LMFDB - Embedded newform 432.2.u.c.385.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(49,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 14]))

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

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

chi := DirichletCharacter("432.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.u (of order $9$, degree $6$, not 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:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.1952986685049.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 27 x^{10} - 80 x^{9} + 186 x^{8} - 330 x^{7} + 463 x^{6} - 504 x^{5} + 420 x^{4} + \cdots + 3 $ x^12 - 6x^11 + 27x^10 - 80x^9 + 186x^8 - 330x^7 + 463x^6 - 504x^5 + 420x^4 - 258x^3 + 108x^2 - 27*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			385.1
Root			$0.500000 + 0.0126039i$ of defining polynomial
Character	$\chi$	$=$	432.385
Dual form			432.2.u.c.193.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.45446 - 0.940501i) q^{3} +(-0.196143 - 1.11238i) q^{5} +(2.99441 + 2.51261i) q^{7} +(1.23092 + 2.73584i) q^{9} +O(q^{10})$	\(q+(-1.45446 - 0.940501i) q^{3} +(-0.196143 - 1.11238i) q^{5} +(2.99441 + 2.51261i) q^{7} +(1.23092 + 2.73584i) q^{9} +(0.324801 - 1.84204i) q^{11} +(0.688417 + 0.250563i) q^{13} +(-0.760915 + 1.80239i) q^{15} +(-0.944822 - 1.63648i) q^{17} +(1.37143 - 2.37538i) q^{19} +(-1.99214 - 6.47073i) q^{21} +(4.46428 - 3.74597i) q^{23} +(3.49954 - 1.27373i) q^{25} +(0.782746 - 5.13686i) q^{27} +(4.99910 - 1.81953i) q^{29} +(-1.02696 + 0.861722i) q^{31} +(-2.20485 + 2.37370i) q^{33} +(2.20765 - 3.82376i) q^{35} +(-1.69806 - 2.94112i) q^{37} +(-0.765621 - 1.01189i) q^{39} +(-1.68800 - 0.614382i) q^{41} +(-0.873477 + 4.95373i) q^{43} +(2.80187 - 1.90587i) q^{45} +(-1.30892 - 1.09832i) q^{47} +(1.43775 + 8.15389i) q^{49} +(-0.164904 + 3.26880i) q^{51} +2.84494 q^{53} -2.11276 q^{55} +(-4.22874 + 2.16507i) q^{57} +(1.95529 + 11.0890i) q^{59} +(4.00710 + 3.36235i) q^{61} +(-3.18824 + 11.2850i) q^{63} +(0.143694 - 0.814930i) q^{65} +(-1.77511 - 0.646086i) q^{67} +(-10.0162 + 1.24972i) q^{69} +(-6.09193 - 10.5515i) q^{71} +(-4.94384 + 8.56298i) q^{73} +(-6.28788 - 1.43873i) q^{75} +(5.60091 - 4.69972i) q^{77} +(11.6079 - 4.22493i) q^{79} +(-5.96969 + 6.73519i) q^{81} +(-10.9786 + 3.99588i) q^{83} +(-1.63507 + 1.37199i) q^{85} +(-8.98227 - 2.05523i) q^{87} +(2.86437 - 4.96123i) q^{89} +(1.43183 + 2.48001i) q^{91} +(2.30412 - 0.287484i) q^{93} +(-2.91133 - 1.05964i) q^{95} +(-0.0596270 + 0.338162i) q^{97} +(5.43934 - 1.37879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7	$ 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{9}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.45446	−	0.940501i	−0.839734	−	0.542999i
$3$	−1.45446	−	0.940501i	−0.839734	−	0.542999i
$4$		0			0
$5$	−0.196143	−	1.11238i	−0.0877179	−	0.497473i	−0.996737	−	0.0807185i	$-0.974279\pi$
$5$	−0.196143	−	1.11238i	−0.0877179	−	0.497473i	0.909019	−	0.416755i	$-0.136833\pi$
$6$		0			0
$7$	2.99441	+	2.51261i	1.13178	+	0.949676i	0.999139	−	0.0414879i	$-0.0132098\pi$
$7$	2.99441	+	2.51261i	1.13178	+	0.949676i	0.132641	+	0.991164i	$0.457654\pi$
$8$		0			0
$9$	1.23092	+	2.73584i	0.410305	+	0.911948i
$10$		0			0
$11$	0.324801	−	1.84204i	0.0979313	−	0.555396i	−0.895878	−	0.444299i	$-0.853453\pi$
$11$	0.324801	−	1.84204i	0.0979313	−	0.555396i	0.993810	−	0.111096i	$-0.0354362\pi$
$12$		0			0
$13$	0.688417	+	0.250563i	0.190932	+	0.0694937i	0.435717	−	0.900084i	$-0.356495\pi$
$13$	0.688417	+	0.250563i	0.190932	+	0.0694937i	−0.244784	+	0.969578i	$0.578717\pi$
$14$		0			0
$15$	−0.760915	+	1.80239i	−0.196467	+	0.465376i
$16$		0			0
$17$	−0.944822	−	1.63648i	−0.229153	−	0.396905i	0.728404	−	0.685147i	$-0.240262\pi$
$17$	−0.944822	−	1.63648i	−0.229153	−	0.396905i	−0.957557	+	0.288243i	$0.906929\pi$
$18$		0			0
$19$	1.37143	−	2.37538i	0.314627	−	0.544950i	−0.664731	−	0.747083i	$-0.731454\pi$
$19$	1.37143	−	2.37538i	0.314627	−	0.544950i	0.979358	+	0.202133i	$0.0647872\pi$
$20$		0			0
$21$	−1.99214	−	6.47073i	−0.434721	−	1.41203i
$22$		0			0
$23$	4.46428	−	3.74597i	0.930866	−	0.781089i	−0.0451066	−	0.998982i	$-0.514363\pi$
$23$	4.46428	−	3.74597i	0.930866	−	0.781089i	0.975973	+	0.217893i	$0.0699183\pi$
$24$		0			0
$25$	3.49954	−	1.27373i	0.699908	−	0.254746i
$26$		0			0
$27$	0.782746	−	5.13686i	0.150640	−	0.988589i
$28$		0			0
$29$	4.99910	−	1.81953i	0.928310	−	0.337877i	0.166771	−	0.985996i	$-0.446666\pi$
$29$	4.99910	−	1.81953i	0.928310	−	0.337877i	0.761540	+	0.648118i	$0.224444\pi$
$30$		0			0
$31$	−1.02696	+	0.861722i	−0.184447	+	0.154770i	−0.730336	−	0.683088i	$-0.760637\pi$
$31$	−1.02696	+	0.861722i	−0.184447	+	0.154770i	0.545889	+	0.837858i	$0.316192\pi$
$32$		0			0
$33$	−2.20485	+	2.37370i	−0.383815	+	0.413208i
$34$		0			0
$35$	2.20765	−	3.82376i	0.373161	−	0.646334i
$36$		0			0
$37$	−1.69806	−	2.94112i	−0.279159	−	0.483517i	0.692017	−	0.721881i	$-0.256722\pi$
$37$	−1.69806	−	2.94112i	−0.279159	−	0.483517i	−0.971176	+	0.238364i	$0.923389\pi$
$38$		0			0
$39$	−0.765621	−	1.01189i	−0.122597	−	0.162032i
$40$		0			0
$41$	−1.68800	−	0.614382i	−0.263621	−	0.0959503i	0.206828	−	0.978377i	$-0.433686\pi$
$41$	−1.68800	−	0.614382i	−0.263621	−	0.0959503i	−0.470449	+	0.882427i	$0.655908\pi$
$42$		0			0
$43$	−0.873477	+	4.95373i	−0.133204	+	0.755437i	0.842890	+	0.538087i	$0.180853\pi$
$43$	−0.873477	+	4.95373i	−0.133204	+	0.755437i	−0.976094	+	0.217351i	$0.930258\pi$
$44$		0			0
$45$	2.80187	−	1.90587i	0.417679	−	0.284110i
$46$		0			0
$47$	−1.30892	−	1.09832i	−0.190926	−	0.160206i	0.542314	−	0.840176i	$-0.317548\pi$
$47$	−1.30892	−	1.09832i	−0.190926	−	0.160206i	−0.733240	+	0.679970i	$0.761993\pi$
$48$		0			0
$49$	1.43775	+	8.15389i	0.205393	+	1.16484i
$50$		0			0
$51$	−0.164904	+	3.26880i	−0.0230912	+	0.457724i
$52$		0			0
$53$	2.84494			0.390783			0.195391	−	0.980725i	$-0.437402\pi$
$53$	2.84494			0.390783			0.195391	+	0.980725i	$0.437402\pi$
$54$		0			0
$55$	−2.11276			−0.284885
$56$		0			0
$57$	−4.22874	+	2.16507i	−0.560110	+	0.286771i
$58$		0			0
$59$	1.95529	+	11.0890i	0.254557	+	1.44366i	0.797208	+	0.603704i	$0.206309\pi$
$59$	1.95529	+	11.0890i	0.254557	+	1.44366i	−0.542652	+	0.839958i	$0.682580\pi$
$60$		0			0
$61$	4.00710	+	3.36235i	0.513056	+	0.430505i	0.862203	−	0.506563i	$-0.169084\pi$
$61$	4.00710	+	3.36235i	0.513056	+	0.430505i	−0.349147	+	0.937068i	$0.613529\pi$
$62$		0			0
$63$	−3.18824	+	11.2850i	−0.401680	+	1.42178i
$64$		0			0
$65$	0.143694	−	0.814930i	0.0178231	−	0.101080i
$66$		0			0
$67$	−1.77511	−	0.646086i	−0.216864	−	0.0789319i	0.231304	−	0.972882i	$-0.425701\pi$
$67$	−1.77511	−	0.646086i	−0.216864	−	0.0789319i	−0.448167	+	0.893950i	$0.647923\pi$
$68$		0			0
$69$	−10.0162	+	1.24972i	−1.20581	+	0.150448i
$70$		0			0
$71$	−6.09193	−	10.5515i	−0.722980	−	1.25224i	−0.959800	−	0.280684i	$-0.909439\pi$
$71$	−6.09193	−	10.5515i	−0.722980	−	1.25224i	0.236821	−	0.971553i	$-0.423895\pi$
$72$		0			0
$73$	−4.94384	+	8.56298i	−0.578633	+	1.00222i	0.417004	+	0.908905i	$0.363080\pi$
$73$	−4.94384	+	8.56298i	−0.578633	+	1.00222i	−0.995637	+	0.0933164i	$0.970253\pi$
$74$		0			0
