LMFDB - Embedded newform 432.2.l.a.107.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("432.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.44953736732$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			107.9
Character	$\chi$	$=$	432.107
Dual form			432.2.l.a.323.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.205193 - 1.39925i) q^{2} +(-1.91579 - 0.574231i) q^{4} +(0.494369 - 0.494369i) q^{5} +4.44678 q^{7} +(-1.19660 + 2.56284i) q^{8} +O(q^{10})$	\(q+(0.205193 - 1.39925i) q^{2} +(-1.91579 - 0.574231i) q^{4} +(0.494369 - 0.494369i) q^{5} +4.44678 q^{7} +(-1.19660 + 2.56284i) q^{8} +(-0.590304 - 0.793186i) q^{10} +(-0.640478 - 0.640478i) q^{11} +(2.56067 - 2.56067i) q^{13} +(0.912446 - 6.22215i) q^{14} +(3.34052 + 2.20021i) q^{16} -2.17390i q^{17} +(-1.65915 - 1.65915i) q^{19} +(-1.23099 + 0.663226i) q^{20} +(-1.02761 + 0.764767i) q^{22} -3.58767i q^{23} +4.51120i q^{25} +(-3.05758 - 4.10845i) q^{26} +(-8.51910 - 2.55348i) q^{28} +(-3.32647 - 3.32647i) q^{29} +6.04970i q^{31} +(3.76410 - 4.22275i) q^{32} +(-3.04183 - 0.446068i) q^{34} +(2.19835 - 2.19835i) q^{35} +(-3.43551 - 3.43551i) q^{37} +(-2.66201 + 1.98112i) q^{38} +(0.675428 + 1.85855i) q^{40} -9.76422 q^{41} +(5.78523 - 5.78523i) q^{43} +(0.859240 + 1.59481i) q^{44} +(-5.02004 - 0.736164i) q^{46} +13.3989 q^{47} +12.7738 q^{49} +(6.31229 + 0.925665i) q^{50} +(-6.37613 + 3.43530i) q^{52} +(-8.04849 + 8.04849i) q^{53} -0.633265 q^{55} +(-5.32101 + 11.3964i) q^{56} +(-5.33713 + 3.97199i) q^{58} +(9.26701 + 9.26701i) q^{59} +(-2.74945 + 2.74945i) q^{61} +(8.46503 + 1.24135i) q^{62} +(-5.13631 - 6.13338i) q^{64} -2.53183i q^{65} +(0.758422 + 0.758422i) q^{67} +(-1.24832 + 4.16474i) q^{68} +(-2.62495 - 3.52712i) q^{70} +12.2617i q^{71} -0.682919i q^{73} +(-5.51208 + 4.10220i) q^{74} +(2.22585 + 4.13132i) q^{76} +(-2.84806 - 2.84806i) q^{77} +6.98551i q^{79} +(2.73917 - 0.563731i) q^{80} +(-2.00355 + 13.6626i) q^{82} +(6.26845 - 6.26845i) q^{83} +(-1.07471 - 1.07471i) q^{85} +(-6.90789 - 9.28207i) q^{86} +(2.40784 - 0.875048i) q^{88} -6.59756 q^{89} +(11.3867 - 11.3867i) q^{91} +(-2.06015 + 6.87323i) q^{92} +(2.74935 - 18.7483i) q^{94} -1.64046 q^{95} +11.5790 q^{97} +(2.62110 - 17.8738i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) $ 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.205193	−	1.39925i	0.145093	−	0.989418i
$2$	0.205193	−	1.39925i	0.145093	−	0.989418i
$3$		0			0
$3$		0			0
$4$	−1.91579	−	0.574231i	−0.957896	−	0.287115i
$5$	0.494369	−	0.494369i	0.221089	−	0.221089i	−0.587868	−	0.808957i	$-0.700033\pi$
$5$	0.494369	−	0.494369i	0.221089	−	0.221089i	0.808957	+	0.587868i	$0.200033\pi$
$6$		0			0
$7$	4.44678			1.68072			0.840362	−	0.542025i	$-0.182342\pi$
$7$	4.44678			1.68072			0.840362	+	0.542025i	$0.182342\pi$
$8$	−1.19660	+	2.56284i	−0.423061	+	0.906101i
$9$		0			0
$10$	−0.590304	−	0.793186i	−0.186671	−	0.250827i
$11$	−0.640478	−	0.640478i	−0.193111	−	0.193111i	0.603928	−	0.797039i	$-0.293602\pi$
$11$	−0.640478	−	0.640478i	−0.193111	−	0.193111i	−0.797039	+	0.603928i	$0.793602\pi$
$12$		0			0
$13$	2.56067	−	2.56067i	0.710202	−	0.710202i	−0.256375	−	0.966577i	$-0.582528\pi$
$13$	2.56067	−	2.56067i	0.710202	−	0.710202i	0.966577	+	0.256375i	$0.0825282\pi$
$14$	0.912446	−	6.22215i	0.243862	−	1.66294i
$15$		0			0
$16$	3.34052	+	2.20021i	0.835129	+	0.550054i
$17$		−	2.17390i		−	0.527248i	−0.964626	−	0.263624i	$-0.915082\pi$
$17$		−	2.17390i		−	0.527248i	0.964626	−	0.263624i	$-0.0849178\pi$
$18$		0			0
$19$	−1.65915	−	1.65915i	−0.380635	−	0.380635i	0.490696	−	0.871331i	$-0.336743\pi$
$19$	−1.65915	−	1.65915i	−0.380635	−	0.380635i	−0.871331	+	0.490696i	$0.836743\pi$
$20$	−1.23099	+	0.663226i	−0.275258	+	0.148302i
$21$		0			0
$22$	−1.02761	+	0.764767i	−0.219087	+	0.163049i
$23$		−	3.58767i		−	0.748081i	−0.927412	−	0.374041i	$-0.877972\pi$
$23$		−	3.58767i		−	0.748081i	0.927412	−	0.374041i	$-0.122028\pi$
$24$		0			0
$25$			4.51120i			0.902240i
$26$	−3.05758	−	4.10845i	−0.599642	−	0.805733i
$27$		0			0
$28$	−8.51910	−	2.55348i	−1.60996	−	0.482562i
$29$	−3.32647	−	3.32647i	−0.617710	−	0.617710i	0.327234	−	0.944944i	$-0.393884\pi$
$29$	−3.32647	−	3.32647i	−0.617710	−	0.617710i	−0.944944	+	0.327234i	$0.893884\pi$
$30$		0			0
$31$			6.04970i			1.08656i	0.839552	+	0.543279i	$0.182817\pi$
$31$			6.04970i			1.08656i	−0.839552	+	0.543279i	$0.817183\pi$
$32$	3.76410	−	4.22275i	0.665404	−	0.746483i
$33$		0			0
$34$	−3.04183	−	0.446068i	−0.521669	−	0.0765001i
$35$	2.19835	−	2.19835i	0.371589	−	0.371589i
$36$		0			0
$37$	−3.43551	−	3.43551i	−0.564795	−	0.564795i	0.365871	−	0.930666i	$-0.380771\pi$
$37$	−3.43551	−	3.43551i	−0.564795	−	0.564795i	−0.930666	+	0.365871i	$0.880771\pi$
$38$	−2.66201	+	1.98112i	−0.431835	+	0.321380i
$39$		0			0
$40$	0.675428	+	1.85855i	0.106795	+	0.293863i
$41$	−9.76422			−1.52491			−0.762457	−	0.647039i	$-0.776007\pi$
$41$	−9.76422			−1.52491			−0.762457	+	0.647039i	$0.776007\pi$
$42$		0			0
$43$	5.78523	−	5.78523i	0.882240	−	0.882240i	−0.111522	−	0.993762i	$-0.535573\pi$
$43$	5.78523	−	5.78523i	0.882240	−	0.882240i	0.993762	+	0.111522i	$0.0355726\pi$
$44$	0.859240	+	1.59481i	0.129535	+	0.240426i
$45$		0			0
$46$	−5.02004	−	0.736164i	−0.740165	−	0.108541i
$47$	13.3989			1.95443			0.977213	−	0.212262i	$-0.0680830\pi$
$47$	13.3989			1.95443			0.977213	+	0.212262i	$0.0680830\pi$
$48$		0			0
$49$	12.7738			1.82483
$50$	6.31229	+	0.925665i	0.892692	+	0.130909i
$51$		0			0
$52$	−6.37613	+	3.43530i	−0.884210	+	0.476390i
$53$	−8.04849	+	8.04849i	−1.10555	+	1.10555i	−0.111817	+	0.993729i	$0.535667\pi$
$53$	−8.04849	+	8.04849i	−1.10555	+	1.10555i	−0.993729	+	0.111817i	$0.964333\pi$
$54$		0			0
$55$	−0.633265			−0.0853894
$56$	−5.32101	+	11.3964i	−0.711049	+	1.52291i
$57$		0			0
$58$	−5.33713	+	3.97199i	−0.700799	+	0.521548i
$59$	9.26701	+	9.26701i	1.20646	+	1.20646i	0.972165	+	0.234297i	$0.0752787\pi$
$59$	9.26701	+	9.26701i	1.20646	+	1.20646i	0.234297	+	0.972165i	$0.424721\pi$
$60$		0			0
$61$	−2.74945	+	2.74945i	−0.352031	+	0.352031i	−0.860865	−	0.508833i	$-0.830077\pi$
$61$	−2.74945	+	2.74945i	−0.352031	+	0.352031i	0.508833	+	0.860865i	$0.330077\pi$
$62$	8.46503	+	1.24135i	1.07506	+	0.157652i
$63$		0			0
$64$	−5.13631	−	6.13338i	−0.642038	−	0.766673i
$65$		−	2.53183i		−	0.314035i
$66$		0			0
$67$	0.758422	+	0.758422i	0.0926560	+	0.0926560i	0.751915	−	0.659260i	$-0.229130\pi$
$67$	0.758422	+	0.758422i	0.0926560	+	0.0926560i	−0.659260	+	0.751915i	$0.729130\pi$
$68$	−1.24832	+	4.16474i	−0.151381	+	0.505049i
$69$		0			0
$70$	−2.62495	−	3.52712i	−0.313742	−	0.421572i
$71$			12.2617i			1.45519i	0.686005	+	0.727597i	$0.259363\pi$
$71$			12.2617i			1.45519i	−0.686005	+	0.727597i	$0.740637\pi$
$72$		0			0
$73$		−	0.682919i		−	0.0799296i	−0.999201	−	0.0399648i	$-0.987275\pi$
$73$		−	0.682919i		−	0.0799296i	0.999201	−	0.0399648i	$-0.0127246\pi$
$74$	−5.51208	+	4.10220i	−0.640766	+	0.476871i
$75$		0			0
$76$	2.22585	+	4.13132i	0.255322	+	0.473895i
$77$	−2.84806	−	2.84806i	−0.324567	−	0.324567i
$78$		0			0
$79$			6.98551i			0.785932i	0.919553	+	0.392966i	$0.128551\pi$
$79$			6.98551i			0.785932i	−0.919553	+	0.392966i	$0.871449\pi$
