LMFDB - Embedded newform 475.2.e.c.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [475,2,Mod(26,475)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(475, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("475.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 475 = 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	475.e (of order $3$, degree $2$, 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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	475.26
Dual form			475.2.e.c.201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +4.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +4.00000 q^{7} +(1.50000 - 2.59808i) q^{9} -1.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(4.00000 + 6.92820i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} +6.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} +(-1.00000 - 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} -4.00000 q^{26} +(-4.00000 + 6.92820i) q^{28} +(-4.50000 + 7.79423i) q^{29} -7.00000 q^{31} +(-4.00000 + 6.92820i) q^{32} +(2.00000 - 3.46410i) q^{34} +(3.00000 + 5.19615i) q^{36} -2.00000 q^{37} +(-8.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{41} +(1.00000 + 1.73205i) q^{43} +(1.00000 - 1.73205i) q^{44} +12.0000 q^{46} +(3.00000 - 5.19615i) q^{47} +9.00000 q^{49} +(-2.00000 - 3.46410i) q^{52} +(2.00000 - 3.46410i) q^{53} -18.0000 q^{58} +(-4.50000 - 7.79423i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-7.00000 - 12.1244i) q^{62} +(6.00000 - 10.3923i) q^{63} -8.00000 q^{64} +(-5.00000 + 8.66025i) q^{67} +4.00000 q^{68} +(-0.500000 - 0.866025i) q^{71} +(5.00000 + 8.66025i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-1.00000 - 8.66025i) q^{76} -4.00000 q^{77} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.00000 - 3.46410i) q^{82} +6.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(5.50000 - 9.52628i) q^{89} +(-4.00000 + 6.92820i) q^{91} +(6.00000 + 10.3923i) q^{92} +12.0000 q^{94} +(-3.00000 - 5.19615i) q^{97} +(9.00000 + 15.5885i) q^{98} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{4} + 8 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^4 + 8 * q^7 + 3 * q^9	$ 2 q + 2 q^{2} - 2 q^{4} + 8 q^{7} + 3 q^{9} - 2 q^{11} - 2 q^{13} + 8 q^{14} + 4 q^{16} - 2 q^{17} + 12 q^{18} - 7 q^{19} - 2 q^{22} + 6 q^{23} - 8 q^{26} - 8 q^{28} - 9 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{34} + 6 q^{36} - 4 q^{37} - 16 q^{38} - 2 q^{41} + 2 q^{43} + 2 q^{44} + 24 q^{46} + 6 q^{47} + 18 q^{49} - 4 q^{52} + 4 q^{53} - 36 q^{58} - 9 q^{59} + 7 q^{61} - 14 q^{62} + 12 q^{63} - 16 q^{64} - 10 q^{67} + 8 q^{68} - q^{71} + 10 q^{73} - 4 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} - 9 q^{81} + 4 q^{82} + 12 q^{83} - 4 q^{86} + 11 q^{89} - 8 q^{91} + 12 q^{92} + 24 q^{94} - 6 q^{97} + 18 q^{98} - 3 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^4 + 8 * q^7 + 3 * q^9 - 2 * q^11 - 2 * q^13 + 8 * q^14 + 4 * q^16 - 2 * q^17 + 12 * q^18 - 7 * q^19 - 2 * q^22 + 6 * q^23 - 8 * q^26 - 8 * q^28 - 9 * q^29 - 14 * q^31 - 8 * q^32 + 4 * q^34 + 6 * q^36 - 4 * q^37 - 16 * q^38 - 2 * q^41 + 2 * q^43 + 2 * q^44 + 24 * q^46 + 6 * q^47 + 18 * q^49 - 4 * q^52 + 4 * q^53 - 36 * q^58 - 9 * q^59 + 7 * q^61 - 14 * q^62 + 12 * q^63 - 16 * q^64 - 10 * q^67 + 8 * q^68 - q^71 + 10 * q^73 - 4 * q^74 - 2 * q^76 - 8 * q^77 - q^79 - 9 * q^81 + 4 * q^82 + 12 * q^83 - 4 * q^86 + 11 * q^89 - 8 * q^91 + 12 * q^92 + 24 * q^94 - 6 * q^97 + 18 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	0.965926	+	0.258819i	$0.0833333\pi$
$2$	1.00000	+	1.73205i	0.707107	+	1.22474i	−0.258819	+	0.965926i	$0.583333\pi$
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	4.00000			1.51186			0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000			1.51186			0.755929	+	0.654654i	$0.227186\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−1.00000			−0.301511			−0.150756	−	0.988571i	$-0.548171\pi$
$11$	−1.00000			−0.301511			−0.150756	+	0.988571i	$0.548171\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	4.00000	+	6.92820i	1.06904	+	1.85164i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$	6.00000			1.41421
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$20$		0			0
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$		0			0
$26$	−4.00000			−0.784465
$27$		0			0
$28$	−4.00000	+	6.92820i	−0.755929	+	1.30931i
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	0.0578882	+	0.998323i	$0.481563\pi$
$29$	−4.50000	+	7.79423i	−0.835629	+	1.44735i	−0.893517	+	0.449029i	$0.851770\pi$
$30$		0			0
$31$	−7.00000			−1.25724			−0.628619	−	0.777714i	$-0.716379\pi$
$31$	−7.00000			−1.25724			−0.628619	+	0.777714i	$0.716379\pi$
$32$	−4.00000	+	6.92820i	−0.707107	+	1.22474i
$33$		0			0
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$		0			0
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	−8.00000	−	3.46410i	−1.29777	−	0.561951i
$39$		0			0
$40$		0			0
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$		0			0
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	0.932145	−	0.362084i	$-0.117935\pi$
$43$	1.00000	+	1.73205i	0.152499	+	0.264135i	−0.779647	+	0.626219i	$0.784601\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$		0			0
$46$	12.0000			1.76930
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$		0			0
$51$		0			0
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	−18.0000			−2.36352
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	−0.994769	−	0.102151i	$-0.967427\pi$
$59$	−4.50000	−	7.79423i	−0.585850	−	1.01472i	0.408919	−	0.912571i	$-0.365906\pi$
$60$		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	$0.0187572\pi$
$62$	−7.00000	−	12.1244i	−0.889001	−	1.53979i
$63$	6.00000	−	10.3923i	0.755929	−	1.30931i
$64$	−8.00000			−1.00000
$65$		0			0
$66$		0			0
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$	4.00000			0.485071
$69$		0			0
$70$		0			0
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	0.834830	−	0.550508i	$-0.185566\pi$
$71$	−0.500000	−	0.866025i	−0.0593391	−	0.102778i	−0.894169	+	0.447730i	$0.852233\pi$
$72$		0			0
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$	−2.00000	−	3.46410i	−0.232495	−	0.402694i
