LMFDB - Embedded newform 475.2.p.b.407.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(107,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("475.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.p (of order $12$, degree $4$, 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:	$3.79289409601$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	475.407
Dual form			475.2.p.b.468.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.36603 - 0.633975i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.00000 - 2.00000i) q^{7} +(2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(2.36603 - 0.633975i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.00000 - 2.00000i) q^{7} +(2.59808 - 1.50000i) q^{9} -1.00000 q^{11} +(3.46410 - 3.46410i) q^{12} +(-0.633975 + 2.36603i) q^{13} +(2.00000 - 3.46410i) q^{16} +(4.09808 - 1.09808i) q^{17} +(-4.33013 + 0.500000i) q^{19} +(-6.00000 - 3.46410i) q^{21} +(5.46410 + 1.46410i) q^{23} +(-5.46410 - 1.46410i) q^{28} +(0.866025 + 1.50000i) q^{29} +8.66025i q^{31} +(-2.36603 + 0.633975i) q^{33} +(3.00000 - 5.19615i) q^{36} +(-3.46410 + 3.46410i) q^{37} +6.00000i q^{39} +(-9.00000 - 5.19615i) q^{41} +(2.92820 + 10.9282i) q^{43} +(-1.73205 + 1.00000i) q^{44} +(1.83013 - 6.83013i) q^{47} +(2.53590 - 9.46410i) q^{48} +1.00000i q^{49} +(9.00000 - 5.19615i) q^{51} +(1.26795 + 4.73205i) q^{52} +(0.633975 - 2.36603i) q^{53} +(-9.92820 + 3.92820i) q^{57} +(0.866025 - 1.50000i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-8.19615 - 2.19615i) q^{63} -8.00000i q^{64} +(2.36603 + 0.633975i) q^{67} +(6.00000 - 6.00000i) q^{68} +13.8564 q^{69} +(7.50000 + 4.33013i) q^{71} +(-0.732051 - 2.73205i) q^{73} +(-7.00000 + 5.19615i) q^{76} +(2.00000 + 2.00000i) q^{77} +(2.59808 - 4.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} -13.8564 q^{84} +(3.00000 + 3.00000i) q^{87} +(-6.06218 - 10.5000i) q^{89} +(6.00000 - 3.46410i) q^{91} +(10.9282 - 2.92820i) q^{92} +(5.49038 + 20.4904i) q^{93} +(-2.53590 - 9.46410i) q^{97} +(-2.59808 + 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} - 8 q^{7}+O(q^{10}) $ 4 * q + 6 * q^3 - 8 * q^7	$ 4 q + 6 q^{3} - 8 q^{7} - 4 q^{11} - 6 q^{13} + 8 q^{16} + 6 q^{17} - 24 q^{21} + 8 q^{23} - 8 q^{28} - 6 q^{33} + 12 q^{36} - 36 q^{41} - 16 q^{43} - 10 q^{47} + 24 q^{48} + 36 q^{51} + 12 q^{52} + 6 q^{53} - 12 q^{57} + 14 q^{61} - 12 q^{63} + 6 q^{67} + 24 q^{68} + 30 q^{71} + 4 q^{73} - 28 q^{76} + 8 q^{77} - 18 q^{81} + 12 q^{87} + 24 q^{91} + 16 q^{92} - 30 q^{93} - 24 q^{97}+O(q^{100}) $ 4 * q + 6 * q^3 - 8 * q^7 - 4 * q^11 - 6 * q^13 + 8 * q^16 + 6 * q^17 - 24 * q^21 + 8 * q^23 - 8 * q^28 - 6 * q^33 + 12 * q^36 - 36 * q^41 - 16 * q^43 - 10 * q^47 + 24 * q^48 + 36 * q^51 + 12 * q^52 + 6 * q^53 - 12 * q^57 + 14 * q^61 - 12 * q^63 + 6 * q^67 + 24 * q^68 + 30 * q^71 + 4 * q^73 - 28 * q^76 + 8 * q^77 - 18 * q^81 + 12 * q^87 + 24 * q^91 + 16 * q^92 - 30 * q^93 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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			0		0.965926	−	0.258819i	$-0.0833333\pi$
$2$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$3$	2.36603	−	0.633975i	1.36603	−	0.366025i	0.500000	−	0.866025i	$-0.333333\pi$
$3$	2.36603	−	0.633975i	1.36603	−	0.366025i	0.866025	+	0.500000i	$0.166667\pi$
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.00000	−	2.00000i	−0.755929	−	0.755929i	0.219650	−	0.975579i	$-0.429509\pi$
$7$	−2.00000	−	2.00000i	−0.755929	−	0.755929i	−0.975579	+	0.219650i	$0.929509\pi$
$8$		0			0
$9$	2.59808	−	1.50000i	0.866025	−	0.500000i
$10$		0			0
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$	3.46410	−	3.46410i	1.00000	−	1.00000i
$13$	−0.633975	+	2.36603i	−0.175833	+	0.656217i	0.820575	+	0.571538i	$0.193653\pi$
$13$	−0.633975	+	2.36603i	−0.175833	+	0.656217i	−0.996408	+	0.0846790i	$0.973014\pi$
$14$		0			0
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	4.09808	−	1.09808i	0.993929	−	0.266323i	0.275029	−	0.961436i	$-0.411312\pi$
$17$	4.09808	−	1.09808i	0.993929	−	0.266323i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	−4.33013	+	0.500000i	−0.993399	+	0.114708i
$19$	−4.33013	+	0.500000i	−0.993399	+	0.114708i
$20$		0			0
$21$	−6.00000	−	3.46410i	−1.30931	−	0.755929i
$22$		0			0
$23$	5.46410	+	1.46410i	1.13934	+	0.305286i	0.778687	−	0.627412i	$-0.215886\pi$
$23$	5.46410	+	1.46410i	1.13934	+	0.305286i	0.360657	+	0.932699i	$0.382553\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	−5.46410	−	1.46410i	−1.03262	−	0.276689i
$29$	0.866025	+	1.50000i	0.160817	+	0.278543i	0.935162	−	0.354221i	$-0.115254\pi$
$29$	0.866025	+	1.50000i	0.160817	+	0.278543i	−0.774345	+	0.632764i	$0.781920\pi$
$30$		0			0
$31$			8.66025i			1.55543i	0.628619	+	0.777714i	$0.283621\pi$
$31$			8.66025i			1.55543i	−0.628619	+	0.777714i	$0.716379\pi$
$32$		0			0
$33$	−2.36603	+	0.633975i	−0.411872	+	0.110361i
$34$		0			0
$35$		0			0
$36$	3.00000	−	5.19615i	0.500000	−	0.866025i
$37$	−3.46410	+	3.46410i	−0.569495	+	0.569495i	−0.931987	−	0.362492i	$-0.881926\pi$
$37$	−3.46410	+	3.46410i	−0.569495	+	0.569495i	0.362492	+	0.931987i	$0.381926\pi$
$38$		0			0
$39$			6.00000i			0.960769i
$40$		0			0
$41$	−9.00000	−	5.19615i	−1.40556	−	0.811503i	−0.410608	−	0.911812i	$-0.634683\pi$
$41$	−9.00000	−	5.19615i	−1.40556	−	0.811503i	−0.994956	+	0.100309i	$0.968017\pi$
$42$		0			0
$43$	2.92820	+	10.9282i	0.446547	+	1.66654i	0.711820	+	0.702362i	$0.247871\pi$
$43$	2.92820	+	10.9282i	0.446547	+	1.66654i	−0.265273	+	0.964173i	$0.585462\pi$
$44$	−1.73205	+	1.00000i	−0.261116	+	0.150756i
$45$		0			0
$46$		0			0
$47$	1.83013	−	6.83013i	0.266951	−	0.996276i	−0.694094	−	0.719885i	$-0.744195\pi$
$47$	1.83013	−	6.83013i	0.266951	−	0.996276i	0.961045	−	0.276392i	$-0.0891387\pi$
$48$	2.53590	−	9.46410i	0.366025	−	1.36603i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	9.00000	−	5.19615i	1.26025	−	0.727607i
$52$	1.26795	+	4.73205i	0.175833	+	0.656217i
$53$	0.633975	−	2.36603i	0.0870831	−	0.324999i	−0.908617	−	0.417630i	$-0.862861\pi$
$53$	0.633975	−	2.36603i	0.0870831	−	0.324999i	0.995701	+	0.0926309i	$0.0295277\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−9.92820	+	3.92820i	−1.31502	+	0.520303i
$58$		0			0
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	−0.804130	−	0.594454i	$-0.797368\pi$
$59$	0.866025	−	1.50000i	0.112747	−	0.195283i	0.916877	+	0.399170i	$0.130702\pi$
$60$		0			0
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$		0			0
$63$	−8.19615	−	2.19615i	−1.03262	−	0.276689i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$		0			0
$67$	2.36603	+	0.633975i	0.289056	+	0.0774523i	0.400433	−	0.916326i	$-0.368860\pi$
$67$	2.36603	+	0.633975i	0.289056	+	0.0774523i	−0.111377	+	0.993778i	$0.535526\pi$
$68$	6.00000	−	6.00000i	0.727607	−	0.727607i
$69$	13.8564			1.66812
$70$		0			0
