LMFDB - Embedded newform 1155.2.l.d.1121.2

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			1121.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.d.1121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.414214 q^{2} +(1.00000 + 1.41421i) q^{3} -1.82843 q^{4} -1.00000i q^{5} +(-0.414214 - 0.585786i) q^{6} +1.00000i q^{7} +1.58579 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q-0.414214 q^{2} +(1.00000 + 1.41421i) q^{3} -1.82843 q^{4} -1.00000i q^{5} +(-0.414214 - 0.585786i) q^{6} +1.00000i q^{7} +1.58579 q^{8} +(-1.00000 + 2.82843i) q^{9} +0.414214i q^{10} +(-1.41421 - 3.00000i) q^{11} +(-1.82843 - 2.58579i) q^{12} -0.414214i q^{14} +(1.41421 - 1.00000i) q^{15} +3.00000 q^{16} -6.82843 q^{17} +(0.414214 - 1.17157i) q^{18} -0.828427i q^{19} +1.82843i q^{20} +(-1.41421 + 1.00000i) q^{21} +(0.585786 + 1.24264i) q^{22} -0.828427i q^{23} +(1.58579 + 2.24264i) q^{24} -1.00000 q^{25} +(-5.00000 + 1.41421i) q^{27} -1.82843i q^{28} -5.65685 q^{29} +(-0.585786 + 0.414214i) q^{30} +0.828427 q^{31} -4.41421 q^{32} +(2.82843 - 5.00000i) q^{33} +2.82843 q^{34} +1.00000 q^{35} +(1.82843 - 5.17157i) q^{36} +6.00000 q^{37} +0.343146i q^{38} -1.58579i q^{40} -7.65685 q^{41} +(0.585786 - 0.414214i) q^{42} -9.65685i q^{43} +(2.58579 + 5.48528i) q^{44} +(2.82843 + 1.00000i) q^{45} +0.343146i q^{46} -10.8284i q^{47} +(3.00000 + 4.24264i) q^{48} -1.00000 q^{49} +0.414214 q^{50} +(-6.82843 - 9.65685i) q^{51} -0.828427i q^{53} +(2.07107 - 0.585786i) q^{54} +(-3.00000 + 1.41421i) q^{55} +1.58579i q^{56} +(1.17157 - 0.828427i) q^{57} +2.34315 q^{58} +0.343146i q^{59} +(-2.58579 + 1.82843i) q^{60} +5.17157i q^{61} -0.343146 q^{62} +(-2.82843 - 1.00000i) q^{63} -4.17157 q^{64} +(-1.17157 + 2.07107i) q^{66} -6.48528 q^{67} +12.4853 q^{68} +(1.17157 - 0.828427i) q^{69} -0.414214 q^{70} -0.343146i q^{71} +(-1.58579 + 4.48528i) q^{72} -12.0000i q^{73} -2.48528 q^{74} +(-1.00000 - 1.41421i) q^{75} +1.51472i q^{76} +(3.00000 - 1.41421i) q^{77} +4.00000i q^{79} -3.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} +3.17157 q^{82} -12.0000 q^{83} +(2.58579 - 1.82843i) q^{84} +6.82843i q^{85} +4.00000i q^{86} +(-5.65685 - 8.00000i) q^{87} +(-2.24264 - 4.75736i) q^{88} -7.65685i q^{89} +(-1.17157 - 0.414214i) q^{90} +1.51472i q^{92} +(0.828427 + 1.17157i) q^{93} +4.48528i q^{94} -0.828427 q^{95} +(-4.41421 - 6.24264i) q^{96} -5.17157 q^{97} +0.414214 q^{98} +(9.89949 - 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 12 q^{8} - 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 12 * q^8 - 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 12 q^{8} - 4 q^{9} + 4 q^{12} + 12 q^{16} - 16 q^{17} - 4 q^{18} + 8 q^{22} + 12 q^{24} - 4 q^{25} - 20 q^{27} - 8 q^{30} - 8 q^{31} - 12 q^{32} + 4 q^{35} - 4 q^{36} + 24 q^{37} - 8 q^{41} + 8 q^{42} + 16 q^{44} + 12 q^{48} - 4 q^{49} - 4 q^{50} - 16 q^{51} - 20 q^{54} - 12 q^{55} + 16 q^{57} + 32 q^{58} - 16 q^{60} - 24 q^{62} - 28 q^{64} - 16 q^{66} + 8 q^{67} + 16 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{72} + 24 q^{74} - 4 q^{75} + 12 q^{77} - 28 q^{81} + 24 q^{82} - 48 q^{83} + 16 q^{84} + 8 q^{88} - 16 q^{90} - 8 q^{93} + 8 q^{95} - 12 q^{96} - 32 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 12 * q^8 - 4 * q^9 + 4 * q^12 + 12 * q^16 - 16 * q^17 - 4 * q^18 + 8 * q^22 + 12 * q^24 - 4 * q^25 - 20 * q^27 - 8 * q^30 - 8 * q^31 - 12 * q^32 + 4 * q^35 - 4 * q^36 + 24 * q^37 - 8 * q^41 + 8 * q^42 + 16 * q^44 + 12 * q^48 - 4 * q^49 - 4 * q^50 - 16 * q^51 - 20 * q^54 - 12 * q^55 + 16 * q^57 + 32 * q^58 - 16 * q^60 - 24 * q^62 - 28 * q^64 - 16 * q^66 + 8 * q^67 + 16 * q^68 + 16 * q^69 + 4 * q^70 - 12 * q^72 + 24 * q^74 - 4 * q^75 + 12 * q^77 - 28 * q^81 + 24 * q^82 - 48 * q^83 + 16 * q^84 + 8 * q^88 - 16 * q^90 - 8 * q^93 + 8 * q^95 - 12 * q^96 - 32 * q^97 - 4 * q^98

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 $

$2$	−0.414214			−0.292893			−0.146447	−	0.989219i	$-0.546784\pi$
$2$	−0.414214			−0.292893			−0.146447	+	0.989219i	$0.546784\pi$
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$3$	1.00000	+	1.41421i	0.577350	+	0.816497i
$4$	−1.82843			−0.914214
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.414214	−	0.585786i	−0.169102	−	0.239146i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	1.58579			0.560660
$9$	−1.00000	+	2.82843i	−0.333333	+	0.942809i
$10$			0.414214i			0.130986i
$11$	−1.41421	−	3.00000i	−0.426401	−	0.904534i
$11$	−1.41421	−	3.00000i	−0.426401	−	0.904534i
$12$	−1.82843	−	2.58579i	−0.527821	−	0.746452i
$13$		0			0		1.00000			$0$
$13$		0			0		−1.00000			$\pi$
$14$		−	0.414214i		−	0.110703i
$15$	1.41421	−	1.00000i	0.365148	−	0.258199i
$16$	3.00000			0.750000
$17$	−6.82843			−1.65614			−0.828068	−	0.560627i	$-0.810560\pi$
$17$	−6.82843			−1.65614			−0.828068	+	0.560627i	$0.810560\pi$
$18$	0.414214	−	1.17157i	0.0976311	−	0.276142i
$19$		−	0.828427i		−	0.190054i	−0.995475	−	0.0950271i	$-0.969706\pi$
$19$		−	0.828427i		−	0.190054i	0.995475	−	0.0950271i	$-0.0302938\pi$
$20$			1.82843i			0.408849i
$21$	−1.41421	+	1.00000i	−0.308607	+	0.218218i
$22$	0.585786	+	1.24264i	0.124890	+	0.264932i
$23$		−	0.828427i		−	0.172739i	−0.996263	−	0.0863695i	$-0.972473\pi$
$23$		−	0.828427i		−	0.172739i	0.996263	−	0.0863695i	$-0.0275266\pi$
$24$	1.58579	+	2.24264i	0.323697	+	0.457777i
$25$	−1.00000			−0.200000
$26$		0			0
$27$	−5.00000	+	1.41421i	−0.962250	+	0.272166i
$28$		−	1.82843i		−	0.345540i
$29$	−5.65685			−1.05045			−0.525226	−	0.850963i	$-0.676019\pi$
$29$	−5.65685			−1.05045			−0.525226	+	0.850963i	$0.676019\pi$
$30$	−0.585786	+	0.414214i	−0.106949	+	0.0756247i
$31$	0.828427			0.148790			0.0743950	−	0.997229i	$-0.476297\pi$
$31$	0.828427			0.148790			0.0743950	+	0.997229i	$0.476297\pi$
$32$	−4.41421			−0.780330
$33$	2.82843	−	5.00000i	0.492366	−	0.870388i
$34$	2.82843			0.485071
$35$	1.00000			0.169031
$36$	1.82843	−	5.17157i	0.304738	−	0.861929i
$37$	6.00000			0.986394			0.493197	−	0.869918i	$-0.335828\pi$
$37$	6.00000			0.986394			0.493197	+	0.869918i	$0.335828\pi$
$38$			0.343146i			0.0556656i
$39$		0			0
$40$		−	1.58579i		−	0.250735i
$41$	−7.65685			−1.19580			−0.597900	−	0.801571i	$-0.703998\pi$
$41$	−7.65685			−1.19580			−0.597900	+	0.801571i	$0.703998\pi$
$42$	0.585786	−	0.414214i	0.0903888	−	0.0639145i
$43$		−	9.65685i		−	1.47266i	−0.676625	−	0.736328i	$-0.736558\pi$
$43$		−	9.65685i		−	1.47266i	0.676625	−	0.736328i	$-0.263442\pi$
$44$	2.58579	+	5.48528i	0.389822	+	0.826937i
$45$	2.82843	+	1.00000i	0.421637	+	0.149071i
$46$			0.343146i			0.0505941i
$47$		−	10.8284i		−	1.57949i	−0.613436	−	0.789744i	$-0.710213\pi$
$47$		−	10.8284i		−	1.57949i	0.613436	−	0.789744i	$-0.289787\pi$
$48$	3.00000	+	4.24264i	0.433013	+	0.612372i
$49$	−1.00000			−0.142857
$50$	0.414214			0.0585786
$51$	−6.82843	−	9.65685i	−0.956171	−	1.35223i
$52$		0			0
$53$		−	0.828427i		−	0.113793i	−0.998380	−	0.0568966i	$-0.981879\pi$
$53$		−	0.828427i		−	0.113793i	0.998380	−	0.0568966i	$-0.0181205\pi$
$54$	2.07107	−	0.585786i	0.281837	−	0.0797154i
$55$	−3.00000	+	1.41421i	−0.404520	+	0.190693i
$56$			1.58579i			0.211910i
$57$	1.17157	−	0.828427i	0.155179	−	0.109728i
$58$	2.34315			0.307670
$59$			0.343146i			0.0446738i	0.999751	+	0.0223369i	$0.00711064\pi$
$59$			0.343146i			0.0446738i	−0.999751	+	0.0223369i	$0.992889\pi$
$60$	−2.58579	+	1.82843i	−0.333824	+	0.236049i
$61$			5.17157i			0.662152i	0.943604	+	0.331076i	$0.107412\pi$
