LMFDB - Embedded newform 400.3.bg.c.113.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [400,3,Mod(17,400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(400, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 0, 13]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("400.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 400 = 2^{4} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	400.bg (of order $20$, degree $8$, 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:	$10.8992105744$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 25)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			113.1
Character	$\chi$	$=$	400.113
Dual form			400.3.bg.c.177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72787 + 3.39113i) q^{3} +(2.36408 + 4.40581i) q^{5} +(2.38950 - 2.38950i) q^{7} +(-3.22416 - 4.43767i) q^{9} +O(q^{10})$	\(q+(-1.72787 + 3.39113i) q^{3} +(2.36408 + 4.40581i) q^{5} +(2.38950 - 2.38950i) q^{7} +(-3.22416 - 4.43767i) q^{9} +(15.4985 + 11.2603i) q^{11} +(16.2234 + 2.56953i) q^{13} +(-19.0255 + 0.404238i) q^{15} +(-2.10364 - 4.12863i) q^{17} +(-1.02742 - 0.333828i) q^{19} +(3.97436 + 12.2318i) q^{21} +(1.81434 + 11.4553i) q^{23} +(-13.8223 + 20.8313i) q^{25} +(-13.2122 + 2.09261i) q^{27} +(-17.5664 + 5.70767i) q^{29} +(6.76718 - 20.8272i) q^{31} +(-64.9643 + 33.1010i) q^{33} +(16.1766 + 4.87872i) q^{35} +(7.13692 - 45.0607i) q^{37} +(-36.7454 + 50.5757i) q^{39} +(-13.3733 + 9.71629i) q^{41} +(-41.9589 - 41.9589i) q^{43} +(11.9294 - 24.6960i) q^{45} +(-20.1364 - 10.2600i) q^{47} +37.5806i q^{49} +17.6355 q^{51} +(-21.6364 + 42.4637i) q^{53} +(-12.9711 + 94.9034i) q^{55} +(2.90730 - 2.90730i) q^{57} +(27.2616 + 37.5224i) q^{59} +(45.3825 + 32.9723i) q^{61} +(-18.3079 - 2.89969i) q^{63} +(27.0324 + 77.5516i) q^{65} +(-2.50707 - 4.92040i) q^{67} +(-41.9814 - 13.6406i) q^{69} +(20.2891 + 62.4433i) q^{71} +(-16.1217 - 101.788i) q^{73} +(-46.7586 - 82.8669i) q^{75} +(63.9400 - 10.1271i) q^{77} +(81.7963 - 26.5772i) q^{79} +(30.9880 - 95.3712i) q^{81} +(-19.1762 + 9.77074i) q^{83} +(13.2168 - 19.0286i) q^{85} +(10.9970 - 69.4320i) q^{87} +(52.7361 - 72.5850i) q^{89} +(44.9056 - 32.6258i) q^{91} +(58.9350 + 58.9350i) q^{93} +(-0.958111 - 5.31580i) q^{95} +(-83.7126 - 42.6537i) q^{97} -105.082i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9}+O(q^{10}) $ 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9	$ 32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9} + 6 q^{11} - 10 q^{13} + 10 q^{15} + 60 q^{17} - 90 q^{19} - 6 q^{21} - 10 q^{23} - 40 q^{25} + 100 q^{27} - 110 q^{29} + 6 q^{31} - 190 q^{33} + 120 q^{35} + 50 q^{37} - 390 q^{39} - 86 q^{41} - 230 q^{43} + 310 q^{45} - 70 q^{47} + 16 q^{51} - 190 q^{53} + 250 q^{55} - 650 q^{57} + 260 q^{59} + 114 q^{61} + 20 q^{63} + 360 q^{65} - 270 q^{67} + 340 q^{69} + 66 q^{71} + 30 q^{73} + 90 q^{75} - 250 q^{77} + 210 q^{79} + 62 q^{81} + 600 q^{85} - 300 q^{87} - 10 q^{89} + 6 q^{91} + 520 q^{93} - 310 q^{95} + 270 q^{97}+O(q^{100}) $ 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9 + 6 * q^11 - 10 * q^13 + 10 * q^15 + 60 * q^17 - 90 * q^19 - 6 * q^21 - 10 * q^23 - 40 * q^25 + 100 * q^27 - 110 * q^29 + 6 * q^31 - 190 * q^33 + 120 * q^35 + 50 * q^37 - 390 * q^39 - 86 * q^41 - 230 * q^43 + 310 * q^45 - 70 * q^47 + 16 * q^51 - 190 * q^53 + 250 * q^55 - 650 * q^57 + 260 * q^59 + 114 * q^61 + 20 * q^63 + 360 * q^65 - 270 * q^67 + 340 * q^69 + 66 * q^71 + 30 * q^73 + 90 * q^75 - 250 * q^77 + 210 * q^79 + 62 * q^81 + 600 * q^85 - 300 * q^87 - 10 * q^89 + 6 * q^91 + 520 * q^93 - 310 * q^95 + 270 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/400\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$351$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.72787	+	3.39113i	−0.575955	+	1.13038i	0.400829	+	0.916153i	$0.368722\pi$
$3$	−1.72787	+	3.39113i	−0.575955	+	1.13038i	−0.976785	+	0.214223i	$0.931278\pi$
$4$		0			0
$5$	2.36408	+	4.40581i	0.472815	+	0.881162i
$5$	2.36408	+	4.40581i	0.472815	+	0.881162i
$6$		0			0
$7$	2.38950	−	2.38950i	0.341357	−	0.341357i	−0.515520	−	0.856877i	$-0.672401\pi$
$7$	2.38950	−	2.38950i	0.341357	−	0.341357i	0.856877	+	0.515520i	$0.172401\pi$
$8$		0			0
$9$	−3.22416	−	4.43767i	−0.358240	−	0.493075i
$10$		0			0
$11$	15.4985	+	11.2603i	1.40895	+	1.02366i	0.993474	+	0.114058i	$0.0363851\pi$
$11$	15.4985	+	11.2603i	1.40895	+	1.02366i	0.415476	+	0.909604i	$0.363615\pi$
$12$		0			0
$13$	16.2234	+	2.56953i	1.24795	+	0.197656i	0.745239	−	0.666798i	$-0.232336\pi$
$13$	16.2234	+	2.56953i	1.24795	+	0.197656i	0.502712	+	0.864454i	$0.332336\pi$
$14$		0			0
$15$	−19.0255	+	0.404238i	−1.26836	+	0.0269492i
$16$		0			0
$17$	−2.10364	−	4.12863i	−0.123744	−	0.242861i	0.820821	−	0.571185i	$-0.193516\pi$
$17$	−2.10364	−	4.12863i	−0.123744	−	0.242861i	−0.944565	+	0.328324i	$0.893516\pi$
$18$		0			0
$19$	−1.02742	−	0.333828i	−0.0540747	−	0.0175699i	0.281855	−	0.959457i	$-0.409050\pi$
$19$	−1.02742	−	0.333828i	−0.0540747	−	0.0175699i	−0.335929	+	0.941887i	$0.609050\pi$
$20$		0			0
$21$	3.97436	+	12.2318i	0.189255	+	0.582468i
$22$		0			0
$23$	1.81434	+	11.4553i	0.0788845	+	0.498057i	0.995221	+	0.0976482i	$0.0311320\pi$
$23$	1.81434	+	11.4553i	0.0788845	+	0.498057i	−0.916336	+	0.400409i	$0.868868\pi$
$24$		0			0
$25$	−13.8223	+	20.8313i	−0.552892	+	0.833253i
$26$		0			0
$27$	−13.2122	+	2.09261i	−0.489341	+	0.0775040i
$28$		0			0
$29$	−17.5664	+	5.70767i	−0.605738	+	0.196816i	−0.595798	−	0.803134i	$-0.703164\pi$
$29$	−17.5664	+	5.70767i	−0.605738	+	0.196816i	−0.00994032	+	0.999951i	$0.503164\pi$
$30$		0			0
$31$	6.76718	−	20.8272i	0.218296	−	0.671846i	−0.780607	−	0.625022i	$-0.785090\pi$
$31$	6.76718	−	20.8272i	0.218296	−	0.671846i	0.998903	−	0.0468241i	$-0.0149100\pi$
$32$		0			0
$33$	−64.9643	+	33.1010i	−1.96862	+	1.00306i
$34$		0			0
$35$	16.1766	+	4.87872i	0.462189	+	0.139392i
$36$		0			0
$37$	7.13692	−	45.0607i	0.192890	−	1.21786i	−0.681201	−	0.732096i	$-0.738542\pi$
$37$	7.13692	−	45.0607i	0.192890	−	1.21786i	0.874091	−	0.485762i	$-0.161458\pi$
$38$		0			0
$39$	−36.7454	+	50.5757i	−0.942190	+	1.29681i
$40$		0			0
$41$	−13.3733	+	9.71629i	−0.326179	+	0.236983i	−0.738807	−	0.673917i	$-0.764611\pi$
$41$	−13.3733	+	9.71629i	−0.326179	+	0.236983i	0.412629	+	0.910899i	$0.364611\pi$
$42$		0			0
$43$	−41.9589	−	41.9589i	−0.975789	−	0.975789i	0.0239244	−	0.999714i	$-0.492384\pi$
$43$	−41.9589	−	41.9589i	−0.975789	−	0.975789i	−0.999714	+	0.0239244i	$0.992384\pi$
$44$		0			0
$45$	11.9294	−	24.6960i	0.265097	−	0.548801i
$46$		0			0
$47$	−20.1364	−	10.2600i	−0.428434	−	0.218298i	0.226457	−	0.974021i	$-0.427286\pi$
$47$	−20.1364	−	10.2600i	−0.428434	−	0.218298i	−0.654891	+	0.755723i	$0.727286\pi$
$48$		0			0
$49$			37.5806i			0.766951i
$50$		0			0
$51$	17.6355			0.345795
$52$		0			0
$53$	−21.6364	+	42.4637i	−0.408233	+	0.801203i	−0.999988	−	0.00491533i	$-0.998435\pi$
$53$	−21.6364	+	42.4637i	−0.408233	+	0.801203i	0.591755	+	0.806118i	$0.298435\pi$
$54$		0			0
$55$	−12.9711	+	94.9034i	−0.235839	+	1.72552i
$56$		0			0
$57$	2.90730	−	2.90730i	0.0510052	−	0.0510052i
$58$		0			0
$59$	27.2616	+	37.5224i	0.462062	+	0.635973i	0.974935	−	0.222491i	$-0.0714189\pi$
