LMFDB - Embedded newform 1083.2.d.b.1082.6

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			1082.6
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	1083.1082
Dual form			1083.2.d.b.1082.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.517638 q^{2} +(1.41421 + 1.00000i) q^{3} -1.73205 q^{4} -1.41421i q^{5} +(0.732051 + 0.517638i) q^{6} -0.267949 q^{7} -1.93185 q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})$	\(q+0.517638 q^{2} +(1.41421 + 1.00000i) q^{3} -1.73205 q^{4} -1.41421i q^{5} +(0.732051 + 0.517638i) q^{6} -0.267949 q^{7} -1.93185 q^{8} +(1.00000 + 2.82843i) q^{9} -0.732051i q^{10} -5.27792i q^{11} +(-2.44949 - 1.73205i) q^{12} -0.267949i q^{13} -0.138701 q^{14} +(1.41421 - 2.00000i) q^{15} +2.46410 q^{16} -4.89898i q^{17} +(0.517638 + 1.46410i) q^{18} +2.44949i q^{20} +(-0.378937 - 0.267949i) q^{21} -2.73205i q^{22} -5.27792i q^{23} +(-2.73205 - 1.93185i) q^{24} +3.00000 q^{25} -0.138701i q^{26} +(-1.41421 + 5.00000i) q^{27} +0.464102 q^{28} -2.07055 q^{29} +(0.732051 - 1.03528i) q^{30} +2.46410i q^{31} +5.13922 q^{32} +(5.27792 - 7.46410i) q^{33} -2.53590i q^{34} +0.378937i q^{35} +(-1.73205 - 4.89898i) q^{36} -7.73205i q^{37} +(0.267949 - 0.378937i) q^{39} +2.73205i q^{40} +5.65685 q^{41} +(-0.196152 - 0.138701i) q^{42} +5.73205 q^{43} +9.14162i q^{44} +(4.00000 - 1.41421i) q^{45} -2.73205i q^{46} -0.757875i q^{47} +(3.48477 + 2.46410i) q^{48} -6.92820 q^{49} +1.55291 q^{50} +(4.89898 - 6.92820i) q^{51} +0.464102i q^{52} +10.9348 q^{53} +(-0.732051 + 2.58819i) q^{54} -7.46410 q^{55} +0.517638 q^{56} -1.07180 q^{58} -11.2122 q^{59} +(-2.44949 + 3.46410i) q^{60} -10.4641 q^{61} +1.27551i q^{62} +(-0.267949 - 0.757875i) q^{63} -2.26795 q^{64} -0.378937 q^{65} +(2.73205 - 3.86370i) q^{66} -1.00000i q^{67} +8.48528i q^{68} +(5.27792 - 7.46410i) q^{69} +0.196152i q^{70} +13.3843 q^{71} +(-1.93185 - 5.46410i) q^{72} -3.00000 q^{73} -4.00240i q^{74} +(4.24264 + 3.00000i) q^{75} +1.41421i q^{77} +(0.138701 - 0.196152i) q^{78} -10.4641i q^{79} -3.48477i q^{80} +(-7.00000 + 5.65685i) q^{81} +2.92820 q^{82} +2.07055i q^{83} +(0.656339 + 0.464102i) q^{84} -6.92820 q^{85} +2.96713 q^{86} +(-2.92820 - 2.07055i) q^{87} +10.1962i q^{88} -7.34847 q^{89} +(2.07055 - 0.732051i) q^{90} +0.0717968i q^{91} +9.14162i q^{92} +(-2.46410 + 3.48477i) q^{93} -0.392305i q^{94} +(7.26795 + 5.13922i) q^{96} +0.535898i q^{97} -3.58630 q^{98} +(14.9282 - 5.27792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.517638			0.366025			0.183013	−	0.983111i	$-0.441415\pi$
$2$	0.517638			0.366025			0.183013	+	0.983111i	$0.441415\pi$
$3$	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	$-0.102416\pi$
$6$	0.732051	+	0.517638i	0.298858	+	0.211325i
$7$	−0.267949			−0.101275			−0.0506376	−	0.998717i	$-0.516125\pi$
$7$	−0.267949			−0.101275			−0.0506376	+	0.998717i	$0.516125\pi$
$8$	−1.93185			−0.683013
$9$	1.00000	+	2.82843i	0.333333	+	0.942809i
$10$		−	0.732051i		−	0.231495i
$11$		−	5.27792i		−	1.59135i	−0.605723	−	0.795676i	$-0.707116\pi$
$11$		−	5.27792i		−	1.59135i	0.605723	−	0.795676i	$-0.292884\pi$
$12$	−2.44949	−	1.73205i	−0.707107	−	0.500000i
$13$		−	0.267949i		−	0.0743157i	−0.999309	−	0.0371579i	$-0.988170\pi$
$13$		−	0.267949i		−	0.0743157i	0.999309	−	0.0371579i	$-0.0118304\pi$
$14$	−0.138701			−0.0370693
$15$	1.41421	−	2.00000i	0.365148	−	0.516398i
$16$	2.46410			0.616025
$17$		−	4.89898i		−	1.18818i	−0.804400	−	0.594089i	$-0.797513\pi$
$17$		−	4.89898i		−	1.18818i	0.804400	−	0.594089i	$-0.202487\pi$
$18$	0.517638	+	1.46410i	0.122008	+	0.345092i
$19$		0			0
$19$		0			0
$20$			2.44949i			0.547723i
$21$	−0.378937	−	0.267949i	−0.0826909	−	0.0584713i
$22$		−	2.73205i		−	0.582475i
$23$		−	5.27792i		−	1.10052i	−0.834993	−	0.550261i	$-0.814528\pi$
$23$		−	5.27792i		−	1.10052i	0.834993	−	0.550261i	$-0.185472\pi$
$24$	−2.73205	−	1.93185i	−0.557678	−	0.394338i
$25$	3.00000			0.600000
$26$		−	0.138701i		−	0.0272014i
$27$	−1.41421	+	5.00000i	−0.272166	+	0.962250i
$28$	0.464102			0.0877070
$29$	−2.07055			−0.384492			−0.192246	−	0.981347i	$-0.561577\pi$
$29$	−2.07055			−0.384492			−0.192246	+	0.981347i	$0.561577\pi$
$30$	0.732051	−	1.03528i	0.133654	−	0.189015i
$31$			2.46410i			0.442566i	0.975210	+	0.221283i	$0.0710244\pi$
$31$			2.46410i			0.442566i	−0.975210	+	0.221283i	$0.928976\pi$
$32$	5.13922			0.908494
$33$	5.27792	−	7.46410i	0.918767	−	1.29933i
$34$		−	2.53590i		−	0.434903i
$35$			0.378937i			0.0640521i
$36$	−1.73205	−	4.89898i	−0.288675	−	0.816497i
$37$		−	7.73205i		−	1.27114i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$		−	7.73205i		−	1.27114i	0.772043	−	0.635571i	$-0.219235\pi$
$38$		0			0
$39$	0.267949	−	0.378937i	0.0429062	−	0.0606785i
$40$			2.73205i			0.431975i
$41$	5.65685			0.883452			0.441726	−	0.897150i	$-0.354366\pi$
$41$	5.65685			0.883452			0.441726	+	0.897150i	$0.354366\pi$
$42$	−0.196152	−	0.138701i	−0.0302670	−	0.0214020i
$43$	5.73205			0.874130			0.437065	−	0.899430i	$-0.356018\pi$
$43$	5.73205			0.874130			0.437065	+	0.899430i	$0.356018\pi$
$44$			9.14162i			1.37815i
$45$	4.00000	−	1.41421i	0.596285	−	0.210819i
$46$		−	2.73205i		−	0.402819i
$47$		−	0.757875i		−	0.110547i	−0.998471	−	0.0552737i	$-0.982397\pi$
$47$		−	0.757875i		−	0.110547i	0.998471	−	0.0552737i	$-0.0176031\pi$
$48$	3.48477	+	2.46410i	0.502983	+	0.355662i
$49$	−6.92820			−0.989743
$50$	1.55291			0.219615
$51$	4.89898	−	6.92820i	0.685994	−	0.970143i
$52$			0.464102i			0.0643593i
$53$	10.9348			1.50201			0.751003	−	0.660299i	$-0.229570\pi$
$53$	10.9348			1.50201			0.751003	+	0.660299i	$0.229570\pi$
$54$	−0.732051	+	2.58819i	−0.0996195	+	0.352208i
$55$	−7.46410			−1.00646
$56$	0.517638			0.0691723
$57$		0			0
$58$	−1.07180			−0.140734
$59$	−11.2122			−1.45970			−0.729850	−	0.683607i	$-0.760410\pi$
$59$	−11.2122			−1.45970			−0.729850	+	0.683607i	$0.760410\pi$
$60$	−2.44949	+	3.46410i	−0.316228	+	0.447214i
$61$	−10.4641			−1.33979			−0.669895	−	0.742455i	$-0.733661\pi$
$61$	−10.4641			−1.33979			−0.669895	+	0.742455i	$0.733661\pi$
$62$			1.27551i			0.161990i
$63$	−0.267949	−	0.757875i	−0.0337584	−	0.0954832i
$64$	−2.26795			−0.283494
$65$	−0.378937			−0.0470014
$66$	2.73205	−	3.86370i	0.336292	−	0.475589i
$67$		−	1.00000i		−	0.122169i	−0.998133	−	0.0610847i	$-0.980544\pi$
$67$		−	1.00000i		−	0.122169i	0.998133	−	0.0610847i	$-0.0194560\pi$
$68$			8.48528i			1.02899i
$69$	5.27792	−	7.46410i	0.635387	−	0.898572i
$70$			0.196152i			0.0234447i
$71$	13.3843			1.58842			0.794210	−	0.607644i	$-0.207885\pi$
$71$	13.3843			1.58842			0.794210	+	0.607644i	$0.207885\pi$
$72$	−1.93185	−	5.46410i	−0.227671	−	0.643951i
$73$	−3.00000			−0.351123			−0.175562	−	0.984468i	$-0.556174\pi$
$73$	−3.00000			−0.351123			−0.175562	+	0.984468i	$0.556174\pi$
$74$		−	4.00240i		−	0.465270i
$75$	4.24264	+	3.00000i	0.489898	+	0.346410i
$76$		0			0
$77$			1.41421i			0.161165i
$78$	0.138701	−	0.196152i	0.0157048	−	0.0222099i
$79$		−	10.4641i		−	1.17730i	−0.808387	−	0.588652i	$-0.799659\pi$
$79$		−	10.4641i		−	1.17730i	0.808387	−	0.588652i	$-0.200341\pi$
$80$		−	3.48477i		−	0.389609i