$80$	2.73917	−	0.563731i	0.306248	−	0.0630270i
$81$		0			0
$82$	−2.00355	+	13.6626i	−0.221255	+	1.50878i
$83$	6.26845	−	6.26845i	0.688052	−	0.688052i	−0.273749	−	0.961801i	$-0.588264\pi$
$83$	6.26845	−	6.26845i	0.688052	−	0.688052i	0.961801	+	0.273749i	$0.0882638\pi$
$84$		0			0
$85$	−1.07471	−	1.07471i	−0.116568	−	0.116568i
$86$	−6.90789	−	9.28207i	−0.744897	−	1.00091i
$87$		0			0
$88$	2.40784	−	0.875048i	0.256676	−	0.0932805i
$89$	−6.59756			−0.699340			−0.349670	−	0.936873i	$-0.613706\pi$
$89$	−6.59756			−0.699340			−0.349670	+	0.936873i	$0.613706\pi$
$90$		0			0
$91$	11.3867	−	11.3867i	1.19365	−	1.19365i
$92$	−2.06015	+	6.87323i	−0.214786	+	0.716584i
$93$		0			0
$94$	2.74935	−	18.7483i	0.283574	−	1.93374i
$95$	−1.64046			−0.168308
$96$		0			0
$97$	11.5790			1.17566			0.587832	−	0.808983i	$-0.299982\pi$
$97$	11.5790			1.17566			0.587832	+	0.808983i	$0.299982\pi$
$98$	2.62110	−	17.8738i	0.264771	−	1.80552i
$99$		0			0
$100$	2.59047	−	8.64252i	0.259047	−	0.864252i
$101$	3.48722	−	3.48722i	0.346991	−	0.346991i	−0.511997	−	0.858988i	$-0.671094\pi$
$101$	3.48722	−	3.48722i	0.346991	−	0.346991i	0.858988	+	0.511997i	$0.171094\pi$
$102$		0			0
$103$	−13.8523			−1.36490			−0.682452	−	0.730931i	$-0.739086\pi$
$103$	−13.8523			−1.36490			−0.682452	+	0.730931i	$0.739086\pi$
$104$	3.49850	+	9.62669i	0.343056	+	0.943974i
$105$		0			0
$106$	9.61035	+	12.9133i	0.933440	+	1.25425i
$107$	−0.0361939	−	0.0361939i	−0.00349900	−	0.00349900i	0.705355	−	0.708854i	$-0.250788\pi$
$107$	−0.0361939	−	0.0361939i	−0.00349900	−	0.00349900i	−0.708854	+	0.705355i	$0.750788\pi$
$108$		0			0
$109$	−12.6566	+	12.6566i	−1.21228	+	1.21228i	−0.242011	+	0.970274i	$0.577807\pi$
$109$	−12.6566	+	12.6566i	−1.21228	+	1.21228i	−0.970274	+	0.242011i	$0.922193\pi$
$110$	−0.129941	+	0.886095i	−0.0123894	+	0.0844858i
$111$		0			0
$112$	14.8545	+	9.78386i	1.40362	+	0.924488i
$113$			17.2251i			1.62040i	0.586152	+	0.810201i	$0.300642\pi$
$113$			17.2251i			1.62040i	−0.586152	+	0.810201i	$0.699358\pi$
$114$		0			0
$115$	−1.77363	−	1.77363i	−0.165392	−	0.165392i
$116$	4.46266	+	8.28299i	0.414348	+	0.769056i
$117$		0			0
$118$	14.8684	−	11.0653i	1.36874	−	1.01865i
$119$		−	9.66685i		−	0.886159i
$120$		0			0
$121$		−	10.1796i		−	0.925416i
$122$	3.28300	+	4.41134i	0.297229	+	0.399384i
$123$		0			0
$124$	3.47393	−	11.5900i	0.311968	−	1.04081i
$125$	4.70204	+	4.70204i	0.420563	+	0.420563i
$126$		0			0
$127$			3.11642i			0.276538i	0.990395	+	0.138269i	$0.0441538\pi$
$127$			3.11642i			0.276538i	−0.990395	+	0.138269i	$0.955846\pi$
$128$	−9.63606	+	5.92844i	−0.851715	+	0.524005i
$129$		0			0
$130$	−3.54266	−	0.519513i	−0.310712	−	0.0455643i
$131$	−10.4918	+	10.4918i	−0.916669	+	0.916669i	−0.996785	−	0.0801168i	$-0.974471\pi$
$131$	−10.4918	+	10.4918i	−0.916669	+	0.916669i	0.0801168	+	0.996785i	$0.474471\pi$
$132$		0			0
$133$	−7.37787	−	7.37787i	−0.639742	−	0.639742i
$134$	1.21684	−	0.905598i	0.105119	−	0.0782317i
$135$		0			0
$136$	5.57136	+	2.60128i	0.477740	+	0.223058i
$137$	11.8257			1.01034			0.505169	−	0.863021i	$-0.331430\pi$
$137$	11.8257			1.01034			0.505169	+	0.863021i	$0.331430\pi$
$138$		0			0
$139$	−1.27713	+	1.27713i	−0.108324	+	0.108324i	−0.759192	−	0.650867i	$-0.774405\pi$
$139$	−1.27713	+	1.27713i	−0.108324	+	0.108324i	0.650867	+	0.759192i	$0.274405\pi$
$140$	−5.47394	+	2.94922i	−0.462632	+	0.249255i
$141$		0			0
$142$	17.1571	+	2.51601i	1.43979	+	0.211139i
$143$	−3.28011			−0.274296
$144$		0			0
$145$	−3.28901			−0.273137
$146$	−0.955573	−	0.140130i	−0.0790838	−	0.0115972i
$147$		0			0
$148$	4.60895	+	8.55451i	0.378854	+	0.703176i
$149$	−4.44080	+	4.44080i	−0.363805	+	0.363805i	−0.865212	−	0.501407i	$-0.832816\pi$
$149$	−4.44080	+	4.44080i	−0.363805	+	0.363805i	0.501407	+	0.865212i	$0.332816\pi$
$150$		0			0
$151$	−9.21822			−0.750168			−0.375084	−	0.926991i	$-0.622386\pi$
$151$	−9.21822			−0.750168			−0.375084	+	0.926991i	$0.622386\pi$
$152$	6.23747	−	2.26680i	0.505926	−	0.183862i
$153$		0			0
$154$	−4.56955	+	3.40075i	−0.368225	+	0.274040i
$155$	2.99078	+	2.99078i	0.240226	+	0.240226i
$156$		0			0
$157$	−4.25176	+	4.25176i	−0.339328	+	0.339328i	−0.856114	−	0.516787i	$-0.827128\pi$
$157$	−4.25176	+	4.25176i	−0.339328	+	0.339328i	0.516787	+	0.856114i	$0.327128\pi$
$158$	9.77447	+	1.43338i	0.777615	+	0.114033i
$159$		0			0
$160$	−0.226742	−	3.94845i	−0.0179256	−	0.312152i
$161$		−	15.9536i		−	1.25732i
$162$		0			0
$163$	−4.71266	−	4.71266i	−0.369124	−	0.369124i	0.498033	−	0.867158i	$-0.334056\pi$
$163$	−4.71266	−	4.71266i	−0.369124	−	0.369124i	−0.867158	+	0.498033i	$0.834056\pi$
$164$	18.7062	+	5.60691i	1.46071	+	0.437827i
$165$		0			0
$166$	−7.48488	−	10.0574i	−0.580939	−	0.780603i
$167$			7.91280i			0.612311i	0.951982	+	0.306155i	$0.0990427\pi$
$167$			7.91280i			0.612311i	−0.951982	+	0.306155i	$0.900957\pi$
$168$		0			0
$169$		−	0.114074i		−	0.00877494i
$170$	−1.72431	+	1.28326i	−0.132248	+	0.0984217i
$171$		0			0
$172$	−14.4054	+	7.76124i	−1.09840	+	0.591789i
$173$	−10.6426	−	10.6426i	−0.809140	−	0.809140i	0.175363	−	0.984504i	$-0.443890\pi$
$173$	−10.6426	−	10.6426i	−0.809140	−	0.809140i	−0.984504	+	0.175363i	$0.943890\pi$
$174$		0			0
$175$			20.0603i			1.51642i
$176$	−0.730339	−	3.54872i	−0.0550514	−	0.267495i
$177$		0			0
$178$	−1.35377	+	9.23162i	−0.101469	+	0.691940i
$179$	15.5780	−	15.5780i	1.16435	−	1.16435i	0.180840	−	0.983512i	$-0.442118\pi$
$179$	15.5780	−	15.5780i	1.16435	−	1.16435i	0.983512	−	0.180840i	$-0.0578818\pi$
$180$		0			0
$181$	−9.45554	−	9.45554i	−0.702825	−	0.702825i	0.262191	−	0.965016i	$-0.415555\pi$
$181$	−9.45554	−	9.45554i	−0.702825	−	0.702825i	−0.965016	+	0.262191i	$0.915555\pi$
$182$	−13.5964	−	18.2693i	−1.00783	−	1.35421i
$183$		0			0
$184$	9.19463	+	4.29300i	0.677837	+	0.316484i
$185$	−3.39682			−0.249739
$186$		0			0
$187$	−1.39234	+	1.39234i	−0.101818	+	0.101818i
$188$	−25.6694	−	7.69404i	−1.87214	−	0.561146i
$189$		0			0
$190$	−0.336611	+	2.29542i	−0.0244203	+	0.166527i
$191$	2.07832			0.150382			0.0751909	−	0.997169i	$-0.476043\pi$
$191$	2.07832			0.150382			0.0751909	+	0.997169i	$0.476043\pi$
$192$		0			0
$193$	7.09317			0.510578			0.255289	−	0.966865i	$-0.417829\pi$
$193$	7.09317			0.510578			0.255289	+	0.966865i	$0.417829\pi$
$194$	2.37592	−	16.2018i	0.170581	−	1.16322i
$195$		0			0
$196$	−24.4720	−	7.33513i	−1.74800	−	0.523938i
$197$	3.69246	−	3.69246i	0.263077	−	0.263077i	−0.563226	−	0.826303i	$-0.690440\pi$
$197$	3.69246	−	3.69246i	0.263077	−	0.263077i	0.826303	+	0.563226i	$0.190440\pi$
$198$		0			0
$199$	4.00998			0.284260			0.142130	−	0.989848i	$-0.454605\pi$
$199$	4.00998			0.284260			0.142130	+	0.989848i	$0.454605\pi$
$200$	−11.5615	−	5.39809i	−0.817520	−	0.381703i
$201$		0			0
$202$	−4.16393	−	5.59503i	−0.292973	−	0.393665i
$203$	−14.7921	−	14.7921i	−1.03820	−	1.03820i
$204$		0			0
$205$	−4.82712	+	4.82712i	−0.337141	+	0.337141i
$206$	−2.84238	+	19.3827i	−0.198038	+	1.35046i
$207$		0			0
$208$	14.1880	−	2.91994i	0.983760	−	0.202462i
$209$			2.12530i			0.147010i
$210$		0			0
$211$	−14.6831	−	14.6831i	−1.01083	−	1.01083i	−0.999941	−	0.0108871i	$-0.996534\pi$
$211$	−14.6831	−	14.6831i	−1.01083	−	1.01083i	−0.0108871	−	0.999941i	$-0.503466\pi$
