LMFDB - Embedded newform 245.2.e.d.226.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(116,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.116"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.95633484952$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			226.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.2.e.d.116.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +6.00000 q^{6} +(-3.00000 + 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(3.00000 - 5.19615i) q^{12} -3.00000 q^{13} -3.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(6.00000 + 10.3923i) q^{18} +(3.00000 - 5.19615i) q^{19} +2.00000 q^{20} -2.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -9.00000 q^{27} -1.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(1.50000 - 2.59808i) q^{33} -6.00000 q^{34} +12.0000 q^{36} +(-6.00000 - 10.3923i) q^{38} +(-4.50000 - 7.79423i) q^{39} -6.00000 q^{41} -6.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-4.50000 + 7.79423i) q^{47} +12.0000 q^{48} -2.00000 q^{50} +(4.50000 - 7.79423i) q^{51} +(3.00000 + 5.19615i) q^{52} +(5.00000 + 8.66025i) q^{53} +(-9.00000 + 15.5885i) q^{54} +1.00000 q^{55} +18.0000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(3.00000 + 5.19615i) q^{60} +12.0000 q^{62} -8.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(7.00000 + 12.1244i) q^{67} +(-3.00000 + 5.19615i) q^{68} +12.0000 q^{69} -8.00000 q^{71} +(3.00000 + 5.19615i) q^{73} +(1.50000 - 2.59808i) q^{75} -12.0000 q^{76} -18.0000 q^{78} +(0.500000 - 0.866025i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{82} -12.0000 q^{83} +3.00000 q^{85} +(-6.00000 + 10.3923i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(6.00000 - 10.3923i) q^{89} -12.0000 q^{90} -8.00000 q^{92} +(-9.00000 + 15.5885i) q^{93} +(9.00000 + 15.5885i) q^{94} +(3.00000 + 5.19615i) q^{95} +(12.0000 - 20.7846i) q^{96} +15.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - q^{5} + 12 q^{6} - 6 q^{9} + 2 q^{10} - q^{11} + 6 q^{12} - 6 q^{13} - 6 q^{15} + 4 q^{16} - 3 q^{17} + 12 q^{18} + 6 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - q^{25}+ \cdots + 12 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - q^5 + 12 * q^6 - 6 * q^9 + 2 * q^10 - q^11 + 6 * q^12 - 6 * q^13 - 6 * q^15 + 4 * q^16 - 3 * q^17 + 12 * q^18 + 6 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - q^25 - 6 * q^26 - 18 * q^27 - 2 * q^29 - 6 * q^30 + 6 * q^31 - 8 * q^32 + 3 * q^33 - 12 * q^34 + 24 * q^36 - 12 * q^38 - 9 * q^39 - 12 * q^41 - 12 * q^43 - 2 * q^44 - 6 * q^45 - 8 * q^46 - 9 * q^47 + 24 * q^48 - 4 * q^50 + 9 * q^51 + 6 * q^52 + 10 * q^53 - 18 * q^54 + 2 * q^55 + 36 * q^57 - 2 * q^58 - 6 * q^59 + 6 * q^60 + 24 * q^62 - 16 * q^64 + 3 * q^65 - 6 * q^66 + 14 * q^67 - 6 * q^68 + 24 * q^69 - 16 * q^71 + 6 * q^73 + 3 * q^75 - 24 * q^76 - 36 * q^78 + q^79 + 4 * q^80 - 9 * q^81 - 12 * q^82 - 24 * q^83 + 6 * q^85 - 12 * q^86 - 3 * q^87 + 12 * q^89 - 24 * q^90 - 16 * q^92 - 18 * q^93 + 18 * q^94 + 6 * q^95 + 24 * q^96 + 30 * q^97 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	1.00000	−	1.73205i	0.707107	−	1.22474i	0.965926	−	0.258819i	$-0.0833333\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	6.00000			2.44949
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	1.00000	+	1.73205i	0.316228	+	0.547723i
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	0.780750	−	0.624844i	$-0.214837\pi$
$11$	−0.500000	−	0.866025i	−0.150756	−	0.261116i	−0.931505	+	0.363727i	$0.881504\pi$
$12$	3.00000	−	5.19615i	0.866025	−	1.50000i
$13$	−3.00000			−0.832050			−0.416025	−	0.909353i	$-0.636577\pi$
$13$	−3.00000			−0.832050			−0.416025	+	0.909353i	$0.636577\pi$
$14$		0			0
$15$	−3.00000			−0.774597
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	0.624780	−	0.780801i	$-0.285189\pi$
$17$	−1.50000	−	2.59808i	−0.363803	−	0.630126i	−0.988583	+	0.150675i	$0.951855\pi$
$18$	6.00000	+	10.3923i	1.41421	+	2.44949i
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	−0.284157	−	0.958778i	$-0.591714\pi$
$19$	3.00000	−	5.19615i	0.688247	−	1.19208i	0.972404	−	0.233301i	$-0.0749529\pi$
$20$	2.00000			0.447214
$21$		0			0
$22$	−2.00000			−0.426401
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$	−9.00000			−1.73205
$28$		0			0
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$	−3.00000	+	5.19615i	−0.547723	+	0.948683i