$81$	−7.00000	+	5.65685i	−0.777778	+	0.628539i
$82$	2.92820			0.323366
$83$			2.07055i			0.227273i	0.993522	+	0.113636i	$0.0362499\pi$
$83$			2.07055i			0.227273i	−0.993522	+	0.113636i	$0.963750\pi$
$84$	0.656339	+	0.464102i	0.0716124	+	0.0506376i
$85$	−6.92820			−0.751469
$86$	2.96713			0.319954
$87$	−2.92820	−	2.07055i	−0.313936	−	0.221987i
$88$			10.1962i			1.08691i
$89$	−7.34847			−0.778936			−0.389468	−	0.921040i	$-0.627341\pi$
$89$	−7.34847			−0.778936			−0.389468	+	0.921040i	$0.627341\pi$
$90$	2.07055	−	0.732051i	0.218255	−	0.0771649i
$91$			0.0717968i			0.00752635i
$92$			9.14162i			0.953080i
$93$	−2.46410	+	3.48477i	−0.255515	+	0.361353i
$94$		−	0.392305i		−	0.0404632i
$95$		0			0
$96$	7.26795	+	5.13922i	0.741782	+	0.524519i
$97$			0.535898i			0.0544122i	0.999630	+	0.0272061i	$0.00866105\pi$
$97$			0.535898i			0.0544122i	−0.999630	+	0.0272061i	$0.991339\pi$
$98$	−3.58630			−0.362271
$99$	14.9282	−	5.27792i	1.50034	−	0.530451i
$100$	−5.19615			−0.519615
$101$		−	2.07055i		−	0.206028i	−0.994680	−	0.103014i	$-0.967151\pi$
$101$		−	2.07055i		−	0.206028i	0.994680	−	0.103014i	$-0.0328486\pi$
$102$	2.53590	−	3.58630i	0.251091	−	0.355097i
$103$			3.53590i			0.348402i	0.984710	+	0.174201i	$0.0557343\pi$
$103$			3.53590i			0.348402i	−0.984710	+	0.174201i	$0.944266\pi$
$104$			0.517638i			0.0507586i
$105$	−0.378937	+	0.535898i	−0.0369805	+	0.0522983i
$106$	5.66025			0.549772
$107$	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
$109$			6.39230i			0.612272i	0.951988	+	0.306136i	$0.0990362\pi$
$109$			6.39230i			0.612272i	−0.951988	+	0.306136i	$0.900964\pi$
$110$	−3.86370			−0.368390
$111$	7.73205	−	10.9348i	0.733894	−	1.03788i
$112$	−0.660254			−0.0623881
$113$	3.96524			0.373018			0.186509	−	0.982453i	$-0.440283\pi$
$113$	3.96524			0.373018			0.186509	+	0.982453i	$0.440283\pi$
$114$		0			0
$115$	−7.46410			−0.696031
$116$	3.58630			0.332980
$117$	0.757875	−	0.267949i	0.0700655	−	0.0247719i
$118$	−5.80385			−0.534287
$119$			1.31268i			0.120333i
$120$	−2.73205	+	3.86370i	−0.249401	+	0.352706i
$121$	−16.8564			−1.53240
$122$	−5.41662			−0.490398
$123$	8.00000	+	5.65685i	0.721336	+	0.510061i
$124$		−	4.26795i		−	0.383273i
$125$		−	11.3137i		−	1.01193i
$126$	−0.138701	−	0.392305i	−0.0123564	−	0.0349493i
$127$			19.8564i			1.76197i	0.473143	+	0.880986i	$0.343119\pi$
$127$			19.8564i			1.76197i	−0.473143	+	0.880986i	$0.656881\pi$
$128$	−11.4524			−1.01226
$129$	8.10634	+	5.73205i	0.713724	+	0.504679i
$130$	−0.196152			−0.0172037
$131$			12.6264i			1.10317i	0.834118	+	0.551586i	$0.185977\pi$
$131$			12.6264i			1.10317i	−0.834118	+	0.551586i	$0.814023\pi$
$132$	−9.14162	+	12.9282i	−0.795676	+	1.12526i
$133$		0			0
$134$		−	0.517638i		−	0.0447171i
$135$	7.07107	+	2.00000i	0.608581	+	0.172133i
$136$			9.46410i			0.811540i
$137$			10.5558i			0.901846i	0.892563	+	0.450923i	$0.148905\pi$
$137$			10.5558i			0.901846i	−0.892563	+	0.450923i	$0.851095\pi$
$138$	2.73205	−	3.86370i	0.232568	−	0.328900i
$139$	2.80385			0.237819			0.118910	−	0.992905i	$-0.462060\pi$
$139$	2.80385			0.237819			0.118910	+	0.992905i	$0.462060\pi$
$140$		−	0.656339i		−	0.0554708i
$141$	0.757875	−	1.07180i	0.0638246	−	0.0902616i
$142$	6.92820			0.581402
$143$	−1.41421			−0.118262
$144$	2.46410	+	6.96953i	0.205342	+	0.580794i
$145$			2.92820i			0.243174i
$146$	−1.55291			−0.128520
$147$	−9.79796	−	6.92820i	−0.808122	−	0.571429i
$148$			13.3923i			1.10084i
$149$		−	2.72689i		−	0.223396i	−0.993742	−	0.111698i	$-0.964371\pi$
$149$		−	2.72689i		−	0.223396i	0.993742	−	0.111698i	$-0.0356289\pi$
$150$	2.19615	+	1.55291i	0.179315	+	0.126795i
$151$		−	2.00000i		−	0.162758i	−0.996683	−	0.0813788i	$-0.974068\pi$
$151$		−	2.00000i		−	0.162758i	0.996683	−	0.0813788i	$-0.0259324\pi$
$152$		0			0
$153$	13.8564	−	4.89898i	1.12022	−	0.396059i
$154$			0.732051i			0.0589903i
$155$	3.48477			0.279903
$156$	−0.464102	+	0.656339i	−0.0371579	+	0.0525492i
$157$	10.4641			0.835126			0.417563	−	0.908648i	$-0.362884\pi$
$157$	10.4641			0.835126			0.417563	+	0.908648i	$0.362884\pi$
$158$		−	5.41662i		−	0.430923i
$159$	15.4641	+	10.9348i	1.22638	+	0.867184i
$160$		−	7.26795i		−	0.574582i
$161$			1.41421i			0.111456i
$162$	−3.62347	+	2.92820i	−0.284686	+	0.230061i
$163$	−5.19615			−0.406994			−0.203497	−	0.979076i	$-0.565231\pi$
$163$	−5.19615			−0.406994			−0.203497	+	0.979076i	$0.565231\pi$
$164$	−9.79796			−0.765092
$165$	−10.5558	−	7.46410i	−0.821771	−	0.581080i
$166$			1.07180i			0.0831876i
$167$	−21.7680			−1.68446			−0.842229	−	0.539119i	$-0.818757\pi$
$167$	−21.7680			−1.68446			−0.842229	+	0.539119i	$0.818757\pi$
$168$	0.732051	+	0.517638i	0.0564789	+	0.0399366i
$169$	12.9282			0.994477
$170$	−3.58630			−0.275057
$171$		0			0
$172$	−9.92820			−0.757018
$173$	17.5254			1.33243			0.666214	−	0.745760i	$-0.267914\pi$
$173$	17.5254			1.33243			0.666214	+	0.745760i	$0.267914\pi$
$174$	−1.51575	−	1.07180i	−0.114909	−	0.0812527i
$175$	−0.803848			−0.0607652
$176$		−	13.0053i		−	0.980313i
$177$	−15.8564	−	11.2122i	−1.19184	−	0.842758i
$178$	−3.80385			−0.285110
$179$	1.41421			0.105703			0.0528516	−	0.998602i	$-0.483169\pi$
$179$	1.41421			0.105703			0.0528516	+	0.998602i	$0.483169\pi$
$180$	−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	$-0.0410940\pi$
$182$			0.0371647i			0.00275483i
$183$	−14.7985	−	10.4641i	−1.09393	−	0.773529i
$184$			10.1962i			0.751670i
$185$	−10.9348			−0.803940
$186$	−1.27551	+	1.80385i	−0.0935251	+	0.132265i
$187$	−25.8564			−1.89081
$188$			1.31268i			0.0957369i
$189$	0.378937	−	1.33975i	0.0275636	−	0.0974522i
$190$		0			0
$191$		−	13.0053i		−	0.941032i	−0.882391	−	0.470516i	$-0.844068\pi$
$191$		−	13.0053i		−	0.941032i	0.882391	−	0.470516i	$-0.155932\pi$
$192$	−3.20736	−	2.26795i	−0.231472	−	0.163675i
$193$			2.80385i			0.201825i	0.994895	+	0.100913i	$0.0321763\pi$
$193$			2.80385i			0.201825i	−0.994895	+	0.100913i	$0.967824\pi$
$194$			0.277401i			0.0199163i
$195$	−0.535898	−	0.378937i	−0.0383765	−	0.0271363i
$196$	12.0000			0.857143
$197$			0.656339i			0.0467622i	0.999727	+	0.0233811i	$0.00744311\pi$
$197$			0.656339i			0.0467622i	−0.999727	+	0.0233811i	$0.992557\pi$
$198$	7.72741	−	2.73205i	0.549163	−	0.194158i
$199$	−23.1962			−1.64433			−0.822166	−	0.569248i	$-0.807234\pi$
$199$	−23.1962			−1.64433			−0.822166	+	0.569248i	$0.807234\pi$
$200$	−5.79555			−0.409808
$201$	1.00000	−	1.41421i	0.0705346	−	0.0997509i
$202$		−	1.07180i		−	0.0754114i
$203$	0.554803			0.0389395
$204$	−8.48528	+	12.0000i	−0.594089	+	0.840168i
$205$		−	8.00000i		−	0.558744i
$206$			1.83032i			0.127524i
$207$	14.9282	−	5.27792i	1.03758	−	0.366841i
$208$		−	0.660254i		−	0.0457804i
$209$		0			0
$210$	−0.196152	+	0.277401i	−0.0135358	+	0.0191425i
$211$		−	11.0000i		−	0.757271i	−0.925546	−	0.378636i	$-0.876393\pi$
$211$		−	11.0000i		−	0.757271i	0.925546	−	0.378636i	$-0.123607\pi$
$212$	−18.9396			−1.30078
$213$	18.9282	+	13.3843i	1.29694	+	0.917074i
$214$	2.53590			0.173350
$215$		−	8.10634i		−	0.552848i
$216$	2.73205	−	9.65926i	0.185893	−	0.657229i
$217$		−	0.660254i		−	0.0448210i