$61$			5.17157i			0.662152i	−0.943604	+	0.331076i	$0.892588\pi$
$62$	−0.343146			−0.0435796
$63$	−2.82843	−	1.00000i	−0.356348	−	0.125988i
$64$	−4.17157			−0.521447
$65$		0			0
$66$	−1.17157	+	2.07107i	−0.144211	+	0.254931i
$67$	−6.48528			−0.792303			−0.396152	−	0.918185i	$-0.629655\pi$
$67$	−6.48528			−0.792303			−0.396152	+	0.918185i	$0.629655\pi$
$68$	12.4853			1.51406
$69$	1.17157	−	0.828427i	0.141041	−	0.0997309i
$70$	−0.414214			−0.0495080
$71$		−	0.343146i		−	0.0407239i	−0.999793	−	0.0203620i	$-0.993518\pi$
$71$		−	0.343146i		−	0.0407239i	0.999793	−	0.0203620i	$-0.00648186\pi$
$72$	−1.58579	+	4.48528i	−0.186887	+	0.528595i
$73$		−	12.0000i		−	1.40449i	−0.711934	−	0.702247i	$-0.752180\pi$
$73$		−	12.0000i		−	1.40449i	0.711934	−	0.702247i	$-0.247820\pi$
$74$	−2.48528			−0.288908
$75$	−1.00000	−	1.41421i	−0.115470	−	0.163299i
$76$			1.51472i			0.173750i
$77$	3.00000	−	1.41421i	0.341882	−	0.161165i
$78$		0			0
$79$			4.00000i			0.450035i	0.974355	+	0.225018i	$0.0722440\pi$
$79$			4.00000i			0.450035i	−0.974355	+	0.225018i	$0.927756\pi$
$80$		−	3.00000i		−	0.335410i
$81$	−7.00000	−	5.65685i	−0.777778	−	0.628539i
$82$	3.17157			0.350242
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	2.58579	−	1.82843i	0.282132	−	0.199498i
$85$			6.82843i			0.740647i
$86$			4.00000i			0.431331i
$87$	−5.65685	−	8.00000i	−0.606478	−	0.857690i
$88$	−2.24264	−	4.75736i	−0.239066	−	0.507136i
$89$		−	7.65685i		−	0.811625i	−0.913956	−	0.405812i	$-0.866989\pi$
$89$		−	7.65685i		−	0.811625i	0.913956	−	0.405812i	$-0.133011\pi$
$90$	−1.17157	−	0.414214i	−0.123495	−	0.0436619i
$91$		0			0
$92$			1.51472i			0.157920i
$93$	0.828427	+	1.17157i	0.0859039	+	0.121486i
$94$			4.48528i			0.462621i
$95$	−0.828427			−0.0849948
$96$	−4.41421	−	6.24264i	−0.450524	−	0.637137i
$97$	−5.17157			−0.525094			−0.262547	−	0.964919i	$-0.584562\pi$
$97$	−5.17157			−0.525094			−0.262547	+	0.964919i	$0.584562\pi$
$98$	0.414214			0.0418419
$99$	9.89949	−	1.00000i	0.994937	−	0.100504i
$100$	1.82843			0.182843
$101$	9.31371			0.926749			0.463374	−	0.886163i	$-0.346639\pi$
$101$	9.31371			0.926749			0.463374	+	0.886163i	$0.346639\pi$
$102$	2.82843	+	4.00000i	0.280056	+	0.396059i
$103$	9.31371			0.917707			0.458853	−	0.888512i	$-0.348260\pi$
$103$	9.31371			0.917707			0.458853	+	0.888512i	$0.348260\pi$
$104$		0			0
$105$	1.00000	+	1.41421i	0.0975900	+	0.138013i
$106$			0.343146i			0.0333293i
$107$	−9.31371			−0.900390			−0.450195	−	0.892930i	$-0.648646\pi$
$107$	−9.31371			−0.900390			−0.450195	+	0.892930i	$0.648646\pi$
$108$	9.14214	−	2.58579i	0.879702	−	0.248817i
$109$		−	9.65685i		−	0.924959i	−0.886630	−	0.462479i	$-0.846960\pi$
$109$		−	9.65685i		−	0.924959i	0.886630	−	0.462479i	$-0.153040\pi$
$110$	1.24264	−	0.585786i	0.118481	−	0.0558525i
$111$	6.00000	+	8.48528i	0.569495	+	0.805387i
$112$			3.00000i			0.283473i
$113$		−	3.17157i		−	0.298356i	−0.988810	−	0.149178i	$-0.952337\pi$
$113$		−	3.17157i		−	0.298356i	0.988810	−	0.149178i	$-0.0476628\pi$
$114$	−0.485281	+	0.343146i	−0.0454508	+	0.0321385i
$115$	−0.828427			−0.0772512
$116$	10.3431			0.960337
$117$		0			0
$118$		−	0.142136i		−	0.0130846i
$119$		−	6.82843i		−	0.625961i
$120$	2.24264	−	1.58579i	0.204724	−	0.144762i
$121$	−7.00000	+	8.48528i	−0.636364	+	0.771389i
$122$		−	2.14214i		−	0.193940i
$123$	−7.65685	−	10.8284i	−0.690395	−	0.976366i
$124$	−1.51472			−0.136026
$125$			1.00000i			0.0894427i
$126$	1.17157	+	0.414214i	0.104372	+	0.0369011i
$127$			13.6569i			1.21185i	0.795522	+	0.605925i	$0.207197\pi$
$127$			13.6569i			1.21185i	−0.795522	+	0.605925i	$0.792803\pi$
$128$	10.5563			0.933058
$129$	13.6569	−	9.65685i	1.20242	−	0.850239i
$130$		0			0
$131$	17.6569			1.54269			0.771343	−	0.636419i	$-0.219585\pi$
$131$	17.6569			1.54269			0.771343	+	0.636419i	$0.219585\pi$
$132$	−5.17157	+	9.14214i	−0.450128	+	0.795721i
$133$	0.828427			0.0718337
$134$	2.68629			0.232060
$135$	1.41421	+	5.00000i	0.121716	+	0.430331i
$136$	−10.8284			−0.928530
$137$			12.8284i			1.09601i	0.836476	+	0.548003i	$0.184612\pi$
$137$			12.8284i			1.09601i	−0.836476	+	0.548003i	$0.815388\pi$
$138$	−0.485281	+	0.343146i	−0.0413099	+	0.0292105i
$139$			6.48528i			0.550074i	0.961434	+	0.275037i	$0.0886902\pi$
$139$			6.48528i			0.550074i	−0.961434	+	0.275037i	$0.911310\pi$
$140$	−1.82843			−0.154530
$141$	15.3137	−	10.8284i	1.28965	−	0.911918i
$142$			0.142136i			0.0119278i
$143$		0			0
$144$	−3.00000	+	8.48528i	−0.250000	+	0.707107i
$145$			5.65685i			0.469776i
$146$			4.97056i			0.411367i
$147$	−1.00000	−	1.41421i	−0.0824786	−	0.116642i
$148$	−10.9706			−0.901775
$149$	−7.31371			−0.599162			−0.299581	−	0.954071i	$-0.596847\pi$
$149$	−7.31371			−0.599162			−0.299581	+	0.954071i	$0.596847\pi$
$150$	0.414214	+	0.585786i	0.0338204	+	0.0478293i
$151$		−	3.31371i		−	0.269666i	−0.990868	−	0.134833i	$-0.956950\pi$
$151$		−	3.31371i		−	0.269666i	0.990868	−	0.134833i	$-0.0430498\pi$
$152$		−	1.31371i		−	0.106556i
$153$	6.82843	−	19.3137i	0.552046	−	1.56142i
$154$	−1.24264	+	0.585786i	−0.100135	+	0.0472040i
$155$		−	0.828427i		−	0.0665409i
$156$		0			0
$157$	−18.8284			−1.50267			−0.751336	−	0.659920i	$-0.770590\pi$
$157$	−18.8284			−1.50267			−0.751336	+	0.659920i	$0.770590\pi$
$158$		−	1.65685i		−	0.131812i
$159$	1.17157	−	0.828427i	0.0929118	−	0.0656985i
$160$			4.41421i			0.348974i
$161$	0.828427			0.0652892
$162$	2.89949	+	2.34315i	0.227806	+	0.184095i
$163$	−1.51472			−0.118642			−0.0593210	−	0.998239i	$-0.518894\pi$
$163$	−1.51472			−0.118642			−0.0593210	+	0.998239i	$0.518894\pi$
$164$	14.0000			1.09322
$165$	−5.00000	−	2.82843i	−0.389249	−	0.220193i
$166$	4.97056			0.385790
$167$	2.34315			0.181318			0.0906590	−	0.995882i	$-0.471103\pi$
$167$	2.34315			0.181318			0.0906590	+	0.995882i	$0.471103\pi$
$168$	−2.24264	+	1.58579i	−0.173023	+	0.122346i
$169$	13.0000			1.00000
$170$		−	2.82843i		−	0.216930i
$171$	2.34315	+	0.828427i	0.179185	+	0.0633514i
$172$			17.6569i			1.34632i
$173$	−10.1421			−0.771092			−0.385546	−	0.922689i	$-0.625987\pi$
$173$	−10.1421			−0.771092			−0.385546	+	0.922689i	$0.625987\pi$
$174$	2.34315	+	3.31371i	0.177633	+	0.251212i
$175$		−	1.00000i		−	0.0755929i
$176$	−4.24264	−	9.00000i	−0.319801	−	0.678401i
$177$	−0.485281	+	0.343146i	−0.0364760	+	0.0257924i
$178$			3.17157i			0.237719i
$179$			11.6569i			0.871274i	0.900122	+	0.435637i	$0.143477\pi$
$179$			11.6569i			0.871274i	−0.900122	+	0.435637i	$0.856523\pi$
$180$	−5.17157	−	1.82843i	−0.385466	−	0.136283i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$		0			0
$183$	−7.31371	+	5.17157i	−0.540645	+	0.382294i
$184$		−	1.31371i		−	0.0968479i
$185$		−	6.00000i		−	0.441129i
$186$	−0.343146	−	0.485281i	−0.0251607	−	0.0355826i
$187$	9.65685	+	20.4853i	0.706179	+	1.49803i
$188$			19.7990i			1.44399i
$189$	−1.41421	−	5.00000i	−0.102869	−	0.363696i
$190$	0.343146			0.0248944
$191$		−	6.00000i		−	0.434145i	−0.976156	−	0.217072i	$-0.930349\pi$
$191$		−	6.00000i		−	0.434145i	0.976156	−	0.217072i	$-0.0696508\pi$
$192$	−4.17157	−	5.89949i	−0.301057	−	0.425759i
$193$			22.4853i			1.61853i	0.587447	+	0.809263i	$0.300133\pi$
$193$			22.4853i			1.61853i	−0.587447	+	0.809263i	$0.699867\pi$
$194$	2.14214			0.153796
$195$		0			0
$196$	1.82843			0.130602
$197$	−14.8284			−1.05648			−0.528241	−	0.849095i	$-0.677148\pi$
$197$	−14.8284			−1.05648			−0.528241	+	0.849095i	$0.677148\pi$
$198$	−4.10051	+	0.414214i	−0.291410	+	0.0294369i
