LMFDB - Embedded newform 432.2.k.d.109.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,2,Mod(109,432)]

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([0, 3, 0]))

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

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

chi := DirichletCharacter("432.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	432.k (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			109.13
Character	$\chi$	$=$	432.109
Dual form			432.2.k.d.325.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.24081 - 0.678517i) q^{2} +(1.07923 - 1.68382i) q^{4} +(-0.920303 + 0.920303i) q^{5} -4.02115i q^{7} +(0.196619 - 2.82158i) q^{8} +O(q^{10})$	\(q+(1.24081 - 0.678517i) q^{2} +(1.07923 - 1.68382i) q^{4} +(-0.920303 + 0.920303i) q^{5} -4.02115i q^{7} +(0.196619 - 2.82158i) q^{8} +(-0.517482 + 1.76636i) q^{10} +(0.00588626 - 0.00588626i) q^{11} +(-1.05208 - 1.05208i) q^{13} +(-2.72841 - 4.98949i) q^{14} +(-1.67053 - 3.63447i) q^{16} +8.16285 q^{17} +(-2.21973 - 2.21973i) q^{19} +(0.556409 + 2.54285i) q^{20} +(0.00330982 - 0.0112977i) q^{22} +4.29419i q^{23} +3.30609i q^{25} +(-2.01929 - 0.591579i) q^{26} +(-6.77090 - 4.33974i) q^{28} +(-1.74222 - 1.74222i) q^{29} +4.60192 q^{31} +(-4.53885 - 3.37621i) q^{32} +(10.1286 - 5.53863i) q^{34} +(3.70067 + 3.70067i) q^{35} +(-3.07984 + 3.07984i) q^{37} +(-4.26039 - 1.24814i) q^{38} +(2.41576 + 2.77766i) q^{40} +9.43396i q^{41} +(6.55387 - 6.55387i) q^{43} +(-0.00355880 - 0.0162641i) q^{44} +(2.91368 + 5.32828i) q^{46} +2.90237 q^{47} -9.16961 q^{49} +(2.24323 + 4.10223i) q^{50} +(-2.90695 + 0.636081i) q^{52} +(-8.65803 + 8.65803i) q^{53} +0.0108343i q^{55} +(-11.3460 - 0.790635i) q^{56} +(-3.34390 - 0.979643i) q^{58} +(-6.98627 + 6.98627i) q^{59} +(-0.243756 - 0.243756i) q^{61} +(5.71012 - 3.12248i) q^{62} +(-7.92268 - 1.10956i) q^{64} +1.93646 q^{65} +(4.55053 + 4.55053i) q^{67} +(8.80959 - 13.7448i) q^{68} +(7.10281 + 2.08087i) q^{70} -10.8858i q^{71} +7.35651i q^{73} +(-1.73178 + 5.91124i) q^{74} +(-6.13323 + 1.34203i) q^{76} +(-0.0236695 - 0.0236695i) q^{77} +8.69300 q^{79} +(4.88220 + 1.80742i) q^{80} +(6.40110 + 11.7058i) q^{82} +(8.93029 + 8.93029i) q^{83} +(-7.51229 + 7.51229i) q^{85} +(3.68521 - 12.5790i) q^{86} +(-0.0154512 - 0.0177659i) q^{88} -9.17677i q^{89} +(-4.23056 + 4.23056i) q^{91} +(7.23065 + 4.63442i) q^{92} +(3.60129 - 1.96930i) q^{94} +4.08565 q^{95} +3.27186 q^{97} +(-11.3778 + 6.22174i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) $ 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	1.24081	−	0.678517i	0.877387	−	0.479784i
$2$	1.24081	−	0.678517i	0.877387	−	0.479784i
$3$		0			0
$3$		0			0
$4$	1.07923	−	1.68382i	0.539615	−	0.841912i
$5$	−0.920303	+	0.920303i	−0.411572	+	0.411572i	−0.882286	−	0.470714i	$-0.843996\pi$
$5$	−0.920303	+	0.920303i	−0.411572	+	0.411572i	0.470714	+	0.882286i	$0.343996\pi$
$6$		0			0
$7$		−	4.02115i		−	1.51985i	−0.650011	−	0.759925i	$-0.725236\pi$
$7$		−	4.02115i		−	1.51985i	0.650011	−	0.759925i	$-0.274764\pi$
$8$	0.196619	−	2.82158i	0.0695154	−	0.997581i
$9$		0			0
$10$	−0.517482	+	1.76636i	−0.163642	+	0.558573i
$11$	0.00588626	−	0.00588626i	0.00177477	−	0.00177477i	−0.706219	−	0.707994i	$-0.749601\pi$
$11$	0.00588626	−	0.00588626i	0.00177477	−	0.00177477i	0.707994	+	0.706219i	$0.249601\pi$
$12$		0			0
$13$	−1.05208	−	1.05208i	−0.291794	−	0.291794i	0.545994	−	0.837789i	$-0.316152\pi$
$13$	−1.05208	−	1.05208i	−0.291794	−	0.291794i	−0.837789	+	0.545994i	$0.816152\pi$
$14$	−2.72841	−	4.98949i	−0.729200	−	1.33350i
$15$		0			0
$16$	−1.67053	−	3.63447i	−0.417631	−	0.908617i
$17$	8.16285			1.97978			0.989890	−	0.141834i	$-0.0452998\pi$
$17$	8.16285			1.97978			0.989890	+	0.141834i	$0.0452998\pi$
$18$		0			0
$19$	−2.21973	−	2.21973i	−0.509241	−	0.509241i	0.405053	−	0.914293i	$-0.367253\pi$
$19$	−2.21973	−	2.21973i	−0.509241	−	0.509241i	−0.914293	+	0.405053i	$0.867253\pi$
$20$	0.556409	+	2.54285i	0.124417	+	0.568598i
$21$		0			0
$22$	0.00330982	−	0.0112977i	0.000705655	−	0.00240867i
$23$			4.29419i			0.895400i	0.894184	+	0.447700i	$0.147757\pi$
$23$			4.29419i			0.895400i	−0.894184	+	0.447700i	$0.852243\pi$
$24$		0			0
$25$			3.30609i			0.661217i
$26$	−2.01929	−	0.591579i	−0.396015	−	0.116018i
$27$		0			0
$28$	−6.77090	−	4.33974i	−1.27958	−	0.820134i
$29$	−1.74222	−	1.74222i	−0.323522	−	0.323522i	0.526594	−	0.850117i	$-0.323469\pi$
$29$	−1.74222	−	1.74222i	−0.323522	−	0.323522i	−0.850117	+	0.526594i	$0.823469\pi$
$30$		0			0
$31$	4.60192			0.826530			0.413265	−	0.910611i	$-0.364388\pi$
$31$	4.60192			0.826530			0.413265	+	0.910611i	$0.364388\pi$
$32$	−4.53885	−	3.37621i	−0.802364	−	0.596835i
$33$		0			0
$34$	10.1286	−	5.53863i	1.73703	−	0.949867i
$35$	3.70067	+	3.70067i	0.625528	+	0.625528i
$36$		0			0
$37$	−3.07984	+	3.07984i	−0.506323	+	0.506323i	−0.913396	−	0.407073i	$-0.866550\pi$
$37$	−3.07984	+	3.07984i	−0.506323	+	0.506323i	0.407073	+	0.913396i	$0.366550\pi$
$38$	−4.26039	−	1.24814i	−0.691127	−	0.202476i
$39$		0			0
$40$	2.41576	+	2.77766i	0.381966	+	0.439187i
$41$			9.43396i			1.47334i	0.676254	+	0.736669i	$0.263602\pi$
$41$			9.43396i			1.47334i	−0.676254	+	0.736669i	$0.736398\pi$
$42$		0			0
$43$	6.55387	−	6.55387i	0.999456	−	0.999456i	−0.000543587	−	1.00000i	$-0.500173\pi$
$43$	6.55387	−	6.55387i	0.999456	−	0.999456i	1.00000		0.000543587i	$0.000173029\pi$
$44$	−0.00355880	−	0.0162641i	−0.000536509	−	0.00245190i
$45$		0			0
$46$	2.91368	+	5.32828i	0.429598	+	0.785612i
$47$	2.90237			0.423354			0.211677	−	0.977340i	$-0.432108\pi$
$47$	2.90237			0.423354			0.211677	+	0.977340i	$0.432108\pi$
$48$		0			0
$49$	−9.16961			−1.30994
$50$	2.24323	+	4.10223i	0.317241	+	0.580143i
$51$		0			0
$52$	−2.90695	+	0.636081i	−0.403122	+	0.0882085i
$53$	−8.65803	+	8.65803i	−1.18927	+	1.18927i	−0.212004	+	0.977269i	$0.567999\pi$
$53$	−8.65803	+	8.65803i	−1.18927	+	1.18927i	−0.977269	+	0.212004i	$0.932001\pi$
$54$		0			0
$55$			0.0108343i			0.00146089i
$56$	−11.3460	−	0.790635i	−1.51617	−	0.105653i
$57$		0			0
$58$	−3.34390	−	0.979643i	−0.439075	−	0.128633i
$59$	−6.98627	+	6.98627i	−0.909534	+	0.909534i	−0.996234	−	0.0867000i	$-0.972368\pi$
$59$	−6.98627	+	6.98627i	−0.909534	+	0.909534i	0.0867000	+	0.996234i	$0.472368\pi$
$60$		0			0
$61$	−0.243756	−	0.243756i	−0.0312098	−	0.0312098i	0.691330	−	0.722539i	$-0.257025\pi$
$61$	−0.243756	−	0.243756i	−0.0312098	−	0.0312098i	−0.722539	+	0.691330i	$0.757025\pi$
$62$	5.71012	−	3.12248i	0.725186	−	0.396555i
$63$		0			0
$64$	−7.92268	−	1.10956i	−0.990335	−	0.138694i
$65$	1.93646			0.240189
$66$		0			0
$67$	4.55053	+	4.55053i	0.555936	+	0.555936i	0.928148	−	0.372212i	$-0.121401\pi$
$67$	4.55053	+	4.55053i	0.555936	+	0.555936i	−0.372212	+	0.928148i	$0.621401\pi$
$68$	8.80959	−	13.7448i	1.06832	−	1.66680i
$69$		0			0
$70$	7.10281	+	2.08087i	0.848948	+	0.248712i
$71$		−	10.8858i		−	1.29191i	−0.763378	−	0.645953i	$-0.776460\pi$
$71$		−	10.8858i		−	1.29191i	0.763378	−	0.645953i	$-0.223540\pi$
$72$		0			0
$73$			7.35651i			0.861014i	0.902587	+	0.430507i	$0.141665\pi$
$73$			7.35651i			0.861014i	−0.902587	+	0.430507i	$0.858335\pi$
$74$	−1.73178	+	5.91124i	−0.201316	+	0.687167i
$75$		0			0
$76$	−6.13323	+	1.34203i	−0.703530	+	0.153942i