$59$	27.2616	+	37.5224i	0.462062	+	0.635973i	−0.512873	+	0.858464i	$0.671419\pi$
$60$		0			0
$61$	45.3825	+	32.9723i	0.743975	+	0.540529i	0.893953	−	0.448160i	$-0.147920\pi$
$61$	45.3825	+	32.9723i	0.743975	+	0.540529i	−0.149979	+	0.988689i	$0.547920\pi$
$62$		0			0
$63$	−18.3079	−	2.89969i	−0.290602	−	0.0460269i
$64$		0			0
$65$	27.0324	+	77.5516i	0.415883	+	1.19310i
$66$		0			0
$67$	−2.50707	−	4.92040i	−0.0374190	−	0.0734388i	0.871540	−	0.490324i	$-0.163122\pi$
$67$	−2.50707	−	4.92040i	−0.0374190	−	0.0734388i	−0.908959	+	0.416885i	$0.863122\pi$
$68$		0			0
$69$	−41.9814	−	13.6406i	−0.608426	−	0.197690i
$70$		0			0
$71$	20.2891	+	62.4433i	0.285761	+	0.879483i	0.986169	+	0.165740i	$0.0530014\pi$
$71$	20.2891	+	62.4433i	0.285761	+	0.879483i	−0.700408	+	0.713743i	$0.746999\pi$
$72$		0			0
$73$	−16.1217	−	101.788i	−0.220845	−	1.39436i	−0.810044	−	0.586370i	$-0.800557\pi$
$73$	−16.1217	−	101.788i	−0.220845	−	1.39436i	0.589199	−	0.807988i	$-0.299443\pi$
$74$		0			0
$75$	−46.7586	−	82.8669i	−0.623449	−	1.10489i
$76$		0			0
$77$	63.9400	−	10.1271i	0.830389	−	0.131521i
$78$		0			0
$79$	81.7963	−	26.5772i	1.03540	−	0.336421i	0.258475	−	0.966018i	$-0.416780\pi$
$79$	81.7963	−	26.5772i	1.03540	−	0.336421i	0.776922	+	0.629597i	$0.216780\pi$
$80$		0			0
$81$	30.9880	−	95.3712i	0.382568	−	1.17742i
$82$		0			0
$83$	−19.1762	+	9.77074i	−0.231038	+	0.117720i	−0.565678	−	0.824626i	$-0.691385\pi$
$83$	−19.1762	+	9.77074i	−0.231038	+	0.117720i	0.334640	+	0.942346i	$0.391385\pi$
$84$		0			0
$85$	13.2168	−	19.0286i	0.155492	−	0.223866i
$86$		0			0
$87$	10.9970	−	69.4320i	0.126402	−	0.798070i
$88$		0			0
$89$	52.7361	−	72.5850i	0.592541	−	0.815562i	−0.402459	−	0.915438i	$-0.631844\pi$
$89$	52.7361	−	72.5850i	0.592541	−	0.815562i	0.995000	+	0.0998756i	$0.0318445\pi$
$90$		0			0
$91$	44.9056	−	32.6258i	0.493468	−	0.358525i
$92$		0			0
$93$	58.9350	+	58.9350i	0.633710	+	0.633710i
$94$		0			0
$95$	−0.958111	−	5.31580i	−0.0100854	−	0.0559558i
$96$		0			0
$97$	−83.7126	−	42.6537i	−0.863017	−	0.439729i	−0.0343096	−	0.999411i	$-0.510923\pi$
$97$	−83.7126	−	42.6537i	−0.863017	−	0.439729i	−0.828707	+	0.559682i	$0.810923\pi$
$98$		0			0
$99$		−	105.082i		−	1.06143i
$100$		0			0
$101$	14.4367			0.142938			0.0714690	−	0.997443i	$-0.477231\pi$
$101$	14.4367			0.142938			0.0714690	+	0.997443i	$0.477231\pi$
$102$		0			0
$103$	−39.3351	+	77.1995i	−0.381894	+	0.749510i	−0.999311	−	0.0371269i	$-0.988179\pi$
$103$	−39.3351	+	77.1995i	−0.381894	+	0.749510i	0.617416	+	0.786637i	$0.288179\pi$
$104$		0			0
$105$	−44.4954	+	46.4272i	−0.423766	+	0.442164i
$106$		0			0
$107$	120.842	−	120.842i	1.12937	−	1.12937i	0.139087	−	0.990280i	$-0.455583\pi$
$107$	120.842	−	120.842i	1.12937	−	1.12937i	0.990280	−	0.139087i	$-0.0444167\pi$
$108$		0			0
$109$	19.5764	+	26.9446i	0.179600	+	0.247198i	0.889320	−	0.457286i	$-0.151178\pi$
$109$	19.5764	+	26.9446i	0.179600	+	0.247198i	−0.709720	+	0.704484i	$0.751178\pi$
$110$		0			0
$111$	140.475	+	102.061i	1.26554	+	0.919470i
$112$		0			0
$113$	−25.8428	−	4.09310i	−0.228697	−	0.0362221i	0.0410338	−	0.999158i	$-0.486935\pi$
$113$	−25.8428	−	4.09310i	−0.228697	−	0.0362221i	−0.269731	+	0.962936i	$0.586935\pi$
$114$		0			0
$115$	−46.1807	+	35.0749i	−0.401571	+	0.304999i
$116$		0			0
$117$	−40.9040	−	80.2786i	−0.349607	−	0.686142i
$118$		0			0
$119$	−14.8920	−	4.83871i	−0.125143	−	0.0406614i
$120$		0			0
$121$	76.0170	+	233.956i	0.628240	+	1.93352i
$122$		0			0
$123$	−9.84186	−	62.1391i	−0.0800151	−	0.505196i
$124$		0			0
$125$	−124.456	−	11.6515i	−0.995646	−	0.0932121i
$126$		0			0
$127$	−73.7930	+	11.6877i	−0.581047	+	0.0920289i	−0.440038	−	0.897979i	$-0.645035\pi$
$127$	−73.7930	+	11.6877i	−0.581047	+	0.0920289i	−0.141010	+	0.990008i	$0.545035\pi$
$128$		0			0
$129$	214.788	−	69.7887i	1.66502	−	0.540998i
$130$		0			0
$131$	25.0313	−	77.0383i	0.191078	−	0.588078i	−0.808922	−	0.587916i	$-0.799948\pi$
$131$	25.0313	−	77.0383i	0.191078	−	0.588078i	1.00000		0.000162070i	$-5.15886e-5\pi$
$132$		0			0
$133$	−3.25270	+	1.65733i	−0.0244564	+	0.0124611i
$134$		0			0
$135$	−40.4543	−	53.2634i	−0.299661	−	0.394544i
$136$		0			0
$137$	24.7567	−	156.308i	0.180706	−	1.14093i	−0.715932	−	0.698170i	$-0.753998\pi$
$137$	24.7567	−	156.308i	0.180706	−	1.14093i	0.896638	−	0.442763i	$-0.146002\pi$
$138$		0			0
$139$	92.2598	−	126.985i	0.663739	−	0.913559i	−0.335859	−	0.941912i	$-0.609026\pi$
$139$	92.2598	−	126.985i	0.663739	−	0.913559i	0.999598	+	0.0283536i	$0.00902645\pi$
$140$		0			0
$141$	69.5860	−	50.5572i	0.493518	−	0.358561i
$142$		0			0
$143$	222.503	+	222.503i	1.55597	+	1.55597i
$144$		0			0
$145$	−66.6753	−	63.9009i	−0.459829	−	0.440696i
$146$		0			0
$147$	−127.441	−	64.9342i	−0.866943	−	0.441729i
$148$		0			0
$149$		−	87.4028i		−	0.586596i	−0.956021	−	0.293298i	$-0.905247\pi$
$149$		−	87.4028i		−	0.586596i	0.956021	−	0.293298i	$-0.0947529\pi$
$150$		0			0
$151$	−172.239			−1.14066			−0.570328	−	0.821417i	$-0.693184\pi$
$151$	−172.239			−1.14066			−0.570328	+	0.821417i	$0.693184\pi$
$152$		0			0
$153$	−11.5390	+	22.6467i	−0.0754186	+	0.148017i
$154$		0			0
$155$	107.759	−	19.4223i	0.695219	−	0.125305i
$156$		0			0
$157$	−53.0884	+	53.0884i	−0.338143	+	0.338143i	−0.855668	−	0.517525i	$-0.826853\pi$
$157$	−53.0884	+	53.0884i	−0.338143	+	0.338143i	0.517525	+	0.855668i	$0.326853\pi$
$158$		0			0
$159$	−106.615	−	146.743i	−0.670536	−	0.922914i
$160$		0			0
$161$	31.7078	+	23.0371i	0.196943	+	0.143088i
$162$		0			0
$163$	−1.91719	−	0.303653i	−0.0117619	−	0.00186290i	0.150551	−	0.988602i	$-0.451895\pi$
$163$	−1.91719	−	0.303653i	−0.0117619	−	0.00186290i	−0.162313	+	0.986739i	$0.551895\pi$
$164$		0			0
$165$	−299.417	−	207.967i	−1.81465	−	1.26041i
$166$		0			0
$167$	5.17831	+	10.1630i	0.0310078	+	0.0608563i	0.905991	−	0.423298i	$-0.139128\pi$
$167$	5.17831	+	10.1630i	0.0310078	+	0.0608563i	−0.874983	+	0.484154i	$0.839128\pi$
$168$		0			0
$169$	95.8665	+	31.1489i	0.567257	+	0.184313i
$170$		0			0
$171$	1.83114	+	5.63567i	0.0107084	+	0.0329571i
$172$		0			0
$173$	31.2522	+	197.319i	0.180649	+	1.14057i	0.896738	+	0.442562i	$0.145930\pi$
$173$	31.2522	+	197.319i	0.180649	+	1.14057i	−0.716089	+	0.698009i	$0.754070\pi$
$174$		0			0
$175$	16.7481	+	82.8048i	0.0957034	+	0.473170i
$176$		0			0
$177$	−174.348	+	27.6140i	−0.985016	+	0.156011i
$178$		0			0
$179$	51.8588	−	16.8499i	0.289714	−	0.0941338i	−0.160555	−	0.987027i	$-0.551328\pi$
$179$	51.8588	−	16.8499i	0.289714	−	0.0941338i	0.450269	+	0.892893i	$0.351328\pi$
$180$		0			0
$181$	42.0315	−	129.360i	0.232218	−	0.714694i	−0.765260	−	0.643721i	$-0.777390\pi$
$181$	42.0315	−	129.360i	0.232218	−	0.714694i	0.997478	−	0.0709726i	$-0.0226103\pi$
$182$		0			0
$183$	−190.228	+	96.9260i	−1.03950	+	0.529650i
$184$		0			0
$185$	215.401	−	75.0831i	1.16433	−	0.405855i
$186$		0			0
$187$	13.8864	−	87.6750i	0.0742586	−	0.468850i
$188$		0			0
$189$	−26.5703	+	36.5708i	−0.140583	+	0.193496i
$190$		0			0
$191$	−73.9512	+	53.7287i	−0.387179	+	0.281302i	−0.764299	−	0.644863i	$-0.776915\pi$
$191$	−73.9512	+	53.7287i	−0.387179	+	0.281302i	0.377119	+	0.926165i	$0.376915\pi$
$192$		0			0
