755	+	0.602981i	$0.793979\pi$
$114$		0			0
$115$	3.95680	+	3.95680i	0.368974	+	0.368974i
$116$	0.474960	+	1.28889i	0.0440989	+	0.119670i
$117$		0			0
$118$	0.787045	+	1.22998i	0.0724534	+	0.113229i
$119$			2.46890i			0.226324i
$120$		0			0
$121$			27.2990i			2.48173i
$122$	−12.3479	+	7.90123i	−1.11793	+	0.715344i
$123$		0			0
$124$	8.05554	−	17.4570i	0.723409	−	1.56769i
$125$	8.52590	+	8.52590i	0.762580	+	0.762580i
$126$		0			0
$127$			1.40699i			0.124850i	0.998050	+	0.0624249i	$0.0198834\pi$
$127$			1.40699i			0.124850i	−0.998050	+	0.0624249i	$0.980117\pi$
$128$	−0.651582	−	11.2949i	−0.0575922	−	0.998340i
$129$		0			0
$130$	−1.01587	+	4.62601i	−0.0890973	+	0.405728i
$131$	−0.494626	+	0.494626i	−0.0432157	+	0.0432157i	−0.728384	−	0.685169i	$-0.759728\pi$
$131$	−0.494626	+	0.494626i	−0.0432157	+	0.0432157i	0.685169	+	0.728384i	$0.259728\pi$
$132$		0			0
$133$	1.59602	+	1.59602i	0.138393	+	0.138393i
$134$	−7.96291	−	12.4443i	−0.687890	−	1.07502i
$135$		0			0
$136$	−3.15702	+	4.16579i	−0.270712	+	0.357213i
$137$	−12.9156			−1.10346			−0.551728	−	0.834024i	$-0.686031\pi$
$137$	−12.9156			−1.10346			−0.551728	+	0.834024i	$0.686031\pi$
$138$		0			0
$139$	15.1838	−	15.1838i	1.28787	−	1.28787i	0.351791	−	0.936078i	$-0.385573\pi$
$139$	15.1838	−	15.1838i	1.28787	−	1.28787i	0.936078	−	0.351791i	$-0.114427\pi$
$140$	−4.93480	+	1.81849i	−0.417067	+	0.153691i
$141$		0			0
$142$	−1.33688	+	6.08784i	−0.112189	+	0.510880i
$143$	−10.5300			−0.880560
$144$		0			0
$145$	1.35183			0.112263
$146$	0.117049	−	0.533012i	0.00968703	−	0.0441124i
$147$		0			0
$148$	−6.84312	−	18.5700i	−0.562501	−	1.52645i
$149$	9.78679	−	9.78679i	0.801765	−	0.801765i	−0.181606	−	0.983371i	$-0.558130\pi$
$149$	9.78679	−	9.78679i	0.801765	−	0.801765i	0.983371	+	0.181606i	$0.0581297\pi$
$150$		0			0
$151$	−18.9203			−1.53971			−0.769857	−	0.638216i	$-0.779673\pi$
$151$	−18.9203			−1.53971			−0.769857	+	0.638216i	$0.779673\pi$
$152$	0.652119	+	4.73382i	0.0528938	+	0.383964i
$153$		0			0
$154$	−6.30216	−	9.84892i	−0.507843	−	0.793648i
$155$	−13.3792	−	13.3792i	−1.07464	−	1.07464i
$156$		0			0
$157$	−12.3331	+	12.3331i	−0.984291	+	0.984291i	−0.999879	−	0.0155875i	$-0.995038\pi$
$157$	−12.3331	+	12.3331i	−0.984291	+	0.984291i	0.0155875	+	0.999879i	$0.495038\pi$
$158$	2.68228	−	12.2145i	0.213391	−	0.971732i
$159$		0			0
$160$	−10.6518	−	3.24184i	−0.842102	−	0.256290i
$161$		−	3.79820i		−	0.299340i
$162$		0			0
$163$	13.6186	+	13.6186i	1.06669	+	1.06669i	0.997611	+	0.0690796i	$0.0220063\pi$
$163$	13.6186	+	13.6186i	1.06669	+	1.06669i	0.0690796	+	0.997611i	$0.477994\pi$
$164$	17.4034	+	8.03081i	1.35898	+	0.627101i
$165$		0			0
$166$	11.3795	−	7.28154i	0.883218	−	0.565157i
$167$			6.27242i			0.485374i	0.970105	+	0.242687i	$0.0780289\pi$
$167$			6.27242i			0.485374i	−0.970105	+	0.242687i	$0.921971\pi$
$168$		0			0
$169$			10.1049i			0.777299i
$170$	2.77253	+	4.33287i	0.212643	+	0.332316i
$171$		0			0
$172$	15.3693	−	5.66365i	1.17190	−	0.431850i
$173$	−8.28143	−	8.28143i	−0.629625	−	0.629625i	0.318348	−	0.947974i	$-0.396872\pi$
$173$	−8.28143	−	8.28143i	−0.629625	−	0.629625i	−0.947974	+	0.318348i	$0.896872\pi$
$174$		0			0
$175$		−	1.50419i		−	0.113706i
$176$	1.96028	−	24.6768i	0.147761	−	1.86008i
$177$		0			0
$178$	−18.5066	−	4.06403i	−1.38713	−	0.304612i
$179$	−2.23413	+	2.23413i	−0.166986	+	0.166986i	−0.785653	−	0.618667i	$-0.787673\pi$
$179$	−2.23413	+	2.23413i	−0.166986	+	0.166986i	0.618667	+	0.785653i	$0.287673\pi$
$180$		0			0
$181$	7.60438	+	7.60438i	0.565229	+	0.565229i	0.930788	−	0.365559i	$-0.119122\pi$
$181$	7.60438	+	7.60438i	0.565229	+	0.565229i	−0.365559	+	0.930788i	$0.619122\pi$
$182$	2.70787	−	1.73272i	0.200720	−	0.128438i
$183$		0			0
$184$	4.85681	−	6.40872i	0.358049	−	0.472457i
$185$	−19.4768			−1.43196
$186$		0			0
$187$	−8.08684	+	8.08684i	−0.591368	+	0.591368i
$188$	−14.6542	−	6.76217i	−1.06877	−	0.493182i
$189$		0			0
$190$	4.59328	+	1.00868i	0.333231	+	0.0731771i
$191$	6.09856			0.441276			0.220638	−	0.975356i	$-0.429186\pi$
$191$	6.09856			0.441276			0.220638	+	0.975356i	$0.429186\pi$
$192$		0			0
$193$	6.42444			0.462441			0.231221	−	0.972901i	$-0.425728\pi$
$193$	6.42444			0.462441			0.231221	+	0.972901i	$0.425728\pi$
$194$	3.88778	+	0.853752i	0.279126	+	0.0612958i
$195$		0			0
$196$	−9.47055	−	4.37019i	−0.676468	−	0.312156i
$197$	−0.305089	+	0.305089i	−0.0217367	+	0.0217367i	−0.717892	−	0.696155i	$-0.754893\pi$
$197$	−0.305089	+	0.305089i	−0.0217367	+	0.0217367i	0.696155	+	0.717892i	$0.254893\pi$
$198$		0			0
$199$	−9.26500			−0.656779			−0.328389	−	0.944542i	$-0.606506\pi$
$199$	−9.26500			−0.656779			−0.328389	+	0.944542i	$0.606506\pi$
$200$	1.92343	−	2.53803i	0.136007	−	0.179466i
$201$		0			0
$202$	−15.4673	+	9.89728i	−1.08828	+	0.696370i
$203$	−0.648821	−	0.648821i	−0.0455383	−	0.0455383i
$204$		0			0
$205$	13.3381	−	13.3381i	0.931574	−	0.931574i
$206$	−1.83306	−	0.402537i	−0.127715	−	0.0280460i
$207$		0			0
$208$	6.78464	+	0.538959i	0.470430	+	0.0373701i
$209$			10.4555i			0.723219i
$210$		0			0
$211$	−1.35580	−	1.35580i	−0.0933374	−	0.0933374i	0.658896	−	0.752234i	$-0.271024\pi$
$211$	−1.35580	−	1.35580i	−0.0933374	−	0.0933374i	−0.752234	+	0.658896i	$0.771024\pi$
$212$	−8.63675	+	3.18268i	−0.593175	+	0.218587i
$213$		0			0
$214$	−9.00833	−	14.0781i	−0.615796	−	0.962357i
$215$		−	16.1198i		−	1.09936i
$216$		0			0
$217$			12.8429i			0.871833i
$218$	−16.5480	+	10.5888i	−1.12077	+	0.717166i
$219$		0			0
$220$	−22.1203	−	10.2074i	−1.49135	−	0.688183i
$221$	−2.22340	−	2.22340i	−0.149562	−	0.149562i
$222$		0			0
$223$		−	1.18959i		−	0.0796606i	−0.999206	−	0.0398303i	$-0.987318\pi$
$223$		−	1.18959i		−	0.0796606i	0.999206	−	0.0398303i	$-0.0126817\pi$
$224$	3.55649	+	6.66840i	0.237628	+	0.445551i
$225$		0			0
$226$	3.88858	−	17.7077i	0.258664	−	1.17790i
$227$	12.7220	−	12.7220i	0.844387	−	0.844387i	−0.145039	−	0.989426i	$-0.546331\pi$
$227$	12.7220	−	12.7220i	0.844387	−	0.844387i	0.989426	+	0.145039i	$0.0463308\pi$