$218$			3.30890i			0.224107i
$219$	−4.24264	−	3.00000i	−0.286691	−	0.202721i
$220$	12.9282			0.871619
$221$	−1.31268			−0.0883003
$222$	4.00240	−	5.66025i	0.268624	−	0.379891i
$223$			11.3923i			0.762885i	0.924393	+	0.381443i	$0.124573\pi$
$223$			11.3923i			0.762885i	−0.924393	+	0.381443i	$0.875427\pi$
$224$	−1.37705			−0.0920079
$225$	3.00000	+	8.48528i	0.200000	+	0.565685i
$226$	2.05256			0.136534
$227$	4.79744			0.318418			0.159209	−	0.987245i	$-0.449106\pi$
$227$	4.79744			0.318418			0.159209	+	0.987245i	$0.449106\pi$
$228$		0			0
$229$	−11.3923			−0.752825			−0.376412	−	0.926452i	$-0.622842\pi$
$229$	−11.3923			−0.752825			−0.376412	+	0.926452i	$0.622842\pi$
$230$	−3.86370			−0.254765
$231$	−1.41421	+	2.00000i	−0.0930484	+	0.131590i
$232$	4.00000			0.262613
$233$			13.3843i			0.876832i	0.898772	+	0.438416i	$0.144460\pi$
$233$			13.3843i			0.876832i	−0.898772	+	0.438416i	$0.855540\pi$
$234$	0.392305	−	0.138701i	0.0256458	−	0.00906715i
$235$	−1.07180			−0.0699163
$236$	19.4201			1.26414
$237$	10.4641	−	14.7985i	0.679716	−	0.961264i
$238$			0.679492i			0.0440449i
$239$			15.2789i			0.988313i	0.869373	+	0.494156i	$0.164523\pi$
$239$			15.2789i			0.988313i	−0.869373	+	0.494156i	$0.835477\pi$
$240$	3.48477	−	4.92820i	0.224941	−	0.318114i
$241$			11.3397i			0.730457i	0.930918	+	0.365229i	$0.119009\pi$
$241$			11.3397i			0.730457i	−0.930918	+	0.365229i	$0.880991\pi$
$242$	−8.72552			−0.560898
$243$	−15.5563	+	1.00000i	−0.997940	+	0.0641500i
$244$	18.1244			1.16029
$245$			9.79796i			0.625969i
$246$	4.14110	+	2.92820i	0.264027	+	0.186695i
$247$		0			0
$248$		−	4.76028i		−	0.302278i
$249$	−2.07055	+	2.92820i	−0.131216	+	0.185567i
$250$		−	5.85641i		−	0.370392i
$251$			14.6969i			0.927663i	0.885924	+	0.463831i	$0.153526\pi$
$251$			14.6969i			0.927663i	−0.885924	+	0.463831i	$0.846474\pi$
$252$	0.464102	+	1.31268i	0.0292357	+	0.0826909i
$253$	−27.8564			−1.75132
$254$			10.2784i			0.644926i
$255$	−9.79796	−	6.92820i	−0.613572	−	0.433861i
$256$	−1.39230			−0.0870191
$257$	8.10634			0.505660			0.252830	−	0.967511i	$-0.418639\pi$
$257$	8.10634			0.505660			0.252830	+	0.967511i	$0.418639\pi$
$258$	4.19615	+	2.96713i	0.261241	+	0.184725i
$259$			2.07180i			0.128735i
$260$	0.656339			0.0407044
$261$	−2.07055	−	5.85641i	−0.128164	−	0.362502i
$262$			6.53590i			0.403789i
$263$		−	28.8391i		−	1.77829i	−0.457622	−	0.889147i	$-0.651299\pi$
$263$		−	28.8391i		−	1.77829i	0.457622	−	0.889147i	$-0.348701\pi$
$264$	−10.1962	+	14.4195i	−0.627530	+	0.887461i
$265$		−	15.4641i		−	0.949952i
$266$		0			0
$267$	−10.3923	−	7.34847i	−0.635999	−	0.449719i
$268$			1.73205i			0.105802i
$269$	10.9348			0.666705			0.333352	−	0.942802i	$-0.391820\pi$
$269$	10.9348			0.666705			0.333352	+	0.942802i	$0.391820\pi$
$270$	3.66025	+	1.03528i	0.222756	+	0.0630049i
$271$	6.92820			0.420858			0.210429	−	0.977609i	$-0.432514\pi$
$271$	6.92820			0.420858			0.210429	+	0.977609i	$0.432514\pi$
$272$		−	12.0716i		−	0.731947i
$273$	−0.0717968	+	0.101536i	−0.00434534	+	0.00614524i
$274$			5.46410i			0.330098i
$275$		−	15.8338i		−	0.954811i
$276$	−9.14162	+	12.9282i	−0.550261	+	0.778186i
$277$	17.8564			1.07289			0.536444	−	0.843936i	$-0.319767\pi$
$277$	17.8564			1.07289			0.536444	+	0.843936i	$0.319767\pi$
$278$	1.45138			0.0870479
$279$	−6.96953	+	2.46410i	−0.417255	+	0.147522i
$280$		−	0.732051i		−	0.0437484i
$281$	9.41902			0.561892			0.280946	−	0.959724i	$-0.409352\pi$
$281$	9.41902			0.561892			0.280946	+	0.959724i	$0.409352\pi$
$282$	0.392305	−	0.554803i	0.0233614	−	0.0330380i
$283$	5.85641			0.348127			0.174064	−	0.984734i	$-0.444310\pi$
$283$	5.85641			0.348127			0.174064	+	0.984734i	$0.444310\pi$
$284$	−23.1822			−1.37561
$285$		0			0
$286$	−0.732051			−0.0432871
$287$	−1.51575			−0.0894719
$288$	5.13922	+	14.5359i	0.302831	+	0.856536i
$289$	−7.00000			−0.411765
$290$			1.51575i			0.0890079i
$291$	−0.535898	+	0.757875i	−0.0314149	+	0.0444274i
$292$	5.19615			0.304082
$293$	13.9391			0.814329			0.407164	−	0.913355i	$-0.366518\pi$
$293$	13.9391			0.814329			0.407164	+	0.913355i	$0.366518\pi$
$294$	−5.07180	−	3.58630i	−0.295793	−	0.209157i
$295$			15.8564i			0.923196i
$296$			14.9372i			0.868206i
$297$	26.3896	+	7.46410i	1.53128	+	0.433111i
$298$		−	1.41154i		−	0.0817685i
$299$	−1.41421			−0.0817861
$300$	−7.34847	−	5.19615i	−0.424264	−	0.300000i
$301$	−1.53590			−0.0885277
$302$		−	1.03528i		−	0.0595734i
$303$	2.07055	−	2.92820i	0.118950	−	0.168221i
$304$		0			0
$305$			14.7985i			0.847358i
$306$	7.17260	−	2.53590i	0.410030	−	0.144968i
$307$			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
$309$	−3.53590	+	5.00052i	−0.201150	+	0.284469i
$310$	1.80385			0.102452
$311$		−	12.4505i		−	0.706004i	−0.935623	−	0.353002i	$-0.885161\pi$
$311$		−	12.4505i		−	0.706004i	0.935623	−	0.353002i	$-0.114839\pi$
$312$	−0.517638	+	0.732051i	−0.0293055	+	0.0414442i
$313$	16.7846			0.948722			0.474361	−	0.880330i	$-0.342679\pi$
$313$	16.7846			0.948722			0.474361	+	0.880330i	$0.342679\pi$
$314$	5.41662			0.305677
$315$	−1.07180	+	0.378937i	−0.0603889	+	0.0213507i
$316$			18.1244i			1.01957i
$317$	−8.86422			−0.497864			−0.248932	−	0.968521i	$-0.580080\pi$
$317$	−8.86422			−0.497864			−0.248932	+	0.968521i	$0.580080\pi$
$318$	8.00481	+	5.66025i	0.448887	+	0.317411i
$319$			10.9282i			0.611862i
$320$			3.20736i			0.179297i
$321$	6.92820	+	4.89898i	0.386695	+	0.273434i
$322$			0.732051i			0.0407956i
$323$		0			0
$324$	12.1244	−	9.79796i	0.673575	−	0.544331i
$325$		−	0.803848i		−	0.0445894i
$326$	−2.68973			−0.148970
$327$	−6.39230	+	9.04008i	−0.353495	+	0.499918i
$328$	−10.9282			−0.603409
$329$			0.203072i			0.0111957i
$330$	−5.46410	−	3.86370i	−0.300789	−	0.212690i
$331$		−	18.0718i		−	0.993316i	−0.867946	−	0.496658i	$-0.834560\pi$
$331$		−	18.0718i		−	0.993316i	0.867946	−	0.496658i	$-0.165440\pi$
$332$		−	3.58630i		−	0.196824i
$333$	21.8695	−	7.73205i	1.19844	−	0.423714i
$334$	−11.2679			−0.616555
$335$	−1.41421			−0.0772667
$336$	−0.933740	−	0.660254i	−0.0509397	−	0.0360198i
$337$			24.6603i			1.34333i	0.740855	+	0.671665i	$0.234420\pi$
$337$			24.6603i			1.34333i	−0.740855	+	0.671665i	$0.765580\pi$
$338$	6.69213			0.364004
$339$	5.60770	+	3.96524i	0.304568	+	0.215362i
$340$	12.0000			0.650791
$341$	13.0053			0.704278
$342$		0			0
$343$	3.73205			0.201512
$344$	−11.0735			−0.597042
$345$	−10.5558	−	7.46410i	−0.568307	−	0.401854i
$346$	9.07180			0.487703
$347$			19.2170i			1.03162i	0.856703	+	0.515811i	$0.172509\pi$
$347$			19.2170i			1.03162i	−0.856703	+	0.515811i	$0.827491\pi$
$348$	5.07180	+	3.58630i	0.271877	+	0.192246i
$349$	9.39230			0.502759			0.251379	−	0.967889i	$-0.419116\pi$
$349$	9.39230			0.502759			0.251379	+	0.967889i	$0.419116\pi$
$350$	−0.416102			−0.0222416
$351$	1.33975	+	0.378937i	0.0715103	+	0.0202262i
$352$		−	27.1244i		−	1.44573i
$353$			2.17209i			0.115609i	0.998328	+	0.0578043i	$0.0184099\pi$
$353$			2.17209i			0.115609i	−0.998328	+	0.0578043i	$0.981590\pi$
$354$	−8.20788	−	5.80385i	−0.436244	−	0.308471i
$355$		−	18.9282i		−	1.00460i
$356$	12.7279			0.674579
