LMFDB - Embedded newform 1083.2.d.b.1082.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1083,2,Mod(1082,1083)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1083, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1083.1082");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1083 = 3 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1083.d (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:	$8.64779853890$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 57)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1082.7
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	1083.1082
Dual form			1083.2.d.b.1082.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.93185 q^{2} +(-1.41421 - 1.00000i) q^{3} +1.73205 q^{4} -1.41421i q^{5} +(-2.73205 - 1.93185i) q^{6} -3.73205 q^{7} -0.517638 q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+1.93185 q^{2} +(-1.41421 - 1.00000i) q^{3} +1.73205 q^{4} -1.41421i q^{5} +(-2.73205 - 1.93185i) q^{6} -3.73205 q^{7} -0.517638 q^{8} +(1.00000 + 2.82843i) q^{9} -2.73205i q^{10} -0.378937i q^{11} +(-2.44949 - 1.73205i) q^{12} +3.73205i q^{13} -7.20977 q^{14} +(-1.41421 + 2.00000i) q^{15} -4.46410 q^{16} +4.89898i q^{17} +(1.93185 + 5.46410i) q^{18} -2.44949i q^{20} +(5.27792 + 3.73205i) q^{21} -0.732051i q^{22} -0.378937i q^{23} +(0.732051 + 0.517638i) q^{24} +3.00000 q^{25} +7.20977i q^{26} +(1.41421 - 5.00000i) q^{27} -6.46410 q^{28} -7.72741 q^{29} +(-2.73205 + 3.86370i) q^{30} +4.46410i q^{31} -7.58871 q^{32} +(-0.378937 + 0.535898i) q^{33} +9.46410i q^{34} +5.27792i q^{35} +(1.73205 + 4.89898i) q^{36} +4.26795i q^{37} +(3.73205 - 5.27792i) q^{39} +0.732051i q^{40} -5.65685 q^{41} +(10.1962 + 7.20977i) q^{42} +2.26795 q^{43} -0.656339i q^{44} +(4.00000 - 1.41421i) q^{45} -0.732051i q^{46} -10.5558i q^{47} +(6.31319 + 4.46410i) q^{48} +6.92820 q^{49} +5.79555 q^{50} +(4.89898 - 6.92820i) q^{51} +6.46410i q^{52} -6.03579 q^{53} +(2.73205 - 9.65926i) q^{54} -0.535898 q^{55} +1.93185 q^{56} -14.9282 q^{58} -8.38375 q^{59} +(-2.44949 + 3.46410i) q^{60} -3.53590 q^{61} +8.62398i q^{62} +(-3.73205 - 10.5558i) q^{63} -5.73205 q^{64} +5.27792 q^{65} +(-0.732051 + 1.03528i) q^{66} +1.00000i q^{67} +8.48528i q^{68} +(-0.378937 + 0.535898i) q^{69} +10.1962i q^{70} -3.58630 q^{71} +(-0.517638 - 1.46410i) q^{72} -3.00000 q^{73} +8.24504i q^{74} +(-4.24264 - 3.00000i) q^{75} +1.41421i q^{77} +(7.20977 - 10.1962i) q^{78} +3.53590i q^{79} +6.31319i q^{80} +(-7.00000 + 5.65685i) q^{81} -10.9282 q^{82} -7.72741i q^{83} +(9.14162 + 6.46410i) q^{84} +6.92820 q^{85} +4.38134 q^{86} +(10.9282 + 7.72741i) q^{87} +0.196152i q^{88} -7.34847 q^{89} +(7.72741 - 2.73205i) q^{90} -13.9282i q^{91} -0.656339i q^{92} +(4.46410 - 6.31319i) q^{93} -20.3923i q^{94} +(10.7321 + 7.58871i) q^{96} -7.46410i q^{97} +13.3843 q^{98} +(1.07180 - 0.378937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{6} - 16 q^{7} + 8 q^{9}+O(q^{10}) $ 8 * q - 8 * q^6 - 16 * q^7 + 8 * q^9	$ 8 q - 8 q^{6} - 16 q^{7} + 8 q^{9} - 8 q^{16} - 8 q^{24} + 24 q^{25} - 24 q^{28} - 8 q^{30} + 16 q^{39} + 40 q^{42} + 32 q^{43} + 32 q^{45} + 8 q^{54} - 32 q^{55} - 64 q^{58} - 56 q^{61} - 16 q^{63} - 32 q^{64} + 8 q^{66} - 24 q^{73} - 56 q^{81} - 32 q^{82} + 32 q^{87} + 8 q^{93} + 72 q^{96} + 64 q^{99}+O(q^{100}) $ 8 * q - 8 * q^6 - 16 * q^7 + 8 * q^9 - 8 * q^16 - 8 * q^24 + 24 * q^25 - 24 * q^28 - 8 * q^30 + 16 * q^39 + 40 * q^42 + 32 * q^43 + 32 * q^45 + 8 * q^54 - 32 * q^55 - 64 * q^58 - 56 * q^61 - 16 * q^63 - 32 * q^64 + 8 * q^66 - 24 * q^73 - 56 * q^81 - 32 * q^82 + 32 * q^87 + 8 * q^93 + 72 * q^96 + 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1083\mathbb{Z}\right)^\times$.

$n$	$362$	$724$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.93185			1.36603			0.683013	−	0.730406i	$-0.260669\pi$
$2$	1.93185			1.36603			0.683013	+	0.730406i	$0.260669\pi$
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$3$	−1.41421	−	1.00000i	−0.816497	−	0.577350i
$4$	1.73205			0.866025
$5$		−	1.41421i		−	0.632456i	−0.948683	−	0.316228i	$-0.897584\pi$
$5$		−	1.41421i		−	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$6$	−2.73205	−	1.93185i	−1.11536	−	0.788675i
$7$	−3.73205			−1.41058			−0.705291	−	0.708918i	$-0.749184\pi$
$7$	−3.73205			−1.41058			−0.705291	+	0.708918i	$0.749184\pi$
$8$	−0.517638			−0.183013
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$		−	2.73205i		−	0.863950i
$11$		−	0.378937i		−	0.114254i	−0.998367	−	0.0571270i	$-0.981806\pi$
$11$		−	0.378937i		−	0.114254i	0.998367	−	0.0571270i	$-0.0181940\pi$
$12$	−2.44949	−	1.73205i	−0.707107	−	0.500000i
$13$			3.73205i			1.03508i	0.855658	+	0.517542i	$0.173153\pi$
$13$			3.73205i			1.03508i	−0.855658	+	0.517542i	$0.826847\pi$
$14$	−7.20977			−1.92689
$15$	−1.41421	+	2.00000i	−0.365148	+	0.516398i
$16$	−4.46410			−1.11603
$17$			4.89898i			1.18818i	0.804400	+	0.594089i	$0.202487\pi$
$17$			4.89898i			1.18818i	−0.804400	+	0.594089i	$0.797513\pi$
$18$	1.93185	+	5.46410i	0.455342	+	1.28790i
$19$		0			0
$19$		0			0
$20$		−	2.44949i		−	0.547723i
$21$	5.27792	+	3.73205i	1.15174	+	0.814400i
$22$		−	0.732051i		−	0.156074i
$23$		−	0.378937i		−	0.0790139i	−0.999219	−	0.0395070i	$-0.987421\pi$
$23$		−	0.378937i		−	0.0790139i	0.999219	−	0.0395070i	$-0.0125787\pi$
$24$	0.732051	+	0.517638i	0.149429	+	0.105662i
$25$	3.00000			0.600000
$26$			7.20977i			1.41395i
$27$	1.41421	−	5.00000i	0.272166	−	0.962250i
$28$	−6.46410			−1.22160
$29$	−7.72741			−1.43494			−0.717472	−	0.696588i	$-0.754701\pi$
$29$	−7.72741			−1.43494			−0.717472	+	0.696588i	$0.754701\pi$
$30$	−2.73205	+	3.86370i	−0.498802	+	0.705412i
$31$			4.46410i			0.801776i	0.916127	+	0.400888i	$0.131298\pi$
$31$			4.46410i			0.801776i	−0.916127	+	0.400888i	$0.868702\pi$
$32$	−7.58871			−1.34151
$33$	−0.378937	+	0.535898i	−0.0659645	+	0.0932879i
$34$			9.46410i			1.62308i
$35$			5.27792i			0.892131i
$36$	1.73205	+	4.89898i	0.288675	+	0.816497i
$37$			4.26795i			0.701647i	0.936442	+	0.350823i	$0.114098\pi$
$37$			4.26795i			0.701647i	−0.936442	+	0.350823i	$0.885902\pi$
$38$		0			0
$39$	3.73205	−	5.27792i	0.597606	−	0.845143i
$40$			0.732051i			0.115747i
$41$	−5.65685			−0.883452			−0.441726	−	0.897150i	$-0.645634\pi$
$41$	−5.65685			−0.883452			−0.441726	+	0.897150i	$0.645634\pi$
$42$	10.1962	+	7.20977i	1.57330	+	1.11249i
$43$	2.26795			0.345859			0.172930	−	0.984934i	$-0.444677\pi$
$43$	2.26795			0.345859			0.172930	+	0.984934i	$0.444677\pi$
$44$		−	0.656339i		−	0.0989468i
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$		−	0.732051i		−	0.107935i
$47$		−	10.5558i		−	1.53973i	−0.638209	−	0.769863i	$-0.720324\pi$
$47$		−	10.5558i		−	1.53973i	0.638209	−	0.769863i	$-0.279676\pi$
$48$	6.31319	+	4.46410i	0.911231	+	0.644338i
$49$	6.92820			0.989743
$50$	5.79555			0.819615
$51$	4.89898	−	6.92820i	0.685994	−	0.970143i
$52$			6.46410i			0.896410i
$53$	−6.03579			−0.829080			−0.414540	−	0.910031i	$-0.636057\pi$
$53$	−6.03579			−0.829080			−0.414540	+	0.910031i	$0.636057\pi$
$54$	2.73205	−	9.65926i	0.371785	−	1.31446i
$55$	−0.535898			−0.0722605
$56$	1.93185			0.258155
$57$		0			0
$58$	−14.9282			−1.96017
$59$	−8.38375			−1.09147			−0.545735	−	0.837958i	$-0.683750\pi$
$59$	−8.38375			−1.09147			−0.545735	+	0.837958i	$0.683750\pi$
$60$	−2.44949	+	3.46410i	−0.316228	+	0.447214i
