LMFDB - Embedded newform 475.2.p.b.107.1

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			107.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	475.107
Dual form			475.2.p.b.293.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.633975 - 2.36603i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-2.00000 - 2.00000i) q^{7} +(-2.59808 - 1.50000i) q^{9} +O(q^{10})$	\(q+(0.633975 - 2.36603i) q^{3} +(-1.73205 - 1.00000i) q^{4} +(-2.00000 - 2.00000i) q^{7} +(-2.59808 - 1.50000i) q^{9} -1.00000 q^{11} +(-3.46410 + 3.46410i) q^{12} +(-2.36603 + 0.633975i) q^{13} +(2.00000 + 3.46410i) q^{16} +(-1.09808 + 4.09808i) q^{17} +(4.33013 + 0.500000i) q^{19} +(-6.00000 + 3.46410i) q^{21} +(-1.46410 - 5.46410i) q^{23} +(1.46410 + 5.46410i) q^{28} +(-0.866025 + 1.50000i) q^{29} -8.66025i q^{31} +(-0.633975 + 2.36603i) q^{33} +(3.00000 + 5.19615i) q^{36} +(3.46410 - 3.46410i) q^{37} +6.00000i q^{39} +(-9.00000 + 5.19615i) q^{41} +(-10.9282 - 2.92820i) q^{43} +(1.73205 + 1.00000i) q^{44} +(-6.83013 + 1.83013i) q^{47} +(9.46410 - 2.53590i) q^{48} +1.00000i q^{49} +(9.00000 + 5.19615i) q^{51} +(4.73205 + 1.26795i) q^{52} +(2.36603 - 0.633975i) q^{53} +(3.92820 - 9.92820i) q^{57} +(-0.866025 - 1.50000i) q^{59} +(3.50000 - 6.06218i) q^{61} +(2.19615 + 8.19615i) q^{63} -8.00000i q^{64} +(0.633975 + 2.36603i) q^{67} +(6.00000 - 6.00000i) q^{68} -13.8564 q^{69} +(7.50000 - 4.33013i) q^{71} +(2.73205 + 0.732051i) q^{73} +(-7.00000 - 5.19615i) q^{76} +(2.00000 + 2.00000i) q^{77} +(-2.59808 - 4.50000i) q^{79} +(-4.50000 - 7.79423i) q^{81} +13.8564 q^{84} +(3.00000 + 3.00000i) q^{87} +(6.06218 - 10.5000i) q^{89} +(6.00000 + 3.46410i) q^{91} +(-2.92820 + 10.9282i) q^{92} +(-20.4904 - 5.49038i) q^{93} +(-9.46410 - 2.53590i) q^{97} +(2.59808 + 1.50000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/475\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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		0.258819	−	0.965926i	$-0.416667\pi$
$2$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$3$	0.633975	−	2.36603i	0.366025	−	1.36603i	−0.500000	−	0.866025i	$-0.666667\pi$
$3$	0.633975	−	2.36603i	0.366025	−	1.36603i	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
$13$	−2.36603	+	0.633975i	−0.656217	+	0.175833i	−0.571538	−	0.820575i	$-0.693653\pi$
$13$	−2.36603	+	0.633975i	−0.656217	+	0.175833i	−0.0846790	+	0.996408i	$0.526986\pi$
$14$		0			0
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−1.09808	+	4.09808i	−0.266323	+	0.993929i	0.695113	+	0.718900i	$0.255354\pi$
$17$	−1.09808	+	4.09808i	−0.266323	+	0.993929i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		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
$23$	−1.46410	−	5.46410i	−0.305286	−	1.13934i	−0.932699	−	0.360657i	$-0.882553\pi$
$23$	−1.46410	−	5.46410i	−0.305286	−	1.13934i	0.627412	−	0.778687i	$-0.284114\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		0			0
$28$	1.46410	+	5.46410i	0.276689	+	1.03262i
$29$	−0.866025	+	1.50000i	−0.160817	+	0.278543i	−0.935162	−	0.354221i	$-0.884746\pi$
$29$	−0.866025	+	1.50000i	−0.160817	+	0.278543i	0.774345	+	0.632764i	$0.218080\pi$
$30$		0			0
$31$		−	8.66025i		−	1.55543i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$		−	8.66025i		−	1.55543i	0.628619	−	0.777714i	$-0.283621\pi$
$32$		0			0
$33$	−0.633975	+	2.36603i	−0.110361	+	0.411872i
$34$		0			0
$35$		0			0
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$	3.46410	−	3.46410i	0.569495	−	0.569495i	−0.362492	−	0.931987i	$-0.618074\pi$
$37$	3.46410	−	3.46410i	0.569495	−	0.569495i	0.931987	+	0.362492i	$0.118074\pi$
$38$		0			0
$39$			6.00000i			0.960769i
$40$		0			0
$41$	−9.00000	+	5.19615i	−1.40556	+	0.811503i	−0.994956	−	0.100309i	$-0.968017\pi$
$41$	−9.00000	+	5.19615i	−1.40556	+	0.811503i	−0.410608	+	0.911812i	$0.634683\pi$
$42$		0			0
$43$	−10.9282	−	2.92820i	−1.66654	−	0.446547i	−0.702362	−	0.711820i	$-0.747871\pi$
$43$	−10.9282	−	2.92820i	−1.66654	−	0.446547i	−0.964173	+	0.265273i	$0.914538\pi$
$44$	1.73205	+	1.00000i	0.261116	+	0.150756i
$45$		0			0
$46$		0			0
$47$	−6.83013	+	1.83013i	−0.996276	+	0.266951i	−0.719885	−	0.694094i	$-0.755805\pi$
$47$	−6.83013	+	1.83013i	−0.996276	+	0.266951i	−0.276392	+	0.961045i	$0.589139\pi$
$48$	9.46410	−	2.53590i	1.36603	−	0.366025i
$49$			1.00000i			0.142857i
$50$		0			0
$51$	9.00000	+	5.19615i	1.26025	+	0.727607i
$52$	4.73205	+	1.26795i	0.656217	+	0.175833i
$53$	2.36603	−	0.633975i	0.324999	−	0.0870831i	−0.0926309	−	0.995701i	$-0.529528\pi$
$53$	2.36603	−	0.633975i	0.324999	−	0.0870831i	0.417630	+	0.908617i	$0.362861\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	3.92820	−	9.92820i	0.520303	−	1.31502i
$58$		0			0
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	0.804130	−	0.594454i	$-0.202632\pi$
$59$	−0.866025	−	1.50000i	−0.112747	−	0.195283i	−0.916877	+	0.399170i	$0.869298\pi$
$60$		0			0
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$		0			0
$63$	2.19615	+	8.19615i	0.276689	+	1.03262i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$		0			0
$67$	0.633975	+	2.36603i	0.0774523	+	0.289056i	0.993778	−	0.111377i	$-0.0355262\pi$
$67$	0.633975	+	2.36603i	0.0774523	+	0.289056i	−0.916326	+	0.400433i	$0.868860\pi$