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−4.00000	−	6.92820i	−0.707107	−	1.22474i
$33$	1.50000	−	2.59808i	0.261116	−	0.452267i
$34$	−6.00000			−1.02899
$35$		0			0
$36$	12.0000			2.00000
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	−6.00000	−	10.3923i	−0.973329	−	1.68585i
$39$	−4.50000	−	7.79423i	−0.720577	−	1.24808i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$		0			0
$43$	−6.00000			−0.914991			−0.457496	−	0.889212i	$-0.651253\pi$
$43$	−6.00000			−0.914991			−0.457496	+	0.889212i	$0.651253\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−3.00000	−	5.19615i	−0.447214	−	0.774597i
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	0.325150	+	0.945662i	$0.394585\pi$
$47$	−4.50000	+	7.79423i	−0.656392	+	1.13691i	−0.981543	+	0.191243i	$0.938748\pi$
$48$	12.0000			1.73205
$49$		0			0
$50$	−2.00000			−0.282843
$51$	4.50000	−	7.79423i	0.630126	−	1.09141i
$52$	3.00000	+	5.19615i	0.416025	+	0.720577i
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	0.972867	+	0.231367i	$0.0743197\pi$
$53$	5.00000	+	8.66025i	0.686803	+	1.18958i	−0.286064	+	0.958211i	$0.592347\pi$
$54$	−9.00000	+	15.5885i	−1.22474	+	2.12132i
$55$	1.00000			0.134840
$56$		0			0
$57$	18.0000			2.38416
$58$	−1.00000	+	1.73205i	−0.131306	+	0.227429i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	3.00000	+	5.19615i	0.387298	+	0.670820i
$61$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$61$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$62$	12.0000			1.52400
$63$		0			0
$64$	−8.00000			−1.00000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$	−3.00000	−	5.19615i	−0.369274	−	0.639602i
$67$	7.00000	+	12.1244i	0.855186	+	1.48123i	0.876472	+	0.481452i	$0.159891\pi$
$67$	7.00000	+	12.1244i	0.855186	+	1.48123i	−0.0212861	+	0.999773i	$0.506776\pi$
$68$	−3.00000	+	5.19615i	−0.363803	+	0.630126i
$69$	12.0000			1.44463
$70$		0			0
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$		0			0
$75$	1.50000	−	2.59808i	0.173205	−	0.300000i
$76$	−12.0000			−1.37649
$77$		0			0
$78$	−18.0000			−2.03810
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$	2.00000	+	3.46410i	0.223607	+	0.387298i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$	−6.00000	+	10.3923i	−0.646997	+	1.12063i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$		0			0
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	−0.350304	−	0.936636i	$-0.613922\pi$
$89$	6.00000	−	10.3923i	0.635999	−	1.10158i	0.986303	−	0.164946i	$-0.0527450\pi$
$90$	−12.0000			−1.26491
$91$		0			0
$92$	−8.00000			−0.834058
$93$	−9.00000	+	15.5885i	−0.933257	+	1.61645i
$94$	9.00000	+	15.5885i	0.928279	+	1.60783i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$	12.0000	−	20.7846i	1.22474	−	2.12132i
$97$	15.0000			1.52302			0.761510	−	0.648154i	$-0.224459\pi$
$97$	15.0000			1.52302			0.761510	+	0.648154i	$0.224459\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.833143	−	0.553058i	$-0.813461\pi$
$101$	−9.00000	−	15.5885i	−0.895533	−	1.55111i	−0.0623905	−	0.998052i	$-0.519872\pi$
$102$	−9.00000	−	15.5885i	−0.891133	−	1.54349i
$103$	−4.50000	+	7.79423i	−0.443398	+	0.767988i	−0.997939	−	0.0641683i	$-0.979561\pi$
$103$	−4.50000	+	7.79423i	−0.443398	+	0.767988i	0.554541	+	0.832156i	$0.312894\pi$
$104$		0			0
$105$		0			0
$106$	20.0000			1.94257
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	−0.813632	−	0.581380i	$-0.802513\pi$
$107$	1.00000	−	1.73205i	0.0966736	−	0.167444i	0.910306	+	0.413936i	$0.135846\pi$
$108$	9.00000	+	15.5885i	0.866025	+	1.50000i
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	0.961645	+	0.274296i	$0.0884447\pi$
$109$	7.50000	+	12.9904i	0.718370	+	1.24425i	−0.243276	+	0.969957i	$0.578222\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$		0			0
$112$		0			0
$113$	8.00000			0.752577			0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000			0.752577			0.376288	+	0.926503i	$0.377200\pi$
$114$	18.0000	−	31.1769i	1.68585	−	2.91999i
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	1.00000	+	1.73205i	0.0928477	+	0.160817i
$117$	9.00000	−	15.5885i	0.832050	−	1.44115i
$118$	−12.0000			−1.10469
$119$		0			0
$120$		0			0
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$		0			0
$123$	−9.00000	−	15.5885i	−0.811503	−	1.40556i
$124$	6.00000	−	10.3923i	0.538816	−	0.933257i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−2.00000			−0.177471			−0.0887357	−	0.996055i	$-0.528283\pi$