$61$	−3.53590			−0.452725			−0.226363	−	0.974043i	$-0.572683\pi$
$61$	−3.53590			−0.452725			−0.226363	+	0.974043i	$0.572683\pi$
$62$			8.62398i			1.09525i
$63$	−3.73205	−	10.5558i	−0.470194	−	1.32991i
$64$	−5.73205			−0.716506
$65$	5.27792			0.654645
$66$	−0.732051	+	1.03528i	−0.0901092	+	0.127434i
$67$			1.00000i			0.122169i	0.998133	+	0.0610847i	$0.0194560\pi$
$67$			1.00000i			0.122169i	−0.998133	+	0.0610847i	$0.980544\pi$
$68$			8.48528i			1.02899i
$69$	−0.378937	+	0.535898i	−0.0456187	+	0.0645146i
$70$			10.1962i			1.21867i
$71$	−3.58630			−0.425616			−0.212808	−	0.977094i	$-0.568261\pi$
$71$	−3.58630			−0.425616			−0.212808	+	0.977094i	$0.568261\pi$
$72$	−0.517638	−	1.46410i	−0.0610042	−	0.172546i
$73$	−3.00000			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$74$			8.24504i			0.958467i
$75$	−4.24264	−	3.00000i	−0.489898	−	0.346410i
$76$		0			0
$77$			1.41421i			0.161165i
$78$	7.20977	−	10.1962i	0.816346	−	1.15449i
$79$			3.53590i			0.397820i	0.980018	+	0.198910i	$0.0637401\pi$
$79$			3.53590i			0.397820i	−0.980018	+	0.198910i	$0.936260\pi$
$80$			6.31319i			0.705836i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	−10.9282			−1.20682
$83$		−	7.72741i		−	0.848193i	−0.905617	−	0.424097i	$-0.860592\pi$
$83$		−	7.72741i		−	0.848193i	0.905617	−	0.424097i	$-0.139408\pi$
$84$	9.14162	+	6.46410i	0.997433	+	0.705291i
$85$	6.92820			0.751469
$86$	4.38134			0.472452
$87$	10.9282	+	7.72741i	1.17163	+	0.828465i
$88$			0.196152i			0.0209099i
$89$	−7.34847			−0.778936			−0.389468	−	0.921040i	$-0.627341\pi$
$89$	−7.34847			−0.778936			−0.389468	+	0.921040i	$0.627341\pi$
$90$	7.72741	−	2.73205i	0.814540	−	0.287983i
$91$		−	13.9282i		−	1.46007i
$92$		−	0.656339i		−	0.0684280i
$93$	4.46410	−	6.31319i	0.462906	−	0.654648i
$94$		−	20.3923i		−	2.10331i
$95$		0			0
$96$	10.7321	+	7.58871i	1.09534	+	0.774519i
$97$		−	7.46410i		−	0.757865i	−0.925424	−	0.378932i	$-0.876291\pi$
$97$		−	7.46410i		−	0.757865i	0.925424	−	0.378932i	$-0.123709\pi$
$98$	13.3843			1.35201
$99$	1.07180	−	0.378937i	0.107720	−	0.0380846i
$100$	5.19615			0.519615
$101$			7.72741i			0.768906i	0.923145	+	0.384453i	$0.125610\pi$
$101$			7.72741i			0.768906i	−0.923145	+	0.384453i	$0.874390\pi$
$102$	9.46410	−	13.3843i	0.937086	−	1.32524i
$103$		−	10.4641i		−	1.03106i	−0.856872	−	0.515529i	$-0.827595\pi$
$103$		−	10.4641i		−	1.03106i	0.856872	−	0.515529i	$-0.172405\pi$
$104$		−	1.93185i		−	0.189434i
$105$	5.27792	−	7.46410i	0.515072	−	0.728422i
$106$	−11.6603			−1.13254
$107$	4.89898			0.473602			0.236801	−	0.971558i	$-0.423901\pi$
$107$	4.89898			0.473602			0.236801	+	0.971558i	$0.423901\pi$
$108$	2.44949	−	8.66025i	0.235702	−	0.833333i
$109$			14.3923i			1.37853i	0.724508	+	0.689266i	$0.242067\pi$
$109$			14.3923i			1.37853i	−0.724508	+	0.689266i	$0.757933\pi$
$110$	−1.03528			−0.0987097
$111$	4.26795	−	6.03579i	0.405096	−	0.572892i
$112$	16.6603			1.57425
$113$	−18.6622			−1.75559			−0.877795	−	0.479036i	$-0.840986\pi$
$113$	−18.6622			−1.75559			−0.877795	+	0.479036i	$0.840986\pi$
$114$		0			0
$115$	−0.535898			−0.0499728
$116$	−13.3843			−1.24270
$117$	−10.5558	+	3.73205i	−0.975887	+	0.345028i
$118$	−16.1962			−1.49098
$119$		−	18.2832i		−	1.67602i
$120$	0.732051	−	1.03528i	0.0668268	−	0.0945074i
$121$	10.8564			0.986946
$122$	−6.83083			−0.618434
$123$	8.00000	+	5.65685i	0.721336	+	0.510061i
$124$			7.73205i			0.694359i
$125$		−	11.3137i		−	1.01193i
$126$	−7.20977	−	20.3923i	−0.642297	−	1.81669i
$127$			7.85641i			0.697143i	0.937282	+	0.348572i	$0.113333\pi$
$127$			7.85641i			0.697143i	−0.937282	+	0.348572i	$0.886667\pi$
$128$	4.10394			0.362740
$129$	−3.20736	−	2.26795i	−0.282393	−	0.199682i
$130$	10.1962			0.894262
$131$		−	6.96953i		−	0.608931i	−0.952523	−	0.304465i	$-0.901522\pi$
$131$		−	6.96953i		−	0.608931i	0.952523	−	0.304465i	$-0.0984778\pi$
$132$	−0.656339	+	0.928203i	−0.0571270	+	0.0807897i
$133$		0			0
$134$			1.93185i			0.166887i
$135$	−7.07107	−	2.00000i	−0.608581	−	0.172133i
$136$		−	2.53590i		−	0.217451i
$137$			0.757875i			0.0647496i	0.999476	+	0.0323748i	$0.0103070\pi$
$137$			0.757875i			0.0647496i	−0.999476	+	0.0323748i	$0.989693\pi$
$138$	−0.732051	+	1.03528i	−0.0623163	+	0.0881286i
$139$	13.1962			1.11928			0.559642	−	0.828735i	$-0.310939\pi$
$139$	13.1962			1.11928			0.559642	+	0.828735i	$0.310939\pi$
$140$			9.14162i			0.772608i
$141$	−10.5558	+	14.9282i	−0.888962	+	1.25718i
$142$	−6.92820			−0.581402
$143$	1.41421			0.118262
$144$	−4.46410	−	12.6264i	−0.372008	−	1.05220i
$145$			10.9282i			0.907538i
$146$	−5.79555			−0.479644
$147$	−9.79796	−	6.92820i	−0.808122	−	0.571429i
$148$			7.39230i			0.607644i
$149$			16.8690i			1.38196i	0.722872	+	0.690982i	$0.242822\pi$
$149$			16.8690i			1.38196i	−0.722872	+	0.690982i	$0.757178\pi$
$150$	−8.19615	−	5.79555i	−0.669213	−	0.473205i
$151$			2.00000i			0.162758i	0.996683	+	0.0813788i	$0.0259324\pi$
$151$			2.00000i			0.162758i	−0.996683	+	0.0813788i	$0.974068\pi$
$152$		0			0
$153$	−13.8564	+	4.89898i	−1.12022	+	0.396059i
$154$			2.73205i			0.220155i
$155$	6.31319			0.507088
$156$	6.46410	−	9.14162i	0.517542	−	0.731915i
$157$	3.53590			0.282195			0.141098	−	0.989996i	$-0.454937\pi$
$157$	3.53590			0.282195			0.141098	+	0.989996i	$0.454937\pi$
$158$			6.83083i			0.543432i
$159$	8.53590	+	6.03579i	0.676941	+	0.478669i
$160$			10.7321i			0.848443i
$161$			1.41421i			0.111456i
$162$	−13.5230	+	10.9282i	−1.06246	+	0.858601i
$163$	5.19615			0.406994			0.203497	−	0.979076i	$-0.434769\pi$
$163$	5.19615			0.406994			0.203497	+	0.979076i	$0.434769\pi$
$164$	−9.79796			−0.765092
$165$	0.757875	+	0.535898i	0.0590005	+	0.0417196i
$166$		−	14.9282i		−	1.15865i
$167$	−7.62587			−0.590108			−0.295054	−	0.955481i	$-0.595338\pi$
$167$	−7.62587			−0.590108			−0.295054	+	0.955481i	$0.595338\pi$
$168$	−2.73205	−	1.93185i	−0.210782	−	0.149046i
$169$	−0.928203			−0.0714002
$170$	13.3843			1.02653
$171$		0			0
$172$	3.92820			0.299523
$173$	11.8685			0.902346			0.451173	−	0.892436i	$-0.351006\pi$
$173$	11.8685			0.902346			0.451173	+	0.892436i	$0.351006\pi$
$174$	21.1117	+	14.9282i	1.60047	+	1.13170i
$175$	−11.1962			−0.846350
$176$			1.69161i			0.127510i
$177$	11.8564	+	8.38375i	0.891182	+	0.630161i
$178$	−14.1962			−1.06405
$179$	−1.41421			−0.105703			−0.0528516	−	0.998602i	$-0.516831\pi$
$179$	−1.41421			−0.105703			−0.0528516	+	0.998602i	$0.516831\pi$
$180$	6.92820	−	2.44949i	0.516398	−	0.182574i
$181$		−	3.46410i		−	0.257485i	−0.991678	−	0.128742i	$-0.958906\pi$
$181$		−	3.46410i		−	0.257485i	0.991678	−	0.128742i	$-0.0410940\pi$
$182$		−	26.9072i		−	1.99450i
$183$	5.00052	+	3.53590i	0.369649	+	0.261381i
$184$			0.196152i			0.0144605i
$185$	6.03579			0.443760
$186$	8.62398	−	12.1962i	0.632341	−	0.894265i
$187$	1.85641			0.135754
$188$		−	18.2832i		−	1.33344i
$189$	−5.27792	+	18.6603i	−0.383912	+	1.35733i
$190$		0			0
$191$			1.69161i			0.122401i	0.998125	+	0.0612005i	$0.0194929\pi$
$191$			1.69161i			0.122401i	−0.998125	+	0.0612005i	$0.980507\pi$
$192$	8.10634	+	5.73205i	0.585025	+	0.413675i
$193$		−	13.1962i		−	0.949880i	−0.880018	−	0.474940i	$-0.842470\pi$
$193$		−	13.1962i		−	0.949880i	0.880018	−	0.474940i	$-0.157530\pi$
$194$		−	14.4195i		−	1.03526i
$195$	−7.46410	−	5.27792i	−0.534515	−	0.377959i
$196$	12.0000			0.857143