$77$	−0.0236695	−	0.0236695i	−0.00269739	−	0.00269739i
$78$		0			0
$79$	8.69300			0.978038			0.489019	−	0.872273i	$-0.337355\pi$
$79$	8.69300			0.978038			0.489019	+	0.872273i	$0.337355\pi$
$80$	4.88220	+	1.80742i	0.545846	+	0.202076i
$81$		0			0
$82$	6.40110	+	11.7058i	0.706883	+	1.29269i
$83$	8.93029	+	8.93029i	0.980227	+	0.980227i	0.999808	−	0.0195813i	$-0.00623333\pi$
$83$	8.93029	+	8.93029i	0.980227	+	0.980227i	−0.0195813	+	0.999808i	$0.506233\pi$
$84$		0			0
$85$	−7.51229	+	7.51229i	−0.814822	+	0.814822i
$86$	3.68521	−	12.5790i	0.397387	−	1.35643i
$87$		0			0
$88$	−0.0154512	−	0.0177659i	−0.00164711	−	0.00189385i
$89$		−	9.17677i		−	0.972735i	−0.873754	−	0.486368i	$-0.838322\pi$
$89$		−	9.17677i		−	0.972735i	0.873754	−	0.486368i	$-0.161678\pi$
$90$		0			0
$91$	−4.23056	+	4.23056i	−0.443484	+	0.443484i
$92$	7.23065	+	4.63442i	0.753848	+	0.483171i
$93$		0			0
$94$	3.60129	−	1.96930i	0.371445	−	0.203118i
$95$	4.08565			0.419178
$96$		0			0
$97$	3.27186			0.332207			0.166103	−	0.986108i	$-0.446881\pi$
$97$	3.27186			0.332207			0.166103	+	0.986108i	$0.446881\pi$
$98$	−11.3778	+	6.22174i	−1.14933	+	0.628490i
$99$		0			0
$100$	5.56687	+	3.56803i	0.556687	+	0.356803i
$101$	8.96020	−	8.96020i	0.891574	−	0.891574i	−0.103098	−	0.994671i	$-0.532875\pi$
$101$	8.96020	−	8.96020i	0.891574	−	0.891574i	0.994671	+	0.103098i	$0.0328754\pi$
$102$		0			0
$103$		−	13.1077i		−	1.29154i	−0.763533	−	0.645769i	$-0.776537\pi$
$103$		−	13.1077i		−	1.29154i	0.763533	−	0.645769i	$-0.223463\pi$
$104$	−3.17539	+	2.76167i	−0.311373	+	0.270804i
$105$		0			0
$106$	−4.86837	+	16.6176i	−0.472858	+	1.61405i
$107$	−7.18511	+	7.18511i	−0.694611	+	0.694611i	−0.963243	−	0.268632i	$-0.913429\pi$
$107$	−7.18511	+	7.18511i	−0.694611	+	0.694611i	0.268632	+	0.963243i	$0.413429\pi$
$108$		0			0
$109$	6.32874	+	6.32874i	0.606184	+	0.606184i	0.941947	−	0.335763i	$-0.108994\pi$
$109$	6.32874	+	6.32874i	0.606184	+	0.606184i	−0.335763	+	0.941947i	$0.608994\pi$
$110$	0.00735124	+	0.0134433i	0.000700913	+	0.00128177i
$111$		0			0
$112$	−14.6147	+	6.71742i	−1.38096	+	0.634737i
$113$	2.18978			0.205997			0.102999	−	0.994681i	$-0.467156\pi$
$113$	2.18978			0.205997			0.102999	+	0.994681i	$0.467156\pi$
$114$		0			0
$115$	−3.95195	−	3.95195i	−0.368521	−	0.368521i
$116$	−4.81385	+	1.05334i	−0.446955	+	0.0977998i
$117$		0			0
$118$	−3.92835	+	13.4089i	−0.361634	+	1.23439i
$119$		−	32.8240i		−	3.00897i
$120$		0			0
$121$			10.9999i			0.999994i
$122$	−0.467849	−	0.137063i	−0.0423571	−	0.0124091i
$123$		0			0
$124$	4.96653	−	7.74883i	0.446008	−	0.695865i
$125$	−7.64411	−	7.64411i	−0.683710	−	0.683710i
$126$		0			0
$127$	−17.4917			−1.55214			−0.776068	−	0.630650i	$-0.782788\pi$
$127$	−17.4917			−1.55214			−0.776068	+	0.630650i	$0.782788\pi$
$128$	−10.5834	+	3.99892i	−0.935450	+	0.353458i
$129$		0			0
$130$	2.40279	−	1.31392i	0.210738	−	0.115239i
$131$	3.88006	+	3.88006i	0.339002	+	0.339002i	0.855992	−	0.516989i	$-0.172947\pi$
$131$	3.88006	+	3.88006i	0.339002	+	0.339002i	−0.516989	+	0.855992i	$0.672947\pi$
$132$		0			0
$133$	−8.92586	+	8.92586i	−0.773970	+	0.773970i
$134$	8.73396	+	2.55874i	0.754500	+	0.221042i
$135$		0			0
$136$	1.60497	−	23.0322i	0.137625	−	1.97499i
$137$			0.768635i			0.0656689i	0.999461	+	0.0328345i	$0.0104534\pi$
$137$			0.768635i			0.0656689i	−0.999461	+	0.0328345i	$0.989547\pi$
$138$		0			0
$139$	12.6620	−	12.6620i	1.07397	−	1.07397i	0.0769370	−	0.997036i	$-0.475486\pi$
$139$	12.6620	−	12.6620i	1.07397	−	1.07397i	0.997036	−	0.0769370i	$-0.0245140\pi$
$140$	10.2252	−	2.23740i	0.864183	−	0.189095i
$141$		0			0
$142$	−7.38619	−	13.5072i	−0.619835	−	1.13350i
$143$	−0.0123856			−0.00103574
$144$		0			0
$145$	3.20674			0.266305
$146$	4.99151	+	9.12805i	0.413101	+	0.755442i
$147$		0			0
$148$	1.86205	+	8.50978i	0.153060	+	0.699499i
$149$	−9.62555	+	9.62555i	−0.788556	+	0.788556i	−0.981257	−	0.192702i	$-0.938275\pi$
$149$	−9.62555	+	9.62555i	−0.788556	+	0.788556i	0.192702	+	0.981257i	$0.438275\pi$
$150$		0			0
$151$			12.6930i			1.03294i	0.856305	+	0.516471i	$0.172754\pi$
$151$			12.6930i			1.03294i	−0.856305	+	0.516471i	$0.827246\pi$
$152$	−6.69960	+	5.82671i	−0.543409	+	0.472609i
$153$		0			0
$154$	−0.0454296	−	0.0133093i	−0.00366082	−	0.00107249i
$155$	−4.23516	+	4.23516i	−0.340176	+	0.340176i
$156$		0			0
$157$	6.01963	+	6.01963i	0.480419	+	0.480419i	0.905265	−	0.424846i	$-0.139672\pi$
$157$	6.01963	+	6.01963i	0.480419	+	0.480419i	−0.424846	+	0.905265i	$0.639672\pi$
$158$	10.7864	−	5.89834i	0.858118	−	0.469247i
$159$		0			0
$160$	7.28426	−	1.06998i	0.575871	−	0.0845896i
$161$	17.2675			1.36087
$162$		0			0
$163$	−2.19865	−	2.19865i	−0.172211	−	0.172211i	0.615739	−	0.787950i	$-0.288858\pi$
$163$	−2.19865	−	2.19865i	−0.172211	−	0.172211i	−0.787950	+	0.615739i	$0.788858\pi$
$164$	15.8851	+	10.1814i	1.24042	+	0.795035i
$165$		0			0
$166$	17.1402	+	5.02146i	1.33034	+	0.389741i
$167$		−	6.77659i		−	0.524389i	−0.965015	−	0.262194i	$-0.915554\pi$
$167$		−	6.77659i		−	0.524389i	0.965015	−	0.262194i	$-0.0844461\pi$
$168$		0			0
$169$		−	10.7863i		−	0.829712i
$170$	−4.22413	+	14.4186i	−0.323976	+	1.10585i
$171$		0			0
$172$	−3.96243	−	18.1087i	−0.302132	−	1.38078i
$173$	−12.6639	−	12.6639i	−0.962816	−	0.962816i	0.0365175	−	0.999333i	$-0.488374\pi$
$173$	−12.6639	−	12.6639i	−0.962816	−	0.962816i	−0.999333	+	0.0365175i	$0.988374\pi$
$174$		0			0
$175$	13.2943			1.00495
$176$	−0.0312266	−	0.0115603i	−0.00235379	−	0.000871388i
$177$		0			0
$178$	−6.22659	−	11.3866i	−0.466703	−	0.853465i
$179$	−10.1309	−	10.1309i	−0.757219	−	0.757219i	0.218597	−	0.975815i	$-0.429852\pi$
$179$	−10.1309	−	10.1309i	−0.757219	−	0.757219i	−0.975815	+	0.218597i	$0.929852\pi$
$180$		0			0
$181$	17.8456	−	17.8456i	1.32645	−	1.32645i	0.418012	−	0.908441i	$-0.362727\pi$
$181$	17.8456	−	17.8456i	1.32645	−	1.32645i	0.908441	−	0.418012i	$-0.137273\pi$
$182$	−2.37883	+	8.11984i	−0.176330	+	0.601883i
$183$		0			0
$184$	12.1164	+	0.844320i	0.893234	+	0.0622441i
$185$		−	5.66878i		−	0.416777i
$186$		0			0
$187$	0.0480486	−	0.0480486i	0.00351366	−	0.00351366i
$188$	3.13232	−	4.88707i	0.228448	−	0.356426i
$189$		0			0
$190$	5.06952	−	2.77218i	0.367782	−	0.201115i
$191$	−19.6804			−1.42402			−0.712011	−	0.702168i	$-0.752216\pi$
$191$	−19.6804			−1.42402			−0.712011	+	0.702168i	$0.752216\pi$
$192$		0			0
$193$	−15.9852			−1.15064			−0.575321	−	0.817927i	$-0.695123\pi$
$193$	−15.9852			−1.15064			−0.575321	+	0.817927i	$0.695123\pi$
$194$	4.05976	−	2.22001i	0.291474	−	0.159387i
$195$		0			0
$196$	−9.89612	+	15.4400i	−0.706866	+	1.10286i
$197$	−9.08050	+	9.08050i	−0.646959	+	0.646959i	−0.952257	−	0.305298i	$-0.901244\pi$
$197$	−9.08050	+	9.08050i	−0.646959	+	0.646959i	0.305298	+	0.952257i	$0.401244\pi$
$198$		0			0
$199$		−	0.266808i		−	0.0189135i	−0.999955	−	0.00945677i	$-0.996990\pi$
$199$		−	0.266808i		−	0.0189135i	0.999955	−	0.00945677i	$-0.00301023\pi$
$200$	9.32840	+	0.650040i	0.659618	+	0.0459648i
$201$		0			0
$202$	5.03828	−	17.1976i	0.354492	−	1.21002i
$203$	−7.00573	+	7.00573i	−0.491706	+	0.491706i
$204$		0			0
$205$	−8.68210	−	8.68210i	−0.606384	−	0.606384i
$206$	−8.89378	−	16.2642i	−0.619659	−	1.13318i
$207$		0			0
$208$	−2.06622	+	5.58127i	−0.143267	+	0.386992i
$209$	−0.0261318			−0.00180758