$75$	−6.28788	−	1.43873i	−0.726062	−	0.166130i
$76$		0			0
$77$	5.60091	−	4.69972i	0.638283	−	0.535583i
$78$		0			0
$79$	11.6079	−	4.22493i	1.30599	−	0.475342i	0.407048	−	0.913407i	$-0.366558\pi$
$79$	11.6079	−	4.22493i	1.30599	−	0.475342i	0.898943	+	0.438065i	$0.144336\pi$
$80$		0			0
$81$	−5.96969	+	6.73519i	−0.663299	+	0.748354i
$82$		0			0
$83$	−10.9786	+	3.99588i	−1.20506	+	0.438605i	−0.864986	−	0.501796i	$-0.832673\pi$
$83$	−10.9786	+	3.99588i	−1.20506	+	0.438605i	−0.340070	+	0.940400i	$0.610451\pi$
$84$		0			0
$85$	−1.63507	+	1.37199i	−0.177349	+	0.148813i
$86$		0			0
$87$	−8.98227	−	2.05523i	−0.963000	−	0.220344i
$88$		0			0
$89$	2.86437	−	4.96123i	0.303622	−	0.525889i	−0.673331	−	0.739341i	$-0.735137\pi$
$89$	2.86437	−	4.96123i	0.303622	−	0.525889i	0.976954	+	0.213452i	$0.0684706\pi$
$90$		0			0
$91$	1.43183	+	2.48001i	0.150097	+	0.259976i
$92$		0			0
$93$	2.30412	−	0.287484i	0.238926	−	0.0298107i
$94$		0			0
$95$	−2.91133	−	1.05964i	−0.298697	−	0.108717i
$96$		0			0
$97$	−0.0596270	+	0.338162i	−0.00605421	+	0.0343351i	−0.987685	−	0.156454i	$-0.949994\pi$
$97$	−0.0596270	+	0.338162i	−0.00605421	+	0.0343351i	0.981631	+	0.190789i	$0.0611047\pi$
$98$		0			0
$99$	5.43934	−	1.37879i	0.546674	−	0.138574i
$100$		0			0
$101$	−13.3309	−	11.1860i	−1.32647	−	1.11304i	−0.984888	−	0.173194i	$-0.944591\pi$
$101$	−13.3309	−	11.1860i	−1.32647	−	1.11304i	−0.341586	−	0.939850i	$-0.610964\pi$
$102$		0			0
$103$	2.74590	+	15.5728i	0.270561	+	1.53443i	0.752717	+	0.658345i	$0.228743\pi$
$103$	2.74590	+	15.5728i	0.270561	+	1.53443i	−0.482155	+	0.876086i	$0.660146\pi$
$104$		0			0
$105$	−6.80719	+	3.48522i	−0.664314	+	0.340122i
$106$		0			0
$107$	16.5298			1.59800			0.798999	−	0.601332i	$-0.205363\pi$
$107$	16.5298			1.59800			0.798999	+	0.601332i	$0.205363\pi$
$108$		0			0
$109$	−4.71844			−0.451945			−0.225972	−	0.974134i	$-0.572556\pi$
$109$	−4.71844			−0.451945			−0.225972	+	0.974134i	$0.572556\pi$
$110$		0			0
$111$	−0.296369	+	5.87477i	−0.0281301	+	0.557608i
$112$		0			0
$113$	3.46338	+	19.6418i	0.325807	+	1.84775i	0.503939	+	0.863739i	$0.331884\pi$
$113$	3.46338	+	19.6418i	0.325807	+	1.84775i	−0.178132	+	0.984007i	$0.557005\pi$
$114$		0			0
$115$	−5.04260	−	4.23124i	−0.470225	−	0.394565i
$116$		0			0
$117$	0.161881	+	2.19182i	0.0149659	+	0.202634i
$118$		0			0
$119$	1.28265	−	7.27425i	0.117580	−	0.666830i
$120$		0			0
$121$	7.04901	+	2.56563i	0.640819	+	0.233239i
$122$		0			0
$123$	1.87730	+	2.48116i	0.169271	+	0.223719i
$124$		0			0
$125$	−4.92714	−	8.53407i	−0.440697	−	0.763310i
$126$		0			0
$127$	0.534728	−	0.926176i	0.0474495	−	0.0821849i	−0.841325	−	0.540529i	$-0.818224\pi$
$127$	0.534728	−	0.926176i	0.0474495	−	0.0821849i	0.888775	+	0.458344i	$0.151557\pi$
$128$		0			0
$129$	5.92943	−	6.38351i	0.522057	−	0.562037i
$130$		0			0
$131$	−5.85281	+	4.91109i	−0.511362	+	0.429084i	−0.861608	−	0.507574i	$-0.830542\pi$
$131$	−5.85281	+	4.91109i	−0.511362	+	0.429084i	0.350246	+	0.936658i	$0.386098\pi$
$132$		0			0
$133$	10.0750	−	3.66701i	0.873615	−	0.317970i
$134$		0			0
$135$	−5.86769	+	0.136846i	−0.505010	+	0.0117778i
$136$		0			0
$137$	−14.7067	+	5.35279i	−1.25647	+	0.457319i	−0.882585	−	0.470154i	$-0.844199\pi$
$137$	−14.7067	+	5.35279i	−1.25647	+	0.457319i	−0.373890	+	0.927473i	$0.621976\pi$
$138$		0			0
$139$	−6.63160	+	5.56457i	−0.562485	+	0.471981i	−0.879142	−	0.476559i	$-0.841884\pi$
$139$	−6.63160	+	5.56457i	−0.562485	+	0.471981i	0.316658	+	0.948540i	$0.397439\pi$
$140$		0			0
$141$	0.870810	+	2.82850i	0.0733354	+	0.238203i
$142$		0			0
$143$	0.685146	−	1.18671i	0.0572948	−	0.0992375i
$144$		0			0
$145$	−3.00455	−	5.20403i	−0.249514	−	0.432172i
$146$		0			0
$147$	5.57759	−	13.2117i	0.460032	−	1.08968i
$148$		0			0
$149$	2.31524	+	0.842677i	0.189672	+	0.0690348i	0.435110	−	0.900377i	$-0.356710\pi$
$149$	2.31524	+	0.842677i	0.189672	+	0.0690348i	−0.245438	+	0.969412i	$0.578932\pi$
$150$		0			0
$151$	1.82563	−	10.3537i	0.148568	−	0.842571i	−0.815865	−	0.578243i	$-0.803739\pi$
$151$	1.82563	−	10.3537i	0.148568	−	0.842571i	0.964433	−	0.264328i	$-0.0851502\pi$
$152$		0			0
$153$	3.31416	−	4.59925i	0.267934	−	0.371828i
$154$		0			0
$155$	1.16000	+	0.973353i	0.0931731	+	0.0781816i
$156$		0			0
$157$	0.0625044	+	0.354480i	0.00498840	+	0.0282906i	0.987200	−	0.159485i	$-0.0509833\pi$
$157$	0.0625044	+	0.354480i	0.00498840	+	0.0282906i	−0.982212	+	0.187776i	$0.939872\pi$
$158$		0			0
$159$	−4.13786	−	2.67567i	−0.328154	−	0.212195i
$160$		0			0
$161$	22.7800			1.79532
$162$		0			0
$163$	−14.6186			−1.14502			−0.572508	−	0.819899i	$-0.694029\pi$
$163$	−14.6186			−1.14502			−0.572508	+	0.819899i	$0.694029\pi$
$164$		0			0
$165$	3.07293	+	1.98706i	0.239227	+	0.154692i
$166$		0			0
$167$	−0.377832	−	2.14279i	−0.0292375	−	0.165814i	0.966693	−	0.255939i	$-0.0823846\pi$
$167$	−0.377832	−	2.14279i	−0.0292375	−	0.165814i	−0.995930	+	0.0901247i	$0.971273\pi$
$168$		0			0
$169$	−9.54744	−	8.01125i	−0.734419	−	0.616250i
$170$		0			0
$171$	8.18679	+	0.828119i	0.626060	+	0.0633278i
$172$		0			0
$173$	−3.05048	+	17.3001i	−0.231924	+	1.31531i	0.617072	+	0.786906i	$0.288319\pi$
$173$	−3.05048	+	17.3001i	−0.231924	+	1.31531i	−0.848996	+	0.528399i	$0.822793\pi$
$174$		0			0
$175$	13.6794	+	4.97890i	1.03407	+	0.376370i
$176$		0			0
$177$	7.58531	−	17.9674i	0.570147	−	1.35052i
$178$		0			0
$179$	0.502236	+	0.869898i	0.0375388	+	0.0650192i	0.884184	−	0.467138i	$-0.154715\pi$
$179$	0.502236	+	0.869898i	0.0375388	+	0.0650192i	−0.846646	+	0.532157i	$0.821382\pi$
$180$		0			0
$181$	10.5866	−	18.3366i	0.786898	−	1.36295i	−0.140961	−	0.990015i	$-0.545019\pi$
$181$	10.5866	−	18.3366i	0.786898	−	1.36295i	0.927859	−	0.372932i	$-0.121647\pi$
$182$		0			0
$183$	−2.66587	−	8.65909i	−0.197067	−	0.640099i
$184$		0			0
$185$	−2.93859	+	2.46577i	−0.216050	+	0.181287i
$186$		0			0
$187$	−3.32134	+	1.20887i	−0.242880	+	0.0884012i
$188$		0			0
$189$	15.2508	−	13.4151i	1.10933	−	0.975806i
$190$		0			0
$191$	−9.23566	+	3.36150i	−0.668269	+	0.243230i	−0.653802	−	0.756665i	$-0.726827\pi$
$191$	−9.23566	+	3.36150i	−0.668269	+	0.243230i	−0.0144664	+	0.999895i	$0.504605\pi$
$192$		0			0
$193$	−8.54606	+	7.17099i	−0.615159	+	0.516179i	−0.896278	−	0.443494i	$-0.853739\pi$
$193$	−8.54606	+	7.17099i	−0.615159	+	0.516179i	0.281119	+	0.959673i	$0.409294\pi$
$194$		0			0
$195$	−0.975440	+	1.05014i	−0.0698527	+	0.0752021i
$196$		0			0
$197$	−4.54497	+	7.87212i	−0.323816	+	0.560865i	−0.981272	−	0.192628i	$-0.938299\pi$
$197$	−4.54497	+	7.87212i	−0.323816	+	0.560865i	0.657456	+	0.753493i	$0.271632\pi$
$198$		0			0
$199$	−7.34694	−	12.7253i	−0.520811	−	0.902071i	−0.999707	−	0.0241994i	$-0.992296\pi$
$199$	−7.34694	−	12.7253i	−0.520811	−	0.902071i	0.478896	−	0.877872i	$-0.341037\pi$
$200$		0			0
$201$	1.97418	+	2.60920i	0.139248	+	0.184038i
$202$		0			0
$203$	19.5411	+	7.11238i	1.37152	+	0.499191i
$204$		0			0
$205$	−0.352339	+	1.99821i	−0.0246084	+	0.139561i
$206$		0			0
$207$	15.7435	+	7.60259i	1.09425	+	0.528417i
$208$		0			0
$209$	−3.93011	−	3.29775i	−0.271851	−	0.228110i
$210$		0			0
$211$	−1.36458	−	7.73891i	−0.0939415	−	0.532769i	−0.995067	−	0.0992096i	$-0.968369\pi$