$212$	20.0409	−	10.7975i	1.37642	−	0.741578i
$213$		0			0
$214$	−0.0580710	+	0.0432176i	−0.00396965	+	0.00295429i
$215$		−	5.72008i		−	0.390106i
$216$		0			0
$217$			26.9017i			1.82620i
$218$	15.1127	+	20.3068i	1.02356	+	1.37535i
$219$		0			0
$220$	1.21320	+	0.363640i	0.0817942	+	0.0245166i
$221$	−5.56664	−	5.56664i	−0.374453	−	0.374453i
$222$		0			0
$223$			8.14815i			0.545641i	0.962065	+	0.272820i	$0.0879565\pi$
$223$			8.14815i			0.545641i	−0.962065	+	0.272820i	$0.912044\pi$
$224$	16.7381	−	18.7776i	1.11836	−	1.25463i
$225$		0			0
$226$	24.1022	+	3.53447i	1.60325	+	0.235109i
$227$	−8.02796	+	8.02796i	−0.532834	+	0.532834i	−0.921415	−	0.388580i	$-0.872966\pi$
$227$	−8.02796	+	8.02796i	−0.532834	+	0.532834i	0.388580	+	0.921415i	$0.372966\pi$
$228$		0			0
$229$	−16.0347	−	16.0347i	−1.05960	−	1.05960i	−0.998107	−	0.0614952i	$-0.980413\pi$
$229$	−16.0347	−	16.0347i	−1.05960	−	1.05960i	−0.0614952	−	0.998107i	$-0.519587\pi$
$230$	−2.84569	+	2.11782i	−0.187639	+	0.139645i
$231$		0			0
$232$	12.5057	−	4.54477i	0.821037	−	0.298378i
$233$	−12.8841			−0.844067			−0.422034	−	0.906580i	$-0.638684\pi$
$233$	−12.8841			−0.844067			−0.422034	+	0.906580i	$0.638684\pi$
$234$		0			0
$235$	6.62398	−	6.62398i	0.432101	−	0.432101i
$236$	−12.4323	−	23.0751i	−0.809271	−	1.50206i
$237$		0			0
$238$	−13.5263	−	1.98357i	−0.876781	−	0.128576i
$239$	13.6434			0.882518			0.441259	−	0.897380i	$-0.354532\pi$
$239$	13.6434			0.882518			0.441259	+	0.897380i	$0.354532\pi$
$240$		0			0
$241$	−14.4368			−0.929956			−0.464978	−	0.885322i	$-0.653938\pi$
$241$	−14.4368			−0.929956			−0.464978	+	0.885322i	$0.653938\pi$
$242$	−14.2438	−	2.08877i	−0.915623	−	0.134271i
$243$		0			0
$244$	6.84620	−	3.68856i	0.438283	−	0.236136i
$245$	6.31499	−	6.31499i	0.403450	−	0.403450i
$246$		0			0
$247$	−8.49707			−0.540656
$248$	−15.5044	−	7.23906i	−0.984532	−	0.459681i
$249$		0			0
$250$	7.54415	−	5.61450i	0.477134	−	0.355092i
$251$	10.6680	+	10.6680i	0.673356	+	0.673356i	0.958488	−	0.285133i	$-0.0920376\pi$
$251$	10.6680	+	10.6680i	0.673356	+	0.673356i	−0.285133	+	0.958488i	$0.592038\pi$
$252$		0			0
$253$	−2.29783	+	2.29783i	−0.144463	+	0.144463i
$254$	4.36065	+	0.639467i	0.273611	+	0.0401237i
$255$		0			0
$256$	6.31811	+	14.6997i	0.394882	+	0.918732i
$257$		−	10.5151i		−	0.655916i	−0.944692	−	0.327958i	$-0.893640\pi$
$257$		−	10.5151i		−	0.655916i	0.944692	−	0.327958i	$-0.106360\pi$
$258$		0			0
$259$	−15.2770	−	15.2770i	−0.949265	−	0.949265i
$260$	−1.45386	+	4.85046i	−0.0901644	+	0.300813i
$261$		0			0
$262$	12.5277	+	16.8334i	0.773966	+	1.03997i
$263$		−	13.2028i		−	0.814120i	−0.913401	−	0.407060i	$-0.866554\pi$
$263$		−	13.2028i		−	0.814120i	0.913401	−	0.407060i	$-0.133446\pi$
$264$		0			0
$265$			7.95785i			0.488847i
$266$	−11.8374	+	8.80959i	−0.725795	+	0.540150i
$267$		0			0
$268$	−1.01747	−	1.88849i	−0.0621518	−	0.115358i
$269$	14.9229	+	14.9229i	0.909863	+	0.909863i	0.996261	−	0.0863977i	$-0.0275356\pi$
$269$	14.9229	+	14.9229i	0.909863	+	0.909863i	−0.0863977	+	0.996261i	$0.527536\pi$
$270$		0			0
$271$			5.85419i			0.355617i	0.984065	+	0.177808i	$0.0569008\pi$
$271$			5.85419i			0.355617i	−0.984065	+	0.177808i	$0.943099\pi$
$272$	4.78304	−	7.26195i	0.290015	−	0.440320i
$273$		0			0
$274$	2.42655	−	16.5471i	0.146593	−	0.999646i
$275$	2.88932	−	2.88932i	0.174233	−	0.174233i
$276$		0			0
$277$	−13.3427	−	13.3427i	−0.801684	−	0.801684i	0.181675	−	0.983359i	$-0.441848\pi$
$277$	−13.3427	−	13.3427i	−0.801684	−	0.801684i	−0.983359	+	0.181675i	$0.941848\pi$
$278$	1.52496	+	2.04907i	0.0914610	+	0.122895i
$279$		0			0
$280$	3.00348	+	8.26456i	0.179492	+	0.493902i
$281$	3.59193			0.214276			0.107138	−	0.994244i	$-0.465831\pi$
$281$	3.59193			0.214276			0.107138	+	0.994244i	$0.465831\pi$
$282$		0			0
$283$	−12.0732	+	12.0732i	−0.717675	+	0.717675i	−0.968129	−	0.250454i	$-0.919420\pi$
$283$	−12.0732	+	12.0732i	−0.717675	+	0.717675i	0.250454	+	0.968129i	$0.419420\pi$
$284$	7.04104	−	23.4908i	0.417809	−	1.39392i
$285$		0			0
$286$	−0.673054	+	4.58969i	−0.0397985	+	0.271394i
$287$	−43.4193			−2.56296
$288$		0			0
$289$	12.2742			0.722009
$290$	−0.674880	+	4.60214i	−0.0396303	+	0.270247i
$291$		0			0
$292$	−0.392153	+	1.30833i	−0.0229490	+	0.0765642i
$293$	0.624182	−	0.624182i	0.0364651	−	0.0364651i	−0.688639	−	0.725104i	$-0.741792\pi$
$293$	0.624182	−	0.624182i	0.0364651	−	0.0364651i	0.725104	+	0.688639i	$0.241792\pi$
$294$		0			0
$295$	9.16264			0.533470
$296$	12.9156	−	4.69375i	0.750704	−	0.272818i
$297$		0			0
$298$	5.30257	+	7.12501i	0.307169	+	0.412741i
$299$	−9.18685	−	9.18685i	−0.531289	−	0.531289i
$300$		0			0
$301$	25.7257	−	25.7257i	1.48280	−	1.48280i
$302$	−1.89151	+	12.8986i	−0.108844	+	0.742230i
$303$		0			0
$304$	−1.89193	−	9.19290i	−0.108510	−	0.527249i
$305$			2.71849i			0.155660i
$306$		0			0
$307$	9.08438	+	9.08438i	0.518473	+	0.518473i	0.917109	−	0.398636i	$-0.130516\pi$
$307$	9.08438	+	9.08438i	0.518473	+	0.518473i	−0.398636	+	0.917109i	$0.630516\pi$
$308$	3.82085	+	7.09175i	0.217713	+	0.404090i
$309$		0			0
$310$	4.79854	−	3.57116i	0.272539	−	0.202828i
$311$			0.747330i			0.0423772i	0.999775	+	0.0211886i	$0.00674504\pi$
$311$			0.747330i			0.0423772i	−0.999775	+	0.0211886i	$0.993255\pi$
$312$		0			0
$313$			10.6738i			0.603321i	0.953415	+	0.301661i	$0.0975409\pi$
$313$			10.6738i			0.603321i	−0.953415	+	0.301661i	$0.902459\pi$
$314$	5.07684	+	6.82170i	0.286503	+	0.384971i
$315$		0			0
$316$	4.01130	−	13.3828i	0.225653	−	0.752841i
$317$	11.0205	+	11.0205i	0.618973	+	0.618973i	0.945268	−	0.326295i	$-0.105800\pi$
$317$	11.0205	+	11.0205i	0.618973	+	0.618973i	−0.326295	+	0.945268i	$0.605800\pi$
$318$		0			0
$319$			4.26106i			0.238574i
$320$	−5.57138	−	0.492923i	−0.311450	−	0.0275553i
$321$		0			0
$322$	−22.3230	−	3.27356i	−1.24401	−	0.182428i
$323$	−3.60682	+	3.60682i	−0.200689	+	0.200689i
$324$		0			0
$325$	11.5517	+	11.5517i	0.640773	+	0.640773i
$326$	−7.56119	+	5.62718i	−0.418776	+	0.311661i
$327$		0			0
$328$	11.6838	−	25.0241i	0.645132	−	1.38173i
$329$	59.5818			3.28485
$330$		0			0
$331$	15.7181	−	15.7181i	0.863945	−	0.863945i	−0.127849	−	0.991794i	$-0.540807\pi$
$331$	15.7181	−	15.7181i	0.863945	−	0.863945i	0.991794	+	0.127849i	$0.0408072\pi$
$332$	−15.6086	+	8.40951i	−0.856633	+	0.461532i
$333$		0			0
$334$	11.0720	+	1.62365i	0.605831	+	0.0888421i
$335$	0.749880			0.0409703
$336$		0			0
$337$	26.2424			1.42952			0.714758	−	0.699372i	$-0.246537\pi$
$337$	26.2424			1.42952			0.714758	+	0.699372i	$0.246537\pi$
$338$	−0.159618	−	0.0234072i	−0.00868208	−	0.00127318i
$339$		0			0
$340$	1.44179	+	2.67605i	0.0781919	+	0.145129i
$341$	3.87470	−	3.87470i	0.209827	−	0.209827i
$342$		0			0
$343$	25.6750			1.38632
$344$	7.90403	+	21.7492i	0.426157	+	1.17264i
$345$		0			0
$346$	−17.0754	+	12.7078i	−0.917979	+	0.683177i
$347$	−17.6976	−	17.6976i	−0.950058	−	0.950058i	0.0487531	−	0.998811i	$-0.484475\pi$
$347$	−17.6976	−	17.6976i	−0.950058	−	0.950058i	−0.998811	+	0.0487531i	$0.984475\pi$
$348$		0			0
$349$	−8.51556	+	8.51556i	−0.455827	+	0.455827i	−0.897283	−	0.441456i	$-0.854462\pi$
$349$	−8.51556	+	8.51556i	−0.455827	+	0.455827i	0.441456	+	0.897283i	$0.354462\pi$
