LMFDB - Embedded newform 1155.2.l.c.1121.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.3
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.c.1121.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000i q^{5} +(1.41421 - 2.00000i) q^{6} -1.00000i q^{7} -2.82843 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})$	\(q+1.41421 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000i q^{5} +(1.41421 - 2.00000i) q^{6} -1.00000i q^{7} -2.82843 q^{8} +(-1.00000 - 2.82843i) q^{9} +1.41421i q^{10} +(3.00000 - 1.41421i) q^{11} -6.24264i q^{13} -1.41421i q^{14} +(1.41421 + 1.00000i) q^{15} -4.00000 q^{16} +0.171573 q^{17} +(-1.41421 - 4.00000i) q^{18} +5.24264i q^{19} +(-1.41421 - 1.00000i) q^{21} +(4.24264 - 2.00000i) q^{22} -7.24264i q^{23} +(-2.82843 + 4.00000i) q^{24} -1.00000 q^{25} -8.82843i q^{26} +(-5.00000 - 1.41421i) q^{27} -0.171573 q^{29} +(2.00000 + 1.41421i) q^{30} -0.242641 q^{31} +(1.00000 - 5.65685i) q^{33} +0.242641 q^{34} +1.00000 q^{35} -0.242641 q^{37} +7.41421i q^{38} +(-8.82843 - 6.24264i) q^{39} -2.82843i q^{40} +7.41421 q^{41} +(-2.00000 - 1.41421i) q^{42} +5.24264i q^{43} +(2.82843 - 1.00000i) q^{45} -10.2426i q^{46} -13.0711i q^{47} +(-4.00000 + 5.65685i) q^{48} -1.00000 q^{49} -1.41421 q^{50} +(0.171573 - 0.242641i) q^{51} +1.58579i q^{53} +(-7.07107 - 2.00000i) q^{54} +(1.41421 + 3.00000i) q^{55} +2.82843i q^{56} +(7.41421 + 5.24264i) q^{57} -0.242641 q^{58} -6.89949i q^{59} +0.757359i q^{61} -0.343146 q^{62} +(-2.82843 + 1.00000i) q^{63} +8.00000 q^{64} +6.24264 q^{65} +(1.41421 - 8.00000i) q^{66} +4.48528 q^{67} +(-10.2426 - 7.24264i) q^{69} +1.41421 q^{70} +10.2426i q^{71} +(2.82843 + 8.00000i) q^{72} +10.4853i q^{73} -0.343146 q^{74} +(-1.00000 + 1.41421i) q^{75} +(-1.41421 - 3.00000i) q^{77} +(-12.4853 - 8.82843i) q^{78} +2.24264i q^{79} -4.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} +10.4853 q^{82} +11.1421 q^{83} +0.171573i q^{85} +7.41421i q^{86} +(-0.171573 + 0.242641i) q^{87} +(-8.48528 + 4.00000i) q^{88} +13.5858i q^{89} +(4.00000 - 1.41421i) q^{90} -6.24264 q^{91} +(-0.242641 + 0.343146i) q^{93} -18.4853i q^{94} -5.24264 q^{95} -7.00000 q^{97} -1.41421 q^{98} +(-7.00000 - 7.07107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^9	$ 4 q + 4 q^{3} - 4 q^{9} + 12 q^{11} - 16 q^{16} + 12 q^{17} - 4 q^{25} - 20 q^{27} - 12 q^{29} + 8 q^{30} + 16 q^{31} + 4 q^{33} - 16 q^{34} + 4 q^{35} + 16 q^{37} - 24 q^{39} + 24 q^{41} - 8 q^{42} - 16 q^{48} - 4 q^{49} + 12 q^{51} + 24 q^{57} + 16 q^{58} - 24 q^{62} + 32 q^{64} + 8 q^{65} - 16 q^{67} - 24 q^{69} - 24 q^{74} - 4 q^{75} - 16 q^{78} - 28 q^{81} + 8 q^{82} - 12 q^{83} - 12 q^{87} + 16 q^{90} - 8 q^{91} + 16 q^{93} - 4 q^{95} - 28 q^{97} - 28 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^9 + 12 * q^11 - 16 * q^16 + 12 * q^17 - 4 * q^25 - 20 * q^27 - 12 * q^29 + 8 * q^30 + 16 * q^31 + 4 * q^33 - 16 * q^34 + 4 * q^35 + 16 * q^37 - 24 * q^39 + 24 * q^41 - 8 * q^42 - 16 * q^48 - 4 * q^49 + 12 * q^51 + 24 * q^57 + 16 * q^58 - 24 * q^62 + 32 * q^64 + 8 * q^65 - 16 * q^67 - 24 * q^69 - 24 * q^74 - 4 * q^75 - 16 * q^78 - 28 * q^81 + 8 * q^82 - 12 * q^83 - 12 * q^87 + 16 * q^90 - 8 * q^91 + 16 * q^93 - 4 * q^95 - 28 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	1.41421			1.00000			0.500000	−	0.866025i	$-0.333333\pi$
$2$	1.41421			1.00000			0.500000	+	0.866025i	$0.333333\pi$
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$3$	1.00000	−	1.41421i	0.577350	−	0.816497i
$4$		0			0
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	1.41421	−	2.00000i	0.577350	−	0.816497i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−2.82843			−1.00000
$9$	−1.00000	−	2.82843i	−0.333333	−	0.942809i
$10$			1.41421i			0.447214i
$11$	3.00000	−	1.41421i	0.904534	−	0.426401i
$11$	3.00000	−	1.41421i	0.904534	−	0.426401i
$12$		0			0
$13$		−	6.24264i		−	1.73140i	−0.500566	−	0.865699i	$-0.666875\pi$
$13$		−	6.24264i		−	1.73140i	0.500566	−	0.865699i	$-0.333125\pi$
$14$		−	1.41421i		−	0.377964i
$15$	1.41421	+	1.00000i	0.365148	+	0.258199i
$16$	−4.00000			−1.00000
$17$	0.171573			0.0416125			0.0208063	−	0.999784i	$-0.493377\pi$
$17$	0.171573			0.0416125			0.0208063	+	0.999784i	$0.493377\pi$
$18$	−1.41421	−	4.00000i	−0.333333	−	0.942809i
$19$			5.24264i			1.20274i	0.798969	+	0.601372i	$0.205379\pi$
$19$			5.24264i			1.20274i	−0.798969	+	0.601372i	$0.794621\pi$
$20$		0			0
$21$	−1.41421	−	1.00000i	−0.308607	−	0.218218i
$22$	4.24264	−	2.00000i	0.904534	−	0.426401i
$23$		−	7.24264i		−	1.51019i	−0.655613	−	0.755097i	$-0.727590\pi$
$23$		−	7.24264i		−	1.51019i	0.655613	−	0.755097i	$-0.272410\pi$
$24$	−2.82843	+	4.00000i	−0.577350	+	0.816497i
$25$	−1.00000			−0.200000
$26$		−	8.82843i		−	1.73140i
$27$	−5.00000	−	1.41421i	−0.962250	−	0.272166i
$28$		0			0
$29$	−0.171573			−0.0318603			−0.0159301	−	0.999873i	$-0.505071\pi$
$29$	−0.171573			−0.0318603			−0.0159301	+	0.999873i	$0.505071\pi$
$30$	2.00000	+	1.41421i	0.365148	+	0.258199i
$31$	−0.242641			−0.0435796			−0.0217898	−	0.999763i	$-0.506936\pi$
$31$	−0.242641			−0.0435796			−0.0217898	+	0.999763i	$0.506936\pi$
$32$		0			0
$33$	1.00000	−	5.65685i	0.174078	−	0.984732i
$34$	0.242641			0.0416125
$35$	1.00000			0.169031
$36$		0			0
$37$	−0.242641			−0.0398899			−0.0199449	−	0.999801i	$-0.506349\pi$
$37$	−0.242641			−0.0398899			−0.0199449	+	0.999801i	$0.506349\pi$
$38$			7.41421i			1.20274i
$39$	−8.82843	−	6.24264i	−1.41368	−	0.999623i
$40$		−	2.82843i		−	0.447214i
$41$	7.41421			1.15791			0.578953	−	0.815361i	$-0.303462\pi$
$41$	7.41421			1.15791			0.578953	+	0.815361i	$0.303462\pi$
$42$	−2.00000	−	1.41421i	−0.308607	−	0.218218i
$43$			5.24264i			0.799495i	0.916625	+	0.399748i	$0.130902\pi$
$43$			5.24264i			0.799495i	−0.916625	+	0.399748i	$0.869098\pi$
$44$		0			0
$45$	2.82843	−	1.00000i	0.421637	−	0.149071i
$46$		−	10.2426i		−	1.51019i
$47$		−	13.0711i		−	1.90661i	−0.302007	−	0.953306i	$-0.597657\pi$
$47$		−	13.0711i		−	1.90661i	0.302007	−	0.953306i	$-0.402343\pi$
$48$	−4.00000	+	5.65685i	−0.577350	+	0.816497i
$49$	−1.00000			−0.142857
$50$	−1.41421			−0.200000
$51$	0.171573	−	0.242641i	0.0240250	−	0.0339765i
$52$		0			0
$53$			1.58579i			0.217825i	0.994051	+	0.108912i	$0.0347368\pi$
$53$			1.58579i			0.217825i	−0.994051	+	0.108912i	$0.965263\pi$
$54$	−7.07107	−	2.00000i	−0.962250	−	0.272166i
$55$	1.41421	+	3.00000i	0.190693	+	0.404520i
$56$			2.82843i			0.377964i
$57$	7.41421	+	5.24264i	0.982037	+	0.694405i
$58$	−0.242641			−0.0318603
$59$		−	6.89949i		−	0.898238i	−0.893472	−	0.449119i	$-0.851738\pi$
$59$		−	6.89949i		−	0.898238i	0.893472	−	0.449119i	$-0.148262\pi$
$60$		0			0
$61$			0.757359i			0.0969699i	0.998824	+	0.0484850i	$0.0154393\pi$
$61$			0.757359i			0.0969699i	−0.998824	+	0.0484850i	$0.984561\pi$
$62$	−0.343146			−0.0435796
$63$	−2.82843	+	1.00000i	−0.356348	+	0.125988i
$64$	8.00000			1.00000
$65$	6.24264			0.774304
$66$	1.41421	−	8.00000i	0.174078	−	0.984732i
$67$	4.48528			0.547964			0.273982	−	0.961735i	$-0.411659\pi$
$67$	4.48528			0.547964			0.273982	+	0.961735i	$0.411659\pi$
