LMFDB - Embedded newform 432.2.k.c.109.9

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:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	432.109
Dual form			432.2.k.c.325.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15725 + 0.812885i) q^{2} +(0.678437 + 1.88142i) q^{4} +(2.39401 - 2.39401i) q^{5} -2.42931i q^{7} +(-0.744255 + 2.72875i) q^{8} +O(q^{10})$	\(q+(1.15725 + 0.812885i) q^{2} +(0.678437 + 1.88142i) q^{4} +(2.39401 - 2.39401i) q^{5} -2.42931i q^{7} +(-0.744255 + 2.72875i) q^{8} +(4.71651 - 0.824404i) q^{10} +(0.803139 - 0.803139i) q^{11} +(0.643126 + 0.643126i) q^{13} +(1.97475 - 2.81131i) q^{14} +(-3.07945 + 2.55284i) q^{16} +0.717454 q^{17} +(-3.76851 - 3.76851i) q^{19} +(6.12831 + 2.87994i) q^{20} +(1.58229 - 0.276570i) q^{22} +7.35083i q^{23} -6.46256i q^{25} +(0.221468 + 1.26704i) q^{26} +(4.57054 - 1.64813i) q^{28} +(6.75619 + 6.75619i) q^{29} -6.69776 q^{31} +(-5.63884 + 0.451033i) q^{32} +(0.830271 + 0.583207i) q^{34} +(-5.81579 - 5.81579i) q^{35} +(-7.02138 + 7.02138i) q^{37} +(-1.29773 - 7.42446i) q^{38} +(4.75090 + 8.31441i) q^{40} +3.53544i q^{41} +(1.31950 - 1.31950i) q^{43} +(2.05592 + 0.966158i) q^{44} +(-5.97538 + 8.50672i) q^{46} -4.02558 q^{47} +1.09844 q^{49} +(5.25332 - 7.47877i) q^{50} +(-0.773667 + 1.64631i) q^{52} +(6.85520 - 6.85520i) q^{53} -3.84544i q^{55} +(6.62899 + 1.80803i) q^{56} +(2.32657 + 13.3106i) q^{58} +(-4.81675 + 4.81675i) q^{59} +(-8.63547 - 8.63547i) q^{61} +(-7.75095 - 5.44451i) q^{62} +(-6.89217 - 4.06177i) q^{64} +3.07930 q^{65} +(11.0938 + 11.0938i) q^{67} +(0.486747 + 1.34983i) q^{68} +(-2.00274 - 11.4579i) q^{70} -8.42199i q^{71} -14.0778i q^{73} +(-13.8330 + 2.41789i) q^{74} +(4.53344 - 9.64684i) q^{76} +(-1.95107 - 1.95107i) q^{77} -5.60141 q^{79} +(-1.26069 + 13.4838i) q^{80} +(-2.87391 + 4.09137i) q^{82} +(-6.14958 - 6.14958i) q^{83} +(1.71759 - 1.71759i) q^{85} +(2.59959 - 0.454385i) q^{86} +(1.59383 + 2.78931i) q^{88} -5.44218i q^{89} +(1.56235 - 1.56235i) q^{91} +(-13.8300 + 4.98708i) q^{92} +(-4.65859 - 3.27234i) q^{94} -18.0437 q^{95} -7.77657 q^{97} +(1.27117 + 0.892909i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 16 q^{4}+O(q^{10}) $ 24 * q + 16 * q^4	$ 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) $ 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

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 $

$2$	1.15725	+	0.812885i	0.818297	+	0.574796i
$2$	1.15725	+	0.812885i	0.818297	+	0.574796i
$3$		0			0
$3$		0			0
$4$	0.678437	+	1.88142i	0.339218	+	0.940708i
$5$	2.39401	−	2.39401i	1.07063	−	1.07063i	0.0733254	−	0.997308i	$-0.476639\pi$
$5$	2.39401	−	2.39401i	1.07063	−	1.07063i	0.997308	−	0.0733254i	$-0.0233612\pi$
$6$		0			0
$7$		−	2.42931i		−	0.918193i	−0.888386	−	0.459097i	$-0.848173\pi$
$7$		−	2.42931i		−	0.918193i	0.888386	−	0.459097i	$-0.151827\pi$
$8$	−0.744255	+	2.72875i	−0.263134	+	0.964759i
$9$		0			0
$10$	4.71651	−	0.824404i	1.49149	−	0.260700i
$11$	0.803139	−	0.803139i	0.242155	−	0.242155i	−0.575586	−	0.817741i	$-0.695226\pi$
$11$	0.803139	−	0.803139i	0.242155	−	0.242155i	0.817741	+	0.575586i	$0.195226\pi$
$12$		0			0
$13$	0.643126	+	0.643126i	0.178371	+	0.178371i	0.790645	−	0.612274i	$-0.209745\pi$
$13$	0.643126	+	0.643126i	0.178371	+	0.178371i	−0.612274	+	0.790645i	$0.709745\pi$
$14$	1.97475	−	2.81131i	0.527774	−	0.751355i
$15$		0			0
$16$	−3.07945	+	2.55284i	−0.769862	+	0.638211i
$17$	0.717454			0.174008			0.0870041	−	0.996208i	$-0.472271\pi$
$17$	0.717454			0.174008			0.0870041	+	0.996208i	$0.472271\pi$
$18$		0			0
$19$	−3.76851	−	3.76851i	−0.864556	−	0.864556i	0.127307	−	0.991863i	$-0.459367\pi$
$19$	−3.76851	−	3.76851i	−0.864556	−	0.864556i	−0.991863	+	0.127307i	$0.959367\pi$
$20$	6.12831	+	2.87994i	1.37033	+	0.643974i
$21$		0			0
$22$	1.58229	−	0.276570i	0.337345	−	0.0589649i
$23$			7.35083i			1.53275i	0.642391	+	0.766377i	$0.277943\pi$
$23$			7.35083i			1.53275i	−0.642391	+	0.766377i	$0.722057\pi$
$24$		0			0
$25$		−	6.46256i		−	1.29251i
$26$	0.221468	+	1.26704i	0.0434334	+	0.248487i
$27$		0			0
$28$	4.57054	−	1.64813i	0.863752	−	0.311468i
$29$	6.75619	+	6.75619i	1.25459	+	1.25459i	0.953638	+	0.300955i	$0.0973054\pi$
$29$	6.75619	+	6.75619i	1.25459	+	1.25459i	0.300955	+	0.953638i	$0.402695\pi$
$30$		0			0
$31$	−6.69776			−1.20295			−0.601476	−	0.798891i	$-0.705421\pi$
$31$	−6.69776			−1.20295			−0.601476	+	0.798891i	$0.705421\pi$
$32$	−5.63884	+	0.451033i	−0.996816	+	0.0797322i
$33$		0			0
$34$	0.830271	+	0.583207i	0.142390	+	0.100019i
$35$	−5.81579	−	5.81579i	−0.983049	−	0.983049i
$36$		0			0
$37$	−7.02138	+	7.02138i	−1.15431	+	1.15431i	−0.168629	+	0.985680i	$0.553934\pi$
$37$	−7.02138	+	7.02138i	−1.15431	+	1.15431i	−0.985680	+	0.168629i	$0.946066\pi$
$38$	−1.29773	−	7.42446i	−0.210520	−	1.20441i
$39$		0			0
$40$	4.75090	+	8.31441i	0.751184	+	1.31462i
$41$			3.53544i			0.552143i	0.961137	+	0.276071i	$0.0890327\pi$
$41$			3.53544i			0.552143i	−0.961137	+	0.276071i	$0.910967\pi$
$42$		0			0
$43$	1.31950	−	1.31950i	0.201222	−	0.201222i	−0.599301	−	0.800523i	$-0.704555\pi$
$43$	1.31950	−	1.31950i	0.201222	−	0.201222i	0.800523	+	0.599301i	$0.204555\pi$
$44$	2.05592	+	0.966158i	0.309941	+	0.145654i
$45$		0			0
$46$	−5.97538	+	8.50672i	−0.881022	+	1.25425i
$47$	−4.02558			−0.587192			−0.293596	−	0.955930i	$-0.594852\pi$
$47$	−4.02558			−0.587192			−0.293596	+	0.955930i	$0.594852\pi$
$48$		0			0
$49$	1.09844			0.156921
$50$	5.25332	−	7.47877i	0.742931	−	1.05766i
$51$		0			0
$52$	−0.773667	+	1.64631i	−0.107288	+	0.228302i
$53$	6.85520	−	6.85520i	0.941634	−	0.941634i	−0.0567538	−	0.998388i	$-0.518075\pi$
$53$	6.85520	−	6.85520i	0.941634	−	0.941634i	0.998388	+	0.0567538i	$0.0180750\pi$
$54$		0			0
$55$		−	3.84544i		−	0.518519i
$56$	6.62899	+	1.80803i	0.885836	+	0.241608i
$57$		0			0
$58$	2.32657	+	13.3106i	0.305494	+	1.74777i
$59$	−4.81675	+	4.81675i	−0.627087	+	0.627087i	−0.947334	−	0.320247i	$-0.896234\pi$
$59$	−4.81675	+	4.81675i	−0.627087	+	0.627087i	0.320247	+	0.947334i	$0.396234\pi$
$60$		0			0
$61$	−8.63547	−	8.63547i	−1.10566	−	1.10566i	−0.993714	−	0.111944i	$-0.964292\pi$
$61$	−8.63547	−	8.63547i	−1.10566	−	1.10566i	−0.111944	−	0.993714i	$-0.535708\pi$
$62$	−7.75095	−	5.44451i	−0.984372	−	0.691453i
$63$		0			0
$64$	−6.89217	−	4.06177i	−0.861521	−	0.507722i
$65$	3.07930			0.381940
$66$		0			0
$67$	11.0938	+	11.0938i	1.35533	+	1.35533i	0.879586	+	0.475740i	$0.157820\pi$
$67$	11.0938	+	11.0938i	1.35533	+	1.35533i	0.475740	+	0.879586i	$0.342180\pi$
$68$	0.486747	+	1.34983i	0.0590268	+	0.163691i
$69$		0			0
$70$	−2.00274	−	11.4579i	−0.239373	−	1.36948i
$71$		−	8.42199i		−	0.999506i	−0.866168	−	0.499753i	$-0.833424\pi$
$71$		−	8.42199i		−	0.999506i	0.866168	−	0.499753i	$-0.166576\pi$
$72$		0			0
$73$		−	14.0778i		−	1.64769i	−0.566818	−	0.823843i	$-0.691826\pi$
$73$		−	14.0778i		−	1.64769i	0.566818	−	0.823843i	$-0.308174\pi$
$74$	−13.8330	+	2.41789i	−1.60806	+	0.281074i
$75$		0			0
$76$	4.53344	−	9.64684i	0.520021	−	1.10657i
$77$	−1.95107	−	1.95107i	−0.222345	−	0.222345i
$78$		0			0
$79$	−5.60141			−0.630208			−0.315104	−	0.949057i	$-0.602039\pi$
$79$	−5.60141			−0.630208			−0.315104	+	0.949057i	$0.602039\pi$