$211$	−1.36458	−	7.73891i	−0.0939415	−	0.532769i	0.901125	−	0.433559i	$-0.142743\pi$
$212$		0			0
$213$	−1.06325	+	21.0763i	−0.0728528	+	1.44412i
$214$		0			0
$215$	5.68178			0.387494
$216$		0			0
$217$	−5.24030			−0.355735
$218$		0			0
$219$	15.2441	−	7.80484i	1.03010	−	0.527402i
$220$		0			0
$221$	−0.240390	−	1.36332i	−0.0161704	−	0.0917067i
$222$		0			0
$223$	6.69591	+	5.61853i	0.448391	+	0.376245i	0.838838	−	0.544380i	$-0.183235\pi$
$223$	6.69591	+	5.61853i	0.448391	+	0.376245i	−0.390447	+	0.920625i	$0.627680\pi$
$224$		0			0
$225$	7.79236	+	8.00634i	0.519490	+	0.533756i
$226$		0			0
$227$	−0.706473	+	4.00661i	−0.0468903	+	0.265928i	−0.999236	−	0.0390942i	$-0.987553\pi$
$227$	−0.706473	+	4.00661i	−0.0468903	+	0.265928i	0.952345	+	0.305022i	$0.0986639\pi$
$228$		0			0
$229$	−15.1816	−	5.52563i	−1.00323	−	0.365144i	−0.212398	−	0.977183i	$-0.568127\pi$
$229$	−15.1816	−	5.52563i	−1.00323	−	0.365144i	−0.790827	+	0.612039i	$0.790349\pi$
$230$		0			0
$231$	−12.5664	+	1.56790i	−0.826808	+	0.103160i
$232$		0			0
$233$	−8.60658	−	14.9070i	−0.563836	−	0.976592i	−0.997157	−	0.0753527i	$-0.975992\pi$
$233$	−8.60658	−	14.9070i	−0.563836	−	0.976592i	0.433321	−	0.901240i	$-0.357342\pi$
$234$		0			0
$235$	−0.965013	+	1.67145i	−0.0629505	+	0.109034i
$236$		0			0
$237$	−20.8568	−	4.77225i	−1.35479	−	0.309991i
$238$		0			0
$239$	1.17621	−	0.986962i	0.0760830	−	0.0638412i	−0.603953	−	0.797020i	$-0.706409\pi$
$239$	1.17621	−	0.986962i	0.0760830	−	0.0638412i	0.680036	+	0.733179i	$0.261964\pi$
$240$		0			0
$241$	5.18868	−	1.88852i	0.334232	−	0.121650i	−0.169452	−	0.985538i	$-0.554200\pi$
$241$	5.18868	−	1.88852i	0.334232	−	0.121650i	0.503684	+	0.863888i	$0.331978\pi$
$242$		0			0
$243$	15.0171	−	4.18157i	0.963350	−	0.268248i
$244$		0			0
$245$	8.78825	−	3.19866i	0.561461	−	0.204355i
$246$		0			0
$247$	1.53930	−	1.29162i	0.0979432	−	0.0821841i
$248$		0			0
$249$	19.7261	+	4.51352i	1.25009	+	0.286033i
$250$		0			0
$251$	−10.7204	+	18.5683i	−0.676668	+	1.17202i	0.299310	+	0.954156i	$0.403244\pi$
$251$	−10.7204	+	18.5683i	−0.676668	+	1.17202i	−0.975978	+	0.217868i	$0.930090\pi$
$252$		0			0
$253$	−5.45023	−	9.44007i	−0.342653	−	0.593492i
$254$		0			0
$255$	3.66851	−	0.457717i	0.229731	−	0.0286634i
$256$		0			0
$257$	13.8947	+	5.05727i	0.866730	+	0.315464i	0.736842	−	0.676065i	$-0.236316\pi$
$257$	13.8947	+	5.05727i	0.866730	+	0.315464i	0.129888	+	0.991529i	$0.458538\pi$
$258$		0			0
$259$	2.30520	−	13.0735i	0.143238	−	0.812346i
$260$		0			0
$261$	11.1314	+	11.4371i	0.689017	+	0.707938i
$262$		0			0
$263$	−2.14704	−	1.80158i	−0.132392	−	0.111090i	0.574187	−	0.818724i	$-0.305318\pi$
$263$	−2.14704	−	1.80158i	−0.132392	−	0.111090i	−0.706579	+	0.707634i	$0.749763\pi$
$264$		0			0
$265$	−0.558016	−	3.16467i	−0.0342787	−	0.194404i
$266$		0			0
$267$	−8.83215	+	4.52197i	−0.540519	+	0.276740i
$268$		0			0
$269$	−0.356528			−0.0217379			−0.0108689	−	0.999941i	$-0.503460\pi$
$269$	−0.356528			−0.0217379			−0.0108689	+	0.999941i	$0.503460\pi$
$270$		0			0
$271$	12.1467			0.737857			0.368928	−	0.929458i	$-0.379725\pi$
$271$	12.1467			0.737857			0.368928	+	0.929458i	$0.379725\pi$
$272$		0			0
$273$	0.249904	−	4.95372i	0.0151249	−	0.299813i
$274$		0			0
$275$	−1.20960	−	6.85999i	−0.0729418	−	0.413673i
$276$		0			0
$277$	19.1434	+	16.0632i	1.15022	+	0.965146i	0.999725	−	0.0234648i	$-0.00746978\pi$
$277$	19.1434	+	16.0632i	1.15022	+	0.965146i	0.150492	+	0.988611i	$0.451914\pi$
$278$		0			0
$279$	−3.62164	−	1.74890i	−0.216822	−	0.104704i
$280$		0			0
$281$	1.27160	−	7.21162i	0.0758575	−	0.430209i	−0.923100	−	0.384560i	$-0.874353\pi$
$281$	1.27160	−	7.21162i	0.0758575	−	0.430209i	0.998958	−	0.0456492i	$-0.0145356\pi$
$282$		0			0
$283$	−13.5204	−	4.92102i	−0.803703	−	0.292524i	−0.0926830	−	0.995696i	$-0.529544\pi$
$283$	−13.5204	−	4.92102i	−0.803703	−	0.292524i	−0.711020	+	0.703172i	$0.751767\pi$
$284$		0			0
$285$	3.23783	+	4.27932i	0.191793	+	0.253485i
$286$		0			0
$287$	−3.51086	−	6.08099i	−0.207240	−	0.358950i
$288$		0			0
$289$	6.71462	−	11.6301i	0.394978	−	0.684122i
$290$		0			0
$291$	0.404767	−	0.435764i	0.0237278	−	0.0255449i
$292$		0			0
$293$	−11.0429	+	9.26611i	−0.645134	+	0.541332i	−0.905590	−	0.424154i	$-0.860572\pi$
$293$	−11.0429	+	9.26611i	−0.645134	+	0.541332i	0.260456	+	0.965486i	$0.416127\pi$
$294$		0			0
$295$	11.9517	−	4.35006i	0.695854	−	0.253270i
$296$		0			0
$297$	−9.20806	−	3.11031i	−0.534306	−	0.180478i
$298$		0			0
$299$	4.01189	−	1.46021i	0.232013	−	0.0844460i
$300$		0			0
$301$	−15.0623	+	12.6388i	−0.868178	+	0.728488i
$302$		0			0
$303$	8.86888	+	28.8073i	0.509504	+	1.65493i
$304$		0			0
$305$	2.95426	−	5.11693i	0.169161	−	0.292995i
$306$		0			0
$307$	−15.2163	−	26.3554i	−0.868440	−	1.50418i	−0.863591	−	0.504193i	$-0.831790\pi$
$307$	−15.2163	−	26.3554i	−0.868440	−	1.50418i	−0.00484869	−	0.999988i	$-0.501543\pi$
$308$		0			0
$309$	10.6524	−	25.2325i	0.605994	−	1.43543i
$310$		0			0
$311$	−13.1516	−	4.78678i	−0.745757	−	0.271433i	−0.0589378	−	0.998262i	$-0.518771\pi$
$311$	−13.1516	−	4.78678i	−0.745757	−	0.271433i	−0.686819	+	0.726828i	$0.740994\pi$
$312$		0			0
$313$	3.83547	−	21.7520i	0.216793	−	1.22950i	−0.660974	−	0.750409i	$-0.729857\pi$
$313$	3.83547	−	21.7520i	0.216793	−	1.22950i	0.877767	−	0.479087i	$-0.159032\pi$
$314$		0			0
$315$	13.1787	+	1.33306i	0.742533	+	0.0751094i
$316$		0			0
$317$	13.3205	+	11.1773i	0.748156	+	0.627777i	0.935014	−	0.354610i	$-0.115386\pi$
$317$	13.3205	+	11.1773i	0.748156	+	0.627777i	−0.186859	+	0.982387i	$0.559831\pi$
$318$		0			0
$319$	−1.72792	−	9.79953i	−0.0967450	−	0.548668i
$320$		0			0
$321$	−24.0420	−	15.5463i	−1.34189	−	0.867711i
$322$		0			0
$323$	−5.18302			−0.288391
$324$		0			0
$325$	2.72829			0.151338
$326$		0			0
$327$	6.86279	+	4.43770i	0.379513	+	0.245405i
$328$		0			0
$329$	−1.15981	−	6.57762i	−0.0639425	−	0.362636i
$330$		0			0
$331$	−0.661975	−	0.555463i	−0.0363855	−	0.0305310i	0.624414	−	0.781094i	$-0.285338\pi$
$331$	−0.661975	−	0.555463i	−0.0363855	−	0.0305310i	−0.660799	+	0.750563i	$0.729782\pi$
$332$		0			0
$333$	5.95628	−	8.26589i	0.326402	−	0.452968i
$334$		0			0
$335$	−0.370520	+	2.10132i	−0.0202437	+	0.114808i
$336$		0			0
$337$	−0.393289	−	0.143145i	−0.0214238	−	0.00779762i	0.331286	−	0.943530i	$-0.392517\pi$
$337$	−0.393289	−	0.143145i	−0.0214238	−	0.00779762i	−0.352710	+	0.935733i	$0.614740\pi$
$338$		0			0
$339$	13.4358	−	31.8256i	0.729732	−	1.72853i
$340$		0			0
$341$	1.25377	+	2.17159i	0.0678953	+	0.117598i
$342$		0			0
$343$	−2.50108	+	4.33199i	−0.135046	+	0.233906i
$344$		0			0
$345$	3.35478	+	10.8967i	0.180615	+	0.586661i
$346$		0			0
$347$	−17.9329	+	15.0475i	−0.962689	+	0.807792i	−0.981388	−	0.192033i	$-0.938492\pi$
$347$	−17.9329	+	15.0475i	−0.962689	+	0.807792i	0.0186996	+	0.999825i	$0.494047\pi$
$348$		0			0
$349$	−19.8993	+	7.24276i	−1.06519	+	0.387696i	−0.814374	−	0.580340i	$-0.802920\pi$
$349$	−19.8993	+	7.24276i	−1.06519	+	0.387696i	−0.250811	+	0.968036i	$0.580697\pi$
$350$		0			0
$351$	1.82596	−	3.34017i	0.0974627	−	0.178285i
$352$		0			0
$353$	−22.1246	+	8.05268i	−1.17757	+	0.428601i	−0.855344	−	0.518061i	$-0.826654\pi$