$75$		0			0
$76$	−1.00000	−	8.66025i	−0.114708	−	0.993399i
$77$	−4.00000			−0.455842
$78$		0			0
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	2.00000	−	3.46410i	0.220863	−	0.382546i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$		0			0
$85$		0			0
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$		0			0
$88$		0			0
$89$	5.50000	−	9.52628i	0.582999	−	1.00978i	−0.412123	−	0.911128i	$-0.635213\pi$
$89$	5.50000	−	9.52628i	0.582999	−	1.00978i	0.995122	−	0.0986553i	$-0.0314541\pi$
$90$		0			0
$91$	−4.00000	+	6.92820i	−0.419314	+	0.726273i
$92$	6.00000	+	10.3923i	0.625543	+	1.08347i
$93$		0			0
$94$	12.0000			1.23771
$95$		0			0
$96$		0			0
$97$	−3.00000	−	5.19615i	−0.304604	−	0.527589i	0.672569	−	0.740034i	$-0.265191\pi$
$97$	−3.00000	−	5.19615i	−0.304604	−	0.527589i	−0.977173	+	0.212445i	$0.931857\pi$
$98$	9.00000	+	15.5885i	0.909137	+	1.57467i
$99$	−1.50000	+	2.59808i	−0.150756	+	0.261116i
$100$		0			0
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	0.203317	+	0.979113i	$0.434828\pi$
$101$	−7.50000	+	12.9904i	−0.746278	+	1.29259i	−0.949595	+	0.313478i	$0.898506\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$		0			0
$105$		0			0
$106$	8.00000			0.777029
$107$	10.0000			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$108$		0			0
$109$	−7.50000	−	12.9904i	−0.718370	−	1.24425i	−0.961645	−	0.274296i	$-0.911555\pi$
$109$	−7.50000	−	12.9904i	−0.718370	−	1.24425i	0.243276	−	0.969957i	$-0.421778\pi$
$110$		0			0
$111$		0			0
$112$	8.00000	+	13.8564i	0.755929	+	1.30931i
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$		0			0
$116$	−9.00000	−	15.5885i	−0.835629	−	1.44735i
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$	9.00000	−	15.5885i	0.828517	−	1.43503i
$119$	−4.00000	−	6.92820i	−0.366679	−	0.635107i
$120$		0			0
$121$	−10.0000			−0.909091
$122$	14.0000			1.26750
$123$		0			0
$124$	7.00000	−	12.1244i	0.628619	−	1.08880i
$125$		0			0
$126$	24.0000			2.13809
$127$	−3.00000	+	5.19615i	−0.266207	+	0.461084i	−0.967879	−	0.251416i	$-0.919104\pi$
$127$	−3.00000	+	5.19615i	−0.266207	+	0.461084i	0.701672	+	0.712500i	$0.252437\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	−0.999602	−	0.0281993i	$-0.991023\pi$
$131$	−6.00000	−	10.3923i	−0.524222	−	0.907980i	0.475380	−	0.879781i	$-0.342311\pi$
$132$		0			0
$133$	−14.0000	+	10.3923i	−1.21395	+	0.901127i
$134$	−20.0000			−1.72774
$135$		0			0
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$		0			0
$141$		0			0
$142$	1.00000	−	1.73205i	0.0839181	−	0.145350i
$143$	1.00000	−	1.73205i	0.0836242	−	0.144841i
$144$	12.0000			1.00000
$145$		0			0
$146$	−10.0000	+	17.3205i	−0.827606	+	1.43346i
$147$		0			0
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	0.885779	−	0.464107i	$-0.153625\pi$
$149$	0.500000	+	0.866025i	0.0409616	+	0.0709476i	−0.844818	+	0.535054i	$0.820291\pi$
$150$		0			0
$151$	9.00000			0.732410			0.366205	−	0.930534i	$-0.380657\pi$
$151$	9.00000			0.732410			0.366205	+	0.930534i	$0.380657\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	−4.00000	−	6.92820i	−0.322329	−	0.558291i
$155$		0			0
$156$		0			0
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	1.00000	−	1.73205i	0.0795557	−	0.137795i
$159$		0			0
$160$		0			0
$161$	12.0000	−	20.7846i	0.945732	−	1.63806i
$162$	9.00000	−	15.5885i	0.707107	−	1.22474i
$163$	−4.00000			−0.313304			−0.156652	−	0.987654i	$-0.550070\pi$
$163$	−4.00000			−0.313304			−0.156652	+	0.987654i	$0.550070\pi$
$164$	4.00000			0.312348
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$		0			0
$171$	1.50000	+	12.9904i	0.114708	+	0.993399i
$172$	−4.00000			−0.304997
$173$	−12.0000	−	20.7846i	−0.912343	−	1.58022i	−0.810745	−	0.585399i	$-0.800938\pi$
$173$	−12.0000	−	20.7846i	−0.912343	−	1.58022i	−0.101598	−	0.994826i	$-0.532395\pi$
$174$		0			0
$175$		0			0
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$		0			0
$178$	22.0000			1.64897
$179$	15.0000			1.12115			0.560576	−	0.828103i	$-0.310580\pi$
$179$	15.0000			1.12115			0.560576	+	0.828103i	$0.310580\pi$
$180$		0			0
$181$	3.00000	−	5.19615i	0.222988	−	0.386227i	−0.732726	−	0.680524i	$-0.761752\pi$
$181$	3.00000	−	5.19615i	0.222988	−	0.386227i	0.955714	+	0.294297i	$0.0950855\pi$
$182$	−16.0000			−1.18600
$183$		0			0
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1.00000	+	1.73205i	0.0731272	+	0.126660i
$188$	6.00000	+	10.3923i	0.437595	+	0.757937i
$189$		0			0
$190$		0			0
$191$	−3.00000			−0.217072			−0.108536	−	0.994092i	$-0.534616\pi$
$191$	−3.00000			−0.217072			−0.108536	+	0.994092i	$0.534616\pi$
$192$		0			0
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	0.995948	+	0.0899262i	$0.0286631\pi$
$193$	8.00000	+	13.8564i	0.575853	+	0.997406i	−0.420096	+	0.907480i	$0.638004\pi$
$194$	6.00000	−	10.3923i	0.430775	−	0.746124i
$195$		0			0
$196$	−9.00000	+	15.5885i	−0.642857	+	1.11346i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−6.00000			−0.426401
$199$	−6.50000	+	11.2583i	−0.460773	+	0.798082i	−0.999000	−	0.0447181i	$-0.985761\pi$
$199$	−6.50000	+	11.2583i	−0.460773	+	0.798082i	0.538227	+	0.842800i	$0.319094\pi$
$200$		0			0
$201$		0			0
$202$	−30.0000			−2.11079
$203$	−18.0000	+	31.1769i	−1.26335	+	2.18819i
$204$		0			0
$205$		0			0
$206$	−16.0000	−	27.7128i	−1.11477	−	1.93084i
$207$	−9.00000	−	15.5885i	−0.625543	−	1.08347i
$208$	−8.00000			−0.554700
$209$	3.50000	−	2.59808i	0.242100	−	0.179713i
$210$		0			0
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	0.767049	−	0.641588i	$-0.221724\pi$
$211$	−2.50000	−	4.33013i	−0.172107	−	0.298098i	−0.939156	+	0.343490i	$0.888391\pi$
$212$	4.00000	+	6.92820i	0.274721	+	0.475831i
$213$		0			0
$214$	10.0000	+	17.3205i	0.683586	+	1.18401i
$215$		0			0
$216$		0			0
$217$	−28.0000			−1.90076
$218$	15.0000	−	25.9808i	1.01593	−	1.75964i
$219$		0			0
$220$		0			0
$221$	4.00000			0.269069
$222$		0			0
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	0.830599	−	0.556871i	$-0.187998\pi$
$223$	−1.00000	−	1.73205i	−0.0669650	−	0.115987i	−0.897564	+	0.440884i	$0.854665\pi$
$224$	−16.0000	+	27.7128i	−1.06904	+	1.85164i
$225$		0			0
$226$	12.0000	+	20.7846i	0.798228	+	1.38257i