$357$	−1.31268	+	1.85641i	−0.0694743	+	0.0982514i
$358$	0.732051			0.0386901
$359$			7.17260i			0.378556i	0.981924	+	0.189278i	$0.0606147\pi$
$359$			7.17260i			0.378556i	−0.981924	+	0.189278i	$0.939385\pi$
$360$	−7.72741	+	2.73205i	−0.407270	+	0.143992i
$361$		0			0
$362$		−	1.79315i		−	0.0942459i
$363$	−23.8386	−	16.8564i	−1.25120	−	0.884732i
$364$		−	0.124356i		−	0.00651801i
$365$			4.24264i			0.222070i
$366$	−7.66025	−	5.41662i	−0.400408	−	0.283131i
$367$	21.0526			1.09893			0.549467	−	0.835515i	$-0.314831\pi$
$367$	21.0526			1.09893			0.549467	+	0.835515i	$0.314831\pi$
$368$		−	13.0053i		−	0.677949i
$369$	5.65685	+	16.0000i	0.294484	+	0.832927i
$370$	−5.66025			−0.294263
$371$	−2.92996			−0.152116
$372$	4.26795	−	6.03579i	0.221283	−	0.312941i
$373$		−	19.4641i		−	1.00781i	−0.863758	−	0.503906i	$-0.831896\pi$
$373$		−	19.4641i		−	1.00781i	0.863758	−	0.503906i	$-0.168104\pi$
$374$	−13.3843			−0.692084
$375$	11.3137	−	16.0000i	0.584237	−	0.826236i
$376$			1.46410i			0.0755053i
$377$			0.554803i			0.0285738i
$378$	0.196152	−	0.693504i	0.0100890	−	0.0356700i
$379$			23.7846i			1.22173i	0.791733	+	0.610867i	$0.209179\pi$
$379$			23.7846i			1.22173i	−0.791733	+	0.610867i	$0.790821\pi$
$380$		0			0
$381$	−19.8564	+	28.0812i	−1.01727	+	1.43864i
$382$		−	6.73205i		−	0.344442i
$383$	−12.5249			−0.639990			−0.319995	−	0.947419i	$-0.603681\pi$
$383$	−12.5249			−0.639990			−0.319995	+	0.947419i	$0.603681\pi$
$384$	−16.1962	−	11.4524i	−0.826506	−	0.584428i
$385$	2.00000			0.101929
$386$			1.45138i			0.0738732i
$387$	5.73205	+	16.2127i	0.291377	+	0.824137i
$388$		−	0.928203i		−	0.0471224i
$389$			14.7985i			0.750312i	0.926962	+	0.375156i	$0.122411\pi$
$389$			14.7985i			0.750312i	−0.926962	+	0.375156i	$0.877589\pi$
$390$	−0.277401	−	0.196152i	−0.0140468	−	0.00993256i
$391$	−25.8564			−1.30761
$392$	13.3843			0.676007
$393$	−12.6264	+	17.8564i	−0.636917	+	0.900737i
$394$			0.339746i			0.0171162i
$395$	−14.7985			−0.744592
$396$	−25.8564	+	9.14162i	−1.29933	+	0.459384i
$397$	−26.3205			−1.32099			−0.660494	−	0.750831i	$-0.729653\pi$
$397$	−26.3205			−1.32099			−0.660494	+	0.750831i	$0.729653\pi$
$398$	−12.0072			−0.601867
$399$		0			0
$400$	7.39230			0.369615
$401$	22.8033			1.13874			0.569371	−	0.822081i	$-0.307187\pi$
$401$	22.8033			1.13874			0.569371	+	0.822081i	$0.307187\pi$
$402$	0.517638	−	0.732051i	0.0258174	−	0.0365114i
$403$	0.660254			0.0328896
$404$			3.58630i			0.178425i
$405$	8.00000	+	9.89949i	0.397523	+	0.491910i
$406$	0.287187			0.0142529
$407$	−40.8091			−2.02283
$408$	−9.46410	+	13.3843i	−0.468543	+	0.662620i
$409$			20.2487i			1.00123i	0.865669	+	0.500617i	$0.166894\pi$
$409$			20.2487i			1.00123i	−0.865669	+	0.500617i	$0.833106\pi$
$410$		−	4.14110i		−	0.204515i
$411$	−10.5558	+	14.9282i	−0.520681	+	0.736354i
$412$		−	6.12436i		−	0.301725i
$413$	3.00429			0.147832
$414$	7.72741	−	2.73205i	0.379781	−	0.134273i
$415$	2.92820			0.143740
$416$		−	1.37705i		−	0.0675154i
$417$	3.96524	+	2.80385i	0.194179	+	0.137305i
$418$		0			0
$419$			7.55154i			0.368917i	0.982840	+	0.184458i	$0.0590531\pi$
$419$			7.55154i			0.368917i	−0.982840	+	0.184458i	$0.940947\pi$
$420$	0.656339	−	0.928203i	0.0320261	−	0.0452917i
$421$		−	28.5359i		−	1.39075i	−0.718645	−	0.695377i	$-0.755237\pi$
$421$		−	28.5359i		−	1.39075i	0.718645	−	0.695377i	$-0.244763\pi$
$422$		−	5.69402i		−	0.277181i
$423$	2.14359	−	0.757875i	0.104225	−	0.0368491i
$424$	−21.1244			−1.02589
$425$		−	14.6969i		−	0.712906i
$426$	9.79796	+	6.92820i	0.474713	+	0.335673i
$427$	2.80385			0.135688
$428$	−8.48528			−0.410152
$429$	−2.00000	−	1.41421i	−0.0965609	−	0.0682789i
$430$		−	4.19615i		−	0.202356i
$431$	25.4558			1.22616			0.613082	−	0.790019i	$-0.289929\pi$
$431$	25.4558			1.22616			0.613082	+	0.790019i	$0.289929\pi$
$432$	−3.48477	+	12.3205i	−0.167661	+	0.592771i
$433$		−	20.6603i		−	0.992868i	−0.868074	−	0.496434i	$-0.834642\pi$
$433$		−	20.6603i		−	0.992868i	0.868074	−	0.496434i	$-0.165358\pi$
$434$		−	0.341773i		−	0.0164056i
$435$	−2.92820	+	4.14110i	−0.140397	+	0.198551i
$436$		−	11.0718i		−	0.530243i
$437$		0			0
$438$	−2.19615	−	1.55291i	−0.104936	−	0.0742011i
$439$			15.5359i			0.741488i	0.928735	+	0.370744i	$0.120897\pi$
$439$			15.5359i			0.741488i	−0.928735	+	0.370744i	$0.879103\pi$
$440$	14.4195			0.687424
$441$	−6.92820	−	19.5959i	−0.329914	−	0.933139i
$442$	−0.679492			−0.0323201
$443$			10.3528i			0.491875i	0.969286	+	0.245937i	$0.0790957\pi$
$443$			10.3528i			0.491875i	−0.969286	+	0.245937i	$0.920904\pi$
$444$	−13.3923	+	18.9396i	−0.635571	+	0.898833i
$445$			10.3923i			0.492642i
$446$			5.89709i			0.279235i
$447$	2.72689	−	3.85641i	0.128978	−	0.182402i
$448$	0.607695			0.0287109
$449$	5.10205			0.240781			0.120390	−	0.992727i	$-0.461585\pi$
$449$	5.10205			0.240781			0.120390	+	0.992727i	$0.461585\pi$
$450$	1.55291	+	4.39230i	0.0732051	+	0.207055i
$451$		−	29.8564i		−	1.40588i
$452$	−6.86800			−0.323043
$453$	2.00000	−	2.82843i	0.0939682	−	0.132891i
$454$	2.48334			0.116549
$455$	0.101536			0.00476008
$456$		0			0
$457$	34.7128			1.62380			0.811898	−	0.583799i	$-0.198434\pi$
$457$	34.7128			1.62380			0.811898	+	0.583799i	$0.198434\pi$
$458$	−5.89709			−0.275553
$459$	24.4949	+	6.92820i	1.14332	+	0.323381i
$460$	12.9282			0.602781
$461$		−	35.7071i		−	1.66304i	−0.555492	−	0.831522i	$-0.687470\pi$
$461$		−	35.7071i		−	1.66304i	0.555492	−	0.831522i	$-0.312530\pi$
$462$	−0.732051	+	1.03528i	−0.0340581	+	0.0481654i
$463$	1.58846			0.0738219			0.0369109	−	0.999319i	$-0.488248\pi$
$463$	1.58846			0.0738219			0.0369109	+	0.999319i	$0.488248\pi$
$464$	−5.10205			−0.236857
$465$	4.92820	+	3.48477i	0.228540	+	0.161602i
$466$			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	$-0.175387\pi$
$468$	−1.31268	+	0.464102i	−0.0606785	+	0.0214531i
$469$			0.267949i			0.0123727i
$470$	−0.554803			−0.0255911
$471$	14.7985	+	10.4641i	0.681878	+	0.482160i
$472$	21.6603			0.996994
$473$		−	30.2533i		−	1.39105i
$474$	5.41662	−	7.66025i	0.248793	−	0.351847i
$475$		0			0
$476$		−	2.27362i		−	0.104211i
$477$	10.9348	+	30.9282i	0.500669	+	1.41611i
$478$			7.90897i			0.361748i
$479$		−	17.5254i		−	0.800754i	−0.916350	−	0.400377i	$-0.868879\pi$
$479$		−	17.5254i		−	0.800754i	0.916350	−	0.400377i	$-0.131121\pi$
$480$	7.26795	−	10.2784i	0.331735	−	0.469144i
$481$	−2.07180			−0.0944658
$482$			5.86988i			0.267366i
$483$	−1.41421	+	2.00000i	−0.0643489	+	0.0910032i
$484$	29.1962			1.32710
$485$	0.757875			0.0344133
$486$	−8.05256	+	0.517638i	−0.365271	+	0.0234805i
$487$			11.0718i			0.501711i	0.968025	+	0.250856i	$0.0807119\pi$
$487$			11.0718i			0.501711i	−0.968025	+	0.250856i	$0.919288\pi$
$488$	20.2151			0.915094
$489$	−7.34847	−	5.19615i	−0.332309	−	0.234978i
$490$			5.07180i			0.229120i
$491$			29.5969i			1.33569i	0.744300	+	0.667846i	$0.232783\pi$
$491$			29.5969i			1.33569i	−0.744300	+	0.667846i	$0.767217\pi$
$492$	−13.8564	−	9.79796i	−0.624695	−	0.441726i
$493$			10.1436i			0.456844i
$494$		0			0
$495$	−7.46410	−	21.1117i	−0.335486	−	0.948899i
$496$			6.07180i			0.272632i
$497$	−3.58630			−0.160868
