LMFDB - Embedded newform 1008.2.t.i.961.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(193,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("1008.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.t (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	10.0.991381711347.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 9x^{8} - 8x^{7} + 40x^{6} - 36x^{5} + 90x^{4} - 3x^{3} + 36x^{2} - 9x + 9 $ x^10 - 2x^9 + 9x^8 - 8x^7 + 40x^6 - 36x^5 + 90x^4 - 3x^3 + 36x^2 - 9*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 63)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.5
Root			$0.920620 + 1.59456i$ of defining polynomial
Character	$\chi$	$=$	1008.961
Dual form			1008.2.t.i.193.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.58800 - 0.691567i) q^{3} +1.33475 q^{5} +(2.54347 + 0.728536i) q^{7} +(2.04347 - 2.19641i) q^{9} +O(q^{10})$	\(q+(1.58800 - 0.691567i) q^{3} +1.33475 q^{5} +(2.54347 + 0.728536i) q^{7} +(2.04347 - 2.19641i) q^{9} -1.51302 q^{11} +(-2.58800 - 4.48254i) q^{13} +(2.11958 - 0.923072i) q^{15} +(0.774463 + 1.34141i) q^{17} +(1.25211 - 2.16872i) q^{19} +(4.54285 - 0.602068i) q^{21} +7.36079 q^{23} -3.21843 q^{25} +(1.72605 - 4.90110i) q^{27} +(-0.0309713 + 0.0536439i) q^{29} +(-1.92388 + 3.33227i) q^{31} +(-2.40267 + 1.04635i) q^{33} +(3.39490 + 0.972416i) q^{35} +(-0.281608 + 0.487760i) q^{37} +(-7.20971 - 5.32849i) q^{39} +(4.51188 + 7.81481i) q^{41} +(-5.09988 + 8.83325i) q^{43} +(2.72753 - 2.93167i) q^{45} +(-4.75925 - 8.24327i) q^{47} +(5.93847 + 3.70602i) q^{49} +(2.15752 + 1.59456i) q^{51} +(0.755374 + 1.30835i) q^{53} -2.01950 q^{55} +(0.488532 - 4.30983i) q^{57} +(-4.22166 + 7.31212i) q^{59} +(-1.61958 - 2.80520i) q^{61} +(6.79767 - 4.09777i) q^{63} +(-3.45434 - 5.98309i) q^{65} +(3.46670 - 6.00449i) q^{67} +(11.6889 - 5.09048i) q^{69} +12.3304 q^{71} +(-1.37936 - 2.38912i) q^{73} +(-5.11086 + 2.22576i) q^{75} +(-3.84831 - 1.10229i) q^{77} +(-2.95969 - 5.12633i) q^{79} +(-0.648467 - 8.97661i) q^{81} +(-2.80111 + 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(-0.0120840 + 0.106605i) q^{87} +(0.703287 - 1.21813i) q^{89} +(-3.31680 - 13.2867i) q^{91} +(-0.750637 + 6.62212i) q^{93} +(1.67126 - 2.89470i) q^{95} +(-6.09713 + 10.5605i) q^{97} +(-3.09180 + 3.32321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) $ 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9	$ 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) $ 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9 + 8 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 7 * q^27 + 7 * q^29 + 3 * q^31 - q^33 - 5 * q^35 - 20 * q^39 + 5 * q^41 + 7 * q^43 - q^45 - 27 * q^47 + 25 * q^49 - 24 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 - 30 * q^59 - 14 * q^61 + 35 * q^63 - 11 * q^65 + 2 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 - 31 * q^75 - 31 * q^77 + 4 * q^79 + 8 * q^81 - 9 * q^83 - 6 * q^85 - 32 * q^87 + 28 * q^89 + 4 * q^91 - 12 * q^93 + 14 * q^95 - 12 * q^97 - 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.58800	−	0.691567i	0.916831	−	0.399277i
$3$	1.58800	−	0.691567i	0.916831	−	0.399277i
$4$		0			0
$5$	1.33475			0.596920			0.298460	−	0.954422i	$-0.403527\pi$
$5$	1.33475			0.596920			0.298460	+	0.954422i	$0.403527\pi$
$6$		0			0
$7$	2.54347	+	0.728536i	0.961341	+	0.275361i
$7$	2.54347	+	0.728536i	0.961341	+	0.275361i
$8$		0			0
$9$	2.04347	−	2.19641i	0.681156	−	0.732138i
$10$		0			0
$11$	−1.51302			−0.456192			−0.228096	−	0.973639i	$-0.573250\pi$
$11$	−1.51302			−0.456192			−0.228096	+	0.973639i	$0.573250\pi$
$12$		0			0
$13$	−2.58800	−	4.48254i	−0.717781	−	1.24323i	−0.961877	−	0.273482i	$-0.911824\pi$
$13$	−2.58800	−	4.48254i	−0.717781	−	1.24323i	0.244096	−	0.969751i	$-0.421509\pi$
$14$		0			0
$15$	2.11958	−	0.923072i	0.547274	−	0.238336i
$16$		0			0
$17$	0.774463	+	1.34141i	0.187835	+	0.325340i	0.944528	−	0.328430i	$-0.106520\pi$
$17$	0.774463	+	1.34141i	0.187835	+	0.325340i	−0.756693	+	0.653770i	$0.773186\pi$
$18$		0			0
$19$	1.25211	−	2.16872i	0.287254	−	0.497538i	−0.685900	−	0.727696i	$-0.740591\pi$
$19$	1.25211	−	2.16872i	0.287254	−	0.497538i	0.973153	+	0.230158i	$0.0739244\pi$
$20$		0			0
$21$	4.54285	−	0.602068i	0.991332	−	0.131382i
$22$		0			0
$23$	7.36079			1.53483			0.767415	−	0.641151i	$-0.221543\pi$
$23$	7.36079			1.53483			0.767415	+	0.641151i	$0.221543\pi$
$24$		0			0
$25$	−3.21843			−0.643687
$26$		0			0
$27$	1.72605	−	4.90110i	0.332179	−	0.943216i
$28$		0			0
$29$	−0.0309713	+	0.0536439i	−0.00575123	+	0.00996143i	−0.868887	−	0.495011i	$-0.835164\pi$
$29$	−0.0309713	+	0.0536439i	−0.00575123	+	0.00996143i	0.863135	+	0.504972i	$0.168497\pi$
$30$		0			0
$31$	−1.92388	+	3.33227i	−0.345540	+	0.598493i	−0.985452	−	0.169956i	$-0.945638\pi$
$31$	−1.92388	+	3.33227i	−0.345540	+	0.598493i	0.639912	+	0.768448i	$0.278971\pi$
$32$		0			0
$33$	−2.40267	+	1.04635i	−0.418250	+	0.182147i
$34$		0			0
$35$	3.39490	+	0.972416i	0.573844	+	0.164368i
$36$		0			0
$37$	−0.281608	+	0.487760i	−0.0462961	+	0.0801872i	−0.888245	−	0.459370i	$-0.848075\pi$
$37$	−0.281608	+	0.487760i	−0.0462961	+	0.0801872i	0.841949	+	0.539557i	$0.181408\pi$
$38$		0			0
$39$	−7.20971	−	5.32849i	−1.15448	−	0.853241i
$40$		0			0
$41$	4.51188	+	7.81481i	0.704638	+	1.22047i	0.966822	+	0.255450i	$0.0822237\pi$
$41$	4.51188	+	7.81481i	0.704638	+	1.22047i	−0.262185	+	0.965018i	$0.584443\pi$
$42$		0			0
$43$	−5.09988	+	8.83325i	−0.777724	+	1.34706i	0.155526	+	0.987832i	$0.450293\pi$
$43$	−5.09988	+	8.83325i	−0.777724	+	1.34706i	−0.933251	+	0.359226i	$0.883041\pi$
$44$		0			0
$45$	2.72753	−	2.93167i	0.406596	−	0.437028i
$46$		0			0
$47$	−4.75925	−	8.24327i	−0.694209	−	1.20240i	−0.970447	−	0.241315i	$-0.922421\pi$
$47$	−4.75925	−	8.24327i	−0.694209	−	1.20240i	0.276238	−	0.961089i	$-0.410912\pi$
$48$		0			0
$49$	5.93847	+	3.70602i	0.848353	+	0.529431i
$50$		0			0
$51$	2.15752	+	1.59456i	0.302113	+	0.223283i
$52$		0			0
$53$	0.755374	+	1.30835i	0.103759	+	0.179715i	0.913230	−	0.407444i	$-0.133580\pi$
$53$	0.755374	+	1.30835i	0.103759	+	0.179715i	−0.809472	+	0.587159i	$0.800246\pi$
$54$		0			0
$55$	−2.01950			−0.272310
$56$		0			0
$57$	0.488532	−	4.30983i	0.0647077	−	0.570851i
$58$		0			0
$59$	−4.22166	+	7.31212i	−0.549613	+	0.951957i	0.448688	+	0.893688i	$0.351891\pi$
$59$	−4.22166	+	7.31212i	−0.549613	+	0.951957i	−0.998301	+	0.0582689i	$0.981442\pi$
$60$		0			0
$61$	−1.61958	−	2.80520i	−0.207367	−	0.359169i	0.743518	−	0.668716i	$-0.233156\pi$
$61$	−1.61958	−	2.80520i	−0.207367	−	0.359169i	−0.950884	+	0.309547i	$0.899823\pi$
$62$		0			0
$63$	6.79767	−	4.09777i	0.856426	−	0.516271i
$64$		0			0
$65$	−3.45434	−	5.98309i	−0.428458	−	0.742111i
$66$		0			0
$67$	3.46670	−	6.00449i	0.423524	−	0.733566i	−0.572757	−	0.819725i	$-0.694126\pi$
$67$	3.46670	−	6.00449i	0.423524	−	0.733566i	0.996281	+	0.0861595i	$0.0274595\pi$
$68$		0			0
$69$	11.6889	−	5.09048i	1.40718	−	0.612822i
$70$		0			0
$71$	12.3304			1.46335			0.731673	−	0.681656i	$-0.238740\pi$
$71$	12.3304			1.46335			0.731673	+	0.681656i	$0.238740\pi$
$72$		0			0