$68$	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	0.0161155	−	0.999870i	$-0.494870\pi$
$71$	7.50000	−	4.33013i	0.890086	−	0.513892i	0.873971	+	0.485979i	$0.161537\pi$
$72$		0			0
$73$	2.73205	+	0.732051i	0.319762	+	0.0856801i	0.415130	−	0.909762i	$-0.363736\pi$
$73$	2.73205	+	0.732051i	0.319762	+	0.0856801i	−0.0953678	+	0.995442i	$0.530403\pi$
$74$		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	$-0.261089\pi$
$79$	−2.59808	−	4.50000i	−0.292306	−	0.506290i	−0.974355	+	0.225018i	$0.927756\pi$
$80$		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	−0.342263	−	0.939604i	$-0.611193\pi$
$89$	6.06218	−	10.5000i	0.642590	−	1.11300i	0.984853	−	0.173394i	$-0.0554733\pi$
$90$		0			0
$91$	6.00000	+	3.46410i	0.628971	+	0.363137i
$92$	−2.92820	+	10.9282i	−0.305286	+	1.13934i
$93$	−20.4904	−	5.49038i	−2.12475	−	0.569326i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.46410	−	2.53590i	−0.960934	−	0.257481i	−0.255938	−	0.966693i	$-0.582384\pi$
$97$	−9.46410	−	2.53590i	−0.960934	−	0.257481i	−0.704996	+	0.709212i	$0.749051\pi$
$98$		0			0
$99$	2.59808	+	1.50000i	0.261116	+	0.150756i
$100$		0			0
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	−0.451190	−	0.892428i	$-0.649000\pi$
$101$	5.50000	−	9.52628i	0.547270	−	0.947900i	0.998460	−	0.0554722i	$-0.0176664\pi$
$102$		0			0
$103$	3.46410	+	3.46410i	0.341328	+	0.341328i	0.856866	−	0.515538i	$-0.172408\pi$
$103$	3.46410	+	3.46410i	0.341328	+	0.341328i	−0.515538	+	0.856866i	$0.672408\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	13.8564	−	13.8564i	1.33955	−	1.33955i	0.443055	−	0.896494i	$-0.353895\pi$
$107$	13.8564	−	13.8564i	1.33955	−	1.33955i	0.896494	−	0.443055i	$-0.146105\pi$
$108$		0			0
$109$	6.06218	+	10.5000i	0.580651	+	1.00572i	0.995402	+	0.0957826i	$0.0305354\pi$
$109$	6.06218	+	10.5000i	0.580651	+	1.00572i	−0.414751	+	0.909935i	$0.636131\pi$
$110$		0			0
$111$	−6.00000	−	10.3923i	−0.569495	−	0.986394i
$112$	2.92820	−	10.9282i	0.276689	−	1.03262i
$113$	12.1244	+	12.1244i	1.14056	+	1.14056i	0.988347	+	0.152216i	$0.0486410\pi$
$113$	12.1244	+	12.1244i	1.14056	+	1.14056i	0.152216	+	0.988347i	$0.451359\pi$
$114$		0			0
$115$		0			0
$116$	3.00000	−	1.73205i	0.278543	−	0.160817i
$117$	7.09808	+	1.90192i	0.656217	+	0.175833i
$118$		0			0
$119$	10.3923	−	6.00000i	0.952661	−	0.550019i
$120$		0			0
$121$	−10.0000			−0.909091
$122$		0			0
$123$	6.58846	+	24.5885i	0.594061	+	2.21707i
$124$	−8.66025	+	15.0000i	−0.777714	+	1.34704i
$125$		0			0
$126$		0			0
$127$	−0.633975	−	2.36603i	−0.0562561	−	0.209951i	0.932077	−	0.362261i	$-0.117995\pi$
$127$	−0.633975	−	2.36603i	−0.0562561	−	0.209951i	−0.988333	+	0.152311i	$0.951329\pi$
$128$		0			0
$129$	−13.8564	+	24.0000i	−1.21999	+	2.11308i
$130$		0			0
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	0.990972	+	0.134069i	$0.0428042\pi$
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	−0.379379	+	0.925241i	$0.623862\pi$
$132$	3.46410	−	3.46410i	0.301511	−	0.301511i
$133$	−7.66025	−	9.66025i	−0.664228	−	0.837650i
$134$		0			0
$135$		0			0
$136$		0			0
$137$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$137$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$138$		0			0
$139$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$139$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$140$		0			0
$141$			17.3205i			1.45865i
$142$		0			0
$143$	2.36603	−	0.633975i	0.197857	−	0.0530156i
$144$		−	12.0000i		−	1.00000i
$145$		0			0
$146$		0			0
$147$	2.36603	+	0.633975i	0.195146	+	0.0522893i
$148$	−9.46410	+	2.53590i	−0.777944	+	0.208450i
$149$	6.06218	−	3.50000i	0.496633	−	0.286731i	−0.230689	−	0.973028i	$-0.574098\pi$
$149$	6.06218	−	3.50000i	0.496633	−	0.286731i	0.727322	+	0.686296i	$0.240765\pi$
$150$		0			0
$151$			1.73205i			0.140952i	0.997513	+	0.0704761i	$0.0224519\pi$
$151$			1.73205i			0.140952i	−0.997513	+	0.0704761i	$0.977548\pi$
$152$		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
$157$	1.83013	−	6.83013i	0.146060	−	0.545103i	−0.853646	−	0.520854i	$-0.825614\pi$
$157$	1.83013	−	6.83013i	0.146060	−	0.545103i	0.999706	−	0.0242497i	$-0.00771967\pi$
$158$		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
$167$	1.26795	+	4.73205i	0.0981169	+	0.366177i	0.997474	−	0.0710385i	$-0.0226313\pi$
$167$	1.26795	+	4.73205i	0.0981169	+	0.366177i	−0.899357	+	0.437216i	$0.855965\pi$
$168$		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
$173$	−2.53590	+	9.46410i	−0.192801	+	0.719542i	0.800024	+	0.599967i	$0.204820\pi$
$173$	−2.53590	+	9.46410i	−0.192801	+	0.719542i	−0.992825	+	0.119575i	$0.961847\pi$
$174$		0			0
$175$		0			0
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$	−4.09808	+	1.09808i	−0.308030	+	0.0825365i
$178$		0			0
$179$	−12.1244			−0.906217			−0.453108	−	0.891455i	$-0.649685\pi$
$179$	−12.1244			−0.906217			−0.453108	+	0.891455i	$0.649685\pi$
$180$		0			0
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	0.384345	−	0.923190i	$-0.374427\pi$
$181$	−3.00000	−	1.73205i	−0.222988	−	0.128742i	−0.607333	+	0.794447i	$0.707761\pi$
$182$		0			0
$183$	−12.1244	−	12.1244i	−0.896258	−	0.896258i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.09808	−	4.09808i	0.0802993	−	0.299681i
