LMFDB - Embedded newform 363.3.b.i.122.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,3,Mod(122,363)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("363.122");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	363.b (of order $2$, degree $1$, 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:	$9.89103359628$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} + 9x^{2} - 8x + 2 $ x^4 - 2x^3 + 9x^2 - 8*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			122.2
Root			$0.500000 + 2.73709i$ of defining polynomial
Character	$\chi$	$=$	363.122
Dual form			363.3.b.i.122.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.64575i q^{2} +(-1.00000 + 2.82843i) q^{3} -3.00000 q^{4} +2.82843i q^{5} +(7.48331 + 2.64575i) q^{6} -7.48331 q^{7} -2.64575i q^{8} +(-7.00000 - 5.65685i) q^{9} +O(q^{10})$	\(q-2.64575i q^{2} +(-1.00000 + 2.82843i) q^{3} -3.00000 q^{4} +2.82843i q^{5} +(7.48331 + 2.64575i) q^{6} -7.48331 q^{7} -2.64575i q^{8} +(-7.00000 - 5.65685i) q^{9} +7.48331 q^{10} +(3.00000 - 8.48528i) q^{12} +22.4499 q^{13} +19.7990i q^{14} +(-8.00000 - 2.82843i) q^{15} -19.0000 q^{16} -21.1660i q^{17} +(-14.9666 + 18.5203i) q^{18} +14.9666 q^{19} -8.48528i q^{20} +(7.48331 - 21.1660i) q^{21} -31.1127i q^{23} +(7.48331 + 2.64575i) q^{24} +17.0000 q^{25} -59.3970i q^{26} +(23.0000 - 14.1421i) q^{27} +22.4499 q^{28} -21.1660i q^{29} +(-7.48331 + 21.1660i) q^{30} +30.0000 q^{31} +39.6863i q^{32} -56.0000 q^{34} -21.1660i q^{35} +(21.0000 + 16.9706i) q^{36} -10.0000 q^{37} -39.5980i q^{38} +(-22.4499 + 63.4980i) q^{39} +7.48331 q^{40} -42.3320i q^{41} +(-56.0000 - 19.7990i) q^{42} -14.9666 q^{43} +(16.0000 - 19.7990i) q^{45} -82.3165 q^{46} +36.7696i q^{47} +(19.0000 - 53.7401i) q^{48} +7.00000 q^{49} -44.9778i q^{50} +(59.8665 + 21.1660i) q^{51} -67.3498 q^{52} -42.4264i q^{53} +(-37.4166 - 60.8523i) q^{54} +19.7990i q^{56} +(-14.9666 + 42.3320i) q^{57} -56.0000 q^{58} +33.9411i q^{59} +(24.0000 + 8.48528i) q^{60} -97.2831 q^{61} -79.3725i q^{62} +(52.3832 + 42.3320i) q^{63} +29.0000 q^{64} +63.4980i q^{65} -42.0000 q^{67} +63.4980i q^{68} +(88.0000 + 31.1127i) q^{69} -56.0000 q^{70} +65.0538i q^{71} +(-14.9666 + 18.5203i) q^{72} +74.8331 q^{73} +26.4575i q^{74} +(-17.0000 + 48.0833i) q^{75} -44.8999 q^{76} +(168.000 + 59.3970i) q^{78} +22.4499 q^{79} -53.7401i q^{80} +(17.0000 + 79.1960i) q^{81} -112.000 q^{82} -21.1660i q^{83} +(-22.4499 + 63.4980i) q^{84} +59.8665 q^{85} +39.5980i q^{86} +(59.8665 + 21.1660i) q^{87} -62.2254i q^{89} +(-52.3832 - 42.3320i) q^{90} -168.000 q^{91} +93.3381i q^{92} +(-30.0000 + 84.8528i) q^{93} +97.2831 q^{94} +42.3320i q^{95} +(-112.250 - 39.6863i) q^{96} +74.0000 q^{97} -18.5203i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{3} - 12 q^{4} - 28 q^{9}+O(q^{10}) $ 4 * q - 4 * q^3 - 12 * q^4 - 28 * q^9	$ 4 q - 4 q^{3} - 12 q^{4} - 28 q^{9} + 12 q^{12} - 32 q^{15} - 76 q^{16} + 68 q^{25} + 92 q^{27} + 120 q^{31} - 224 q^{34} + 84 q^{36} - 40 q^{37} - 224 q^{42} + 64 q^{45} + 76 q^{48} + 28 q^{49} - 224 q^{58} + 96 q^{60} + 116 q^{64} - 168 q^{67} + 352 q^{69} - 224 q^{70} - 68 q^{75} + 672 q^{78} + 68 q^{81} - 448 q^{82} - 672 q^{91} - 120 q^{93} + 296 q^{97}+O(q^{100}) $ 4 * q - 4 * q^3 - 12 * q^4 - 28 * q^9 + 12 * q^12 - 32 * q^15 - 76 * q^16 + 68 * q^25 + 92 * q^27 + 120 * q^31 - 224 * q^34 + 84 * q^36 - 40 * q^37 - 224 * q^42 + 64 * q^45 + 76 * q^48 + 28 * q^49 - 224 * q^58 + 96 * q^60 + 116 * q^64 - 168 * q^67 + 352 * q^69 - 224 * q^70 - 68 * q^75 + 672 * q^78 + 68 * q^81 - 448 * q^82 - 672 * q^91 - 120 * q^93 + 296 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	2.64575i		−	1.32288i	−0.750000	−	0.661438i	$-0.769947\pi$
$2$		−	2.64575i		−	1.32288i	0.750000	−	0.661438i	$-0.230053\pi$
$3$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$3$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$4$	−3.00000			−0.750000
$5$			2.82843i			0.565685i	0.959166	+	0.282843i	$0.0912774\pi$
$5$			2.82843i			0.565685i	−0.959166	+	0.282843i	$0.908723\pi$
$6$	7.48331	+	2.64575i	1.24722	+	0.440959i
$7$	−7.48331			−1.06904			−0.534522	−	0.845154i	$-0.679509\pi$
$7$	−7.48331			−1.06904			−0.534522	+	0.845154i	$0.679509\pi$
$8$		−	2.64575i		−	0.330719i
$9$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$10$	7.48331			0.748331
$11$		0			0
$11$		0			0
$12$	3.00000	−	8.48528i	0.250000	−	0.707107i
$13$	22.4499			1.72692			0.863459	−	0.504418i	$-0.168293\pi$
$13$	22.4499			1.72692			0.863459	+	0.504418i	$0.168293\pi$
$14$			19.7990i			1.41421i
$15$	−8.00000	−	2.82843i	−0.533333	−	0.188562i
$16$	−19.0000			−1.18750
$17$		−	21.1660i		−	1.24506i	−0.782596	−	0.622530i	$-0.786105\pi$
$17$		−	21.1660i		−	1.24506i	0.782596	−	0.622530i	$-0.213895\pi$
$18$	−14.9666	+	18.5203i	−0.831479	+	1.02890i
$19$	14.9666			0.787717			0.393859	−	0.919171i	$-0.371140\pi$
$19$	14.9666			0.787717			0.393859	+	0.919171i	$0.371140\pi$
$20$		−	8.48528i		−	0.424264i
$21$	7.48331	−	21.1660i	0.356348	−	1.00791i
$22$		0			0
$23$		−	31.1127i		−	1.35273i	−0.736568	−	0.676363i	$-0.763555\pi$
$23$		−	31.1127i		−	1.35273i	0.736568	−	0.676363i	$-0.236445\pi$
$24$	7.48331	+	2.64575i	0.311805	+	0.110240i
$25$	17.0000			0.680000
$26$		−	59.3970i		−	2.28450i
$27$	23.0000	−	14.1421i	0.851852	−	0.523783i
$28$	22.4499			0.801784
$29$		−	21.1660i		−	0.729862i	−0.931034	−	0.364931i	$-0.881093\pi$
$29$		−	21.1660i		−	0.729862i	0.931034	−	0.364931i	$-0.118907\pi$
$30$	−7.48331	+	21.1660i	−0.249444	+	0.705534i
$31$	30.0000			0.967742			0.483871	−	0.875139i	$-0.339230\pi$
$31$	30.0000			0.967742			0.483871	+	0.875139i	$0.339230\pi$
$32$			39.6863i			1.24020i
$33$		0			0
$34$	−56.0000			−1.64706
$35$		−	21.1660i		−	0.604743i
$36$	21.0000	+	16.9706i	0.583333	+	0.471405i
$37$	−10.0000			−0.270270			−0.135135	−	0.990827i	$-0.543147\pi$
$37$	−10.0000			−0.270270			−0.135135	+	0.990827i	$0.543147\pi$
$38$		−	39.5980i		−	1.04205i
$39$	−22.4499	+	63.4980i	−0.575640	+	1.62815i
$40$	7.48331			0.187083
$41$		−	42.3320i		−	1.03249i	−0.856441	−	0.516244i	$-0.827330\pi$
$41$		−	42.3320i		−	1.03249i	0.856441	−	0.516244i	$-0.172670\pi$
$42$	−56.0000	−	19.7990i	−1.33333	−	0.471405i
$43$	−14.9666			−0.348061			−0.174031	−	0.984740i	$-0.555679\pi$
$43$	−14.9666			−0.348061			−0.174031	+	0.984740i	$0.555679\pi$
$44$		0			0
$45$	16.0000	−	19.7990i	0.355556	−	0.439978i
$46$	−82.3165			−1.78949
$47$			36.7696i			0.782331i	0.920320	+	0.391165i	$0.127928\pi$
$47$			36.7696i			0.782331i	−0.920320	+	0.391165i	$0.872072\pi$
$48$	19.0000	−	53.7401i	0.395833	−	1.11959i
$49$	7.00000			0.142857
$50$		−	44.9778i		−	0.899555i
$51$	59.8665	+	21.1660i	1.17385	+	0.415020i
$52$	−67.3498			−1.29519
$53$		−	42.4264i		−	0.800498i	−0.916406	−	0.400249i	$-0.868924\pi$
$53$		−	42.4264i		−	0.800498i	0.916406	−	0.400249i	$-0.131076\pi$
$54$	−37.4166	−	60.8523i	−0.692900	−	1.12689i
$55$		0			0
$56$			19.7990i			0.353553i
$57$	−14.9666	+	42.3320i	−0.262572	+	0.742667i
$58$	−56.0000			−0.965517
$59$			33.9411i			0.575273i	0.957740	+	0.287637i	$0.0928695\pi$
$59$			33.9411i			0.575273i	−0.957740	+	0.287637i	$0.907130\pi$
$60$	24.0000	+	8.48528i	0.400000	+	0.141421i
$61$	−97.2831			−1.59480			−0.797402	−	0.603448i	$-0.793793\pi$
$61$	−97.2831			−1.59480			−0.797402	+	0.603448i	$0.793793\pi$