$80$	−1.26069	+	13.4838i	−0.140950	+	1.50753i
$81$		0			0
$82$	−2.87391	+	4.09137i	−0.317370	+	0.451817i
$83$	−6.14958	−	6.14958i	−0.675004	−	0.675004i	0.283862	−	0.958865i	$-0.408384\pi$
$83$	−6.14958	−	6.14958i	−0.675004	−	0.675004i	−0.958865	+	0.283862i	$0.908384\pi$
$84$		0			0
$85$	1.71759	−	1.71759i	0.186299	−	0.186299i
$86$	2.59959	−	0.454385i	0.280321	−	0.0489976i
$87$		0			0
$88$	1.59383	+	2.78931i	0.169902	+	0.297341i
$89$		−	5.44218i		−	0.576870i	−0.957500	−	0.288435i	$-0.906865\pi$
$89$		−	5.44218i		−	0.576870i	0.957500	−	0.288435i	$-0.0931349\pi$
$90$		0			0
$91$	1.56235	−	1.56235i	0.163779	−	0.163779i
$92$	−13.8300	+	4.98708i	−1.44187	+	0.519939i
$93$		0			0
$94$	−4.65859	−	3.27234i	−0.480497	−	0.337516i
$95$	−18.0437			−1.85125
$96$		0			0
$97$	−7.77657			−0.789591			−0.394795	−	0.918769i	$-0.629185\pi$
$97$	−7.77657			−0.789591			−0.394795	+	0.918769i	$0.629185\pi$
$98$	1.27117	+	0.892909i	0.128408	+	0.0901974i
$99$		0			0
$100$	12.1588	−	4.38444i	1.21588	−	0.438444i
$101$	−5.02217	+	5.02217i	−0.499725	+	0.499725i	−0.911352	−	0.411627i	$-0.864961\pi$
$101$	−5.02217	+	5.02217i	−0.499725	+	0.499725i	0.411627	+	0.911352i	$0.364961\pi$
$102$		0			0
$103$		−	10.4881i		−	1.03342i	−0.856160	−	0.516710i	$-0.827157\pi$
$103$		−	10.4881i		−	1.03342i	0.856160	−	0.516710i	$-0.172843\pi$
$104$	−2.23358	+	1.27628i	−0.219021	+	0.125150i
$105$		0			0
$106$	13.5056	−	2.36067i	1.31178	−	0.229288i
$107$	−2.96908	+	2.96908i	−0.287032	+	0.287032i	−0.835905	−	0.548874i	$-0.815057\pi$
$107$	−2.96908	+	2.96908i	−0.287032	+	0.287032i	0.548874	+	0.835905i	$0.315057\pi$
$108$		0			0
$109$	11.4372	+	11.4372i	1.09549	+	1.09549i	0.994931	+	0.100557i	$0.0320625\pi$
$109$	11.4372	+	11.4372i	1.09549	+	1.09549i	0.100557	+	0.994931i	$0.467938\pi$
$110$	3.12590	−	4.45012i	0.298043	−	0.424303i
$111$		0			0
$112$	6.20165	+	7.48094i	0.586001	+	0.706882i
$113$	10.3566			0.974266			0.487133	−	0.873328i	$-0.338043\pi$
$113$	10.3566			0.974266			0.487133	+	0.873328i	$0.338043\pi$
$114$		0			0
$115$	17.5980	+	17.5980i	1.64102	+	1.64102i
$116$	−8.12755	+	17.2949i	−0.754624	+	1.60579i
$117$		0			0
$118$	−9.48963	+	1.65870i	−0.873591	+	0.152696i
$119$		−	1.74292i		−	0.159773i
$120$		0			0
$121$			9.70994i			0.882722i
$122$	−2.97372	−	17.0130i	−0.269228	−	1.54029i
$123$		0			0
$124$	−4.54401	−	12.6013i	−0.408064	−	1.13163i
$125$	−3.50138	−	3.50138i	−0.313173	−	0.313173i
$126$		0			0
$127$	−9.05695			−0.803674			−0.401837	−	0.915711i	$-0.631628\pi$
$127$	−9.05695			−0.803674			−0.401837	+	0.915711i	$0.631628\pi$
$128$	−4.67418	−	10.3030i	−0.413143	−	0.910666i
$129$		0			0
$130$	3.56351	+	2.50312i	0.312540	+	0.219538i
$131$	10.5185	+	10.5185i	0.919005	+	0.919005i	0.996957	−	0.0779523i	$-0.0248382\pi$
$131$	10.5185	+	10.5185i	0.919005	+	0.919005i	−0.0779523	+	0.996957i	$0.524838\pi$
$132$		0			0
$133$	−9.15489	+	9.15489i	−0.793830	+	0.793830i
$134$	3.82028	+	21.8563i	0.330022	+	1.88809i
$135$		0			0
$136$	−0.533969	+	1.95775i	−0.0457874	+	0.167876i
$137$		−	15.3049i		−	1.30759i	−0.756673	−	0.653793i	$-0.773177\pi$
$137$		−	15.3049i		−	1.30759i	0.756673	−	0.653793i	$-0.226823\pi$
$138$		0			0
$139$	3.55470	−	3.55470i	0.301506	−	0.301506i	−0.540097	−	0.841603i	$-0.681612\pi$
$139$	3.55470	−	3.55470i	0.301506	−	0.301506i	0.841603	+	0.540097i	$0.181612\pi$
$140$	6.99627	−	14.8876i	0.591293	−	1.25823i
$141$		0			0
$142$	6.84610	−	9.74631i	0.574512	−	0.817892i
$143$	1.03304			0.0863870
$144$		0			0
$145$	32.3488			2.68642
$146$	11.4437	−	16.2915i	0.947084	−	1.34830i
$147$		0			0
$148$	−17.9737	−	8.44657i	−1.47743	−	0.694304i
$149$	−2.84139	+	2.84139i	−0.232776	+	0.232776i	−0.813850	−	0.581074i	$-0.802633\pi$
$149$	−2.84139	+	2.84139i	−0.232776	+	0.232776i	0.581074	+	0.813850i	$0.302633\pi$
$150$		0			0
$151$			4.90577i			0.399226i	0.979875	+	0.199613i	$0.0639684\pi$
$151$			4.90577i			0.399226i	−0.979875	+	0.199613i	$0.936032\pi$
$152$	13.0881	−	7.47860i	1.06158	−	0.606595i
$153$		0			0
$154$	−0.671874	−	3.84387i	−0.0541412	−	0.309748i
$155$	−16.0345	+	16.0345i	−1.28792	+	1.28792i
$156$		0			0
$157$	5.36412	+	5.36412i	0.428103	+	0.428103i	0.887982	−	0.459879i	$-0.152107\pi$
$157$	5.36412	+	5.36412i	0.428103	+	0.428103i	−0.459879	+	0.887982i	$0.652107\pi$
$158$	−6.48221	−	4.55330i	−0.515697	−	0.362241i
$159$		0			0
$160$	−12.4197	+	14.5792i	−0.981861	+	1.15259i
$161$	17.8575			1.40737
$162$		0			0
$163$	−3.68855	−	3.68855i	−0.288910	−	0.288910i	0.547739	−	0.836649i	$-0.315489\pi$
$163$	−3.68855	−	3.68855i	−0.288910	−	0.288910i	−0.836649	+	0.547739i	$0.815489\pi$
$164$	−6.65163	+	2.39857i	−0.519405	+	0.187297i
$165$		0			0
$166$	−2.11768	−	12.1155i	−0.164364	−	0.940343i
$167$		−	4.89629i		−	0.378887i	−0.981892	−	0.189443i	$-0.939332\pi$
$167$		−	4.89629i		−	0.378887i	0.981892	−	0.189443i	$-0.0606683\pi$
$168$		0			0
$169$		−	12.1728i		−	0.936368i
$170$	3.38388	−	0.591472i	0.259532	−	0.0453639i
$171$		0			0
$172$	3.37773	+	1.58733i	0.257549	+	0.121033i
$173$	−0.362404	−	0.362404i	−0.0275531	−	0.0275531i	0.693196	−	0.720749i	$-0.256202\pi$
$173$	−0.362404	−	0.362404i	−0.0275531	−	0.0275531i	−0.720749	+	0.693196i	$0.756202\pi$
$174$		0			0
$175$	−15.6996			−1.18678
$176$	−0.422935	+	4.52351i	−0.0318799	+	0.340972i
$177$		0			0
$178$	4.42386	−	6.29794i	0.331583	−	0.472051i
$179$	2.96908	+	2.96908i	0.221919	+	0.221919i	0.809306	−	0.587387i	$-0.199843\pi$
$179$	2.96908	+	2.96908i	0.221919	+	0.221919i	−0.587387	+	0.809306i	$0.699843\pi$
$180$		0			0
$181$	−8.50927	+	8.50927i	−0.632489	+	0.632489i	−0.948692	−	0.316203i	$-0.897592\pi$
$181$	−8.50927	+	8.50927i	−0.632489	+	0.632489i	0.316203	+	0.948692i	$0.397592\pi$
$182$	3.07804	−	0.538014i	0.228160	−	0.0398803i
$183$		0			0
$184$	−20.0586	−	5.47090i	−1.47874	−	0.403320i
$185$			33.6185i			2.47168i
$186$		0			0
$187$	0.576215	−	0.576215i	0.0421370	−	0.0421370i
$188$	−2.73111	−	7.57380i	−0.199186	−	0.552376i
$189$		0			0
$190$	−20.8810	−	14.6675i	−1.51487	−	1.06409i
$191$	12.4358			0.899823			0.449911	−	0.893073i	$-0.351456\pi$
$191$	12.4358			0.899823			0.449911	+	0.893073i	$0.351456\pi$
$192$		0			0
$193$	4.89006			0.351994			0.175997	−	0.984391i	$-0.443685\pi$
$193$	4.89006			0.351994			0.175997	+	0.984391i	$0.443685\pi$
$194$	−8.99940	−	6.32145i	−0.646119	−	0.453854i
$195$		0			0
$196$	0.745226	+	2.06663i	0.0532304	+	0.147616i
$197$	−4.31292	+	4.31292i	−0.307283	+	0.307283i	−0.843855	−	0.536572i	$-0.819719\pi$
$197$	−4.31292	+	4.31292i	−0.307283	+	0.307283i	0.536572	+	0.843855i	$0.319719\pi$
$198$		0			0
$199$		−	3.77894i		−	0.267882i	−0.990989	−	0.133941i	$-0.957237\pi$
$199$		−	3.77894i		−	0.267882i	0.990989	−	0.133941i	$-0.0427633\pi$
$200$	17.6347	+	4.80979i	1.24696	+	0.340104i
$201$		0			0
$202$	−9.89434	+	1.72944i	−0.696163	+	0.121683i
$203$	16.4129	−	16.4129i	1.15196	−	1.15196i
$204$		0			0
$205$	8.46388	+	8.46388i	0.591143	+	0.591143i
$206$	8.52559	−	12.1373i	0.594006	−	0.845644i
$207$		0			0
$208$	−3.62227	−	0.338672i	−0.251159	−	0.0234827i
$209$	−6.05328			−0.418714
$210$		0			0
$211$	2.07230	+	2.07230i	0.142663	+	0.142663i	0.774831	−	0.632168i	$-0.217835\pi$
$211$	2.07230	+	2.07230i	0.142663	+	0.142663i	−0.632168	+	0.774831i	$0.717835\pi$