$498$	−1.07180	+	1.51575i	−0.0480284	+	0.0679224i
$499$	8.12436			0.363696			0.181848	−	0.983327i	$-0.441792\pi$
$499$	8.12436			0.363696			0.181848	+	0.983327i	$0.441792\pi$
$500$			19.5959i			0.876356i
$501$	−30.7846	−	21.7680i	−1.37535	−	0.972523i
$502$			7.60770i			0.339548i
$503$		−	1.31268i		−	0.0585294i	−0.999572	−	0.0292647i	$-0.990683\pi$
$503$		−	1.31268i		−	0.0585294i	0.999572	−	0.0292647i	$-0.00931657\pi$
$504$	0.517638	+	1.46410i	0.0230574	+	0.0652163i
$505$	−2.92820			−0.130303
$506$	−14.4195			−0.641027
$507$	18.2832	+	12.9282i	0.811987	+	0.574162i
$508$		−	34.3923i		−	1.52591i
$509$	42.9812			1.90511			0.952554	−	0.304369i	$-0.0984455\pi$
$509$	42.9812			1.90511			0.952554	+	0.304369i	$0.0984455\pi$
$510$	−5.07180	−	3.58630i	−0.224583	−	0.158804i
$511$	0.803848			0.0355601
$512$	22.1841			0.980408
$513$		0			0
$514$	4.19615			0.185084
$515$	5.00052			0.220349
$516$	−14.0406	−	9.92820i	−0.618103	−	0.437065i
$517$	−4.00000			−0.175920
$518$			1.07244i			0.0471203i
$519$	24.7846	+	17.5254i	1.08792	+	0.769278i
$520$	0.732051			0.0321026
$521$	10.1769			0.445858			0.222929	−	0.974835i	$-0.428438\pi$
$521$	10.1769			0.445858			0.222929	+	0.974835i	$0.428438\pi$
$522$	−1.07180	−	3.03150i	−0.0469113	−	0.132685i
$523$		−	10.8564i		−	0.474718i	−0.971422	−	0.237359i	$-0.923718\pi$
$523$		−	10.8564i		−	0.474718i	0.971422	−	0.237359i	$-0.0762817\pi$
$524$		−	21.8695i		−	0.955375i
$525$	−1.13681	−	0.803848i	−0.0496145	−	0.0350828i
$526$		−	14.9282i		−	0.650901i
$527$	12.0716			0.525846
$528$	13.0053	−	18.3923i	0.565984	−	0.800422i
$529$	−4.85641			−0.211148
$530$		−	8.00481i		−	0.347707i
$531$	−11.2122	−	31.7128i	−0.486567	−	1.37622i
$532$		0			0
$533$		−	1.51575i		−	0.0656544i
$534$	−5.37945	−	3.80385i	−0.232792	−	0.164609i
$535$		−	6.92820i		−	0.299532i
$536$			1.93185i			0.0834433i
$537$	2.00000	+	1.41421i	0.0863064	+	0.0610278i
$538$	5.66025			0.244031
$539$			36.5665i			1.57503i
$540$	−12.2474	−	3.46410i	−0.527046	−	0.149071i
$541$	−24.4641			−1.05179			−0.525897	−	0.850548i	$-0.676270\pi$
$541$	−24.4641			−1.05179			−0.525897	+	0.850548i	$0.676270\pi$
$542$	3.58630			0.154045
$543$	3.46410	−	4.89898i	0.148659	−	0.210235i
$544$		−	25.1769i		−	1.07945i
$545$	9.04008			0.387235
$546$	−0.0371647	+	0.0525589i	−0.00159050	+	0.00224931i
$547$		−	14.8564i		−	0.635214i	−0.948222	−	0.317607i	$-0.897121\pi$
$547$		−	14.8564i		−	0.635214i	0.948222	−	0.317607i	$-0.102879\pi$
$548$		−	18.2832i		−	0.781021i
$549$	−10.4641	−	29.5969i	−0.446597	−	1.26317i
$550$		−	8.19615i		−	0.349485i
$551$		0			0
$552$	−10.1962	+	14.4195i	−0.433977	+	0.613736i
$553$			2.80385i			0.119232i
$554$	9.24316			0.392704
$555$	−15.4641	−	10.9348i	−0.656415	−	0.464155i
$556$	−4.85641			−0.205958
$557$		−	26.0106i		−	1.10211i	−0.834470	−	0.551053i	$-0.814226\pi$
$557$		−	26.0106i		−	1.10211i	0.834470	−	0.551053i	$-0.185774\pi$
$558$	−3.60770	+	1.27551i	−0.152726	+	0.0539968i
$559$		−	1.53590i		−	0.0649616i
$560$			0.933740i			0.0394577i
$561$	−36.5665	−	25.8564i	−1.54384	−	1.09166i
$562$	4.87564			0.205667
$563$	−26.0106			−1.09622			−0.548109	−	0.836407i	$-0.684652\pi$
$563$	−26.0106			−1.09622			−0.548109	+	0.836407i	$0.684652\pi$
$564$	−1.31268	+	1.85641i	−0.0552737	+	0.0781688i
$565$		−	5.60770i		−	0.235918i
$566$	3.03150			0.127423
$567$	1.87564	−	1.51575i	0.0787697	−	0.0636555i
$568$	−25.8564			−1.08491
$569$	25.2528			1.05865			0.529326	−	0.848419i	$-0.322445\pi$
$569$	25.2528			1.05865			0.529326	+	0.848419i	$0.322445\pi$
$570$		0			0
$571$	14.8038			0.619522			0.309761	−	0.950814i	$-0.399751\pi$
$571$	14.8038			0.619522			0.309761	+	0.950814i	$0.399751\pi$
$572$	2.44949			0.102418
$573$	13.0053	−	18.3923i	0.543305	−	0.768350i
$574$	−0.784610			−0.0327490
$575$		−	15.8338i		−	0.660313i
$576$	−2.26795	−	6.41473i	−0.0944979	−	0.267280i
$577$	29.0718			1.21027			0.605137	−	0.796121i	$-0.293118\pi$
$577$	29.0718			1.21027			0.605137	+	0.796121i	$0.293118\pi$
$578$	−3.62347			−0.150716
$579$	−2.80385	+	3.96524i	−0.116524	+	0.164790i
$580$		−	5.07180i		−	0.210595i
$581$		−	0.554803i		−	0.0230171i
$582$	−0.277401	+	0.392305i	−0.0114987	+	0.0162616i
$583$		−	57.7128i		−	2.39022i
$584$	5.79555			0.239822
$585$	−0.378937	−	1.07180i	−0.0156671	−	0.0443133i
$586$	7.21539			0.298065
$587$		−	33.3591i		−	1.37688i	−0.725294	−	0.688439i	$-0.758296\pi$
$587$		−	33.3591i		−	1.37688i	0.725294	−	0.688439i	$-0.241704\pi$
$588$	16.9706	+	12.0000i	0.699854	+	0.494872i
$589$		0			0
$590$			8.20788i			0.337913i
$591$	−0.656339	+	0.928203i	−0.0269982	+	0.0381812i
$592$		−	19.0526i		−	0.783055i
$593$		−	33.6365i		−	1.38129i	−0.723196	−	0.690643i	$-0.757328\pi$
$593$		−	33.6365i		−	1.38129i	0.723196	−	0.690643i	$-0.242672\pi$
$594$	13.6603	+	3.86370i	0.560487	+	0.158530i
$595$	1.85641			0.0761052
$596$			4.72311i			0.193466i
$597$	−32.8043	−	23.1962i	−1.34259	−	0.949355i
$598$	−0.732051			−0.0299358
$599$	−2.72689			−0.111418			−0.0557089	−	0.998447i	$-0.517742\pi$
$599$	−2.72689			−0.111418			−0.0557089	+	0.998447i	$0.517742\pi$
$600$	−8.19615	−	5.79555i	−0.334607	−	0.236603i
$601$		−	28.3731i		−	1.15736i	−0.815554	−	0.578681i	$-0.803568\pi$
$601$		−	28.3731i		−	1.15736i	0.815554	−	0.578681i	$-0.196432\pi$
$602$	−0.795040			−0.0324034
$603$	2.82843	−	1.00000i	0.115182	−	0.0407231i
$604$			3.46410i			0.140952i
$605$			23.8386i			0.969175i
$606$	1.07180	−	1.51575i	0.0435388	−	0.0615731i
$607$			35.2487i			1.43070i	0.698766	+	0.715351i	$0.253733\pi$
$607$			35.2487i			1.43070i	−0.698766	+	0.715351i	$0.746267\pi$
$608$		0			0
$609$	0.784610	+	0.554803i	0.0317940	+	0.0224817i
$610$			7.66025i			0.310155i
$611$	−0.203072			−0.00821541
$612$	−24.0000	+	8.48528i	−0.970143	+	0.342997i
$613$	−46.6410			−1.88381			−0.941906	−	0.335875i	$-0.890968\pi$
$613$	−46.6410			−1.88381			−0.941906	+	0.335875i	$0.890968\pi$
$614$			7.17260i			0.289463i
$615$	8.00000	−	11.3137i	0.322591	−	0.456213i
$616$		−	2.73205i		−	0.110077i
$617$			23.0807i			0.929193i	0.885522	+	0.464597i	$0.153801\pi$
$617$			23.0807i			0.929193i	−0.885522	+	0.464597i	$0.846199\pi$
$618$	−1.83032	+	2.58846i	−0.0736261	+	0.104123i
$619$	13.1962			0.530398			0.265199	−	0.964194i	$-0.414562\pi$
$619$	13.1962			0.530398			0.265199	+	0.964194i	$0.414562\pi$
$620$	−6.03579			−0.242403
$621$	26.3896	+	7.46410i	1.05898	+	0.299524i
$622$		−	6.44486i		−	0.258415i
$623$	1.96902			0.0788870
$624$	0.660254	−	0.933740i	0.0264313	−	0.0373795i
$625$	−1.00000			−0.0400000
$626$	8.68835			0.347256
$627$		0			0
$628$	−18.1244			−0.723241
$629$	−37.8792			−1.51034
$630$	−0.554803	+	0.196152i	−0.0221039	+	0.00781490i
$631$	10.9474			0.435811			0.217905	−	0.975970i	$-0.430078\pi$
$631$	10.9474			0.435811			0.217905	+	0.975970i	$0.430078\pi$
$632$			20.2151i			0.804113i
$633$	11.0000	−	15.5563i	0.437211	−	0.618309i
$634$	−4.58846			−0.182231
$635$	28.0812			1.11437
$636$	−26.7846	−	18.9396i	−1.06208	−	0.751003i
$637$			1.85641i			0.0735535i
$638$			5.65685i			0.223957i
$639$	13.3843	+	37.8564i	0.529473	+	1.49758i
$640$			16.1962i			0.640209i