$68$		0			0
$69$	−10.2426	−	7.24264i	−1.23307	−	0.871911i
$70$	1.41421			0.169031
$71$			10.2426i			1.21558i	0.794099	+	0.607789i	$0.207943\pi$
$71$			10.2426i			1.21558i	−0.794099	+	0.607789i	$0.792057\pi$
$72$	2.82843	+	8.00000i	0.333333	+	0.942809i
$73$			10.4853i			1.22721i	0.789613	+	0.613605i	$0.210281\pi$
$73$			10.4853i			1.22721i	−0.789613	+	0.613605i	$0.789719\pi$
$74$	−0.343146			−0.0398899
$75$	−1.00000	+	1.41421i	−0.115470	+	0.163299i
$76$		0			0
$77$	−1.41421	−	3.00000i	−0.161165	−	0.341882i
$78$	−12.4853	−	8.82843i	−1.41368	−	0.999623i
$79$			2.24264i			0.252317i	0.992010	+	0.126158i	$0.0402648\pi$
$79$			2.24264i			0.252317i	−0.992010	+	0.126158i	$0.959735\pi$
$80$		−	4.00000i		−	0.447214i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	10.4853			1.15791
$83$	11.1421			1.22301			0.611504	−	0.791241i	$-0.290565\pi$
$83$	11.1421			1.22301			0.611504	+	0.791241i	$0.290565\pi$
$84$		0			0
$85$			0.171573i			0.0186097i
$86$			7.41421i			0.799495i
$87$	−0.171573	+	0.242641i	−0.0183945	+	0.0260138i
$88$	−8.48528	+	4.00000i	−0.904534	+	0.426401i
$89$			13.5858i			1.44009i	0.693927	+	0.720045i	$0.255879\pi$
$89$			13.5858i			1.44009i	−0.693927	+	0.720045i	$0.744121\pi$
$90$	4.00000	−	1.41421i	0.421637	−	0.149071i
$91$	−6.24264			−0.654407
$92$		0			0
$93$	−0.242641	+	0.343146i	−0.0251607	+	0.0355826i
$94$		−	18.4853i		−	1.90661i
$95$	−5.24264			−0.537884
$96$		0			0
$97$	−7.00000			−0.710742			−0.355371	−	0.934725i	$-0.615646\pi$
$97$	−7.00000			−0.710742			−0.355371	+	0.934725i	$0.615646\pi$
$98$	−1.41421			−0.142857
$99$	−7.00000	−	7.07107i	−0.703526	−	0.710669i
$100$		0			0
$101$	14.4853			1.44134			0.720670	−	0.693279i	$-0.243834\pi$
$101$	14.4853			1.44134			0.720670	+	0.693279i	$0.243834\pi$
$102$	0.242641	−	0.343146i	0.0240250	−	0.0339765i
$103$	−17.4853			−1.72288			−0.861438	−	0.507863i	$-0.830436\pi$
$103$	−17.4853			−1.72288			−0.861438	+	0.507863i	$0.830436\pi$
$104$			17.6569i			1.73140i
$105$	1.00000	−	1.41421i	0.0975900	−	0.138013i
$106$			2.24264i			0.217825i
$107$	−4.58579			−0.443325			−0.221662	−	0.975123i	$-0.571148\pi$
$107$	−4.58579			−0.443325			−0.221662	+	0.975123i	$0.571148\pi$
$108$		0			0
$109$			12.2426i			1.17263i	0.810082	+	0.586316i	$0.199422\pi$
$109$			12.2426i			1.17263i	−0.810082	+	0.586316i	$0.800578\pi$
$110$	2.00000	+	4.24264i	0.190693	+	0.404520i
$111$	−0.242641	+	0.343146i	−0.0230304	+	0.0325700i
$112$			4.00000i			0.377964i
$113$			0.899495i			0.0846174i	0.999105	+	0.0423087i	$0.0134713\pi$
$113$			0.899495i			0.0846174i	−0.999105	+	0.0423087i	$0.986529\pi$
$114$	10.4853	+	7.41421i	0.982037	+	0.694405i
$115$	7.24264			0.675380
$116$		0			0
$117$	−17.6569	+	6.24264i	−1.63238	+	0.577132i
$118$		−	9.75736i		−	0.898238i
$119$		−	0.171573i		−	0.0157281i
$120$	−4.00000	−	2.82843i	−0.365148	−	0.258199i
$121$	7.00000	−	8.48528i	0.636364	−	0.771389i
$122$			1.07107i			0.0969699i
$123$	7.41421	−	10.4853i	0.668517	−	0.945426i
$124$		0			0
$125$		−	1.00000i		−	0.0894427i
$126$	−4.00000	+	1.41421i	−0.356348	+	0.125988i
$127$			4.75736i			0.422147i	0.977470	+	0.211074i	$0.0676960\pi$
$127$			4.75736i			0.422147i	−0.977470	+	0.211074i	$0.932304\pi$
$128$	11.3137			1.00000
$129$	7.41421	+	5.24264i	0.652785	+	0.461589i
$130$	8.82843			0.774304
$131$	16.5858			1.44911			0.724553	−	0.689219i	$-0.242046\pi$
$131$	16.5858			1.44911			0.724553	+	0.689219i	$0.242046\pi$
$132$		0			0
$133$	5.24264			0.454595
$134$	6.34315			0.547964
$135$	1.41421	−	5.00000i	0.121716	−	0.430331i
$136$	−0.485281			−0.0416125
$137$		−	2.48528i		−	0.212332i	−0.994348	−	0.106166i	$-0.966143\pi$
$137$		−	2.48528i		−	0.212332i	0.994348	−	0.106166i	$-0.0338575\pi$
$138$	−14.4853	−	10.2426i	−1.23307	−	0.871911i
$139$			4.48528i			0.380437i	0.981742	+	0.190218i	$0.0609196\pi$
$139$			4.48528i			0.380437i	−0.981742	+	0.190218i	$0.939080\pi$
$140$		0			0
$141$	−18.4853	−	13.0711i	−1.55674	−	1.10078i
$142$			14.4853i			1.21558i
$143$	−8.82843	−	18.7279i	−0.738270	−	1.56611i
$144$	4.00000	+	11.3137i	0.333333	+	0.942809i
$145$		−	0.171573i		−	0.0142484i
$146$			14.8284i			1.22721i
$147$	−1.00000	+	1.41421i	−0.0824786	+	0.116642i
$148$		0			0
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$	−1.41421	+	2.00000i	−0.115470	+	0.163299i
$151$			10.0000i			0.813788i	0.913475	+	0.406894i	$0.133388\pi$
$151$			10.0000i			0.813788i	−0.913475	+	0.406894i	$0.866612\pi$
$152$		−	14.8284i		−	1.20274i
$153$	−0.171573	−	0.485281i	−0.0138708	−	0.0392327i
$154$	−2.00000	−	4.24264i	−0.161165	−	0.341882i
$155$		−	0.242641i		−	0.0194894i
$156$		0			0
$157$	11.0000			0.877896			0.438948	−	0.898513i	$-0.355351\pi$
$157$	11.0000			0.877896			0.438948	+	0.898513i	$0.355351\pi$
$158$			3.17157i			0.252317i
$159$	2.24264	+	1.58579i	0.177853	+	0.125761i
$160$		0			0
$161$	−7.24264			−0.570800
$162$	−9.89949	+	8.00000i	−0.777778	+	0.628539i
$163$	−6.24264			−0.488961			−0.244481	−	0.969654i	$-0.578617\pi$
$163$	−6.24264			−0.488961			−0.244481	+	0.969654i	$0.578617\pi$
$164$		0			0
$165$	5.65685	+	1.00000i	0.440386	+	0.0778499i
$166$	15.7574			1.22301
$167$	8.14214			0.630057			0.315029	−	0.949082i	$-0.397986\pi$
$167$	8.14214			0.630057			0.315029	+	0.949082i	$0.397986\pi$
$168$	4.00000	+	2.82843i	0.308607	+	0.218218i
$169$	−25.9706			−1.99774
$170$			0.242641i			0.0186097i
$171$	14.8284	−	5.24264i	1.13396	−	0.400915i
$172$		0			0
$173$	−2.82843			−0.215041			−0.107521	−	0.994203i	$-0.534291\pi$
$173$	−2.82843			−0.215041			−0.107521	+	0.994203i	$0.534291\pi$
$174$	−0.242641	+	0.343146i	−0.0183945	+	0.0260138i
$175$			1.00000i			0.0755929i
$176$	−12.0000	+	5.65685i	−0.904534	+	0.426401i
$177$	−9.75736	−	6.89949i	−0.733408	−	0.518598i
$178$			19.2132i			1.44009i
$179$		−	10.5858i		−	0.791219i	−0.918419	−	0.395609i	$-0.870533\pi$
$179$		−	10.5858i		−	0.791219i	0.918419	−	0.395609i	$-0.129467\pi$
$180$		0			0
$181$	22.9706			1.70739			0.853694	−	0.520775i	$-0.174357\pi$
$181$	22.9706			1.70739			0.853694	+	0.520775i	$0.174357\pi$
$182$	−8.82843			−0.654407
$183$	1.07107	+	0.757359i	0.0791756	+	0.0559856i
$184$			20.4853i			1.51019i
$185$		−	0.242641i		−	0.0178393i
$186$	−0.343146	+	0.485281i	−0.0251607	+	0.0355826i
$187$	0.514719	−	0.242641i	0.0376400	−	0.0177436i
$188$		0			0
$189$	−1.41421	+	5.00000i	−0.102869	+	0.363696i
$190$	−7.41421			−0.537884
$191$			14.8284i			1.07295i	0.843917	+	0.536474i	$0.180244\pi$
$191$			14.8284i			1.07295i	−0.843917	+	0.536474i	$0.819756\pi$
$192$	8.00000	−	11.3137i	0.577350	−	0.816497i
$193$		−	10.0000i		−	0.719816i	−0.932988	−	0.359908i	$-0.882808\pi$
$193$		−	10.0000i		−	0.719816i	0.932988	−	0.359908i	$-0.117192\pi$
$194$	−9.89949			−0.710742
$195$	6.24264	−	8.82843i	0.447045	−	0.632217i
$196$		0			0
$197$	−6.00000			−0.427482			−0.213741	−	0.976890i	$-0.568565\pi$
$197$	−6.00000			−0.427482			−0.213741	+	0.976890i	$0.568565\pi$
$198$	−9.89949	−	10.0000i	−0.703526	−	0.710669i
$199$	24.4853			1.73572			0.867858	−	0.496813i	$-0.165496\pi$
$199$	24.4853			1.73572			0.867858	+	0.496813i	$0.165496\pi$