$197$		−	9.14162i		−	0.651313i	−0.945488	−	0.325657i	$-0.894415\pi$
$197$		−	9.14162i		−	0.651313i	0.945488	−	0.325657i	$-0.105585\pi$
$198$	2.07055	−	0.732051i	0.147148	−	0.0520246i
$199$	−12.8038			−0.907641			−0.453820	−	0.891093i	$-0.649939\pi$
$199$	−12.8038			−0.907641			−0.453820	+	0.891093i	$0.649939\pi$
$200$	−1.55291			−0.109808
$201$	1.00000	−	1.41421i	0.0705346	−	0.0997509i
$202$			14.9282i			1.05034i
$203$	28.8391			2.02411
$204$	8.48528	−	12.0000i	0.594089	−	0.840168i
$205$			8.00000i			0.558744i
$206$		−	20.2151i		−	1.40845i
$207$	1.07180	−	0.378937i	0.0744950	−	0.0263380i
$208$		−	16.6603i		−	1.15518i
$209$		0			0
$210$	10.1962	−	14.4195i	0.703601	−	0.995043i
$211$			11.0000i			0.757271i	0.925546	+	0.378636i	$0.123607\pi$
$211$			11.0000i			0.757271i	−0.925546	+	0.378636i	$0.876393\pi$
$212$	−10.4543			−0.718004
$213$	5.07180	+	3.58630i	0.347514	+	0.245729i
$214$	9.46410			0.646953
$215$		−	3.20736i		−	0.218740i
$216$	−0.732051	+	2.58819i	−0.0498097	+	0.176104i
$217$		−	16.6603i		−	1.13097i
$218$			27.8038i			1.88311i
$219$	4.24264	+	3.00000i	0.286691	+	0.202721i
$220$	−0.928203			−0.0625794
$221$	−18.2832			−1.22986
$222$	8.24504	−	11.6603i	0.553371	−	0.782585i
$223$			9.39230i			0.628955i	0.949265	+	0.314478i	$0.101829\pi$
$223$			9.39230i			0.628955i	−0.949265	+	0.314478i	$0.898171\pi$
$224$	28.3214			1.89231
$225$	3.00000	+	8.48528i	0.200000	+	0.565685i
$226$	−36.0526			−2.39818
$227$	24.5964			1.63252			0.816261	−	0.577683i	$-0.196043\pi$
$227$	24.5964			1.63252			0.816261	+	0.577683i	$0.196043\pi$
$228$		0			0
$229$	9.39230			0.620661			0.310330	−	0.950629i	$-0.399560\pi$
$229$	9.39230			0.620661			0.310330	+	0.950629i	$0.399560\pi$
$230$	−1.03528			−0.0682641
$231$	1.41421	−	2.00000i	0.0930484	−	0.131590i
$232$	4.00000			0.262613
$233$			3.58630i			0.234946i	0.993076	+	0.117473i	$0.0374794\pi$
$233$			3.58630i			0.234946i	−0.993076	+	0.117473i	$0.962521\pi$
$234$	−20.3923	+	7.20977i	−1.33309	+	0.471317i
$235$	−14.9282			−0.973809
$236$	−14.5211			−0.945241
$237$	3.53590	−	5.00052i	0.229681	−	0.324818i
$238$		−	35.3205i		−	2.28949i
$239$			29.9759i			1.93898i	0.245133	+	0.969489i	$0.421168\pi$
$239$			29.9759i			1.93898i	−0.245133	+	0.969489i	$0.578832\pi$
$240$	6.31319	−	8.92820i	0.407515	−	0.576313i
$241$		−	28.6603i		−	1.84617i	−0.384597	−	0.923085i	$-0.625660\pi$
$241$		−	28.6603i		−	1.84617i	0.384597	−	0.923085i	$-0.374340\pi$
$242$	20.9730			1.34819
$243$	15.5563	−	1.00000i	0.997940	−	0.0641500i
$244$	−6.12436			−0.392072
$245$		−	9.79796i		−	0.625969i
$246$	15.4548	+	10.9282i	0.985363	+	0.696757i
$247$		0			0
$248$		−	2.31079i		−	0.146735i
$249$	−7.72741	+	10.9282i	−0.489704	+	0.692547i
$250$		−	21.8564i		−	1.38232i
$251$		−	14.6969i		−	0.927663i	−0.885924	−	0.463831i	$-0.846474\pi$
$251$		−	14.6969i		−	0.927663i	0.885924	−	0.463831i	$-0.153526\pi$
$252$	−6.46410	−	18.2832i	−0.407200	−	1.15174i
$253$	−0.143594			−0.00902765
$254$			15.1774i			0.952316i
$255$	−9.79796	−	6.92820i	−0.613572	−	0.433861i
$256$	19.3923			1.21202
$257$	−3.20736			−0.200070			−0.100035	−	0.994984i	$-0.531895\pi$
$257$	−3.20736			−0.200070			−0.100035	+	0.994984i	$0.531895\pi$
$258$	−6.19615	−	4.38134i	−0.385756	−	0.272770i
$259$		−	15.9282i		−	0.989730i
$260$	9.14162			0.566939
$261$	−7.72741	−	21.8564i	−0.478314	−	1.35288i
$262$		−	13.4641i		−	0.831815i
$263$			0.554803i			0.0342106i	0.999854	+	0.0171053i	$0.00544505\pi$
$263$			0.554803i			0.0342106i	−0.999854	+	0.0171053i	$0.994555\pi$
$264$	0.196152	−	0.277401i	0.0120723	−	0.0170729i
$265$			8.53590i			0.524356i
$266$		0			0
$267$	10.3923	+	7.34847i	0.635999	+	0.449719i
$268$			1.73205i			0.105802i
$269$	−6.03579			−0.368009			−0.184004	−	0.982925i	$-0.558906\pi$
$269$	−6.03579			−0.368009			−0.184004	+	0.982925i	$0.558906\pi$
$270$	−13.6603	−	3.86370i	−0.831337	−	0.235137i
$271$	−6.92820			−0.420858			−0.210429	−	0.977609i	$-0.567486\pi$
$271$	−6.92820			−0.420858			−0.210429	+	0.977609i	$0.567486\pi$
$272$		−	21.8695i		−	1.32604i
$273$	−13.9282	+	19.6975i	−0.842973	+	1.19214i
$274$			1.46410i			0.0884496i
$275$		−	1.13681i		−	0.0685524i
$276$	−0.656339	+	0.928203i	−0.0395070	+	0.0558713i
$277$	−9.85641			−0.592214			−0.296107	−	0.955155i	$-0.595689\pi$
$277$	−9.85641			−0.592214			−0.296107	+	0.955155i	$0.595689\pi$
$278$	25.4930			1.52897
$279$	−12.6264	+	4.46410i	−0.755922	+	0.267259i
$280$		−	2.73205i		−	0.163271i
$281$	15.0759			0.899351			0.449676	−	0.893192i	$-0.351540\pi$
$281$	15.0759			0.899351			0.449676	+	0.893192i	$0.351540\pi$
$282$	−20.3923	+	28.8391i	−1.21434	+	1.71734i
$283$	−21.8564			−1.29923			−0.649614	−	0.760264i	$-0.725070\pi$
$283$	−21.8564			−1.29923			−0.649614	+	0.760264i	$0.725070\pi$
$284$	−6.21166			−0.368594
$285$		0			0
$286$	2.73205			0.161550
$287$	21.1117			1.24618
$288$	−7.58871	−	21.4641i	−0.447169	−	1.26478i
$289$	−7.00000			−0.411765
$290$			21.1117i			1.23972i
$291$	−7.46410	+	10.5558i	−0.437553	+	0.618794i
$292$	−5.19615			−0.304082
$293$	25.2528			1.47528			0.737641	−	0.675193i	$-0.235940\pi$
$293$	25.2528			1.47528			0.737641	+	0.675193i	$0.235940\pi$
$294$	−18.9282	−	13.3843i	−1.10392	−	0.780586i
$295$			11.8564i			0.690307i
$296$		−	2.20925i		−	0.128410i
$297$	−1.89469	−	0.535898i	−0.109941	−	0.0310960i
$298$			32.5885i			1.88780i
$299$	1.41421			0.0817861
$300$	−7.34847	−	5.19615i	−0.424264	−	0.300000i
$301$	−8.46410			−0.487863
$302$			3.86370i			0.222331i
$303$	7.72741	−	10.9282i	0.443928	−	0.627809i
$304$		0			0
$305$			5.00052i			0.286329i
$306$	−26.7685	+	9.46410i	−1.53025	+	0.541027i
$307$			13.8564i			0.790827i	0.918503	+	0.395413i	$0.129399\pi$
$307$			13.8564i			0.790827i	−0.918503	+	0.395413i	$0.870601\pi$
$308$			2.44949i			0.139573i
$309$	−10.4641	+	14.7985i	−0.595282	+	0.841856i
$310$	12.1962			0.692695
$311$		−	27.1475i		−	1.53939i	−0.638411	−	0.769696i	$-0.720408\pi$
$311$		−	27.1475i		−	1.53939i	0.638411	−	0.769696i	$-0.279592\pi$
$312$	−1.93185	+	2.73205i	−0.109370	+	0.154672i
$313$	−24.7846			−1.40091			−0.700454	−	0.713697i	$-0.747019\pi$
$313$	−24.7846			−1.40091			−0.700454	+	0.713697i	$0.747019\pi$
$314$	6.83083			0.385486
$315$	−14.9282	+	5.27792i	−0.841109	+	0.297377i
$316$			6.12436i			0.344522i
$317$	13.7632			0.773018			0.386509	−	0.922286i	$-0.373681\pi$
$317$	13.7632			0.773018			0.386509	+	0.922286i	$0.373681\pi$
$318$	16.4901	+	11.6603i	0.924718	+	0.653875i
$319$			2.92820i			0.163948i
$320$			8.10634i			0.453158i
$321$	−6.92820	−	4.89898i	−0.386695	−	0.273434i
$322$			2.73205i			0.152251i
$323$		0			0
$324$	−12.1244	+	9.79796i	−0.673575	+	0.544331i
$325$			11.1962i			0.621051i
$326$	10.0382			0.555964
$327$	14.3923	−	20.3538i	0.795896	−	1.12557i
$328$	2.92820			0.161683
$329$			39.3949i			2.17191i
$330$	1.46410	+	1.03528i	0.0805961	+	0.0569901i
$331$			31.9282i			1.75493i	0.479638	+	0.877466i	$0.340768\pi$
$331$			31.9282i			1.75493i	−0.479638	+	0.877466i	$0.659232\pi$
$332$		−	13.3843i		−	0.734557i
$333$	−12.0716	+	4.26795i	−0.661519	+	0.233882i
$334$	−14.7321			−0.806102
$335$	1.41421			0.0772667
$336$	−23.5612	−	16.6603i	−1.28537	−	0.908891i
$337$		−	7.33975i		−	0.399821i	−0.979814	−	0.199911i	$-0.935935\pi$
$337$		−	7.33975i		−	0.399821i	0.979814	−	0.199911i	$-0.0640652\pi$
$338$	−1.79315			−0.0975346
$339$	26.3923	+	18.6622i	1.43343	+	1.01359i
$340$	12.0000			0.650791