$62$		−	79.3725i		−	1.28020i
$63$	52.3832	+	42.3320i	0.831479	+	0.671937i
$64$	29.0000			0.453125
$65$			63.4980i			0.976893i
$66$		0			0
$67$	−42.0000			−0.626866			−0.313433	−	0.949610i	$-0.601479\pi$
$67$	−42.0000			−0.626866			−0.313433	+	0.949610i	$0.601479\pi$
$68$			63.4980i			0.933795i
$69$	88.0000	+	31.1127i	1.27536	+	0.450909i
$70$	−56.0000			−0.800000
$71$			65.0538i			0.916251i	0.888888	+	0.458126i	$0.151479\pi$
$71$			65.0538i			0.916251i	−0.888888	+	0.458126i	$0.848521\pi$
$72$	−14.9666	+	18.5203i	−0.207870	+	0.257226i
$73$	74.8331			1.02511			0.512556	−	0.858654i	$-0.328699\pi$
$73$	74.8331			1.02511			0.512556	+	0.858654i	$0.328699\pi$
$74$			26.4575i			0.357534i
$75$	−17.0000	+	48.0833i	−0.226667	+	0.641110i
$76$	−44.8999			−0.590788
$77$		0			0
$78$	168.000	+	59.3970i	2.15385	+	0.761500i
$79$	22.4499			0.284177			0.142088	−	0.989854i	$-0.454618\pi$
$79$	22.4499			0.284177			0.142088	+	0.989854i	$0.454618\pi$
$80$		−	53.7401i		−	0.671751i
$81$	17.0000	+	79.1960i	0.209877	+	0.977728i
$82$	−112.000			−1.36585
$83$		−	21.1660i		−	0.255012i	−0.991838	−	0.127506i	$-0.959303\pi$
$83$		−	21.1660i		−	0.255012i	0.991838	−	0.127506i	$-0.0406972\pi$
$84$	−22.4499	+	63.4980i	−0.267261	+	0.755929i
$85$	59.8665			0.704312
$86$			39.5980i			0.460442i
$87$	59.8665	+	21.1660i	0.688121	+	0.243287i
$88$		0			0
$89$		−	62.2254i		−	0.699162i	−0.936906	−	0.349581i	$-0.886324\pi$
$89$		−	62.2254i		−	0.699162i	0.936906	−	0.349581i	$-0.113676\pi$
$90$	−52.3832	−	42.3320i	−0.582036	−	0.470356i
$91$	−168.000			−1.84615
$92$			93.3381i			1.01454i
$93$	−30.0000	+	84.8528i	−0.322581	+	0.912396i
$94$	97.2831			1.03493
$95$			42.3320i			0.445600i
$96$	−112.250	−	39.6863i	−1.16927	−	0.413399i
$97$	74.0000			0.762887			0.381443	−	0.924392i	$-0.375427\pi$
$97$	74.0000			0.762887			0.381443	+	0.924392i	$0.375427\pi$
$98$		−	18.5203i		−	0.188982i
$99$		0			0
$100$	−51.0000			−0.510000
$101$		−	148.162i		−	1.46695i	−0.679716	−	0.733476i	$-0.737897\pi$
$101$		−	148.162i		−	1.46695i	0.679716	−	0.733476i	$-0.262103\pi$
$102$	56.0000	−	158.392i	0.549020	−	1.55286i
$103$	34.0000			0.330097			0.165049	−	0.986285i	$-0.447222\pi$
$103$	34.0000			0.330097			0.165049	+	0.986285i	$0.447222\pi$
$104$		−	59.3970i		−	0.571125i
$105$	59.8665	+	21.1660i	0.570157	+	0.201581i
$106$	−112.250			−1.05896
$107$		−	42.3320i		−	0.395626i	−0.980240	−	0.197813i	$-0.936616\pi$
$107$		−	42.3320i		−	0.395626i	0.980240	−	0.197813i	$-0.0633839\pi$
$108$	−69.0000	+	42.4264i	−0.638889	+	0.392837i
$109$	67.3498			0.617888			0.308944	−	0.951080i	$-0.400024\pi$
$109$	67.3498			0.617888			0.308944	+	0.951080i	$0.400024\pi$
$110$		0			0
$111$	10.0000	−	28.2843i	0.0900901	−	0.254813i
$112$	142.183			1.26949
$113$		−	118.794i		−	1.05127i	−0.850709	−	0.525637i	$-0.823827\pi$
$113$		−	118.794i		−	1.05127i	0.850709	−	0.525637i	$-0.176173\pi$
$114$	112.000	+	39.5980i	0.982456	+	0.347351i
$115$	88.0000			0.765217
$116$			63.4980i			0.547397i
$117$	−157.150	−	126.996i	−1.34316	−	1.08544i
$118$	89.7998			0.761015
$119$			158.392i			1.33102i
$120$	−7.48331	+	21.1660i	−0.0623610	+	0.176383i
$121$		0			0
$122$			257.387i			2.10973i
$123$	119.733	+	42.3320i	0.973439	+	0.344163i
$124$	−90.0000			−0.725806
$125$			118.794i			0.950352i
$126$	112.000	−	138.593i	0.888889	−	1.09994i
$127$	67.3498			0.530314			0.265157	−	0.964205i	$-0.414576\pi$
$127$	67.3498			0.530314			0.265157	+	0.964205i	$0.414576\pi$
$128$			82.0183i			0.640768i
$129$	14.9666	−	42.3320i	0.116020	−	0.328155i
$130$	168.000			1.29231
$131$		−	232.826i		−	1.77730i	−0.458587	−	0.888649i	$-0.651644\pi$
$131$		−	232.826i		−	1.77730i	0.458587	−	0.888649i	$-0.348356\pi$
$132$		0			0
$133$	−112.000			−0.842105
$134$			111.122i			0.829265i
$135$	40.0000	+	65.0538i	0.296296	+	0.481880i
$136$	−56.0000			−0.411765
$137$			158.392i			1.15615i	0.815985	+	0.578073i	$0.196195\pi$
$137$			158.392i			1.15615i	−0.815985	+	0.578073i	$0.803805\pi$
$138$	82.3165	−	232.826i	0.596496	−	1.68715i
$139$	−89.7998			−0.646042			−0.323021	−	0.946392i	$-0.604698\pi$
$139$	−89.7998			−0.646042			−0.323021	+	0.946392i	$0.604698\pi$
$140$			63.4980i			0.453557i
$141$	−104.000	−	36.7696i	−0.737589	−	0.260777i
$142$	172.116			1.21209
$143$		0			0
$144$	133.000	+	107.480i	0.923611	+	0.746390i
$145$	59.8665			0.412873
$146$		−	197.990i		−	1.35610i
$147$	−7.00000	+	19.7990i	−0.0476190	+	0.134687i
$148$	30.0000			0.202703
$149$		−	21.1660i		−	0.142054i	−0.997474	−	0.0710269i	$-0.977372\pi$
$149$		−	21.1660i		−	0.142054i	0.997474	−	0.0710269i	$-0.0226276\pi$
$150$	127.216	+	44.9778i	0.848109	+	0.299852i
$151$	−67.3498			−0.446025			−0.223013	−	0.974816i	$-0.571589\pi$
$151$	−67.3498			−0.446025			−0.223013	+	0.974816i	$0.571589\pi$
$152$		−	39.5980i		−	0.260513i
$153$	−119.733	+	148.162i	−0.782569	+	0.968380i
$154$		0			0
$155$			84.8528i			0.547438i
$156$	67.3498	−	190.494i	0.431730	−	1.22112i
$157$	86.0000			0.547771			0.273885	−	0.961762i	$-0.411691\pi$
$157$	86.0000			0.547771			0.273885	+	0.961762i	$0.411691\pi$
$158$		−	59.3970i		−	0.375930i
$159$	120.000	+	42.4264i	0.754717	+	0.266833i
$160$	−112.250			−0.701561
$161$			232.826i			1.44612i
$162$	209.533	−	44.9778i	1.29341	−	0.277641i
$163$	−14.0000			−0.0858896			−0.0429448	−	0.999077i	$-0.513674\pi$
$163$	−14.0000			−0.0858896			−0.0429448	+	0.999077i	$0.513674\pi$
$164$			126.996i			0.774366i
$165$		0			0
$166$	−56.0000			−0.337349
$167$			84.6640i			0.506970i	0.967339	+	0.253485i	$0.0815769\pi$
$167$			84.6640i			0.506970i	−0.967339	+	0.253485i	$0.918423\pi$
$168$	−56.0000	−	19.7990i	−0.333333	−	0.117851i
$169$	335.000			1.98225
$170$		−	158.392i		−	0.931717i
$171$	−104.766	−	84.6640i	−0.612669	−	0.495111i
$172$	44.8999			0.261046
$173$			190.494i			1.10112i	0.834795	+	0.550561i	$0.185586\pi$
$173$			190.494i			1.10112i	−0.834795	+	0.550561i	$0.814414\pi$
$174$	56.0000	−	158.392i	0.321839	−	0.910298i
$175$	−127.216			−0.726951
$176$		0			0
$177$	−96.0000	−	33.9411i	−0.542373	−	0.191758i
$178$	−164.633			−0.924904
$179$			316.784i			1.76974i	0.465836	+	0.884871i	$0.345754\pi$
$179$			316.784i			1.76974i	−0.465836	+	0.884871i	$0.654246\pi$
$180$	−48.0000	+	59.3970i	−0.266667	+	0.329983i
$181$	−262.000			−1.44751			−0.723757	−	0.690055i	$-0.757586\pi$
$181$	−262.000			−1.44751			−0.723757	+	0.690055i	$0.757586\pi$
$182$			444.486i			2.44223i
$183$	97.2831	−	275.158i	0.531602	−	1.50360i
$184$	−82.3165			−0.447372
$185$		−	28.2843i		−	0.152888i
$186$	224.499	+	79.3725i	1.20699	+	0.426734i
$187$		0			0
$188$		−	110.309i		−	0.586748i
$189$	−172.116	+	105.830i	−0.910668	+	0.559947i
$190$	112.000			0.589474
$191$		−	59.3970i		−	0.310979i	−0.987838	−	0.155489i	$-0.950305\pi$
$191$		−	59.3970i		−	0.310979i	0.987838	−	0.155489i	$-0.0496955\pi$
$192$	−29.0000	+	82.0244i	−0.151042	+	0.427210i
$193$	149.666			0.775473			0.387737	−	0.921770i	$-0.373257\pi$
$193$	149.666			0.775473			0.387737	+	0.921770i	$0.373257\pi$
$194$		−	195.786i		−	1.00920i
$195$	−179.600	−	63.4980i	−0.921023	−	0.325631i
$196$	−21.0000			−0.107143
$197$		−	232.826i		−	1.18186i	−0.806723	−	0.590929i	$-0.798761\pi$
$197$		−	232.826i		−	1.18186i	0.806723	−	0.590929i	$-0.201239\pi$
$198$		0			0