$228$		0			0
$229$	−12.5661	−	12.5661i	−0.830393	−	0.830393i	0.157177	−	0.987570i	$-0.449761\pi$
$229$	−12.5661	−	12.5661i	−0.830393	−	0.830393i	−0.987570	+	0.157177i	$0.949761\pi$
$230$	−4.26531	−	6.66575i	−0.281246	−	0.439527i
$231$		0			0
$232$	−0.265102	−	1.92441i	−0.0174048	−	0.126344i
$233$	17.2312			1.12885			0.564427	−	0.825483i	$-0.309097\pi$
$233$	17.2312			1.12885			0.564427	+	0.825483i	$0.309097\pi$
$234$		0			0
$235$	−11.2311	+	11.2311i	−0.732634	+	0.732634i
$236$	−0.714053	−	1.93771i	−0.0464809	−	0.126134i
$237$		0			0
$238$	0.748897	−	3.41030i	0.0485438	−	0.221057i
$239$	17.6216			1.13985			0.569925	−	0.821697i	$-0.306972\pi$
$239$	17.6216			1.13985			0.569925	+	0.821697i	$0.306972\pi$
$240$		0			0
$241$	−4.55260			−0.293259			−0.146629	−	0.989191i	$-0.546842\pi$
$241$	−4.55260			−0.293259			−0.146629	+	0.989191i	$0.546842\pi$
$242$	8.28066	−	37.7082i	0.532301	−	2.42397i
$243$		0			0
$244$	19.4529	−	7.16846i	1.24534	−	0.458914i
$245$	−7.25830	+	7.25830i	−0.463716	+	0.463716i
$246$		0			0
$247$	−2.87463			−0.182908
$248$	−16.4224	+	21.6699i	−1.04282	+	1.37604i
$249$		0			0
$250$	−9.19065	−	14.3630i	−0.581268	−	0.908396i
$251$	13.6040	+	13.6040i	0.858677	+	0.858677i	0.991182	−	0.132505i	$-0.0423022\pi$
$251$	13.6040	+	13.6040i	0.858677	+	0.858677i	−0.132505	+	0.991182i	$0.542302\pi$
$252$		0			0
$253$	12.4409	−	12.4409i	0.782154	−	0.782154i
$254$	0.426783	−	1.94347i	0.0267788	−	0.121944i
$255$		0			0
$256$	−2.52608	+	15.7993i	−0.157880	+	0.987458i
$257$		−	21.0374i		−	1.31228i	−0.754640	−	0.656139i	$-0.772189\pi$
$257$		−	21.0374i		−	1.31228i	0.754640	−	0.656139i	$-0.227811\pi$
$258$		0			0
$259$	9.34807	+	9.34807i	0.580861	+	0.580861i
$260$	2.80643	−	6.08176i	0.174047	−	0.377175i
$261$		0			0
$262$	0.833263	−	0.533191i	0.0514792	−	0.0329407i
$263$		−	5.35347i		−	0.330109i	−0.986284	−	0.165055i	$-0.947220\pi$
$263$		−	5.35347i		−	0.330109i	0.986284	−	0.165055i	$-0.0527800\pi$
$264$		0			0
$265$			9.05849i			0.556459i
$266$	−1.72046	−	2.68871i	−0.105488	−	0.164855i
$267$		0			0
$268$	7.22441	+	19.6047i	0.441301	+	1.19755i
$269$	−18.2302	−	18.2302i	−1.11151	−	1.11151i	−0.992946	−	0.118569i	$-0.962169\pi$
$269$	−18.2302	−	18.2302i	−1.11151	−	1.11151i	−0.118569	−	0.992946i	$-0.537831\pi$
$270$		0			0
$271$			6.32505i			0.384219i	0.981373	+	0.192110i	$0.0615329\pi$
$271$			6.32505i			0.384219i	−0.981373	+	0.192110i	$0.938467\pi$
$272$	5.62441	−	4.79658i	0.341030	−	0.290835i
$273$		0			0
$274$	17.8404	+	3.91772i	1.07778	+	0.236678i
$275$	4.92695	−	4.92695i	0.297107	−	0.297107i
$276$		0			0
$277$	−4.50389	−	4.50389i	−0.270612	−	0.270612i	0.558734	−	0.829347i	$-0.311287\pi$
$277$	−4.50389	−	4.50389i	−0.270612	−	0.270612i	−0.829347	+	0.558734i	$0.811287\pi$
$278$	−25.5790	+	16.3676i	−1.53413	+	0.981664i
$279$		0			0
$280$	7.36805	−	1.01500i	0.440325	−	0.0606581i
$281$	−20.6398			−1.23127			−0.615634	−	0.788033i	$-0.711100\pi$
$281$	−20.6398			−1.23127			−0.615634	+	0.788033i	$0.711100\pi$
$282$		0			0
$283$	16.8888	−	16.8888i	1.00393	−	1.00393i	0.00394063	−	0.999992i	$-0.498746\pi$
$283$	16.8888	−	16.8888i	1.00393	−	1.00393i	0.999992	−	0.00394063i	$-0.00125434\pi$
$284$	3.69327	−	8.00362i	0.219155	−	0.474927i
$285$		0			0
$286$	14.5450	+	3.19407i	0.860066	+	0.188869i
$287$	−12.8035			−0.755766
$288$		0			0
$289$	13.5849			0.799113
$290$	−1.86728	−	0.410051i	−0.109650	−	0.0240790i
$291$		0			0
$292$	−0.323359	+	0.700745i	−0.0189232	+	0.0410080i
$293$	−10.0125	+	10.0125i	−0.584934	+	0.584934i	−0.936255	−	0.351321i	$-0.885733\pi$
$293$	−10.0125	+	10.0125i	−0.584934	+	0.584934i	0.351321	+	0.936255i	$0.385733\pi$
$294$		0			0
$295$	−2.03233			−0.118327
$296$	3.81953	+	27.7265i	0.222006	+	1.61157i
$297$		0			0
$298$	−16.4871	+	10.5498i	−0.955074	+	0.611136i
$299$	3.42052	+	3.42052i	0.197814	+	0.197814i
$300$		0			0
$301$	−7.73685	+	7.73685i	−0.445945	+	0.445945i
$302$	26.1346	+	5.73913i	1.50388	+	0.330250i
$303$		0			0
$304$	0.535146	−	6.73664i	0.0306927	−	0.386373i
$305$		−	20.4028i		−	1.16826i
$306$		0			0
$307$	13.0816	+	13.0816i	0.746607	+	0.746607i	0.973840	−	0.227233i	$-0.0729679\pi$
$307$	13.0816	+	13.0816i	0.746607	+	0.746607i	−0.227233	+	0.973840i	$0.572968\pi$
$308$	5.71769	+	15.5160i	0.325796	+	0.884104i
$309$		0			0
$310$	14.4223	+	22.5390i	0.819133	+	1.28013i
$311$			2.77454i			0.157330i	0.996901	+	0.0786648i	$0.0250657\pi$
$311$			2.77454i			0.157330i	−0.996901	+	0.0786648i	$0.974934\pi$
$312$		0			0
$313$		−	3.90643i		−	0.220804i	−0.993887	−	0.110402i	$-0.964786\pi$
$313$		−	3.90643i		−	0.220804i	0.993887	−	0.110402i	$-0.0352139\pi$
$314$	20.7768	−	13.2947i	1.17250	−	0.750265i
$315$		0			0
$316$	−7.41008	+	16.0582i	−0.416849	+	0.903347i
$317$	4.99649	+	4.99649i	0.280631	+	0.280631i	0.833361	−	0.552730i	$-0.186414\pi$
$317$	4.99649	+	4.99649i	0.280631	+	0.280631i	−0.552730	+	0.833361i	$0.686414\pi$
$318$		0			0
$319$		−	4.25039i		−	0.237976i
$320$	13.7300	+	7.70900i	0.767532	+	0.430946i
$321$		0			0
$322$	−1.15212	+	5.24646i	−0.0642049	+	0.292374i
$323$	−2.20767	+	2.20767i	−0.122838	+	0.122838i
$324$		0			0
$325$	1.35462	+	1.35462i	0.0751408	+	0.0751408i
$326$	−14.6804	−	22.9423i	−0.813073	−	1.27066i
$327$		0			0
$328$	−21.6034	−	16.3720i	−1.19285	−	0.903991i
$329$	10.7809			0.594370
$330$		0			0
$331$	−3.18235	+	3.18235i	−0.174918	+	0.174918i	−0.789136	−	0.614218i	$-0.789471\pi$
$331$	−3.18235	+	3.18235i	−0.174918	+	0.174918i	0.614218	+	0.789136i	$0.289471\pi$
$332$	−17.9272	+	6.60623i	−0.983882	+	0.362564i
$333$		0			0
$334$	1.90262	−	8.66409i	0.104107	−	0.474078i
$335$	20.5620			1.12342
$336$		0			0
$337$	−33.8660			−1.84480			−0.922399	−	0.386238i	$-0.873774\pi$
$337$	−33.8660			−1.84480			−0.922399	+	0.386238i	$0.873774\pi$
$338$	3.06513	−	13.9579i	0.166721	−	0.759209i
$339$		0			0
$340$	−2.51540	−	6.82598i	−0.136417	−	0.370191i
$341$	−42.0666	+	42.0666i	−2.27804	+	2.27804i
$342$		0			0
$343$	16.3193			0.881161
