LMFDB - Embedded newform 1014.3.f.a.775.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,3,Mod(577,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1014.577");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1014.f (of order $4$, 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:	$27.6294988061$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 78)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			775.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1014.775
Dual form			1014.3.f.a.577.1

$q$-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 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(-4.73205 - 4.73205i) q^{5} +(1.73205 + 1.73205i) q^{6} +(2.73205 - 2.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +9.46410i q^{10} +(-1.73205 + 1.73205i) q^{11} -3.46410i q^{12} -5.46410 q^{14} +(8.19615 + 8.19615i) q^{15} -4.00000 q^{16} -29.3205i q^{17} +(-3.00000 - 3.00000i) q^{18} +(11.2679 + 11.2679i) q^{19} +(9.46410 - 9.46410i) q^{20} +(-4.73205 + 4.73205i) q^{21} +3.46410 q^{22} -29.3205i q^{23} +(-3.46410 + 3.46410i) q^{24} +19.7846i q^{25} -5.19615 q^{27} +(5.46410 + 5.46410i) q^{28} +31.8564 q^{29} -16.3923i q^{30} +(-26.9808 - 26.9808i) q^{31} +(4.00000 + 4.00000i) q^{32} +(3.00000 - 3.00000i) q^{33} +(-29.3205 + 29.3205i) q^{34} -25.8564 q^{35} +6.00000i q^{36} +(30.8564 - 30.8564i) q^{37} -22.5359i q^{38} -18.9282 q^{40} +(14.4449 + 14.4449i) q^{41} +9.46410 q^{42} -25.1769i q^{43} +(-3.46410 - 3.46410i) q^{44} +(-14.1962 - 14.1962i) q^{45} +(-29.3205 + 29.3205i) q^{46} +(41.1962 - 41.1962i) q^{47} +6.92820 q^{48} +34.0718i q^{49} +(19.7846 - 19.7846i) q^{50} +50.7846i q^{51} +2.28719 q^{53} +(5.19615 + 5.19615i) q^{54} +16.3923 q^{55} -10.9282i q^{56} +(-19.5167 - 19.5167i) q^{57} +(-31.8564 - 31.8564i) q^{58} +(-54.6218 + 54.6218i) q^{59} +(-16.3923 + 16.3923i) q^{60} -7.42563 q^{61} +53.9615i q^{62} +(8.19615 - 8.19615i) q^{63} -8.00000i q^{64} -6.00000 q^{66} +(60.6936 + 60.6936i) q^{67} +58.6410 q^{68} +50.7846i q^{69} +(25.8564 + 25.8564i) q^{70} +(-38.9090 - 38.9090i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-40.3205 + 40.3205i) q^{73} -61.7128 q^{74} -34.2679i q^{75} +(-22.5359 + 22.5359i) q^{76} +9.46410i q^{77} -148.210 q^{79} +(18.9282 + 18.9282i) q^{80} +9.00000 q^{81} -28.8897i q^{82} +(-73.7987 - 73.7987i) q^{83} +(-9.46410 - 9.46410i) q^{84} +(-138.746 + 138.746i) q^{85} +(-25.1769 + 25.1769i) q^{86} -55.1769 q^{87} +6.92820i q^{88} +(-25.5167 + 25.5167i) q^{89} +28.3923i q^{90} +58.6410 q^{92} +(46.7321 + 46.7321i) q^{93} -82.3923 q^{94} -106.641i q^{95} +(-6.92820 - 6.92820i) q^{96} +(86.0333 + 86.0333i) q^{97} +(34.0718 - 34.0718i) q^{98} +(-5.19615 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 12 q^{5} + 4 q^{7} + 8 q^{8} + 12 q^{9} - 8 q^{14} + 12 q^{15} - 16 q^{16} - 12 q^{18} + 52 q^{19} + 24 q^{20} - 12 q^{21} + 8 q^{28} + 72 q^{29} - 4 q^{31} + 16 q^{32} + 12 q^{33} - 48 q^{34}+ \cdots + 164 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 12 * q^5 + 4 * q^7 + 8 * q^8 + 12 * q^9 - 8 * q^14 + 12 * q^15 - 16 * q^16 - 12 * q^18 + 52 * q^19 + 24 * q^20 - 12 * q^21 + 8 * q^28 + 72 * q^29 - 4 * q^31 + 16 * q^32 + 12 * q^33 - 48 * q^34 - 48 * q^35 + 68 * q^37 - 48 * q^40 - 60 * q^41 + 24 * q^42 - 36 * q^45 - 48 * q^46 + 144 * q^47 - 4 * q^50 + 120 * q^53 + 24 * q^55 + 12 * q^57 - 72 * q^58 + 24 * q^59 - 24 * q^60 + 192 * q^61 + 12 * q^63 - 24 * q^66 + 28 * q^67 + 96 * q^68 + 48 * q^70 - 24 * q^71 + 24 * q^72 - 92 * q^73 - 136 * q^74 - 104 * q^76 - 288 * q^79 + 48 * q^80 + 36 * q^81 + 72 * q^83 - 24 * q^84 - 264 * q^85 + 24 * q^86 - 96 * q^87 - 12 * q^89 + 96 * q^92 + 180 * q^93 - 288 * q^94 + 164 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$

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	−	1.00000i	−0.500000	−	0.500000i
$2$	−1.00000	−	1.00000i	−0.500000	−	0.500000i
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$			2.00000i			0.500000i
$5$	−4.73205	−	4.73205i	−0.946410	−	0.946410i	0.0522252	−	0.998635i	$-0.483369\pi$
$5$	−4.73205	−	4.73205i	−0.946410	−	0.946410i	−0.998635	+	0.0522252i	$0.983369\pi$
$6$	1.73205	+	1.73205i	0.288675	+	0.288675i
$7$	2.73205	−	2.73205i	0.390293	−	0.390293i	−0.484499	−	0.874792i	$-0.660998\pi$
$7$	2.73205	−	2.73205i	0.390293	−	0.390293i	0.874792	+	0.484499i	$0.160998\pi$
$8$	2.00000	−	2.00000i	0.250000	−	0.250000i
$9$	3.00000			0.333333
$10$			9.46410i			0.946410i
$11$	−1.73205	+	1.73205i	−0.157459	+	0.157459i	−0.781440	−	0.623981i	$-0.785514\pi$
$11$	−1.73205	+	1.73205i	−0.157459	+	0.157459i	0.623981	+	0.781440i	$0.285514\pi$
$12$		−	3.46410i		−	0.288675i
$13$		0			0
$13$		0			0
$14$	−5.46410			−0.390293
$15$	8.19615	+	8.19615i	0.546410	+	0.546410i
$16$	−4.00000			−0.250000
$17$		−	29.3205i		−	1.72474i	−0.506282	−	0.862368i	$-0.668981\pi$
$17$		−	29.3205i		−	1.72474i	0.506282	−	0.862368i	$-0.331019\pi$
$18$	−3.00000	−	3.00000i	−0.166667	−	0.166667i
$19$	11.2679	+	11.2679i	0.593050	+	0.593050i	0.938454	−	0.345404i	$-0.112258\pi$
$19$	11.2679	+	11.2679i	0.593050	+	0.593050i	−0.345404	+	0.938454i	$0.612258\pi$
$20$	9.46410	−	9.46410i	0.473205	−	0.473205i
$21$	−4.73205	+	4.73205i	−0.225336	+	0.225336i
$22$	3.46410			0.157459
$23$		−	29.3205i		−	1.27480i	−0.770531	−	0.637402i	$-0.780009\pi$
$23$		−	29.3205i		−	1.27480i	0.770531	−	0.637402i	$-0.219991\pi$
$24$	−3.46410	+	3.46410i	−0.144338	+	0.144338i
$25$			19.7846i			0.791384i
$26$		0			0
$27$	−5.19615			−0.192450
$28$	5.46410	+	5.46410i	0.195146	+	0.195146i
$29$	31.8564			1.09850			0.549248	−	0.835659i	$-0.314914\pi$
$29$	31.8564			1.09850			0.549248	+	0.835659i	$0.314914\pi$
$30$		−	16.3923i		−	0.546410i
$31$	−26.9808	−	26.9808i	−0.870347	−	0.870347i	0.122163	−	0.992510i	$-0.461017\pi$
$31$	−26.9808	−	26.9808i	−0.870347	−	0.870347i	−0.992510	+	0.122163i	$0.961017\pi$
$32$	4.00000	+	4.00000i	0.125000	+	0.125000i
$33$	3.00000	−	3.00000i	0.0909091	−	0.0909091i
$34$	−29.3205	+	29.3205i	−0.862368	+	0.862368i
$35$	−25.8564			−0.738754
$36$			6.00000i			0.166667i
$37$	30.8564	−	30.8564i	0.833957	−	0.833957i	−0.154099	−	0.988055i	$-0.549247\pi$
$37$	30.8564	−	30.8564i	0.833957	−	0.833957i	0.988055	+	0.154099i	$0.0492473\pi$
$38$		−	22.5359i		−	0.593050i
$39$		0			0
$40$	−18.9282			−0.473205
$41$	14.4449	+	14.4449i	0.352314	+	0.352314i	0.860970	−	0.508656i	$-0.169858\pi$
$41$	14.4449	+	14.4449i	0.352314	+	0.352314i	−0.508656	+	0.860970i	$0.669858\pi$
$42$	9.46410			0.225336
$43$		−	25.1769i		−	0.585510i	−0.956188	−	0.292755i	$-0.905428\pi$
$43$		−	25.1769i		−	0.585510i	0.956188	−	0.292755i	$-0.0945720\pi$
$44$	−3.46410	−	3.46410i	−0.0787296	−	0.0787296i
$45$	−14.1962	−	14.1962i	−0.315470	−	0.315470i
$46$	−29.3205	+	29.3205i	−0.637402	+	0.637402i
$47$	41.1962	−	41.1962i	0.876514	−	0.876514i	−0.116658	−	0.993172i	$-0.537218\pi$
$47$	41.1962	−	41.1962i	0.876514	−	0.876514i	0.993172	+	0.116658i	$0.0372182\pi$
$48$	6.92820			0.144338
$49$			34.0718i			0.695343i
$50$	19.7846	−	19.7846i	0.395692	−	0.395692i
$51$			50.7846i			0.995777i
$52$		0			0
$53$	2.28719			0.0431545			0.0215772	−	0.999767i	$-0.493131\pi$
$53$	2.28719			0.0431545			0.0215772	+	0.999767i	$0.493131\pi$
$54$	5.19615	+	5.19615i	0.0962250	+	0.0962250i
$55$	16.3923			0.298042
$56$		−	10.9282i		−	0.195146i
$57$	−19.5167	−	19.5167i	−0.342398	−	0.342398i
$58$	−31.8564	−	31.8564i	−0.549248	−	0.549248i
$59$	−54.6218	+	54.6218i	−0.925793	+	0.925793i	−0.997431	−	0.0716379i	$-0.977177\pi$
$59$	−54.6218	+	54.6218i	−0.925793	+	0.925793i	0.0716379	+	0.997431i	$0.477177\pi$
$60$	−16.3923	+	16.3923i	−0.273205	+	0.273205i
$61$	−7.42563			−0.121732			−0.0608658	−	0.998146i	$-0.519386\pi$
$61$	−7.42563			−0.121732			−0.0608658	+	0.998146i	$0.519386\pi$
$62$			53.9615i			0.870347i
$63$	8.19615	−	8.19615i	0.130098	−	0.130098i