$341$	1.69161			0.0916061
$342$		0			0
$343$	0.267949			0.0144679
$344$	−1.17398			−0.0632966
$345$	0.757875	+	0.535898i	0.0408026	+	0.0288518i
$346$	22.9282			1.23263
$347$		−	24.8738i		−	1.33530i	−0.744476	−	0.667649i	$-0.767301\pi$
$347$		−	24.8738i		−	1.33530i	0.744476	−	0.667649i	$-0.232699\pi$
$348$	18.9282	+	13.3843i	1.01466	+	0.717472i
$349$	−11.3923			−0.609816			−0.304908	−	0.952382i	$-0.598626\pi$
$349$	−11.3923			−0.609816			−0.304908	+	0.952382i	$0.598626\pi$
$350$	−21.6293			−1.15614
$351$	18.6603	+	5.27792i	0.996011	+	0.281714i
$352$			2.87564i			0.153272i
$353$			11.9700i			0.637101i	0.947906	+	0.318551i	$0.103196\pi$
$353$			11.9700i			0.637101i	−0.947906	+	0.318551i	$0.896804\pi$
$354$	22.9048	+	16.1962i	1.21738	+	0.860816i
$355$			5.07180i			0.269183i
$356$	−12.7279			−0.674579
$357$	−18.2832	+	25.8564i	−0.967652	+	1.36847i
$358$	−2.73205			−0.144393
$359$			26.7685i			1.41279i	0.707819	+	0.706394i	$0.249679\pi$
$359$			26.7685i			1.41279i	−0.707819	+	0.706394i	$0.750321\pi$
$360$	−2.07055	+	0.732051i	−0.109128	+	0.0385825i
$361$		0			0
$362$		−	6.69213i		−	0.351731i
$363$	−15.3533	−	10.8564i	−0.805838	−	0.569814i
$364$		−	24.1244i		−	1.26446i
$365$			4.24264i			0.222070i
$366$	9.66025	+	6.83083i	0.504950	+	0.357053i
$367$	−17.0526			−0.890136			−0.445068	−	0.895497i	$-0.646821\pi$
$367$	−17.0526			−0.890136			−0.445068	+	0.895497i	$0.646821\pi$
$368$			1.69161i			0.0881815i
$369$	−5.65685	−	16.0000i	−0.294484	−	0.832927i
$370$	11.6603			0.606188
$371$	22.5259			1.16949
$372$	7.73205	−	10.9348i	0.400888	−	0.566941i
$373$			12.5359i			0.649084i	0.945871	+	0.324542i	$0.105210\pi$
$373$			12.5359i			0.649084i	−0.945871	+	0.324542i	$0.894790\pi$
$374$	3.58630			0.185443
$375$	−11.3137	+	16.0000i	−0.584237	+	0.826236i
$376$			5.46410i			0.281790i
$377$		−	28.8391i		−	1.48529i
$378$	−10.1962	+	36.0488i	−0.524433	+	1.85415i
$379$			17.7846i			0.913534i	0.889586	+	0.456767i	$0.150993\pi$
$379$			17.7846i			0.913534i	−0.889586	+	0.456767i	$0.849007\pi$
$380$		0			0
$381$	7.85641	−	11.1106i	0.402496	−	0.569215i
$382$			3.26795i			0.167203i
$383$	−26.6670			−1.36262			−0.681310	−	0.731995i	$-0.738589\pi$
$383$	−26.6670			−1.36262			−0.681310	+	0.731995i	$0.738589\pi$
$384$	−5.80385	−	4.10394i	−0.296176	−	0.209428i
$385$	2.00000			0.101929
$386$		−	25.4930i		−	1.29756i
$387$	2.26795	+	6.41473i	0.115286	+	0.326079i
$388$		−	12.9282i		−	0.656330i
$389$			5.00052i			0.253536i	0.991932	+	0.126768i	$0.0404604\pi$
$389$			5.00052i			0.253536i	−0.991932	+	0.126768i	$0.959540\pi$
$390$	−14.4195	−	10.1962i	−0.730162	−	0.516302i
$391$	1.85641			0.0938825
$392$	−3.58630			−0.181136
$393$	−6.96953	+	9.85641i	−0.351566	+	0.497190i
$394$		−	17.6603i		−	0.889711i
$395$	5.00052			0.251603
$396$	1.85641	−	0.656339i	0.0932879	−	0.0329823i
$397$	8.32051			0.417594			0.208797	−	0.977959i	$-0.433045\pi$
$397$	8.32051			0.417594			0.208797	+	0.977959i	$0.433045\pi$
$398$	−24.7351			−1.23986
$399$		0			0
$400$	−13.3923			−0.669615
$401$	11.4896			0.573762			0.286881	−	0.957966i	$-0.407382\pi$
$401$	11.4896			0.573762			0.286881	+	0.957966i	$0.407382\pi$
$402$	1.93185	−	2.73205i	0.0963520	−	0.136262i
$403$	−16.6603			−0.829906
$404$			13.3843i			0.665892i
$405$	8.00000	+	9.89949i	0.397523	+	0.491910i
$406$	55.7128			2.76498
$407$	1.61729			0.0801659
$408$	−2.53590	+	3.58630i	−0.125546	+	0.177548i
$409$			28.2487i			1.39681i	0.715703	+	0.698404i	$0.246106\pi$
$409$			28.2487i			1.39681i	−0.715703	+	0.698404i	$0.753894\pi$
$410$			15.4548i			0.763259i
$411$	0.757875	−	1.07180i	0.0373832	−	0.0528678i
$412$		−	18.1244i		−	0.892923i
$413$	31.2886			1.53961
$414$	2.07055	−	0.732051i	0.101762	−	0.0359783i
$415$	−10.9282			−0.536444
$416$		−	28.3214i		−	1.38857i
$417$	−18.6622	−	13.1962i	−0.913891	−	0.646218i
$418$		0			0
$419$			32.0464i			1.56557i	0.622292	+	0.782785i	$0.286202\pi$
$419$			32.0464i			1.56557i	−0.622292	+	0.782785i	$0.713798\pi$
$420$	9.14162	−	12.9282i	0.446065	−	0.630832i
$421$			35.4641i			1.72841i	0.503136	+	0.864207i	$0.332179\pi$
$421$			35.4641i			1.72841i	−0.503136	+	0.864207i	$0.667821\pi$
$422$			21.2504i			1.03445i
$423$	29.8564	−	10.5558i	1.45167	−	0.513242i
$424$	3.12436			0.151732
$425$			14.6969i			0.712906i
$426$	9.79796	+	6.92820i	0.474713	+	0.335673i
$427$	13.1962			0.638607
$428$	8.48528			0.410152
$429$	−2.00000	−	1.41421i	−0.0965609	−	0.0682789i
$430$		−	6.19615i		−	0.298805i
$431$	−25.4558			−1.22616			−0.613082	−	0.790019i	$-0.710071\pi$
$431$	−25.4558			−1.22616			−0.613082	+	0.790019i	$0.710071\pi$
$432$	−6.31319	+	22.3205i	−0.303744	+	1.07390i
$433$			3.33975i			0.160498i	0.996775	+	0.0802490i	$0.0255715\pi$
$433$			3.33975i			0.160498i	−0.996775	+	0.0802490i	$0.974428\pi$
$434$		−	32.1851i		−	1.54494i
$435$	10.9282	−	15.4548i	0.523967	−	0.741002i
$436$			24.9282i			1.19384i
$437$		0			0
$438$	8.19615	+	5.79555i	0.391627	+	0.276922i
$439$		−	22.4641i		−	1.07215i	−0.844169	−	0.536077i	$-0.819906\pi$
$439$		−	22.4641i		−	1.07215i	0.844169	−	0.536077i	$-0.180094\pi$
$440$	0.277401			0.0132246
$441$	6.92820	+	19.5959i	0.329914	+	0.933139i
$442$	−35.3205			−1.68003
$443$		−	38.6370i		−	1.83570i	−0.396926	−	0.917850i	$-0.629923\pi$
$443$		−	38.6370i		−	1.83570i	0.396926	−	0.917850i	$-0.370077\pi$
$444$	7.39230	−	10.4543i	0.350823	−	0.496139i
$445$			10.3923i			0.492642i
$446$			18.1445i			0.859169i
$447$	16.8690	−	23.8564i	0.797878	−	1.12837i
$448$	21.3923			1.01069
$449$	−34.4959			−1.62796			−0.813982	−	0.580890i	$-0.802704\pi$
$449$	−34.4959			−1.62796			−0.813982	+	0.580890i	$0.802704\pi$
$450$	5.79555	+	16.3923i	0.273205	+	0.772741i
$451$			2.14359i			0.100938i
$452$	−32.3238			−1.52039
$453$	2.00000	−	2.82843i	0.0939682	−	0.132891i
$454$	47.5167			2.23007
$455$	−19.6975			−0.923431
$456$		0			0
$457$	−20.7128			−0.968905			−0.484452	−	0.874818i	$-0.660981\pi$
$457$	−20.7128			−0.968905			−0.484452	+	0.874818i	$0.660981\pi$
$458$	18.1445			0.847839
$459$	24.4949	+	6.92820i	1.14332	+	0.323381i
$460$	−0.928203			−0.0432777
$461$			32.8786i			1.53131i	0.643251	+	0.765656i	$0.277585\pi$
$461$			32.8786i			1.53131i	−0.643251	+	0.765656i	$0.722415\pi$
$462$	2.73205	−	3.86370i	0.127107	−	0.179756i
$463$	−29.5885			−1.37509			−0.687546	−	0.726141i	$-0.741312\pi$
$463$	−29.5885			−1.37509			−0.687546	+	0.726141i	$0.741312\pi$
$464$	34.4959			1.60143
$465$	−8.92820	−	6.31319i	−0.414036	−	0.292767i
$466$			6.92820i			0.320943i
$467$		−	22.6274i		−	1.04707i	−0.852004	−	0.523536i	$-0.824613\pi$
$467$		−	22.6274i		−	1.04707i	0.852004	−	0.523536i	$-0.175387\pi$
$468$	−18.2832	+	6.46410i	−0.845143	+	0.298803i
$469$		−	3.73205i		−	0.172330i
$470$	−28.8391			−1.33025
$471$	−5.00052	−	3.53590i	−0.230412	−	0.162926i
$472$	4.33975			0.199753
$473$		−	0.859411i		−	0.0395157i
$474$	6.83083	−	9.66025i	0.313750	−	0.443710i
$475$		0			0
$476$		−	31.6675i		−	1.45148i
$477$	−6.03579	−	17.0718i	−0.276360	−	0.781664i
$478$			57.9090i			2.64869i
$479$			11.8685i			0.542286i	0.962539	+	0.271143i	$0.0874017\pi$
$479$			11.8685i			0.542286i	−0.962539	+	0.271143i	$0.912598\pi$
$480$	10.7321	−	15.1774i	0.489849	−	0.692751i
$481$	−15.9282			−0.726264
$482$		−	55.3674i		−	2.52191i
$483$	1.41421	−	2.00000i	0.0643489	−	0.0910032i
$484$	18.8038			0.854720
$485$	−10.5558			−0.479316