$227$	−14.0000			−0.929213			−0.464606	−	0.885517i	$-0.653804\pi$
$227$	−14.0000			−0.929213			−0.464606	+	0.885517i	$0.653804\pi$
$228$		0			0
$229$	17.0000			1.12339			0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000			1.12339			0.561696	+	0.827344i	$0.310149\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−4.00000	−	6.92820i	−0.262049	−	0.453882i	0.704737	−	0.709468i	$-0.251065\pi$
$233$	−4.00000	−	6.92820i	−0.262049	−	0.453882i	−0.966786	+	0.255586i	$0.917731\pi$
$234$	−6.00000	+	10.3923i	−0.392232	+	0.679366i
$235$		0			0
$236$	18.0000			1.17170
$237$		0			0
$238$	8.00000	−	13.8564i	0.518563	−	0.898177i
$239$	−19.0000			−1.22901			−0.614504	−	0.788914i	$-0.710644\pi$
$239$	−19.0000			−1.22901			−0.614504	+	0.788914i	$0.710644\pi$
$240$		0			0
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$	−10.0000	−	17.3205i	−0.642824	−	1.11340i
$243$		0			0
$244$	7.00000	+	12.1244i	0.448129	+	0.776182i
$245$		0			0
$246$		0			0
$247$	−1.00000	−	8.66025i	−0.0636285	−	0.551039i
$248$		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	$0.301234\pi$
$252$	12.0000	+	20.7846i	0.755929	+	1.30931i
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	−12.0000			−0.752947
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	−0.944294	−	0.329104i	$-0.893253\pi$
$257$	−3.00000	+	5.19615i	−0.187135	+	0.324127i	0.757159	+	0.653231i	$0.226587\pi$
$258$		0			0
$259$	−8.00000			−0.497096
$260$		0			0
$261$	13.5000	+	23.3827i	0.835629	+	1.44735i
$262$	12.0000	−	20.7846i	0.741362	−	1.28408i
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$		0			0
$265$		0			0
$266$	−32.0000	−	13.8564i	−1.96205	−	0.849591i
$267$		0			0
$268$	−10.0000	−	17.3205i	−0.610847	−	1.05802i
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	0.816668	−	0.577108i	$-0.195819\pi$
$269$	−1.50000	−	2.59808i	−0.0914566	−	0.158408i	−0.908124	+	0.418701i	$0.862486\pi$
$270$		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	$0.862378\pi$
$272$	4.00000	−	6.92820i	0.242536	−	0.420084i
$273$		0			0
$274$	24.0000			1.44989
$275$		0			0
$276$		0			0
$277$	28.0000			1.68236			0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000			1.68236			0.841178	+	0.540758i	$0.181862\pi$
$278$	−40.0000			−2.39904
$279$	−10.5000	+	18.1865i	−0.628619	+	1.08880i
$280$		0			0
$281$	−5.00000	+	8.66025i	−0.298275	+	0.516627i	−0.975741	−	0.218926i	$-0.929745\pi$
$281$	−5.00000	+	8.66025i	−0.298275	+	0.516627i	0.677466	+	0.735554i	$0.263078\pi$
$282$		0			0
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	2.00000			0.118678
$285$		0			0
$286$	4.00000			0.236525
$287$	−4.00000	−	6.92820i	−0.236113	−	0.408959i
$288$	12.0000	+	20.7846i	0.707107	+	1.22474i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$		0			0
$292$	−20.0000			−1.17041
$293$	−4.00000			−0.233682			−0.116841	−	0.993151i	$-0.537277\pi$
$293$	−4.00000			−0.233682			−0.116841	+	0.993151i	$0.537277\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$	−1.00000	+	1.73205i	−0.0579284	+	0.100335i
$299$	6.00000	+	10.3923i	0.346989	+	0.601003i
$300$		0			0
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	9.00000	+	15.5885i	0.517892	+	0.897015i
$303$		0			0
$304$	−16.0000	−	6.92820i	−0.917663	−	0.397360i
$305$		0			0
$306$	−6.00000	−	10.3923i	−0.342997	−	0.594089i
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	0.998778	−	0.0494267i	$-0.0157394\pi$
$307$	8.00000	+	13.8564i	0.456584	+	0.790827i	−0.542194	+	0.840254i	$0.682406\pi$
$308$	4.00000	−	6.92820i	0.227921	−	0.394771i
$309$		0			0
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$		0			0
$313$	15.0000	−	25.9808i	0.847850	−	1.46852i	−0.0352727	−	0.999378i	$-0.511230\pi$
$313$	15.0000	−	25.9808i	0.847850	−	1.46852i	0.883123	−	0.469142i	$-0.155437\pi$
$314$	−4.00000	+	6.92820i	−0.225733	+	0.390981i
$315$		0			0
$316$	2.00000			0.112509
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	−0.892741	−	0.450570i	$-0.851221\pi$
$317$	−1.00000	+	1.73205i	−0.0561656	+	0.0972817i	0.836576	+	0.547852i	$0.184554\pi$
$318$		0			0
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$		0			0
$322$	48.0000			2.67494
$323$	8.00000	+	3.46410i	0.445132	+	0.192748i
$324$	18.0000			1.00000
$325$		0			0
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$		0			0
$328$		0			0
$329$	12.0000	−	20.7846i	0.661581	−	1.14589i
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$	−3.00000	+	5.19615i	−0.164399	+	0.284747i
$334$	−24.0000			−1.31322
$335$		0			0
$336$		0			0
$337$	17.0000	+	29.4449i	0.926049	+	1.60396i	0.789865	+	0.613280i	$0.210150\pi$
$337$	17.0000	+	29.4449i	0.926049	+	1.60396i	0.136184	+	0.990684i	$0.456516\pi$
$338$	−9.00000	+	15.5885i	−0.489535	+	0.847900i
$339$		0			0
$340$		0			0
$341$	7.00000			0.379071
$342$	−21.0000	+	15.5885i	−1.13555	+	0.842927i
$343$	8.00000			0.431959
$344$		0			0
$345$		0			0
$346$	24.0000	−	41.5692i	1.29025	−	2.23478i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$		0			0
$352$	4.00000	−	6.92820i	0.213201	−	0.369274i
$353$	8.00000			0.425797			0.212899	−	0.977074i	$-0.431710\pi$
$353$	8.00000			0.425797			0.212899	+	0.977074i	$0.431710\pi$
$354$		0			0
$355$		0			0
$356$	11.0000	+	19.0526i	0.582999	+	1.00978i
$357$		0			0
$358$	15.0000	+	25.9808i	0.792775	+	1.37313i
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	12.0000			0.630706
$363$		0			0
$364$	−8.00000	−	13.8564i	−0.419314	−	0.726273i
$365$		0			0
$366$		0			0
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	−0.995697	−	0.0926670i	$-0.970461\pi$
$367$	−8.00000	+	13.8564i	−0.417597	+	0.723299i	0.578101	+	0.815966i	$0.303794\pi$
$368$	24.0000			1.25109
$369$	−6.00000			−0.312348
$370$		0			0
$371$	8.00000	−	13.8564i	0.415339	−	0.719389i
$372$		0			0
$373$	12.0000			0.621336			0.310668	−	0.950518i	$-0.399447\pi$
$373$	12.0000			0.621336			0.310668	+	0.950518i	$0.399447\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$		0			0
$376$		0			0
$377$	−9.00000	−	15.5885i	−0.463524	−	0.802846i
$378$		0			0
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$		0			0
$381$		0			0
$382$	−3.00000	−	5.19615i	−0.153493	−	0.265858i