$200$	2.82843			0.200000
$201$	4.48528	−	6.34315i	0.316367	−	0.447411i
$202$	20.4853			1.44134
$203$			0.171573i			0.0120421i
$204$		0			0
$205$			7.41421i			0.517831i
$206$	−24.7279			−1.72288
$207$	−20.4853	+	7.24264i	−1.42383	+	0.503398i
$208$			24.9706i			1.73140i
$209$	7.41421	+	15.7279i	0.512852	+	1.08792i
$210$	1.41421	−	2.00000i	0.0975900	−	0.138013i
$211$			8.00000i			0.550743i	0.961338	+	0.275371i	$0.0888008\pi$
$211$			8.00000i			0.550743i	−0.961338	+	0.275371i	$0.911199\pi$
$212$		0			0
$213$	14.4853	+	10.2426i	0.992515	+	0.701814i
$214$	−6.48528			−0.443325
$215$	−5.24264			−0.357545
$216$	14.1421	+	4.00000i	0.962250	+	0.272166i
$217$			0.242641i			0.0164715i
$218$			17.3137i			1.17263i
$219$	14.8284	+	10.4853i	1.00201	+	0.708530i
$220$		0			0
$221$		−	1.07107i		−	0.0720478i
$222$	−0.343146	+	0.485281i	−0.0230304	+	0.0325700i
$223$	17.0000			1.13840			0.569202	−	0.822198i	$-0.307252\pi$
$223$	17.0000			1.13840			0.569202	+	0.822198i	$0.307252\pi$
$224$		0			0
$225$	1.00000	+	2.82843i	0.0666667	+	0.188562i
$226$			1.27208i			0.0846174i
$227$	11.8284			0.785080			0.392540	−	0.919735i	$-0.371596\pi$
$227$	11.8284			0.785080			0.392540	+	0.919735i	$0.371596\pi$
$228$		0			0
$229$	−6.72792			−0.444594			−0.222297	−	0.974979i	$-0.571355\pi$
$229$	−6.72792			−0.444594			−0.222297	+	0.974979i	$0.571355\pi$
$230$	10.2426			0.675380
$231$	−5.65685	−	1.00000i	−0.372194	−	0.0657952i
$232$	0.485281			0.0318603
$233$	−21.5563			−1.41220			−0.706102	−	0.708110i	$-0.749548\pi$
$233$	−21.5563			−1.41220			−0.706102	+	0.708110i	$0.749548\pi$
$234$	−24.9706	+	8.82843i	−1.63238	+	0.577132i
$235$	13.0711			0.852662
$236$		0			0
$237$	3.17157	+	2.24264i	0.206016	+	0.145675i
$238$		−	0.242641i		−	0.0157281i
$239$	−2.65685			−0.171858			−0.0859288	−	0.996301i	$-0.527386\pi$
$239$	−2.65685			−0.171858			−0.0859288	+	0.996301i	$0.527386\pi$
$240$	−5.65685	−	4.00000i	−0.365148	−	0.258199i
$241$		−	26.4853i		−	1.70607i	−0.521856	−	0.853033i	$-0.674760\pi$
$241$		−	26.4853i		−	1.70607i	0.521856	−	0.853033i	$-0.325240\pi$
$242$	9.89949	−	12.0000i	0.636364	−	0.771389i
$243$	1.00000	+	15.5563i	0.0641500	+	0.997940i
$244$		0			0
$245$		−	1.00000i		−	0.0638877i
$246$	10.4853	−	14.8284i	0.668517	−	0.945426i
$247$	32.7279			2.08243
$248$	0.686292			0.0435796
$249$	11.1421	−	15.7574i	0.706104	−	0.998582i
$250$		−	1.41421i		−	0.0894427i
$251$			4.97056i			0.313739i	0.987619	+	0.156870i	$0.0501402\pi$
$251$			4.97056i			0.313739i	−0.987619	+	0.156870i	$0.949860\pi$
$252$		0			0
$253$	−10.2426	−	21.7279i	−0.643949	−	1.36602i
$254$			6.72792i			0.422147i
$255$	0.242641	+	0.171573i	0.0151947	+	0.0107443i
$256$		0			0
$257$		−	13.7574i		−	0.858160i	−0.903266	−	0.429080i	$-0.858838\pi$
$257$		−	13.7574i		−	0.858160i	0.903266	−	0.429080i	$-0.141162\pi$
$258$	10.4853	+	7.41421i	0.652785	+	0.461589i
$259$			0.242641i			0.0150770i
$260$		0			0
$261$	0.171573	+	0.485281i	0.0106201	+	0.0300382i
$262$	23.4558			1.44911
$263$	15.1716			0.935519			0.467760	−	0.883856i	$-0.345061\pi$
$263$	15.1716			0.935519			0.467760	+	0.883856i	$0.345061\pi$
$264$	−2.82843	+	16.0000i	−0.174078	+	0.984732i
$265$	−1.58579			−0.0974141
$266$	7.41421			0.454595
$267$	19.2132	+	13.5858i	1.17583	+	0.831437i
$268$		0			0
$269$		−	30.5563i		−	1.86305i	−0.363673	−	0.931527i	$-0.618477\pi$
$269$		−	30.5563i		−	1.86305i	0.363673	−	0.931527i	$-0.381523\pi$
$270$	2.00000	−	7.07107i	0.121716	−	0.430331i
$271$		−	23.2426i		−	1.41189i	−0.708267	−	0.705945i	$-0.750523\pi$
$271$		−	23.2426i		−	1.41189i	0.708267	−	0.705945i	$-0.249477\pi$
$272$	−0.686292			−0.0416125
$273$	−6.24264	+	8.82843i	−0.377822	+	0.534321i
$274$		−	3.51472i		−	0.212332i
$275$	−3.00000	+	1.41421i	−0.180907	+	0.0852803i
$276$		0			0
$277$		−	8.48528i		−	0.509831i	−0.966963	−	0.254916i	$-0.917952\pi$
$277$		−	8.48528i		−	0.509831i	0.966963	−	0.254916i	$-0.0820477\pi$
$278$			6.34315i			0.380437i
$279$	0.242641	+	0.686292i	0.0145265	+	0.0410872i
$280$	−2.82843			−0.169031
$281$	−17.3137			−1.03285			−0.516425	−	0.856333i	$-0.672737\pi$
$281$	−17.3137			−1.03285			−0.516425	+	0.856333i	$0.672737\pi$
$282$	−26.1421	−	18.4853i	−1.55674	−	1.10078i
$283$			13.2132i			0.785443i	0.919657	+	0.392722i	$0.128466\pi$
$283$			13.2132i			0.785443i	−0.919657	+	0.392722i	$0.871534\pi$
$284$		0			0
$285$	−5.24264	+	7.41421i	−0.310547	+	0.439180i
$286$	−12.4853	−	26.4853i	−0.738270	−	1.56611i
$287$		−	7.41421i		−	0.437647i
$288$		0			0
$289$	−16.9706			−0.998268
$290$		−	0.242641i		−	0.0142484i
$291$	−7.00000	+	9.89949i	−0.410347	+	0.580319i
$292$		0			0
$293$	−14.6569			−0.856263			−0.428131	−	0.903717i	$-0.640828\pi$
$293$	−14.6569			−0.856263			−0.428131	+	0.903717i	$0.640828\pi$
$294$	−1.41421	+	2.00000i	−0.0824786	+	0.116642i
$295$	6.89949			0.401704
$296$	0.686292			0.0398899
$297$	−17.0000	+	2.82843i	−0.986440	+	0.164122i
$298$		0			0
$299$	−45.2132			−2.61475
$300$		0			0
$301$	5.24264			0.302181
$302$			14.1421i			0.813788i
$303$	14.4853	−	20.4853i	0.832158	−	1.17685i
$304$		−	20.9706i		−	1.20274i
$305$	−0.757359			−0.0433663
$306$	−0.242641	−	0.686292i	−0.0138708	−	0.0392327i
$307$		−	3.51472i		−	0.200596i	−0.994957	−	0.100298i	$-0.968020\pi$
$307$		−	3.51472i		−	0.200596i	0.994957	−	0.100298i	$-0.0319796\pi$
$308$		0			0
$309$	−17.4853	+	24.7279i	−0.994703	+	1.40672i
$310$		−	0.343146i		−	0.0194894i
$311$			9.17157i			0.520072i	0.965599	+	0.260036i	$0.0837345\pi$
$311$			9.17157i			0.520072i	−0.965599	+	0.260036i	$0.916266\pi$
$312$	24.9706	+	17.6569i	1.41368	+	0.999623i
$313$	24.4558			1.38233			0.691163	−	0.722699i	$-0.257099\pi$
$313$	24.4558			1.38233			0.691163	+	0.722699i	$0.257099\pi$
$314$	15.5563			0.877896
$315$	−1.00000	−	2.82843i	−0.0563436	−	0.159364i
$316$		0			0
$317$		−	27.1716i		−	1.52611i	−0.646335	−	0.763054i	$-0.723699\pi$
$317$		−	27.1716i		−	1.52611i	0.646335	−	0.763054i	$-0.276301\pi$
$318$	3.17157	+	2.24264i	0.177853	+	0.125761i
$319$	−0.514719	+	0.242641i	−0.0288187	+	0.0135853i
$320$			8.00000i			0.447214i
$321$	−4.58579	+	6.48528i	−0.255954	+	0.361973i
$322$	−10.2426			−0.570800
$323$			0.899495i			0.0500492i
$324$		0			0
$325$			6.24264i			0.346279i
$326$	−8.82843			−0.488961
$327$	17.3137	+	12.2426i	0.957450	+	0.677020i
$328$	−20.9706			−1.15791
$329$	−13.0711			−0.720631
$330$	8.00000	+	1.41421i	0.440386	+	0.0778499i
$331$	19.4853			1.07101			0.535504	−	0.844533i	$-0.320122\pi$
$331$	19.4853			1.07101			0.535504	+	0.844533i	$0.320122\pi$
$332$		0			0
$333$	0.242641	+	0.686292i	0.0132966	+	0.0376085i
$334$	11.5147			0.630057
$335$			4.48528i			0.245057i
$336$	5.65685	+	4.00000i	0.308607	+	0.218218i
$337$			18.7574i			1.02178i	0.859647	+	0.510889i	$0.170684\pi$
$337$			18.7574i			1.02178i	−0.859647	+	0.510889i	$0.829316\pi$
$338$	−36.7279			−1.99774
$339$	1.27208	+	0.899495i	0.0690898	+	0.0488539i
$340$		0			0
$341$	−0.727922	+	0.343146i	−0.0394192	+	0.0185824i
$342$	20.9706	−	7.41421i	1.13396	−	0.400915i
$343$			1.00000i			0.0539949i
$344$		−	14.8284i		−	0.799495i
$345$	7.24264	−	10.2426i	0.389931	−	0.551445i