$199$	222.000			1.11558			0.557789	−	0.829983i	$-0.311650\pi$
$199$	222.000			1.11558			0.557789	+	0.829983i	$0.311650\pi$
$200$		−	44.9778i		−	0.224889i
$201$	42.0000	−	118.794i	0.208955	−	0.591015i
$202$	−392.000			−1.94059
$203$			158.392i			0.780256i
$204$	−179.600	−	63.4980i	−0.880390	−	0.311265i
$205$	119.733			0.584064
$206$		−	89.9555i		−	0.436677i
$207$	−176.000	+	217.789i	−0.850242	+	1.05212i
$208$	−426.549			−2.05072
$209$		0			0
$210$	56.0000	−	158.392i	0.266667	−	0.754247i
$211$	−389.132			−1.84423			−0.922115	−	0.386917i	$-0.873540\pi$
$211$	−389.132			−1.84423			−0.922115	+	0.386917i	$0.873540\pi$
$212$			127.279i			0.600374i
$213$	−184.000	−	65.0538i	−0.863850	−	0.305417i
$214$	−112.000			−0.523364
$215$		−	42.3320i		−	0.196893i
$216$	−37.4166	−	60.8523i	−0.173225	−	0.281724i
$217$	−224.499			−1.03456
$218$		−	178.191i		−	0.817389i
$219$	−74.8331	+	211.660i	−0.341704	+	0.966484i
$220$		0			0
$221$		−	475.176i		−	2.15012i
$222$	−74.8331	−	26.4575i	−0.337086	−	0.119178i
$223$	−46.0000			−0.206278			−0.103139	−	0.994667i	$-0.532889\pi$
$223$	−46.0000			−0.206278			−0.103139	+	0.994667i	$0.532889\pi$
$224$		−	296.985i		−	1.32583i
$225$	−119.000	−	96.1665i	−0.528889	−	0.427407i
$226$	−314.299			−1.39070
$227$			211.660i			0.932423i	0.884673	+	0.466212i	$0.154381\pi$
$227$			211.660i			0.932423i	−0.884673	+	0.466212i	$0.845619\pi$
$228$	44.8999	−	126.996i	0.196929	−	0.557000i
$229$	118.000			0.515284			0.257642	−	0.966240i	$-0.417055\pi$
$229$	118.000			0.515284			0.257642	+	0.966240i	$0.417055\pi$
$230$		−	232.826i		−	1.01229i
$231$		0			0
$232$	−56.0000			−0.241379
$233$			84.6640i			0.363365i	0.983357	+	0.181682i	$0.0581543\pi$
$233$			84.6640i			0.363365i	−0.983357	+	0.181682i	$0.941846\pi$
$234$	−336.000	+	415.779i	−1.43590	+	1.77683i
$235$	−104.000			−0.442553
$236$		−	101.823i		−	0.431455i
$237$	−22.4499	+	63.4980i	−0.0947255	+	0.267924i
$238$	419.066			1.76078
$239$		−	42.3320i		−	0.177121i	−0.996071	−	0.0885607i	$-0.971773\pi$
$239$		−	42.3320i		−	0.177121i	0.996071	−	0.0885607i	$-0.0282267\pi$
$240$	152.000	+	53.7401i	0.633333	+	0.223917i
$241$	149.666			0.621022			0.310511	−	0.950570i	$-0.399500\pi$
$241$	149.666			0.621022			0.310511	+	0.950570i	$0.399500\pi$
$242$		0			0
$243$	−241.000	−	31.1127i	−0.991770	−	0.128036i
$244$	291.849			1.19610
$245$			19.7990i			0.0808122i
$246$	112.000	−	316.784i	0.455285	−	1.28774i
$247$	336.000			1.36032
$248$		−	79.3725i		−	0.320051i
$249$	59.8665	+	21.1660i	0.240428	+	0.0850041i
$250$	314.299			1.25720
$251$			50.9117i			0.202835i	0.994844	+	0.101418i	$0.0323379\pi$
$251$			50.9117i			0.202835i	−0.994844	+	0.101418i	$0.967662\pi$
$252$	−157.150	−	126.996i	−0.623610	−	0.503953i
$253$		0			0
$254$		−	178.191i		−	0.701539i
$255$	−59.8665	+	169.328i	−0.234771	+	0.664032i
$256$	333.000			1.30078
$257$			96.1665i			0.374189i	0.982342	+	0.187094i	$0.0599070\pi$
$257$			96.1665i			0.374189i	−0.982342	+	0.187094i	$0.940093\pi$
$258$	−112.000	−	39.5980i	−0.434109	−	0.153481i
$259$	74.8331			0.288931
$260$		−	190.494i		−	0.732670i
$261$	−119.733	+	148.162i	−0.458747	+	0.567671i
$262$	−616.000			−2.35115
$263$			465.652i			1.77054i	0.465077	+	0.885270i	$0.346027\pi$
$263$			465.652i			1.77054i	−0.465077	+	0.885270i	$0.653973\pi$
$264$		0			0
$265$	120.000			0.452830
$266$			296.324i			1.11400i
$267$	176.000	+	62.2254i	0.659176	+	0.233054i
$268$	126.000			0.470149
$269$		−	370.524i		−	1.37741i	−0.725040	−	0.688706i	$-0.758179\pi$
$269$		−	370.524i		−	1.37741i	0.725040	−	0.688706i	$-0.241821\pi$
$270$	172.116	−	105.830i	0.637468	−	0.391963i
$271$	−336.749			−1.24262			−0.621308	−	0.783566i	$-0.713399\pi$
$271$	−336.749			−1.24262			−0.621308	+	0.783566i	$0.713399\pi$
$272$			402.154i			1.47851i
$273$	168.000	−	475.176i	0.615385	−	1.74057i
$274$	419.066			1.52944
$275$		0			0
$276$	−264.000	−	93.3381i	−0.956522	−	0.338182i
$277$	22.4499			0.0810467			0.0405234	−	0.999179i	$-0.487097\pi$
$277$	22.4499			0.0810467			0.0405234	+	0.999179i	$0.487097\pi$
$278$			237.588i			0.854633i
$279$	−210.000	−	169.706i	−0.752688	−	0.608264i
$280$	−56.0000			−0.200000
$281$		−	21.1660i		−	0.0753239i	−0.999291	−	0.0376619i	$-0.988009\pi$
$281$		−	21.1660i		−	0.0753239i	0.999291	−	0.0376619i	$-0.0119910\pi$
$282$	−97.2831	+	275.158i	−0.344976	+	0.975738i
$283$	179.600			0.634627			0.317314	−	0.948321i	$-0.397219\pi$
$283$	179.600			0.634627			0.317314	+	0.948321i	$0.397219\pi$
$284$		−	195.161i		−	0.687188i
$285$	−119.733	−	42.3320i	−0.420116	−	0.148533i
$286$		0			0
$287$			316.784i			1.10378i
$288$	224.499	−	277.804i	0.779512	−	0.964597i
$289$	−159.000			−0.550173
$290$		−	158.392i		−	0.546179i
$291$	−74.0000	+	209.304i	−0.254296	+	0.719256i
$292$	−224.499			−0.768834
$293$		−	21.1660i		−	0.0722389i	−0.999347	−	0.0361195i	$-0.988500\pi$
$293$		−	21.1660i		−	0.0722389i	0.999347	−	0.0361195i	$-0.0114997\pi$
$294$	52.3832	+	18.5203i	0.178174	+	0.0629941i
$295$	−96.0000			−0.325424
$296$			26.4575i			0.0893835i
$297$		0			0
$298$	−56.0000			−0.187919
$299$		−	698.478i		−	2.33605i
$300$	51.0000	−	144.250i	0.170000	−	0.480833i
$301$	112.000			0.372093
$302$			178.191i			0.590036i
$303$	419.066	+	148.162i	1.38305	+	0.488984i
$304$	−284.366			−0.935414
$305$		−	275.158i		−	0.902158i
$306$	392.000	+	316.784i	1.28105	+	1.03524i
$307$	149.666			0.487512			0.243756	−	0.969837i	$-0.421620\pi$
$307$	149.666			0.487512			0.243756	+	0.969837i	$0.421620\pi$
$308$		0			0
$309$	−34.0000	+	96.1665i	−0.110032	+	0.311219i
$310$	224.499			0.724192
$311$		−	25.4558i		−	0.0818516i	−0.999162	−	0.0409258i	$-0.986969\pi$
$311$		−	25.4558i		−	0.0818516i	0.999162	−	0.0409258i	$-0.0130307\pi$
$312$	168.000	+	59.3970i	0.538462	+	0.190375i
$313$	398.000			1.27157			0.635783	−	0.771868i	$-0.280677\pi$
$313$	398.000			1.27157			0.635783	+	0.771868i	$0.280677\pi$
$314$		−	227.535i		−	0.724633i
$315$	−119.733	+	148.162i	−0.380105	+	0.470356i
$316$	−67.3498			−0.213132
$317$		−	415.779i		−	1.31161i	−0.754932	−	0.655803i	$-0.772330\pi$
$317$		−	415.779i		−	1.31161i	0.754932	−	0.655803i	$-0.227670\pi$
$318$	112.250	−	317.490i	0.352987	−	0.998397i
$319$		0			0
$320$			82.0244i			0.256326i
$321$	119.733	+	42.3320i	0.373000	+	0.131875i
$322$	616.000			1.91304
$323$		−	316.784i		−	0.980755i
$324$	−51.0000	−	237.588i	−0.157407	−	0.733296i
$325$	381.649			1.17430
$326$			37.0405i			0.113621i
$327$	−67.3498	+	190.494i	−0.205963	+	0.582551i
$328$	−112.000			−0.341463
$329$		−	275.158i		−	0.836347i
$330$		0			0
$331$	178.000			0.537764			0.268882	−	0.963173i	$-0.413346\pi$
$331$	178.000			0.537764			0.268882	+	0.963173i	$0.413346\pi$
$332$			63.4980i			0.191259i
$333$	70.0000	+	56.5685i	0.210210	+	0.169876i
$334$	224.000			0.670659
$335$		−	118.794i		−	0.354609i
$336$	−142.183	+	402.154i	−0.423164	+	1.19689i
$337$	−254.433			−0.754993			−0.377497	−	0.926011i	$-0.623215\pi$
$337$	−254.433			−0.754993			−0.377497	+	0.926011i	$0.623215\pi$
$338$		−	886.327i		−	2.62227i
$339$	336.000	+	118.794i	0.991150	+	0.350425i
$340$	−179.600			−0.528234
$341$		0			0
$342$	−224.000	+	277.186i	−0.654971	+	0.810485i
$343$	314.299			0.916324
$344$			39.5980i			0.115110i
$345$	−88.0000	+	248.902i	−0.255072	+	0.721454i
$346$	504.000			1.45665