$344$	−22.9476	+	3.16120i	−1.23725	+	0.170441i
$345$		0			0
$346$	8.92712	+	13.9512i	0.479925	+	0.750019i
$347$	0.987636	+	0.987636i	0.0530191	+	0.0530191i	0.733119	−	0.680100i	$-0.238064\pi$
$347$	0.987636	+	0.987636i	0.0530191	+	0.0530191i	−0.680100	+	0.733119i	$0.738064\pi$
$348$		0			0
$349$	−17.8420	+	17.8420i	−0.955060	+	0.955060i	−0.999033	−	0.0439726i	$-0.985999\pi$
$349$	−17.8420	+	17.8420i	−0.955060	+	0.955060i	0.0439726	+	0.999033i	$0.485999\pi$
$350$	−0.456270	+	2.07774i	−0.0243886	+	0.111060i
$351$		0			0
$352$	−10.1930	+	33.4914i	−0.543287	+	1.78510i
$353$			10.3421i			0.550455i	0.961379	+	0.275228i	$0.0887532\pi$
$353$			10.3421i			0.550455i	−0.961379	+	0.275228i	$0.911247\pi$
$354$		0			0
$355$	−6.13403	−	6.13403i	−0.325560	−	0.325560i
$356$	24.3305	+	11.2273i	1.28951	+	0.595045i
$357$		0			0
$358$	3.76368	−	2.40832i	0.198917	−	0.127284i
$359$		−	9.51484i		−	0.502174i	−0.967965	−	0.251087i	$-0.919212\pi$
$359$		−	9.51484i		−	0.502174i	0.967965	−	0.251087i	$-0.0807880\pi$
$360$		0			0
$361$		−	16.1457i		−	0.849774i
$362$	−8.19729	−	12.8106i	−0.430840	−	0.673309i
$363$		0			0
$364$	−4.26597	+	1.57202i	−0.223597	+	0.0823965i
$365$	0.537056	+	0.537056i	0.0281108	+	0.0281108i
$366$		0			0
$367$		−	15.9015i		−	0.830051i	−0.909810	−	0.415026i	$-0.863773\pi$
$367$		−	15.9015i		−	0.830051i	0.909810	−	0.415026i	$-0.136227\pi$
$368$	−8.65268	+	7.37914i	−0.451052	+	0.384664i
$369$		0			0
$370$	26.9033	+	5.90793i	1.39864	+	0.307139i
$371$	4.34770	−	4.34770i	0.225722	−	0.225722i
$372$		0			0
$373$	8.33818	+	8.33818i	0.431735	+	0.431735i	0.889218	−	0.457483i	$-0.151249\pi$
$373$	8.33818	+	8.33818i	0.431735	+	0.431735i	−0.457483	+	0.889218i	$0.651249\pi$
$374$	13.6233	−	8.71736i	0.704446	−	0.450764i
$375$		0			0
$376$	18.1906	+	13.7857i	0.938110	+	0.710941i
$377$	1.16861			0.0601863
$378$		0			0
$379$	9.86499	−	9.86499i	0.506731	−	0.506731i	−0.406791	−	0.913521i	$-0.633352\pi$
$379$	9.86499	−	9.86499i	0.506731	−	0.506731i	0.913521	+	0.406791i	$0.133352\pi$
$380$	−6.03873	−	2.78657i	−0.309780	−	0.142948i
$381$		0			0
$382$	−8.42394	−	1.84988i	−0.431006	−	0.0946483i
$383$	24.8050			1.26748			0.633738	−	0.773548i	$-0.281520\pi$
$383$	24.8050			1.26748			0.633738	+	0.773548i	$0.281520\pi$
$384$		0			0
$385$	16.2736			0.829380
$386$	−8.87407	−	1.94873i	−0.451679	−	0.0991880i
$387$		0			0
$388$	−5.11122	−	2.35857i	−0.259483	−	0.119738i
$389$	18.5481	−	18.5481i	0.940428	−	0.940428i	−0.0578943	−	0.998323i	$-0.518439\pi$
$389$	18.5481	−	18.5481i	0.940428	−	0.940428i	0.998323	+	0.0578943i	$0.0184386\pi$
$390$		0			0
$391$	5.25380			0.265696
$392$	11.7561	+	8.90926i	0.593771	+	0.449985i
$393$		0			0
$394$	0.513962	−	0.328876i	0.0258930	−	0.0165685i
$395$	12.3071	+	12.3071i	0.619240	+	0.619240i
$396$		0			0
$397$	9.27587	−	9.27587i	0.465542	−	0.465542i	−0.434924	−	0.900467i	$-0.643225\pi$
$397$	9.27587	−	9.27587i	0.465542	−	0.465542i	0.900467	+	0.434924i	$0.143225\pi$
$398$	12.7977	+	2.81037i	0.641493	+	0.140871i
$399$		0			0
$400$	−3.42670	+	2.92235i	−0.171335	+	0.146117i
$401$			32.5487i			1.62540i	0.582680	+	0.812702i	$0.302004\pi$
$401$			32.5487i			1.62540i	−0.582680	+	0.812702i	$0.697996\pi$
$402$		0			0
$403$	−11.5658	−	11.5658i	−0.576135	−	0.576135i
$404$	24.3672	−	8.97939i	1.21231	−	0.446741i
$405$		0			0
$406$	0.699408	+	1.09302i	0.0347110	+	0.0542459i
$407$			61.2387i			3.03549i
$408$		0			0
$409$		−	14.8204i		−	0.732819i	−0.930454	−	0.366410i	$-0.880587\pi$
$409$		−	14.8204i		−	0.732819i	0.930454	−	0.366410i	$-0.119413\pi$
$410$	−22.4698	+	14.3781i	−1.10970	+	0.710082i
$411$		0			0
$412$	2.40990	+	1.11205i	0.118727	+	0.0547866i
$413$	0.975434	+	0.975434i	0.0479980	+	0.0479980i
$414$		0			0
$415$			18.8026i			0.922982i
$416$	−9.20814	−	2.80246i	−0.451466	−	0.137402i
$417$		0			0
$418$	3.17147	−	14.4421i	0.155122	−	0.706387i
$419$	0.857617	−	0.857617i	0.0418973	−	0.0418973i	−0.685848	−	0.727745i	$-0.740568\pi$
$419$	0.857617	−	0.857617i	0.0418973	−	0.0418973i	0.727745	+	0.685848i	$0.240568\pi$
$420$		0			0
$421$	−23.1613	−	23.1613i	−1.12881	−	1.12881i	−0.990370	−	0.138445i	$-0.955790\pi$
$421$	−23.1613	−	23.1613i	−1.12881	−	1.12881i	−0.138445	−	0.990370i	$-0.544210\pi$
$422$	1.46151	+	2.28403i	0.0711454	+	0.111185i
$423$		0			0
$424$	12.8954	−	1.77643i	0.626254	−	0.0862711i
$425$	2.08065			0.100926
$426$		0			0
$427$	−9.79250	+	9.79250i	−0.473892	+	0.473892i
$428$	8.17288	+	22.1785i	0.395051	+	1.07204i
$429$		0			0
$430$	−4.88965	+	22.2663i	−0.235800	+	1.07378i
$431$	2.42928			0.117014			0.0585072	−	0.998287i	$-0.481366\pi$
$431$	2.42928			0.117014			0.0585072	+	0.998287i	$0.481366\pi$
$432$		0			0
$433$	8.16178			0.392230			0.196115	−	0.980581i	$-0.437167\pi$
$433$	8.16178			0.392230			0.196115	+	0.980581i	$0.437167\pi$
$434$	3.89566	−	17.7399i	0.186998	−	0.851543i
$435$		0			0
$436$	26.0697	−	9.60680i	1.24851	−	0.460082i
$437$	3.39631	−	3.39631i	0.162468	−	0.162468i
$438$		0			0
$439$	2.09986			0.100221			0.0501104	−	0.998744i	$-0.484043\pi$
$439$	2.09986			0.100221			0.0501104	+	0.998744i	$0.484043\pi$
$440$	27.4585	+	20.8093i	1.30903	+	0.992043i
$441$		0			0
$442$	2.39676	+	3.74561i	0.114002	+	0.178161i
$443$	−7.58622	−	7.58622i	−0.360432	−	0.360432i	0.503540	−	0.863972i	$-0.332031\pi$
$443$	−7.58622	−	7.58622i	−0.360432	−	0.360432i	−0.863972	+	0.503540i	$0.832031\pi$
$444$		0			0
$445$	18.6470	−	18.6470i	0.883954	−	0.883954i
$446$	−0.360839	+	1.64317i	−0.0170862	+	0.0778066i
$447$		0			0
$448$	−2.88985	−	10.2899i	−0.136532	−	0.486150i
$449$		−	1.07314i		−	0.0506445i	−0.999679	−	0.0253223i	$-0.991939\pi$
$449$		−	1.07314i		−	0.0506445i	0.999679	−	0.0253223i	$-0.00806119\pi$
$450$		0			0
$451$	−41.9375	−	41.9375i	−1.97476	−	1.97476i
$452$	−10.7426	+	23.2801i	−0.505289	+	1.09500i
$453$		0			0
$454$	−21.4318	+	13.7139i	−1.00585	+	0.643624i
$455$			4.47428i			0.209757i
$456$		0			0
$457$		−	22.2121i		−	1.03904i	−0.854459	−	0.519519i	$-0.826111\pi$
$457$		−	22.2121i		−	1.03904i	0.854459	−	0.519519i	$-0.173889\pi$