$350$	28.0693	+	4.11623i	1.50037	+	0.220022i
$351$		0			0
$352$	−5.11540	+	0.293755i	−0.272652	+	0.0156572i
$353$			27.0583i			1.44017i	0.693887	+	0.720084i	$0.255897\pi$
$353$			27.0583i			1.44017i	−0.693887	+	0.720084i	$0.744103\pi$
$354$		0			0
$355$	6.06179	+	6.06179i	0.321727	+	0.321727i
$356$	12.6396	+	3.78852i	0.669895	+	0.200791i
$357$		0			0
$358$	−18.6010	−	24.9940i	−0.983092	−	1.32097i
$359$			15.0498i			0.794300i	0.917754	+	0.397150i	$0.130001\pi$
$359$			15.0498i			0.794300i	−0.917754	+	0.397150i	$0.869999\pi$
$360$		0			0
$361$		−	13.4944i		−	0.710234i
$362$	−15.1709	+	11.2904i	−0.797362	+	0.593412i
$363$		0			0
$364$	−28.3532	+	15.2760i	−1.48611	+	0.800680i
$365$	−0.337614	−	0.337614i	−0.0176715	−	0.0176715i
$366$		0			0
$367$		−	25.2454i		−	1.31780i	−0.752230	−	0.658901i	$-0.771022\pi$
$367$		−	25.2454i		−	1.31780i	0.752230	−	0.658901i	$-0.228978\pi$
$368$	7.89365	−	11.9847i	0.411485	−	0.624745i
$369$		0			0
$370$	−0.697003	+	4.75300i	−0.0362355	+	0.247097i
$371$	−35.7899	+	35.7899i	−1.85812	+	1.85812i
$372$		0			0
$373$	21.3893	+	21.3893i	1.10750	+	1.10750i	0.993479	+	0.114018i	$0.0363722\pi$
$373$	21.3893	+	21.3893i	1.10750	+	1.10750i	0.114018	+	0.993479i	$0.463628\pi$
$374$	1.66253	+	2.23392i	0.0859672	+	0.115513i
$375$		0			0
$376$	−16.0331	+	34.3392i	−0.826842	+	1.77091i
$377$	−17.0360			−0.877398
$378$		0			0
$379$	7.09652	−	7.09652i	0.364524	−	0.364524i	−0.500952	−	0.865475i	$-0.667017\pi$
$379$	7.09652	−	7.09652i	0.364524	−	0.364524i	0.865475	+	0.500952i	$0.167017\pi$
$380$	3.14279	+	0.942005i	0.161222	+	0.0483238i
$381$		0			0
$382$	0.426456	−	2.90808i	0.0218194	−	0.148790i
$383$	−3.20914			−0.163979			−0.0819896	−	0.996633i	$-0.526127\pi$
$383$	−3.20914			−0.163979			−0.0819896	+	0.996633i	$0.526127\pi$
$384$		0			0
$385$	−2.81599			−0.143516
$386$	1.45547	−	9.92511i	0.0740813	−	0.505175i
$387$		0			0
$388$	−22.1829	−	6.64899i	−1.12616	−	0.337551i
$389$	12.5208	−	12.5208i	0.634827	−	0.634827i	−0.314447	−	0.949275i	$-0.601819\pi$
$389$	12.5208	−	12.5208i	0.634827	−	0.634827i	0.949275	+	0.314447i	$0.101819\pi$
$390$		0			0
$391$	−7.79924			−0.394424
$392$	−15.2852	+	32.7373i	−0.772017	+	1.65348i
$393$		0			0
$394$	−4.40900	−	5.92433i	−0.222122	−	0.298463i
$395$	3.45342	+	3.45342i	0.173760	+	0.173760i
$396$		0			0
$397$	−3.51914	+	3.51914i	−0.176621	+	0.176621i	−0.789881	−	0.613260i	$-0.789858\pi$
$397$	−3.51914	+	3.51914i	−0.176621	+	0.176621i	0.613260	+	0.789881i	$0.289858\pi$
$398$	0.822818	−	5.61096i	0.0412441	−	0.281252i
$399$		0			0
$400$	−9.92560	+	15.0697i	−0.496280	+	0.753487i
$401$		−	13.3391i		−	0.666121i	−0.942905	−	0.333061i	$-0.891919\pi$
$401$		−	13.3391i		−	0.666121i	0.942905	−	0.333061i	$-0.108081\pi$
$402$		0			0
$403$	15.4913	+	15.4913i	0.771676	+	0.771676i
$404$	−8.68325	+	4.67831i	−0.432008	+	0.232755i
$405$		0			0
$406$	−23.7330	+	17.6626i	−1.17785	+	0.876578i
$407$			4.40074i			0.218137i
$408$		0			0
$409$		−	37.9280i		−	1.87542i	−0.347417	−	0.937711i	$-0.612941\pi$
$409$		−	37.9280i		−	1.87542i	0.347417	−	0.937711i	$-0.387059\pi$
$410$	5.76386	+	7.74484i	0.284657	+	0.382490i
$411$		0			0
$412$	26.5380	+	7.95439i	1.30744	+	0.391885i
$413$	41.2083	+	41.2083i	2.02773	+	2.02773i
$414$		0			0
$415$		−	6.19786i		−	0.304241i
$416$	−1.17445	−	20.4517i	−0.0575822	−	1.00273i
$417$		0			0
$418$	2.97382	+	0.436095i	0.145454	+	0.0213301i
$419$	−2.71590	+	2.71590i	−0.132681	+	0.132681i	−0.770328	−	0.637648i	$-0.779908\pi$
$419$	−2.71590	+	2.71590i	−0.132681	+	0.132681i	0.637648	+	0.770328i	$0.279908\pi$
$420$		0			0
$421$	22.1859	+	22.1859i	1.08127	+	1.08127i	0.996391	+	0.0848816i	$0.0270512\pi$
$421$	22.1859	+	22.1859i	1.08127	+	1.08127i	0.0848816	+	0.996391i	$0.472949\pi$
$422$	−23.5582	+	17.5325i	−1.14680	+	0.853467i
$423$		0			0
$424$	−10.9962	−	30.2578i	−0.534022	−	1.46945i
$425$	9.80689			0.475704
$426$		0			0
$427$	−12.2262	+	12.2262i	−0.591668	+	0.591668i
$428$	0.0485564	+	0.0901237i	0.00234706	+	0.00435629i
$429$		0			0
$430$	−8.00381	−	1.17372i	−0.385978	−	0.0566017i
$431$	−23.7125			−1.14219			−0.571096	−	0.820883i	$-0.693482\pi$
$431$	−23.7125			−1.14219			−0.571096	+	0.820883i	$0.693482\pi$
$432$		0			0
$433$	−12.2365			−0.588047			−0.294024	−	0.955798i	$-0.594994\pi$
$433$	−12.2365			−0.588047			−0.294024	+	0.955798i	$0.594994\pi$
$434$	37.6421	+	5.52003i	1.80688	+	0.264970i
$435$		0			0
$436$	31.5153	−	16.9796i	1.50931	−	0.813177i
$437$	−5.95248	+	5.95248i	−0.284746	+	0.284746i
$438$		0			0
$439$	0.701786			0.0334944			0.0167472	−	0.999860i	$-0.494669\pi$
$439$	0.701786			0.0334944			0.0167472	+	0.999860i	$0.494669\pi$
$440$	0.757764	−	1.62296i	0.0361250	−	0.0773714i
$441$		0			0
$442$	−8.93135	+	6.64688i	−0.424821	+	0.316160i
$443$	−6.59069	−	6.59069i	−0.313133	−	0.313133i	0.532989	−	0.846122i	$-0.321069\pi$
$443$	−6.59069	−	6.59069i	−0.313133	−	0.313133i	−0.846122	+	0.532989i	$0.821069\pi$
$444$		0			0
$445$	−3.26163	+	3.26163i	−0.154616	+	0.154616i
$446$	11.4013	+	1.67194i	0.539867	+	0.0791687i
$447$		0			0
$448$	−22.8400	−	27.2738i	−1.07909	−	1.28857i
$449$		−	29.3950i		−	1.38724i	−0.720342	−	0.693619i	$-0.756015\pi$
$449$		−	29.3950i		−	1.38724i	0.720342	−	0.693619i	$-0.243985\pi$
$450$		0			0
$451$	6.25377	+	6.25377i	0.294478	+	0.294478i
$452$	9.89119	−	32.9997i	0.465242	−	1.55218i
$453$		0			0
$454$	9.58583	+	12.8804i	0.449885	+	0.604507i
$455$		−	11.2585i		−	0.527807i
$456$		0			0
$457$		−	11.9379i		−	0.558431i	−0.960228	−	0.279216i	$-0.909926\pi$
$457$		−	11.9379i		−	0.558431i	0.960228	−	0.279216i	$-0.0900744\pi$
$458$	−25.7267	+	19.1463i	−1.20213	+	0.894649i
$459$		0			0
$460$	2.37944	+	4.41639i	0.110942	+	0.205915i
$461$	−24.7614	−	24.7614i	−1.15325	−	1.15325i	−0.985896	−	0.167358i	$-0.946476\pi$
$461$	−24.7614	−	24.7614i	−1.15325	−	1.15325i	−0.167358	−	0.985896i	$-0.553524\pi$
$462$		0			0
$463$			1.67006i			0.0776145i	0.999247	+	0.0388072i	$0.0123558\pi$
$463$			1.67006i			0.0776145i	−0.999247	+	0.0388072i	$0.987644\pi$
$464$	−3.79318	−	18.4311i	−0.176094	−	0.855641i
$465$		0			0
$466$	−2.64373	+	18.0281i	−0.122468	+	0.835136i
$467$	19.3267	−	19.3267i	0.894333	−	0.894333i	−0.100595	−	0.994928i	$-0.532074\pi$
$467$	19.3267	−	19.3267i	0.894333	−	0.894333i	0.994928	+	0.100595i	$0.0320745\pi$
$468$		0			0
$469$	3.37253	+	3.37253i	0.155729	+	0.155729i
$470$	−7.90940	−	10.6278i	−0.364834	−	0.490223i
$471$		0			0
$472$	−34.8388	+	12.6610i	−1.60358	+	0.582769i
$473$	−7.41063			−0.340741
$474$		0			0
$475$	7.48475	−	7.48475i	0.343424	−	0.343424i
$476$	−5.55100	+	18.5197i	−0.254430	+	0.848848i
$477$		0			0
$478$	2.79952	−	19.0905i	0.128047	−	0.873179i
$479$	11.4065			0.521176			0.260588	−	0.965450i	$-0.416084\pi$
$479$	11.4065			0.521176			0.260588	+	0.965450i	$0.416084\pi$
$480$		0			0
$481$	−17.5944			−0.802238
$482$	−2.96233	+	20.2007i	−0.134930	+	0.920115i
$483$		0			0
$484$	−5.84543	+	19.5019i	−0.265701	+	0.886452i
$485$	5.72427	−	5.72427i	0.259926	−	0.259926i
$486$		0			0
$487$	−16.7834			−0.760527			−0.380263	−	0.924878i	$-0.624167\pi$
$487$	−16.7834			−0.760527			−0.380263	+	0.924878i	$0.624167\pi$
$488$	−3.75642	−	10.3364i	−0.170045	−	0.467907i
$489$		0			0