$353$	−22.1246	+	8.05268i	−1.17757	+	0.428601i	−0.322228	+	0.946662i	$0.604432\pi$
$354$		0			0
$355$	−10.5425	+	8.84618i	−0.559536	+	0.469507i
$356$		0			0
$357$	−8.70700	+	9.37379i	−0.460823	+	0.496114i
$358$		0			0
$359$	−5.23047	+	9.05943i	−0.276053	+	0.478139i	−0.970400	−	0.241502i	$-0.922360\pi$
$359$	−5.23047	+	9.05943i	−0.276053	+	0.478139i	0.694347	+	0.719640i	$0.255693\pi$
$360$		0			0
$361$	5.73837	+	9.93915i	0.302019	+	0.523113i
$362$		0			0
$363$	−7.83953	−	10.3612i	−0.411469	−	0.543822i
$364$		0			0
$365$	10.4950	+	3.81988i	0.549335	+	0.199941i
$366$		0			0
$367$	−3.69146	+	20.9353i	−0.192693	+	1.09281i	0.722974	+	0.690875i	$0.242775\pi$
$367$	−3.69146	+	20.9353i	−0.192693	+	1.09281i	−0.915666	+	0.401939i	$0.868336\pi$
$368$		0			0
$369$	−0.396932	−	5.37436i	−0.0206635	−	0.279778i
$370$		0			0
$371$	8.51892	+	7.14822i	0.442280	+	0.371117i
$372$		0			0
$373$	0.401142	+	2.27499i	0.0207704	+	0.117795i	0.993430	−	0.114440i	$-0.0365074\pi$
$373$	0.401142	+	2.27499i	0.0207704	+	0.117795i	−0.972660	+	0.232235i	$0.925396\pi$
$374$		0			0
$375$	−0.859956	+	17.0465i	−0.0444079	+	0.880275i
$376$		0			0
$377$	3.89737			0.200725
$378$		0			0
$379$	−12.5539			−0.644850			−0.322425	−	0.946595i	$-0.604498\pi$
$379$	−12.5539			−0.644850			−0.322425	+	0.946595i	$0.604498\pi$
$380$		0			0
$381$	−1.64881	+	0.844175i	−0.0844712	+	0.0432484i
$382$		0			0
$383$	3.41297	+	19.3559i	0.174395	+	0.989042i	0.938840	+	0.344353i	$0.111902\pi$
$383$	3.41297	+	19.3559i	0.174395	+	0.989042i	−0.764445	+	0.644689i	$0.776987\pi$
$384$		0			0
$385$	−6.32647	−	5.30854i	−0.322427	−	0.270548i
$386$		0			0
$387$	−14.6278	+	3.70793i	−0.743574	+	0.188485i
$388$		0			0
$389$	−3.27198	+	18.5563i	−0.165896	+	0.940843i	0.782240	+	0.622978i	$0.214077\pi$
$389$	−3.27198	+	18.5563i	−0.165896	+	0.940843i	−0.948136	+	0.317866i	$0.897034\pi$
$390$		0			0
$391$	−10.3482	−	3.76642i	−0.523329	−	0.190476i
$392$		0			0
$393$	13.1316	−	1.63842i	0.662400	−	0.0826472i
$394$		0			0
$395$	−6.97656	−	12.0838i	−0.351029	−	0.608000i
$396$		0			0
$397$	−10.0589	+	17.4225i	−0.504841	+	0.874410i	0.495143	+	0.868811i	$0.335116\pi$
$397$	−10.0589	+	17.4225i	−0.504841	+	0.874410i	−0.999984	+	0.00559897i	$0.998218\pi$
$398$		0			0
$399$	−18.1026	−	4.14205i	−0.906261	−	0.207362i
$400$		0			0
$401$	−23.5985	+	19.8015i	−1.17845	+	0.988840i	−0.178466	+	0.983946i	$0.557113\pi$
$401$	−23.5985	+	19.8015i	−1.17845	+	0.988840i	−0.999988	+	0.00489430i	$0.998442\pi$
$402$		0			0
$403$	−0.922892	+	0.335905i	−0.0459725	+	0.0167326i
$404$		0			0
$405$	8.66303	+	5.31953i	0.430469	+	0.264330i
$406$		0			0
$407$	−5.96919	+	2.17261i	−0.295882	+	0.107692i
$408$		0			0
$409$	30.4059	−	25.5136i	1.50347	−	1.26156i	0.628086	−	0.778144i	$-0.283839\pi$
$409$	30.4059	−	25.5136i	1.50347	−	1.26156i	0.875388	−	0.483421i	$-0.160606\pi$
$410$		0			0
$411$	26.4246	+	6.04621i	1.30343	+	0.298237i
$412$		0			0
$413$	−22.0073	+	38.1178i	−1.08291	+	1.87565i
$414$		0			0
$415$	6.59832	+	11.4286i	0.323899	+	0.561010i
$416$		0			0
$417$	14.8789	−	1.85643i	0.728622	−	0.0909097i
$418$		0			0
$419$	14.5099	+	5.28118i	0.708856	+	0.258002i	0.671187	−	0.741288i	$-0.265785\pi$
$419$	14.5099	+	5.28118i	0.708856	+	0.258002i	0.0376687	+	0.999290i	$0.488007\pi$
$420$		0			0
$421$	−3.14193	+	17.8188i	−0.153128	+	0.868433i	0.807349	+	0.590074i	$0.200902\pi$
$421$	−3.14193	+	17.8188i	−0.153128	+	0.868433i	−0.960477	+	0.278359i	$0.910210\pi$
$422$		0			0
$423$	1.39365	−	4.93294i	0.0677616	−	0.239848i
$424$		0			0
$425$	−5.39087	−	4.52348i	−0.261496	−	0.219421i
$426$		0			0
$427$	3.55061	+	20.1365i	0.171826	+	0.974475i
$428$		0			0
$429$	−2.11262	+	1.08164i	−0.101998	+	0.0522221i
$430$		0			0
$431$	28.9683			1.39535			0.697677	−	0.716412i	$-0.254217\pi$
$431$	28.9683			1.39535			0.697677	+	0.716412i	$0.254217\pi$
$432$		0			0
$433$	−37.5902			−1.80647			−0.903235	−	0.429146i	$-0.858815\pi$
$433$	−37.5902			−1.80647			−0.903235	+	0.429146i	$0.858815\pi$
$434$		0			0
$435$	−0.524397	+	10.3949i	−0.0251429	+	0.498395i
$436$		0			0
$437$	−2.77569	−	15.7417i	−0.132779	−	0.753028i
$438$		0			0
$439$	−7.86232	−	6.59727i	−0.375248	−	0.314871i	0.435585	−	0.900147i	$-0.356541\pi$
$439$	−7.86232	−	6.59727i	−0.375248	−	0.314871i	−0.810834	+	0.585277i	$0.800986\pi$
$440$		0			0
$441$	−20.5380	+	13.9702i	−0.978001	+	0.665248i
$442$		0			0
$443$	−3.80437	+	21.5757i	−0.180751	+	1.02509i	0.750543	+	0.660822i	$0.229792\pi$
$443$	−3.80437	+	21.5757i	−0.180751	+	1.02509i	−0.931294	+	0.364269i	$0.881319\pi$
$444$		0			0
$445$	−6.08062	−	2.21316i	−0.288249	−	0.104914i
$446$		0			0
$447$	−2.57488	−	3.40312i	−0.121788	−	0.160962i
$448$		0			0
$449$	−4.98565	−	8.63540i	−0.235287	−	0.407530i	0.724069	−	0.689728i	$-0.242270\pi$
$449$	−4.98565	−	8.63540i	−0.235287	−	0.407530i	−0.959356	+	0.282198i	$0.908936\pi$
$450$		0			0
$451$	−1.67998	+	2.90981i	−0.0791072	+	0.137018i
$452$		0			0
$453$	−12.3930	+	13.3420i	−0.582272	+	0.626863i
$454$		0			0
$455$	2.47788	−	2.07919i	0.116165	−	0.0974738i
$456$		0			0
$457$	7.15867	−	2.60554i	0.334869	−	0.121882i	−0.169113	−	0.985597i	$-0.554090\pi$
$457$	7.15867	−	2.60554i	0.334869	−	0.121882i	0.503981	+	0.863715i	$0.331868\pi$
$458$		0			0
$459$	−9.14592	+	3.57247i	−0.426895	+	0.166748i
$460$		0			0
$461$	21.4255	−	7.79824i	0.997885	−	0.363200i	0.209116	−	0.977891i	$-0.432941\pi$
$461$	21.4255	−	7.79824i	0.997885	−	0.363200i	0.788768	+	0.614690i	$0.210719\pi$
$462$		0			0
$463$	6.73792	−	5.65379i	0.313138	−	0.262754i	−0.472650	−	0.881250i	$-0.656702\pi$
$463$	6.73792	−	5.65379i	0.313138	−	0.262754i	0.785787	+	0.618497i	$0.212258\pi$
$464$		0			0
$465$	−0.771731	−	2.50668i	−0.0357882	−	0.116245i
$466$		0			0
$467$	−5.49878	+	9.52416i	−0.254453	+	0.440726i	−0.964747	−	0.263180i	$-0.915229\pi$
$467$	−5.49878	+	9.52416i	−0.254453	+	0.440726i	0.710294	+	0.703905i	$0.248562\pi$
$468$		0			0
$469$	−3.69203	−	6.39479i	−0.170482	−	0.295284i
$470$		0			0
$471$	0.242479	−	0.574363i	0.0111728	−	0.0264653i
$472$		0			0
$473$	8.84127	+	3.21796i	0.406522	+	0.147962i
$474$		0			0
$475$	1.77377	−	10.0596i	0.0813863	−	0.461565i
$476$		0			0
$477$	3.50188	+	7.78332i	0.160340	+	0.356374i
$478$		0			0
$479$	−19.6816	−	16.5148i	−0.899276	−	0.754582i	0.0707730	−	0.997492i	$-0.477453\pi$
$479$	−19.6816	−	16.5148i	−0.899276	−	0.754582i	−0.970049	+	0.242911i	$0.921898\pi$
$480$		0			0
$481$	−0.432034	−	2.45019i	−0.0196991	−	0.111719i
$482$		0			0
$483$	−33.1327	−	21.4246i	−1.50759	−	0.974855i
$484$		0			0
$485$	0.387861			0.0176119
$486$		0			0
$487$	30.3800			1.37665			0.688325	−	0.725402i	$-0.258346\pi$
$487$	30.3800			1.37665			0.688325	+	0.725402i	$0.258346\pi$
$488$		0			0
$489$	21.2621	+	13.7488i	0.961508	+	0.621742i
$490$		0			0
$491$	−1.51218	−	8.57597i	−0.0682435	−	0.387028i	−0.999730	−	0.0232514i	$-0.992598\pi$
$491$	−1.51218	−	8.57597i	−0.0682435	−	0.387028i	0.931486	−	0.363777i	$-0.118513\pi$
$492$		0			0
$493$	−7.70088	−	6.46180i	−0.346830	−	0.291025i
$494$		0			0
$495$	−2.60063	−	5.78019i	−0.116890	−	0.259800i
$496$		0			0
$497$	8.27013	−	46.9023i	0.370966	−	2.10385i
$498$		0			0
$499$	10.9338	+	3.97957i	0.489463	+	0.178150i	0.574949	−	0.818189i	$-0.305022\pi$