$486$	30.0526	−	1.93185i	1.36321	−	0.0876306i
$487$		−	24.9282i		−	1.12960i	−0.825226	−	0.564802i	$-0.808952\pi$
$487$		−	24.9282i		−	1.12960i	0.825226	−	0.564802i	$-0.191048\pi$
$488$	1.83032			0.0828545
$489$	−7.34847	−	5.19615i	−0.332309	−	0.234978i
$490$		−	18.9282i		−	0.855089i
$491$			10.0010i			0.451340i	0.974204	+	0.225670i	$0.0724571\pi$
$491$			10.0010i			0.451340i	−0.974204	+	0.225670i	$0.927543\pi$
$492$	13.8564	+	9.79796i	0.624695	+	0.441726i
$493$		−	37.8564i		−	1.70497i
$494$		0			0
$495$	−0.535898	−	1.51575i	−0.0240868	−	0.0681279i
$496$		−	19.9282i		−	0.894803i
$497$	13.3843			0.600366
$498$	−14.9282	+	21.1117i	−0.668949	+	0.946036i
$499$	−16.1244			−0.721825			−0.360913	−	0.932600i	$-0.617535\pi$
$499$	−16.1244			−0.721825			−0.360913	+	0.932600i	$0.617535\pi$
$500$		−	19.5959i		−	0.876356i
$501$	10.7846	+	7.62587i	0.481821	+	0.340699i
$502$		−	28.3923i		−	1.26721i
$503$			18.2832i			0.815209i	0.913158	+	0.407605i	$0.133636\pi$
$503$			18.2832i			0.815209i	−0.913158	+	0.407605i	$0.866364\pi$
$504$	1.93185	+	5.46410i	0.0860515	+	0.243390i
$505$	10.9282			0.486299
$506$	−0.277401			−0.0123320
$507$	1.31268	+	0.928203i	0.0582981	+	0.0412230i
$508$			13.6077i			0.603744i
$509$	−13.5873			−0.602248			−0.301124	−	0.953585i	$-0.597362\pi$
$509$	−13.5873			−0.602248			−0.301124	+	0.953585i	$0.597362\pi$
$510$	−18.9282	−	13.3843i	−0.838155	−	0.592665i
$511$	11.1962			0.495289
$512$	29.2552			1.29291
$513$		0			0
$514$	−6.19615			−0.273301
$515$	−14.7985			−0.652099
$516$	−5.55532	−	3.92820i	−0.244559	−	0.172930i
$517$	−4.00000			−0.175920
$518$		−	30.7709i		−	1.35200i
$519$	−16.7846	−	11.8685i	−0.736763	−	0.520970i
$520$	−2.73205			−0.119808
$521$	4.52004			0.198027			0.0990133	−	0.995086i	$-0.468431\pi$
$521$	4.52004			0.198027			0.0990133	+	0.995086i	$0.468431\pi$
$522$	−14.9282	−	42.2233i	−0.653390	−	1.84807i
$523$		−	16.8564i		−	0.737079i	−0.929612	−	0.368540i	$-0.879858\pi$
$523$		−	16.8564i		−	0.737079i	0.929612	−	0.368540i	$-0.120142\pi$
$524$		−	12.0716i		−	0.527350i
$525$	15.8338	+	11.1962i	0.691042	+	0.488640i
$526$			1.07180i			0.0467326i
$527$	−21.8695			−0.952652
$528$	1.69161	−	2.39230i	0.0736181	−	0.104112i
$529$	22.8564			0.993757
$530$			16.4901i			0.716284i
$531$	−8.38375	−	23.7128i	−0.363824	−	1.02905i
$532$		0			0
$533$		−	21.1117i		−	0.914448i
$534$	20.0764	+	14.1962i	0.868790	+	0.614328i
$535$		−	6.92820i		−	0.299532i
$536$		−	0.517638i		−	0.0223586i
$537$	2.00000	+	1.41421i	0.0863064	+	0.0610278i
$538$	−11.6603			−0.502709
$539$		−	2.62536i		−	0.113082i
$540$	−12.2474	−	3.46410i	−0.527046	−	0.149071i
$541$	−17.5359			−0.753927			−0.376964	−	0.926228i	$-0.623032\pi$
$541$	−17.5359			−0.753927			−0.376964	+	0.926228i	$0.623032\pi$
$542$	−13.3843			−0.574903
$543$	−3.46410	+	4.89898i	−0.148659	+	0.210235i
$544$		−	37.1769i		−	1.59395i
$545$	20.3538			0.871861
$546$	−26.9072	+	38.0526i	−1.15152	+	1.62850i
$547$		−	12.8564i		−	0.549700i	−0.961487	−	0.274850i	$-0.911372\pi$
$547$		−	12.8564i		−	0.549700i	0.961487	−	0.274850i	$-0.0886282\pi$
$548$			1.31268i			0.0560748i
$549$	−3.53590	−	10.0010i	−0.150908	−	0.426834i
$550$		−	2.19615i		−	0.0936443i
$551$		0			0
$552$	0.196152	−	0.277401i	0.00834880	−	0.0118070i
$553$		−	13.1962i		−	0.561157i
$554$	−19.0411			−0.808979
$555$	−8.53590	−	6.03579i	−0.362329	−	0.256205i
$556$	22.8564			0.969328
$557$			3.38323i			0.143352i	0.997428	+	0.0716760i	$0.0228348\pi$
$557$			3.38323i			0.143352i	−0.997428	+	0.0716760i	$0.977165\pi$
$558$	−24.3923	+	8.62398i	−1.03261	+	0.365082i
$559$			8.46410i			0.357993i
$560$		−	23.5612i		−	0.995641i
$561$	−2.62536	−	1.85641i	−0.110843	−	0.0783775i
$562$	29.1244			1.22854
$563$	−3.38323			−0.142586			−0.0712931	−	0.997455i	$-0.522713\pi$
$563$	−3.38323			−0.142586			−0.0712931	+	0.997455i	$0.522713\pi$
$564$	−18.2832	+	25.8564i	−0.769863	+	1.08875i
$565$			26.3923i			1.11033i
$566$	−42.2233			−1.77478
$567$	26.1244	−	21.1117i	1.09712	−	0.886607i
$568$	1.85641			0.0778931
$569$	13.9391			0.584356			0.292178	−	0.956364i	$-0.405620\pi$
$569$	13.9391			0.584356			0.292178	+	0.956364i	$0.405620\pi$
$570$		0			0
$571$	25.1962			1.05443			0.527213	−	0.849733i	$-0.323237\pi$
$571$	25.1962			1.05443			0.527213	+	0.849733i	$0.323237\pi$
$572$	2.44949			0.102418
$573$	1.69161	−	2.39230i	0.0706682	−	0.0999400i
$574$	40.7846			1.70232
$575$		−	1.13681i		−	0.0474083i
$576$	−5.73205	−	16.2127i	−0.238835	−	0.675529i
$577$	42.9282			1.78712			0.893562	−	0.448939i	$-0.148198\pi$
$577$	42.9282			1.78712			0.893562	+	0.448939i	$0.148198\pi$
$578$	−13.5230			−0.562481
$579$	−13.1962	+	18.6622i	−0.548413	+	0.775574i
$580$			18.9282i			0.785951i
$581$			28.8391i			1.19645i
$582$	−14.4195	+	20.3923i	−0.597709	+	0.845288i
$583$			2.28719i			0.0947256i
$584$	1.55291			0.0642600
$585$	5.27792	+	14.9282i	0.218215	+	0.617205i
$586$	48.7846			2.01527
$587$			10.7317i			0.442945i	0.975167	+	0.221472i	$0.0710862\pi$
$587$			10.7317i			0.442945i	−0.975167	+	0.221472i	$0.928914\pi$
$588$	−16.9706	−	12.0000i	−0.699854	−	0.494872i
$589$		0			0
$590$			22.9048i			0.942976i
$591$	−9.14162	+	12.9282i	−0.376036	+	0.531795i
$592$		−	19.0526i		−	0.783055i
$593$			25.1512i			1.03284i	0.856336	+	0.516419i	$0.172735\pi$
$593$			25.1512i			1.03284i	−0.856336	+	0.516419i	$0.827265\pi$
$594$	−3.66025	−	1.03528i	−0.150182	−	0.0424779i
$595$	−25.8564			−1.06001
$596$			29.2180i			1.19682i
$597$	18.1074	+	12.8038i	0.741086	+	0.524027i
$598$	2.73205			0.111722
$599$	−16.8690			−0.689250			−0.344625	−	0.938740i	$-0.611994\pi$
$599$	−16.8690			−0.689250			−0.344625	+	0.938740i	$0.611994\pi$
$600$	2.19615	+	1.55291i	0.0896575	+	0.0633975i
$601$		−	44.3731i		−	1.81002i	−0.425395	−	0.905008i	$-0.639865\pi$
$601$		−	44.3731i		−	1.81002i	0.425395	−	0.905008i	$-0.360135\pi$
$602$	−16.3514			−0.666433
$603$	−2.82843	+	1.00000i	−0.115182	+	0.0407231i
$604$			3.46410i			0.140952i
$605$		−	15.3533i		−	0.624199i
$606$	14.9282	−	21.1117i	0.606417	−	0.857603i
$607$			13.2487i			0.537749i	0.963175	+	0.268874i	$0.0866516\pi$
$607$			13.2487i			0.537749i	−0.963175	+	0.268874i	$0.913348\pi$
$608$		0			0
$609$	−40.7846	−	28.8391i	−1.65268	−	1.16862i
$610$			9.66025i			0.391132i
$611$	39.3949			1.59375
$612$	−24.0000	+	8.48528i	−0.970143	+	0.342997i
$613$	22.6410			0.914462			0.457231	−	0.889348i	$-0.348841\pi$
$613$	22.6410			0.914462			0.457231	+	0.889348i	$0.348841\pi$
$614$			26.7685i			1.08029i
$615$	8.00000	−	11.3137i	0.322591	−	0.456213i
$616$		−	0.732051i		−	0.0294952i
$617$		−	25.9091i		−	1.04306i	−0.853232	−	0.521531i	$-0.825361\pi$
$617$		−	25.9091i		−	1.04306i	0.853232	−	0.521531i	$-0.174639\pi$
$618$	−20.2151	+	28.5885i	−0.813170	+	1.15000i
$619$	2.80385			0.112696			0.0563481	−	0.998411i	$-0.482054\pi$
$619$	2.80385			0.112696			0.0563481	+	0.998411i	$0.482054\pi$
$620$	10.9348			0.439151
$621$	−1.89469	−	0.535898i	−0.0760312	−	0.0215049i
$622$		−	52.4449i		−	2.10285i
$623$	27.4249			1.09875
$624$	−16.6603	+	23.5612i	−0.666944	+	0.943201i
$625$	−1.00000			−0.0400000
$626$	−47.8802			−1.91368
$627$		0			0
$628$	6.12436			0.244388
$629$	−20.9086			−0.833680
$630$	−28.8391	+	10.1962i	−1.14898	+	0.406224i
$631$	49.0526			1.95275			0.976376	−	0.216080i	$-0.0693270\pi$
$631$	49.0526			1.95275			0.976376	+	0.216080i	$0.0693270\pi$