$127$	−2.00000			−0.177471			−0.0887357	+	0.996055i	$0.528283\pi$
$128$		0			0
$129$	−9.00000	−	15.5885i	−0.792406	−	1.37249i
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$	28.0000			2.41883
$135$	4.50000	−	7.79423i	0.387298	−	0.670820i
$136$		0			0
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	0.643013	−	0.765855i	$-0.277684\pi$
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	−0.984757	+	0.173939i	$0.944351\pi$
$138$	12.0000	−	20.7846i	1.02151	−	1.76930i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−27.0000			−2.27381
$142$	−8.00000	+	13.8564i	−0.671345	+	1.16280i
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$	12.0000	+	20.7846i	1.00000	+	1.73205i
$145$	0.500000	−	0.866025i	0.0415227	−	0.0719195i
$146$	12.0000			0.993127
$147$		0			0
$148$		0			0
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$	−3.00000	−	5.19615i	−0.244949	−	0.424264i
$151$	−7.50000	−	12.9904i	−0.610341	−	1.05714i	−0.991183	−	0.132502i	$-0.957699\pi$
$151$	−7.50000	−	12.9904i	−0.610341	−	1.05714i	0.380841	−	0.924640i	$-0.375634\pi$
$152$		0			0
$153$	18.0000			1.45521
$154$		0			0
$155$	−6.00000			−0.481932
$156$	−9.00000	+	15.5885i	−0.720577	+	1.24808i
$157$	9.00000	+	15.5885i	0.718278	+	1.24409i	0.961681	+	0.274169i	$0.0884028\pi$
$157$	9.00000	+	15.5885i	0.718278	+	1.24409i	−0.243403	+	0.969925i	$0.578264\pi$
$158$	−1.00000	−	1.73205i	−0.0795557	−	0.137795i
$159$	−15.0000	+	25.9808i	−1.18958	+	2.06041i
$160$	8.00000			0.632456
$161$		0			0
$162$	−18.0000			−1.41421
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	0.361619	+	0.932326i	$0.382224\pi$
$163$	−8.00000	+	13.8564i	−0.626608	+	1.08532i	−0.988227	+	0.152992i	$0.951109\pi$
$164$	6.00000	+	10.3923i	0.468521	+	0.811503i
$165$	1.50000	+	2.59808i	0.116775	+	0.202260i
$166$	−12.0000	+	20.7846i	−0.931381	+	1.61320i
$167$	−3.00000			−0.232147			−0.116073	−	0.993241i	$-0.537031\pi$
$167$	−3.00000			−0.232147			−0.116073	+	0.993241i	$0.537031\pi$
$168$		0			0
$169$	−4.00000			−0.307692
$170$	3.00000	−	5.19615i	0.230089	−	0.398527i
$171$	18.0000	+	31.1769i	1.37649	+	2.38416i
$172$	6.00000	+	10.3923i	0.457496	+	0.792406i
$173$	−1.50000	+	2.59808i	−0.114043	+	0.197528i	−0.917397	−	0.397974i	$-0.869713\pi$
$173$	−1.50000	+	2.59808i	−0.114043	+	0.197528i	0.803354	+	0.595502i	$0.203047\pi$
$174$	−6.00000			−0.454859
$175$		0			0
$176$	−4.00000			−0.301511
$177$	9.00000	−	15.5885i	0.676481	−	1.17170i
$178$	−12.0000	−	20.7846i	−0.899438	−	1.55787i
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	0.781551	−	0.623841i	$-0.214429\pi$
$179$	−2.00000	−	3.46410i	−0.149487	−	0.258919i	−0.931038	+	0.364922i	$0.881096\pi$
$180$	−6.00000	+	10.3923i	−0.447214	+	0.774597i
$181$	6.00000			0.445976			0.222988	−	0.974821i	$-0.428419\pi$
$181$	6.00000			0.445976			0.222988	+	0.974821i	$0.428419\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$		0			0
$186$	18.0000	+	31.1769i	1.31982	+	2.28600i
$187$	−1.50000	+	2.59808i	−0.109691	+	0.189990i
$188$	18.0000			1.31278
$189$		0			0
$190$	12.0000			0.870572
$191$	−8.50000	+	14.7224i	−0.615038	+	1.06528i	0.375339	+	0.926887i	$0.377526\pi$
$191$	−8.50000	+	14.7224i	−0.615038	+	1.06528i	−0.990378	+	0.138390i	$0.955807\pi$
$192$	−12.0000	−	20.7846i	−0.866025	−	1.50000i
$193$	−6.00000	−	10.3923i	−0.431889	−	0.748054i	0.565147	−	0.824991i	$-0.308820\pi$
$193$	−6.00000	−	10.3923i	−0.431889	−	0.748054i	−0.997036	+	0.0769360i	$0.975486\pi$
$194$	15.0000	−	25.9808i	1.07694	−	1.86531i
$195$	9.00000			0.644503
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$	6.00000	−	10.3923i	0.426401	−	0.738549i
$199$	3.00000	+	5.19615i	0.212664	+	0.368345i	0.952548	−	0.304390i	$-0.0984526\pi$
$199$	3.00000	+	5.19615i	0.212664	+	0.368345i	−0.739883	+	0.672735i	$0.765119\pi$
$200$		0			0
$201$	−21.0000	+	36.3731i	−1.48123	+	2.56556i
$202$	−36.0000			−2.53295
$203$		0			0
$204$	−18.0000			−1.26025
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	9.00000	+	15.5885i	0.627060	+	1.08610i
$207$	12.0000	+	20.7846i	0.834058	+	1.44463i
$208$	−6.00000	+	10.3923i	−0.416025	+	0.720577i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	15.0000			1.03264			0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000			1.03264			0.516321	+	0.856395i	$0.327301\pi$
$212$	10.0000	−	17.3205i	0.686803	−	1.18958i
$213$	−12.0000	−	20.7846i	−0.822226	−	1.42414i
$214$	−2.00000	−	3.46410i	−0.136717	−	0.236801i