$188$	13.6603	+	3.66025i	0.996276	+	0.266951i
$189$		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	$0.187132\pi$
$192$	−18.9282	−	5.07180i	−1.36603	−	0.366025i
$193$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$193$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$194$		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	$-0.229987\pi$
$199$	7.79423	+	4.50000i	0.552518	+	0.318997i	−0.197619	+	0.980279i	$0.563321\pi$
$200$		0			0
$201$	6.00000			0.423207
$202$		0			0
$203$	4.73205	−	1.26795i	0.332125	−	0.0889926i
$204$	−10.3923	−	18.0000i	−0.727607	−	1.26025i
$205$		0			0
$206$		0			0
$207$	−4.39230	+	16.3923i	−0.305286	+	1.13934i
$208$	−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	−0.987164	−	0.159708i	$-0.948945\pi$
$211$	−19.5000	+	11.2583i	−1.34244	+	0.775055i	−0.355271	+	0.934763i	$0.615611\pi$
$212$	−4.73205	−	1.26795i	−0.324999	−	0.0870831i
$213$	−5.49038	−	20.4904i	−0.376195	−	1.40398i
$214$		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
$223$	3.80385	−	14.1962i	0.254724	−	0.950645i	−0.713519	−	0.700636i	$-0.752900\pi$
$223$	3.80385	−	14.1962i	0.254724	−	0.950645i	0.968244	−	0.250009i	$-0.0804335\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.92820	+	6.92820i	−0.459841	+	0.459841i	−0.898603	−	0.438762i	$-0.855417\pi$
$227$	−6.92820	+	6.92820i	−0.459841	+	0.459841i	0.438762	+	0.898603i	$0.355417\pi$
$228$	−16.7321	+	13.2679i	−1.10811	+	0.878691i
$229$		−	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
$233$	−1.36603	−	0.366025i	−0.0894913	−	0.0239791i	0.213796	−	0.976878i	$-0.431417\pi$
$233$	−1.36603	−	0.366025i	−0.0894913	−	0.0239791i	−0.303287	+	0.952899i	$0.598084\pi$
$234$		0			0
$235$		0			0
$236$			3.46410i			0.225494i
$237$	−12.2942	+	3.29423i	−0.798596	+	0.213983i
$238$		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	0.348013	−	0.937490i	$-0.386857\pi$
$241$	−4.50000	−	2.59808i	−0.289870	−	0.167357i	−0.637883	+	0.770133i	$0.720190\pi$
$242$		0			0
$243$	−21.2942	+	5.70577i	−1.36603	+	0.366025i
$244$	−12.1244	+	7.00000i	−0.776182	+	0.448129i
$245$		0			0
$246$		0			0
$247$	−10.5622	+	1.56218i	−0.672055	+	0.0993990i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−6.50000	+	11.2583i	−0.410276	+	0.710620i	−0.994920	−	0.100671i	$-0.967901\pi$
$251$	−6.50000	+	11.2583i	−0.410276	+	0.710620i	0.584643	+	0.811290i	$0.301234\pi$
$252$	4.39230	−	16.3923i	0.276689	−	1.03262i
$253$	1.46410	+	5.46410i	0.0920473	+	0.343525i
$254$		0			0
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−0.633975	−	2.36603i	−0.0395462	−	0.147589i	0.943330	−	0.331857i	$-0.107675\pi$
$257$	−0.633975	−	2.36603i	−0.0395462	−	0.147589i	−0.982876	+	0.184268i	$0.941008\pi$
$258$		0			0
$259$	−13.8564			−0.860995
$260$		0			0
$261$	4.50000	−	2.59808i	0.278543	−	0.160817i
$262$		0			0
$263$	12.2942	+	3.29423i	0.758095	+	0.203131i	0.617106	−	0.786880i	$-0.288305\pi$
$263$	12.2942	+	3.29423i	0.758095	+	0.203131i	0.140989	+	0.990011i	$0.454972\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−21.0000	−	21.0000i	−1.28518	−	1.28518i
$268$	1.26795	−	4.73205i	0.0774523	−	0.289056i
$269$	−7.79423	−	13.5000i	−0.475223	−	0.823110i	0.524375	−	0.851488i	$-0.324299\pi$
$269$	−7.79423	−	13.5000i	−0.475223	−	0.823110i	−0.999597	+	0.0283781i	$0.990966\pi$
$270$		0			0
$271$	−1.50000	−	2.59808i	−0.0911185	−	0.157822i	0.816864	−	0.576831i	$-0.195711\pi$
$271$	−1.50000	−	2.59808i	−0.0911185	−	0.157822i	−0.907982	+	0.419009i	$0.862378\pi$
$272$	−16.3923	+	4.39230i	−0.993929	+	0.266323i
$273$	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	0.0973670	−	0.995249i	$-0.468958\pi$
$281$	−12.0000	−	6.92820i	−0.715860	−	0.413302i	−0.813227	+	0.581947i	$0.802291\pi$
$282$		0			0
$283$	9.56218	+	2.56218i	0.568412	+	0.152306i	0.531568	−	0.847015i	$-0.321603\pi$
$283$	9.56218	+	2.56218i	0.568412	+	0.152306i	0.0368441	+	0.999321i	$0.488270\pi$
$284$	−17.3205			−1.02778
$285$		0			0
$286$		0			0
$287$	28.3923	+	7.60770i	1.67594	+	0.449068i
$288$		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	0.942194	−	0.335069i	$-0.108760\pi$
$293$	10.3923	+	10.3923i	0.607125	+	0.607125i	−0.335069	+	0.942194i	$0.608760\pi$
$294$		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
$307$	16.5622	+	4.43782i	0.945253	+	0.253280i	0.698347	−	0.715759i	$-0.253919\pi$
$307$	16.5622	+	4.43782i	0.945253	+	0.253280i	0.246906	+	0.969039i	$0.420586\pi$
$308$	−1.46410	−	5.46410i	−0.0834249	−	0.311346i
$309$	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
$313$	1.83013	+	6.83013i	0.103445	+	0.386062i	0.998164	−	0.0605675i	$-0.0192910\pi$
$313$	1.83013	+	6.83013i	0.103445	+	0.386062i	−0.894719	+	0.446629i	$0.852624\pi$
$314$		0			0
$315$		0			0
$316$			10.3923i			0.584613i
$317$	6.33975	+	23.6603i	0.356076	+	1.32889i	0.879126	+	0.476590i	$0.158127\pi$
$317$	6.33975	+	23.6603i	0.356076	+	1.32889i	−0.523050	+	0.852302i	$0.675206\pi$
$318$		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
$323$	−6.80385	+	17.1962i	−0.378576	+	0.956820i
$324$			18.0000i			1.00000i
$325$		0			0
$326$		0			0
$327$	28.6865	−	7.68653i	1.58637	−	0.425066i
$328$		0			0
