LMFDB - Embedded newform 864.2.w.a.107.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [864,2,Mod(107,864)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(864, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 5, 4]))

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

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

chi := DirichletCharacter("864.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.w (of order $8$, degree $4$, 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:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			107.20
Character	$\chi$	$=$	864.107
Dual form			864.2.w.a.323.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.394008 + 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(2.44724 + 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(-2.11938 - 1.87302i) q^{8} +O(q^{10})$	\(q+(0.394008 + 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(2.44724 + 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(-2.11938 - 1.87302i) q^{8} +(-0.412566 + 3.72328i) q^{10} +(-4.19398 - 1.73720i) q^{11} +(2.12813 + 5.13777i) q^{13} +(5.93786 + 3.26747i) q^{14} +(1.70892 - 3.61657i) q^{16} +3.78123 q^{17} +(6.01757 - 2.49256i) q^{19} +(-5.21959 + 0.906648i) q^{20} +(0.707039 - 6.38081i) q^{22} +(-0.521933 + 0.521933i) q^{23} +(1.42590 + 1.42590i) q^{25} +(-6.13971 + 4.91479i) q^{26} +(-2.09837 + 9.35232i) q^{28} +(1.96141 + 4.73526i) q^{29} -2.30887i q^{31} +(5.58542 + 0.896134i) q^{32} +(1.48984 + 5.13574i) q^{34} +(11.7282 - 4.85798i) q^{35} +(0.301775 - 0.728548i) q^{37} +(5.75641 + 7.19109i) q^{38} +(-3.28799 - 6.73211i) q^{40} +(-5.11319 - 5.11319i) q^{41} +(-1.04025 + 2.51140i) q^{43} +(8.94511 - 1.55378i) q^{44} +(-0.914544 - 0.503253i) q^{46} +6.05530i q^{47} -15.9673i q^{49} +(-1.37487 + 2.49850i) q^{50} +(-9.09446 - 6.40260i) q^{52} +(-3.39385 + 8.19348i) q^{53} +(-8.50270 - 8.50270i) q^{55} +(-13.5293 + 0.834842i) q^{56} +(-5.65871 + 4.52976i) q^{58} +(-3.61257 + 8.72153i) q^{59} +(-0.171884 + 0.0711965i) q^{61} +(3.13594 - 0.909712i) q^{62} +(0.983556 + 7.93931i) q^{64} +14.7306i q^{65} +(0.155362 + 0.375078i) q^{67} +(-6.38845 + 4.04705i) q^{68} +(11.2192 + 14.0154i) q^{70} +(4.96412 + 4.96412i) q^{71} +(-1.96331 + 1.96331i) q^{73} +(1.10843 + 0.122822i) q^{74} +(-7.49899 + 10.6518i) q^{76} +(-20.0993 + 8.32540i) q^{77} -8.19131 q^{79} +(7.84819 - 7.11831i) q^{80} +(4.93019 - 8.95946i) q^{82} +(-4.85181 - 11.7133i) q^{83} +(9.25358 + 3.83296i) q^{85} +(-3.82089 - 0.423382i) q^{86} +(5.63482 + 11.5372i) q^{88} +(6.59205 - 6.59205i) q^{89} +(24.6223 + 10.1989i) q^{91} +(0.323190 - 1.44044i) q^{92} +(-8.22442 + 2.38584i) q^{94} +17.2531 q^{95} -6.02797 q^{97} +(21.6870 - 6.29123i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q+O(q^{10}) $ 128 * q	$ 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) $ 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$-1$	$-1$

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 $

$2$	0.394008	+	1.35822i	0.278606	+	0.960406i
$2$	0.394008	+	1.35822i	0.278606	+	0.960406i
$3$		0			0
$3$		0			0
$4$	−1.68952	+	1.07030i	−0.844758	+	0.535149i
$5$	2.44724	+	1.01368i	1.09444	+	0.453331i	0.855552	−	0.517716i	$-0.173218\pi$
$5$	2.44724	+	1.01368i	1.09444	+	0.453331i	0.238886	+	0.971048i	$0.423218\pi$
$6$		0			0
$7$	3.38875	−	3.38875i	1.28083	−	1.28083i	0.340630	−	0.940197i	$-0.389360\pi$
$7$	3.38875	−	3.38875i	1.28083	−	1.28083i	0.940197	−	0.340630i	$-0.110640\pi$
$8$	−2.11938	−	1.87302i	−0.749315	−	0.662214i
$9$		0			0
$10$	−0.412566	+	3.72328i	−0.130465	+	1.17741i
$11$	−4.19398	−	1.73720i	−1.26453	−	0.523786i	−0.353234	−	0.935535i	$-0.614918\pi$
$11$	−4.19398	−	1.73720i	−1.26453	−	0.523786i	−0.911297	+	0.411749i	$0.864918\pi$
$12$		0			0
$13$	2.12813	+	5.13777i	0.590238	+	1.42496i	0.883273	+	0.468859i	$0.155335\pi$
$13$	2.12813	+	5.13777i	0.590238	+	1.42496i	−0.293035	+	0.956102i	$0.594665\pi$
$14$	5.93786	+	3.26747i	1.58696	+	0.873268i
$15$		0			0
$16$	1.70892	−	3.61657i	0.427231	−	0.904143i
$17$	3.78123			0.917084			0.458542	−	0.888673i	$-0.348372\pi$
$17$	3.78123			0.917084			0.458542	+	0.888673i	$0.348372\pi$
$18$		0			0
$19$	6.01757	−	2.49256i	1.38053	−	0.571832i	0.435903	−	0.899993i	$-0.356429\pi$
$19$	6.01757	−	2.49256i	1.38053	−	0.571832i	0.944622	+	0.328161i	$0.106429\pi$
$20$	−5.21959	+	0.906648i	−1.16714	+	0.202733i
$21$		0			0
$22$	0.707039	−	6.38081i	0.150741	−	1.36039i
$23$	−0.521933	+	0.521933i	−0.108830	+	0.108830i	−0.759425	−	0.650595i	$-0.774520\pi$
$23$	−0.521933	+	0.521933i	−0.108830	+	0.108830i	0.650595	+	0.759425i	$0.274520\pi$
$24$		0			0
$25$	1.42590	+	1.42590i	0.285180	+	0.285180i
$26$	−6.13971	+	4.91479i	−1.20410	+	0.963871i
$27$		0			0
$28$	−2.09837	+	9.35232i	−0.396555	+	1.76742i
$29$	1.96141	+	4.73526i	0.364225	+	0.879316i	0.994673	+	0.103085i	$0.0328713\pi$
$29$	1.96141	+	4.73526i	0.364225	+	0.879316i	−0.630448	+	0.776232i	$0.717129\pi$
$30$		0			0
$31$		−	2.30887i		−	0.414684i	−0.978268	−	0.207342i	$-0.933519\pi$
$31$		−	2.30887i		−	0.414684i	0.978268	−	0.207342i	$-0.0664814\pi$
$32$	5.58542	+	0.896134i	0.987373	+	0.158416i
$33$		0			0
$34$	1.48984	+	5.13574i	0.255505	+	0.880773i
$35$	11.7282	−	4.85798i	1.98243	−	0.821148i
$36$		0			0
$37$	0.301775	−	0.728548i	0.0496114	−	0.119773i	−0.897131	−	0.441765i	$-0.854353\pi$
$37$	0.301775	−	0.728548i	0.0496114	−	0.119773i	0.946742	+	0.321992i	$0.104353\pi$
$38$	5.75641	+	7.19109i	0.933813	+	1.16655i
$39$		0			0
$40$	−3.28799	−	6.73211i	−0.519876	−	1.06444i
$41$	−5.11319	−	5.11319i	−0.798546	−	0.798546i	0.184321	−	0.982866i	$-0.440992\pi$
$41$	−5.11319	−	5.11319i	−0.798546	−	0.798546i	−0.982866	+	0.184321i	$0.940992\pi$
$42$		0			0
$43$	−1.04025	+	2.51140i	−0.158637	+	0.382984i	−0.983135	−	0.182881i	$-0.941458\pi$
$43$	−1.04025	+	2.51140i	−0.158637	+	0.382984i	0.824498	+	0.565865i	$0.191458\pi$
$44$	8.94511	−	1.55378i	1.34853	−	0.234241i
$45$		0			0
$46$	−0.914544	−	0.503253i	−0.134842	−	0.0742006i
$47$			6.05530i			0.883256i	0.897198	+	0.441628i	$0.145599\pi$
$47$			6.05530i			0.883256i	−0.897198	+	0.441628i	$0.854401\pi$
$48$		0			0
$49$		−	15.9673i		−	2.28104i
$50$	−1.37487	+	2.49850i	−0.194436	+	0.353341i
$51$		0			0
$52$	−9.09446	−	6.40260i	−1.26117	−	0.887881i
$53$	−3.39385	+	8.19348i	−0.466181	+	1.12546i	0.499635	+	0.866236i	$0.333467\pi$
$53$	−3.39385	+	8.19348i	−0.466181	+	1.12546i	−0.965817	+	0.259226i	$0.916533\pi$
$54$		0			0
$55$	−8.50270	−	8.50270i	−1.14650	−	1.14650i
$56$	−13.5293	+	0.834842i	−1.80792	+	0.111560i
$57$		0			0
$58$	−5.65871	+	4.52976i	−0.743025	+	0.594786i
$59$	−3.61257	+	8.72153i	−0.470317	+	1.13545i	0.493706	+	0.869629i	$0.335642\pi$
$59$	−3.61257	+	8.72153i	−0.470317	+	1.13545i	−0.964023	+	0.265817i	$0.914358\pi$
$60$		0			0
$61$	−0.171884	+	0.0711965i	−0.0220074	+	0.00911578i	−0.393660	−	0.919256i	$-0.628791\pi$
$61$	−0.171884	+	0.0711965i	−0.0220074	+	0.00911578i	0.371653	+	0.928372i	$0.378791\pi$
$62$	3.13594	−	0.909712i	0.398265	−	0.115533i
$63$		0			0
$64$	0.983556	+	7.93931i	0.122945	+	0.992414i
$65$			14.7306i			1.82711i
$66$		0			0
$67$	0.155362	+	0.375078i	0.0189805	+	0.0458231i	0.933086	−	0.359654i	$-0.117105\pi$
$67$	0.155362	+	0.375078i	0.0189805	+	0.0458231i	−0.914105	+	0.405477i	$0.867105\pi$
$68$	−6.38845	+	4.04705i	−0.774714	+	0.490777i
$69$		0			0
$70$	11.2192	+	14.0154i	1.34095	+	1.67516i
$71$	4.96412	+	4.96412i	0.589132	+	0.589132i	0.937396	−	0.348264i	$-0.113229\pi$
$71$	4.96412	+	4.96412i	0.589132	+	0.589132i	−0.348264	+	0.937396i	$0.613229\pi$