$458$	13.5459	+	21.1693i	0.632958	+	0.989176i
$459$		0			0
$460$	3.86974	+	10.5012i	0.180427	+	0.489621i
$461$	0.113003	+	0.113003i	0.00526308	+	0.00526308i	0.709733	−	0.704470i	$-0.248815\pi$
$461$	0.113003	+	0.113003i	0.00526308	+	0.00526308i	−0.704470	+	0.709733i	$0.748815\pi$
$462$		0			0
$463$		−	21.8420i		−	1.01509i	−0.861627	−	0.507543i	$-0.830554\pi$
$463$		−	21.8420i		−	1.01509i	0.861627	−	0.507543i	$-0.169446\pi$
$464$	−0.217550	+	2.73860i	−0.0100995	+	0.127136i
$465$		0			0
$466$	−23.8015	−	5.22677i	−1.10258	−	0.242126i
$467$	16.6910	−	16.6910i	0.772366	−	0.772366i	−0.206154	−	0.978520i	$-0.566095\pi$
$467$	16.6910	−	16.6910i	0.772366	−	0.772366i	0.978520	+	0.206154i	$0.0660947\pi$
$468$		0			0
$469$	−9.86893	−	9.86893i	−0.455705	−	0.455705i
$470$	18.9202	−	12.1067i	0.872724	−	0.558442i
$471$		0			0
$472$	0.398553	+	2.89315i	0.0183449	+	0.133168i
$473$	−50.6838			−2.33044
$474$		0			0
$475$	1.34504	−	1.34504i	0.0617144	−	0.0617144i
$476$	−2.06890	+	4.48348i	−0.0948280	+	0.205500i
$477$		0			0
$478$	−24.3408	−	5.34520i	−1.11332	−	0.244484i
$479$	38.9267			1.77861			0.889304	−	0.457317i	$-0.151189\pi$
$479$	38.9267			1.77861			0.889304	+	0.457317i	$0.151189\pi$
$480$		0			0
$481$	−16.8370			−0.767702
$482$	6.28851	+	1.38095i	0.286434	+	0.0629005i
$483$		0			0
$484$	−22.8762	+	49.5745i	−1.03983	+	2.25339i
$485$	−3.91728	+	3.91728i	−0.177874	+	0.177874i
$486$		0			0
$487$	−34.6434			−1.56984			−0.784921	−	0.619595i	$-0.787297\pi$
$487$	−34.6434			−1.56984			−0.784921	+	0.619595i	$0.787297\pi$
$488$	−29.0447	+	4.00112i	−1.31479	+	0.181122i
$489$		0			0
$490$	12.2276	−	7.82422i	0.552385	−	0.353462i
$491$	−25.0776	−	25.0776i	−1.13174	−	1.13174i	−0.989888	−	0.141848i	$-0.954696\pi$
$491$	−25.0776	−	25.0776i	−1.13174	−	1.13174i	−0.141848	−	0.989888i	$-0.545304\pi$
$492$		0			0
$493$	0.897470	−	0.897470i	0.0404200	−	0.0404200i
$494$	3.97073	+	0.871966i	0.178651	+	0.0392316i
$495$		0			0
$496$	29.2574	−	24.9512i	1.31370	−	1.12034i
$497$			5.88816i			0.264120i
$498$		0			0
$499$	0.744492	+	0.744492i	0.0333280	+	0.0333280i	0.723574	−	0.690246i	$-0.242498\pi$
$499$	0.744492	+	0.744492i	0.0333280	+	0.0333280i	−0.690246	+	0.723574i	$0.742498\pi$
$500$	8.33830	+	22.6274i	0.372900	+	1.01193i
$501$		0			0
$502$	−14.6647	−	22.9177i	−0.654517	−	1.02287i
$503$		−	25.4114i		−	1.13304i	−0.824049	−	0.566518i	$-0.808290\pi$
$503$		−	25.4114i		−	1.13304i	0.824049	−	0.566518i	$-0.191710\pi$
$504$		0			0
$505$		−	25.5570i		−	1.13727i
$506$	−20.9584	+	13.4109i	−0.931714	+	0.596188i
$507$		0			0
$508$	−1.17903	+	2.55506i	−0.0523110	+	0.113362i
$509$	−6.08160	−	6.08160i	−0.269562	−	0.269562i	0.559362	−	0.828924i	$-0.311046\pi$
$509$	−6.08160	−	6.08160i	−0.269562	−	0.269562i	−0.828924	+	0.559362i	$0.811046\pi$
$510$		0			0
$511$		−	0.515530i		−	0.0228057i
$512$	8.28171	−	21.0574i	0.366003	−	0.930614i
$513$		0			0
$514$	−6.38131	+	29.0590i	−0.281468	+	1.28174i
$515$	1.84696	−	1.84696i	0.0813869	−	0.0813869i
$516$		0			0
$517$	35.3126	+	35.3126i	1.55305	+	1.55305i
$518$	−10.0769	−	15.7481i	−0.442755	−	0.691930i
$519$		0			0
$520$	−5.72131	+	7.54946i	−0.250896	+	0.331066i
$521$	2.71599			0.118990			0.0594949	−	0.998229i	$-0.481051\pi$
$521$	2.71599			0.118990			0.0594949	+	0.998229i	$0.481051\pi$
$522$		0			0
$523$	3.25885	−	3.25885i	0.142500	−	0.142500i	−0.632258	−	0.774758i	$-0.717872\pi$
$523$	3.25885	−	3.25885i	0.142500	−	0.142500i	0.774758	+	0.632258i	$0.217872\pi$
$524$	−1.31272	+	0.483742i	−0.0573464	+	0.0211324i
$525$		0			0
$526$	−1.62388	+	7.39475i	−0.0708044	+	0.322426i
$527$	−17.7647			−0.773844
$528$		0			0
$529$	14.9175			0.648585
$530$	2.74773	−	12.5125i	0.119354	−	0.543508i
$531$		0			0
$532$	1.56090	+	4.23578i	0.0676737	+	0.183644i
$533$	11.5303	−	11.5303i	0.499434	−	0.499434i
$534$		0			0
$535$	23.2615			1.00568
$536$	−4.03235	−	29.2714i	−0.174171	−	1.26433i
$537$		0			0
$538$	19.6516	+	30.7112i	0.847240	+	1.32405i
$539$	22.8215	+	22.8215i	0.982990	+	0.982990i
$540$		0			0
$541$	−25.1883	+	25.1883i	−1.08293	+	1.08293i	−0.0866938	+	0.996235i	$0.527630\pi$
$541$	−25.1883	+	25.1883i	−1.08293	+	1.08293i	−0.996235	+	0.0866938i	$0.972370\pi$
$542$	1.91859	−	8.73679i	0.0824104	−	0.375277i
$543$		0			0
$544$	−9.22395	+	4.91946i	−0.395473	+	0.210920i
$545$		−	27.3427i		−	1.17123i
$546$		0			0
$547$	−13.9678	−	13.9678i	−0.597220	−	0.597220i	0.342352	−	0.939572i	$-0.388776\pi$
$547$	−13.9678	−	13.9678i	−0.597220	−	0.597220i	−0.939572	+	0.342352i	$0.888776\pi$
$548$	−23.4545	−	10.8231i	−1.00193	−	0.462340i
$549$		0			0
$550$	−8.30010	+	5.31110i	−0.353918	+	0.226466i
$551$		−	1.16034i		−	0.0494320i
$552$		0			0
$553$		−	11.8139i		−	0.502376i
$554$	4.85505	+	7.58739i	0.206271	+	0.322357i
$555$		0			0
$556$	40.2972	−	14.8497i	1.70898	−	0.629766i
$557$	−24.4470	−	24.4470i	−1.03585	−	1.03585i	−0.999333	−	0.0365217i	$-0.988372\pi$
$557$	−24.4470	−	24.4470i	−1.03585	−	1.03585i	−0.0365217	−	0.999333i	$-0.511628\pi$
$558$		0			0
$559$		−	13.9350i		−	0.589389i
$560$	−10.4854	−	0.832939i	−0.443088	−	0.0351981i
$561$		0			0
$562$	28.5098	+	6.26070i	1.20261	+	0.264092i
$563$	−1.69941	+	1.69941i	−0.0716217	+	0.0716217i	−0.742010	−	0.670389i	$-0.766127\pi$
$563$	−1.69941	+	1.69941i	−0.0716217	+	0.0716217i	0.670389	+	0.742010i	$0.266127\pi$
$564$		0			0
$565$	17.8420	+	17.8420i	0.750618	+	0.750618i
$566$	−28.4513	+	18.2056i	−1.19590	+	0.765237i
$567$		0			0
$568$	−7.52927	+	9.93511i	−0.315921	+	0.416868i
$569$	−2.63311			−0.110386			−0.0551929	−	0.998476i	$-0.517577\pi$
$569$	−2.63311			−0.110386			−0.0551929	+	0.998476i	$0.517577\pi$
$570$		0			0
$571$	−7.58069	+	7.58069i	−0.317242	+	0.317242i	−0.847707	−	0.530465i	$-0.822017\pi$
$571$	−7.58069	+	7.58069i	−0.317242	+	0.317242i	0.530465	+	0.847707i	$0.322017\pi$
$572$	−19.1222	−	8.82394i	−0.799539	−	0.368948i
$573$		0			0
$574$	17.6855	+	3.88370i	0.738177	+	0.162103i
$575$	−3.20091			−0.133487
$576$		0			0