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	0.932436	−	0.361335i	$-0.117679\pi$
$383$	3.00000	+	5.19615i	0.153293	+	0.265511i	−0.779143	+	0.626846i	$0.784346\pi$
$384$		0			0
$385$		0			0
$386$	−16.0000	+	27.7128i	−0.814379	+	1.41055i
$387$	6.00000			0.304997
$388$	12.0000			0.609208
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	−0.0561516	−	0.998422i	$-0.517883\pi$
$389$	16.5000	−	28.5788i	0.836583	−	1.44900i	0.892735	−	0.450582i	$-0.148784\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$		0			0
$393$		0			0
$394$	18.0000	+	31.1769i	0.906827	+	1.57067i
$395$		0			0
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	0.748017	−	0.663679i	$-0.231006\pi$
$397$	−4.00000	−	6.92820i	−0.200754	−	0.347717i	−0.948772	+	0.315963i	$0.897673\pi$
$398$	−26.0000			−1.30326
$399$		0			0
$400$		0			0
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	7.00000	−	12.1244i	0.348695	−	0.603957i
$404$	−15.0000	−	25.9808i	−0.746278	−	1.29259i
$405$		0			0
$406$	−72.0000			−3.57330
$407$	2.00000			0.0991363
$408$		0			0
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	−0.797574	−	0.603220i	$-0.793884\pi$
$409$	2.50000	−	4.33013i	0.123617	−	0.214111i	0.921192	+	0.389109i	$0.127217\pi$
$410$		0			0
$411$		0			0
$412$	16.0000	−	27.7128i	0.788263	−	1.36531i
$413$	−18.0000	−	31.1769i	−0.885722	−	1.53412i
$414$	18.0000	−	31.1769i	0.884652	−	1.53226i
$415$		0			0
$416$	−8.00000	−	13.8564i	−0.392232	−	0.679366i
$417$		0			0
$418$	8.00000	+	3.46410i	0.391293	+	0.169435i
$419$	9.00000			0.439679			0.219839	−	0.975536i	$-0.429447\pi$
$419$	9.00000			0.439679			0.219839	+	0.975536i	$0.429447\pi$
$420$		0			0
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	0.988861	−	0.148844i	$-0.0475552\pi$
$421$	7.50000	+	12.9904i	0.365528	+	0.633112i	−0.623333	+	0.781956i	$0.714222\pi$
$422$	5.00000	−	8.66025i	0.243396	−	0.421575i
$423$	−9.00000	−	15.5885i	−0.437595	−	0.757937i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	14.0000	−	24.2487i	0.677507	−	1.17348i
$428$	−10.0000	+	17.3205i	−0.483368	+	0.837218i
$429$		0			0
$430$		0			0
$431$	−10.5000	+	18.1865i	−0.505767	+	0.876014i	0.494211	+	0.869342i	$0.335457\pi$
$431$	−10.5000	+	18.1865i	−0.505767	+	0.876014i	−0.999978	+	0.00667224i	$0.997876\pi$
$432$		0			0
$433$	−2.00000	+	3.46410i	−0.0961139	+	0.166474i	−0.910073	−	0.414448i	$-0.863975\pi$
$433$	−2.00000	+	3.46410i	−0.0961139	+	0.166474i	0.813959	+	0.580922i	$0.197308\pi$
$434$	−28.0000	−	48.4974i	−1.34404	−	2.32795i
$435$		0			0
$436$	30.0000			1.43674
$437$	3.00000	+	25.9808i	0.143509	+	1.24283i
$438$		0			0
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	0.978412	−	0.206666i	$-0.0662612\pi$
$439$	6.50000	+	11.2583i	0.310228	+	0.537331i	−0.668184	+	0.743996i	$0.732928\pi$
$440$		0			0
$441$	13.5000	−	23.3827i	0.642857	−	1.11346i
$442$	4.00000	+	6.92820i	0.190261	+	0.329541i
$443$	2.00000	−	3.46410i	0.0950229	−	0.164584i	−0.814595	−	0.580030i	$-0.803041\pi$
$443$	2.00000	−	3.46410i	0.0950229	−	0.164584i	0.909618	+	0.415445i	$0.136374\pi$
$444$		0			0
$445$		0			0
$446$	2.00000	−	3.46410i	0.0947027	−	0.164030i
$447$		0			0
$448$	−32.0000			−1.51186
$449$	31.0000			1.46298			0.731490	−	0.681852i	$-0.238825\pi$
$449$	31.0000			1.46298			0.731490	+	0.681852i	$0.238825\pi$
$450$		0			0
$451$	1.00000	+	1.73205i	0.0470882	+	0.0815591i
$452$	−12.0000	+	20.7846i	−0.564433	+	0.977626i
$453$		0			0
$454$	−14.0000	−	24.2487i	−0.657053	−	1.13805i
$455$		0			0
$456$		0			0
$457$	−34.0000			−1.59045			−0.795226	−	0.606313i	$-0.792648\pi$
$457$	−34.0000			−1.59045			−0.795226	+	0.606313i	$0.792648\pi$
$458$	17.0000	+	29.4449i	0.794358	+	1.37587i
$459$		0			0
$460$		0			0
$461$	12.5000	+	21.6506i	0.582183	+	1.00837i	0.995220	+	0.0976564i	$0.0311346\pi$
$461$	12.5000	+	21.6506i	0.582183	+	1.00837i	−0.413037	+	0.910714i	$0.635532\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	−36.0000			−1.67126
$465$		0			0
$466$	8.00000	−	13.8564i	0.370593	−	0.641886i
$467$	−10.0000			−0.462745			−0.231372	−	0.972865i	$-0.574322\pi$
$467$	−10.0000			−0.462745			−0.231372	+	0.972865i	$0.574322\pi$
$468$	−12.0000			−0.554700
$469$	−20.0000	+	34.6410i	−0.923514	+	1.59957i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.00000	−	1.73205i	−0.0459800	−	0.0796398i
$474$		0			0
$475$		0			0
$476$	16.0000			0.733359
$477$	−6.00000	−	10.3923i	−0.274721	−	0.475831i
$478$	−19.0000	−	32.9090i	−0.869040	−	1.50522i
$479$	−7.50000	+	12.9904i	−0.342684	+	0.593546i	−0.984930	−	0.172953i	$-0.944669\pi$
$479$	−7.50000	+	12.9904i	−0.342684	+	0.593546i	0.642246	+	0.766498i	$0.278003\pi$
$480$		0			0
$481$	2.00000	−	3.46410i	0.0911922	−	0.157949i
$482$	−2.00000			−0.0910975
$483$		0			0
$484$	10.0000	−	17.3205i	0.454545	−	0.787296i
$485$		0			0
$486$		0			0
$487$	38.0000			1.72194			0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000			1.72194			0.860972	+	0.508652i	$0.169856\pi$
$488$		0			0
$489$		0			0
$490$		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	$0.928100\pi$
$492$		0			0
$493$	18.0000			0.810679
$494$	14.0000	−	10.3923i	0.629890	−	0.467572i
$495$		0			0
$496$	−14.0000	−	24.2487i	−0.628619	−	1.08880i
$497$	−2.00000	−	3.46410i	−0.0897123	−	0.155386i
$498$		0			0
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	−0.988204	−	0.153141i	$-0.951061\pi$
$499$	−14.0000	−	24.2487i	−0.626726	−	1.08552i	0.361478	−	0.932381i	$-0.382272\pi$
$500$		0			0
$501$		0			0
$502$	−26.0000			−1.16044
$503$	−13.0000	+	22.5167i	−0.579641	+	1.00397i	0.415879	+	0.909420i	$0.363474\pi$
$503$	−13.0000	+	22.5167i	−0.579641	+	1.00397i	−0.995520	+	0.0945483i	$0.969859\pi$
$504$		0			0
$505$		0			0
$506$	−12.0000			−0.533465
$507$		0			0
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$		0			0
$511$	20.0000	+	34.6410i	0.884748	+	1.53243i
$512$	−32.0000			−1.41421
$513$		0			0
$514$	−12.0000			−0.529297
$515$		0			0
$516$		0			0
$517$	−3.00000	+	5.19615i	−0.131940	+	0.228527i
$518$	−8.00000	−	13.8564i	−0.351500	−	0.608816i
$519$		0			0
$520$		0			0
$521$	15.0000			0.657162			0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$	−27.0000	+	46.7654i	−1.18176	+	2.04686i