$64$		−	8.00000i		−	0.125000i
$65$		0			0
$66$	−6.00000			−0.0909091
$67$	60.6936	+	60.6936i	0.905874	+	0.905874i	0.995936	−	0.0900619i	$-0.0287065\pi$
$67$	60.6936	+	60.6936i	0.905874	+	0.905874i	−0.0900619	+	0.995936i	$0.528706\pi$
$68$	58.6410			0.862368
$69$			50.7846i			0.736009i
$70$	25.8564	+	25.8564i	0.369377	+	0.369377i
$71$	−38.9090	−	38.9090i	−0.548014	−	0.548014i	0.377852	−	0.925866i	$-0.376663\pi$
$71$	−38.9090	−	38.9090i	−0.548014	−	0.548014i	−0.925866	+	0.377852i	$0.876663\pi$
$72$	6.00000	−	6.00000i	0.0833333	−	0.0833333i
$73$	−40.3205	+	40.3205i	−0.552336	+	0.552336i	−0.927114	−	0.374779i	$-0.877719\pi$
$73$	−40.3205	+	40.3205i	−0.552336	+	0.552336i	0.374779	+	0.927114i	$0.377719\pi$
$74$	−61.7128			−0.833957
$75$		−	34.2679i		−	0.456906i
$76$	−22.5359	+	22.5359i	−0.296525	+	0.296525i
$77$			9.46410i			0.122910i
$78$		0			0
$79$	−148.210			−1.87608			−0.938039	−	0.346528i	$-0.887360\pi$
$79$	−148.210			−1.87608			−0.938039	+	0.346528i	$0.887360\pi$
$80$	18.9282	+	18.9282i	0.236603	+	0.236603i
$81$	9.00000			0.111111
$82$		−	28.8897i		−	0.352314i
$83$	−73.7987	−	73.7987i	−0.889141	−	0.889141i	0.105300	−	0.994441i	$-0.466420\pi$
$83$	−73.7987	−	73.7987i	−0.889141	−	0.889141i	−0.994441	+	0.105300i	$0.966420\pi$
$84$	−9.46410	−	9.46410i	−0.112668	−	0.112668i
$85$	−138.746	+	138.746i	−1.63231	+	1.63231i
$86$	−25.1769	+	25.1769i	−0.292755	+	0.292755i
$87$	−55.1769			−0.634217
$88$			6.92820i			0.0787296i
$89$	−25.5167	+	25.5167i	−0.286704	+	0.286704i	−0.835775	−	0.549071i	$-0.814981\pi$
$89$	−25.5167	+	25.5167i	−0.286704	+	0.286704i	0.549071	+	0.835775i	$0.314981\pi$
$90$			28.3923i			0.315470i
$91$		0			0
$92$	58.6410			0.637402
$93$	46.7321	+	46.7321i	0.502495	+	0.502495i
$94$	−82.3923			−0.876514
$95$		−	106.641i		−	1.12254i
$96$	−6.92820	−	6.92820i	−0.0721688	−	0.0721688i
$97$	86.0333	+	86.0333i	0.886941	+	0.886941i	0.994228	−	0.107287i	$-0.0342163\pi$
$97$	86.0333	+	86.0333i	0.886941	+	0.886941i	−0.107287	+	0.994228i	$0.534216\pi$
$98$	34.0718	−	34.0718i	0.347671	−	0.347671i
$99$	−5.19615	+	5.19615i	−0.0524864	+	0.0524864i
$100$	−39.5692			−0.395692
$101$		−	104.536i		−	1.03501i	−0.855681	−	0.517504i	$-0.826861\pi$
$101$		−	104.536i		−	1.03501i	0.855681	−	0.517504i	$-0.173139\pi$
$102$	50.7846	−	50.7846i	0.497888	−	0.497888i
$103$		−	36.6795i		−	0.356112i	−0.984020	−	0.178056i	$-0.943019\pi$
$103$		−	36.6795i		−	0.356112i	0.984020	−	0.178056i	$-0.0569808\pi$
$104$		0			0
$105$	44.7846			0.426520
$106$	−2.28719	−	2.28719i	−0.0215772	−	0.0215772i
$107$	−123.464			−1.15387			−0.576935	−	0.816790i	$-0.695751\pi$
$107$	−123.464			−1.15387			−0.576935	+	0.816790i	$0.695751\pi$
$108$		−	10.3923i		−	0.0962250i
$109$	−119.315	−	119.315i	−1.09464	−	1.09464i	−0.995027	−	0.0996097i	$-0.968241\pi$
$109$	−119.315	−	119.315i	−1.09464	−	1.09464i	−0.0996097	−	0.995027i	$-0.531759\pi$
$110$	−16.3923	−	16.3923i	−0.149021	−	0.149021i
$111$	−53.4449	+	53.4449i	−0.481485	+	0.481485i
$112$	−10.9282	+	10.9282i	−0.0975732	+	0.0975732i
$113$	−184.277			−1.63077			−0.815384	−	0.578920i	$-0.803474\pi$
$113$	−184.277			−1.63077			−0.815384	+	0.578920i	$0.803474\pi$
$114$			39.0333i			0.342398i
$115$	−138.746	+	138.746i	−1.20649	+	1.20649i
$116$			63.7128i			0.549248i
$117$		0			0
$118$	109.244			0.925793
$119$	−80.1051	−	80.1051i	−0.673152	−	0.673152i
$120$	32.7846			0.273205
$121$			115.000i			0.950413i
$122$	7.42563	+	7.42563i	0.0608658	+	0.0608658i
$123$	−25.0192	−	25.0192i	−0.203408	−	0.203408i
$124$	53.9615	−	53.9615i	0.435174	−	0.435174i
$125$	−24.6795	+	24.6795i	−0.197436	+	0.197436i
$126$	−16.3923			−0.130098
$127$			173.962i			1.36978i	0.728648	+	0.684888i	$0.240149\pi$
$127$			173.962i			1.36978i	−0.728648	+	0.684888i	$0.759851\pi$
$128$	−8.00000	+	8.00000i	−0.0625000	+	0.0625000i
$129$			43.6077i			0.338044i
$130$		0			0
$131$	121.110			0.924506			0.462253	−	0.886748i	$-0.347041\pi$
$131$	121.110			0.924506			0.462253	+	0.886748i	$0.347041\pi$
$132$	6.00000	+	6.00000i	0.0454545	+	0.0454545i
$133$	61.5692			0.462926
$134$		−	121.387i		−	0.905874i
$135$	24.5885	+	24.5885i	0.182137	+	0.182137i
$136$	−58.6410	−	58.6410i	−0.431184	−	0.431184i
$137$	130.053	−	130.053i	0.949289	−	0.949289i	−0.0494861	−	0.998775i	$-0.515758\pi$
$137$	130.053	−	130.053i	0.949289	−	0.949289i	0.998775	+	0.0494861i	$0.0157583\pi$
$138$	50.7846	−	50.7846i	0.368004	−	0.368004i
$139$	−27.1384			−0.195241			−0.0976203	−	0.995224i	$-0.531123\pi$
$139$	−27.1384			−0.195241			−0.0976203	+	0.995224i	$0.531123\pi$
$140$		−	51.7128i		−	0.369377i
$141$	−71.3538	+	71.3538i	−0.506056	+	0.506056i
$142$			77.8179i			0.548014i
$143$		0			0
$144$	−12.0000			−0.0833333
$145$	−150.746	−	150.746i	−1.03963	−	1.03963i
$146$	80.6410			0.552336
$147$		−	59.0141i		−	0.401456i
$148$	61.7128	+	61.7128i	0.416978	+	0.416978i
$149$	168.224	+	168.224i	1.12902	+	1.12902i	0.990336	+	0.138686i	$0.0442878\pi$
$149$	168.224	+	168.224i	1.12902	+	1.12902i	0.138686	+	0.990336i	$0.455712\pi$
$150$	−34.2679	+	34.2679i	−0.228453	+	0.228453i
$151$	38.4064	−	38.4064i	0.254347	−	0.254347i	−0.568403	−	0.822750i	$-0.692439\pi$
$151$	38.4064	−	38.4064i	0.254347	−	0.254347i	0.822750	+	0.568403i	$0.192439\pi$
$152$	45.0718			0.296525
$153$		−	87.9615i		−	0.574912i
$154$	9.46410	−	9.46410i	0.0614552	−	0.0614552i
$155$			255.349i			1.64741i
$156$		0			0
$157$	−227.215			−1.44723			−0.723616	−	0.690203i	$-0.757521\pi$
$157$	−227.215			−1.44723			−0.723616	+	0.690203i	$0.757521\pi$
$158$	148.210	+	148.210i	0.938039	+	0.938039i
$159$	−3.96152			−0.0249152
$160$		−	37.8564i		−	0.236603i
$161$	−80.1051	−	80.1051i	−0.497547	−	0.497547i
$162$	−9.00000	−	9.00000i	−0.0555556	−	0.0555556i
$163$	−12.4449	+	12.4449i	−0.0763489	+	0.0763489i	−0.744250	−	0.667901i	$-0.767193\pi$
$163$	−12.4449	+	12.4449i	−0.0763489	+	0.0763489i	0.667901	+	0.744250i	$0.267193\pi$
$164$	−28.8897	+	28.8897i	−0.176157	+	0.176157i
$165$	−28.3923			−0.172075
$166$			147.597i			0.889141i
$167$	−119.512	+	119.512i	−0.715638	+	0.715638i	−0.967709	−	0.252071i	$-0.918888\pi$
$167$	−119.512	+	119.512i	−0.715638	+	0.715638i	0.252071	+	0.967709i	$0.418888\pi$
$168$			18.9282i			0.112668i
$169$		0			0
$170$	277.492			1.63231
$171$	33.8038	+	33.8038i	0.197683	+	0.197683i
$172$	50.3538			0.292755
$173$		−	69.3975i		−	0.401141i	−0.979679	−	0.200571i	$-0.935720\pi$
$173$		−	69.3975i		−	0.401141i	0.979679	−	0.200571i	$-0.0642796\pi$
$174$	55.1769	+	55.1769i	0.317109	+	0.317109i
$175$	54.0526	+	54.0526i	0.308872	+	0.308872i
$176$	6.92820	−	6.92820i	0.0393648	−	0.0393648i
$177$	94.6077	−	94.6077i	0.534507	−	0.534507i
$178$	51.0333			0.286704
$179$			165.282i			0.923363i	0.887046	+	0.461682i	$0.152754\pi$
$179$			165.282i			0.923363i	−0.887046	+	0.461682i	$0.847246\pi$
$180$	28.3923	−	28.3923i	0.157735	−	0.157735i
$181$		−	283.856i		−	1.56827i	−0.620592	−	0.784134i	$-0.713108\pi$
$181$		−	283.856i		−	1.56827i	0.620592	−	0.784134i	$-0.286892\pi$
$182$		0			0
$183$	12.8616			0.0702818
$184$	−58.6410	−	58.6410i	−0.318701	−	0.318701i
$185$	−292.028			−1.57853
$186$		−	93.4641i		−	0.502495i
$187$	50.7846	+	50.7846i	0.271575	+	0.271575i
$188$	82.3923	+	82.3923i	0.438257	+	0.438257i
$189$	−14.1962	+	14.1962i	−0.0751119	+	0.0751119i
$190$	−106.641	+	106.641i	−0.561269	+	0.561269i
$191$	9.28203			0.0485970			0.0242985	−	0.999705i	$-0.492265\pi$
$191$	9.28203			0.0485970			0.0242985	+	0.999705i	$0.492265\pi$
$192$			13.8564i			0.0721688i
$193$	21.7180	−	21.7180i	0.112528	−	0.112528i	−0.648601	−	0.761129i	$-0.724645\pi$
$193$	21.7180	−	21.7180i	0.112528	−	0.112528i	0.761129	+	0.648601i	$0.224645\pi$
$194$		−	172.067i		−	0.886941i
$195$		0			0
$196$	−68.1436			−0.347671
$197$	112.732	+	112.732i	0.572244	+	0.572244i	0.932755	−	0.360511i	$-0.117398\pi$
$197$	112.732	+	112.732i	0.572244	+	0.572244i	−0.360511	+	0.932755i	$0.617398\pi$