$212$	17.5483	+	8.24666i	1.20522	+	0.566383i
$213$		0			0
$214$	−5.84947	+	1.02244i	−0.399862	+	0.0698923i
$215$		−	6.31780i		−	0.430870i
$216$		0			0
$217$			16.2709i			1.10454i
$218$	3.93854	+	22.5328i	0.266752	+	1.52612i
$219$		0			0
$220$	7.23487	−	2.60889i	0.487775	−	0.175891i
$221$	0.461413	+	0.461413i	0.0310380	+	0.0310380i
$222$		0			0
$223$	14.3199			0.958932			0.479466	−	0.877561i	$-0.340830\pi$
$223$	14.3199			0.958932			0.479466	+	0.877561i	$0.340830\pi$
$224$	1.09570	+	13.6985i	0.0732095	+	0.915270i
$225$		0			0
$226$	11.9851	+	8.41871i	0.797238	+	0.560004i
$227$	9.01457	+	9.01457i	0.598318	+	0.598318i	0.939865	−	0.341547i	$-0.110951\pi$
$227$	9.01457	+	9.01457i	0.598318	+	0.598318i	−0.341547	+	0.939865i	$0.610951\pi$
$228$		0			0
$229$	−16.3000	+	16.3000i	−1.07713	+	1.07713i	−0.0803678	+	0.996765i	$0.525609\pi$
$229$	−16.3000	+	16.3000i	−1.07713	+	1.07713i	−0.996765	+	0.0803678i	$0.974391\pi$
$230$	6.06006	+	34.6703i	0.399589	+	2.28609i
$231$		0			0
$232$	−23.4643	+	13.4076i	−1.54051	+	0.880255i
$233$		−	15.9507i		−	1.04497i	−0.852649	−	0.522484i	$-0.825006\pi$
$233$		−	15.9507i		−	1.04497i	0.852649	−	0.522484i	$-0.174994\pi$
$234$		0			0
$235$	−9.63729	+	9.63729i	−0.628667	+	0.628667i
$236$	−12.3302	−	5.79445i	−0.802626	−	0.377186i
$237$		0			0
$238$	1.41679	−	2.01699i	0.0918370	−	0.130742i
$239$	−0.0356301			−0.00230472			−0.00115236	−	0.999999i	$-0.500367\pi$
$239$	−0.0356301			−0.00230472			−0.00115236	+	0.999999i	$0.500367\pi$
$240$		0			0
$241$	6.54514			0.421610			0.210805	−	0.977528i	$-0.432392\pi$
$241$	6.54514			0.421610			0.210805	+	0.977528i	$0.432392\pi$
$242$	−7.89306	+	11.2368i	−0.507385	+	0.722328i
$243$		0			0
$244$	10.3883	−	22.1055i	0.665042	−	1.41516i
$245$	2.62969	−	2.62969i	0.168005	−	0.168005i
$246$		0			0
$247$		−	4.84726i		−	0.308424i
$248$	4.98484	−	18.2765i	0.316538	−	1.16056i
$249$		0			0
$250$	−1.20574	−	6.89818i	−0.0762578	−	0.436279i
$251$	13.6016	−	13.6016i	0.858527	−	0.858527i	−0.132638	−	0.991165i	$-0.542345\pi$
$251$	13.6016	−	13.6016i	0.858527	−	0.858527i	0.991165	+	0.132638i	$0.0423447\pi$
$252$		0			0
$253$	5.90374	+	5.90374i	0.371165	+	0.371165i
$254$	−10.4811	−	7.36225i	−0.657644	−	0.461949i
$255$		0			0
$256$	2.96598	−	15.7227i	0.185374	−	0.982668i
$257$	−3.18566			−0.198716			−0.0993579	−	0.995052i	$-0.531679\pi$
$257$	−3.18566			−0.198716			−0.0993579	+	0.995052i	$0.531679\pi$
$258$		0			0
$259$	17.0571	+	17.0571i	1.05988	+	1.05988i
$260$	2.08911	+	5.79344i	0.129561	+	0.359294i
$261$		0			0
$262$	3.62216	+	20.7228i	0.223778	+	1.28026i
$263$			0.585410i			0.0360979i	0.999837	+	0.0180490i	$0.00574547\pi$
$263$			0.585410i			0.0360979i	−0.999837	+	0.0180490i	$0.994255\pi$
$264$		0			0
$265$		−	32.8228i		−	2.01629i
$266$	−18.0363	+	3.15259i	−1.10588	+	0.193298i
$267$		0			0
$268$	−13.3456	+	28.3985i	−0.815214	+	1.73472i
$269$	3.53355	+	3.53355i	0.215444	+	0.215444i	0.806575	−	0.591131i	$-0.201318\pi$
$269$	3.53355	+	3.53355i	0.215444	+	0.215444i	−0.591131	+	0.806575i	$0.701318\pi$
$270$		0			0
$271$	−10.2234			−0.621029			−0.310514	−	0.950569i	$-0.600501\pi$
$271$	−10.2234			−0.621029			−0.310514	+	0.950569i	$0.600501\pi$
$272$	−2.20936	+	1.83155i	−0.133962	+	0.111054i
$273$		0			0
$274$	12.4411	−	17.7115i	0.751596	−	1.06999i
$275$	−5.19033	−	5.19033i	−0.312989	−	0.312989i
$276$		0			0
$277$	1.50587	−	1.50587i	0.0904791	−	0.0904791i	−0.660419	−	0.750898i	$-0.729621\pi$
$277$	1.50587	−	1.50587i	0.0904791	−	0.0904791i	0.750898	+	0.660419i	$0.229621\pi$
$278$	7.00322	−	1.22410i	0.420025	−	0.0734167i
$279$		0			0
$280$	20.1983	−	11.5414i	1.20708	−	0.689732i
$281$		−	10.1639i		−	0.606328i	−0.952938	−	0.303164i	$-0.901957\pi$
$281$		−	10.1639i		−	0.606328i	0.952938	−	0.303164i	$-0.0980430\pi$
$282$		0			0
$283$	4.30935	−	4.30935i	0.256164	−	0.256164i	−0.567328	−	0.823492i	$-0.692023\pi$
$283$	4.30935	−	4.30935i	0.256164	−	0.256164i	0.823492	+	0.567328i	$0.192023\pi$
$284$	15.8453	−	5.71379i	0.940243	−	0.339051i
$285$		0			0
$286$	1.19548	+	0.839741i	0.0706902	+	0.0496549i
$287$	8.58869			0.506974
$288$		0			0
$289$	−16.4853			−0.969721
$290$	37.4355	+	26.2958i	2.19829	+	1.54414i
$291$		0			0
$292$	26.4862	−	9.55092i	1.54999	−	0.558925i
$293$	3.40085	−	3.40085i	0.198680	−	0.198680i	−0.600754	−	0.799434i	$-0.705133\pi$
$293$	3.40085	−	3.40085i	0.198680	−	0.198680i	0.799434	+	0.600754i	$0.205133\pi$
$294$		0			0
$295$			23.0627i			1.34276i
$296$	−13.9339	−	24.3853i	−0.809892	−	1.41737i
$297$		0			0
$298$	−5.59791	+	0.978466i	−0.324278	+	0.0566810i
$299$	−4.72751	+	4.72751i	−0.273399	+	0.273399i
$300$		0			0
$301$	−3.20548	−	3.20548i	−0.184761	−	0.184761i
$302$	−3.98782	+	5.67718i	−0.229473	+	0.326685i
$303$		0			0
$304$	21.2254	+	1.98451i	1.21736	+	0.113819i
$305$	−41.3468			−2.36751
$306$		0			0
$307$	5.90918	+	5.90918i	0.337255	+	0.337255i	0.855333	−	0.518079i	$-0.173352\pi$
$307$	5.90918	+	5.90918i	0.337255	+	0.337255i	−0.518079	+	0.855333i	$0.673352\pi$
$308$	2.34710	−	4.99446i	0.133738	−	0.284586i
$309$		0			0
$310$	−31.5901	+	5.52166i	−1.79419	+	0.313609i
$311$			11.1601i			0.632830i	0.948621	+	0.316415i	$0.102479\pi$
$311$			11.1601i			0.632830i	−0.948621	+	0.316415i	$0.897521\pi$
$312$		0			0
$313$		−	13.7600i		−	0.777764i	−0.921288	−	0.388882i	$-0.872861\pi$
$313$		−	13.7600i		−	0.777764i	0.921288	−	0.388882i	$-0.127139\pi$
$314$	1.84719	+	10.5680i	0.104243	+	0.596387i
$315$		0			0
$316$	−3.80020	−	10.5386i	−0.213778	−	0.592841i
$317$	7.48941	+	7.48941i	0.420647	+	0.420647i	0.885427	−	0.464779i	$-0.153866\pi$
$317$	7.48941	+	7.48941i	0.420647	+	0.420647i	−0.464779	+	0.885427i	$0.653866\pi$
$318$		0			0
$319$	10.8523			0.607613
$320$	−26.2238	+	6.77599i	−1.46596	+	0.378789i
$321$		0			0
$322$	20.6655	+	14.5161i	1.15164	+	0.808949i
$323$	−2.70374	−	2.70374i	−0.150440	−	0.150440i
$324$		0			0
$325$	4.15624	−	4.15624i	0.230547	−	0.230547i
$326$	−1.27020	−	7.26693i	−0.0703496	−	0.402478i
$327$		0			0
$328$	−9.64734	−	2.63127i	−0.532685	−	0.145288i
$329$			9.77940i			0.539156i
$330$		0			0
$331$	8.77866	−	8.77866i	0.482519	−	0.482519i	−0.423416	−	0.905935i	$-0.639169\pi$
$331$	8.77866	−	8.77866i	0.482519	−	0.482519i	0.905935	+	0.423416i	$0.139169\pi$
$332$	7.39781	−	15.7420i	0.406007	−	0.863955i
$333$		0			0
$334$	3.98012	−	5.66622i	0.217783	−	0.310042i
$335$	53.1174			2.90211
$336$		0			0
$337$	8.61527			0.469304			0.234652	−	0.972079i	$-0.424605\pi$
$337$	8.61527			0.469304			0.234652	+	0.972079i	$0.424605\pi$
$338$	9.89506	−	14.0869i	0.538221	−	0.766226i
$339$		0			0
$340$	4.39678	+	2.06623i	0.238449	+	0.112057i
$341$	−5.37923	+	5.37923i	−0.291302	+	0.291302i
$342$		0			0
$343$		−	19.6736i		−	1.06228i
$344$	2.61855	+	4.58264i	0.141182	+	0.247079i
$345$		0			0
$346$	−0.124798	−	0.713983i	−0.00670918	−	0.0383840i
$347$	18.7627	−	18.7627i	1.00723	−	1.00723i	0.00726010	−	0.999974i	$-0.497689\pi$
$347$	18.7627	−	18.7627i	1.00723	−	1.00723i	0.999974	−	0.00726010i	$-0.00231098\pi$
$348$		0			0
$349$	−24.2289	−	24.2289i	−1.29695	−	1.29695i	−0.930400	−	0.366546i	$-0.880540\pi$
$349$	−24.2289	−	24.2289i	−1.29695	−	1.29695i	−0.366546	−	0.930400i	$-0.619460\pi$