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$	24.0000			1.04844
$525$		0			0
$526$		0			0
$527$	7.00000	+	12.1244i	0.304925	+	0.528145i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$		0			0
$531$	−27.0000			−1.17170
$532$	−4.00000	−	34.6410i	−0.173422	−	1.50188i
$533$	4.00000			0.173259
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	3.00000	−	5.19615i	0.129339	−	0.224022i
$539$	−9.00000			−0.387657
$540$		0			0
$541$	−11.5000	+	19.9186i	−0.494424	+	0.856367i	−0.999979	−	0.00642713i	$-0.997954\pi$
$541$	−11.5000	+	19.9186i	−0.494424	+	0.856367i	0.505556	+	0.862794i	$0.331288\pi$
$542$	3.00000	−	5.19615i	0.128861	−	0.223194i
$543$		0			0
$544$	16.0000			0.685994
$545$		0			0
$546$		0			0
$547$	11.0000	−	19.0526i	0.470326	−	0.814629i	−0.529098	−	0.848561i	$-0.677470\pi$
$547$	11.0000	−	19.0526i	0.470326	−	0.814629i	0.999424	+	0.0339321i	$0.0108030\pi$
$548$	12.0000	+	20.7846i	0.512615	+	0.887875i
$549$	−10.5000	−	18.1865i	−0.448129	−	0.776182i
$550$		0			0
$551$	−4.50000	−	38.9711i	−0.191706	−	1.66023i
$552$		0			0
$553$	−2.00000	−	3.46410i	−0.0850487	−	0.147309i
$554$	28.0000	+	48.4974i	1.18961	+	2.06046i
$555$		0			0
$556$	−20.0000	−	34.6410i	−0.848189	−	1.46911i
$557$	7.00000	−	12.1244i	0.296600	−	0.513725i	−0.678756	−	0.734364i	$-0.737481\pi$
$557$	7.00000	−	12.1244i	0.296600	−	0.513725i	0.975356	+	0.220638i	$0.0708140\pi$
$558$	−42.0000			−1.77800
$559$	−4.00000			−0.169182
$560$		0			0
$561$		0			0
$562$	−20.0000			−0.843649
$563$	24.0000			1.01148			0.505740	−	0.862686i	$-0.331220\pi$
$563$	24.0000			1.01148			0.505740	+	0.862686i	$0.331220\pi$
$564$		0			0
$565$		0			0
$566$	−14.0000	+	24.2487i	−0.588464	+	1.01925i
$567$	−18.0000	−	31.1769i	−0.755929	−	1.30931i
$568$		0			0
$569$	15.0000			0.628833			0.314416	−	0.949285i	$-0.398191\pi$
$569$	15.0000			0.628833			0.314416	+	0.949285i	$0.398191\pi$
$570$		0			0
$571$	13.0000			0.544033			0.272017	−	0.962293i	$-0.412309\pi$
$571$	13.0000			0.544033			0.272017	+	0.962293i	$0.412309\pi$
$572$	2.00000	+	3.46410i	0.0836242	+	0.144841i
$573$		0			0
$574$	8.00000	−	13.8564i	0.333914	−	0.578355i
$575$		0			0
$576$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$577$	−6.00000			−0.249783			−0.124892	−	0.992170i	$-0.539858\pi$
$577$	−6.00000			−0.249783			−0.124892	+	0.992170i	$0.539858\pi$
$578$	26.0000			1.08146
$579$		0			0
$580$		0			0
$581$	24.0000			0.995688
$582$		0			0
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$		0			0
$585$		0			0
$586$	−4.00000	−	6.92820i	−0.165238	−	0.286201i
$587$	−12.0000	−	20.7846i	−0.495293	−	0.857873i	0.504692	−	0.863299i	$-0.331606\pi$
$587$	−12.0000	−	20.7846i	−0.495293	−	0.857873i	−0.999985	+	0.00542667i	$0.998273\pi$
$588$		0			0
$589$	24.5000	−	18.1865i	1.00950	−	0.749363i
$590$		0			0
$591$		0			0
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	−16.0000	+	27.7128i	−0.657041	+	1.13803i	0.324337	+	0.945942i	$0.394859\pi$
$593$	−16.0000	+	27.7128i	−0.657041	+	1.13803i	−0.981378	+	0.192087i	$0.938474\pi$
$594$		0			0
$595$		0			0
$596$	−2.00000			−0.0819232
$597$		0			0
$598$	−12.0000	+	20.7846i	−0.490716	+	0.849946i
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	17.0000			0.693444			0.346722	−	0.937968i	$-0.387295\pi$
$601$	17.0000			0.693444			0.346722	+	0.937968i	$0.387295\pi$
$602$	−8.00000	+	13.8564i	−0.326056	+	0.564745i
$603$	15.0000	+	25.9808i	0.610847	+	1.05802i
$604$	−9.00000	+	15.5885i	−0.366205	+	0.634285i
$605$		0			0
$606$		0			0
$607$	14.0000			0.568242			0.284121	−	0.958788i	$-0.408298\pi$
$607$	14.0000			0.568242			0.284121	+	0.958788i	$0.408298\pi$
$608$	−4.00000	−	34.6410i	−0.162221	−	1.40488i
$609$		0			0
$610$		0			0
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$	6.00000	−	10.3923i	0.242536	−	0.420084i
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	0.999845	−	0.0176058i	$-0.00560439\pi$
$613$	12.0000	+	20.7846i	0.484675	+	0.839482i	−0.515170	+	0.857088i	$0.672271\pi$
$614$	−16.0000	+	27.7128i	−0.645707	+	1.11840i
$615$		0			0
$616$		0			0
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$		0			0
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	22.0000	−	38.1051i	0.881411	−	1.52665i
$624$		0			0
$625$		0			0
$626$	60.0000			2.39808
$627$		0			0
$628$	−8.00000			−0.319235
$629$	2.00000	+	3.46410i	0.0797452	+	0.138123i
$630$		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
$633$		0			0
$634$	−4.00000			−0.158860
$635$		0			0
$636$		0			0
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$	18.0000			0.712627
$639$	−3.00000			−0.118678
$640$		0			0
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	0.580674	−	0.814136i	$-0.302789\pi$
$641$	−10.5000	−	18.1865i	−0.414725	−	0.718325i	−0.995400	+	0.0958109i	$0.969456\pi$
$642$		0			0
$643$	−23.0000	−	39.8372i	−0.907031	−	1.57102i	−0.818167	−	0.574981i	$-0.805009\pi$
$643$	−23.0000	−	39.8372i	−0.907031	−	1.57102i	−0.0888646	−	0.996044i	$-0.528324\pi$
$644$	24.0000	+	41.5692i	0.945732	+	1.63806i
$645$		0			0
$646$	2.00000	+	17.3205i	0.0786889	+	0.681466i
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$		0			0
$649$	4.50000	+	7.79423i	0.176640	+	0.305950i
$650$		0			0
$651$		0			0
$652$	4.00000	−	6.92820i	0.156652	−	0.271329i
$653$	−10.0000			−0.391330			−0.195665	−	0.980671i	$-0.562687\pi$
$653$	−10.0000			−0.391330			−0.195665	+	0.980671i	$0.562687\pi$
$654$		0			0
$655$		0			0
$656$	4.00000	−	6.92820i	0.156174	−	0.270501i
$657$	30.0000			1.17041
$658$	48.0000			1.87123
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	−0.992388	−	0.123148i	$-0.960701\pi$
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	0.602844	+	0.797859i	$0.294034\pi$
$660$		0			0
$661$	7.50000	−	12.9904i	0.291716	−	0.505267i	−0.682499	−	0.730886i	$-0.739107\pi$
$661$	7.50000	−	12.9904i	0.291716	−	0.505267i	0.974216	+	0.225619i	$0.0724404\pi$
$662$	20.0000	+	34.6410i	0.777322	+	1.34636i
$663$		0			0
$664$		0			0
$665$		0			0
$666$	−12.0000			−0.464991
$667$	27.0000	+	46.7654i	1.04544	+	1.81076i
$668$	−12.0000	−	20.7846i	−0.464294	−	0.804181i
$669$		0			0
$670$		0			0
$671$	−3.50000	+	6.06218i	−0.135116	+	0.234028i
$672$		0			0