$198$	10.3923			0.0524864
$199$			245.100i			1.23166i	0.787880	+	0.615829i	$0.211179\pi$
$199$			245.100i			1.23166i	−0.787880	+	0.615829i	$0.788821\pi$
$200$	39.5692	+	39.5692i	0.197846	+	0.197846i
$201$	−105.124	−	105.124i	−0.523007	−	0.523007i
$202$	−104.536	+	104.536i	−0.517504	+	0.517504i
$203$	87.0333	−	87.0333i	0.428736	−	0.428736i
$204$	−101.569			−0.497888
$205$		−	136.708i		−	0.666867i
$206$	−36.6795	+	36.6795i	−0.178056	+	0.178056i
$207$		−	87.9615i		−	0.424935i
$208$		0			0
$209$	−39.0333			−0.186762
$210$	−44.7846	−	44.7846i	−0.213260	−	0.213260i
$211$	345.282			1.63641			0.818204	−	0.574928i	$-0.194970\pi$
$211$	345.282			1.63641			0.818204	+	0.574928i	$0.194970\pi$
$212$			4.57437i			0.0215772i
$213$	67.3923	+	67.3923i	0.316396	+	0.316396i
$214$	123.464	+	123.464i	0.576935	+	0.576935i
$215$	−119.138	+	119.138i	−0.554132	+	0.554132i
$216$	−10.3923	+	10.3923i	−0.0481125	+	0.0481125i
$217$	−147.426			−0.679381
$218$			238.631i			1.09464i
$219$	69.8372	−	69.8372i	0.318891	−	0.318891i
$220$			32.7846i			0.149021i
$221$		0			0
$222$	106.890			0.481485
$223$	−170.588	−	170.588i	−0.764971	−	0.764971i	0.212246	−	0.977216i	$-0.431922\pi$
$223$	−170.588	−	170.588i	−0.764971	−	0.764971i	−0.977216	+	0.212246i	$0.931922\pi$
$224$	21.8564			0.0975732
$225$			59.3538i			0.263795i
$226$	184.277	+	184.277i	0.815384	+	0.815384i
$227$	−169.368	−	169.368i	−0.746114	−	0.746114i	0.227633	−	0.973747i	$-0.426901\pi$
$227$	−169.368	−	169.368i	−0.746114	−	0.746114i	−0.973747	+	0.227633i	$0.926901\pi$
$228$	39.0333	−	39.0333i	0.171199	−	0.171199i
$229$	−141.823	+	141.823i	−0.619315	+	0.619315i	−0.945356	−	0.326041i	$-0.894285\pi$
$229$	−141.823	+	141.823i	−0.619315	+	0.619315i	0.326041	+	0.945356i	$0.394285\pi$
$230$	277.492			1.20649
$231$		−	16.3923i		−	0.0709624i
$232$	63.7128	−	63.7128i	0.274624	−	0.274624i
$233$			128.038i			0.549521i	0.961513	+	0.274761i	$0.0885986\pi$
$233$			128.038i			0.549521i	−0.961513	+	0.274761i	$0.911401\pi$
$234$		0			0
$235$	−389.885			−1.65908
$236$	−109.244	−	109.244i	−0.462896	−	0.462896i
$237$	256.708			1.08315
$238$			160.210i			0.673152i
$239$	−88.0192	−	88.0192i	−0.368281	−	0.368281i	0.498569	−	0.866850i	$-0.333859\pi$
$239$	−88.0192	−	88.0192i	−0.368281	−	0.368281i	−0.866850	+	0.498569i	$0.833859\pi$
$240$	−32.7846	−	32.7846i	−0.136603	−	0.136603i
$241$	147.459	−	147.459i	0.611863	−	0.611863i	−0.331568	−	0.943431i	$-0.607578\pi$
$241$	147.459	−	147.459i	0.611863	−	0.611863i	0.943431	+	0.331568i	$0.107578\pi$
$242$	115.000	−	115.000i	0.475207	−	0.475207i
$243$	−15.5885			−0.0641500
$244$		−	14.8513i		−	0.0608658i
$245$	161.229	−	161.229i	0.658079	−	0.658079i
$246$			50.0385i			0.203408i
$247$		0			0
$248$	−107.923			−0.435174
$249$	127.823	+	127.823i	0.513346	+	0.513346i
$250$	49.3590			0.197436
$251$			181.377i			0.722617i	0.932446	+	0.361308i	$0.117670\pi$
$251$			181.377i			0.722617i	−0.932446	+	0.361308i	$0.882330\pi$
$252$	16.3923	+	16.3923i	0.0650488	+	0.0650488i
$253$	50.7846	+	50.7846i	0.200730	+	0.200730i
$254$	173.962	−	173.962i	0.684888	−	0.684888i
$255$	240.315	−	240.315i	0.942413	−	0.942413i
$256$	16.0000			0.0625000
$257$		−	297.664i		−	1.15823i	−0.815247	−	0.579113i	$-0.803399\pi$
$257$		−	297.664i		−	1.15823i	0.815247	−	0.579113i	$-0.196601\pi$
$258$	43.6077	−	43.6077i	0.169022	−	0.169022i
$259$		−	168.603i		−	0.650975i
$260$		0			0
$261$	95.5692			0.366166
$262$	−121.110	−	121.110i	−0.462253	−	0.462253i
$263$	22.8897			0.0870332			0.0435166	−	0.999053i	$-0.486144\pi$
$263$	22.8897			0.0870332			0.0435166	+	0.999053i	$0.486144\pi$
$264$		−	12.0000i		−	0.0454545i
$265$	−10.8231	−	10.8231i	−0.0408418	−	0.0408418i
$266$	−61.5692	−	61.5692i	−0.231463	−	0.231463i
$267$	44.1962	−	44.1962i	0.165529	−	0.165529i
$268$	−121.387	+	121.387i	−0.452937	+	0.452937i
$269$	220.774			0.820722			0.410361	−	0.911923i	$-0.365403\pi$
$269$	220.774			0.820722			0.410361	+	0.911923i	$0.365403\pi$
$270$		−	49.1769i		−	0.182137i
$271$	−148.953	+	148.953i	−0.549641	+	0.549641i	−0.926337	−	0.376696i	$-0.877060\pi$
$271$	−148.953	+	148.953i	−0.549641	+	0.549641i	0.376696	+	0.926337i	$0.377060\pi$
$272$			117.282i			0.431184i
$273$		0			0
$274$	−260.105			−0.949289
$275$	−34.2679	−	34.2679i	−0.124611	−	0.124611i
$276$	−101.569			−0.368004
$277$			27.2154i			0.0982505i	0.998793	+	0.0491253i	$0.0156434\pi$
$277$			27.2154i			0.0982505i	−0.998793	+	0.0491253i	$0.984357\pi$
$278$	27.1384	+	27.1384i	0.0976203	+	0.0976203i
$279$	−80.9423	−	80.9423i	−0.290116	−	0.290116i
$280$	−51.7128	+	51.7128i	−0.184689	+	0.184689i
$281$	51.6218	−	51.6218i	0.183707	−	0.183707i	−0.609262	−	0.792969i	$-0.708534\pi$
$281$	51.6218	−	51.6218i	0.183707	−	0.183707i	0.792969	+	0.609262i	$0.208534\pi$
$282$	142.708			0.506056
$283$		−	93.8076i		−	0.331476i	−0.986170	−	0.165738i	$-0.946999\pi$
$283$		−	93.8076i		−	0.331476i	0.986170	−	0.165738i	$-0.0530006\pi$
$284$	77.8179	−	77.8179i	0.274007	−	0.274007i
$285$			184.708i			0.648097i
$286$		0			0
$287$	78.9282			0.275011
$288$	12.0000	+	12.0000i	0.0416667	+	0.0416667i
$289$	−570.692			−1.97471
$290$			301.492i			1.03963i
$291$	−149.014	−	149.014i	−0.512076	−	0.512076i
$292$	−80.6410	−	80.6410i	−0.276168	−	0.276168i
$293$	120.042	−	120.042i	0.409701	−	0.409701i	−0.471934	−	0.881634i	$-0.656444\pi$
$293$	120.042	−	120.042i	0.409701	−	0.409701i	0.881634	+	0.471934i	$0.156444\pi$
$294$	−59.0141	+	59.0141i	−0.200728	+	0.200728i
$295$	516.946			1.75236
$296$		−	123.426i		−	0.416978i
$297$	9.00000	−	9.00000i	0.0303030	−	0.0303030i
$298$		−	336.449i		−	1.12902i
$299$		0			0
$300$	68.5359			0.228453
$301$	−68.7846	−	68.7846i	−0.228520	−	0.228520i
$302$	−76.8128			−0.254347
$303$			181.061i			0.597563i
$304$	−45.0718	−	45.0718i	−0.148262	−	0.148262i
$305$	35.1384	+	35.1384i	0.115208	+	0.115208i
$306$	−87.9615	+	87.9615i	−0.287456	+	0.287456i
$307$	−7.48849	+	7.48849i	−0.0243925	+	0.0243925i	−0.719198	−	0.694805i	$-0.755491\pi$
$307$	−7.48849	+	7.48849i	−0.0243925	+	0.0243925i	0.694805	+	0.719198i	$0.255491\pi$
$308$	−18.9282			−0.0614552
$309$			63.5307i			0.205601i
$310$	255.349	−	255.349i	0.823705	−	0.823705i
$311$		−	289.377i		−	0.930472i	−0.885187	−	0.465236i	$-0.845969\pi$
$311$		−	289.377i		−	0.930472i	0.885187	−	0.465236i	$-0.154031\pi$
$312$		0			0
$313$	346.841			1.10812			0.554059	−	0.832477i	$-0.313078\pi$
$313$	346.841			1.10812			0.554059	+	0.832477i	$0.313078\pi$
$314$	227.215	+	227.215i	0.723616	+	0.723616i
$315$	−77.5692			−0.246251
$316$		−	296.420i		−	0.938039i
$317$	97.0192	+	97.0192i	0.306054	+	0.306054i	0.843377	−	0.537322i	$-0.180564\pi$
$317$	97.0192	+	97.0192i	0.306054	+	0.306054i	−0.537322	+	0.843377i	$0.680564\pi$
$318$	3.96152	+	3.96152i	0.0124576	+	0.0124576i
$319$	−55.1769	+	55.1769i	−0.172968	+	0.172968i
$320$	−37.8564	+	37.8564i	−0.118301	+	0.118301i
$321$	213.846			0.666187
$322$			160.210i			0.497547i
$323$	330.382	−	330.382i	1.02285	−	1.02285i
$324$			18.0000i			0.0555556i
$325$		0			0
$326$	24.8897			0.0763489
$327$	206.660	+	206.660i	0.631989	+	0.631989i
$328$	57.7795			0.176157
$329$		−	225.100i		−	0.684194i
$330$	28.3923	+	28.3923i	0.0860373	+	0.0860373i
$331$	126.130	+	126.130i	0.381056	+	0.381056i	0.871483	−	0.490427i	$-0.163159\pi$
$331$	126.130	+	126.130i	0.381056	+	0.381056i	−0.490427	+	0.871483i	$0.663159\pi$
$332$	147.597	−	147.597i	0.444570	−	0.444570i
$333$	92.5692	−	92.5692i	0.277986	−	0.277986i
$334$	239.023			0.715638
$335$		−	574.410i		−	1.71466i
$336$	18.9282	−	18.9282i	0.0563339	−	0.0563339i
$337$		−	423.061i		−	1.25538i	−0.778465	−	0.627688i	$-0.784002\pi$
$337$		−	423.061i		−	1.25538i	0.778465	−	0.627688i	$-0.215998\pi$
$338$		0			0
$339$	319.177			0.941525
$340$	−277.492	−	277.492i	−0.816154	−	0.816154i
$341$	93.4641			0.274088
$342$		−	67.6077i		−	0.197683i