$350$	−18.1683	−	12.7619i	−0.971135	−	0.682155i
$351$		0			0
$352$	−4.16653	+	4.89102i	−0.222077	+	0.260692i
$353$	−8.48757			−0.451748			−0.225874	−	0.974157i	$-0.572524\pi$
$353$	−8.48757			−0.451748			−0.225874	+	0.974157i	$0.572524\pi$
$354$		0			0
$355$	−20.1623	−	20.1623i	−1.07010	−	1.07010i
$356$	10.2390	−	3.69218i	0.542666	−	0.195685i
$357$		0			0
$358$	1.02244	+	5.84947i	0.0540374	+	0.309154i
$359$			30.8247i			1.62687i	0.581658	+	0.813433i	$0.302404\pi$
$359$			30.8247i			1.62687i	−0.581658	+	0.813433i	$0.697596\pi$
$360$		0			0
$361$			9.40338i			0.494915i
$362$	−16.7644	+	2.93026i	−0.881116	+	0.154011i
$363$		0			0
$364$	3.99939	+	1.87948i	0.209625	+	0.0985114i
$365$	−33.7025	−	33.7025i	−1.76407	−	1.76407i
$366$		0			0
$367$	18.1569			0.947784			0.473892	−	0.880583i	$-0.342849\pi$
$367$	18.1569			0.947784			0.473892	+	0.880583i	$0.342849\pi$
$368$	−18.7655	−	22.6365i	−0.978221	−	1.18001i
$369$		0			0
$370$	−27.3280	+	38.9049i	−1.42071	+	2.02257i
$371$	−16.6534	−	16.6534i	−0.864603	−	0.864603i
$372$		0			0
$373$	11.3337	−	11.3337i	0.586838	−	0.586838i	−0.349935	−	0.936774i	$-0.613796\pi$
$373$	11.3337	−	11.3337i	0.586838	−	0.586838i	0.936774	+	0.349935i	$0.113796\pi$
$374$	1.13522	−	0.198426i	0.0587008	−	0.0102604i
$375$		0			0
$376$	2.99606	−	10.9848i	0.154510	−	0.566499i
$377$			8.69017i			0.447566i
$378$		0			0
$379$	13.2886	−	13.2886i	0.682590	−	0.682590i	−0.277993	−	0.960583i	$-0.589669\pi$
$379$	13.2886	−	13.2886i	0.682590	−	0.682590i	0.960583	+	0.277993i	$0.0896692\pi$
$380$	−12.2415	−	33.9477i	−0.627977	−	1.74148i
$381$		0			0
$382$	14.3913	+	10.1089i	0.736322	+	0.517215i
$383$	−26.7493			−1.36682			−0.683412	−	0.730033i	$-0.739505\pi$
$383$	−26.7493			−1.36682			−0.683412	+	0.730033i	$0.739505\pi$
$384$		0			0
$385$	−9.34178			−0.476101
$386$	5.65900	+	3.97505i	0.288035	+	0.202325i
$387$		0			0
$388$	−5.27591	−	14.6310i	−0.267844	−	0.742774i
$389$	−15.2105	+	15.2105i	−0.771205	+	0.771205i	−0.978317	−	0.207112i	$-0.933594\pi$
$389$	−15.2105	+	15.2105i	−0.771205	+	0.771205i	0.207112	+	0.978317i	$0.433594\pi$
$390$		0			0
$391$			5.27389i			0.266712i
$392$	−0.817523	+	2.99738i	−0.0412912	+	0.151391i
$393$		0			0
$394$	−8.49701	+	1.48520i	−0.428073	+	0.0748234i
$395$	−13.4098	+	13.4098i	−0.674722	+	0.674722i
$396$		0			0
$397$	−0.493782	−	0.493782i	−0.0247822	−	0.0247822i	0.694607	−	0.719389i	$-0.255578\pi$
$397$	−0.493782	−	0.493782i	−0.0247822	−	0.0247822i	−0.719389	+	0.694607i	$0.755578\pi$
$398$	3.07185	−	4.37317i	0.153978	−	0.219207i
$399$		0			0
$400$	16.4979	+	19.9011i	0.824895	+	0.995056i
$401$	−35.8192			−1.78873			−0.894363	−	0.447341i	$-0.852371\pi$
$401$	−35.8192			−1.78873			−0.894363	+	0.447341i	$0.852371\pi$
$402$		0			0
$403$	−4.30750	−	4.30750i	−0.214572	−	0.214572i
$404$	−12.8560	−	6.04157i	−0.639611	−	0.300579i
$405$		0			0
$406$	32.3356	−	5.65197i	1.60479	−	0.280502i
$407$			11.2783i			0.559044i
$408$		0			0
$409$			1.57250i			0.0777553i	0.999244	+	0.0388777i	$0.0123783\pi$
$409$			1.57250i			0.0777553i	−0.999244	+	0.0388777i	$0.987622\pi$
$410$	2.91463	+	16.6749i	0.143943	+	0.823517i
$411$		0			0
$412$	19.7324	−	7.11549i	0.972146	−	0.350555i
$413$	11.7014	+	11.7014i	0.575788	+	0.575788i
$414$		0			0
$415$	−29.4443			−1.44536
$416$	−3.91656	−	3.33642i	−0.192025	−	0.163581i
$417$		0			0
$418$	−7.00513	−	4.92062i	−0.342632	−	0.240675i
$419$	15.6458	+	15.6458i	0.764345	+	0.764345i	0.977105	−	0.212759i	$-0.0682450\pi$
$419$	15.6458	+	15.6458i	0.764345	+	0.764345i	−0.212759	+	0.977105i	$0.568245\pi$
$420$		0			0
$421$	−10.0780	+	10.0780i	−0.491170	+	0.491170i	−0.908675	−	0.417505i	$-0.862905\pi$
$421$	−10.0780	+	10.0780i	−0.491170	+	0.491170i	0.417505	+	0.908675i	$0.362905\pi$
$422$	0.713622	+	4.08271i	0.0347386	+	0.198743i
$423$		0			0
$424$	13.6041	+	23.8082i	0.660675	+	1.15623i
$425$		−	4.63659i		−	0.224908i
$426$		0			0
$427$	−20.9783	+	20.9783i	−1.01521	+	1.01521i
$428$	−7.60040	−	3.57174i	−0.367379	−	0.172646i
$429$		0			0
$430$	5.13564	−	7.31124i	0.247663	−	0.352580i
$431$	−11.6123			−0.559346			−0.279673	−	0.960095i	$-0.590226\pi$
$431$	−11.6123			−0.559346			−0.279673	+	0.960095i	$0.590226\pi$
$432$		0			0
$433$	−12.9093			−0.620379			−0.310190	−	0.950675i	$-0.600393\pi$
$433$	−12.9093			−0.620379			−0.310190	+	0.950675i	$0.600393\pi$
$434$	−13.2264	+	18.8295i	−0.634888	+	0.903844i
$435$		0			0
$436$	−13.7587	+	29.2776i	−0.658924	+	1.40214i
$437$	27.7017	−	27.7017i	1.32515	−	1.32515i
$438$		0			0
$439$		−	10.7468i		−	0.512919i	−0.966555	−	0.256460i	$-0.917444\pi$
$439$		−	10.7468i		−	0.512919i	0.966555	−	0.256460i	$-0.0825561\pi$
$440$	10.4933	+	2.86199i	0.500246	+	0.136440i
$441$		0			0
$442$	0.158893	+	0.909045i	0.00755777	+	0.0432388i
$443$	4.28706	−	4.28706i	0.203684	−	0.203684i	−0.597892	−	0.801577i	$-0.703995\pi$
$443$	4.28706	−	4.28706i	0.203684	−	0.203684i	0.801577	+	0.597892i	$0.203995\pi$
$444$		0			0
$445$	−13.0286	−	13.0286i	−0.617616	−	0.617616i
$446$	16.5716	+	11.6404i	0.784690	+	0.551190i
$447$		0			0
$448$	−9.86732	+	16.7432i	−0.466187	+	0.791043i
$449$	−13.4929			−0.636767			−0.318384	−	0.947962i	$-0.603140\pi$
$449$	−13.4929			−0.636767			−0.318384	+	0.947962i	$0.603140\pi$
$450$		0			0
$451$	2.83945	+	2.83945i	0.133704	+	0.133704i
$452$	7.02629	+	19.4850i	0.330489	+	0.916499i
$453$		0			0
$454$	3.10427	+	17.7599i	0.145691	+	0.833513i
$455$		−	7.48058i		−	0.350695i
$456$		0			0
$457$			12.2812i			0.574490i	0.957857	+	0.287245i	$0.0927394\pi$
$457$			12.2812i			0.574490i	−0.957857	+	0.287245i	$0.907261\pi$
$458$	−32.1131	+	5.61308i	−1.50055	+	0.262282i
$459$		0			0
$460$	−21.1700	+	45.0482i	−0.987055	+	2.10038i
$461$	−0.297450	−	0.297450i	−0.0138536	−	0.0138536i	0.700146	−	0.714000i	$-0.253118\pi$
$461$	−0.297450	−	0.297450i	−0.0138536	−	0.0138536i	−0.714000	+	0.700146i	$0.753118\pi$
$462$		0			0
$463$	3.55638			0.165279			0.0826395	−	0.996580i	$-0.473665\pi$
$463$	3.55638			0.165279			0.0826395	+	0.996580i	$0.473665\pi$
$464$	−38.0528	−	3.55783i	−1.76656	−	0.165168i
$465$		0			0
$466$	12.9661	−	18.4589i	0.600643	−	0.855093i
$467$	15.8492	+	15.8492i	0.733414	+	0.733414i	0.971294	−	0.237880i	$-0.0764526\pi$
$467$	15.8492	+	15.8492i	0.733414	+	0.733414i	−0.237880	+	0.971294i	$0.576453\pi$
$468$		0			0
$469$	26.9503	−	26.9503i	1.24445	−	1.24445i
$470$	−18.9867	+	3.31871i	−0.875792	+	0.153081i
$471$		0			0
$472$	−9.55882	−	16.7286i	−0.439980	−	0.769996i
$473$		−	2.11948i		−	0.0974540i
$474$		0			0
$475$	−24.3542	+	24.3542i	−1.11745	+	1.11745i
$476$	3.27916	−	1.18246i	0.150300	−	0.0541980i
$477$		0			0
$478$	−0.0412328	−	0.0289632i	−0.00188594	−	0.00132474i
$479$	6.66729			0.304636			0.152318	−	0.988332i	$-0.451326\pi$
$479$	6.66729			0.304636			0.152318	+	0.988332i	$0.451326\pi$
$480$		0			0
$481$	−9.03127			−0.411790
$482$	7.57434	+	5.32044i	0.345002	+	0.242340i
$483$		0			0
$484$	−18.2684	+	6.58758i	−0.830383	+	0.299435i
$485$	−18.6172	+	18.6172i	−0.845362	+	0.845362i
$486$		0			0
$487$		−	24.5540i		−	1.11265i	−0.830965	−	0.556324i	$-0.812211\pi$
$487$		−	24.5540i		−	1.11265i	0.830965	−	0.556324i	$-0.187789\pi$
$488$	29.9910	−	17.1371i	1.35763	−	0.775758i
$489$		0			0