$193$	62.2572	+	62.2572i	0.322576	+	0.322576i	0.849755	−	0.527178i	$-0.176750\pi$
$193$	62.2572	+	62.2572i	0.322576	+	0.322576i	−0.527178	+	0.849755i	$0.676750\pi$
$194$		0			0
$195$	−309.696	−	42.3284i	−1.58818	−	0.217069i
$196$		0			0
$197$	232.265	+	118.345i	1.17901	+	0.600736i	0.929926	−	0.367746i	$-0.119870\pi$
$197$	232.265	+	118.345i	1.17901	+	0.600736i	0.249084	+	0.968482i	$0.419870\pi$
$198$		0			0
$199$			198.360i			0.996782i	0.866952	+	0.498391i	$0.166076\pi$
$199$			198.360i			0.996782i	−0.866952	+	0.498391i	$0.833924\pi$
$200$		0			0
$201$	21.0176			0.104565
$202$		0			0
$203$	−28.3364	+	55.6134i	−0.139588	+	0.273958i
$204$		0			0
$205$	−74.4236	−	35.9502i	−0.363042	−	0.175367i
$206$		0			0
$207$	44.9853	−	44.9853i	0.217320	−	0.217320i
$208$		0			0
$209$	−12.1644	−	16.7429i	−0.0582028	−	0.0801093i
$210$		0			0
$211$	32.1898	+	23.3872i	0.152558	+	0.110840i	0.661446	−	0.749993i	$-0.269943\pi$
$211$	32.1898	+	23.3872i	0.152558	+	0.110840i	−0.508888	+	0.860833i	$0.669943\pi$
$212$		0			0
$213$	−246.810	−	39.0909i	−1.15873	−	0.183525i
$214$		0			0
$215$	85.6689	−	284.057i	0.398460	−	1.32120i
$216$		0			0
$217$	−33.5965	−	65.9368i	−0.154822	−	0.303856i
$218$		0			0
$219$	373.033	+	121.206i	1.70334	+	0.553450i
$220$		0			0
$221$	−23.5195	−	72.3857i	−0.106423	−	0.327537i
$222$		0			0
$223$	10.9708	+	69.2671i	0.0491966	+	0.310615i	1.00000		0.000819017i	$0.000260701\pi$
$223$	10.9708	+	69.2671i	0.0491966	+	0.310615i	−0.950803	+	0.309796i	$0.899739\pi$
$224$		0			0
$225$	137.008	−	5.82470i	0.608924	−	0.0258876i
$226$		0			0
$227$	46.0077	−	7.28690i	0.202677	−	0.0321009i	−0.0542703	−	0.998526i	$-0.517283\pi$
$227$	46.0077	−	7.28690i	0.202677	−	0.0321009i	0.256947	+	0.966425i	$0.417283\pi$
$228$		0			0
$229$	−17.5687	+	5.70843i	−0.0767194	+	0.0249276i	−0.347125	−	0.937819i	$-0.612842\pi$
$229$	−17.5687	+	5.70843i	−0.0767194	+	0.0249276i	0.270406	+	0.962746i	$0.412842\pi$
$230$		0			0
$231$	−76.1374	+	234.327i	−0.329599	+	1.01440i
$232$		0			0
$233$	364.992	−	185.972i	1.56649	−	0.798165i	0.566817	−	0.823844i	$-0.308175\pi$
$233$	364.992	−	185.972i	1.56649	−	0.798165i	0.999670	+	0.0256786i	$0.00817466\pi$
$234$		0			0
$235$	−2.40035	−	112.973i	−0.0102143	−	0.480734i
$236$		0			0
$237$	−51.2063	+	323.304i	−0.216060	+	1.36415i
$238$		0			0
$239$	241.175	−	331.949i	1.00910	−	1.38891i	0.0895301	−	0.995984i	$-0.471463\pi$
$239$	241.175	−	331.949i	1.00910	−	1.38891i	0.919571	−	0.392924i	$-0.128537\pi$
$240$		0			0
$241$	−284.923	+	207.009i	−1.18225	+	0.858958i	−0.992424	−	0.122859i	$-0.960794\pi$
$241$	−284.923	+	207.009i	−1.18225	+	0.858958i	−0.189830	+	0.981817i	$0.560794\pi$
$242$		0			0
$243$	184.743	+	184.743i	0.760259	+	0.760259i
$244$		0			0
$245$	−165.573	+	88.8434i	−0.675808	+	0.362626i
$246$		0			0
$247$	−15.8104	−	8.05580i	−0.0640097	−	0.0326146i
$248$		0			0
$249$		−	81.9114i		−	0.328961i
$250$		0			0
$251$	−99.8650			−0.397869			−0.198934	−	0.980013i	$-0.563748\pi$
$251$	−99.8650			−0.397869			−0.198934	+	0.980013i	$0.563748\pi$
$252$		0			0
$253$	−100.871	+	197.970i	−0.398698	+	0.782489i
$254$		0			0
$255$	41.6917	+	77.6988i	0.163497	+	0.304701i
$256$		0			0
$257$	−138.476	+	138.476i	−0.538818	+	0.538818i	−0.923182	−	0.384363i	$-0.874421\pi$
$257$	−138.476	+	138.476i	−0.538818	+	0.538818i	0.384363	+	0.923182i	$0.374421\pi$
$258$		0			0
$259$	−90.6189	−	124.726i	−0.349880	−	0.481568i
$260$		0			0
$261$	81.9657	+	59.5516i	0.314045	+	0.228167i
$262$		0			0
$263$	−208.637	−	33.0448i	−0.793296	−	0.125646i	−0.253382	−	0.967366i	$-0.581543\pi$
$263$	−208.637	−	33.0448i	−0.793296	−	0.125646i	−0.539914	+	0.841720i	$0.681543\pi$
$264$		0			0
$265$	−238.237	+	5.06187i	−0.899008	+	0.0191014i
$266$		0			0
$267$	155.024	+	304.252i	0.580615	+	1.13952i
$268$		0			0
$269$	326.227	+	105.998i	1.21274	+	0.394043i	0.844433	−	0.535661i	$-0.179938\pi$
$269$	326.227	+	105.998i	1.21274	+	0.394043i	0.368307	+	0.929704i	$0.379938\pi$
$270$		0			0
$271$	71.5216	+	220.121i	0.263918	+	0.812255i	0.991941	+	0.126702i	$0.0404393\pi$
$271$	71.5216	+	220.121i	0.263918	+	0.812255i	−0.728023	+	0.685552i	$0.759561\pi$
$272$		0			0
$273$	33.0475	+	208.654i	0.121053	+	0.764299i
$274$		0			0
$275$	−448.791	+	167.210i	−1.63197	+	0.608038i
$276$		0			0
$277$	395.109	−	62.5791i	1.42639	−	0.225917i	0.604971	−	0.796247i	$-0.293185\pi$
$277$	395.109	−	62.5791i	1.42639	−	0.225917i	0.821416	+	0.570330i	$0.193185\pi$
$278$		0			0
$279$	−114.243	+	37.1198i	−0.409473	+	0.133046i
$280$		0			0
$281$	−41.2543	+	126.968i	−0.146813	+	0.451843i	−0.997240	−	0.0742504i	$-0.976344\pi$
$281$	−41.2543	+	126.968i	−0.146813	+	0.451843i	0.850427	+	0.526093i	$0.176344\pi$
$282$		0			0
$283$	222.492	−	113.365i	0.786190	−	0.400584i	−0.0143241	−	0.999897i	$-0.504560\pi$
$283$	222.492	−	113.365i	0.786190	−	0.400584i	0.800515	+	0.599313i	$0.204560\pi$
$284$		0			0
$285$	19.6821	+	5.93592i	0.0690599	+	0.0208278i
$286$		0			0
$287$	−8.73848	+	55.1726i	−0.0304477	+	0.192239i
$288$		0			0
$289$	157.250	−	216.436i	0.544116	−	0.748912i
$290$		0			0
$291$	289.288	−	210.180i	0.994118	−	0.722269i
$292$		0			0
$293$	279.769	+	279.769i	0.954844	+	0.954844i	0.999024	−	0.0441800i	$-0.0140675\pi$
$293$	279.769	+	279.769i	0.954844	+	0.954844i	−0.0441800	+	0.999024i	$0.514068\pi$
$294$		0			0
$295$	−100.868	+	208.815i	−0.341925	+	0.707849i
$296$		0			0
$297$	−228.332	−	116.341i	−0.768795	−	0.391721i
$298$		0			0
$299$			190.506i			0.637143i
$300$		0			0
$301$	−200.522			−0.666185
$302$		0			0
$303$	−24.9447	+	48.9568i	−0.0823258	+	0.161574i
$304$		0			0
$305$	−37.9820	+	277.895i	−0.124531	+	0.911133i
$306$		0			0
$307$	−292.963	+	292.963i	−0.954277	+	0.954277i	−0.998999	−	0.0447226i	$-0.985760\pi$
$307$	−292.963	+	292.963i	−0.954277	+	0.954277i	0.0447226	+	0.998999i	$0.485760\pi$
$308$		0			0
$309$	−193.828	−	266.781i	−0.627274	−	0.863368i
$310$		0			0
$311$	56.9351	+	41.3658i	0.183071	+	0.133009i	0.675546	−	0.737318i	$-0.263908\pi$
$311$	56.9351	+	41.3658i	0.183071	+	0.133009i	−0.492475	+	0.870326i	$0.663908\pi$
$312$		0			0
$313$	−551.569	−	87.3599i	−1.76220	−	0.279105i	−0.810412	−	0.585860i	$-0.800757\pi$
$313$	−551.569	−	87.3599i	−1.76220	−	0.279105i	−0.951788	+	0.306755i	$0.900757\pi$
$314$		0			0
$315$	−30.5059	−	87.5164i	−0.0968440	−	0.277830i
$316$		0			0
$317$	−283.718	−	556.827i	−0.895008	−	1.75655i	−0.597581	−	0.801808i	$-0.703871\pi$
$317$	−283.718	−	556.827i	−0.895008	−	1.75655i	−0.297427	−	0.954744i	$-0.596129\pi$
$318$		0			0
$319$	−336.522	−	109.343i	−1.05493	−	0.342767i
$320$		0			0
$321$	200.992	+	618.591i	0.626144	+	1.92707i
$322$		0			0
$323$	0.783067	+	4.94409i	0.00242436	+	0.0153068i
$324$		0			0
$325$	−277.771	+	302.437i	−0.854679	+	0.930577i
$326$		0			0
$327$	−125.198	+	19.8294i	−0.382868	+	0.0606403i
$328$		0			0
$329$	−72.6321	+	23.5996i	−0.220766	+	0.0717314i
$330$		0			0
$331$	98.3145	−	302.581i	0.297023	−	0.914142i	−0.685512	−	0.728062i	$-0.740421\pi$
$331$	98.3145	−	302.581i	0.297023	−	0.914142i	0.982535	−	0.186080i	$-0.0595785\pi$
$332$		0			0
$333$	−222.975	+	113.612i	−0.669596	+	0.341176i
$334$		0			0
$335$	15.7514	−	22.6779i	0.0470192	−	0.0676951i
$336$		0			0
$337$	52.4267	−	331.009i	0.155569	−	0.982223i	−0.779151	−	0.626837i	$-0.784349\pi$