$343$	226.956	+	226.956i	0.661680	+	0.661680i
$344$	−50.3538	−	50.3538i	−0.146377	−	0.146377i
$345$	240.315	−	240.315i	0.696566	−	0.696566i
$346$	−69.3975	+	69.3975i	−0.200571	+	0.200571i
$347$	−191.867			−0.552930			−0.276465	−	0.961024i	$-0.589163\pi$
$347$	−191.867			−0.552930			−0.276465	+	0.961024i	$0.589163\pi$
$348$		−	110.354i		−	0.317109i
$349$	−36.7898	+	36.7898i	−0.105415	+	0.105415i	−0.757847	−	0.652432i	$-0.773749\pi$
$349$	−36.7898	+	36.7898i	−0.105415	+	0.105415i	0.652432	+	0.757847i	$0.273749\pi$
$350$		−	108.105i		−	0.308872i
$351$		0			0
$352$	−13.8564			−0.0393648
$353$	−117.870	−	117.870i	−0.333911	−	0.333911i	0.520159	−	0.854070i	$-0.325873\pi$
$353$	−117.870	−	117.870i	−0.333911	−	0.333911i	−0.854070	+	0.520159i	$0.825873\pi$
$354$	−189.215			−0.534507
$355$			368.238i			1.03729i
$356$	−51.0333	−	51.0333i	−0.143352	−	0.143352i
$357$	138.746	+	138.746i	0.388645	+	0.388645i
$358$	165.282	−	165.282i	0.461682	−	0.461682i
$359$	−13.1192	+	13.1192i	−0.0365437	+	0.0365437i	−0.725143	−	0.688599i	$-0.758226\pi$
$359$	−13.1192	+	13.1192i	−0.0365437	+	0.0365437i	0.688599	+	0.725143i	$0.258226\pi$
$360$	−56.7846			−0.157735
$361$		−	107.067i		−	0.296583i
$362$	−283.856	+	283.856i	−0.784134	+	0.784134i
$363$		−	199.186i		−	0.548721i
$364$		0			0
$365$	381.597			1.04547
$366$	−12.8616	−	12.8616i	−0.0351409	−	0.0351409i
$367$	−600.708			−1.63681			−0.818403	−	0.574645i	$-0.805140\pi$
$367$	−600.708			−1.63681			−0.818403	+	0.574645i	$0.805140\pi$
$368$			117.282i			0.318701i
$369$	43.3346	+	43.3346i	0.117438	+	0.117438i
$370$	292.028	+	292.028i	0.789265	+	0.789265i
$371$	6.24871	−	6.24871i	0.0168429	−	0.0168429i
$372$	−93.4641	+	93.4641i	−0.251248	+	0.251248i
$373$	671.836			1.80117			0.900584	−	0.434682i	$-0.143139\pi$
$373$	671.836			1.80117			0.900584	+	0.434682i	$0.143139\pi$
$374$		−	101.569i		−	0.271575i
$375$	42.7461	−	42.7461i	0.113990	−	0.113990i
$376$		−	164.785i		−	0.438257i
$377$		0			0
$378$	28.3923			0.0751119
$379$	−158.799	−	158.799i	−0.418994	−	0.418994i	0.465863	−	0.884857i	$-0.345744\pi$
$379$	−158.799	−	158.799i	−0.418994	−	0.418994i	−0.884857	+	0.465863i	$0.845744\pi$
$380$	213.282			0.561269
$381$		−	301.310i		−	0.790840i
$382$	−9.28203	−	9.28203i	−0.0242985	−	0.0242985i
$383$	−233.445	−	233.445i	−0.609517	−	0.609517i	0.333303	−	0.942820i	$-0.391837\pi$
$383$	−233.445	−	233.445i	−0.609517	−	0.609517i	−0.942820	+	0.333303i	$0.891837\pi$
$384$	13.8564	−	13.8564i	0.0360844	−	0.0360844i
$385$	44.7846	−	44.7846i	0.116324	−	0.116324i
$386$	−43.4359			−0.112528
$387$		−	75.5307i		−	0.195170i
$388$	−172.067	+	172.067i	−0.443471	+	0.443471i
$389$			27.6950i			0.0711953i	0.999366	+	0.0355976i	$0.0113335\pi$
$389$			27.6950i			0.0711953i	−0.999366	+	0.0355976i	$0.988667\pi$
$390$		0			0
$391$	−859.692			−2.19870
$392$	68.1436	+	68.1436i	0.173836	+	0.173836i
$393$	−209.769			−0.533764
$394$		−	225.464i		−	0.572244i
$395$	701.338	+	701.338i	1.77554	+	1.77554i
$396$	−10.3923	−	10.3923i	−0.0262432	−	0.0262432i
$397$	398.692	−	398.692i	1.00426	−	1.00426i	0.00427158	−	0.999991i	$-0.498640\pi$
$397$	398.692	−	398.692i	1.00426	−	1.00426i	0.999991	−	0.00427158i	$-0.00135969\pi$
$398$	245.100	−	245.100i	0.615829	−	0.615829i
$399$	−106.641			−0.267271
$400$		−	79.1384i		−	0.197846i
$401$	139.450	−	139.450i	0.347756	−	0.347756i	−0.511517	−	0.859273i	$-0.670916\pi$
$401$	139.450	−	139.450i	0.347756	−	0.347756i	0.859273	+	0.511517i	$0.170916\pi$
$402$			210.249i			0.523007i
$403$		0			0
$404$	209.072			0.517504
$405$	−42.5885	−	42.5885i	−0.105157	−	0.105157i
$406$	−174.067			−0.428736
$407$			106.890i			0.262628i
$408$	101.569	+	101.569i	0.248944	+	0.248944i
$409$	−401.813	−	401.813i	−0.982427	−	0.982427i	0.0174209	−	0.999848i	$-0.494454\pi$
$409$	−401.813	−	401.813i	−0.982427	−	0.982427i	−0.999848	+	0.0174209i	$0.994454\pi$
$410$	−136.708	+	136.708i	−0.333433	+	0.333433i
$411$	−225.258	+	225.258i	−0.548072	+	0.548072i
$412$	73.3590			0.178056
$413$			298.459i			0.722661i
$414$	−87.9615	+	87.9615i	−0.212467	+	0.212467i
$415$			698.438i			1.68298i
$416$		0			0
$417$	47.0052			0.112722
$418$	39.0333	+	39.0333i	0.0933812	+	0.0933812i
$419$	139.177			0.332164			0.166082	−	0.986112i	$-0.446888\pi$
$419$	139.177			0.332164			0.166082	+	0.986112i	$0.446888\pi$
$420$			89.5692i			0.213260i
$421$	−360.244	−	360.244i	−0.855685	−	0.855685i	0.135141	−	0.990826i	$-0.456851\pi$
$421$	−360.244	−	360.244i	−0.855685	−	0.855685i	−0.990826	+	0.135141i	$0.956851\pi$
$422$	−345.282	−	345.282i	−0.818204	−	0.818204i
$423$	123.588	−	123.588i	0.292171	−	0.292171i
$424$	4.57437	−	4.57437i	0.0107886	−	0.0107886i
$425$	580.095			1.36493
$426$		−	134.785i		−	0.316396i
$427$	−20.2872	+	20.2872i	−0.0475110	+	0.0475110i
$428$		−	246.928i		−	0.576935i
$429$		0			0
$430$	238.277			0.554132
$431$	−213.522	−	213.522i	−0.495410	−	0.495410i	0.414596	−	0.910006i	$-0.363923\pi$
$431$	−213.522	−	213.522i	−0.495410	−	0.495410i	−0.910006	+	0.414596i	$0.863923\pi$
$432$	20.7846			0.0481125
$433$			446.708i			1.03166i	0.856692	+	0.515829i	$0.172516\pi$
$433$			446.708i			1.03166i	−0.856692	+	0.515829i	$0.827484\pi$
$434$	147.426	+	147.426i	0.339690	+	0.339690i
$435$	261.100	+	261.100i	0.600230	+	0.600230i
$436$	238.631	−	238.631i	0.547318	−	0.547318i
$437$	330.382	−	330.382i	0.756023	−	0.756023i
$438$	−139.674			−0.318891
$439$			164.238i			0.374119i	0.982349	+	0.187060i	$0.0598958\pi$
$439$			164.238i			0.374119i	−0.982349	+	0.187060i	$0.940104\pi$
$440$	32.7846	−	32.7846i	0.0745105	−	0.0745105i
$441$			102.215i			0.231781i
$442$		0			0
$443$	−458.736			−1.03552			−0.517761	−	0.855526i	$-0.673234\pi$
$443$	−458.736			−1.03552			−0.517761	+	0.855526i	$0.673234\pi$
$444$	−106.890	−	106.890i	−0.240743	−	0.240743i
$445$	241.492			0.542679
$446$			341.177i			0.764971i
$447$	−291.373	−	291.373i	−0.651841	−	0.651841i
$448$	−21.8564	−	21.8564i	−0.0487866	−	0.0487866i
$449$	−221.776	+	221.776i	−0.493932	+	0.493932i	−0.909543	−	0.415610i	$-0.863568\pi$
$449$	−221.776	+	221.776i	−0.493932	+	0.493932i	0.415610	+	0.909543i	$0.363568\pi$
$450$	59.3538	−	59.3538i	0.131897	−	0.131897i
$451$	−50.0385			−0.110950
$452$		−	368.554i		−	0.815384i
$453$	−66.5218	+	66.5218i	−0.146847	+	0.146847i
$454$			338.736i			0.746114i
$455$		0			0
$456$	−78.0666			−0.171199
$457$	−52.9615	−	52.9615i	−0.115890	−	0.115890i	0.646784	−	0.762673i	$-0.276114\pi$
$457$	−52.9615	−	52.9615i	−0.115890	−	0.115890i	−0.762673	+	0.646784i	$0.776114\pi$
$458$	283.646			0.619315
$459$			152.354i			0.331926i
$460$	−277.492	−	277.492i	−0.603244	−	0.603244i
$461$	−67.4500	−	67.4500i	−0.146312	−	0.146312i	0.630156	−	0.776468i	$-0.282991\pi$
$461$	−67.4500	−	67.4500i	−0.146312	−	0.146312i	−0.776468	+	0.630156i	$0.782991\pi$
$462$	−16.3923	+	16.3923i	−0.0354812	+	0.0354812i
$463$	−549.247	+	549.247i	−1.18628	+	1.18628i	−0.208191	+	0.978088i	$0.566758\pi$
$463$	−549.247	+	549.247i	−1.18628	+	1.18628i	−0.978088	+	0.208191i	$0.933242\pi$
$464$	−127.426			−0.274624
$465$		−	442.277i		−	0.951133i
$466$	128.038	−	128.038i	0.274761	−	0.274761i
$467$		−	30.1821i		−	0.0646297i	−0.999478	−	0.0323148i	$-0.989712\pi$
$467$		−	30.1821i		−	0.0646297i	0.999478	−	0.0323148i	$-0.0102879\pi$
$468$		0			0
$469$	331.636			0.707113
$470$	389.885	+	389.885i	0.829542	+	0.829542i
$471$	393.549			0.835560
$472$			218.487i			0.462896i
$473$	43.6077	+	43.6077i	0.0921939	+	0.0921939i
$474$	−256.708	−	256.708i	−0.541577	−	0.541577i
$475$	−222.932	+	222.932i	−0.469330	+	0.469330i
$476$	160.210	−	160.210i	0.336576	−	0.336576i
$477$	6.86156			0.0143848
$478$			176.038i			0.368281i
$479$	258.870	−	258.870i	0.540439	−	0.540439i	−0.383218	−	0.923658i	$-0.625184\pi$
$479$	258.870	−	258.870i	0.540439	−	0.540439i	0.923658	+	0.383218i	$0.125184\pi$
$480$			65.5692i			0.136603i