$347$		−	486.818i		−	1.40293i	−0.712702	−	0.701467i	$-0.752529\pi$
$347$		−	486.818i		−	1.40293i	0.712702	−	0.701467i	$-0.247471\pi$
$348$	−179.600	−	63.4980i	−0.516091	−	0.182466i
$349$	−67.3498			−0.192979			−0.0964897	−	0.995334i	$-0.530761\pi$
$349$	−67.3498			−0.192979			−0.0964897	+	0.995334i	$0.530761\pi$
$350$			336.583i			0.961665i
$351$	516.349	−	317.490i	1.47108	−	0.904530i
$352$		0			0
$353$			124.451i			0.352552i	0.984341	+	0.176276i	$0.0564051\pi$
$353$			124.451i			0.352552i	−0.984341	+	0.176276i	$0.943595\pi$
$354$	−89.7998	+	253.992i	−0.253672	+	0.717492i
$355$	−184.000			−0.518310
$356$			186.676i			0.524371i
$357$	−448.000	−	158.392i	−1.25490	−	0.443675i
$358$	838.131			2.34115
$359$		−	253.992i		−	0.707499i	−0.935340	−	0.353749i	$-0.884907\pi$
$359$		−	253.992i		−	0.707499i	0.935340	−	0.353749i	$-0.115093\pi$
$360$	−52.3832	−	42.3320i	−0.145509	−	0.117589i
$361$	−137.000			−0.379501
$362$			693.187i			1.91488i
$363$		0			0
$364$	504.000			1.38462
$365$			211.660i			0.579891i
$366$	−728.000	−	257.387i	−1.98907	−	0.703243i
$367$	−142.000			−0.386921			−0.193460	−	0.981108i	$-0.561971\pi$
$367$	−142.000			−0.386921			−0.193460	+	0.981108i	$0.561971\pi$
$368$			591.141i			1.60636i
$369$	−239.466	+	296.324i	−0.648960	+	0.803046i
$370$	−74.8331			−0.202252
$371$			317.490i			0.855769i
$372$	90.0000	−	254.558i	0.241935	−	0.684297i
$373$	−426.549			−1.14356			−0.571781	−	0.820406i	$-0.693747\pi$
$373$	−426.549			−1.14356			−0.571781	+	0.820406i	$0.693747\pi$
$374$		0			0
$375$	−336.000	−	118.794i	−0.896000	−	0.316784i
$376$	97.2831			0.258732
$377$		−	475.176i		−	1.26041i
$378$	280.000	+	455.377i	0.740741	+	1.20470i
$379$	−350.000			−0.923483			−0.461741	−	0.887015i	$-0.652775\pi$
$379$	−350.000			−0.923483			−0.461741	+	0.887015i	$0.652775\pi$
$380$		−	126.996i		−	0.334200i
$381$	−67.3498	+	190.494i	−0.176771	+	0.499984i
$382$	−157.150			−0.411386
$383$			517.602i			1.35144i	0.737158	+	0.675721i	$0.236168\pi$
$383$			517.602i			1.35144i	−0.737158	+	0.675721i	$0.763832\pi$
$384$	−231.983	−	82.0183i	−0.604122	−	0.213589i
$385$		0			0
$386$		−	395.980i		−	1.02585i
$387$	104.766	+	84.6640i	0.270714	+	0.218770i
$388$	−222.000			−0.572165
$389$			438.406i			1.12701i	0.826113	+	0.563504i	$0.190547\pi$
$389$			438.406i			1.12701i	−0.826113	+	0.563504i	$0.809453\pi$
$390$	−168.000	+	475.176i	−0.430769	+	1.21840i
$391$	−658.532			−1.68422
$392$		−	18.5203i		−	0.0472456i
$393$	658.532	+	232.826i	1.67565	+	0.592433i
$394$	−616.000			−1.56345
$395$			63.4980i			0.160755i
$396$		0			0
$397$	442.000			1.11335			0.556675	−	0.830730i	$-0.312077\pi$
$397$	442.000			1.11335			0.556675	+	0.830730i	$0.312077\pi$
$398$		−	587.357i		−	1.47577i
$399$	112.000	−	316.784i	0.280702	−	0.793944i
$400$	−323.000			−0.807500
$401$		−	526.087i		−	1.31194i	−0.754787	−	0.655969i	$-0.772260\pi$
$401$		−	526.087i		−	1.31194i	0.754787	−	0.655969i	$-0.227740\pi$
$402$	−314.299	−	111.122i	−0.781839	−	0.276422i
$403$	673.498			1.67121
$404$			444.486i			1.10021i
$405$	−224.000	+	48.0833i	−0.553086	+	0.118724i
$406$	419.066			1.03218
$407$		0			0
$408$	56.0000	−	158.392i	0.137255	−	0.388215i
$409$	−224.499			−0.548898			−0.274449	−	0.961602i	$-0.588496\pi$
$409$	−224.499			−0.548898			−0.274449	+	0.961602i	$0.588496\pi$
$410$		−	316.784i		−	0.772644i
$411$	−448.000	−	158.392i	−1.09002	−	0.385382i
$412$	−102.000			−0.247573
$413$		−	253.992i		−	0.614993i
$414$	576.215	+	465.652i	1.39182	+	1.12476i
$415$	59.8665			0.144257
$416$			890.955i			2.14172i
$417$	89.7998	−	253.992i	0.215347	−	0.609094i
$418$		0			0
$419$			684.479i			1.63360i	0.576919	+	0.816801i	$0.304255\pi$
$419$			684.479i			1.63360i	−0.576919	+	0.816801i	$0.695745\pi$
$420$	−179.600	−	63.4980i	−0.427618	−	0.151186i
$421$	−266.000			−0.631829			−0.315914	−	0.948788i	$-0.602311\pi$
$421$	−266.000			−0.631829			−0.315914	+	0.948788i	$0.602311\pi$
$422$			1029.55i			2.43969i
$423$	208.000	−	257.387i	0.491726	−	0.608480i
$424$	−112.250			−0.264740
$425$		−	359.822i		−	0.846640i
$426$	−172.116	+	486.818i	−0.404029	+	1.14277i
$427$	728.000			1.70492
$428$			126.996i			0.296720i
$429$		0			0
$430$	−112.000			−0.260465
$431$			550.316i			1.27684i	0.769690	+	0.638418i	$0.220411\pi$
$431$			550.316i			1.27684i	−0.769690	+	0.638418i	$0.779589\pi$
$432$	−437.000	+	268.701i	−1.01157	+	0.621992i
$433$	738.000			1.70439			0.852194	−	0.523226i	$-0.175272\pi$
$433$	738.000			1.70439			0.852194	+	0.523226i	$0.175272\pi$
$434$			593.970i			1.36859i
$435$	−59.8665	+	169.328i	−0.137624	+	0.389260i
$436$	−202.049			−0.463416
$437$		−	465.652i		−	1.06557i
$438$	560.000	+	197.990i	1.27854	+	0.452032i
$439$	−426.549			−0.971638			−0.485819	−	0.874060i	$-0.661479\pi$
$439$	−426.549			−0.971638			−0.485819	+	0.874060i	$0.661479\pi$
$440$		0			0
$441$	−49.0000	−	39.5980i	−0.111111	−	0.0897913i
$442$	−1257.20			−2.84434
$443$		−	118.794i		−	0.268158i	−0.990971	−	0.134079i	$-0.957192\pi$
$443$		−	118.794i		−	0.268158i	0.990971	−	0.134079i	$-0.0428076\pi$
$444$	−30.0000	+	84.8528i	−0.0675676	+	0.191110i
$445$	176.000			0.395506
$446$			121.705i			0.272880i
$447$	59.8665	+	21.1660i	0.133930	+	0.0473513i
$448$	−217.016			−0.484411
$449$		−	509.117i		−	1.13389i	−0.823755	−	0.566945i	$-0.808125\pi$
$449$		−	509.117i		−	1.13389i	0.823755	−	0.566945i	$-0.191875\pi$
$450$	−254.433	+	314.844i	−0.565406	+	0.699654i
$451$		0			0
$452$			356.382i			0.788455i
$453$	67.3498	−	190.494i	0.148675	−	0.420517i
$454$	560.000			1.23348
$455$		−	475.176i		−	1.04434i
$456$	112.000	+	39.5980i	0.245614	+	0.0868377i
$457$	−673.498			−1.47374			−0.736869	−	0.676035i	$-0.763697\pi$
$457$	−673.498			−1.47374			−0.736869	+	0.676035i	$0.763697\pi$
$458$		−	312.199i		−	0.681656i
$459$	−299.333	−	486.818i	−0.652141	−	1.06061i
$460$	−264.000			−0.573913
$461$			698.478i			1.51514i	0.652755	+	0.757569i	$0.273613\pi$
$461$			698.478i			1.51514i	−0.652755	+	0.757569i	$0.726387\pi$
$462$		0			0
$463$	882.000			1.90497			0.952484	−	0.304589i	$-0.0985192\pi$
$463$	882.000			1.90497			0.952484	+	0.304589i	$0.0985192\pi$
$464$			402.154i			0.866712i
$465$	−240.000	−	84.8528i	−0.516129	−	0.182479i
$466$	224.000			0.480687
$467$			531.744i			1.13864i	0.822116	+	0.569319i	$0.192793\pi$
$467$			531.744i			1.13864i	−0.822116	+	0.569319i	$0.807207\pi$
$468$	471.449	+	380.988i	1.00737	+	0.814077i
$469$	314.299			0.670148
$470$			275.158i			0.585443i
$471$	−86.0000	+	243.245i	−0.182590	+	0.516443i
$472$	89.7998			0.190254
$473$		0			0
$474$	168.000	+	59.3970i	0.354430	+	0.125310i
$475$	254.433			0.535648
$476$		−	475.176i		−	0.998268i
$477$	−240.000	+	296.985i	−0.503145	+	0.622610i
$478$	−112.000			−0.234310
$479$			677.312i			1.41401i	0.707207	+	0.707007i	$0.249955\pi$
$479$			677.312i			1.41401i	−0.707207	+	0.707007i	$0.750045\pi$
$480$	112.250	−	317.490i	0.233854	−	0.661438i
$481$	−224.499			−0.466735
$482$		−	395.980i		−	0.821535i
$483$	−658.532	−	232.826i	−1.36342	−	0.482042i
$484$		0			0
$485$			209.304i			0.431554i
$486$	−82.3165	+	637.626i	−0.169375	+	1.31199i
$487$	350.000			0.718686			0.359343	−	0.933206i	$-0.383001\pi$
$487$	350.000			0.718686			0.359343	+	0.933206i	$0.383001\pi$
$488$			257.387i			0.527432i
$489$	14.0000	−	39.5980i	0.0286299	−	0.0809775i