$490$	−7.54045	−	10.1320i	−0.340643	−	0.457718i
$491$	12.4312	+	12.4312i	0.561012	+	0.561012i	0.929595	−	0.368583i	$-0.120157\pi$
$491$	12.4312	+	12.4312i	0.561012	+	0.561012i	−0.368583	+	0.929595i	$0.620157\pi$
$492$		0			0
$493$	−7.23141	+	7.23141i	−0.325686	+	0.325686i
$494$	−1.74354	+	11.8895i	−0.0784454	+	0.534934i
$495$		0			0
$496$	−13.3106	+	20.2091i	−0.597665	+	0.907417i
$497$			54.5250i			2.44578i
$498$		0			0
$499$	8.84852	+	8.84852i	0.396114	+	0.396114i	0.876860	−	0.480746i	$-0.159634\pi$
$499$	8.84852	+	8.84852i	0.396114	+	0.396114i	−0.480746	+	0.876860i	$0.659634\pi$
$500$	−6.30807	−	11.7082i	−0.282106	−	0.523606i
$501$		0			0
$502$	17.1161	−	12.7381i	0.763929	−	0.568531i
$503$			3.17356i			0.141502i	0.997494	+	0.0707511i	$0.0225396\pi$
$503$			3.17356i			0.141502i	−0.997494	+	0.0707511i	$0.977460\pi$
$504$		0			0
$505$		−	3.44794i		−	0.153431i
$506$	2.74373	+	3.68673i	0.121974	+	0.163895i
$507$		0			0
$508$	1.78955	−	5.97041i	0.0793983	−	0.264894i
$509$	8.04783	+	8.04783i	0.356714	+	0.356714i	0.862600	−	0.505886i	$-0.168835\pi$
$509$	8.04783	+	8.04783i	0.356714	+	0.356714i	−0.505886	+	0.862600i	$0.668835\pi$
$510$		0			0
$511$		−	3.03679i		−	0.134340i
$512$	21.8650	−	5.82434i	0.966304	−	0.257402i
$513$		0			0
$514$	−14.7133	−	2.15763i	−0.648975	−	0.0951688i
$515$	−6.84812	+	6.84812i	−0.301764	+	0.301764i
$516$		0			0
$517$	−8.58168	−	8.58168i	−0.377422	−	0.377422i
$518$	−24.5110	+	18.2416i	−1.07695	+	0.801488i
$519$		0			0
$520$	6.48868	+	3.02959i	0.284548	+	0.132856i
$521$	26.9791			1.18198			0.590988	−	0.806681i	$-0.298738\pi$
$521$	26.9791			1.18198			0.590988	+	0.806681i	$0.298738\pi$
$522$		0			0
$523$	−12.8344	+	12.8344i	−0.561210	+	0.561210i	−0.929651	−	0.368441i	$-0.879892\pi$
$523$	−12.8344	+	12.8344i	−0.561210	+	0.561210i	0.368441	+	0.929651i	$0.379892\pi$
$524$	26.1247	−	14.0753i	1.14126	−	0.614883i
$525$		0			0
$526$	−18.4740	−	2.70912i	−0.805505	−	0.118123i
$527$	13.1514			0.572886
$528$		0			0
$529$	10.1286			0.440374
$530$	11.1350	+	1.63289i	0.483674	+	0.0709283i
$531$		0			0
$532$	9.89786	+	18.3711i	0.429127	+	0.796487i
$533$	−25.0029	+	25.0029i	−1.08300	+	1.08300i
$534$		0			0
$535$	−0.0357863			−0.00154718
$536$	−2.85124	+	1.03619i	−0.123155	+	0.0447565i
$537$		0			0
$538$	23.9429	−	17.8187i	1.03225	−	0.768220i
$539$	−8.18136	−	8.18136i	−0.352396	−	0.352396i
$540$		0			0
$541$	13.5281	−	13.5281i	0.581618	−	0.581618i	−0.353730	−	0.935348i	$-0.615087\pi$
$541$	13.5281	−	13.5281i	0.581618	−	0.581618i	0.935348	+	0.353730i	$0.115087\pi$
$542$	8.19147	+	1.20124i	0.351854	+	0.0515976i
$543$		0			0
$544$	−9.17983	−	8.18277i	−0.393582	−	0.350833i
$545$			12.5141i			0.536044i
$546$		0			0
$547$	30.1918	+	30.1918i	1.29091	+	1.29091i	0.934225	+	0.356684i	$0.116093\pi$
$547$	30.1918	+	30.1918i	1.29091	+	1.29091i	0.356684	+	0.934225i	$0.383907\pi$
$548$	−22.6556	−	6.79068i	−0.967798	−	0.290084i
$549$		0			0
$550$	−3.45001	−	4.63575i	−0.147109	−	0.197669i
$551$			11.0382i			0.470244i
$552$		0			0
$553$			31.0630i			1.32093i
$554$	−21.4075	+	15.9319i	−0.909520	+	0.676882i
$555$		0			0
$556$	3.18007	−	1.71334i	0.134865	−	0.0726619i
$557$	−15.2950	−	15.2950i	−0.648072	−	0.648072i	0.304455	−	0.952527i	$-0.401526\pi$
$557$	−15.2950	−	15.2950i	−0.648072	−	0.648072i	−0.952527	+	0.304455i	$0.901526\pi$
$558$		0			0
$559$		−	29.6282i		−	1.25314i
$560$	12.1805	−	2.50678i	0.514718	−	0.105931i
$561$		0			0
$562$	0.737037	−	5.02600i	0.0310900	−	0.212009i
$563$	−8.19485	+	8.19485i	−0.345372	+	0.345372i	−0.858382	−	0.513011i	$-0.828530\pi$
$563$	−8.19485	+	8.19485i	−0.345372	+	0.345372i	0.513011	+	0.858382i	$0.328530\pi$
$564$		0			0
$565$	8.51556	+	8.51556i	0.358252	+	0.358252i
$566$	14.4160	+	19.3707i	0.605951	+	0.814210i
$567$		0			0
$568$	−31.4247	−	14.6723i	−1.31855	−	0.615636i
$569$	−21.8115			−0.914384			−0.457192	−	0.889368i	$-0.651145\pi$
$569$	−21.8115			−0.914384			−0.457192	+	0.889368i	$0.651145\pi$
$570$		0			0
$571$	13.7828	−	13.7828i	0.576791	−	0.576791i	−0.357226	−	0.934018i	$-0.616278\pi$
$571$	13.7828	−	13.7828i	0.576791	−	0.576791i	0.934018	+	0.357226i	$0.116278\pi$
$572$	6.28400	+	1.88354i	0.262747	+	0.0787547i
$573$		0			0
$574$	−8.90932	+	60.7544i	−0.371868	+	2.53584i
$575$	16.1847			0.674949
$576$		0			0
$577$	0.694745			0.0289226			0.0144613	−	0.999895i	$-0.495397\pi$
$577$	0.694745			0.0289226			0.0144613	+	0.999895i	$0.495397\pi$
$578$	2.51857	−	17.1746i	0.104759	−	0.714369i
$579$		0			0
$580$	6.30105	+	1.88865i	0.261637	+	0.0784219i
$581$	27.8744	−	27.8744i	1.15643	−	1.15643i
$582$		0			0
$583$	10.3098			0.426987
$584$	1.75021	+	0.817179i	0.0724243	+	0.0338151i
$585$		0			0
$586$	−0.745308	−	1.00146i	−0.0307884	−	0.0413701i
$587$	7.24278	+	7.24278i	0.298941	+	0.298941i	0.840599	−	0.541658i	$-0.182203\pi$
$587$	7.24278	+	7.24278i	0.298941	+	0.298941i	−0.541658	+	0.840599i	$0.682203\pi$
$588$		0			0
$589$	10.0374	−	10.0374i	0.413582	−	0.413582i
$590$	1.88011	−	12.8208i	0.0774028	−	0.527824i
$591$		0			0
$592$	−3.91753	−	19.0353i	−0.161009	−	0.782345i
$593$		−	43.5829i		−	1.78973i	−0.446332	−	0.894867i	$-0.647270\pi$
$593$		−	43.5829i		−	1.78973i	0.446332	−	0.894867i	$-0.352730\pi$
$594$		0			0
$595$	−4.77899	−	4.77899i	−0.195919	−	0.195919i
$596$	11.0577	−	5.95761i	0.452941	−	0.244033i
$597$		0			0
$598$	−14.7398	+	10.9696i	−0.602753	+	0.448581i
$599$		−	11.5201i		−	0.470698i	−0.971911	−	0.235349i	$-0.924377\pi$
$599$		−	11.5201i		−	0.470698i	0.971911	−	0.235349i	$-0.0756233\pi$
$600$		0			0
$601$		−	15.4445i		−	0.629993i	−0.949093	−	0.314997i	$-0.897997\pi$
$601$		−	15.4445i		−	0.629993i	0.949093	−	0.314997i	$-0.102003\pi$
$602$	−30.7179	−	41.2753i	−1.25197	−	1.68226i
$603$		0			0
$604$	17.6602	+	5.29339i	0.718583	+	0.215385i
$605$	−5.03247	−	5.03247i	−0.204599	−	0.204599i
$606$		0			0
$607$		−	33.9517i		−	1.37806i	−0.724735	−	0.689028i	$-0.758038\pi$
$607$		−	33.9517i		−	1.37806i	0.724735	−	0.689028i	$-0.241962\pi$
$608$	−13.2514	+	0.760969i	−0.537414	+	0.0308614i
$609$		0			0
$610$	3.80384	+	0.557814i	0.154013	+	0.0225852i
$611$	34.3101	−	34.3101i	1.38804	−	1.38804i
$612$		0			0
$613$	4.91614	+	4.91614i	0.198561	+	0.198561i	0.799383	−	0.600822i	$-0.205160\pi$
$613$	4.91614	+	4.91614i	0.198561	+	0.198561i	−0.600822	+	0.799383i	$0.705160\pi$
$614$	14.5753	−	10.8473i	0.588213	−	0.437759i
$615$		0			0
$616$	10.7071	−	3.89115i	0.431402	−	0.156779i
$617$	−20.8689			−0.840152			−0.420076	−	0.907489i	$-0.637997\pi$
$617$	−20.8689			−0.840152			−0.420076	+	0.907489i	$0.637997\pi$
$618$		0			0
$619$	−23.2338	+	23.2338i	−0.933845	+	0.933845i	−0.997944	−	0.0640985i	$-0.979583\pi$
$619$	−23.2338	+	23.2338i	−0.933845	+	0.933845i	0.0640985	+	0.997944i	$0.479583\pi$
$620$	−4.01232	−	7.44712i	−0.161139	−	0.299084i
$621$		0			0
$622$	1.04570	+	0.153347i	0.0419287	+	0.00614864i
$623$	−29.3379			−1.17540
$624$		0			0
$625$	−17.9069			−0.716276
$626$	14.9354	+	2.19019i	0.596937	+	0.0875377i
$627$		0			0
$628$	10.5870	−	5.70400i	0.422467	−	0.227614i
$629$	−7.46846	+	7.46846i	−0.297787	+	0.297787i
$630$		0			0
$631$	8.60506			0.342562			0.171281	−	0.985222i	$-0.445209\pi$
$631$	8.60506			0.342562			0.171281	+	0.985222i	$0.445209\pi$