$72$		0			0
$73$	−1.96331	+	1.96331i	−0.229788	+	0.229788i	−0.812604	−	0.582816i	$-0.801951\pi$
$73$	−1.96331	+	1.96331i	−0.229788	+	0.229788i	0.582816	+	0.812604i	$0.301951\pi$
$74$	1.10843	+	0.122822i	0.128852	+	0.0142778i
$75$		0			0
$76$	−7.49899	+	10.6518i	−0.860194	+	1.22185i
$77$	−20.0993	+	8.32540i	−2.29053	+	0.948767i
$78$		0			0
$79$	−8.19131			−0.921594			−0.460797	−	0.887505i	$-0.652436\pi$
$79$	−8.19131			−0.921594			−0.460797	+	0.887505i	$0.652436\pi$
$80$	7.84819	−	7.11831i	0.877454	−	0.795851i
$81$		0			0
$82$	4.93019	−	8.95946i	0.544448	−	0.989407i
$83$	−4.85181	−	11.7133i	−0.532555	−	1.28570i	−0.929826	−	0.368000i	$-0.880043\pi$
$83$	−4.85181	−	11.7133i	−0.532555	−	1.28570i	0.397271	−	0.917701i	$-0.369957\pi$
$84$		0			0
$85$	9.25358	+	3.83296i	1.00369	+	0.415743i
$86$	−3.82089	−	0.423382i	−0.412017	−	0.0456545i
$87$		0			0
$88$	5.63482	+	11.5372i	0.600673	+	1.22987i
$89$	6.59205	−	6.59205i	0.698756	−	0.698756i	−0.265386	−	0.964142i	$-0.585499\pi$
$89$	6.59205	−	6.59205i	0.698756	−	0.698756i	0.964142	+	0.265386i	$0.0854995\pi$
$90$		0			0
$91$	24.6223	+	10.1989i	2.58112	+	1.06914i
$92$	0.323190	−	1.44044i	0.0336948	−	0.150176i
$93$		0			0
$94$	−8.22442	+	2.38584i	−0.848284	+	0.246080i
$95$	17.2531			1.77013
$96$		0			0
$97$	−6.02797			−0.612048			−0.306024	−	0.952024i	$-0.598999\pi$
$97$	−6.02797			−0.612048			−0.306024	+	0.952024i	$0.598999\pi$
$98$	21.6870	−	6.29123i	2.19072	−	0.635510i
$99$		0			0
$100$	−3.93522	−	0.882941i	−0.393522	−	0.0882941i
$101$	−1.74724	−	0.723731i	−0.173857	−	0.0720140i	0.294057	−	0.955788i	$-0.404994\pi$
$101$	−1.74724	−	0.723731i	−0.173857	−	0.0720140i	−0.467914	+	0.883774i	$0.654994\pi$
$102$		0			0
$103$	5.68112	−	5.68112i	0.559777	−	0.559777i	−0.369467	−	0.929244i	$-0.620460\pi$
$103$	5.68112	−	5.68112i	0.559777	−	0.559777i	0.929244	+	0.369467i	$0.120460\pi$
$104$	5.11284	−	14.8749i	0.501356	−	1.45861i
$105$		0			0
$106$	−12.4657	−	1.38129i	−1.21078	−	0.134163i
$107$	−11.3023	−	4.68159i	−1.09264	−	0.452586i	−0.237713	−	0.971335i	$-0.576398\pi$
$107$	−11.3023	−	4.68159i	−1.09264	−	0.452586i	−0.854926	+	0.518749i	$0.826398\pi$
$108$		0			0
$109$	−2.63231	−	6.35496i	−0.252130	−	0.608695i	0.746246	−	0.665670i	$-0.231854\pi$
$109$	−2.63231	−	6.35496i	−0.252130	−	0.608695i	−0.998376	+	0.0569753i	$0.981854\pi$
$110$	8.19839	−	14.8987i	0.781686	−	1.42053i
$111$		0			0
$112$	−6.46454	−	18.0468i	−0.610842	−	1.70526i
$113$	−16.8015			−1.58055			−0.790276	−	0.612751i	$-0.790063\pi$
$113$	−16.8015			−1.58055			−0.790276	+	0.612751i	$0.790063\pi$
$114$		0			0
$115$	−1.80637	+	0.748222i	−0.168445	+	0.0697720i
$116$	−8.38198	−	5.90101i	−0.778247	−	0.547895i
$117$		0			0
$118$	−13.2691	−	1.47031i	−1.22152	−	0.135353i
$119$	12.8137	−	12.8137i	1.17463	−	1.17463i
$120$		0			0
$121$	6.79340	+	6.79340i	0.617582	+	0.617582i
$122$	−0.164424	−	0.205403i	−0.0148862	−	0.0185964i
$123$		0			0
$124$	2.47117	+	3.90086i	0.221918	+	0.350308i
$125$	−3.02429	−	7.30128i	−0.270500	−	0.653046i
$126$		0			0
$127$			9.50016i			0.843003i	0.906828	+	0.421501i	$0.138497\pi$
$127$			9.50016i			0.843003i	−0.906828	+	0.421501i	$0.861503\pi$
$128$	−10.3958	+	4.46404i	−0.918866	+	0.394569i
$129$		0			0
$130$	−20.0074	+	5.80398i	−1.75476	+	0.509042i
$131$	19.3884	−	8.03093i	1.69397	−	0.701666i	0.694137	−	0.719843i	$-0.255786\pi$
$131$	19.3884	−	8.03093i	1.69397	−	0.701666i	0.999835	+	0.0181772i	$0.00578631\pi$
$132$		0			0
$133$	11.9454	−	28.8387i	1.03580	−	2.50063i
$134$	−0.448224	+	0.358800i	−0.0387206	+	0.0309956i
$135$		0			0
$136$	−8.01388	−	7.08235i	−0.687184	−	0.607306i
$137$	10.5560	+	10.5560i	0.901864	+	0.901864i	0.995597	−	0.0937337i	$-0.0298802\pi$
$137$	10.5560	+	10.5560i	0.901864	+	0.901864i	−0.0937337	+	0.995597i	$0.529880\pi$
$138$		0			0
$139$	−0.124526	+	0.300633i	−0.0105622	+	0.0254994i	−0.929073	−	0.369897i	$-0.879393\pi$
$139$	−0.124526	+	0.300633i	−0.0105622	+	0.0254994i	0.918510	+	0.395397i	$0.129393\pi$
$140$	−14.6155	+	20.7603i	−1.23523	+	1.75456i
$141$		0			0
$142$	−4.78645	+	8.69826i	−0.401670	+	0.729942i
$143$		−	25.2447i		−	2.11107i
$144$		0			0
$145$			13.5766i			1.12747i
$146$	−3.44017	−	1.89305i	−0.284710	−	0.156670i
$147$		0			0
$148$	0.269911	+	1.55388i	0.0221866	+	0.127728i
$149$	2.37298	−	5.72888i	0.194402	−	0.469328i	−0.796380	−	0.604797i	$-0.793254\pi$
$149$	2.37298	−	5.72888i	0.194402	−	0.469328i	0.990782	+	0.135469i	$0.0432542\pi$
$150$		0			0
$151$	−9.09870	−	9.09870i	−0.740442	−	0.740442i	0.232221	−	0.972663i	$-0.425401\pi$
$151$	−9.09870	−	9.09870i	−0.740442	−	0.740442i	−0.972663	+	0.232221i	$0.925401\pi$
$152$	−17.4222	−	5.98837i	−1.41312	−	0.485721i
$153$		0			0
$154$	−19.2270	−	24.0190i	−1.54936	−	1.93550i
$155$	2.34045	−	5.65035i	0.187989	−	0.453847i
$156$		0			0
$157$	14.6827	−	6.08178i	1.17181	−	0.485379i	0.290018	−	0.957021i	$-0.406339\pi$
$157$	14.6827	−	6.08178i	1.17181	−	0.485379i	0.881790	+	0.471642i	$0.156339\pi$
$158$	−3.22744	−	11.1256i	−0.256762	−	0.885104i
$159$		0			0
$160$	12.7605	+	7.85488i	1.00880	+	0.620983i
$161$			3.53740i			0.278786i
$162$		0			0
$163$	2.81351	+	6.79241i	0.220371	+	0.532023i	0.994940	−	0.100466i	$-0.0320334\pi$
$163$	2.81351	+	6.79241i	0.220371	+	0.532023i	−0.774569	+	0.632489i	$0.782033\pi$
$164$	14.1114	+	3.16617i	1.10192	+	0.247237i
$165$		0			0
$166$	13.9976	−	11.2049i	1.08642	−	0.869673i
$167$	−10.4693	−	10.4693i	−0.810140	−	0.810140i	0.174515	−	0.984655i	$-0.444164\pi$
$167$	−10.4693	−	10.4693i	−0.810140	−	0.810140i	−0.984655	+	0.174515i	$0.944164\pi$
$168$		0			0
$169$	−12.6753	+	12.6753i	−0.975026	+	0.975026i
$170$	−1.56001	+	14.0786i	−0.119647	+	1.07978i
$171$		0			0
$172$	−0.930417	−	5.35642i	−0.0709436	−	0.408423i
$173$	−14.7918	+	6.12697i	−1.12460	+	0.465825i	−0.865942	−	0.500144i	$-0.833280\pi$
$173$	−14.7918	+	6.12697i	−1.12460	+	0.465825i	−0.258658	+	0.965969i	$0.583280\pi$
$174$		0			0
$175$	9.66403			0.730532
$176$	−13.4499	+	12.1991i	−1.01382	+	0.919539i
$177$		0			0
$178$	11.5508	+	6.35612i	0.865766	+	0.476412i
$179$	−2.32212	−	5.60609i	−0.173563	−	0.419019i	0.813029	−	0.582223i	$-0.197817\pi$
$179$	−2.32212	−	5.60609i	−0.173563	−	0.419019i	−0.986592	+	0.163204i	$0.947817\pi$
$180$		0			0
$181$	9.25503	+	3.83356i	0.687921	+	0.284946i	0.699134	−	0.714991i	$-0.253569\pi$
$181$	9.25503	+	3.83356i	0.687921	+	0.284946i	−0.0112129	+	0.999937i	$0.503569\pi$
$182$	−4.15094	+	37.4610i	−0.307688	+	2.77679i
$183$		0			0
$184$	2.08377	−	0.128582i	0.153617	−	0.00947916i
$185$	1.47703	−	1.47703i	0.108593	−	0.108593i
$186$		0			0
$187$	−15.8584	−	6.56877i	−1.15968	−	0.480356i
$188$	−6.48098	−	10.2305i	−0.472674	−	0.746137i
$189$		0			0
$190$	6.79786	+	23.4335i	0.493168	+	1.70004i
$191$	−7.97826			−0.577287			−0.288643	−	0.957437i	$-0.593204\pi$
$191$	−7.97826			−0.577287			−0.288643	+	0.957437i	$0.593204\pi$
$192$		0			0
$193$	−11.9488			−0.860091			−0.430045	−	0.902807i	$-0.641502\pi$
$193$	−11.9488			−0.860091			−0.430045	+	0.902807i	$0.641502\pi$
$194$	−2.37507	−	8.18731i	−0.170520	−	0.587814i
$195$		0			0
$196$	17.0897	+	26.9769i	1.22070	+	1.92692i
$197$	4.88423	+	2.02312i	0.347987	+	0.144141i	0.549829	−	0.835277i	$-0.314693\pi$
$197$	4.88423	+	2.02312i	0.347987	+	0.144141i	−0.201842	+	0.979418i	$0.564693\pi$
$198$		0			0
$199$	15.8193	−	15.8193i	1.12140	−	1.12140i	0.129871	−	0.991531i	$-0.458544\pi$
$199$	15.8193	−	15.8193i	1.12140	−	1.12140i	0.991531	−	0.129871i	$-0.0414563\pi$
$200$	−0.351280	−	5.69277i	−0.0248392	−	0.402539i