$632$		−	1.83032i		−	0.0728060i
$633$	11.0000	−	15.5563i	0.437211	−	0.618309i
$634$	26.5885			1.05596
$635$	11.1106			0.440912
$636$	14.7846	+	10.4543i	0.586248	+	0.414540i
$637$			25.8564i			1.02447i
$638$			5.65685i			0.223957i
$639$	−3.58630	−	10.1436i	−0.141872	−	0.401274i
$640$		−	5.80385i		−	0.229417i
$641$	−12.8295			−0.506733			−0.253367	−	0.967370i	$-0.581538\pi$
$641$	−12.8295			−0.506733			−0.253367	+	0.967370i	$0.581538\pi$
$642$	−13.3843	−	9.46410i	−0.528235	−	0.373518i
$643$	−43.5885			−1.71896			−0.859480	−	0.511169i	$-0.829213\pi$
$643$	−43.5885			−1.71896			−0.859480	+	0.511169i	$0.829213\pi$
$644$			2.44949i			0.0965234i
$645$	−3.20736	+	4.53590i	−0.126290	+	0.178601i
$646$		0			0
$647$		−	20.5569i		−	0.808174i	−0.914721	−	0.404087i	$-0.867589\pi$
$647$		−	20.5569i		−	0.808174i	0.914721	−	0.404087i	$-0.132411\pi$
$648$	3.62347	−	2.92820i	0.142343	−	0.115031i
$649$			3.17691i			0.124705i
$650$			21.6293i			0.848371i
$651$	−16.6603	+	23.5612i	−0.652967	+	0.923435i
$652$	9.00000			0.352467
$653$			47.1223i			1.84404i	0.387144	+	0.922019i	$0.373462\pi$
$653$			47.1223i			1.84404i	−0.387144	+	0.922019i	$0.626538\pi$
$654$	27.8038	−	39.3205i	1.08721	−	1.53755i
$655$	−9.85641			−0.385122
$656$	25.2528			0.985955
$657$	−3.00000	−	8.48528i	−0.117041	−	0.331042i
$658$			76.1051i			2.96689i
$659$	−33.0817			−1.28868			−0.644340	−	0.764739i	$-0.722868\pi$
$659$	−33.0817			−1.28868			−0.644340	+	0.764739i	$0.722868\pi$
$660$	1.31268	+	0.928203i	0.0510959	+	0.0361303i
$661$			6.14359i			0.238958i	0.992837	+	0.119479i	$0.0381224\pi$
$661$			6.14359i			0.238958i	−0.992837	+	0.119479i	$0.961878\pi$
$662$			61.6806i			2.39728i
$663$	25.8564	+	18.2832i	1.00418	+	0.710062i
$664$			4.00000i			0.155230i
$665$		0			0
$666$	−23.3205	+	8.24504i	−0.903651	+	0.319489i
$667$			2.92820i			0.113380i
$668$	−13.2084			−0.511048
$669$	9.39230	−	13.2827i	0.363127	−	0.513540i
$670$	2.73205			0.105548
$671$			1.33988i			0.0517257i
$672$	−40.0526	−	28.3214i	−1.54506	−	1.09252i
$673$			21.9808i			0.847296i	0.905827	+	0.423648i	$0.139251\pi$
$673$			21.9808i			0.847296i	−0.905827	+	0.423648i	$0.860749\pi$
$674$		−	14.1793i		−	0.546166i
$675$	4.24264	−	15.0000i	0.163299	−	0.577350i
$676$	−1.60770			−0.0618344
$677$	18.8380			0.724005			0.362002	−	0.932177i	$-0.382093\pi$
$677$	18.8380			0.724005			0.362002	+	0.932177i	$0.382093\pi$
$678$	50.9860	+	36.0526i	1.95811	+	1.38459i
$679$			27.8564i			1.06903i
$680$	−3.58630			−0.137528
$681$	−34.7846	−	24.5964i	−1.33295	−	0.942537i
$682$	3.26795			0.125136
$683$	16.3142			0.624246			0.312123	−	0.950042i	$-0.398960\pi$
$683$	16.3142			0.624246			0.312123	+	0.950042i	$0.398960\pi$
$684$		0			0
$685$	1.07180			0.0409512
$686$	0.517638			0.0197635
$687$	−13.2827	−	9.39230i	−0.506768	−	0.358339i
$688$	−10.1244			−0.385987
$689$		−	22.5259i		−	0.858168i
$690$	1.46410	+	1.03528i	0.0557374	+	0.0394123i
$691$	9.85641			0.374955			0.187478	−	0.982269i	$-0.439969\pi$
$691$	9.85641			0.374955			0.187478	+	0.982269i	$0.439969\pi$
$692$	20.5569			0.781455
$693$	−4.00000	+	1.41421i	−0.151947	+	0.0537215i
$694$		−	48.0526i		−	1.82405i
$695$		−	18.6622i		−	0.707897i
$696$	−5.65685	−	4.00000i	−0.214423	−	0.151620i
$697$		−	27.7128i		−	1.04970i
$698$	−22.0082			−0.833024
$699$	3.58630	−	5.07180i	0.135646	−	0.191833i
$700$	−19.3923			−0.732960
$701$			19.9005i			0.751632i	0.926694	+	0.375816i	$0.122638\pi$
$701$			19.9005i			0.751632i	−0.926694	+	0.375816i	$0.877362\pi$
$702$	36.0488	+	10.1962i	1.36058	+	0.384829i
$703$		0			0
$704$			2.17209i			0.0818637i
$705$	21.1117	+	14.9282i	0.795111	+	0.562229i
$706$			23.1244i			0.870297i
$707$		−	28.8391i		−	1.08461i
$708$	20.5359	+	14.5211i	0.771786	+	0.545735i
$709$	42.3205			1.58938			0.794690	−	0.607015i	$-0.207633\pi$
$709$	42.3205			1.58938			0.794690	+	0.607015i	$0.207633\pi$
$710$			9.79796i			0.367711i
$711$	−10.0010	+	3.53590i	−0.375068	+	0.132607i
$712$	3.80385			0.142555
$713$	1.69161			0.0633515
$714$	−35.3205	+	49.9507i	−1.32184	+	1.86936i
$715$		−	2.00000i		−	0.0747958i
$716$	−2.44949			−0.0915417
$717$	29.9759	−	42.3923i	1.11947	−	1.58317i
$718$			51.7128i			1.92991i
$719$		−	6.03579i		−	0.225097i	−0.993646	−	0.112549i	$-0.964099\pi$
$719$		−	6.03579i		−	0.225097i	0.993646	−	0.112549i	$-0.0359014\pi$
$720$	−17.8564	+	6.31319i	−0.665469	+	0.235279i
$721$			39.0526i			1.45439i
$722$		0			0
$723$	−28.6603	+	40.5317i	−1.06589	+	1.50739i
$724$		−	6.00000i		−	0.222988i
$725$	−23.1822			−0.860966
$726$	−29.6603	−	20.9730i	−1.10080	−	0.778380i
$727$	−13.5885			−0.503968			−0.251984	−	0.967731i	$-0.581083\pi$
$727$	−13.5885			−0.503968			−0.251984	+	0.967731i	$0.581083\pi$
$728$			7.20977i			0.267212i
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$			8.19615i			0.303353i
$731$			11.1106i			0.410942i
$732$	8.66115	+	6.12436i	0.320125	+	0.226363i
$733$	−35.7128			−1.31908			−0.659541	−	0.751668i	$-0.729249\pi$
$733$	−35.7128			−1.31908			−0.659541	+	0.751668i	$0.729249\pi$
$734$	−32.9430			−1.21595
$735$	−9.79796	+	13.8564i	−0.361403	+	0.511101i
$736$			2.87564i			0.105998i
$737$	0.378937			0.0139583
$738$	−10.9282	−	30.9096i	−0.402273	−	1.13780i
$739$	−34.8038			−1.28028			−0.640140	−	0.768258i	$-0.721124\pi$
$739$	−34.8038			−1.28028			−0.640140	+	0.768258i	$0.721124\pi$
$740$	10.4543			0.384308
$741$		0			0
$742$	43.5167			1.59755
$743$	7.07107			0.259412			0.129706	−	0.991552i	$-0.458597\pi$
$743$	7.07107			0.259412			0.129706	+	0.991552i	$0.458597\pi$
$744$	−2.31079	+	3.26795i	−0.0847176	+	0.119809i
$745$	23.8564			0.874031
$746$			24.2175i			0.886666i
$747$	21.8564	−	7.72741i	0.799684	−	0.282731i
$748$	3.21539			0.117566
$749$	−18.2832			−0.668055
$750$	−21.8564	+	30.9096i	−0.798083	+	1.12866i
$751$		−	8.60770i		−	0.314099i	−0.987591	−	0.157050i	$-0.949802\pi$
$751$		−	8.60770i		−	0.314099i	0.987591	−	0.157050i	$-0.0501983\pi$
$752$			47.1223i			1.71837i
$753$	−14.6969	+	20.7846i	−0.535586	+	0.757433i
$754$		−	55.7128i		−	2.02894i
$755$	2.82843			0.102937
$756$	−9.14162	+	32.3205i	−0.332478	+	1.17549i
$757$	4.60770			0.167470			0.0837348	−	0.996488i	$-0.473315\pi$
$757$	4.60770			0.167470			0.0837348	+	0.996488i	$0.473315\pi$
$758$			34.3572i			1.24791i
$759$	0.203072	+	0.143594i	0.00737104	+	0.00521212i
$760$		0			0
$761$		−	46.2629i		−	1.67703i	−0.544879	−	0.838514i	$-0.683425\pi$
$761$		−	46.2629i		−	1.67703i	0.544879	−	0.838514i	$-0.316575\pi$
$762$	15.1774	−	21.4641i	0.549820	−	0.777562i
$763$		−	53.7128i		−	1.94453i
$764$			2.92996i			0.106002i
$765$	6.92820	+	19.5959i	0.250490	+	0.708492i
$766$	−51.5167			−1.86137
$767$		−	31.2886i		−	1.12976i
$768$	−27.4249	−	19.3923i	−0.989609	−	0.699760i
$769$	−0.856406			−0.0308828			−0.0154414	−	0.999881i	$-0.504915\pi$
$769$	−0.856406			−0.0308828			−0.0154414	+	0.999881i	$0.504915\pi$
$770$	3.86370			0.139238
$771$	4.53590	+	3.20736i	0.163356	+	0.115510i
$772$		−	22.8564i		−	0.822620i
$773$	−18.0802			−0.650298			−0.325149	−	0.945663i	$-0.605415\pi$
$773$	−18.0802			−0.650298			−0.325149	+	0.945663i	$0.605415\pi$
$774$	4.38134	+	12.3923i	0.157484	+	0.445432i
$775$			13.3923i			0.481066i
$776$			3.86370i			0.138699i
$777$	−15.9282	+	22.5259i	−0.571421	+	0.808111i
$778$			9.66025i			0.346337i
$779$		0			0
$780$	−12.9282	−	9.14162i	−0.462904	−	0.327323i
$781$			1.35898i			0.0486283i