$632$	−17.9028	−	8.35885i	−0.712133	−	0.332497i
$633$		0			0
$634$	17.6817	−	13.1591i	0.702231	−	0.522614i
$635$	1.54066	+	1.54066i	0.0611393	+	0.0611393i
$636$		0			0
$637$	32.7096	−	32.7096i	1.29600	−	1.29600i
$638$	5.96228	+	0.874339i	0.236049	+	0.0346154i
$639$		0			0
$640$	−1.83293	+	7.69460i	−0.0724529	+	0.304156i
$641$		−	40.6285i		−	1.60473i	−0.596834	−	0.802364i	$-0.703575\pi$
$641$		−	40.6285i		−	1.60473i	0.596834	−	0.802364i	$-0.296425\pi$
$642$		0			0
$643$	7.43436	+	7.43436i	0.293182	+	0.293182i	0.838336	−	0.545154i	$-0.183529\pi$
$643$	7.43436	+	7.43436i	0.293182	+	0.293182i	−0.545154	+	0.838336i	$0.683529\pi$
$644$	−9.16104	+	30.5637i	−0.360996	+	1.20438i
$645$		0			0
$646$	4.30675	+	5.78694i	0.169447	+	0.227684i
$647$		−	21.0939i		−	0.829288i	−0.909984	−	0.414644i	$-0.863906\pi$
$647$		−	21.0939i		−	0.829288i	0.909984	−	0.414644i	$-0.136094\pi$
$648$		0			0
$649$		−	11.8706i		−	0.465963i
$650$	18.5340	−	13.7934i	0.726964	−	0.541020i
$651$		0			0
$652$	6.32233	+	11.7346i	0.247601	+	0.459564i
$653$	−30.8573	−	30.8573i	−1.20754	−	1.20754i	−0.971822	−	0.235716i	$-0.924257\pi$
$653$	−30.8573	−	30.8573i	−1.20754	−	1.20754i	−0.235716	−	0.971822i	$-0.575743\pi$
$654$		0			0
$655$			10.3736i			0.405330i
$656$	−32.6175	−	21.4834i	−1.27350	−	0.838784i
$657$		0			0
$658$	12.2257	−	83.3697i	0.476609	−	3.25009i
$659$	−6.31965	+	6.31965i	−0.246179	+	0.246179i	−0.819400	−	0.573222i	$-0.805693\pi$
$659$	−6.31965	+	6.31965i	−0.246179	+	0.246179i	0.573222	+	0.819400i	$0.305693\pi$
$660$		0			0
$661$	24.0639	+	24.0639i	0.935975	+	0.935975i	0.998070	−	0.0620949i	$-0.0197781\pi$
$661$	24.0639	+	24.0639i	0.935975	+	0.935975i	−0.0620949	+	0.998070i	$0.519778\pi$
$662$	−18.7683	−	25.2188i	−0.729450	−	0.980155i
$663$		0			0
$664$	8.56423	+	23.5659i	0.332356	+	0.914533i
$665$	−7.29478			−0.282879
$666$		0			0
$667$	−11.9343	+	11.9343i	−0.462097	+	0.462097i
$668$	4.54378	−	15.1593i	0.175804	−	0.586530i
$669$		0			0
$670$	0.153870	−	1.04927i	0.00594451	−	0.0405368i
$671$	3.52193			0.135963
$672$		0			0
$673$	−11.6635			−0.449593			−0.224797	−	0.974406i	$-0.572172\pi$
$673$	−11.6635			−0.449593			−0.224797	+	0.974406i	$0.572172\pi$
$674$	5.38475	−	36.7197i	0.207413	−	1.41439i
$675$		0			0
$676$	−0.0655049	+	0.218542i	−0.00251942	+	0.00840548i
$677$	−3.79004	+	3.79004i	−0.145663	+	0.145663i	−0.776178	−	0.630514i	$-0.782844\pi$
$677$	−3.79004	+	3.79004i	−0.145663	+	0.145663i	0.630514	+	0.776178i	$0.282844\pi$
$678$		0			0
$679$	51.4890			1.97597
$680$	4.04030	−	1.46831i	0.154938	−	0.0563072i
$681$		0			0
$682$	−4.62661	−	6.21673i	−0.177162	−	0.238051i
$683$	−3.69050	−	3.69050i	−0.141213	−	0.141213i	0.632966	−	0.774179i	$-0.281837\pi$
$683$	−3.69050	−	3.69050i	−0.141213	−	0.141213i	−0.774179	+	0.632966i	$0.781837\pi$
$684$		0			0
$685$	5.84626	−	5.84626i	0.223374	−	0.223374i
$686$	5.26832	−	35.9257i	0.201145	−	1.37165i
$687$		0			0
$688$	32.0544	−	6.59692i	1.22206	−	0.251505i
$689$			41.2191i			1.57032i
$690$		0			0
$691$	−27.8100	−	27.8100i	−1.05794	−	1.05794i	−0.998215	−	0.0597295i	$-0.980976\pi$
$691$	−27.8100	−	27.8100i	−1.05794	−	1.05794i	−0.0597295	−	0.998215i	$-0.519024\pi$
$692$	14.2777	+	26.5003i	0.542756	+	1.00739i
$693$		0			0
$694$	−28.3948	+	21.1319i	−1.07785	+	0.802157i
$695$			1.26274i			0.0478986i
$696$		0			0
$697$			21.2264i			0.804008i
$698$	10.1681	+	13.6627i	0.384866	+	0.517141i
$699$		0			0
$700$	11.5192	−	38.4314i	0.435387	−	1.45257i
$701$	9.55994	+	9.55994i	0.361074	+	0.361074i	0.864208	−	0.503134i	$-0.167820\pi$
$701$	9.55994	+	9.55994i	0.361074	+	0.361074i	−0.503134	+	0.864208i	$0.667820\pi$
$702$		0			0
$703$			11.4001i			0.429961i
$704$	−0.638605	+	7.21799i	−0.0240683	+	0.272038i
$705$		0			0
$706$	37.8613	+	5.55217i	1.42493	+	0.208959i
$707$	15.5069	−	15.5069i	0.583196	−	0.583196i
$708$		0			0
$709$	5.67813	+	5.67813i	0.213247	+	0.213247i	0.805645	−	0.592399i	$-0.201819\pi$
$709$	5.67813	+	5.67813i	0.213247	+	0.213247i	−0.592399	+	0.805645i	$0.701819\pi$
$710$	9.72579	−	7.23812i	0.365002	−	0.271642i
$711$		0			0
$712$	7.89463	−	16.9085i	0.295864	−	0.633673i
$713$	21.7043			0.812834
$714$		0			0
$715$	−1.62158	+	1.62158i	−0.0606438	+	0.0606438i
$716$	−38.7895	+	20.8988i	−1.44963	+	0.781025i
$717$		0			0
$718$	21.0585	+	3.08812i	0.785895	+	0.115248i
$719$	−25.3473			−0.945294			−0.472647	−	0.881252i	$-0.656701\pi$
$719$	−25.3473			−0.945294			−0.472647	+	0.881252i	$0.656701\pi$
$720$		0			0
$721$	−61.5979			−2.29403
$722$	−18.8821	−	2.76896i	−0.702718	−	0.103050i
$723$		0			0
$724$	12.6852	+	23.5445i	0.471441	+	0.875025i
$725$	15.0064	−	15.0064i	0.557323	−	0.557323i
$726$		0			0
$727$	−16.3215			−0.605333			−0.302666	−	0.953097i	$-0.597877\pi$
$727$	−16.3215			−0.605333			−0.302666	+	0.953097i	$0.597877\pi$
$728$	15.5570	+	42.8077i	0.576582	+	1.58656i
$729$		0			0
$730$	−0.541681	+	0.403130i	−0.0200485	+	0.0149205i
$731$	−12.5765	−	12.5765i	−0.465159	−	0.465159i
$732$		0			0
$733$	−22.1647	+	22.1647i	−0.818674	+	0.818674i	−0.985916	−	0.167242i	$-0.946514\pi$
$733$	−22.1647	+	22.1647i	−0.818674	+	0.818674i	0.167242	+	0.985916i	$0.446514\pi$
$734$	−35.3246	−	5.18018i	−1.30386	−	0.191204i
$735$		0			0
$736$	−15.1498	−	13.5043i	−0.558430	−	0.497777i
$737$		−	0.971505i		−	0.0357859i
$738$		0			0
$739$	−32.5325	−	32.5325i	−1.19673	−	1.19673i	−0.975141	−	0.221585i	$-0.928877\pi$
$739$	−32.5325	−	32.5325i	−1.19673	−	1.19673i	−0.221585	−	0.975141i	$-0.571123\pi$
$740$	6.50761	+	1.95056i	0.239224	+	0.0717041i
$741$		0			0
$742$	42.7351	+	57.4227i	1.56885	+	2.10805i
$743$		−	18.3002i		−	0.671369i	−0.941975	−	0.335684i	$-0.891032\pi$
$743$		−	18.3002i		−	0.671369i	0.941975	−	0.335684i	$-0.108968\pi$
$744$		0			0
$745$			4.39079i			0.160866i
$746$	34.3179	−	25.5400i	1.25647	−	0.935087i
$747$		0			0
$748$	3.46695	−	1.86790i	0.126764	−	0.0682973i
$749$	−0.160946	−	0.160946i	−0.00588085	−	0.00588085i
$750$		0			0
$751$		−	20.4746i		−	0.747128i	−0.927604	−	0.373564i	$-0.878136\pi$
$751$		−	20.4746i		−	0.747128i	0.927604	−	0.373564i	$-0.121864\pi$
$752$	44.7591	+	29.4804i	1.63220	+	1.07504i
$753$		0			0
$754$	−3.49566	+	23.8376i	−0.127304	+	0.868114i
$755$	−4.55720	+	4.55720i	−0.165854	+	0.165854i
$756$		0			0
$757$	−14.9556	−	14.9556i	−0.543572	−	0.543572i	0.381002	−	0.924574i	$-0.375579\pi$
$757$	−14.9556	−	14.9556i	−0.543572	−	0.543572i	−0.924574	+	0.381002i	$0.875579\pi$
$758$	−8.47364	−	11.3859i	−0.307776	−	0.413556i
$759$		0			0
$760$	1.96298	−	4.20425i	0.0712046	−	0.152504i
$761$	−17.8234			−0.646097			−0.323048	−	0.946382i	$-0.604708\pi$
$761$	−17.8234			−0.646097			−0.323048	+	0.946382i	$0.604708\pi$
$762$		0			0
$763$	−56.2812	+	56.2812i	−2.03752	+	2.03752i
$764$	−3.98162	−	1.19343i	−0.144050	−	0.0431769i
$765$		0			0
$766$	−0.658492	+	4.49038i	−0.0237923	+	0.162244i
$767$	47.4595			1.71366
$768$		0			0
$769$	−49.7923			−1.79556			−0.897779	−	0.440446i	$-0.854820\pi$
$769$	−49.7923			−1.79556			−0.897779	+	0.440446i	$0.854820\pi$
$770$	−0.577820	+	3.94027i	−0.0208232	+	0.141997i
$771$		0			0
$772$	−13.5890	−	4.07312i	−0.489080	−	0.146595i
$773$	−7.65398	+	7.65398i	−0.275294	+	0.275294i	−0.831227	−	0.555933i	$-0.812361\pi$