$201$		0			0
$202$	0.294558	−	2.65829i	0.0207250	−	0.187037i
$203$	22.6934	+	9.39990i	1.59276	+	0.659743i
$204$		0			0
$205$	−7.33006	−	17.6963i	−0.511953	−	1.23596i
$206$	9.95461	+	5.47779i	0.693570	+	0.381656i
$207$		0			0
$208$	22.2179	+	1.08351i	1.54054	+	0.0751279i
$209$	−29.5676			−2.04524
$210$		0			0
$211$	−25.3944	+	10.5187i	−1.74823	+	0.724139i	−0.750207	+	0.661202i	$0.770046\pi$
$211$	−25.3944	+	10.5187i	−1.74823	+	0.724139i	−0.998018	+	0.0629360i	$0.979954\pi$
$212$	−3.03551	−	17.4754i	−0.208479	−	1.20022i
$213$		0			0
$214$	1.90540	−	17.1956i	0.130250	−	1.17547i
$215$	−5.09150	+	5.09150i	−0.347237	+	0.347237i
$216$		0			0
$217$	−7.82417	−	7.82417i	−0.531139	−	0.531139i
$218$	7.59428	−	6.07916i	0.514349	−	0.411733i
$219$		0			0
$220$	23.4659	+	5.26502i	1.58207	+	0.354967i
$221$	8.04697	+	19.4271i	0.541298	+	1.30681i
$222$		0			0
$223$		−	11.8736i		−	0.795117i	−0.917577	−	0.397558i	$-0.869858\pi$
$223$		−	11.8736i		−	0.795117i	0.917577	−	0.397558i	$-0.130142\pi$
$224$	21.9644	−	15.8908i	1.46756	−	1.06175i
$225$		0			0
$226$	−6.61992	−	22.8201i	−0.440351	−	1.51797i
$227$	−16.0487	+	6.64758i	−1.06519	+	0.441215i	−0.845290	−	0.534308i	$-0.820572\pi$
$227$	−16.0487	+	6.64758i	−1.06519	+	0.441215i	−0.219898	+	0.975523i	$0.570572\pi$
$228$		0			0
$229$	−0.190035	+	0.458786i	−0.0125579	+	0.0303174i	−0.930034	−	0.367473i	$-0.880223\pi$
$229$	−0.190035	+	0.458786i	−0.0125579	+	0.0303174i	0.917476	+	0.397791i	$0.130223\pi$
$230$	−1.72797	−	2.15864i	−0.113939	−	0.142336i
$231$		0			0
$232$	4.71229	−	13.7096i	0.309377	−	0.900079i
$233$	4.46281	+	4.46281i	0.292369	+	0.292369i	0.838015	−	0.545647i	$-0.183716\pi$
$233$	4.46281	+	4.46281i	0.292369	+	0.292369i	−0.545647	+	0.838015i	$0.683716\pi$
$234$		0			0
$235$	−6.13813	+	14.8188i	−0.400408	+	0.966670i
$236$	−3.23113	−	18.6017i	−0.210329	−	1.21087i
$237$		0			0
$238$	22.4524	+	12.3551i	1.45538	+	0.800860i
$239$		−	8.12218i		−	0.525380i	−0.964880	−	0.262690i	$-0.915390\pi$
$239$		−	8.12218i		−	0.525380i	0.964880	−	0.262690i	$-0.0846096\pi$
$240$		0			0
$241$			3.91627i			0.252269i	0.992013	+	0.126135i	$0.0402571\pi$
$241$			3.91627i			0.252269i	−0.992013	+	0.126135i	$0.959743\pi$
$242$	−6.55027	+	11.9036i	−0.421067	+	0.765191i
$243$		0			0
$244$	0.214198	−	0.304254i	0.0137126	−	0.0194779i
$245$	16.1857	−	39.0757i	1.03407	−	2.49646i
$246$		0			0
$247$	25.6124	+	25.6124i	1.62968	+	1.62968i
$248$	−4.32456	+	4.89337i	−0.274610	+	0.310729i
$249$		0			0
$250$	8.72513	−	6.98440i	0.551826	−	0.441733i
$251$	−3.33165	+	8.04332i	−0.210292	+	0.507690i	−0.993468	−	0.114110i	$-0.963598\pi$
$251$	−3.33165	+	8.04332i	−0.210292	+	0.507690i	0.783176	+	0.621800i	$0.213598\pi$
$252$		0			0
$253$	3.09568	−	1.28227i	0.194624	−	0.0806157i
$254$	−12.9033	+	3.74314i	−0.809625	+	0.234865i
$255$		0			0
$256$	−10.1592	−	12.3609i	−0.634948	−	0.772555i
$257$		−	4.79986i		−	0.299407i	−0.988731	−	0.149704i	$-0.952168\pi$
$257$		−	4.79986i		−	0.299407i	0.988731	−	0.149704i	$-0.0478319\pi$
$258$		0			0
$259$	−1.44623	−	3.49151i	−0.0898643	−	0.216952i
$260$	−15.7661	−	24.8876i	−0.977774	−	1.54346i
$261$		0			0
$262$	18.5469	+	23.1694i	1.14583	+	1.43141i
$263$	6.41988	+	6.41988i	0.395867	+	0.395867i	0.876772	−	0.480906i	$-0.159692\pi$
$263$	6.41988	+	6.41988i	0.395867	+	0.395867i	−0.480906	+	0.876772i	$0.659692\pi$
$264$		0			0
$265$	−16.6111	+	16.6111i	−1.02041	+	1.02041i
$266$	43.8758	+	4.86176i	2.69020	+	0.298093i
$267$		0			0
$268$	−0.663932	−	0.467416i	−0.0405561	−	0.0285520i
$269$	24.9505	−	10.3349i	1.52126	−	0.630127i	0.543418	−	0.839462i	$-0.317130\pi$
$269$	24.9505	−	10.3349i	1.52126	−	0.630127i	0.977844	+	0.209335i	$0.0671299\pi$
$270$		0			0
$271$	−13.2069			−0.802264			−0.401132	−	0.916020i	$-0.631383\pi$
$271$	−13.2069			−0.802264			−0.401132	+	0.916020i	$0.631383\pi$
$272$	6.46184	−	13.6751i	0.391807	−	0.829175i
$273$		0			0
$274$	−10.1782	+	18.4966i	−0.614890	+	1.11742i
$275$	−3.50311	−	8.45726i	−0.211246	−	0.509992i
$276$		0			0
$277$	24.2560	+	10.0471i	1.45740	+	0.603675i	0.963946	−	0.266098i	$-0.0857344\pi$
$277$	24.2560	+	10.0471i	1.45740	+	0.603675i	0.493453	+	0.869772i	$0.335734\pi$
$278$	−0.457390	−	0.0506821i	−0.0274324	−	0.00303971i
$279$		0			0
$280$	−33.9556	−	11.6713i	−2.02924	−	0.697493i
$281$	−4.07978	+	4.07978i	−0.243379	+	0.243379i	−0.818247	−	0.574867i	$-0.805054\pi$
$281$	−4.07978	+	4.07978i	−0.243379	+	0.243379i	0.574867	+	0.818247i	$0.305054\pi$
$282$		0			0
$283$	22.5628	+	9.34580i	1.34122	+	0.555550i	0.933834	−	0.357707i	$-0.116441\pi$
$283$	22.5628	+	9.34580i	1.34122	+	0.555550i	0.407383	+	0.913257i	$0.366441\pi$
$284$	−13.7000	−	3.07387i	−0.812948	−	0.182400i
$285$		0			0
$286$	34.2878	−	9.94661i	2.02748	−	0.588156i
$287$	−34.6546			−2.04560
$288$		0			0
$289$	−2.70227			−0.158957
$290$	−18.4399	+	5.34928i	−1.08283	+	0.314120i
$291$		0			0
$292$	1.21572	−	5.41837i	0.0711444	−	0.317086i
$293$	−18.8574	−	7.81101i	−1.10166	−	0.456324i	−0.243604	−	0.969875i	$-0.578330\pi$
$293$	−18.8574	−	7.81101i	−1.10166	−	0.456324i	−0.858059	+	0.513551i	$0.828330\pi$
$294$		0			0
$295$	−17.6817	+	17.6817i	−1.02947	+	1.02947i
$296$	−2.00416	+	0.978841i	−0.116490	+	0.0568940i
$297$		0			0
$298$	8.71604	+	0.965800i	0.504907	+	0.0559473i
$299$	−3.79231	−	1.57083i	−0.219315	−	0.0908433i
$300$		0			0
$301$	4.98533	+	12.0357i	0.287350	+	0.693724i
$302$	8.77306	−	15.9430i	0.504833	−	0.917416i
$303$		0			0
$304$	1.26905	−	26.0226i	0.0727851	−	1.49250i
$305$	−0.492811			−0.0282182
$306$		0			0
$307$	−8.73142	+	3.61667i	−0.498328	+	0.206414i	−0.617668	−	0.786439i	$-0.711922\pi$
$307$	−8.73142	+	3.61667i	−0.498328	+	0.206414i	0.119339	+	0.992854i	$0.461922\pi$
$308$	25.0474	−	35.5781i	1.42721	−	2.02725i
$309$		0			0
$310$	8.59656	+	0.952560i	0.488252	+	0.0541018i
$311$	1.57810	−	1.57810i	0.0894860	−	0.0894860i	−0.660947	−	0.750433i	$-0.729845\pi$
$311$	1.57810	−	1.57810i	0.0894860	−	0.0894860i	0.750433	+	0.660947i	$0.229845\pi$
$312$		0			0
$313$	−11.4730	−	11.4730i	−0.648492	−	0.648492i	0.304137	−	0.952628i	$-0.401632\pi$
$313$	−11.4730	−	11.4730i	−0.648492	−	0.648492i	−0.952628	+	0.304137i	$0.901632\pi$
$314$	14.0455	+	17.5461i	0.792633	+	0.990182i
$315$		0			0
$316$	13.8393	−	8.76714i	0.778524	−	0.493190i
$317$	9.79160	+	23.6390i	0.549951	+	1.32770i	0.917515	+	0.397701i	$0.130192\pi$
$317$	9.79160	+	23.6390i	0.549951	+	1.32770i	−0.367564	+	0.929998i	$0.619808\pi$
$318$		0			0
$319$		−	23.2670i		−	1.30270i
$320$	−5.64092	+	20.4264i	−0.315337	+	1.14187i
$321$		0			0
$322$	−4.80456	+	1.39376i	−0.267748	+	0.0776714i
$323$	22.7538	−	9.42495i	1.26606	−	0.524418i
$324$		0			0
$325$	−4.29144	+	10.3604i	−0.238046	+	0.574694i
$326$	−8.11703	+	6.49762i	−0.449561	+	0.359870i
$327$		0			0
$328$	1.25967	+	20.4139i	0.0695535	+	1.12717i
$329$	20.5199	+	20.5199i	1.13130	+	1.13130i
$330$		0			0
$331$	0.460135	−	1.11086i	0.0252913	−	0.0610586i	−0.910729	−	0.413004i	$-0.864480\pi$
$331$	0.460135	−	1.11086i	0.0252913	−	0.0610586i	0.936021	+	0.351945i	$0.114480\pi$
$332$	20.7339	+	14.5969i	1.13792	+	0.801110i
$333$		0			0
$334$	10.0946	−	18.3446i	0.552353	−	1.00377i
$335$			1.07539i			0.0587550i
$336$		0			0
$337$			28.2686i			1.53989i	0.638110	+	0.769945i	$0.279716\pi$
$337$			28.2686i			1.53989i	−0.638110	+	0.769945i	$0.720284\pi$
$338$	−22.2101	−	12.2217i	−1.20807	−	0.664773i
$339$		0			0
$340$	−19.7365	+	3.42825i	−1.07036	+	0.185923i
$341$	−4.01097	+	9.68333i	−0.217206	+	0.524382i
$342$		0			0
$343$	−30.3878	−	30.3878i	−1.64079	−	1.64079i