$499$	10.9338	+	3.97957i	0.489463	+	0.178150i	−0.0854858	+	0.996339i	$0.527244\pi$
$500$		0			0
$501$	−1.46576	+	3.47196i	−0.0654851	+	0.155116i
$502$		0			0
$503$	−18.8996	−	32.7350i	−0.842689	−	1.45958i	−0.887613	−	0.460590i	$-0.847638\pi$
$503$	−18.8996	−	32.7350i	−0.842689	−	1.45958i	0.0449234	−	0.998990i	$-0.485696\pi$
$504$		0			0
$505$	−9.82831	+	17.0231i	−0.437354	+	0.757519i
$506$		0			0
$507$	6.35179	+	20.6314i	0.282093	+	0.916274i
$508$		0			0
$509$	18.0585	−	15.1528i	0.800427	−	0.671638i	−0.147875	−	0.989006i	$-0.547243\pi$
$509$	18.0585	−	15.1528i	0.800427	−	0.671638i	0.948302	+	0.317368i	$0.102799\pi$
$510$		0			0
$511$	−36.3193	+	13.2191i	−1.60667	+	0.584780i
$512$		0			0
$513$	−11.1285	−	8.90415i	−0.491336	−	0.393128i
$514$		0			0
$515$	16.7843	−	6.10899i	0.739605	−	0.269194i
$516$		0			0
$517$	−2.44828	+	2.05435i	−0.107675	+	0.0903503i
$518$		0			0
$519$	20.7076	−	22.2934i	0.908963	−	0.978572i
$520$		0			0
$521$	−3.93474	+	6.81517i	−0.172384	+	0.298578i	−0.939253	−	0.343226i	$-0.888480\pi$
$521$	−3.93474	+	6.81517i	−0.172384	+	0.298578i	0.766869	+	0.641804i	$0.221814\pi$
$522$		0			0
$523$	16.6467	+	28.8330i	0.727911	+	1.26078i	0.957765	+	0.287554i	$0.0928419\pi$
$523$	16.6467	+	28.8330i	0.727911	+	1.26078i	−0.229854	+	0.973225i	$0.573825\pi$
$524$		0			0
$525$	−15.2135	−	20.1071i	−0.663973	−	0.877547i
$526$		0			0
$527$	2.38048	+	0.866425i	0.103695	+	0.0377421i
$528$		0			0
$529$	1.90355	−	10.7955i	0.0827628	−	0.469371i
$530$		0			0
$531$	−27.9309	+	18.9990i	−1.21210	+	0.824485i
$532$		0			0
$533$	−1.00811	−	0.845902i	−0.0436659	−	0.0366401i
$534$		0			0
$535$	−3.24221	−	18.3875i	−0.140173	−	0.794961i
$536$		0			0
$537$	0.0876573	−	1.73759i	0.00378269	−	0.0749823i
$538$		0			0
$539$	15.4868			0.667062
$540$		0			0
$541$	22.4283			0.964266			0.482133	−	0.876098i	$-0.339862\pi$
$541$	22.4283			0.964266			0.482133	+	0.876098i	$0.339862\pi$
$542$		0			0
$543$	−32.6434	+	16.7131i	−1.40086	+	0.717228i
$544$		0			0
$545$	0.925490	+	5.24872i	0.0396436	+	0.224830i
$546$		0			0
$547$	16.0036	+	13.4286i	0.684262	+	0.574164i	0.917248	−	0.398316i	$-0.130405\pi$
$547$	16.0036	+	13.4286i	0.684262	+	0.574164i	−0.232986	+	0.972480i	$0.574850\pi$
$548$		0			0
$549$	−4.26648	+	15.1016i	−0.182089	+	0.644519i
$550$		0			0
$551$	2.53384	−	14.3701i	0.107945	−	0.612188i
$552$		0			0
$553$	45.3744	+	16.5149i	1.92952	+	0.702286i
$554$		0			0
$555$	6.59313	−	0.822620i	0.279863	−	0.0349183i
$556$		0			0
$557$	−4.28920	−	7.42911i	−0.181739	−	0.314782i	0.760734	−	0.649064i	$-0.224839\pi$
$557$	−4.28920	−	7.42911i	−0.181739	−	0.314782i	−0.942473	+	0.334283i	$0.891506\pi$
$558$		0			0
$559$	−1.84254	+	3.19137i	−0.0779311	+	0.134981i
$560$		0			0
$561$	5.96770	+	1.36547i	0.251957	+	0.0576502i
$562$		0			0
$563$	12.0383	−	10.1013i	0.507354	−	0.425720i	−0.352843	−	0.935682i	$-0.614785\pi$
$563$	12.0383	−	10.1013i	0.507354	−	0.425720i	0.860197	+	0.509962i	$0.170341\pi$
$564$		0			0
$565$	21.1699	−	7.70522i	0.890625	−	0.324161i
$566$		0			0
$567$	−34.7986	+	5.16841i	−1.46140	+	0.217053i
$568$		0			0
$569$	−11.9085	+	4.33435i	−0.499231	+	0.181705i	−0.579348	−	0.815080i	$-0.696693\pi$
$569$	−11.9085	+	4.33435i	−0.499231	+	0.181705i	0.0801169	+	0.996785i	$0.474471\pi$
$570$		0			0
$571$	20.1644	−	16.9199i	0.843852	−	0.708076i	−0.114575	−	0.993415i	$-0.536551\pi$
$571$	20.1644	−	16.9199i	0.843852	−	0.708076i	0.958427	+	0.285339i	$0.0921061\pi$
$572$		0			0
$573$	16.5944	+	3.79697i	0.693241	+	0.158621i
$574$		0			0
$575$	10.8516	−	18.7954i	0.452541	−	0.783824i
$576$		0			0
$577$	11.0577	+	19.1525i	0.460338	+	0.797329i	0.998978	−	0.0452074i	$-0.0143949\pi$
$577$	11.0577	+	19.1525i	0.460338	+	0.797329i	−0.538640	+	0.842536i	$0.681062\pi$
$578$		0			0
$579$	19.1742	−	2.39236i	0.796854	−	0.0994230i
$580$		0			0
$581$	−42.9144	−	15.6196i	−1.78039	−	0.648009i
$582$		0			0
$583$	0.924041	−	5.24050i	0.0382699	−	0.217039i
$584$		0			0
$585$	2.40640	−	0.609985i	0.0994923	−	0.0252198i
$586$		0			0
$587$	−10.9568	−	9.19388i	−0.452237	−	0.379472i	0.388028	−	0.921647i	$-0.373156\pi$
$587$	−10.9568	−	9.19388i	−0.452237	−	0.379472i	−0.840265	+	0.542176i	$0.817601\pi$
$588$		0			0
$589$	0.638517	+	3.62121i	0.0263097	+	0.149209i
$590$		0			0
$591$	14.0142	−	7.17514i	0.576468	−	0.295146i
$592$		0			0
$593$	47.7300			1.96004			0.980018	−	0.198908i	$-0.0637397\pi$
$593$	47.7300			1.96004			0.980018	+	0.198908i	$0.0637397\pi$
$594$		0			0
$595$	−8.34334			−0.342044
$596$		0			0
$597$	−1.28229	+	25.4182i	−0.0524808	+	1.04030i
$598$		0			0
$599$	0.0867493	+	0.491980i	0.00354448	+	0.0201018i	0.986529	−	0.163588i	$-0.0523069\pi$
$599$	0.0867493	+	0.491980i	0.00354448	+	0.0201018i	−0.982984	+	0.183690i	$0.941196\pi$
$600$		0			0
$601$	−12.9669	−	10.8805i	−0.528931	−	0.443826i	0.338801	−	0.940858i	$-0.389979\pi$
$601$	−12.9669	−	10.8805i	−0.528931	−	0.443826i	−0.867732	+	0.497032i	$0.834423\pi$
$602$		0			0
$603$	−0.417415	−	5.65169i	−0.0169985	−	0.230155i
$604$		0			0
$605$	1.47135	−	8.34443i	0.0598188	−	0.339249i
$606$		0			0
$607$	0.652741	+	0.237578i	0.0264939	+	0.00964301i	0.355233	−	0.934778i	$-0.384401\pi$
$607$	0.652741	+	0.237578i	0.0264939	+	0.00964301i	−0.328739	+	0.944421i	$0.606624\pi$
$608$		0			0
$609$	−21.7326	−	28.7231i	−0.880649	−	1.16392i
$610$		0			0
$611$	−0.625887	−	1.08407i	−0.0253207	−	0.0438567i
$612$		0			0
$613$	16.3317	−	28.2873i	0.659630	−	1.14251i	−0.321081	−	0.947052i	$-0.604046\pi$
$613$	16.3317	−	28.2873i	0.659630	−	1.14251i	0.980711	−	0.195461i	$-0.0626204\pi$
$614$		0			0
$615$	2.39178	−	2.57495i	0.0964460	−	0.103832i
$616$		0			0
$617$	17.5305	−	14.7098i	0.705751	−	0.592195i	−0.217652	−	0.976026i	$-0.569840\pi$
$617$	17.5305	−	14.7098i	0.705751	−	0.592195i	0.923403	+	0.383831i	$0.125395\pi$
$618$		0			0
$619$	7.97398	−	2.90229i	0.320501	−	0.116653i	−0.176759	−	0.984254i	$-0.556561\pi$
$619$	7.97398	−	2.90229i	0.320501	−	0.116653i	0.497261	+	0.867601i	$0.334339\pi$
$620$		0			0
$621$	−15.7481	−	25.8645i	−0.631951	−	1.03791i
$622$		0			0
$623$	21.0427	−	7.65892i	0.843058	−	0.306848i
$624$		0			0
$625$	5.73752	−	4.81435i	0.229501	−	0.192574i
$626$		0			0
$627$	2.61465	+	8.49272i	0.104419	+	0.339167i
$628$		0			0
$629$	−3.20872	+	5.55767i	−0.127940	+	0.221599i
$630$		0			0
$631$	0.795865	+	1.37848i	0.0316829	+	0.0548763i	0.881432	−	0.472311i	$-0.156580\pi$
$631$	0.795865	+	1.37848i	0.0316829	+	0.0548763i	−0.849749	+	0.527187i	$0.823247\pi$
$632$		0			0
$633$	−5.29373	+	12.5393i	−0.210407	+	0.498394i
$634$		0			0
$635$	−1.13515	−	0.413160i	−0.0450469	−	0.0163957i
$636$		0			0
$637$	−1.05329	+	5.97352i	−0.0417330	+	0.236680i
$638$		0			0
$639$	21.3687	−	29.6546i	0.845333	−	1.17312i
$640$		0			0
$641$	16.6038	+	13.9322i	0.655809	+	0.550289i	0.908827	−	0.417173i	$-0.136979\pi$
$641$	16.6038	+	13.9322i	0.655809	+	0.550289i	−0.253019	+	0.967461i	$0.581423\pi$
$642$		0			0
$643$	1.19853	+	6.79720i	0.0472654	+	0.268056i	0.999278	−	0.0380047i	$-0.0121002\pi$
$643$	1.19853	+	6.79720i	0.0472654	+	0.268056i	−0.952012	+	0.306060i	$0.900989\pi$
$644$		0			0
$645$	−8.26393	−	5.34372i	−0.325392	−	0.210409i
$646$		0			0
$647$	6.18972			0.243343			0.121671	−	0.992570i	$-0.461175\pi$