$337$	52.4267	−	331.009i	0.155569	−	0.982223i	0.934719	−	0.355387i	$-0.115651\pi$
$338$		0			0
$339$	58.5331	−	80.5640i	0.172664	−	0.237652i
$340$		0			0
$341$	339.401	−	246.590i	0.995312	−	0.723136i
$342$		0			0
$343$	206.884	+	206.884i	0.603161	+	0.603161i
$344$		0			0
$345$	−39.1494	−	217.209i	−0.113477	−	0.629592i
$346$		0			0
$347$	−368.200	−	187.607i	−1.06110	−	0.540655i	−0.165815	−	0.986157i	$-0.553025\pi$
$347$	−368.200	−	187.607i	−1.06110	−	0.540655i	−0.895281	+	0.445501i	$0.853025\pi$
$348$		0			0
$349$			234.141i			0.670891i	0.942060	+	0.335445i	$0.108887\pi$
$349$			234.141i			0.670891i	−0.942060	+	0.335445i	$0.891113\pi$
$350$		0			0
$351$	−219.723			−0.625993
$352$		0			0
$353$	93.3076	−	183.126i	0.264327	−	0.518772i	−0.720251	−	0.693713i	$-0.755974\pi$
$353$	93.3076	−	183.126i	0.264327	−	0.518772i	0.984579	+	0.174941i	$0.0559736\pi$
$354$		0			0
$355$	−227.148	+	237.010i	−0.639854	+	0.667635i
$356$		0			0
$357$	42.1401	−	42.1401i	0.118039	−	0.118039i
$358$		0			0
$359$	203.218	+	279.706i	0.566068	+	0.779126i	0.992082	−	0.125591i	$-0.0400826\pi$
$359$	203.218	+	279.706i	0.566068	+	0.779126i	−0.426014	+	0.904717i	$0.640083\pi$
$360$		0			0
$361$	−291.111	−	211.505i	−0.806402	−	0.585885i
$362$		0			0
$363$	−924.723	−	146.462i	−2.54745	−	0.403476i
$364$		0			0
$365$	410.346	−	311.664i	1.12424	−	0.853873i
$366$		0			0
$367$	−241.897	−	474.749i	−0.659119	−	1.29359i	−0.942378	−	0.334551i	$-0.891415\pi$
$367$	−241.897	−	474.749i	−0.659119	−	1.29359i	0.283258	−	0.959044i	$-0.408585\pi$
$368$		0			0
$369$	86.2354	+	28.0196i	0.233700	+	0.0759338i
$370$		0			0
$371$	49.7670	+	153.167i	0.134143	+	0.412849i
$372$		0			0
$373$	−9.51134	−	60.0522i	−0.0254996	−	0.160998i	0.971653	−	0.236413i	$-0.0759718\pi$
$373$	−9.51134	−	60.0522i	−0.0254996	−	0.160998i	−0.997152	+	0.0754151i	$0.975972\pi$
$374$		0			0
$375$	254.555	−	401.913i	0.678812	−	1.07177i
$376$		0			0
$377$	−299.652	+	47.4603i	−0.794834	+	0.125889i
$378$		0			0
$379$	−185.112	+	60.1464i	−0.488421	+	0.158698i	−0.542866	−	0.839819i	$-0.682661\pi$
$379$	−185.112	+	60.1464i	−0.488421	+	0.158698i	0.0544453	+	0.998517i	$0.482661\pi$
$380$		0			0
$381$	87.8701	−	270.436i	0.230630	−	0.709807i
$382$		0			0
$383$	446.637	−	227.573i	1.16615	−	0.594186i	0.239794	−	0.970824i	$-0.422920\pi$
$383$	446.637	−	227.573i	1.16615	−	0.594186i	0.926361	+	0.376638i	$0.122920\pi$
$384$		0			0
$385$	195.777	+	257.766i	0.508512	+	0.669522i
$386$		0			0
$387$	−50.9178	+	321.482i	−0.131571	+	0.830704i
$388$		0			0
$389$	96.3944	−	132.676i	0.247801	−	0.341068i	−0.666939	−	0.745112i	$-0.732396\pi$
$389$	96.3944	−	132.676i	0.247801	−	0.341068i	0.914739	+	0.404044i	$0.132396\pi$
$390$		0			0
$391$	43.4781	−	31.5887i	0.111197	−	0.0807894i
$392$		0			0
$393$	217.996	+	217.996i	0.554697	+	0.554697i
$394$		0			0
$395$	310.467	+	297.548i	0.785992	+	0.753287i
$396$		0			0
$397$	306.180	+	156.006i	0.771234	+	0.392963i	0.794887	−	0.606757i	$-0.207530\pi$
$397$	306.180	+	156.006i	0.771234	+	0.392963i	−0.0236537	+	0.999720i	$0.507530\pi$
$398$		0			0
$399$		−	13.8940i		−	0.0348220i
$400$		0			0
$401$	−355.216			−0.885825			−0.442912	−	0.896565i	$-0.646055\pi$
$401$	−355.216			−0.885825			−0.442912	+	0.896565i	$0.646055\pi$
$402$		0			0
$403$	163.303	−	320.499i	0.405217	−	0.795283i
$404$		0			0
$405$	493.445	−	88.9377i	1.21838	−	0.219599i
$406$		0			0
$407$	618.008	−	618.008i	1.51845	−	1.51845i
$408$		0			0
$409$	−221.160	−	304.400i	−0.540733	−	0.744255i	0.447986	−	0.894041i	$-0.352142\pi$
$409$	−221.160	−	304.400i	−0.540733	−	0.744255i	−0.988718	+	0.149786i	$0.952142\pi$
$410$		0			0
$411$	487.283	+	354.032i	1.18560	+	0.861392i
$412$		0			0
$413$	154.801	+	24.5181i	0.374822	+	0.0593659i
$414$		0			0
$415$	−88.3819	−	61.3877i	−0.212969	−	0.147922i
$416$		0			0
$417$	271.209	+	532.277i	0.650381	+	1.27644i
$418$		0			0
$419$	581.123	+	188.818i	1.38693	+	0.450640i	0.904941	−	0.425538i	$-0.139915\pi$
$419$	581.123	+	188.818i	1.38693	+	0.450640i	0.481987	+	0.876178i	$0.339915\pi$
$420$		0			0
$421$	−63.7783	−	196.289i	−0.151492	−	0.466245i	0.846296	−	0.532712i	$-0.178827\pi$
$421$	−63.7783	−	196.289i	−0.151492	−	0.466245i	−0.997789	+	0.0664671i	$0.978827\pi$
$422$		0			0
$423$	19.3924	+	122.439i	0.0458449	+	0.289453i
$424$		0			0
$425$	115.082	+	13.2455i	0.270781	+	0.0311658i
$426$		0			0
$427$	187.229	−	29.6541i	0.438474	−	0.0694475i
$428$		0			0
$429$	−1138.99	+	370.081i	−2.65500	+	0.862661i
$430$		0			0
$431$	75.3165	−	231.800i	0.174748	−	0.537820i	−0.824874	−	0.565317i	$-0.808754\pi$
$431$	75.3165	−	231.800i	0.174748	−	0.537820i	0.999622	+	0.0274974i	$0.00875381\pi$
$432$		0			0
$433$	−347.221	+	176.918i	−0.801896	+	0.408586i	−0.806376	−	0.591404i	$-0.798574\pi$
$433$	−347.221	+	176.918i	−0.801896	+	0.408586i	0.00447992	+	0.999990i	$0.498574\pi$
$434$		0			0
$435$	331.902	−	115.692i	0.762993	−	0.265959i
$436$		0			0
$437$	1.96002	−	12.3751i	0.00448517	−	0.0283183i
$438$		0			0
$439$	−213.132	+	293.351i	−0.485494	+	0.668225i	−0.979549	−	0.201206i	$-0.935514\pi$
$439$	−213.132	+	293.351i	−0.485494	+	0.668225i	0.494055	+	0.869430i	$0.335514\pi$
$440$		0			0
$441$	166.770	−	121.166i	0.378164	−	0.274752i
$442$		0			0
$443$	−464.820	−	464.820i	−1.04926	−	1.04926i	−0.998722	−	0.0505328i	$-0.983908\pi$
$443$	−464.820	−	464.820i	−1.04926	−	1.04926i	−0.0505328	−	0.998722i	$-0.516092\pi$
$444$		0			0
$445$	444.468	+	60.7487i	0.998804	+	0.136514i
$446$		0			0
$447$	296.394	+	151.020i	0.663074	+	0.337853i
$448$		0			0
$449$			516.794i			1.15099i	0.817806	+	0.575495i	$0.195190\pi$
$449$			516.794i			1.15099i	−0.817806	+	0.575495i	$0.804810\pi$
$450$		0			0
$451$	−316.674			−0.702160
$452$		0			0
$453$	297.606	−	584.085i	0.656967	−	1.28937i
$454$		0			0
$455$	249.903	+	120.715i	0.549238	+	0.265309i
$456$		0			0
$457$	276.799	−	276.799i	0.605687	−	0.605687i	−0.336129	−	0.941816i	$-0.609118\pi$
$457$	276.799	−	276.799i	0.605687	−	0.605687i	0.941816	+	0.336129i	$0.109118\pi$
$458$		0			0
$459$	36.4334	+	50.1463i	0.0793756	+	0.109251i
$460$		0			0
$461$	692.843	+	503.380i	1.50291	+	1.09193i	0.969203	+	0.246264i	$0.0792029\pi$
$461$	692.843	+	503.380i	1.50291	+	1.09193i	0.533711	+	0.845667i	$0.320797\pi$
$462$		0			0
$463$	138.978	+	22.0119i	0.300168	+	0.0475419i	0.304702	−	0.952448i	$-0.401443\pi$
$463$	138.978	+	22.0119i	0.300168	+	0.0475419i	−0.00453395	+	0.999990i	$0.501443\pi$
$464$		0			0
$465$	−120.330	+	398.983i	−0.258773	+	0.858028i
$466$		0			0
$467$	164.433	+	322.718i	0.352105	+	0.691045i	0.997336	−	0.0729424i	$-0.0232389\pi$
$467$	164.433	+	322.718i	0.352105	+	0.691045i	−0.645231	+	0.763987i	$0.723239\pi$
$468$		0			0
$469$	−17.7479	−	5.76665i	−0.0378421	−	0.0122956i
$470$		0			0
$471$	−88.2999	−	271.759i	−0.187473	−	0.576983i
$472$		0			0
$473$	−177.829	−	1122.77i	−0.375960	−	2.37372i
$474$		0			0
$475$	21.1554	−	16.7882i	0.0445376	−	0.0353436i
$476$		0			0
$477$	258.199	−	40.8948i	0.541298	−	0.0857333i
$478$		0			0
$479$	−326.819	+	106.190i	−0.682293	+	0.221691i	−0.629599	−	0.776920i	$-0.716781\pi$
$479$	−326.819	+	106.190i	−0.682293	+	0.221691i	−0.0526943	+	0.998611i	$0.516781\pi$