$215$	3.00000	−	5.19615i	0.204598	−	0.354375i
$216$		0			0
$217$		0			0
$218$	30.0000			2.03186
$219$	−9.00000	+	15.5885i	−0.608164	+	1.05337i
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	4.50000	+	7.79423i	0.302703	+	0.524297i
$222$		0			0
$223$	−3.00000			−0.200895			−0.100447	−	0.994942i	$-0.532027\pi$
$223$	−3.00000			−0.200895			−0.100447	+	0.994942i	$0.532027\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$	8.00000	−	13.8564i	0.532152	−	0.921714i
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$	−18.0000	−	31.1769i	−1.19208	−	2.06474i
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	−0.947960	−	0.318390i	$-0.896858\pi$
$229$	−3.00000	+	5.19615i	−0.198246	+	0.343371i	0.749714	+	0.661762i	$0.230191\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$		0			0
$233$	4.00000	−	6.92820i	0.262049	−	0.453882i	−0.704737	−	0.709468i	$-0.748935\pi$
$233$	4.00000	−	6.92820i	0.262049	−	0.453882i	0.966786	+	0.255586i	$0.0822686\pi$
$234$	−18.0000	−	31.1769i	−1.17670	−	2.03810i
$235$	−4.50000	−	7.79423i	−0.293548	−	0.508439i
$236$	−6.00000	+	10.3923i	−0.390567	+	0.676481i
$237$	3.00000			0.194871
$238$		0			0
$239$	7.00000			0.452792			0.226396	−	0.974035i	$-0.427306\pi$
$239$	7.00000			0.452792			0.226396	+	0.974035i	$0.427306\pi$
$240$	−6.00000	+	10.3923i	−0.387298	+	0.670820i
$241$	−12.0000	−	20.7846i	−0.772988	−	1.33885i	−0.935918	−	0.352217i	$-0.885428\pi$
$241$	−12.0000	−	20.7846i	−0.772988	−	1.33885i	0.162930	−	0.986638i	$-0.447905\pi$
$242$	−10.0000	−	17.3205i	−0.642824	−	1.11340i
$243$		0			0
$244$		0			0
$245$		0			0
$246$	−36.0000			−2.29528
$247$	−9.00000	+	15.5885i	−0.572656	+	0.991870i
$248$		0			0
$249$	−18.0000	−	31.1769i	−1.14070	−	1.97576i
$250$	1.00000	−	1.73205i	0.0632456	−	0.109545i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	−4.00000			−0.251478
$254$	−2.00000	+	3.46410i	−0.125491	+	0.217357i
$255$	4.50000	+	7.79423i	0.281801	+	0.488094i
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$	−36.0000			−2.24126
$259$		0			0
$260$	−6.00000			−0.372104
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	−12.0000	−	20.7846i	−0.741362	−	1.28408i
$263$	5.00000	+	8.66025i	0.308313	+	0.534014i	0.977993	−	0.208635i	$-0.0669022\pi$
$263$	5.00000	+	8.66025i	0.308313	+	0.534014i	−0.669680	+	0.742650i	$0.733569\pi$
$264$		0			0
$265$	−10.0000			−0.614295
$266$		0			0
$267$	36.0000			2.20316
$268$	14.0000	−	24.2487i	0.855186	−	1.48123i
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	0.956176	+	0.292791i	$0.0945841\pi$
$269$	12.0000	+	20.7846i	0.731653	+	1.26726i	−0.224523	+	0.974469i	$0.572083\pi$
$270$	−9.00000	−	15.5885i	−0.547723	−	0.948683i
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$	−12.0000			−0.727607
$273$		0			0
$274$	−16.0000			−0.966595
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$	−12.0000	−	20.7846i	−0.722315	−	1.25109i
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	0.888899	+	0.458103i	$0.151471\pi$
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	−0.0477206	+	0.998861i	$0.515196\pi$
$278$		0			0
$279$	−36.0000			−2.15526
$280$		0			0
$281$	−5.00000			−0.298275			−0.149137	−	0.988816i	$-0.547650\pi$
$281$	−5.00000			−0.298275			−0.149137	+	0.988816i	$0.547650\pi$
$282$	−27.0000	+	46.7654i	−1.60783	+	2.78484i
$283$	10.5000	+	18.1865i	0.624160	+	1.08108i	0.988703	+	0.149890i	$0.0478921\pi$
$283$	10.5000	+	18.1865i	0.624160	+	1.08108i	−0.364542	+	0.931187i	$0.618775\pi$
$284$	8.00000	+	13.8564i	0.474713	+	0.822226i
$285$	−9.00000	+	15.5885i	−0.533114	+	0.923381i
$286$	6.00000			0.354787
$287$		0			0
$288$	48.0000			2.82843
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−1.00000	−	1.73205i	−0.0587220	−	0.101710i
$291$	22.5000	+	38.9711i	1.31897	+	2.28453i
$292$	6.00000	−	10.3923i	0.351123	−	0.608164i
$293$	−9.00000			−0.525786			−0.262893	−	0.964825i	$-0.584677\pi$
$293$	−9.00000			−0.525786			−0.262893	+	0.964825i	$0.584677\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$		0			0
$297$	4.50000	+	7.79423i	0.261116	+	0.452267i
$298$	10.0000	+	17.3205i	0.579284	+	1.00335i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$	−6.00000			−0.346410
$301$		0			0
$302$	−30.0000			−1.72631
$303$	27.0000	−	46.7654i	1.55111	−	2.68660i
$304$	−12.0000	−	20.7846i	−0.688247	−	1.19208i
$305$		0			0
$306$	18.0000	−	31.1769i	1.02899	−	1.78227i