$73$	−1.37936	−	2.38912i	−0.161442	−	0.279625i	0.773944	−	0.633254i	$-0.218281\pi$
$73$	−1.37936	−	2.38912i	−0.161442	−	0.279625i	−0.935386	+	0.353629i	$0.884948\pi$
$74$		0			0
$75$	−5.11086	+	2.22576i	−0.590152	+	0.257009i
$76$		0			0
$77$	−3.84831	−	1.10229i	−0.438556	−	0.125617i
$78$		0			0
$79$	−2.95969	−	5.12633i	−0.332991	−	0.576758i	0.650106	−	0.759844i	$-0.274725\pi$
$79$	−2.95969	−	5.12633i	−0.332991	−	0.576758i	−0.983097	+	0.183086i	$0.941391\pi$
$80$		0			0
$81$	−0.648467	−	8.97661i	−0.0720519	−	0.997401i
$82$		0			0
$83$	−2.80111	+	4.85167i	−0.307462	+	0.532540i	−0.977806	−	0.209510i	$-0.932813\pi$
$83$	−2.80111	+	4.85167i	−0.307462	+	0.532540i	0.670344	+	0.742050i	$0.266146\pi$
$84$		0			0
$85$	1.03372	+	1.79045i	0.112122	+	0.194202i
$86$		0			0
$87$	−0.0120840	+	0.106605i	−0.00129554	+	0.0114293i
$88$		0			0
$89$	0.703287	−	1.21813i	0.0745483	−	0.129121i	−0.826341	−	0.563169i	$-0.809582\pi$
$89$	0.703287	−	1.21813i	0.0745483	−	0.129121i	0.900890	+	0.434048i	$0.142915\pi$
$90$		0			0
$91$	−3.31680	−	13.2867i	−0.347695	−	1.39282i
$92$		0			0
$93$	−0.750637	+	6.62212i	−0.0778374	+	0.686682i
$94$		0			0
$95$	1.67126	−	2.89470i	0.171467	−	0.296990i
$96$		0			0
$97$	−6.09713	+	10.5605i	−0.619070	+	1.07226i	0.370586	+	0.928798i	$0.379157\pi$
$97$	−6.09713	+	10.5605i	−0.619070	+	1.07226i	−0.989656	+	0.143462i	$0.954176\pi$
$98$		0			0
$99$	−3.09180	+	3.32321i	−0.310738	+	0.333995i
$100$		0			0
$101$	1.11867			0.111312			0.0556560	−	0.998450i	$-0.482275\pi$
$101$	1.11867			0.111312			0.0556560	+	0.998450i	$0.482275\pi$
$102$		0			0
$103$	−1.93045			−0.190213			−0.0951063	−	0.995467i	$-0.530319\pi$
$103$	−1.93045			−0.190213			−0.0951063	+	0.995467i	$0.530319\pi$
$104$		0			0
$105$	6.06359	−	0.803612i	0.591746	−	0.0784245i
$106$		0			0
$107$	−2.88969	+	5.00509i	−0.279357	+	0.483860i	−0.971225	−	0.238163i	$-0.923455\pi$
$107$	−2.88969	+	5.00509i	−0.279357	+	0.483860i	0.691868	+	0.722024i	$0.256788\pi$
$108$		0			0
$109$	−4.12106	−	7.13788i	−0.394726	−	0.683685i	0.598340	−	0.801242i	$-0.295827\pi$
$109$	−4.12106	−	7.13788i	−0.394726	−	0.683685i	−0.993066	+	0.117557i	$0.962494\pi$
$110$		0			0
$111$	−0.109874	+	0.969312i	−0.0104288	+	0.0920030i
$112$		0			0
$113$	7.25105	+	12.5592i	0.682121	+	1.18147i	0.974332	+	0.225115i	$0.0722758\pi$
$113$	7.25105	+	12.5592i	0.682121	+	1.18147i	−0.292211	+	0.956354i	$0.594391\pi$
$114$		0			0
$115$	9.82483			0.916170
$116$		0			0
$117$	−15.1340	−	3.47562i	−1.39914	−	0.321322i
$118$		0			0
$119$	0.992558	+	3.97606i	0.0909877	+	0.364485i
$120$		0			0
$121$	−8.71078			−0.791889
$122$		0			0
$123$	12.5693	+	9.28962i	1.13334	+	0.837617i
$124$		0			0
$125$	−10.9696			−0.981149
$126$		0			0
$127$	−8.50004			−0.754257			−0.377128	−	0.926161i	$-0.623088\pi$
$127$	−8.50004			−0.754257			−0.377128	+	0.926161i	$0.623088\pi$
$128$		0			0
$129$	−1.98981	+	17.5541i	−0.175193	+	1.54555i
$130$		0			0
$131$	2.01346			0.175917			0.0879585	−	0.996124i	$-0.471966\pi$
$131$	2.01346			0.175917			0.0879585	+	0.996124i	$0.471966\pi$
$132$		0			0
$133$	4.76469	−	4.60386i	0.413151	−	0.399205i
$134$		0			0
$135$	2.30386	−	6.54175i	0.198285	−	0.563024i
$136$		0			0
$137$	2.21740			0.189445			0.0947225	−	0.995504i	$-0.469804\pi$
$137$	2.21740			0.189445			0.0947225	+	0.995504i	$0.469804\pi$
$138$		0			0
$139$	−0.377669	−	0.654143i	−0.0320335	−	0.0554836i	0.849564	−	0.527485i	$-0.176865\pi$
$139$	−0.377669	−	0.654143i	−0.0320335	−	0.0554836i	−0.881598	+	0.472002i	$0.843532\pi$
$140$		0			0
$141$	−13.2585	−	9.79894i	−1.11656	−	0.825220i
$142$		0			0
$143$	3.91568	+	6.78216i	0.327446	+	0.567153i
$144$		0			0
$145$	−0.0413391	+	0.0716014i	−0.00343303	+	0.00594618i
$146$		0			0
$147$	11.9932	+	1.77829i	0.989185	+	0.146671i
$148$		0			0
$149$	6.58499			0.539463			0.269732	−	0.962936i	$-0.413065\pi$
$149$	6.58499			0.539463			0.269732	+	0.962936i	$0.413065\pi$
$150$		0			0
$151$	−12.6671			−1.03083			−0.515417	−	0.856939i	$-0.672363\pi$
$151$	−12.6671			−1.03083			−0.515417	+	0.856939i	$0.672363\pi$
$152$		0			0
$153$	4.52888	+	1.04009i	0.366138	+	0.0840861i
$154$		0			0
$155$	−2.56791	+	4.44775i	−0.206260	+	0.357252i
$156$		0			0
$157$	8.65372	−	14.9887i	0.690642	−	1.19623i	−0.280986	−	0.959712i	$-0.590662\pi$
$157$	8.65372	−	14.9887i	0.690642	−	1.19623i	0.971628	−	0.236515i	$-0.0760052\pi$
$158$		0			0
$159$	2.10434	+	1.55526i	0.166885	+	0.123340i
$160$		0			0
$161$	18.7219	+	5.36260i	1.47549	+	0.422632i
$162$		0			0
$163$	−6.10963	+	10.5822i	−0.478543	+	0.828861i	−0.999697	−	0.0246014i	$-0.992168\pi$
$163$	−6.10963	+	10.5822i	−0.478543	+	0.828861i	0.521154	+	0.853463i	$0.325502\pi$
$164$		0			0
$165$	−3.20697	+	1.39662i	−0.249662	+	0.108727i
$166$		0			0
$167$	−1.76248	−	3.05270i	−0.136385	−	0.236225i	0.789741	−	0.613440i	$-0.210215\pi$
$167$	−1.76248	−	3.05270i	−0.136385	−	0.236225i	−0.926126	+	0.377215i	$0.876882\pi$
$168$		0			0
$169$	−6.89546	+	11.9433i	−0.530420	+	0.918714i
$170$		0			0
$171$	−2.20475	−	7.18186i	−0.168602	−	0.549210i
$172$		0			0
$173$	−5.07046	−	8.78229i	−0.385500	−	0.667705i	0.606339	−	0.795206i	$-0.292638\pi$
$173$	−5.07046	−	8.78229i	−0.385500	−	0.667705i	−0.991838	+	0.127502i	$0.959304\pi$
$174$		0			0
$175$	−8.18599	−	2.34474i	−0.618802	−	0.177246i
$176$		0			0
$177$	−1.64715	+	14.5312i	−0.123808	+	1.09223i
$178$		0			0
$179$	−0.850579	−	1.47325i	−0.0635752	−	0.110116i	0.832486	−	0.554046i	$-0.186917\pi$
$179$	−0.850579	−	1.47325i	−0.0635752	−	0.110116i	−0.896061	+	0.443931i	$0.853584\pi$
$180$		0			0
$181$	−16.9941			−1.26316			−0.631581	−	0.775310i	$-0.717594\pi$
$181$	−16.9941			−1.26316			−0.631581	+	0.775310i	$0.717594\pi$
$182$		0			0
$183$	−4.51188	−	3.33460i	−0.333528	−	0.246501i
$184$		0			0
$185$	−0.375877	+	0.651039i	−0.0276351	+	0.0478653i
$186$		0			0
$187$	−1.17178	−	2.02957i	−0.0856887	−	0.148417i
$188$		0			0
$189$	7.96079	−	11.2083i	0.579062	−	0.815283i
$190$		0			0
$191$	11.3470	+	19.6535i	0.821038	+	1.42208i	0.904910	+	0.425603i	$0.139938\pi$
$191$	11.3470	+	19.6535i	0.821038	+	1.42208i	−0.0838717	+	0.996477i	$0.526729\pi$
$192$		0			0
$193$	−3.09349	+	5.35808i	−0.222674	+	0.385683i	−0.955619	−	0.294605i	$-0.904812\pi$
$193$	−3.09349	+	5.35808i	−0.222674	+	0.385683i	0.732945	+	0.680288i	$0.238145\pi$
$194$		0			0
$195$	−9.62319	−	7.11222i	−0.689131	−	0.509317i
$196$		0			0
$197$	9.77010			0.696091			0.348045	−	0.937478i	$-0.386846\pi$
$197$	9.77010			0.696091			0.348045	+	0.937478i	$0.386846\pi$
$198$		0			0
$199$	4.33973	+	7.51664i	0.307636	+	0.532840i	0.977845	−	0.209332i	$-0.0671289\pi$
$199$	4.33973	+	7.51664i	0.307636	+	0.532840i	−0.670209	+	0.742172i	$0.733796\pi$
$200$		0			0
$201$	1.35259	−	11.9326i	0.0954044	−	0.841659i
$202$		0			0
$203$	−0.117856	+	0.113878i	−0.00827188	+	0.00799267i
$204$		0			0
$205$	6.02225	+	10.4308i	0.420612	+	0.728522i
$206$		0			0
$207$	15.0415	−	16.1673i	1.04546	−	1.12371i
$208$		0			0
$209$	−1.89446	+	3.28130i	−0.131043	+	0.226973i
$210$		0			0
$211$	2.84219	+	4.92283i	0.195665	+	0.338901i	0.947118	−	0.320885i	$-0.103980\pi$