$71$	7.50000	+	4.33013i	0.890086	+	0.513892i	0.873971	−	0.485979i	$-0.161537\pi$
$71$	7.50000	+	4.33013i	0.890086	+	0.513892i	0.0161155	+	0.999870i	$0.494870\pi$
$72$		0			0
$73$	−0.732051	−	2.73205i	−0.0856801	−	0.319762i	0.909762	−	0.415130i	$-0.136264\pi$
$73$	−0.732051	−	2.73205i	−0.0856801	−	0.319762i	−0.995442	+	0.0953678i	$0.969597\pi$
$74$		0			0
$75$		0			0
$76$	−7.00000	+	5.19615i	−0.802955	+	0.596040i
$77$	2.00000	+	2.00000i	0.227921	+	0.227921i
$78$		0			0
$79$	2.59808	−	4.50000i	0.292306	−	0.506290i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$	2.59808	−	4.50000i	0.292306	−	0.506290i	0.974355	+	0.225018i	$0.0722440\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$83$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$84$	−13.8564			−1.51186
$85$		0			0
$86$		0			0
$87$	3.00000	+	3.00000i	0.321634	+	0.321634i
$88$		0			0
$89$	−6.06218	−	10.5000i	−0.642590	−	1.11300i	−0.984853	−	0.173394i	$-0.944527\pi$
$89$	−6.06218	−	10.5000i	−0.642590	−	1.11300i	0.342263	−	0.939604i	$-0.388807\pi$
$90$		0			0
$91$	6.00000	−	3.46410i	0.628971	−	0.363137i
$92$	10.9282	−	2.92820i	1.13934	−	0.305286i
$93$	5.49038	+	20.4904i	0.569326	+	2.12475i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−2.53590	−	9.46410i	−0.257481	−	0.960934i	−0.966693	−	0.255938i	$-0.917616\pi$
$97$	−2.53590	−	9.46410i	−0.257481	−	0.960934i	0.709212	−	0.704996i	$-0.249051\pi$
$98$		0			0
$99$	−2.59808	+	1.50000i	−0.261116	+	0.150756i
$100$		0			0
$101$	5.50000	+	9.52628i	0.547270	+	0.947900i	0.998460	+	0.0554722i	$0.0176664\pi$
$101$	5.50000	+	9.52628i	0.547270	+	0.947900i	−0.451190	+	0.892428i	$0.649000\pi$
$102$		0			0
$103$	−3.46410	−	3.46410i	−0.341328	−	0.341328i	0.515538	−	0.856866i	$-0.327592\pi$
$103$	−3.46410	−	3.46410i	−0.341328	−	0.341328i	−0.856866	+	0.515538i	$0.827592\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−13.8564	+	13.8564i	−1.33955	+	1.33955i	−0.443055	+	0.896494i	$0.646105\pi$
$107$	−13.8564	+	13.8564i	−1.33955	+	1.33955i	−0.896494	+	0.443055i	$0.853895\pi$
$108$		0			0
$109$	−6.06218	+	10.5000i	−0.580651	+	1.00572i	0.414751	+	0.909935i	$0.363869\pi$
$109$	−6.06218	+	10.5000i	−0.580651	+	1.00572i	−0.995402	+	0.0957826i	$0.969465\pi$
$110$		0			0
$111$	−6.00000	+	10.3923i	−0.569495	+	0.986394i
$112$	−10.9282	+	2.92820i	−1.03262	+	0.276689i
$113$	−12.1244	−	12.1244i	−1.14056	−	1.14056i	−0.988347	−	0.152216i	$-0.951359\pi$
$113$	−12.1244	−	12.1244i	−1.14056	−	1.14056i	−0.152216	−	0.988347i	$-0.548641\pi$
$114$		0			0
$115$		0			0
$116$	3.00000	+	1.73205i	0.278543	+	0.160817i
$117$	1.90192	+	7.09808i	0.175833	+	0.656217i
$118$		0			0
$119$	−10.3923	−	6.00000i	−0.952661	−	0.550019i
$120$		0			0
$121$	−10.0000			−0.909091
$122$		0			0
$123$	−24.5885	−	6.58846i	−2.21707	−	0.594061i
$124$	8.66025	+	15.0000i	0.777714	+	1.34704i
$125$		0			0
$126$		0			0
$127$	−2.36603	−	0.633975i	−0.209951	−	0.0562561i	0.152311	−	0.988333i	$-0.451329\pi$
$127$	−2.36603	−	0.633975i	−0.209951	−	0.0562561i	−0.362261	+	0.932077i	$0.617995\pi$
$128$		0			0
$129$	13.8564	+	24.0000i	1.21999	+	2.11308i
$130$		0			0
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	−0.379379	−	0.925241i	$-0.623862\pi$
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	0.990972	−	0.134069i	$-0.0428042\pi$
$132$	−3.46410	+	3.46410i	−0.301511	+	0.301511i
$133$	9.66025	+	7.66025i	0.837650	+	0.664228i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$137$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$138$		0			0
$139$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$139$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$140$		0			0
$141$		−	17.3205i		−	1.45865i
$142$		0			0
$143$	0.633975	−	2.36603i	0.0530156	−	0.197857i
$144$		−	12.0000i		−	1.00000i
$145$		0			0
$146$		0			0
$147$	0.633975	+	2.36603i	0.0522893	+	0.195146i
$148$	−2.53590	+	9.46410i	−0.208450	+	0.777944i
$149$	−6.06218	−	3.50000i	−0.496633	−	0.286731i	0.230689	−	0.973028i	$-0.425902\pi$
$149$	−6.06218	−	3.50000i	−0.496633	−	0.286731i	−0.727322	+	0.686296i	$0.759235\pi$
$150$		0			0
$151$		−	1.73205i		−	0.140952i	−0.997513	−	0.0704761i	$-0.977548\pi$
$151$		−	1.73205i		−	0.140952i	0.997513	−	0.0704761i	$-0.0224519\pi$
$152$		0			0
$153$	9.00000	−	9.00000i	0.727607	−	0.727607i
$154$		0			0
$155$		0			0
$156$	6.00000	+	10.3923i	0.480384	+	0.832050i
$157$	−6.83013	+	1.83013i	−0.545103	+	0.146060i	−0.520854	−	0.853646i	$-0.674386\pi$
$157$	−6.83013	+	1.83013i	−0.545103	+	0.146060i	−0.0242497	+	0.999706i	$0.507720\pi$
$158$		0			0
$159$		−	6.00000i		−	0.475831i
$160$		0			0
$161$	−8.00000	−	13.8564i	−0.630488	−	1.09204i
$162$		0			0
$163$	7.00000	−	7.00000i	0.548282	−	0.548282i	−0.377661	−	0.925944i	$-0.623272\pi$
$163$	7.00000	−	7.00000i	0.548282	−	0.548282i	0.925944	+	0.377661i	$0.123272\pi$
$164$	−20.7846			−1.62301
$165$		0			0
$166$		0			0
$167$	4.73205	+	1.26795i	0.366177	+	0.0981169i	0.437216	−	0.899357i	$-0.355965\pi$
$167$	4.73205	+	1.26795i	0.366177	+	0.0981169i	−0.0710385	+	0.997474i	$0.522631\pi$
$168$		0			0
$169$	6.06218	+	3.50000i	0.466321	+	0.269231i
$170$		0			0
$171$	−10.5000	+	7.79423i	−0.802955	+	0.596040i
$172$	16.0000	+	16.0000i	1.21999	+	1.21999i
$173$	−9.46410	+	2.53590i	−0.719542	+	0.192801i	−0.599967	−	0.800024i	$-0.704820\pi$
$173$	−9.46410	+	2.53590i	−0.719542	+	0.192801i	−0.119575	+	0.992825i	$0.538153\pi$
$174$		0			0
$175$		0			0
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$	1.09808	−	4.09808i	0.0825365	−	0.308030i
$178$		0			0
$179$	12.1244			0.906217			0.453108	−	0.891455i	$-0.350315\pi$
$179$	12.1244			0.906217			0.453108	+	0.891455i	$0.350315\pi$
$180$		0			0
$181$	−3.00000	+	1.73205i	−0.222988	+	0.128742i	−0.607333	−	0.794447i	$-0.707761\pi$
$181$	−3.00000	+	1.73205i	−0.222988	+	0.128742i	0.384345	+	0.923190i	$0.374427\pi$
$182$		0			0
$183$	12.1244	+	12.1244i	0.896258	+	0.896258i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	−4.09808	+	1.09808i	−0.299681	+	0.0802993i
$188$	−3.66025	−	13.6603i	−0.266951	−	0.996276i
$189$		0			0
$190$		0			0
$191$	23.0000			1.66422			0.832111	−	0.554609i	$-0.187132\pi$
$191$	23.0000			1.66422			0.832111	+	0.554609i	$0.187132\pi$
$192$	−5.07180	−	18.9282i	−0.366025	−	1.36603i
$193$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$193$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$194$		0			0
$195$		0			0
$196$	1.00000	+	1.73205i	0.0714286	+	0.123718i
$197$	1.00000	+	1.00000i	0.0712470	+	0.0712470i	0.741832	−	0.670585i	$-0.233957\pi$
$197$	1.00000	+	1.00000i	0.0712470	+	0.0712470i	−0.670585	+	0.741832i	$0.733957\pi$
$198$		0			0
$199$	−7.79423	+	4.50000i	−0.552518	+	0.318997i	−0.750137	−	0.661282i	$-0.770013\pi$
$199$	−7.79423	+	4.50000i	−0.552518	+	0.318997i	0.197619	+	0.980279i	$0.436679\pi$
$200$		0			0
$201$	6.00000			0.423207
$202$		0			0
$203$	1.26795	−	4.73205i	0.0889926	−	0.332125i