$481$		0			0
$482$	−294.918			−0.611863
$483$	138.746	+	138.746i	0.287259	+	0.287259i
$484$	−230.000			−0.475207
$485$		−	814.228i		−	1.67882i
$486$	15.5885	+	15.5885i	0.0320750	+	0.0320750i
$487$	274.560	+	274.560i	0.563779	+	0.563779i	0.930379	−	0.366600i	$-0.119478\pi$
$487$	274.560	+	274.560i	0.563779	+	0.563779i	−0.366600	+	0.930379i	$0.619478\pi$
$488$	−14.8513	+	14.8513i	−0.0304329	+	0.0304329i
$489$	21.5551	−	21.5551i	0.0440800	−	0.0440800i
$490$	−322.459			−0.658079
$491$			220.726i			0.449543i	0.974412	+	0.224771i	$0.0721635\pi$
$491$			220.726i			0.449543i	−0.974412	+	0.224771i	$0.927836\pi$
$492$	50.0385	−	50.0385i	0.101704	−	0.101704i
$493$		−	934.046i		−	1.89462i
$494$		0			0
$495$	49.1769			0.0993473
$496$	107.923	+	107.923i	0.217587	+	0.217587i
$497$	−212.603			−0.427772
$498$		−	255.646i		−	0.513346i
$499$	625.065	+	625.065i	1.25264	+	1.25264i	0.954534	+	0.298102i	$0.0963534\pi$
$499$	625.065	+	625.065i	1.25264	+	1.25264i	0.298102	+	0.954534i	$0.403647\pi$
$500$	−49.3590	−	49.3590i	−0.0987180	−	0.0987180i
$501$	207.000	−	207.000i	0.413174	−	0.413174i
$502$	181.377	−	181.377i	0.361308	−	0.361308i
$503$	−696.018			−1.38373			−0.691867	−	0.722025i	$-0.743211\pi$
$503$	−696.018			−1.38373			−0.691867	+	0.722025i	$0.743211\pi$
$504$		−	32.7846i		−	0.0650488i
$505$	−494.669	+	494.669i	−0.979543	+	0.979543i
$506$		−	101.569i		−	0.200730i
$507$		0			0
$508$	−347.923			−0.684888
$509$	−401.678	−	401.678i	−0.789151	−	0.789151i	0.192204	−	0.981355i	$-0.438437\pi$
$509$	−401.678	−	401.678i	−0.789151	−	0.789151i	−0.981355	+	0.192204i	$0.938437\pi$
$510$	−480.631			−0.942413
$511$			220.315i			0.431146i
$512$	−16.0000	−	16.0000i	−0.0312500	−	0.0312500i
$513$	−58.5500	−	58.5500i	−0.114133	−	0.114133i
$514$	−297.664	+	297.664i	−0.579113	+	0.579113i
$515$	−173.569	+	173.569i	−0.337028	+	0.337028i
$516$	−87.2154			−0.169022
$517$			142.708i			0.276030i
$518$	−168.603	+	168.603i	−0.325488	+	0.325488i
$519$			120.200i			0.231599i
$520$		0			0
$521$	−602.651			−1.15672			−0.578360	−	0.815782i	$-0.696307\pi$
$521$	−602.651			−1.15672			−0.578360	+	0.815782i	$0.696307\pi$
$522$	−95.5692	−	95.5692i	−0.183083	−	0.183083i
$523$	854.677			1.63418			0.817091	−	0.576509i	$-0.195586\pi$
$523$	854.677			1.63418			0.817091	+	0.576509i	$0.195586\pi$
$524$			242.221i			0.462253i
$525$	−93.6218	−	93.6218i	−0.178327	−	0.178327i
$526$	−22.8897	−	22.8897i	−0.0435166	−	0.0435166i
$527$	−791.090	+	791.090i	−1.50112	+	1.50112i
$528$	−12.0000	+	12.0000i	−0.0227273	+	0.0227273i
$529$	−330.692			−0.625127
$530$			21.6462i			0.0408418i
$531$	−163.865	+	163.865i	−0.308598	+	0.308598i
$532$			123.138i			0.231463i
$533$		0			0
$534$	−88.3923			−0.165529
$535$	584.238	+	584.238i	1.09203	+	1.09203i
$536$	242.774			0.452937
$537$		−	286.277i		−	0.533104i
$538$	−220.774	−	220.774i	−0.410361	−	0.410361i
$539$	−59.0141	−	59.0141i	−0.109488	−	0.109488i
$540$	−49.1769	+	49.1769i	−0.0910684	+	0.0910684i
$541$	344.244	−	344.244i	0.636310	−	0.636310i	−0.313333	−	0.949643i	$-0.601446\pi$
$541$	344.244	−	344.244i	0.636310	−	0.636310i	0.949643	+	0.313333i	$0.101446\pi$
$542$	297.905			0.549641
$543$			491.654i			0.905440i
$544$	117.282	−	117.282i	0.215592	−	0.215592i
$545$			1129.21i			2.07195i
$546$		0			0
$547$	842.200			1.53967			0.769835	−	0.638242i	$-0.220338\pi$
$547$	842.200			1.53967			0.769835	+	0.638242i	$0.220338\pi$
$548$	260.105	+	260.105i	0.474644	+	0.474644i
$549$	−22.2769			−0.0405772
$550$			68.5359i			0.124611i
$551$	358.956	+	358.956i	0.651463	+	0.651463i
$552$	101.569	+	101.569i	0.184002	+	0.184002i
$553$	−404.918	+	404.918i	−0.732220	+	0.732220i
$554$	27.2154	−	27.2154i	0.0491253	−	0.0491253i
$555$	505.808			0.911365
$556$		−	54.2769i		−	0.0976203i
$557$	−99.2576	+	99.2576i	−0.178200	+	0.178200i	−0.790571	−	0.612370i	$-0.790216\pi$
$557$	−99.2576	+	99.2576i	−0.178200	+	0.178200i	0.612370	+	0.790571i	$0.290216\pi$
$558$			161.885i			0.290116i
$559$		0			0
$560$	103.426			0.184689
$561$	−87.9615	−	87.9615i	−0.156794	−	0.156794i
$562$	−103.244			−0.183707
$563$			647.174i			1.14951i	0.818326	+	0.574755i	$0.194903\pi$
$563$			647.174i			1.14951i	−0.818326	+	0.574755i	$0.805097\pi$
$564$	−142.708	−	142.708i	−0.253028	−	0.253028i
$565$	872.008	+	872.008i	1.54338	+	1.54338i
$566$	−93.8076	+	93.8076i	−0.165738	+	0.165738i
$567$	24.5885	−	24.5885i	0.0433659	−	0.0433659i
$568$	−155.636			−0.274007
$569$			701.223i			1.23238i	0.787598	+	0.616189i	$0.211324\pi$
$569$			701.223i			1.23238i	−0.787598	+	0.616189i	$0.788676\pi$
$570$	184.708	−	184.708i	0.324049	−	0.324049i
$571$			218.746i			0.383093i	0.981484	+	0.191547i	$0.0613503\pi$
$571$			218.746i			0.383093i	−0.981484	+	0.191547i	$0.938650\pi$
$572$		0			0
$573$	−16.0770			−0.0280575
$574$	−78.9282	−	78.9282i	−0.137506	−	0.137506i
$575$	580.095			1.00886
$576$		−	24.0000i		−	0.0416667i
$577$	12.3590	+	12.3590i	0.0214194	+	0.0214194i	0.717735	−	0.696316i	$-0.245179\pi$
$577$	12.3590	+	12.3590i	0.0214194	+	0.0214194i	−0.696316	+	0.717735i	$0.745179\pi$
$578$	570.692	+	570.692i	0.987357	+	0.987357i
$579$	−37.6166	+	37.6166i	−0.0649683	+	0.0649683i
$580$	301.492	−	301.492i	0.519814	−	0.519814i
$581$	−403.244			−0.694051
$582$			298.028i			0.512076i
$583$	−3.96152	+	3.96152i	−0.00679507	+	0.00679507i
$584$			161.282i			0.276168i
$585$		0			0
$586$	−240.084			−0.409701
$587$	106.219	+	106.219i	0.180953	+	0.180953i	0.791771	−	0.610818i	$-0.209159\pi$
$587$	106.219	+	106.219i	0.180953	+	0.180953i	−0.610818	+	0.791771i	$0.709159\pi$
$588$	118.028			0.200728
$589$		−	608.036i		−	1.03232i
$590$	−516.946	−	516.946i	−0.876180	−	0.876180i
$591$	−195.258	−	195.258i	−0.330385	−	0.330385i
$592$	−123.426	+	123.426i	−0.208489	+	0.208489i
$593$	−770.645	+	770.645i	−1.29957	+	1.29957i	−0.370895	+	0.928675i	$0.620949\pi$
$593$	−770.645	+	770.645i	−1.29957	+	1.29957i	−0.928675	+	0.370895i	$0.879051\pi$
$594$	−18.0000			−0.0303030
$595$			758.123i			1.27416i
$596$	−336.449	+	336.449i	−0.564511	+	0.564511i
$597$		−	424.526i		−	0.711098i
$598$		0			0
$599$	−130.392			−0.217683			−0.108842	−	0.994059i	$-0.534714\pi$
$599$	−130.392			−0.217683			−0.108842	+	0.994059i	$0.534714\pi$
$600$	−68.5359	−	68.5359i	−0.114226	−	0.114226i
$601$	−551.108			−0.916984			−0.458492	−	0.888698i	$-0.651610\pi$
$601$	−551.108			−0.916984			−0.458492	+	0.888698i	$0.651610\pi$
$602$			137.569i			0.228520i
$603$	182.081	+	182.081i	0.301958	+	0.301958i
$604$	76.8128	+	76.8128i	0.127173	+	0.127173i
$605$	544.186	−	544.186i	0.899481	−	0.899481i
$606$	181.061	−	181.061i	0.298781	−	0.298781i
$607$	63.6001			0.104778			0.0523889	−	0.998627i	$-0.483316\pi$
$607$	63.6001			0.104778			0.0523889	+	0.998627i	$0.483316\pi$
$608$			90.1436i			0.148262i
$609$	−150.746	+	150.746i	−0.247531	+	0.247531i
$610$		−	70.2769i		−	0.115208i
$611$		0			0
$612$	175.923			0.287456
$613$	26.3487	+	26.3487i	0.0429832	+	0.0429832i	0.728272	−	0.685289i	$-0.240324\pi$
$613$	26.3487	+	26.3487i	0.0429832	+	0.0429832i	−0.685289	+	0.728272i	$0.740324\pi$
$614$	14.9770			0.0243925
$615$			236.785i			0.385016i
$616$	18.9282	+	18.9282i	0.0307276	+	0.0307276i
$617$	−375.391	−	375.391i	−0.608413	−	0.608413i	0.334118	−	0.942531i	$-0.391562\pi$
$617$	−375.391	−	375.391i	−0.608413	−	0.608413i	−0.942531	+	0.334118i	$0.891562\pi$
$618$	63.5307	−	63.5307i	0.102801	−	0.102801i
$619$	−264.070	+	264.070i	−0.426608	+	0.426608i	−0.887471	−	0.460863i	$-0.847540\pi$
$619$	−264.070	+	264.070i	−0.426608	+	0.426608i	0.460863	+	0.887471i	$0.347540\pi$
$620$	−510.697			−0.823705
$621$			152.354i			0.245336i
$622$	−289.377	+	289.377i	−0.465236	+	0.465236i
$623$			139.426i			0.223797i
$624$		0			0
$625$	728.184			1.16510
$626$	−346.841	−	346.841i	−0.554059	−	0.554059i
$627$	67.6077			0.107827
$628$		−	454.431i		−	0.723616i
$629$	−904.726	−	904.726i	−1.43836	−	1.43836i