$782$	3.58630			0.128246
$783$	−10.9282	+	38.6370i	−0.390542	+	1.38077i
$784$	−30.9282			−1.10458
$785$		−	5.00052i		−	0.178476i
$786$	−13.4641	+	19.0411i	−0.480249	+	0.679174i
$787$		−	24.0718i		−	0.858067i	−0.903289	−	0.429033i	$-0.858854\pi$
$787$		−	24.0718i		−	0.858067i	0.903289	−	0.429033i	$-0.141146\pi$
$788$		−	15.8338i		−	0.564054i
$789$	0.554803	−	0.784610i	0.0197515	−	0.0279328i
$790$	9.66025			0.343696
$791$	69.6482			2.47640
$792$	−0.554803	+	0.196152i	−0.0197141	+	0.00696997i
$793$		−	13.1962i		−	0.468609i
$794$	16.0740			0.570444
$795$	8.53590	−	12.0716i	0.302737	−	0.428135i
$796$	−22.1769			−0.786040
$797$	−14.4939			−0.513399			−0.256700	−	0.966491i	$-0.582635\pi$
$797$	−14.4939			−0.513399			−0.256700	+	0.966491i	$0.582635\pi$
$798$		0			0
$799$	51.7128			1.82947
$800$	−22.7661			−0.804904
$801$	−7.34847	−	20.7846i	−0.259645	−	0.734388i
$802$	22.1962			0.783773
$803$			1.13681i			0.0401172i
$804$	1.73205	−	2.44949i	0.0610847	−	0.0863868i
$805$	2.00000			0.0704907
$806$	−32.1851			−1.13367
$807$	8.53590	+	6.03579i	0.300478	+	0.212470i
$808$		−	4.00000i		−	0.140720i
$809$		−	51.1619i		−	1.79876i	−0.437172	−	0.899378i	$-0.644020\pi$
$809$		−	51.1619i		−	1.79876i	0.437172	−	0.899378i	$-0.355980\pi$
$810$	15.4548	+	19.1244i	0.543027	+	0.671961i
$811$			21.7128i			0.762440i	0.924484	+	0.381220i	$0.124496\pi$
$811$			21.7128i			0.762440i	−0.924484	+	0.381220i	$0.875504\pi$
$812$	49.9507			1.75293
$813$	9.79796	+	6.92820i	0.343629	+	0.242983i
$814$	3.12436			0.109509
$815$		−	7.34847i		−	0.257406i
$816$	−21.8695	+	30.9282i	−0.765587	+	1.08270i
$817$		0			0
$818$			54.5723i			1.90808i
$819$	39.3949	−	13.9282i	1.37657	−	0.486691i
$820$			13.8564i			0.483887i
$821$		−	34.4959i		−	1.20392i	−0.798528	−	0.601958i	$-0.794387\pi$
$821$		−	34.4959i		−	1.20392i	0.798528	−	0.601958i	$-0.205613\pi$
$822$	1.46410	−	2.07055i	0.0510664	−	0.0722188i
$823$	−8.00000			−0.278862			−0.139431	−	0.990232i	$-0.544527\pi$
$823$	−8.00000			−0.278862			−0.139431	+	0.990232i	$0.544527\pi$
$824$			5.41662i			0.188697i
$825$	−1.13681	+	1.60770i	−0.0395787	+	0.0559728i
$826$	60.4449			2.10315
$827$	−24.4949			−0.851771			−0.425886	−	0.904777i	$-0.640037\pi$
$827$	−24.4949			−0.851771			−0.425886	+	0.904777i	$0.640037\pi$
$828$	1.85641	−	0.656339i	0.0645146	−	0.0228093i
$829$			38.6603i			1.34273i	0.741129	+	0.671363i	$0.234291\pi$
$829$			38.6603i			1.34273i	−0.741129	+	0.671363i	$0.765709\pi$
$830$	−21.1117			−0.732797
$831$	13.9391	+	9.85641i	0.483541	+	0.341915i
$832$		−	21.3923i		−	0.741645i
$833$			33.9411i			1.17599i
$834$	−36.0526	−	25.4930i	−1.24840	−	0.882751i
$835$			10.7846i			0.373217i
$836$		0			0
$837$	22.3205	+	6.31319i	0.771510	+	0.218216i
$838$			61.9090i			2.13861i
$839$	5.75839			0.198802			0.0994009	−	0.995047i	$-0.468307\pi$
$839$	5.75839			0.198802			0.0994009	+	0.995047i	$0.468307\pi$
$840$	−2.73205	+	3.86370i	−0.0942647	+	0.133310i
$841$	30.7128			1.05906
$842$			68.5114i			2.36106i
$843$	−21.3205	−	15.0759i	−0.734317	−	0.519241i
$844$			19.0526i			0.655816i
$845$			1.31268i			0.0451575i
$846$	57.6781	−	20.3923i	1.98302	−	0.701102i
$847$	−40.5167			−1.39217
$848$	26.9444			0.925274
$849$	30.9096	+	21.8564i	1.06082	+	0.750110i
$850$			28.3923i			0.973848i
$851$	1.61729			0.0554398
$852$	8.78461	+	6.21166i	0.300956	+	0.212808i
$853$	19.6795			0.673813			0.336906	−	0.941538i	$-0.390619\pi$
$853$	19.6795			0.673813			0.336906	+	0.941538i	$0.390619\pi$
$854$	25.4930			0.872353
$855$		0			0
$856$	−2.53590			−0.0866752
$857$	3.03150			0.103554			0.0517770	−	0.998659i	$-0.483511\pi$
$857$	3.03150			0.103554			0.0517770	+	0.998659i	$0.483511\pi$
$858$	−3.86370	−	2.73205i	−0.131905	−	0.0932707i
$859$	−4.66025			−0.159006			−0.0795029	−	0.996835i	$-0.525333\pi$
$859$	−4.66025			−0.159006			−0.0795029	+	0.996835i	$0.525333\pi$
$860$		−	5.55532i		−	0.189435i
$861$	−29.8564	−	21.1117i	−1.01750	−	0.719484i
$862$	−49.1769			−1.67497
$863$	−18.2832			−0.622369			−0.311184	−	0.950350i	$-0.600726\pi$
$863$	−18.2832			−0.622369			−0.311184	+	0.950350i	$0.600726\pi$
$864$	−10.7321	+	37.9435i	−0.365112	+	1.29087i
$865$		−	16.7846i		−	0.570694i
$866$			6.45189i			0.219244i
$867$	9.89949	+	7.00000i	0.336204	+	0.237732i
$868$		−	28.8564i		−	0.979450i
$869$	1.33988			0.0454525
$870$	21.1117	−	29.8564i	0.715753	−	1.01223i
$871$	−3.73205			−0.126456
$872$		−	7.45001i		−	0.252289i
$873$	21.1117	−	7.46410i	0.714522	−	0.252622i
$874$		0			0
$875$			42.2233i			1.42741i
$876$	7.34847	+	5.19615i	0.248282	+	0.175562i
$877$			3.73205i			0.126022i	0.998013	+	0.0630112i	$0.0200704\pi$
$877$			3.73205i			0.126022i	−0.998013	+	0.0630112i	$0.979930\pi$
$878$		−	43.3973i		−	1.46459i
$879$	−35.7128	−	25.2528i	−1.20456	−	0.851755i
$880$	2.39230			0.0806446
$881$			39.8482i			1.34252i	0.741222	+	0.671260i	$0.234246\pi$
$881$			39.8482i			1.34252i	−0.741222	+	0.671260i	$0.765754\pi$
$882$	13.3843	+	37.8564i	0.450672	+	1.27469i
$883$	−22.2679			−0.749376			−0.374688	−	0.927151i	$-0.622250\pi$
$883$	−22.2679			−0.749376			−0.374688	+	0.927151i	$0.622250\pi$
$884$	−31.6675			−1.06509
$885$	11.8564	−	16.7675i	0.398549	−	0.563633i
$886$		−	74.6410i		−	2.50761i
$887$	−11.9700			−0.401915			−0.200957	−	0.979600i	$-0.564405\pi$
$887$	−11.9700			−0.401915			−0.200957	+	0.979600i	$0.564405\pi$
$888$	−2.20925	+	3.12436i	−0.0741377	+	0.104847i
$889$		−	29.3205i		−	0.983378i
$890$			20.0764i			0.672962i
$891$	2.14359	+	2.65256i	0.0718131	+	0.0888642i
$892$			16.2679i			0.544691i
$893$		0			0
$894$	32.5885	−	46.0870i	1.08992	−	1.54138i
$895$			2.00000i			0.0668526i
$896$	−15.3161			−0.511675
$897$	−2.00000	−	1.41421i	−0.0667781	−	0.0472192i
$898$	−66.6410			−2.22384
$899$		−	34.4959i		−	1.15050i
$900$	5.19615	+	14.6969i	0.173205	+	0.489898i
$901$		−	29.5692i		−	0.985094i
$902$			4.14110i			0.137884i
$903$	11.9700	+	8.46410i	0.398338	+	0.281668i
$904$	9.66025			0.321295
$905$	−4.89898			−0.162848
$906$	3.86370	−	5.46410i	0.128363	−	0.181533i
$907$		−	40.9282i		−	1.35900i	−0.733676	−	0.679499i	$-0.762197\pi$
$907$		−	40.9282i		−	1.35900i	0.733676	−	0.679499i	$-0.237803\pi$
$908$	42.6023			1.41381
$909$	−21.8564	+	7.72741i	−0.724931	+	0.256302i
$910$	−38.0526			−1.26143
$911$	40.9107			1.35543			0.677715	−	0.735324i	$-0.262970\pi$
$911$	40.9107			1.35543			0.677715	+	0.735324i	$0.262970\pi$
$912$		0			0
$913$	−2.92820			−0.0969094
$914$	−40.0141			−1.32355
$915$	5.00052	−	7.07180i	0.165312	−	0.233786i
$916$	16.2679			0.537508
$917$			26.0106i			0.858947i
$918$	47.3205	+	13.3843i	1.56181	+	0.441746i
$919$	−31.9808			−1.05495			−0.527474	−	0.849571i	$-0.676861\pi$
$919$	−31.9808			−1.05495			−0.527474	+	0.849571i	$0.676861\pi$
$920$	0.277401			0.00914565
$921$	13.8564	−	19.5959i	0.456584	−	0.645707i
$922$			63.5167i			2.09181i
$923$		−	13.3843i		−	0.440548i
$924$	2.44949	−	3.46410i	0.0805823	−	0.113961i
$925$			12.8038i			0.420988i
$926$	−57.1605			−1.87841
$927$	29.5969	−	10.4641i	0.972091	−	0.343686i
$928$	58.6410			1.92499
$929$			20.4553i			0.671118i	0.942019	+	0.335559i	$0.108925\pi$
$929$			20.4553i			0.671118i	−0.942019	+	0.335559i	$0.891075\pi$
$930$	−17.2480	−	12.1962i	−0.565583	−	0.399928i
$931$		0			0
$932$			6.21166i			0.203470i
$933$	−27.1475	+	38.3923i	−0.888768	+	1.25691i
$934$		−	43.7128i		−	1.43033i