$211$	2.84219	+	4.92283i	0.195665	+	0.338901i	−0.751453	+	0.659786i	$0.770647\pi$
$212$		0			0
$213$	19.5806	−	8.52728i	1.34164	−	0.584280i
$214$		0			0
$215$	−6.80708	+	11.7902i	−0.464239	+	0.804086i
$216$		0			0
$217$	−7.32102	+	7.07390i	−0.496983	+	0.480207i
$218$		0			0
$219$	−3.84265	−	2.83999i	−0.259662	−	0.191909i
$220$		0			0
$221$	4.00862	−	6.94313i	0.269649	−	0.467045i
$222$		0			0
$223$	−5.86133	+	10.1521i	−0.392503	+	0.679836i	−0.992779	−	0.119957i	$-0.961724\pi$
$223$	−5.86133	+	10.1521i	−0.392503	+	0.679836i	0.600276	+	0.799793i	$0.295058\pi$
$224$		0			0
$225$	−6.57677	+	7.06901i	−0.438451	+	0.471267i
$226$		0			0
$227$	−11.1831			−0.742247			−0.371123	−	0.928584i	$-0.621027\pi$
$227$	−11.1831			−0.742247			−0.371123	+	0.928584i	$0.621027\pi$
$228$		0			0
$229$	−9.65647			−0.638118			−0.319059	−	0.947735i	$-0.603367\pi$
$229$	−9.65647			−0.638118			−0.319059	+	0.947735i	$0.603367\pi$
$230$		0			0
$231$	−6.87341	+	0.910938i	−0.452237	+	0.0599353i
$232$		0			0
$233$	−9.64492	+	16.7055i	−0.631860	+	1.09441i	0.355311	+	0.934748i	$0.384375\pi$
$233$	−9.64492	+	16.7055i	−0.631860	+	1.09441i	−0.987171	+	0.159666i	$0.948958\pi$
$234$		0			0
$235$	−6.35243	−	11.0027i	−0.414387	−	0.717739i
$236$		0			0
$237$	−8.24519	−	6.09378i	−0.535582	−	0.395833i
$238$		0			0
$239$	0.194641	+	0.337128i	0.0125903	+	0.0218070i	0.872252	−	0.489057i	$-0.162659\pi$
$239$	0.194641	+	0.337128i	0.0125903	+	0.0218070i	−0.859662	+	0.510864i	$0.829326\pi$
$240$		0			0
$241$	10.6361			0.685134			0.342567	−	0.939493i	$-0.388704\pi$
$241$	10.6361			0.685134			0.342567	+	0.939493i	$0.388704\pi$
$242$		0			0
$243$	−7.23769	−	13.8064i	−0.464298	−	0.885679i
$244$		0			0
$245$	7.92639	+	4.94662i	0.506399	+	0.316028i
$246$		0			0
$247$	−12.9618			−0.824741
$248$		0			0
$249$	−1.09290	+	9.64159i	−0.0692599	+	0.611011i
$250$		0			0
$251$	3.26628			0.206166			0.103083	−	0.994673i	$-0.467129\pi$
$251$	3.26628			0.206166			0.103083	+	0.994673i	$0.467129\pi$
$252$		0			0
$253$	−11.1370			−0.700176
$254$		0			0
$255$	2.87976	+	2.12835i	0.180337	+	0.133282i
$256$		0			0
$257$	−4.69573			−0.292912			−0.146456	−	0.989217i	$-0.546787\pi$
$257$	−4.69573			−0.292912			−0.146456	+	0.989217i	$0.546787\pi$
$258$		0			0
$259$	−1.07161	+	1.03544i	−0.0665867	+	0.0643391i
$260$		0			0
$261$	0.0545353	+	0.177646i	0.00337565	+	0.0109960i
$262$		0			0
$263$	−19.5498			−1.20549			−0.602747	−	0.797932i	$-0.705927\pi$
$263$	−19.5498			−1.20549			−0.602747	+	0.797932i	$0.705927\pi$
$264$		0			0
$265$	1.00824	+	1.74632i	0.0619355	+	0.107276i
$266$		0			0
$267$	0.274400	−	2.42076i	0.0167930	−	0.148148i
$268$		0			0
$269$	7.88365	+	13.6549i	0.480675	+	0.832553i	0.999754	−	0.0221730i	$-0.00705846\pi$
$269$	7.88365	+	13.6549i	0.480675	+	0.832553i	−0.519079	+	0.854726i	$0.673725\pi$
$270$		0			0
$271$	−7.39882	+	12.8151i	−0.449446	+	0.778464i	−0.998350	−	0.0574218i	$-0.981712\pi$
$271$	−7.39882	+	12.8151i	−0.449446	+	0.778464i	0.548904	+	0.835886i	$0.315045\pi$
$272$		0			0
$273$	−14.4557	−	18.8054i	−0.874898	−	1.13815i
$274$		0			0
$275$	4.86954			0.293644
$276$		0			0
$277$	−7.45122			−0.447701			−0.223850	−	0.974624i	$-0.571863\pi$
$277$	−7.45122			−0.447701			−0.223850	+	0.974624i	$0.571863\pi$
$278$		0			0
$279$	3.38764	+	11.0350i	0.202812	+	0.660650i
$280$		0			0
$281$	−12.9938	+	22.5060i	−0.775146	+	1.34259i	0.159566	+	0.987187i	$0.448991\pi$
$281$	−12.9938	+	22.5060i	−0.775146	+	1.34259i	−0.934712	+	0.355406i	$0.884343\pi$
$282$		0			0
$283$	9.37768	−	16.2426i	0.557445	−	0.965524i	−0.440263	−	0.897869i	$-0.645115\pi$
$283$	9.37768	−	16.2426i	0.557445	−	0.965524i	0.997709	−	0.0676550i	$-0.0215517\pi$
$284$		0			0
$285$	0.652070	−	5.75257i	0.0386253	−	0.340753i
$286$		0			0
$287$	5.78246	+	23.1638i	0.341328	+	1.36732i
$288$		0			0
$289$	7.30041	−	12.6447i	0.429436	−	0.743805i
$290$		0			0
$291$	−2.37890	+	20.9867i	−0.139454	+	1.23026i
$292$		0			0
$293$	−1.23089	−	2.13196i	−0.0719093	−	0.124551i	0.827829	−	0.560981i	$-0.189576\pi$
$293$	−1.23089	−	2.13196i	−0.0719093	−	0.124551i	−0.899738	+	0.436430i	$0.856243\pi$
$294$		0			0
$295$	−5.63487	+	9.75988i	−0.328075	+	0.568242i
$296$		0			0
$297$	−2.61155	+	7.41544i	−0.151537	+	0.430287i
$298$		0			0
$299$	−19.0497	−	32.9950i	−1.10167	−	1.90815i
$300$		0			0
$301$	−19.4067	+	18.7517i	−1.11858	+	1.08083i
$302$		0			0
$303$	1.77645	−	0.773637i	0.102054	−	0.0444443i
$304$		0			0
$305$	−2.16175	−	3.74425i	−0.123781	−	0.214395i
$306$		0			0
$307$	4.66277			0.266118			0.133059	−	0.991108i	$-0.457520\pi$
$307$	4.66277			0.266118			0.133059	+	0.991108i	$0.457520\pi$
$308$		0			0
$309$	−3.06555	+	1.33503i	−0.174393	+	0.0759475i
$310$		0			0
$311$	13.7410	−	23.8002i	0.779183	−	1.34958i	−0.153231	−	0.988190i	$-0.548968\pi$
$311$	13.7410	−	23.8002i	0.779183	−	1.34958i	0.932413	−	0.361393i	$-0.117699\pi$
$312$		0			0
$313$	−2.74666	−	4.75735i	−0.155250	−	0.268901i	0.777900	−	0.628388i	$-0.216285\pi$
$313$	−2.74666	−	4.75735i	−0.155250	−	0.268901i	−0.933150	+	0.359487i	$0.882952\pi$
$314$		0			0
$315$	9.07321	−	5.46951i	0.511217	−	0.308172i
$316$		0			0
$317$	−4.93879	−	8.55424i	−0.277390	−	0.480454i	0.693345	−	0.720606i	$-0.256136\pi$
$317$	−4.93879	−	8.55424i	−0.277390	−	0.480454i	−0.970735	+	0.240152i	$0.922803\pi$
$318$		0			0
$319$	0.0468601	−	0.0811641i	0.00262366	−	0.00454432i
$320$		0			0
$321$	−1.12746	+	9.94649i	−0.0629288	+	0.555159i
$322$		0			0
$323$	3.87885			0.215825
$324$		0			0
$325$	8.32930	+	14.4268i	0.462026	+	0.800253i
$326$		0			0
$327$	−11.4806	−	8.48494i	−0.634876	−	0.469218i
$328$		0			0
$329$	−6.09950	−	24.4338i	−0.336276	−	1.34708i
$330$		0			0
$331$	−10.3471	−	17.9217i	−0.568729	−	0.985067i	−0.996692	−	0.0812710i	$-0.974102\pi$
$331$	−10.3471	−	17.9217i	−0.568729	−	0.985067i	0.427963	−	0.903796i	$-0.359231\pi$
$332$		0			0
$333$	0.495864	+	1.61525i	0.0271732	+	0.0885152i
$334$		0			0
$335$	4.62718	−	8.01452i	0.252810	−	0.437880i
$336$		0			0
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	0.885698	−	0.464261i	$-0.153680\pi$
$337$	0.748747	+	1.29687i	0.0407869	+	0.0706449i	−0.844911	+	0.534906i	$0.820347\pi$
$338$		0			0
$339$	20.2002	+	14.9294i	1.09712	+	0.810852i
$340$		0			0
$341$	2.91087	−	5.04177i	0.157632	−	0.273027i
$342$		0			0
$343$	12.4044	+	13.7525i	0.669772	+	0.742567i
$344$		0			0
$345$	15.6018	−	6.79453i	0.839973	−	0.365805i
$346$		0			0
$347$	−14.7694	+	25.5813i	−0.792862	+	1.37328i	0.131326	+	0.991339i	$0.458077\pi$
$347$	−14.7694	+	25.5813i	−0.792862	+	1.37328i	−0.924188	+	0.381938i	$0.875257\pi$
$348$		0			0
$349$	18.0006	−	31.1780i	0.963551	−	1.66892i	0.250094	−	0.968222i	$-0.419539\pi$
$349$	18.0006	−	31.1780i	0.963551	−	1.66892i	0.713458	−	0.700698i	$-0.247128\pi$
$350$		0			0
$351$	−26.4364	+	4.94691i	−1.41107	+	0.264046i
$352$		0			0
$353$	−29.4930			−1.56975			−0.784877	−	0.619652i	$-0.787274\pi$
$353$	−29.4930			−1.56975			−0.784877	+	0.619652i	$0.787274\pi$
$354$		0			0
$355$	16.4580			0.873500
$356$		0			0
$357$	4.32589	+	5.62755i	0.228950	+	0.297841i
$358$		0			0