$490$	52.3832			0.106904
$491$		−	253.992i		−	0.517296i	−0.965972	−	0.258648i	$-0.916723\pi$
$491$		−	253.992i		−	0.517296i	0.965972	−	0.258648i	$-0.0832769\pi$
$492$	−359.199	−	126.996i	−0.730079	−	0.258122i
$493$	−448.000			−0.908722
$494$		−	888.972i		−	1.79954i
$495$		0			0
$496$	−570.000			−1.14919
$497$		−	486.818i		−	0.979514i
$498$	56.0000	−	158.392i	0.112450	−	0.318056i
$499$	−98.0000			−0.196393			−0.0981964	−	0.995167i	$-0.531307\pi$
$499$	−98.0000			−0.196393			−0.0981964	+	0.995167i	$0.531307\pi$
$500$		−	356.382i		−	0.712764i
$501$	−239.466	−	84.6640i	−0.477976	−	0.168990i
$502$	134.700			0.268326
$503$		−	507.984i		−	1.00991i	−0.863146	−	0.504955i	$-0.831509\pi$
$503$		−	507.984i		−	1.00991i	0.863146	−	0.504955i	$-0.168491\pi$
$504$	112.000	−	138.593i	0.222222	−	0.274986i
$505$	419.066			0.829833
$506$		0			0
$507$	−335.000	+	947.523i	−0.660750	+	1.86888i
$508$	−202.049			−0.397735
$509$			161.220i			0.316739i	0.987380	+	0.158370i	$0.0506238\pi$
$509$			161.220i			0.316739i	−0.987380	+	0.158370i	$0.949376\pi$
$510$	448.000	+	158.392i	0.878431	+	0.310572i
$511$	−560.000			−1.09589
$512$		−	552.962i		−	1.08000i
$513$	344.232	−	211.660i	0.671018	−	0.412593i
$514$	254.433			0.495005
$515$			96.1665i			0.186731i
$516$	−44.8999	+	126.996i	−0.0870153	+	0.246116i
$517$		0			0
$518$		−	197.990i		−	0.382220i
$519$	−538.799	−	190.494i	−1.03815	−	0.367041i
$520$	168.000			0.323077
$521$		−	152.735i		−	0.293158i	−0.989199	−	0.146579i	$-0.953174\pi$
$521$		−	152.735i		−	0.293158i	0.989199	−	0.146579i	$-0.0468262\pi$
$522$	392.000	+	316.784i	0.750958	+	0.606866i
$523$	−14.9666			−0.0286169			−0.0143084	−	0.999898i	$-0.504555\pi$
$523$	−14.9666			−0.0286169			−0.0143084	+	0.999898i	$0.504555\pi$
$524$			698.478i			1.33297i
$525$	127.216	−	359.822i	0.242317	−	0.685376i
$526$	1232.00			2.34221
$527$		−	634.980i		−	1.20490i
$528$		0			0
$529$	−439.000			−0.829868
$530$		−	317.490i		−	0.599038i
$531$	192.000	−	237.588i	0.361582	−	0.447435i
$532$	336.000			0.631579
$533$		−	950.352i		−	1.78302i
$534$	164.633	−	465.652i	0.308301	−	0.872008i
$535$	119.733			0.223800
$536$			111.122i			0.207316i
$537$	−896.000	−	316.784i	−1.66853	−	0.589914i
$538$	−980.314			−1.82215
$539$		0			0
$540$	−120.000	−	195.161i	−0.222222	−	0.361410i
$541$	516.349			0.954434			0.477217	−	0.878786i	$-0.341646\pi$
$541$	516.349			0.954434			0.477217	+	0.878786i	$0.341646\pi$
$542$			890.955i			1.64383i
$543$	262.000	−	741.048i	0.482505	−	1.36473i
$544$	840.000			1.54412
$545$			190.494i			0.349530i
$546$	−1257.20	−	444.486i	−2.30256	−	0.814077i
$547$	673.498			1.23126			0.615629	−	0.788036i	$-0.288902\pi$
$547$	673.498			1.23126			0.615629	+	0.788036i	$0.288902\pi$
$548$		−	475.176i		−	0.867109i
$549$	680.982	+	550.316i	1.24040	+	1.00240i
$550$		0			0
$551$		−	316.784i		−	0.574925i
$552$	82.3165	−	232.826i	0.149124	−	0.421786i
$553$	−168.000			−0.303797
$554$		−	59.3970i		−	0.107215i
$555$	80.0000	+	28.2843i	0.144144	+	0.0509627i
$556$	269.399			0.484531
$557$			444.486i			0.798000i	0.916951	+	0.399000i	$0.130643\pi$
$557$			444.486i			0.798000i	−0.916951	+	0.399000i	$0.869357\pi$
$558$	−448.999	+	555.608i	−0.804658	+	0.995713i
$559$	−336.000			−0.601073
$560$			402.154i			0.718132i
$561$		0			0
$562$	−56.0000			−0.0996441
$563$			550.316i			0.977471i	0.872432	+	0.488736i	$0.162542\pi$
$563$			550.316i			0.977471i	−0.872432	+	0.488736i	$0.837458\pi$
$564$	312.000	+	110.309i	0.553191	+	0.195583i
$565$	336.000			0.594690
$566$		−	475.176i		−	0.839533i
$567$	−127.216	−	592.648i	−0.224367	−	1.04524i
$568$	172.116			0.303022
$569$			1121.80i			1.97153i	0.168139	+	0.985763i	$0.446224\pi$
$569$			1121.80i			1.97153i	−0.168139	+	0.985763i	$0.553776\pi$
$570$	−112.000	+	316.784i	−0.196491	+	0.555761i
$571$	808.198			1.41541			0.707704	−	0.706509i	$-0.249731\pi$
$571$	808.198			1.41541			0.707704	+	0.706509i	$0.249731\pi$
$572$		0			0
$573$	168.000	+	59.3970i	0.293194	+	0.103660i
$574$	838.131			1.46016
$575$		−	528.916i		−	0.919854i
$576$	−203.000	−	164.049i	−0.352431	−	0.284807i
$577$	310.000			0.537262			0.268631	−	0.963243i	$-0.413429\pi$
$577$	310.000			0.537262			0.268631	+	0.963243i	$0.413429\pi$
$578$			420.674i			0.727810i
$579$	−149.666	+	423.320i	−0.258491	+	0.731123i
$580$	−179.600			−0.309654
$581$			158.392i			0.272619i
$582$	553.765	+	195.786i	0.951487	+	0.336401i
$583$		0			0
$584$		−	197.990i		−	0.339024i
$585$	359.199	−	444.486i	0.614016	−	0.759806i
$586$	−56.0000			−0.0955631
$587$		−	961.665i		−	1.63827i	−0.573600	−	0.819136i	$-0.694454\pi$
$587$		−	961.665i		−	1.63827i	0.573600	−	0.819136i	$-0.305546\pi$
$588$	21.0000	−	59.3970i	0.0357143	−	0.101015i
$589$	448.999			0.762307
$590$			253.992i			0.430495i
$591$	658.532	+	232.826i	1.11427	+	0.393953i
$592$	190.000			0.320946
$593$			232.826i			0.392624i	0.980541	+	0.196312i	$0.0628966\pi$
$593$			232.826i			0.392624i	−0.980541	+	0.196312i	$0.937103\pi$
$594$		0			0
$595$	−448.000			−0.752941
$596$			63.4980i			0.106540i
$597$	−222.000	+	627.911i	−0.371859	+	1.05178i
$598$	−1848.00			−3.09030
$599$			873.984i			1.45907i	0.683943	+	0.729536i	$0.260264\pi$
$599$			873.984i			1.45907i	−0.683943	+	0.729536i	$0.739736\pi$
$600$	127.216	+	44.9778i	0.212027	+	0.0749630i
$601$	−583.699			−0.971212			−0.485606	−	0.874178i	$-0.661401\pi$
$601$	−583.699			−0.971212			−0.485606	+	0.874178i	$0.661401\pi$
$602$		−	296.324i		−	0.492233i
$603$	294.000	+	237.588i	0.487562	+	0.394010i
$604$	202.049			0.334519
$605$		0			0
$606$	392.000	−	1108.74i	0.646865	−	1.82961i
$607$	845.615			1.39310			0.696552	−	0.717506i	$-0.254716\pi$
$607$	845.615			1.39310			0.696552	+	0.717506i	$0.254716\pi$
$608$			593.970i			0.976924i
$609$	−448.000	−	158.392i	−0.735632	−	0.260085i
$610$	−728.000			−1.19344
$611$			825.474i			1.35102i
$612$	359.199	−	444.486i	0.586927	−	0.726285i
$613$	591.182			0.964408			0.482204	−	0.876059i	$-0.339836\pi$
$613$	591.182			0.964408			0.482204	+	0.876059i	$0.339836\pi$
$614$		−	395.980i		−	0.644918i
$615$	−119.733	+	338.656i	−0.194688	+	0.550660i
$616$		0			0
$617$		−	435.578i		−	0.705961i	−0.935631	−	0.352980i	$-0.885168\pi$
$617$		−	435.578i		−	0.705961i	0.935631	−	0.352980i	$-0.114832\pi$
$618$	254.433	+	89.9555i	0.411703	+	0.145559i
$619$	−838.000			−1.35380			−0.676898	−	0.736077i	$-0.736676\pi$
$619$	−838.000			−1.35380			−0.676898	+	0.736077i	$0.736676\pi$
$620$		−	254.558i		−	0.410578i
$621$	−440.000	−	715.592i	−0.708535	−	1.15232i
$622$	−67.3498			−0.108279
$623$			465.652i			0.747435i
$624$	426.549	−	1206.46i	0.683572	−	1.93343i
$625$	89.0000			0.142400
$626$		−	1053.01i		−	1.68212i
$627$		0			0
$628$	−258.000			−0.410828
$629$			211.660i			0.336503i
$630$	392.000	+	316.784i	0.622222	+	0.502831i
$631$	254.000			0.402536			0.201268	−	0.979536i	$-0.435494\pi$
$631$	254.000			0.402536			0.201268	+	0.979536i	$0.435494\pi$
$632$		−	59.3970i		−	0.0939825i
$633$	389.132	−	1100.63i	0.614743	−	1.73876i
$634$	−1100.05			−1.73509
$635$			190.494i			0.299991i
$636$	−360.000	−	127.279i	−0.566038	−	0.200125i
$637$	157.150			0.246703
$638$		0			0
$639$	368.000	−	455.377i	0.575900	−	0.712640i
$640$	−231.983			−0.362473
$641$		−	118.794i		−	0.185326i	−0.995698	−	0.0926630i	$-0.970462\pi$