$346$	−4.00000			−0.215041
$347$	−21.1716			−1.13655			−0.568275	−	0.822839i	$-0.692389\pi$
$347$	−21.1716			−1.13655			−0.568275	+	0.822839i	$0.692389\pi$
$348$		0			0
$349$		−	21.2426i		−	1.13709i	−0.822651	−	0.568546i	$-0.807506\pi$
$349$		−	21.2426i		−	1.13709i	0.822651	−	0.568546i	$-0.192494\pi$
$350$			1.41421i			0.0755929i
$351$	−8.82843	+	31.2132i	−0.471227	+	1.66604i
$352$		0			0
$353$			18.0000i			0.958043i	0.877803	+	0.479022i	$0.159008\pi$
$353$			18.0000i			0.958043i	−0.877803	+	0.479022i	$0.840992\pi$
$354$	−13.7990	−	9.75736i	−0.733408	−	0.518598i
$355$	−10.2426			−0.543623
$356$		0			0
$357$	−0.242641	−	0.171573i	−0.0128419	−	0.00908060i
$358$		−	14.9706i		−	0.791219i
$359$	−31.6274			−1.66923			−0.834616	−	0.550833i	$-0.814310\pi$
$359$	−31.6274			−1.66923			−0.834616	+	0.550833i	$0.814310\pi$
$360$	−8.00000	+	2.82843i	−0.421637	+	0.149071i
$361$	−8.48528			−0.446594
$362$	32.4853			1.70739
$363$	−5.00000	−	18.3848i	−0.262432	−	0.964951i
$364$		0			0
$365$	−10.4853			−0.548825
$366$	1.51472	+	1.07107i	0.0791756	+	0.0559856i
$367$	3.00000			0.156599			0.0782994	−	0.996930i	$-0.475051\pi$
$367$	3.00000			0.156599			0.0782994	+	0.996930i	$0.475051\pi$
$368$			28.9706i			1.51019i
$369$	−7.41421	−	20.9706i	−0.385969	−	1.09168i
$370$		−	0.343146i		−	0.0178393i
$371$	1.58579			0.0823299
$372$		0			0
$373$			36.2132i			1.87505i	0.347920	+	0.937524i	$0.386888\pi$
$373$			36.2132i			1.87505i	−0.347920	+	0.937524i	$0.613112\pi$
$374$	0.727922	−	0.343146i	0.0376400	−	0.0177436i
$375$	−1.41421	−	1.00000i	−0.0730297	−	0.0516398i
$376$			36.9706i			1.90661i
$377$			1.07107i			0.0551628i
$378$	−2.00000	+	7.07107i	−0.102869	+	0.363696i
$379$	−32.4558			−1.66714			−0.833572	−	0.552410i	$-0.813708\pi$
$379$	−32.4558			−1.66714			−0.833572	+	0.552410i	$0.813708\pi$
$380$		0			0
$381$	6.72792	+	4.75736i	0.344682	+	0.243727i
$382$			20.9706i			1.07295i
$383$		−	34.5858i		−	1.76725i	−0.468194	−	0.883626i	$-0.655095\pi$
$383$		−	34.5858i		−	1.76725i	0.468194	−	0.883626i	$-0.344905\pi$
$384$	11.3137	−	16.0000i	0.577350	−	0.816497i
$385$	3.00000	−	1.41421i	0.152894	−	0.0720750i
$386$		−	14.1421i		−	0.719816i
$387$	14.8284	−	5.24264i	0.753771	−	0.266498i
$388$		0			0
$389$			10.2426i			0.519322i	0.965700	+	0.259661i	$0.0836109\pi$
$389$			10.2426i			0.519322i	−0.965700	+	0.259661i	$0.916389\pi$
$390$	8.82843	−	12.4853i	0.447045	−	0.632217i
$391$		−	1.24264i		−	0.0628430i
$392$	2.82843			0.142857
$393$	16.5858	−	23.4558i	0.836642	−	1.18319i
$394$	−8.48528			−0.427482
$395$	−2.24264			−0.112839
$396$		0			0
$397$	−34.0000			−1.70641			−0.853206	−	0.521575i	$-0.825345\pi$
$397$	−34.0000			−1.70641			−0.853206	+	0.521575i	$0.825345\pi$
$398$	34.6274			1.73572
$399$	5.24264	−	7.41421i	0.262460	−	0.371175i
$400$	4.00000			0.200000
$401$			30.7279i			1.53448i	0.641361	+	0.767240i	$0.278370\pi$
$401$			30.7279i			1.53448i	−0.641361	+	0.767240i	$0.721630\pi$
$402$	6.34315	−	8.97056i	0.316367	−	0.447411i
$403$			1.51472i			0.0754535i
$404$		0			0
$405$	−5.65685	−	7.00000i	−0.281091	−	0.347833i
$406$			0.242641i			0.0120421i
$407$	−0.727922	+	0.343146i	−0.0360818	+	0.0170091i
$408$	−0.485281	+	0.686292i	−0.0240250	+	0.0339765i
$409$		−	1.51472i		−	0.0748980i	−0.999299	−	0.0374490i	$-0.988077\pi$
$409$		−	1.51472i		−	0.0748980i	0.999299	−	0.0374490i	$-0.0119232\pi$
$410$			10.4853i			0.517831i
$411$	−3.51472	−	2.48528i	−0.173368	−	0.122590i
$412$		0			0
$413$	−6.89949			−0.339502
$414$	−28.9706	+	10.2426i	−1.42383	+	0.503398i
$415$			11.1421i			0.546946i
$416$		0			0
$417$	6.34315	+	4.48528i	0.310625	+	0.219645i
$418$	10.4853	+	22.2426i	0.512852	+	1.08792i
$419$			28.4142i			1.38813i	0.719915	+	0.694063i	$0.244181\pi$
$419$			28.4142i			1.38813i	−0.719915	+	0.694063i	$0.755819\pi$
$420$		0			0
$421$	−4.51472			−0.220034			−0.110017	−	0.993930i	$-0.535091\pi$
$421$	−4.51472			−0.220034			−0.110017	+	0.993930i	$0.535091\pi$
$422$			11.3137i			0.550743i
$423$	−36.9706	+	13.0711i	−1.79757	+	0.635537i
$424$		−	4.48528i		−	0.217825i
$425$	−0.171573			−0.00832251
$426$	20.4853	+	14.4853i	0.992515	+	0.701814i
$427$	0.757359			0.0366512
$428$		0			0
$429$	−35.3137	−	6.24264i	−1.70496	−	0.301398i
$430$	−7.41421			−0.357545
$431$	12.3431			0.594548			0.297274	−	0.954792i	$-0.403922\pi$
$431$	12.3431			0.594548			0.297274	+	0.954792i	$0.403922\pi$
$432$	20.0000	+	5.65685i	0.962250	+	0.272166i
$433$	−12.0000			−0.576683			−0.288342	−	0.957528i	$-0.593104\pi$
$433$	−12.0000			−0.576683			−0.288342	+	0.957528i	$0.593104\pi$
$434$			0.343146i			0.0164715i
$435$	−0.242641	−	0.171573i	−0.0116337	−	0.00822629i
$436$		0			0
$437$	37.9706			1.81638
$438$	20.9706	+	14.8284i	1.00201	+	0.708530i
$439$		−	3.24264i		−	0.154763i	−0.997002	−	0.0773814i	$-0.975344\pi$
$439$		−	3.24264i		−	0.154763i	0.997002	−	0.0773814i	$-0.0246559\pi$
$440$	−4.00000	−	8.48528i	−0.190693	−	0.404520i
$441$	1.00000	+	2.82843i	0.0476190	+	0.134687i
$442$		−	1.51472i		−	0.0720478i
$443$			11.3137i			0.537531i	0.963206	+	0.268765i	$0.0866156\pi$
$443$			11.3137i			0.537531i	−0.963206	+	0.268765i	$0.913384\pi$
$444$		0			0
$445$	−13.5858			−0.644028
$446$	24.0416			1.13840
$447$		0			0
$448$		−	8.00000i		−	0.377964i
$449$		−	36.7279i		−	1.73330i	−0.498919	−	0.866649i	$-0.666269\pi$
$449$		−	36.7279i		−	1.73330i	0.498919	−	0.866649i	$-0.333731\pi$
$450$	1.41421	+	4.00000i	0.0666667	+	0.188562i
$451$	22.2426	−	10.4853i	1.04737	−	0.493733i
$452$		0			0
$453$	14.1421	+	10.0000i	0.664455	+	0.469841i
$454$	16.7279			0.785080
$455$		−	6.24264i		−	0.292660i
$456$	−20.9706	−	14.8284i	−0.982037	−	0.694405i
$457$		−	10.2132i		−	0.477754i	−0.971050	−	0.238877i	$-0.923221\pi$
$457$		−	10.2132i		−	0.477754i	0.971050	−	0.238877i	$-0.0767792\pi$
$458$	−9.51472			−0.444594
$459$	−0.857864	−	0.242641i	−0.0400417	−	0.0113255i
$460$		0			0
$461$	−29.6569			−1.38126			−0.690629	−	0.723210i	$-0.742666\pi$
$461$	−29.6569			−1.38126			−0.690629	+	0.723210i	$0.742666\pi$
$462$	−8.00000	−	1.41421i	−0.372194	−	0.0657952i
$463$	26.0000			1.20832			0.604161	−	0.796862i	$-0.293508\pi$
$463$	26.0000			1.20832			0.604161	+	0.796862i	$0.293508\pi$
$464$	0.686292			0.0318603
$465$	−0.343146	−	0.242641i	−0.0159130	−	0.0112522i
$466$	−30.4853			−1.41220
$467$		−	0.343146i		−	0.0158789i	−0.999968	−	0.00793945i	$-0.997473\pi$
$467$		−	0.343146i		−	0.0158789i	0.999968	−	0.00793945i	$-0.00252723\pi$
$468$		0			0
$469$		−	4.48528i		−	0.207111i
$470$	18.4853			0.852662
$471$	11.0000	−	15.5563i	0.506853	−	0.716799i
$472$			19.5147i			0.898238i
$473$	7.41421	+	15.7279i	0.340906	+	0.723171i
$474$	4.48528	+	3.17157i	0.206016	+	0.145675i
$475$		−	5.24264i		−	0.240549i
$476$		0			0
$477$	4.48528	−	1.58579i	0.205367	−	0.0726082i
$478$	−3.75736			−0.171858
$479$	27.2132			1.24340			0.621702	−	0.783254i	$-0.286442\pi$
$479$	27.2132			1.24340			0.621702	+	0.783254i	$0.286442\pi$
$480$		0			0
$481$			1.51472i			0.0690652i
$482$		−	37.4558i		−	1.70607i
$483$	−7.24264	+	10.2426i	−0.329552	+	0.466056i
$484$		0			0
$485$		−	7.00000i		−	0.317854i