$359$	−2.70535	+	4.68580i	−0.142783	+	0.247307i	−0.928544	−	0.371224i	$-0.878938\pi$
$359$	−2.70535	+	4.68580i	−0.142783	+	0.247307i	0.785761	+	0.618531i	$0.212272\pi$
$360$		0			0
$361$	6.36444	+	11.0235i	0.334971	+	0.580186i
$362$		0			0
$363$	−13.8327	+	6.02409i	−0.726028	+	0.316183i
$364$		0			0
$365$	−1.84110	−	3.18888i	−0.0963676	−	0.166914i
$366$		0			0
$367$	23.0843			1.20499			0.602496	−	0.798122i	$-0.294173\pi$
$367$	23.0843			1.20499			0.602496	+	0.798122i	$0.294173\pi$
$368$		0			0
$369$	26.3844	+	6.05936i	1.37352	+	0.315438i
$370$		0			0
$371$	0.968093	+	3.87805i	0.0502609	+	0.201339i
$372$		0			0
$373$	21.5030			1.11338			0.556692	−	0.830719i	$-0.312070\pi$
$373$	21.5030			1.11338			0.556692	+	0.830719i	$0.312070\pi$
$374$		0			0
$375$	−17.4197	+	7.58620i	−0.899548	+	0.391750i
$376$		0			0
$377$	0.320615			0.0165125
$378$		0			0
$379$	−5.72168			−0.293903			−0.146952	−	0.989144i	$-0.546946\pi$
$379$	−5.72168			−0.293903			−0.146952	+	0.989144i	$0.546946\pi$
$380$		0			0
$381$	−13.4980	+	5.87835i	−0.691526	+	0.301157i
$382$		0			0
$383$	34.9209			1.78437			0.892187	−	0.451666i	$-0.149170\pi$
$383$	34.9209			1.78437			0.892187	+	0.451666i	$0.149170\pi$
$384$		0			0
$385$	−5.13654	−	1.47128i	−0.261783	−	0.0749834i
$386$		0			0
$387$	8.98003	+	29.2519i	0.456480	+	1.48696i
$388$		0			0
$389$	−28.8822			−1.46438			−0.732192	−	0.681098i	$-0.761503\pi$
$389$	−28.8822			−1.46438			−0.732192	+	0.681098i	$0.761503\pi$
$390$		0			0
$391$	5.70066	+	9.87383i	0.288295	+	0.499341i
$392$		0			0
$393$	3.19737	−	1.39244i	0.161286	−	0.0702395i
$394$		0			0
$395$	−3.95046	−	6.84239i	−0.198769	−	0.344278i
$396$		0			0
$397$	5.59226	−	9.68607i	0.280667	−	0.486130i	−0.690882	−	0.722968i	$-0.742778\pi$
$397$	5.59226	−	9.68607i	0.280667	−	0.486130i	0.971549	+	0.236838i	$0.0761109\pi$
$398$		0			0
$399$	4.38243	−	10.6060i	0.219396	−	0.530965i
$400$		0			0
$401$	−1.08212			−0.0540386			−0.0270193	−	0.999635i	$-0.508602\pi$
$401$	−1.08212			−0.0540386			−0.0270193	+	0.999635i	$0.508602\pi$
$402$		0			0
$403$	19.9160			0.992088
$404$		0			0
$405$	−0.865544	−	11.9816i	−0.0430092	−	0.595368i
$406$		0			0
$407$	0.426078	−	0.737988i	0.0211199	−	0.0365807i
$408$		0			0
$409$	10.8674	−	18.8229i	0.537360	−	0.930735i	−0.461685	−	0.887044i	$-0.652755\pi$
$409$	10.8674	−	18.8229i	0.537360	−	0.930735i	0.999045	−	0.0436908i	$-0.0139116\pi$
$410$		0			0
$411$	3.52122	−	1.53348i	0.173689	−	0.0756410i
$412$		0			0
$413$	−16.0648	+	15.5225i	−0.790497	+	0.763814i
$414$		0			0
$415$	−3.73879	+	6.47578i	−0.183530	+	0.317884i
$416$		0			0
$417$	−1.05212	−	0.777593i	−0.0515226	−	0.0380789i
$418$		0			0
$419$	−12.5906	−	21.8075i	−0.615090	−	1.06537i	−0.990369	−	0.138455i	$-0.955787\pi$
$419$	−12.5906	−	21.8075i	−0.615090	−	1.06537i	0.375279	−	0.926912i	$-0.377547\pi$
$420$		0			0
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	0.237090	+	0.971488i	$0.423806\pi$
$421$	−14.8304	+	25.6869i	−0.722788	+	1.25191i	−0.959878	+	0.280418i	$0.909527\pi$
$422$		0			0
$423$	−27.8310	−	6.39158i	−1.35319	−	0.310769i
$424$		0			0
$425$	−2.49256	−	4.31724i	−0.120907	−	0.209417i
$426$		0			0
$427$	−2.07567	−	8.31487i	−0.100449	−	0.402385i
$428$		0			0
$429$	10.9084	+	8.06209i	0.526663	+	0.389241i
$430$		0			0
$431$	−2.44517	−	4.23516i	−0.117780	−	0.204000i	0.801108	−	0.598520i	$-0.204244\pi$
$431$	−2.44517	−	4.23516i	−0.117780	−	0.204000i	−0.918887	+	0.394520i	$0.870911\pi$
$432$		0			0
$433$	9.71430			0.466839			0.233420	−	0.972376i	$-0.425008\pi$
$433$	9.71430			0.466839			0.233420	+	0.972376i	$0.425008\pi$
$434$		0			0
$435$	−0.0161292	+	0.142292i	−0.000773334	+	0.00682236i
$436$		0			0
$437$	9.21651	−	15.9635i	0.440885	−	0.763636i
$438$		0			0
$439$	−7.41176	−	12.8375i	−0.353744	−	0.612703i	0.633158	−	0.774022i	$-0.281758\pi$
$439$	−7.41176	−	12.8375i	−0.353744	−	0.612703i	−0.986902	+	0.161320i	$0.948425\pi$
$440$		0			0
$441$	20.2750	−	5.47021i	0.965478	−	0.260486i
$442$		0			0
$443$	−10.9510	−	18.9676i	−0.520297	−	0.901180i	−0.999722	−	0.0235972i	$-0.992488\pi$
$443$	−10.9510	−	18.9676i	−0.520297	−	0.901180i	0.479425	−	0.877583i	$-0.340845\pi$
$444$		0			0
$445$	0.938715	−	1.62590i	0.0444994	−	0.0770751i
$446$		0			0
$447$	10.4569	−	4.55396i	0.494596	−	0.215395i
$448$		0			0
$449$	21.4952			1.01442			0.507212	−	0.861822i	$-0.330676\pi$
$449$	21.4952			1.01442			0.507212	+	0.861822i	$0.330676\pi$
$450$		0			0
$451$	−6.82655	−	11.8239i	−0.321450	−	0.556767i
$452$		0			0
$453$	−20.1153	+	8.76016i	−0.945101	+	0.411588i
$454$		0			0
$455$	−4.42711	−	17.7344i	−0.207546	−	0.831402i
$456$		0			0
$457$	−20.3128	−	35.1827i	−0.950190	−	1.64578i	−0.745009	−	0.667054i	$-0.767555\pi$
$457$	−20.3128	−	35.1827i	−0.950190	−	1.64578i	−0.205181	−	0.978724i	$-0.565778\pi$
$458$		0			0
$459$	7.91114	−	1.48037i	0.369261	−	0.0690978i
$460$		0			0
$461$	1.41541	−	2.45155i	0.0659220	−	0.114180i	−0.831181	−	0.556003i	$-0.812334\pi$
$461$	1.41541	−	2.45155i	0.0659220	−	0.114180i	0.897103	+	0.441822i	$0.145668\pi$
$462$		0			0
$463$	13.9324	+	24.1317i	0.647494	+	1.12149i	0.983719	+	0.179711i	$0.0575164\pi$
$463$	13.9324	+	24.1317i	0.647494	+	1.12149i	−0.336225	+	0.941782i	$0.609150\pi$
$464$		0			0
$465$	−1.00192	+	8.83890i	−0.0464627	+	0.409894i
$466$		0			0
$467$	13.3219	−	23.0742i	0.616464	−	1.06775i	−0.373661	−	0.927565i	$-0.621898\pi$
$467$	13.3219	−	23.0742i	0.616464	−	1.06775i	0.990126	−	0.140182i	$-0.0447689\pi$
$468$		0			0
$469$	13.1919	−	12.7466i	0.609146	−	0.588585i
$470$		0			0
$471$	3.37640	−	29.7866i	0.155576	−	1.37249i
$472$		0			0
$473$	7.71620	−	13.3648i	0.354791	−	0.614516i
$474$		0			0
$475$	−4.02983	+	6.97987i	−0.184901	+	0.320258i
$476$		0			0
$477$	4.41725	+	1.01445i	0.202252	+	0.0464485i
$478$		0			0
$479$	31.5791			1.44289			0.721443	−	0.692474i	$-0.243479\pi$
$479$	31.5791			1.44289			0.721443	+	0.692474i	$0.243479\pi$
$480$		0			0
$481$	2.91520			0.132922
$482$		0			0
$483$	33.4390	−	4.43169i	1.52153	−	0.201649i
$484$		0			0
$485$	−8.13817	+	14.0957i	−0.369535	+	0.640054i
$486$		0			0
$487$	0.153087	+	0.265154i	0.00693703	+	0.0120153i	0.869473	−	0.493980i	$-0.164459\pi$
$487$	0.153087	+	0.265154i	0.00693703	+	0.0120153i	−0.862536	+	0.505996i	$0.831125\pi$
$488$		0			0
$489$	−2.38378	+	21.0297i	−0.107798	+	0.950996i
$490$		0			0
$491$	9.06981	+	15.7094i	0.409315	+	0.708954i	0.994813	−	0.101720i	$-0.0324345\pi$
$491$	9.06981	+	15.7094i	0.409315	+	0.708954i	−0.585498	+	0.810674i	$0.699101\pi$
$492$		0			0
$493$	−0.0959447			−0.00432113
$494$		0			0
$495$	−4.12679	+	4.43567i	−0.185486	+	0.199368i
$496$		0			0
$497$	31.3619	+	8.98311i	1.40677	+	0.402948i
$498$		0			0
$499$	21.3091			0.953928			0.476964	−	0.878923i	$-0.341737\pi$
$499$	21.3091			0.953928			0.476964	+	0.878923i	$0.341737\pi$
$500$		0			0
$501$	−4.90996	−	3.62881i	−0.219361	−	0.162123i
$502$		0			0
$503$	17.0738			0.761285			0.380642	−	0.924722i	$-0.375703\pi$
$503$	17.0738			0.761285			0.380642	+	0.924722i	$0.375703\pi$
$504$		0			0
$505$	1.49315			0.0664443
$506$		0			0
$507$	−2.69038	+	23.7346i	−0.119484	+	1.05409i
$508$		0			0