$673$	20.0000			0.770943			0.385472	−	0.922720i	$-0.374039\pi$
$673$	20.0000			0.770943			0.385472	+	0.922720i	$0.374039\pi$
$674$	−34.0000	+	58.8897i	−1.30963	+	2.26835i
$675$		0			0
$676$	−18.0000			−0.692308
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$		0			0
$681$		0			0
$682$	7.00000	+	12.1244i	0.268044	+	0.464266i
$683$	−30.0000			−1.14792			−0.573959	−	0.818884i	$-0.694593\pi$
$683$	−30.0000			−1.14792			−0.573959	+	0.818884i	$0.694593\pi$
$684$	−24.0000	−	10.3923i	−0.917663	−	0.397360i
$685$		0			0
$686$	8.00000	+	13.8564i	0.305441	+	0.529040i
$687$		0			0
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	4.00000	+	6.92820i	0.152388	+	0.263944i
$690$		0			0
$691$	3.00000			0.114125			0.0570627	−	0.998371i	$-0.481827\pi$
$691$	3.00000			0.114125			0.0570627	+	0.998371i	$0.481827\pi$
$692$	48.0000			1.82469
$693$	−6.00000	+	10.3923i	−0.227921	+	0.394771i
$694$	12.0000	−	20.7846i	0.455514	−	0.788973i
$695$		0			0
$696$		0			0
$697$	−2.00000	+	3.46410i	−0.0757554	+	0.131212i
$698$	14.0000	+	24.2487i	0.529908	+	0.917827i
$699$		0			0
$700$		0			0
$701$	−3.00000	−	5.19615i	−0.113308	−	0.196256i	0.803794	−	0.594908i	$-0.202811\pi$
$701$	−3.00000	−	5.19615i	−0.113308	−	0.196256i	−0.917102	+	0.398652i	$0.869478\pi$
$702$		0			0
$703$	7.00000	−	5.19615i	0.264010	−	0.195977i
$704$	8.00000			0.301511
$705$		0			0
$706$	8.00000	+	13.8564i	0.301084	+	0.521493i
$707$	−30.0000	+	51.9615i	−1.12827	+	1.95421i
$708$		0			0
$709$	−12.5000	+	21.6506i	−0.469447	+	0.813107i	−0.999390	−	0.0349269i	$-0.988880\pi$
$709$	−12.5000	+	21.6506i	−0.469447	+	0.813107i	0.529943	+	0.848034i	$0.322213\pi$
$710$		0			0
$711$	−3.00000			−0.112509
$712$		0			0
$713$	−21.0000	+	36.3731i	−0.786456	+	1.36218i
$714$		0			0
$715$		0			0
$716$	−15.0000	+	25.9808i	−0.560576	+	0.970947i
$717$		0			0
$718$	−20.0000	+	34.6410i	−0.746393	+	1.29279i
$719$	10.5000	+	18.1865i	0.391584	+	0.678243i	0.992659	−	0.120950i	$-0.0385939\pi$
$719$	10.5000	+	18.1865i	0.391584	+	0.678243i	−0.601075	+	0.799193i	$0.705261\pi$
$720$		0			0
$721$	−64.0000			−2.38348
$722$	37.0000	−	8.66025i	1.37700	−	0.322301i
$723$		0			0
$724$	6.00000	+	10.3923i	0.222988	+	0.386227i
$725$		0			0
$726$		0			0
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	2.00000	−	3.46410i	0.0739727	−	0.128124i
$732$		0			0
$733$	6.00000			0.221615			0.110808	−	0.993842i	$-0.464656\pi$
$733$	6.00000			0.221615			0.110808	+	0.993842i	$0.464656\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	24.0000	+	41.5692i	0.884652	+	1.53226i
$737$	5.00000	−	8.66025i	0.184177	−	0.319005i
$738$	−6.00000	−	10.3923i	−0.220863	−	0.382546i
$739$	14.5000	+	25.1147i	0.533391	+	0.923861i	0.999239	+	0.0389959i	$0.0124159\pi$
$739$	14.5000	+	25.1147i	0.533391	+	0.923861i	−0.465848	+	0.884865i	$0.654251\pi$
$740$		0			0
$741$		0			0
$742$	32.0000			1.17476
$743$	25.0000	+	43.3013i	0.917161	+	1.58857i	0.803706	+	0.595026i	$0.202858\pi$
$743$	25.0000	+	43.3013i	0.917161	+	1.58857i	0.113455	+	0.993543i	$0.463808\pi$
$744$		0			0
$745$		0			0
$746$	12.0000	+	20.7846i	0.439351	+	0.760979i
$747$	9.00000	−	15.5885i	0.329293	−	0.570352i
$748$	−4.00000			−0.146254
$749$	40.0000			1.46157
$750$		0			0
$751$	−20.5000	+	35.5070i	−0.748056	+	1.29567i	0.200698	+	0.979653i	$0.435679\pi$
$751$	−20.5000	+	35.5070i	−0.748056	+	1.29567i	−0.948753	+	0.316017i	$0.897654\pi$
$752$	24.0000			0.875190
$753$		0			0
$754$	18.0000	−	31.1769i	0.655521	−	1.13540i
$755$		0			0
$756$		0			0
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	0.999505	−	0.0314762i	$-0.0100208\pi$
$757$	13.0000	+	22.5167i	0.472493	+	0.818382i	−0.527011	+	0.849858i	$0.676688\pi$
$758$	−29.0000	−	50.2295i	−1.05333	−	1.82442i
$759$		0			0
$760$		0			0
$761$	−18.0000			−0.652499			−0.326250	−	0.945284i	$-0.605785\pi$
$761$	−18.0000			−0.652499			−0.326250	+	0.945284i	$0.605785\pi$
$762$		0			0
$763$	−30.0000	−	51.9615i	−1.08607	−	1.88113i
$764$	3.00000	−	5.19615i	0.108536	−	0.187990i
$765$		0			0
$766$	−6.00000	+	10.3923i	−0.216789	+	0.375489i
$767$	18.0000			0.649942
$768$		0			0
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	−0.907575	−	0.419890i	$-0.862069\pi$
$769$	−2.50000	+	4.33013i	−0.0901523	+	0.156148i	0.817423	+	0.576038i	$0.195402\pi$
$770$		0			0
$771$		0			0
$772$	−32.0000			−1.15171
$773$	17.0000	−	29.4449i	0.611448	−	1.05906i	−0.379549	−	0.925172i	$-0.623921\pi$
$773$	17.0000	−	29.4449i	0.611448	−	1.05906i	0.990997	−	0.133887i	$-0.0427458\pi$
$774$	6.00000	+	10.3923i	0.215666	+	0.373544i
$775$		0			0
$776$		0			0
$777$		0			0
$778$	66.0000			2.36621
$779$	8.00000	+	3.46410i	0.286630	+	0.124114i
$780$		0			0
$781$	0.500000	+	0.866025i	0.0178914	+	0.0309888i
$782$	−12.0000	−	20.7846i	−0.429119	−	0.743256i
$783$		0			0
$784$	18.0000	+	31.1769i	0.642857	+	1.11346i
$785$		0			0
$786$		0			0
$787$	−22.0000			−0.784215			−0.392108	−	0.919919i	$-0.628254\pi$
$787$	−22.0000			−0.784215			−0.392108	+	0.919919i	$0.628254\pi$
$788$	−18.0000	+	31.1769i	−0.641223	+	1.11063i
$789$		0			0
$790$		0			0
$791$	48.0000			1.70668
$792$		0			0
$793$	7.00000	+	12.1244i	0.248577	+	0.430548i
$794$	8.00000	−	13.8564i	0.283909	−	0.491745i
$795$		0			0
$796$	−13.0000	−	22.5167i	−0.460773	−	0.798082i
$797$	−24.0000			−0.850124			−0.425062	−	0.905164i	$-0.639748\pi$
$797$	−24.0000			−0.850124			−0.425062	+	0.905164i	$0.639748\pi$
$798$		0			0
$799$	−12.0000			−0.424529
$800$		0			0
$801$	−16.5000	−	28.5788i	−0.582999	−	1.00978i
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	−5.00000	−	8.66025i	−0.176446	−	0.305614i
$804$		0			0
$805$		0			0
$806$	28.0000			0.986258
$807$		0			0
$808$		0			0
$809$	−43.0000			−1.51180			−0.755900	−	0.654687i	$-0.772800\pi$
$809$	−43.0000			−1.51180			−0.755900	+	0.654687i	$0.772800\pi$
$810$		0			0
$811$	−4.50000	+	7.79423i	−0.158016	+	0.273692i	−0.934153	−	0.356872i	$-0.883843\pi$
$811$	−4.50000	+	7.79423i	−0.158016	+	0.273692i	0.776137	+	0.630564i	$0.217177\pi$
$812$	−36.0000	−	62.3538i	−1.26335	−	2.18819i
$813$		0			0
$814$	2.00000	+	3.46410i	0.0701000	+	0.121417i
$815$		0			0
$816$		0			0
$817$	−8.00000	−	3.46410i	−0.279885	−	0.121194i
$818$	10.0000			0.349642