$641$		−	118.794i		−	0.185326i	0.995698	−	0.0926630i	$-0.0295379\pi$
$642$	112.000	−	316.784i	0.174455	−	0.493433i
$643$	−438.000			−0.681182			−0.340591	−	0.940212i	$-0.610627\pi$
$643$	−438.000			−0.681182			−0.340591	+	0.940212i	$0.610627\pi$
$644$		−	698.478i		−	1.08459i
$645$	119.733	+	42.3320i	0.185633	+	0.0656310i
$646$	−838.131			−1.29742
$647$			330.926i			0.511478i	0.966746	+	0.255739i	$0.0823187\pi$
$647$			330.926i			0.511478i	−0.966746	+	0.255739i	$0.917681\pi$
$648$	209.533	−	44.9778i	0.323353	−	0.0694101i
$649$		0			0
$650$		−	1009.75i		−	1.55346i
$651$	224.499	−	634.980i	0.344853	−	0.975392i
$652$	42.0000			0.0644172
$653$			625.082i			0.957247i	0.878020	+	0.478624i	$0.158864\pi$
$653$			625.082i			0.957247i	−0.878020	+	0.478624i	$0.841136\pi$
$654$	504.000	+	178.191i	0.770642	+	0.272463i
$655$	658.532			1.00539
$656$			804.308i			1.22608i
$657$	−523.832	−	423.320i	−0.797309	−	0.644323i
$658$	−728.000			−1.10638
$659$		−	465.652i		−	0.706604i	−0.935509	−	0.353302i	$-0.885059\pi$
$659$		−	465.652i		−	0.706604i	0.935509	−	0.353302i	$-0.114941\pi$
$660$		0			0
$661$	−394.000			−0.596067			−0.298033	−	0.954555i	$-0.596331\pi$
$661$	−394.000			−0.596067			−0.298033	+	0.954555i	$0.596331\pi$
$662$		−	470.944i		−	0.711395i
$663$	1344.00	+	475.176i	2.02715	+	0.716706i
$664$	−56.0000			−0.0843373
$665$		−	316.784i		−	0.476367i
$666$	149.666	−	185.203i	0.224724	−	0.278082i
$667$	−658.532			−0.987304
$668$		−	253.992i		−	0.380228i
$669$	46.0000	−	130.108i	0.0687593	−	0.194481i
$670$	−314.299			−0.469103
$671$		0			0
$672$	840.000	+	296.985i	1.25000	+	0.441942i
$673$	−883.031			−1.31208			−0.656041	−	0.754725i	$-0.727770\pi$
$673$	−883.031			−1.31208			−0.656041	+	0.754725i	$0.727770\pi$
$674$			673.166i			0.998762i
$675$	391.000	−	240.416i	0.579259	−	0.356172i
$676$	−1005.00			−1.48669
$677$			910.138i			1.34437i	0.740383	+	0.672185i	$0.234644\pi$
$677$			910.138i			1.34437i	−0.740383	+	0.672185i	$0.765356\pi$
$678$	314.299	−	888.972i	0.463568	−	1.31117i
$679$	−553.765			−0.815560
$680$		−	158.392i		−	0.232929i
$681$	−598.665	−	211.660i	−0.879097	−	0.310808i
$682$		0			0
$683$			435.578i			0.637742i	0.947798	+	0.318871i	$0.103304\pi$
$683$			435.578i			0.637742i	−0.947798	+	0.318871i	$0.896696\pi$
$684$	314.299	+	253.992i	0.459502	+	0.371334i
$685$	−448.000			−0.654015
$686$		−	831.558i		−	1.21218i
$687$	−118.000	+	333.754i	−0.171761	+	0.485814i
$688$	284.366			0.413323
$689$		−	952.470i		−	1.38240i
$690$	658.532	+	232.826i	0.954394	+	0.337429i
$691$	426.000			0.616498			0.308249	−	0.951306i	$-0.400257\pi$
$691$	426.000			0.616498			0.308249	+	0.951306i	$0.400257\pi$
$692$		−	571.482i		−	0.825841i
$693$		0			0
$694$	−1288.00			−1.85591
$695$		−	253.992i		−	0.365456i
$696$	56.0000	−	158.392i	0.0804598	−	0.227575i
$697$	−896.000			−1.28551
$698$			178.191i			0.255288i
$699$	−239.466	−	84.6640i	−0.342584	−	0.121122i
$700$	381.649			0.545213
$701$		−	275.158i		−	0.392522i	−0.980552	−	0.196261i	$-0.937120\pi$
$701$		−	275.158i		−	0.392522i	0.980552	−	0.196261i	$-0.0628800\pi$
$702$	−840.000	−	1366.13i	−1.19658	−	1.94605i
$703$	−149.666			−0.212897
$704$		0			0
$705$	104.000	−	294.156i	0.147518	−	0.417243i
$706$	329.266			0.466382
$707$			1108.74i			1.56824i
$708$	288.000	+	101.823i	0.406780	+	0.143818i
$709$	−42.0000			−0.0592384			−0.0296192	−	0.999561i	$-0.509429\pi$
$709$	−42.0000			−0.0592384			−0.0296192	+	0.999561i	$0.509429\pi$
$710$			486.818i			0.685659i
$711$	−157.150	−	126.996i	−0.221026	−	0.178616i
$712$	−164.633			−0.231226
$713$		−	933.381i		−	1.30909i
$714$	−419.066	+	1185.30i	−0.586927	+	1.66008i
$715$		0			0
$716$		−	950.352i		−	1.32731i
$717$	119.733	+	42.3320i	0.166992	+	0.0590405i
$718$	−672.000			−0.935933
$719$		−	432.749i		−	0.601877i	−0.953644	−	0.300938i	$-0.902700\pi$
$719$		−	432.749i		−	0.601877i	0.953644	−	0.300938i	$-0.0972998\pi$
$720$	−304.000	+	376.181i	−0.422222	+	0.522473i
$721$	−254.433			−0.352889
$722$			362.468i			0.502033i
$723$	−149.666	+	423.320i	−0.207007	+	0.585505i
$724$	786.000			1.08564
$725$		−	359.822i		−	0.496306i
$726$		0			0
$727$	1102.00			1.51582			0.757909	−	0.652360i	$-0.226221\pi$
$727$	1102.00			1.51582			0.757909	+	0.652360i	$0.226221\pi$
$728$			444.486i			0.610558i
$729$	329.000	−	650.538i	0.451303	−	0.892371i
$730$	560.000			0.767123
$731$			316.784i			0.433357i
$732$	−291.849	+	825.474i	−0.398701	+	1.12770i
$733$	486.415			0.663595			0.331798	−	0.943351i	$-0.392345\pi$
$733$	486.415			0.663595			0.331798	+	0.943351i	$0.392345\pi$
$734$			375.697i			0.511848i
$735$	−56.0000	−	19.7990i	−0.0761905	−	0.0269374i
$736$	1234.75			1.67765
$737$		0			0
$738$	784.000	+	633.568i	1.06233	+	0.858493i
$739$	−1047.66			−1.41768			−0.708839	−	0.705370i	$-0.750781\pi$
$739$	−1047.66			−1.41768			−0.708839	+	0.705370i	$0.750781\pi$
$740$			84.8528i			0.114666i
$741$	−336.000	+	950.352i	−0.453441	+	1.28253i
$742$	840.000			1.13208
$743$		−	253.992i		−	0.341847i	−0.985284	−	0.170923i	$-0.945325\pi$
$743$		−	253.992i		−	0.341847i	0.985284	−	0.170923i	$-0.0546751\pi$
$744$	224.499	+	79.3725i	0.301747	+	0.106684i
$745$	59.8665			0.0803577
$746$			1128.54i			1.51279i
$747$	−119.733	+	148.162i	−0.160285	+	0.198343i
$748$		0			0
$749$			316.784i			0.422942i
$750$	−314.299	+	888.972i	−0.419066	+	1.18530i
$751$	350.000			0.466045			0.233023	−	0.972471i	$-0.425138\pi$
$751$	350.000			0.466045			0.233023	+	0.972471i	$0.425138\pi$
$752$		−	698.621i		−	0.929018i
$753$	−144.000	−	50.9117i	−0.191235	−	0.0676118i
$754$	−1257.20			−1.66737
$755$		−	190.494i		−	0.252310i
$756$	516.349	−	317.490i	0.683001	−	0.419961i
$757$	294.000			0.388375			0.194188	−	0.980964i	$-0.437793\pi$
$757$	294.000			0.388375			0.194188	+	0.980964i	$0.437793\pi$
$758$			926.013i			1.22165i
$759$		0			0
$760$	112.000			0.147368
$761$			783.142i			1.02910i	0.857461	+	0.514548i	$0.172040\pi$
$761$			783.142i			1.02910i	−0.857461	+	0.514548i	$0.827960\pi$
$762$	504.000	+	178.191i	0.661417	+	0.233846i
$763$	−504.000			−0.660550
$764$			178.191i			0.233234i
$765$	−419.066	−	338.656i	−0.547798	−	0.442688i
$766$	1369.45			1.78779
$767$			761.976i			0.993450i
$768$	−333.000	+	941.866i	−0.433594	+	1.22639i
$769$	−838.131			−1.08990			−0.544949	−	0.838469i	$-0.683451\pi$
$769$	−838.131			−1.08990			−0.544949	+	0.838469i	$0.683451\pi$
$770$		0			0
$771$	−272.000	−	96.1665i	−0.352789	−	0.124730i
$772$	−448.999			−0.581605
$773$			410.122i			0.530559i	0.964172	+	0.265279i	$0.0854642\pi$
$773$			410.122i			0.530559i	−0.964172	+	0.265279i	$0.914536\pi$
$774$	224.000	−	277.186i	0.289406	−	0.358121i
$775$	510.000			0.658065
$776$		−	195.786i		−	0.252301i
$777$	−74.8331	+	211.660i	−0.0963104	+	0.272407i
$778$	1159.91			1.49089
$779$		−	633.568i		−	0.813309i
$780$	538.799	+	190.494i	0.690768	+	0.244223i
$781$		0			0
$782$			1742.31i			2.22802i
$783$	−299.333	−	486.818i	−0.382289	−	0.621735i
$784$	−133.000			−0.169643
$785$			243.245i			0.309866i
$786$	616.000	−	1742.31i	0.783715	−	2.21668i
$787$	314.299			0.399364			0.199682	−	0.979861i	$-0.436009\pi$
$787$	314.299			0.399364			0.199682	+	0.979861i	$0.436009\pi$
$788$			698.478i			0.886394i
$789$	−1317.06	−	465.652i	−1.66928	−	0.590180i
$790$	168.000			0.212658