$509$	36.7735			1.62996			0.814979	−	0.579490i	$-0.196748\pi$
$509$	36.7735			1.62996			0.814979	+	0.579490i	$0.196748\pi$
$510$		0			0
$511$	−1.76780	−	7.08155i	−0.0782027	−	0.313270i
$512$		0			0
$513$	−8.46788	−	9.88003i	−0.373866	−	0.436214i
$514$		0			0
$515$	−2.57667			−0.113542
$516$		0			0
$517$	7.20083	+	12.4722i	0.316692	+	0.548527i
$518$		0			0
$519$	−14.1254	−	10.4397i	−0.620037	−	0.458251i
$520$		0			0
$521$	−9.57535	−	16.5850i	−0.419504	−	0.726602i	0.576386	−	0.817178i	$-0.304463\pi$
$521$	−9.57535	−	16.5850i	−0.419504	−	0.726602i	−0.995890	+	0.0905758i	$0.971129\pi$
$522$		0			0
$523$	20.9715	−	36.3236i	0.917018	−	1.58832i	0.113097	−	0.993584i	$-0.463923\pi$
$523$	20.9715	−	36.3236i	0.917018	−	1.58832i	0.803920	−	0.594737i	$-0.202744\pi$
$524$		0			0
$525$	−14.6209	+	1.93771i	−0.638107	+	0.0845688i
$526$		0			0
$527$	−5.95991			−0.259618
$528$		0			0
$529$	31.1812			1.35570
$530$		0			0
$531$	7.43362	+	24.2146i	0.322592	+	1.05082i
$532$		0			0
$533$	23.3535	−	40.4494i	1.01155	−	1.75206i
$534$		0			0
$535$	−3.85702	+	6.68056i	−0.166754	+	0.288826i
$536$		0			0
$537$	−2.36956	−	1.75128i	−0.102254	−	0.0755732i
$538$		0			0
$539$	−8.98500	−	5.60726i	−0.387011	−	0.241522i
$540$		0			0
$541$	−1.44272	+	2.49886i	−0.0620273	+	0.107434i	−0.895371	−	0.445320i	$-0.853090\pi$
$541$	−1.44272	+	2.49886i	−0.0620273	+	0.107434i	0.833344	+	0.552754i	$0.186423\pi$
$542$		0			0
$543$	−26.9866	+	11.7526i	−1.15811	+	0.504351i
$544$		0			0
$545$	−5.50059	−	9.52731i	−0.235620	−	0.408105i
$546$		0			0
$547$	−1.38738	+	2.40301i	−0.0593201	+	0.102745i	−0.894160	−	0.447747i	$-0.852227\pi$
$547$	−1.38738	+	2.40301i	−0.0593201	+	0.102745i	0.834840	+	0.550492i	$0.185560\pi$
$548$		0			0
$549$	−9.47096	−	2.17507i	−0.404211	−	0.0928296i
$550$		0			0
$551$	0.0775590	+	0.134336i	0.00330413	+	0.00572291i
$552$		0			0
$553$	−3.79316	−	15.1949i	−0.161302	−	0.646154i
$554$		0			0
$555$	−0.146655	+	1.29379i	−0.00622516	+	0.0549184i
$556$		0			0
$557$	15.5344	+	26.9064i	0.658214	+	1.14006i	0.981078	+	0.193614i	$0.0620211\pi$
$557$	15.5344	+	26.9064i	0.658214	+	1.14006i	−0.322864	+	0.946445i	$0.604646\pi$
$558$		0			0
$559$	52.7939			2.23294
$560$		0			0
$561$	−3.26436	−	2.41260i	−0.137822	−	0.101860i
$562$		0			0
$563$	0.144020	−	0.249451i	0.00606973	−	0.0105131i	−0.862975	−	0.505247i	$-0.831401\pi$
$563$	0.144020	−	0.249451i	0.00606973	−	0.0105131i	0.869044	+	0.494734i	$0.164735\pi$
$564$		0			0
$565$	9.67836	+	16.7634i	0.407172	+	0.705242i
$566$		0			0
$567$	4.89042	−	23.3042i	0.205378	−	0.978683i
$568$		0			0
$569$	8.04004	+	13.9258i	0.337056	+	0.583798i	0.983878	−	0.178843i	$-0.0572354\pi$
$569$	8.04004	+	13.9258i	0.337056	+	0.583798i	−0.646821	+	0.762641i	$0.723902\pi$
$570$		0			0
$571$	−7.64289	+	13.2379i	−0.319845	+	0.553988i	−0.980456	−	0.196741i	$-0.936964\pi$
$571$	−7.64289	+	13.2379i	−0.319845	+	0.553988i	0.660610	+	0.750729i	$0.270298\pi$
$572$		0			0
$573$	31.6107	+	23.3626i	1.32056	+	0.975985i
$574$		0			0
$575$	−23.6902			−0.987950
$576$		0			0
$577$	12.0812	+	20.9253i	0.502949	+	0.871133i	0.999994	+	0.00340833i	$0.00108491\pi$
$577$	12.0812	+	20.9253i	0.502949	+	0.871133i	−0.497045	+	0.867725i	$0.665582\pi$
$578$		0			0
$579$	−1.20698	+	10.6480i	−0.0501603	+	0.442515i
$580$		0			0
$581$	−10.6592	+	10.2994i	−0.442216	+	0.427289i
$582$		0			0
$583$	−1.14289	−	1.97955i	−0.0473338	−	0.0819845i
$584$		0			0
$585$	−20.2002	−	4.63910i	−0.835174	−	0.191803i
$586$		0			0
$587$	−18.0145	+	31.2020i	−0.743537	+	1.28784i	0.207339	+	0.978269i	$0.433520\pi$
$587$	−18.0145	+	31.2020i	−0.743537	+	1.28784i	−0.950875	+	0.309574i	$0.899814\pi$
$588$		0			0
$589$	4.81783	+	8.34472i	0.198515	+	0.343838i
$590$		0			0
$591$	15.5149	−	6.75668i	0.638197	−	0.277933i
$592$		0			0
$593$	12.4668	−	21.5932i	0.511951	−	0.886726i	−0.487953	−	0.872870i	$-0.662256\pi$
$593$	12.4668	−	21.5932i	0.511951	−	0.886726i	0.999904	−	0.0138558i	$-0.00441057\pi$
$594$		0			0
$595$	1.32482	+	5.30706i	0.0543124	+	0.217568i
$596$		0			0
$597$	12.0897	+	8.93518i	0.494800	+	0.365693i
$598$		0			0
$599$	19.7642	−	34.2325i	0.807542	−	1.39870i	−0.107019	−	0.994257i	$-0.534131\pi$
$599$	19.7642	−	34.2325i	0.807542	−	1.39870i	0.914561	−	0.404447i	$-0.132536\pi$
$600$		0			0
$601$	1.86447	−	3.22936i	0.0760534	−	0.131728i	−0.825490	−	0.564416i	$-0.809101\pi$
$601$	1.86447	−	3.22936i	0.0760534	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$602$		0			0
$603$	−6.10427	−	19.8843i	−0.248585	−	0.809751i
$604$		0			0
$605$	−11.6267			−0.472694
$606$		0			0
$607$	−23.6528			−0.960036			−0.480018	−	0.877259i	$-0.659370\pi$
$607$	−23.6528			−0.960036			−0.480018	+	0.877259i	$0.659370\pi$
$608$		0			0
$609$	−0.108401	+	0.262343i	−0.00439263	+	0.0106307i
$610$		0			0
$611$	−24.6339	+	42.6671i	−0.996580	+	1.72613i
$612$		0			0
$613$	1.89952	+	3.29006i	0.0767208	+	0.132884i	0.901833	−	0.432084i	$-0.142222\pi$
$613$	1.89952	+	3.29006i	0.0767208	+	0.132884i	−0.825113	+	0.564968i	$0.808888\pi$
$614$		0			0
$615$	16.7769	+	12.3994i	0.676512	+	0.499990i
$616$		0			0
$617$	−17.5615	−	30.4174i	−0.706999	−	1.22456i	−0.965965	−	0.258672i	$-0.916715\pi$
$617$	−17.5615	−	30.4174i	−0.706999	−	1.22456i	0.258966	−	0.965886i	$-0.416618\pi$
$618$		0			0
$619$	21.1632			0.850622			0.425311	−	0.905047i	$-0.360165\pi$
$619$	21.1632			0.850622			0.425311	+	0.905047i	$0.360165\pi$
$620$		0			0
$621$	12.7051	−	36.0759i	0.509839	−	1.44768i
$622$		0			0
$623$	2.67624	−	2.58590i	0.107221	−	0.103602i
$624$		0			0
$625$	1.45048			0.0580192
$626$		0			0
$627$	−0.739157	+	6.52085i	−0.0295191	+	0.260418i
$628$		0			0
$629$	−0.872381			−0.0347841
$630$		0			0
$631$	−4.74845			−0.189033			−0.0945164	−	0.995523i	$-0.530130\pi$
$631$	−4.74845			−0.189033			−0.0945164	+	0.995523i	$0.530130\pi$
$632$		0			0
$633$	7.91786	+	5.85186i	0.314707	+	0.232591i
$634$		0			0
$635$	−11.3455			−0.450231
$636$		0			0
$637$	1.24363	−	36.2106i	0.0492745	−	1.43472i
$638$		0			0
$639$	25.1967	−	27.0826i	0.996767	−	1.07137i
$640$		0			0
$641$	−9.87469			−0.390027			−0.195013	−	0.980801i	$-0.562475\pi$
$641$	−9.87469			−0.390027			−0.195013	+	0.980801i	$0.562475\pi$
$642$		0			0
$643$	−21.9748	−	38.0615i	−0.866602	−	1.50100i	−0.865448	−	0.501000i	$-0.832966\pi$
$643$	−21.9748	−	38.0615i	−0.866602	−	1.50100i	−0.00115462	−	0.999999i	$-0.500368\pi$
$644$		0			0
$645$	−2.65590	+	23.4304i	−0.104576	+	0.922570i
$646$		0			0
$647$	−22.1936	−	38.4404i	−0.872521	−	1.51125i	−0.859381	−	0.511336i	$-0.829151\pi$
$647$	−22.1936	−	38.4404i	−0.872521	−	1.51125i	−0.0131398	−	0.999914i	$-0.504183\pi$
$648$		0			0
$649$	6.38743	−	11.0634i	0.250729	−	0.434275i
$650$		0			0
$651$	−6.73368	+	16.2963i	−0.263914	+	0.638703i
$652$		0			0
$653$	41.9912			1.64324			0.821622	−	0.570033i	$-0.193070\pi$
$653$	41.9912			1.64324			0.821622	+	0.570033i	$0.193070\pi$
$654$		0			0
$655$	2.68748			0.105008
$656$		0			0
$657$	−8.06616	−	1.85245i	−0.314691	−	0.0722708i
$658$		0			0
$659$	19.6365	−	34.0114i	0.764928	−	1.32489i	−0.175356	−	0.984505i	$-0.556108\pi$