$935$		−	2.62536i		−	0.0858583i
$936$	5.46410	−	1.93185i	0.178600	−	0.0631445i
$937$	5.78461			0.188975			0.0944875	−	0.995526i	$-0.469879\pi$
$937$	5.78461			0.188975			0.0944875	+	0.995526i	$0.469879\pi$
$938$		−	7.20977i		−	0.235407i
$939$	35.0507	+	24.7846i	1.14384	+	0.808815i
$940$	−25.8564			−0.843343
$941$	−13.9391			−0.454400			−0.227200	−	0.973848i	$-0.572957\pi$
$941$	−13.9391			−0.454400			−0.227200	+	0.973848i	$0.572957\pi$
$942$	−9.66025	−	6.83083i	−0.314748	−	0.222561i
$943$			2.14359i			0.0698050i
$944$	37.4259			1.21811
$945$	26.3896	+	7.46410i	0.858453	+	0.242807i
$946$		−	1.66025i		−	0.0539795i
$947$			44.2939i			1.43936i	0.694307	+	0.719679i	$0.255711\pi$
$947$			44.2939i			1.43936i	−0.694307	+	0.719679i	$0.744289\pi$
$948$	6.12436	−	8.66115i	0.198910	−	0.281301i
$949$		−	11.1962i		−	0.363442i
$950$		0			0
$951$	−19.4641	−	13.7632i	−0.631167	−	0.446302i
$952$			9.46410i			0.306733i
$953$	42.6023			1.38002			0.690011	−	0.723798i	$-0.257605\pi$
$953$	42.6023			1.38002			0.690011	+	0.723798i	$0.257605\pi$
$954$	−11.6603	−	32.9802i	−0.377515	−	1.06777i
$955$	2.39230			0.0774132
$956$			51.9198i			1.67920i
$957$	2.92820	−	4.14110i	0.0946554	−	0.133863i
$958$			22.9282i			0.740777i
$959$		−	2.82843i		−	0.0913347i
$960$	8.10634	−	11.4641i	0.261631	−	0.370002i
$961$	11.0718			0.357155
$962$	−30.7709			−0.992094
$963$	4.89898	+	13.8564i	0.157867	+	0.446516i
$964$		−	49.6410i		−	1.59883i
$965$	−18.6622			−0.600757
$966$	2.73205	−	3.86370i	0.0879023	−	0.124313i
$967$	−8.80385			−0.283113			−0.141556	−	0.989930i	$-0.545211\pi$
$967$	−8.80385			−0.283113			−0.141556	+	0.989930i	$0.545211\pi$
$968$	−5.61969			−0.180624
$969$		0			0
$970$	−20.3923			−0.654757
$971$	−14.3452			−0.460360			−0.230180	−	0.973148i	$-0.573931\pi$
$971$	−14.3452			−0.460360			−0.230180	+	0.973148i	$0.573931\pi$
$972$	26.9444	−	1.73205i	0.864242	−	0.0555556i
$973$	−49.2487			−1.57884
$974$		−	48.1576i		−	1.54307i
$975$	11.1962	−	15.8338i	0.358564	−	0.507086i
$976$	15.7846			0.505253
$977$	−20.3538			−0.651176			−0.325588	−	0.945512i	$-0.605562\pi$
$977$	−20.3538			−0.651176			−0.325588	+	0.945512i	$0.605562\pi$
$978$	−14.1962	−	10.0382i	−0.453943	−	0.320986i
$979$			2.78461i			0.0889965i
$980$		−	16.9706i		−	0.542105i
$981$	−40.7076	+	14.3923i	−1.29969	+	0.459511i
$982$			19.3205i			0.616542i
$983$	32.5269			1.03745			0.518724	−	0.854942i	$-0.326407\pi$
$983$	32.5269			1.03745			0.518724	+	0.854942i	$0.326407\pi$
$984$	−4.14110	−	2.92820i	−0.132014	−	0.0933477i
$985$	−12.9282			−0.411927
$986$		−	73.1330i		−	2.32903i
$987$	39.3949	−	55.7128i	1.25395	−	1.77336i
$988$		0			0
$989$		−	0.859411i		−	0.0273277i
$990$	−1.03528	−	2.92820i	−0.0329032	−	0.0930644i
$991$			4.17691i			0.132684i	0.997797	+	0.0663420i	$0.0211328\pi$
$991$			4.17691i			0.132684i	−0.997797	+	0.0663420i	$0.978867\pi$
$992$		−	33.8768i		−	1.07559i
$993$	31.9282	−	45.1533i	1.01321	−	1.43290i
$994$	25.8564			0.820115
$995$			18.1074i			0.574042i
$996$	−13.3843	+	18.9282i	−0.424097	+	0.599763i
$997$	50.1769			1.58912			0.794559	−	0.607186i	$-0.207702\pi$
$997$	50.1769			1.58912			0.794559	+	0.607186i	$0.207702\pi$
$998$	−31.1499			−0.986032
$999$	21.3397	+	6.03579i	0.675160	+	0.190964i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1083.2.d.b.1082.7		8
3.2	odd	2	inner	1083.2.d.b.1082.1		8
19.7	even	3		57.2.f.a.8.1	✓	8
19.8	odd	6		57.2.f.a.50.4	yes	8
19.18	odd	2	inner	1083.2.d.b.1082.2		8
57.8	even	6		57.2.f.a.50.1	yes	8
57.26	odd	6		57.2.f.a.8.4	yes	8
57.56	even	2	inner	1083.2.d.b.1082.8		8
76.7	odd	6		912.2.bn.m.65.1		8
76.27	even	6		912.2.bn.m.449.2		8
228.83	even	6		912.2.bn.m.65.2		8
228.179	odd	6		912.2.bn.m.449.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.f.a.8.1	✓	8	19.7	even	3
57.2.f.a.8.4	yes	8	57.26	odd	6
57.2.f.a.50.1	yes	8	57.8	even	6
57.2.f.a.50.4	yes	8	19.8	odd	6
912.2.bn.m.65.1		8	76.7	odd	6
912.2.bn.m.65.2		8	228.83	even	6
912.2.bn.m.449.1		8	228.179	odd	6
912.2.bn.m.449.2		8	76.27	even	6
1083.2.d.b.1082.1		8	3.2	odd	2	inner
1083.2.d.b.1082.2		8	19.18	odd	2	inner
1083.2.d.b.1082.7		8	1.1	even	1	trivial
1083.2.d.b.1082.8		8	57.56	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:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1083.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.93185 q^{2} +(-1.41421 - 1.00000i) q^{3} +1.73205 q^{4} -1.41421i q^{5} +(-2.73205 - 1.93185i) q^{6} -3.73205 q^{7} -0.517638 q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+1.93185 q^{2} +(-1.41421 - 1.00000i) q^{3} +1.73205 q^{4} -1.41421i q^{5} +(-2.73205 - 1.93185i) q^{6} -3.73205 q^{7} -0.517638 q^{8} +(1.00000 + 2.82843i) q^{9} -2.73205i q^{10} -0.378937i q^{11} +(-2.44949 - 1.73205i) q^{12} +3.73205i q^{13} -7.20977 q^{14} +(-1.41421 + 2.00000i) q^{15} -4.46410 q^{16} +4.89898i q^{17} +(1.93185 + 5.46410i) q^{18} -2.44949i q^{20} +(5.27792 + 3.73205i) q^{21} -0.732051i q^{22} -0.378937i q^{23} +(0.732051 + 0.517638i) q^{24} +3.00000 q^{25} +7.20977i q^{26} +(1.41421 - 5.00000i) q^{27} -6.46410 q^{28} -7.72741 q^{29} +(-2.73205 + 3.86370i) q^{30} +4.46410i q^{31} -7.58871 q^{32} +(-0.378937 + 0.535898i) q^{33} +9.46410i q^{34} +5.27792i q^{35} +(1.73205 + 4.89898i) q^{36} +4.26795i q^{37} +(3.73205 - 5.27792i) q^{39} +0.732051i q^{40} -5.65685 q^{41} +(10.1962 + 7.20977i) q^{42} +2.26795 q^{43} -0.656339i q^{44} +(4.00000 - 1.41421i) q^{45} -0.732051i q^{46} -10.5558i q^{47} +(6.31319 + 4.46410i) q^{48} +6.92820 q^{49} +5.79555 q^{50} +(4.89898 - 6.92820i) q^{51} +6.46410i q^{52} -6.03579 q^{53} +(2.73205 - 9.65926i) q^{54} -0.535898 q^{55} +1.93185 q^{56} -14.9282 q^{58} -8.38375 q^{59} +(-2.44949 + 3.46410i) q^{60} -3.53590 q^{61} +8.62398i q^{62} +(-3.73205 - 10.5558i) q^{63} -5.73205 q^{64} +5.27792 q^{65} +(-0.732051 + 1.03528i) q^{66} +1.00000i q^{67} +8.48528i q^{68} +(-0.378937 + 0.535898i) q^{69} +10.1962i q^{70} -3.58630 q^{71} +(-0.517638 - 1.46410i) q^{72} -3.00000 q^{73} +8.24504i q^{74} +(-4.24264 - 3.00000i) q^{75} +1.41421i q^{77} +(7.20977 - 10.1962i) q^{78} +3.53590i q^{79} +6.31319i q^{80} +(-7.00000 + 5.65685i) q^{81} -10.9282 q^{82} -7.72741i q^{83} +(9.14162 + 6.46410i) q^{84} +6.92820 q^{85} +4.38134 q^{86} +(10.9282 + 7.72741i) q^{87} +0.196152i q^{88} -7.34847 q^{89} +(7.72741 - 2.73205i) q^{90} -13.9282i q^{91} -0.656339i q^{92} +(4.46410 - 6.31319i) q^{93} -20.3923i q^{94} +(10.7321 + 7.58871i) q^{96} -7.46410i q^{97} +13.3843 q^{98} +(1.07180 - 0.378937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{6} - 16 q^{7} + 8 q^{9}+O(q^{10}) \) 8 * q - 8 * q^6 - 16 * q^7 + 8 * q^9	\( 8 q - 8 q^{6} - 16 q^{7} + 8 q^{9} - 8 q^{16} - 8 q^{24} + 24 q^{25} - 24 q^{28} - 8 q^{30} + 16 q^{39} + 40 q^{42} + 32 q^{43} + 32 q^{45} + 8 q^{54} - 32 q^{55} - 64 q^{58} - 56 q^{61} - 16 q^{63} - 32 q^{64} + 8 q^{66} - 24 q^{73} - 56 q^{81} - 32 q^{82} + 32 q^{87} + 8 q^{93} + 72 q^{96} + 64 q^{99}+O(q^{100}) \) 8 * q - 8 * q^6 - 16 * q^7 + 8 * q^9 - 8 * q^16 - 8 * q^24 + 24 * q^25 - 24 * q^28 - 8 * q^30 + 16 * q^39 + 40 * q^42 + 32 * q^43 + 32 * q^45 + 8 * q^54 - 32 * q^55 - 64 * q^58 - 56 * q^61 - 16 * q^63 - 32 * q^64 + 8 * q^66 - 24 * q^73 - 56 * q^81 - 32 * q^82 + 32 * q^87 + 8 * q^93 + 72 * q^96 + 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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