$199$	−14.4853			−1.02683			−0.513417	−	0.858139i	$-0.671621\pi$
$199$	−14.4853			−1.02683			−0.513417	+	0.858139i	$0.671621\pi$
$200$	−1.58579			−0.112132
$201$	−6.48528	−	9.17157i	−0.457436	−	0.646913i
$202$	−3.85786			−0.271438
$203$		−	5.65685i		−	0.397033i
$204$	12.4853	+	17.6569i	0.874145	+	1.23623i
$205$			7.65685i			0.534778i
$206$	−3.85786			−0.268790
$207$	2.34315	+	0.828427i	0.162860	+	0.0575797i
$208$		0			0
$209$	−2.48528	+	1.17157i	−0.171911	+	0.0810394i
$210$	−0.414214	−	0.585786i	−0.0285835	−	0.0404231i
$211$			16.9706i			1.16830i	0.811645	+	0.584151i	$0.198572\pi$
$211$			16.9706i			1.16830i	−0.811645	+	0.584151i	$0.801428\pi$
$212$			1.51472i			0.104031i
$213$	0.485281	−	0.343146i	0.0332509	−	0.0235120i
$214$	3.85786			0.263718
$215$	−9.65685			−0.658592
$216$	−7.92893	+	2.24264i	−0.539496	+	0.152592i
$217$			0.828427i			0.0562373i
$218$			4.00000i			0.270914i
$219$	16.9706	−	12.0000i	1.14676	−	0.810885i
$220$	5.48528	−	2.58579i	0.369818	−	0.174334i
$221$		0			0
$222$	−2.48528	−	3.51472i	−0.166801	−	0.235892i
$223$	−14.9706			−1.00250			−0.501252	−	0.865302i	$-0.667127\pi$
$223$	−14.9706			−1.00250			−0.501252	+	0.865302i	$0.667127\pi$
$224$		−	4.41421i		−	0.294937i
$225$	1.00000	−	2.82843i	0.0666667	−	0.188562i
$226$			1.31371i			0.0873866i
$227$	−14.3431			−0.951988			−0.475994	−	0.879449i	$-0.657912\pi$
$227$	−14.3431			−0.951988			−0.475994	+	0.879449i	$0.657912\pi$
$228$	−2.14214	+	1.51472i	−0.141866	+	0.100315i
$229$	−9.31371			−0.615467			−0.307734	−	0.951473i	$-0.599571\pi$
$229$	−9.31371			−0.615467			−0.307734	+	0.951473i	$0.599571\pi$
$230$	0.343146			0.0226264
$231$	5.00000	+	2.82843i	0.328976	+	0.186097i
$232$	−8.97056			−0.588946
$233$	11.7990			0.772978			0.386489	−	0.922294i	$-0.373688\pi$
$233$	11.7990			0.772978			0.386489	+	0.922294i	$0.373688\pi$
$234$		0			0
$235$	−10.8284			−0.706369
$236$		−	0.627417i		−	0.0408414i
$237$	−5.65685	+	4.00000i	−0.367452	+	0.259828i
$238$			2.82843i			0.183340i
$239$	2.82843			0.182956			0.0914779	−	0.995807i	$-0.470841\pi$
$239$	2.82843			0.182956			0.0914779	+	0.995807i	$0.470841\pi$
$240$	4.24264	−	3.00000i	0.273861	−	0.193649i
$241$		−	22.8284i		−	1.47051i	−0.677792	−	0.735254i	$-0.737063\pi$
$241$		−	22.8284i		−	1.47051i	0.677792	−	0.735254i	$-0.262937\pi$
$242$	2.89949	−	3.51472i	0.186387	−	0.225935i
$243$	1.00000	−	15.5563i	0.0641500	−	0.997940i
$244$		−	9.45584i		−	0.605348i
$245$			1.00000i			0.0638877i
$246$	3.17157	+	4.48528i	0.202212	+	0.285971i
$247$		0			0
$248$	1.31371			0.0834206
$249$	−12.0000	−	16.9706i	−0.760469	−	1.07547i
$250$		−	0.414214i		−	0.0261972i
$251$			20.6274i			1.30199i	0.759082	+	0.650996i	$0.225648\pi$
$251$			20.6274i			1.30199i	−0.759082	+	0.650996i	$0.774352\pi$
$252$	5.17157	+	1.82843i	0.325778	+	0.115180i
$253$	−2.48528	+	1.17157i	−0.156248	+	0.0736562i
$254$		−	5.65685i		−	0.354943i
$255$	−9.65685	+	6.82843i	−0.604736	+	0.427613i
$256$	3.97056			0.248160
$257$			13.3137i			0.830486i	0.909710	+	0.415243i	$0.136304\pi$
$257$			13.3137i			0.830486i	−0.909710	+	0.415243i	$0.863696\pi$
$258$	−5.65685	+	4.00000i	−0.352180	+	0.249029i
$259$			6.00000i			0.372822i
$260$		0			0
$261$	5.65685	−	16.0000i	0.350150	−	0.990375i
$262$	−7.31371			−0.451842
$263$	17.3137			1.06761			0.533805	−	0.845608i	$-0.320762\pi$
$263$	17.3137			1.06761			0.533805	+	0.845608i	$0.320762\pi$
$264$	4.48528	−	7.92893i	0.276050	−	0.487992i
$265$	−0.828427			−0.0508899
$266$	−0.343146			−0.0210396
$267$	10.8284	−	7.65685i	0.662689	−	0.468592i
$268$	11.8579			0.724334
$269$			17.3137i			1.05564i	0.849358	+	0.527818i	$0.176990\pi$
$269$			17.3137i			1.05564i	−0.849358	+	0.527818i	$0.823010\pi$
$270$	−0.585786	−	2.07107i	−0.0356498	−	0.126041i
$271$		−	2.48528i		−	0.150970i	−0.997147	−	0.0754850i	$-0.975949\pi$
$271$		−	2.48528i		−	0.150970i	0.997147	−	0.0754850i	$-0.0240505\pi$
$272$	−20.4853			−1.24210
$273$		0			0
$274$		−	5.31371i		−	0.321013i
$275$	1.41421	+	3.00000i	0.0852803	+	0.180907i
$276$	−2.14214	+	1.51472i	−0.128941	+	0.0911753i
$277$			4.82843i			0.290112i	0.989423	+	0.145056i	$0.0463362\pi$
$277$			4.82843i			0.290112i	−0.989423	+	0.145056i	$0.953664\pi$
$278$		−	2.68629i		−	0.161113i
$279$	−0.828427	+	2.34315i	−0.0495966	+	0.140280i
$280$	1.58579			0.0947689
$281$	28.9706			1.72824			0.864119	−	0.503287i	$-0.167876\pi$
$281$	28.9706			1.72824			0.864119	+	0.503287i	$0.167876\pi$
$282$	−6.34315	+	4.48528i	−0.377729	+	0.267095i
$283$			28.9706i			1.72212i	0.508502	+	0.861061i	$0.330199\pi$
$283$			28.9706i			1.72212i	−0.508502	+	0.861061i	$0.669801\pi$
$284$			0.627417i			0.0372303i
$285$	−0.828427	−	1.17157i	−0.0490718	−	0.0693980i
$286$		0			0
$287$		−	7.65685i		−	0.451970i
$288$	4.41421	−	12.4853i	0.260110	−	0.735702i
$289$	29.6274			1.74279
$290$		−	2.34315i		−	0.137594i
$291$	−5.17157	−	7.31371i	−0.303163	−	0.428737i
$292$			21.9411i			1.28401i
$293$	18.8284			1.09997			0.549984	−	0.835175i	$-0.314634\pi$
$293$	18.8284			1.09997			0.549984	+	0.835175i	$0.314634\pi$
$294$	0.414214	+	0.585786i	0.0241574	+	0.0341638i
$295$	0.343146			0.0199787
$296$	9.51472			0.553032
$297$	11.3137	+	13.0000i	0.656488	+	0.754337i
$298$	3.02944			0.175491
$299$		0			0
$300$	1.82843	+	2.58579i	0.105564	+	0.149290i
$301$	9.65685			0.556612
$302$			1.37258i			0.0789833i
$303$	9.31371	+	13.1716i	0.535059	+	0.756687i
$304$		−	2.48528i		−	0.142541i
$305$	5.17157			0.296123
$306$	−2.82843	+	8.00000i	−0.161690	+	0.457330i
$307$		−	8.97056i		−	0.511977i	−0.966680	−	0.255989i	$-0.917599\pi$
$307$		−	8.97056i		−	0.511977i	0.966680	−	0.255989i	$-0.0824009\pi$
$308$	−5.48528	+	2.58579i	−0.312553	+	0.147339i
$309$	9.31371	+	13.1716i	0.529838	+	0.749305i
$310$			0.343146i			0.0194894i
$311$			24.6274i			1.39649i	0.715858	+	0.698246i	$0.246036\pi$
$311$			24.6274i			1.39649i	−0.715858	+	0.698246i	$0.753964\pi$
$312$		0			0
$313$	13.1716			0.744501			0.372251	−	0.928132i	$-0.378586\pi$
$313$	13.1716			0.744501			0.372251	+	0.928132i	$0.378586\pi$
$314$	7.79899			0.440122
$315$	−1.00000	+	2.82843i	−0.0563436	+	0.159364i
$316$		−	7.31371i		−	0.411428i
$317$		−	28.8284i		−	1.61917i	−0.587006	−	0.809583i	$-0.699693\pi$
$317$		−	28.8284i		−	1.61917i	0.587006	−	0.809583i	$-0.300307\pi$
$318$	−0.485281	+	0.343146i	−0.0272132	+	0.0192427i
$319$	8.00000	+	16.9706i	0.447914	+	0.950169i
$320$			4.17157i			0.233198i
$321$	−9.31371	−	13.1716i	−0.519841	−	0.735166i
$322$	−0.343146			−0.0191228
$323$			5.65685i			0.314756i
$324$	12.7990	+	10.3431i	0.711055	+	0.574619i
$325$		0			0
$326$	0.627417			0.0347494
$327$	13.6569	−	9.65685i	0.755226	−	0.534025i
$328$	−12.1421			−0.670437
$329$	10.8284			0.596991
$330$	2.07107	+	1.17157i	0.114009	+	0.0644930i
$331$	−10.3431			−0.568511			−0.284255	−	0.958749i	$-0.591746\pi$
$331$	−10.3431			−0.568511			−0.284255	+	0.958749i	$0.591746\pi$
$332$	21.9411			1.20418
$333$	−6.00000	+	16.9706i	−0.328798	+	0.929981i
$334$	−0.970563			−0.0531068
$335$			6.48528i			0.354329i
$336$	−4.24264	+	3.00000i	−0.231455	+	0.163663i
$337$		−	2.48528i		−	0.135382i	−0.997706	−	0.0676910i	$-0.978437\pi$
$337$		−	2.48528i		−	0.135382i	0.997706	−	0.0676910i	$-0.0215632\pi$
$338$	−5.38478			−0.292893
$339$	4.48528	−	3.17157i	0.243607	−	0.172256i
$340$		−	12.4853i		−	0.677109i
$341$	−1.17157	−	2.48528i	−0.0634442	−	0.134586i
$342$	−0.970563	−	0.343146i	−0.0524820	−	0.0185552i
$343$		−	1.00000i		−	0.0539949i