$204$	10.3923	−	18.0000i	0.727607	−	1.26025i
$205$		0			0
$206$		0			0
$207$	16.3923	−	4.39230i	1.13934	−	0.305286i
$208$	6.92820	+	6.92820i	0.480384	+	0.480384i
$209$	4.33013	−	0.500000i	0.299521	−	0.0345857i
$210$		0			0
$211$	−19.5000	−	11.2583i	−1.34244	−	0.775055i	−0.355271	−	0.934763i	$-0.615611\pi$
$211$	−19.5000	−	11.2583i	−1.34244	−	0.775055i	−0.987164	+	0.159708i	$0.948945\pi$
$212$	−1.26795	−	4.73205i	−0.0870831	−	0.324999i
$213$	20.4904	+	5.49038i	1.40398	+	0.376195i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	17.3205	−	17.3205i	1.17579	−	1.17579i
$218$		0			0
$219$	−3.46410	−	6.00000i	−0.234082	−	0.405442i
$220$		0			0
$221$			10.3923i			0.699062i
$222$		0			0
$223$	14.1962	−	3.80385i	0.950645	−	0.254724i	0.250009	−	0.968244i	$-0.419566\pi$
$223$	14.1962	−	3.80385i	0.950645	−	0.254724i	0.700636	+	0.713519i	$0.252900\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	6.92820	−	6.92820i	0.459841	−	0.459841i	−0.438762	−	0.898603i	$-0.644583\pi$
$227$	6.92820	−	6.92820i	0.459841	−	0.459841i	0.898603	+	0.438762i	$0.144583\pi$
$228$	−13.2679	+	16.7321i	−0.878691	+	1.10811i
$229$		−	9.00000i		−	0.594737i	−0.954763	−	0.297368i	$-0.903891\pi$
$229$		−	9.00000i		−	0.594737i	0.954763	−	0.297368i	$-0.0961089\pi$
$230$		0			0
$231$	6.00000	+	3.46410i	0.394771	+	0.227921i
$232$		0			0
$233$	0.366025	+	1.36603i	0.0239791	+	0.0894913i	0.976878	−	0.213796i	$-0.0685826\pi$
$233$	0.366025	+	1.36603i	0.0239791	+	0.0894913i	−0.952899	+	0.303287i	$0.901916\pi$
$234$		0			0
$235$		0			0
$236$		−	3.46410i		−	0.225494i
$237$	3.29423	−	12.2942i	0.213983	−	0.798596i
$238$		0			0
$239$		−	7.00000i		−	0.452792i	−0.974035	−	0.226396i	$-0.927306\pi$
$239$		−	7.00000i		−	0.452792i	0.974035	−	0.226396i	$-0.0726944\pi$
$240$		0			0
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	−0.637883	−	0.770133i	$-0.720190\pi$
$241$	−4.50000	+	2.59808i	−0.289870	+	0.167357i	0.348013	+	0.937490i	$0.386857\pi$
$242$		0			0
$243$	−5.70577	+	21.2942i	−0.366025	+	1.36603i
$244$	12.1244	+	7.00000i	0.776182	+	0.448129i
$245$		0			0
$246$		0			0
$247$	1.56218	−	10.5622i	0.0993990	−	0.672055i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	0.584643	−	0.811290i	$-0.301234\pi$
$251$	−6.50000	−	11.2583i	−0.410276	−	0.710620i	−0.994920	+	0.100671i	$0.967901\pi$
$252$	−16.3923	+	4.39230i	−1.03262	+	0.276689i
$253$	−5.46410	−	1.46410i	−0.343525	−	0.0920473i
$254$		0			0
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−2.36603	−	0.633975i	−0.147589	−	0.0395462i	0.184268	−	0.982876i	$-0.441008\pi$
$257$	−2.36603	−	0.633975i	−0.147589	−	0.0395462i	−0.331857	+	0.943330i	$0.607675\pi$
$258$		0			0
$259$	13.8564			0.860995
$260$		0			0
$261$	4.50000	+	2.59808i	0.278543	+	0.160817i
$262$		0			0
$263$	−3.29423	−	12.2942i	−0.203131	−	0.758095i	−0.990011	−	0.140989i	$-0.954972\pi$
$263$	−3.29423	−	12.2942i	−0.203131	−	0.758095i	0.786880	−	0.617106i	$-0.211695\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−21.0000	−	21.0000i	−1.28518	−	1.28518i
$268$	4.73205	−	1.26795i	0.289056	−	0.0774523i
$269$	7.79423	−	13.5000i	0.475223	−	0.823110i	−0.524375	−	0.851488i	$-0.675701\pi$
$269$	7.79423	−	13.5000i	0.475223	−	0.823110i	0.999597	+	0.0283781i	$0.00903423\pi$
$270$		0			0
$271$	−1.50000	+	2.59808i	−0.0911185	+	0.157822i	−0.907982	−	0.419009i	$-0.862378\pi$
$271$	−1.50000	+	2.59808i	−0.0911185	+	0.157822i	0.816864	+	0.576831i	$0.195711\pi$
$272$	4.39230	−	16.3923i	0.266323	−	0.993929i
$273$	12.0000	−	12.0000i	0.726273	−	0.726273i
$274$		0			0
$275$		0			0
$276$	24.0000	−	13.8564i	1.44463	−	0.834058i
$277$	−8.00000	−	8.00000i	−0.480673	−	0.480673i	0.424673	−	0.905347i	$-0.360389\pi$
$277$	−8.00000	−	8.00000i	−0.480673	−	0.480673i	−0.905347	+	0.424673i	$0.860389\pi$
$278$		0			0
$279$	12.9904	+	22.5000i	0.777714	+	1.34704i
$280$		0			0
$281$	−12.0000	+	6.92820i	−0.715860	+	0.413302i	−0.813227	−	0.581947i	$-0.802291\pi$
$281$	−12.0000	+	6.92820i	−0.715860	+	0.413302i	0.0973670	+	0.995249i	$0.468958\pi$
$282$		0			0
$283$	−2.56218	−	9.56218i	−0.152306	−	0.568412i	−0.999321	−	0.0368441i	$-0.988270\pi$
$283$	−2.56218	−	9.56218i	−0.152306	−	0.568412i	0.847015	−	0.531568i	$-0.178397\pi$
$284$	17.3205			1.02778
$285$		0			0
$286$		0			0
$287$	7.60770	+	28.3923i	0.449068	+	1.67594i
$288$		0			0
$289$	0.866025	−	0.500000i	0.0509427	−	0.0294118i
$290$		0			0
$291$	−12.0000	−	20.7846i	−0.703452	−	1.21842i
$292$	−4.00000	−	4.00000i	−0.234082	−	0.234082i
$293$	−10.3923	−	10.3923i	−0.607125	−	0.607125i	0.335069	−	0.942194i	$-0.391240\pi$
$293$	−10.3923	−	10.3923i	−0.607125	−	0.607125i	−0.942194	+	0.335069i	$0.891240\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−6.92820	+	12.0000i	−0.400668	+	0.693978i
$300$		0			0
$301$	16.0000	−	27.7128i	0.922225	−	1.59734i
$302$		0			0
$303$	19.0526	+	19.0526i	1.09454	+	1.09454i
$304$	−6.92820	+	16.0000i	−0.397360	+	0.917663i
$305$		0			0
$306$		0			0
$307$	4.43782	+	16.5622i	0.253280	+	0.945253i	0.969039	+	0.246906i	$0.0794140\pi$
$307$	4.43782	+	16.5622i	0.253280	+	0.945253i	−0.715759	+	0.698347i	$0.753919\pi$
$308$	5.46410	+	1.46410i	0.311346	+	0.0834249i
$309$	−10.3923	−	6.00000i	−0.591198	−	0.341328i
$310$		0			0
$311$	26.0000			1.47432			0.737162	−	0.675716i	$-0.236165\pi$
$311$	26.0000			1.47432			0.737162	+	0.675716i	$0.236165\pi$
$312$		0			0
$313$	−6.83013	−	1.83013i	−0.386062	−	0.103445i	0.0605675	−	0.998164i	$-0.480709\pi$
$313$	−6.83013	−	1.83013i	−0.386062	−	0.103445i	−0.446629	+	0.894719i	$0.647376\pi$
$314$		0			0
$315$		0			0
$316$		−	10.3923i		−	0.584613i
$317$	23.6603	+	6.33975i	1.32889	+	0.356076i	0.852302	−	0.523050i	$-0.175206\pi$
$317$	23.6603	+	6.33975i	1.32889	+	0.356076i	0.476590	+	0.879126i	$0.341873\pi$
$318$		0			0
$319$	−0.866025	−	1.50000i	−0.0484881	−	0.0839839i
$320$		0			0
$321$	−24.0000	+	41.5692i	−1.33955	+	2.32017i
$322$		0			0
$323$	−17.1962	+	6.80385i	−0.956820	+	0.378576i
$324$			18.0000i			1.00000i
$325$		0			0
$326$		0			0
$327$	−7.68653	+	28.6865i	−0.425066	+	1.58637i
$328$		0			0
$329$	−17.3205	+	10.0000i	−0.954911	+	0.551318i
$330$		0			0
$331$			27.7128i			1.52323i	0.648027	+	0.761617i	$0.275594\pi$
$331$			27.7128i			1.52323i	−0.648027	+	0.761617i	$0.724406\pi$
$332$		0			0
$333$	−3.80385	+	14.1962i	−0.208450	+	0.777944i
$334$		0			0
$335$		0			0
$336$	−24.0000	+	13.8564i	−1.30931	+	0.755929i
$337$	−6.33975	−	23.6603i	−0.345348	−	1.28886i	−0.892205	−	0.451630i	$-0.850843\pi$
$337$	−6.33975	−	23.6603i	−0.345348	−	1.28886i	0.546857	−	0.837226i	$-0.315824\pi$
$338$		0			0
$339$	−36.3731	−	21.0000i	−1.97551	−	1.14056i
$340$		0			0
$341$		−	8.66025i		−	0.468979i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	16.3923	−	4.39230i	0.879985	−	0.235791i	0.209584	−	0.977791i	$-0.432789\pi$
$347$	16.3923	−	4.39230i	0.879985	−	0.235791i	0.670401	+	0.741999i	$0.266122\pi$
$348$	8.19615	+	2.19615i	0.439360	+	0.117726i