$630$	77.5692	+	77.5692i	0.123126	+	0.123126i
$631$	441.594	−	441.594i	0.699831	−	0.699831i	−0.264543	−	0.964374i	$-0.585221\pi$
$631$	441.594	−	441.594i	0.699831	−	0.699831i	0.964374	+	0.264543i	$0.0852210\pi$
$632$	−296.420	+	296.420i	−0.469020	+	0.469020i
$633$	−598.046			−0.944780
$634$		−	194.038i		−	0.306054i
$635$	823.195	−	823.195i	1.29637	−	1.29637i
$636$		−	7.92305i		−	0.0124576i
$637$		0			0
$638$	110.354			0.172968
$639$	−116.727	−	116.727i	−0.182671	−	0.182671i
$640$	75.7128			0.118301
$641$		−	829.910i		−	1.29471i	−0.762188	−	0.647356i	$-0.775875\pi$
$641$		−	829.910i		−	1.29471i	0.762188	−	0.647356i	$-0.224125\pi$
$642$	−213.846	−	213.846i	−0.333094	−	0.333094i
$643$	−424.196	−	424.196i	−0.659714	−	0.659714i	0.295598	−	0.955312i	$-0.404481\pi$
$643$	−424.196	−	424.196i	−0.659714	−	0.659714i	−0.955312	+	0.295598i	$0.904481\pi$
$644$	160.210	−	160.210i	0.248774	−	0.248774i
$645$	206.354	−	206.354i	0.319928	−	0.319928i
$646$	−660.764			−1.02285
$647$			477.913i			0.738660i	0.929298	+	0.369330i	$0.120413\pi$
$647$			477.913i			0.738660i	−0.929298	+	0.369330i	$0.879587\pi$
$648$	18.0000	−	18.0000i	0.0277778	−	0.0277778i
$649$		−	189.215i		−	0.291549i
$650$		0			0
$651$	255.349			0.392241
$652$	−24.8897	−	24.8897i	−0.0381744	−	0.0381744i
$653$	−243.380			−0.372710			−0.186355	−	0.982482i	$-0.559667\pi$
$653$	−243.380			−0.372710			−0.186355	+	0.982482i	$0.559667\pi$
$654$		−	413.321i		−	0.631989i
$655$	−573.100	−	573.100i	−0.874962	−	0.874962i
$656$	−57.7795	−	57.7795i	−0.0880784	−	0.0880784i
$657$	−120.962	+	120.962i	−0.184112	+	0.184112i
$658$	−225.100	+	225.100i	−0.342097	+	0.342097i
$659$	−190.677			−0.289343			−0.144671	−	0.989480i	$-0.546212\pi$
$659$	−190.677			−0.289343			−0.144671	+	0.989480i	$0.546212\pi$
$660$		−	56.7846i		−	0.0860373i
$661$	446.149	−	446.149i	0.674960	−	0.674960i	−0.283895	−	0.958855i	$-0.591627\pi$
$661$	446.149	−	446.149i	0.674960	−	0.674960i	0.958855	+	0.283895i	$0.0916267\pi$
$662$		−	252.259i		−	0.381056i
$663$		0			0
$664$	−295.195			−0.444570
$665$	−291.349	−	291.349i	−0.438118	−	0.438118i
$666$	−185.138			−0.277986
$667$		−	934.046i		−	1.40037i
$668$	−239.023	−	239.023i	−0.357819	−	0.357819i
$669$	295.468	+	295.468i	0.441656	+	0.441656i
$670$	−574.410	+	574.410i	−0.857329	+	0.857329i
$671$	12.8616	−	12.8616i	0.0191678	−	0.0191678i
$672$	−37.8564			−0.0563339
$673$		−	176.221i		−	0.261843i	−0.991393	−	0.130922i	$-0.958206\pi$
$673$		−	176.221i		−	0.261843i	0.991393	−	0.130922i	$-0.0417936\pi$
$674$	−423.061	+	423.061i	−0.627688	+	0.627688i
$675$		−	102.804i		−	0.152302i
$676$		0			0
$677$	672.600			0.993500			0.496750	−	0.867894i	$-0.334527\pi$
$677$	672.600			0.993500			0.496750	+	0.867894i	$0.334527\pi$
$678$	−319.177	−	319.177i	−0.470762	−	0.470762i
$679$	470.095			0.692334
$680$			554.985i			0.816154i
$681$	293.354	+	293.354i	0.430769	+	0.430769i
$682$	−93.4641	−	93.4641i	−0.137044	−	0.137044i
$683$	−306.191	+	306.191i	−0.448303	+	0.448303i	−0.894790	−	0.446487i	$-0.852675\pi$
$683$	−306.191	+	306.191i	−0.448303	+	0.448303i	0.446487	+	0.894790i	$0.352675\pi$
$684$	−67.6077	+	67.6077i	−0.0988417	+	0.0988417i
$685$	−1230.83			−1.79683
$686$		−	453.913i		−	0.661680i
$687$	245.645	−	245.645i	0.357562	−	0.357562i
$688$			100.708i			0.146377i
$689$		0			0
$690$	−480.631			−0.696566
$691$	474.865	+	474.865i	0.687215	+	0.687215i	0.961615	−	0.274401i	$-0.0884795\pi$
$691$	474.865	+	474.865i	0.687215	+	0.687215i	−0.274401	+	0.961615i	$0.588479\pi$
$692$	138.795			0.200571
$693$			28.3923i			0.0409701i
$694$	191.867	+	191.867i	0.276465	+	0.276465i
$695$	128.420	+	128.420i	0.184778	+	0.184778i
$696$	−110.354	+	110.354i	−0.158554	+	0.158554i
$697$	423.531	−	423.531i	0.607648	−	0.607648i
$698$	73.5795			0.105415
$699$		−	221.769i		−	0.317266i
$700$	−108.105	+	108.105i	−0.154436	+	0.154436i
$701$			204.480i			0.291697i	0.989307	+	0.145848i	$0.0465912\pi$
$701$			204.480i			0.291697i	−0.989307	+	0.145848i	$0.953409\pi$
$702$		0			0
$703$	695.377			0.989156
$704$	13.8564	+	13.8564i	0.0196824	+	0.0196824i
$705$	675.300			0.957872
$706$			235.741i			0.333911i
$707$	−285.597	−	285.597i	−0.403957	−	0.403957i
$708$	189.215	+	189.215i	0.267253	+	0.267253i
$709$	629.018	−	629.018i	0.887190	−	0.887190i	−0.107062	−	0.994252i	$-0.534144\pi$
$709$	629.018	−	629.018i	0.887190	−	0.887190i	0.994252	+	0.107062i	$0.0341444\pi$
$710$	368.238	−	368.238i	0.518646	−	0.518646i
$711$	−444.631			−0.625360
$712$			102.067i			0.143352i
$713$	−791.090	+	791.090i	−1.10952	+	1.10952i
$714$		−	277.492i		−	0.388645i
$715$		0			0
$716$	−330.564			−0.461682
$717$	152.454	+	152.454i	0.212627	+	0.212627i
$718$	26.2384			0.0365437
$719$		−	863.290i		−	1.20068i	−0.799745	−	0.600340i	$-0.795032\pi$
$719$		−	863.290i		−	1.20068i	0.799745	−	0.600340i	$-0.204968\pi$
$720$	56.7846	+	56.7846i	0.0788675	+	0.0788675i
$721$	−100.210	−	100.210i	−0.138988	−	0.138988i
$722$	−107.067	+	107.067i	−0.148292	+	0.148292i
$723$	−255.406	+	255.406i	−0.353259	+	0.353259i
$724$	567.713			0.784134
$725$			630.267i			0.869333i
$726$	−199.186	+	199.186i	−0.274361	+	0.274361i
$727$			605.577i			0.832980i	0.909140	+	0.416490i	$0.136740\pi$
$727$			605.577i			0.832980i	−0.909140	+	0.416490i	$0.863260\pi$
$728$		0			0
$729$	27.0000			0.0370370
$730$	−381.597	−	381.597i	−0.522736	−	0.522736i
$731$	−738.200			−1.00985
$732$			25.7231i			0.0351409i
$733$	−205.946	−	205.946i	−0.280963	−	0.280963i	0.552530	−	0.833493i	$-0.313663\pi$
$733$	−205.946	−	205.946i	−0.280963	−	0.280963i	−0.833493	+	0.552530i	$0.813663\pi$
$734$	600.708	+	600.708i	0.818403	+	0.818403i
$735$	−279.258	+	279.258i	−0.379942	+	0.379942i
$736$	117.282	−	117.282i	0.159351	−	0.159351i
$737$	−210.249			−0.285276
$738$		−	86.6692i		−	0.117438i
$739$	58.7884	−	58.7884i	0.0795513	−	0.0795513i	−0.666212	−	0.745763i	$-0.732085\pi$
$739$	58.7884	−	58.7884i	0.0795513	−	0.0795513i	0.745763	+	0.666212i	$0.232085\pi$
$740$		−	584.056i		−	0.789265i
$741$		0			0
$742$	−12.4974			−0.0168429
$743$	885.509	+	885.509i	1.19180	+	1.19180i	0.976561	+	0.215241i	$0.0690536\pi$
$743$	885.509	+	885.509i	1.19180	+	1.19180i	0.215241	+	0.976561i	$0.430946\pi$
$744$	186.928			0.251248
$745$		−	1592.09i		−	2.13704i
$746$	−671.836	−	671.836i	−0.900584	−	0.900584i
$747$	−221.396	−	221.396i	−0.296380	−	0.296380i
$748$	−101.569	+	101.569i	−0.135788	+	0.135788i
$749$	−337.310	+	337.310i	−0.450347	+	0.450347i
$750$	−85.4923			−0.113990
$751$		−	19.5720i		−	0.0260612i	−0.999915	−	0.0130306i	$-0.995852\pi$
$751$		−	19.5720i		−	0.0260612i	0.999915	−	0.0130306i	$-0.00414789\pi$
$752$	−164.785	+	164.785i	−0.219128	+	0.219128i
$753$		−	314.154i		−	0.417203i
$754$		0			0
$755$	−363.482			−0.481433
$756$	−28.3923	−	28.3923i	−0.0375560	−	0.0375560i
$757$	677.836			0.895424			0.447712	−	0.894178i	$-0.352239\pi$
$757$	677.836			0.895424			0.447712	+	0.894178i	$0.352239\pi$
$758$			317.597i			0.418994i
$759$	−87.9615	−	87.9615i	−0.115891	−	0.115891i
$760$	−213.282	−	213.282i	−0.280634	−	0.280634i
$761$	62.4449	−	62.4449i	0.0820563	−	0.0820563i	−0.664887	−	0.746944i	$-0.731520\pi$
$761$	62.4449	−	62.4449i	0.0820563	−	0.0820563i	0.746944	+	0.664887i	$0.231520\pi$
$762$	−301.310	+	301.310i	−0.395420	+	0.395420i
$763$	−651.951			−0.854458
$764$			18.5641i			0.0242985i
$765$	−416.238	+	416.238i	−0.544102	+	0.544102i
$766$			466.890i			0.609517i
$767$		0			0
$768$	−27.7128			−0.0360844
$769$	71.5950	+	71.5950i	0.0931014	+	0.0931014i	0.752124	−	0.659022i	$-0.229030\pi$
$769$	71.5950	+	71.5950i	0.0931014	+	0.0931014i	−0.659022	+	0.752124i	$0.729030\pi$
$770$	−89.5692			−0.116324
$771$			515.569i			0.668702i
$772$	43.4359	+	43.4359i	0.0562642	+	0.0562642i
$773$	778.817	+	778.817i	1.00752	+	1.00752i	0.999971	+	0.00755317i	$0.00240427\pi$