$490$	5.18083	−	0.905563i	0.234046	−	0.0409092i
$491$	28.4818	−	28.4818i	1.28537	−	1.28537i	0.347794	−	0.937571i	$-0.386931\pi$
$491$	28.4818	−	28.4818i	1.28537	−	1.28537i	0.937571	−	0.347794i	$-0.113069\pi$
$492$		0			0
$493$	4.84726	+	4.84726i	0.218310	+	0.218310i
$494$	3.94026	−	5.60947i	0.177281	−	0.252382i
$495$		0			0
$496$	20.6254	−	17.0983i	0.926107	−	0.767738i
$497$	−20.4596			−0.917740
$498$		0			0
$499$	−27.5736	−	27.5736i	−1.23437	−	1.23437i	−0.962270	−	0.272095i	$-0.912283\pi$
$499$	−27.5736	−	27.5736i	−1.23437	−	1.23437i	−0.272095	−	0.962270i	$-0.587717\pi$
$500$	4.21209	−	8.96303i	0.188370	−	0.400839i
$501$		0			0
$502$	26.7970	−	4.68387i	1.19601	−	0.209052i
$503$		−	26.3403i		−	1.17446i	−0.809421	−	0.587228i	$-0.800219\pi$
$503$		−	26.3403i		−	1.17446i	0.809421	−	0.587228i	$-0.199781\pi$
$504$		0			0
$505$			24.0463i			1.07004i
$506$	2.03302	+	11.6311i	0.0903787	+	0.517067i
$507$		0			0
$508$	−6.14457	−	17.0399i	−0.272621	−	0.756022i
$509$	−12.6205	−	12.6205i	−0.559392	−	0.559392i	0.369742	−	0.929134i	$-0.379446\pi$
$509$	−12.6205	−	12.6205i	−0.559392	−	0.559392i	−0.929134	+	0.369742i	$0.879446\pi$
$510$		0			0
$511$	−34.1994			−1.51289
$512$	16.2131	−	15.7840i	0.716525	−	0.697562i
$513$		0			0
$514$	−3.68659	−	2.58957i	−0.162608	−	0.114221i
$515$	−25.1085	−	25.1085i	−1.10641	−	1.10641i
$516$		0			0
$517$	−3.23310	+	3.23310i	−0.142192	+	0.142192i
$518$	5.87382	+	33.6048i	0.258081	+	1.47651i
$519$		0			0
$520$	−2.29178	+	8.40264i	−0.100501	+	0.368480i
$521$			6.18166i			0.270823i	0.990789	+	0.135412i	$0.0432357\pi$
$521$			6.18166i			0.270823i	−0.990789	+	0.135412i	$0.956764\pi$
$522$		0			0
$523$	25.4662	−	25.4662i	1.11356	−	1.11356i	0.120896	−	0.992665i	$-0.461423\pi$
$523$	25.4662	−	25.4662i	1.11356	−	1.11356i	0.992665	−	0.120896i	$-0.0385767\pi$
$524$	−12.6535	+	26.9258i	−0.552771	+	1.17626i
$525$		0			0
$526$	−0.475871	+	0.677463i	−0.0207489	+	0.0295388i
$527$	−4.80533			−0.209324
$528$		0			0
$529$	−31.0348			−1.34934
$530$	26.6812	−	37.9841i	1.15896	−	1.64992i
$531$		0			0
$532$	−23.4352	−	11.0131i	−1.01604	−	0.477480i
$533$	−2.27373	+	2.27373i	−0.0984863	+	0.0984863i
$534$		0			0
$535$			14.2160i			0.614611i
$536$	−38.5289	+	22.0156i	−1.66420	+	0.950931i
$537$		0			0
$538$	1.21682	+	6.96155i	0.0524607	+	0.300134i
$539$	0.882203	−	0.882203i	0.0379992	−	0.0379992i
$540$		0			0
$541$	−1.20787	−	1.20787i	−0.0519306	−	0.0519306i	0.680665	−	0.732595i	$-0.261691\pi$
$541$	−1.20787	−	1.20787i	−0.0519306	−	0.0519306i	−0.732595	+	0.680665i	$0.761691\pi$
$542$	−11.8310	−	8.31046i	−0.508185	−	0.356965i
$543$		0			0
$544$	−4.04561	+	0.323596i	−0.173454	+	0.0138740i
$545$	54.7617			2.34573
$546$		0			0
$547$	−28.0845	−	28.0845i	−1.20080	−	1.20080i	−0.973922	−	0.226882i	$-0.927147\pi$
$547$	−28.0845	−	28.0845i	−1.20080	−	1.20080i	−0.226882	−	0.973922i	$-0.572853\pi$
$548$	28.7949	−	10.3834i	1.23006	−	0.443557i
$549$		0			0
$550$	−1.78735	−	10.2256i	−0.0762129	−	0.436022i
$551$		−	50.9216i		−	2.16933i
$552$		0			0
$553$			13.6076i			0.578653i
$554$	2.96677	−	0.518565i	0.126046	−	0.0220317i
$555$		0			0
$556$	9.09950	+	4.27623i	0.385905	+	0.181352i
$557$	−7.73448	−	7.73448i	−0.327720	−	0.327720i	0.523999	−	0.851719i	$-0.324440\pi$
$557$	−7.73448	−	7.73448i	−0.327720	−	0.327720i	−0.851719	+	0.523999i	$0.824440\pi$
$558$		0			0
$559$	1.69721			0.0717844
$560$	32.7562	+	3.06262i	1.38420	+	0.129419i
$561$		0			0
$562$	8.26209	−	11.7621i	0.348515	−	0.496156i
$563$	16.8387	+	16.8387i	0.709667	+	0.709667i	0.966465	−	0.256798i	$-0.0826676\pi$
$563$	16.8387	+	16.8387i	0.709667	+	0.709667i	−0.256798	+	0.966465i	$0.582668\pi$
$564$		0			0
$565$	24.7938	−	24.7938i	1.04308	−	1.04308i
$566$	8.48998	−	1.48397i	0.356861	−	0.0623761i
$567$		0			0
$568$	22.9815	+	6.26811i	0.964283	+	0.263004i
$569$			0.430002i			0.0180266i	0.999959	+	0.00901331i	$0.00286906\pi$
$569$			0.430002i			0.0180266i	−0.999959	+	0.00901331i	$0.997131\pi$
$570$		0			0
$571$	14.8125	−	14.8125i	0.619884	−	0.619884i	−0.325618	−	0.945502i	$-0.605572\pi$
$571$	14.8125	−	14.8125i	0.619884	−	0.619884i	0.945502	+	0.325618i	$0.105572\pi$
$572$	0.700852	+	1.94357i	0.0293041	+	0.0812649i
$573$		0			0
$574$	9.93922	+	6.98161i	0.414855	+	0.291407i
$575$	47.5052			1.98110
$576$		0			0
$577$	−1.89410			−0.0788524			−0.0394262	−	0.999222i	$-0.512553\pi$
$577$	−1.89410			−0.0788524			−0.0394262	+	0.999222i	$0.512553\pi$
$578$	−19.0775	−	13.4006i	−0.793519	−	0.557392i
$579$		0			0
$580$	21.9466	+	60.8615i	0.911283	+	2.52714i
$581$	−14.9392	+	14.9392i	−0.619784	+	0.619784i
$582$		0			0
$583$		−	11.0114i		−	0.456044i
$584$	38.4149	+	10.4775i	1.58962	+	0.433562i
$585$		0			0
$586$	6.70012	−	1.17112i	0.276780	−	0.0483786i
$587$	−15.3826	+	15.3826i	−0.634910	+	0.634910i	−0.949295	−	0.314386i	$-0.898202\pi$
$587$	−15.3826	+	15.3826i	−0.634910	+	0.634910i	0.314386	+	0.949295i	$0.398202\pi$
$588$		0			0
$589$	25.2406	+	25.2406i	1.04002	+	1.04002i
$590$	−18.7473	+	26.6892i	−0.771814	+	1.09878i
$591$		0			0
$592$	3.69748	−	39.5465i	0.151966	−	1.62535i
$593$	45.0304			1.84918			0.924589	−	0.380966i	$-0.124409\pi$
$593$	45.0304			1.84918			0.924589	+	0.380966i	$0.124409\pi$
$594$		0			0
$595$	−4.17257	−	4.17257i	−0.171059	−	0.171059i
$596$	−7.27354	−	3.41813i	−0.297936	−	0.140012i
$597$		0			0
$598$	−9.31382	+	1.62797i	−0.380870	+	0.0665728i
$599$			17.0476i			0.696547i	0.937393	+	0.348274i	$0.113232\pi$
$599$			17.0476i			0.696547i	−0.937393	+	0.348274i	$0.886768\pi$
$600$		0			0
$601$			4.99596i			0.203789i	0.994795	+	0.101895i	$0.0324905\pi$
$601$			4.99596i			0.203789i	−0.994795	+	0.101895i	$0.967510\pi$
$602$	−1.10384	−	6.31521i	−0.0449893	−	0.257389i
$603$		0			0
$604$	−9.22978	+	3.32825i	−0.375555	+	0.135425i
$605$	23.2457	+	23.2457i	0.945071	+	0.945071i
$606$		0			0
$607$	39.8609			1.61790			0.808951	−	0.587876i	$-0.200036\pi$
$607$	39.8609			1.61790			0.808951	+	0.587876i	$0.200036\pi$
$608$	22.9498	+	19.5503i	0.930737	+	0.792871i
$609$		0			0
$610$	−47.8484	−	33.6102i	−1.93733	−	1.36084i
$611$	−2.58896	−	2.58896i	−0.104738	−	0.104738i
$612$		0			0
$613$	30.1934	−	30.1934i	1.21950	−	1.21950i	0.251693	−	0.967807i	$-0.419013\pi$
$613$	30.1934	−	30.1934i	1.21950	−	1.21950i	0.967807	−	0.251693i	$-0.0809873\pi$
$614$	2.03489	+	11.6419i	0.0821216	+	0.469827i
$615$		0			0
$616$	6.77609	−	3.87190i	0.273017	−	0.156003i
$617$		−	25.9722i		−	1.04560i	−0.852455	−	0.522800i	$-0.824887\pi$
$617$		−	25.9722i		−	1.04560i	0.852455	−	0.522800i	$-0.175113\pi$
$618$		0			0
$619$	5.23851	−	5.23851i	0.210553	−	0.210553i	−0.593949	−	0.804503i	$-0.702432\pi$
$619$	5.23851	−	5.23851i	0.210553	−	0.210553i	0.804503	+	0.593949i	$0.202432\pi$
$620$	−41.0459	−	19.2891i	−1.64844	−	0.774671i
$621$		0			0
$622$	−9.07186	+	12.9150i	−0.363749	+	0.517843i
$623$	−13.2207			−0.529678
$624$		0			0
$625$	15.5481			0.621924
$626$	11.1853	−	15.9238i	0.447056	−	0.636441i
$627$		0			0
$628$	−6.45291	+	13.7313i	−0.257499	+	0.547940i
$629$	−5.03752	+	5.03752i	−0.200859	+	0.200859i
$630$		0			0
$631$			38.5898i			1.53623i	0.640309	+	0.768117i	$0.278806\pi$
$631$			38.5898i			1.53623i	−0.640309	+	0.768117i	$0.721194\pi$