$210$		0			0
$211$	−1.62057	−	1.62057i	−0.111565	−	0.111565i	0.649121	−	0.760685i	$-0.275137\pi$
$211$	−1.62057	−	1.62057i	−0.111565	−	0.111565i	−0.760685	+	0.649121i	$0.775137\pi$
$212$	5.23459	+	23.9226i	0.359513	+	1.64301i
$213$		0			0
$214$	−4.04016	+	13.7906i	−0.276179	+	0.942706i
$215$			12.0631i			0.822696i
$216$		0			0
$217$		−	18.5050i		−	1.25620i
$218$	12.1469	+	3.55862i	0.822695	+	0.241020i
$219$		0			0
$220$	0.0182430	+	0.0116927i	0.00122994	+	0.000788320i
$221$	−8.58796	−	8.58796i	−0.577689	−	0.577689i
$222$		0			0
$223$	−8.71414			−0.583542			−0.291771	−	0.956488i	$-0.594245\pi$
$223$	−8.71414			−0.583542			−0.291771	+	0.956488i	$0.594245\pi$
$224$	−13.5762	+	18.2514i	−0.907101	+	1.21947i
$225$		0			0
$226$	2.71711	−	1.48580i	0.180739	−	0.0988342i
$227$	2.54467	+	2.54467i	0.168896	+	0.168896i	0.786494	−	0.617598i	$-0.211894\pi$
$227$	2.54467	+	2.54467i	0.168896	+	0.168896i	−0.617598	+	0.786494i	$0.711894\pi$
$228$		0			0
$229$	−1.51727	+	1.51727i	−0.100264	+	0.100264i	−0.755459	−	0.655195i	$-0.772586\pi$
$229$	−1.51727	+	1.51727i	−0.100264	+	0.100264i	0.655195	+	0.755459i	$0.272586\pi$
$230$	−7.58509	−	2.22216i	−0.500146	−	0.146525i
$231$		0			0
$232$	−5.25838	+	4.57327i	−0.345230	+	0.300250i
$233$		−	4.94845i		−	0.324184i	−0.986776	−	0.162092i	$-0.948176\pi$
$233$		−	4.94845i		−	0.324184i	0.986776	−	0.162092i	$-0.0518241\pi$
$234$		0			0
$235$	−2.67105	+	2.67105i	−0.174240	+	0.174240i
$236$	4.22385	+	19.3034i	0.274949	+	1.25655i
$237$		0			0
$238$	−22.2716	−	40.7284i	−1.44366	−	2.64003i
$239$	−3.73190			−0.241397			−0.120698	−	0.992689i	$-0.538513\pi$
$239$	−3.73190			−0.241397			−0.120698	+	0.992689i	$0.538513\pi$
$240$		0			0
$241$	−14.0581			−0.905563			−0.452781	−	0.891622i	$-0.649568\pi$
$241$	−14.0581			−0.905563			−0.452781	+	0.891622i	$0.649568\pi$
$242$	7.46364	+	13.6488i	0.479781	+	0.877381i
$243$		0			0
$244$	−0.673512	+	0.147374i	−0.0431172	+	0.00943463i
$245$	8.43882	−	8.43882i	0.539136	−	0.539136i
$246$		0			0
$247$			4.67066i			0.297187i
$248$	0.904826	−	12.9847i	0.0574565	−	0.824530i
$249$		0			0
$250$	−14.6716	−	4.29825i	−0.927911	−	0.271845i
$251$	9.52436	−	9.52436i	0.601173	−	0.601173i	−0.339451	−	0.940624i	$-0.610241\pi$
$251$	9.52436	−	9.52436i	0.601173	−	0.601173i	0.940624	+	0.339451i	$0.110241\pi$
$252$		0			0
$253$	0.0252767	+	0.0252767i	0.00158913	+	0.00158913i
$254$	−21.7039	+	11.8684i	−1.36182	+	0.744689i
$255$		0			0
$256$	−10.4187	+	12.1429i	−0.651168	+	0.758933i
$257$	26.7736			1.67009			0.835045	−	0.550182i	$-0.185442\pi$
$257$	26.7736			1.67009			0.835045	+	0.550182i	$0.185442\pi$
$258$		0			0
$259$	12.3845	+	12.3845i	0.769536	+	0.769536i
$260$	2.08989	−	3.26066i	0.129609	−	0.202218i
$261$		0			0
$262$	7.44711	+	2.18174i	0.460084	+	0.134788i
$263$		−	11.6499i		−	0.718362i	−0.933268	−	0.359181i	$-0.883056\pi$
$263$		−	11.6499i		−	0.718362i	0.933268	−	0.359181i	$-0.116944\pi$
$264$		0			0
$265$		−	15.9360i		−	0.978942i
$266$	−5.01897	+	17.1317i	−0.307733	+	1.05041i
$267$		0			0
$268$	12.5734	−	2.75122i	0.768040	−	0.168058i
$269$	−14.9093	−	14.9093i	−0.909037	−	0.909037i	0.0871578	−	0.996195i	$-0.472222\pi$
$269$	−14.9093	−	14.9093i	−0.909037	−	0.909037i	−0.996195	+	0.0871578i	$0.972222\pi$
$270$		0			0
$271$	3.23266			0.196370			0.0981849	−	0.995168i	$-0.468696\pi$
$271$	3.23266			0.196370			0.0981849	+	0.995168i	$0.468696\pi$
$272$	−13.6362	−	29.6676i	−0.826818	−	1.79886i
$273$		0			0
$274$	0.521532	+	0.953732i	0.0315069	+	0.0576170i
$275$	0.0194605	+	0.0194605i	0.00117351	+	0.00117351i
$276$		0			0
$277$	9.07782	−	9.07782i	0.545433	−	0.545433i	−0.379683	−	0.925117i	$-0.623967\pi$
$277$	9.07782	−	9.07782i	0.545433	−	0.545433i	0.925117	+	0.379683i	$0.123967\pi$
$278$	7.11976	−	24.3025i	0.427015	−	1.45756i
$279$		0			0
$280$	11.1694	−	9.71413i	0.667498	−	0.580531i
$281$			14.2092i			0.847649i	0.905744	+	0.423825i	$0.139313\pi$
$281$			14.2092i			0.847649i	−0.905744	+	0.423825i	$0.860687\pi$
$282$		0			0
$283$	−6.14943	+	6.14943i	−0.365546	+	0.365546i	−0.865850	−	0.500304i	$-0.833222\pi$
$283$	−6.14943	+	6.14943i	−0.365546	+	0.365546i	0.500304	+	0.865850i	$0.333222\pi$
$284$	−18.3297	−	11.7483i	−1.08767	−	0.697131i
$285$		0			0
$286$	−0.0153682	+	0.00840385i	−0.000908743	+	0.000496930i
$287$	37.9353			2.23925
$288$		0			0
$289$	49.6321			2.91953
$290$	3.97897	−	2.17583i	0.233653	−	0.127769i
$291$		0			0
$292$	12.3871	+	7.93936i	0.724898	+	0.464616i
$293$	−16.2785	+	16.2785i	−0.950999	+	0.950999i	−0.998854	−	0.0478555i	$-0.984761\pi$
$293$	−16.2785	+	16.2785i	−0.950999	+	0.950999i	0.0478555	+	0.998854i	$0.484761\pi$
$294$		0			0
$295$		−	12.8590i		−	0.748678i
$296$	8.08449	+	9.29560i	0.469901	+	0.540296i
$297$		0			0
$298$	−5.41240	+	18.4746i	−0.313532	+	1.07020i
$299$	4.51782	−	4.51782i	0.261273	−	0.261273i
$300$		0			0
$301$	−26.3541	−	26.3541i	−1.51902	−	1.51902i
$302$	8.61241	+	15.7496i	0.495589	+	0.906289i
$303$		0			0
$304$	−4.35942	+	11.7756i	−0.250030	+	0.675380i
$305$	0.448660			0.0256902
$306$		0			0
$307$	−11.5850	−	11.5850i	−0.661191	−	0.661191i	0.294470	−	0.955661i	$-0.404857\pi$
$307$	−11.5850	−	11.5850i	−0.661191	−	0.661191i	−0.955661	+	0.294470i	$0.904857\pi$
$308$	−0.0654001	+	0.0143104i	−0.00372652	+	0.000815413i
$309$		0			0
$310$	−2.38141	+	8.12867i	−0.135255	+	0.461677i
$311$		−	7.81755i		−	0.443293i	−0.975127	−	0.221646i	$-0.928857\pi$
$311$		−	7.81755i		−	0.443293i	0.975127	−	0.221646i	$-0.0711430\pi$
$312$		0			0
$313$			24.3436i			1.37598i	0.725719	+	0.687992i	$0.241507\pi$
$313$			24.3436i			1.37598i	−0.725719	+	0.687992i	$0.758493\pi$
$314$	11.5537	+	3.38481i	0.652011	+	0.191016i
$315$		0			0
$316$	9.38174	−	14.6375i	0.527764	−	0.823422i
$317$	13.1199	+	13.1199i	0.736886	+	0.736886i	0.971974	−	0.235088i	$-0.0755380\pi$
$317$	13.1199	+	13.1199i	0.736886	+	0.736886i	−0.235088	+	0.971974i	$0.575538\pi$
$318$		0			0
$319$	−0.0205103			−0.00114836
$320$	8.31239	−	6.27014i	0.464677	−	0.350511i
$321$		0			0
$322$	21.4258	−	11.7163i	1.19401	−	0.652925i
$323$	−18.1193	−	18.1193i	−1.00819	−	1.00819i
$324$		0			0
$325$	3.47826	−	3.47826i	0.192939	−	0.192939i
$326$	−4.21992	−	1.23629i	−0.233720	−	0.0684717i
$327$		0			0
$328$	26.6187	+	1.85490i	1.46977	+	0.102420i
$329$		−	11.6708i		−	0.643434i
$330$		0			0
$331$	−23.2983	+	23.2983i	−1.28059	+	1.28059i	−0.340260	+	0.940331i	$0.610515\pi$
$331$	−23.2983	+	23.2983i	−1.28059	+	1.28059i	−0.940331	+	0.340260i	$0.889485\pi$
$332$	24.6749	−	5.39920i	1.35421	−	0.296320i
$333$		0			0
$334$	−4.59803	−	8.40848i	−0.251593	−	0.460092i
$335$	−8.37573			−0.457615
$336$		0			0
$337$	15.5184			0.845339			0.422669	−	0.906284i	$-0.361093\pi$
$337$	15.5184			0.845339			0.422669	+	0.906284i	$0.361093\pi$
$338$	−7.31866	−	13.3837i	−0.398082	−	0.727978i
$339$		0			0
$340$	4.54188	+	20.7569i	0.246318	+	1.12570i
$341$	0.0270881	−	0.0270881i	0.00146690	−	0.00146690i
$342$		0			0
$343$			8.72433i			0.471070i
$344$	−17.2037	−	19.7809i	−0.927561	−	1.06652i
$345$		0			0
$346$	−24.3061	−	7.12083i	−1.30670	−	0.382818i
$347$	3.12567	−	3.12567i	0.167795	−	0.167795i	−0.618215	−	0.786009i	$-0.712144\pi$
$347$	3.12567	−	3.12567i	0.167795	−	0.167795i	0.786009	+	0.618215i	$0.212144\pi$
$348$		0			0