$773$	−7.65398	+	7.65398i	−0.275294	+	0.275294i	0.555933	+	0.831227i	$0.312361\pi$
$774$		0			0
$775$	−27.2914			−0.980336
$776$	−13.8554	+	29.6750i	−0.497378	+	1.06527i
$777$		0			0
$778$	−14.9505	−	20.0888i	−0.536001	−	0.720219i
$779$	16.2003	+	16.2003i	0.580436	+	0.580436i
$780$		0			0
$781$	7.85334	−	7.85334i	0.281014	−	0.281014i
$782$	−1.60035	+	10.9131i	−0.0572283	+	0.390251i
$783$		0			0
$784$	42.6712	+	28.1052i	1.52397	+	1.00376i
$785$			4.20388i			0.150043i
$786$		0			0
$787$	4.90186	+	4.90186i	0.174732	+	0.174732i	0.789055	−	0.614323i	$-0.210571\pi$
$787$	4.90186	+	4.90186i	0.174732	+	0.174732i	−0.614323	+	0.789055i	$0.710571\pi$
$788$	−9.19430	+	4.95366i	−0.327533	+	0.176467i
$789$		0			0
$790$	5.54081	−	4.12358i	0.197133	−	0.146710i
$791$			76.5962i			2.72345i
$792$		0			0
$793$			14.0809i			0.500027i
$794$	4.20205	+	5.64625i	0.149125	+	0.200378i
$795$		0			0
$796$	−7.68228	−	2.30265i	−0.272291	−	0.0816154i
$797$	18.3529	+	18.3529i	0.650093	+	0.650093i	0.953015	−	0.302922i	$-0.0979623\pi$
$797$	18.3529	+	18.3529i	0.650093	+	0.650093i	−0.302922	+	0.953015i	$0.597962\pi$
$798$		0			0
$799$		−	29.1278i		−	1.03047i
$800$	19.0496	+	16.9806i	0.673507	+	0.600354i
$801$		0			0
$802$	−18.6647	−	2.73708i	−0.659072	−	0.0966496i
$803$	−0.437394	+	0.437394i	−0.0154353	+	0.0154353i
$804$		0			0
$805$	−7.88695	−	7.88695i	−0.277979	−	0.277979i
$806$	24.8549	−	18.4975i	0.875475	−	0.651546i
$807$		0			0
$808$	4.76438	+	13.1100i	0.167610	+	0.461207i
$809$	−11.8725			−0.417415			−0.208708	−	0.977978i	$-0.566926\pi$
$809$	−11.8725			−0.417415			−0.208708	+	0.977978i	$0.566926\pi$
$810$		0			0
$811$	−32.5638	+	32.5638i	−1.14347	+	1.14347i	−0.155661	+	0.987811i	$0.549751\pi$
$811$	−32.5638	+	32.5638i	−1.14347	+	1.14347i	−0.987811	+	0.155661i	$0.950249\pi$
$812$	19.8445	+	36.8326i	0.696404	+	1.29257i
$813$		0			0
$814$	6.15773	+	0.903000i	0.215828	+	0.0316501i
$815$	−4.65959			−0.163218
$816$		0			0
$817$	−19.1971			−0.671623
$818$	−53.0708	−	7.78256i	−1.85558	−	0.272111i
$819$		0			0
$820$	12.0197	−	6.47588i	0.419744	−	0.226148i
$821$	−21.8050	+	21.8050i	−0.760998	+	0.760998i	−0.976503	−	0.215505i	$-0.930860\pi$
$821$	−21.8050	+	21.8050i	−0.760998	+	0.760998i	0.215505	+	0.976503i	$0.430860\pi$
$822$		0			0
$823$	3.57439			0.124595			0.0622977	−	0.998058i	$-0.480157\pi$
$823$	3.57439			0.124595			0.0622977	+	0.998058i	$0.480157\pi$
$824$	16.5756	−	35.5011i	0.577438	−	1.23674i
$825$		0			0
$826$	66.1163	−	49.2050i	2.30048	−	1.71206i
$827$	−1.65970	−	1.65970i	−0.0577135	−	0.0577135i	0.677661	−	0.735374i	$-0.262994\pi$
$827$	−1.65970	−	1.65970i	−0.0577135	−	0.0577135i	−0.735374	+	0.677661i	$0.762994\pi$
$828$		0			0
$829$	9.37290	−	9.37290i	0.325534	−	0.325534i	−0.525351	−	0.850885i	$-0.676066\pi$
$829$	9.37290	−	9.37290i	0.325534	−	0.325534i	0.850885	+	0.525351i	$0.176066\pi$
$830$	−8.67234	−	1.27175i	−0.301021	−	0.0441432i
$831$		0			0
$832$	−28.8580	−	2.55318i	−1.00047	−	0.0885157i
$833$		−	27.7690i		−	0.962140i
$834$		0			0
$835$	3.91184	+	3.91184i	0.135375	+	0.135375i
$836$	1.22041	−	4.07163i	0.0422088	−	0.140820i
$837$		0			0
$838$	3.24294	+	4.35751i	0.112026	+	0.150528i
$839$		−	20.7551i		−	0.716546i	−0.933617	−	0.358273i	$-0.883366\pi$
$839$		−	20.7551i		−	0.716546i	0.933617	−	0.358273i	$-0.116634\pi$
$840$		0			0
$841$		−	6.86919i		−	0.236869i
$842$	35.5959	−	26.4912i	1.22672	−	0.912945i
$843$		0			0
$844$	19.6983	+	36.5613i	0.678044	+	1.25849i
$845$	−0.0563947	−	0.0563947i	−0.00194004	−	0.00194004i
$846$		0			0
$847$		−	45.2663i		−	1.55537i
$848$	−44.5945	+	9.17772i	−1.53138	+	0.315164i
$849$		0			0
$850$	2.01230	−	13.7223i	0.0690214	−	0.470670i
$851$	−12.3255	+	12.3255i	−0.422513	+	0.422513i
$852$		0			0
$853$	11.8144	+	11.8144i	0.404517	+	0.404517i	0.879821	−	0.475304i	$-0.157662\pi$
$853$	11.8144	+	11.8144i	0.404517	+	0.404517i	−0.475304	+	0.879821i	$0.657662\pi$
$854$	14.5988	+	19.6162i	0.499560	+	0.671254i
$855$		0			0
$856$	0.136069	−	0.0494497i	0.00465074	−	0.00169016i
$857$	−4.43559			−0.151517			−0.0757585	−	0.997126i	$-0.524138\pi$
$857$	−4.43559			−0.151517			−0.0757585	+	0.997126i	$0.524138\pi$
$858$		0			0
$859$	−13.8476	+	13.8476i	−0.472474	+	0.472474i	−0.902714	−	0.430240i	$-0.858429\pi$
$859$	−13.8476	+	13.8476i	−0.472474	+	0.472474i	0.430240	+	0.902714i	$0.358429\pi$
$860$	−3.28465	+	10.9585i	−0.112006	+	0.373681i
$861$		0			0
$862$	−4.86563	+	33.1797i	−0.165724	+	1.13011i
$863$	33.4529			1.13875			0.569375	−	0.822078i	$-0.307185\pi$
$863$	33.4529			1.13875			0.569375	+	0.822078i	$0.307185\pi$
$864$		0			0
$865$	−10.5227			−0.357783
$866$	−2.51083	+	17.1219i	−0.0853216	+	0.581824i
$867$		0			0
$868$	15.4478	−	51.5380i	0.524332	−	1.74931i
$869$	4.47407	−	4.47407i	0.151772	−	0.151772i
$870$		0			0
$871$	3.88414			0.131609
$872$	−17.2920	−	47.5818i	−0.585582	−	1.61132i
$873$		0			0
$874$	7.10760	+	9.55041i	0.240418	+	0.323047i
$875$	20.9089	+	20.9089i	0.706851	+	0.706851i
$876$		0			0
$877$	−12.6035	+	12.6035i	−0.425590	+	0.425590i	−0.887123	−	0.461533i	$-0.847299\pi$
$877$	−12.6035	+	12.6035i	−0.425590	+	0.425590i	0.461533	+	0.887123i	$0.347299\pi$
$878$	0.144001	−	0.981973i	0.00485981	−	0.0331400i
$879$		0			0
$880$	−2.11543	−	1.39332i	−0.0713112	−	0.0469688i
$881$			31.4115i			1.05828i	0.848535	+	0.529139i	$0.177485\pi$
$881$			31.4115i			1.05828i	−0.848535	+	0.529139i	$0.822515\pi$
$882$		0			0
$883$	35.8039	+	35.8039i	1.20490	+	1.20490i	0.972659	+	0.232237i	$0.0746045\pi$
$883$	35.8039	+	35.8039i	1.20490	+	1.20490i	0.232237	+	0.972659i	$0.425395\pi$
$884$	7.46799	+	13.8611i	0.251176	+	0.466198i
$885$		0			0
$886$	−10.5744	+	7.86966i	−0.355253	+	0.264386i
$887$		−	31.7006i		−	1.06440i	−0.846618	−	0.532201i	$-0.821365\pi$
$887$		−	31.7006i		−	1.06440i	0.846618	−	0.532201i	$-0.178635\pi$
$888$		0			0
$889$			13.8580i			0.464784i
$890$	3.89457	+	5.23309i	0.130546	+	0.175414i
$891$		0			0
$892$	4.67892	−	15.6102i	0.156662	−	0.522667i
$893$	−22.2307	−	22.2307i	−0.743923	−	0.743923i
$894$		0			0
$895$		−	15.4025i		−	0.514850i
$896$	−42.8494	+	26.3625i	−1.43150	+	0.880708i
$897$		0			0
$898$	−41.1310	−	6.03165i	−1.37256	−	0.201279i
$899$	20.1241	−	20.1241i	0.671178	−	0.671178i
$900$		0			0
$901$	17.4966	+	17.4966i	0.582897	+	0.582897i
$902$	10.0338	−	7.46734i	0.334089	−	0.248635i
$903$		0			0
$904$	−44.1452	−	20.6115i	−1.46825	−	0.685529i
$905$	−9.34905			−0.310773
$906$		0			0
$907$	16.2449	−	16.2449i	0.539404	−	0.539404i	−0.383950	−	0.923354i	$-0.625436\pi$
$907$	16.2449	−	16.2449i	0.539404	−	0.539404i	0.923354	+	0.383950i	$0.125436\pi$
$908$	19.9898	−	10.7700i	0.663385	−	0.357415i
$909$		0			0
$910$	−15.7534	−	2.31016i	−0.522221	−	0.0765811i
$911$	20.9490			0.694070			0.347035	−	0.937852i	$-0.387189\pi$
$911$	20.9490			0.694070			0.347035	+	0.937852i	$0.387189\pi$
$912$		0			0
$913$	−8.02961			−0.265741
$914$	−16.7041	−	2.44957i	−0.552522	−	0.0810245i
$915$		0			0
$916$	21.5115	+	39.9268i	0.710761	+	1.31922i
$917$	−46.6545	+	46.6545i	−1.54067	+	1.54067i
$918$		0			0
$919$	−2.90670			−0.0958832			−0.0479416	−	0.998850i	$-0.515266\pi$
$919$	−2.90670			−0.0958832			−0.0479416	+	0.998850i	$0.515266\pi$