$329$	17.3205	+	10.0000i	0.954911	+	0.551318i
$330$		0			0
$331$		−	27.7128i		−	1.52323i	−0.648027	−	0.761617i	$-0.724406\pi$
$331$		−	27.7128i		−	1.52323i	0.648027	−	0.761617i	$-0.275594\pi$
$332$		0			0
$333$	−14.1962	+	3.80385i	−0.777944	+	0.208450i
$334$		0			0
$335$		0			0
$336$	−24.0000	−	13.8564i	−1.30931	−	0.755929i
$337$	−23.6603	−	6.33975i	−1.28886	−	0.345348i	−0.451630	−	0.892205i	$-0.649157\pi$
$337$	−23.6603	−	6.33975i	−1.28886	−	0.345348i	−0.837226	+	0.546857i	$0.815824\pi$
$338$		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
$347$	−4.39230	+	16.3923i	−0.235791	+	0.879985i	0.741999	+	0.670401i	$0.233878\pi$
$347$	−4.39230	+	16.3923i	−0.235791	+	0.879985i	−0.977791	+	0.209584i	$0.932789\pi$
$348$	−2.19615	−	8.19615i	−0.117726	−	0.439360i
$349$		−	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
$357$	−7.60770	−	28.3923i	−0.402642	−	1.50268i
$358$		0			0
$359$	−8.66025	+	5.00000i	−0.457071	+	0.263890i	−0.710812	−	0.703382i	$-0.751672\pi$
$359$	−8.66025	+	5.00000i	−0.457071	+	0.263890i	0.253741	+	0.967272i	$0.418339\pi$
$360$		0			0
$361$	18.5000	+	4.33013i	0.973684	+	0.227901i
$362$		0			0
$363$	−6.33975	+	23.6603i	−0.332750	+	1.24184i
$364$	−6.92820	−	12.0000i	−0.363137	−	0.628971i
$365$		0			0
$366$		0			0
$367$	27.3205	−	7.32051i	1.42612	−	0.382127i	0.538469	−	0.842646i	$-0.319003\pi$
$367$	27.3205	−	7.32051i	1.42612	−	0.382127i	0.887650	+	0.460518i	$0.152336\pi$
$368$	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	0.384875	−	0.922969i	$-0.374244\pi$
$373$	−10.3923	−	10.3923i	−0.538093	−	0.538093i	−0.922969	+	0.384875i	$0.874244\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.09808	−	4.09808i	0.0565538	−	0.211062i
$378$		0			0
$379$	−15.5885			−0.800725			−0.400363	−	0.916357i	$-0.631116\pi$
$379$	−15.5885			−0.800725			−0.400363	+	0.916357i	$0.631116\pi$
$380$		0			0
$381$	−6.00000			−0.307389
$382$		0			0
$383$	−0.633975	+	2.36603i	−0.0323946	+	0.120898i	−0.980230	−	0.197863i	$-0.936600\pi$
$383$	−0.633975	+	2.36603i	−0.0323946	+	0.120898i	0.947835	+	0.318761i	$0.103267\pi$
$384$		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	$-0.0455430\pi$
$389$	26.8468	+	15.5000i	1.36119	+	0.785881i	0.371404	+	0.928471i	$0.378876\pi$
$390$		0			0
$391$	24.0000			1.21373
$392$		0			0
$393$	33.1244	−	8.87564i	1.67090	−	0.447717i
$394$		0			0
$395$		0			0
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	0.732051	−	2.73205i	0.0367406	−	0.137118i	−0.945119	−	0.326725i	$-0.894055\pi$
$397$	0.732051	−	2.73205i	0.0367406	−	0.137118i	0.981860	+	0.189607i	$0.0607215\pi$
$398$		0			0
$399$	−27.7128	+	12.0000i	−1.38738	+	0.600751i
$400$		0			0
$401$	13.5000	−	7.79423i	0.674158	−	0.389225i	−0.123492	−	0.992346i	$-0.539409\pi$
$401$	13.5000	−	7.79423i	0.674158	−	0.389225i	0.797650	+	0.603120i	$0.206076\pi$
$402$		0			0
$403$	5.49038	+	20.4904i	0.273495	+	1.02070i
$404$	−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	−0.342578	−	0.939490i	$-0.611300\pi$
$409$	12.9904	−	22.5000i	0.642333	−	1.11255i	0.984911	−	0.173064i	$-0.0553667\pi$
$410$		0			0
$411$		0			0
$412$	−2.53590	−	9.46410i	−0.124935	−	0.466263i
$413$	−1.26795	+	4.73205i	−0.0623917	+	0.232849i
$414$		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	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−1.50000	+	0.866025i	−0.0731055	+	0.0422075i	0.463002	+	0.886357i	$0.346772\pi$
$422$		0			0
$423$	20.4904	+	5.49038i	0.996276	+	0.266951i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−19.1244	+	5.12436i	−0.925492	+	0.247985i
$428$	−37.8564	+	10.1436i	−1.82986	+	0.490309i
$429$		−	6.00000i		−	0.289683i
$430$		0			0
$431$	13.5000	+	7.79423i	0.650272	+	0.375435i	0.788560	−	0.614957i	$-0.210827\pi$
$431$	13.5000	+	7.79423i	0.650272	+	0.375435i	−0.138288	+	0.990392i	$0.544160\pi$
$432$		0			0
$433$	−14.1962	+	3.80385i	−0.682224	+	0.182801i	−0.583255	−	0.812289i	$-0.698221\pi$
$433$	−14.1962	+	3.80385i	−0.682224	+	0.182801i	−0.0989688	+	0.995091i	$0.531554\pi$
$434$		0			0
$435$		0			0
$436$		−	24.2487i		−	1.16130i
$437$	−3.60770	−	24.3923i	−0.172579	−	1.16684i
$438$		0			0
$439$	11.2583	+	19.5000i	0.537331	+	0.930684i	0.999047	+	0.0436563i	$0.0139007\pi$
$439$	11.2583	+	19.5000i	0.537331	+	0.930684i	−0.461716	+	0.887028i	$0.652766\pi$
$440$		0			0
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$		0			0
$443$	−2.92820	−	10.9282i	−0.139123	−	0.519215i	−0.999947	−	0.0103113i	$-0.996718\pi$
$443$	−2.92820	−	10.9282i	−0.139123	−	0.519215i	0.860824	−	0.508903i	$-0.169949\pi$
$444$			24.0000i			1.13899i
$445$		0			0
$446$		0			0
$447$	−4.43782	−	16.5622i	−0.209902	−	0.783364i
$448$	−16.0000	+	16.0000i	−0.755929	+	0.755929i
$449$	−19.0526			−0.899146			−0.449573	−	0.893244i	$-0.648424\pi$
$449$	−19.0526			−0.899146			−0.449573	+	0.893244i	$0.648424\pi$
$450$		0			0
$451$	9.00000	−	5.19615i	0.423793	−	0.244677i
$452$	−8.87564	−	33.1244i	−0.417475	−	1.55804i
$453$	4.09808	+	1.09808i	0.192544	+	0.0515921i
$454$		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	0.854147	−	0.520032i	$-0.174080\pi$
$461$	−0.500000	−	0.866025i	−0.0232873	−	0.0403348i	−0.877434	+	0.479697i	$0.840747\pi$