$647$	6.18972			0.243343			0.121671	+	0.992570i	$0.461175\pi$
$648$		0			0
$649$	21.0614			0.826733
$650$		0			0
$651$	7.62182	+	4.92851i	0.298723	+	0.193164i
$652$		0			0
$653$	−4.72574	−	26.8010i	−0.184933	−	1.04881i	−0.926042	−	0.377421i	$-0.876811\pi$
$653$	−4.72574	−	26.8010i	−0.184933	−	1.04881i	0.741109	−	0.671384i	$-0.234300\pi$
$654$		0			0
$655$	6.61100	+	5.54729i	0.258313	+	0.216751i
$656$		0			0
$657$	−29.5124	−	2.98527i	−1.15139	−	0.116467i
$658$		0			0
$659$	−0.917209	+	5.20175i	−0.0357294	+	0.202631i	−0.997447	−	0.0714110i	$-0.977250\pi$
$659$	−0.917209	+	5.20175i	−0.0357294	+	0.202631i	0.961718	+	0.274043i	$0.0883609\pi$
$660$		0			0
$661$	−10.9616	−	3.98968i	−0.426355	−	0.155181i	0.119925	−	0.992783i	$-0.461734\pi$
$661$	−10.9616	−	3.98968i	−0.426355	−	0.155181i	−0.546280	+	0.837602i	$0.683957\pi$
$662$		0			0
$663$	−0.932564	+	2.20898i	−0.0362178	+	0.0857897i
$664$		0			0
$665$	−6.05527	−	10.4880i	−0.234813	−	0.406708i
$666$		0			0
$667$	15.5015	−	26.8494i	0.600220	−	1.03961i
$668$		0			0
$669$	−4.45470	−	14.4694i	−0.172229	−	0.559421i
$670$		0			0
$671$	7.49510	−	6.28913i	0.289345	−	0.242789i
$672$		0			0
$673$	−46.1412	+	16.7940i	−1.77861	+	0.647362i	−0.778814	+	0.627255i	$0.784178\pi$
$673$	−46.1412	+	16.7940i	−1.77861	+	0.647362i	−0.999798	+	0.0201071i	$0.993599\pi$
$674$		0			0
$675$	−3.80371	−	18.9736i	−0.146405	−	0.730295i
$676$		0			0
$677$	21.2550	−	7.73617i	0.816894	−	0.297325i	0.100426	−	0.994945i	$-0.467980\pi$
$677$	21.2550	−	7.73617i	0.816894	−	0.297325i	0.716469	+	0.697619i	$0.245757\pi$
$678$		0			0
$679$	−1.02822	+	0.862775i	−0.0394593	+	0.0331103i
$680$		0			0
$681$	4.79576	−	5.16302i	0.183774	−	0.197847i
$682$		0			0
$683$	−8.56931	+	14.8425i	−0.327896	+	0.567932i	−0.982094	−	0.188391i	$-0.939673\pi$
$683$	−8.56931	+	14.8425i	−0.327896	+	0.567932i	0.654198	+	0.756323i	$0.273006\pi$
$684$		0			0
$685$	8.83897	+	15.3095i	0.337720	+	0.584947i
$686$		0			0
$687$	16.8841	+	22.3151i	0.644169	+	0.851374i
$688$		0			0
$689$	1.95851	+	0.712838i	0.0746132	+	0.0271570i
$690$		0			0
$691$	−3.17011	+	17.9786i	−0.120597	+	0.683937i	0.863230	+	0.504811i	$0.168438\pi$
$691$	−3.17011	+	17.9786i	−0.120597	+	0.683937i	−0.983826	+	0.179126i	$0.942673\pi$
$692$		0			0
$693$	19.7520	+	9.53826i	0.750315	+	0.362328i
$694$		0			0
$695$	7.49068	+	6.28543i	0.284138	+	0.238420i
$696$		0			0
$697$	0.589436	+	3.34286i	0.0223265	+	0.126620i
$698$		0			0
$699$	−1.50214	+	29.7762i	−0.0568163	+	1.12624i
$700$		0			0
$701$	−2.92075			−0.110315			−0.0551575	−	0.998478i	$-0.517566\pi$
$701$	−2.92075			−0.110315			−0.0551575	+	0.998478i	$0.517566\pi$
$702$		0			0
$703$	−9.31505			−0.351324
$704$		0			0
$705$	2.97558	−	1.52347i	0.112067	−	0.0573771i
$706$		0			0
$707$	−11.8123	−	66.9906i	−0.444246	−	2.51944i
$708$		0			0
$709$	23.0023	+	19.3012i	0.863868	+	0.724872i	0.962798	−	0.270223i	$-0.0870974\pi$
$709$	23.0023	+	19.3012i	0.863868	+	0.724872i	−0.0989295	+	0.995094i	$0.531542\pi$
$710$		0			0
$711$	25.8471	+	26.5569i	0.969342	+	0.995961i
$712$		0			0
$713$	−1.35665	+	7.69393i	−0.0508068	+	0.288140i
$714$		0			0
$715$	−1.45446	−	0.529381i	−0.0543938	−	0.0197977i
$716$		0			0
$717$	−2.63900	+	0.329266i	−0.0985552	+	0.0122967i
$718$		0			0
$719$	20.0285	+	34.6903i	0.746936	+	1.29373i	0.949285	+	0.314418i	$0.101809\pi$
$719$	20.0285	+	34.6903i	0.746936	+	1.29373i	−0.202349	+	0.979314i	$0.564857\pi$
$720$		0			0
$721$	−30.9059	+	53.5306i	−1.15100	+	1.99358i
$722$		0			0
$723$	−9.32289	−	2.13317i	−0.346722	−	0.0793335i
$724$		0			0
$725$	15.1770	−	12.7350i	0.563659	−	0.472966i
$726$		0			0
$727$	−1.44598	+	0.526294i	−0.0536285	+	0.0195192i	−0.368695	−	0.929550i	$-0.620195\pi$
$727$	−1.44598	+	0.526294i	−0.0536285	+	0.0195192i	0.315067	+	0.949070i	$0.397973\pi$
$728$		0			0
$729$	−25.7746	−	8.04171i	−0.954615	−	0.297841i
$730$		0			0
$731$	8.93196	−	3.25097i	0.330361	−	0.120241i
$732$		0			0
$733$	−1.15818	+	0.971827i	−0.0427783	+	0.0358952i	−0.663926	−	0.747798i	$-0.731111\pi$
$733$	−1.15818	+	0.971827i	−0.0427783	+	0.0358952i	0.621148	+	0.783693i	$0.286667\pi$
$734$		0			0
$735$	−15.7905	−	3.61303i	−0.582442	−	0.133269i
$736$		0			0
$737$	−1.76667	+	3.05997i	−0.0650762	+	0.112715i
$738$		0			0
$739$	10.6779	+	18.4946i	0.392792	+	0.680336i	0.992817	−	0.119646i	$-0.0381758\pi$
$739$	10.6779	+	18.4946i	0.392792	+	0.680336i	−0.600024	+	0.799982i	$0.704843\pi$
$740$		0			0
$741$	−3.45362	+	0.430906i	−0.126872	+	0.0158297i
$742$		0			0
$743$	−19.1028	−	6.95284i	−0.700812	−	0.255075i	−0.0330547	−	0.999454i	$-0.510524\pi$
$743$	−19.1028	−	6.95284i	−0.700812	−	0.255075i	−0.667758	+	0.744379i	$0.732746\pi$
$744$		0			0
$745$	0.483262	−	2.74072i	0.0177054	−	0.100412i
$746$		0			0
$747$	−24.4458	−	25.1171i	−0.894425	−	0.918987i
$748$		0			0
$749$	49.4970	+	41.5329i	1.80858	+	1.51758i
$750$		0			0
$751$	−0.740289	−	4.19839i	−0.0270135	−	0.153201i	0.968317	−	0.249723i	$-0.0803395\pi$
$751$	−0.740289	−	4.19839i	−0.0270135	−	0.153201i	−0.995331	+	0.0965214i	$0.969228\pi$
$752$		0			0
$753$	33.0560	−	16.9244i	1.20463	−	0.616758i
$754$		0			0
$755$	−11.8754			−0.432189
$756$		0			0
$757$	54.3419			1.97509			0.987546	−	0.157332i	$-0.0502892\pi$
$757$	54.3419			1.97509			0.987546	+	0.157332i	$0.0502892\pi$
$758$		0			0
$759$	−0.951252	+	18.8562i	−0.0345282	+	0.684435i
$760$		0			0
$761$	3.15364	+	17.8852i	0.114319	+	0.648338i	0.987085	+	0.160198i	$0.0512133\pi$
$761$	3.15364	+	17.8852i	0.114319	+	0.648338i	−0.872765	+	0.488140i	$0.837676\pi$
$762$		0			0
$763$	−14.1289	−	11.8556i	−0.511502	−	0.429201i
$764$		0			0
$765$	−5.76618	−	2.78450i	−0.208477	−	0.100674i
$766$		0			0
$767$	−1.43244	+	8.12376i	−0.0517224	+	0.293332i
$768$		0			0
$769$	−23.3558	−	8.50082i	−0.842232	−	0.306547i	−0.115363	−	0.993323i	$-0.536803\pi$
$769$	−23.3558	−	8.50082i	−0.842232	−	0.306547i	−0.726869	+	0.686776i	$0.759025\pi$
$770$		0			0
$771$	−15.4530	−	20.4236i	−0.556526	−	0.735539i
$772$		0			0
$773$	−19.2416	−	33.3274i	−0.692071	−	1.19870i	−0.971158	−	0.238437i	$-0.923365\pi$
$773$	−19.2416	−	33.3274i	−0.692071	−	1.19870i	0.279087	−	0.960266i	$-0.409968\pi$
$774$		0			0
$775$	−2.49629	+	4.32369i	−0.0896692	+	0.155312i
$776$		0			0
$777$	−15.6484	+	16.8468i	−0.561385	+	0.604376i
$778$		0			0
$779$	−3.77436	+	3.16707i	−0.135231	+	0.113472i
$780$		0			0
$781$	−21.4150	+	7.79443i	−0.766290	+	0.278907i
$782$		0			0
$783$	−5.43361	−	27.1039i	−0.194181	−	0.968615i
$784$		0			0
$785$	0.382058	−	0.139058i	0.0136362	−	0.00496319i
$786$		0			0
$787$	0.821566	−	0.689376i	0.0292857	−	0.0245736i	−0.628027	−	0.778191i	$-0.716137\pi$
$787$	0.821566	−	0.689376i	0.0292857	−	0.0245736i	0.657313	+	0.753618i	$0.271693\pi$
$788$		0			0
$789$	1.42840	+	4.63962i	0.0508523	+	0.165175i
$790$		0			0
$791$	−38.9814	+	67.5177i	−1.38602	+	2.40065i
$792$		0			0
$793$	1.91607	+	3.31873i	0.0680417	+	0.117852i
$794$		0			0
$795$	−2.16476	+	5.12770i	−0.0767761	+	0.181861i
$796$		0			0
$797$	−23.7246	−	8.63505i	−0.840369	−	0.305869i	−0.114262	−	0.993451i	$-0.536450\pi$
$797$	−23.7246	−	8.63505i	−0.840369	−	0.305869i	−0.726107	+	0.687581i	$0.758672\pi$
$798$		0			0