$349$	17.5029	+	17.5029i	0.936911	+	0.936911i	0.998125	−	0.0612142i	$-0.0194973\pi$
$349$	17.5029	+	17.5029i	0.936911	+	0.936911i	−0.0612142	+	0.998125i	$0.519497\pi$
$350$	16.4957	−	9.02037i	0.881731	−	0.482159i
$351$		0			0
$352$	−0.0465901	+	0.00684362i	−0.00248326	+	0.000364766i
$353$	−14.5375			−0.773752			−0.386876	−	0.922132i	$-0.626446\pi$
$353$	−14.5375			−0.773752			−0.386876	+	0.922132i	$0.626446\pi$
$354$		0			0
$355$	10.0182	+	10.0182i	0.531712	+	0.531712i
$356$	−15.4521	−	9.90384i	−0.818957	−	0.524903i
$357$		0			0
$358$	−19.4445	−	5.69656i	−1.02768	−	0.301072i
$359$			27.0384i			1.42703i	0.700639	+	0.713516i	$0.252898\pi$
$359$			27.0384i			1.42703i	−0.700639	+	0.713516i	$0.747102\pi$
$360$		0			0
$361$		−	9.14560i		−	0.481347i
$362$	10.0345	−	34.2516i	0.527402	−	1.80022i
$363$		0			0
$364$	2.55777	+	11.6893i	0.134064	+	0.612685i
$365$	−6.77021	−	6.77021i	−0.354369	−	0.354369i
$366$		0			0
$367$	−16.9489			−0.884724			−0.442362	−	0.896837i	$-0.645859\pi$
$367$	−16.9489			−0.884724			−0.442362	+	0.896837i	$0.645859\pi$
$368$	15.6071	−	7.17355i	0.813575	−	0.373947i
$369$		0			0
$370$	−3.84636	−	7.03389i	−0.199963	−	0.365675i
$371$	34.8152	+	34.8152i	1.80752	+	1.80752i
$372$		0			0
$373$	1.75899	−	1.75899i	0.0910772	−	0.0910772i	−0.660100	−	0.751177i	$-0.729486\pi$
$373$	1.75899	−	1.75899i	0.0910772	−	0.0910772i	0.751177	+	0.660100i	$0.229486\pi$
$374$	0.0270175	−	0.0922211i	0.00139704	−	0.00476864i
$375$		0			0
$376$	0.570661	−	8.18927i	0.0294296	−	0.422329i
$377$			3.66591i			0.188804i
$378$		0			0
$379$	−19.3755	+	19.3755i	−0.995254	+	0.995254i	−0.999989	−	0.00473496i	$-0.998493\pi$
$379$	−19.3755	+	19.3755i	−0.995254	+	0.995254i	0.00473496	+	0.999989i	$0.498493\pi$
$380$	4.40935	−	6.87951i	0.226195	−	0.352911i
$381$		0			0
$382$	−24.4197	+	13.3535i	−1.24942	+	0.683223i
$383$	−15.7187			−0.803189			−0.401594	−	0.915818i	$-0.631544\pi$
$383$	−15.7187			−0.803189			−0.401594	+	0.915818i	$0.631544\pi$
$384$		0			0
$385$	0.0435662			0.00222034
$386$	−19.8347	+	10.8463i	−1.00956	+	0.552060i
$387$		0			0
$388$	3.53108	−	5.50923i	0.179264	−	0.279689i
$389$	6.48805	−	6.48805i	0.328957	−	0.328957i	−0.523233	−	0.852190i	$-0.675274\pi$
$389$	6.48805	−	6.48805i	0.328957	−	0.328957i	0.852190	+	0.523233i	$0.175274\pi$
$390$		0			0
$391$			35.0528i			1.77270i
$392$	−1.80292	+	25.8728i	−0.0910613	+	1.30678i
$393$		0			0
$394$	−5.10592	+	17.4285i	−0.257233	+	0.878033i
$395$	−8.00019	+	8.00019i	−0.402533	+	0.402533i
$396$		0			0
$397$	10.7411	+	10.7411i	0.539083	+	0.539083i	0.923260	−	0.384177i	$-0.125515\pi$
$397$	10.7411	+	10.7411i	0.539083	+	0.539083i	−0.384177	+	0.923260i	$0.625515\pi$
$398$	−0.181034	−	0.331059i	−0.00907441	−	0.0165945i
$399$		0			0
$400$	12.0159	−	5.52290i	0.600793	−	0.276145i
$401$	−7.98281			−0.398642			−0.199321	−	0.979934i	$-0.563874\pi$
$401$	−7.98281			−0.398642			−0.199321	+	0.979934i	$0.563874\pi$
$402$		0			0
$403$	−4.84159	−	4.84159i	−0.241177	−	0.241177i
$404$	−5.41728	−	24.7575i	−0.269520	−	1.23173i
$405$		0			0
$406$	−3.93929	+	13.4463i	−0.195504	+	0.667328i
$407$			0.0362575i			0.00179722i
$408$		0			0
$409$			4.94668i			0.244598i	0.992493	+	0.122299i	$0.0390266\pi$
$409$			4.94668i			0.244598i	−0.992493	+	0.122299i	$0.960973\pi$
$410$	−16.6638	−	4.88191i	−0.822967	−	0.241100i
$411$		0			0
$412$	−22.0710	−	14.1462i	−1.08736	−	0.696934i
$413$	28.0928	+	28.0928i	1.38236	+	1.38236i
$414$		0			0
$415$	−16.4371			−0.806868
$416$	1.22319	+	8.32728i	0.0599719	+	0.408278i
$417$		0			0
$418$	−0.0324247	+	0.0177309i	−0.00158594	+	0.000867245i
$419$	13.9899	+	13.9899i	0.683452	+	0.683452i	0.960776	−	0.277324i	$-0.0894477\pi$
$419$	13.9899	+	13.9899i	0.683452	+	0.683452i	−0.277324	+	0.960776i	$0.589448\pi$
$420$		0			0
$421$	3.76418	−	3.76418i	0.183455	−	0.183455i	−0.609405	−	0.792859i	$-0.708591\pi$
$421$	3.76418	−	3.76418i	0.183455	−	0.183455i	0.792859	+	0.609405i	$0.208591\pi$
$422$	−3.11041	−	0.911241i	−0.151413	−	0.0443585i
$423$		0			0
$424$	22.7270	+	26.1317i	1.10372	+	1.26907i
$425$			26.9871i			1.30907i
$426$		0			0
$427$	−0.980180	+	0.980180i	−0.0474343	+	0.0474343i
$428$	4.34408	+	19.8529i	0.209979	+	0.959624i
$429$		0			0
$430$	8.18501	+	14.9680i	0.394716	+	0.721823i
$431$	1.83169			0.0882293			0.0441146	−	0.999026i	$-0.485953\pi$
$431$	1.83169			0.0882293			0.0441146	+	0.999026i	$0.485953\pi$
$432$		0			0
$433$	−26.3059			−1.26418			−0.632092	−	0.774894i	$-0.717803\pi$
$433$	−26.3059			−1.26418			−0.632092	+	0.774894i	$0.717803\pi$
$434$	−12.5560	−	22.9612i	−0.602705	−	1.10217i
$435$		0			0
$436$	17.4867	−	3.82632i	0.837459	−	0.183247i
$437$	9.53193	−	9.53193i	0.455974	−	0.455974i
$438$		0			0
$439$			7.73329i			0.369090i	0.982824	+	0.184545i	$0.0590811\pi$
$439$			7.73329i			0.369090i	−0.982824	+	0.184545i	$0.940919\pi$
$440$	0.0305698	+	0.00213023i	0.00145736	+	0.000101555i
$441$		0			0
$442$	−16.4831	−	4.82897i	−0.784022	−	0.229691i
$443$	−22.2288	+	22.2288i	−1.05612	+	1.05612i	−0.0577927	+	0.998329i	$0.518406\pi$
$443$	−22.2288	+	22.2288i	−1.05612	+	1.05612i	−0.998329	+	0.0577927i	$0.981594\pi$
$444$		0			0
$445$	8.44540	+	8.44540i	0.400351	+	0.400351i
$446$	−10.8126	+	5.91269i	−0.511992	+	0.279974i
$447$		0			0
$448$	−4.46168	+	31.8583i	−0.210795	+	1.50516i
$449$	8.44617			0.398600			0.199300	−	0.979939i	$-0.436133\pi$
$449$	8.44617			0.398600			0.199300	+	0.979939i	$0.436133\pi$
$450$		0			0
$451$	0.0555307	+	0.0555307i	0.00261484	+	0.00261484i
$452$	2.36328	−	3.68721i	0.111159	−	0.173432i
$453$		0			0
$454$	4.88406	+	1.43086i	0.229220	+	0.0671535i
$455$		−	7.78680i		−	0.365051i
$456$		0			0
$457$		−	12.6386i		−	0.591208i	−0.955311	−	0.295604i	$-0.904479\pi$
$457$		−	12.6386i		−	0.591208i	0.955311	−	0.295604i	$-0.0955209\pi$
$458$	−0.853154	+	2.91214i	−0.0398653	+	0.136075i
$459$		0			0
$460$	−10.9195	+	2.38933i	−0.509122	+	0.111403i
$461$	14.0437	+	14.0437i	0.654081	+	0.654081i	0.953973	−	0.299892i	$-0.0969506\pi$
$461$	14.0437	+	14.0437i	0.654081	+	0.654081i	−0.299892	+	0.953973i	$0.596951\pi$
$462$		0			0
$463$	3.86221			0.179492			0.0897462	−	0.995965i	$-0.471394\pi$
$463$	3.86221			0.179492			0.0897462	+	0.995965i	$0.471394\pi$
$464$	−3.42162	+	9.24247i	−0.158845	+	0.429071i
$465$		0			0
$466$	−3.35761	−	6.14010i	−0.155538	−	0.284435i
$467$	−13.9631	−	13.9631i	−0.646137	−	0.646137i	0.305920	−	0.952057i	$-0.401036\pi$
$467$	−13.9631	−	13.9631i	−0.646137	−	0.646137i	−0.952057	+	0.305920i	$0.901036\pi$
$468$		0			0
$469$	18.2983	−	18.2983i	0.844939	−	0.844939i
$470$	−1.50192	+	5.12663i	−0.0692785	+	0.236474i
$471$		0			0
$472$	18.3387	+	21.0860i	0.844108	+	0.970561i
$473$		−	0.0771556i		−	0.00354762i
$474$		0			0
$475$	7.33862	−	7.33862i	0.336719	−	0.336719i
$476$	−55.2698	−	35.4246i	−2.53329	−	1.62369i
$477$		0			0
$478$	−4.63059	+	2.53216i	−0.211798	+	0.115818i
$479$	−0.403935			−0.0184563			−0.00922814	−	0.999957i	$-0.502937\pi$
$479$	−0.403935			−0.0184563			−0.00922814	+	0.999957i	$0.502937\pi$
$480$		0			0
$481$	6.48048			0.295485
$482$	−17.4435	+	9.53867i	−0.794529	+	0.434474i
$483$		0			0
$484$	18.5219	+	11.8715i	0.841907	+	0.539612i
$485$	−3.01110	+	3.01110i	−0.136727	+	0.136727i
$486$		0			0
$487$			12.4256i			0.563058i	0.959553	+	0.281529i	$0.0908416\pi$