$344$	6.90860	−	3.37418i	0.372487	−	0.181924i
$345$		0			0
$346$	−14.1498	−	17.6764i	−0.760701	−	0.950291i
$347$	3.19400	−	7.71101i	0.171463	−	0.413949i	−0.814666	−	0.579931i	$-0.803080\pi$
$347$	3.19400	−	7.71101i	0.171463	−	0.413949i	0.986129	+	0.165982i	$0.0530795\pi$
$348$		0			0
$349$	−15.0741	+	6.24391i	−0.806900	+	0.334229i	−0.747716	−	0.664018i	$-0.768850\pi$
$349$	−15.0741	+	6.24391i	−0.806900	+	0.334229i	−0.0591837	+	0.998247i	$0.518850\pi$
$350$	3.80771	+	13.1259i	0.203531	+	0.701607i
$351$		0			0
$352$	−21.8684	−	13.4614i	−1.16559	−	0.717494i
$353$		−	25.0652i		−	1.33409i	−0.745019	−	0.667043i	$-0.767560\pi$
$353$		−	25.0652i		−	1.33409i	0.745019	−	0.667043i	$-0.232440\pi$
$354$		0			0
$355$	7.11636	+	17.1804i	0.377697	+	0.911841i
$356$	−4.08191	+	18.1928i	−0.216341	+	0.964218i
$357$		0			0
$358$	6.69936	−	5.36279i	0.354072	−	0.283432i
$359$	12.3171	+	12.3171i	0.650069	+	0.650069i	0.953010	−	0.302940i	$-0.0979682\pi$
$359$	12.3171	+	12.3171i	0.650069	+	0.650069i	−0.302940	+	0.953010i	$0.597968\pi$
$360$		0			0
$361$	16.5633	−	16.5633i	0.871751	−	0.871751i
$362$	−1.56025	+	14.0808i	−0.0820051	+	0.740070i
$363$		0			0
$364$	−52.5157	+	9.12204i	−2.75257	+	0.478125i
$365$	−6.79486	+	2.81452i	−0.355659	+	0.147319i
$366$		0			0
$367$	1.24387			0.0649297			0.0324649	−	0.999473i	$-0.489664\pi$
$367$	1.24387			0.0649297			0.0324649	+	0.999473i	$0.489664\pi$
$368$	0.995663	+	2.77955i	0.0519025	+	0.144894i
$369$		0			0
$370$	2.58809	+	1.42417i	0.134548	+	0.0740389i
$371$	16.2648	+	39.2666i	0.844424	+	2.03862i
$372$		0			0
$373$	−14.2613	−	5.90724i	−0.738424	−	0.305865i	−0.0184154	−	0.999830i	$-0.505862\pi$
$373$	−14.2613	−	5.90724i	−0.738424	−	0.305865i	−0.720009	+	0.693965i	$0.755862\pi$
$374$	2.67348	−	24.1273i	0.138242	−	1.24759i
$375$		0			0
$376$	11.3417	−	12.8335i	0.584905	−	0.661837i
$377$	−20.1546	+	20.1546i	−1.03801	+	1.03801i
$378$		0			0
$379$	−6.21100	−	2.57268i	−0.319037	−	0.132150i	0.217417	−	0.976079i	$-0.430237\pi$
$379$	−6.21100	−	2.57268i	−0.319037	−	0.132150i	−0.536455	+	0.843929i	$0.680237\pi$
$380$	−29.1494	+	18.4659i	−1.49533	+	0.947283i
$381$		0			0
$382$	−3.14350	−	10.8362i	−0.160835	−	0.554429i
$383$	−13.6072			−0.695296			−0.347648	−	0.937625i	$-0.613020\pi$
$383$	−13.6072			−0.695296			−0.347648	+	0.937625i	$0.613020\pi$
$384$		0			0
$385$	−57.6271			−2.93695
$386$	−4.70791	−	16.2290i	−0.239626	−	0.826036i
$387$		0			0
$388$	10.1844	−	6.45173i	0.517032	−	0.327537i
$389$	−2.68660	−	1.11283i	−0.136216	−	0.0564226i	0.313534	−	0.949577i	$-0.398487\pi$
$389$	−2.68660	−	1.11283i	−0.136216	−	0.0564226i	−0.449750	+	0.893154i	$0.648487\pi$
$390$		0			0
$391$	−1.97355	+	1.97355i	−0.0998067	+	0.0998067i
$392$	−29.9071	+	33.8407i	−1.51054	+	1.70921i
$393$		0			0
$394$	−0.823406	+	7.43098i	−0.0414826	+	0.374367i
$395$	−20.0461	−	8.30336i	−1.00863	−	0.417788i
$396$		0			0
$397$	2.81875	+	6.80507i	0.141469	+	0.341537i	0.978695	−	0.205321i	$-0.0658239\pi$
$397$	2.81875	+	6.80507i	0.141469	+	0.341537i	−0.837226	+	0.546858i	$0.815824\pi$
$398$	27.7190	+	15.2532i	1.38943	+	0.764572i
$399$		0			0
$400$	7.59362	−	2.72011i	0.379681	−	0.136006i
$401$	−33.3220			−1.66402			−0.832012	−	0.554758i	$-0.812811\pi$
$401$	−33.3220			−1.66402			−0.832012	+	0.554758i	$0.812811\pi$
$402$		0			0
$403$	11.8624	−	4.91358i	0.590909	−	0.244763i
$404$	3.72660	−	0.647315i	0.185405	−	0.0322051i
$405$		0			0
$406$	−3.82575	+	34.5262i	−0.189869	+	1.71351i
$407$	−2.53127	+	2.53127i	−0.125470	+	0.125470i
$408$		0			0
$409$	8.50034	+	8.50034i	0.420315	+	0.420315i	0.885312	−	0.464997i	$-0.153945\pi$
$409$	8.50034	+	8.50034i	0.420315	+	0.420315i	−0.464997	+	0.885312i	$0.653945\pi$
$410$	21.1474	−	16.9283i	1.04439	−	0.836030i
$411$		0			0
$412$	−3.51785	+	15.6788i	−0.173312	+	0.772440i
$413$	17.3130	+	41.7972i	0.851915	+	2.05671i
$414$		0			0
$415$		−	33.5834i		−	1.64855i
$416$	7.28240	+	30.6037i	0.357049	+	1.50047i
$417$		0			0
$418$	−11.6499	−	40.1593i	−0.569815	−	1.96426i
$419$	8.90474	−	3.68846i	0.435025	−	0.180193i	−0.154414	−	0.988006i	$-0.549349\pi$
$419$	8.90474	−	3.68846i	0.435025	−	0.180193i	0.589439	+	0.807813i	$0.299349\pi$
$420$		0			0
$421$	−9.24819	+	22.3271i	−0.450729	+	1.08816i	0.521316	+	0.853363i	$0.325441\pi$
$421$	−9.24819	+	22.3271i	−0.450729	+	1.08816i	−0.972045	+	0.234793i	$0.924559\pi$
$422$	−24.2923	−	30.3467i	−1.18253	−	1.47726i
$423$		0			0
$424$	22.5395	−	11.0083i	1.09461	−	0.534613i
$425$	5.39166	+	5.39166i	0.261534	+	0.261534i
$426$		0			0
$427$	−0.341203	+	0.823738i	−0.0165120	+	0.0398635i
$428$	24.1062	−	4.18727i	1.16522	−	0.202399i
$429$		0			0
$430$	−8.92146	−	4.90928i	−0.430231	−	0.236746i
$431$		−	34.2686i		−	1.65066i	−0.564650	−	0.825331i	$-0.690989\pi$
$431$		−	34.2686i		−	1.65066i	0.564650	−	0.825331i	$-0.309011\pi$
$432$		0			0
$433$		−	0.323021i		−	0.0155234i	−0.999970	−	0.00776171i	$-0.997529\pi$
$433$		−	0.323021i		−	0.0155234i	0.999970	−	0.00776171i	$-0.00247065\pi$
$434$	7.54415	−	13.7097i	0.362131	−	0.658088i
$435$		0			0
$436$	11.2490	+	7.91945i	0.538731	+	0.379273i
$437$	−1.83982	+	4.44171i	−0.0880104	+	0.212476i
$438$		0			0
$439$	−1.22080	−	1.22080i	−0.0582654	−	0.0582654i	0.677374	−	0.735639i	$-0.263118\pi$
$439$	−1.22080	−	1.22080i	−0.0582654	−	0.0582654i	−0.735639	+	0.677374i	$0.763118\pi$
$440$	2.09470	+	33.9462i	0.0998608	+	1.61832i
$441$		0			0
$442$	−23.2157	+	18.5840i	−1.10426	+	0.883950i
$443$	3.37120	−	8.13880i	0.160171	−	0.386686i	−0.823337	−	0.567553i	$-0.807890\pi$
$443$	3.37120	−	8.13880i	0.160171	−	0.386686i	0.983508	+	0.180867i	$0.0578903\pi$
$444$		0			0
$445$	22.8145	−	9.45009i	1.08151	−	0.447977i
$446$	16.1270	−	4.67830i	0.763635	−	0.221524i
$447$		0			0
$448$	30.2374	+	23.5713i	1.42858	+	1.11364i
$449$			4.83707i			0.228276i	0.993465	+	0.114138i	$0.0364105\pi$
$449$			4.83707i			0.228276i	−0.993465	+	0.114138i	$0.963589\pi$
$450$		0			0
$451$	12.5620	+	30.3272i	0.591519	+	1.42805i
$452$	28.3864	−	17.9826i	1.33518	−	0.845831i
$453$		0			0
$454$	−15.3522	−	19.1784i	−0.720513	−	0.900087i
$455$	49.9183	+	49.9183i	2.34021	+	2.34021i
$456$		0			0
$457$	−7.23423	+	7.23423i	−0.338403	+	0.338403i	−0.855766	−	0.517363i	$-0.826914\pi$
$457$	−7.23423	+	7.23423i	−0.338403	+	0.338403i	0.517363	+	0.855766i	$0.326914\pi$
$458$	−0.698006	−	0.0773441i	−0.0326157	−	0.00361405i
$459$		0			0
$460$	2.25106	−	3.19748i	0.104956	−	0.149083i
$461$	4.04570	−	1.67578i	0.188427	−	0.0780490i	−0.286475	−	0.958088i	$-0.592484\pi$
$461$	4.04570	−	1.67578i	0.188427	−	0.0780490i	0.474902	+	0.880039i	$0.342484\pi$
$462$		0			0
$463$	−39.1299			−1.81852			−0.909261	−	0.416227i	$-0.863352\pi$
$463$	−39.1299			−1.81852			−0.909261	+	0.416227i	$0.863352\pi$
$464$	20.4773	+	0.998625i	0.950635	+	0.0463600i
$465$		0			0
$466$	−4.30309	+	7.81986i	−0.199337	+	0.362248i
$467$	−2.71550	−	6.55579i	−0.125658	−	0.303366i	0.848514	−	0.529173i	$-0.177498\pi$
$467$	−2.71550	−	6.55579i	−0.125658	−	0.303366i	−0.974172	+	0.225808i	$0.927498\pi$
$468$		0			0
$469$	1.79753	+	0.744561i	0.0830022	+	0.0343807i
$470$	−22.5456	−	2.49821i	−1.03995	−	0.115234i
$471$		0			0
$472$	23.9921	−	11.7178i	1.10432	−	0.539356i
$473$	8.72560	−	8.72560i	0.401204	−	0.401204i
$474$		0			0
$475$	12.1346	+	5.02631i	0.556773	+	0.230623i
$476$	−7.93444	+	35.3633i	−0.363674	+	1.62087i
$477$		0			0
$478$	11.0317	−	3.20020i	0.504578	−	0.146374i
$479$	−19.3768			−0.885349			−0.442674	−	0.896682i	$-0.645970\pi$
$479$	−19.3768			−0.885349			−0.442674	+	0.896682i	$0.645970\pi$