$344$		−	15.3137i		−	0.825660i
$345$	−0.828427	−	1.17157i	−0.0446010	−	0.0630754i
$346$	4.20101			0.225848
$347$	−12.3431			−0.662615			−0.331307	−	0.943523i	$-0.607490\pi$
$347$	−12.3431			−0.662615			−0.331307	+	0.943523i	$0.607490\pi$
$348$	10.3431	+	14.6274i	0.554451	+	0.784112i
$349$		−	32.4853i		−	1.73890i	−0.494023	−	0.869449i	$-0.664474\pi$
$349$		−	32.4853i		−	1.73890i	0.494023	−	0.869449i	$-0.335526\pi$
$350$			0.414214i			0.0221406i
$351$		0			0
$352$	6.24264	+	13.2426i	0.332734	+	0.705835i
$353$		−	0.343146i		−	0.0182638i	−0.999958	−	0.00913190i	$-0.997093\pi$
$353$		−	0.343146i		−	0.0182638i	0.999958	−	0.00913190i	$-0.00290682\pi$
$354$	0.201010	−	0.142136i	0.0106836	−	0.00755442i
$355$	−0.343146			−0.0182123
$356$			14.0000i			0.741999i
$357$	9.65685	−	6.82843i	0.511095	−	0.361399i
$358$		−	4.82843i		−	0.255190i
$359$	−8.48528			−0.447836			−0.223918	−	0.974608i	$-0.571885\pi$
$359$	−8.48528			−0.447836			−0.223918	+	0.974608i	$0.571885\pi$
$360$	4.48528	+	1.58579i	0.236395	+	0.0835783i
$361$	18.3137			0.963879
$362$	0.828427			0.0435412
$363$	−19.0000	−	1.41421i	−0.997241	−	0.0742270i
$364$		0			0
$365$	−12.0000			−0.628109
$366$	3.02944	−	2.14214i	0.158351	−	0.111971i
$367$	−18.0000			−0.939592			−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000			−0.939592			−0.469796	+	0.882775i	$0.655673\pi$
$368$		−	2.48528i		−	0.129554i
$369$	7.65685	−	21.6569i	0.398600	−	1.12741i
$370$			2.48528i			0.129204i
$371$	0.828427			0.0430098
$372$	−1.51472	−	2.14214i	−0.0785345	−	0.111065i
$373$			4.14214i			0.214472i	0.994234	+	0.107236i	$0.0342000\pi$
$373$			4.14214i			0.214472i	−0.994234	+	0.107236i	$0.965800\pi$
$374$	−4.00000	−	8.48528i	−0.206835	−	0.438763i
$375$	−1.41421	+	1.00000i	−0.0730297	+	0.0516398i
$376$		−	17.1716i		−	0.885556i
$377$		0			0
$378$	0.585786	+	2.07107i	0.0301296	+	0.106524i
$379$	−37.9411			−1.94890			−0.974452	−	0.224594i	$-0.927894\pi$
$379$	−37.9411			−1.94890			−0.974452	+	0.224594i	$0.927894\pi$
$380$	1.51472			0.0777034
$381$	−19.3137	+	13.6569i	−0.989471	+	0.699662i
$382$			2.48528i			0.127158i
$383$			23.7990i			1.21607i	0.793910	+	0.608036i	$0.208042\pi$
$383$			23.7990i			1.21607i	−0.793910	+	0.608036i	$0.791958\pi$
$384$	10.5563	+	14.9289i	0.538701	+	0.761839i
$385$	−1.41421	−	3.00000i	−0.0720750	−	0.152894i
$386$		−	9.31371i		−	0.474055i
$387$	27.3137	+	9.65685i	1.38843	+	0.490885i
$388$	9.45584			0.480048
$389$			10.6274i			0.538831i	0.963024	+	0.269416i	$0.0868306\pi$
$389$			10.6274i			0.538831i	−0.963024	+	0.269416i	$0.913169\pi$
$390$		0			0
$391$			5.65685i			0.286079i
$392$	−1.58579			−0.0800943
$393$	17.6569	+	24.9706i	0.890670	+	1.25960i
$394$	6.14214			0.309436
$395$	4.00000			0.201262
$396$	−18.1005	+	1.82843i	−0.909585	+	0.0918819i
$397$	20.4853			1.02813			0.514063	−	0.857752i	$-0.328140\pi$
$397$	20.4853			1.02813			0.514063	+	0.857752i	$0.328140\pi$
$398$	6.00000			0.300753
$399$	0.828427	+	1.17157i	0.0414732	+	0.0586520i
$400$	−3.00000			−0.150000
$401$		−	4.68629i		−	0.234022i	−0.993131	−	0.117011i	$-0.962669\pi$
$401$		−	4.68629i		−	0.234022i	0.993131	−	0.117011i	$-0.0373313\pi$
$402$	2.68629	+	3.79899i	0.133980	+	0.189476i
$403$		0			0
$404$	−17.0294			−0.847246
$405$	−5.65685	+	7.00000i	−0.281091	+	0.347833i
$406$			2.34315i			0.116288i
$407$	−8.48528	−	18.0000i	−0.420600	−	0.892227i
$408$	−10.8284	−	15.3137i	−0.536087	−	0.758142i
$409$		−	37.4558i		−	1.85207i	−0.377435	−	0.926036i	$-0.623194\pi$
$409$		−	37.4558i		−	1.85207i	0.377435	−	0.926036i	$-0.376806\pi$
$410$		−	3.17157i		−	0.156633i
$411$	−18.1421	+	12.8284i	−0.894886	+	0.632780i
$412$	−17.0294			−0.838980
$413$	−0.343146			−0.0168851
$414$	−0.970563	−	0.343146i	−0.0477006	−	0.0168647i
$415$			12.0000i			0.589057i
$416$		0			0
$417$	−9.17157	+	6.48528i	−0.449134	+	0.317586i
$418$	1.02944	−	0.485281i	0.0503514	−	0.0237359i
$419$			25.3137i			1.23666i	0.785920	+	0.618328i	$0.212190\pi$
$419$			25.3137i			1.23666i	−0.785920	+	0.618328i	$0.787810\pi$
$420$	−1.82843	−	2.58579i	−0.0892181	−	0.126173i
$421$	18.0000			0.877266			0.438633	−	0.898666i	$-0.355463\pi$
$421$	18.0000			0.877266			0.438633	+	0.898666i	$0.355463\pi$
$422$		−	7.02944i		−	0.342188i
$423$	30.6274	+	10.8284i	1.48916	+	0.526496i
$424$		−	1.31371i		−	0.0637993i
$425$	6.82843			0.331227
$426$	−0.201010	+	0.142136i	−0.00973897	+	0.00688649i
$427$	−5.17157			−0.250270
$428$	17.0294			0.823149
$429$		0			0
$430$	4.00000			0.192897
$431$	18.1421			0.873876			0.436938	−	0.899492i	$-0.356063\pi$
$431$	18.1421			0.873876			0.436938	+	0.899492i	$0.356063\pi$
$432$	−15.0000	+	4.24264i	−0.721688	+	0.204124i
$433$	−34.8284			−1.67375			−0.836874	−	0.547396i	$-0.815619\pi$
$433$	−34.8284			−1.67375			−0.836874	+	0.547396i	$0.815619\pi$
$434$		−	0.343146i		−	0.0164715i
$435$	−8.00000	+	5.65685i	−0.383571	+	0.271225i
$436$			17.6569i			0.845610i
$437$	−0.686292			−0.0328298
$438$	−7.02944	+	4.97056i	−0.335880	+	0.237503i
$439$		−	19.4558i		−	0.928577i	−0.885684	−	0.464288i	$-0.846310\pi$
$439$		−	19.4558i		−	0.928577i	0.885684	−	0.464288i	$-0.153690\pi$
$440$	−4.75736	+	2.24264i	−0.226798	+	0.106914i
$441$	1.00000	−	2.82843i	0.0476190	−	0.134687i
$442$		0			0
$443$		−	37.7990i		−	1.79588i	−0.440114	−	0.897942i	$-0.645062\pi$
$443$		−	37.7990i		−	1.79588i	0.440114	−	0.897942i	$-0.354938\pi$
$444$	−10.9706	−	15.5147i	−0.520640	−	0.736296i
$445$	−7.65685			−0.362970
$446$	6.20101			0.293626
$447$	−7.31371	−	10.3431i	−0.345927	−	0.489214i
$448$		−	4.17157i		−	0.197088i
$449$		−	6.34315i		−	0.299352i	−0.988735	−	0.149676i	$-0.952177\pi$
$449$		−	6.34315i		−	0.299352i	0.988735	−	0.149676i	$-0.0478230\pi$
$450$	−0.414214	+	1.17157i	−0.0195262	+	0.0552285i
$451$	10.8284	+	22.9706i	0.509891	+	1.08164i
$452$			5.79899i			0.272762i
$453$	4.68629	−	3.31371i	0.220181	−	0.155692i
$454$	5.94113			0.278831
$455$		0			0
$456$	1.85786	−	1.31371i	0.0870025	−	0.0615200i
$457$		−	26.4853i		−	1.23893i	−0.785025	−	0.619465i	$-0.787350\pi$
$457$		−	26.4853i		−	1.23893i	0.785025	−	0.619465i	$-0.212650\pi$
$458$	3.85786			0.180266
$459$	34.1421	−	9.65685i	1.59362	−	0.450743i
$460$	1.51472			0.0706241
$461$	12.3431			0.574878			0.287439	−	0.957799i	$-0.407196\pi$
$461$	12.3431			0.574878			0.287439	+	0.957799i	$0.407196\pi$
$462$	−2.07107	−	1.17157i	−0.0963548	−	0.0545065i
$463$	−39.4558			−1.83367			−0.916834	−	0.399268i	$-0.869264\pi$
$463$	−39.4558			−1.83367			−0.916834	+	0.399268i	$0.869264\pi$
$464$	−16.9706			−0.787839
$465$	1.17157	−	0.828427i	0.0543304	−	0.0384174i
$466$	−4.88730			−0.226400
$467$		−	1.17157i		−	0.0542139i	−0.999633	−	0.0271070i	$-0.991371\pi$
$467$		−	1.17157i		−	0.0542139i	0.999633	−	0.0271070i	$-0.00862947\pi$
$468$		0			0
$469$		−	6.48528i		−	0.299462i
$470$	4.48528			0.206891
$471$	−18.8284	−	26.6274i	−0.867568	−	1.22693i
$472$			0.544156i			0.0250468i
$473$	−28.9706	+	13.6569i	−1.33207	+	0.627943i
$474$	2.34315	−	1.65685i	0.107624	−	0.0761018i
$475$			0.828427i			0.0380108i
$476$			12.4853i			0.572262i
$477$	2.34315	+	0.828427i	0.107285	+	0.0379311i
$478$	−1.17157			−0.0535865
$479$	−11.3137			−0.516937			−0.258468	−	0.966020i	$-0.583218\pi$
$479$	−11.3137			−0.516937			−0.258468	+	0.966020i	$0.583218\pi$
$480$	−6.24264	+	4.41421i	−0.284936	+	0.201480i
$481$		0			0
$482$			9.45584i			0.430702i
$483$	0.828427	+	1.17157i	0.0376947	+	0.0533084i
$484$	12.7990	−	15.5147i	0.581772	−	0.705214i