$487$			12.4256i			0.563058i	−0.959553	+	0.281529i	$0.909158\pi$
$488$	−0.735707	+	0.639852i	−0.0333039	+	0.0289648i
$489$		0			0
$490$	4.74511	−	16.1969i	0.214362	−	0.731700i
$491$	17.8700	−	17.8700i	0.806461	−	0.806461i	−0.177636	−	0.984096i	$-0.556845\pi$
$491$	17.8700	−	17.8700i	0.806461	−	0.806461i	0.984096	+	0.177636i	$0.0568449\pi$
$492$		0			0
$493$	−14.2215	−	14.2215i	−0.640504	−	0.640504i
$494$	3.16912	+	5.79542i	0.142586	+	0.260748i
$495$		0			0
$496$	−7.68763	−	16.7255i	−0.345185	−	0.750998i
$497$	−43.7733			−1.96350
$498$		0			0
$499$	7.82074	+	7.82074i	0.350104	+	0.350104i	0.860148	−	0.510044i	$-0.170371\pi$
$499$	7.82074	+	7.82074i	0.350104	+	0.350104i	−0.510044	+	0.860148i	$0.670371\pi$
$500$	−21.1211	+	4.62158i	−0.944564	+	0.206683i
$501$		0			0
$502$	5.35551	−	18.2804i	0.239028	−	0.815894i
$503$			24.4633i			1.09076i	0.838188	+	0.545382i	$0.183615\pi$
$503$			24.4633i			1.09076i	−0.838188	+	0.545382i	$0.816385\pi$
$504$		0			0
$505$			16.4922i			0.733893i
$506$	0.0485143	+	0.0142130i	0.00215672	+	0.000631844i
$507$		0			0
$508$	−18.8775	+	29.4529i	−0.837555	+	1.30676i
$509$	25.0074	+	25.0074i	1.10843	+	1.10843i	0.993357	+	0.115077i	$0.0367114\pi$
$509$	25.0074	+	25.0074i	1.10843	+	1.10843i	0.115077	+	0.993357i	$0.463289\pi$
$510$		0			0
$511$	29.5816			1.30861
$512$	−4.68846	+	22.1364i	−0.207202	+	0.978298i
$513$		0			0
$514$	33.2210	−	18.1663i	1.46531	−	0.801282i
$515$	12.0630	+	12.0630i	0.531561	+	0.531561i
$516$		0			0
$517$	0.0170841	−	0.0170841i	0.000751357	−	0.000751357i
$518$	23.7699	+	6.96375i	1.04439	+	0.305970i
$519$		0			0
$520$	0.380746	−	5.46389i	0.0166968	−	0.239608i
$521$		−	5.27524i		−	0.231113i	−0.993301	−	0.115556i	$-0.963135\pi$
$521$		−	5.27524i		−	0.231113i	0.993301	−	0.115556i	$-0.0368651\pi$
$522$		0			0
$523$	−0.113382	+	0.113382i	−0.00495786	+	0.00495786i	−0.709581	−	0.704624i	$-0.751116\pi$
$523$	−0.113382	+	0.113382i	−0.00495786	+	0.00495786i	0.704624	+	0.709581i	$0.251116\pi$
$524$	10.7208	−	2.34586i	0.468341	−	0.102479i
$525$		0			0
$526$	−7.90464	−	14.4553i	−0.344659	−	0.630281i
$527$	37.5648			1.63635
$528$		0			0
$529$	4.55996			0.198259
$530$	−10.8129	−	19.7736i	−0.469681	−	0.858911i
$531$		0			0
$532$	5.39652	+	24.6626i	0.233969	+	1.06926i
$533$	9.92527	−	9.92527i	0.429911	−	0.429911i
$534$		0			0
$535$		−	13.2250i		−	0.571765i
$536$	13.7344	−	11.9450i	0.593237	−	0.515945i
$537$		0			0
$538$	−28.6159	−	8.38344i	−1.23372	−	0.361436i
$539$	−0.0539747	+	0.0539747i	−0.00232486	+	0.00232486i
$540$		0			0
$541$	−12.3932	−	12.3932i	−0.532827	−	0.532827i	0.388586	−	0.921413i	$-0.372964\pi$
$541$	−12.3932	−	12.3932i	−0.532827	−	0.532827i	−0.921413	+	0.388586i	$0.872964\pi$
$542$	4.01112	−	2.19341i	0.172292	−	0.0942151i
$543$		0			0
$544$	−37.0500	−	27.5595i	−1.58850	−	1.18160i
$545$	−11.6487			−0.498976
$546$		0			0
$547$	−5.79572	−	5.79572i	−0.247807	−	0.247807i	0.572263	−	0.820070i	$-0.306066\pi$
$547$	−5.79572	−	5.79572i	−0.247807	−	0.247807i	−0.820070	+	0.572263i	$0.806066\pi$
$548$	1.29425	+	0.829534i	0.0552874	+	0.0354359i
$549$		0			0
$550$	0.0373511	+	0.0109425i	0.00159265	+	0.000466591i
$551$			7.73452i			0.329502i
$552$		0			0
$553$		−	34.9558i		−	1.48647i
$554$	5.10442	−	17.4233i	0.216866	−	0.740246i
$555$		0			0
$556$	−7.65534	−	34.9857i	−0.324659	−	1.48372i
$557$	16.0511	+	16.0511i	0.680109	+	0.680109i	0.960025	−	0.279916i	$-0.0903065\pi$
$557$	16.0511	+	16.0511i	0.680109	+	0.680109i	−0.279916	+	0.960025i	$0.590307\pi$
$558$		0			0
$559$	−13.7904			−0.583271
$560$	7.26790	−	19.6320i	0.307125	−	0.829605i
$561$		0			0
$562$	9.64117	+	17.6309i	0.406688	+	0.743716i
$563$	−28.1803	−	28.1803i	−1.18766	−	1.18766i	−0.977714	−	0.209942i	$-0.932672\pi$
$563$	−28.1803	−	28.1803i	−1.18766	−	1.18766i	−0.209942	−	0.977714i	$-0.567328\pi$
$564$		0			0
$565$	−2.01526	+	2.01526i	−0.0847828	+	0.0847828i
$566$	−3.45780	+	11.8028i	−0.145342	+	0.496108i
$567$		0			0
$568$	−30.7152	−	2.14035i	−1.28878	−	0.0898073i
$569$			11.9105i			0.499313i	0.968335	+	0.249656i	$0.0803176\pi$
$569$			11.9105i			0.499313i	−0.968335	+	0.249656i	$0.919682\pi$
$570$		0			0
$571$	6.44280	−	6.44280i	0.269623	−	0.269623i	−0.559325	−	0.828948i	$-0.688940\pi$
$571$	6.44280	−	6.44280i	0.269623	−	0.269623i	0.828948	+	0.559325i	$0.188940\pi$
$572$	−0.0133669	+	0.0208552i	−0.000558900	+	0.000872000i
$573$		0			0
$574$	47.0706	−	25.7398i	1.96469	−	1.07436i
$575$	−14.1969			−0.592054
$576$		0			0
$577$	0.452776			0.0188493			0.00942466	−	0.999956i	$-0.497000\pi$
$577$	0.452776			0.0188493			0.00942466	+	0.999956i	$0.497000\pi$
$578$	61.5841	−	33.6762i	2.56156	−	1.40074i
$579$		0			0
$580$	3.46081	−	5.39959i	0.143702	−	0.224206i
$581$	35.9100	−	35.9100i	1.48980	−	1.48980i
$582$		0			0
$583$			0.101927i			0.00422138i
$584$	20.7570	+	1.44643i	0.858931	+	0.0598537i
$585$		0			0
$586$	−9.15331	+	31.2438i	−0.378120	+	1.29067i
$587$	−5.22754	+	5.22754i	−0.215764	+	0.215764i	−0.806711	−	0.590947i	$-0.798754\pi$
$587$	−5.22754	+	5.22754i	−0.215764	+	0.215764i	0.590947	+	0.806711i	$0.298754\pi$
$588$		0			0
$589$	−10.2150	−	10.2150i	−0.420903	−	0.420903i
$590$	−8.72502	−	15.9556i	−0.359203	−	0.656880i
$591$		0			0
$592$	16.3385	+	6.04863i	0.671510	+	0.248597i
$593$	−2.08355			−0.0855613			−0.0427806	−	0.999084i	$-0.513622\pi$
$593$	−2.08355			−0.0855613			−0.0427806	+	0.999084i	$0.513622\pi$
$594$		0			0
$595$	30.2080	+	30.2080i	1.23841	+	1.23841i
$596$	5.81955	+	26.5959i	0.238378	+	1.08941i
$597$		0			0
$598$	2.54035	−	8.67119i	0.103883	−	0.354591i
$599$			24.2289i			0.989965i	0.868903	+	0.494983i	$0.164826\pi$
$599$			24.2289i			0.989965i	−0.868903	+	0.494983i	$0.835174\pi$
$600$		0			0
$601$		−	32.8682i		−	1.34072i	−0.742035	−	0.670362i	$-0.766139\pi$
$601$		−	32.8682i		−	1.34072i	0.742035	−	0.670362i	$-0.233861\pi$
$602$	−50.5821	−	14.8188i	−2.06157	−	0.603968i
$603$		0			0
$604$	21.3728	+	13.6987i	0.869646	+	0.557391i
$605$	−10.1233	−	10.1233i	−0.411569	−	0.411569i
$606$		0			0
$607$	−4.95329			−0.201048			−0.100524	−	0.994935i	$-0.532052\pi$
$607$	−4.95329			−0.201048			−0.100524	+	0.994935i	$0.532052\pi$
$608$	2.58075	+	17.5693i	0.104663	+	0.712529i
$609$		0			0
$610$	0.556702	−	0.304423i	0.0225402	−	0.0123257i
$611$	−3.05352	−	3.05352i	−0.123532	−	0.123532i
$612$		0			0
$613$	−27.4680	+	27.4680i	−1.10942	+	1.10942i	−0.116194	+	0.993227i	$0.537069\pi$
$613$	−27.4680	+	27.4680i	−1.10942	+	1.10942i	−0.993227	+	0.116194i	$0.962931\pi$
$614$	−22.2354	−	6.51420i	−0.897349	−	0.262892i
$615$		0			0
$616$	−0.0714394	+	0.0621316i	−0.00287838	+	0.00250336i
$617$		−	26.5857i		−	1.07030i	−0.844757	−	0.535151i	$-0.820255\pi$
$617$		−	26.5857i		−	1.07030i	0.844757	−	0.535151i	$-0.179745\pi$
$618$		0			0
$619$	8.54410	−	8.54410i	0.343416	−	0.343416i	−0.514234	−	0.857650i	$-0.671924\pi$
$619$	8.54410	−	8.54410i	0.343416	−	0.343416i	0.857650	+	0.514234i	$0.171924\pi$
$620$	2.56055	+	11.7020i	0.102834	+	0.469963i
$621$		0			0
$622$	−5.30434	−	9.70011i	−0.212685	−	0.388939i
$623$	−36.9011			−1.47841
$624$		0			0
$625$	−2.46063			−0.0984253
$626$	16.5176	+	30.2059i	0.660175	+	1.20727i
$627$		0			0
$628$	16.6326	−	3.63943i	0.663712	−	0.145229i
$629$	−25.1403	+	25.1403i	−1.00241	+	1.00241i
$630$		0			0