$799$	−0.560674	+	3.17974i	−0.0198352	+	0.112491i
$800$		0			0
$801$	17.0989	+	1.72961i	0.604161	+	0.0611127i
$802$		0			0
$803$	14.1676	+	11.8880i	0.499963	+	0.419519i
$804$		0			0
$805$	−4.46815	−	25.3401i	−0.157482	−	0.893122i
$806$		0			0
$807$	0.518556	+	0.335315i	0.0182540	+	0.0118036i
$808$		0			0
$809$	−11.7337			−0.412536			−0.206268	−	0.978495i	$-0.566132\pi$
$809$	−11.7337			−0.412536			−0.206268	+	0.978495i	$0.566132\pi$
$810$		0			0
$811$	38.4085			1.34871			0.674353	−	0.738409i	$-0.264423\pi$
$811$	38.4085			1.34871			0.674353	+	0.738409i	$0.264423\pi$
$812$		0			0
$813$	−17.6668	−	11.4239i	−0.619603	−	0.400655i
$814$		0			0
$815$	2.86733	+	16.2615i	0.100438	+	0.569614i
$816$		0			0
$817$	10.5691	+	8.86853i	0.369766	+	0.310271i
$818$		0			0
$819$	−5.02246	+	6.96996i	−0.175499	+	0.243550i
$820$		0			0
$821$	4.64197	−	26.3259i	0.162006	−	0.918781i	−0.790092	−	0.612988i	$-0.789967\pi$
$821$	4.64197	−	26.3259i	0.162006	−	0.918781i	0.952098	−	0.305793i	$-0.0989216\pi$
$822$		0			0
$823$	4.10107	+	1.49267i	0.142954	+	0.0520311i	0.412506	−	0.910955i	$-0.364653\pi$
$823$	4.10107	+	1.49267i	0.142954	+	0.0520311i	−0.269552	+	0.962986i	$0.586876\pi$
$824$		0			0
$825$	−4.69251	+	11.1152i	−0.163372	+	0.386983i
$826$		0			0
$827$	−19.5727	−	33.9009i	−0.680610	−	1.17885i	−0.974795	−	0.223102i	$-0.928382\pi$
$827$	−19.5727	−	33.9009i	−0.680610	−	1.17885i	0.294185	−	0.955748i	$-0.404952\pi$
$828$		0			0
$829$	16.4433	−	28.4807i	0.571101	−	0.989176i	−0.425352	−	0.905028i	$-0.639850\pi$
$829$	16.4433	−	28.4807i	0.571101	−	0.989176i	0.996453	−	0.0841481i	$-0.0268169\pi$
$830$		0			0
$831$	−12.7359	−	41.3678i	−0.441803	−	1.43503i
$832$		0			0
$833$	11.9853	−	10.0568i	0.415264	−	0.348448i
$834$		0			0
$835$	−2.30950	+	0.840588i	−0.0799234	+	0.0290898i
$836$		0			0
$837$	3.62269	+	5.94986i	0.125219	+	0.205657i
$838$		0			0
$839$	29.7322	−	10.8216i	1.02647	−	0.373604i	0.226734	−	0.973957i	$-0.427195\pi$
$839$	29.7322	−	10.8216i	1.02647	−	0.373604i	0.799735	+	0.600353i	$0.204973\pi$
$840$		0			0
$841$	−0.534920	+	0.448851i	−0.0184455	+	0.0154776i
$842$		0			0
$843$	−8.63203	+	9.29308i	−0.297303	+	0.320071i
$844$		0			0
$845$	−7.03892	+	12.1918i	−0.242146	+	0.419410i
$846$		0			0
$847$	14.6612	+	25.3939i	0.503764	+	0.872545i
$848$		0			0
$849$	15.0366	+	19.8734i	0.516056	+	0.682052i
$850$		0			0
$851$	−18.5980	−	6.76910i	−0.637530	−	0.232042i
$852$		0			0
$853$	−0.982440	+	5.57169i	−0.0336381	+	0.190771i	−0.996997	−	0.0774461i	$-0.975323\pi$
$853$	−0.982440	+	5.57169i	−0.0336381	+	0.190771i	0.963358	+	0.268217i	$0.0864345\pi$
$854$		0			0
$855$	−0.684599	−	9.26928i	−0.0234128	−	0.317003i
$856$		0			0
$857$	−31.5690	−	26.4895i	−1.07838	−	0.904864i	−0.0825904	−	0.996584i	$-0.526319\pi$
$857$	−31.5690	−	26.4895i	−1.07838	−	0.904864i	−0.995785	+	0.0917193i	$0.970764\pi$
$858$		0			0
$859$	−6.22605	−	35.3097i	−0.212430	−	1.20475i	−0.885311	−	0.465000i	$-0.846054\pi$
$859$	−6.22605	−	35.3097i	−0.212430	−	1.20475i	0.672880	−	0.739751i	$-0.265057\pi$
$860$		0			0
$861$	−0.612766	+	12.1465i	−0.0208830	+	0.413953i
$862$		0			0
$863$	−20.9694			−0.713806			−0.356903	−	0.934142i	$-0.616167\pi$
$863$	−20.9694			−0.713806			−0.356903	+	0.934142i	$0.616167\pi$
$864$		0			0
$865$	19.8427			0.674673
$866$		0			0
$867$	−20.7043	+	10.6004i	−0.703153	+	0.360008i
$868$		0			0
$869$	−4.01223	−	22.7545i	−0.136106	−	0.771893i
$870$		0			0
$871$	−1.06013	−	0.889553i	−0.0359210	−	0.0301413i
$872$		0			0
$873$	−0.998554	+	0.253118i	−0.0337959	+	0.00856675i
$874$		0			0
$875$	6.68887	−	37.9345i	0.226125	−	1.28242i
$876$		0			0
$877$	−19.2735	−	7.01498i	−0.650819	−	0.236879i	−0.00455171	−	0.999990i	$-0.501449\pi$
$877$	−19.2735	−	7.01498i	−0.650819	−	0.236879i	−0.646268	+	0.763111i	$0.723671\pi$
$878$		0			0
$879$	24.7763	−	3.09132i	0.835684	−	0.104268i
$880$		0			0
$881$	19.1438	+	33.1581i	0.644972	+	1.11712i	0.984308	+	0.176459i	$0.0564644\pi$
$881$	19.1438	+	33.1581i	0.644972	+	1.11712i	−0.339336	+	0.940665i	$0.610202\pi$
$882$		0			0
$883$	−8.72326	+	15.1091i	−0.293561	+	0.508463i	−0.974649	−	0.223739i	$-0.928174\pi$
$883$	−8.72326	+	15.1091i	−0.293561	+	0.508463i	0.681088	+	0.732201i	$0.261507\pi$
$884$		0			0
$885$	−21.4745	−	4.91358i	−0.721857	−	0.165168i
$886$		0			0
$887$	41.5325	−	34.8499i	1.39453	−	1.17015i	0.431058	−	0.902324i	$-0.358140\pi$
$887$	41.5325	−	34.8499i	1.39453	−	1.17015i	0.963468	−	0.267823i	$-0.0863041\pi$
$888$		0			0
$889$	3.92831	−	1.42979i	0.131751	−	0.0479536i
$890$		0			0
$891$	10.4675	+	13.1840i	0.350675	+	0.441681i
$892$		0			0
$893$	−4.40402	+	1.60293i	−0.147375	+	0.0536400i
$894$		0			0
$895$	0.869150	−	0.729303i	0.0290525	−	0.0243779i
$896$		0			0
$897$	−7.20846	−	1.64937i	−0.240683	−	0.0550708i
$898$		0			0
$899$	−3.56595	+	6.17641i	−0.118931	+	0.205995i
$900$		0			0
$901$	−2.68796	−	4.65569i	−0.0895491	−	0.155104i
$902$		0			0
$903$	33.7944	−	4.21650i	1.12461	−	0.140316i
$904$		0			0
$905$	−22.4738	−	8.17979i	−0.747054	−	0.271906i
$906$		0			0
$907$	−4.98078	+	28.2474i	−0.165384	+	0.937939i	0.783284	+	0.621665i	$0.213543\pi$
$907$	−4.98078	+	28.2474i	−0.165384	+	0.937939i	−0.948668	+	0.316275i	$0.897568\pi$
$908$		0			0
$909$	14.1938	−	50.2402i	0.470779	−	1.66636i
$910$		0			0
$911$	21.7416	+	18.2433i	0.720330	+	0.604429i	0.927477	−	0.373881i	$-0.121973\pi$
$911$	21.7416	+	18.2433i	0.720330	+	0.604429i	−0.207146	+	0.978310i	$0.566418\pi$
$912$		0			0
$913$	3.79471	+	21.5208i	0.125586	+	0.712236i
$914$		0			0
$915$	−9.10934	+	4.66389i	−0.301146	+	0.154184i
$916$		0			0
$917$	−29.8653			−0.986240
$918$		0			0
$919$	−37.7786			−1.24620			−0.623101	−	0.782141i	$-0.714127\pi$
$919$	−37.7786			−1.24620			−0.623101	+	0.782141i	$0.714127\pi$
$920$		0			0
$921$	−2.65576	+	52.6438i	−0.0875104	+	1.73467i
$922$		0			0
$923$	−1.54996	−	8.79027i	−0.0510176	−	0.289335i
$924$		0			0
$925$	−9.68860	−	8.12970i	−0.318559	−	0.267303i
$926$		0			0
$927$	−39.2247	+	26.6811i	−1.28831	+	0.876323i
$928$		0			0
$929$	−6.00421	+	34.0516i	−0.196992	+	1.11720i	0.712562	+	0.701609i	$0.247535\pi$
$929$	−6.00421	+	34.0516i	−0.196992	+	1.11720i	−0.909554	+	0.415586i	$0.863576\pi$
$930$		0			0
$931$	21.3404	+	7.76726i	0.699403	+	0.254562i
$932$		0			0
$933$	14.6265	+	19.3312i	0.478849	+	0.632877i
$934$		0			0
$935$	1.99618	+	3.45749i	0.0652822	+	0.113072i
$936$		0			0
$937$	9.71839	−	16.8328i	0.317486	−	0.549902i	−0.662477	−	0.749082i	$-0.730495\pi$
$937$	9.71839	−	16.8328i	0.317486	−	0.549902i	0.979963	+	0.199180i	$0.0638280\pi$
$938$		0			0
$939$	−26.0363	+	28.0302i	−0.849663	+	0.914731i
$940$		0			0
$941$	7.61330	−	6.38832i	0.248187	−	0.208253i	−0.510204	−	0.860053i	$-0.670430\pi$
$941$	7.61330	−	6.38832i	0.248187	−	0.208253i	0.758391	+	0.651800i	$0.225986\pi$
$942$		0			0
$943$	−9.83716	+	3.58043i	−0.320342	+	0.116595i
$944$		0			0
$945$	−17.9141	−	14.3334i	−0.582746	−	0.466266i
$946$		0			0
$947$	15.8909	−	5.78380i	0.516384	−	0.187948i	−0.0706647	−	0.997500i	$-0.522512\pi$
$947$	15.8909	−	5.78380i	0.516384	−	0.187948i	0.587048	+	0.809552i	$0.300290\pi$
$948$		0			0
$949$	−5.54899	+	4.65616i	−0.180128	+	0.151145i
$950$		0			0