$480$		0			0
$481$	231.570	−	712.698i	0.481434	−	1.48170i
$482$		0			0
$483$	−132.909	+	67.7203i	−0.275173	+	0.140208i
$484$		0			0
$485$	−9.97893	−	469.658i	−0.0205751	−	0.968368i
$486$		0			0
$487$	109.417	−	690.831i	0.224675	−	1.41854i	−0.575021	−	0.818139i	$-0.695006\pi$
$487$	109.417	−	690.831i	0.224675	−	1.41854i	0.799696	−	0.600405i	$-0.204994\pi$
$488$		0			0
$489$	4.34237	−	5.97676i	0.00888011	−	0.0122224i
$490$		0			0
$491$	281.430	−	204.471i	0.573177	−	0.416438i	−0.263081	−	0.964774i	$-0.584739\pi$
$491$	281.430	−	204.471i	0.573177	−	0.416438i	0.836258	+	0.548336i	$0.184739\pi$
$492$		0			0
$493$	60.5184	+	60.5184i	0.122755	+	0.122755i
$494$		0			0
$495$	462.971	−	248.422i	0.935296	−	0.501863i
$496$		0			0
$497$	197.689	+	100.727i	0.397764	+	0.202671i
$498$		0			0
$499$		−	90.5909i		−	0.181545i	−0.995872	−	0.0907724i	$-0.971066\pi$
$499$		−	90.5909i		−	0.181545i	0.995872	−	0.0907724i	$-0.0289336\pi$
$500$		0			0
$501$	−43.4114			−0.0866496
$502$		0			0
$503$	360.023	−	706.585i	0.715751	−	1.40474i	−0.190365	−	0.981713i	$-0.560967\pi$
$503$	360.023	−	706.585i	0.715751	−	1.40474i	0.906117	−	0.423028i	$-0.139033\pi$
$504$		0			0
$505$	34.1295	+	63.6055i	0.0675832	+	0.125951i
$506$		0			0
$507$	−271.274	+	271.274i	−0.535058	+	0.535058i
$508$		0			0
$509$	361.411	+	497.439i	0.710041	+	0.977287i	0.999796	+	0.0201863i	$0.00642593\pi$
$509$	361.411	+	497.439i	0.710041	+	0.977287i	−0.289756	+	0.957101i	$0.593574\pi$
$510$		0			0
$511$	−281.745	−	204.700i	−0.551360	−	0.400587i
$512$		0			0
$513$	14.2730	+	2.26063i	0.0278227	+	0.00440668i
$514$		0			0
$515$	−433.117	+	9.20254i	−0.841004	+	0.0178690i
$516$		0			0
$517$	−196.552	−	385.756i	−0.380179	−	0.746143i
$518$		0			0
$519$	−723.133	−	234.960i	−1.39332	−	0.452717i
$520$		0			0
$521$	−204.980	−	630.864i	−0.393436	−	1.21087i	−0.930173	−	0.367121i	$-0.880343\pi$
$521$	−204.980	−	630.864i	−0.393436	−	1.21087i	0.536737	−	0.843749i	$-0.319657\pi$
$522$		0			0
$523$	−37.7042	−	238.055i	−0.0720921	−	0.455172i	−0.997156	−	0.0753609i	$-0.975989\pi$
$523$	−37.7042	−	238.055i	−0.0720921	−	0.455172i	0.925064	−	0.379811i	$-0.124011\pi$
$524$		0			0
$525$	−309.740	−	86.2806i	−0.589981	−	0.164344i
$526$		0			0
$527$	−100.224	+	15.8739i	−0.190178	+	0.0301212i
$528$		0			0
$529$	375.176	−	121.902i	0.709218	−	0.230439i
$530$		0			0
$531$	78.6164	−	241.957i	0.148054	−	0.455662i
$532$		0			0
$533$	−241.926	+	123.268i	−0.453896	+	0.231271i
$534$		0			0
$535$	818.088	+	246.728i	1.52914	+	0.461173i
$536$		0			0
$537$	−32.4647	+	204.974i	−0.0604557	+	0.381703i
$538$		0			0
$539$	−423.168	+	582.441i	−0.785099	+	1.08060i
$540$		0			0
$541$	−755.213	+	548.694i	−1.39596	+	1.01422i	−0.400776	+	0.916176i	$0.631259\pi$
$541$	−755.213	+	548.694i	−1.39596	+	1.01422i	−0.995182	+	0.0980465i	$0.968741\pi$
$542$		0			0
$543$	366.050	+	366.050i	0.674125	+	0.674125i
$544$		0			0
$545$	−72.4326	+	149.949i	−0.132904	+	0.275135i
$546$		0			0
$547$	926.420	+	472.034i	1.69364	+	0.862951i	0.988014	+	0.154364i	$0.0493328\pi$
$547$	926.420	+	472.034i	1.69364	+	0.862951i	0.705623	+	0.708587i	$0.250667\pi$
$548$		0			0
$549$		−	307.701i		−	0.560475i
$550$		0			0
$551$	19.9534			0.0362131
$552$		0			0
$553$	131.946	−	258.958i	0.238600	−	0.468279i
$554$		0			0
$555$	−117.568	+	860.187i	−0.211834	+	1.54989i
$556$		0			0
$557$	−162.407	+	162.407i	−0.291575	+	0.291575i	−0.837702	−	0.546127i	$-0.816102\pi$
$557$	−162.407	+	162.407i	−0.291575	+	0.291575i	0.546127	+	0.837702i	$0.316102\pi$
$558$		0			0
$559$	−572.900	−	788.530i	−1.02487	−	1.41061i
$560$		0			0
$561$	273.323	+	198.581i	0.487208	+	0.353977i
$562$		0			0
$563$	228.223	+	36.1470i	0.405370	+	0.0642043i	0.355790	−	0.934566i	$-0.384212\pi$
$563$	228.223	+	36.1470i	0.405370	+	0.0642043i	0.0495798	+	0.998770i	$0.484212\pi$
$564$		0			0
$565$	−43.0610	−	123.535i	−0.0762141	−	0.218646i
$566$		0			0
$567$	−153.844	−	301.935i	−0.271329	−	0.532513i
$568$		0			0
$569$	−124.308	−	40.3900i	−0.218467	−	0.0709842i	0.197739	−	0.980255i	$-0.436640\pi$
$569$	−124.308	−	40.3900i	−0.218467	−	0.0709842i	−0.416205	+	0.909271i	$0.636640\pi$
$570$		0			0
$571$	−154.922	−	476.802i	−0.271318	−	0.835030i	−0.990170	−	0.139867i	$-0.955332\pi$
$571$	−154.922	−	476.802i	−0.271318	−	0.835030i	0.718853	−	0.695163i	$-0.244668\pi$
$572$		0			0
$573$	−54.4231	−	343.614i	−0.0949793	−	0.599675i
$574$		0			0
$575$	−263.708	−	120.544i	−0.458623	−	0.209641i
$576$		0			0
$577$	372.888	−	59.0596i	0.646252	−	0.102356i	0.175300	−	0.984515i	$-0.443910\pi$
$577$	372.888	−	59.0596i	0.646252	−	0.102356i	0.470952	+	0.882159i	$0.343910\pi$
$578$		0			0
$579$	−318.694	+	103.550i	−0.550422	+	0.178843i
$580$		0			0
$581$	−22.4742	+	69.1686i	−0.0386820	+	0.119051i
$582$		0			0
$583$	−813.484	+	414.491i	−1.39534	+	0.710962i
$584$		0			0
$585$	256.992	−	370.000i	0.439302	−	0.632478i
$586$		0			0
$587$	−138.085	+	871.835i	−0.235239	+	1.48524i	0.533568	+	0.845757i	$0.320851\pi$
$587$	−138.085	+	871.835i	−0.235239	+	1.48524i	−0.768807	+	0.639481i	$0.779149\pi$
$588$		0			0
$589$	−13.9054	+	19.1392i	−0.0236086	+	0.0324944i
$590$		0			0
$591$	−802.646	+	583.156i	−1.35811	+	0.986728i
$592$		0			0
$593$	128.291	+	128.291i	0.216342	+	0.216342i	0.806955	−	0.590613i	$-0.201114\pi$
$593$	128.291	+	128.291i	0.216342	+	0.216342i	−0.590613	+	0.806955i	$0.701114\pi$
$594$		0			0
$595$	−13.8874	−	77.0504i	−0.0233402	−	0.129496i
$596$		0			0
$597$	−672.663	−	342.739i	−1.12674	−	0.574102i
$598$		0			0
$599$		−	543.188i		−	0.906825i	−0.891301	−	0.453412i	$-0.850207\pi$
$599$		−	543.188i		−	0.906825i	0.891301	−	0.453412i	$-0.149793\pi$
$600$		0			0
$601$	228.860			0.380799			0.190399	−	0.981707i	$-0.439022\pi$
$601$	228.860			0.380799			0.190399	+	0.981707i	$0.439022\pi$
$602$		0			0
$603$	−13.7519	+	26.9897i	−0.0228059	+	0.0447591i
$604$		0			0
$605$	−851.056	+	888.007i	−1.40670	+	1.46778i
$606$		0			0
$607$	−241.898	+	241.898i	−0.398514	+	0.398514i	−0.877709	−	0.479195i	$-0.840929\pi$
$607$	−241.898	+	241.898i	−0.398514	+	0.398514i	0.479195	+	0.877709i	$0.340929\pi$
$608$		0			0
$609$	−139.631	−	192.185i	−0.229278	−	0.315575i
$610$		0			0
$611$	−300.317	−	218.193i	−0.491517	−	0.357108i
$612$		0			0
$613$	−58.4076	−	9.25086i	−0.0952816	−	0.0150911i	0.108612	−	0.994084i	$-0.465360\pi$
$613$	−58.4076	−	9.25086i	−0.0952816	−	0.0150911i	−0.203893	+	0.978993i	$0.565360\pi$
$614$		0			0
$615$	250.506	−	190.263i	0.407327	−	0.309370i
$616$		0			0
$617$	352.094	+	691.024i	0.570656	+	1.11997i	0.978370	+	0.206865i	$0.0663260\pi$
$617$	352.094	+	691.024i	0.570656	+	1.11997i	−0.407714	+	0.913110i	$0.633674\pi$
$618$		0			0
$619$	537.492	+	174.642i	0.868323	+	0.282135i	0.709100	−	0.705108i	$-0.249101\pi$
$619$	537.492	+	174.642i	0.868323	+	0.282135i	0.159222	+	0.987243i	$0.449101\pi$
$620$		0			0
$621$	−47.9430	−	147.553i	−0.0772029	−	0.237606i
$622$		0			0
$623$	−47.4290	−	299.455i	−0.0761300	−	0.480666i
$624$		0			0
$625$	−242.889	−	575.873i	−0.388622	−	0.921397i
$626$		0			0
$627$	77.7956	−	12.3216i	0.124076	−	0.0196517i
$628$		0			0
$629$	−201.053	+	65.3260i	−0.319639	+	0.103857i
$630$		0			0
$631$	187.092	−	575.810i	0.296501	−	0.912536i	−0.686212	−	0.727401i	$-0.740728\pi$