$659$	19.6365	−	34.0114i	0.764928	−	1.32489i	0.940284	−	0.340390i	$-0.110559\pi$
$660$		0			0
$661$	0.0933694	−	0.161721i	0.00363165	−	0.00629020i	−0.864204	−	0.503142i	$-0.832177\pi$
$661$	0.0933694	−	0.161721i	0.00363165	−	0.00629020i	0.867836	+	0.496852i	$0.165511\pi$
$662$		0			0
$663$	1.56403	−	13.7979i	0.0607419	−	0.535866i
$664$		0			0
$665$	6.35969	−	6.14502i	0.246618	−	0.238293i
$666$		0			0
$667$	−0.227973	+	0.394862i	−0.00882717	+	0.0152891i
$668$		0			0
$669$	−2.28690	+	20.1750i	−0.0884166	+	0.780012i
$670$		0			0
$671$	2.45046	+	4.24432i	0.0945989	+	0.163850i
$672$		0			0
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	−0.951544	−	0.307512i	$-0.900503\pi$
$673$	−5.43382	+	9.41166i	−0.209458	+	0.362793i	0.742086	+	0.670305i	$0.233837\pi$
$674$		0			0
$675$	−5.55519	+	15.7738i	−0.213819	+	0.607136i
$676$		0			0
$677$	−14.1950	−	24.5865i	−0.545560	−	0.944937i	−0.998571	−	0.0534326i	$-0.982984\pi$
$677$	−14.1950	−	24.5865i	−0.545560	−	0.944937i	0.453012	−	0.891505i	$-0.350350\pi$
$678$		0			0
$679$	−23.2016	+	22.4184i	−0.890396	+	0.860341i
$680$		0			0
$681$	−17.7587	+	7.73385i	−0.680514	+	0.296362i
$682$		0			0
$683$	−5.92034	−	10.2543i	−0.226536	−	0.392371i	0.730243	−	0.683187i	$-0.239407\pi$
$683$	−5.92034	−	10.2543i	−0.226536	−	0.392371i	−0.956779	+	0.290816i	$0.906073\pi$
$684$		0			0
$685$	2.95968			0.113083
$686$		0			0
$687$	−15.3345	+	6.67810i	−0.585046	+	0.254786i
$688$		0			0
$689$	3.90981	−	6.77199i	0.148952	−	0.257992i
$690$		0			0
$691$	5.95416	+	10.3129i	0.226507	+	0.392321i	0.956770	−	0.290844i	$-0.0939361\pi$
$691$	5.95416	+	10.3129i	0.226507	+	0.392321i	−0.730264	+	0.683165i	$0.760603\pi$
$692$		0			0
$693$	−10.2850	+	6.19999i	−0.390694	+	0.235518i
$694$		0			0
$695$	−0.504096	−	0.873119i	−0.0191214	−	0.0331193i
$696$		0			0
$697$	−6.98857	+	12.1046i	−0.264711	+	0.458493i
$698$		0			0
$699$	−3.76313	+	33.1984i	−0.142335	+	1.25568i
$700$		0			0
$701$	−31.3902			−1.18559			−0.592795	−	0.805353i	$-0.701976\pi$
$701$	−31.3902			−1.18559			−0.592795	+	0.805353i	$0.701976\pi$
$702$		0			0
$703$	0.705208	+	1.22146i	0.0265974	+	0.0460681i
$704$		0			0
$705$	−17.6968	−	13.0792i	−0.666499	−	0.492590i
$706$		0			0
$707$	2.84531	+	0.814992i	0.107009	+	0.0306509i
$708$		0			0
$709$	−0.312609	−	0.541455i	−0.0117403	−	0.0203348i	0.860096	−	0.510133i	$-0.170404\pi$
$709$	−0.312609	−	0.541455i	−0.0117403	−	0.0203348i	−0.871836	+	0.489798i	$0.837070\pi$
$710$		0			0
$711$	−17.3076	−	3.97480i	−0.649085	−	0.149067i
$712$		0			0
$713$	−14.1613	+	24.5281i	−0.530345	+	0.918584i
$714$		0			0
$715$	5.22647	+	9.05251i	0.195459	+	0.338545i
$716$		0			0
$717$	0.542236	+	0.400751i	0.0202502	+	0.0149663i
$718$		0			0
$719$	−12.1969	+	21.1257i	−0.454869	+	0.787857i	−0.998681	−	0.0513506i	$-0.983647\pi$
$719$	−12.1969	+	21.1257i	−0.454869	+	0.787857i	0.543811	+	0.839208i	$0.316981\pi$
$720$		0			0
$721$	−4.91003	−	1.40640i	−0.182859	−	0.0523771i
$722$		0			0
$723$	16.8902	−	7.35561i	0.628152	−	0.273558i
$724$		0			0
$725$	0.0996792	−	0.172649i	0.00370199	−	0.00641204i
$726$		0			0
$727$	18.9253	−	32.7796i	0.701900	−	1.21573i	−0.265899	−	0.964001i	$-0.585669\pi$
$727$	18.9253	−	32.7796i	0.701900	−	1.21573i	0.967799	−	0.251726i	$-0.0809980\pi$
$728$		0			0
$729$	−21.0415	−	16.9191i	−0.779314	−	0.626634i
$730$		0			0
$731$	−15.7987			−0.584335
$732$		0			0
$733$	2.40155			0.0887033			0.0443516	−	0.999016i	$-0.485878\pi$
$733$	2.40155			0.0887033			0.0443516	+	0.999016i	$0.485878\pi$
$734$		0			0
$735$	16.0080	+	2.37358i	0.590464	+	0.0875508i
$736$		0			0
$737$	−5.24517	+	9.08490i	−0.193208	+	0.334646i
$738$		0			0
$739$	15.1940	+	26.3167i	0.558920	+	0.968077i	0.997587	+	0.0694277i	$0.0221173\pi$
$739$	15.1940	+	26.3167i	0.558920	+	0.968077i	−0.438667	+	0.898650i	$0.644549\pi$
$740$		0			0
$741$	−20.5833	+	8.96397i	−0.756148	+	0.329300i
$742$		0			0
$743$	2.54785	+	4.41300i	0.0934715	+	0.161897i	0.908970	−	0.416862i	$-0.136870\pi$
$743$	2.54785	+	4.41300i	0.0934715	+	0.161897i	−0.815498	+	0.578760i	$0.803537\pi$
$744$		0			0
$745$	8.78934			0.322016
$746$		0			0
$747$	4.93228	+	16.0666i	0.180463	+	0.587847i
$748$		0			0
$749$	−10.9962	+	10.6251i	−0.401793	+	0.388231i
$750$		0			0
$751$	0.975011			0.0355787			0.0177893	−	0.999842i	$-0.494337\pi$
$751$	0.975011			0.0355787			0.0177893	+	0.999842i	$0.494337\pi$
$752$		0			0
$753$	5.18685	−	2.25885i	0.189019	−	0.0823172i
$754$		0			0
$755$	−16.9075			−0.615326
$756$		0			0
$757$	11.6346			0.422865			0.211433	−	0.977393i	$-0.432187\pi$
$757$	11.6346			0.422865			0.211433	+	0.977393i	$0.432187\pi$
$758$		0			0
$759$	−17.6855	+	7.70198i	−0.641943	+	0.279564i
$760$		0			0
$761$	−54.1749			−1.96384			−0.981920	−	0.189298i	$-0.939379\pi$
$761$	−54.1749			−1.96384			−0.981920	+	0.189298i	$0.939379\pi$
$762$		0			0
$763$	−5.28158	−	21.1573i	−0.191206	−	0.765946i
$764$		0			0
$765$	6.04494	+	1.38826i	0.218555	+	0.0501927i
$766$		0			0
$767$	43.7025			1.57801
$768$		0			0
$769$	−10.4326	−	18.0698i	−0.376208	−	0.651612i	0.614299	−	0.789074i	$-0.289439\pi$
$769$	−10.4326	−	18.0698i	−0.376208	−	0.651612i	−0.990507	+	0.137462i	$0.956106\pi$
$770$		0			0
$771$	−7.45681	+	3.24742i	−0.268551	+	0.116953i
$772$		0			0
$773$	−27.4972	−	47.6266i	−0.989007	−	1.71301i	−0.622561	−	0.782572i	$-0.713908\pi$
$773$	−27.4972	−	47.6266i	−0.989007	−	1.71301i	−0.366447	−	0.930439i	$-0.619426\pi$
$774$		0			0
$775$	6.19189	−	10.7247i	0.222419	−	0.385242i
$776$		0			0
$777$	−0.985640	+	2.38537i	−0.0353596	+	0.0855746i
$778$		0			0
$779$	22.5975			0.809639
$780$		0			0
$781$	−18.6560			−0.667566
$782$		0			0
$783$	0.209456	+	0.244386i	0.00748534	+	0.00873364i
$784$		0			0
$785$	11.5506	−	20.0062i	0.412258	−	0.714051i
$786$		0			0
$787$	4.59475	−	7.95833i	0.163785	−	0.283684i	−0.772438	−	0.635090i	$-0.780963\pi$
$787$	4.59475	−	7.95833i	0.163785	−	0.283684i	0.936223	+	0.351406i	$0.114296\pi$
$788$		0			0
$789$	−31.0451	+	13.5200i	−1.10523	+	0.481325i
$790$		0			0
$791$	9.29301	+	37.2266i	0.330421	+	1.32362i
$792$		0			0
$793$	−8.38296	+	14.5197i	−0.297688	+	0.515610i
$794$		0			0
$795$	2.80878	+	2.07588i	0.0996170	+	0.0736241i
$796$		0			0
$797$	3.53774	+	6.12754i	0.125313	+	0.217049i	0.921855	−	0.387534i	$-0.126673\pi$
$797$	3.53774	+	6.12754i	0.125313	+	0.217049i	−0.796542	+	0.604583i	$0.793340\pi$
$798$		0			0
$799$	7.37174	−	12.7682i	0.260793	−	0.451707i
$800$		0			0
$801$	−1.23837	−	4.03392i	−0.0437556	−	0.142532i
$802$		0			0
$803$	2.08699	+	3.61477i	0.0736483	+	0.127563i
$804$		0			0
$805$	24.9892	+	7.15774i	0.880752	+	0.252277i
$806$		0			0
$807$	21.9625	+	16.2318i	0.773116	+	0.571388i
$808$		0			0
$809$	−2.97060	−	5.14522i	−0.104441	−	0.180896i	0.809069	−	0.587714i	$-0.199972\pi$
$809$	−2.97060	−	5.14522i	−0.104441	−	0.180896i	−0.913510	+	0.406817i	$0.866639\pi$
$810$		0			0
$811$	−44.4139			−1.55958			−0.779791	−	0.626039i	$-0.784675\pi$
$811$	−44.4139			−1.55958			−0.779791	+	0.626039i	$0.784675\pi$
$812$		0			0
$813$	−2.88678	+	25.4672i	−0.101244	+	0.893173i
$814$		0			0
$815$	−8.15485	+	14.1246i	−0.285652	+	0.494764i
$816$		0			0