$349$		−	24.0000i		−	1.28469i	−0.766415	−	0.642345i	$-0.777962\pi$
$349$		−	24.0000i		−	1.28469i	0.766415	−	0.642345i	$-0.222038\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	22.0000	−	22.0000i	1.17094	−	1.17094i	0.188956	−	0.981985i	$-0.439490\pi$
$353$	22.0000	−	22.0000i	1.17094	−	1.17094i	0.981985	−	0.188956i	$-0.0605105\pi$
$354$		0			0
$355$		0			0
$356$	−21.0000	−	12.1244i	−1.11300	−	0.642590i
$357$	−28.3923	−	7.60770i	−1.50268	−	0.402642i
$358$		0			0
$359$	8.66025	+	5.00000i	0.457071	+	0.263890i	0.710812	−	0.703382i	$-0.248328\pi$
$359$	8.66025	+	5.00000i	0.457071	+	0.263890i	−0.253741	+	0.967272i	$0.581661\pi$
$360$		0			0
$361$	18.5000	−	4.33013i	0.973684	−	0.227901i
$362$		0			0
$363$	−23.6603	+	6.33975i	−1.24184	+	0.332750i
$364$	6.92820	−	12.0000i	0.363137	−	0.628971i
$365$		0			0
$366$		0			0
$367$	−7.32051	+	27.3205i	−0.382127	+	1.42612i	0.460518	+	0.887650i	$0.347664\pi$
$367$	−7.32051	+	27.3205i	−0.382127	+	1.42612i	−0.842646	+	0.538469i	$0.819003\pi$
$368$	16.0000	−	16.0000i	0.834058	−	0.834058i
$369$	−31.1769			−1.62301
$370$		0			0
$371$	−6.00000	+	3.46410i	−0.311504	+	0.179847i
$372$	30.0000	+	30.0000i	1.55543	+	1.55543i
$373$	10.3923	+	10.3923i	0.538093	+	0.538093i	0.922969	−	0.384875i	$-0.125756\pi$
$373$	10.3923	+	10.3923i	0.538093	+	0.538093i	−0.384875	+	0.922969i	$0.625756\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−4.09808	+	1.09808i	−0.211062	+	0.0565538i
$378$		0			0
$379$	15.5885			0.800725			0.400363	−	0.916357i	$-0.368884\pi$
$379$	15.5885			0.800725			0.400363	+	0.916357i	$0.368884\pi$
$380$		0			0
$381$	−6.00000			−0.307389
$382$		0			0
$383$	−2.36603	+	0.633975i	−0.120898	+	0.0323946i	−0.318761	−	0.947835i	$-0.603267\pi$
$383$	−2.36603	+	0.633975i	−0.120898	+	0.0323946i	0.197863	+	0.980230i	$0.436600\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	24.0000	+	24.0000i	1.21999	+	1.21999i
$388$	−13.8564	−	13.8564i	−0.703452	−	0.703452i
$389$	−26.8468	+	15.5000i	−1.36119	+	0.785881i	−0.989782	−	0.142590i	$-0.954457\pi$
$389$	−26.8468	+	15.5000i	−1.36119	+	0.785881i	−0.371404	+	0.928471i	$0.621124\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$		0			0
$393$	8.87564	−	33.1244i	0.447717	−	1.67090i
$394$		0			0
$395$		0			0
$396$	−3.00000	+	5.19615i	−0.150756	+	0.261116i
$397$	−2.73205	+	0.732051i	−0.137118	+	0.0367406i	−0.326725	−	0.945119i	$-0.605945\pi$
$397$	−2.73205	+	0.732051i	−0.137118	+	0.0367406i	0.189607	+	0.981860i	$0.439278\pi$
$398$		0			0
$399$	27.7128	+	12.0000i	1.38738	+	0.600751i
$400$		0			0
$401$	13.5000	+	7.79423i	0.674158	+	0.389225i	0.797650	−	0.603120i	$-0.206076\pi$
$401$	13.5000	+	7.79423i	0.674158	+	0.389225i	−0.123492	+	0.992346i	$0.539409\pi$
$402$		0			0
$403$	−20.4904	−	5.49038i	−1.02070	−	0.273495i
$404$	19.0526	+	11.0000i	0.947900	+	0.547270i
$405$		0			0
$406$		0			0
$407$	3.46410	−	3.46410i	0.171709	−	0.171709i
$408$		0			0
$409$	−12.9904	−	22.5000i	−0.642333	−	1.11255i	−0.984911	−	0.173064i	$-0.944633\pi$
$409$	−12.9904	−	22.5000i	−0.642333	−	1.11255i	0.342578	−	0.939490i	$-0.388700\pi$
$410$		0			0
$411$		0			0
$412$	−9.46410	−	2.53590i	−0.466263	−	0.124935i
$413$	−4.73205	+	1.26795i	−0.232849	+	0.0623917i
$414$		0			0
$415$		0			0
$416$		0			0
$417$		0			0
$418$		0			0
$419$		−	23.0000i		−	1.12362i	−0.827265	−	0.561812i	$-0.810105\pi$
$419$		−	23.0000i		−	1.12362i	0.827265	−	0.561812i	$-0.189895\pi$
$420$		0			0
$421$	−1.50000	−	0.866025i	−0.0731055	−	0.0422075i	0.463002	−	0.886357i	$-0.346772\pi$
$421$	−1.50000	−	0.866025i	−0.0731055	−	0.0422075i	−0.536107	+	0.844150i	$0.680106\pi$
$422$		0			0
$423$	−5.49038	−	20.4904i	−0.266951	−	0.996276i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	5.12436	−	19.1244i	0.247985	−	0.925492i
$428$	−10.1436	+	37.8564i	−0.490309	+	1.82986i
$429$		−	6.00000i		−	0.289683i
$430$		0			0
$431$	13.5000	−	7.79423i	0.650272	−	0.375435i	−0.138288	−	0.990392i	$-0.544160\pi$
$431$	13.5000	−	7.79423i	0.650272	−	0.375435i	0.788560	+	0.614957i	$0.210827\pi$
$432$		0			0
$433$	−3.80385	+	14.1962i	−0.182801	+	0.682224i	0.812289	+	0.583255i	$0.198221\pi$
$433$	−3.80385	+	14.1962i	−0.182801	+	0.682224i	−0.995091	+	0.0989688i	$0.968446\pi$
$434$		0			0
$435$		0			0
$436$			24.2487i			1.16130i
$437$	−24.3923	−	3.60770i	−1.16684	−	0.172579i
$438$		0			0
$439$	−11.2583	+	19.5000i	−0.537331	+	0.930684i	0.461716	+	0.887028i	$0.347234\pi$
$439$	−11.2583	+	19.5000i	−0.537331	+	0.930684i	−0.999047	+	0.0436563i	$0.986099\pi$
$440$		0			0
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$		0			0
$443$	10.9282	+	2.92820i	0.519215	+	0.139123i	0.508903	−	0.860824i	$-0.330051\pi$
$443$	10.9282	+	2.92820i	0.519215	+	0.139123i	0.0103113	+	0.999947i	$0.496718\pi$
$444$			24.0000i			1.13899i
$445$		0			0
$446$		0			0
$447$	−16.5622	−	4.43782i	−0.783364	−	0.209902i
$448$	−16.0000	+	16.0000i	−0.755929	+	0.755929i
$449$	19.0526			0.899146			0.449573	−	0.893244i	$-0.351576\pi$
$449$	19.0526			0.899146			0.449573	+	0.893244i	$0.351576\pi$
$450$		0			0
$451$	9.00000	+	5.19615i	0.423793	+	0.244677i
$452$	−33.1244	−	8.87564i	−1.55804	−	0.417475i
$453$	−1.09808	−	4.09808i	−0.0515921	−	0.192544i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	1.00000	+	1.00000i	0.0467780	+	0.0467780i	0.730109	−	0.683331i	$-0.239469\pi$
$457$	1.00000	+	1.00000i	0.0467780	+	0.0467780i	−0.683331	+	0.730109i	$0.739469\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−0.500000	+	0.866025i	−0.0232873	+	0.0403348i	−0.877434	−	0.479697i	$-0.840747\pi$
$461$	−0.500000	+	0.866025i	−0.0232873	+	0.0403348i	0.854147	+	0.520032i	$0.174080\pi$
$462$		0			0
$463$	4.00000	−	4.00000i	0.185896	−	0.185896i	−0.608023	−	0.793919i	$-0.708037\pi$
$463$	4.00000	−	4.00000i	0.185896	−	0.185896i	0.793919	+	0.608023i	$0.208037\pi$
$464$	6.92820			0.321634
$465$		0			0
$466$		0			0
$467$	8.00000	+	8.00000i	0.370196	+	0.370196i	0.867548	−	0.497353i	$-0.165694\pi$
$467$	8.00000	+	8.00000i	0.370196	+	0.370196i	−0.497353	+	0.867548i	$0.665694\pi$
$468$	10.3923	+	10.3923i	0.480384	+	0.480384i
$469$	−3.46410	−	6.00000i	−0.159957	−	0.277054i
$470$		0			0
$471$	−15.0000	+	8.66025i	−0.691164	+	0.399043i
$472$		0			0
$473$	−2.92820	−	10.9282i	−0.134639	−	0.502479i
$474$		0			0
$475$		0			0
$476$	−24.0000			−1.10004
$477$	−1.90192	−	7.09808i	−0.0870831	−	0.324999i
$478$		0			0
$479$	0.866025	−	0.500000i	0.0395697	−	0.0228456i	−0.480085	−	0.877222i	$-0.659394\pi$
$479$	0.866025	−	0.500000i	0.0395697	−	0.0228456i	0.519654	+	0.854377i	$0.326061\pi$
$480$		0			0
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$		0			0
$483$	−27.7128	−	27.7128i	−1.26098	−	1.26098i
$484$	−17.3205	+	10.0000i	−0.787296	+	0.454545i
$485$		0			0
$486$		0			0
$487$	−15.5885	+	15.5885i	−0.706380	+	0.706380i	−0.965772	−	0.259392i	$-0.916478\pi$