$632$	4.16888	−	15.2849i	0.165829	−	0.607999i
$633$		0			0
$634$	2.57907	+	14.7551i	0.102428	+	0.586001i
$635$	−21.6824	+	21.6824i	−0.860441	+	0.860441i
$636$		0			0
$637$	0.706438	+	0.706438i	0.0279901	+	0.0279901i
$638$	12.5588	+	8.82168i	0.497208	+	0.349254i
$639$		0			0
$640$	−35.8555	−	13.4755i	−1.41731	−	0.532665i
$641$	7.77685			0.307167			0.153584	−	0.988136i	$-0.450919\pi$
$641$	7.77685			0.307167			0.153584	+	0.988136i	$0.450919\pi$
$642$		0			0
$643$	21.9416	+	21.9416i	0.865293	+	0.865293i	0.991947	−	0.126654i	$-0.0404239\pi$
$643$	21.9416	+	21.9416i	0.865293	+	0.865293i	−0.126654	+	0.991947i	$0.540424\pi$
$644$	12.1152	+	33.5973i	0.477404	+	1.32392i
$645$		0			0
$646$	−0.931062	−	5.32671i	−0.0366321	−	0.209577i
$647$			44.9113i			1.76564i	0.469707	+	0.882822i	$0.344360\pi$
$647$			44.9113i			1.76564i	−0.469707	+	0.882822i	$0.655640\pi$
$648$		0			0
$649$			7.73703i			0.303705i
$650$	8.18834	−	1.43125i	0.321173	−	0.0561382i
$651$		0			0
$652$	4.43725	−	9.44215i	0.173776	−	0.369783i
$653$	−17.2512	−	17.2512i	−0.675091	−	0.675091i	0.283794	−	0.958885i	$-0.408407\pi$
$653$	−17.2512	−	17.2512i	−0.675091	−	0.675091i	−0.958885	+	0.283794i	$0.908407\pi$
$654$		0			0
$655$	50.3627			1.96783
$656$	−9.02542	−	10.8872i	−0.352384	−	0.425074i
$657$		0			0
$658$	−7.94952	+	11.3172i	−0.309905	+	0.441189i
$659$	28.6843	+	28.6843i	1.11738	+	1.11738i	0.992124	+	0.125257i	$0.0399754\pi$
$659$	28.6843	+	28.6843i	1.11738	+	1.11738i	0.125257	+	0.992124i	$0.460025\pi$
$660$		0			0
$661$	−20.0295	+	20.0295i	−0.779058	+	0.779058i	−0.979671	−	0.200612i	$-0.935707\pi$
$661$	−20.0295	+	20.0295i	−0.779058	+	0.779058i	0.200612	+	0.979671i	$0.435707\pi$
$662$	17.2951	−	3.02303i	0.672194	−	0.117494i
$663$		0			0
$664$	21.3575	−	12.2038i	0.828833	−	0.473600i
$665$			43.8338i			1.69980i
$666$		0			0
$667$	−49.6637	+	49.6637i	−1.92298	+	1.92298i
$668$	9.21196	−	3.32183i	0.356421	−	0.128525i
$669$		0			0
$670$	61.4699	+	43.1783i	2.37479	+	1.66812i
$671$	−13.8710			−0.535482
$672$		0			0
$673$	37.2460			1.43573			0.717864	−	0.696183i	$-0.245120\pi$
$673$	37.2460			1.43573			0.717864	+	0.696183i	$0.245120\pi$
$674$	9.96999	+	7.00322i	0.384030	+	0.269754i
$675$		0			0
$676$	22.9020	−	8.25846i	0.880848	−	0.317633i
$677$	−21.6296	+	21.6296i	−0.831294	+	0.831294i	−0.987694	−	0.156400i	$-0.950011\pi$
$677$	−21.6296	+	21.6296i	−0.831294	+	0.831294i	0.156400	+	0.987694i	$0.450011\pi$
$678$		0			0
$679$			18.8917i			0.724997i
$680$	3.40855	+	5.96521i	0.130712	+	0.228755i
$681$		0			0
$682$	−10.5978	+	1.85240i	−0.405810	+	0.0709320i
$683$	−24.7282	+	24.7282i	−0.946199	+	0.946199i	−0.998625	−	0.0524260i	$-0.983305\pi$
$683$	−24.7282	+	24.7282i	−0.946199	+	0.946199i	0.0524260	+	0.998625i	$0.483305\pi$
$684$		0			0
$685$	−36.6401	−	36.6401i	−1.39995	−	1.39995i
$686$	15.9924	−	22.7673i	0.610593	−	0.869258i
$687$		0			0
$688$	−0.694853	+	7.43181i	−0.0264910	+	0.283335i
$689$	8.81752			0.335921
$690$		0			0
$691$	−17.7724	−	17.7724i	−0.676093	−	0.676093i	0.283021	−	0.959114i	$-0.408664\pi$
$691$	−17.7724	−	17.7724i	−0.676093	−	0.676093i	−0.959114	+	0.283021i	$0.908664\pi$
$692$	0.435964	−	0.927700i	0.0165729	−	0.0352659i
$693$		0			0
$694$	36.9649	−	6.46114i	1.40317	−	0.245262i
$695$		−	17.0200i		−	0.645604i
$696$		0			0
$697$			2.53652i			0.0960774i
$698$	−8.34351	−	47.7342i	−0.315807	−	1.80677i
$699$		0			0
$700$	−10.6512	−	29.5374i	−0.402576	−	1.11641i
$701$	28.9738	+	28.9738i	1.09432	+	1.09432i	0.995061	+	0.0992626i	$0.0316484\pi$
$701$	28.9738	+	28.9738i	1.09432	+	1.09432i	0.0992626	+	0.995061i	$0.468352\pi$
$702$		0			0
$703$	52.9204			1.99593
$704$	−8.79753	+	2.27320i	−0.331570	+	0.0856744i
$705$		0			0
$706$	−9.82220	−	6.89941i	−0.369663	−	0.259663i
$707$	12.2004	+	12.2004i	0.458844	+	0.458844i
$708$		0			0
$709$	4.82706	−	4.82706i	0.181284	−	0.181284i	−0.610631	−	0.791915i	$-0.709084\pi$
$709$	4.82706	−	4.82706i	0.181284	−	0.181284i	0.791915	+	0.610631i	$0.209084\pi$
$710$	−6.94312	−	39.7224i	−0.260571	−	1.49076i
$711$		0			0
$712$	14.8504	+	4.05037i	0.556540	+	0.151794i
$713$		−	49.2341i		−	1.84383i
$714$		0			0
$715$	2.47310	−	2.47310i	0.0924888	−	0.0924888i
$716$	−3.57174	+	7.60040i	−0.133482	+	0.284040i
$717$		0			0
$718$	−25.0570	+	35.6718i	−0.935117	+	1.33126i
$719$	−44.1619			−1.64696			−0.823481	−	0.567344i	$-0.807971\pi$
$719$	−44.1619			−1.64696			−0.823481	+	0.567344i	$0.807971\pi$
$720$		0			0
$721$	−25.4788			−0.948880
$722$	−7.64387	+	10.8820i	−0.284475	+	0.404987i
$723$		0			0
$724$	−21.7825	−	10.2365i	−0.809539	−	0.380435i
$725$	43.6623	−	43.6623i	1.62158	−	1.62158i
$726$		0			0
$727$			15.1668i			0.562507i	0.959634	+	0.281253i	$0.0907502\pi$
$727$			15.1668i			0.562507i	−0.959634	+	0.281253i	$0.909250\pi$
$728$	3.10048	+	5.42606i	0.114912	+	0.201103i
$729$		0			0
$730$	−11.6058	−	66.3983i	−0.429551	−	2.45751i
$731$	0.946681	−	0.946681i	0.0350143	−	0.0350143i
$732$		0			0
$733$	4.75924	+	4.75924i	0.175787	+	0.175787i	0.789516	−	0.613730i	$-0.210331\pi$
$733$	4.75924	+	4.75924i	0.175787	+	0.175787i	−0.613730	+	0.789516i	$0.710331\pi$
$734$	21.0120	+	14.7595i	0.775568	+	0.544782i
$735$		0			0
$736$	−3.31547	−	41.4502i	−0.122210	−	1.52788i
$737$	17.8197			0.656399
$738$		0			0
$739$	−16.7000	−	16.7000i	−0.614321	−	0.614321i	0.329748	−	0.944069i	$-0.393036\pi$
$739$	−16.7000	−	16.7000i	−0.614321	−	0.614321i	−0.944069	+	0.329748i	$0.893036\pi$
$740$	−63.2504	+	22.8080i	−2.32513	+	0.838440i
$741$		0			0
$742$	−5.73480	−	32.8094i	−0.210531	−	1.20447i
$743$		−	37.0929i		−	1.36081i	−0.732838	−	0.680403i	$-0.761805\pi$
$743$		−	37.0929i		−	1.36081i	0.732838	−	0.680403i	$-0.238195\pi$
$744$		0			0
$745$			13.6046i			0.498435i
$746$	22.3289	−	3.90290i	0.817520	−	0.142895i
$747$		0			0
$748$	1.47503	+	0.693174i	0.0539323	+	0.0253450i
$749$	7.21281	+	7.21281i	0.263550	+	0.263550i
$750$		0			0
$751$	14.0418			0.512392			0.256196	−	0.966625i	$-0.417531\pi$
$751$	14.0418			0.512392			0.256196	+	0.966625i	$0.417531\pi$
$752$	12.3966	−	10.2767i	0.452056	−	0.374752i
$753$		0			0
$754$	−7.06410	+	10.0567i	−0.257259	+	0.366242i
$755$	11.7444	+	11.7444i	0.427424	+	0.427424i
$756$		0			0
$757$	−30.1151	+	30.1151i	−1.09455	+	1.09455i	−0.0995178	+	0.995036i	$0.531730\pi$
$757$	−30.1151	+	30.1151i	−1.09455	+	1.09455i	−0.995036	+	0.0995178i	$0.968270\pi$
$758$	26.1803	−	4.57609i	0.950912	−	0.166211i
$759$		0			0
$760$	13.4291	−	49.2368i	0.487125	−	1.78601i
$761$			35.2054i			1.27619i	0.769956	+	0.638097i	$0.220278\pi$
$761$			35.2054i			1.27619i	−0.769956	+	0.638097i	$0.779722\pi$
$762$		0			0
$763$	27.7846	−	27.7846i	1.00587	−	1.00587i
$764$	8.43690	+	23.3969i	0.305236	+	0.846470i
$765$		0			0
$766$	−30.9555	−	21.7441i	−1.11847	−	0.785645i
$767$	−6.19555			−0.223708
$768$		0			0
$769$	−32.5212			−1.17274			−0.586372	−	0.810042i	$-0.699444\pi$
$769$	−32.5212			−1.17274			−0.586372	+	0.810042i	$0.699444\pi$
$770$	−10.8107	−	7.59379i	−0.389592	−	0.273661i
$771$		0			0
$772$	3.31760	+	9.20023i	0.119403	+	0.331123i
$773$	3.97440	−	3.97440i	0.142949	−	0.142949i	−0.632011	−	0.774960i	$-0.717770\pi$
$773$	3.97440	−	3.97440i	0.142949	−	0.142949i	0.774960	+	0.632011i	$0.217770\pi$
$774$		0			0