$480$		0			0
$481$	4.38533			0.199954
$482$	−5.31915	+	1.54304i	−0.242281	+	0.0702837i
$483$		0			0
$484$	−18.7485	−	4.20659i	−0.852206	−	0.191209i
$485$	−14.7519	−	6.11044i	−0.669849	−	0.277461i
$486$		0			0
$487$	−28.1905	+	28.1905i	−1.27743	+	1.27743i	−0.335334	+	0.942099i	$0.608849\pi$
$487$	−28.1905	+	28.1905i	−1.27743	+	1.27743i	−0.942099	+	0.335334i	$0.891151\pi$
$488$	0.497640	+	0.171050i	0.0225271	+	0.00774305i
$489$		0			0
$490$	59.4507	+	6.58756i	2.68571	+	0.297596i
$491$	21.4812	+	8.89781i	0.969434	+	0.401553i	0.810501	−	0.585737i	$-0.199195\pi$
$491$	21.4812	+	8.89781i	0.969434	+	0.401553i	0.158933	+	0.987289i	$0.449195\pi$
$492$		0			0
$493$	7.41655	+	17.9051i	0.334025	+	0.806407i
$494$	−24.6957	+	44.8787i	−1.11111	+	2.01919i
$495$		0			0
$496$	−8.35017	−	3.94567i	−0.374934	−	0.177166i
$497$	33.6443			1.50915
$498$		0			0
$499$	24.2391	−	10.0402i	1.08509	−	0.449459i	0.232798	−	0.972525i	$-0.425212\pi$
$499$	24.2391	−	10.0402i	1.08509	−	0.449459i	0.852292	+	0.523066i	$0.175212\pi$
$500$	12.9241	+	9.09873i	0.577984	+	0.406907i
$501$		0			0
$502$	−12.2373	−	1.35598i	−0.546177	−	0.0605203i
$503$	−8.27072	+	8.27072i	−0.368773	+	0.368773i	−0.867030	−	0.498256i	$-0.833974\pi$
$503$	−8.27072	+	8.27072i	−0.368773	+	0.368773i	0.498256	+	0.867030i	$0.333974\pi$
$504$		0			0
$505$	−3.54229	−	3.54229i	−0.157630	−	0.157630i
$506$	2.96133	+	3.69938i	0.131647	+	0.164458i
$507$		0			0
$508$	−10.1680	−	16.0507i	−0.451132	−	0.712133i
$509$	−14.1181	−	34.0841i	−0.625774	−	1.51075i	−0.844827	−	0.535039i	$-0.820297\pi$
$509$	−14.1181	−	34.0841i	−0.625774	−	1.51075i	0.219054	−	0.975713i	$-0.429703\pi$
$510$		0			0
$511$			13.3063i			0.588638i
$512$	12.7860	−	18.6686i	0.565066	−	0.825046i
$513$		0			0
$514$	6.51926	−	1.89118i	0.287552	−	0.0834166i
$515$	19.6619	−	8.14422i	0.866406	−	0.358877i
$516$		0			0
$517$	10.5193	−	25.3958i	0.462637	−	1.11691i
$518$	4.17240	−	3.33998i	0.183325	−	0.146750i
$519$		0			0
$520$	27.5908	−	31.2198i	1.20994	−	1.36908i
$521$	6.11354	+	6.11354i	0.267839	+	0.267839i	0.828229	−	0.560390i	$-0.189349\pi$
$521$	6.11354	+	6.11354i	0.267839	+	0.267839i	−0.560390	+	0.828229i	$0.689349\pi$
$522$		0			0
$523$	−10.2211	+	24.6760i	−0.446939	+	1.07901i	0.526524	+	0.850160i	$0.323495\pi$
$523$	−10.2211	+	24.6760i	−0.446939	+	1.07901i	−0.973463	+	0.228846i	$0.926505\pi$
$524$	−24.1615	+	34.3197i	−1.05550	+	1.49926i
$525$		0			0
$526$	−6.19012	+	11.2491i	−0.269902	+	0.490483i
$527$		−	8.73036i		−	0.380300i
$528$		0			0
$529$			22.4552i			0.976312i
$530$	−29.1065	−	16.0166i	−1.26430	−	0.695718i
$531$		0			0
$532$	10.6841	+	61.5086i	0.463215	+	2.66673i
$533$	15.3888	−	37.1519i	0.666564	−	1.60923i
$534$		0			0
$535$	−22.9139	−	22.9139i	−0.990655	−	0.990655i
$536$	0.373258	−	1.08593i	0.0161223	−	0.0469051i
$537$		0			0
$538$	23.8677	+	29.8163i	1.02901	+	1.28547i
$539$	−27.7384	+	66.9664i	−1.19478	+	2.88445i
$540$		0			0
$541$	−26.2040	+	10.8540i	−1.12660	+	0.466652i	−0.866623	−	0.498964i	$-0.833714\pi$
$541$	−26.2040	+	10.8540i	−1.12660	+	0.466652i	−0.259974	+	0.965616i	$0.583714\pi$
$542$	−5.20364	−	17.9379i	−0.223515	−	0.770498i
$543$		0			0
$544$	21.1198	+	3.38849i	0.905504	+	0.145280i
$545$		−	18.2204i		−	0.780478i
$546$		0			0
$547$	−2.86307	−	6.91207i	−0.122416	−	0.295539i	0.850777	−	0.525526i	$-0.176131\pi$
$547$	−2.86307	−	6.91207i	−0.122416	−	0.295539i	−0.973194	+	0.229987i	$0.926131\pi$
$548$	−29.1327	−	6.53648i	−1.24449	−	0.279225i
$549$		0			0
$550$	10.1066	−	8.09022i	0.430945	−	0.344968i
$551$	23.6058	+	23.6058i	1.00564	+	1.00564i
$552$		0			0
$553$	−27.7583	+	27.7583i	−1.18040	+	1.18040i
$554$	−4.08918	+	36.9035i	−0.173733	+	1.56788i
$555$		0			0
$556$	−0.111378	−	0.641205i	−0.00472348	−	0.0271931i
$557$	9.83837	−	4.07519i	0.416865	−	0.172671i	−0.164385	−	0.986396i	$-0.552564\pi$
$557$	9.83837	−	4.07519i	0.416865	−	0.172671i	0.581250	+	0.813725i	$0.302564\pi$
$558$		0			0
$559$	−15.1168			−0.639371
$560$	2.47337	−	50.7177i	0.104519	−	2.14322i
$561$		0			0
$562$	−7.14870	−	3.93377i	−0.301550	−	0.165936i
$563$	−1.54232	−	3.72350i	−0.0650012	−	0.156927i	0.888041	−	0.459764i	$-0.152066\pi$
$563$	−1.54232	−	3.72350i	−0.0650012	−	0.156927i	−0.953042	+	0.302837i	$0.902066\pi$
$564$		0			0
$565$	−41.1173	−	17.0313i	−1.72982	−	0.716513i
$566$	−3.80373	+	34.3275i	−0.159883	+	1.44289i
$567$		0			0
$568$	−1.22294	−	19.8188i	−0.0513136	−	0.831577i
$569$	8.57127	−	8.57127i	0.359327	−	0.359327i	−0.504238	−	0.863565i	$-0.668227\pi$
$569$	8.57127	−	8.57127i	0.359327	−	0.359327i	0.863565	+	0.504238i	$0.168227\pi$
$570$		0			0
$571$	−26.2074	−	10.8554i	−1.09674	−	0.454286i	−0.240390	−	0.970676i	$-0.577275\pi$
$571$	−26.2074	−	10.8554i	−1.09674	−	0.454286i	−0.856353	+	0.516390i	$0.827275\pi$
$572$	27.0194	+	42.6513i	1.12974	+	1.78334i
$573$		0			0
$574$	−13.6542	−	47.0686i	−0.569916	−	1.96460i
$575$	−1.48845			−0.0620725
$576$		0			0
$577$	40.8448			1.70039			0.850196	−	0.526466i	$-0.176483\pi$
$577$	40.8448			1.70039			0.850196	+	0.526466i	$0.176483\pi$
$578$	−1.06472	−	3.67027i	−0.0442863	−	0.152663i
$579$		0			0
$580$	−14.5310	−	22.9378i	−0.603366	−	0.952441i
$581$	−56.1350	−	23.2519i	−2.32887	−	0.964651i
$582$		0			0
$583$	28.4675	−	28.4675i	1.17900	−	1.17900i
$584$	7.83834	−	0.483675i	0.324353	−	0.0200146i
$585$		0			0
$586$	3.17907	−	28.6901i	0.131326	−	1.18518i
$587$	−30.3985	−	12.5915i	−1.25468	−	0.519705i	−0.346407	−	0.938084i	$-0.612598\pi$
$587$	−30.3985	−	12.5915i	−1.25468	−	0.519705i	−0.908273	+	0.418379i	$0.862598\pi$
$588$		0			0
$589$	−5.75498	−	13.8938i	−0.237130	−	0.572482i
$590$	−30.9823	−	17.0488i	−1.27552	−	0.701890i
$591$		0			0
$592$	−2.11914	−	2.33642i	−0.0870960	−	0.0960264i
$593$	5.64301			0.231731			0.115865	−	0.993265i	$-0.463036\pi$
$593$	5.64301			0.231731			0.115865	+	0.993265i	$0.463036\pi$
$594$		0			0
$595$	44.3470	−	18.3691i	1.81805	−	0.753062i
$596$	2.12242	+	12.2188i	0.0869379	+	0.500502i
$597$		0			0
$598$	0.639325	−	5.76971i	0.0261439	−	0.235941i
$599$	−5.75089	+	5.75089i	−0.234975	+	0.234975i	−0.814766	−	0.579790i	$-0.803134\pi$
$599$	−5.75089	+	5.75089i	−0.234975	+	0.234975i	0.579790	+	0.814766i	$0.303134\pi$
$600$		0			0
$601$	−22.4340	−	22.4340i	−0.915102	−	0.915102i	0.0815662	−	0.996668i	$-0.474008\pi$
$601$	−22.4340	−	22.4340i	−0.915102	−	0.915102i	−0.996668	+	0.0815662i	$0.974008\pi$
$602$	−14.3828	+	11.5133i	−0.586199	+	0.469248i
$603$		0			0
$604$	25.1107	+	5.63407i	1.02174	+	0.229247i
$605$	9.73875	+	23.5114i	0.395936	+	0.955875i
$606$		0			0
$607$			7.67228i			0.311408i	0.987804	+	0.155704i	$0.0497647\pi$
$607$			7.67228i			0.311408i	−0.987804	+	0.155704i	$0.950235\pi$
$608$	35.8443	−	8.52945i	1.45368	−	0.345915i
$609$		0			0
$610$	−0.194171	−	0.669344i	−0.00786177	−	0.0271010i
$611$	−31.1107	+	12.8865i	−1.25861	+	0.521332i
$612$		0			0
$613$	−3.65989	+	8.83576i	−0.147822	+	0.356873i	−0.980395	−	0.197042i	$-0.936867\pi$
$613$	−3.65989	+	8.83576i	−0.147822	+	0.356873i	0.832573	+	0.553915i	$0.186867\pi$
$614$	−8.35248	−	10.4342i	−0.337079	−	0.421089i
$615$		0			0
$616$	58.1918	+	20.0018i	2.34461	+	0.805895i
$617$	7.16767	+	7.16767i	0.288560	+	0.288560i	0.836511	−	0.547951i	$-0.184592\pi$
$617$	7.16767	+	7.16767i	0.288560	+	0.288560i	−0.547951	+	0.836511i	$0.684592\pi$
$618$		0			0
$619$	−13.8565	+	33.4525i	−0.556939	+	1.34457i	0.355239	+	0.934776i	$0.384400\pi$
$619$	−13.8565	+	33.4525i	−0.556939	+	1.34457i	−0.912178	+	0.409794i	$0.865600\pi$
$620$	2.09333	+	12.0513i	0.0840701	+	0.483993i