$487$	−15.5885	+	15.5885i	−0.706380	+	0.706380i	0.259392	+	0.965772i	$0.416478\pi$
$488$		0			0
$489$	12.1244	−	21.0000i	0.548282	−	0.949653i
$490$		0			0
$491$	−6.50000	+	11.2583i	−0.293341	+	0.508081i	−0.974598	−	0.223963i	$-0.928100\pi$
$491$	−6.50000	+	11.2583i	−0.293341	+	0.508081i	0.681257	+	0.732045i	$0.261434\pi$
$492$	−49.1769	+	13.1769i	−2.21707	+	0.594061i
$493$	5.19615	+	5.19615i	0.234023	+	0.234023i
$494$		0			0
$495$		0			0
$496$	30.0000	+	17.3205i	1.34704	+	0.777714i
$497$	−6.33975	−	23.6603i	−0.284376	−	1.06131i
$498$		0			0
$499$	25.9808	+	15.0000i	1.16306	+	0.671492i	0.952035	−	0.305989i	$-0.0989870\pi$
$499$	25.9808	+	15.0000i	1.16306	+	0.671492i	0.211024	+	0.977481i	$0.432320\pi$
$500$		0			0
$501$	12.0000			0.536120
$502$		0			0
$503$	4.09808	+	1.09808i	0.182724	+	0.0489608i	0.349021	−	0.937115i	$-0.386514\pi$
$503$	4.09808	+	1.09808i	0.182724	+	0.0489608i	−0.166297	+	0.986076i	$0.553181\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	16.5622	+	4.43782i	0.735552	+	0.197091i
$508$	−4.73205	+	1.26795i	−0.209951	+	0.0562561i
$509$	1.73205	+	3.00000i	0.0767718	+	0.132973i	0.901855	−	0.432038i	$-0.142205\pi$
$509$	1.73205	+	3.00000i	0.0767718	+	0.132973i	−0.825084	+	0.565011i	$0.808872\pi$
$510$		0			0
$511$	−4.00000	+	6.92820i	−0.176950	+	0.306486i
$512$		0			0
$513$		0			0
$514$		0			0
$515$		0			0
$516$	48.0000	+	27.7128i	2.11308	+	1.21999i
$517$	−1.83013	+	6.83013i	−0.0804889	+	0.300389i
$518$		0			0
$519$	−20.7846	+	12.0000i	−0.912343	+	0.526742i
$520$		0			0
$521$		−	22.5167i		−	0.986473i	−0.869895	−	0.493236i	$-0.835814\pi$
$521$		−	22.5167i		−	0.986473i	0.869895	−	0.493236i	$-0.164186\pi$
$522$		0			0
$523$	3.16987	−	11.8301i	0.138609	−	0.517295i	−0.861348	−	0.508015i	$-0.830379\pi$
$523$	3.16987	−	11.8301i	0.138609	−	0.517295i	0.999957	−	0.00928008i	$-0.00295398\pi$
$524$		−	28.0000i		−	1.22319i
$525$		0			0
$526$		0			0
$527$	9.50962	+	35.4904i	0.414246	+	1.54599i
$528$	−2.53590	+	9.46410i	−0.110361	+	0.411872i
$529$	7.79423	+	4.50000i	0.338880	+	0.195652i
$530$		0			0
$531$		−	5.19615i		−	0.225494i
$532$	24.3923	+	3.60770i	1.05754	+	0.156413i
$533$	18.0000	−	18.0000i	0.779667	−	0.779667i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	28.6865	−	7.68653i	1.23792	−	0.331698i
$538$		0			0
$539$		−	1.00000i		−	0.0430730i
$540$		0			0
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	0.896468	−	0.443109i	$-0.146125\pi$
$541$	1.50000	+	2.59808i	0.0644900	+	0.111700i	−0.831978	+	0.554809i	$0.812791\pi$
$542$		0			0
$543$	−6.00000	+	6.00000i	−0.257485	+	0.257485i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−4.73205	−	1.26795i	−0.202328	−	0.0542136i	0.156232	−	0.987720i	$-0.450065\pi$
$547$	−4.73205	−	1.26795i	−0.202328	−	0.0542136i	−0.358560	+	0.933507i	$0.616732\pi$
$548$		0			0
$549$	18.1865	+	10.5000i	0.776182	+	0.448129i
$550$		0			0
$551$	−4.50000	−	6.06218i	−0.191706	−	0.258257i
$552$		0			0
$553$	−14.1962	+	3.80385i	−0.603682	+	0.161756i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	7.32051	−	27.3205i	0.310180	−	1.15761i	−0.618214	−	0.786010i	$-0.712144\pi$
$557$	7.32051	−	27.3205i	0.310180	−	1.15761i	0.928394	−	0.371597i	$-0.121190\pi$
$558$		0			0
$559$	−27.7128			−1.17213
$560$		0			0
$561$	−9.00000	+	5.19615i	−0.379980	+	0.219382i
$562$		0			0
$563$	25.9808	+	25.9808i	1.09496	+	1.09496i	0.994991	+	0.0999679i	$0.0318740\pi$
$563$	25.9808	+	25.9808i	1.09496	+	1.09496i	0.0999679	+	0.994991i	$0.468126\pi$
$564$	−17.3205	−	30.0000i	−0.729325	−	1.26323i
$565$		0			0
$566$		0			0
$567$	24.5885	−	6.58846i	1.03262	−	0.276689i
$568$		0			0
$569$	−32.9090			−1.37962			−0.689808	−	0.723993i	$-0.742305\pi$
$569$	−32.9090			−1.37962			−0.689808	+	0.723993i	$0.742305\pi$
$570$		0			0
$571$	−39.0000			−1.63210			−0.816050	−	0.577982i	$-0.803840\pi$
$571$	−39.0000			−1.63210			−0.816050	+	0.577982i	$0.803840\pi$
$572$	−1.26795	−	4.73205i	−0.0530156	−	0.197857i
$573$	54.4186	−	14.5814i	2.27337	−	0.609147i
$574$		0			0
$575$		0			0
$576$	−12.0000	−	20.7846i	−0.500000	−	0.866025i
$577$	20.0000	+	20.0000i	0.832611	+	0.832611i	0.987873	−	0.155262i	$-0.0496223\pi$
$577$	20.0000	+	20.0000i	0.832611	+	0.832611i	−0.155262	+	0.987873i	$0.549622\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−0.633975	+	2.36603i	−0.0262565	+	0.0979908i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	2.73205	−	0.732051i	0.112764	−	0.0302150i	−0.201996	−	0.979386i	$-0.564743\pi$
$587$	2.73205	−	0.732051i	0.112764	−	0.0302150i	0.314760	+	0.949171i	$0.398076\pi$
$588$	3.46410	+	3.46410i	0.142857	+	0.142857i
$589$	−4.33013	−	37.5000i	−0.178420	−	1.54516i
$590$		0			0
$591$	3.00000	+	1.73205i	0.123404	+	0.0712470i
$592$	5.07180	+	18.9282i	0.208450	+	0.777944i
$593$	−32.7846	−	8.78461i	−1.34630	−	0.360741i	−0.487534	−	0.873104i	$-0.662103\pi$
$593$	−32.7846	−	8.78461i	−1.34630	−	0.360741i	−0.858769	+	0.512363i	$0.828770\pi$
$594$		0			0
$595$		0			0
$596$	−14.0000			−0.573462
$597$	−15.5885	+	15.5885i	−0.637993	+	0.637993i
$598$		0			0
$599$	13.8564	+	24.0000i	0.566157	+	0.980613i	0.996941	+	0.0781581i	$0.0249039\pi$
$599$	13.8564	+	24.0000i	0.566157	+	0.980613i	−0.430784	+	0.902455i	$0.641763\pi$
$600$		0			0
$601$		−	29.4449i		−	1.20108i	−0.799594	−	0.600541i	$-0.794952\pi$
$601$		−	29.4449i		−	1.20108i	0.799594	−	0.600541i	$-0.205048\pi$
$602$		0			0
$603$	7.09808	−	1.90192i	0.289056	−	0.0774523i
$604$	−1.73205	−	3.00000i	−0.0704761	−	0.122068i
$605$		0			0
$606$		0			0
$607$	5.19615	−	5.19615i	0.210905	−	0.210905i	−0.593747	−	0.804652i	$-0.702352\pi$
$607$	5.19615	−	5.19615i	0.210905	−	0.210905i	0.804652	+	0.593747i	$0.202352\pi$
$608$		0			0
$609$		−	12.0000i		−	0.486265i
$610$		0			0
$611$	15.0000	+	8.66025i	0.606835	+	0.350356i
$612$	6.58846	−	24.5885i	0.266323	−	0.993929i
$613$	−4.75833	−	17.7583i	−0.192187	−	0.717252i	−0.992977	−	0.118307i	$-0.962253\pi$
$613$	−4.75833	−	17.7583i	−0.192187	−	0.717252i	0.800790	−	0.598945i	$-0.204413\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.58846	+	24.5885i	−0.265241	+	0.989894i	0.696861	+	0.717206i	$0.254579\pi$
$617$	−6.58846	+	24.5885i	−0.265241	+	0.989894i	−0.962103	+	0.272688i	$0.912087\pi$
$618$		0			0
$619$			30.0000i			1.20580i	0.797816	+	0.602901i	$0.205989\pi$
$619$			30.0000i			1.20580i	−0.797816	+	0.602901i	$0.794011\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−8.87564	+	33.1244i	−0.355595	+	1.32710i
$624$	20.7846	+	12.0000i	0.832050	+	0.480384i
$625$		0			0
$626$		0			0
$627$	9.92820	−	3.92820i	0.396494	−	0.156877i
$628$	−10.0000	+	10.0000i	−0.399043	+	0.399043i
$629$	−10.3923	+	18.0000i	−0.414368	+	0.717707i
$630$		0			0
$631$	−0.500000	−	0.866025i	−0.0199047	−	0.0344759i	0.855901	−	0.517139i	$-0.173003\pi$
$631$	−0.500000	−	0.866025i	−0.0199047	−	0.0344759i	−0.875806	+	0.482663i	$0.839670\pi$
$632$		0			0
$633$	−53.2750	−	14.2750i	−2.11749	−	0.567380i