$307$	3.00000			0.171219			0.0856095	−	0.996329i	$-0.472716\pi$
$307$	3.00000			0.171219			0.0856095	+	0.996329i	$0.472716\pi$
$308$		0			0
$309$	−27.0000			−1.53598
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$		0			0
$313$	1.50000	−	2.59808i	0.0847850	−	0.146852i	−0.820515	−	0.571626i	$-0.806313\pi$
$313$	1.50000	−	2.59808i	0.0847850	−	0.146852i	0.905300	+	0.424774i	$0.139646\pi$
$314$	36.0000			2.03160
$315$		0			0
$316$	−2.00000			−0.112509
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	−0.372061	−	0.928208i	$-0.621349\pi$
$317$	11.0000	−	19.0526i	0.617822	−	1.07010i	0.989882	−	0.141890i	$-0.0453179\pi$
$318$	30.0000	+	51.9615i	1.68232	+	2.91386i
$319$	0.500000	+	0.866025i	0.0279946	+	0.0484881i
$320$	4.00000	−	6.92820i	0.223607	−	0.387298i
$321$	6.00000			0.334887
$322$		0			0
$323$	−18.0000			−1.00155
$324$	−9.00000	+	15.5885i	−0.500000	+	0.866025i
$325$	1.50000	+	2.59808i	0.0832050	+	0.144115i
$326$	16.0000	+	27.7128i	0.886158	+	1.53487i
$327$	−22.5000	+	38.9711i	−1.24425	+	2.15511i
$328$		0			0
$329$		0			0
$330$	6.00000			0.330289
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	−0.982470	−	0.186421i	$-0.940311\pi$
$331$	−6.00000	+	10.3923i	−0.329790	+	0.571213i	0.652680	+	0.757634i	$0.273645\pi$
$332$	12.0000	+	20.7846i	0.658586	+	1.14070i
$333$		0			0
$334$	−3.00000	+	5.19615i	−0.164153	+	0.284321i
$335$	−14.0000			−0.764902
$336$		0			0
$337$	−24.0000			−1.30736			−0.653682	−	0.756770i	$-0.726776\pi$
$337$	−24.0000			−1.30736			−0.653682	+	0.756770i	$0.726776\pi$
$338$	−4.00000	+	6.92820i	−0.217571	+	0.376845i
$339$	12.0000	+	20.7846i	0.651751	+	1.12887i
$340$	−3.00000	−	5.19615i	−0.162698	−	0.281801i
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$	72.0000			3.89331
$343$		0			0
$344$		0			0
$345$	−6.00000	+	10.3923i	−0.323029	+	0.559503i
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	0.567363	−	0.823468i	$-0.307964\pi$
$347$	−8.00000	−	13.8564i	−0.429463	−	0.743851i	−0.996826	+	0.0796169i	$0.974630\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	30.0000			1.60586			0.802932	−	0.596071i	$-0.203272\pi$
$349$	30.0000			1.60586			0.802932	+	0.596071i	$0.203272\pi$
$350$		0			0
$351$	27.0000			1.44115
$352$	−4.00000	+	6.92820i	−0.213201	+	0.369274i
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	0.823343	−	0.567545i	$-0.192107\pi$
$353$	−1.50000	−	2.59808i	−0.0798369	−	0.138282i	−0.903179	+	0.429263i	$0.858773\pi$
$354$	−18.0000	−	31.1769i	−0.956689	−	1.65703i
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$	−24.0000			−1.27200
$357$		0			0
$358$	−8.00000			−0.422813
$359$	−16.0000	+	27.7128i	−0.844448	+	1.46263i	0.0416523	+	0.999132i	$0.486738\pi$
$359$	−16.0000	+	27.7128i	−0.844448	+	1.46263i	−0.886100	+	0.463494i	$0.846596\pi$
$360$		0			0
$361$	−8.50000	−	14.7224i	−0.447368	−	0.774865i
$362$	6.00000	−	10.3923i	0.315353	−	0.546207i
$363$	30.0000			1.57459
$364$		0			0
$365$	−6.00000			−0.314054
$366$		0			0
$367$	−16.5000	−	28.5788i	−0.861293	−	1.49180i	−0.870681	−	0.491847i	$-0.836322\pi$
$367$	−16.5000	−	28.5788i	−0.861293	−	1.49180i	0.00938849	−	0.999956i	$-0.497012\pi$
$368$	−8.00000	−	13.8564i	−0.417029	−	0.722315i
$369$	18.0000	−	31.1769i	0.937043	−	1.62301i
$370$		0			0
$371$		0			0
$372$	36.0000			1.86651
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	−0.913147	−	0.407630i	$-0.866355\pi$
$373$	−2.00000	+	3.46410i	−0.103556	+	0.179364i	0.809591	+	0.586994i	$0.199689\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$	1.50000	+	2.59808i	0.0774597	+	0.134164i
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−24.0000			−1.23280			−0.616399	−	0.787434i	$-0.711409\pi$
$379$	−24.0000			−1.23280			−0.616399	+	0.787434i	$0.711409\pi$
$380$	6.00000	−	10.3923i	0.307794	−	0.533114i
$381$	−3.00000	−	5.19615i	−0.153695	−	0.266207i
$382$	17.0000	+	29.4449i	0.869796	+	1.50653i
$383$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$383$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$384$		0			0
$385$		0			0
$386$	−24.0000			−1.22157
$387$	18.0000	−	31.1769i	0.914991	−	1.58481i
$388$	−15.0000	−	25.9808i	−0.761510	−	1.31897i
$389$	−6.50000	−	11.2583i	−0.329563	−	0.570820i	0.652862	−	0.757477i	$-0.273568\pi$
$389$	−6.50000	−	11.2583i	−0.329563	−	0.570820i	−0.982425	+	0.186657i	$0.940235\pi$
$390$	9.00000	−	15.5885i	0.455733	−	0.789352i
$391$	−12.0000			−0.606866
$392$		0			0
$393$	36.0000			1.81596