$621$		0			0
$622$	2.76519	+	1.52162i	0.110874	+	0.0610115i
$623$		−	44.6776i		−	1.78997i
$624$		0			0
$625$		−	31.0163i		−	1.24065i
$626$	11.0624	−	20.1033i	0.442141	−	0.803488i
$627$		0			0
$628$	−18.2973	+	25.9901i	−0.730144	+	1.03712i
$629$	1.14108	−	2.75481i	0.0454979	−	0.109842i
$630$		0			0
$631$	4.00538	+	4.00538i	0.159452	+	0.159452i	0.782324	−	0.622872i	$-0.214034\pi$
$631$	4.00538	+	4.00538i	0.159452	+	0.159452i	−0.622872	+	0.782324i	$0.714034\pi$
$632$	17.3605	+	15.3425i	0.690564	+	0.610293i
$633$		0			0
$634$	−28.2490	+	22.6131i	−1.12191	+	0.898081i
$635$	−9.63012	+	23.2492i	−0.382160	+	0.922615i
$636$		0			0
$637$	82.0361	−	33.9805i	3.25039	−	1.34636i
$638$	31.6016	−	9.16737i	1.25112	−	0.362940i
$639$		0			0
$640$	−29.9661	+	0.386566i	−1.18451	+	0.0152804i
$641$			0.320061i			0.0126416i	0.999980	+	0.00632082i	$0.00201199\pi$
$641$			0.320061i			0.0126416i	−0.999980	+	0.00632082i	$0.997988\pi$
$642$		0			0
$643$	15.3875	+	37.1487i	0.606824	+	1.46500i	0.866435	+	0.499289i	$0.166405\pi$
$643$	15.3875	+	37.1487i	0.606824	+	1.46500i	−0.259612	+	0.965713i	$0.583595\pi$
$644$	−3.78607	−	5.97649i	−0.149192	−	0.235507i
$645$		0			0
$646$	21.7663	+	27.1912i	0.856385	+	1.06982i
$647$	11.1884	+	11.1884i	0.439863	+	0.439863i	0.891966	−	0.452103i	$-0.149326\pi$
$647$	11.1884	+	11.1884i	0.439863	+	0.439863i	−0.452103	+	0.891966i	$0.649326\pi$
$648$		0			0
$649$	30.3021	−	30.3021i	1.18946	−	1.18946i
$650$	−15.7626	−	1.74661i	−0.618260	−	0.0685077i
$651$		0			0
$652$	−12.0234	−	8.46459i	−0.470871	−	0.331499i
$653$	44.2880	−	18.3447i	1.73312	−	0.717884i	0.733870	−	0.679290i	$-0.237712\pi$
$653$	44.2880	−	18.3447i	1.73312	−	0.717884i	0.999255	−	0.0385936i	$-0.0122878\pi$
$654$		0			0
$655$	55.5888			2.17203
$656$	−27.2302	+	9.75415i	−1.06316	+	0.380836i
$657$		0			0
$658$	−19.7855	+	35.9555i	−0.771319	+	1.40169i
$659$	−7.81320	−	18.8627i	−0.304359	−	0.734788i	−0.999868	−	0.0162701i	$-0.994821\pi$
$659$	−7.81320	−	18.8627i	−0.304359	−	0.734788i	0.695509	−	0.718518i	$-0.255179\pi$
$660$		0			0
$661$	−19.8609	−	8.22666i	−0.772500	−	0.319980i	−0.0386153	−	0.999254i	$-0.512295\pi$
$661$	−19.8609	−	8.22666i	−0.772500	−	0.319980i	−0.733885	+	0.679274i	$0.762295\pi$
$662$	1.69009	+	0.187274i	0.0656873	+	0.00727863i
$663$		0			0
$664$	−11.6565	+	33.9125i	−0.452359	+	1.31606i
$665$	58.4664	−	58.4664i	2.26723	−	2.26723i
$666$		0			0
$667$	−3.49521	−	1.44776i	−0.135335	−	0.0560577i
$668$	28.8934	+	6.48278i	1.11792	+	0.250826i
$669$		0			0
$670$	−1.46062	+	0.423714i	−0.0564286	+	0.0163695i
$671$	0.844558			0.0326038
$672$		0			0
$673$	43.3143			1.66964			0.834821	−	0.550522i	$-0.185571\pi$
$673$	43.3143			1.66964			0.834821	+	0.550522i	$0.185571\pi$
$674$	−38.3950	+	11.1381i	−1.47892	+	0.429022i
$675$		0			0
$676$	7.84879	−	34.9816i	0.301876	−	1.34545i
$677$	39.7727	+	16.4744i	1.52859	+	0.633162i	0.979290	−	0.202465i	$-0.0648951\pi$
$677$	39.7727	+	16.4744i	1.52859	+	0.633162i	0.549298	+	0.835626i	$0.314895\pi$
$678$		0			0
$679$	−20.4273	+	20.4273i	−0.783928	+	0.783928i
$680$	−12.4326	−	25.4557i	−0.476770	−	0.976181i
$681$		0			0
$682$	−14.7324	−	1.63246i	−0.564134	−	0.0625101i
$683$	−5.40622	−	2.23933i	−0.206863	−	0.0856856i	0.276846	−	0.960914i	$-0.410711\pi$
$683$	−5.40622	−	2.23933i	−0.206863	−	0.0856856i	−0.483709	+	0.875229i	$0.660711\pi$
$684$		0			0
$685$	15.1327	+	36.5336i	0.578191	+	1.39588i
$686$	29.3003	−	53.2464i	1.11869	−	2.03296i
$687$		0			0
$688$	7.30492	+	8.05393i	0.278498	+	0.307053i
$689$	−49.3188			−1.87890
$690$		0			0
$691$	−17.4054	+	7.20955i	−0.662132	+	0.274264i	−0.688336	−	0.725392i	$-0.741658\pi$
$691$	−17.4054	+	7.20955i	−0.662132	+	0.274264i	0.0262032	+	0.999657i	$0.491658\pi$
$692$	18.4333	−	26.1832i	0.700729	−	0.995338i
$693$		0			0
$694$	11.7317	+	1.29996i	0.445329	+	0.0493457i
$695$	−0.609492	+	0.609492i	−0.0231193	+	0.0231193i
$696$		0			0
$697$	−19.3342	−	19.3342i	−0.732333	−	0.732333i
$698$	−14.4199	−	18.0138i	−0.545802	−	0.681833i
$699$		0			0
$700$	−16.3275	+	10.3434i	−0.617123	+	0.390944i
$701$	−10.6696	−	25.7586i	−0.402984	−	0.972889i	−0.986938	−	0.161102i	$-0.948495\pi$
$701$	−10.6696	−	25.7586i	−0.402984	−	0.972889i	0.583954	−	0.811787i	$-0.301505\pi$
$702$		0			0
$703$		−	5.13628i		−	0.193719i
$704$	9.66717	−	35.0059i	0.364345	−	1.31934i
$705$		0			0
$706$	34.0440	−	9.87589i	1.28126	−	0.371684i
$707$	−8.37351	+	3.46842i	−0.314918	+	0.130443i
$708$		0			0
$709$	−0.671243	+	1.62052i	−0.0252091	+	0.0608601i	−0.935983	−	0.352046i	$-0.885486\pi$
$709$	−0.671243	+	1.62052i	−0.0252091	+	0.0608601i	0.910774	+	0.412906i	$0.135486\pi$
$710$	−20.5308	+	16.4348i	−0.770509	+	0.616787i
$711$		0			0
$712$	−26.3181	+	1.62400i	−0.986314	+	0.0608618i
$713$	1.20507	+	1.20507i	0.0451303	+	0.0451303i
$714$		0			0
$715$	25.5900	−	61.7798i	0.957013	−	2.31043i
$716$	9.92344	+	6.98622i	0.370857	+	0.261087i
$717$		0			0
$718$	−11.8762	+	21.5823i	−0.443217	+	0.805443i
$719$			22.7818i			0.849618i	0.905283	+	0.424809i	$0.139659\pi$
$719$			22.7818i			0.849618i	−0.905283	+	0.424809i	$0.860341\pi$
$720$		0			0
$721$		−	38.5038i		−	1.43396i
$722$	29.0226	+	15.9705i	1.08011	+	0.594359i
$723$		0			0
$724$	−19.7396	+	3.42878i	−0.733615	+	0.127430i
$725$	−3.95523	+	9.54878i	−0.146894	+	0.354633i
$726$		0			0
$727$	12.5833	+	12.5833i	0.466688	+	0.466688i	0.900840	−	0.434152i	$-0.142952\pi$
$727$	12.5833	+	12.5833i	0.466688	+	0.466688i	−0.434152	+	0.900840i	$0.642952\pi$
$728$	−33.0813	−	67.7336i	−1.22608	−	2.51038i
$729$		0			0
$730$	−6.49997	−	8.11996i	−0.240575	−	0.300533i
$731$	−3.93344	+	9.49617i	−0.145484	+	0.351229i
$732$		0			0
$733$	35.2843	−	14.6152i	1.30326	−	0.539826i	0.380347	−	0.924844i	$-0.375805\pi$
$733$	35.2843	−	14.6152i	1.30326	−	0.539826i	0.922909	+	0.385017i	$0.125805\pi$
$734$	0.490096	+	1.68945i	0.0180898	+	0.0623588i
$735$		0			0
$736$	−3.38294	+	2.44749i	−0.124697	+	0.0902158i
$737$		−	1.84296i		−	0.0678865i
$738$		0			0
$739$	14.2438	+	34.3875i	0.523965	+	1.26496i	0.935421	+	0.353535i	$0.115020\pi$
$739$	14.2438	+	34.3875i	0.523965	+	1.26496i	−0.411456	+	0.911430i	$0.634980\pi$
$740$	−0.914602	+	4.07632i	−0.0336214	+	0.149849i
$741$		0			0
$742$	−46.9242	+	37.5624i	−1.72264	+	1.37896i
$743$	5.48927	+	5.48927i	0.201382	+	0.201382i	0.800592	−	0.599210i	$-0.204519\pi$
$743$	5.48927	+	5.48927i	0.201382	+	0.201382i	−0.599210	+	0.800592i	$0.704519\pi$
$744$		0			0
$745$	11.6145	−	11.6145i	0.425522	−	0.425522i
$746$	2.40424	−	21.6975i	0.0880255	−	0.794402i
$747$		0			0
$748$	33.8236	−	5.87519i	1.23671	−	0.214818i
$749$	−54.1656	+	22.4361i	−1.97917	+	0.819798i
$750$		0			0
$751$	13.1151			0.478576			0.239288	−	0.970949i	$-0.423086\pi$
$751$	13.1151			0.478576			0.239288	+	0.970949i	$0.423086\pi$
$752$	21.8994	+	10.3480i	0.798590	+	0.377354i
$753$		0			0
$754$	−35.3153	−	19.4332i	−1.28611	−	0.707717i
$755$	−13.0435	−	31.4899i	−0.474702	−	1.14603i
$756$		0			0
$757$	24.2944	+	10.0631i	0.882994	+	0.365748i	0.777657	−	0.628689i	$-0.216408\pi$
$757$	24.2944	+	10.0631i	0.882994	+	0.365748i	0.105337	+	0.994437i	$0.466408\pi$
$758$	1.04708	−	9.44955i	0.0380316	−	0.343223i
$759$		0			0
$760$	−36.5659	−	32.3155i	−1.32638	−	1.17220i
$761$	10.1791	−	10.1791i	0.368993	−	0.368993i	−0.498117	−	0.867110i	$-0.665975\pi$
$761$	10.1791	−	10.1791i	0.368993	−	0.368993i	0.867110	+	0.498117i	$0.165975\pi$
$762$		0			0
$763$	−30.4556	−	12.6151i	−1.10257	−	0.456699i
$764$	13.4794	−	8.53912i	0.487667	−	0.308934i
$765$		0			0
$766$	−5.36135	−	18.4816i	−0.193713	−	0.667766i