$485$			5.17157i			0.234829i
$486$	−0.414214	+	6.44365i	−0.0187891	+	0.292290i
$487$	26.4853			1.20016			0.600081	−	0.799939i	$-0.295135\pi$
$487$	26.4853			1.20016			0.600081	+	0.799939i	$0.295135\pi$
$488$			8.20101i			0.371242i
$489$	−1.51472	−	2.14214i	−0.0684979	−	0.0968707i
$490$		−	0.414214i		−	0.0187123i
$491$	18.1421			0.818743			0.409372	−	0.912368i	$-0.365748\pi$
$491$	18.1421			0.818743			0.409372	+	0.912368i	$0.365748\pi$
$492$	14.0000	+	19.7990i	0.631169	+	0.892607i
$493$	38.6274			1.73969
$494$		0			0
$495$	−1.00000	−	9.89949i	−0.0449467	−	0.444949i
$496$	2.48528			0.111592
$497$	0.343146			0.0153922
$498$	4.97056	+	7.02944i	0.222736	+	0.314997i
$499$	36.0000			1.61158			0.805791	−	0.592200i	$-0.201741\pi$
$499$	36.0000			1.61158			0.805791	+	0.592200i	$0.201741\pi$
$500$		−	1.82843i		−	0.0817697i
$501$	2.34315	+	3.31371i	0.104684	+	0.148046i
$502$		−	8.54416i		−	0.381344i
$503$	−25.6569			−1.14398			−0.571991	−	0.820260i	$-0.693829\pi$
$503$	−25.6569			−1.14398			−0.571991	+	0.820260i	$0.693829\pi$
$504$	−4.48528	−	1.58579i	−0.199790	−	0.0706365i
$505$		−	9.31371i		−	0.414455i
$506$	1.02944	−	0.485281i	0.0457641	−	0.0215734i
$507$	13.0000	+	18.3848i	0.577350	+	0.816497i
$508$		−	24.9706i		−	1.10789i
$509$		−	10.9706i		−	0.486262i	−0.969994	−	0.243131i	$-0.921826\pi$
$509$		−	10.9706i		−	0.486262i	0.969994	−	0.243131i	$-0.0781744\pi$
$510$	4.00000	−	2.82843i	0.177123	−	0.125245i
$511$	12.0000			0.530849
$512$	−22.7574			−1.00574
$513$	1.17157	+	4.14214i	0.0517262	+	0.182880i
$514$		−	5.51472i		−	0.243244i
$515$		−	9.31371i		−	0.410411i
$516$	−24.9706	+	17.6569i	−1.09927	+	0.777300i
$517$	−32.4853	+	15.3137i	−1.42870	+	0.673496i
$518$		−	2.48528i		−	0.109197i
$519$	−10.1421	−	14.3431i	−0.445190	−	0.629594i
$520$		0			0
$521$			9.31371i			0.408041i	0.978967	+	0.204020i	$0.0654009\pi$
$521$			9.31371i			0.408041i	−0.978967	+	0.204020i	$0.934599\pi$
$522$	−2.34315	+	6.62742i	−0.102557	+	0.290074i
$523$		−	12.9706i		−	0.567163i	−0.958948	−	0.283582i	$-0.908477\pi$
$523$		−	12.9706i		−	0.567163i	0.958948	−	0.283582i	$-0.0915227\pi$
$524$	−32.2843			−1.41034
$525$	1.41421	−	1.00000i	0.0617213	−	0.0436436i
$526$	−7.17157			−0.312695
$527$	−5.65685			−0.246416
$528$	8.48528	−	15.0000i	0.369274	−	0.652791i
$529$	22.3137			0.970161
$530$	0.343146			0.0149053
$531$	−0.970563	−	0.343146i	−0.0421188	−	0.0148913i
$532$	−1.51472			−0.0656714
$533$		0			0
$534$	−4.48528	+	3.17157i	−0.194097	+	0.137247i
$535$			9.31371i			0.402667i
$536$	−10.2843			−0.444213
$537$	−16.4853	+	11.6569i	−0.711392	+	0.503030i
$538$		−	7.17157i		−	0.309188i
$539$	1.41421	+	3.00000i	0.0609145	+	0.129219i
$540$	−2.58579	−	9.14214i	−0.111275	−	0.393415i
$541$		−	28.9706i		−	1.24554i	−0.782404	−	0.622771i	$-0.786007\pi$
$541$		−	28.9706i		−	1.24554i	0.782404	−	0.622771i	$-0.213993\pi$
$542$			1.02944i			0.0442181i
$543$	−2.00000	−	2.82843i	−0.0858282	−	0.121379i
$544$	30.1421			1.29233
$545$	−9.65685			−0.413654
$546$		0			0
$547$		−	32.2843i		−	1.38038i	−0.723630	−	0.690188i	$-0.757528\pi$
$547$		−	32.2843i		−	1.38038i	0.723630	−	0.690188i	$-0.242472\pi$
$548$		−	23.4558i		−	1.00198i
$549$	−14.6274	−	5.17157i	−0.624283	−	0.220717i
$550$	−0.585786	−	1.24264i	−0.0249780	−	0.0529864i
$551$			4.68629i			0.199643i
$552$	1.85786	−	1.31371i	0.0790760	−	0.0559151i
$553$	−4.00000			−0.170097
$554$		−	2.00000i		−	0.0849719i
$555$	8.48528	−	6.00000i	0.360180	−	0.254686i
$556$		−	11.8579i		−	0.502885i
$557$	−44.4853			−1.88490			−0.942451	−	0.334344i	$-0.891485\pi$
$557$	−44.4853			−1.88490			−0.942451	+	0.334344i	$0.891485\pi$
$558$	0.343146	−	0.970563i	0.0145265	−	0.0410872i
$559$		0			0
$560$	3.00000			0.126773
$561$	−19.3137	+	34.1421i	−0.815425	+	1.44148i
$562$	−12.0000			−0.506189
$563$	−7.02944			−0.296255			−0.148128	−	0.988968i	$-0.547325\pi$
$563$	−7.02944			−0.296255			−0.148128	+	0.988968i	$0.547325\pi$
$564$	−28.0000	+	19.7990i	−1.17901	+	0.833688i
$565$	−3.17157			−0.133429
$566$		−	12.0000i		−	0.504398i
$567$	5.65685	−	7.00000i	0.237566	−	0.293972i
$568$		−	0.544156i		−	0.0228323i
$569$	23.3137			0.977362			0.488681	−	0.872463i	$-0.337478\pi$
$569$	23.3137			0.977362			0.488681	+	0.872463i	$0.337478\pi$
$570$	0.343146	+	0.485281i	0.0143728	+	0.0203262i
$571$		−	4.97056i		−	0.208012i	−0.994577	−	0.104006i	$-0.966834\pi$
$571$		−	4.97056i		−	0.208012i	0.994577	−	0.104006i	$-0.0331660\pi$
$572$		0			0
$573$	8.48528	−	6.00000i	0.354478	−	0.250654i
$574$			3.17157i			0.132379i
$575$			0.828427i			0.0345478i
$576$	4.17157	−	11.7990i	0.173816	−	0.491625i
$577$	−20.4853			−0.852813			−0.426407	−	0.904532i	$-0.640221\pi$
$577$	−20.4853			−0.852813			−0.426407	+	0.904532i	$0.640221\pi$
$578$	−12.2721			−0.510451
$579$	−31.7990	+	22.4853i	−1.32152	+	0.934456i
$580$		−	10.3431i		−	0.429476i
$581$		−	12.0000i		−	0.497844i
$582$	2.14214	+	3.02944i	0.0887944	+	0.125574i
$583$	−2.48528	+	1.17157i	−0.102930	+	0.0485216i
$584$		−	19.0294i		−	0.787444i
$585$		0			0
$586$	−7.79899			−0.322173
$587$		−	37.4558i		−	1.54597i	−0.634425	−	0.772984i	$-0.718763\pi$
$587$		−	37.4558i		−	1.54597i	0.634425	−	0.772984i	$-0.281237\pi$
$588$	1.82843	+	2.58579i	0.0754031	+	0.106636i
$589$		−	0.686292i		−	0.0282781i
$590$	−0.142136			−0.00585163
$591$	−14.8284	−	20.9706i	−0.609960	−	0.862614i
$592$	18.0000			0.739795
$593$	−17.1716			−0.705152			−0.352576	−	0.935783i	$-0.614694\pi$
$593$	−17.1716			−0.705152			−0.352576	+	0.935783i	$0.614694\pi$
$594$	−4.68629	−	5.38478i	−0.192281	−	0.220940i
$595$	−6.82843			−0.279938
$596$	13.3726			0.547762
$597$	−14.4853	−	20.4853i	−0.592843	−	0.838407i
$598$		0			0
$599$		−	39.9411i		−	1.63195i	−0.578087	−	0.815975i	$-0.696201\pi$
$599$		−	39.9411i		−	1.63195i	0.578087	−	0.815975i	$-0.303799\pi$
$600$	−1.58579	−	2.24264i	−0.0647395	−	0.0915554i
$601$		−	5.45584i		−	0.222549i	−0.993790	−	0.111274i	$-0.964507\pi$
$601$		−	5.45584i		−	0.222549i	0.993790	−	0.111274i	$-0.0354932\pi$
$602$	−4.00000			−0.163028
$603$	6.48528	−	18.3431i	0.264101	−	0.746991i
$604$			6.05887i			0.246532i
$605$	8.48528	+	7.00000i	0.344976	+	0.284590i
$606$	−3.85786	−	5.45584i	−0.156715	−	0.221629i
$607$			36.0000i			1.46119i	0.682808	+	0.730597i	$0.260758\pi$
$607$			36.0000i			1.46119i	−0.682808	+	0.730597i	$0.739242\pi$
$608$			3.65685i			0.148305i
$609$	8.00000	−	5.65685i	0.324176	−	0.229227i
$610$	−2.14214			−0.0867325
$611$		0			0
$612$	−12.4853	+	35.3137i	−0.504688	+	1.42747i
$613$			5.79899i			0.234219i	0.993119	+	0.117109i	$0.0373628\pi$
$613$			5.79899i			0.234219i	−0.993119	+	0.117109i	$0.962637\pi$
$614$			3.71573i			0.149955i
$615$	−10.8284	+	7.65685i	−0.436644	+	0.308754i
$616$	4.75736	−	2.24264i	0.191679	−	0.0903586i
$617$		−	19.4558i		−	0.783263i	−0.920122	−	0.391631i	$-0.871911\pi$
$617$		−	19.4558i		−	0.783263i	0.920122	−	0.391631i	$-0.128089\pi$
$618$	−3.85786	−	5.45584i	−0.155186	−	0.219466i
$619$	−21.7990			−0.876175			−0.438088	−	0.898932i	$-0.644344\pi$
$619$	−21.7990			−0.876175			−0.438088	+	0.898932i	$0.644344\pi$
$620$			1.51472i			0.0608326i
$621$	1.17157	+	4.14214i	0.0470136	+	0.166218i
$622$		−	10.2010i		−	0.409023i
$623$	7.65685			0.306765
$624$		0			0
$625$	1.00000			0.0400000
$626$	−5.45584			−0.218059
$627$	−4.14214	−	2.34315i	−0.165421	−	0.0935762i
$628$	34.4264			1.37376
$629$	−40.9706			−1.63360
$630$	0.414214	−	1.17157i	0.0165027	−	0.0466766i