$791$			888.972i			1.12386i
$792$		0			0
$793$	−2184.00			−2.75410
$794$		−	1169.42i		−	1.47282i
$795$	−120.000	+	339.411i	−0.150943	+	0.426932i
$796$	−666.000			−0.836683
$797$		−	246.073i		−	0.308749i	−0.988012	−	0.154375i	$-0.950664\pi$
$797$		−	246.073i		−	0.308749i	0.988012	−	0.154375i	$-0.0493363\pi$
$798$	−838.131	−	296.324i	−1.05029	−	0.371334i
$799$	778.265			0.974048
$800$			674.667i			0.843333i
$801$	−352.000	+	435.578i	−0.439451	+	0.543792i
$802$	−1391.90			−1.73553
$803$		0			0
$804$	−126.000	+	356.382i	−0.156716	+	0.443261i
$805$	−658.532			−0.818052
$806$		−	1781.91i		−	2.21081i
$807$	1048.00	+	370.524i	1.29864	+	0.459137i
$808$	−392.000			−0.485149
$809$		−	253.992i		−	0.313958i	−0.987602	−	0.156979i	$-0.949824\pi$
$809$		−	253.992i		−	0.313958i	0.987602	−	0.156979i	$-0.0501755\pi$
$810$	127.216	+	592.648i	0.157057	+	0.731665i
$811$	−972.831			−1.19954			−0.599772	−	0.800171i	$-0.704742\pi$
$811$	−972.831			−1.19954			−0.599772	+	0.800171i	$0.704742\pi$
$812$		−	475.176i		−	0.585192i
$813$	336.749	−	952.470i	0.414206	−	1.17155i
$814$		0			0
$815$		−	39.5980i		−	0.0485865i
$816$	−1137.46	−	402.154i	−1.39395	−	0.492836i
$817$	−224.000			−0.274174
$818$			593.970i			0.726124i
$819$	1176.00	+	950.352i	1.43590	+	1.16038i
$820$	−359.199			−0.438048
$821$		−	486.818i		−	0.592958i	−0.955039	−	0.296479i	$-0.904188\pi$
$821$		−	486.818i		−	0.592958i	0.955039	−	0.296479i	$-0.0958124\pi$
$822$	−419.066	+	1185.30i	−0.509812	+	1.44197i
$823$	1042.00			1.26610			0.633050	−	0.774111i	$-0.281803\pi$
$823$	1042.00			1.26610			0.633050	+	0.774111i	$0.281803\pi$
$824$		−	89.9555i		−	0.109169i
$825$		0			0
$826$	−672.000			−0.813559
$827$			1248.79i			1.51003i	0.655708	+	0.755015i	$0.272370\pi$
$827$			1248.79i			1.51003i	−0.655708	+	0.755015i	$0.727630\pi$
$828$	528.000	−	653.367i	0.637681	−	0.789090i
$829$	1178.00			1.42099			0.710495	−	0.703703i	$-0.248471\pi$
$829$	1178.00			1.42099			0.710495	+	0.703703i	$0.248471\pi$
$830$		−	158.392i		−	0.190834i
$831$	−22.4499	+	63.4980i	−0.0270156	+	0.0764116i
$832$	651.048			0.782510
$833$		−	148.162i		−	0.177866i
$834$	−672.000	−	237.588i	−0.805755	−	0.284878i
$835$	−239.466			−0.286786
$836$		0			0
$837$	690.000	−	424.264i	0.824373	−	0.506887i
$838$	1810.96			2.16105
$839$		−	1021.06i		−	1.21700i	−0.793554	−	0.608500i	$-0.791772\pi$
$839$		−	1021.06i		−	1.21700i	0.793554	−	0.608500i	$-0.208228\pi$
$840$	56.0000	−	158.392i	0.0666667	−	0.188562i
$841$	393.000			0.467301
$842$			703.770i			0.835831i
$843$	59.8665	+	21.1660i	0.0710160	+	0.0251080i
$844$	1167.40			1.38317
$845$			947.523i			1.12133i
$846$	−680.982	−	550.316i	−0.804943	−	0.650492i
$847$		0			0
$848$			806.102i			0.950592i
$849$	−179.600	+	507.984i	−0.211542	+	0.598332i
$850$	−952.000			−1.12000
$851$			311.127i			0.365602i
$852$	552.000	+	195.161i	0.647887	+	0.229063i
$853$	−591.182			−0.693062			−0.346531	−	0.938039i	$-0.612640\pi$
$853$	−591.182			−0.693062			−0.346531	+	0.938039i	$0.612640\pi$
$854$		−	1926.11i		−	2.25539i
$855$	239.466	−	296.324i	0.280077	−	0.346578i
$856$	−112.000			−0.130841
$857$		0			0		1.00000			$0$
$857$		0			0		−1.00000			$\pi$
$858$		0			0
$859$	706.000			0.821886			0.410943	−	0.911661i	$-0.365200\pi$
$859$	706.000			0.821886			0.410943	+	0.911661i	$0.365200\pi$
$860$			126.996i			0.147670i
$861$	−896.000	−	316.784i	−1.04065	−	0.367925i
$862$	1456.00			1.68910
$863$		−	494.975i		−	0.573551i	−0.957998	−	0.286776i	$-0.907417\pi$
$863$		−	494.975i		−	0.573551i	0.957998	−	0.286776i	$-0.0925834\pi$
$864$	561.249	+	912.784i	0.649593	+	1.05646i
$865$	−538.799			−0.622889
$866$		−	1952.56i		−	2.25469i
$867$	159.000	−	449.720i	0.183391	−	0.518708i
$868$	673.498			0.775920
$869$		0			0
$870$	448.000	+	158.392i	0.514943	+	0.182060i
$871$	−942.898			−1.08255
$872$		−	178.191i		−	0.204347i
$873$	−518.000	−	418.607i	−0.593356	−	0.479504i
$874$	−1232.00			−1.40961
$875$		−	888.972i		−	1.01597i
$876$	224.499	−	634.980i	0.256278	−	0.724863i
$877$	97.2831			0.110927			0.0554636	−	0.998461i	$-0.482336\pi$
$877$	97.2831			0.110927			0.0554636	+	0.998461i	$0.482336\pi$
$878$			1128.54i			1.28536i
$879$	59.8665	+	21.1660i	0.0681075	+	0.0240796i
$880$		0			0
$881$		−	1493.41i		−	1.69513i	−0.530692	−	0.847565i	$-0.678068\pi$
$881$		−	1493.41i		−	1.69513i	0.530692	−	0.847565i	$-0.321932\pi$
$882$	−104.766	+	129.642i	−0.118783	+	0.146986i
$883$	86.0000			0.0973952			0.0486976	−	0.998814i	$-0.484493\pi$
$883$	86.0000			0.0973952			0.0486976	+	0.998814i	$0.484493\pi$
$884$			1425.53i			1.61259i
$885$	96.0000	−	271.529i	0.108475	−	0.306812i
$886$	−314.299			−0.354740
$887$		−	253.992i		−	0.286350i	−0.989697	−	0.143175i	$-0.954269\pi$
$887$		−	253.992i		−	0.286350i	0.989697	−	0.143175i	$-0.0457311\pi$
$888$	−74.8331	−	26.4575i	−0.0842716	−	0.0297945i
$889$	−504.000			−0.566929
$890$		−	465.652i		−	0.523205i
$891$		0			0
$892$	138.000			0.154709
$893$			550.316i			0.616256i
$894$	56.0000	−	158.392i	0.0626398	−	0.177172i
$895$	−896.000			−1.00112
$896$		−	613.769i		−	0.685010i
$897$	1975.60	+	698.478i	2.20245	+	0.778683i
$898$	−1347.00			−1.50000
$899$		−	634.980i		−	0.706318i
$900$	357.000	+	288.500i	0.396667	+	0.320555i
$901$	−897.998			−0.996668
$902$		0			0
$903$	−112.000	+	316.784i	−0.124031	+	0.350813i
$904$	−314.299			−0.347676
$905$		−	741.048i		−	0.818837i
$906$	−504.000	−	178.191i	−0.556291	−	0.196679i
$907$	−966.000			−1.06505			−0.532525	−	0.846414i	$-0.678757\pi$
$907$	−966.000			−1.06505			−0.532525	+	0.846414i	$0.678757\pi$
$908$		−	634.980i		−	0.699318i
$909$	−838.131	+	1037.13i	−0.922037	+	1.14096i
$910$	−1257.20			−1.38154
$911$			1450.98i			1.59274i	0.604812	+	0.796368i	$0.293248\pi$
$911$			1450.98i			1.59274i	−0.604812	+	0.796368i	$0.706752\pi$
$912$	284.366	−	804.308i	0.311805	−	0.881917i
$913$		0			0
$914$			1781.91i			1.94957i
$915$	778.265	+	275.158i	0.850563	+	0.300719i
$916$	−354.000			−0.386463
$917$			1742.31i			1.90001i
$918$	−1288.00	+	791.960i	−1.40305	+	0.862701i
$919$	396.616			0.431573			0.215787	−	0.976441i	$-0.430768\pi$
$919$	396.616			0.431573			0.215787	+	0.976441i	$0.430768\pi$
$920$		−	232.826i		−	0.253072i
$921$	−149.666	+	423.320i	−0.162504	+	0.459631i
$922$	1848.00			2.00434
$923$			1460.45i			1.58229i
$924$		0			0
$925$	−170.000			−0.183784
$926$		−	2333.55i		−	2.52004i
$927$	−238.000	−	192.333i	−0.256742	−	0.207479i
$928$	840.000			0.905172
$929$			1527.35i			1.64408i	0.569429	+	0.822040i	$0.307164\pi$
$929$			1527.35i			1.64408i	−0.569429	+	0.822040i	$0.692836\pi$
$930$	−224.499	+	634.980i	−0.241397	+	0.682775i
$931$	104.766			0.112531
$932$		−	253.992i		−	0.272524i
$933$	72.0000	+	25.4558i	0.0771704	+	0.0272839i
$934$	1406.86			1.50628
$935$		0			0
$936$	−336.000	+	415.779i	−0.358974	+	0.444208i
$937$	1257.20			1.34173			0.670863	−	0.741581i	$-0.265924\pi$
$937$	1257.20			1.34173			0.670863	+	0.741581i	$0.265924\pi$
$938$		−	831.558i		−	0.886522i
$939$	−398.000	+	1125.71i	−0.423855	+	1.19884i
$940$	312.000			0.331915
$941$		−	486.818i		−	0.517341i	−0.965966	−	0.258671i	$-0.916716\pi$
$941$		−	486.818i		−	0.517341i	0.965966	−	0.258671i	$-0.0832844\pi$
$942$	643.565	+	227.535i	0.683190	+	0.241544i
$943$	−1317.06			−1.39667
$944$		−	644.881i		−	0.683137i