$767$	−52.4972			−1.89557
$768$		0			0
$769$	10.7380			0.387221			0.193611	−	0.981078i	$-0.437980\pi$
$769$	10.7380			0.387221			0.193611	+	0.981078i	$0.437980\pi$
$770$	−22.7055	−	78.2701i	−0.818250	−	2.82066i
$771$		0			0
$772$	20.1876	−	12.7887i	0.726568	−	0.460277i
$773$	27.6103	+	11.4366i	0.993073	+	0.411344i	0.819252	−	0.573433i	$-0.194389\pi$
$773$	27.6103	+	11.4366i	0.993073	+	0.411344i	0.173820	+	0.984777i	$0.444389\pi$
$774$		0			0
$775$	3.29221	−	3.29221i	0.118260	−	0.118260i
$776$	12.7756	+	11.2905i	0.458617	+	0.405307i
$777$		0			0
$778$	0.452920	−	4.08746i	0.0162380	−	0.146543i
$779$	−43.5139	−	18.0240i	−1.55905	−	0.645778i
$780$		0			0
$781$	−12.1957	−	29.4431i	−0.436397	−	1.05356i
$782$	−3.45811	−	1.90292i	−0.123662	−	0.0680482i
$783$		0			0
$784$	−57.7467	−	27.2868i	−2.06238	−	0.974530i
$785$	42.0971			1.50251
$786$		0			0
$787$	−6.96385	+	2.88452i	−0.248234	+	0.102822i	−0.503331	−	0.864093i	$-0.667893\pi$
$787$	−6.96385	+	2.88452i	−0.248234	+	0.102822i	0.255097	+	0.966915i	$0.417893\pi$
$788$	−10.4173	+	1.80950i	−0.371102	+	0.0644608i
$789$		0			0
$790$	3.37946	−	30.4986i	0.120236	−	1.08509i
$791$	−56.9361	+	56.9361i	−2.02441	+	2.02441i
$792$		0			0
$793$	−0.731582	−	0.731582i	−0.0259793	−	0.0259793i
$794$	−8.13216	+	6.50973i	−0.288600	+	0.231022i
$795$		0			0
$796$	−9.79559	+	43.6584i	−0.347196	+	1.54743i
$797$	2.21940	+	5.35811i	0.0786152	+	0.189794i	0.958301	−	0.285762i	$-0.0922468\pi$
$797$	2.21940	+	5.35811i	0.0786152	+	0.189794i	−0.879685	+	0.475556i	$0.842247\pi$
$798$		0			0
$799$			22.8965i			0.810020i
$800$	6.68645	+	9.24204i	0.236402	+	0.326756i
$801$		0			0
$802$	−13.1292	−	45.2586i	−0.463607	−	1.59814i
$803$	11.6448	−	4.82342i	0.410935	−	0.170215i
$804$		0			0
$805$	−3.58579	+	8.65686i	−0.126382	+	0.305114i
$806$	11.3476	+	14.1758i	0.399702	+	0.499320i
$807$		0			0
$808$	2.34751	+	4.80649i	0.0825850	+	0.169092i
$809$	15.3959	+	15.3959i	0.541290	+	0.541290i	0.923907	−	0.382617i	$-0.124977\pi$
$809$	15.3959	+	15.3959i	0.541290	+	0.541290i	−0.382617	+	0.923907i	$0.624977\pi$
$810$		0			0
$811$	−10.0739	+	24.3205i	−0.353742	+	0.854009i	0.642409	+	0.766362i	$0.277935\pi$
$811$	−10.0739	+	24.3205i	−0.353742	+	0.854009i	−0.996152	+	0.0876474i	$0.972065\pi$
$812$	−48.4015	+	8.40739i	−1.69856	+	0.295042i
$813$		0			0
$814$	−4.43536	−	2.44068i	−0.155459	−	0.0855458i
$815$			19.4746i			0.682167i
$816$		0			0
$817$			17.7054i			0.619433i
$818$	−8.19612	+	14.8945i	−0.286570	+	0.520775i
$819$		0			0
$820$	31.3246	+	22.0529i	1.09390	+	0.770119i
$821$	2.78461	−	6.72263i	0.0971834	−	0.234622i	−0.867810	−	0.496897i	$-0.834473\pi$
$821$	2.78461	−	6.72263i	0.0971834	−	0.234622i	0.964993	+	0.262275i	$0.0844728\pi$
$822$		0			0
$823$	12.2411	+	12.2411i	0.426697	+	0.426697i	0.887502	−	0.460805i	$-0.152439\pi$
$823$	12.2411	+	12.2411i	0.426697	+	0.426697i	−0.460805	+	0.887502i	$0.652439\pi$
$824$	−22.6813	+	1.39958i	−0.790142	+	0.0487567i
$825$		0			0
$826$	−49.9483	+	39.9832i	−1.73792	+	1.39119i
$827$	1.55210	−	3.74709i	0.0539716	−	0.130299i	−0.894594	−	0.446880i	$-0.852535\pi$
$827$	1.55210	−	3.74709i	0.0539716	−	0.130299i	0.948565	+	0.316581i	$0.102535\pi$
$828$		0			0
$829$	−43.2888	+	17.9308i	−1.50348	+	0.622763i	−0.974201	−	0.225682i	$-0.927539\pi$
$829$	−43.2888	+	17.9308i	−1.50348	+	0.622763i	−0.529283	+	0.848446i	$0.677539\pi$
$830$	45.6136	−	13.2321i	1.58327	−	0.459294i
$831$		0			0
$832$	−38.6972	+	21.9492i	−1.34158	+	0.760952i
$833$		−	60.3760i		−	2.09190i
$834$		0			0
$835$	−15.0084	−	36.2335i	−0.519387	−	1.25391i
$836$	49.9550	−	31.6462i	1.72773	−	1.09451i
$837$		0			0
$838$	8.51828	+	10.6413i	0.294259	+	0.367597i
$839$	−17.0010	−	17.0010i	−0.586938	−	0.586938i	0.349863	−	0.936801i	$-0.386228\pi$
$839$	−17.0010	−	17.0010i	−0.586938	−	0.586938i	−0.936801	+	0.349863i	$0.886228\pi$
$840$		0			0
$841$	1.93051	−	1.93051i	0.0665691	−	0.0665691i
$842$	−33.9689	−	3.76400i	−1.17065	−	0.129716i
$843$		0			0
$844$	31.6461	−	44.9512i	1.08930	−	1.54728i
$845$	−43.8683	+	18.1709i	−1.50912	+	0.625097i
$846$		0			0
$847$	46.0423			1.58203
$848$	23.8325	+	26.2761i	0.818411	+	0.902326i
$849$		0			0
$850$	−5.19869	+	9.44741i	−0.178314	+	0.324043i
$851$	0.222747	+	0.537759i	0.00763567	+	0.0184341i
$852$		0			0
$853$	39.7985	+	16.4851i	1.36267	+	0.564438i	0.939792	−	0.341746i	$-0.111018\pi$
$853$	39.7985	+	16.4851i	1.36267	+	0.564438i	0.422882	+	0.906185i	$0.361018\pi$
$854$	−1.25325	−	0.138869i	−0.0428854	−	0.00475201i
$855$		0			0
$856$	15.1853	+	31.0916i	0.519022	+	1.06269i
$857$	40.7725	−	40.7725i	1.39276	−	1.39276i	0.573690	−	0.819073i	$-0.305512\pi$
$857$	40.7725	−	40.7725i	1.39276	−	1.39276i	0.819073	−	0.573690i	$-0.194488\pi$
$858$		0			0
$859$	18.6301	+	7.71683i	0.635650	+	0.263295i	0.677152	−	0.735844i	$-0.263214\pi$
$859$	18.6301	+	7.71683i	0.635650	+	0.263295i	−0.0415015	+	0.999138i	$0.513214\pi$
$860$	3.15274	−	14.0516i	0.107508	−	0.479155i
$861$		0			0
$862$	46.5443	−	13.5021i	1.58530	−	0.459884i
$863$	18.0443			0.614237			0.307118	−	0.951671i	$-0.400635\pi$
$863$	18.0443			0.614237			0.307118	+	0.951671i	$0.400635\pi$
$864$		0			0
$865$	−42.4099			−1.44198
$866$	0.438734	−	0.127273i	0.0149088	−	0.00432491i
$867$		0			0
$868$	21.5932	+	4.84486i	0.732923	+	0.164445i
$869$	34.3542	+	14.2300i	1.16539	+	0.482718i
$870$		0			0
$871$	−1.59643	+	1.59643i	−0.0540931	+	0.0540931i
$872$	−6.32413	+	18.3990i	−0.214162	+	0.623068i
$873$		0			0
$874$	−6.75772	−	0.748804i	−0.228583	−	0.0253287i
$875$	−34.9908	−	14.4936i	−1.18290	−	0.489975i
$876$		0			0
$877$	−15.6405	−	37.7594i	−0.528141	−	1.27505i	−0.932739	−	0.360551i	$-0.882589\pi$
$877$	−15.6405	−	37.7594i	−0.528141	−	1.27505i	0.404598	−	0.914494i	$-0.367411\pi$
$878$	1.17710	−	2.13911i	0.0397254	−	0.0721915i
$879$		0			0
$880$	−45.2811	+	16.2201i	−1.52642	+	0.546781i
$881$	−37.5483			−1.26503			−0.632517	−	0.774546i	$-0.717978\pi$
$881$	−37.5483			−1.26503			−0.632517	+	0.774546i	$0.717978\pi$
$882$		0			0
$883$	11.9128	−	4.93445i	0.400898	−	0.166058i	−0.173118	−	0.984901i	$-0.555384\pi$
$883$	11.9128	−	4.93445i	0.400898	−	0.166058i	0.574017	+	0.818843i	$0.305384\pi$
$884$	−34.3883	−	24.2097i	−1.15660	−	0.814262i
$885$		0			0
$886$	12.3826	+	1.37208i	0.416000	+	0.0460958i
$887$	4.91841	−	4.91841i	0.165144	−	0.165144i	−0.619697	−	0.784841i	$-0.712744\pi$
$887$	4.91841	−	4.91841i	0.165144	−	0.165144i	0.784841	+	0.619697i	$0.212744\pi$
$888$		0			0
$889$	32.1937	+	32.1937i	1.07974	+	1.07974i
$890$	21.8244	+	27.2637i	0.731556	+	0.913882i
$891$		0			0
$892$	12.7083	+	20.0607i	0.425506	+	0.671681i
$893$	15.0932	+	36.4382i	0.505074	+	1.21936i
$894$		0			0
$895$		−	16.0733i		−	0.537272i
$896$	−20.1012	+	50.3562i	−0.671535	+	1.68228i
$897$		0			0
$898$	−6.56980	+	1.90585i	−0.219237	+	0.0635989i
$899$	10.9331	−	4.52863i	0.364639	−	0.151038i
$900$		0			0
$901$	−12.8329	+	30.9815i	−0.427528	+	1.03214i
$902$	−36.2415	+	29.0111i	−1.20671	+	0.965962i
$903$		0			0
$904$	35.6088	+	31.4696i	1.18433	+	1.04666i
$905$	18.7633	+	18.7633i	0.623712	+	0.623712i
$906$		0			0
$907$	20.9645	−	50.6128i	0.696115	−	1.68057i	−0.0359677	−	0.999353i	$-0.511451\pi$
$907$	20.9645	−	50.6128i	0.696115	−	1.68057i	0.732082	−	0.681216i	$-0.238549\pi$
$908$	19.9996	−	28.4081i	0.663710	−	0.942755i
$909$		0			0
$910$	−48.1318	+	87.4682i	−1.59555	+	2.89954i
$911$			35.8156i			1.18662i	0.804973	+	0.593312i	$0.202180\pi$
$911$			35.8156i			1.18662i	−0.804973	+	0.593312i	$0.797820\pi$
$912$		0			0
$913$			57.5539i			1.90476i