$462$		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
$473$	10.9282	+	2.92820i	0.502479	+	0.134639i
$474$		0			0
$475$		0			0
$476$	−24.0000			−1.10004
$477$	−7.09808	−	1.90192i	−0.324999	−	0.0870831i
$478$		0			0
$479$	−0.866025	−	0.500000i	−0.0395697	−	0.0228456i	0.480085	−	0.877222i	$-0.340606\pi$
$479$	−0.866025	−	0.500000i	−0.0395697	−	0.0228456i	−0.519654	+	0.854377i	$0.673939\pi$
$480$		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	−0.259392	−	0.965772i	$-0.583522\pi$
$487$	15.5885	−	15.5885i	0.706380	−	0.706380i	0.965772	+	0.259392i	$0.0835221\pi$
$488$		0			0
$489$	−12.1244	−	21.0000i	−0.548282	−	0.949653i
$490$		0			0
$491$	−6.50000	−	11.2583i	−0.293341	−	0.508081i	0.681257	−	0.732045i	$-0.261434\pi$
$491$	−6.50000	−	11.2583i	−0.293341	−	0.508081i	−0.974598	+	0.223963i	$0.928100\pi$
$492$	13.1769	−	49.1769i	0.594061	−	2.21707i
$493$	−5.19615	−	5.19615i	−0.234023	−	0.234023i
$494$		0			0
$495$		0			0
$496$	30.0000	−	17.3205i	1.34704	−	0.777714i
$497$	−23.6603	−	6.33975i	−1.06131	−	0.284376i
$498$		0			0
$499$	−25.9808	+	15.0000i	−1.16306	+	0.671492i	−0.952035	−	0.305989i	$-0.901013\pi$
$499$	−25.9808	+	15.0000i	−1.16306	+	0.671492i	−0.211024	+	0.977481i	$0.567680\pi$
$500$		0			0
$501$	12.0000			0.536120
$502$		0			0
$503$	−1.09808	−	4.09808i	−0.0489608	−	0.182724i	0.937115	−	0.349021i	$-0.113486\pi$
$503$	−1.09808	−	4.09808i	−0.0489608	−	0.182724i	−0.986076	+	0.166297i	$0.946819\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	4.43782	+	16.5622i	0.197091	+	0.735552i
$508$	−1.26795	+	4.73205i	−0.0562561	+	0.209951i
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	−0.901855	−	0.432038i	$-0.857795\pi$
$509$	−1.73205	+	3.00000i	−0.0767718	+	0.132973i	0.825084	+	0.565011i	$0.191128\pi$
$510$		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
$517$	6.83013	−	1.83013i	0.300389	−	0.0804889i
$518$		0			0
$519$	20.7846	+	12.0000i	0.912343	+	0.526742i
$520$		0			0
$521$			22.5167i			0.986473i	0.869895	+	0.493236i	$0.164186\pi$
$521$			22.5167i			0.986473i	−0.869895	+	0.493236i	$0.835814\pi$
$522$		0			0
$523$	11.8301	−	3.16987i	0.517295	−	0.138609i	0.00928008	−	0.999957i	$-0.497046\pi$
$523$	11.8301	−	3.16987i	0.517295	−	0.138609i	0.508015	+	0.861348i	$0.330379\pi$
$524$		−	28.0000i		−	1.22319i
$525$		0			0
$526$		0			0
$527$	35.4904	+	9.50962i	1.54599	+	0.414246i
$528$	−9.46410	+	2.53590i	−0.411872	+	0.110361i
$529$	−7.79423	+	4.50000i	−0.338880	+	0.195652i
$530$		0			0
$531$			5.19615i			0.225494i
$532$	3.60770	+	24.3923i	0.156413	+	1.05754i
$533$	18.0000	−	18.0000i	0.779667	−	0.779667i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−7.68653	+	28.6865i	−0.331698	+	1.23792i
$538$		0			0
$539$		−	1.00000i		−	0.0430730i
$540$		0			0
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	−0.831978	−	0.554809i	$-0.812791\pi$
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	0.896468	+	0.443109i	$0.146125\pi$
$542$		0			0
$543$	−6.00000	+	6.00000i	−0.257485	+	0.257485i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−1.26795	−	4.73205i	−0.0542136	−	0.202328i	0.933507	−	0.358560i	$-0.116732\pi$
$547$	−1.26795	−	4.73205i	−0.0542136	−	0.202328i	−0.987720	+	0.156232i	$0.950065\pi$
$548$		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
$553$	−3.80385	+	14.1962i	−0.161756	+	0.603682i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−27.3205	+	7.32051i	−1.15761	+	0.310180i	−0.786010	−	0.618214i	$-0.787856\pi$
$557$	−27.3205	+	7.32051i	−1.15761	+	0.310180i	−0.371597	+	0.928394i	$0.621190\pi$
$558$		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	$-0.968126\pi$
$563$	−25.9808	−	25.9808i	−1.09496	−	1.09496i	−0.0999679	−	0.994991i	$-0.531874\pi$
$564$	17.3205	−	30.0000i	0.729325	−	1.26323i
$565$		0			0
$566$		0			0
$567$	−6.58846	+	24.5885i	−0.276689	+	1.03262i
$568$		0			0
$569$	32.9090			1.37962			0.689808	−	0.723993i	$-0.257695\pi$
$569$	32.9090			1.37962			0.689808	+	0.723993i	$0.257695\pi$
$570$		0			0
$571$	−39.0000			−1.63210			−0.816050	−	0.577982i	$-0.803840\pi$
$571$	−39.0000			−1.63210			−0.816050	+	0.577982i	$0.803840\pi$
$572$	−4.73205	−	1.26795i	−0.197857	−	0.0530156i
$573$	14.5814	−	54.4186i	0.609147	−	2.27337i
$574$		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
$583$	−2.36603	+	0.633975i	−0.0979908	+	0.0262565i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.732051	+	2.73205i	−0.0302150	+	0.112764i	−0.979386	−	0.201996i	$-0.935257\pi$
$587$	−0.732051	+	2.73205i	−0.0302150	+	0.112764i	0.949171	+	0.314760i	$0.101924\pi$
$588$	−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
$592$	18.9282	+	5.07180i	0.777944	+	0.208450i
$593$	8.78461	+	32.7846i	0.360741	+	1.34630i	0.873104	+	0.487534i	$0.162103\pi$
$593$	8.78461	+	32.7846i	0.360741	+	1.34630i	−0.512363	+	0.858769i	$0.671230\pi$
$594$		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	0.430784	+	0.902455i	$0.358237\pi$
$599$	−13.8564	+	24.0000i	−0.566157	+	0.980613i	−0.996941	+	0.0781581i	$0.975096\pi$
$600$		0			0
$601$			29.4449i			1.20108i	0.799594	+	0.600541i	$0.205048\pi$
$601$			29.4449i			1.20108i	−0.799594	+	0.600541i	$0.794952\pi$
$602$		0			0
$603$	1.90192	−	7.09808i	0.0774523	−	0.289056i