$631$	187.092	−	575.810i	0.296501	−	0.912536i	0.982713	−	0.185134i	$-0.0592721\pi$
$632$		0			0
$633$	−134.929	+	68.7496i	−0.213158	+	0.108609i
$634$		0			0
$635$	−225.946	−	297.487i	−0.355820	−	0.468484i
$636$		0			0
$637$	−96.5644	+	609.684i	−0.151592	+	0.957117i
$638$		0			0
$639$	211.688	−	291.363i	0.331280	−	0.455968i
$640$		0			0
$641$	621.687	−	451.682i	0.969870	−	0.704652i	0.0144481	−	0.999896i	$-0.495401\pi$
$641$	621.687	−	451.682i	0.969870	−	0.704652i	0.955422	+	0.295244i	$0.0954009\pi$
$642$		0			0
$643$	485.126	+	485.126i	0.754472	+	0.754472i	0.975310	−	0.220838i	$-0.0708792\pi$
$643$	485.126	+	485.126i	0.754472	+	0.754472i	−0.220838	+	0.975310i	$0.570879\pi$
$644$		0			0
$645$	815.250	+	781.327i	1.26395	+	1.21136i
$646$		0			0
$647$	−438.563	−	223.459i	−0.677840	−	0.345377i	0.0809441	−	0.996719i	$-0.474206\pi$
$647$	−438.563	−	223.459i	−0.677840	−	0.345377i	−0.758785	+	0.651342i	$0.774206\pi$
$648$		0			0
$649$			888.513i			1.36905i
$650$		0			0
$651$	281.650			0.432642
$652$		0			0
$653$	330.468	−	648.579i	0.506076	−	0.993230i	−0.486736	−	0.873549i	$-0.661813\pi$
$653$	330.468	−	648.579i	0.506076	−	0.993230i	0.992812	−	0.119681i	$-0.0381873\pi$
$654$		0			0
$655$	398.592	−	71.8414i	0.608537	−	0.109682i
$656$		0			0
$657$	−399.724	+	399.724i	−0.608408	+	0.608408i
$658$		0			0
$659$	285.023	+	392.301i	0.432509	+	0.595297i	0.968527	−	0.248909i	$-0.0800722\pi$
$659$	285.023	+	392.301i	0.432509	+	0.595297i	−0.536018	+	0.844206i	$0.680072\pi$
$660$		0			0
$661$	−837.490	−	608.472i	−1.26700	−	0.920533i	−0.267925	−	0.963440i	$-0.586338\pi$
$661$	−837.490	−	608.472i	−1.26700	−	0.920533i	−0.999079	+	0.0429071i	$0.986338\pi$
$662$		0			0
$663$	286.108	+	45.3150i	0.431535	+	0.0683484i
$664$		0			0
$665$	−14.9915	−	10.4127i	−0.0225436	−	0.0156582i
$666$		0			0
$667$	−97.2548	−	190.873i	−0.145809	−	0.286167i
$668$		0			0
$669$	−253.850	−	82.4808i	−0.379447	−	0.123290i
$670$		0			0
$671$	332.081	+	1022.04i	0.494904	+	1.52316i
$672$		0			0
$673$	143.361	+	905.147i	0.213018	+	1.34494i	0.829910	+	0.557897i	$0.188391\pi$
$673$	143.361	+	905.147i	0.213018	+	1.34494i	−0.616892	+	0.787048i	$0.711609\pi$
$674$		0			0
$675$	139.031	−	304.153i	0.205972	−	0.450596i
$676$		0			0
$677$	−1316.25	+	208.473i	−1.94424	+	0.307937i	−0.999785	−	0.0207152i	$-0.993406\pi$
$677$	−1316.25	+	208.473i	−1.94424	+	0.307937i	−0.944451	+	0.328652i	$0.893406\pi$
$678$		0			0
$679$	−301.952	+	98.1102i	−0.444701	+	0.144492i
$680$		0			0
$681$	−54.7843	+	168.609i	−0.0804469	+	0.247590i
$682$		0			0
$683$	−553.314	+	281.927i	−0.810123	+	0.412778i	−0.809426	−	0.587222i	$-0.800222\pi$
$683$	−553.314	+	281.927i	−0.810123	+	0.412778i	−0.000696453		1.00000i	$0.500222\pi$
$684$		0			0
$685$	747.189	−	260.450i	1.09079	−	0.380219i
$686$		0			0
$687$	10.9984	−	69.4413i	0.0160093	−	0.101079i
$688$		0			0
$689$	−460.126	+	633.310i	−0.667818	+	0.919172i
$690$		0			0
$691$	−651.607	+	473.420i	−0.942992	+	0.685123i	−0.949139	−	0.314858i	$-0.898043\pi$
$691$	−651.607	+	473.420i	−0.942992	+	0.685123i	0.00614739	+	0.999981i	$0.498043\pi$
$692$		0			0
$693$	−251.093	−	251.093i	−0.362328	−	0.362328i
$694$		0			0
$695$	777.579	+	106.277i	1.11882	+	0.152917i
$696$		0			0
$697$	68.2477	+	34.7739i	0.0979163	+	0.0498908i
$698$		0			0
$699$			1559.07i			2.23043i
$700$		0			0
$701$	−570.439			−0.813751			−0.406876	−	0.913484i	$-0.633382\pi$
$701$	−570.439			−0.813751			−0.406876	+	0.913484i	$0.633382\pi$
$702$		0			0
$703$	−22.3752	+	43.9137i	−0.0318281	+	0.0624662i
$704$		0			0
$705$	387.252	+	187.061i	0.549293	+	0.265335i
$706$		0			0
$707$	34.4965	−	34.4965i	0.0487928	−	0.0487928i
$708$		0			0
$709$	341.238	+	469.674i	0.481295	+	0.662445i	0.978753	−	0.205043i	$-0.0657333\pi$
$709$	341.238	+	469.674i	0.481295	+	0.662445i	−0.497458	+	0.867488i	$0.665733\pi$
$710$		0			0
$711$	−381.665	−	277.296i	−0.536801	−	0.390009i
$712$		0			0
$713$	250.861	+	39.7324i	0.351838	+	0.0557257i
$714$		0			0
$715$	−454.292	+	1506.32i	−0.635374	+	2.10674i
$716$		0			0
$717$	708.963	+	1391.42i	0.988791	+	1.94061i
$718$		0			0
$719$	497.061	+	161.505i	0.691322	+	0.224624i	0.633546	−	0.773705i	$-0.281599\pi$
$719$	497.061	+	161.505i	0.691322	+	0.224624i	0.0577767	+	0.998330i	$0.481599\pi$
$720$		0			0
$721$	90.4769	+	278.459i	0.125488	+	0.386213i
$722$		0			0
$723$	−209.684	−	1323.89i	−0.290020	−	1.83111i
$724$		0			0
$725$	123.910	−	444.825i	0.170910	−	0.613552i
$726$		0			0
$727$	412.828	−	65.3856i	0.567852	−	0.0899389i	0.134094	−	0.990969i	$-0.457187\pi$
$727$	412.828	−	65.3856i	0.567852	−	0.0899389i	0.433757	+	0.901030i	$0.357187\pi$
$728$		0			0
$729$	−87.3564	+	28.3838i	−0.119830	+	0.0389353i
$730$		0			0
$731$	−84.9664	+	261.500i	−0.116233	+	0.357729i
$732$		0			0
$733$	641.297	−	326.757i	0.874894	−	0.445781i	0.0419378	−	0.999120i	$-0.486647\pi$
$733$	641.297	−	326.757i	0.874894	−	0.445781i	0.832956	+	0.553340i	$0.186647\pi$
$734$		0			0
$735$	−15.1915	−	714.988i	−0.0206687	−	0.972773i
$736$		0			0
$737$	16.5494	−	104.489i	0.0224551	−	0.141776i
$738$		0			0
$739$	560.278	−	771.157i	0.758158	−	1.04351i	−0.239208	−	0.970968i	$-0.576888\pi$
$739$	560.278	−	771.157i	0.758158	−	1.04351i	0.997365	−	0.0725458i	$-0.0231124\pi$
$740$		0			0
$741$	54.6365	−	39.6957i	0.0737335	−	0.0535705i
$742$		0			0
$743$	973.452	+	973.452i	1.31016	+	1.31016i	0.921292	+	0.388872i	$0.127135\pi$
$743$	973.452	+	973.452i	1.31016	+	1.31016i	0.388872	+	0.921292i	$0.372865\pi$
$744$		0			0
$745$	385.080	−	206.627i	0.516886	−	0.277352i
$746$		0			0
$747$	105.186	+	53.5951i	0.140812	+	0.0717472i
$748$		0			0
$749$		−	577.505i		−	0.771034i
$750$		0			0
$751$	−815.196			−1.08548			−0.542740	−	0.839901i	$-0.682613\pi$
$751$	−815.196			−1.08548			−0.542740	+	0.839901i	$0.682613\pi$
$752$		0			0
$753$	172.553	−	338.655i	0.229155	−	0.449741i
$754$		0			0
$755$	−407.186	−	758.852i	−0.539320	−	1.00510i
$756$		0			0
$757$	266.404	−	266.404i	0.351920	−	0.351920i	−0.508903	−	0.860824i	$-0.669949\pi$
$757$	266.404	−	266.404i	0.351920	−	0.351920i	0.860824	+	0.508903i	$0.169949\pi$
$758$		0			0
$759$	−497.050	−	684.131i	−0.654875	−	0.901358i
$760$		0			0
$761$	−875.638	−	636.188i	−1.15064	−	0.835989i	−0.162075	−	0.986778i	$-0.551819\pi$
$761$	−875.638	−	636.188i	−1.15064	−	0.835989i	−0.988566	+	0.150789i	$0.951819\pi$
$762$		0			0
$763$	111.162	+	17.6063i	0.145690	+	0.0230751i
$764$		0			0
$765$	−127.056	+	2.69959i	−0.166086	+	0.00352887i
$766$		0			0
$767$	345.860	+	678.789i	0.450926	+	0.884993i
$768$		0			0
$769$	−749.913	−	243.662i	−0.975180	−	0.316855i	−0.222275	−	0.974984i	$-0.571348\pi$
$769$	−749.913	−	243.662i	−0.975180	−	0.316855i	−0.752905	+	0.658129i	$0.771348\pi$
$770$		0			0
$771$	−230.322	−	708.860i	−0.298732	−	0.919403i
$772$		0			0
$773$	56.0962	+	354.177i	0.0725694	+	0.458185i	0.997037	+	0.0769245i	$0.0245100\pi$
$773$	56.0962	+	354.177i	0.0725694	+	0.458185i	−0.924467	+	0.381261i	$0.875490\pi$
$774$		0			0
$775$	340.321	+	428.849i	0.439124	+	0.553354i
$776$		0			0
$777$	579.540	−	91.7901i	0.745869	−	0.118134i
$778$		0			0
$779$	16.9836	−	5.51830i	0.0218018	−	0.00708382i
$780$		0			0