$577$	−23.4358			−0.975643			−0.487822	−	0.872943i	$-0.662208\pi$
$577$	−23.4358			−0.975643			−0.487822	+	0.872943i	$0.662208\pi$
$578$	−18.7649	−	4.12074i	−0.780515	−	0.171400i
$579$		0			0
$580$	2.45489	+	1.13281i	0.101934	+	0.0470373i
$581$	9.02447	−	9.02447i	0.374398	−	0.374398i
$582$		0			0
$583$	28.4816			1.17959
$584$	0.659214	−	0.869855i	0.0272785	−	0.0359948i
$585$		0			0
$586$	16.8673	−	10.7931i	0.696782	−	0.445860i
$587$	12.5335	+	12.5335i	0.517313	+	0.517313i	0.916757	−	0.399445i	$-0.130797\pi$
$587$	12.5335	+	12.5335i	0.517313	+	0.517313i	−0.399445	+	0.916757i	$0.630797\pi$
$588$		0			0
$589$	−11.4840	+	11.4840i	−0.473190	+	0.473190i
$590$	2.80726	+	0.616470i	0.115573	+	0.0253796i
$591$		0			0
$592$	3.13441	−	39.4572i	0.128823	−	1.62168i
$593$		−	0.818182i		−	0.0335987i	−0.999859	−	0.0167994i	$-0.994652\pi$
$593$		−	0.818182i		−	0.0335987i	0.999859	−	0.0167994i	$-0.00534765\pi$
$594$		0			0
$595$	3.43617	+	3.43617i	0.140869	+	0.140869i
$596$	25.9738	−	9.57144i	1.06393	−	0.392061i
$597$		0			0
$598$	−3.68721	−	5.76231i	−0.150781	−	0.235638i
$599$		−	26.8601i		−	1.09747i	−0.835995	−	0.548737i	$-0.815109\pi$
$599$		−	26.8601i		−	1.09747i	0.835995	−	0.548737i	$-0.184891\pi$
$600$		0			0
$601$			13.9878i			0.570573i	0.958442	+	0.285286i	$0.0920887\pi$
$601$			13.9878i			0.570573i	−0.958442	+	0.285286i	$0.907911\pi$
$602$	13.0337	−	8.34008i	0.531216	−	0.339916i
$603$		0			0
$604$	−34.3589	−	15.8549i	−1.39804	−	0.645128i
$605$	37.9943	+	37.9943i	1.54469	+	1.54469i
$606$		0			0
$607$			12.5530i			0.509512i	0.967005	+	0.254756i	$0.0819952\pi$
$607$			12.5530i			0.509512i	−0.967005	+	0.254756i	$0.918005\pi$
$608$	−2.78263	+	9.14299i	−0.112851	+	0.370797i
$609$		0			0
$610$	−6.18881	+	28.1824i	−0.250578	+	1.14107i
$611$	−9.70886	+	9.70886i	−0.392778	+	0.392778i
$612$		0			0
$613$	1.35533	+	1.35533i	0.0547411	+	0.0547411i	0.733947	−	0.679206i	$-0.237676\pi$
$613$	1.35533	+	1.35533i	0.0547411	+	0.0547411i	−0.679206	+	0.733947i	$0.737676\pi$
$614$	−14.1016	−	22.0377i	−0.569093	−	0.889369i
$615$		0			0
$616$	−3.19136	−	23.1665i	−0.128584	−	0.933407i
$617$	3.03958			0.122369			0.0611845	−	0.998126i	$-0.480512\pi$
$617$	3.03958			0.122369			0.0611845	+	0.998126i	$0.480512\pi$
$618$		0			0
$619$	−12.8492	+	12.8492i	−0.516453	+	0.516453i	−0.916496	−	0.400043i	$-0.868995\pi$
$619$	−12.8492	+	12.8492i	−0.516453	+	0.516453i	0.400043	+	0.916496i	$0.368995\pi$
$620$	−13.0848	−	35.5078i	−0.525497	−	1.42603i
$621$		0			0
$622$	0.841605	−	3.83247i	0.0337453	−	0.153668i
$623$	−17.8996			−0.717133
$624$		0			0
$625$	18.1029			0.724114
$626$	−1.18494	+	5.39595i	−0.0473599	+	0.215666i
$627$		0			0
$628$	−32.7317	+	12.0617i	−1.30614	+	0.481316i
$629$	−12.9306	+	12.9306i	−0.515575	+	0.515575i
$630$		0			0
$631$	43.7376			1.74117			0.870583	−	0.492022i	$-0.163742\pi$
$631$	43.7376			1.74117			0.870583	+	0.492022i	$0.163742\pi$
$632$	15.1065	−	19.9335i	0.600905	−	0.792914i
$633$		0			0
$634$	−5.38606	−	8.41725i	−0.213908	−	0.334292i
$635$	1.95821	+	1.95821i	0.0777093	+	0.0777093i
$636$		0			0
$637$	−6.27454	+	6.27454i	−0.248606	+	0.248606i
$638$	−1.28928	+	5.87107i	−0.0510430	+	0.232438i
$639$		0			0
$640$	−16.6269	−	14.8132i	−0.657236	−	0.585543i
$641$			17.4093i			0.687628i	0.939038	+	0.343814i	$0.111719\pi$
$641$			17.4093i			0.687628i	−0.939038	+	0.343814i	$0.888281\pi$
$642$		0			0
$643$	−4.85280	−	4.85280i	−0.191376	−	0.191376i	0.604915	−	0.796290i	$-0.293207\pi$
$643$	−4.85280	−	4.85280i	−0.191376	−	0.191376i	−0.796290	+	0.604915i	$0.793207\pi$
$644$	3.18283	−	6.89746i	0.125421	−	0.271798i
$645$		0			0
$646$	3.71911	−	2.37980i	0.146326	−	0.0936319i
$647$		−	19.3043i		−	0.758930i	−0.925206	−	0.379465i	$-0.876108\pi$
$647$		−	19.3043i		−	0.758930i	0.925206	−	0.379465i	$-0.123892\pi$
$648$		0			0
$649$			6.39002i			0.250830i
$650$	−1.46024	−	2.28204i	−0.0572752	−	0.0895088i
$651$		0			0
$652$	13.3189	+	36.1433i	0.521610	+	1.41548i
$653$	−22.7421	−	22.7421i	−0.889968	−	0.889968i	0.104552	−	0.994519i	$-0.466659\pi$
$653$	−22.7421	−	22.7421i	−0.889968	−	0.889968i	−0.994519	+	0.104552i	$0.966659\pi$
$654$		0			0
$655$			1.37682i			0.0537969i
$656$	24.8746	+	29.1676i	0.971189	+	1.13880i
$657$		0			0
$658$	−14.8917	−	3.27019i	−0.580537	−	0.127485i
$659$	−1.27511	+	1.27511i	−0.0496711	+	0.0496711i	−0.731506	−	0.681835i	$-0.761182\pi$
$659$	−1.27511	+	1.27511i	−0.0496711	+	0.0496711i	0.681835	+	0.731506i	$0.261182\pi$
$660$		0			0
$661$	−15.1257	−	15.1257i	−0.588323	−	0.588323i	0.348854	−	0.937177i	$-0.386571\pi$
$661$	−15.1257	−	15.1257i	−0.588323	−	0.588323i	−0.937177	+	0.348854i	$0.886571\pi$
$662$	5.36109	−	3.43047i	0.208365	−	0.133329i
$663$		0			0
$664$	26.7667	−	3.68731i	1.03875	−	0.143095i
$665$	4.44262			0.172277
$666$		0			0
$667$	−1.38068	+	1.38068i	−0.0534603	+	0.0534603i
$668$	−5.25619	+	11.3906i	−0.203368	+	0.440715i
$669$		0			0
$670$	−28.4023	−	6.23712i	−1.09728	−	0.240961i
$671$	−64.1502			−2.47649
$672$		0			0
$673$	19.7749			0.762265			0.381133	−	0.924520i	$-0.375534\pi$
$673$	19.7749			0.762265			0.381133	+	0.924520i	$0.375534\pi$
$674$	46.7791	+	10.2726i	1.80186	+	0.395687i
$675$		0			0
$676$	−8.46773	+	18.3503i	−0.325682	+	0.705780i
$677$	14.8386	−	14.8386i	0.570295	−	0.570295i	−0.361916	−	0.932211i	$-0.617877\pi$
$677$	14.8386	−	14.8386i	0.570295	−	0.570295i	0.932211	+	0.361916i	$0.117877\pi$
$678$		0			0
$679$	3.76026			0.144306
$680$	1.40399	+	10.1917i	0.0538404	+	0.390835i
$681$		0			0
$682$	70.8668	−	45.3465i	2.71363	−	1.73641i
$683$	5.57200	+	5.57200i	0.213207	+	0.213207i	0.805628	−	0.592422i	$-0.201828\pi$
$683$	5.57200	+	5.57200i	0.213207	+	0.213207i	−0.592422	+	0.805628i	$0.701828\pi$
$684$		0			0
$685$	−17.9757	+	17.9757i	−0.686816	+	0.686816i
$686$	−22.5419	−	4.95017i	−0.860653	−	0.188998i
$687$		0			0
$688$	32.6564	+	2.59417i	1.24501	+	0.0989017i
$689$			7.83075i			0.298328i
$690$		0			0
$691$	21.1504	+	21.1504i	0.804598	+	0.804598i	0.983810	−	0.179212i	$-0.0573549\pi$