$631$	32.9706			1.31254			0.656269	−	0.754527i	$-0.272134\pi$
$631$	32.9706			1.31254			0.656269	+	0.754527i	$0.272134\pi$
$632$			6.34315i			0.252317i
$633$	−24.0000	+	16.9706i	−0.953914	+	0.674519i
$634$			11.9411i			0.474243i
$635$	13.6569			0.541956
$636$	−2.14214	+	1.51472i	−0.0849412	+	0.0600625i
$637$		0			0
$638$	−3.31371	−	7.02944i	−0.131191	−	0.278298i
$639$	0.970563	+	0.343146i	0.0383949	+	0.0135746i
$640$		−	10.5563i		−	0.417276i
$641$			16.6863i			0.659069i	0.944144	+	0.329534i	$0.106892\pi$
$641$			16.6863i			0.659069i	−0.944144	+	0.329534i	$0.893108\pi$
$642$	3.85786	+	5.45584i	0.152258	+	0.215325i
$643$	−10.9706			−0.432637			−0.216318	−	0.976323i	$-0.569405\pi$
$643$	−10.9706			−0.432637			−0.216318	+	0.976323i	$0.569405\pi$
$644$	−1.51472			−0.0596883
$645$	−9.65685	−	13.6569i	−0.380238	−	0.537738i
$646$		−	2.34315i		−	0.0921898i
$647$		−	4.20101i		−	0.165159i	−0.996584	−	0.0825794i	$-0.973684\pi$
$647$		−	4.20101i		−	0.165159i	0.996584	−	0.0825794i	$-0.0263158\pi$
$648$	−11.1005	−	8.97056i	−0.436069	−	0.352397i
$649$	1.02944	−	0.485281i	0.0404089	−	0.0190490i
$650$		0			0
$651$	−1.17157	+	0.828427i	−0.0459176	+	0.0324686i
$652$	2.76955			0.108464
$653$		−	26.4853i		−	1.03645i	−0.855245	−	0.518225i	$-0.826593\pi$
$653$		−	26.4853i		−	1.03645i	0.855245	−	0.518225i	$-0.173407\pi$
$654$	−5.65685	+	4.00000i	−0.221201	+	0.156412i
$655$		−	17.6569i		−	0.689910i
$656$	−22.9706			−0.896850
$657$	33.9411	+	12.0000i	1.32417	+	0.468165i
$658$	−4.48528			−0.174854
$659$	44.4853			1.73290			0.866450	−	0.499263i	$-0.166396\pi$
$659$	44.4853			1.73290			0.866450	+	0.499263i	$0.166396\pi$
$660$	9.14214	+	5.17157i	0.355857	+	0.201303i
$661$	−46.9706			−1.82694			−0.913472	−	0.406903i	$-0.866609\pi$
$661$	−46.9706			−1.82694			−0.913472	+	0.406903i	$0.866609\pi$
$662$	4.28427			0.166513
$663$		0			0
$664$	−19.0294			−0.738485
$665$		−	0.828427i		−	0.0321250i
$666$	2.48528	−	7.02944i	0.0963027	−	0.272385i
$667$			4.68629i			0.181454i
$668$	−4.28427			−0.165763
$669$	−14.9706	−	21.1716i	−0.578795	−	0.818540i
$670$		−	2.68629i		−	0.103780i
$671$	15.5147	−	7.31371i	0.598939	−	0.282343i
$672$	6.24264	−	4.41421i	0.240815	−	0.170282i
$673$		−	25.5147i		−	0.983520i	−0.870731	−	0.491760i	$-0.836354\pi$
$673$		−	25.5147i		−	0.983520i	0.870731	−	0.491760i	$-0.163646\pi$
$674$			1.02944i			0.0396524i
$675$	5.00000	−	1.41421i	0.192450	−	0.0544331i
$676$	−23.7696			−0.914214
$677$	−40.7696			−1.56690			−0.783451	−	0.621454i	$-0.786542\pi$
$677$	−40.7696			−1.56690			−0.783451	+	0.621454i	$0.786542\pi$
$678$	−1.85786	+	1.31371i	−0.0713509	+	0.0504527i
$679$		−	5.17157i		−	0.198467i
$680$			10.8284i			0.415251i
$681$	−14.3431	−	20.2843i	−0.549631	−	0.777295i
$682$	0.485281	+	1.02944i	0.0185824	+	0.0394192i
$683$			37.7990i			1.44634i	0.690671	+	0.723169i	$0.257315\pi$
$683$			37.7990i			1.44634i	−0.690671	+	0.723169i	$0.742685\pi$
$684$	−4.28427	−	1.51472i	−0.163813	−	0.0579167i
$685$	12.8284			0.490149
$686$			0.414214i			0.0158147i
$687$	−9.31371	−	13.1716i	−0.355340	−	0.502527i
$688$		−	28.9706i		−	1.10449i
$689$		0			0
$690$	0.343146	+	0.485281i	0.0130633	+	0.0184743i
$691$	−5.51472			−0.209790			−0.104895	−	0.994483i	$-0.533451\pi$
$691$	−5.51472			−0.209790			−0.104895	+	0.994483i	$0.533451\pi$
$692$	18.5442			0.704943
$693$	1.00000	+	9.89949i	0.0379869	+	0.376051i
$694$	5.11270			0.194075
$695$	6.48528			0.246001
$696$	−8.97056	−	12.6863i	−0.340028	−	0.480873i
$697$	52.2843			1.98041
$698$			13.4558i			0.509311i
$699$	11.7990	+	16.6863i	0.446279	+	0.631134i
$700$			1.82843i			0.0691080i
$701$	−31.5980			−1.19344			−0.596720	−	0.802450i	$-0.703530\pi$
$701$	−31.5980			−1.19344			−0.596720	+	0.802450i	$0.703530\pi$
$702$		0			0
$703$		−	4.97056i		−	0.187468i
$704$	5.89949	+	12.5147i	0.222346	+	0.471666i
$705$	−10.8284	−	15.3137i	−0.407822	−	0.576748i
$706$			0.142136i			0.00534934i
$707$			9.31371i			0.350278i
$708$	0.887302	−	0.627417i	0.0333468	−	0.0235798i
$709$	30.0000			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$710$	0.142136			0.00533425
$711$	−11.3137	−	4.00000i	−0.424297	−	0.150012i
$712$		−	12.1421i		−	0.455046i
$713$		−	0.686292i		−	0.0257018i
$714$	−4.00000	+	2.82843i	−0.149696	+	0.105851i
$715$		0			0
$716$		−	21.3137i		−	0.796531i
$717$	2.82843	+	4.00000i	0.105630	+	0.149383i
$718$	3.51472			0.131168
$719$		−	6.68629i		−	0.249357i	−0.992197	−	0.124678i	$-0.960210\pi$
$719$		−	6.68629i		−	0.249357i	0.992197	−	0.124678i	$-0.0397899\pi$
$720$	8.48528	+	3.00000i	0.316228	+	0.111803i
$721$			9.31371i			0.346861i
$722$	−7.58579			−0.282314
$723$	32.2843	−	22.8284i	1.20066	−	0.848998i
$724$	3.65685			0.135906
$725$	5.65685			0.210090
$726$	7.87006	+	0.585786i	0.292085	+	0.0217406i
$727$	42.0000			1.55769			0.778847	−	0.627214i	$-0.215805\pi$
$727$	42.0000			1.55769			0.778847	+	0.627214i	$0.215805\pi$
$728$		0			0
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	4.97056			0.183969
$731$			65.9411i			2.43892i
$732$	13.3726	−	9.45584i	0.494265	−	0.349498i
$733$			29.9411i			1.10590i	0.833214	+	0.552950i	$0.186498\pi$
$733$			29.9411i			1.10590i	−0.833214	+	0.552950i	$0.813502\pi$
$734$	7.45584			0.275200
$735$	−1.41421	+	1.00000i	−0.0521641	+	0.0368856i
$736$			3.65685i			0.134793i
$737$	9.17157	+	19.4558i	0.337839	+	0.716665i
$738$	−3.17157	+	8.97056i	−0.116747	+	0.330211i
$739$			20.2843i			0.746169i	0.927797	+	0.373084i	$0.121700\pi$
$739$			20.2843i			0.746169i	−0.927797	+	0.373084i	$0.878300\pi$
$740$			10.9706i			0.403286i
$741$		0			0
$742$	−0.343146			−0.0125973
$743$	−22.6863			−0.832279			−0.416140	−	0.909301i	$-0.636617\pi$
$743$	−22.6863			−0.832279			−0.416140	+	0.909301i	$0.636617\pi$
$744$	1.31371	+	1.85786i	0.0481629	+	0.0681126i
$745$			7.31371i			0.267954i
$746$		−	1.71573i		−	0.0628173i
$747$	12.0000	−	33.9411i	0.439057	−	1.24184i
$748$	−17.6569	−	37.4558i	−0.645599	−	1.36952i
$749$		−	9.31371i		−	0.340316i
$750$	0.585786	−	0.414214i	0.0213899	−	0.0151249i
$751$	−29.9411			−1.09257			−0.546284	−	0.837600i	$-0.683958\pi$
$751$	−29.9411			−1.09257			−0.546284	+	0.837600i	$0.683958\pi$
$752$		−	32.4853i		−	1.18462i
$753$	−29.1716	+	20.6274i	−1.06307	+	0.751705i
$754$		0			0
$755$	−3.31371			−0.120598
$756$	2.58579	+	9.14214i	0.0940441	+	0.332496i
$757$	39.9411			1.45168			0.725842	−	0.687861i	$-0.241450\pi$
$757$	39.9411			1.45168			0.725842	+	0.687861i	$0.241450\pi$
$758$	15.7157			0.570821
$759$	−4.14214	−	2.34315i	−0.150350	−	0.0850508i
$760$	−1.31371			−0.0476532
$761$	36.3431			1.31744			0.658719	−	0.752389i	$-0.271099\pi$
$761$	36.3431			1.31744			0.658719	+	0.752389i	$0.271099\pi$
$762$	8.00000	−	5.65685i	0.289809	−	0.204926i
$763$	9.65685			0.349602
$764$			10.9706i			0.396901i
$765$	−19.3137	−	6.82843i	−0.698289	−	0.246882i
$766$		−	9.85786i		−	0.356179i
$767$		0			0
$768$	3.97056	+	5.61522i	0.143275	+	0.202622i
$769$		−	20.4853i		−	0.738718i	−0.929287	−	0.369359i	$-0.879577\pi$
$769$		−	20.4853i		−	0.738718i	0.929287	−	0.369359i	$-0.120423\pi$
$770$	0.585786	+	1.24264i	0.0211103	+	0.0447817i
$771$	−18.8284	+	13.3137i	−0.678089	+	0.479481i
$772$		−	41.1127i		−	1.47968i
$773$		−	2.68629i		−	0.0966192i	−0.998832	−	0.0483096i	$-0.984617\pi$
$773$		−	2.68629i		−	0.0966192i	0.998832	−	0.0483096i	$-0.0153834\pi$
$774$	−11.3137	−	4.00000i	−0.406663	−	0.143777i
$775$	−0.828427			−0.0297580
$776$	−8.20101			−0.294399
$777$	−8.48528	+	6.00000i	−0.304408	+	0.215249i