$634$		0			0
$635$		0			0
$636$	−6.00000	−	10.3923i	−0.237915	−	0.412082i
$637$	−2.36603	−	0.633975i	−0.0937453	−	0.0251190i
$638$		0			0
$639$	25.9808			1.02778
$640$		0			0
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	0.278093	−	0.960554i	$-0.410298\pi$
$641$	−10.5000	−	6.06218i	−0.414725	−	0.239442i	−0.692818	+	0.721113i	$0.743631\pi$
$642$		0			0
$643$	−8.41858	−	31.4186i	−0.331997	−	1.23903i	−0.907089	−	0.420939i	$-0.861700\pi$
$643$	−8.41858	−	31.4186i	−0.331997	−	1.23903i	0.575092	−	0.818089i	$-0.304966\pi$
$644$	−27.7128	−	16.0000i	−1.09204	−	0.630488i
$645$		0			0
$646$		0			0
$647$	−9.00000	−	9.00000i	−0.353827	−	0.353827i	0.507705	−	0.861531i	$-0.330494\pi$
$647$	−9.00000	−	9.00000i	−0.353827	−	0.353827i	−0.861531	+	0.507705i	$0.830494\pi$
$648$		0			0
$649$	−0.866025	+	1.50000i	−0.0339945	+	0.0588802i
$650$		0			0
$651$	30.0000	−	51.9615i	1.17579	−	2.03653i
$652$	5.12436	−	19.1244i	0.200685	−	0.748968i
$653$	6.00000	−	6.00000i	0.234798	−	0.234798i	−0.579894	−	0.814692i	$-0.696906\pi$
$653$	6.00000	−	6.00000i	0.234798	−	0.234798i	0.814692	+	0.579894i	$0.196906\pi$
$654$		0			0
$655$		0			0
$656$	−36.0000	+	20.7846i	−1.40556	+	0.811503i
$657$	−6.00000	−	6.00000i	−0.234082	−	0.234082i
$658$		0			0
$659$	6.92820	+	12.0000i	0.269884	+	0.467454i	0.968832	−	0.247720i	$-0.0796812\pi$
$659$	6.92820	+	12.0000i	0.269884	+	0.467454i	−0.698947	+	0.715173i	$0.746348\pi$
$660$		0			0
$661$	−34.5000	+	19.9186i	−1.34189	+	0.774743i	−0.987085	−	0.160196i	$-0.948788\pi$
$661$	−34.5000	+	19.9186i	−1.34189	+	0.774743i	−0.354809	+	0.934939i	$0.615454\pi$
$662$		0			0
$663$	6.58846	+	24.5885i	0.255874	+	0.954937i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	2.53590	+	9.46410i	0.0981904	+	0.366451i
$668$	9.46410	−	2.53590i	0.366177	−	0.0981169i
$669$	31.1769	−	18.0000i	1.20537	−	0.695920i
$670$		0			0
$671$	−3.50000	−	6.06218i	−0.135116	−	0.234028i
$672$		0			0
$673$	20.7846	+	20.7846i	0.801188	+	0.801188i	0.983281	−	0.182093i	$-0.0582873\pi$
$673$	20.7846	+	20.7846i	0.801188	+	0.801188i	−0.182093	+	0.983281i	$0.558287\pi$
$674$		0			0
$675$		0			0
$676$	14.0000			0.538462
$677$	17.3205	−	17.3205i	0.665681	−	0.665681i	−0.291032	−	0.956713i	$-0.593999\pi$
$677$	17.3205	−	17.3205i	0.665681	−	0.665681i	0.956713	+	0.291032i	$0.0939986\pi$
$678$		0			0
$679$	−13.8564	+	24.0000i	−0.531760	+	0.921035i
$680$		0			0
$681$	12.0000	−	20.7846i	0.459841	−	0.796468i
$682$		0			0
$683$	12.1244	+	12.1244i	0.463926	+	0.463926i	0.899940	−	0.436014i	$-0.143610\pi$
$683$	12.1244	+	12.1244i	0.463926	+	0.463926i	−0.436014	+	0.899940i	$0.643610\pi$
$684$	−10.3923	+	24.0000i	−0.397360	+	0.917663i
$685$		0			0
$686$		0			0
$687$	−5.70577	−	21.2942i	−0.217689	−	0.812425i
$688$	43.7128	+	11.7128i	1.66654	+	0.446547i
$689$	5.19615	+	3.00000i	0.197958	+	0.114291i
$690$		0			0
$691$	3.00000			0.114125			0.0570627	−	0.998371i	$-0.481827\pi$
$691$	3.00000			0.114125			0.0570627	+	0.998371i	$0.481827\pi$
$692$	−13.8564	+	13.8564i	−0.526742	+	0.526742i
$693$	8.19615	+	2.19615i	0.311346	+	0.0834249i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−42.5885	−	11.4115i	−1.61315	−	0.432243i
$698$		0			0
$699$	1.73205	+	3.00000i	0.0655122	+	0.113470i
$700$		0			0
$701$	10.0000	−	17.3205i	0.377695	−	0.654187i	−0.613032	−	0.790058i	$-0.710050\pi$
$701$	10.0000	−	17.3205i	0.377695	−	0.654187i	0.990726	+	0.135872i	$0.0433835\pi$
$702$		0			0
$703$	13.2679	−	16.7321i	0.500410	−	0.631061i
$704$			8.00000i			0.301511i
$705$		0			0
$706$		0			0
$707$	8.05256	−	30.0526i	0.302848	−	1.13024i
$708$	−2.19615	−	8.19615i	−0.0825365	−	0.308030i
$709$	44.1673	−	25.5000i	1.65874	−	0.957673i	0.685439	−	0.728130i	$-0.259610\pi$
$709$	44.1673	−	25.5000i	1.65874	−	0.957673i	0.973299	−	0.229543i	$-0.0737230\pi$
$710$		0			0
$711$		−	15.5885i		−	0.584613i
$712$		0			0
$713$	−12.6795	+	47.3205i	−0.474851	+	1.77217i
$714$		0			0
$715$		0			0
$716$	21.0000	−	12.1244i	0.784807	−	0.453108i
$717$	−4.43782	−	16.5622i	−0.165734	−	0.618526i
$718$		0			0
$719$	−32.0429	−	18.5000i	−1.19500	−	0.689934i	−0.235564	−	0.971859i	$-0.575694\pi$
$719$	−32.0429	−	18.5000i	−1.19500	−	0.689934i	−0.959436	+	0.281925i	$0.909027\pi$
$720$		0			0
$721$			13.8564i			0.516040i
$722$		0			0
$723$	−9.00000	+	9.00000i	−0.334714	+	0.334714i
$724$	−3.46410	+	6.00000i	−0.128742	+	0.222988i
$725$		0			0
$726$		0			0
$727$	9.56218	−	2.56218i	0.354642	−	0.0950259i	−0.0770998	−	0.997023i	$-0.524566\pi$
$727$	9.56218	−	2.56218i	0.354642	−	0.0950259i	0.431741	+	0.901997i	$0.357899\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$	33.1244	+	8.87564i	1.22431	+	0.328053i
$733$	26.0000	−	26.0000i	0.960332	−	0.960332i	−0.0389108	−	0.999243i	$-0.512389\pi$
$733$	26.0000	−	26.0000i	0.960332	−	0.960332i	0.999243	+	0.0389108i	$0.0123888\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−2.36603	−	0.633975i	−0.0871537	−	0.0233528i
$738$		0			0
$739$	−19.9186	−	11.5000i	−0.732717	−	0.423034i	0.0866983	−	0.996235i	$-0.472368\pi$
$739$	−19.9186	−	11.5000i	−0.732717	−	0.423034i	−0.819415	+	0.573200i	$0.805702\pi$
$740$		0			0
$741$	−3.00000	−	25.9808i	−0.110208	−	0.954427i
$742$		0			0
$743$	14.1962	−	3.80385i	0.520806	−	0.139550i	0.0111668	−	0.999938i	$-0.496445\pi$
$743$	14.1962	−	3.80385i	0.520806	−	0.139550i	0.509640	+	0.860388i	$0.329779\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		0			0
$748$	−6.00000	+	6.00000i	−0.219382	+	0.219382i
$749$	55.4256			2.02521
$750$		0			0
$751$	−7.50000	+	4.33013i	−0.273679	+	0.158009i	−0.630558	−	0.776142i	$-0.717174\pi$
$751$	−7.50000	+	4.33013i	−0.273679	+	0.158009i	0.356879	+	0.934150i	$0.383841\pi$
$752$	−20.0000	−	20.0000i	−0.729325	−	0.729325i
$753$	−22.5167	−	22.5167i	−0.820553	−	0.820553i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−23.2224	+	6.22243i	−0.844034	+	0.226158i	−0.654827	−	0.755779i	$-0.727258\pi$
$757$	−23.2224	+	6.22243i	−0.844034	+	0.226158i	−0.189207	+	0.981937i	$0.560592\pi$
$758$		0			0
$759$	−13.8564			−0.502956
$760$		0			0
$761$	8.00000			0.290000			0.145000	−	0.989432i	$-0.453682\pi$
$761$	8.00000			0.290000			0.145000	+	0.989432i	$0.453682\pi$
$762$		0			0
$763$	33.1244	−	8.87564i	1.19918	−	0.321320i
$764$	39.8372	−	23.0000i	1.44126	−	0.832111i
$765$		0			0
$766$		0			0
$767$	3.00000	+	3.00000i	0.108324	+	0.108324i
$768$	−27.7128	−	27.7128i	−1.00000	−	1.00000i
$769$	2.59808	−	1.50000i	0.0936890	−	0.0540914i	−0.452423	−	0.891803i	$-0.649440\pi$
$769$	2.59808	−	1.50000i	0.0936890	−	0.0540914i	0.546113	+	0.837712i	$0.316107\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$		0			0
$773$	−9.50962	+	35.4904i	−0.342037	+	1.27650i	0.553998	+	0.832518i	$0.313101\pi$
$773$	−9.50962	+	35.4904i	−0.342037	+	1.27650i	−0.896035	+	0.443982i	$0.853565\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	32.7846	−	8.78461i	1.17614	−	0.315146i