$819$	12.0000	+	20.7846i	0.419314	+	0.726273i
$820$		0			0
$821$	−10.5000	+	18.1865i	−0.366453	+	0.634714i	−0.989008	−	0.147861i	$-0.952761\pi$
$821$	−10.5000	+	18.1865i	−0.366453	+	0.634714i	0.622556	+	0.782576i	$0.286094\pi$
$822$		0			0
$823$	−15.0000	+	25.9808i	−0.522867	+	0.905632i	0.476779	+	0.879023i	$0.341804\pi$
$823$	−15.0000	+	25.9808i	−0.522867	+	0.905632i	−0.999646	+	0.0266091i	$0.991529\pi$
$824$		0			0
$825$		0			0
$826$	36.0000	−	62.3538i	1.25260	−	2.16957i
$827$	3.00000	−	5.19615i	0.104320	−	0.180688i	−0.809140	−	0.587616i	$-0.800067\pi$
$827$	3.00000	−	5.19615i	0.104320	−	0.180688i	0.913460	+	0.406928i	$0.133400\pi$
$828$	36.0000			1.25109
$829$	2.00000			0.0694629			0.0347314	−	0.999397i	$-0.488942\pi$
$829$	2.00000			0.0694629			0.0347314	+	0.999397i	$0.488942\pi$
$830$		0			0
$831$		0			0
$832$	8.00000	−	13.8564i	0.277350	−	0.480384i
$833$	−9.00000	−	15.5885i	−0.311832	−	0.540108i
$834$		0			0
$835$		0			0
$836$	1.00000	+	8.66025i	0.0345857	+	0.299521i
$837$		0			0
$838$	9.00000	+	15.5885i	0.310900	+	0.538494i
$839$	−24.0000	−	41.5692i	−0.828572	−	1.43513i	−0.899158	−	0.437623i	$-0.855820\pi$
$839$	−24.0000	−	41.5692i	−0.828572	−	1.43513i	0.0705865	−	0.997506i	$-0.477513\pi$
$840$		0			0
$841$	−26.0000	−	45.0333i	−0.896552	−	1.55287i
$842$	−15.0000	+	25.9808i	−0.516934	+	0.895356i
$843$		0			0
$844$	10.0000			0.344214
$845$		0			0
$846$	18.0000	−	31.1769i	0.618853	−	1.07188i
$847$	−40.0000			−1.37442
$848$	16.0000			0.549442
$849$		0			0
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	−8.00000	−	13.8564i	−0.273915	−	0.474434i	0.695946	−	0.718094i	$-0.254985\pi$
$853$	−8.00000	−	13.8564i	−0.273915	−	0.474434i	−0.969861	+	0.243660i	$0.921652\pi$
$854$	56.0000			1.91628
$855$		0			0
$856$		0			0
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	0.670366	−	0.742030i	$-0.266137\pi$
$857$	−9.00000	−	15.5885i	−0.307434	−	0.532492i	−0.977800	+	0.209539i	$0.932804\pi$
$858$		0			0
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	−0.874429	−	0.485153i	$-0.838764\pi$
$859$	−0.500000	+	0.866025i	−0.0170598	+	0.0295484i	0.857369	+	0.514701i	$0.172097\pi$
$860$		0			0
$861$		0			0
$862$	−42.0000			−1.43053
$863$	−20.0000			−0.680808			−0.340404	−	0.940279i	$-0.610564\pi$
$863$	−20.0000			−0.680808			−0.340404	+	0.940279i	$0.610564\pi$
$864$		0			0
$865$		0			0
$866$	−8.00000			−0.271851
$867$		0			0
$868$	28.0000	−	48.4974i	0.950382	−	1.64611i
$869$	0.500000	+	0.866025i	0.0169613	+	0.0293779i
$870$		0			0
$871$	−10.0000	−	17.3205i	−0.338837	−	0.586883i
$872$		0			0
$873$	−18.0000			−0.609208
$874$	−42.0000	+	31.1769i	−1.42067	+	1.05457i
$875$		0			0
$876$		0			0
$877$	−29.0000	−	50.2295i	−0.979260	−	1.69613i	−0.665092	−	0.746762i	$-0.731608\pi$
$877$	−29.0000	−	50.2295i	−0.979260	−	1.69613i	−0.314169	−	0.949367i	$-0.601726\pi$
$878$	−13.0000	+	22.5167i	−0.438729	+	0.759900i
$879$		0			0
$880$		0			0
$881$	37.0000			1.24656			0.623281	−	0.781998i	$-0.285799\pi$
$881$	37.0000			1.24656			0.623281	+	0.781998i	$0.285799\pi$
$882$	54.0000			1.81827
$883$	−4.00000	+	6.92820i	−0.134611	+	0.233153i	−0.925449	−	0.378873i	$-0.876312\pi$
$883$	−4.00000	+	6.92820i	−0.134611	+	0.233153i	0.790838	+	0.612026i	$0.209645\pi$
$884$	−4.00000	+	6.92820i	−0.134535	+	0.233021i
$885$		0			0
$886$	8.00000			0.268765
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	−0.968504	−	0.248998i	$-0.919899\pi$
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	0.699890	+	0.714250i	$0.253232\pi$
$888$		0			0
$889$	−12.0000	+	20.7846i	−0.402467	+	0.697093i
$890$		0			0
$891$	4.50000	+	7.79423i	0.150756	+	0.261116i
$892$	4.00000			0.133930
$893$	3.00000	+	25.9808i	0.100391	+	0.869413i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	31.0000	+	53.6936i	1.03448	+	1.79178i
$899$	31.5000	−	54.5596i	1.05058	−	1.81966i
$900$		0			0
$901$	−8.00000			−0.266519
$902$	−2.00000	+	3.46410i	−0.0665927	+	0.115342i
$903$		0			0
$904$		0			0
$905$		0			0
$906$		0			0
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	14.0000	−	24.2487i	0.464606	−	0.804722i
$909$	22.5000	+	38.9711i	0.746278	+	1.29259i
$910$		0			0
$911$	41.0000			1.35839			0.679195	−	0.733958i	$-0.262329\pi$
$911$	41.0000			1.35839			0.679195	+	0.733958i	$0.262329\pi$
$912$		0			0
$913$	−6.00000			−0.198571
$914$	−34.0000	−	58.8897i	−1.12462	−	1.94790i
$915$		0			0
$916$	−17.0000	+	29.4449i	−0.561696	+	0.972886i
$917$	−24.0000	−	41.5692i	−0.792550	−	1.37274i
$918$		0			0
$919$	16.0000			0.527791			0.263896	−	0.964551i	$-0.414993\pi$
$919$	16.0000			0.527791			0.263896	+	0.964551i	$0.414993\pi$
$920$		0			0
$921$		0			0
$922$	−25.0000	+	43.3013i	−0.823331	+	1.42605i
$923$	2.00000			0.0658308
$924$		0			0
$925$		0			0
$926$	4.00000	+	6.92820i	0.131448	+	0.227675i
$927$	−24.0000	+	41.5692i	−0.788263	+	1.36531i
$928$	−36.0000	−	62.3538i	−1.18176	−	2.04686i
$929$	−25.5000	−	44.1673i	−0.836628	−	1.44908i	−0.892698	−	0.450655i	$-0.851190\pi$
$929$	−25.5000	−	44.1673i	−0.836628	−	1.44908i	0.0560703	−	0.998427i	$-0.482143\pi$
$930$		0			0
$931$	−31.5000	+	23.3827i	−1.03237	+	0.766337i
$932$	16.0000			0.524097
$933$		0			0
$934$	−10.0000	−	17.3205i	−0.327210	−	0.566744i
$935$		0			0
$936$		0			0
$937$	−28.0000	+	48.4974i	−0.914720	+	1.58434i	−0.107410	+	0.994215i	$0.534256\pi$
$937$	−28.0000	+	48.4974i	−0.914720	+	1.58434i	−0.807311	+	0.590127i	$0.799078\pi$
$938$	−80.0000			−2.61209
$939$		0			0
$940$		0			0
$941$	−17.5000	+	30.3109i	−0.570484	+	0.988107i	0.426033	+	0.904708i	$0.359911\pi$
$941$	−17.5000	+	30.3109i	−0.570484	+	0.988107i	−0.996516	+	0.0833989i	$0.973422\pi$
$942$		0			0
$943$	−12.0000			−0.390774
$944$	18.0000	−	31.1769i	0.585850	−	1.01472i
$945$		0			0
$946$	2.00000	−	3.46410i	0.0650256	−	0.112628i
$947$	−21.0000	−	36.3731i	−0.682408	−	1.18197i	−0.974244	−	0.225497i	$-0.927599\pi$
$947$	−21.0000	−	36.3731i	−0.682408	−	1.18197i	0.291835	−	0.956469i	$-0.405734\pi$
$948$		0			0
$949$	−20.0000			−0.649227
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−12.0000	−	20.7846i	−0.388718	−	0.673280i	0.603559	−	0.797318i	$-0.293749\pi$
$953$	−12.0000	−	20.7846i	−0.388718	−	0.673280i	−0.992277	+	0.124039i	$0.960415\pi$