$778$		−	4.40202i		−	0.157820i
$779$			6.34315i			0.227267i
$780$		0			0
$781$	−1.02944	+	0.485281i	−0.0368362	+	0.0173647i
$782$		−	2.34315i		−	0.0837907i
$783$	28.2843	−	8.00000i	1.01080	−	0.285897i
$784$	−3.00000			−0.107143
$785$			18.8284i			0.672015i
$786$	−7.31371	−	10.3431i	−0.260871	−	0.368928i
$787$		−	37.9411i		−	1.35246i	−0.736693	−	0.676228i	$-0.763614\pi$
$787$		−	37.9411i		−	1.35246i	0.736693	−	0.676228i	$-0.236386\pi$
$788$	27.1127			0.965850
$789$	17.3137	+	24.4853i	0.616384	+	0.871699i
$790$	−1.65685			−0.0589482
$791$	3.17157			0.112768
$792$	15.6985	−	1.58579i	0.557821	−	0.0563485i
$793$		0			0
$794$	−8.48528			−0.301131
$795$	−0.828427	−	1.17157i	−0.0293813	−	0.0415514i
$796$	26.4853			0.938746
$797$		−	16.6274i		−	0.588973i	−0.955656	−	0.294487i	$-0.904851\pi$
$797$		−	16.6274i		−	0.588973i	0.955656	−	0.294487i	$-0.0951487\pi$
$798$	−0.343146	−	0.485281i	−0.0121472	−	0.0171788i
$799$			73.9411i			2.61585i
$800$	4.41421			0.156066
$801$	21.6569	+	7.65685i	0.765207	+	0.270542i
$802$			1.94113i			0.0685435i
$803$	−36.0000	+	16.9706i	−1.27041	+	0.598878i
$804$	11.8579	+	16.7696i	0.418195	+	0.591417i
$805$		−	0.828427i		−	0.0291982i
$806$		0			0
$807$	−24.4853	+	17.3137i	−0.861923	+	0.609471i
$808$	14.7696			0.519591
$809$	10.6274			0.373640			0.186820	−	0.982394i	$-0.440182\pi$
$809$	10.6274			0.373640			0.186820	+	0.982394i	$0.440182\pi$
$810$	2.34315	−	2.89949i	0.0823297	−	0.101878i
$811$			17.5147i			0.615025i	0.951544	+	0.307512i	$0.0994966\pi$
$811$			17.5147i			0.615025i	−0.951544	+	0.307512i	$0.900503\pi$
$812$			10.3431i			0.362973i
$813$	3.51472	−	2.48528i	0.123267	−	0.0871626i
$814$	3.51472	+	7.45584i	0.123191	+	0.261327i
$815$			1.51472i			0.0530583i
$816$	−20.4853	−	28.9706i	−0.717128	−	1.01417i
$817$	−8.00000			−0.279885
$818$			15.5147i			0.542459i
$819$		0			0
$820$		−	14.0000i		−	0.488901i
$821$	6.62742			0.231298			0.115649	−	0.993290i	$-0.463105\pi$
$821$	6.62742			0.231298			0.115649	+	0.993290i	$0.463105\pi$
$822$	7.51472	−	5.31371i	0.262106	−	0.185337i
$823$	−0.142136			−0.00495454			−0.00247727	−	0.999997i	$-0.500789\pi$
$823$	−0.142136			−0.00495454			−0.00247727	+	0.999997i	$0.500789\pi$
$824$	14.7696			0.514522
$825$	−2.82843	+	5.00000i	−0.0984732	+	0.174078i
$826$	0.142136			0.00494553
$827$	51.2548			1.78231			0.891153	−	0.453704i	$-0.149898\pi$
$827$	51.2548			1.78231			0.891153	+	0.453704i	$0.149898\pi$
$828$	−4.28427	−	1.51472i	−0.148889	−	0.0526401i
$829$	−50.9706			−1.77028			−0.885140	−	0.465324i	$-0.845938\pi$
$829$	−50.9706			−1.77028			−0.885140	+	0.465324i	$0.845938\pi$
$830$		−	4.97056i		−	0.172531i
$831$	−6.82843	+	4.82843i	−0.236876	+	0.167496i
$832$		0			0
$833$	6.82843			0.236591
$834$	3.79899	−	2.68629i	0.131548	−	0.0930187i
$835$		−	2.34315i		−	0.0810879i
$836$	4.54416	−	2.14214i	0.157163	−	0.0740873i
$837$	−4.14214	+	1.17157i	−0.143173	+	0.0404955i
$838$		−	10.4853i		−	0.362208i
$839$			51.6569i			1.78339i	0.452634	+	0.891696i	$0.350484\pi$
$839$			51.6569i			1.78339i	−0.452634	+	0.891696i	$0.649516\pi$
$840$	1.58579	+	2.24264i	0.0547148	+	0.0773785i
$841$	3.00000			0.103448
$842$	−7.45584			−0.256945
$843$	28.9706	+	40.9706i	0.997799	+	1.41110i
$844$		−	31.0294i		−	1.06808i
$845$		−	13.0000i		−	0.447214i
$846$	−12.6863	−	4.48528i	−0.436164	−	0.154207i
$847$	−8.48528	−	7.00000i	−0.291558	−	0.240523i
$848$		−	2.48528i		−	0.0853449i
$849$	−40.9706	+	28.9706i	−1.40611	+	0.994267i
$850$	−2.82843			−0.0970143
$851$		−	4.97056i		−	0.170389i
$852$	−0.887302	+	0.627417i	−0.0303985	+	0.0214950i
$853$		−	28.9706i		−	0.991933i	−0.868342	−	0.495967i	$-0.834814\pi$
$853$		−	28.9706i		−	0.991933i	0.868342	−	0.495967i	$-0.165186\pi$
$854$	2.14214			0.0733024
$855$	0.828427	−	2.34315i	0.0283316	−	0.0801339i
$856$	−14.7696			−0.504813
$857$	−23.1127			−0.789515			−0.394757	−	0.918785i	$-0.629171\pi$
$857$	−23.1127			−0.789515			−0.394757	+	0.918785i	$0.629171\pi$
$858$		0			0
$859$	−35.4558			−1.20974			−0.604869	−	0.796325i	$-0.706774\pi$
$859$	−35.4558			−1.20974			−0.604869	+	0.796325i	$0.706774\pi$
$860$	17.6569			0.602094
$861$	10.8284	−	7.65685i	0.369032	−	0.260945i
$862$	−7.51472			−0.255952
$863$		−	40.1421i		−	1.36645i	−0.730206	−	0.683227i	$-0.760576\pi$
$863$		−	40.1421i		−	1.36645i	0.730206	−	0.683227i	$-0.239424\pi$
$864$	22.0711	−	6.24264i	0.750873	−	0.212379i
$865$			10.1421i			0.344843i
$866$	14.4264			0.490229
$867$	29.6274	+	41.8995i	1.00620	+	1.42298i
$868$		−	1.51472i		−	0.0514129i
$869$	12.0000	−	5.65685i	0.407072	−	0.191896i
$870$	3.31371	−	2.34315i	0.112345	−	0.0794401i
$871$		0			0
$872$		−	15.3137i		−	0.518588i
$873$	5.17157	−	14.6274i	0.175031	−	0.495063i
$874$	0.284271			0.00961562
$875$	−1.00000			−0.0338062
$876$	−31.0294	+	21.9411i	−1.04839	+	0.741322i
$877$			29.7990i			1.00624i	0.864216	+	0.503120i	$0.167815\pi$
$877$			29.7990i			1.00624i	−0.864216	+	0.503120i	$0.832185\pi$
$878$			8.05887i			0.271974i
$879$	18.8284	+	26.6274i	0.635067	+	0.898120i
$880$	−9.00000	+	4.24264i	−0.303390	+	0.143019i
$881$		−	24.3431i		−	0.820141i	−0.912054	−	0.410071i	$-0.865504\pi$
$881$		−	24.3431i		−	0.820141i	0.912054	−	0.410071i	$-0.134496\pi$
$882$	−0.414214	+	1.17157i	−0.0139473	+	0.0394489i
$883$	17.1127			0.575888			0.287944	−	0.957647i	$-0.407028\pi$
$883$	17.1127			0.575888			0.287944	+	0.957647i	$0.407028\pi$
$884$		0			0
$885$	0.343146	+	0.485281i	0.0115347	+	0.0163126i
$886$			15.6569i			0.526002i
$887$	36.6863			1.23181			0.615903	−	0.787822i	$-0.288791\pi$
$887$	36.6863			1.23181			0.615903	+	0.787822i	$0.288791\pi$
$888$	9.51472	+	13.4558i	0.319293	+	0.451549i
$889$	−13.6569			−0.458036
$890$	3.17157			0.106311
$891$	−7.07107	+	29.0000i	−0.236890	+	0.971537i
$892$	27.3726			0.916502
$893$	−8.97056			−0.300188
$894$	3.02944	+	4.28427i	0.101320	+	0.143287i
$895$	11.6569			0.389646
$896$			10.5563i			0.352663i
$897$		0			0
$898$			2.62742i			0.0876780i
$899$	−4.68629			−0.156297
$900$	−1.82843	+	5.17157i	−0.0609476	+	0.172386i
$901$			5.65685i			0.188457i
$902$	−4.48528	−	9.51472i	−0.149344	−	0.316805i
$903$	9.65685	+	13.6569i	0.321360	+	0.454472i
$904$		−	5.02944i		−	0.167277i
$905$			2.00000i			0.0664822i
$906$	−1.94113	+	1.37258i	−0.0644896	+	0.0456010i
$907$	−12.8284			−0.425961			−0.212980	−	0.977056i	$-0.568317\pi$
$907$	−12.8284			−0.425961			−0.212980	+	0.977056i	$0.568317\pi$
$908$	26.2254			0.870320
$909$	−9.31371	+	26.3431i	−0.308916	+	0.873747i
$910$		0			0
$911$		−	12.6274i		−	0.418365i	−0.977877	−	0.209182i	$-0.932920\pi$
$911$		−	12.6274i		−	0.418365i	0.977877	−	0.209182i	$-0.0670803\pi$
$912$	3.51472	−	2.48528i	0.116384	−	0.0822959i
$913$	16.9706	+	36.0000i	0.561644	+	1.19143i
$914$			10.9706i			0.362874i
$915$	5.17157	+	7.31371i	0.170967	+	0.241784i
$916$	17.0294			0.562668
$917$			17.6569i			0.583081i
$918$	−14.1421	+	4.00000i	−0.466760	+	0.132020i
$919$			58.9117i			1.94332i	0.236388	+	0.971659i	$0.424036\pi$
$919$			58.9117i			1.94332i	−0.236388	+	0.971659i	$0.575964\pi$
$920$	−1.31371			−0.0433117
$921$	12.6863	−	8.97056i	0.418028	−	0.295590i
$922$	−5.11270			−0.168378
$923$		0			0
$924$	−9.14214	−	5.17157i	−0.300754	−	0.170132i
$925$	−6.00000			−0.197279
$926$	16.3431			0.537069
$927$	−9.31371	+	26.3431i	−0.305902	+	0.865222i
$928$	24.9706			0.819699
$929$		−	31.6569i		−	1.03863i	−0.854584	−	0.519314i	$-0.826188\pi$
$929$		−	31.6569i		−	1.03863i	0.854584	−	0.519314i	$-0.173812\pi$