$778$		0			0
$779$	41.5692	+	18.0000i	1.48937	+	0.644917i
$780$		0			0
$781$	−7.50000	−	4.33013i	−0.268371	−	0.154944i
$782$		0			0
$783$		0			0
$784$	3.46410	+	2.00000i	0.123718	+	0.0714286i
$785$		0			0
$786$		0			0
$787$	36.3731	−	36.3731i	1.29656	−	1.29656i	0.365909	−	0.930651i	$-0.380758\pi$
$787$	36.3731	−	36.3731i	1.29656	−	1.29656i	0.930651	−	0.365909i	$-0.119242\pi$
$788$	2.73205	+	0.732051i	0.0973253	+	0.0260782i
$789$	−15.5885	−	27.0000i	−0.554964	−	0.961225i
$790$		0			0
$791$			48.4974i			1.72437i
$792$		0			0
$793$	−16.5622	+	4.43782i	−0.588140	+	0.157592i
$794$		0			0
$795$		0			0
$796$	−9.00000	+	15.5885i	−0.318997	+	0.552518i
$797$	−29.4449	+	29.4449i	−1.04299	+	1.04299i	−0.0439572	+	0.999033i	$0.513997\pi$
$797$	−29.4449	+	29.4449i	−1.04299	+	1.04299i	−0.999033	+	0.0439572i	$0.986003\pi$
$798$		0			0
$799$		−	30.0000i		−	1.06132i
$800$		0			0
$801$	−31.5000	−	18.1865i	−1.11300	−	0.642590i
$802$		0			0
$803$	0.732051	+	2.73205i	0.0258335	+	0.0964120i
$804$	10.3923	−	6.00000i	0.366508	−	0.211604i
$805$		0			0
$806$		0			0
$807$	9.88269	−	36.8827i	0.347887	−	1.29833i
$808$		0			0
$809$		−	23.0000i		−	0.808637i	−0.914618	−	0.404318i	$-0.867509\pi$
$809$		−	23.0000i		−	0.808637i	0.914618	−	0.404318i	$-0.132491\pi$
$810$		0			0
$811$	10.5000	−	6.06218i	0.368705	−	0.212872i	−0.304188	−	0.952612i	$-0.598385\pi$
$811$	10.5000	−	6.06218i	0.368705	−	0.212872i	0.672892	+	0.739740i	$0.265052\pi$
$812$	−2.53590	−	9.46410i	−0.0889926	−	0.332125i
$813$	−1.90192	+	7.09808i	−0.0667034	+	0.248940i
$814$		0			0
$815$		0			0
$816$		−	41.5692i		−	1.45521i
$817$	−18.1436	−	45.8564i	−0.634764	−	1.60431i
$818$		0			0
$819$	10.3923	−	18.0000i	0.363137	−	0.628971i
$820$		0			0
$821$	2.50000	+	4.33013i	0.0872506	+	0.151122i	0.906348	−	0.422532i	$-0.138859\pi$
$821$	2.50000	+	4.33013i	0.0872506	+	0.151122i	−0.819097	+	0.573654i	$0.805525\pi$
$822$		0			0
$823$	15.0263	+	4.02628i	0.523783	+	0.140347i	0.511016	−	0.859571i	$-0.329269\pi$
$823$	15.0263	+	4.02628i	0.523783	+	0.140347i	0.0127672	+	0.999918i	$0.495936\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−16.5622	−	4.43782i	−0.575923	−	0.154318i	−0.0409115	−	0.999163i	$-0.513026\pi$
$827$	−16.5622	−	4.43782i	−0.575923	−	0.154318i	−0.535012	+	0.844845i	$0.679693\pi$
$828$	24.0000	−	24.0000i	0.834058	−	0.834058i
$829$	−10.3923			−0.360940			−0.180470	−	0.983581i	$-0.557762\pi$
$829$	−10.3923			−0.360940			−0.180470	+	0.983581i	$0.557762\pi$
$830$		0			0
$831$	−24.0000	−	13.8564i	−0.832551	−	0.480673i
$832$	18.9282	+	5.07180i	0.656217	+	0.175833i
$833$	1.09808	+	4.09808i	0.0380461	+	0.141990i
$834$		0			0
$835$		0			0
$836$	7.00000	−	5.19615i	0.242100	−	0.179713i
$837$		0			0
$838$		0			0
$839$	−10.3923	+	18.0000i	−0.358782	+	0.621429i	−0.987758	−	0.155996i	$-0.950141\pi$
$839$	−10.3923	+	18.0000i	−0.358782	+	0.621429i	0.628975	+	0.777425i	$0.283475\pi$
$840$		0			0
$841$	13.0000	−	22.5167i	0.448276	−	0.776437i
$842$		0			0
$843$	−24.0000	+	24.0000i	−0.826604	+	0.826604i
$844$	−45.0333			−1.55011
$845$		0			0
$846$		0			0
$847$	20.0000	+	20.0000i	0.687208	+	0.687208i
$848$	−6.92820	−	6.92820i	−0.237915	−	0.237915i
$849$	−12.1244	−	21.0000i	−0.416107	−	0.720718i
$850$		0			0
$851$	−24.0000	+	13.8564i	−0.822709	+	0.474991i
$852$	40.9808	−	10.9808i	1.40398	−	0.376195i
$853$	13.5429	+	50.5429i	0.463701	+	1.73056i	0.661159	+	0.750246i	$0.270065\pi$
$853$	13.5429	+	50.5429i	0.463701	+	1.73056i	−0.197458	+	0.980311i	$0.563268\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	10.1436	+	37.8564i	0.346499	+	1.29315i	0.890852	+	0.454294i	$0.150108\pi$
$857$	10.1436	+	37.8564i	0.346499	+	1.29315i	−0.544353	+	0.838856i	$0.683225\pi$
$858$		0			0
$859$	−14.7224	+	8.50000i	−0.502323	+	0.290016i	−0.729672	−	0.683797i	$-0.760327\pi$
$859$	−14.7224	+	8.50000i	−0.502323	+	0.290016i	0.227349	+	0.973813i	$0.426994\pi$
$860$		0			0
$861$	36.0000	+	62.3538i	1.22688	+	2.12501i
$862$		0			0
$863$	36.3731	+	36.3731i	1.23815	+	1.23815i	0.960755	+	0.277399i	$0.0894723\pi$
$863$	36.3731	+	36.3731i	1.23815	+	1.23815i	0.277399	+	0.960755i	$0.410528\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	1.73205	−	1.73205i	0.0588235	−	0.0588235i
$868$	12.6795	−	47.3205i	0.430370	−	1.60616i
$869$	−2.59808	+	4.50000i	−0.0881337	+	0.152652i
$870$		0			0
$871$	−3.00000	+	5.19615i	−0.101651	+	0.176065i
$872$		0			0
$873$	−20.7846	−	20.7846i	−0.703452	−	0.703452i
$874$		0			0
$875$		0			0
$876$	−12.0000	−	6.92820i	−0.405442	−	0.234082i
$877$	13.9474	+	52.0526i	0.470972	+	1.75769i	0.636290	+	0.771450i	$0.280468\pi$
$877$	13.9474	+	52.0526i	0.470972	+	1.75769i	−0.165319	+	0.986240i	$0.552865\pi$
$878$		0			0
$879$	−31.1769	−	18.0000i	−1.05157	−	0.607125i
$880$		0			0
$881$	37.0000			1.24656			0.623281	−	0.781998i	$-0.285799\pi$
$881$	37.0000			1.24656			0.623281	+	0.781998i	$0.285799\pi$
$882$		0			0
$883$	−27.3205	−	7.32051i	−0.919408	−	0.246355i	−0.232076	−	0.972698i	$-0.574552\pi$
$883$	−27.3205	−	7.32051i	−0.919408	−	0.246355i	−0.687332	+	0.726343i	$0.741218\pi$
$884$	10.3923	+	18.0000i	0.349531	+	0.605406i
$885$		0			0
$886$		0			0
$887$	9.46410	+	2.53590i	0.317773	+	0.0851471i	0.414180	−	0.910195i	$-0.364068\pi$
$887$	9.46410	+	2.53590i	0.317773	+	0.0851471i	−0.0964068	+	0.995342i	$0.530735\pi$
$888$		0			0
$889$	3.46410	+	6.00000i	0.116182	+	0.201234i
$890$		0			0
$891$	4.50000	−	7.79423i	0.150756	−	0.261116i
$892$	20.7846	−	20.7846i	0.695920	−	0.695920i
$893$	−4.50962	+	30.4904i	−0.150909	+	1.02032i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−8.78461	+	32.7846i	−0.293310	+	1.09465i
$898$		0			0
$899$	−12.9904	+	7.50000i	−0.433253	+	0.250139i
$900$		0			0
$901$		−	10.3923i		−	0.346218i
$902$		0			0
$903$	20.2872	−	75.7128i	0.675115	−	2.51956i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−5.07180	−	18.9282i	−0.168406	−	0.628501i	−0.997581	−	0.0695114i	$-0.977856\pi$
$907$	−5.07180	−	18.9282i	−0.168406	−	0.628501i	0.829175	−	0.558989i	$-0.188811\pi$
$908$	5.07180	−	18.9282i	0.168313	−	0.628154i
$909$	28.5788	+	16.5000i	0.947900	+	0.547270i
$910$		0			0
$911$			22.5167i			0.746010i	0.927829	+	0.373005i	$0.121673\pi$
$911$			22.5167i			0.746010i	−0.927829	+	0.373005i	$0.878327\pi$
$912$	−6.24871	+	42.2487i	−0.206916	+	1.39899i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−9.00000	−	15.5885i	−0.297368	−	0.515057i
$917$	−38.2487	+	10.2487i	−1.26308	+	0.338442i
$918$		0			0
$919$		−	14.0000i		−	0.461817i	−0.972975	−	0.230909i	$-0.925830\pi$
$919$		−	14.0000i		−	0.461817i	0.972975	−	0.230909i	$-0.0741699\pi$
$920$		0			0
$921$	21.0000	+	36.3731i	0.691974	+	1.19853i
$922$		0			0
$923$	−15.0000	+	15.0000i	−0.493731	+	0.493731i
$924$	13.8564			0.455842
$925$		0			0
$926$		0			0
$927$	−14.1962	−	3.80385i	−0.466263	−	0.124935i
$928$		0			0
$929$	16.4545	+	9.50000i	0.539854	+	0.311685i	0.745020	−	0.667042i	$-0.232440\pi$