$781$	−388.680	+	1196.24i	−0.497670	+	1.53167i
$782$		0			0
$783$	220.147	−	112.171i	0.281159	−	0.143257i
$784$		0			0
$785$	−359.402	−	108.392i	−0.457837	−	0.138079i
$786$		0			0
$787$	−197.057	+	1244.17i	−0.250390	+	1.58090i	0.467021	+	0.884246i	$0.345327\pi$
$787$	−197.057	+	1244.17i	−0.250390	+	1.58090i	−0.717410	+	0.696651i	$0.754673\pi$
$788$		0			0
$789$	472.556	−	650.417i	0.598930	−	0.824356i
$790$		0			0
$791$	−71.5318	+	51.9709i	−0.0904321	+	0.0657028i
$792$		0			0
$793$	651.533	+	651.533i	0.821605	+	0.821605i
$794$		0			0
$795$	394.476	−	816.639i	0.496197	−	1.02722i
$796$		0			0
$797$	748.686	+	381.474i	0.939380	+	0.478638i	0.855480	−	0.517836i	$-0.173262\pi$
$797$	748.686	+	381.474i	0.939380	+	0.478638i	0.0839000	+	0.996474i	$0.473262\pi$
$798$		0			0
$799$			104.719i			0.131063i
$800$		0			0
$801$	−492.138			−0.614405
$802$		0			0
$803$	896.303	−	1759.09i	1.11619	−	2.19065i
$804$		0			0
$805$	−26.5373	+	194.160i	−0.0329656	+	0.241193i
$806$		0			0
$807$	−923.128	+	923.128i	−1.14390	+	1.14390i
$808$		0			0
$809$	−668.124	−	919.594i	−0.825864	−	1.13670i	−0.988679	−	0.150048i	$-0.952057\pi$
$809$	−668.124	−	919.594i	−0.825864	−	1.13670i	0.162814	−	0.986657i	$-0.447943\pi$
$810$		0			0
$811$	−1006.65	−	731.378i	−1.24125	−	0.901822i	−0.243570	−	0.969883i	$-0.578319\pi$
$811$	−1006.65	−	731.378i	−1.24125	−	0.901822i	−0.997681	+	0.0680614i	$0.978319\pi$
$812$		0			0
$813$	−870.038	−	137.801i	−1.07016	−	0.169496i
$814$		0			0
$815$	−3.19454	−	9.16463i	−0.00391969	−	0.0112449i
$816$		0			0
$817$	29.1023	+	57.1165i	0.0356209	+	0.0699100i
$818$		0			0
$819$	−289.566	−	94.0855i	−0.353560	−	0.114879i
$820$		0			0
$821$	3.49825	+	10.7665i	0.00426096	+	0.0131139i	0.953164	−	0.302453i	$-0.0978054\pi$
$821$	3.49825	+	10.7665i	0.00426096	+	0.0131139i	−0.948903	+	0.315567i	$0.897805\pi$
$822$		0			0
$823$	65.6724	+	414.639i	0.0797964	+	0.503815i	0.994922	+	0.100646i	$0.0320911\pi$
$823$	65.6724	+	414.639i	0.0797964	+	0.503815i	−0.915126	+	0.403168i	$0.867909\pi$
$824$		0			0
$825$	208.418	−	1810.82i	0.252628	−	2.19494i
$826$		0			0
$827$	−1100.78	+	174.346i	−1.33105	+	0.210817i	−0.781113	−	0.624390i	$-0.785348\pi$
$827$	−1100.78	+	174.346i	−1.33105	+	0.210817i	−0.549936	+	0.835207i	$0.685348\pi$
$828$		0			0
$829$	494.260	−	160.595i	0.596213	−	0.193721i	0.00466205	−	0.999989i	$-0.498516\pi$
$829$	494.260	−	160.595i	0.596213	−	0.193721i	0.591551	+	0.806268i	$0.298516\pi$
$830$		0			0
$831$	−470.482	+	1447.99i	−0.566163	+	1.74247i
$832$		0			0
$833$	155.156	−	79.0562i	0.186262	−	0.0949054i
$834$		0			0
$835$	−32.5343	+	46.8407i	−0.0389632	+	0.0560967i
$836$		0			0
$837$	−45.8261	+	289.335i	−0.0547504	+	0.345681i
$838$		0			0
$839$	−657.552	+	905.043i	−0.783733	+	1.07872i	0.211127	+	0.977459i	$0.432287\pi$
$839$	−657.552	+	905.043i	−0.783733	+	1.07872i	−0.994860	+	0.101257i	$0.967713\pi$
$840$		0			0
$841$	−404.382	+	293.801i	−0.480835	+	0.349347i
$842$		0			0
$843$	−359.282	−	359.282i	−0.426194	−	0.426194i
$844$		0			0
$845$	89.3995	+	496.008i	0.105798	+	0.586991i
$846$		0			0
$847$	740.681	+	377.396i	0.874475	+	0.445567i
$848$		0			0
$849$			950.378i			1.11941i
$850$		0			0
$851$	529.134			0.621779
$852$		0			0
$853$	281.083	−	551.657i	0.329523	−	0.646725i	−0.665497	−	0.746401i	$-0.731780\pi$
$853$	281.083	−	551.657i	0.329523	−	0.646725i	0.995020	+	0.0996751i	$0.0317803\pi$
$854$		0			0
$855$	−20.5007	+	21.3908i	−0.0239774	+	0.0250185i
$856$		0			0
$857$	312.684	−	312.684i	0.364858	−	0.364858i	−0.500740	−	0.865598i	$-0.666939\pi$
$857$	312.684	−	312.684i	0.364858	−	0.364858i	0.865598	+	0.500740i	$0.166939\pi$
$858$		0			0
$859$	−59.1889	−	81.4665i	−0.0689044	−	0.0948387i	0.773174	−	0.634194i	$-0.218668\pi$
$859$	−59.1889	−	81.4665i	−0.0689044	−	0.0948387i	−0.842078	+	0.539355i	$0.818668\pi$
$860$		0			0
$861$	−171.998	−	124.964i	−0.199766	−	0.145138i
$862$		0			0
$863$	158.959	+	25.1766i	0.184194	+	0.0291734i	0.247850	−	0.968798i	$-0.420276\pi$
$863$	158.959	+	25.1766i	0.184194	+	0.0291734i	−0.0636561	+	0.997972i	$0.520276\pi$
$864$		0			0
$865$	−795.466	+	604.168i	−0.919614	+	0.698460i
$866$		0			0
$867$	462.254	+	907.225i	0.533165	+	1.04640i
$868$		0			0
$869$	1566.98	+	509.144i	1.80320	+	0.585896i
$870$		0			0
$871$	−28.0300	−	86.2675i	−0.0321814	−	0.0990442i
$872$		0			0
$873$	80.6196	+	509.012i	0.0923477	+	0.583061i
$874$		0			0
$875$	−325.228	+	269.546i	−0.371689	+	0.308052i
$876$		0			0
$877$	−889.491	+	140.882i	−1.01424	+	0.160640i	−0.641362	−	0.767239i	$-0.721630\pi$
$877$	−889.491	+	140.882i	−1.01424	+	0.160640i	−0.372882	+	0.927879i	$0.621630\pi$
$878$		0			0
$879$	−1432.14	+	465.329i	−1.62928	+	0.529385i
$880$		0			0
$881$	−310.239	+	954.819i	−0.352145	+	1.08379i	0.605502	+	0.795844i	$0.292972\pi$
$881$	−310.239	+	954.819i	−0.352145	+	1.08379i	−0.957647	+	0.287946i	$0.907028\pi$
$882$		0			0
$883$	−322.466	+	164.305i	−0.365193	+	0.186075i	−0.626952	−	0.779058i	$-0.715698\pi$
$883$	−322.466	+	164.305i	−0.365193	+	0.186075i	0.261758	+	0.965133i	$0.415698\pi$
$884$		0			0
$885$	−533.833	−	702.861i	−0.603201	−	0.794193i
$886$		0			0
$887$	172.488	−	1089.05i	0.194463	−	1.22779i	−0.676501	−	0.736442i	$-0.736505\pi$
$887$	172.488	−	1089.05i	0.194463	−	1.22779i	0.870964	−	0.491347i	$-0.163495\pi$
$888$		0			0
$889$	−148.401	+	204.256i	−0.166930	+	0.229759i
$890$		0			0
$891$	1554.17	−	1129.17i	1.74430	−	1.26731i
$892$		0			0
$893$	17.2634	+	17.2634i	0.0193319	+	0.0193319i
$894$		0			0
$895$	196.836	+	188.645i	0.219928	+	0.210777i
$896$		0			0
$897$	−646.030	−	329.169i	−0.720211	−	0.366966i
$898$		0			0
$899$			404.485i			0.449927i
$900$		0			0
$901$	220.832			0.245097
$902$		0			0
$903$	346.475	−	679.995i	0.383693	−	0.753039i
$904$		0			0
$905$	669.299	−	120.633i	0.739557	−	0.133296i
$906$		0			0
$907$	−183.638	+	183.638i	−0.202468	+	0.202468i	−0.801056	−	0.598589i	$-0.795728\pi$
$907$	−183.638	+	183.638i	−0.202468	+	0.202468i	0.598589	+	0.801056i	$0.295728\pi$
$908$		0			0
$909$	−46.5463	−	64.0655i	−0.0512061	−	0.0704791i
$910$		0			0
$911$	−922.010	−	669.880i	−1.01209	−	0.735323i	−0.0474403	−	0.998874i	$-0.515106\pi$
$911$	−922.010	−	669.880i	−1.01209	−	0.735323i	−0.964646	+	0.263551i	$0.915106\pi$
$912$		0			0
$913$	−407.222	−	64.4977i	−0.446027	−	0.0706437i
$914$		0			0
$915$	−876.751	−	608.968i	−0.958198	−	0.665539i
$916$		0			0
$917$	−124.271	−	243.895i	−0.135519	−	0.265971i
$918$		0			0
$919$	1036.37	+	336.736i	1.12771	+	0.366416i	0.812706	−	0.582674i	$-0.197993\pi$
$919$	1036.37	+	336.736i	1.12771	+	0.366416i	0.315006	+	0.949090i	$0.397993\pi$
$920$		0			0
$921$	−487.274	−	1499.68i	−0.529071	−	1.62831i
$922$		0			0
$923$	168.707	+	1065.17i	0.182781	+	1.15403i
$924$		0			0
$925$	840.027	+	771.514i	0.908137	+	0.834069i
$926$		0			0
$927$	469.409	−	74.3471i	0.506374	−	0.0802018i
$928$		0			0
$929$	−832.928	+	270.635i	−0.896585	+	0.291318i	−0.720827	−	0.693115i	$-0.756238\pi$
$929$	−832.928	+	270.635i	−0.896585	+	0.291318i	−0.175758	+	0.984433i	$0.556238\pi$
$930$		0			0
$931$	12.5455	−	38.6110i	0.0134753	−	0.0414726i
$932$		0			0
$933$	−238.653	+	121.600i	−0.255791	+	0.130332i
$934$		0			0
$935$	419.108	−	146.090i	0.448244	−	0.156246i