$486$	1.41421	+	22.0000i	0.0641500	+	0.997940i
$487$	3.02944			0.137277			0.0686385	−	0.997642i	$-0.478135\pi$
$487$	3.02944			0.137277			0.0686385	+	0.997642i	$0.478135\pi$
$488$		−	2.14214i		−	0.0969699i
$489$	−6.24264	+	8.82843i	−0.282302	+	0.399235i
$490$		−	1.41421i		−	0.0638877i
$491$	−15.3431			−0.692426			−0.346213	−	0.938156i	$-0.612533\pi$
$491$	−15.3431			−0.692426			−0.346213	+	0.938156i	$0.612533\pi$
$492$		0			0
$493$	−0.0294373			−0.00132579
$494$	46.2843			2.08243
$495$	7.07107	−	7.00000i	0.317821	−	0.314627i
$496$	0.970563			0.0435796
$497$	10.2426			0.459445
$498$	15.7574	−	22.2843i	0.706104	−	0.998582i
$499$	−11.4853			−0.514152			−0.257076	−	0.966391i	$-0.582759\pi$
$499$	−11.4853			−0.514152			−0.257076	+	0.966391i	$0.582759\pi$
$500$		0			0
$501$	8.14214	−	11.5147i	0.363764	−	0.514440i
$502$			7.02944i			0.313739i
$503$	−10.4558			−0.466203			−0.233102	−	0.972452i	$-0.574887\pi$
$503$	−10.4558			−0.466203			−0.233102	+	0.972452i	$0.574887\pi$
$504$	8.00000	−	2.82843i	0.356348	−	0.125988i
$505$			14.4853i			0.644587i
$506$	−14.4853	−	30.7279i	−0.643949	−	1.36602i
$507$	−25.9706	+	36.7279i	−1.15339	+	1.63114i
$508$		0			0
$509$			28.7574i			1.27465i	0.770596	+	0.637324i	$0.219959\pi$
$509$			28.7574i			1.27465i	−0.770596	+	0.637324i	$0.780041\pi$
$510$	0.343146	+	0.242641i	0.0151947	+	0.0107443i
$511$	10.4853			0.463842
$512$	−22.6274			−1.00000
$513$	7.41421	−	26.2132i	0.327346	−	1.15734i
$514$		−	19.4558i		−	0.858160i
$515$		−	17.4853i		−	0.770494i
$516$		0			0
$517$	−18.4853	−	39.2132i	−0.812982	−	1.72459i
$518$			0.343146i			0.0150770i
$519$	−2.82843	+	4.00000i	−0.124154	+	0.175581i
$520$	−17.6569			−0.774304
$521$			7.58579i			0.332339i	0.986097	+	0.166170i	$0.0531399\pi$
$521$			7.58579i			0.332339i	−0.986097	+	0.166170i	$0.946860\pi$
$522$	0.242641	+	0.686292i	0.0106201	+	0.0300382i
$523$			26.9706i			1.17934i	0.807644	+	0.589670i	$0.200742\pi$
$523$			26.9706i			1.17934i	−0.807644	+	0.589670i	$0.799258\pi$
$524$		0			0
$525$	1.41421	+	1.00000i	0.0617213	+	0.0436436i
$526$	21.4558			0.935519
$527$	−0.0416306			−0.00181346
$528$	−4.00000	+	22.6274i	−0.174078	+	0.984732i
$529$	−29.4558			−1.28069
$530$	−2.24264			−0.0974141
$531$	−19.5147	+	6.89949i	−0.846867	+	0.299413i
$532$		0			0
$533$		−	46.2843i		−	2.00479i
$534$	27.1716	+	19.2132i	1.17583	+	0.831437i
$535$		−	4.58579i		−	0.198261i
$536$	−12.6863			−0.547964
$537$	−14.9706	−	10.5858i	−0.646027	−	0.456810i
$538$		−	43.2132i		−	1.86305i
$539$	−3.00000	+	1.41421i	−0.129219	+	0.0609145i
$540$		0			0
$541$		−	14.7279i		−	0.633203i	−0.948559	−	0.316601i	$-0.897458\pi$
$541$		−	14.7279i		−	0.633203i	0.948559	−	0.316601i	$-0.102542\pi$
$542$		−	32.8701i		−	1.41189i
$543$	22.9706	−	32.4853i	0.985761	−	1.39408i
$544$		0			0
$545$	−12.2426			−0.524417
$546$	−8.82843	+	12.4853i	−0.377822	+	0.534321i
$547$		−	14.7574i		−	0.630979i	−0.948929	−	0.315490i	$-0.897831\pi$
$547$		−	14.7574i		−	0.630979i	0.948929	−	0.315490i	$-0.102169\pi$
$548$		0			0
$549$	2.14214	−	0.757359i	0.0914241	−	0.0323233i
$550$	−4.24264	+	2.00000i	−0.180907	+	0.0852803i
$551$		−	0.899495i		−	0.0383198i
$552$	28.9706	+	20.4853i	1.23307	+	0.871911i
$553$	2.24264			0.0953668
$554$		−	12.0000i		−	0.509831i
$555$	−0.343146	−	0.242641i	−0.0145657	−	0.0102995i
$556$		0			0
$557$	32.8284			1.39099			0.695493	−	0.718533i	$-0.255186\pi$
$557$	32.8284			1.39099			0.695493	+	0.718533i	$0.255186\pi$
$558$	0.343146	+	0.970563i	0.0145265	+	0.0410872i
$559$	32.7279			1.38424
$560$	−4.00000			−0.169031
$561$	0.171573	−	0.970563i	0.00724381	−	0.0409772i
$562$	−24.4853			−1.03285
$563$	37.1127			1.56411			0.782057	−	0.623207i	$-0.214171\pi$
$563$	37.1127			1.56411			0.782057	+	0.623207i	$0.214171\pi$
$564$		0			0
$565$	−0.899495			−0.0378420
$566$			18.6863i			0.785443i
$567$	5.65685	+	7.00000i	0.237566	+	0.293972i
$568$		−	28.9706i		−	1.21558i
$569$	11.1421			0.467103			0.233551	−	0.972344i	$-0.424965\pi$
$569$	11.1421			0.467103			0.233551	+	0.972344i	$0.424965\pi$
$570$	−7.41421	+	10.4853i	−0.310547	+	0.439180i
$571$			36.1838i			1.51424i	0.653274	+	0.757122i	$0.273395\pi$
$571$			36.1838i			1.51424i	−0.653274	+	0.757122i	$0.726605\pi$
$572$		0			0
$573$	20.9706	+	14.8284i	0.876058	+	0.619466i
$574$		−	10.4853i		−	0.437647i
$575$			7.24264i			0.302039i
$576$	−8.00000	−	22.6274i	−0.333333	−	0.942809i
$577$	29.4558			1.22626			0.613131	−	0.789981i	$-0.289910\pi$
$577$	29.4558			1.22626			0.613131	+	0.789981i	$0.289910\pi$
$578$	−24.0000			−0.998268
$579$	−14.1421	−	10.0000i	−0.587727	−	0.415586i
$580$		0			0
$581$		−	11.1421i		−	0.462254i
$582$	−9.89949	+	14.0000i	−0.410347	+	0.580319i
$583$	2.24264	+	4.75736i	0.0928807	+	0.197030i
$584$		−	29.6569i		−	1.22721i
$585$	−6.24264	−	17.6569i	−0.258101	−	0.730021i
$586$	−20.7279			−0.856263
$587$			12.0416i			0.497011i	0.968630	+	0.248506i	$0.0799395\pi$
$587$			12.0416i			0.497011i	−0.968630	+	0.248506i	$0.920061\pi$
$588$		0			0
$589$		−	1.27208i		−	0.0524151i
$590$	9.75736			0.401704
$591$	−6.00000	+	8.48528i	−0.246807	+	0.349038i
$592$	0.970563			0.0398899
$593$	21.1716			0.869412			0.434706	−	0.900572i	$-0.356852\pi$
$593$	21.1716			0.869412			0.434706	+	0.900572i	$0.356852\pi$
$594$	−24.0416	+	4.00000i	−0.986440	+	0.164122i
$595$	0.171573			0.00703380
$596$		0			0
$597$	24.4853	−	34.6274i	1.00212	−	1.41721i
$598$	−63.9411			−2.61475
$599$		−	37.1127i		−	1.51638i	−0.652032	−	0.758192i	$-0.726083\pi$
$599$		−	37.1127i		−	1.51638i	0.652032	−	0.758192i	$-0.273917\pi$
$600$	2.82843	−	4.00000i	0.115470	−	0.163299i
$601$		−	29.7279i		−	1.21263i	−0.795226	−	0.606314i	$-0.792648\pi$
$601$		−	29.7279i		−	1.21263i	0.795226	−	0.606314i	$-0.207352\pi$
$602$	7.41421			0.302181
$603$	−4.48528	−	12.6863i	−0.182655	−	0.516626i
$604$		0			0
$605$	8.48528	+	7.00000i	0.344976	+	0.284590i
$606$	20.4853	−	28.9706i	0.832158	−	1.17685i
$607$		−	9.51472i		−	0.386191i	−0.981180	−	0.193095i	$-0.938147\pi$
$607$		−	9.51472i		−	0.386191i	0.981180	−	0.193095i	$-0.0618526\pi$
$608$		0			0
$609$	0.242641	+	0.171573i	0.00983230	+	0.00695248i
$610$	−1.07107			−0.0433663
$611$	−81.5980			−3.30110
$612$		0			0
$613$			1.51472i			0.0611789i	0.999532	+	0.0305895i	$0.00973844\pi$
$613$			1.51472i			0.0611789i	−0.999532	+	0.0305895i	$0.990262\pi$
$614$		−	4.97056i		−	0.200596i
$615$	10.4853	+	7.41421i	0.422807	+	0.298970i
$616$	4.00000	+	8.48528i	0.161165	+	0.341882i
$617$			17.3137i			0.697024i	0.937304	+	0.348512i	$0.113313\pi$
$617$			17.3137i			0.697024i	−0.937304	+	0.348512i	$0.886687\pi$
$618$	−24.7279	+	34.9706i	−0.994703	+	1.40672i
$619$	−14.4853			−0.582213			−0.291106	−	0.956691i	$-0.594023\pi$
$619$	−14.4853			−0.582213			−0.291106	+	0.956691i	$0.594023\pi$
$620$		0			0
$621$	−10.2426	+	36.2132i	−0.411023	+	1.45319i
$622$			12.9706i			0.520072i
$623$	13.5858			0.544303
$624$	35.3137	+	24.9706i	1.41368	+	0.999623i
$625$	1.00000			0.0400000
$626$	34.5858			1.38233
$627$	29.6569	+	5.24264i	1.18438	+	0.209371i
$628$		0			0
$629$	−0.0416306			−0.00165992
$630$	−1.41421	−	4.00000i	−0.0563436	−	0.159364i