$631$		−	29.6417i		−	1.18002i	−0.807397	−	0.590009i	$-0.799124\pi$
$631$		−	29.6417i		−	1.18002i	0.807397	−	0.590009i	$-0.200876\pi$
$632$	1.70921	−	24.5280i	0.0679887	−	0.975672i
$633$		0			0
$634$	25.1814	+	7.37725i	1.00008	+	0.292988i
$635$	16.0976	−	16.0976i	0.638815	−	0.638815i
$636$		0			0
$637$	9.64716	+	9.64716i	0.382234	+	0.382234i
$638$	−0.0254495	+	0.0139166i	−0.00100755	+	0.000550964i
$639$		0			0
$640$	6.05972	−	13.4202i	0.239532	−	0.530478i
$641$	−26.8712			−1.06135			−0.530674	−	0.847576i	$-0.678061\pi$
$641$	−26.8712			−1.06135			−0.530674	+	0.847576i	$0.678061\pi$
$642$		0			0
$643$	−30.6951	−	30.6951i	−1.21050	−	1.21050i	−0.970863	−	0.239635i	$-0.922972\pi$
$643$	−30.6951	−	30.6951i	−1.21050	−	1.21050i	−0.239635	−	0.970863i	$-0.577028\pi$
$644$	18.6357	−	29.0755i	0.734348	−	1.14574i
$645$		0			0
$646$	−34.7769	−	10.1884i	−1.36828	−	0.400858i
$647$			17.8060i			0.700027i	0.936745	+	0.350014i	$0.113823\pi$
$647$			17.8060i			0.700027i	−0.936745	+	0.350014i	$0.886177\pi$
$648$		0			0
$649$			0.0822460i			0.00322844i
$650$	1.95581	−	6.67593i	0.0767133	−	0.261852i
$651$		0			0
$652$	−6.07498	+	1.32929i	−0.237914	+	0.0520589i
$653$	−1.29719	−	1.29719i	−0.0507628	−	0.0507628i	0.681270	−	0.732033i	$-0.261428\pi$
$653$	−1.29719	−	1.29719i	−0.0507628	−	0.0507628i	−0.732033	+	0.681270i	$0.761428\pi$
$654$		0			0
$655$	−7.14166			−0.279048
$656$	34.2874	−	15.7597i	1.33870	−	0.615312i
$657$		0			0
$658$	−7.91886	−	14.4813i	−0.308709	−	0.564540i
$659$	−6.63308	−	6.63308i	−0.258388	−	0.258388i	0.566010	−	0.824398i	$-0.308486\pi$
$659$	−6.63308	−	6.63308i	−0.258388	−	0.258388i	−0.824398	+	0.566010i	$0.808486\pi$
$660$		0			0
$661$	2.45705	−	2.45705i	0.0955683	−	0.0955683i	−0.657706	−	0.753275i	$-0.728473\pi$
$661$	2.45705	−	2.45705i	0.0955683	−	0.0955683i	0.753275	+	0.657706i	$0.228473\pi$
$662$	−13.1005	+	44.7171i	−0.509167	+	1.73798i
$663$		0			0
$664$	26.9534	−	23.4417i	1.04600	−	0.909715i
$665$		−	16.4290i		−	0.637089i
$666$		0			0
$667$	7.48142	−	7.48142i	0.289682	−	0.289682i
$668$	−11.4106	−	7.31350i	−0.441489	−	0.282968i
$669$		0			0
$670$	−10.3927	+	5.68307i	−0.401505	+	0.219556i
$671$	−0.00286963			−0.000110781
$672$		0			0
$673$	26.8720			1.03584			0.517920	−	0.855429i	$-0.326706\pi$
$673$	26.8720			1.03584			0.517920	+	0.855429i	$0.326706\pi$
$674$	19.2554	−	10.5295i	0.741689	−	0.405580i
$675$		0			0
$676$	−18.1622	−	11.6409i	−0.698545	−	0.447725i
$677$	16.8184	−	16.8184i	0.646382	−	0.646382i	−0.305735	−	0.952117i	$-0.598902\pi$
$677$	16.8184	−	16.8184i	0.646382	−	0.646382i	0.952117	+	0.305735i	$0.0989021\pi$
$678$		0			0
$679$		−	13.1566i		−	0.504904i
$680$	19.7195	+	22.6736i	0.756208	+	0.869494i
$681$		0			0
$682$	0.0152315	−	0.0519910i	0.000583245	−	0.00199084i
$683$	31.2845	−	31.2845i	1.19707	−	1.19707i	0.222026	−	0.975041i	$-0.428733\pi$
$683$	31.2845	−	31.2845i	1.19707	−	1.19707i	0.975041	−	0.222026i	$-0.0712669\pi$
$684$		0			0
$685$	−0.707377	−	0.707377i	−0.0270275	−	0.0270275i
$686$	5.91960	+	10.8253i	0.226012	+	0.413310i
$687$		0			0
$688$	−34.7682	−	12.8714i	−1.32553	−	0.490718i
$689$	18.2179			0.694046
$690$		0			0
$691$	6.40836	+	6.40836i	0.243785	+	0.243785i	0.818414	−	0.574629i	$-0.194854\pi$
$691$	6.40836	+	6.40836i	0.243785	+	0.243785i	−0.574629	+	0.818414i	$0.694854\pi$
$692$	−34.9909	+	7.65649i	−1.33016	+	0.291056i
$693$		0			0
$694$	1.75755	−	5.99919i	0.0667157	−	0.227726i
$695$			23.3057i			0.884034i
$696$		0			0
$697$			77.0080i			2.91689i
$698$	33.5939	+	9.84182i	1.27155	+	0.372518i
$699$		0			0
$700$	14.3476	−	22.3852i	0.542287	−	0.846080i
$701$	−36.3613	−	36.3613i	−1.37335	−	1.37335i	−0.855434	−	0.517911i	$-0.826710\pi$
$701$	−36.3613	−	36.3613i	−1.37335	−	1.37335i	−0.517911	−	0.855434i	$-0.673290\pi$
$702$		0			0
$703$	13.6728			0.515681
$704$	−0.0531661	+	0.0401038i	−0.00200377	+	0.00151147i
$705$		0			0
$706$	−18.0383	+	9.86392i	−0.678880	+	0.371234i
$707$	−36.0303	−	36.0303i	−1.35506	−	1.35506i
$708$		0			0
$709$	6.37360	−	6.37360i	0.239366	−	0.239366i	−0.577222	−	0.816587i	$-0.695863\pi$
$709$	6.37360	−	6.37360i	0.239366	−	0.239366i	0.816587	+	0.577222i	$0.195863\pi$
$710$	19.2283	+	5.63320i	0.721624	+	0.211410i
$711$		0			0
$712$	−25.8930	−	1.80433i	−0.970382	−	0.0676201i
$713$			19.7615i			0.740074i
$714$		0			0
$715$	0.0113985	−	0.0113985i	0.000426281	−	0.000426281i
$716$	−27.9922	+	6.12508i	−1.04612	+	0.228905i
$717$		0			0
$718$	18.3460	+	33.5496i	0.684667	+	1.25206i
$719$	6.46690			0.241175			0.120587	−	0.992703i	$-0.461522\pi$
$719$	6.46690			0.241175			0.120587	+	0.992703i	$0.461522\pi$
$720$		0			0
$721$	−52.7079			−1.96295
$722$	−6.20544	−	11.3480i	−0.230943	−	0.422328i
$723$		0			0
$724$	−10.7893	−	49.3084i	−0.400983	−	1.83253i
$725$	5.75993	−	5.75993i	0.213919	−	0.213919i
$726$		0			0
$727$		−	9.60335i		−	0.356169i	−0.984015	−	0.178084i	$-0.943010\pi$
$727$		−	9.60335i		−	0.356169i	0.984015	−	0.178084i	$-0.0569900\pi$
$728$	11.1051	+	12.7687i	0.411582	+	0.473240i
$729$		0			0
$730$	−12.9943	−	3.80686i	−0.480939	−	0.140898i
$731$	53.4983	−	53.4983i	1.97870	−	1.97870i
$732$		0			0
$733$	35.8445	+	35.8445i	1.32395	+	1.32395i	0.910552	+	0.413395i	$0.135657\pi$
$733$	35.8445	+	35.8445i	1.32395	+	1.32395i	0.413395	+	0.910552i	$0.364343\pi$
$734$	−21.0304	+	11.5001i	−0.776245	+	0.424476i
$735$		0			0
$736$	14.4981	−	19.4907i	0.534406	−	0.718436i
$737$	0.0535712			0.00197332
$738$		0			0
$739$	−29.2535	−	29.2535i	−1.07611	−	1.07611i	−0.996855	−	0.0792526i	$-0.974747\pi$
$739$	−29.2535	−	29.2535i	−1.07611	−	1.07611i	−0.0792526	−	0.996855i	$-0.525253\pi$
$740$	−9.54522	−	6.11792i	−0.350889	−	0.224899i
$741$		0			0
$742$	66.8219	+	19.5764i	2.45311	+	0.718674i
$743$			13.4556i			0.493640i	0.969061	+	0.246820i	$0.0793856\pi$
$743$			13.4556i			0.493640i	−0.969061	+	0.246820i	$0.920614\pi$
$744$		0			0
$745$		−	17.7168i		−	0.649095i
$746$	0.989073	−	3.37608i	0.0362125	−	0.123607i
$747$		0			0
$748$	−0.0290499	−	0.132761i	−0.00106217	−	0.00485422i
$749$	28.8924	+	28.8924i	1.05571	+	1.05571i
$750$		0			0
$751$	−38.9583			−1.42161			−0.710805	−	0.703389i	$-0.751669\pi$
$751$	−38.9583			−1.42161			−0.710805	+	0.703389i	$0.751669\pi$
$752$	−4.84847	−	10.5485i	−0.176806	−	0.384666i
$753$		0			0
$754$	2.48738	+	4.54871i	0.0905851	+	0.165654i
$755$	−11.6814	−	11.6814i	−0.425130	−	0.425130i
$756$		0			0
$757$	7.60768	−	7.60768i	0.276506	−	0.276506i	−0.555207	−	0.831713i	$-0.687361\pi$
$757$	7.60768	−	7.60768i	0.276506	−	0.276506i	0.831713	+	0.555207i	$0.187361\pi$
$758$	−10.8948	+	37.1880i	−0.395716	+	1.35073i
$759$		0			0
$760$	0.803317	−	11.5280i	0.0291394	−	0.418164i
$761$		−	8.39507i		−	0.304321i	−0.988356	−	0.152160i	$-0.951377\pi$
$761$		−	8.39507i		−	0.304321i	0.988356	−	0.152160i	$-0.0486231\pi$
$762$		0			0
$763$	25.4488	−	25.4488i	0.921308	−	0.921308i
$764$	−21.2397	+	33.1383i	−0.768424	+	1.19890i
$765$		0			0
$766$	−19.5040	+	10.6654i	−0.704707	+	0.385357i
$767$	14.7002			0.530794
$768$		0			0
$769$	−4.62097			−0.166636			−0.0833182	−	0.996523i	$-0.526552\pi$
$769$	−4.62097			−0.166636			−0.0833182	+	0.996523i	$0.526552\pi$
$770$	0.0540575	−	0.0295604i	0.00194810	−	0.00106528i
$771$		0			0
$772$	−17.2518	+	26.9163i	−0.620904	+	0.968740i