$604$	1.73205	−	3.00000i	0.0704761	−	0.122068i
$605$		0			0
$606$		0			0
$607$	−5.19615	+	5.19615i	−0.210905	+	0.210905i	−0.804652	−	0.593747i	$-0.797648\pi$
$607$	−5.19615	+	5.19615i	−0.210905	+	0.210905i	0.593747	+	0.804652i	$0.297648\pi$
$608$		0			0
$609$		−	12.0000i		−	0.486265i
$610$		0			0
$611$	15.0000	−	8.66025i	0.606835	−	0.350356i
$612$	−24.5885	+	6.58846i	−0.993929	+	0.266323i
$613$	17.7583	+	4.75833i	0.717252	+	0.192187i	0.598945	−	0.800790i	$-0.295587\pi$
$613$	17.7583	+	4.75833i	0.717252	+	0.192187i	0.118307	+	0.992977i	$0.462253\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	24.5885	−	6.58846i	0.989894	−	0.265241i	0.272688	−	0.962103i	$-0.412087\pi$
$617$	24.5885	−	6.58846i	0.989894	−	0.265241i	0.717206	+	0.696861i	$0.245421\pi$
$618$		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
$623$	−33.1244	+	8.87564i	−1.32710	+	0.355595i
$624$	−20.7846	+	12.0000i	−0.832050	+	0.480384i
$625$		0			0
$626$		0			0
$627$	−3.92820	+	9.92820i	−0.156877	+	0.396494i
$628$	−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	−0.875806	−	0.482663i	$-0.839670\pi$
$631$	−0.500000	+	0.866025i	−0.0199047	+	0.0344759i	0.855901	+	0.517139i	$0.173003\pi$
$632$		0			0
$633$	14.2750	+	53.2750i	0.567380	+	2.11749i
$634$		0			0
$635$		0			0
$636$	−6.00000	+	10.3923i	−0.237915	+	0.412082i
$637$	−0.633975	−	2.36603i	−0.0251190	−	0.0937453i
$638$		0			0
$639$	−25.9808			−1.02778
$640$		0			0
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	−0.692818	−	0.721113i	$-0.743631\pi$
$641$	−10.5000	+	6.06218i	−0.414725	+	0.239442i	0.278093	+	0.960554i	$0.410298\pi$
$642$		0			0
$643$	31.4186	+	8.41858i	1.23903	+	0.331997i	0.818089	−	0.575092i	$-0.195034\pi$
$643$	31.4186	+	8.41858i	1.23903	+	0.331997i	0.420939	+	0.907089i	$0.361700\pi$
$644$	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
$652$	−19.1244	+	5.12436i	−0.748968	+	0.200685i
$653$	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	$-0.920319\pi$
$659$	−6.92820	+	12.0000i	−0.269884	+	0.467454i	0.698947	+	0.715173i	$0.253652\pi$
$660$		0			0
$661$	−34.5000	−	19.9186i	−1.34189	−	0.774743i	−0.354809	−	0.934939i	$-0.615454\pi$
$661$	−34.5000	−	19.9186i	−1.34189	−	0.774743i	−0.987085	+	0.160196i	$0.948788\pi$
$662$		0			0
$663$	−24.5885	−	6.58846i	−0.954937	−	0.255874i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.46410	+	2.53590i	0.366451	+	0.0981904i
$668$	2.53590	−	9.46410i	0.0981169	−	0.366177i
$669$	−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	0.182093	−	0.983281i	$-0.441713\pi$
$673$	−20.7846	−	20.7846i	−0.801188	−	0.801188i	−0.983281	+	0.182093i	$0.941713\pi$
$674$		0			0
$675$		0			0
$676$	14.0000			0.538462
$677$	−17.3205	+	17.3205i	−0.665681	+	0.665681i	−0.956713	−	0.291032i	$-0.906001\pi$
$677$	−17.3205	+	17.3205i	−0.665681	+	0.665681i	0.291032	+	0.956713i	$0.406001\pi$
$678$		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	0.436014	−	0.899940i	$-0.356390\pi$
$683$	−12.1244	−	12.1244i	−0.463926	−	0.463926i	−0.899940	+	0.436014i	$0.856390\pi$
$684$	10.3923	+	24.0000i	0.397360	+	0.917663i
$685$		0			0
$686$		0			0
$687$	−21.2942	−	5.70577i	−0.812425	−	0.217689i
$688$	−11.7128	−	43.7128i	−0.446547	−	1.66654i
$689$	−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
$693$	−2.19615	−	8.19615i	−0.0834249	−	0.311346i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−11.4115	−	42.5885i	−0.432243	−	1.61315i
$698$		0			0
$699$	−1.73205	+	3.00000i	−0.0655122	+	0.113470i
$700$		0			0
$701$	10.0000	+	17.3205i	0.377695	+	0.654187i	0.990726	−	0.135872i	$-0.0433835\pi$
$701$	10.0000	+	17.3205i	0.377695	+	0.654187i	−0.613032	+	0.790058i	$0.710050\pi$
$702$		0			0
$703$	16.7321	−	13.2679i	0.631061	−	0.500410i
$704$			8.00000i			0.301511i
$705$		0			0
$706$		0			0
$707$	−30.0526	+	8.05256i	−1.13024	+	0.302848i
$708$	8.19615	+	2.19615i	0.308030	+	0.0825365i
$709$	−44.1673	−	25.5000i	−1.65874	−	0.957673i	−0.973299	−	0.229543i	$-0.926277\pi$
$709$	−44.1673	−	25.5000i	−1.65874	−	0.957673i	−0.685439	−	0.728130i	$-0.740390\pi$
$710$		0			0
$711$			15.5885i			0.584613i
$712$		0			0
$713$	−47.3205	+	12.6795i	−1.77217	+	0.474851i
$714$		0			0
$715$		0			0
$716$	21.0000	+	12.1244i	0.784807	+	0.453108i
$717$	−16.5622	−	4.43782i	−0.618526	−	0.165734i
$718$		0			0
$719$	32.0429	−	18.5000i	1.19500	−	0.689934i	0.235564	−	0.971859i	$-0.424306\pi$
$719$	32.0429	−	18.5000i	1.19500	−	0.689934i	0.959436	+	0.281925i	$0.0909730\pi$
$720$		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
$727$	−2.56218	+	9.56218i	−0.0950259	+	0.354642i	−0.997023	−	0.0770998i	$-0.975434\pi$
$727$	−2.56218	+	9.56218i	−0.0950259	+	0.354642i	0.901997	+	0.431741i	$0.142101\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$		0			0
$731$	24.0000	−	41.5692i	0.887672	−	1.53749i
$732$	8.87564	+	33.1244i	0.328053	+	1.22431i
$733$	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
$737$	−0.633975	−	2.36603i	−0.0233528	−	0.0871537i
$738$		0			0
$739$	19.9186	−	11.5000i	0.732717	−	0.423034i	−0.0866983	−	0.996235i	$-0.527632\pi$
$739$	19.9186	−	11.5000i	0.732717	−	0.423034i	0.819415	+	0.573200i	$0.194298\pi$
$740$		0			0
$741$	−3.00000	+	25.9808i	−0.110208	+	0.954427i
$742$		0			0