$929$	16.4545	+	9.50000i	0.539854	+	0.311685i	−0.205166	+	0.978727i	$0.565773\pi$
$930$		0			0
$931$	−0.500000	−	4.33013i	−0.0163868	−	0.141914i
$932$	2.00000	+	2.00000i	0.0655122	+	0.0655122i
$933$	61.5167	−	16.4833i	2.01397	−	0.539640i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−6.22243	+	23.2224i	−0.203278	+	0.758644i	0.786690	+	0.617349i	$0.211793\pi$
$937$	−6.22243	+	23.2224i	−0.203278	+	0.758644i	−0.989968	+	0.141295i	$0.954873\pi$
$938$		0			0
$939$	−17.3205			−0.565233
$940$		0			0
$941$	−28.5000	+	16.4545i	−0.929073	+	0.536401i	−0.886518	−	0.462693i	$-0.846883\pi$
$941$	−28.5000	+	16.4545i	−0.929073	+	0.536401i	−0.0425550	+	0.999094i	$0.513550\pi$
$942$		0			0
$943$	−41.5692	−	41.5692i	−1.35368	−	1.35368i
$944$	−3.46410	−	6.00000i	−0.112747	−	0.195283i
$945$		0			0
$946$		0			0
$947$	−53.2750	+	14.2750i	−1.73120	+	0.463875i	−0.980460	−	0.196718i	$-0.936972\pi$
$947$	−53.2750	+	14.2750i	−1.73120	+	0.463875i	−0.750744	+	0.660593i	$0.770305\pi$
$948$	−6.58846	−	24.5885i	−0.213983	−	0.798596i
$949$	6.92820			0.224899
$950$		0			0
$951$	60.0000			1.94563
$952$		0			0
$953$	−9.46410	+	2.53590i	−0.306572	+	0.0821458i	−0.408825	−	0.912613i	$-0.634062\pi$
$953$	−9.46410	+	2.53590i	−0.306572	+	0.0821458i	0.102253	+	0.994758i	$0.467395\pi$
$954$		0			0
$955$		0			0
$956$	−7.00000	−	12.1244i	−0.226396	−	0.392130i
$957$	−3.00000	−	3.00000i	−0.0969762	−	0.0969762i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−44.0000			−1.41935
$962$		0			0
$963$	−15.2154	+	56.7846i	−0.490309	+	1.82986i
$964$	−5.19615	+	9.00000i	−0.167357	+	0.289870i
$965$		0			0
$966$		0			0
$967$	−21.8564	+	5.85641i	−0.702855	+	0.188329i	−0.592509	−	0.805564i	$-0.701862\pi$
$967$	−21.8564	+	5.85641i	−0.702855	+	0.188329i	−0.110346	+	0.993893i	$0.535196\pi$
$968$		0			0
$969$	−36.3731	+	27.0000i	−1.16847	+	0.867365i
$970$		0			0
$971$	−24.0000	−	13.8564i	−0.770197	−	0.444673i	0.0627481	−	0.998029i	$-0.480014\pi$
$971$	−24.0000	−	13.8564i	−0.770197	−	0.444673i	−0.832945	+	0.553356i	$0.813347\pi$
$972$	11.4115	+	42.5885i	0.366025	+	1.36603i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	28.0000			0.896258
$977$	24.2487	−	24.2487i	0.775785	−	0.775785i	−0.203326	−	0.979111i	$-0.565175\pi$
$977$	24.2487	−	24.2487i	0.775785	−	0.775785i	0.979111	+	0.203326i	$0.0651751\pi$
$978$		0			0
$979$	6.06218	+	10.5000i	0.193748	+	0.335581i
$980$		0			0
$981$			36.3731i			1.16130i
$982$		0			0
$983$	−56.7846	+	15.2154i	−1.81115	+	0.485296i	−0.995626	−	0.0934305i	$-0.970217\pi$
$983$	−56.7846	+	15.2154i	−1.81115	+	0.485296i	−0.815522	+	0.578726i	$0.803550\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−34.6410	+	34.6410i	−1.10264	+	1.10264i
$988$	−7.85641	−	19.8564i	−0.249946	−	0.631716i
$989$			64.0000i			2.03508i
$990$		0			0
$991$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$991$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$992$		0			0
$993$	17.5692	+	65.5692i	0.557542	+	2.08078i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−10.6147	+	39.6147i	−0.336172	+	1.25461i	0.566421	+	0.824116i	$0.308328\pi$
$997$	−10.6147	+	39.6147i	−0.336172	+	1.25461i	−0.902593	+	0.430495i	$0.858339\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.p.b.407.1		4
5.2	odd	4		95.2.l.b.8.1	✓	4
5.3	odd	4	inner	475.2.p.b.293.1		4
5.4	even	2		95.2.l.b.27.1	yes	4
15.2	even	4		855.2.cj.b.388.1		4
15.14	odd	2		855.2.cj.b.217.1		4
19.12	odd	6	inner	475.2.p.b.107.1		4
95.12	even	12		95.2.l.b.88.1	yes	4
95.69	odd	6		95.2.l.b.12.1	yes	4
95.88	even	12	inner	475.2.p.b.468.1		4
285.107	odd	12		855.2.cj.b.658.1		4
285.164	even	6		855.2.cj.b.487.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.l.b.8.1	✓	4	5.2	odd	4
95.2.l.b.12.1	yes	4	95.69	odd	6
95.2.l.b.27.1	yes	4	5.4	even	2
95.2.l.b.88.1	yes	4	95.12	even	12
475.2.p.b.107.1		4	19.12	odd	6	inner
475.2.p.b.293.1		4	5.3	odd	4	inner
475.2.p.b.407.1		4	1.1	even	1	trivial
475.2.p.b.468.1		4	95.88	even	12	inner
855.2.cj.b.217.1		4	15.14	odd	2
855.2.cj.b.388.1		4	15.2	even	4
855.2.cj.b.487.1		4	285.164	even	6
855.2.cj.b.658.1		4	285.107	odd	12

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:	\( N \)	\(=\)	\( 475 = 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	475.p (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.36603 - 0.633975i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.00000 - 2.00000i) q^{7} +(2.59808 - 1.50000i) q^{9} +O(q^{10})\)	\(q+(2.36603 - 0.633975i) q^{3} +(1.73205 - 1.00000i) q^{4} +(-2.00000 - 2.00000i) q^{7} +(2.59808 - 1.50000i) q^{9} -1.00000 q^{11} +(3.46410 - 3.46410i) q^{12} +(-0.633975 + 2.36603i) q^{13} +(2.00000 - 3.46410i) q^{16} +(4.09808 - 1.09808i) q^{17} +(-4.33013 + 0.500000i) q^{19} +(-6.00000 - 3.46410i) q^{21} +(5.46410 + 1.46410i) q^{23} +(-5.46410 - 1.46410i) q^{28} +(0.866025 + 1.50000i) q^{29} +8.66025i q^{31} +(-2.36603 + 0.633975i) q^{33} +(3.00000 - 5.19615i) q^{36} +(-3.46410 + 3.46410i) q^{37} +6.00000i q^{39} +(-9.00000 - 5.19615i) q^{41} +(2.92820 + 10.9282i) q^{43} +(-1.73205 + 1.00000i) q^{44} +(1.83013 - 6.83013i) q^{47} +(2.53590 - 9.46410i) q^{48} +1.00000i q^{49} +(9.00000 - 5.19615i) q^{51} +(1.26795 + 4.73205i) q^{52} +(0.633975 - 2.36603i) q^{53} +(-9.92820 + 3.92820i) q^{57} +(0.866025 - 1.50000i) q^{59} +(3.50000 + 6.06218i) q^{61} +(-8.19615 - 2.19615i) q^{63} -8.00000i q^{64} +(2.36603 + 0.633975i) q^{67} +(6.00000 - 6.00000i) q^{68} +13.8564 q^{69} +(7.50000 + 4.33013i) q^{71} +(-0.732051 - 2.73205i) q^{73} +(-7.00000 + 5.19615i) q^{76} +(2.00000 + 2.00000i) q^{77} +(2.59808 - 4.50000i) q^{79} +(-4.50000 + 7.79423i) q^{81} -13.8564 q^{84} +(3.00000 + 3.00000i) q^{87} +(-6.06218 - 10.5000i) q^{89} +(6.00000 - 3.46410i) q^{91} +(10.9282 - 2.92820i) q^{92} +(5.49038 + 20.4904i) q^{93} +(-2.53590 - 9.46410i) q^{97} +(-2.59808 + 1.50000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} - 8 q^{7}+O(q^{10}) \) 4 * q + 6 * q^3 - 8 * q^7	\( 4 q + 6 q^{3} - 8 q^{7} - 4 q^{11} - 6 q^{13} + 8 q^{16} + 6 q^{17} - 24 q^{21} + 8 q^{23} - 8 q^{28} - 6 q^{33} + 12 q^{36} - 36 q^{41} - 16 q^{43} - 10 q^{47} + 24 q^{48} + 36 q^{51} + 12 q^{52} + 6 q^{53} - 12 q^{57} + 14 q^{61} - 12 q^{63} + 6 q^{67} + 24 q^{68} + 30 q^{71} + 4 q^{73} - 28 q^{76} + 8 q^{77} - 18 q^{81} + 12 q^{87} + 24 q^{91} + 16 q^{92} - 30 q^{93} - 24 q^{97}+O(q^{100}) \) 4 * q + 6 * q^3 - 8 * q^7 - 4 * q^11 - 6 * q^13 + 8 * q^16 + 6 * q^17 - 24 * q^21 + 8 * q^23 - 8 * q^28 - 6 * q^33 + 12 * q^36 - 36 * q^41 - 16 * q^43 - 10 * q^47 + 24 * q^48 + 36 * q^51 + 12 * q^52 + 6 * q^53 - 12 * q^57 + 14 * q^61 - 12 * q^63 + 6 * q^67 + 24 * q^68 + 30 * q^71 + 4 * q^73 - 28 * q^76 + 8 * q^77 - 18 * q^81 + 12 * q^87 + 24 * q^91 + 16 * q^92 - 30 * q^93 - 24 * q^97

Introduction

L-functions

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