$920$	6.66787	−	2.42321i	0.219833	−	0.0798910i
$921$		0			0
$922$	−39.7282	+	29.5665i	−1.30838	+	0.973721i
$923$	31.3981	+	31.3981i	1.03348	+	1.03348i
$924$		0			0
$925$	15.4983	−	15.4983i	0.509581	−	0.509581i
$926$	2.33683	+	0.342685i	0.0767932	+	0.0112613i
$927$		0			0
$928$	−26.5680	+	1.52569i	−0.872137	+	0.0500831i
$929$			7.03464i			0.230799i	0.993319	+	0.115399i	$0.0368148\pi$
$929$			7.03464i			0.230799i	−0.993319	+	0.115399i	$0.963185\pi$
$930$		0			0
$931$	−21.1937	−	21.1937i	−0.694596	−	0.694596i
$932$	24.6833	+	7.39847i	0.808529	+	0.242345i
$933$		0			0
$934$	−23.0772	−	31.0085i	−0.755108	−	1.01463i
$935$			1.37665i			0.0450214i
$936$		0			0
$937$		−	33.6191i		−	1.09829i	−0.835727	−	0.549145i	$-0.814954\pi$
$937$		−	33.6191i		−	1.09829i	0.835727	−	0.549145i	$-0.185046\pi$
$938$	5.41103	−	4.02699i	0.176676	−	0.131486i
$939$		0			0
$940$	−16.4939	+	8.88648i	−0.537971	+	0.289845i
$941$	−21.1595	−	21.1595i	−0.689781	−	0.689781i	0.272403	−	0.962183i	$-0.412182\pi$
$941$	−21.1595	−	21.1595i	−0.689781	−	0.689781i	−0.962183	+	0.272403i	$0.912182\pi$
$942$		0			0
$943$			35.0308i			1.14076i
$944$	10.5672	+	51.3460i	0.343933	+	1.67117i
$945$		0			0
$946$	−1.52061	+	10.3693i	−0.0494392	+	0.337135i
$947$	10.8619	−	10.8619i	0.352964	−	0.352964i	−0.508247	−	0.861211i	$-0.669706\pi$
$947$	10.8619	−	10.8619i	0.352964	−	0.352964i	0.861211	+	0.508247i	$0.169706\pi$
$948$		0			0
$949$	−1.74873	−	1.74873i	−0.0567662	−	0.0567662i
$950$	−8.93721	−	12.0088i	−0.289961	−	0.389618i
$951$		0			0
$952$	24.7746	+	11.5673i	0.802949	+	0.374899i
$953$	−51.0258			−1.65289			−0.826444	−	0.563020i	$-0.809640\pi$
$953$	−51.0258			−1.65289			−0.826444	+	0.563020i	$0.809640\pi$
$954$		0			0
$955$	1.02746	−	1.02746i	0.0332477	−	0.0332477i
$956$	−26.1379	−	7.83446i	−0.845360	−	0.253385i
$957$		0			0
$958$	2.34053	−	15.9605i	0.0756191	−	0.515661i
$959$	52.5862			1.69810
$960$		0			0
$961$	−5.59888			−0.180609
$962$	−3.61025	+	24.6190i	−0.116399	+	0.793748i
$963$		0			0
$964$	27.6579	+	8.29006i	0.890801	+	0.267005i
$965$	3.50664	−	3.50664i	0.112883	−	0.112883i
$966$		0			0
$967$	−5.24792			−0.168762			−0.0843809	−	0.996434i	$-0.526891\pi$
$967$	−5.24792			−0.168762			−0.0843809	+	0.996434i	$0.526891\pi$
$968$	26.0886	+	12.1809i	0.838520	+	0.391508i
$969$		0			0
$970$	−6.83510	−	9.18426i	−0.219462	−	0.294889i
$971$	23.3352	+	23.3352i	0.748863	+	0.748863i	0.974266	−	0.225402i	$-0.0723697\pi$
$971$	23.3352	+	23.3352i	0.748863	+	0.748863i	−0.225402	+	0.974266i	$0.572370\pi$
$972$		0			0
$973$	−5.67910	+	5.67910i	−0.182063	+	0.182063i
$974$	−3.44382	+	23.4841i	−0.110347	+	0.752479i
$975$		0			0
$976$	−15.2340	+	3.13521i	−0.487628	+	0.100356i
$977$			22.0048i			0.703997i	0.936001	+	0.351999i	$0.114498\pi$
$977$			22.0048i			0.703997i	−0.936001	+	0.351999i	$0.885502\pi$
$978$		0			0
$979$	4.22559	+	4.22559i	0.135051	+	0.135051i
$980$	−15.7245	+	8.47194i	−0.502300	+	0.270626i
$981$		0			0
$982$	19.9451	−	14.8435i	0.636474	−	0.473676i
$983$			57.9445i			1.84814i	0.382220	+	0.924071i	$0.375160\pi$
$983$			57.9445i			1.84814i	−0.382220	+	0.924071i	$0.624840\pi$
$984$		0			0
$985$		−	3.65087i		−	0.116326i
$986$	8.63471	+	11.6024i	0.274985	+	0.369495i
$987$		0			0
$988$	16.2786	+	4.87928i	0.517892	+	0.155231i
$989$	−20.7555	−	20.7555i	−0.659987	−	0.659987i
$990$		0			0
$991$			40.5730i			1.28884i	0.764670	+	0.644422i	$0.222902\pi$
$991$			40.5730i			1.28884i	−0.764670	+	0.644422i	$0.777098\pi$
$992$	25.5463	+	22.7717i	0.811097	+	0.723001i
$993$		0			0
$994$	76.2940	+	11.1881i	2.41990	+	0.354866i
$995$	1.98241	−	1.98241i	0.0628466	−	0.0628466i
$996$		0			0
$997$	−2.42600	−	2.42600i	−0.0768323	−	0.0768323i	0.667646	−	0.744479i	$-0.267302\pi$
$997$	−2.42600	−	2.42600i	−0.0768323	−	0.0768323i	−0.744479	+	0.667646i	$0.767302\pi$
$998$	14.1969	−	10.5656i	0.449396	−	0.334449i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.2.l.a.107.9	yes	32
3.2	odd	2	inner	432.2.l.a.107.8	✓	32
4.3	odd	2		1728.2.l.a.1295.10		32
12.11	even	2		1728.2.l.a.1295.7		32
16.3	odd	4	inner	432.2.l.a.323.8	yes	32
16.13	even	4		1728.2.l.a.431.7		32
48.29	odd	4		1728.2.l.a.431.10		32
48.35	even	4	inner	432.2.l.a.323.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
432.2.l.a.107.8	✓	32	3.2	odd	2	inner
432.2.l.a.107.9	yes	32	1.1	even	1	trivial
432.2.l.a.323.8	yes	32	16.3	odd	4	inner
432.2.l.a.323.9	yes	32	48.35	even	4	inner
1728.2.l.a.431.7		32	16.13	even	4
1728.2.l.a.431.10		32	48.29	odd	4
1728.2.l.a.1295.7		32	12.11	even	2
1728.2.l.a.1295.10		32	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.205193 - 1.39925i) q^{2} +(-1.91579 - 0.574231i) q^{4} +(0.494369 - 0.494369i) q^{5} +4.44678 q^{7} +(-1.19660 + 2.56284i) q^{8} +O(q^{10})\)	\(q+(0.205193 - 1.39925i) q^{2} +(-1.91579 - 0.574231i) q^{4} +(0.494369 - 0.494369i) q^{5} +4.44678 q^{7} +(-1.19660 + 2.56284i) q^{8} +(-0.590304 - 0.793186i) q^{10} +(-0.640478 - 0.640478i) q^{11} +(2.56067 - 2.56067i) q^{13} +(0.912446 - 6.22215i) q^{14} +(3.34052 + 2.20021i) q^{16} -2.17390i q^{17} +(-1.65915 - 1.65915i) q^{19} +(-1.23099 + 0.663226i) q^{20} +(-1.02761 + 0.764767i) q^{22} -3.58767i q^{23} +4.51120i q^{25} +(-3.05758 - 4.10845i) q^{26} +(-8.51910 - 2.55348i) q^{28} +(-3.32647 - 3.32647i) q^{29} +6.04970i q^{31} +(3.76410 - 4.22275i) q^{32} +(-3.04183 - 0.446068i) q^{34} +(2.19835 - 2.19835i) q^{35} +(-3.43551 - 3.43551i) q^{37} +(-2.66201 + 1.98112i) q^{38} +(0.675428 + 1.85855i) q^{40} -9.76422 q^{41} +(5.78523 - 5.78523i) q^{43} +(0.859240 + 1.59481i) q^{44} +(-5.02004 - 0.736164i) q^{46} +13.3989 q^{47} +12.7738 q^{49} +(6.31229 + 0.925665i) q^{50} +(-6.37613 + 3.43530i) q^{52} +(-8.04849 + 8.04849i) q^{53} -0.633265 q^{55} +(-5.32101 + 11.3964i) q^{56} +(-5.33713 + 3.97199i) q^{58} +(9.26701 + 9.26701i) q^{59} +(-2.74945 + 2.74945i) q^{61} +(8.46503 + 1.24135i) q^{62} +(-5.13631 - 6.13338i) q^{64} -2.53183i q^{65} +(0.758422 + 0.758422i) q^{67} +(-1.24832 + 4.16474i) q^{68} +(-2.62495 - 3.52712i) q^{70} +12.2617i q^{71} -0.682919i q^{73} +(-5.51208 + 4.10220i) q^{74} +(2.22585 + 4.13132i) q^{76} +(-2.84806 - 2.84806i) q^{77} +6.98551i q^{79} +(2.73917 - 0.563731i) q^{80} +(-2.00355 + 13.6626i) q^{82} +(6.26845 - 6.26845i) q^{83} +(-1.07471 - 1.07471i) q^{85} +(-6.90789 - 9.28207i) q^{86} +(2.40784 - 0.875048i) q^{88} -6.59756 q^{89} +(11.3867 - 11.3867i) q^{91} +(-2.06015 + 6.87323i) q^{92} +(2.74935 - 18.7483i) q^{94} -1.64046 q^{95} +11.5790 q^{97} +(2.62110 - 17.8738i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q - 4 q^{10} - 20 q^{16} + 8 q^{19} + 4 q^{22} - 12 q^{28} - 36 q^{34} - 12 q^{40} + 32 q^{43} - 16 q^{46} + 32 q^{49} - 60 q^{52} + 64 q^{55} - 48 q^{58} - 16 q^{61} + 48 q^{64} - 32 q^{67} - 72 q^{70} - 96 q^{76} + 40 q^{82} - 16 q^{85} + 36 q^{88} + 24 q^{91} - 36 q^{94}+O(q^{100}) \) 32 * q - 4 * q^10 - 20 * q^16 + 8 * q^19 + 4 * q^22 - 12 * q^28 - 36 * q^34 - 12 * q^40 + 32 * q^43 - 16 * q^46 + 32 * q^49 - 60 * q^52 + 64 * q^55 - 48 * q^58 - 16 * q^61 + 48 * q^64 - 32 * q^67 - 72 * q^70 - 96 * q^76 + 40 * q^82 - 16 * q^85 + 36 * q^88 + 24 * q^91 - 36 * q^94

Introduction

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