$691$	21.1504	+	21.1504i	0.804598	+	0.804598i	−0.179212	+	0.983810i	$0.557355\pi$
$692$	−8.09920	−	21.9786i	−0.307885	−	0.835502i
$693$		0			0
$694$	−1.06464	−	1.66380i	−0.0404132	−	0.0631571i
$695$		−	42.2649i		−	1.60320i
$696$		0			0
$697$		−	17.7102i		−	0.670822i
$698$	30.0572	−	19.2331i	1.13768	−	0.727984i
$699$		0			0
$700$	1.26049	−	2.73159i	0.0476421	−	0.103244i
$701$	16.7025	+	16.7025i	0.630846	+	0.630846i	0.948280	−	0.317434i	$-0.102821\pi$
$701$	16.7025	+	16.7025i	0.630846	+	0.630846i	−0.317434	+	0.948280i	$0.602821\pi$
$702$		0			0
$703$			16.7179i			0.630527i
$704$	24.2385	−	43.1698i	0.913525	−	1.62702i
$705$		0			0
$706$	3.13709	−	14.2856i	0.118066	−	0.537644i
$707$	−12.2663	+	12.2663i	−0.461322	+	0.461322i
$708$		0			0
$709$	15.2575	+	15.2575i	0.573009	+	0.573009i	0.932968	−	0.359959i	$-0.117209\pi$
$709$	15.2575	+	15.2575i	0.573009	+	0.573009i	−0.359959	+	0.932968i	$0.617209\pi$
$710$	6.61229	+	10.3336i	0.248155	+	0.387812i
$711$		0			0
$712$	−30.2021	−	22.8885i	−1.13187	−	0.857781i
$713$	27.3296			1.02350
$714$		0			0
$715$	−14.6554	+	14.6554i	−0.548080	+	0.548080i
$716$	−5.92929	+	2.18497i	−0.221588	+	0.0816560i
$717$		0			0
$718$	−2.88615	+	13.1428i	−0.107710	+	0.490487i
$719$	−16.7129			−0.623287			−0.311643	−	0.950199i	$-0.600879\pi$
$719$	−16.7129			−0.623287			−0.311643	+	0.950199i	$0.600879\pi$
$720$		0			0
$721$	−1.77293			−0.0660274
$722$	−4.89750	+	22.3021i	−0.182266	+	0.829997i
$723$		0			0
$724$	7.43705	+	20.1818i	0.276396	+	0.750049i
$725$	−0.546789	+	0.546789i	−0.0203072	+	0.0203072i
$726$		0			0
$727$	24.4451			0.906619			0.453309	−	0.891353i	$-0.350243\pi$
$727$	24.4451			0.906619			0.453309	+	0.891353i	$0.350243\pi$
$728$	6.36942	−	0.877435i	0.236067	−	0.0325199i
$729$		0			0
$730$	−0.578930	−	0.904742i	−0.0214271	−	0.0334860i
$731$	−10.7019	−	10.7019i	−0.395823	−	0.395823i
$732$		0			0
$733$	−7.43009	+	7.43009i	−0.274437	+	0.274437i	−0.830883	−	0.556447i	$-0.812164\pi$
$733$	−7.43009	+	7.43009i	−0.274437	+	0.274437i	0.556447	+	0.830883i	$0.312164\pi$
$734$	−4.82343	+	21.9647i	−0.178036	+	0.810733i
$735$		0			0
$736$	14.1903	−	7.56818i	0.523060	−	0.278967i
$737$		−	64.6509i		−	2.38145i
$738$		0			0
$739$	−8.91352	−	8.91352i	−0.327889	−	0.327889i	0.523894	−	0.851783i	$-0.324479\pi$
$739$	−8.91352	−	8.91352i	−0.327889	−	0.327889i	−0.851783	+	0.523894i	$0.824479\pi$
$740$	−35.3695	−	16.3213i	−1.30021	−	0.599981i
$741$		0			0
$742$	−7.32428	+	4.68669i	−0.268883	+	0.172054i
$743$			40.2146i			1.47533i	0.675167	+	0.737665i	$0.264072\pi$
$743$			40.2146i			1.47533i	−0.675167	+	0.737665i	$0.735928\pi$
$744$		0			0
$745$		−	27.2421i		−	0.998073i
$746$	−8.98830	−	14.0468i	−0.329085	−	0.514289i
$747$		0			0
$748$	−21.4622	+	7.90889i	−0.784735	+	0.289178i
$749$	−11.1646	−	11.1646i	−0.407945	−	0.407945i
$750$		0			0
$751$			46.3705i			1.69209i	0.533115	+	0.846043i	$0.321021\pi$
$751$			46.3705i			1.69209i	−0.533115	+	0.846043i	$0.678979\pi$
$752$	−20.9451	−	24.5599i	−0.763789	−	0.895609i
$753$		0			0
$754$	−1.61420	−	0.354475i	−0.0587855	−	0.0129092i
$755$	−26.3329	+	26.3329i	−0.958353	+	0.958353i
$756$		0			0
$757$	16.1930	+	16.1930i	0.588546	+	0.588546i	0.937237	−	0.348692i	$-0.113374\pi$
$757$	16.1930	+	16.1930i	0.588546	+	0.588546i	−0.348692	+	0.937237i	$0.613374\pi$
$758$	−16.6189	+	10.6341i	−0.603625	+	0.386250i
$759$		0			0
$760$	7.49604	+	5.68083i	0.271910	+	0.206065i
$761$	10.8371			0.392843			0.196422	−	0.980520i	$-0.437068\pi$
$761$	10.8371			0.392843			0.196422	+	0.980520i	$0.437068\pi$
$762$		0			0
$763$	−13.1234	+	13.1234i	−0.475099	+	0.475099i
$764$	11.0749	+	5.11049i	0.400674	+	0.184891i
$765$		0			0
$766$	−34.2632	−	7.52414i	−1.23798	−	0.271858i
$767$	−1.75688			−0.0634371
$768$		0			0
$769$	30.0426			1.08336			0.541681	−	0.840584i	$-0.317788\pi$
$769$	30.0426			1.08336			0.541681	+	0.840584i	$0.317788\pi$
$770$	−22.4787	−	4.93630i	−0.810078	−	0.177892i
$771$		0			0
$772$	11.6666	+	5.38358i	0.419892	+	0.193759i
$773$	7.38305	−	7.38305i	0.265550	−	0.265550i	−0.561754	−	0.827304i	$-0.689873\pi$
$773$	7.38305	−	7.38305i	0.265550	−	0.265550i	0.827304	+	0.561754i	$0.189873\pi$
$774$		0			0
$775$	10.8233			0.388783
$776$	6.34470	+	4.80830i	0.227762	+	0.172608i
$777$		0			0
$778$	−31.2468	+	19.9943i	−1.12025	+	0.716831i
$779$	−11.4487	−	11.4487i	−0.410194	−	0.410194i
$780$		0			0
$781$	−19.2865	+	19.2865i	−0.690127	+	0.690127i
$782$	−7.25708	−	1.59364i	−0.259513	−	0.0569886i
$783$		0			0
$784$	−13.5362	−	15.8723i	−0.483435	−	0.566869i
$785$			34.3300i			1.22529i
$786$		0			0
$787$	−19.8336	−	19.8336i	−0.706990	−	0.706990i	0.258911	−	0.965901i	$-0.416636\pi$
$787$	−19.8336	−	19.8336i	−0.706990	−	0.706990i	−0.965901	+	0.258911i	$0.916636\pi$
$788$	−0.809694	+	0.298375i	−0.0288442	+	0.0106292i
$789$		0			0
$790$	−13.2667	−	20.7330i	−0.472009	−	0.737648i
$791$		−	17.1269i		−	0.608961i
$792$		0			0
$793$		−	17.6375i		−	0.626326i
$794$	−15.6264	+	9.99909i	−0.554561	+	0.354855i
$795$		0			0
$796$	−16.8251	−	7.76392i	−0.596348	−	0.275185i
$797$	12.3065	+	12.3065i	0.435918	+	0.435918i	0.890636	−	0.454718i	$-0.150260\pi$
$797$	12.3065	+	12.3065i	0.435918	+	0.435918i	−0.454718	+	0.890636i	$0.650260\pi$
$798$		0			0
$799$			14.9125i			0.527566i
$800$	5.61974	−	2.99721i	0.198688	−	0.105967i
$801$		0			0
$802$	9.87304	−	44.9595i	0.348629	−	1.58757i
$803$	1.68861	−	1.68861i	0.0595896	−	0.0595896i
$804$		0			0
$805$	−5.28626	−	5.28626i	−0.186316	−	0.186316i
$806$	12.4676	+	19.4842i	0.439152	+	0.686300i
$807$		0			0
$808$	−36.3821	+	5.01190i	−1.27992	+	0.176318i
$809$	38.4080			1.35035			0.675176	−	0.737657i	$-0.264068\pi$
$809$	38.4080			1.35035			0.675176	+	0.737657i	$0.264068\pi$
$810$		0			0
$811$	−35.1507	+	35.1507i	−1.23431	+	1.23431i	−0.272013	+	0.962294i	$0.587689\pi$
$811$	−35.1507	+	35.1507i	−1.23431	+	1.23431i	−0.962294	+	0.272013i	$0.912311\pi$
$812$	−0.634544	−	1.72195i	−0.0222681	−	0.0604285i
$813$		0			0
$814$	18.5757	−	84.5891i	0.651076	−	2.96485i