$945$	−299.333	−	486.818i	−0.316754	−	0.515152i
$946$		0			0
$947$		−	435.578i		−	0.459955i	−0.973196	−	0.229978i	$-0.926135\pi$
$947$		−	435.578i		−	0.459955i	0.973196	−	0.229978i	$-0.0738653\pi$
$948$	67.3498	−	190.494i	0.0710441	−	0.200943i
$949$	1680.00			1.77028
$950$		−	673.166i		−	0.708595i
$951$	1176.00	+	415.779i	1.23659	+	0.437202i
$952$	419.066			0.440195
$953$			1608.62i			1.68795i	0.536382	+	0.843975i	$0.319791\pi$
$953$			1608.62i			1.68795i	−0.536382	+	0.843975i	$0.680209\pi$
$954$	785.748	+	634.980i	0.823635	+	0.665598i
$955$	168.000			0.175916
$956$			126.996i			0.132841i
$957$		0			0
$958$	1792.00			1.87056
$959$		−	1185.30i		−	1.23597i
$960$	−232.000	−	82.0244i	−0.241667	−	0.0854421i
$961$	−61.0000			−0.0634755
$962$			593.970i			0.617432i
$963$	−239.466	+	296.324i	−0.248667	+	0.307709i
$964$	−448.999			−0.465766
$965$			423.320i			0.438674i
$966$	−616.000	+	1742.31i	−0.637681	+	1.80363i
$967$	1055.15			1.09116			0.545578	−	0.838060i	$-0.316310\pi$
$967$	1055.15			1.09116			0.545578	+	0.838060i	$0.316310\pi$
$968$		0			0
$969$	896.000	+	316.784i	0.924665	+	0.326918i
$970$	553.765			0.570892
$971$			254.558i			0.262161i	0.991372	+	0.131081i	$0.0418447\pi$
$971$			254.558i			0.262161i	−0.991372	+	0.131081i	$0.958155\pi$
$972$	723.000	+	93.3381i	0.743827	+	0.0960268i
$973$	672.000			0.690647
$974$		−	926.013i		−	0.950732i
$975$	−381.649	+	1079.47i	−0.391435	+	1.10715i
$976$	1848.38			1.89383
$977$		−	1442.50i		−	1.47646i	−0.674551	−	0.738228i	$-0.735663\pi$
$977$		−	1442.50i		−	1.47646i	0.674551	−	0.738228i	$-0.264337\pi$
$978$	−104.766	−	37.0405i	−0.107123	−	0.0378737i
$979$		0			0
$980$		−	59.3970i		−	0.0606092i
$981$	−471.449	−	380.988i	−0.480580	−	0.388367i
$982$	−672.000			−0.684318
$983$			687.308i			0.699194i	0.936900	+	0.349597i	$0.113682\pi$
$983$			687.308i			0.699194i	−0.936900	+	0.349597i	$0.886318\pi$
$984$	112.000	−	316.784i	0.113821	−	0.321935i
$985$	658.532			0.668560
$986$			1185.30i			1.20213i
$987$	778.265	+	275.158i	0.788515	+	0.278782i
$988$	−1008.00			−1.02024
$989$			465.652i			0.470831i
$990$		0			0
$991$	574.000			0.579213			0.289606	−	0.957146i	$-0.406476\pi$
$991$	574.000			0.579213			0.289606	+	0.957146i	$0.406476\pi$
$992$			1190.59i			1.20019i
$993$	−178.000	+	503.460i	−0.179255	+	0.507009i
$994$	−1288.00			−1.29577
$995$			627.911i			0.631066i
$996$	−179.600	−	63.4980i	−0.180321	−	0.0637530i
$997$	−1324.55			−1.32853			−0.664266	−	0.747496i	$-0.731256\pi$
$997$	−1324.55			−1.32853			−0.664266	+	0.747496i	$0.731256\pi$
$998$			259.284i			0.259803i
$999$	−230.000	+	141.421i	−0.230230	+	0.141563i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.3.b.i.122.2	yes	4
3.2	odd	2	inner	363.3.b.i.122.3	yes	4
11.2	odd	10		363.3.h.k.323.4		16
11.3	even	5		363.3.h.k.251.1		16
11.4	even	5		363.3.h.k.269.4		16
11.5	even	5		363.3.h.k.245.3		16
11.6	odd	10		363.3.h.k.245.1		16
11.7	odd	10		363.3.h.k.269.2		16
11.8	odd	10		363.3.h.k.251.3		16
11.9	even	5		363.3.h.k.323.2		16
11.10	odd	2	inner	363.3.b.i.122.4	yes	4
33.2	even	10		363.3.h.k.323.1		16
33.5	odd	10		363.3.h.k.245.2		16
33.8	even	10		363.3.h.k.251.2		16
33.14	odd	10		363.3.h.k.251.4		16
33.17	even	10		363.3.h.k.245.4		16
33.20	odd	10		363.3.h.k.323.3		16
33.26	odd	10		363.3.h.k.269.1		16
33.29	even	10		363.3.h.k.269.3		16
33.32	even	2	inner	363.3.b.i.122.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.3.b.i.122.1	✓	4	33.32	even	2	inner
363.3.b.i.122.2	yes	4	1.1	even	1	trivial
363.3.b.i.122.3	yes	4	3.2	odd	2	inner
363.3.b.i.122.4	yes	4	11.10	odd	2	inner
363.3.h.k.245.1		16	11.6	odd	10
363.3.h.k.245.2		16	33.5	odd	10
363.3.h.k.245.3		16	11.5	even	5
363.3.h.k.245.4		16	33.17	even	10
363.3.h.k.251.1		16	11.3	even	5
363.3.h.k.251.2		16	33.8	even	10
363.3.h.k.251.3		16	11.8	odd	10
363.3.h.k.251.4		16	33.14	odd	10
363.3.h.k.269.1		16	33.26	odd	10
363.3.h.k.269.2		16	11.7	odd	10
363.3.h.k.269.3		16	33.29	even	10
363.3.h.k.269.4		16	11.4	even	5
363.3.h.k.323.1		16	33.2	even	10
363.3.h.k.323.2		16	11.9	even	5
363.3.h.k.323.3		16	33.20	odd	10
363.3.h.k.323.4		16	11.2	odd	10

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:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	363.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.64575i q^{2} +(-1.00000 + 2.82843i) q^{3} -3.00000 q^{4} +2.82843i q^{5} +(7.48331 + 2.64575i) q^{6} -7.48331 q^{7} -2.64575i q^{8} +(-7.00000 - 5.65685i) q^{9} +O(q^{10})\)	\(q-2.64575i q^{2} +(-1.00000 + 2.82843i) q^{3} -3.00000 q^{4} +2.82843i q^{5} +(7.48331 + 2.64575i) q^{6} -7.48331 q^{7} -2.64575i q^{8} +(-7.00000 - 5.65685i) q^{9} +7.48331 q^{10} +(3.00000 - 8.48528i) q^{12} +22.4499 q^{13} +19.7990i q^{14} +(-8.00000 - 2.82843i) q^{15} -19.0000 q^{16} -21.1660i q^{17} +(-14.9666 + 18.5203i) q^{18} +14.9666 q^{19} -8.48528i q^{20} +(7.48331 - 21.1660i) q^{21} -31.1127i q^{23} +(7.48331 + 2.64575i) q^{24} +17.0000 q^{25} -59.3970i q^{26} +(23.0000 - 14.1421i) q^{27} +22.4499 q^{28} -21.1660i q^{29} +(-7.48331 + 21.1660i) q^{30} +30.0000 q^{31} +39.6863i q^{32} -56.0000 q^{34} -21.1660i q^{35} +(21.0000 + 16.9706i) q^{36} -10.0000 q^{37} -39.5980i q^{38} +(-22.4499 + 63.4980i) q^{39} +7.48331 q^{40} -42.3320i q^{41} +(-56.0000 - 19.7990i) q^{42} -14.9666 q^{43} +(16.0000 - 19.7990i) q^{45} -82.3165 q^{46} +36.7696i q^{47} +(19.0000 - 53.7401i) q^{48} +7.00000 q^{49} -44.9778i q^{50} +(59.8665 + 21.1660i) q^{51} -67.3498 q^{52} -42.4264i q^{53} +(-37.4166 - 60.8523i) q^{54} +19.7990i q^{56} +(-14.9666 + 42.3320i) q^{57} -56.0000 q^{58} +33.9411i q^{59} +(24.0000 + 8.48528i) q^{60} -97.2831 q^{61} -79.3725i q^{62} +(52.3832 + 42.3320i) q^{63} +29.0000 q^{64} +63.4980i q^{65} -42.0000 q^{67} +63.4980i q^{68} +(88.0000 + 31.1127i) q^{69} -56.0000 q^{70} +65.0538i q^{71} +(-14.9666 + 18.5203i) q^{72} +74.8331 q^{73} +26.4575i q^{74} +(-17.0000 + 48.0833i) q^{75} -44.8999 q^{76} +(168.000 + 59.3970i) q^{78} +22.4499 q^{79} -53.7401i q^{80} +(17.0000 + 79.1960i) q^{81} -112.000 q^{82} -21.1660i q^{83} +(-22.4499 + 63.4980i) q^{84} +59.8665 q^{85} +39.5980i q^{86} +(59.8665 + 21.1660i) q^{87} -62.2254i q^{89} +(-52.3832 - 42.3320i) q^{90} -168.000 q^{91} +93.3381i q^{92} +(-30.0000 + 84.8528i) q^{93} +97.2831 q^{94} +42.3320i q^{95} +(-112.250 - 39.6863i) q^{96} +74.0000 q^{97} -18.5203i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{3} - 12 q^{4} - 28 q^{9}+O(q^{10}) \) 4 * q - 4 * q^3 - 12 * q^4 - 28 * q^9	\( 4 q - 4 q^{3} - 12 q^{4} - 28 q^{9} + 12 q^{12} - 32 q^{15} - 76 q^{16} + 68 q^{25} + 92 q^{27} + 120 q^{31} - 224 q^{34} + 84 q^{36} - 40 q^{37} - 224 q^{42} + 64 q^{45} + 76 q^{48} + 28 q^{49} - 224 q^{58} + 96 q^{60} + 116 q^{64} - 168 q^{67} + 352 q^{69} - 224 q^{70} - 68 q^{75} + 672 q^{78} + 68 q^{81} - 448 q^{82} - 672 q^{91} - 120 q^{93} + 296 q^{97}+O(q^{100}) \) 4 * q - 4 * q^3 - 12 * q^4 - 28 * q^9 + 12 * q^12 - 32 * q^15 - 76 * q^16 + 68 * q^25 + 92 * q^27 + 120 * q^31 - 224 * q^34 + 84 * q^36 - 40 * q^37 - 224 * q^42 + 64 * q^45 + 76 * q^48 + 28 * q^49 - 224 * q^58 + 96 * q^60 + 116 * q^64 - 168 * q^67 + 352 * q^69 - 224 * q^70 - 68 * q^75 + 672 * q^78 + 68 * q^81 - 448 * q^82 - 672 * q^91 - 120 * q^93 + 296 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more