$394$	−2.00000	+	3.46410i	−0.100759	+	0.174519i
$395$	0.500000	+	0.866025i	0.0251577	+	0.0435745i
$396$	−6.00000	−	10.3923i	−0.301511	−	0.522233i
$397$	4.50000	−	7.79423i	0.225849	−	0.391181i	−0.730725	−	0.682672i	$-0.760818\pi$
$397$	4.50000	−	7.79423i	0.225849	−	0.391181i	0.956574	+	0.291491i	$0.0941512\pi$
$398$	12.0000			0.601506
$399$		0			0
$400$	−4.00000			−0.200000
$401$	9.50000	−	16.4545i	0.474407	−	0.821698i	−0.525163	−	0.851002i	$-0.675996\pi$
$401$	9.50000	−	16.4545i	0.474407	−	0.821698i	0.999571	+	0.0293039i	$0.00932905\pi$
$402$	42.0000	+	72.7461i	2.09477	+	3.62825i
$403$	−9.00000	−	15.5885i	−0.448322	−	0.776516i
$404$	−18.0000	+	31.1769i	−0.895533	+	1.55111i
$405$	9.00000			0.447214
$406$		0			0
$407$		0			0
$408$		0			0
$409$	15.0000	+	25.9808i	0.741702	+	1.28467i	0.951720	+	0.306968i	$0.0993146\pi$
$409$	15.0000	+	25.9808i	0.741702	+	1.28467i	−0.210017	+	0.977698i	$0.567352\pi$
$410$	−6.00000	−	10.3923i	−0.296319	−	0.513239i
$411$	12.0000	−	20.7846i	0.591916	−	1.02523i
$412$	18.0000			0.886796
$413$		0			0
$414$	48.0000			2.35907
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$	12.0000	+	20.7846i	0.588348	+	1.01905i
$417$		0			0
$418$	−6.00000	+	10.3923i	−0.293470	+	0.508304i
$419$	6.00000			0.293119			0.146560	−	0.989202i	$-0.453180\pi$
$419$	6.00000			0.293119			0.146560	+	0.989202i	$0.453180\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	15.0000	−	25.9808i	0.730189	−	1.26472i
$423$	−27.0000	−	46.7654i	−1.31278	−	2.27381i
$424$		0			0
$425$	−1.50000	+	2.59808i	−0.0727607	+	0.126025i
$426$	−48.0000			−2.32561
$427$		0			0
$428$	−4.00000			−0.193347
$429$	−4.50000	+	7.79423i	−0.217262	+	0.376309i
$430$	−6.00000	−	10.3923i	−0.289346	−	0.501161i
$431$	−2.50000	−	4.33013i	−0.120421	−	0.208575i	0.799513	−	0.600649i	$-0.205091\pi$
$431$	−2.50000	−	4.33013i	−0.120421	−	0.208575i	−0.919934	+	0.392074i	$0.871758\pi$
$432$	−18.0000	+	31.1769i	−0.866025	+	1.50000i
$433$	30.0000			1.44171			0.720854	−	0.693087i	$-0.243750\pi$
$433$	30.0000			1.44171			0.720854	+	0.693087i	$0.243750\pi$
$434$		0			0
$435$	3.00000			0.143839
$436$	15.0000	−	25.9808i	0.718370	−	1.24425i
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$	18.0000	+	31.1769i	0.860073	+	1.48969i
$439$	6.00000	−	10.3923i	0.286364	−	0.495998i	−0.686575	−	0.727059i	$-0.740887\pi$
$439$	6.00000	−	10.3923i	0.286364	−	0.495998i	0.972939	+	0.231062i	$0.0742199\pi$
$440$		0			0
$441$		0			0
$442$	18.0000			0.856173
$443$	−17.0000	+	29.4449i	−0.807694	+	1.39897i	0.106763	+	0.994285i	$0.465952\pi$
$443$	−17.0000	+	29.4449i	−0.807694	+	1.39897i	−0.914457	+	0.404683i	$0.867382\pi$
$444$		0			0
$445$	6.00000	+	10.3923i	0.284427	+	0.492642i
$446$	−3.00000	+	5.19615i	−0.142054	+	0.246045i
$447$	−30.0000			−1.41895
$448$		0			0
$449$	23.0000			1.08544			0.542719	−	0.839915i	$-0.317395\pi$
$449$	23.0000			1.08544			0.542719	+	0.839915i	$0.317395\pi$
$450$	6.00000	−	10.3923i	0.282843	−	0.489898i
$451$	3.00000	+	5.19615i	0.141264	+	0.244677i
$452$	−8.00000	−	13.8564i	−0.376288	−	0.651751i
$453$	22.5000	−	38.9711i	1.05714	−	1.83102i
$454$	6.00000			0.281594
$455$		0			0
$456$		0			0
$457$	−3.00000	+	5.19615i	−0.140334	+	0.243066i	−0.927622	−	0.373519i	$-0.878151\pi$
$457$	−3.00000	+	5.19615i	−0.140334	+	0.243066i	0.787288	+	0.616585i	$0.211484\pi$
$458$	6.00000	+	10.3923i	0.280362	+	0.485601i
$459$	13.5000	+	23.3827i	0.630126	+	1.09141i
$460$	4.00000	−	6.92820i	0.186501	−	0.323029i
$461$	−36.0000			−1.67669			−0.838344	−	0.545142i	$-0.816476\pi$
$461$	−36.0000			−1.67669			−0.838344	+	0.545142i	$0.816476\pi$
$462$		0			0
$463$	−4.00000			−0.185896			−0.0929479	−	0.995671i	$-0.529629\pi$
$463$	−4.00000			−0.185896			−0.0929479	+	0.995671i	$0.529629\pi$
$464$	−2.00000	+	3.46410i	−0.0928477	+	0.160817i
$465$	−9.00000	−	15.5885i	−0.417365	−	0.722897i
$466$	−8.00000	−	13.8564i	−0.370593	−	0.641886i
$467$	−7.50000	+	12.9904i	−0.347059	+	0.601123i	−0.985726	−	0.168360i	$-0.946153\pi$
$467$	−7.50000	+	12.9904i	−0.347059	+	0.601123i	0.638667	+	0.769483i	$0.279486\pi$
$468$	−36.0000			−1.66410
$469$		0			0
$470$	−18.0000			−0.830278
$471$	−27.0000	+	46.7654i	−1.24409	+	2.15483i
$472$		0			0
$473$	3.00000	+	5.19615i	0.137940	+	0.238919i
$474$	3.00000	−	5.19615i	0.137795	−	0.238667i
$475$	−6.00000			−0.275299
$476$		0			0
$477$	−60.0000			−2.74721
$478$	7.00000	−	12.1244i	0.320173	−	0.554555i