$773$	−24.9897	+	24.9897i	−0.898815	+	0.898815i	−0.995331	−	0.0965162i	$-0.969230\pi$
$773$	−24.9897	+	24.9897i	−0.898815	+	0.898815i	0.0965162	+	0.995331i	$0.469230\pi$
$774$		0			0
$775$			15.2143i			0.546516i
$776$	0.643310	−	9.23182i	0.0230935	−	0.331403i
$777$		0			0
$778$	3.64820	−	12.4527i	0.130794	−	0.446451i
$779$	20.9408	−	20.9408i	0.750284	−	0.750284i
$780$		0			0
$781$	−0.0640766	−	0.0640766i	−0.00229284	−	0.00229284i
$782$	23.7839	+	43.4939i	0.850511	+	1.55534i
$783$		0			0
$784$	15.3181	+	33.3267i	0.547074	+	1.19024i
$785$	−11.0798			−0.395454
$786$		0			0
$787$	−12.6207	−	12.6207i	−0.449880	−	0.449880i	0.445435	−	0.895315i	$-0.353049\pi$
$787$	−12.6207	−	12.6207i	−0.449880	−	0.449880i	−0.895315	+	0.445435i	$0.853049\pi$
$788$	5.49001	+	25.0899i	0.195574	+	0.893791i
$789$		0			0
$790$	−4.49847	+	15.3550i	−0.160048	+	0.546306i
$791$		−	8.80544i		−	0.313085i
$792$		0			0
$793$			0.512902i			0.0182137i
$794$	20.6158	+	6.03970i	0.731627	+	0.214341i
$795$		0			0
$796$	−0.449258	−	0.287947i	−0.0159235	−	0.0102060i
$797$	−20.0528	−	20.0528i	−0.710308	−	0.710308i	0.256292	−	0.966599i	$-0.417499\pi$
$797$	−20.0528	−	20.0528i	−0.710308	−	0.710308i	−0.966599	+	0.256292i	$0.917499\pi$
$798$		0			0
$799$	23.6916			0.838147
$800$	11.1620	−	15.0058i	0.394638	−	0.530537i
$801$		0			0
$802$	−9.90516	+	5.41647i	−0.349764	+	0.191262i
$803$	0.0433023	+	0.0433023i	0.00152811	+	0.00152811i
$804$		0			0
$805$	−15.8914	+	15.8914i	−0.560097	+	0.560097i
$806$	−9.29260	−	2.72240i	−0.327318	−	0.0958925i
$807$		0			0
$808$	−23.5202	−	27.0437i	−0.827439	−	0.951395i
$809$		−	31.3494i		−	1.10219i	−0.834444	−	0.551093i	$-0.814211\pi$
$809$		−	31.3494i		−	1.10219i	0.834444	−	0.551093i	$-0.185789\pi$
$810$		0			0
$811$	22.7477	−	22.7477i	0.798779	−	0.798779i	−0.184124	−	0.982903i	$-0.558945\pi$
$811$	22.7477	−	22.7477i	0.798779	−	0.798779i	0.982903	+	0.184124i	$0.0589449\pi$
$812$	4.23562	+	19.3572i	0.148641	+	0.679305i
$813$		0			0
$814$	0.0246013	+	0.0449888i	0.000862277	+	0.00157686i
$815$	4.04684			0.141755
$816$		0			0
$817$	−29.0957			−1.01793
$818$	3.35640	+	6.13790i	0.117354	+	0.214607i
$819$		0			0
$820$	−23.9891	+	5.24914i	−0.837736	+	0.183308i
$821$	15.7194	−	15.7194i	0.548612	−	0.548612i	−0.377427	−	0.926039i	$-0.623191\pi$
$821$	15.7194	−	15.7194i	0.548612	−	0.548612i	0.926039	+	0.377427i	$0.123191\pi$
$822$		0			0
$823$		−	11.9624i		−	0.416984i	−0.978024	−	0.208492i	$-0.933144\pi$
$823$		−	11.9624i		−	0.416984i	0.978024	−	0.208492i	$-0.0668556\pi$
$824$	−36.9844	−	2.57722i	−1.28841	−	0.0897818i
$825$		0			0
$826$	53.9193	+	15.7965i	1.87609	+	0.549629i
$827$	−15.2128	+	15.2128i	−0.528999	+	0.528999i	−0.920274	−	0.391275i	$-0.872034\pi$
$827$	−15.2128	+	15.2128i	−0.528999	+	0.528999i	0.391275	+	0.920274i	$0.372034\pi$
$828$		0			0
$829$	15.5031	+	15.5031i	0.538446	+	0.538446i	0.923072	−	0.384626i	$-0.125670\pi$
$829$	15.5031	+	15.5031i	0.538446	+	0.538446i	−0.384626	+	0.923072i	$0.625670\pi$
$830$	−20.3954	+	11.1529i	−0.707935	+	0.387122i
$831$		0			0
$832$	7.16795	+	9.50263i	0.248504	+	0.329444i
$833$	−74.8501			−2.59340
$834$		0			0
$835$	6.23652	+	6.23652i	0.215824	+	0.215824i
$836$	−0.0282022	+	0.0440014i	−0.000975395	+	0.00152182i
$837$		0			0
$838$	26.8512	+	7.86647i	0.927561	+	0.271743i
$839$			18.9078i			0.652769i	0.945237	+	0.326384i	$0.105830\pi$
$839$			18.9078i			0.652769i	−0.945237	+	0.326384i	$0.894170\pi$
$840$		0			0
$841$		−	22.9293i		−	0.790666i
$842$	2.11658	−	7.22469i	0.0729421	−	0.248979i
$843$		0			0
$844$	−4.47773	+	0.979788i	−0.154130	+	0.0337257i
$845$	9.92662	+	9.92662i	0.341486	+	0.341486i
$846$		0			0
$847$	44.2323			1.51984
$848$	45.9308	+	17.0039i	1.57727	+	0.583915i
$849$		0			0
$850$	18.3112	+	33.4859i	0.628068	+	1.14856i
$851$	−13.2254	−	13.2254i	−0.453362	−	0.453362i
$852$		0			0
$853$	12.6167	−	12.6167i	0.431989	−	0.431989i	−0.457315	−	0.889305i	$-0.651189\pi$
$853$	12.6167	−	12.6167i	0.431989	−	0.431989i	0.889305	+	0.457315i	$0.151189\pi$
$854$	−0.551151	+	1.88129i	−0.0188600	+	0.0643764i
$855$		0			0
$856$	18.8607	+	21.6861i	0.644645	+	0.741217i
$857$		−	12.9552i		−	0.442543i	−0.975212	−	0.221271i	$-0.928979\pi$
$857$		−	12.9552i		−	0.442543i	0.975212	−	0.221271i	$-0.0710207\pi$
$858$		0			0
$859$	15.7020	−	15.7020i	0.535746	−	0.535746i	−0.386530	−	0.922277i	$-0.626327\pi$
$859$	15.7020	−	15.7020i	0.535746	−	0.535746i	0.922277	+	0.386530i	$0.126327\pi$
$860$	20.3121	+	13.0189i	0.692638	+	0.443939i
$861$		0			0
$862$	2.27278	−	1.24283i	0.0774112	−	0.0423310i
$863$	−40.8333			−1.38998			−0.694990	−	0.719019i	$-0.744591\pi$
$863$	−40.8333			−1.38998			−0.694990	+	0.719019i	$0.744591\pi$
$864$		0			0
$865$	23.3092			0.792536
$866$	−32.6407	+	17.8490i	−1.10918	+	0.606535i
$867$		0			0
$868$	−31.1592	−	19.9711i	−1.05761	−	0.677865i
$869$	0.0511692	−	0.0511692i	0.00173580	−	0.00173580i
$870$		0			0
$871$		−	9.57504i		−	0.324438i
$872$	19.1014	−	16.6127i	0.646856	−	0.562578i
$873$		0			0
$874$	5.35976	−	18.2949i	0.181297	−	0.618835i
$875$	−30.7381	+	30.7381i	−1.03914	+	1.03914i
$876$		0			0
$877$	−4.00311	−	4.00311i	−0.135175	−	0.135175i	0.636282	−	0.771457i	$-0.280472\pi$
$877$	−4.00311	−	4.00311i	−0.135175	−	0.135175i	−0.771457	+	0.636282i	$0.780472\pi$
$878$	5.24716	+	9.59556i	0.177083	+	0.323834i
$879$		0			0
$880$	0.0393768	−	0.0180989i	0.00132739	−	0.000610115i
$881$	28.7204			0.967615			0.483807	−	0.875175i	$-0.339254\pi$
$881$	28.7204			0.967615			0.483807	+	0.875175i	$0.339254\pi$
$882$		0			0
$883$	21.6320	+	21.6320i	0.727975	+	0.727975i	0.970216	−	0.242241i	$-0.0778824\pi$
$883$	21.6320	+	21.6320i	0.727975	+	0.727975i	−0.242241	+	0.970216i	$0.577882\pi$
$884$	−23.7290	+	5.19223i	−0.798093	+	0.174634i
$885$		0			0
$886$	−12.4991	+	42.6643i	−0.419917	+	1.43334i
$887$			25.2127i			0.846559i	0.905999	+	0.423279i	$0.139121\pi$
$887$			25.2127i			0.846559i	−0.905999	+	0.423279i	$0.860879\pi$
$888$		0			0
$889$			70.3366i			2.35901i
$890$	16.2095	+	4.74881i	0.543344	+	0.159181i
$891$		0			0
$892$	−9.40456	+	14.6731i	−0.314888	+	0.491291i
$893$	−6.44247	−	6.44247i	−0.215589	−	0.215589i
$894$		0			0
$895$	18.6470			0.623300
$896$	16.0802	+	42.5574i	0.537203	+	1.42174i
$897$		0			0
$898$	10.4801	−	5.73087i	0.349726	−	0.191242i
$899$	−8.01757	−	8.01757i	−0.267401	−	0.267401i
$900$		0			0
$901$	−70.6742	+	70.6742i	−2.35450	+	2.35450i
$902$	0.106582	+	0.0312247i	0.00354878	+	0.00103967i
$903$		0			0
$904$	0.430553	−	6.17866i	0.0143200	−	0.205499i
$905$			32.8467i			1.09186i
$906$		0			0
$907$	−27.4465	+	27.4465i	−0.911346	+	0.911346i	−0.996378	−	0.0850318i	$-0.972901\pi$
$907$	−27.4465	+	27.4465i	−0.911346	+	0.911346i	0.0850318	+	0.996378i	$0.472901\pi$
$908$	7.03107	−	1.53849i	0.233334	−	0.0510567i
$909$		0			0
$910$	−5.28347	−	9.66196i	−0.175145	−	0.320291i
$911$	−24.4762			−0.810934			−0.405467	−	0.914110i	$-0.632891\pi$
$911$	−24.4762			−0.810934			−0.405467	+	0.914110i	$0.632891\pi$
$912$		0			0
$913$	0.105132			0.00347936
$914$	−8.57549	−	15.6821i	−0.283652	−	0.518718i
$915$		0			0
$916$	0.917332	+	4.19230i	0.0303095	+	0.138517i
$917$	15.6023	−	15.6023i	0.515233	−	0.515233i
$918$		0			0
$919$			2.71829i			0.0896681i	0.998994	+	0.0448340i	$0.0142759\pi$
$919$			2.71829i			0.0896681i	−0.998994	+	0.0448340i	$0.985724\pi$