$743$	3.80385	−	14.1962i	0.139550	−	0.520806i	−0.860388	−	0.509640i	$-0.829779\pi$
$743$	3.80385	−	14.1962i	0.139550	−	0.520806i	0.999938	−	0.0111668i	$-0.00355457\pi$
$744$		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	0.356879	−	0.934150i	$-0.383841\pi$
$751$	−7.50000	−	4.33013i	−0.273679	−	0.158009i	−0.630558	+	0.776142i	$0.717174\pi$
$752$	−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
$757$	6.22243	−	23.2224i	0.226158	−	0.844034i	−0.755779	−	0.654827i	$-0.772742\pi$
$757$	6.22243	−	23.2224i	0.226158	−	0.844034i	0.981937	−	0.189207i	$-0.0605917\pi$
$758$		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
$763$	8.87564	−	33.1244i	0.321320	−	1.19918i
$764$	−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	$-0.350560\pi$
$769$	−2.59808	−	1.50000i	−0.0936890	−	0.0540914i	−0.546113	+	0.837712i	$0.683893\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$		0			0
$773$	−35.4904	+	9.50962i	−1.27650	+	0.342037i	−0.832518	−	0.553998i	$-0.813101\pi$
$773$	−35.4904	+	9.50962i	−1.27650	+	0.342037i	−0.443982	+	0.896035i	$0.646435\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−8.78461	+	32.7846i	−0.315146	+	1.17614i
$778$		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	$0.619242\pi$
$787$	−36.3731	+	36.3731i	−1.29656	+	1.29656i	−0.930651	+	0.365909i	$0.880758\pi$
$788$	−0.732051	−	2.73205i	−0.0260782	−	0.0973253i
$789$	15.5885	−	27.0000i	0.554964	−	0.961225i
$790$		0			0
$791$		−	48.4974i		−	1.72437i
$792$		0			0
$793$	−4.43782	+	16.5622i	−0.157592	+	0.588140i
$794$		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	$-0.486003\pi$
$797$	29.4449	−	29.4449i	1.04299	−	1.04299i	0.999033	−	0.0439572i	$-0.0139965\pi$
$798$		0			0
$799$		−	30.0000i		−	1.06132i
$800$		0			0
$801$	−31.5000	+	18.1865i	−1.11300	+	0.642590i
$802$		0			0
$803$	−2.73205	−	0.732051i	−0.0964120	−	0.0258335i
$804$	−10.3923	−	6.00000i	−0.366508	−	0.211604i
$805$		0			0
$806$		0			0
$807$	−36.8827	+	9.88269i	−1.29833	+	0.347887i
$808$		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	0.672892	−	0.739740i	$-0.265052\pi$
$811$	10.5000	+	6.06218i	0.368705	+	0.212872i	−0.304188	+	0.952612i	$0.598385\pi$
$812$	−9.46410	−	2.53590i	−0.332125	−	0.0889926i
$813$	−7.09808	+	1.90192i	−0.248940	+	0.0667034i
$814$		0			0
$815$		0			0
$816$			41.5692i			1.45521i
$817$	−45.8564	−	18.1436i	−1.60431	−	0.634764i
$818$		0			0
$819$	−10.3923	−	18.0000i	−0.363137	−	0.628971i
$820$		0			0
$821$	2.50000	−	4.33013i	0.0872506	−	0.151122i	−0.819097	−	0.573654i	$-0.805525\pi$
$821$	2.50000	−	4.33013i	0.0872506	−	0.151122i	0.906348	+	0.422532i	$0.138859\pi$
$822$		0			0
$823$	−4.02628	−	15.0263i	−0.140347	−	0.523783i	−0.999918	−	0.0127672i	$-0.995936\pi$
$823$	−4.02628	−	15.0263i	−0.140347	−	0.523783i	0.859571	−	0.511016i	$-0.170731\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−4.43782	−	16.5622i	−0.154318	−	0.575923i	−0.999163	−	0.0409115i	$-0.986974\pi$
$827$	−4.43782	−	16.5622i	−0.154318	−	0.575923i	0.844845	−	0.535012i	$-0.179693\pi$
$828$	24.0000	−	24.0000i	0.834058	−	0.834058i
$829$	10.3923			0.360940			0.180470	−	0.983581i	$-0.442238\pi$
$829$	10.3923			0.360940			0.180470	+	0.983581i	$0.442238\pi$
$830$		0			0
$831$	−24.0000	+	13.8564i	−0.832551	+	0.480673i
$832$	5.07180	+	18.9282i	0.175833	+	0.656217i
$833$	−4.09808	−	1.09808i	−0.141990	−	0.0380461i
$834$		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	$-0.0498587\pi$
$839$	10.3923	+	18.0000i	0.358782	+	0.621429i	−0.628975	+	0.777425i	$0.716525\pi$
$840$		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
$852$	−10.9808	+	40.9808i	−0.376195	+	1.40398i
$853$	−50.5429	−	13.5429i	−1.73056	−	0.463701i	−0.750246	−	0.661159i	$-0.770065\pi$
$853$	−50.5429	−	13.5429i	−1.73056	−	0.463701i	−0.980311	+	0.197458i	$0.936732\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	37.8564	+	10.1436i	1.29315	+	0.346499i	0.838856	−	0.544353i	$-0.183225\pi$
$857$	37.8564	+	10.1436i	1.29315	+	0.346499i	0.454294	+	0.890852i	$0.349892\pi$
$858$		0			0
$859$	14.7224	+	8.50000i	0.502323	+	0.290016i	0.729672	−	0.683797i	$-0.239673\pi$
$859$	14.7224	+	8.50000i	0.502323	+	0.290016i	−0.227349	+	0.973813i	$0.573006\pi$
$860$		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	$-0.910528\pi$
$863$	−36.3731	−	36.3731i	−1.23815	−	1.23815i	−0.277399	−	0.960755i	$-0.589472\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.73205	+	1.73205i	−0.0588235	+	0.0588235i
$868$	47.3205	−	12.6795i	1.60616	−	0.430370i
$869$	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
$877$	52.0526	+	13.9474i	1.75769	+	0.470972i	0.986240	−	0.165319i	$-0.0528652\pi$
$877$	52.0526	+	13.9474i	1.75769	+	0.470972i	0.771450	+	0.636290i	$0.219532\pi$
$878$		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
$883$	7.32051	+	27.3205i	0.246355	+	0.919408i	0.972698	+	0.232076i	$0.0745518\pi$
$883$	7.32051	+	27.3205i	0.246355	+	0.919408i	−0.726343	+	0.687332i	$0.758782\pi$
$884$	−10.3923	+	18.0000i	−0.349531	+	0.605406i
$885$		0			0
$886$		0			0
$887$	2.53590	+	9.46410i	0.0851471	+	0.317773i	0.995342	−	0.0964068i	$-0.0307350\pi$
$887$	2.53590	+	9.46410i	0.0851471	+	0.317773i	−0.910195	+	0.414180i	$0.864068\pi$