$773$	778.817	+	778.817i	1.00752	+	1.00752i	0.00755317	+	0.999971i	$0.497596\pi$
$774$	−75.5307	+	75.5307i	−0.0975849	+	0.0975849i
$775$	533.804	−	533.804i	0.688779	−	0.688779i
$776$	344.133			0.443471
$777$			292.028i			0.375841i
$778$	27.6950	−	27.6950i	0.0355976	−	0.0355976i
$779$			325.528i			0.417879i
$780$		0			0
$781$	134.785			0.172580
$782$	859.692	+	859.692i	1.09935	+	1.09935i
$783$	−165.531			−0.211406
$784$		−	136.287i		−	0.173836i
$785$	1075.19	+	1075.19i	1.36967	+	1.36967i
$786$	209.769	+	209.769i	0.266882	+	0.266882i
$787$	−548.883	+	548.883i	−0.697437	+	0.697437i	−0.963857	−	0.266420i	$-0.914159\pi$
$787$	−548.883	+	548.883i	−0.697437	+	0.697437i	0.266420	+	0.963857i	$0.414159\pi$
$788$	−225.464	+	225.464i	−0.286122	+	0.286122i
$789$	−39.6462			−0.0502486
$790$		−	1402.68i		−	1.77554i
$791$	−503.454	+	503.454i	−0.636478	+	0.636478i
$792$			20.7846i			0.0262432i
$793$		0			0
$794$	−797.384			−1.00426
$795$	18.7461	+	18.7461i	0.0235800	+	0.0235800i
$796$	−490.200			−0.615829
$797$		−	41.5871i		−	0.0521795i	−0.999660	−	0.0260898i	$-0.991694\pi$
$797$		−	41.5871i		−	0.0521795i	0.999660	−	0.0260898i	$-0.00830557\pi$
$798$	106.641	+	106.641i	0.133635	+	0.133635i
$799$	−1207.89	−	1207.89i	−1.51175	−	1.51175i
$800$	−79.1384	+	79.1384i	−0.0989230	+	0.0989230i
$801$	−76.5500	+	76.5500i	−0.0955680	+	0.0955680i
$802$	−278.900			−0.347756
$803$		−	139.674i		−	0.173941i
$804$	210.249	−	210.249i	0.261503	−	0.261503i
$805$			758.123i			0.941768i
$806$		0			0
$807$	−382.392			−0.473844
$808$	−209.072	−	209.072i	−0.258752	−	0.258752i
$809$	−1338.40			−1.65439			−0.827194	−	0.561916i	$-0.810064\pi$
$809$	−1338.40			−1.65439			−0.827194	+	0.561916i	$0.810064\pi$
$810$			85.1769i			0.105157i
$811$	−257.258	−	257.258i	−0.317210	−	0.317210i	0.530484	−	0.847695i	$-0.322010\pi$
$811$	−257.258	−	257.258i	−0.317210	−	0.317210i	−0.847695	+	0.530484i	$0.822010\pi$
$812$	174.067	+	174.067i	0.214368	+	0.214368i
$813$	257.993	−	257.993i	0.317335	−	0.317335i
$814$	106.890	−	106.890i	0.131314	−	0.131314i
$815$	117.779			0.144515
$816$		−	203.138i		−	0.248944i
$817$	283.692	−	283.692i	0.347236	−	0.347236i
$818$			803.626i			0.982427i
$819$		0			0
$820$	273.415			0.333433
$821$	306.873	+	306.873i	0.373779	+	0.373779i	0.868852	−	0.495072i	$-0.164858\pi$
$821$	306.873	+	306.873i	0.373779	+	0.373779i	−0.495072	+	0.868852i	$0.664858\pi$
$822$	450.515			0.548072
$823$			1037.92i			1.26114i	0.776131	+	0.630571i	$0.217179\pi$
$823$			1037.92i			1.26114i	−0.776131	+	0.630571i	$0.782821\pi$
$824$	−73.3590	−	73.3590i	−0.0890279	−	0.0890279i
$825$	59.3538	+	59.3538i	0.0719440	+	0.0719440i
$826$	298.459	−	298.459i	0.361330	−	0.361330i
$827$	−658.153	+	658.153i	−0.795831	+	0.795831i	−0.982435	−	0.186604i	$-0.940252\pi$
$827$	−658.153	+	658.153i	−0.795831	+	0.795831i	0.186604	+	0.982435i	$0.440252\pi$
$828$	175.923			0.212467
$829$			372.354i			0.449160i	0.974456	+	0.224580i	$0.0721010\pi$
$829$			372.354i			0.449160i	−0.974456	+	0.224580i	$0.927899\pi$
$830$	698.438	−	698.438i	0.841492	−	0.841492i
$831$		−	47.1384i		−	0.0567250i
$832$		0			0
$833$	999.002			1.19928
$834$	−47.0052	−	47.0052i	−0.0563611	−	0.0563611i
$835$	1131.07			1.35457
$836$		−	78.0666i		−	0.0933812i
$837$	140.196	+	140.196i	0.167498	+	0.167498i
$838$	−139.177	−	139.177i	−0.166082	−	0.166082i
$839$	−1018.87	+	1018.87i	−1.21438	+	1.21438i	−0.244813	+	0.969570i	$0.578727\pi$
$839$	−1018.87	+	1018.87i	−1.21438	+	1.21438i	−0.969570	+	0.244813i	$0.921273\pi$
$840$	89.5692	−	89.5692i	0.106630	−	0.106630i
$841$	173.831			0.206695
$842$			720.487i			0.855685i
$843$	−89.4115	+	89.4115i	−0.106064	+	0.106064i
$844$			690.564i			0.818204i
$845$		0			0
$846$	−247.177			−0.292171
$847$	314.186	+	314.186i	0.370940	+	0.370940i
$848$	−9.14875			−0.0107886
$849$			162.480i			0.191378i
$850$	−580.095	−	580.095i	−0.682464	−	0.682464i
$851$	−904.726	−	904.726i	−1.06313	−	1.06313i
$852$	−134.785	+	134.785i	−0.158198	+	0.158198i
$853$	366.790	−	366.790i	0.430000	−	0.430000i	−0.458628	−	0.888628i	$-0.651659\pi$
$853$	366.790	−	366.790i	0.430000	−	0.430000i	0.888628	+	0.458628i	$0.151659\pi$
$854$	40.5744			0.0475110
$855$		−	319.923i		−	0.374179i
$856$	−246.928	+	246.928i	−0.288468	+	0.288468i
$857$		−	469.244i		−	0.547542i	−0.961795	−	0.273771i	$-0.911729\pi$
$857$		−	469.244i		−	0.547542i	0.961795	−	0.273771i	$-0.0882711\pi$
$858$		0			0
$859$	−1238.66			−1.44197			−0.720987	−	0.692948i	$-0.756311\pi$
$859$	−1238.66			−1.44197			−0.720987	+	0.692948i	$0.756311\pi$
$860$	−238.277	−	238.277i	−0.277066	−	0.277066i
$861$	−136.708			−0.158778
$862$			427.044i			0.495410i
$863$	5.71143	+	5.71143i	0.00661811	+	0.00661811i	0.710408	−	0.703790i	$-0.248510\pi$
$863$	5.71143	+	5.71143i	0.00661811	+	0.00661811i	−0.703790	+	0.710408i	$0.748510\pi$
$864$	−20.7846	−	20.7846i	−0.0240563	−	0.0240563i
$865$	−328.392	+	328.392i	−0.379644	+	0.379644i
$866$	446.708	−	446.708i	0.515829	−	0.515829i
$867$	988.468			1.14010
$868$		−	294.851i		−	0.339690i
$869$	256.708	−	256.708i	0.295406	−	0.295406i
$870$		−	522.200i		−	0.600230i
$871$		0			0
$872$	−477.261			−0.547318
$873$	258.100	+	258.100i	0.295647	+	0.295647i
$874$	−660.764			−0.756023
$875$			134.851i			0.154116i
$876$	139.674	+	139.674i	0.159446	+	0.159446i
$877$	−591.287	−	591.287i	−0.674216	−	0.674216i	0.284469	−	0.958685i	$-0.408183\pi$
$877$	−591.287	−	591.287i	−0.674216	−	0.674216i	−0.958685	+	0.284469i	$0.908183\pi$
$878$	164.238	−	164.238i	0.187060	−	0.187060i
$879$	−207.919	+	207.919i	−0.236541	+	0.236541i
$880$	−65.5692			−0.0745105
$881$		−	663.997i		−	0.753686i	−0.926277	−	0.376843i	$-0.877010\pi$
$881$		−	663.997i		−	0.753686i	0.926277	−	0.376843i	$-0.122990\pi$
$882$	102.215	−	102.215i	0.115890	−	0.115890i
$883$			570.192i			0.645744i	0.946443	+	0.322872i	$0.104648\pi$
$883$			570.192i			0.645744i	−0.946443	+	0.322872i	$0.895352\pi$
$884$		0			0
$885$	−895.377			−1.01173
$886$	458.736	+	458.736i	0.517761	+	0.517761i
$887$	481.031			0.542312			0.271156	−	0.962535i	$-0.412594\pi$
$887$	481.031			0.542312			0.271156	+	0.962535i	$0.412594\pi$
$888$			213.779i			0.240743i
$889$	475.272	+	475.272i	0.534614	+	0.534614i
$890$	−241.492	−	241.492i	−0.271340	−	0.271340i
$891$	−15.5885	+	15.5885i	−0.0174955	+	0.0174955i
$892$	341.177	−	341.177i	0.382485	−	0.382485i
$893$	928.392			1.03963
$894$			582.746i			0.651841i
$895$	782.123	−	782.123i	0.873880	−	0.873880i
$896$			43.7128i			0.0487866i
$897$		0			0
$898$	443.551			0.493932
$899$	−859.510	−	859.510i	−0.956074	−	0.956074i
$900$	−118.708			−0.131897
$901$		−	67.0615i		−	0.0744301i
$902$	50.0385	+	50.0385i	0.0554750	+	0.0554750i
$903$	119.138	+	119.138i	0.131936	+	0.131936i
$904$	−368.554	+	368.554i	−0.407692	+	0.407692i
$905$	−1343.22	+	1343.22i	−1.48422	+	1.48422i
$906$	133.044			0.146847
$907$		−	193.331i		−	0.213154i	−0.994304	−	0.106577i	$-0.966011\pi$
$907$		−	193.331i		−	0.213154i	0.994304	−	0.106577i	$-0.0339891\pi$
$908$	338.736	−	338.736i	0.373057	−	0.373057i
$909$		−	313.608i		−	0.345003i
$910$		0			0
$911$	−868.743			−0.953615			−0.476808	−	0.879008i	$-0.658206\pi$
$911$	−868.743			−0.953615			−0.476808	+	0.879008i	$0.658206\pi$
$912$	78.0666	+	78.0666i	0.0855994	+	0.0855994i
$913$	255.646			0.280007
$914$			105.923i			0.115890i
$915$	−60.8616	−	60.8616i	−0.0665154	−	0.0665154i
$916$	−283.646	−	283.646i	−0.309657	−	0.309657i
$917$	330.879	−	330.879i	0.360828	−	0.360828i
$918$	152.354	−	152.354i	0.165963	−	0.165963i
$919$	389.108			0.423403			0.211702	−	0.977334i	$-0.432100\pi$
$919$	389.108			0.423403			0.211702	+	0.977334i	$0.432100\pi$
$920$			554.985i			0.603244i
$921$	12.9705	−	12.9705i	0.0140830	−	0.0140830i
$922$			134.900i			0.146312i
$923$		0			0
$924$	32.7846			0.0354812
$925$	610.482	+	610.482i	0.659980	+	0.659980i
$926$	1098.49			1.18628