$930$	−0.485281	+	0.343146i	−0.0159130	+	0.0112522i
$931$			0.828427i			0.0271506i
$932$	−21.5736			−0.706667
$933$	−34.8284	+	24.6274i	−1.14023	+	0.806265i
$934$			0.485281i			0.0158789i
$935$	20.4853	−	9.65685i	0.669940	−	0.315813i
$936$		0			0
$937$			12.9706i			0.423730i	0.977299	+	0.211865i	$0.0679537\pi$
$937$			12.9706i			0.423730i	−0.977299	+	0.211865i	$0.932046\pi$
$938$			2.68629i			0.0877105i
$939$	13.1716	+	18.6274i	0.429838	+	0.607883i
$940$	19.7990			0.645772
$941$	−22.9706			−0.748819			−0.374409	−	0.927263i	$-0.622155\pi$
$941$	−22.9706			−0.748819			−0.374409	+	0.927263i	$0.622155\pi$
$942$	7.79899	+	11.0294i	0.254105	+	0.359358i
$943$			6.34315i			0.206561i
$944$			1.02944i			0.0335053i
$945$	−5.00000	+	1.41421i	−0.162650	+	0.0460044i
$946$	12.0000	−	5.65685i	0.390154	−	0.183920i
$947$			47.1716i			1.53287i	0.642322	+	0.766435i	$0.277971\pi$
$947$			47.1716i			1.53287i	−0.642322	+	0.766435i	$0.722029\pi$
$948$	10.3431	−	7.31371i	0.335930	−	0.237538i
$949$		0			0
$950$		−	0.343146i		−	0.0111331i
$951$	40.7696	−	28.8284i	1.32204	−	0.934826i
$952$		−	10.8284i		−	0.350951i
$953$	37.1716			1.20411			0.602053	−	0.798456i	$-0.294350\pi$
$953$	37.1716			1.20411			0.602053	+	0.798456i	$0.294350\pi$
$954$	−0.970563	−	0.343146i	−0.0314231	−	0.0111098i
$955$	−6.00000			−0.194155
$956$	−5.17157			−0.167261
$957$	−16.0000	+	28.2843i	−0.517207	+	0.914301i
$958$	4.68629			0.151407
$959$	−12.8284			−0.414252
$960$	−5.89949	+	4.17157i	−0.190405	+	0.134637i
$961$	−30.3137			−0.977862
$962$		0			0
$963$	9.31371	−	26.3431i	0.300130	−	0.848896i
$964$			41.7401i			1.34436i
$965$	22.4853			0.723827
$966$	−0.343146	−	0.485281i	−0.0110405	−	0.0156137i
$967$		−	12.2843i		−	0.395036i	−0.980299	−	0.197518i	$-0.936712\pi$
$967$		−	12.2843i		−	0.395036i	0.980299	−	0.197518i	$-0.0632880\pi$
$968$	−11.1005	+	13.4558i	−0.356784	+	0.432487i
$969$	−8.00000	+	5.65685i	−0.256997	+	0.181724i
$970$		−	2.14214i		−	0.0687798i
$971$		−	30.2843i		−	0.971869i	−0.873995	−	0.485934i	$-0.838479\pi$
$971$		−	30.2843i		−	0.971869i	0.873995	−	0.485934i	$-0.161521\pi$
$972$	−1.82843	+	28.4437i	−0.0586468	+	0.912331i
$973$	−6.48528			−0.207909
$974$	−10.9706			−0.351520
$975$		0			0
$976$			15.5147i			0.496614i
$977$			7.17157i			0.229439i	0.993398	+	0.114719i	$0.0365969\pi$
$977$			7.17157i			0.229439i	−0.993398	+	0.114719i	$0.963403\pi$
$978$	0.627417	+	0.887302i	0.0200626	+	0.0283728i
$979$	−22.9706	+	10.8284i	−0.734142	+	0.346078i
$980$		−	1.82843i		−	0.0584070i
$981$	27.3137	+	9.65685i	0.872060	+	0.308320i
$982$	−7.51472			−0.239804
$983$		−	2.82843i		−	0.0902128i	−0.998982	−	0.0451064i	$-0.985637\pi$
$983$		−	2.82843i		−	0.0902128i	0.998982	−	0.0451064i	$-0.0143627\pi$
$984$	−12.1421	−	17.1716i	−0.387077	−	0.547410i
$985$			14.8284i			0.472473i
$986$	−16.0000			−0.509544
$987$	10.8284	+	15.3137i	0.344673	+	0.487441i
$988$		0			0
$989$	−8.00000			−0.254385
$990$	0.414214	+	4.10051i	0.0131646	+	0.130323i
$991$	45.6569			1.45034			0.725169	−	0.688571i	$-0.241762\pi$
$991$	45.6569			1.45034			0.725169	+	0.688571i	$0.241762\pi$
$992$	−3.65685			−0.116105
$993$	−10.3431	−	14.6274i	−0.328230	−	0.464187i
$994$	−0.142136			−0.00450827
$995$			14.4853i			0.459214i
$996$	21.9411	+	31.0294i	0.695231	+	0.983205i
$997$		−	44.2843i		−	1.40250i	−0.712917	−	0.701248i	$-0.752626\pi$
$997$		−	44.2843i		−	1.40250i	0.712917	−	0.701248i	$-0.247374\pi$
$998$	−14.9117			−0.472021
$999$	−30.0000	+	8.48528i	−0.949158	+	0.268462i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.a.1121.3	✓	4	3.2	odd	2
1155.2.l.a.1121.4	yes	4	11.10	odd	2
1155.2.l.d.1121.1	yes	4	33.32	even	2	inner
1155.2.l.d.1121.2	yes	4	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-0.414214 q^{2} +(1.00000 + 1.41421i) q^{3} -1.82843 q^{4} -1.00000i q^{5} +(-0.414214 - 0.585786i) q^{6} +1.00000i q^{7} +1.58579 q^{8} +(-1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q-0.414214 q^{2} +(1.00000 + 1.41421i) q^{3} -1.82843 q^{4} -1.00000i q^{5} +(-0.414214 - 0.585786i) q^{6} +1.00000i q^{7} +1.58579 q^{8} +(-1.00000 + 2.82843i) q^{9} +0.414214i q^{10} +(-1.41421 - 3.00000i) q^{11} +(-1.82843 - 2.58579i) q^{12} -0.414214i q^{14} +(1.41421 - 1.00000i) q^{15} +3.00000 q^{16} -6.82843 q^{17} +(0.414214 - 1.17157i) q^{18} -0.828427i q^{19} +1.82843i q^{20} +(-1.41421 + 1.00000i) q^{21} +(0.585786 + 1.24264i) q^{22} -0.828427i q^{23} +(1.58579 + 2.24264i) q^{24} -1.00000 q^{25} +(-5.00000 + 1.41421i) q^{27} -1.82843i q^{28} -5.65685 q^{29} +(-0.585786 + 0.414214i) q^{30} +0.828427 q^{31} -4.41421 q^{32} +(2.82843 - 5.00000i) q^{33} +2.82843 q^{34} +1.00000 q^{35} +(1.82843 - 5.17157i) q^{36} +6.00000 q^{37} +0.343146i q^{38} -1.58579i q^{40} -7.65685 q^{41} +(0.585786 - 0.414214i) q^{42} -9.65685i q^{43} +(2.58579 + 5.48528i) q^{44} +(2.82843 + 1.00000i) q^{45} +0.343146i q^{46} -10.8284i q^{47} +(3.00000 + 4.24264i) q^{48} -1.00000 q^{49} +0.414214 q^{50} +(-6.82843 - 9.65685i) q^{51} -0.828427i q^{53} +(2.07107 - 0.585786i) q^{54} +(-3.00000 + 1.41421i) q^{55} +1.58579i q^{56} +(1.17157 - 0.828427i) q^{57} +2.34315 q^{58} +0.343146i q^{59} +(-2.58579 + 1.82843i) q^{60} +5.17157i q^{61} -0.343146 q^{62} +(-2.82843 - 1.00000i) q^{63} -4.17157 q^{64} +(-1.17157 + 2.07107i) q^{66} -6.48528 q^{67} +12.4853 q^{68} +(1.17157 - 0.828427i) q^{69} -0.414214 q^{70} -0.343146i q^{71} +(-1.58579 + 4.48528i) q^{72} -12.0000i q^{73} -2.48528 q^{74} +(-1.00000 - 1.41421i) q^{75} +1.51472i q^{76} +(3.00000 - 1.41421i) q^{77} +4.00000i q^{79} -3.00000i q^{80} +(-7.00000 - 5.65685i) q^{81} +3.17157 q^{82} -12.0000 q^{83} +(2.58579 - 1.82843i) q^{84} +6.82843i q^{85} +4.00000i q^{86} +(-5.65685 - 8.00000i) q^{87} +(-2.24264 - 4.75736i) q^{88} -7.65685i q^{89} +(-1.17157 - 0.414214i) q^{90} +1.51472i q^{92} +(0.828427 + 1.17157i) q^{93} +4.48528i q^{94} -0.828427 q^{95} +(-4.41421 - 6.24264i) q^{96} -5.17157 q^{97} +0.414214 q^{98} +(9.89949 - 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 12 q^{8} - 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 12 * q^8 - 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{6} + 12 q^{8} - 4 q^{9} + 4 q^{12} + 12 q^{16} - 16 q^{17} - 4 q^{18} + 8 q^{22} + 12 q^{24} - 4 q^{25} - 20 q^{27} - 8 q^{30} - 8 q^{31} - 12 q^{32} + 4 q^{35} - 4 q^{36} + 24 q^{37} - 8 q^{41} + 8 q^{42} + 16 q^{44} + 12 q^{48} - 4 q^{49} - 4 q^{50} - 16 q^{51} - 20 q^{54} - 12 q^{55} + 16 q^{57} + 32 q^{58} - 16 q^{60} - 24 q^{62} - 28 q^{64} - 16 q^{66} + 8 q^{67} + 16 q^{68} + 16 q^{69} + 4 q^{70} - 12 q^{72} + 24 q^{74} - 4 q^{75} + 12 q^{77} - 28 q^{81} + 24 q^{82} - 48 q^{83} + 16 q^{84} + 8 q^{88} - 16 q^{90} - 8 q^{93} + 8 q^{95} - 12 q^{96} - 32 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^6 + 12 * q^8 - 4 * q^9 + 4 * q^12 + 12 * q^16 - 16 * q^17 - 4 * q^18 + 8 * q^22 + 12 * q^24 - 4 * q^25 - 20 * q^27 - 8 * q^30 - 8 * q^31 - 12 * q^32 + 4 * q^35 - 4 * q^36 + 24 * q^37 - 8 * q^41 + 8 * q^42 + 16 * q^44 + 12 * q^48 - 4 * q^49 - 4 * q^50 - 16 * q^51 - 20 * q^54 - 12 * q^55 + 16 * q^57 + 32 * q^58 - 16 * q^60 - 24 * q^62 - 28 * q^64 - 16 * q^66 + 8 * q^67 + 16 * q^68 + 16 * q^69 + 4 * q^70 - 12 * q^72 + 24 * q^74 - 4 * q^75 + 12 * q^77 - 28 * q^81 + 24 * q^82 - 48 * q^83 + 16 * q^84 + 8 * q^88 - 16 * q^90 - 8 * q^93 + 8 * q^95 - 12 * q^96 - 32 * q^97 - 4 * q^98

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