$815$	37.9082			1.32787
$816$		0			0
$817$	−13.8364			−0.484075
$818$	−4.49548	+	20.4714i	−0.157181	+	0.715764i
$819$		0			0
$820$	35.3989	−	13.0446i	1.23618	−	0.455538i
$821$	0.263864	−	0.263864i	0.00920890	−	0.00920890i	−0.702487	−	0.711696i	$-0.747927\pi$
$821$	0.263864	−	0.263864i	0.00920890	−	0.00920890i	0.711696	+	0.702487i	$0.247927\pi$
$822$		0			0
$823$	6.00341			0.209266			0.104633	−	0.994511i	$-0.466633\pi$
$823$	6.00341			0.209266			0.104633	+	0.994511i	$0.466633\pi$
$824$	−2.99147	−	2.26707i	−0.104213	−	0.0789771i
$825$		0			0
$826$	−1.05149	−	1.64325i	−0.0365859	−	0.0571759i
$827$	−5.50493	−	5.50493i	−0.191425	−	0.191425i	0.604887	−	0.796312i	$-0.293218\pi$
$827$	−5.50493	−	5.50493i	−0.191425	−	0.191425i	−0.796312	+	0.604887i	$0.793218\pi$
$828$		0			0
$829$	−13.2457	+	13.2457i	−0.460041	+	0.460041i	−0.898669	−	0.438628i	$-0.855465\pi$
$829$	−13.2457	+	13.2457i	−0.460041	+	0.460041i	0.438628	+	0.898669i	$0.355465\pi$
$830$	5.70342	−	25.9720i	0.197969	−	0.901502i
$831$		0			0
$832$	11.8691	+	6.66416i	0.411488	+	0.231038i
$833$			9.63749i			0.333919i
$834$		0			0
$835$	8.72982	+	8.72982i	0.302108	+	0.302108i
$836$	−8.76151	+	18.9869i	−0.303023	+	0.656676i
$837$		0			0
$838$	−1.44477	+	0.924484i	−0.0499087	+	0.0319358i
$839$			25.5283i			0.881334i	0.897671	+	0.440667i	$0.145258\pi$
$839$			25.5283i			0.881334i	−0.897671	+	0.440667i	$0.854742\pi$
$840$		0			0
$841$		−	28.5283i		−	0.983734i
$842$	24.9672	+	39.0183i	0.860426	+	1.34466i
$843$		0			0
$844$	−1.32597	−	3.59826i	−0.0456418	−	0.123857i
$845$	14.0638	+	14.0638i	0.483809	+	0.483809i
$846$		0			0
$847$		−	36.4714i		−	1.25317i
$848$	−18.3512	−	1.45779i	−0.630183	−	0.0500606i
$849$		0			0
$850$	−2.87400	−	0.631127i	−0.0985775	−	0.0216475i
$851$	19.8926	−	19.8926i	0.681909	−	0.681909i
$852$		0			0
$853$	13.7071	+	13.7071i	0.469321	+	0.469321i	0.901695	−	0.432373i	$-0.142324\pi$
$853$	13.7071	+	13.7071i	0.469321	+	0.469321i	−0.432373	+	0.901695i	$0.642324\pi$
$854$	16.4967	−	10.5560i	0.564507	−	0.361219i
$855$		0			0
$856$	−4.56174	−	33.1143i	−0.155917	−	1.13182i
$857$	−16.8324			−0.574982			−0.287491	−	0.957783i	$-0.592821\pi$
$857$	−16.8324			−0.574982			−0.287491	+	0.957783i	$0.592821\pi$
$858$		0			0
$859$	−9.49208	+	9.49208i	−0.323866	+	0.323866i	−0.850248	−	0.526382i	$-0.823548\pi$
$859$	−9.49208	+	9.49208i	−0.323866	+	0.323866i	0.526382	+	0.850248i	$0.323548\pi$
$860$	13.5082	−	29.2733i	0.460624	−	0.998210i
$861$		0			0
$862$	−3.35557	−	0.736878i	−0.114291	−	0.0250982i
$863$	−51.2834			−1.74571			−0.872853	−	0.487982i	$-0.837733\pi$
$863$	−51.2834			−1.74571			−0.872853	+	0.487982i	$0.837733\pi$
$864$		0			0
$865$	−23.0518			−0.783786
$866$	−11.2739	−	2.47573i	−0.383101	−	0.0841286i
$867$		0			0
$868$	−10.7621	+	23.3225i	−0.365291	+	0.791616i
$869$	38.6960	−	38.6960i	1.31267	−	1.31267i
$870$		0			0
$871$	17.7752			0.602288
$872$	−38.9242	+	5.36209i	−1.31814	+	0.181583i
$873$		0			0
$874$	−5.72154	+	3.66112i	−0.193534	+	0.123839i
$875$	−11.3906	−	11.3906i	−0.385071	−	0.385071i
$876$		0			0
$877$	−9.23767	+	9.23767i	−0.311934	+	0.311934i	−0.845658	−	0.533724i	$-0.820792\pi$
$877$	−9.23767	+	9.23767i	−0.311934	+	0.311934i	0.533724	+	0.845658i	$0.320792\pi$
$878$	−2.90054	−	0.636954i	−0.0978884	−	0.0214962i
$879$		0			0
$880$	−31.6163	−	37.0729i	−1.06579	−	1.24973i
$881$			44.2215i			1.48986i	0.667143	+	0.744929i	$0.267517\pi$
$881$			44.2215i			1.48986i	−0.667143	+	0.744929i	$0.732483\pi$
$882$		0			0
$883$	3.93847	+	3.93847i	0.132540	+	0.132540i	0.770265	−	0.637724i	$-0.220124\pi$
$883$	3.93847	+	3.93847i	0.132540	+	0.132540i	−0.637724	+	0.770265i	$0.720124\pi$
$884$	−2.17448	−	5.90082i	−0.0731356	−	0.198466i
$885$		0			0
$886$	8.17771	+	12.7800i	0.274735	+	0.429352i
$887$			18.4211i			0.618518i	0.950978	+	0.309259i	$0.100081\pi$
$887$			18.4211i			0.618518i	−0.950978	+	0.309259i	$0.899919\pi$
$888$		0			0
$889$		−	1.87972i		−	0.0630439i
$890$	−31.4134	+	20.1009i	−1.05298	+	0.673784i
$891$		0			0
$892$	0.996854	−	2.16026i	0.0333771	−	0.0723310i
$893$	9.64016	+	9.64016i	0.322596	+	0.322596i
$894$		0			0
$895$			6.21882i			0.207872i
$896$	0.870509	+	15.0900i	0.0290817	+	0.504120i
$897$		0			0
$898$	−0.325517	+	1.48233i	−0.0108626	+	0.0494659i
$899$	4.66852	−	4.66852i	0.155704	−	0.155704i
$900$		0			0
$901$	6.01389	+	6.01389i	0.200352	+	0.200352i
$902$	45.2073	+	70.6493i	1.50524	+	2.35236i
$903$		0			0
$904$	21.9003	−	28.8982i	0.728393	−	0.961139i
$905$	21.1673			0.703623
$906$		0			0
$907$	24.4813	−	24.4813i	0.812887	−	0.812887i	−0.172179	−	0.985066i	$-0.555081\pi$
$907$	24.4813	−	24.4813i	0.812887	−	0.812887i	0.985066	+	0.172179i	$0.0550806\pi$
$908$	33.7637	−	12.4420i	1.12049	−	0.412903i
$909$		0			0
$910$	1.35719	−	6.18032i	0.0449904	−	0.204876i
$911$	17.6487			0.584728			0.292364	−	0.956307i	$-0.405558\pi$
$911$	17.6487			0.584728			0.292364	+	0.956307i	$0.405558\pi$
$912$		0			0
$913$	59.1189			1.95655
$914$	−6.73763	+	30.6816i	−0.222861	+	1.01486i
$915$		0			0
$916$	−12.2896	−	33.3500i	−0.406060	−	1.10192i
$917$	0.660818	−	0.660818i	0.0218221	−	0.0218221i
$918$		0			0
$919$	15.6259			0.515452			0.257726	−	0.966218i	$-0.417027\pi$
$919$	15.6259			0.515452			0.257726	+	0.966218i	$0.417027\pi$
$920$	−2.15992	−	15.6791i	−0.0712103	−	0.516926i
$921$		0			0
$922$	−0.121814	−	0.190369i	−0.00401172	−	0.00626946i
$923$	−5.30265	−	5.30265i	−0.174539	−	0.174539i
$924$		0			0
$925$	7.87802	−	7.87802i	0.259028	−	0.259028i
$926$	−6.62538	+	30.1704i	−0.217724	+	0.991461i
$927$		0			0
$928$	1.13121	−	3.71684i	0.0371337	−	0.122011i
$929$		−	45.6109i		−	1.49644i	−0.663448	−	0.748222i	$-0.730908\pi$
$929$		−	45.6109i		−	1.49644i	0.663448	−	0.748222i	$-0.269092\pi$
$930$		0			0
$931$	6.23015	+	6.23015i	0.204185	+	0.204185i
$932$	31.2915	+	14.4395i	1.02499	+	0.472981i
$933$		0			0
$934$	−28.1181	+	17.9923i	−0.920053	+	0.588727i
$935$			22.5102i			0.736162i
$936$		0			0
$937$			44.9133i			1.46725i	0.679553	+	0.733626i	$0.262174\pi$