$914$	−12.6760	−	6.97532i	−0.419285	−	0.230723i
$915$		0			0
$916$	−0.169970	−	0.978519i	−0.00561597	−	0.0323312i
$917$	38.4876	−	92.9173i	1.27097	−	3.06840i
$918$		0			0
$919$	−11.8886	−	11.8886i	−0.392168	−	0.392168i	0.483291	−	0.875459i	$-0.339441\pi$
$919$	−11.8886	−	11.8886i	−0.392168	−	0.392168i	−0.875459	+	0.483291i	$0.839441\pi$
$920$	5.22982	+	1.79760i	0.172422	+	0.0592652i
$921$		0			0
$922$	3.87012	+	4.83467i	0.127456	+	0.159221i
$923$	−14.9402	+	36.0688i	−0.491762	+	1.18722i
$924$		0			0
$925$	1.46914	−	0.608536i	0.0483049	−	0.0200085i
$926$	−15.4175	−	53.1470i	−0.506650	−	1.74652i
$927$		0			0
$928$	6.71188	+	28.2061i	0.220328	+	0.925912i
$929$			36.9856i			1.21346i	0.794908	+	0.606730i	$0.207519\pi$
$929$			36.9856i			1.21346i	−0.794908	+	0.606730i	$0.792481\pi$
$930$		0			0
$931$	−39.7994	−	96.0841i	−1.30437	−	3.14903i
$932$	−12.3165	−	2.76345i	−0.403442	−	0.0905198i
$933$		0			0
$934$	7.83427	−	6.27127i	0.256345	−	0.205202i
$935$	−32.1507	−	32.1507i	−1.05144	−	1.05144i
$936$		0			0
$937$	−6.76308	+	6.76308i	−0.220940	+	0.220940i	−0.808894	−	0.587954i	$-0.799934\pi$
$937$	−6.76308	+	6.76308i	−0.220940	+	0.220940i	0.587954	+	0.808894i	$0.299934\pi$
$938$	−0.303036	+	2.73480i	−0.00989446	+	0.0892945i
$939$		0			0
$940$	−5.49003	−	31.6062i	−0.179065	−	1.03088i
$941$	−1.86301	+	0.771684i	−0.0607324	+	0.0251562i	−0.412843	−	0.910802i	$-0.635464\pi$
$941$	−1.86301	+	0.771684i	−0.0607324	+	0.0251562i	0.352110	+	0.935958i	$0.385464\pi$
$942$		0			0
$943$	5.33748			0.173812
$944$	25.3684	+	27.9696i	0.825671	+	0.910331i
$945$		0			0
$946$	15.2892	+	8.41332i	0.497096	+	0.273541i
$947$	5.04250	+	12.1737i	0.163859	+	0.395591i	0.984388	−	0.176015i	$-0.0563207\pi$
$947$	5.04250	+	12.1737i	0.163859	+	0.395591i	−0.820528	+	0.571606i	$0.806321\pi$
$948$		0			0
$949$	−14.2652	−	5.90885i	−0.463069	−	0.191810i
$950$	−2.04570	+	18.4618i	−0.0663713	+	0.598981i
$951$		0			0
$952$	−51.1573	+	3.15673i	−1.65802	+	0.102310i
$953$	−3.83903	+	3.83903i	−0.124358	+	0.124358i	−0.766547	−	0.642188i	$-0.778027\pi$
$953$	−3.83903	+	3.83903i	−0.124358	+	0.124358i	0.642188	+	0.766547i	$0.278027\pi$
$954$		0			0
$955$	−19.5247	−	8.08740i	−0.631805	−	0.261702i
$956$	8.69315	+	13.7225i	0.281157	+	0.443819i
$957$		0			0
$958$	−7.63462	−	26.3179i	−0.246663	−	0.850294i
$959$	71.5436			2.31026
$960$		0			0
$961$	25.6691			0.828037
$962$	1.72786	+	5.95624i	0.0557083	+	0.192037i
$963$		0			0
$964$	−4.19158	−	6.61660i	−0.135002	−	0.213106i
$965$	−29.2415	−	12.1122i	−0.941316	−	0.389906i
$966$		0			0
$967$	20.0812	−	20.0812i	0.645767	−	0.645767i	−0.306200	−	0.951967i	$-0.599058\pi$
$967$	20.0812	−	20.0812i	0.645767	−	0.645767i	0.951967	+	0.306200i	$0.0990578\pi$
$968$	−1.67360	−	27.1220i	−0.0537916	−	0.871735i
$969$		0			0
$970$	2.48694	−	22.4439i	0.0798508	−	0.720629i
$971$	20.3039	+	8.41013i	0.651582	+	0.269894i	0.683891	−	0.729584i	$-0.260286\pi$
$971$	20.3039	+	8.41013i	0.651582	+	0.269894i	−0.0323095	+	0.999478i	$0.510286\pi$
$972$		0			0
$973$	0.596782	+	1.44076i	0.0191320	+	0.0461887i
$974$	−49.3961	−	27.1816i	−1.58275	−	0.870954i
$975$		0			0
$976$	−0.0362487	+	0.743298i	−0.00116029	+	0.0237924i
$977$	−26.6502			−0.852616			−0.426308	−	0.904578i	$-0.640186\pi$
$977$	−26.6502			−0.852616			−0.426308	+	0.904578i	$0.640186\pi$
$978$		0			0
$979$	−39.0986	+	16.1952i	−1.24960	+	0.517600i
$980$	14.4767	+	83.3425i	0.462441	+	2.66228i
$981$		0			0
$982$	−3.62140	+	32.6820i	−0.115564	+	1.04292i
$983$	25.5264	−	25.5264i	0.814167	−	0.814167i	−0.171089	−	0.985256i	$-0.554729\pi$
$983$	25.5264	−	25.5264i	0.814167	−	0.814167i	0.985256	+	0.171089i	$0.0547285\pi$
$984$		0			0
$985$	9.90210	+	9.90210i	0.315507	+	0.315507i
$986$	−21.3969	+	17.1281i	−0.681417	+	0.545469i
$987$		0			0
$988$	−70.6854	−	15.8596i	−2.24880	−	0.504562i
$989$	−0.767837	−	1.85372i	−0.0244158	−	0.0589449i
$990$		0			0
$991$		−	40.2503i		−	1.27859i	−0.768961	−	0.639296i	$-0.779226\pi$
$991$		−	40.2503i		−	1.27859i	0.768961	−	0.639296i	$-0.220774\pi$
$992$	2.06905	−	12.8960i	0.0656925	−	0.409448i
$993$		0			0
$994$	13.2561	+	45.6963i	0.420459	+	1.44940i
$995$	54.7494	−	22.6779i	1.73567	−	0.718939i
$996$		0			0
$997$	17.7030	−	42.7389i	0.560661	−	1.35356i	−0.348577	−	0.937280i	$-0.613335\pi$
$997$	17.7030	−	42.7389i	0.560661	−	1.35356i	0.909238	−	0.416276i	$-0.136665\pi$
$998$	23.1871	+	28.9661i	0.733975	+	0.916905i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.w.a.107.20	yes	128
3.2	odd	2	inner	864.2.w.a.107.13	✓	128
32.3	odd	8	inner	864.2.w.a.323.13	yes	128
96.35	even	8	inner	864.2.w.a.323.20	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
864.2.w.a.107.13	✓	128	3.2	odd	2	inner
864.2.w.a.107.20	yes	128	1.1	even	1	trivial
864.2.w.a.323.13	yes	128	32.3	odd	8	inner
864.2.w.a.323.20	yes	128	96.35	even	8	inner

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.394008 + 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(2.44724 + 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(-2.11938 - 1.87302i) q^{8} +O(q^{10})\)	\(q+(0.394008 + 1.35822i) q^{2} +(-1.68952 + 1.07030i) q^{4} +(2.44724 + 1.01368i) q^{5} +(3.38875 - 3.38875i) q^{7} +(-2.11938 - 1.87302i) q^{8} +(-0.412566 + 3.72328i) q^{10} +(-4.19398 - 1.73720i) q^{11} +(2.12813 + 5.13777i) q^{13} +(5.93786 + 3.26747i) q^{14} +(1.70892 - 3.61657i) q^{16} +3.78123 q^{17} +(6.01757 - 2.49256i) q^{19} +(-5.21959 + 0.906648i) q^{20} +(0.707039 - 6.38081i) q^{22} +(-0.521933 + 0.521933i) q^{23} +(1.42590 + 1.42590i) q^{25} +(-6.13971 + 4.91479i) q^{26} +(-2.09837 + 9.35232i) q^{28} +(1.96141 + 4.73526i) q^{29} -2.30887i q^{31} +(5.58542 + 0.896134i) q^{32} +(1.48984 + 5.13574i) q^{34} +(11.7282 - 4.85798i) q^{35} +(0.301775 - 0.728548i) q^{37} +(5.75641 + 7.19109i) q^{38} +(-3.28799 - 6.73211i) q^{40} +(-5.11319 - 5.11319i) q^{41} +(-1.04025 + 2.51140i) q^{43} +(8.94511 - 1.55378i) q^{44} +(-0.914544 - 0.503253i) q^{46} +6.05530i q^{47} -15.9673i q^{49} +(-1.37487 + 2.49850i) q^{50} +(-9.09446 - 6.40260i) q^{52} +(-3.39385 + 8.19348i) q^{53} +(-8.50270 - 8.50270i) q^{55} +(-13.5293 + 0.834842i) q^{56} +(-5.65871 + 4.52976i) q^{58} +(-3.61257 + 8.72153i) q^{59} +(-0.171884 + 0.0711965i) q^{61} +(3.13594 - 0.909712i) q^{62} +(0.983556 + 7.93931i) q^{64} +14.7306i q^{65} +(0.155362 + 0.375078i) q^{67} +(-6.38845 + 4.04705i) q^{68} +(11.2192 + 14.0154i) q^{70} +(4.96412 + 4.96412i) q^{71} +(-1.96331 + 1.96331i) q^{73} +(1.10843 + 0.122822i) q^{74} +(-7.49899 + 10.6518i) q^{76} +(-20.0993 + 8.32540i) q^{77} -8.19131 q^{79} +(7.84819 - 7.11831i) q^{80} +(4.93019 - 8.95946i) q^{82} +(-4.85181 - 11.7133i) q^{83} +(9.25358 + 3.83296i) q^{85} +(-3.82089 - 0.423382i) q^{86} +(5.63482 + 11.5372i) q^{88} +(6.59205 - 6.59205i) q^{89} +(24.6223 + 10.1989i) q^{91} +(0.323190 - 1.44044i) q^{92} +(-8.22442 + 2.38584i) q^{94} +17.2531 q^{95} -6.02797 q^{97} +(21.6870 - 6.29123i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q+O(q^{10}) \) 128 * q	\( 128 q - 16 q^{10} + 32 q^{16} + 16 q^{22} - 32 q^{40} - 32 q^{46} + 16 q^{52} - 32 q^{55} - 32 q^{58} - 64 q^{61} - 48 q^{64} - 64 q^{67} + 96 q^{70} - 32 q^{76} + 64 q^{79} - 80 q^{82} - 80 q^{88} + 96 q^{91} - 144 q^{94}+O(q^{100}) \) 128 * q - 16 * q^10 + 32 * q^16 + 16 * q^22 - 32 * q^40 - 32 * q^46 + 16 * q^52 - 32 * q^55 - 32 * q^58 - 64 * q^61 - 48 * q^64 - 64 * q^67 + 96 * q^70 - 32 * q^76 + 64 * q^79 - 80 * q^82 - 80 * q^88 + 96 * q^91 - 144 * q^94

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