$631$	15.0000			0.597141			0.298570	−	0.954388i	$-0.403490\pi$
$631$	15.0000			0.597141			0.298570	+	0.954388i	$0.403490\pi$
$632$		−	6.34315i		−	0.252317i
$633$	11.3137	+	8.00000i	0.449680	+	0.317971i
$634$		−	38.4264i		−	1.52611i
$635$	−4.75736			−0.188790
$636$		0			0
$637$			6.24264i			0.247342i
$638$	−0.727922	+	0.343146i	−0.0288187	+	0.0135853i
$639$	28.9706	−	10.2426i	1.14606	−	0.405193i
$640$			11.3137i			0.447214i
$641$		−	19.4558i		−	0.768460i	−0.923237	−	0.384230i	$-0.874467\pi$
$641$		−	19.4558i		−	0.768460i	0.923237	−	0.384230i	$-0.125533\pi$
$642$	−6.48528	+	9.17157i	−0.255954	+	0.361973i
$643$	17.9706			0.708690			0.354345	−	0.935115i	$-0.384704\pi$
$643$	17.9706			0.708690			0.354345	+	0.935115i	$0.384704\pi$
$644$		0			0
$645$	−5.24264	+	7.41421i	−0.206429	+	0.291934i
$646$			1.27208i			0.0500492i
$647$			4.20101i			0.165159i	0.996584	+	0.0825794i	$0.0263158\pi$
$647$			4.20101i			0.165159i	−0.996584	+	0.0825794i	$0.973684\pi$
$648$	19.7990	−	16.0000i	0.777778	−	0.628539i
$649$	−9.75736	−	20.6985i	−0.383010	−	0.812487i
$650$			8.82843i			0.346279i
$651$	0.343146	+	0.242641i	0.0134489	+	0.00950984i
$652$		0			0
$653$		−	24.2132i		−	0.947536i	−0.880650	−	0.473768i	$-0.842894\pi$
$653$		−	24.2132i		−	0.947536i	0.880650	−	0.473768i	$-0.157106\pi$
$654$	24.4853	+	17.3137i	0.957450	+	0.677020i
$655$			16.5858i			0.648060i
$656$	−29.6569			−1.15791
$657$	29.6569	−	10.4853i	1.15702	−	0.409070i
$658$	−18.4853			−0.720631
$659$	43.2843			1.68612			0.843058	−	0.537823i	$-0.180753\pi$
$659$	43.2843			1.68612			0.843058	+	0.537823i	$0.180753\pi$
$660$		0			0
$661$	−25.2132			−0.980680			−0.490340	−	0.871531i	$-0.663127\pi$
$661$	−25.2132			−0.980680			−0.490340	+	0.871531i	$0.663127\pi$
$662$	27.5563			1.07101
$663$	−1.51472	−	1.07107i	−0.0588268	−	0.0415968i
$664$	−31.5147			−1.22301
$665$			5.24264i			0.203301i
$666$	0.343146	+	0.970563i	0.0132966	+	0.0376085i
$667$			1.24264i			0.0481152i
$668$		0			0
$669$	17.0000	−	24.0416i	0.657258	−	0.929503i
$670$			6.34315i			0.245057i
$671$	1.07107	+	2.27208i	0.0413481	+	0.0877126i
$672$		0			0
$673$			35.7279i			1.37721i	0.725137	+	0.688605i	$0.241777\pi$
$673$			35.7279i			1.37721i	−0.725137	+	0.688605i	$0.758223\pi$
$674$			26.5269i			1.02178i
$675$	5.00000	+	1.41421i	0.192450	+	0.0544331i
$676$		0			0
$677$	−11.8284			−0.454603			−0.227302	−	0.973824i	$-0.572990\pi$
$677$	−11.8284			−0.454603			−0.227302	+	0.973824i	$0.572990\pi$
$678$	1.79899	+	1.27208i	0.0690898	+	0.0488539i
$679$			7.00000i			0.268635i
$680$		−	0.485281i		−	0.0186097i
$681$	11.8284	−	16.7279i	0.453266	−	0.641015i
$682$	−1.02944	+	0.485281i	−0.0394192	+	0.0185824i
$683$		−	0.343146i		−	0.0131301i	−0.999978	−	0.00656505i	$-0.997910\pi$
$683$		−	0.343146i		−	0.0131301i	0.999978	−	0.00656505i	$-0.00208974\pi$
$684$		0			0
$685$	2.48528			0.0949577
$686$			1.41421i			0.0539949i
$687$	−6.72792	+	9.51472i	−0.256686	+	0.363009i
$688$		−	20.9706i		−	0.799495i
$689$	9.89949			0.377141
$690$	10.2426	−	14.4853i	0.389931	−	0.551445i
$691$	−42.9706			−1.63468			−0.817339	−	0.576158i	$-0.804551\pi$
$691$	−42.9706			−1.63468			−0.817339	+	0.576158i	$0.804551\pi$
$692$		0			0
$693$	−7.07107	+	7.00000i	−0.268608	+	0.265908i
$694$	−29.9411			−1.13655
$695$	−4.48528			−0.170136
$696$	0.485281	−	0.686292i	0.0183945	−	0.0260138i
$697$	1.27208			0.0481834
$698$		−	30.0416i		−	1.13709i
$699$	−21.5563	+	30.4853i	−0.815336	+	1.15306i
$700$		0			0
$701$	4.02944			0.152190			0.0760949	−	0.997101i	$-0.475755\pi$
$701$	4.02944			0.152190			0.0760949	+	0.997101i	$0.475755\pi$
$702$	−12.4853	+	44.1421i	−0.471227	+	1.66604i
$703$		−	1.27208i		−	0.0479773i
$704$	24.0000	−	11.3137i	0.904534	−	0.426401i
$705$	13.0711	−	18.4853i	0.492285	−	0.696196i
$706$			25.4558i			0.958043i
$707$		−	14.4853i		−	0.544775i
$708$		0			0
$709$	16.9411			0.636237			0.318119	−	0.948051i	$-0.396949\pi$
$709$	16.9411			0.636237			0.318119	+	0.948051i	$0.396949\pi$
$710$	−14.4853			−0.543623
$711$	6.34315	−	2.24264i	0.237887	−	0.0841056i
$712$		−	38.4264i		−	1.44009i
$713$			1.75736i			0.0658136i
$714$	−0.343146	−	0.242641i	−0.0128419	−	0.00908060i
$715$	18.7279	−	8.82843i	0.700385	−	0.330164i
$716$		0			0
$717$	−2.65685	+	3.75736i	−0.0992220	+	0.140321i
$718$	−44.7279			−1.66923
$719$			17.5269i			0.653644i	0.945086	+	0.326822i	$0.105978\pi$
$719$			17.5269i			0.653644i	−0.945086	+	0.326822i	$0.894022\pi$
$720$	−11.3137	+	4.00000i	−0.421637	+	0.149071i
$721$			17.4853i			0.651186i
$722$	−12.0000			−0.446594
$723$	−37.4558	−	26.4853i	−1.39300	−	0.984998i
$724$		0			0
$725$	0.171573			0.00637206
$726$	−7.07107	−	26.0000i	−0.262432	−	0.964951i
$727$	−30.4558			−1.12954			−0.564772	−	0.825247i	$-0.691036\pi$
$727$	−30.4558			−1.12954			−0.564772	+	0.825247i	$0.691036\pi$
$728$	17.6569			0.654407
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	−14.8284			−0.548825
$731$			0.899495i			0.0332690i
$732$		0			0
$733$			29.4558i			1.08798i	0.839093	+	0.543988i	$0.183086\pi$
$733$			29.4558i			1.08798i	−0.839093	+	0.543988i	$0.816914\pi$
$734$	4.24264			0.156599
$735$	−1.41421	−	1.00000i	−0.0521641	−	0.0368856i
$736$		0			0
$737$	13.4558	−	6.34315i	0.495652	−	0.233653i
$738$	−10.4853	−	29.6569i	−0.385969	−	1.09168i
$739$			13.5147i			0.497147i	0.968613	+	0.248573i	$0.0799617\pi$
$739$			13.5147i			0.497147i	−0.968613	+	0.248573i	$0.920038\pi$
$740$		0			0
$741$	32.7279	−	46.2843i	1.20229	−	1.70030i
$742$	2.24264			0.0823299
$743$	−1.37258			−0.0503552			−0.0251776	−	0.999683i	$-0.508015\pi$
$743$	−1.37258			−0.0503552			−0.0251776	+	0.999683i	$0.508015\pi$
$744$	0.686292	−	0.970563i	0.0251607	−	0.0355826i
$745$		0			0
$746$			51.2132i			1.87505i
$747$	−11.1421	−	31.5147i	−0.407669	−	1.15306i
$748$		0			0
$749$			4.58579i			0.167561i
$750$	−2.00000	−	1.41421i	−0.0730297	−	0.0516398i
$751$	−25.9706			−0.947679			−0.473840	−	0.880611i	$-0.657132\pi$
$751$	−25.9706			−0.947679			−0.473840	+	0.880611i	$0.657132\pi$
$752$			52.2843i			1.90661i
$753$	7.02944	+	4.97056i	0.256167	+	0.181137i
$754$			1.51472i			0.0551628i
$755$	−10.0000			−0.363937
$756$		0			0
$757$	41.4558			1.50674			0.753369	−	0.657598i	$-0.228427\pi$
$757$	41.4558			1.50674			0.753369	+	0.657598i	$0.228427\pi$
$758$	−45.8995			−1.66714
$759$	−40.9706	−	7.24264i	−1.48714	−	0.262891i
$760$	14.8284			0.537884
$761$	−40.9706			−1.48518			−0.742591	−	0.669745i	$-0.766403\pi$
$761$	−40.9706			−1.48518			−0.742591	+	0.669745i	$0.766403\pi$
$762$	9.51472	+	6.72792i	0.344682	+	0.243727i
$763$	12.2426			0.443213
$764$		0			0
$765$	0.485281	−	0.171573i	0.0175454	−	0.00620323i
$766$		−	48.9117i		−	1.76725i
$767$	−43.0711			−1.55521
$768$		0			0
$769$			41.6690i			1.50262i	0.659947	+	0.751312i	$0.270579\pi$
$769$			41.6690i			1.50262i	−0.659947	+	0.751312i	$0.729421\pi$
$770$	4.24264	−	2.00000i	0.152894	−	0.0720750i
$771$	−19.4558	−	13.7574i	−0.700685	−	0.495459i
$772$		0			0
$773$		−	9.17157i		−	0.329879i	−0.986304	−	0.164939i	$-0.947257\pi$
$773$		−	9.17157i		−	0.329879i	0.986304	−	0.164939i	$-0.0527428\pi$