$641$	32.4254			1.28073			0.640363	−	0.768073i	$-0.278784\pi$
$641$	32.4254			1.28073			0.640363	+	0.768073i	$0.278784\pi$
$642$	3.58630	+	2.53590i	0.141540	+	0.100084i
$643$	−12.4115			−0.489463			−0.244732	−	0.969591i	$-0.578700\pi$
$643$	−12.4115			−0.489463			−0.244732	+	0.969591i	$0.578700\pi$
$644$		−	2.44949i		−	0.0965234i
$645$	8.10634	−	11.4641i	0.319187	−	0.451399i
$646$		0			0
$647$		−	30.3548i		−	1.19337i	−0.802475	−	0.596686i	$-0.796484\pi$
$647$		−	30.3548i		−	1.19337i	0.802475	−	0.596686i	$-0.203516\pi$
$648$	13.5230	−	10.9282i	0.531232	−	0.429300i
$649$			59.1769i			2.32290i
$650$		−	0.416102i		−	0.0163209i
$651$	0.660254	−	0.933740i	0.0258774	−	0.0365962i
$652$	9.00000			0.352467
$653$		−	1.86748i		−	0.0730802i	−0.999332	−	0.0365401i	$-0.988366\pi$
$653$		−	1.86748i		−	0.0730802i	0.999332	−	0.0365401i	$-0.0116337\pi$
$654$	−3.30890	+	4.67949i	−0.129388	+	0.182983i
$655$	17.8564			0.697708
$656$	13.9391			0.544229
$657$	−3.00000	−	8.48528i	−0.117041	−	0.331042i
$658$			0.105118i			0.00409792i
$659$	3.68784			0.143658			0.0718289	−	0.997417i	$-0.477116\pi$
$659$	3.68784			0.143658			0.0718289	+	0.997417i	$0.477116\pi$
$660$	18.2832	+	12.9282i	0.711674	+	0.503230i
$661$		−	33.8564i		−	1.31686i	−0.752641	−	0.658431i	$-0.771221\pi$
$661$		−	33.8564i		−	1.31686i	0.752641	−	0.658431i	$-0.228779\pi$
$662$		−	9.35465i		−	0.363579i
$663$	−1.85641	−	1.31268i	−0.0720969	−	0.0509802i
$664$		−	4.00000i		−	0.155230i
$665$		0			0
$666$	11.3205	−	4.00240i	0.438661	−	0.155090i
$667$			10.9282i			0.423142i
$668$	37.7033			1.45878
$669$	−11.3923	+	16.1112i	−0.440452	+	0.622893i
$670$	−0.732051			−0.0282816
$671$			55.2287i			2.13208i
$672$	−1.94744	−	1.37705i	−0.0751242	−	0.0531208i
$673$			29.9808i			1.15567i	0.816152	+	0.577837i	$0.196103\pi$
$673$			29.9808i			1.15567i	−0.816152	+	0.577837i	$0.803897\pi$
$674$			12.7651i			0.491693i
$675$	−4.24264	+	15.0000i	−0.163299	+	0.577350i
$676$	−22.3923			−0.861242
$677$	30.1518			1.15883			0.579413	−	0.815034i	$-0.303282\pi$
$677$	30.1518			1.15883			0.579413	+	0.815034i	$0.303282\pi$
$678$	2.90276	+	2.05256i	0.111480	+	0.0788280i
$679$		−	0.143594i		−	0.00551061i
$680$	13.3843			0.513263
$681$	6.78461	+	4.79744i	0.259987	+	0.183838i
$682$	6.73205			0.257784
$683$	−26.1122			−0.999155			−0.499577	−	0.866269i	$-0.666511\pi$
$683$	−26.1122			−0.999155			−0.499577	+	0.866269i	$0.666511\pi$
$684$		0			0
$685$	14.9282			0.570377
$686$	1.93185			0.0737584
$687$	−16.1112	−	11.3923i	−0.614679	−	0.434644i
$688$	14.1244			0.538486
$689$		−	2.92996i		−	0.111623i
$690$	−5.46410	−	3.86370i	−0.208015	−	0.147089i
$691$	−17.8564			−0.679290			−0.339645	−	0.940554i	$-0.610307\pi$
$691$	−17.8564			−0.679290			−0.339645	+	0.940554i	$0.610307\pi$
$692$	−30.3548			−1.15392
$693$	−4.00000	+	1.41421i	−0.151947	+	0.0537215i
$694$			9.94744i			0.377600i
$695$		−	3.96524i		−	0.150410i
$696$	5.65685	+	4.00000i	0.214423	+	0.151620i
$697$		−	27.7128i		−	1.04970i
$698$	4.86181			0.184022
$699$	−13.3843	+	18.9282i	−0.506239	+	0.715930i
$700$	1.39230			0.0526242
$701$			39.4964i			1.49176i	0.666080	+	0.745880i	$0.267971\pi$
$701$			39.4964i			1.49176i	−0.666080	+	0.745880i	$0.732029\pi$
$702$	0.693504	+	0.196152i	0.0261746	+	0.00740330i
$703$		0			0
$704$			11.9700i			0.451138i
$705$	−1.51575	−	1.07180i	−0.0570864	−	0.0403662i
$706$			1.12436i			0.0423157i
$707$			0.554803i			0.0208655i
$708$	27.4641	+	19.4201i	1.03216	+	0.729850i
$709$	7.67949			0.288409			0.144205	−	0.989548i	$-0.453938\pi$
$709$	7.67949			0.288409			0.144205	+	0.989548i	$0.453938\pi$
$710$		−	9.79796i		−	0.367711i
$711$	29.5969	−	10.4641i	1.10997	−	0.392434i
$712$	14.1962			0.532023
$713$	13.0053			0.487053
$714$	−0.679492	+	0.960947i	−0.0254293	+	0.0359625i
$715$			2.00000i			0.0747958i
$716$	−2.44949			−0.0915417
$717$	−15.2789	+	21.6077i	−0.570603	+	0.806954i
$718$			3.71281i			0.138561i
$719$		−	10.9348i		−	0.407798i	−0.978992	−	0.203899i	$-0.934639\pi$
$719$		−	10.9348i		−	0.407798i	0.978992	−	0.203899i	$-0.0653614\pi$
$720$	9.85641	−	3.48477i	0.367327	−	0.129870i
$721$		−	0.947441i		−	0.0352846i
$722$		0			0
$723$	−11.3397	+	16.0368i	−0.421730	+	0.596416i
$724$			6.00000i			0.222988i
$725$	−6.21166			−0.230695
$726$	−12.3397	−	8.72552i	−0.457971	−	0.323834i
$727$	17.5885			0.652320			0.326160	−	0.945315i	$-0.394245\pi$
$727$	17.5885			0.652320			0.326160	+	0.945315i	$0.394245\pi$
$728$		−	0.138701i		−	0.00514059i
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$			2.19615i			0.0812832i
$731$		−	28.0812i		−	1.03862i
$732$	25.6317	+	18.1244i	0.947375	+	0.669895i
$733$	19.7128			0.728109			0.364055	−	0.931378i	$-0.381392\pi$
$733$	19.7128			0.728109			0.364055	+	0.931378i	$0.381392\pi$
$734$	10.8976			0.402238
$735$	−9.79796	+	13.8564i	−0.361403	+	0.511101i
$736$		−	27.1244i		−	0.999817i
$737$	−5.27792			−0.194415
$738$	2.92820	+	8.28221i	0.107789	+	0.304872i
$739$	−45.1962			−1.66257			−0.831284	−	0.555848i	$-0.812393\pi$
$739$	−45.1962			−1.66257			−0.831284	+	0.555848i	$0.812393\pi$
$740$	18.9396			0.696233
$741$		0			0
$742$	−1.51666			−0.0556784
$743$	−7.07107			−0.259412			−0.129706	−	0.991552i	$-0.541403\pi$
$743$	−7.07107			−0.259412			−0.129706	+	0.991552i	$0.541403\pi$
$744$	4.76028	−	6.73205i	0.174520	−	0.246809i
$745$	−3.85641			−0.141288
$746$		−	10.0754i		−	0.368885i
$747$	−5.85641	+	2.07055i	−0.214275	+	0.0757575i
$748$	44.7846			1.63749
$749$	−1.31268			−0.0479642
$750$	5.85641	−	8.28221i	0.213846	−	0.302424i
$751$			29.3923i			1.07254i	0.844046	+	0.536270i	$0.180167\pi$
$751$			29.3923i			1.07254i	−0.844046	+	0.536270i	$0.819833\pi$
$752$		−	1.86748i		−	0.0681000i
$753$	−14.6969	+	20.7846i	−0.535586	+	0.757433i
$754$			0.287187i			0.0104587i
$755$	−2.82843			−0.102937
$756$	−0.656339	+	2.32051i	−0.0238708	+	0.0843961i
$757$	25.3923			0.922899			0.461450	−	0.887166i	$-0.347330\pi$
$757$	25.3923			0.922899			0.461450	+	0.887166i	$0.347330\pi$
$758$			12.3118i			0.447185i
$759$	−39.3949	−	27.8564i	−1.42994	−	1.01112i
$760$		0			0
$761$			32.1208i			1.16438i	0.813054	+	0.582188i	$0.197803\pi$
$761$			32.1208i			1.16438i	−0.813054	+	0.582188i	$0.802197\pi$
$762$	−10.2784	+	14.5359i	−0.372348	+	0.526580i
$763$		−	1.71281i		−	0.0620080i
$764$			22.5259i			0.814958i
$765$	−6.92820	−	19.5959i	−0.250490	−	0.708492i
$766$	−6.48334			−0.234253
$767$			3.00429i			0.108479i
$768$	−1.96902	−	1.39230i	−0.0710508	−	0.0502405i
$769$	26.8564			0.968467			0.484233	−	0.874939i	$-0.339099\pi$
$769$	26.8564			0.968467			0.484233	+	0.874939i	$0.339099\pi$
$770$	1.03528			0.0373088
$771$	11.4641	+	8.10634i	0.412870	+	0.291943i
$772$		−	4.85641i		−	0.174786i
$773$	−40.7076			−1.46415			−0.732075	−	0.681224i	$-0.761448\pi$
$773$	−40.7076			−1.46415			−0.732075	+	0.681224i	$0.761448\pi$
$774$	2.96713	+	8.39230i	0.106651	+	0.301655i
$775$			7.39230i			0.265539i
$776$		−	1.03528i		−	0.0371642i
$777$	−2.07180	+	2.92996i	−0.0743253	+	0.105112i
$778$			7.66025i			0.274633i
$779$		0			0
$780$	0.928203	+	0.656339i	0.0332350	+	0.0235007i
$781$		−	70.6410i		−	2.52773i