$937$			44.9133i			1.46725i	−0.679553	+	0.733626i	$0.737826\pi$
$938$	10.6384	+	16.6255i	0.347356	+	0.542842i
$939$		0			0
$940$	−29.8068	+	10.9839i	−0.972192	+	0.358256i
$941$	19.7625	+	19.7625i	0.644241	+	0.644241i	0.951595	−	0.307355i	$-0.0994438\pi$
$941$	19.7625	+	19.7625i	0.644241	+	0.644241i	−0.307355	+	0.951595i	$0.599444\pi$
$942$		0			0
$943$			27.2457i			0.887241i
$944$	0.327063	−	4.11720i	0.0106450	−	0.134004i
$945$		0			0
$946$	70.0095	+	15.3740i	2.27620	+	0.499851i
$947$	−28.1515	+	28.1515i	−0.914802	+	0.914802i	−0.996645	−	0.0818429i	$-0.973919\pi$
$947$	−28.1515	+	28.1515i	−0.914802	+	0.914802i	0.0818429	+	0.996645i	$0.473919\pi$
$948$		0			0
$949$	0.464266	+	0.464266i	0.0150707	+	0.0150707i
$950$	−2.26589	+	1.44991i	−0.0735151	+	0.0470411i
$951$		0			0
$952$	4.21776	−	5.56547i	0.136698	−	0.180378i
$953$	−5.21912			−0.169064			−0.0845319	−	0.996421i	$-0.526939\pi$
$953$	−5.21912			−0.169064			−0.0845319	+	0.996421i	$0.526939\pi$
$954$		0			0
$955$	8.48785	−	8.48785i	0.274660	−	0.274660i
$956$	32.0005	+	14.7667i	1.03497	+	0.477588i
$957$		0			0
$958$	−53.7695	−	11.8077i	−1.73721	−	0.381490i
$959$	17.2552			0.557200
$960$		0			0
$961$	−61.4097			−1.98096
$962$	23.2570	+	5.10720i	0.749835	+	0.164663i
$963$		0			0
$964$	−8.26743	−	3.81501i	−0.266276	−	0.122873i
$965$	8.94140	−	8.94140i	0.287834	−	0.287834i
$966$		0			0
$967$	1.57917			0.0507827			0.0253914	−	0.999678i	$-0.491917\pi$
$967$	1.57917			0.0507827			0.0253914	+	0.999678i	$0.491917\pi$
$968$	46.6364	−	61.5382i	1.49895	−	1.97791i
$969$		0			0
$970$	6.59917	−	4.22270i	0.211887	−	0.135583i
$971$	−27.7225	−	27.7225i	−0.889658	−	0.889658i	0.104832	−	0.994490i	$-0.466570\pi$
$971$	−27.7225	−	27.7225i	−0.889658	−	0.889658i	−0.994490	+	0.104832i	$0.966570\pi$
$972$		0			0
$973$	−20.2854	+	20.2854i	−0.650321	+	0.650321i
$974$	47.8530	+	10.5084i	1.53331	+	0.336712i
$975$		0			0
$976$	41.3331	+	3.28342i	1.32304	+	0.105100i
$977$			19.1443i			0.612480i	0.951954	+	0.306240i	$0.0990711\pi$
$977$			19.1443i			0.612480i	−0.951954	+	0.306240i	$0.900929\pi$
$978$		0			0
$979$	−58.6298	−	58.6298i	−1.87382	−	1.87382i
$980$	−19.2633	+	7.09858i	−0.615342	+	0.226756i
$981$		0			0
$982$	27.0329	+	42.2465i	0.862653	+	1.34814i
$983$			59.3747i			1.89376i	0.321588	+	0.946880i	$0.395783\pi$
$983$			59.3747i			1.89376i	−0.321588	+	0.946880i	$0.604217\pi$
$984$		0			0
$985$			0.849233i			0.0270588i
$986$	−1.51191	+	0.967444i	−0.0481489	+	0.0308097i
$987$		0			0
$988$	−5.22027	−	2.40889i	−0.166079	−	0.0766371i
$989$	16.4639	+	16.4639i	0.523523	+	0.523523i
$990$		0			0
$991$		−	15.2515i		−	0.484481i	−0.970216	−	0.242241i	$-0.922118\pi$
$991$		−	15.2515i		−	0.484481i	0.970216	−	0.242241i	$-0.0778823\pi$
$992$	−47.9817	+	25.5903i	−1.52342	+	0.812494i
$993$		0			0
$994$	1.78607	−	8.13332i	0.0566506	−	0.257973i
$995$	−12.8948	+	12.8948i	−0.408794	+	0.408794i
$996$		0			0
$997$	31.2388	+	31.2388i	0.989344	+	0.989344i	0.999944	−	0.0106003i	$-0.00337423\pi$
$997$	31.2388	+	31.2388i	0.989344	+	0.989344i	−0.0106003	+	0.999944i	$0.503374\pi$
$998$	−0.802539	−	1.25419i	−0.0254039	−	0.0397008i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.a.107.2	✓	32
3.2	odd	2	inner	432.2.l.a.107.15	yes	32
4.3	odd	2		1728.2.l.a.1295.13		32
12.11	even	2		1728.2.l.a.1295.4		32
16.3	odd	4	inner	432.2.l.a.323.15	yes	32
16.13	even	4		1728.2.l.a.431.4		32
48.29	odd	4		1728.2.l.a.431.13		32
48.35	even	4	inner	432.2.l.a.323.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.a.107.2	✓	32	1.1	even	1	trivial
432.2.l.a.107.15	yes	32	3.2	odd	2	inner
432.2.l.a.323.2	yes	32	48.35	even	4	inner
432.2.l.a.323.15	yes	32	16.3	odd	4	inner
1728.2.l.a.431.4		32	16.13	even	4
1728.2.l.a.431.13		32	48.29	odd	4
1728.2.l.a.1295.4		32	12.11	even	2
1728.2.l.a.1295.13		32	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	432.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38130 - 0.303332i) q^{2} +(1.81598 + 0.837984i) q^{4} +(1.39178 - 1.39178i) q^{5} -1.33599 q^{7} +(-2.25423 - 1.70835i) q^{8} +O(q^{10})\)	\(q+(-1.38130 - 0.303332i) q^{2} +(1.81598 + 0.837984i) q^{4} +(1.39178 - 1.39178i) q^{5} -1.33599 q^{7} +(-2.25423 - 1.70835i) q^{8} +(-2.34464 + 1.50029i) q^{10} +(-4.37602 - 4.37602i) q^{11} +(1.20314 - 1.20314i) q^{13} +(1.84541 + 0.405249i) q^{14} +(2.59557 + 3.04352i) q^{16} -1.84799i q^{17} +(-1.19463 - 1.19463i) q^{19} +(3.69373 - 1.36115i) q^{20} +(4.71721 + 7.37198i) q^{22} +2.84298i q^{23} +1.12590i q^{25} +(-2.02686 + 1.29695i) q^{26} +(-2.42614 - 1.11954i) q^{28} +(0.485646 + 0.485646i) q^{29} -9.61300i q^{31} +(-2.66206 - 4.99134i) q^{32} +(-0.560554 + 2.55263i) q^{34} +(-1.85941 + 1.85941i) q^{35} +(-6.99709 - 6.99709i) q^{37} +(1.28778 + 2.01251i) q^{38} +(-5.51503 + 0.759737i) q^{40} +9.58349 q^{41} +(5.79108 - 5.79108i) q^{43} +(-4.27973 - 11.6138i) q^{44} +(0.862366 - 3.92701i) q^{46} -8.06957 q^{47} -5.21512 q^{49} +(0.341521 - 1.55520i) q^{50} +(3.19310 - 1.17667i) q^{52} +(-3.25428 + 3.25428i) q^{53} -12.1809 q^{55} +(3.01163 + 2.28235i) q^{56} +(-0.523511 - 0.818135i) q^{58} +(-0.730119 - 0.730119i) q^{59} +(7.32974 - 7.32974i) q^{61} +(-2.91593 + 13.2784i) q^{62} +(2.16307 + 7.70202i) q^{64} -3.34902i q^{65} +(7.38696 + 7.38696i) q^{67} +(1.54859 - 3.35591i) q^{68} +(3.13242 - 2.00438i) q^{70} -4.40733i q^{71} +0.385877i q^{73} +(7.54264 + 11.7875i) q^{74} +(-1.16834 - 3.17051i) q^{76} +(5.84633 + 5.84633i) q^{77} +8.84274i q^{79} +(7.84837 + 0.623460i) q^{80} +(-13.2377 - 2.90698i) q^{82} +(-6.75487 + 6.75487i) q^{83} +(-2.57200 - 2.57200i) q^{85} +(-9.75584 + 6.24260i) q^{86} +(2.38876 + 17.3403i) q^{88} +13.3980 q^{89} +(-1.60739 + 1.60739i) q^{91} +(-2.38237 + 5.16279i) q^{92} +(11.1465 + 2.44776i) q^{94} -3.32533 q^{95} -2.81458 q^{97} +(7.20365 + 1.58191i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) \) 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Introduction

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