$774$	20.9706	−	7.41421i	0.753771	−	0.266498i
$775$	0.242641			0.00871591
$776$	19.7990			0.710742
$777$	0.343146	+	0.242641i	0.0123103	+	0.00870469i
$778$			14.4853i			0.519322i
$779$			38.8701i			1.39266i
$780$		0			0
$781$	14.4853	+	30.7279i	0.518324	+	1.09953i
$782$		−	1.75736i		−	0.0628430i
$783$	0.857864	+	0.242641i	0.0306576	+	0.00867127i
$784$	4.00000			0.142857
$785$			11.0000i			0.392607i
$786$	23.4558	−	33.1716i	0.836642	−	1.18319i
$787$		−	35.4558i		−	1.26386i	−0.775024	−	0.631932i	$-0.782262\pi$
$787$		−	35.4558i		−	1.26386i	0.775024	−	0.631932i	$-0.217738\pi$
$788$		0			0
$789$	15.1716	−	21.4558i	0.540122	−	0.763848i
$790$	−3.17157			−0.112839
$791$	0.899495			0.0319824
$792$	19.7990	+	20.0000i	0.703526	+	0.710669i
$793$	4.72792			0.167893
$794$	−48.0833			−1.70641
$795$	−1.58579	+	2.24264i	−0.0562420	+	0.0795383i
$796$		0			0
$797$		−	31.7990i		−	1.12638i	−0.826328	−	0.563189i	$-0.809574\pi$
$797$		−	31.7990i		−	1.12638i	0.826328	−	0.563189i	$-0.190426\pi$
$798$	7.41421	−	10.4853i	0.262460	−	0.371175i
$799$		−	2.24264i		−	0.0793389i
$800$		0			0
$801$	38.4264	−	13.5858i	1.35773	−	0.480030i
$802$			43.4558i			1.53448i
$803$	14.8284	+	31.4558i	0.523284	+	1.11005i
$804$		0			0
$805$		−	7.24264i		−	0.255270i
$806$			2.14214i			0.0754535i
$807$	−43.2132	−	30.5563i	−1.52118	−	1.07563i
$808$	−40.9706			−1.44134
$809$	−26.8284			−0.943237			−0.471619	−	0.881803i	$-0.656330\pi$
$809$	−26.8284			−0.943237			−0.471619	+	0.881803i	$0.656330\pi$
$810$	−8.00000	−	9.89949i	−0.281091	−	0.347833i
$811$		−	2.00000i		−	0.0702295i	−0.999383	−	0.0351147i	$-0.988820\pi$
$811$		−	2.00000i		−	0.0702295i	0.999383	−	0.0351147i	$-0.0111797\pi$
$812$		0			0
$813$	−32.8701	−	23.2426i	−1.15280	−	0.815155i
$814$	−1.02944	+	0.485281i	−0.0360818	+	0.0170091i
$815$		−	6.24264i		−	0.218670i
$816$	−0.686292	+	0.970563i	−0.0240250	+	0.0339765i
$817$	−27.4853			−0.961588
$818$		−	2.14214i		−	0.0748980i
$819$	6.24264	+	17.6569i	0.218136	+	0.616980i
$820$		0			0
$821$	29.1421			1.01707			0.508534	−	0.861042i	$-0.330188\pi$
$821$	29.1421			1.01707			0.508534	+	0.861042i	$0.330188\pi$
$822$	−4.97056	−	3.51472i	−0.173368	−	0.122590i
$823$	−1.21320			−0.0422896			−0.0211448	−	0.999776i	$-0.506731\pi$
$823$	−1.21320			−0.0422896			−0.0211448	+	0.999776i	$0.506731\pi$
$824$	49.4558			1.72288
$825$	−1.00000	+	5.65685i	−0.0348155	+	0.196946i
$826$	−9.75736			−0.339502
$827$	−6.00000			−0.208640			−0.104320	−	0.994544i	$-0.533267\pi$
$827$	−6.00000			−0.208640			−0.104320	+	0.994544i	$0.533267\pi$
$828$		0			0
$829$	−36.9706			−1.28404			−0.642020	−	0.766688i	$-0.721904\pi$
$829$	−36.9706			−1.28404			−0.642020	+	0.766688i	$0.721904\pi$
$830$			15.7574i			0.546946i
$831$	−12.0000	−	8.48528i	−0.416275	−	0.294351i
$832$		−	49.9411i		−	1.73140i
$833$	−0.171573			−0.00594465
$834$	8.97056	+	6.34315i	0.310625	+	0.219645i
$835$			8.14214i			0.281770i
$836$		0			0
$837$	1.21320	+	0.343146i	0.0419344	+	0.0118609i
$838$			40.1838i			1.38813i
$839$		−	1.58579i		−	0.0547474i	−0.999625	−	0.0273737i	$-0.991286\pi$
$839$		−	1.58579i		−	0.0547474i	0.999625	−	0.0273737i	$-0.00871441\pi$
$840$	−2.82843	+	4.00000i	−0.0975900	+	0.138013i
$841$	−28.9706			−0.998985
$842$	−6.38478			−0.220034
$843$	−17.3137	+	24.4853i	−0.596316	+	0.843318i
$844$		0			0
$845$		−	25.9706i		−	0.893415i
$846$	−52.2843	+	18.4853i	−1.79757	+	0.635537i
$847$	−8.48528	−	7.00000i	−0.291558	−	0.240523i
$848$		−	6.34315i		−	0.217825i
$849$	18.6863	+	13.2132i	0.641312	+	0.453476i
$850$	−0.242641			−0.00832251
$851$			1.75736i			0.0602415i
$852$		0			0
$853$		−	44.2426i		−	1.51484i	−0.652928	−	0.757420i	$-0.726460\pi$
$853$		−	44.2426i		−	1.51484i	0.652928	−	0.757420i	$-0.273540\pi$
$854$	1.07107			0.0366512
$855$	5.24264	+	14.8284i	0.179295	+	0.507122i
$856$	12.9706			0.443325
$857$	−34.9706			−1.19457			−0.597286	−	0.802028i	$-0.703754\pi$
$857$	−34.9706			−1.19457			−0.597286	+	0.802028i	$0.703754\pi$
$858$	−49.9411	−	8.82843i	−1.70496	−	0.301398i
$859$	44.1838			1.50753			0.753765	−	0.657144i	$-0.228236\pi$
$859$	44.1838			1.50753			0.753765	+	0.657144i	$0.228236\pi$
$860$		0			0
$861$	−10.4853	−	7.41421i	−0.357337	−	0.252676i
$862$	17.4558			0.594548
$863$			23.8701i			0.812546i	0.913752	+	0.406273i	$0.133172\pi$
$863$			23.8701i			0.812546i	−0.913752	+	0.406273i	$0.866828\pi$
$864$		0			0
$865$		−	2.82843i		−	0.0961694i
$866$	−16.9706			−0.576683
$867$	−16.9706	+	24.0000i	−0.576351	+	0.815083i
$868$		0			0
$869$	3.17157	+	6.72792i	0.107588	+	0.228229i
$870$	−0.343146	−	0.242641i	−0.0116337	−	0.00822629i
$871$		−	28.0000i		−	0.948744i
$872$		−	34.6274i		−	1.17263i
$873$	7.00000	+	19.7990i	0.236914	+	0.670094i
$874$	53.6985			1.81638
$875$	−1.00000			−0.0338062
$876$		0			0
$877$		−	21.7279i		−	0.733700i	−0.930280	−	0.366850i	$-0.880436\pi$
$877$		−	21.7279i		−	0.733700i	0.930280	−	0.366850i	$-0.119564\pi$
$878$		−	4.58579i		−	0.154763i
$879$	−14.6569	+	20.7279i	−0.494363	+	0.699135i
$880$	−5.65685	−	12.0000i	−0.190693	−	0.404520i
$881$		−	24.2132i		−	0.815764i	−0.913035	−	0.407882i	$-0.866268\pi$
$881$		−	24.2132i		−	0.815764i	0.913035	−	0.407882i	$-0.133732\pi$
$882$	1.41421	+	4.00000i	0.0476190	+	0.134687i
$883$	28.9706			0.974937			0.487469	−	0.873141i	$-0.337920\pi$
$883$	28.9706			0.974937			0.487469	+	0.873141i	$0.337920\pi$
$884$		0			0
$885$	6.89949	−	9.75736i	0.231924	−	0.327990i
$886$			16.0000i			0.537531i
$887$	30.9411			1.03890			0.519451	−	0.854500i	$-0.326137\pi$
$887$	30.9411			1.03890			0.519451	+	0.854500i	$0.326137\pi$
$888$	0.686292	−	0.970563i	0.0230304	−	0.0325700i
$889$	4.75736			0.159557
$890$	−19.2132			−0.644028
$891$	−13.0000	+	26.8701i	−0.435516	+	0.900181i
$892$		0			0
$893$	68.5269			2.29317
$894$		0			0
$895$	10.5858			0.353844
$896$		−	11.3137i		−	0.377964i
$897$	−45.2132	+	63.9411i	−1.50962	+	2.13493i
$898$		−	51.9411i		−	1.73330i
$899$	0.0416306			0.00138846
$900$		0			0
$901$			0.272078i			0.00906423i
$902$	31.4558	−	14.8284i	1.04737	−	0.493733i
$903$	5.24264	−	7.41421i	0.174464	−	0.246730i
$904$		−	2.54416i		−	0.0846174i
$905$			22.9706i			0.763567i
$906$	20.0000	+	14.1421i	0.664455	+	0.469841i
$907$	5.27208			0.175056			0.0875282	−	0.996162i	$-0.472103\pi$
$907$	5.27208			0.175056			0.0875282	+	0.996162i	$0.472103\pi$
$908$		0			0
$909$	−14.4853	−	40.9706i	−0.480446	−	1.35891i
$910$		−	8.82843i		−	0.292660i
$911$			58.2843i			1.93104i	0.260321	+	0.965522i	$0.416171\pi$
$911$			58.2843i			1.93104i	−0.260321	+	0.965522i	$0.583829\pi$
$912$	−29.6569	−	20.9706i	−0.982037	−	0.694405i
$913$	33.4264	−	15.7574i	1.10625	−	0.521492i
$914$		−	14.4437i		−	0.477754i
$915$	−0.757359	+	1.07107i	−0.0250375	+	0.0354084i
$916$		0			0
$917$		−	16.5858i		−	0.547711i
$918$	−1.21320	−	0.343146i	−0.0400417	−	0.0113255i
$919$		−	15.0294i		−	0.495775i	−0.968789	−	0.247888i	$-0.920264\pi$
$919$		−	15.0294i		−	0.495775i	0.968789	−	0.247888i	$-0.0797364\pi$
$920$	−20.4853			−0.675380
$921$	−4.97056	−	3.51472i	−0.163786	−	0.115814i
$922$	−41.9411			−1.38126
$923$	63.9411			2.10465
$924$		0			0