$927$		−	110.038i		−	0.118704i
$928$	127.426	+	127.426i	0.137312	+	0.137312i
$929$	429.870	+	429.870i	0.462724	+	0.462724i	0.899547	−	0.436823i	$-0.143897\pi$
$929$	429.870	+	429.870i	0.462724	+	0.462724i	−0.436823	+	0.899547i	$0.643897\pi$
$930$	−442.277	+	442.277i	−0.475567	+	0.475567i
$931$	−383.919	+	383.919i	−0.412373	+	0.412373i
$932$	−256.077			−0.274761
$933$			501.215i			0.537208i
$934$	−30.1821	+	30.1821i	−0.0323148	+	0.0323148i
$935$		−	480.631i		−	0.514044i
$936$		0			0
$937$	916.441			0.978059			0.489029	−	0.872267i	$-0.337351\pi$
$937$	916.441			0.978059			0.489029	+	0.872267i	$0.337351\pi$
$938$	−331.636	−	331.636i	−0.353556	−	0.353556i
$939$	−600.746			−0.639772
$940$		−	779.769i		−	0.829542i
$941$	−835.601	−	835.601i	−0.887993	−	0.887993i	0.106337	−	0.994330i	$-0.466088\pi$
$941$	−835.601	−	835.601i	−0.887993	−	0.887993i	−0.994330	+	0.106337i	$0.966088\pi$
$942$	−393.549	−	393.549i	−0.417780	−	0.417780i
$943$	423.531	−	423.531i	0.449131	−	0.449131i
$944$	218.487	−	218.487i	0.231448	−	0.231448i
$945$	134.354			0.142173
$946$		−	87.2154i		−	0.0921939i
$947$	378.506	−	378.506i	0.399690	−	0.399690i	−0.478434	−	0.878124i	$-0.658795\pi$
$947$	378.506	−	378.506i	0.399690	−	0.399690i	0.878124	+	0.478434i	$0.158795\pi$
$948$			513.415i			0.541577i
$949$		0			0
$950$	445.864			0.469330
$951$	−168.042	−	168.042i	−0.176701	−	0.176701i
$952$	−320.420			−0.336576
$953$			839.556i			0.880961i	0.897762	+	0.440481i	$0.145192\pi$
$953$			839.556i			0.880961i	−0.897762	+	0.440481i	$0.854808\pi$
$954$	−6.86156	−	6.86156i	−0.00719241	−	0.00719241i
$955$	−43.9230	−	43.9230i	−0.0459927	−	0.0459927i
$956$	176.038	−	176.038i	0.184141	−	0.184141i
$957$	95.5692	−	95.5692i	0.0998633	−	0.0998633i
$958$	−517.741			−0.540439
$959$		−	710.620i		−	0.741001i
$960$	65.5692	−	65.5692i	0.0683013	−	0.0683013i
$961$			494.923i			0.515008i
$962$		0			0
$963$	−370.392			−0.384623
$964$	294.918	+	294.918i	0.305931	+	0.305931i
$965$	−205.541			−0.212996
$966$		−	277.492i		−	0.287259i
$967$	375.745	+	375.745i	0.388567	+	0.388567i	0.874176	−	0.485609i	$-0.161402\pi$
$967$	375.745	+	375.745i	0.388567	+	0.388567i	−0.485609	+	0.874176i	$0.661402\pi$
$968$	230.000	+	230.000i	0.237603	+	0.237603i
$969$	−572.238	+	572.238i	−0.590545	+	0.590545i
$970$	−814.228	+	814.228i	−0.839410	+	0.839410i
$971$	134.523			0.138541			0.0692703	−	0.997598i	$-0.477933\pi$
$971$	134.523			0.138541			0.0692703	+	0.997598i	$0.477933\pi$
$972$		−	31.1769i		−	0.0320750i
$973$	−74.1436	+	74.1436i	−0.0762010	+	0.0762010i
$974$		−	549.121i		−	0.563779i
$975$		0			0
$976$	29.7025			0.0304329
$977$	−708.060	−	708.060i	−0.724729	−	0.724729i	0.244836	−	0.969565i	$-0.421266\pi$
$977$	−708.060	−	708.060i	−0.724729	−	0.724729i	−0.969565	+	0.244836i	$0.921266\pi$
$978$	−43.1103			−0.0440800
$979$		−	88.3923i		−	0.0902884i
$980$	322.459	+	322.459i	0.329040	+	0.329040i
$981$	−357.946	−	357.946i	−0.364879	−	0.364879i
$982$	220.726	−	220.726i	0.224771	−	0.224771i
$983$	904.881	−	904.881i	0.920530	−	0.920530i	−0.0765369	−	0.997067i	$-0.524386\pi$
$983$	904.881	−	904.881i	0.920530	−	0.920530i	0.997067	+	0.0765369i	$0.0243863\pi$
$984$	−100.077			−0.101704
$985$		−	1066.91i		−	1.08315i
$986$	−934.046	+	934.046i	−0.947308	+	0.947308i
$987$			389.885i			0.395020i
$988$		0			0
$989$	−738.200			−0.746410
$990$	−49.1769	−	49.1769i	−0.0496737	−	0.0496737i
$991$	29.0155			0.0292790			0.0146395	−	0.999893i	$-0.495340\pi$
$991$	29.0155			0.0292790			0.0146395	+	0.999893i	$0.495340\pi$
$992$		−	215.846i		−	0.217587i
$993$	−218.463	−	218.463i	−0.220003	−	0.220003i
$994$	212.603	+	212.603i	0.213886	+	0.213886i
$995$	1159.83	−	1159.83i	1.16565	−	1.16565i
$996$	−255.646	+	255.646i	−0.256673	+	0.256673i
$997$	336.123			0.337134			0.168567	−	0.985690i	$-0.446086\pi$
$997$	336.123			0.337134			0.168567	+	0.985690i	$0.446086\pi$
$998$		−	1250.13i		−	1.25264i
$999$	−160.335	+	160.335i	−0.160495	+	0.160495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.3.f.a.775.1		4
13.5	odd	4	inner	1014.3.f.a.577.1		4
13.8	odd	4		78.3.f.a.31.1	✓	4
13.12	even	2		78.3.f.a.73.1	yes	4
39.8	even	4		234.3.i.b.109.1		4
39.38	odd	2		234.3.i.b.73.1		4
52.47	even	4		624.3.ba.a.577.2		4
52.51	odd	2		624.3.ba.a.385.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
78.3.f.a.31.1	✓	4	13.8	odd	4
78.3.f.a.73.1	yes	4	13.12	even	2
234.3.i.b.73.1		4	39.38	odd	2
234.3.i.b.109.1		4	39.8	even	4
624.3.ba.a.385.2		4	52.51	odd	2
624.3.ba.a.577.2		4	52.47	even	4
1014.3.f.a.577.1		4	13.5	odd	4	inner
1014.3.f.a.775.1		4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1014.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.00000i) q^{2} -1.73205 q^{3} +2.00000i q^{4} +(-4.73205 - 4.73205i) q^{5} +(1.73205 + 1.73205i) q^{6} +(2.73205 - 2.73205i) q^{7} +(2.00000 - 2.00000i) q^{8} +3.00000 q^{9} +9.46410i q^{10} +(-1.73205 + 1.73205i) q^{11} -3.46410i q^{12} -5.46410 q^{14} +(8.19615 + 8.19615i) q^{15} -4.00000 q^{16} -29.3205i q^{17} +(-3.00000 - 3.00000i) q^{18} +(11.2679 + 11.2679i) q^{19} +(9.46410 - 9.46410i) q^{20} +(-4.73205 + 4.73205i) q^{21} +3.46410 q^{22} -29.3205i q^{23} +(-3.46410 + 3.46410i) q^{24} +19.7846i q^{25} -5.19615 q^{27} +(5.46410 + 5.46410i) q^{28} +31.8564 q^{29} -16.3923i q^{30} +(-26.9808 - 26.9808i) q^{31} +(4.00000 + 4.00000i) q^{32} +(3.00000 - 3.00000i) q^{33} +(-29.3205 + 29.3205i) q^{34} -25.8564 q^{35} +6.00000i q^{36} +(30.8564 - 30.8564i) q^{37} -22.5359i q^{38} -18.9282 q^{40} +(14.4449 + 14.4449i) q^{41} +9.46410 q^{42} -25.1769i q^{43} +(-3.46410 - 3.46410i) q^{44} +(-14.1962 - 14.1962i) q^{45} +(-29.3205 + 29.3205i) q^{46} +(41.1962 - 41.1962i) q^{47} +6.92820 q^{48} +34.0718i q^{49} +(19.7846 - 19.7846i) q^{50} +50.7846i q^{51} +2.28719 q^{53} +(5.19615 + 5.19615i) q^{54} +16.3923 q^{55} -10.9282i q^{56} +(-19.5167 - 19.5167i) q^{57} +(-31.8564 - 31.8564i) q^{58} +(-54.6218 + 54.6218i) q^{59} +(-16.3923 + 16.3923i) q^{60} -7.42563 q^{61} +53.9615i q^{62} +(8.19615 - 8.19615i) q^{63} -8.00000i q^{64} -6.00000 q^{66} +(60.6936 + 60.6936i) q^{67} +58.6410 q^{68} +50.7846i q^{69} +(25.8564 + 25.8564i) q^{70} +(-38.9090 - 38.9090i) q^{71} +(6.00000 - 6.00000i) q^{72} +(-40.3205 + 40.3205i) q^{73} -61.7128 q^{74} -34.2679i q^{75} +(-22.5359 + 22.5359i) q^{76} +9.46410i q^{77} -148.210 q^{79} +(18.9282 + 18.9282i) q^{80} +9.00000 q^{81} -28.8897i q^{82} +(-73.7987 - 73.7987i) q^{83} +(-9.46410 - 9.46410i) q^{84} +(-138.746 + 138.746i) q^{85} +(-25.1769 + 25.1769i) q^{86} -55.1769 q^{87} +6.92820i q^{88} +(-25.5167 + 25.5167i) q^{89} +28.3923i q^{90} +58.6410 q^{92} +(46.7321 + 46.7321i) q^{93} -82.3923 q^{94} -106.641i q^{95} +(-6.92820 - 6.92820i) q^{96} +(86.0333 + 86.0333i) q^{97} +(34.0718 - 34.0718i) q^{98} +(-5.19615 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 12 q^{5} + 4 q^{7} + 8 q^{8} + 12 q^{9} - 8 q^{14} + 12 q^{15} - 16 q^{16} - 12 q^{18} + 52 q^{19} + 24 q^{20} - 12 q^{21} + 8 q^{28} + 72 q^{29} - 4 q^{31} + 16 q^{32} + 12 q^{33} - 48 q^{34}+ \cdots + 164 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 12 * q^5 + 4 * q^7 + 8 * q^8 + 12 * q^9 - 8 * q^14 + 12 * q^15 - 16 * q^16 - 12 * q^18 + 52 * q^19 + 24 * q^20 - 12 * q^21 + 8 * q^28 + 72 * q^29 - 4 * q^31 + 16 * q^32 + 12 * q^33 - 48 * q^34 - 48 * q^35 + 68 * q^37 - 48 * q^40 - 60 * q^41 + 24 * q^42 - 36 * q^45 - 48 * q^46 + 144 * q^47 - 4 * q^50 + 120 * q^53 + 24 * q^55 + 12 * q^57 - 72 * q^58 + 24 * q^59 - 24 * q^60 + 192 * q^61 + 12 * q^63 - 24 * q^66 + 28 * q^67 + 96 * q^68 + 48 * q^70 - 24 * q^71 + 24 * q^72 - 92 * q^73 - 136 * q^74 - 104 * q^76 - 288 * q^79 + 48 * q^80 + 36 * q^81 + 72 * q^83 - 24 * q^84 - 264 * q^85 + 24 * q^86 - 96 * q^87 - 12 * q^89 + 96 * q^92 + 180 * q^93 - 288 * q^94 + 164 * q^97 + 164 * q^98

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