$954$	12.0000	−	20.7846i	0.388514	−	0.672927i
$955$		0			0
$956$	19.0000	−	32.9090i	0.614504	−	1.06435i
$957$		0			0
$958$	−30.0000			−0.969256
$959$	24.0000	−	41.5692i	0.775000	−	1.34234i
$960$		0			0
$961$	18.0000			0.580645
$962$	8.00000			0.257930
$963$	15.0000	−	25.9808i	0.483368	−	0.837218i
$964$	−1.00000	−	1.73205i	−0.0322078	−	0.0557856i
$965$		0			0
$966$		0			0
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515777\pi$
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$		0			0
$973$	−40.0000	+	69.2820i	−1.28234	+	2.22108i
$974$	38.0000	+	65.8179i	1.21760	+	2.10894i
$975$		0			0
$976$	28.0000			0.896258
$977$	44.0000			1.40768			0.703842	−	0.710356i	$-0.251466\pi$
$977$	44.0000			1.40768			0.703842	+	0.710356i	$0.251466\pi$
$978$		0			0
$979$	−5.50000	+	9.52628i	−0.175781	+	0.304461i
$980$		0			0
$981$	−45.0000			−1.43674
$982$	13.0000	−	22.5167i	0.414847	−	0.718536i
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$		0			0
$985$		0			0
$986$	18.0000	+	31.1769i	0.573237	+	0.992875i
$987$		0			0
$988$	16.0000	+	6.92820i	0.509028	+	0.220416i
$989$	12.0000			0.381578
$990$		0			0
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	−0.968864	−	0.247592i	$-0.920361\pi$
$991$	−22.0000	−	38.1051i	−0.698853	−	1.21045i	0.270011	−	0.962857i	$-0.412973\pi$
$992$	28.0000	−	48.4974i	0.889001	−	1.53979i
$993$		0			0
$994$	4.00000	−	6.92820i	0.126872	−	0.219749i
$995$		0			0
$996$		0			0
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	−0.583363	−	0.812211i	$-0.698264\pi$
$997$	13.0000	−	22.5167i	0.411714	−	0.713110i	0.995077	+	0.0991016i	$0.0315969\pi$
$998$	28.0000	−	48.4974i	0.886325	−	1.53516i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	475.2.e.c.26.1		2
5.2	odd	4		95.2.i.a.64.1	yes	4
5.3	odd	4		95.2.i.a.64.2	yes	4
5.4	even	2		475.2.e.a.26.1		2
15.2	even	4		855.2.be.a.64.2		4
15.8	even	4		855.2.be.a.64.1		4
19.7	even	3		9025.2.a.b.1.1		1
19.11	even	3	inner	475.2.e.c.201.1		2
19.12	odd	6		9025.2.a.j.1.1		1
95.7	odd	12		1805.2.b.b.1084.1		2
95.12	even	12		1805.2.b.a.1084.2		2
95.49	even	6		475.2.e.a.201.1		2
95.64	even	6		9025.2.a.i.1.1		1
95.68	odd	12		95.2.i.a.49.1	✓	4
95.69	odd	6		9025.2.a.a.1.1		1
95.83	odd	12		1805.2.b.b.1084.2		2
95.87	odd	12		95.2.i.a.49.2	yes	4
95.88	even	12		1805.2.b.a.1084.1		2
285.68	even	12		855.2.be.a.334.2		4
285.182	even	12		855.2.be.a.334.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.a.49.1	✓	4	95.68	odd	12
95.2.i.a.49.2	yes	4	95.87	odd	12
95.2.i.a.64.1	yes	4	5.2	odd	4
95.2.i.a.64.2	yes	4	5.3	odd	4
475.2.e.a.26.1		2	5.4	even	2
475.2.e.a.201.1		2	95.49	even	6
475.2.e.c.26.1		2	1.1	even	1	trivial
475.2.e.c.201.1		2	19.11	even	3	inner
855.2.be.a.64.1		4	15.8	even	4
855.2.be.a.64.2		4	15.2	even	4
855.2.be.a.334.1		4	285.182	even	12
855.2.be.a.334.2		4	285.68	even	12
1805.2.b.a.1084.1		2	95.88	even	12
1805.2.b.a.1084.2		2	95.12	even	12
1805.2.b.b.1084.1		2	95.7	odd	12
1805.2.b.b.1084.2		2	95.83	odd	12
9025.2.a.a.1.1		1	95.69	odd	6
9025.2.a.b.1.1		1	19.7	even	3
9025.2.a.i.1.1		1	95.64	even	6
9025.2.a.j.1.1		1	19.12	odd	6

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.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +4.00000 q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +4.00000 q^{7} +(1.50000 - 2.59808i) q^{9} -1.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(4.00000 + 6.92820i) q^{14} +(2.00000 + 3.46410i) q^{16} +(-1.00000 - 1.73205i) q^{17} +6.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} +(-1.00000 - 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} -4.00000 q^{26} +(-4.00000 + 6.92820i) q^{28} +(-4.50000 + 7.79423i) q^{29} -7.00000 q^{31} +(-4.00000 + 6.92820i) q^{32} +(2.00000 - 3.46410i) q^{34} +(3.00000 + 5.19615i) q^{36} -2.00000 q^{37} +(-8.00000 - 3.46410i) q^{38} +(-1.00000 - 1.73205i) q^{41} +(1.00000 + 1.73205i) q^{43} +(1.00000 - 1.73205i) q^{44} +12.0000 q^{46} +(3.00000 - 5.19615i) q^{47} +9.00000 q^{49} +(-2.00000 - 3.46410i) q^{52} +(2.00000 - 3.46410i) q^{53} -18.0000 q^{58} +(-4.50000 - 7.79423i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-7.00000 - 12.1244i) q^{62} +(6.00000 - 10.3923i) q^{63} -8.00000 q^{64} +(-5.00000 + 8.66025i) q^{67} +4.00000 q^{68} +(-0.500000 - 0.866025i) q^{71} +(5.00000 + 8.66025i) q^{73} +(-2.00000 - 3.46410i) q^{74} +(-1.00000 - 8.66025i) q^{76} -4.00000 q^{77} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(2.00000 - 3.46410i) q^{82} +6.00000 q^{83} +(-2.00000 + 3.46410i) q^{86} +(5.50000 - 9.52628i) q^{89} +(-4.00000 + 6.92820i) q^{91} +(6.00000 + 10.3923i) q^{92} +12.0000 q^{94} +(-3.00000 - 5.19615i) q^{97} +(9.00000 + 15.5885i) q^{98} +(-1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{4} + 8 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^4 + 8 * q^7 + 3 * q^9	\( 2 q + 2 q^{2} - 2 q^{4} + 8 q^{7} + 3 q^{9} - 2 q^{11} - 2 q^{13} + 8 q^{14} + 4 q^{16} - 2 q^{17} + 12 q^{18} - 7 q^{19} - 2 q^{22} + 6 q^{23} - 8 q^{26} - 8 q^{28} - 9 q^{29} - 14 q^{31} - 8 q^{32} + 4 q^{34} + 6 q^{36} - 4 q^{37} - 16 q^{38} - 2 q^{41} + 2 q^{43} + 2 q^{44} + 24 q^{46} + 6 q^{47} + 18 q^{49} - 4 q^{52} + 4 q^{53} - 36 q^{58} - 9 q^{59} + 7 q^{61} - 14 q^{62} + 12 q^{63} - 16 q^{64} - 10 q^{67} + 8 q^{68} - q^{71} + 10 q^{73} - 4 q^{74} - 2 q^{76} - 8 q^{77} - q^{79} - 9 q^{81} + 4 q^{82} + 12 q^{83} - 4 q^{86} + 11 q^{89} - 8 q^{91} + 12 q^{92} + 24 q^{94} - 6 q^{97} + 18 q^{98} - 3 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^4 + 8 * q^7 + 3 * q^9 - 2 * q^11 - 2 * q^13 + 8 * q^14 + 4 * q^16 - 2 * q^17 + 12 * q^18 - 7 * q^19 - 2 * q^22 + 6 * q^23 - 8 * q^26 - 8 * q^28 - 9 * q^29 - 14 * q^31 - 8 * q^32 + 4 * q^34 + 6 * q^36 - 4 * q^37 - 16 * q^38 - 2 * q^41 + 2 * q^43 + 2 * q^44 + 24 * q^46 + 6 * q^47 + 18 * q^49 - 4 * q^52 + 4 * q^53 - 36 * q^58 - 9 * q^59 + 7 * q^61 - 14 * q^62 + 12 * q^63 - 16 * q^64 - 10 * q^67 + 8 * q^68 - q^71 + 10 * q^73 - 4 * q^74 - 2 * q^76 - 8 * q^77 - q^79 - 9 * q^81 + 4 * q^82 + 12 * q^83 - 4 * q^86 + 11 * q^89 - 8 * q^91 + 12 * q^92 + 24 * q^94 - 6 * q^97 + 18 * q^98 - 3 * q^99

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