$925$	0.242641			0.00797798
$926$	36.7696			1.20832
$927$	17.4853	+	49.4558i	0.574292	+	1.62434i
$928$		0			0
$929$		−	19.7990i		−	0.649584i	−0.945786	−	0.324792i	$-0.894706\pi$
$929$		−	19.7990i		−	0.649584i	0.945786	−	0.324792i	$-0.105294\pi$
$930$	−0.485281	−	0.343146i	−0.0159130	−	0.0112522i
$931$		−	5.24264i		−	0.171821i
$932$		0			0
$933$	12.9706	+	9.17157i	0.424637	+	0.300264i
$934$		−	0.485281i		−	0.0158789i
$935$	0.242641	+	0.514719i	0.00793520	+	0.0168331i
$936$	49.9411	−	17.6569i	1.63238	−	0.577132i
$937$		−	11.2721i		−	0.368243i	−0.982904	−	0.184121i	$-0.941056\pi$
$937$		−	11.2721i		−	0.368243i	0.982904	−	0.184121i	$-0.0589439\pi$
$938$		−	6.34315i		−	0.207111i
$939$	24.4558	−	34.5858i	0.798086	−	1.12866i
$940$		0			0
$941$	24.3848			0.794921			0.397460	−	0.917619i	$-0.369892\pi$
$941$	24.3848			0.794921			0.397460	+	0.917619i	$0.369892\pi$
$942$	15.5563	−	22.0000i	0.506853	−	0.716799i
$943$		−	53.6985i		−	1.74866i
$944$			27.5980i			0.898238i
$945$	−5.00000	−	1.41421i	−0.162650	−	0.0460044i
$946$	10.4853	+	22.2426i	0.340906	+	0.723171i
$947$			26.3553i			0.856433i	0.903676	+	0.428217i	$0.140858\pi$
$947$			26.3553i			0.856433i	−0.903676	+	0.428217i	$0.859142\pi$
$948$		0			0
$949$	65.4558			2.12479
$950$		−	7.41421i		−	0.240549i
$951$	−38.4264	−	27.1716i	−1.24606	−	0.881099i
$952$			0.485281i			0.0157281i
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$	6.34315	−	2.24264i	0.205367	−	0.0726082i
$955$	−14.8284			−0.479837
$956$		0			0
$957$	−0.171573	+	0.970563i	−0.00554616	+	0.0313738i
$958$	38.4853			1.24340
$959$	−2.48528			−0.0802539
$960$	11.3137	+	8.00000i	0.365148	+	0.258199i
$961$	−30.9411			−0.998101
$962$			2.14214i			0.0690652i
$963$	4.58579	+	12.9706i	0.147775	+	0.417971i
$964$		0			0
$965$	10.0000			0.321911
$966$	−10.2426	+	14.4853i	−0.329552	+	0.466056i
$967$		−	2.21320i		−	0.0711718i	−0.999367	−	0.0355859i	$-0.988670\pi$
$967$		−	2.21320i		−	0.0711718i	0.999367	−	0.0355859i	$-0.0113297\pi$
$968$	−19.7990	+	24.0000i	−0.636364	+	0.771389i
$969$	1.27208	+	0.899495i	0.0408650	+	0.0288959i
$970$		−	9.89949i		−	0.317854i
$971$			53.8701i			1.72877i	0.502828	+	0.864386i	$0.332293\pi$
$971$			53.8701i			1.72877i	−0.502828	+	0.864386i	$0.667707\pi$
$972$		0			0
$973$	4.48528			0.143792
$974$	4.28427			0.137277
$975$	8.82843	+	6.24264i	0.282736	+	0.199925i
$976$		−	3.02944i		−	0.0969699i
$977$			42.8995i			1.37248i	0.727377	+	0.686238i	$0.240739\pi$
$977$			42.8995i			1.37248i	−0.727377	+	0.686238i	$0.759261\pi$
$978$	−8.82843	+	12.4853i	−0.282302	+	0.399235i
$979$	19.2132	+	40.7574i	0.614057	+	1.30261i
$980$		0			0
$981$	34.6274	−	12.2426i	1.10557	−	0.390877i
$982$	−21.6985			−0.692426
$983$			22.6274i			0.721703i	0.932623	+	0.360851i	$0.117514\pi$
$983$			22.6274i			0.721703i	−0.932623	+	0.360851i	$0.882486\pi$
$984$	−20.9706	+	29.6569i	−0.668517	+	0.945426i
$985$		−	6.00000i		−	0.191176i
$986$	−0.0416306			−0.00132579
$987$	−13.0711	+	18.4853i	−0.416057	+	0.588393i
$988$		0			0
$989$	37.9706			1.20739
$990$	10.0000	−	9.89949i	0.317821	−	0.314627i
$991$	61.4853			1.95314			0.976572	−	0.215190i	$-0.0690371\pi$
$991$	61.4853			1.95314			0.976572	+	0.215190i	$0.0690371\pi$
$992$		0			0
$993$	19.4853	−	27.5563i	0.618347	−	0.874474i
$994$	14.4853			0.459445
$995$			24.4853i			0.776236i
$996$		0			0
$997$		−	40.9706i		−	1.29755i	−0.760980	−	0.648775i	$-0.775281\pi$
$997$		−	40.9706i		−	1.29755i	0.760980	−	0.648775i	$-0.224719\pi$
$998$	−16.2426			−0.514152
$999$	1.21320	+	0.343146i	0.0383841	+	0.0108567i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.c.1121.3	yes	4
3.2	odd	2		1155.2.l.b.1121.2	yes	4
11.10	odd	2		1155.2.l.b.1121.1	✓	4
33.32	even	2	inner	1155.2.l.c.1121.4	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.b.1121.1	✓	4	11.10	odd	2
1155.2.l.b.1121.2	yes	4	3.2	odd	2
1155.2.l.c.1121.3	yes	4	1.1	even	1	trivial
1155.2.l.c.1121.4	yes	4	33.32	even	2	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000i q^{5} +(1.41421 - 2.00000i) q^{6} -1.00000i q^{7} -2.82843 q^{8} +(-1.00000 - 2.82843i) q^{9} +O(q^{10})\)	\(q+1.41421 q^{2} +(1.00000 - 1.41421i) q^{3} +1.00000i q^{5} +(1.41421 - 2.00000i) q^{6} -1.00000i q^{7} -2.82843 q^{8} +(-1.00000 - 2.82843i) q^{9} +1.41421i q^{10} +(3.00000 - 1.41421i) q^{11} -6.24264i q^{13} -1.41421i q^{14} +(1.41421 + 1.00000i) q^{15} -4.00000 q^{16} +0.171573 q^{17} +(-1.41421 - 4.00000i) q^{18} +5.24264i q^{19} +(-1.41421 - 1.00000i) q^{21} +(4.24264 - 2.00000i) q^{22} -7.24264i q^{23} +(-2.82843 + 4.00000i) q^{24} -1.00000 q^{25} -8.82843i q^{26} +(-5.00000 - 1.41421i) q^{27} -0.171573 q^{29} +(2.00000 + 1.41421i) q^{30} -0.242641 q^{31} +(1.00000 - 5.65685i) q^{33} +0.242641 q^{34} +1.00000 q^{35} -0.242641 q^{37} +7.41421i q^{38} +(-8.82843 - 6.24264i) q^{39} -2.82843i q^{40} +7.41421 q^{41} +(-2.00000 - 1.41421i) q^{42} +5.24264i q^{43} +(2.82843 - 1.00000i) q^{45} -10.2426i q^{46} -13.0711i q^{47} +(-4.00000 + 5.65685i) q^{48} -1.00000 q^{49} -1.41421 q^{50} +(0.171573 - 0.242641i) q^{51} +1.58579i q^{53} +(-7.07107 - 2.00000i) q^{54} +(1.41421 + 3.00000i) q^{55} +2.82843i q^{56} +(7.41421 + 5.24264i) q^{57} -0.242641 q^{58} -6.89949i q^{59} +0.757359i q^{61} -0.343146 q^{62} +(-2.82843 + 1.00000i) q^{63} +8.00000 q^{64} +6.24264 q^{65} +(1.41421 - 8.00000i) q^{66} +4.48528 q^{67} +(-10.2426 - 7.24264i) q^{69} +1.41421 q^{70} +10.2426i q^{71} +(2.82843 + 8.00000i) q^{72} +10.4853i q^{73} -0.343146 q^{74} +(-1.00000 + 1.41421i) q^{75} +(-1.41421 - 3.00000i) q^{77} +(-12.4853 - 8.82843i) q^{78} +2.24264i q^{79} -4.00000i q^{80} +(-7.00000 + 5.65685i) q^{81} +10.4853 q^{82} +11.1421 q^{83} +0.171573i q^{85} +7.41421i q^{86} +(-0.171573 + 0.242641i) q^{87} +(-8.48528 + 4.00000i) q^{88} +13.5858i q^{89} +(4.00000 - 1.41421i) q^{90} -6.24264 q^{91} +(-0.242641 + 0.343146i) q^{93} -18.4853i q^{94} -5.24264 q^{95} -7.00000 q^{97} -1.41421 q^{98} +(-7.00000 - 7.07107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^9	\( 4 q + 4 q^{3} - 4 q^{9} + 12 q^{11} - 16 q^{16} + 12 q^{17} - 4 q^{25} - 20 q^{27} - 12 q^{29} + 8 q^{30} + 16 q^{31} + 4 q^{33} - 16 q^{34} + 4 q^{35} + 16 q^{37} - 24 q^{39} + 24 q^{41} - 8 q^{42} - 16 q^{48} - 4 q^{49} + 12 q^{51} + 24 q^{57} + 16 q^{58} - 24 q^{62} + 32 q^{64} + 8 q^{65} - 16 q^{67} - 24 q^{69} - 24 q^{74} - 4 q^{75} - 16 q^{78} - 28 q^{81} + 8 q^{82} - 12 q^{83} - 12 q^{87} + 16 q^{90} - 8 q^{91} + 16 q^{93} - 4 q^{95} - 28 q^{97} - 28 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^9 + 12 * q^11 - 16 * q^16 + 12 * q^17 - 4 * q^25 - 20 * q^27 - 12 * q^29 + 8 * q^30 + 16 * q^31 + 4 * q^33 - 16 * q^34 + 4 * q^35 + 16 * q^37 - 24 * q^39 + 24 * q^41 - 8 * q^42 - 16 * q^48 - 4 * q^49 + 12 * q^51 + 24 * q^57 + 16 * q^58 - 24 * q^62 + 32 * q^64 + 8 * q^65 - 16 * q^67 - 24 * q^69 - 24 * q^74 - 4 * q^75 - 16 * q^78 - 28 * q^81 + 8 * q^82 - 12 * q^83 - 12 * q^87 + 16 * q^90 - 8 * q^91 + 16 * q^93 - 4 * q^95 - 28 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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