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	−0.998392	−	0.0566937i	$-0.981944\pi$
$479$	−12.0000	−	20.7846i	−0.548294	−	0.949673i	0.450098	−	0.892979i	$-0.351389\pi$
$480$	12.0000	+	20.7846i	0.547723	+	0.948683i
$481$		0			0
$482$	−48.0000			−2.18634
$483$		0			0
$484$	−20.0000			−0.909091
$485$	−7.50000	+	12.9904i	−0.340557	+	0.589863i
$486$		0			0
$487$	−18.0000	−	31.1769i	−0.815658	−	1.41276i	−0.908855	−	0.417113i	$-0.863042\pi$
$487$	−18.0000	−	31.1769i	−0.815658	−	1.41276i	0.0931967	−	0.995648i	$-0.470291\pi$
$488$		0			0
$489$	−48.0000			−2.17064
$490$		0			0
$491$	23.0000			1.03798			0.518988	−	0.854782i	$-0.326309\pi$
$491$	23.0000			1.03798			0.518988	+	0.854782i	$0.326309\pi$
$492$	−18.0000	+	31.1769i	−0.811503	+	1.40556i
$493$	1.50000	+	2.59808i	0.0675566	+	0.117011i
$494$	18.0000	+	31.1769i	0.809858	+	1.40272i
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$	24.0000			1.07763
$497$		0			0
$498$	−72.0000			−3.22640
$499$	13.5000	−	23.3827i	0.604343	−	1.04675i	−0.387812	−	0.921739i	$-0.626769\pi$
$499$	13.5000	−	23.3827i	0.604343	−	1.04675i	0.992155	−	0.125014i	$-0.0398977\pi$
$500$	−1.00000	−	1.73205i	−0.0447214	−	0.0774597i
$501$	−4.50000	−	7.79423i	−0.201045	−	0.348220i
$502$	12.0000	−	20.7846i	0.535586	−	0.927663i
$503$	−9.00000			−0.401290			−0.200645	−	0.979664i	$-0.564304\pi$
$503$	−9.00000			−0.401290			−0.200645	+	0.979664i	$0.564304\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$	−6.00000	−	10.3923i	−0.266469	−	0.461538i
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	−12.0000	+	20.7846i	−0.531891	+	0.921262i	0.467416	+	0.884037i	$0.345185\pi$
$509$	−12.0000	+	20.7846i	−0.531891	+	0.921262i	−0.999307	+	0.0372243i	$0.988148\pi$
$510$	18.0000			0.797053
$511$		0			0
$512$	−32.0000			−1.41421
$513$	−27.0000	+	46.7654i	−1.19208	+	2.06474i
$514$	−18.0000	−	31.1769i	−0.793946	−	1.37515i
$515$	−4.50000	−	7.79423i	−0.198294	−	0.343455i
$516$	−18.0000	+	31.1769i	−0.792406	+	1.37249i
$517$	9.00000			0.395820
$518$		0			0
$519$	−9.00000			−0.395056
$520$		0			0
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	0.598714	−	0.800963i	$-0.295679\pi$
$521$	−9.00000	−	15.5885i	−0.394297	−	0.682943i	−0.993011	+	0.118020i	$0.962345\pi$
$522$	−6.00000	−	10.3923i	−0.262613	−	0.454859i
$523$	12.0000	−	20.7846i	0.524723	−	0.908848i	−0.474862	−	0.880060i	$-0.657502\pi$
$523$	12.0000	−	20.7846i	0.524723	−	0.908848i	0.999586	−	0.0287874i	$-0.00916457\pi$
$524$	−24.0000			−1.04844
$525$		0			0
$526$	20.0000			0.872041
$527$	9.00000	−	15.5885i	0.392046	−	0.679044i
$528$	−6.00000	−	10.3923i	−0.261116	−	0.452267i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	−10.0000	+	17.3205i	−0.434372	+	0.752355i
$531$	36.0000			1.56227
$532$		0			0
$533$	18.0000			0.779667
$534$	36.0000	−	62.3538i	1.55787	−	2.69831i
$535$	1.00000	+	1.73205i	0.0432338	+	0.0748831i
$536$		0			0
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$	48.0000			2.06943
$539$		0			0
$540$	−18.0000			−0.774597
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	−0.959697	−	0.281037i	$-0.909322\pi$
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	0.723234	+	0.690604i	$0.242655\pi$
$542$	−24.0000	−	41.5692i	−1.03089	−	1.78555i
$543$	9.00000	+	15.5885i	0.386227	+	0.668965i
$544$	−12.0000	+	20.7846i	−0.514496	+	0.891133i
$545$	−15.0000			−0.642529
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−8.00000	+	13.8564i	−0.341743	+	0.591916i
$549$		0			0
$550$	1.00000	+	1.73205i	0.0426401	+	0.0738549i
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$		0			0
$553$		0			0
$554$	56.0000			2.37921
$555$		0			0
$556$		0			0
$557$	−2.00000	−	3.46410i	−0.0847427	−	0.146779i	0.820539	−	0.571591i	$-0.193674\pi$
$557$	−2.00000	−	3.46410i	−0.0847427	−	0.146779i	−0.905282	+	0.424812i	$0.860340\pi$
$558$	−36.0000	+	62.3538i	−1.52400	+	2.63965i
$559$	18.0000			0.761319
$560$		0			0
$561$	−9.00000			−0.379980
$562$	−5.00000	+	8.66025i	−0.210912	+	0.365311i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$	27.0000	+	46.7654i	1.13691	+	1.96918i
$565$	−4.00000	+	6.92820i	−0.168281	+	0.291472i
$566$	42.0000			1.76539
$567$		0			0
$568$		0			0
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	−0.125347	−	0.992113i	$-0.540004\pi$
$569$	19.0000	−	32.9090i	0.796521	−	1.37962i	0.921869	−	0.387503i	$-0.126662\pi$
$570$	18.0000	+	31.1769i	0.753937	+	1.30586i