$817$	12.7712	+	22.1204i	0.446808	+	0.773894i
$818$		0			0
$819$	−35.9608	−	19.8658i	−1.25657	−	0.694168i
$820$		0			0
$821$	−3.17761	−	5.50378i	−0.110899	−	0.192083i	0.805234	−	0.592958i	$-0.202040\pi$
$821$	−3.17761	−	5.50378i	−0.110899	−	0.192083i	−0.916133	+	0.400874i	$0.868706\pi$
$822$		0			0
$823$	−4.73216	+	8.19635i	−0.164953	+	0.285707i	−0.936639	−	0.350297i	$-0.886081\pi$
$823$	−4.73216	+	8.19635i	−0.164953	+	0.285707i	0.771686	+	0.636004i	$0.219414\pi$
$824$		0			0
$825$	7.73282	−	3.36762i	0.269222	−	0.117245i
$826$		0			0
$827$	4.86261			0.169090			0.0845448	−	0.996420i	$-0.473056\pi$
$827$	4.86261			0.169090			0.0845448	+	0.996420i	$0.473056\pi$
$828$		0			0
$829$	20.3926	+	35.3211i	0.708266	+	1.22675i	0.965500	+	0.260403i	$0.0838555\pi$
$829$	20.3926	+	35.3211i	0.708266	+	1.22675i	−0.257234	+	0.966349i	$0.582811\pi$
$830$		0			0
$831$	−11.8325	+	5.15302i	−0.410466	+	0.178756i
$832$		0			0
$833$	−0.372159	+	10.8361i	−0.0128946	+	0.375449i
$834$		0			0
$835$	−2.35247	−	4.07460i	−0.0814107	−	0.141007i
$836$		0			0
$837$	13.0110	+	15.1808i	0.449727	+	0.524726i
$838$		0			0
$839$	−9.60171	+	16.6307i	−0.331488	+	0.574154i	−0.982804	−	0.184653i	$-0.940884\pi$
$839$	−9.60171	+	16.6307i	−0.331488	+	0.574154i	0.651316	+	0.758807i	$0.274217\pi$
$840$		0			0
$841$	14.4981	+	25.1114i	0.499934	+	0.865911i
$842$		0			0
$843$	−5.06976	+	44.7255i	−0.174612	+	1.54043i
$844$		0			0
$845$	−9.20374	+	15.9413i	−0.316618	+	0.548399i
$846$		0			0
$847$	−22.1556	−	6.34612i	−0.761276	−	0.218055i
$848$		0			0
$849$	3.65886	−	32.2785i	0.125572	−	1.10780i
$850$		0			0
$851$	−2.07286	+	3.59029i	−0.0710566	+	0.123074i
$852$		0			0
$853$	−6.95055	+	12.0387i	−0.237982	+	0.412198i	−0.960135	−	0.279536i	$-0.909819\pi$
$853$	−6.95055	+	12.0387i	−0.237982	+	0.412198i	0.722153	+	0.691734i	$0.243153\pi$
$854$		0			0
$855$	−2.94280	−	9.58601i	−0.100642	−	0.327835i
$856$		0			0
$857$	56.9838			1.94653			0.973265	−	0.229686i	$-0.0737700\pi$
$857$	56.9838			1.94653			0.973265	+	0.229686i	$0.0737700\pi$
$858$		0			0
$859$	20.1002			0.685810			0.342905	−	0.939370i	$-0.388589\pi$
$859$	20.1002			0.685810			0.342905	+	0.939370i	$0.388589\pi$
$860$		0			0
$861$	25.2019	+	32.7851i	0.858877	+	1.11731i
$862$		0			0
$863$	3.08893	−	5.35018i	0.105148	−	0.182122i	−0.808650	−	0.588289i	$-0.799802\pi$
$863$	3.08893	−	5.35018i	0.105148	−	0.182122i	0.913799	+	0.406167i	$0.133135\pi$
$864$		0			0
$865$	−6.76781	−	11.7222i	−0.230112	−	0.398566i
$866$		0			0
$867$	2.84838	−	25.1285i	0.0967361	−	0.853407i
$868$		0			0
$869$	4.47806	+	7.75623i	0.151908	+	0.263112i
$870$		0			0
$871$	−35.8872			−1.21599
$872$		0			0
$873$	10.7360	+	34.9720i	0.363359	+	1.18362i
$874$		0			0
$875$	−27.9008	−	7.99173i	−0.943219	−	0.270170i
$876$		0			0
$877$	−37.2574			−1.25809			−0.629046	−	0.777368i	$-0.716554\pi$
$877$	−37.2574			−1.25809			−0.629046	+	0.777368i	$0.716554\pi$
$878$		0			0
$879$	−3.42905	−	2.53431i	−0.115659	−	0.0854801i
$880$		0			0
$881$	−11.7848			−0.397041			−0.198520	−	0.980097i	$-0.563614\pi$
$881$	−11.7848			−0.397041			−0.198520	+	0.980097i	$0.563614\pi$
$882$		0			0
$883$	29.2308			0.983693			0.491847	−	0.870682i	$-0.336322\pi$
$883$	29.2308			0.983693			0.491847	+	0.870682i	$0.336322\pi$
$884$		0			0
$885$	−2.19854	+	19.3956i	−0.0739032	+	0.651974i
$886$		0			0
$887$	−28.5161			−0.957479			−0.478739	−	0.877957i	$-0.658906\pi$
$887$	−28.5161			−0.957479			−0.478739	+	0.877957i	$0.658906\pi$
$888$		0			0
$889$	−21.6196	−	6.19258i	−0.725098	−	0.207693i
$890$		0			0
$891$	0.981141	+	13.5818i	0.0328695	+	0.455006i
$892$		0			0
$893$	−23.8364			−0.797656
$894$		0			0
$895$	−1.13531	−	1.96642i	−0.0379493	−	0.0657301i
$896$		0			0
$897$	−53.0691	−	39.2219i	−1.77193	−	1.30958i
$898$		0			0
$899$	−0.119171	−	0.206410i	−0.00397456	−	0.00688414i
$900$		0			0
$901$	−1.17002	+	2.02653i	−0.0389790	+	0.0675135i
$902$		0			0
$903$	−17.8498	+	43.1986i	−0.594004	+	1.43756i
$904$		0			0
$905$	−22.6829			−0.754006
$906$		0			0
$907$	7.89155			0.262035			0.131017	−	0.991380i	$-0.458176\pi$
$907$	7.89155			0.262035			0.131017	+	0.991380i	$0.458176\pi$
$908$		0			0
$909$	2.28597	−	2.45707i	0.0758209	−	0.0814957i
$910$		0			0
$911$	14.2206	−	24.6308i	0.471150	−	0.816055i	−0.528306	−	0.849054i	$-0.677173\pi$
$911$	14.2206	−	24.6308i	0.471150	−	0.816055i	0.999455	+	0.0329991i	$0.0105058\pi$
$912$		0			0
$913$	4.23813	−	7.34065i	0.140262	−	0.242940i
$914$		0			0
$915$	−6.02225	−	4.45087i	−0.199089	−	0.147141i
$916$		0			0
$917$	5.12118	+	1.46688i	0.169116	+	0.0484406i
$918$		0			0
$919$	−3.99271	+	6.91558i	−0.131707	+	0.228124i	−0.924335	−	0.381582i	$-0.875379\pi$
$919$	−3.99271	+	6.91558i	−0.131707	+	0.228124i	0.792627	+	0.609706i	$0.208713\pi$
$920$		0			0
$921$	7.40446	−	3.22462i	0.243985	−	0.106255i
$922$		0			0
$923$	−31.9110	−	55.2714i	−1.05036	−	1.81928i
$924$		0			0
$925$	0.906337	−	1.56982i	0.0298002	−	0.0516154i
$926$		0			0
$927$	−3.94481	+	4.24006i	−0.129565	+	0.139262i
$928$		0			0
$929$	−9.40031	−	16.2818i	−0.308414	−	0.534189i	0.669601	−	0.742721i	$-0.266465\pi$
$929$	−9.40031	−	16.2818i	−0.308414	−	0.534189i	−0.978016	+	0.208531i	$0.933132\pi$
$930$		0			0
$931$	15.4729	−	8.23853i	0.507104	−	0.270007i
$932$		0			0
$933$	5.36130	−	47.2974i	0.175521	−	1.54845i
$934$		0			0
$935$	−1.56403	−	2.70898i	−0.0511493	−	0.0885932i
$936$		0			0
$937$	48.5788			1.58700			0.793500	−	0.608570i	$-0.208256\pi$
$937$	48.5788			1.58700			0.793500	+	0.608570i	$0.208256\pi$
$938$		0			0
$939$	−7.65172	−	5.65516i	−0.249704	−	0.184549i
$940$		0			0
$941$	−10.2425	+	17.7406i	−0.333898	+	0.578328i	−0.983272	−	0.182141i	$-0.941697\pi$
$941$	−10.2425	+	17.7406i	−0.333898	+	0.578328i	0.649375	+	0.760468i	$0.275031\pi$
$942$		0			0
$943$	33.2110	+	57.5231i	1.08150	+	1.87321i
$944$		0			0
$945$	10.6257	−	14.9603i	0.345654	−	0.486659i
$946$		0			0
$947$	−7.42524	−	12.8609i	−0.241288	−	0.417923i	0.719793	−	0.694188i	$-0.244236\pi$
$947$	−7.42524	−	12.8609i	−0.241288	−	0.417923i	−0.961081	+	0.276265i	$0.910903\pi$
$948$		0			0
$949$	−7.13954	+	12.3661i	−0.231759	+	0.401419i
$950$		0			0
$951$	−13.7586	−	10.1686i	−0.446154	−	0.329739i
$952$		0			0
$953$	46.4678			1.50524			0.752620	−	0.658456i	$-0.228790\pi$
$953$	46.4678			1.50524			0.752620	+	0.658456i	$0.228790\pi$
$954$		0			0
$955$	15.1454	+	26.2326i	0.490094	+	0.848868i
$956$		0			0
$957$	0.0182833	−	0.161295i	0.000591015	−	0.00521394i
$958$		0			0
$959$	5.63988	+	1.61545i	0.182121	+	0.0521657i
$960$		0			0
$961$	8.09733	+	14.0250i	0.261204	+	0.452419i
$962$		0			0
$963$	5.08826	+	16.5747i	0.163967	+	0.534112i
$964$		0			0
$965$	−4.12905	+	7.15172i	−0.132919	+	0.230222i
$966$		0			0
$967$	−0.863670	−	1.49592i	−0.0277738	−	0.0481056i	0.851804	−	0.523860i	$-0.175508\pi$
$967$	−0.863670	−	1.49592i	−0.0277738	−	0.0481056i	−0.879578	+	0.475754i	$0.842175\pi$
$968$		0			0
$969$	6.15960	−	2.68249i	0.197875	−	0.0861739i
$970$		0			0
$971$	3.78085	−	6.54863i	0.121333	−	0.210156i	−0.798960	−	0.601384i	$-0.794616\pi$
$971$	3.78085	−	6.54863i	0.121333	−	0.210156i	0.920294	+	0.391228i	$0.127950\pi$