$920$	−11.9278	+	10.3737i	−0.393248	+	0.342012i
$921$		0			0
$922$	26.9545	+	7.89672i	0.887700	+	0.260065i
$923$	−11.4527	+	11.4527i	−0.376971	+	0.376971i
$924$		0			0
$925$	−10.1822	−	10.1822i	−0.334790	−	0.334790i
$926$	4.79228	−	2.62058i	0.157484	−	0.0861175i
$927$		0			0
$928$	2.02558	+	13.7898i	0.0664930	+	0.452672i
$929$	−29.1769			−0.957262			−0.478631	−	0.878016i	$-0.658867\pi$
$929$	−29.1769			−0.957262			−0.478631	+	0.878016i	$0.658867\pi$
$930$		0			0
$931$	20.3541	+	20.3541i	0.667077	+	0.667077i
$932$	−8.33232	−	5.34052i	−0.272934	−	0.174934i
$933$		0			0
$934$	−26.7999	−	7.85141i	−0.876919	−	0.256906i
$935$			0.0884386i			0.00289225i
$936$		0			0
$937$			31.3347i			1.02366i	0.859086	+	0.511831i	$0.171032\pi$
$937$			31.3347i			1.02366i	−0.859086	+	0.511831i	$0.828968\pi$
$938$	10.2891	−	35.1205i	0.335950	−	1.14673i
$939$		0			0
$940$	1.61490	+	7.38027i	0.0526723	+	0.240718i
$941$	17.0685	+	17.0685i	0.556419	+	0.556419i	0.928286	−	0.371867i	$-0.121282\pi$
$941$	17.0685	+	17.0685i	0.556419	+	0.556419i	−0.371867	+	0.928286i	$0.621282\pi$
$942$		0			0
$943$	−40.5112			−1.31923
$944$	37.0621	+	13.7206i	1.20627	+	0.446568i
$945$		0			0
$946$	−0.0523514	−	0.0957356i	−0.00170209	−	0.00311263i
$947$	−22.9244	−	22.9244i	−0.744942	−	0.744942i	0.228583	−	0.973525i	$-0.426591\pi$
$947$	−22.9244	−	22.9244i	−0.744942	−	0.744942i	−0.973525	+	0.228583i	$0.926591\pi$
$948$		0			0
$949$	7.73963	−	7.73963i	0.251239	−	0.251239i
$950$	4.12647	−	14.0852i	0.133880	−	0.456985i
$951$		0			0
$952$	−92.6157	−	6.45383i	−3.00169	−	0.209170i
$953$		−	31.0152i		−	1.00468i	−0.864669	−	0.502341i	$-0.832472\pi$
$953$		−	31.0152i		−	1.00468i	0.864669	−	0.502341i	$-0.167528\pi$
$954$		0			0
$955$	18.1119	−	18.1119i	0.586088	−	0.586088i
$956$	−4.02758	+	6.28387i	−0.130261	+	0.203235i
$957$		0			0
$958$	−0.501208	+	0.274077i	−0.0161933	+	0.00885502i
$959$	3.09079			0.0998069
$960$		0			0
$961$	−9.82232			−0.316849
$962$	8.04106	−	4.39712i	0.259254	−	0.141769i
$963$		0			0
$964$	−15.1719	+	23.6714i	−0.488655	+	0.762404i
$965$	14.7113	−	14.7113i	0.473572	−	0.473572i
$966$		0			0
$967$		−	6.33233i		−	0.203634i	−0.994803	−	0.101817i	$-0.967534\pi$
$967$		−	6.33233i		−	0.203634i	0.994803	−	0.101817i	$-0.0324656\pi$
$968$	31.0372	+	2.16280i	0.997575	+	0.0695150i
$969$		0			0
$970$	−1.69313	+	5.77929i	−0.0543630	+	0.185562i
$971$	13.1578	−	13.1578i	0.422253	−	0.422253i	−0.463726	−	0.885979i	$-0.653488\pi$
$971$	13.1578	−	13.1578i	0.422253	−	0.422253i	0.885979	+	0.463726i	$0.153488\pi$
$972$		0			0
$973$	−50.9156	−	50.9156i	−1.63228	−	1.63228i
$974$	8.43099	+	15.4179i	0.270146	+	0.494020i
$975$		0			0
$976$	−0.478723	+	1.29313i	−0.0153236	+	0.0413920i
$977$	−15.2607			−0.488232			−0.244116	−	0.969746i	$-0.578498\pi$
$977$	−15.2607			−0.488232			−0.244116	+	0.969746i	$0.578498\pi$
$978$		0			0
$979$	−0.0540168	−	0.0540168i	−0.00172639	−	0.00172639i
$980$	−5.10206	−	23.3169i	−0.162979	−	0.744831i
$981$		0			0
$982$	10.0482	−	34.2984i	0.320651	−	1.09450i
$983$		−	37.7317i		−	1.20346i	−0.798701	−	0.601728i	$-0.794479\pi$
$983$		−	37.7317i		−	1.20346i	0.798701	−	0.601728i	$-0.205521\pi$
$984$		0			0
$985$		−	16.7136i		−	0.532540i
$986$	−27.2957	−	7.99668i	−0.869273	−	0.254666i
$987$		0			0
$988$	7.86457	+	5.04072i	0.250205	+	0.160367i
$989$	28.1436	+	28.1436i	0.894913	+	0.894913i
$990$		0			0
$991$	53.2311			1.69094			0.845470	−	0.534023i	$-0.179320\pi$
$991$	53.2311			1.69094			0.845470	+	0.534023i	$0.179320\pi$
$992$	−20.8875	−	15.5371i	−0.663177	−	0.493302i
$993$		0			0
$994$	−54.3145	+	29.7009i	−1.72275	+	0.942057i
$995$	0.245544	+	0.245544i	0.00778428	+	0.00778428i
$996$		0			0
$997$	−30.3998	+	30.3998i	−0.962771	+	0.962771i	−0.999331	−	0.0365604i	$-0.988360\pi$
$997$	−30.3998	+	30.3998i	−0.962771	+	0.962771i	0.0365604	+	0.999331i	$0.488360\pi$
$998$	15.0106	+	4.39756i	0.475151	+	0.139202i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.d.109.13	yes	32
3.2	odd	2	inner	432.2.k.d.109.4	✓	32
4.3	odd	2		1728.2.k.d.1297.7		32
12.11	even	2		1728.2.k.d.1297.10		32
16.5	even	4	inner	432.2.k.d.325.13	yes	32
16.11	odd	4		1728.2.k.d.433.7		32
48.5	odd	4	inner	432.2.k.d.325.4	yes	32
48.11	even	4		1728.2.k.d.433.10		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.d.109.4	✓	32	3.2	odd	2	inner
432.2.k.d.109.13	yes	32	1.1	even	1	trivial
432.2.k.d.325.4	yes	32	48.5	odd	4	inner
432.2.k.d.325.13	yes	32	16.5	even	4	inner
1728.2.k.d.433.7		32	16.11	odd	4
1728.2.k.d.433.10		32	48.11	even	4
1728.2.k.d.1297.7		32	4.3	odd	2
1728.2.k.d.1297.10		32	12.11	even	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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.24081 - 0.678517i) q^{2} +(1.07923 - 1.68382i) q^{4} +(-0.920303 + 0.920303i) q^{5} -4.02115i q^{7} +(0.196619 - 2.82158i) q^{8} +O(q^{10})\)	\(q+(1.24081 - 0.678517i) q^{2} +(1.07923 - 1.68382i) q^{4} +(-0.920303 + 0.920303i) q^{5} -4.02115i q^{7} +(0.196619 - 2.82158i) q^{8} +(-0.517482 + 1.76636i) q^{10} +(0.00588626 - 0.00588626i) q^{11} +(-1.05208 - 1.05208i) q^{13} +(-2.72841 - 4.98949i) q^{14} +(-1.67053 - 3.63447i) q^{16} +8.16285 q^{17} +(-2.21973 - 2.21973i) q^{19} +(0.556409 + 2.54285i) q^{20} +(0.00330982 - 0.0112977i) q^{22} +4.29419i q^{23} +3.30609i q^{25} +(-2.01929 - 0.591579i) q^{26} +(-6.77090 - 4.33974i) q^{28} +(-1.74222 - 1.74222i) q^{29} +4.60192 q^{31} +(-4.53885 - 3.37621i) q^{32} +(10.1286 - 5.53863i) q^{34} +(3.70067 + 3.70067i) q^{35} +(-3.07984 + 3.07984i) q^{37} +(-4.26039 - 1.24814i) q^{38} +(2.41576 + 2.77766i) q^{40} +9.43396i q^{41} +(6.55387 - 6.55387i) q^{43} +(-0.00355880 - 0.0162641i) q^{44} +(2.91368 + 5.32828i) q^{46} +2.90237 q^{47} -9.16961 q^{49} +(2.24323 + 4.10223i) q^{50} +(-2.90695 + 0.636081i) q^{52} +(-8.65803 + 8.65803i) q^{53} +0.0108343i q^{55} +(-11.3460 - 0.790635i) q^{56} +(-3.34390 - 0.979643i) q^{58} +(-6.98627 + 6.98627i) q^{59} +(-0.243756 - 0.243756i) q^{61} +(5.71012 - 3.12248i) q^{62} +(-7.92268 - 1.10956i) q^{64} +1.93646 q^{65} +(4.55053 + 4.55053i) q^{67} +(8.80959 - 13.7448i) q^{68} +(7.10281 + 2.08087i) q^{70} -10.8858i q^{71} +7.35651i q^{73} +(-1.73178 + 5.91124i) q^{74} +(-6.13323 + 1.34203i) q^{76} +(-0.0236695 - 0.0236695i) q^{77} +8.69300 q^{79} +(4.88220 + 1.80742i) q^{80} +(6.40110 + 11.7058i) q^{82} +(8.93029 + 8.93029i) q^{83} +(-7.51229 + 7.51229i) q^{85} +(3.68521 - 12.5790i) q^{86} +(-0.0154512 - 0.0177659i) q^{88} -9.17677i q^{89} +(-4.23056 + 4.23056i) q^{91} +(7.23065 + 4.63442i) q^{92} +(3.60129 - 1.96930i) q^{94} +4.08565 q^{95} +3.27186 q^{97} +(-11.3778 + 6.22174i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 8 q^{10} + 24 q^{16} + 16 q^{19} + 32 q^{22} + 24 q^{28} - 8 q^{34} + 56 q^{40} - 16 q^{43} - 32 q^{49} - 16 q^{52} - 32 q^{61} + 24 q^{64} + 32 q^{67} - 96 q^{70} - 48 q^{76} - 32 q^{79} + 32 q^{85} - 88 q^{88} - 48 q^{91} - 96 q^{94}+O(q^{100}) \) 32 * q - 8 * q^10 + 24 * q^16 + 16 * q^19 + 32 * q^22 + 24 * q^28 - 8 * q^34 + 56 * q^40 - 16 * q^43 - 32 * q^49 - 16 * q^52 - 32 * q^61 + 24 * q^64 + 32 * q^67 - 96 * q^70 - 48 * q^76 - 32 * q^79 + 32 * q^85 - 88 * q^88 - 48 * q^91 - 96 * q^94

Introduction

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