$951$	−8.86198	−	28.7849i	−0.287369	−	0.933413i
$952$		0			0
$953$	−8.67866	+	15.0319i	−0.281129	+	0.486930i	−0.971663	−	0.236370i	$-0.924042\pi$
$953$	−8.67866	+	15.0319i	−0.281129	+	0.486930i	0.690534	+	0.723300i	$0.257376\pi$
$954$		0			0
$955$	5.55079	+	9.61426i	0.179620	+	0.311110i
$956$		0			0
$957$	−6.70327	+	15.8782i	−0.216686	+	0.513268i
$958$		0			0
$959$	−57.4872	−	20.9236i	−1.85636	−	0.675659i
$960$		0			0
$961$	−5.07101	+	28.7591i	−0.163581	+	0.927714i
$962$		0			0
$963$	20.3468	+	45.2230i	0.655667	+	1.45729i
$964$		0			0
$965$	9.65315	+	8.09995i	0.310746	+	0.260747i
$966$		0			0
$967$	2.91440	+	16.5284i	0.0937207	+	0.531517i	0.995132	+	0.0985525i	$0.0314212\pi$
$967$	2.91440	+	16.5284i	0.0937207	+	0.531517i	−0.901411	+	0.432964i	$0.857468\pi$
$968$		0			0
$969$	7.53850	+	4.87464i	0.242172	+	0.156596i
$970$		0			0
$971$	33.4811			1.07446			0.537230	−	0.843436i	$-0.319471\pi$
$971$	33.4811			1.07446			0.537230	+	0.843436i	$0.319471\pi$
$972$		0			0
$973$	−33.8393			−1.08484
$974$		0			0
$975$	−3.96819	−	2.56596i	−0.127084	−	0.0821765i
$976$		0			0
$977$	3.94786	+	22.3894i	0.126303	+	0.716302i	0.980525	+	0.196393i	$0.0629229\pi$
$977$	3.94786	+	22.3894i	0.126303	+	0.716302i	−0.854222	+	0.519909i	$0.825966\pi$
$978$		0			0
$979$	−8.20843	−	6.88769i	−0.262342	−	0.220131i
$980$		0			0
$981$	−5.80800	−	12.9089i	−0.185435	−	0.412150i
$982$		0			0
$983$	−8.18917	+	46.4431i	−0.261194	+	1.48131i	0.518464	+	0.855100i	$0.326504\pi$
$983$	−8.18917	+	46.4431i	−0.261194	+	1.48131i	−0.779658	+	0.626206i	$0.784607\pi$
$984$		0			0
$985$	9.64828	+	3.51169i	0.307420	+	0.111892i
$986$		0			0
$987$	−4.49936	+	10.6577i	−0.143216	+	0.339238i
$988$		0			0
$989$	14.6571	+	25.3869i	0.466069	+	0.807255i
$990$		0			0
$991$	−2.18837	+	3.79036i	−0.0695158	+	0.120405i	−0.898688	−	0.438588i	$-0.855479\pi$
$991$	−2.18837	+	3.79036i	−0.0695158	+	0.120405i	0.829172	+	0.558993i	$0.188812\pi$
$992$		0			0
$993$	0.440404	+	1.43049i	0.0139758	+	0.0453952i
$994$		0			0
$995$	−12.7143	+	10.6686i	−0.403072	+	0.338217i
$996$		0			0
$997$	2.01517	−	0.733462i	0.0638211	−	0.0232290i	−0.309912	−	0.950765i	$-0.600300\pi$
$997$	2.01517	−	0.733462i	0.0638211	−	0.0232290i	0.373733	+	0.927536i	$0.378077\pi$
$998$		0			0
$999$	−16.4373	+	6.42052i	−0.520052	+	0.203136i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.u.c.385.1		12
4.3	odd	2		27.2.e.a.7.1	yes	12
12.11	even	2		81.2.e.a.19.2		12
20.3	even	4		675.2.u.b.574.4		24
20.7	even	4		675.2.u.b.574.1		24
20.19	odd	2		675.2.l.c.601.2		12
27.4	even	9	inner	432.2.u.c.193.1		12
36.7	odd	6		243.2.e.d.136.2		12
36.11	even	6		243.2.e.a.136.1		12
36.23	even	6		243.2.e.b.217.1		12
36.31	odd	6		243.2.e.c.217.2		12
108.7	odd	18		729.2.c.e.487.1		12
108.11	even	18		729.2.c.b.244.6		12
108.23	even	18		81.2.e.a.64.2		12
108.31	odd	18		27.2.e.a.4.1	✓	12
108.43	odd	18		729.2.c.e.244.1		12
108.47	even	18		729.2.c.b.487.6		12
108.59	even	18		243.2.e.b.28.1		12
108.67	odd	18		243.2.e.d.109.2		12
108.79	odd	18		729.2.a.a.1.6		6
108.83	even	18		729.2.a.d.1.1		6
108.95	even	18		243.2.e.a.109.1		12
108.103	odd	18		243.2.e.c.28.2		12
540.139	odd	18		675.2.l.c.301.2		12
540.247	even	36		675.2.u.b.274.4		24
540.463	even	36		675.2.u.b.274.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.4.1	✓	12	108.31	odd	18
27.2.e.a.7.1	yes	12	4.3	odd	2
81.2.e.a.19.2		12	12.11	even	2
81.2.e.a.64.2		12	108.23	even	18
243.2.e.a.109.1		12	108.95	even	18
243.2.e.a.136.1		12	36.11	even	6
243.2.e.b.28.1		12	108.59	even	18
243.2.e.b.217.1		12	36.23	even	6
243.2.e.c.28.2		12	108.103	odd	18
243.2.e.c.217.2		12	36.31	odd	6
243.2.e.d.109.2		12	108.67	odd	18
243.2.e.d.136.2		12	36.7	odd	6
432.2.u.c.193.1		12	27.4	even	9	inner
432.2.u.c.385.1		12	1.1	even	1	trivial
675.2.l.c.301.2		12	540.139	odd	18
675.2.l.c.601.2		12	20.19	odd	2
675.2.u.b.274.1		24	540.463	even	36
675.2.u.b.274.4		24	540.247	even	36
675.2.u.b.574.1		24	20.7	even	4
675.2.u.b.574.4		24	20.3	even	4
729.2.a.a.1.6		6	108.79	odd	18
729.2.a.d.1.1		6	108.83	even	18
729.2.c.b.244.6		12	108.11	even	18
729.2.c.b.487.6		12	108.47	even	18
729.2.c.e.244.1		12	108.43	odd	18
729.2.c.e.487.1		12	108.7	odd	18

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.u (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.45446 - 0.940501i) q^{3} +(-0.196143 - 1.11238i) q^{5} +(2.99441 + 2.51261i) q^{7} +(1.23092 + 2.73584i) q^{9} +O(q^{10})\)	\(q+(-1.45446 - 0.940501i) q^{3} +(-0.196143 - 1.11238i) q^{5} +(2.99441 + 2.51261i) q^{7} +(1.23092 + 2.73584i) q^{9} +(0.324801 - 1.84204i) q^{11} +(0.688417 + 0.250563i) q^{13} +(-0.760915 + 1.80239i) q^{15} +(-0.944822 - 1.63648i) q^{17} +(1.37143 - 2.37538i) q^{19} +(-1.99214 - 6.47073i) q^{21} +(4.46428 - 3.74597i) q^{23} +(3.49954 - 1.27373i) q^{25} +(0.782746 - 5.13686i) q^{27} +(4.99910 - 1.81953i) q^{29} +(-1.02696 + 0.861722i) q^{31} +(-2.20485 + 2.37370i) q^{33} +(2.20765 - 3.82376i) q^{35} +(-1.69806 - 2.94112i) q^{37} +(-0.765621 - 1.01189i) q^{39} +(-1.68800 - 0.614382i) q^{41} +(-0.873477 + 4.95373i) q^{43} +(2.80187 - 1.90587i) q^{45} +(-1.30892 - 1.09832i) q^{47} +(1.43775 + 8.15389i) q^{49} +(-0.164904 + 3.26880i) q^{51} +2.84494 q^{53} -2.11276 q^{55} +(-4.22874 + 2.16507i) q^{57} +(1.95529 + 11.0890i) q^{59} +(4.00710 + 3.36235i) q^{61} +(-3.18824 + 11.2850i) q^{63} +(0.143694 - 0.814930i) q^{65} +(-1.77511 - 0.646086i) q^{67} +(-10.0162 + 1.24972i) q^{69} +(-6.09193 - 10.5515i) q^{71} +(-4.94384 + 8.56298i) q^{73} +(-6.28788 - 1.43873i) q^{75} +(5.60091 - 4.69972i) q^{77} +(11.6079 - 4.22493i) q^{79} +(-5.96969 + 6.73519i) q^{81} +(-10.9786 + 3.99588i) q^{83} +(-1.63507 + 1.37199i) q^{85} +(-8.98227 - 2.05523i) q^{87} +(2.86437 - 4.96123i) q^{89} +(1.43183 + 2.48001i) q^{91} +(2.30412 - 0.287484i) q^{93} +(-2.91133 - 1.05964i) q^{95} +(-0.0596270 + 0.338162i) q^{97} +(5.43934 - 1.37879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7}+O(q^{10}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7	\( 12 q + 6 q^{3} - 3 q^{5} + 6 q^{7} - 3 q^{11} - 6 q^{13} - 9 q^{15} + 9 q^{17} + 3 q^{19} - 12 q^{21} + 12 q^{23} + 3 q^{25} + 9 q^{27} - 6 q^{29} - 3 q^{31} - 12 q^{35} - 3 q^{37} - 33 q^{39} + 15 q^{41} - 3 q^{43} - 9 q^{45} + 15 q^{47} + 12 q^{49} + 18 q^{51} - 18 q^{53} + 12 q^{55} - 3 q^{57} + 12 q^{59} + 12 q^{61} - 9 q^{63} + 3 q^{65} + 15 q^{67} + 9 q^{69} - 27 q^{71} + 6 q^{73} - 39 q^{75} + 15 q^{77} + 42 q^{79} + 36 q^{81} - 39 q^{83} - 27 q^{85} - 9 q^{87} + 9 q^{89} - 6 q^{91} - 39 q^{93} + 33 q^{95} + 3 q^{97} + 27 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 - 3 * q^5 + 6 * q^7 - 3 * q^11 - 6 * q^13 - 9 * q^15 + 9 * q^17 + 3 * q^19 - 12 * q^21 + 12 * q^23 + 3 * q^25 + 9 * q^27 - 6 * q^29 - 3 * q^31 - 12 * q^35 - 3 * q^37 - 33 * q^39 + 15 * q^41 - 3 * q^43 - 9 * q^45 + 15 * q^47 + 12 * q^49 + 18 * q^51 - 18 * q^53 + 12 * q^55 - 3 * q^57 + 12 * q^59 + 12 * q^61 - 9 * q^63 + 3 * q^65 + 15 * q^67 + 9 * q^69 - 27 * q^71 + 6 * q^73 - 39 * q^75 + 15 * q^77 + 42 * q^79 + 36 * q^81 - 39 * q^83 - 27 * q^85 - 9 * q^87 + 9 * q^89 - 6 * q^91 - 39 * q^93 + 33 * q^95 + 3 * q^97 + 27 * q^99

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