$972$		0			0
$973$	−0.484024	−	1.93894i	−0.0155171	−	0.0621595i
$974$		0			0
$975$	23.2040	+	17.1494i	0.743122	+	0.549220i
$976$		0			0
$977$	28.3101	−	49.0345i	0.905721	−	1.56875i	0.0857737	−	0.996315i	$-0.472664\pi$
$977$	28.3101	−	49.0345i	0.905721	−	1.56875i	0.819947	−	0.572440i	$-0.194003\pi$
$978$		0			0
$979$	−1.06408	+	1.84305i	−0.0340083	+	0.0589041i
$980$		0			0
$981$	−24.0990	−	5.53449i	−0.769422	−	0.176703i
$982$		0			0
$983$	−32.2972			−1.03012			−0.515061	−	0.857154i	$-0.672231\pi$
$983$	−32.2972			−1.03012			−0.515061	+	0.857154i	$0.672231\pi$
$984$		0			0
$985$	13.0407			0.415510
$986$		0			0
$987$	−26.5836	−	34.5826i	−0.846165	−	1.10078i
$988$		0			0
$989$	−37.5391	+	65.0197i	−1.19367	+	2.06750i
$990$		0			0
$991$	7.15502	+	12.3929i	0.227287	+	0.393672i	0.957003	−	0.290078i	$-0.0936812\pi$
$991$	7.15502	+	12.3929i	0.227287	+	0.393672i	−0.729716	+	0.683750i	$0.760348\pi$
$992$		0			0
$993$	−28.8253	−	21.3039i	−0.914742	−	0.676059i
$994$		0			0
$995$	5.79247	+	10.0329i	0.183634	+	0.318063i
$996$		0			0
$997$	56.2524			1.78153			0.890765	−	0.454463i	$-0.150169\pi$
$997$	56.2524			1.78153			0.890765	+	0.454463i	$0.150169\pi$
$998$		0			0
$999$	1.90449	+	2.22209i	0.0602553	+	0.0703038i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.t.i.961.5		10
3.2	odd	2		3024.2.t.i.289.2		10
4.3	odd	2		63.2.g.b.16.4	yes	10
7.4	even	3		1008.2.q.i.529.2		10
9.4	even	3		1008.2.q.i.625.2		10
9.5	odd	6		3024.2.q.i.2305.4		10
12.11	even	2		189.2.g.b.100.2		10
21.11	odd	6		3024.2.q.i.2881.4		10
28.3	even	6		441.2.h.f.214.2		10
28.11	odd	6		63.2.h.b.25.2	yes	10
28.19	even	6		441.2.f.f.295.4		10
28.23	odd	6		441.2.f.e.295.4		10
28.27	even	2		441.2.g.f.79.4		10
36.7	odd	6		567.2.e.f.163.4		10
36.11	even	6		567.2.e.e.163.2		10
36.23	even	6		189.2.h.b.37.4		10
36.31	odd	6		63.2.h.b.58.2	yes	10
63.4	even	3	inner	1008.2.t.i.193.5		10
63.32	odd	6		3024.2.t.i.1873.2		10
84.11	even	6		189.2.h.b.46.4		10
84.23	even	6		1323.2.f.e.883.2		10
84.47	odd	6		1323.2.f.f.883.2		10
84.59	odd	6		1323.2.h.f.802.4		10
84.83	odd	2		1323.2.g.f.667.2		10
252.11	even	6		567.2.e.e.487.2		10
252.23	even	6		1323.2.f.e.442.2		10
252.31	even	6		441.2.g.f.67.4		10
252.47	odd	6		3969.2.a.bb.1.4		5
252.59	odd	6		1323.2.g.f.361.2		10
252.67	odd	6		63.2.g.b.4.4	✓	10
252.79	odd	6		3969.2.a.z.1.2		5
252.95	even	6		189.2.g.b.172.2		10
252.103	even	6		441.2.f.f.148.4		10
252.131	odd	6		1323.2.f.f.442.2		10
252.139	even	6		441.2.h.f.373.2		10
252.151	odd	6		567.2.e.f.487.4		10
252.167	odd	6		1323.2.h.f.226.4		10
252.187	even	6		3969.2.a.ba.1.2		5
252.191	even	6		3969.2.a.bc.1.4		5
252.247	odd	6		441.2.f.e.148.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.2.g.b.4.4	✓	10	252.67	odd	6
63.2.g.b.16.4	yes	10	4.3	odd	2
63.2.h.b.25.2	yes	10	28.11	odd	6
63.2.h.b.58.2	yes	10	36.31	odd	6
189.2.g.b.100.2		10	12.11	even	2
189.2.g.b.172.2		10	252.95	even	6
189.2.h.b.37.4		10	36.23	even	6
189.2.h.b.46.4		10	84.11	even	6
441.2.f.e.148.4		10	252.247	odd	6
441.2.f.e.295.4		10	28.23	odd	6
441.2.f.f.148.4		10	252.103	even	6
441.2.f.f.295.4		10	28.19	even	6
441.2.g.f.67.4		10	252.31	even	6
441.2.g.f.79.4		10	28.27	even	2
441.2.h.f.214.2		10	28.3	even	6
441.2.h.f.373.2		10	252.139	even	6
567.2.e.e.163.2		10	36.11	even	6
567.2.e.e.487.2		10	252.11	even	6
567.2.e.f.163.4		10	36.7	odd	6
567.2.e.f.487.4		10	252.151	odd	6
1008.2.q.i.529.2		10	7.4	even	3
1008.2.q.i.625.2		10	9.4	even	3
1008.2.t.i.193.5		10	63.4	even	3	inner
1008.2.t.i.961.5		10	1.1	even	1	trivial
1323.2.f.e.442.2		10	252.23	even	6
1323.2.f.e.883.2		10	84.23	even	6
1323.2.f.f.442.2		10	252.131	odd	6
1323.2.f.f.883.2		10	84.47	odd	6
1323.2.g.f.361.2		10	252.59	odd	6
1323.2.g.f.667.2		10	84.83	odd	2
1323.2.h.f.226.4		10	252.167	odd	6
1323.2.h.f.802.4		10	84.59	odd	6
3024.2.q.i.2305.4		10	9.5	odd	6
3024.2.q.i.2881.4		10	21.11	odd	6
3024.2.t.i.289.2		10	3.2	odd	2
3024.2.t.i.1873.2		10	63.32	odd	6
3969.2.a.z.1.2		5	252.79	odd	6
3969.2.a.ba.1.2		5	252.187	even	6
3969.2.a.bb.1.4		5	252.47	odd	6
3969.2.a.bc.1.4		5	252.191	even	6

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:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.t (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.58800 - 0.691567i) q^{3} +1.33475 q^{5} +(2.54347 + 0.728536i) q^{7} +(2.04347 - 2.19641i) q^{9} +O(q^{10})\)	\(q+(1.58800 - 0.691567i) q^{3} +1.33475 q^{5} +(2.54347 + 0.728536i) q^{7} +(2.04347 - 2.19641i) q^{9} -1.51302 q^{11} +(-2.58800 - 4.48254i) q^{13} +(2.11958 - 0.923072i) q^{15} +(0.774463 + 1.34141i) q^{17} +(1.25211 - 2.16872i) q^{19} +(4.54285 - 0.602068i) q^{21} +7.36079 q^{23} -3.21843 q^{25} +(1.72605 - 4.90110i) q^{27} +(-0.0309713 + 0.0536439i) q^{29} +(-1.92388 + 3.33227i) q^{31} +(-2.40267 + 1.04635i) q^{33} +(3.39490 + 0.972416i) q^{35} +(-0.281608 + 0.487760i) q^{37} +(-7.20971 - 5.32849i) q^{39} +(4.51188 + 7.81481i) q^{41} +(-5.09988 + 8.83325i) q^{43} +(2.72753 - 2.93167i) q^{45} +(-4.75925 - 8.24327i) q^{47} +(5.93847 + 3.70602i) q^{49} +(2.15752 + 1.59456i) q^{51} +(0.755374 + 1.30835i) q^{53} -2.01950 q^{55} +(0.488532 - 4.30983i) q^{57} +(-4.22166 + 7.31212i) q^{59} +(-1.61958 - 2.80520i) q^{61} +(6.79767 - 4.09777i) q^{63} +(-3.45434 - 5.98309i) q^{65} +(3.46670 - 6.00449i) q^{67} +(11.6889 - 5.09048i) q^{69} +12.3304 q^{71} +(-1.37936 - 2.38912i) q^{73} +(-5.11086 + 2.22576i) q^{75} +(-3.84831 - 1.10229i) q^{77} +(-2.95969 - 5.12633i) q^{79} +(-0.648467 - 8.97661i) q^{81} +(-2.80111 + 4.85167i) q^{83} +(1.03372 + 1.79045i) q^{85} +(-0.0120840 + 0.106605i) q^{87} +(0.703287 - 1.21813i) q^{89} +(-3.31680 - 13.2867i) q^{91} +(-0.750637 + 6.62212i) q^{93} +(1.67126 - 2.89470i) q^{95} +(-6.09713 + 10.5605i) q^{97} +(-3.09180 + 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9}+O(q^{10}) \) 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9	\( 10 q - 2 q^{3} - 8 q^{5} + q^{7} - 4 q^{9} + 8 q^{11} - 8 q^{13} + 19 q^{15} + 12 q^{17} - q^{19} - 2 q^{21} + 6 q^{23} + 2 q^{25} + 7 q^{27} + 7 q^{29} + 3 q^{31} - q^{33} - 5 q^{35} - 20 q^{39} + 5 q^{41} + 7 q^{43} - q^{45} - 27 q^{47} + 25 q^{49} - 24 q^{51} - 21 q^{53} - 4 q^{55} - 4 q^{57} - 30 q^{59} - 14 q^{61} + 35 q^{63} - 11 q^{65} + 2 q^{67} + 15 q^{69} + 6 q^{71} + 15 q^{73} - 31 q^{75} - 31 q^{77} + 4 q^{79} + 8 q^{81} - 9 q^{83} - 6 q^{85} - 32 q^{87} + 28 q^{89} + 4 q^{91} - 12 q^{93} + 14 q^{95} - 12 q^{97} - 35 q^{99}+O(q^{100}) \) 10 * q - 2 * q^3 - 8 * q^5 + q^7 - 4 * q^9 + 8 * q^11 - 8 * q^13 + 19 * q^15 + 12 * q^17 - q^19 - 2 * q^21 + 6 * q^23 + 2 * q^25 + 7 * q^27 + 7 * q^29 + 3 * q^31 - q^33 - 5 * q^35 - 20 * q^39 + 5 * q^41 + 7 * q^43 - q^45 - 27 * q^47 + 25 * q^49 - 24 * q^51 - 21 * q^53 - 4 * q^55 - 4 * q^57 - 30 * q^59 - 14 * q^61 + 35 * q^63 - 11 * q^65 + 2 * q^67 + 15 * q^69 + 6 * q^71 + 15 * q^73 - 31 * q^75 - 31 * q^77 + 4 * q^79 + 8 * q^81 - 9 * q^83 - 6 * q^85 - 32 * q^87 + 28 * q^89 + 4 * q^91 - 12 * q^93 + 14 * q^95 - 12 * q^97 - 35 * q^99

Introduction

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