$888$		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
$893$	−30.4904	+	4.50962i	−1.02032	+	0.150909i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	32.7846	−	8.78461i	1.09465	−	0.293310i
$898$		0			0
$899$	12.9904	+	7.50000i	0.433253	+	0.250139i
$900$		0			0
$901$			10.3923i			0.346218i
$902$		0			0
$903$	75.7128	−	20.2872i	2.51956	−	0.675115i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	−18.9282	−	5.07180i	−0.628501	−	0.168406i	−0.0695114	−	0.997581i	$-0.522144\pi$
$907$	−18.9282	−	5.07180i	−0.628501	−	0.168406i	−0.558989	+	0.829175i	$0.688811\pi$
$908$	18.9282	−	5.07180i	0.628154	−	0.168313i
$909$	−28.5788	+	16.5000i	−0.947900	+	0.547270i
$910$		0			0
$911$		−	22.5167i		−	0.746010i	−0.927829	−	0.373005i	$-0.878327\pi$
$911$		−	22.5167i		−	0.746010i	0.927829	−	0.373005i	$-0.121673\pi$
$912$	42.2487	−	6.24871i	1.39899	−	0.206916i
$913$		0			0
$914$		0			0
$915$		0			0
$916$	−9.00000	+	15.5885i	−0.297368	+	0.515057i
$917$	10.2487	−	38.2487i	0.338442	−	1.26308i
$918$		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
$927$	−3.80385	−	14.1962i	−0.124935	−	0.466263i
$928$		0			0
$929$	−16.4545	+	9.50000i	−0.539854	+	0.311685i	−0.745020	−	0.667042i	$-0.767560\pi$
$929$	−16.4545	+	9.50000i	−0.539854	+	0.311685i	0.205166	+	0.978727i	$0.434227\pi$
$930$		0			0
$931$	−0.500000	+	4.33013i	−0.0163868	+	0.141914i
$932$	2.00000	+	2.00000i	0.0655122	+	0.0655122i
$933$	16.4833	−	61.5167i	0.539640	−	2.01397i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	23.2224	−	6.22243i	0.758644	−	0.203278i	0.141295	−	0.989968i	$-0.454873\pi$
$937$	23.2224	−	6.22243i	0.758644	−	0.203278i	0.617349	+	0.786690i	$0.288207\pi$
$938$		0			0
$939$	17.3205			0.565233
$940$		0			0
$941$	−28.5000	−	16.4545i	−0.929073	−	0.536401i	−0.0425550	−	0.999094i	$-0.513550\pi$
$941$	−28.5000	−	16.4545i	−0.929073	−	0.536401i	−0.886518	+	0.462693i	$0.846883\pi$
$942$		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
$947$	14.2750	−	53.2750i	0.463875	−	1.73120i	−0.196718	−	0.980460i	$-0.563028\pi$
$947$	14.2750	−	53.2750i	0.463875	−	1.73120i	0.660593	−	0.750744i	$-0.270305\pi$
$948$	24.5885	+	6.58846i	0.798596	+	0.213983i
$949$	−6.92820			−0.224899
$950$		0			0
$951$	60.0000			1.94563
$952$		0			0
$953$	−2.53590	+	9.46410i	−0.0821458	+	0.306572i	−0.994758	−	0.102253i	$-0.967395\pi$
$953$	−2.53590	+	9.46410i	−0.0821458	+	0.306572i	0.912613	+	0.408825i	$0.134062\pi$
$954$		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
$963$	−56.7846	+	15.2154i	−1.82986	+	0.490309i
$964$	5.19615	+	9.00000i	0.167357	+	0.289870i
$965$		0			0
$966$		0			0
$967$	5.85641	−	21.8564i	0.188329	−	0.702855i	−0.805564	−	0.592509i	$-0.798138\pi$
$967$	5.85641	−	21.8564i	0.188329	−	0.702855i	0.993893	−	0.110346i	$-0.0351958\pi$
$968$		0			0
$969$	36.3731	+	27.0000i	1.16847	+	0.867365i
$970$		0			0
$971$	−24.0000	+	13.8564i	−0.770197	+	0.444673i	−0.832945	−	0.553356i	$-0.813347\pi$
$971$	−24.0000	+	13.8564i	−0.770197	+	0.444673i	0.0627481	+	0.998029i	$0.480014\pi$
$972$	42.5885	+	11.4115i	1.36603	+	0.366025i
$973$		0			0
$974$		0			0
$975$		0			0
$976$	28.0000			0.896258
$977$	−24.2487	+	24.2487i	−0.775785	+	0.775785i	−0.979111	−	0.203326i	$-0.934825\pi$
$977$	−24.2487	+	24.2487i	−0.775785	+	0.775785i	0.203326	+	0.979111i	$0.434825\pi$
$978$		0			0
$979$	−6.06218	+	10.5000i	−0.193748	+	0.335581i
$980$		0			0
$981$		−	36.3731i		−	1.16130i
$982$		0			0
$983$	−15.2154	+	56.7846i	−0.485296	+	1.81115i	0.0934305	+	0.995626i	$0.470217\pi$
$983$	−15.2154	+	56.7846i	−0.485296	+	1.81115i	−0.578726	+	0.815522i	$0.696450\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	34.6410	−	34.6410i	1.10264	−	1.10264i
$988$	19.8564	+	7.85641i	0.631716	+	0.249946i
$989$			64.0000i			2.03508i
$990$		0			0
$991$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$991$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$992$		0			0
$993$	−65.5692	−	17.5692i	−2.08078	−	0.557542i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	39.6147	−	10.6147i	1.25461	−	0.336172i	0.430495	−	0.902593i	$-0.358339\pi$
$997$	39.6147	−	10.6147i	1.25461	−	0.336172i	0.824116	+	0.566421i	$0.191672\pi$
$998$		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.107.1		4
5.2	odd	4		95.2.l.b.88.1	yes	4
5.3	odd	4	inner	475.2.p.b.468.1		4
5.4	even	2		95.2.l.b.12.1	yes	4
15.2	even	4		855.2.cj.b.658.1		4
15.14	odd	2		855.2.cj.b.487.1		4
19.8	odd	6	inner	475.2.p.b.407.1		4
95.8	even	12	inner	475.2.p.b.293.1		4
95.27	even	12		95.2.l.b.8.1	✓	4
95.84	odd	6		95.2.l.b.27.1	yes	4
285.122	odd	12		855.2.cj.b.388.1		4
285.179	even	6		855.2.cj.b.217.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.l.b.8.1	✓	4	95.27	even	12
95.2.l.b.12.1	yes	4	5.4	even	2
95.2.l.b.27.1	yes	4	95.84	odd	6
95.2.l.b.88.1	yes	4	5.2	odd	4
475.2.p.b.107.1		4	1.1	even	1	trivial
475.2.p.b.293.1		4	95.8	even	12	inner
475.2.p.b.407.1		4	19.8	odd	6	inner
475.2.p.b.468.1		4	5.3	odd	4	inner
855.2.cj.b.217.1		4	285.179	even	6
855.2.cj.b.388.1		4	285.122	odd	12
855.2.cj.b.487.1		4	15.14	odd	2
855.2.cj.b.658.1		4	15.2	even	4

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)

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