$775$			43.2847i			1.55483i
$776$	5.78775	−	21.2203i	0.207768	−	0.761765i
$777$		0			0
$778$	−29.9668	+	5.23792i	−1.07436	+	0.187789i
$779$	13.3234	−	13.3234i	0.477359	−	0.477359i
$780$		0			0
$781$	−6.76402	−	6.76402i	−0.242036	−	0.242036i
$782$	−4.28706	+	6.10318i	−0.153305	+	0.218249i
$783$		0			0
$784$	−3.38260	+	2.80416i	−0.120807	+	0.100148i
$785$	25.6835			0.916683
$786$		0			0
$787$	7.04602	+	7.04602i	0.251163	+	0.251163i	0.821448	−	0.570284i	$-0.193167\pi$
$787$	7.04602	+	7.04602i	0.251163	+	0.251163i	−0.570284	+	0.821448i	$0.693167\pi$
$788$	−11.0404	−	5.18835i	−0.393299	−	0.184827i
$789$		0			0
$790$	−26.4191	+	4.61783i	−0.939950	+	0.164295i
$791$		−	25.1594i		−	0.894564i
$792$		0			0
$793$		−	11.1074i		−	0.394435i
$794$	−0.170039	−	0.972815i	−0.00603447	−	0.0345239i
$795$		0			0
$796$	7.10976	−	2.56378i	0.251999	−	0.0908706i
$797$	−8.86644	−	8.86644i	−0.314065	−	0.314065i	0.532417	−	0.846482i	$-0.321284\pi$
$797$	−8.86644	−	8.86644i	−0.314065	−	0.314065i	−0.846482	+	0.532417i	$0.821284\pi$
$798$		0			0
$799$	−2.88817			−0.102176
$800$	2.91483	+	36.4414i	0.103055	+	1.28840i
$801$		0			0
$802$	−41.4517	−	29.1169i	−1.46371	−	1.02815i
$803$	−11.3064	−	11.3064i	−0.398996	−	0.398996i
$804$		0			0
$805$	42.7509	−	42.7509i	1.50677	−	1.50677i
$806$	−1.48334	−	8.48634i	−0.0522483	−	0.298919i
$807$		0			0
$808$	−9.96649	−	17.4420i	−0.350620	−	0.613609i
$809$		−	28.3480i		−	0.996663i	−0.866987	−	0.498332i	$-0.833946\pi$
$809$		−	28.3480i		−	0.996663i	0.866987	−	0.498332i	$-0.166054\pi$
$810$		0			0
$811$	−11.2891	+	11.2891i	−0.396415	+	0.396415i	−0.876966	−	0.480552i	$-0.840436\pi$
$811$	−11.2891	+	11.2891i	−0.396415	+	0.396415i	0.480552	+	0.876966i	$0.340436\pi$
$812$	42.0146	+	19.7444i	1.47442	+	0.692891i
$813$		0			0
$814$	−9.16795	+	13.0518i	−0.321336	+	0.457464i
$815$	−17.6609			−0.618633
$816$		0			0
$817$	−9.94512			−0.347936
$818$	−1.27826	+	1.81977i	−0.0446935	+	0.0636269i
$819$		0			0
$820$	−10.1819	+	21.6663i	−0.355566	+	0.756619i
$821$	10.0814	−	10.0814i	0.351845	−	0.351845i	−0.508951	−	0.860796i	$-0.669967\pi$
$821$	10.0814	−	10.0814i	0.351845	−	0.351845i	0.860796	+	0.508951i	$0.169967\pi$
$822$		0			0
$823$			40.0394i			1.39569i	0.716251	+	0.697843i	$0.245857\pi$
$823$			40.0394i			1.39569i	−0.716251	+	0.697843i	$0.754143\pi$
$824$	28.6193	+	7.80580i	0.997002	+	0.271928i
$825$		0			0
$826$	4.02951	+	23.0533i	0.140204	+	0.802126i
$827$	−11.4276	+	11.4276i	−0.397376	+	0.397376i	−0.877306	−	0.479931i	$-0.840662\pi$
$827$	−11.4276	+	11.4276i	−0.397376	+	0.397376i	0.479931	+	0.877306i	$0.340662\pi$
$828$		0			0
$829$	26.8520	+	26.8520i	0.932609	+	0.932609i	0.997868	−	0.0652592i	$-0.0207874\pi$
$829$	26.8520	+	26.8520i	0.932609	+	0.932609i	−0.0652592	+	0.997868i	$0.520787\pi$
$830$	−34.0743	−	23.9348i	−1.18274	−	0.830789i
$831$		0			0
$832$	−1.82030	−	7.04477i	−0.0631076	−	0.244233i
$833$	0.788084			0.0273055
$834$		0			0
$835$	−11.7218	−	11.7218i	−0.405649	−	0.405649i
$836$	−4.10677	−	11.3887i	−0.142035	−	0.393887i
$837$		0			0
$838$	5.38780	+	30.8242i	0.186118	+	1.06480i
$839$			51.7727i			1.78739i	0.448672	+	0.893697i	$0.351897\pi$
$839$			51.7727i			1.78739i	−0.448672	+	0.893697i	$0.648103\pi$
$840$		0			0
$841$			62.2923i			2.14801i
$842$	−19.8549	+	3.47046i	−0.684245	+	0.119600i
$843$		0			0
$844$	−2.49294	+	5.30479i	−0.0858105	+	0.182599i
$845$	−29.1417	−	29.1417i	−1.00251	−	1.00251i
$846$		0			0
$847$	23.5885			0.810509
$848$	−3.60997	+	38.6105i	−0.123967	+	1.32589i
$849$		0			0
$850$	3.76901	−	5.36568i	0.129276	−	0.184041i
$851$	−51.6130	−	51.6130i	−1.76927	−	1.76927i
$852$		0			0
$853$	8.74587	−	8.74587i	0.299453	−	0.299453i	−0.541347	−	0.840800i	$-0.682085\pi$
$853$	8.74587	−	8.74587i	0.299453	−	0.299453i	0.840800	+	0.541347i	$0.182085\pi$
$854$	−41.3299	+	7.22410i	−1.41428	+	0.247204i
$855$		0			0
$856$	−5.89212	−	10.3116i	−0.201389	−	0.352444i
$857$		−	31.6621i		−	1.08156i	−0.841166	−	0.540778i	$-0.818130\pi$
$857$		−	31.6621i		−	1.08156i	0.841166	−	0.540778i	$-0.181870\pi$
$858$		0			0
$859$	−21.6426	+	21.6426i	−0.738436	+	0.738436i	−0.972275	−	0.233839i	$-0.924871\pi$
$859$	−21.6426	+	21.6426i	−0.738436	+	0.738436i	0.233839	+	0.972275i	$0.424871\pi$
$860$	11.8864	−	4.28623i	0.405323	−	0.146159i
$861$		0			0
$862$	−13.4383	−	9.43947i	−0.457711	−	0.321510i
$863$	27.4127			0.933141			0.466570	−	0.884484i	$-0.345489\pi$
$863$	27.4127			0.933141			0.466570	+	0.884484i	$0.345489\pi$
$864$		0			0
$865$	−1.73520			−0.0589985
$866$	−14.9392	−	10.4937i	−0.507654	−	0.356592i
$867$		0			0
$868$	−30.6124	+	11.0388i	−1.03905	+	0.374682i
$869$	−4.49871	+	4.49871i	−0.152608	+	0.152608i
$870$		0			0
$871$			14.2694i			0.483502i
$872$	−39.7216	+	22.6971i	−1.34514	+	0.768622i
$873$		0			0
$874$	54.5760	−	9.53940i	1.84606	−	0.322675i
$875$	−8.50595	+	8.50595i	−0.287554	+	0.287554i
$876$		0			0
$877$	−20.6328	−	20.6328i	−0.696721	−	0.696721i	0.266981	−	0.963702i	$-0.413974\pi$
$877$	−20.6328	−	20.6328i	−0.696721	−	0.696721i	−0.963702	+	0.266981i	$0.913974\pi$
$878$	8.73595	−	12.4367i	0.294824	−	0.419720i
$879$		0			0
$880$	9.81681	+	11.8418i	0.330925	+	0.399188i
$881$	−38.0432			−1.28171			−0.640854	−	0.767663i	$-0.721419\pi$
$881$	−38.0432			−1.28171			−0.640854	+	0.767663i	$0.721419\pi$
$882$		0			0
$883$	12.6242	+	12.6242i	0.424838	+	0.424838i	0.886866	−	0.462028i	$-0.152878\pi$
$883$	12.6242	+	12.6242i	0.424838	+	0.424838i	−0.462028	+	0.886866i	$0.652878\pi$
$884$	−0.555070	+	1.18115i	−0.0186690	+	0.0397264i
$885$		0			0
$886$	8.44607	−	1.47630i	0.283751	−	0.0495972i
$887$		−	4.75345i		−	0.159605i	−0.996811	−	0.0798026i	$-0.974571\pi$
$887$		−	4.75345i		−	0.159605i	0.996811	−	0.0798026i	$-0.0254290\pi$
$888$		0			0
$889$			22.0022i			0.737928i
$890$	−4.48656	−	25.6681i	−0.150390	−	0.860397i
$891$		0			0
$892$	9.71515	+	26.9417i	0.325287	+	0.902074i
$893$	15.1705	+	15.1705i	0.507660	+	0.507660i
$894$		0			0
$895$	14.2160			0.475188
$896$	−25.0292	+	11.3550i	−0.836168	+	0.379345i
$897$		0			0
$898$	−15.6146	−	10.9681i	−0.521065	−	0.366012i
$899$	−45.2513	−	45.2513i	−1.50922	−	1.50922i
$900$		0			0
$901$	4.91829	−	4.91829i	0.163852	−	0.163852i
$902$	0.977796	+	5.59408i	0.0325571	+	0.186263i
$903$		0			0
$904$	−7.70794	+	28.2605i	−0.256362	+	0.939932i
$905$			40.7425i			1.35433i
$906$		0			0
$907$	−12.2203	+	12.2203i	−0.405768	+	0.405768i	−0.880260	−	0.474492i	$-0.842632\pi$
$907$	−12.2203	+	12.2203i	−0.405768	+	0.405768i	0.474492	+	0.880260i	$0.342632\pi$
$908$	−10.8443	+	23.0760i	−0.359882	+	0.765803i
$909$		0			0
$910$	6.08085	−	8.65687i	0.201578	−	0.286972i
$911$	−23.1374			−0.766577			−0.383289	−	0.923629i	$-0.625209\pi$
$911$	−23.1374			−0.766577			−0.383289	+	0.923629i	$0.625209\pi$
$912$		0			0
$913$	−9.87792			−0.326912
$914$	−9.98320	+	14.2124i	−0.330215	+	0.470103i
$915$		0			0
$916$	−41.7255	−	19.6085i	−1.37865	−	0.647884i
$917$	25.5527	−	25.5527i	0.843824	−	0.843824i
$918$		0			0
$919$			0.363863i			0.0120027i	0.999982	+	0.00600137i	$0.00191031\pi$
$919$			0.363863i			0.0120027i	−0.999982	+	0.00600137i	$0.998090\pi$
$920$	−61.1178	+	34.9231i	−2.01500	+	1.15138i
$921$		0			0
$922$	−0.102430	−	0.586016i	−0.00337337	−	0.0192994i