$936$		0			0
$937$	10.8140	−	68.2770i	0.0115411	−	0.0728676i	−0.981246	−	0.192762i	$-0.938256\pi$
$937$	10.8140	−	68.2770i	0.0115411	−	0.0728676i	0.992787	+	0.119894i	$0.0382555\pi$
$938$		0			0
$939$	1249.29	−	1719.49i	1.33044	−	1.83120i
$940$		0			0
$941$	−300.146	+	218.068i	−0.318964	+	0.231741i	−0.735733	−	0.677271i	$-0.763162\pi$
$941$	−300.146	+	218.068i	−0.318964	+	0.231741i	0.416769	+	0.909012i	$0.363162\pi$
$942$		0			0
$943$	−135.567	−	135.567i	−0.143761	−	0.143761i
$944$		0			0
$945$	−223.938	−	30.6073i	−0.236972	−	0.0323886i
$946$		0			0
$947$	47.7905	+	24.3505i	0.0504651	+	0.0257133i	0.479041	−	0.877793i	$-0.340985\pi$
$947$	47.7905	+	24.3505i	0.0504651	+	0.0257133i	−0.428576	+	0.903506i	$0.640985\pi$
$948$		0			0
$949$		−	1692.77i		−	1.78374i
$950$		0			0
$951$	2378.50			2.50105
$952$		0			0
$953$	−62.8579	+	123.366i	−0.0659580	+	0.129450i	−0.921632	−	0.388066i	$-0.873143\pi$
$953$	−62.8579	+	123.366i	−0.0659580	+	0.129450i	0.855674	+	0.517516i	$0.173143\pi$
$954$		0			0
$955$	−411.545	−	198.796i	−0.430937	−	0.208163i
$956$		0			0
$957$	952.261	−	952.261i	0.995048	−	0.995048i
$958$		0			0
$959$	−314.341	−	432.653i	−0.327780	−	0.451151i
$960$		0			0
$961$	389.487	+	282.979i	0.405293	+	0.294463i
$962$		0			0
$963$	−925.873	−	146.644i	−0.961447	−	0.152278i
$964$		0			0
$965$	−127.113	+	421.474i	−0.131723	+	0.436761i
$966$		0			0
$967$	−358.090	−	702.791i	−0.370310	−	0.726775i	0.628382	−	0.777905i	$-0.283718\pi$
$967$	−358.090	−	702.791i	−0.370310	−	0.726775i	−0.998692	+	0.0511303i	$0.983718\pi$
$968$		0			0
$969$	−18.1191	−	5.88724i	−0.0186987	−	0.00607559i
$970$		0			0
$971$	−295.128	−	908.310i	−0.303942	−	0.935438i	−0.980070	−	0.198653i	$-0.936343\pi$
$971$	−295.128	−	908.310i	−0.303942	−	0.935438i	0.676128	−	0.736784i	$-0.263657\pi$
$972$		0			0
$973$	−82.9751	−	523.884i	−0.0852776	−	0.538422i
$974$		0			0
$975$	−545.654	−	1464.53i	−0.559645	−	1.50208i
$976$		0			0
$977$	699.516	−	110.792i	0.715984	−	0.113401i	0.212195	−	0.977227i	$-0.431939\pi$
$977$	699.516	−	110.792i	0.715984	−	0.113401i	0.503789	+	0.863827i	$0.331939\pi$
$978$		0			0
$979$	1634.66	−	531.132i	1.66972	−	0.542525i
$980$		0			0
$981$	56.4539	−	173.747i	0.0575473	−	0.177112i
$982$		0			0
$983$	−375.050	+	191.097i	−0.381536	+	0.194402i	−0.634231	−	0.773144i	$-0.718683\pi$
$983$	−375.050	+	191.097i	−0.381536	+	0.194402i	0.252695	+	0.967546i	$0.418683\pi$
$984$		0			0
$985$	27.6871	+	1303.09i	0.0281087	+	1.32294i
$986$		0			0
$987$	45.4693	−	287.082i	0.0460682	−	0.290863i
$988$		0			0
$989$	404.525	−	556.781i	0.409024	−	0.562974i
$990$		0			0
$991$	−984.068	+	714.967i	−0.993005	+	0.721460i	−0.960577	−	0.278014i	$-0.910324\pi$
$991$	−984.068	+	714.967i	−0.993005	+	0.721460i	−0.0324279	+	0.999474i	$0.510324\pi$
$992$		0			0
$993$	856.216	+	856.216i	0.862252	+	0.862252i
$994$		0			0
$995$	−873.934	+	468.937i	−0.878326	+	0.471294i
$996$		0			0
$997$	31.4577	+	16.0285i	0.0315523	+	0.0160767i	0.469695	−	0.882828i	$-0.344364\pi$
$997$	31.4577	+	16.0285i	0.0315523	+	0.0160767i	−0.438143	+	0.898905i	$0.644364\pi$
$998$		0			0
$999$			610.287i			0.610898i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	400.3.bg.c.113.1		32
4.3	odd	2		25.3.f.a.13.3	yes	32
12.11	even	2		225.3.r.a.163.2		32
20.3	even	4		125.3.f.b.82.2		32
20.7	even	4		125.3.f.a.82.3		32
20.19	odd	2		125.3.f.c.43.2		32
25.2	odd	20	inner	400.3.bg.c.177.1		32
100.11	odd	10		125.3.f.a.93.3		32
100.23	even	20		125.3.f.c.32.2		32
100.27	even	20		25.3.f.a.2.3	✓	32
100.39	odd	10		125.3.f.b.93.2		32
300.227	odd	20		225.3.r.a.127.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.2.3	✓	32	100.27	even	20
25.3.f.a.13.3	yes	32	4.3	odd	2
125.3.f.a.82.3		32	20.7	even	4
125.3.f.a.93.3		32	100.11	odd	10
125.3.f.b.82.2		32	20.3	even	4
125.3.f.b.93.2		32	100.39	odd	10
125.3.f.c.32.2		32	100.23	even	20
125.3.f.c.43.2		32	20.19	odd	2
225.3.r.a.127.2		32	300.227	odd	20
225.3.r.a.163.2		32	12.11	even	2
400.3.bg.c.113.1		32	1.1	even	1	trivial
400.3.bg.c.177.1		32	25.2	odd	20	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:	\( N \)	\(=\)	\( 400 = 2^{4} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	400.bg (of order \(20\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.72787 + 3.39113i) q^{3} +(2.36408 + 4.40581i) q^{5} +(2.38950 - 2.38950i) q^{7} +(-3.22416 - 4.43767i) q^{9} +O(q^{10})\)	\(q+(-1.72787 + 3.39113i) q^{3} +(2.36408 + 4.40581i) q^{5} +(2.38950 - 2.38950i) q^{7} +(-3.22416 - 4.43767i) q^{9} +(15.4985 + 11.2603i) q^{11} +(16.2234 + 2.56953i) q^{13} +(-19.0255 + 0.404238i) q^{15} +(-2.10364 - 4.12863i) q^{17} +(-1.02742 - 0.333828i) q^{19} +(3.97436 + 12.2318i) q^{21} +(1.81434 + 11.4553i) q^{23} +(-13.8223 + 20.8313i) q^{25} +(-13.2122 + 2.09261i) q^{27} +(-17.5664 + 5.70767i) q^{29} +(6.76718 - 20.8272i) q^{31} +(-64.9643 + 33.1010i) q^{33} +(16.1766 + 4.87872i) q^{35} +(7.13692 - 45.0607i) q^{37} +(-36.7454 + 50.5757i) q^{39} +(-13.3733 + 9.71629i) q^{41} +(-41.9589 - 41.9589i) q^{43} +(11.9294 - 24.6960i) q^{45} +(-20.1364 - 10.2600i) q^{47} +37.5806i q^{49} +17.6355 q^{51} +(-21.6364 + 42.4637i) q^{53} +(-12.9711 + 94.9034i) q^{55} +(2.90730 - 2.90730i) q^{57} +(27.2616 + 37.5224i) q^{59} +(45.3825 + 32.9723i) q^{61} +(-18.3079 - 2.89969i) q^{63} +(27.0324 + 77.5516i) q^{65} +(-2.50707 - 4.92040i) q^{67} +(-41.9814 - 13.6406i) q^{69} +(20.2891 + 62.4433i) q^{71} +(-16.1217 - 101.788i) q^{73} +(-46.7586 - 82.8669i) q^{75} +(63.9400 - 10.1271i) q^{77} +(81.7963 - 26.5772i) q^{79} +(30.9880 - 95.3712i) q^{81} +(-19.1762 + 9.77074i) q^{83} +(13.2168 - 19.0286i) q^{85} +(10.9970 - 69.4320i) q^{87} +(52.7361 - 72.5850i) q^{89} +(44.9056 - 32.6258i) q^{91} +(58.9350 + 58.9350i) q^{93} +(-0.958111 - 5.31580i) q^{95} +(-83.7126 - 42.6537i) q^{97} -105.082i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9}+O(q^{10}) \) 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9	\( 32 q + 10 q^{3} - 10 q^{5} + 10 q^{7} - 10 q^{9} + 6 q^{11} - 10 q^{13} + 10 q^{15} + 60 q^{17} - 90 q^{19} - 6 q^{21} - 10 q^{23} - 40 q^{25} + 100 q^{27} - 110 q^{29} + 6 q^{31} - 190 q^{33} + 120 q^{35} + 50 q^{37} - 390 q^{39} - 86 q^{41} - 230 q^{43} + 310 q^{45} - 70 q^{47} + 16 q^{51} - 190 q^{53} + 250 q^{55} - 650 q^{57} + 260 q^{59} + 114 q^{61} + 20 q^{63} + 360 q^{65} - 270 q^{67} + 340 q^{69} + 66 q^{71} + 30 q^{73} + 90 q^{75} - 250 q^{77} + 210 q^{79} + 62 q^{81} + 600 q^{85} - 300 q^{87} - 10 q^{89} + 6 q^{91} + 520 q^{93} - 310 q^{95} + 270 q^{97}+O(q^{100}) \) 32 * q + 10 * q^3 - 10 * q^5 + 10 * q^7 - 10 * q^9 + 6 * q^11 - 10 * q^13 + 10 * q^15 + 60 * q^17 - 90 * q^19 - 6 * q^21 - 10 * q^23 - 40 * q^25 + 100 * q^27 - 110 * q^29 + 6 * q^31 - 190 * q^33 + 120 * q^35 + 50 * q^37 - 390 * q^39 - 86 * q^41 - 230 * q^43 + 310 * q^45 - 70 * q^47 + 16 * q^51 - 190 * q^53 + 250 * q^55 - 650 * q^57 + 260 * q^59 + 114 * q^61 + 20 * q^63 + 360 * q^65 - 270 * q^67 + 340 * q^69 + 66 * q^71 + 30 * q^73 + 90 * q^75 - 250 * q^77 + 210 * q^79 + 62 * q^81 + 600 * q^85 - 300 * q^87 - 10 * q^89 + 6 * q^91 + 520 * q^93 - 310 * q^95 + 270 * q^97

Introduction

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