$782$	−13.3843			−0.478620
$783$	2.92820	−	10.3528i	0.104645	−	0.369978i
$784$	−17.0718			−0.609707
$785$		−	14.7985i		−	0.528180i
$786$	−6.53590	+	9.24316i	−0.233128	+	0.329692i
$787$			37.9282i			1.35199i	0.736904	+	0.675997i	$0.236287\pi$
$787$			37.9282i			1.35199i	−0.736904	+	0.675997i	$0.763713\pi$
$788$		−	1.13681i		−	0.0404973i
$789$	28.8391	−	40.7846i	1.02670	−	1.45197i
$790$	−7.66025			−0.272540
$791$	−1.06248			−0.0377775
$792$	−28.8391	+	10.1962i	−1.02475	+	0.362305i
$793$			2.80385i			0.0995675i
$794$	−13.6245			−0.483515
$795$	15.4641	−	21.8695i	0.548455	−	0.775633i
$796$	40.1769			1.42403
$797$	−54.0918			−1.91603			−0.958016	−	0.286716i	$-0.907437\pi$
$797$	−54.0918			−1.91603			−0.958016	+	0.286716i	$0.907437\pi$
$798$		0			0
$799$	−3.71281			−0.131350
$800$	15.4176			0.545096
$801$	−7.34847	−	20.7846i	−0.259645	−	0.734388i
$802$	11.8038			0.416808
$803$			15.8338i			0.558761i
$804$	−1.73205	+	2.44949i	−0.0610847	+	0.0863868i
$805$	2.00000			0.0704907
$806$	0.341773			0.0120384
$807$	15.4641	+	10.9348i	0.544362	+	0.384922i
$808$			4.00000i			0.140720i
$809$			37.0197i			1.30155i	0.759273	+	0.650773i	$0.225555\pi$
$809$			37.0197i			1.30155i	−0.759273	+	0.650773i	$0.774445\pi$
$810$	4.14110	+	5.12436i	0.145504	+	0.180052i
$811$			33.7128i			1.18382i	0.806005	+	0.591908i	$0.201625\pi$
$811$			33.7128i			1.18382i	−0.806005	+	0.591908i	$0.798375\pi$
$812$	−0.960947			−0.0337226
$813$	9.79796	+	6.92820i	0.343629	+	0.242983i
$814$	−21.1244			−0.740408
$815$			7.34847i			0.257406i
$816$	12.0716	−	17.0718i	0.422590	−	0.597632i
$817$		0			0
$818$			10.4815i			0.366477i
$819$	−0.203072	+	0.0717968i	−0.00709591	+	0.00250878i
$820$			13.8564i			0.483887i
$821$		−	5.10205i		−	0.178063i	−0.996029	−	0.0890314i	$-0.971623\pi$
$821$		−	5.10205i		−	0.178063i	0.996029	−	0.0890314i	$-0.0283772\pi$
$822$	−5.46410	+	7.72741i	−0.190582	+	0.269524i
$823$	−8.00000			−0.278862			−0.139431	−	0.990232i	$-0.544527\pi$
$823$	−8.00000			−0.278862			−0.139431	+	0.990232i	$0.544527\pi$
$824$		−	6.83083i		−	0.237963i
$825$	15.8338	−	22.3923i	0.551260	−	0.779600i
$826$	1.55514			0.0541101
$827$	−24.4949			−0.851771			−0.425886	−	0.904777i	$-0.640037\pi$
$827$	−24.4949			−0.851771			−0.425886	+	0.904777i	$0.640037\pi$
$828$	−25.8564	+	9.14162i	−0.898572	+	0.317693i
$829$		−	21.3397i		−	0.741160i	−0.928801	−	0.370580i	$-0.879159\pi$
$829$		−	21.3397i		−	0.741160i	0.928801	−	0.370580i	$-0.120841\pi$
$830$	1.51575			0.0526124
$831$	25.2528	+	17.8564i	0.876009	+	0.619432i
$832$			0.607695i			0.0210680i
$833$			33.9411i			1.17599i
$834$	2.05256	+	1.45138i	0.0710743	+	0.0502571i
$835$			30.7846i			1.06535i
$836$		0			0
$837$	−12.3205	−	3.48477i	−0.425859	−	0.120451i
$838$			3.90897i			0.135033i
$839$	−25.3543			−0.875328			−0.437664	−	0.899139i	$-0.644194\pi$
$839$	−25.3543			−0.875328			−0.437664	+	0.899139i	$0.644194\pi$
$840$	0.732051	−	1.03528i	0.0252582	−	0.0357204i
$841$	−24.7128			−0.852166
$842$		−	14.7713i		−	0.509052i
$843$	13.3205	+	9.41902i	0.458783	+	0.324408i
$844$			19.0526i			0.655816i
$845$		−	18.2832i		−	0.628963i
$846$	1.10961	−	0.392305i	0.0381490	−	0.0134877i
$847$	4.51666			0.155194
$848$	26.9444			0.925274
$849$	8.28221	+	5.85641i	0.284245	+	0.200991i
$850$		−	7.60770i		−	0.260942i
$851$	−40.8091			−1.39892
$852$	−32.7846	−	23.1822i	−1.12318	−	0.794210i
$853$	54.3205			1.85990			0.929949	−	0.367688i	$-0.119850\pi$
$853$	54.3205			1.85990			0.929949	+	0.367688i	$0.119850\pi$
$854$	1.45138			0.0496651
$855$		0			0
$856$	−9.46410			−0.323476
$857$	−42.2233			−1.44232			−0.721161	−	0.692768i	$-0.756391\pi$
$857$	−42.2233			−1.44232			−0.721161	+	0.692768i	$0.756391\pi$
$858$	−1.03528	−	0.732051i	−0.0353437	−	0.0249918i
$859$	12.6603			0.431962			0.215981	−	0.976398i	$-0.430705\pi$
$859$	12.6603			0.431962			0.215981	+	0.976398i	$0.430705\pi$
$860$			14.0406i			0.478780i
$861$	−2.14359	−	1.51575i	−0.0730535	−	0.0516566i
$862$	13.1769			0.448807
$863$	−1.31268			−0.0446841			−0.0223420	−	0.999750i	$-0.507112\pi$
$863$	−1.31268			−0.0446841			−0.0223420	+	0.999750i	$0.507112\pi$
$864$	−7.26795	+	25.6961i	−0.247261	+	0.874198i
$865$		−	24.7846i		−	0.842702i
$866$		−	10.6945i		−	0.363415i
$867$	−9.89949	−	7.00000i	−0.336204	−	0.237732i
$868$			1.14359i			0.0388161i
$869$	−55.2287			−1.87350
$870$	−1.51575	+	2.14359i	−0.0513887	+	0.0726746i
$871$	−0.267949			−0.00907911
$872$		−	12.3490i		−	0.418189i
$873$	−1.51575	+	0.535898i	−0.0513003	+	0.0181374i
$874$		0			0
$875$			3.03150i			0.102483i
$876$	7.34847	+	5.19615i	0.248282	+	0.175562i
$877$		−	0.267949i		−	0.00904800i	−0.999990	−	0.00452400i	$-0.998560\pi$
$877$		−	0.267949i		−	0.00904800i	0.999990	−	0.00452400i	$-0.00144004\pi$
$878$			8.04197i			0.271403i
$879$	19.7128	+	13.9391i	0.664897	+	0.470153i
$880$	−18.3923			−0.620004
$881$		−	48.3335i		−	1.62840i	−0.580588	−	0.814198i	$-0.697177\pi$
$881$		−	48.3335i		−	1.62840i	0.580588	−	0.814198i	$-0.302823\pi$
$882$	−3.58630	−	10.1436i	−0.120757	−	0.341553i
$883$	−25.7321			−0.865952			−0.432976	−	0.901405i	$-0.642537\pi$
$883$	−25.7321			−0.865952			−0.432976	+	0.901405i	$0.642537\pi$
$884$	2.27362			0.0764703
$885$	−15.8564	+	22.4243i	−0.533007	+	0.753786i
$886$			5.35898i			0.180039i
$887$	2.17209			0.0729316			0.0364658	−	0.999335i	$-0.488390\pi$
$887$	2.17209			0.0729316			0.0364658	+	0.999335i	$0.488390\pi$
$888$	−14.9372	+	21.1244i	−0.501259	+	0.708887i
$889$		−	5.32051i		−	0.178444i
$890$			5.37945i			0.180320i
$891$	29.8564	+	36.9454i	1.00023	+	1.23772i
$892$		−	19.7321i		−	0.660678i
$893$		0			0
$894$	1.41154	−	1.99622i	0.0472091	−	0.0667637i
$895$		−	2.00000i		−	0.0668526i
$896$	3.06866			0.102517
$897$	−2.00000	−	1.41421i	−0.0667781	−	0.0472192i
$898$	2.64102			0.0881319
$899$		−	5.10205i		−	0.170163i
$900$	−5.19615	−	14.6969i	−0.173205	−	0.489898i
$901$		−	53.5692i		−	1.78465i
$902$		−	15.4548i		−	0.514589i
$903$	−2.17209	−	1.53590i	−0.0722826	−	0.0511115i
$904$	−7.66025			−0.254776
$905$	−4.89898			−0.162848
$906$	1.03528	−	1.46410i	0.0343947	−	0.0486415i
$907$			27.0718i			0.898904i	0.893304	+	0.449452i	$0.148381\pi$
$907$			27.0718i			0.898904i	−0.893304	+	0.449452i	$0.851619\pi$
$908$	−8.30942			−0.275758
$909$	5.85641	−	2.07055i	0.194245	−	0.0686759i
$910$	0.0525589			0.00174231
$911$	−21.3147			−0.706189			−0.353094	−	0.935588i	$-0.614871\pi$
$911$	−21.3147			−0.706189			−0.353094	+	0.935588i	$0.614871\pi$
$912$		0			0
$913$	10.9282			0.361671
$914$	17.9687			0.594351
$915$	−14.7985	+	20.9282i	−0.489222	+	0.691865i
$916$	19.7321			0.651965
$917$		−	3.38323i		−	0.111724i
$918$	12.6795	+	3.58630i	0.418486	+	0.118366i
$919$	19.9808			0.659105			0.329552	−	0.944137i	$-0.393102\pi$
$919$	19.9808			0.659105			0.329552	+	0.944137i	$0.393102\pi$
$920$	14.4195			0.475398
$921$	−13.8564	+	19.5959i	−0.456584	+	0.645707i
$922$		−	18.4833i		−	0.608716i
$923$		−	3.58630i		−	0.118045i
$924$	2.44949	−	3.46410i	0.0805823	−	0.113961i
$925$		−	23.1962i		−	0.762685i
$926$	0.822246			0.0270207
$927$	−10.0010	+	3.53590i	−0.328477	+	0.116134i
$928$	−10.6410			−0.349308