$923$	5.41640	−	5.41640i	0.178283	−	0.178283i
$924$		0			0
$925$	45.3761	+	45.3761i	1.49196	+	1.49196i
$926$	4.11561	+	2.89093i	0.135247	+	0.0950018i
$927$		0			0
$928$	−41.1444	−	35.0499i	−1.35063	−	1.15057i
$929$	42.2453			1.38602			0.693012	−	0.720926i	$-0.256283\pi$
$929$	42.2453			1.38602			0.693012	+	0.720926i	$0.256283\pi$
$930$		0			0
$931$	−4.13950	−	4.13950i	−0.135667	−	0.135667i
$932$	30.0099	−	10.8216i	0.983008	−	0.354472i
$933$		0			0
$934$	5.45786	+	31.2250i	0.178587	+	1.02171i
$935$		−	2.75893i		−	0.0902266i
$936$		0			0
$937$		−	19.9323i		−	0.651160i	−0.945515	−	0.325580i	$-0.894441\pi$
$937$		−	19.9323i		−	0.651160i	0.945515	−	0.325580i	$-0.105559\pi$
$938$	53.0957	−	9.28066i	1.73364	−	0.303024i
$939$		0			0
$940$	−24.6700	−	11.5934i	−0.804648	−	0.378137i
$941$	33.6416	+	33.6416i	1.09669	+	1.09669i	0.994796	+	0.101891i	$0.0324892\pi$
$941$	33.6416	+	33.6416i	1.09669	+	1.09669i	0.101891	+	0.994796i	$0.467511\pi$
$942$		0			0
$943$	−25.9884			−0.846300
$944$	2.53652	−	27.1293i	0.0825565	−	0.882985i
$945$		0			0
$946$	1.72290	−	2.45276i	0.0560162	−	0.0797463i
$947$	−11.9878	−	11.9878i	−0.389550	−	0.389550i	0.484977	−	0.874527i	$-0.338828\pi$
$947$	−11.9878	−	11.9878i	−0.389550	−	0.389550i	−0.874527	+	0.484977i	$0.838828\pi$
$948$		0			0
$949$	9.05382	−	9.05382i	0.293899	−	0.293899i
$950$	−47.9810	+	8.38666i	−1.55671	+	0.272099i
$951$		0			0
$952$	4.75599	+	1.29718i	0.154143	+	0.0420417i
$953$			15.0018i			0.485955i	0.970032	+	0.242977i	$0.0781241\pi$
$953$			15.0018i			0.485955i	−0.970032	+	0.242977i	$0.921876\pi$
$954$		0			0
$955$	29.7714	−	29.7714i	0.963380	−	0.963380i
$956$	−0.0241728	−	0.0670350i	−0.000781804	−	0.00216807i
$957$		0			0
$958$	7.71570	+	5.41974i	0.249283	+	0.175104i
$959$	−37.1804			−1.20062
$960$		0			0
$961$	13.8600			0.447096
$962$	−10.4514	−	7.34138i	−0.336967	−	0.236696i
$963$		0			0
$964$	4.44047	+	12.3141i	0.143018	+	0.396611i
$965$	11.7068	−	11.7068i	0.376857	−	0.376857i
$966$		0			0
$967$		−	54.4570i		−	1.75122i	−0.483019	−	0.875610i	$-0.660460\pi$
$967$		−	54.4570i		−	1.75122i	0.483019	−	0.875610i	$-0.339540\pi$
$968$	−26.4960	−	7.22667i	−0.851614	−	0.232274i
$969$		0			0
$970$	−36.6783	+	6.41104i	−1.17767	+	0.205846i
$971$	−7.58358	+	7.58358i	−0.243369	+	0.243369i	−0.818242	−	0.574874i	$-0.805051\pi$
$971$	−7.58358	+	7.58358i	−0.243369	+	0.243369i	0.574874	+	0.818242i	$0.305051\pi$
$972$		0			0
$973$	−8.63547	−	8.63547i	−0.276841	−	0.276841i
$974$	19.9596	−	28.4150i	0.639546	−	0.910476i
$975$		0			0
$976$	48.6375	+	4.54747i	1.55685	+	0.145561i
$977$	−37.6490			−1.20450			−0.602250	−	0.798308i	$-0.705729\pi$
$977$	−37.6490			−1.20450			−0.602250	+	0.798308i	$0.705729\pi$
$978$		0			0
$979$	−4.37082	−	4.37082i	−0.139692	−	0.139692i
$980$	6.73161	+	3.16346i	0.215033	+	0.101053i
$981$		0			0
$982$	56.1128	−	9.80803i	1.79063	−	0.312987i
$983$			28.2828i			0.902081i	0.892504	+	0.451040i	$0.148947\pi$
$983$			28.2828i			0.902081i	−0.892504	+	0.451040i	$0.851053\pi$
$984$		0			0
$985$			20.6503i			0.657974i
$986$	1.66921	+	9.54973i	0.0531584	+	0.304125i
$987$		0			0
$988$	9.11970	−	3.28856i	0.290136	−	0.104623i
$989$	9.69943	+	9.69943i	0.308424	+	0.308424i
$990$		0			0
$991$	30.2284			0.960237			0.480119	−	0.877204i	$-0.340594\pi$
$991$	30.2284			0.960237			0.480119	+	0.877204i	$0.340594\pi$
$992$	37.7676	−	3.02091i	1.19912	−	0.0959140i
$993$		0			0
$994$	−23.6768	−	16.6313i	−0.750983	−	0.527513i
$995$	−9.04683	−	9.04683i	−0.286804	−	0.286804i
$996$		0			0
$997$	18.6910	−	18.6910i	0.591951	−	0.591951i	−0.346207	−	0.938158i	$-0.612530\pi$
$997$	18.6910	−	18.6910i	0.591951	−	0.591951i	0.938158	+	0.346207i	$0.112530\pi$
$998$	−9.49530	−	54.3237i	−0.300568	−	1.71959i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.k.c.109.9	yes	24
3.2	odd	2	inner	432.2.k.c.109.4	✓	24
4.3	odd	2		1728.2.k.c.1297.11		24
12.11	even	2		1728.2.k.c.1297.2		24
16.5	even	4	inner	432.2.k.c.325.9	yes	24
16.11	odd	4		1728.2.k.c.433.11		24
48.5	odd	4	inner	432.2.k.c.325.4	yes	24
48.11	even	4		1728.2.k.c.433.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.k.c.109.4	✓	24	3.2	odd	2	inner
432.2.k.c.109.9	yes	24	1.1	even	1	trivial
432.2.k.c.325.4	yes	24	48.5	odd	4	inner
432.2.k.c.325.9	yes	24	16.5	even	4	inner
1728.2.k.c.433.2		24	48.11	even	4
1728.2.k.c.433.11		24	16.11	odd	4
1728.2.k.c.1297.2		24	12.11	even	2
1728.2.k.c.1297.11		24	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.15725 + 0.812885i) q^{2} +(0.678437 + 1.88142i) q^{4} +(2.39401 - 2.39401i) q^{5} -2.42931i q^{7} +(-0.744255 + 2.72875i) q^{8} +O(q^{10})\)	\(q+(1.15725 + 0.812885i) q^{2} +(0.678437 + 1.88142i) q^{4} +(2.39401 - 2.39401i) q^{5} -2.42931i q^{7} +(-0.744255 + 2.72875i) q^{8} +(4.71651 - 0.824404i) q^{10} +(0.803139 - 0.803139i) q^{11} +(0.643126 + 0.643126i) q^{13} +(1.97475 - 2.81131i) q^{14} +(-3.07945 + 2.55284i) q^{16} +0.717454 q^{17} +(-3.76851 - 3.76851i) q^{19} +(6.12831 + 2.87994i) q^{20} +(1.58229 - 0.276570i) q^{22} +7.35083i q^{23} -6.46256i q^{25} +(0.221468 + 1.26704i) q^{26} +(4.57054 - 1.64813i) q^{28} +(6.75619 + 6.75619i) q^{29} -6.69776 q^{31} +(-5.63884 + 0.451033i) q^{32} +(0.830271 + 0.583207i) q^{34} +(-5.81579 - 5.81579i) q^{35} +(-7.02138 + 7.02138i) q^{37} +(-1.29773 - 7.42446i) q^{38} +(4.75090 + 8.31441i) q^{40} +3.53544i q^{41} +(1.31950 - 1.31950i) q^{43} +(2.05592 + 0.966158i) q^{44} +(-5.97538 + 8.50672i) q^{46} -4.02558 q^{47} +1.09844 q^{49} +(5.25332 - 7.47877i) q^{50} +(-0.773667 + 1.64631i) q^{52} +(6.85520 - 6.85520i) q^{53} -3.84544i q^{55} +(6.62899 + 1.80803i) q^{56} +(2.32657 + 13.3106i) q^{58} +(-4.81675 + 4.81675i) q^{59} +(-8.63547 - 8.63547i) q^{61} +(-7.75095 - 5.44451i) q^{62} +(-6.89217 - 4.06177i) q^{64} +3.07930 q^{65} +(11.0938 + 11.0938i) q^{67} +(0.486747 + 1.34983i) q^{68} +(-2.00274 - 11.4579i) q^{70} -8.42199i q^{71} -14.0778i q^{73} +(-13.8330 + 2.41789i) q^{74} +(4.53344 - 9.64684i) q^{76} +(-1.95107 - 1.95107i) q^{77} -5.60141 q^{79} +(-1.26069 + 13.4838i) q^{80} +(-2.87391 + 4.09137i) q^{82} +(-6.14958 - 6.14958i) q^{83} +(1.71759 - 1.71759i) q^{85} +(2.59959 - 0.454385i) q^{86} +(1.59383 + 2.78931i) q^{88} -5.44218i q^{89} +(1.56235 - 1.56235i) q^{91} +(-13.8300 + 4.98708i) q^{92} +(-4.65859 - 3.27234i) q^{94} -18.0437 q^{95} -7.77657 q^{97} +(1.27117 + 0.892909i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 16 q^{4}+O(q^{10}) \) 24 * q + 16 * q^4	\( 24 q + 16 q^{4} - 4 q^{10} + 16 q^{13} - 20 q^{16} - 16 q^{19} - 12 q^{22} - 12 q^{28} + 32 q^{31} + 28 q^{34} - 8 q^{37} - 36 q^{40} - 64 q^{46} - 16 q^{49} - 36 q^{52} - 32 q^{58} - 16 q^{61} + 16 q^{64} + 48 q^{67} - 24 q^{70} + 16 q^{76} - 48 q^{79} - 16 q^{82} - 16 q^{85} - 60 q^{88} + 96 q^{91} + 84 q^{94} + 8 q^{97}+O(q^{100}) \) 24 * q + 16 * q^4 - 4 * q^10 + 16 * q^13 - 20 * q^16 - 16 * q^19 - 12 * q^22 - 12 * q^28 + 32 * q^31 + 28 * q^34 - 8 * q^37 - 36 * q^40 - 64 * q^46 - 16 * q^49 - 36 * q^52 - 32 * q^58 - 16 * q^61 + 16 * q^64 + 48 * q^67 - 24 * q^70 + 16 * q^76 - 48 * q^79 - 16 * q^82 - 16 * q^85 - 60 * q^88 + 96 * q^91 + 84 * q^94 + 8 * q^97

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