$929$			10.6574i			0.349657i	0.984599	+	0.174828i	$0.0559371\pi$
$929$			10.6574i			0.349657i	−0.984599	+	0.174828i	$0.944063\pi$
$930$	2.55103	+	1.80385i	0.0836514	+	0.0591505i
$931$		0			0
$932$		−	23.1822i		−	0.759359i
$933$	12.4505	−	17.6077i	0.407612	−	0.576450i
$934$		−	11.7128i		−	0.383255i
$935$			36.5665i			1.19585i
$936$	−1.46410	+	0.517638i	−0.0478557	+	0.0169195i
$937$	−35.7846			−1.16903			−0.584516	−	0.811382i	$-0.698716\pi$
$937$	−35.7846			−1.16903			−0.584516	+	0.811382i	$0.698716\pi$
$938$			0.138701i			0.00452874i
$939$	23.7370	+	16.7846i	0.774628	+	0.547745i
$940$	1.85641			0.0605493
$941$	−25.2528			−0.823217			−0.411608	−	0.911361i	$-0.635033\pi$
$941$	−25.2528			−0.823217			−0.411608	+	0.911361i	$0.635033\pi$
$942$	7.66025	+	5.41662i	0.249585	+	0.176483i
$943$		−	29.8564i		−	0.972258i
$944$	−27.6279			−0.899213
$945$	−1.89469	−	0.535898i	−0.0616342	−	0.0174328i
$946$		−	15.6603i		−	0.509159i
$947$		−	4.69591i		−	0.152596i	−0.997085	−	0.0762982i	$-0.975690\pi$
$947$		−	4.69591i		−	0.152596i	0.997085	−	0.0762982i	$-0.0243101\pi$
$948$	−18.1244	+	25.6317i	−0.588652	+	0.832479i
$949$			0.803848i			0.0260940i
$950$		0			0
$951$	−12.5359	−	8.86422i	−0.406504	−	0.287442i
$952$		−	2.53590i		−	0.0821889i
$953$	−8.30942			−0.269168			−0.134584	−	0.990902i	$-0.542970\pi$
$953$	−8.30942			−0.269168			−0.134584	+	0.990902i	$0.542970\pi$
$954$	5.66025	+	16.0096i	0.183257	+	0.518330i
$955$	−18.3923			−0.595161
$956$		−	26.4639i		−	0.855904i
$957$	−10.9282	+	15.4548i	−0.353259	+	0.499583i
$958$		−	9.07180i		−	0.293096i
$959$		−	2.82843i		−	0.0913347i
$960$	−3.20736	+	4.53590i	−0.103517	+	0.146395i
$961$	24.9282			0.804136
$962$	−1.07244			−0.0345769
$963$	4.89898	+	13.8564i	0.157867	+	0.446516i
$964$		−	19.6410i		−	0.632595i
$965$	3.96524			0.127646
$966$	−0.732051	+	1.03528i	−0.0235533	+	0.0333095i
$967$	−19.1962			−0.617307			−0.308653	−	0.951175i	$-0.599878\pi$
$967$	−19.1962			−0.617307			−0.308653	+	0.951175i	$0.599878\pi$
$968$	32.5641			1.04665
$969$		0			0
$970$	0.392305			0.0125961
$971$	53.5370			1.71809			0.859043	−	0.511904i	$-0.171060\pi$
$971$	53.5370			1.71809			0.859043	+	0.511904i	$0.171060\pi$
$972$	26.9444	−	1.73205i	0.864242	−	0.0555556i
$973$	−0.751289			−0.0240852
$974$			5.73118i			0.183639i
$975$	0.803848	−	1.13681i	0.0257437	−	0.0364071i
$976$	−25.7846			−0.825345
$977$	−9.04008			−0.289218			−0.144609	−	0.989489i	$-0.546192\pi$
$977$	−9.04008			−0.289218			−0.144609	+	0.989489i	$0.546192\pi$
$978$	−3.80385	−	2.68973i	−0.121634	−	0.0860080i
$979$			38.7846i			1.23956i
$980$		−	16.9706i		−	0.542105i
$981$	−18.0802	+	6.39230i	−0.577255	+	0.204091i
$982$			15.3205i			0.488897i
$983$	−32.5269			−1.03745			−0.518724	−	0.854942i	$-0.673593\pi$
$983$	−32.5269			−1.03745			−0.518724	+	0.854942i	$0.673593\pi$
$984$	−15.4548	−	10.9282i	−0.492681	−	0.348378i
$985$	0.928203			0.0295750
$986$			5.25071i			0.167217i
$987$	−0.203072	+	0.287187i	−0.00646385	+	0.00914127i
$988$		0			0
$989$		−	30.2533i		−	0.961999i
$990$	−3.86370	−	10.9282i	−0.122797	−	0.347321i
$991$			58.1769i			1.84805i	0.382331	+	0.924025i	$0.375121\pi$
$991$			58.1769i			1.84805i	−0.382331	+	0.924025i	$0.624879\pi$
$992$			12.6636i			0.402068i
$993$	18.0718	−	25.5574i	0.573491	−	0.811039i
$994$	−1.85641			−0.0588816
$995$			32.8043i			1.03997i
$996$	3.58630	−	5.07180i	0.113636	−	0.160706i
$997$	−12.1769			−0.385647			−0.192823	−	0.981233i	$-0.561764\pi$
$997$	−12.1769			−0.385647			−0.192823	+	0.981233i	$0.561764\pi$
$998$	4.20548			0.133122
$999$	38.6603	+	10.9348i	1.22316	+	0.345961i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1083.2.d.b.1082.6		8
3.2	odd	2	inner	1083.2.d.b.1082.4		8
19.7	even	3		57.2.f.a.8.2	✓	8
19.8	odd	6		57.2.f.a.50.3	yes	8
19.18	odd	2	inner	1083.2.d.b.1082.3		8
57.8	even	6		57.2.f.a.50.2	yes	8
57.26	odd	6		57.2.f.a.8.3	yes	8
57.56	even	2	inner	1083.2.d.b.1082.5		8
76.7	odd	6		912.2.bn.m.65.4		8
76.27	even	6		912.2.bn.m.449.3		8
228.83	even	6		912.2.bn.m.65.3		8
228.179	odd	6		912.2.bn.m.449.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.f.a.8.2	✓	8	19.7	even	3
57.2.f.a.8.3	yes	8	57.26	odd	6
57.2.f.a.50.2	yes	8	57.8	even	6
57.2.f.a.50.3	yes	8	19.8	odd	6
912.2.bn.m.65.3		8	228.83	even	6
912.2.bn.m.65.4		8	76.7	odd	6
912.2.bn.m.449.3		8	76.27	even	6
912.2.bn.m.449.4		8	228.179	odd	6
1083.2.d.b.1082.3		8	19.18	odd	2	inner
1083.2.d.b.1082.4		8	3.2	odd	2	inner
1083.2.d.b.1082.5		8	57.56	even	2	inner
1083.2.d.b.1082.6		8	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:	\( N \)	\(=\)	\( 1083 = 3 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1083.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.517638 q^{2} +(1.41421 + 1.00000i) q^{3} -1.73205 q^{4} -1.41421i q^{5} +(0.732051 + 0.517638i) q^{6} -0.267949 q^{7} -1.93185 q^{8} +(1.00000 + 2.82843i) q^{9} +O(q^{10})\)	\(q+0.517638 q^{2} +(1.41421 + 1.00000i) q^{3} -1.73205 q^{4} -1.41421i q^{5} +(0.732051 + 0.517638i) q^{6} -0.267949 q^{7} -1.93185 q^{8} +(1.00000 + 2.82843i) q^{9} -0.732051i q^{10} -5.27792i q^{11} +(-2.44949 - 1.73205i) q^{12} -0.267949i q^{13} -0.138701 q^{14} +(1.41421 - 2.00000i) q^{15} +2.46410 q^{16} -4.89898i q^{17} +(0.517638 + 1.46410i) q^{18} +2.44949i q^{20} +(-0.378937 - 0.267949i) q^{21} -2.73205i q^{22} -5.27792i q^{23} +(-2.73205 - 1.93185i) q^{24} +3.00000 q^{25} -0.138701i q^{26} +(-1.41421 + 5.00000i) q^{27} +0.464102 q^{28} -2.07055 q^{29} +(0.732051 - 1.03528i) q^{30} +2.46410i q^{31} +5.13922 q^{32} +(5.27792 - 7.46410i) q^{33} -2.53590i q^{34} +0.378937i q^{35} +(-1.73205 - 4.89898i) q^{36} -7.73205i q^{37} +(0.267949 - 0.378937i) q^{39} +2.73205i q^{40} +5.65685 q^{41} +(-0.196152 - 0.138701i) q^{42} +5.73205 q^{43} +9.14162i q^{44} +(4.00000 - 1.41421i) q^{45} -2.73205i q^{46} -0.757875i q^{47} +(3.48477 + 2.46410i) q^{48} -6.92820 q^{49} +1.55291 q^{50} +(4.89898 - 6.92820i) q^{51} +0.464102i q^{52} +10.9348 q^{53} +(-0.732051 + 2.58819i) q^{54} -7.46410 q^{55} +0.517638 q^{56} -1.07180 q^{58} -11.2122 q^{59} +(-2.44949 + 3.46410i) q^{60} -10.4641 q^{61} +1.27551i q^{62} +(-0.267949 - 0.757875i) q^{63} -2.26795 q^{64} -0.378937 q^{65} +(2.73205 - 3.86370i) q^{66} -1.00000i q^{67} +8.48528i q^{68} +(5.27792 - 7.46410i) q^{69} +0.196152i q^{70} +13.3843 q^{71} +(-1.93185 - 5.46410i) q^{72} -3.00000 q^{73} -4.00240i q^{74} +(4.24264 + 3.00000i) q^{75} +1.41421i q^{77} +(0.138701 - 0.196152i) q^{78} -10.4641i q^{79} -3.48477i q^{80} +(-7.00000 + 5.65685i) q^{81} +2.92820 q^{82} +2.07055i q^{83} +(0.656339 + 0.464102i) q^{84} -6.92820 q^{85} +2.96713 q^{86} +(-2.92820 - 2.07055i) q^{87} +10.1962i q^{88} -7.34847 q^{89} +(2.07055 - 0.732051i) q^{90} +0.0717968i q^{91} +9.14162i q^{92} +(-2.46410 + 3.48477i) q^{93} -0.392305i q^{94} +(7.26795 + 5.13922i) q^{96} +0.535898i q^{97} -3.58630 q^{98} +(14.9282 - 5.27792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{6} - 16 q^{7} + 8 q^{9}+O(q^{10}) \) 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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