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	3.00000	−	5.19615i	0.125436	−	0.217262i
$573$	−51.0000			−2.13056
$574$		0			0
$575$	−4.00000			−0.166812
$576$	24.0000	−	41.5692i	1.00000	−	1.73205i
$577$	7.50000	+	12.9904i	0.312229	+	0.540797i	0.978845	−	0.204605i	$-0.0655910\pi$
$577$	7.50000	+	12.9904i	0.312229	+	0.540797i	−0.666616	+	0.745402i	$0.732258\pi$
$578$	−8.00000	−	13.8564i	−0.332756	−	0.576351i
$579$	18.0000	−	31.1769i	0.748054	−	1.29567i
$580$	−2.00000			−0.0830455
$581$		0			0
$582$	90.0000			3.73062
$583$	5.00000	−	8.66025i	0.207079	−	0.358671i
$584$		0			0
$585$	9.00000	+	15.5885i	0.372104	+	0.644503i
$586$	−9.00000	+	15.5885i	−0.371787	+	0.643953i
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	36.0000			1.48335
$590$	6.00000	−	10.3923i	0.247016	−	0.427844i
$591$	−3.00000	−	5.19615i	−0.123404	−	0.213741i
$592$		0			0
$593$	−22.5000	+	38.9711i	−0.923964	+	1.60035i	−0.130746	+	0.991416i	$0.541737\pi$
$593$	−22.5000	+	38.9711i	−0.923964	+	1.60035i	−0.793219	+	0.608937i	$0.791596\pi$
$594$	18.0000			0.738549
$595$		0			0
$596$	20.0000			0.819232
$597$	−9.00000	+	15.5885i	−0.368345	+	0.637993i
$598$	12.0000	+	20.7846i	0.490716	+	0.849946i
$599$	−8.50000	−	14.7224i	−0.347301	−	0.601542i	0.638468	−	0.769648i	$-0.279568\pi$
$599$	−8.50000	−	14.7224i	−0.347301	−	0.601542i	−0.985769	+	0.168106i	$0.946235\pi$
$600$		0			0
$601$	30.0000			1.22373			0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000			1.22373			0.611863	+	0.790964i	$0.290420\pi$
$602$		0			0
$603$	−84.0000			−3.42074
$604$	−15.0000	+	25.9808i	−0.610341	+	1.05714i
$605$	5.00000	+	8.66025i	0.203279	+	0.352089i
$606$	−54.0000	−	93.5307i	−2.19360	−	3.79943i
$607$	10.5000	−	18.1865i	0.426182	−	0.738169i	−0.570348	−	0.821403i	$-0.693192\pi$
$607$	10.5000	−	18.1865i	0.426182	−	0.738169i	0.996530	+	0.0832344i	$0.0265250\pi$
$608$	−48.0000			−1.94666
$609$		0			0
$610$		0			0
$611$	13.5000	−	23.3827i	0.546152	−	0.945962i
$612$	−18.0000	−	31.1769i	−0.727607	−	1.26025i
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	0.885514	−	0.464614i	$-0.153807\pi$
$613$	1.00000	+	1.73205i	0.0403896	+	0.0699569i	−0.845124	+	0.534570i	$0.820473\pi$
$614$	3.00000	−	5.19615i	0.121070	−	0.209700i
$615$	18.0000			0.725830
$616$		0			0
$617$	4.00000			0.161034			0.0805170	−	0.996753i	$-0.474343\pi$
$617$	4.00000			0.161034			0.0805170	+	0.996753i	$0.474343\pi$
$618$	−27.0000	+	46.7654i	−1.08610	+	1.88118i
$619$	−12.0000	−	20.7846i	−0.482321	−	0.835404i	0.517473	−	0.855699i	$-0.326873\pi$
$619$	−12.0000	−	20.7846i	−0.482321	−	0.835404i	−0.999794	+	0.0202954i	$0.993539\pi$
$620$	6.00000	+	10.3923i	0.240966	+	0.417365i
$621$	−18.0000	+	31.1769i	−0.722315	+	1.25109i
$622$	−12.0000			−0.481156
$623$		0			0
$624$	−36.0000			−1.44115
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	−9.00000	−	15.5885i	−0.359425	−	0.622543i
$628$	18.0000	−	31.1769i	0.718278	−	1.24409i
$629$		0			0
$630$		0			0
$631$	−11.0000			−0.437903			−0.218952	−	0.975736i	$-0.570264\pi$
$631$	−11.0000			−0.437903			−0.218952	+	0.975736i	$0.570264\pi$
$632$		0			0
$633$	22.5000	+	38.9711i	0.894295	+	1.54896i
$634$	−22.0000	−	38.1051i	−0.873732	−	1.51335i
$635$	1.00000	−	1.73205i	0.0396838	−	0.0687343i
$636$	60.0000			2.37915
$637$		0			0
$638$	2.00000			0.0791808
$639$	24.0000	−	41.5692i	0.949425	−	1.64445i
$640$		0			0
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	0.885098	−	0.465404i	$-0.154091\pi$
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	−0.845601	+	0.533816i	$0.820758\pi$
$642$	6.00000	−	10.3923i	0.236801	−	0.410152i
$643$	−27.0000			−1.06478			−0.532388	−	0.846500i	$-0.678705\pi$
$643$	−27.0000			−1.06478			−0.532388	+	0.846500i	$0.678705\pi$
$644$		0			0
$645$	18.0000			0.708749
$646$	−18.0000	+	31.1769i	−0.708201	+	1.22664i
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	0.959529	−	0.281609i	$-0.0908680\pi$
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	−0.723645	+	0.690172i	$0.757535\pi$
$648$		0			0
$649$	−3.00000	+	5.19615i	−0.117760	+	0.203967i
$650$	6.00000			0.235339
$651$		0			0
$652$	32.0000			1.25322
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$	45.0000	+	77.9423i	1.75964	+	3.04778i
$655$	6.00000	+	10.3923i	0.234439	+	0.406061i
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$	−36.0000			−1.40449
$658$		0			0
$659$	−19.0000			−0.740135			−0.370067	−	0.929005i	$-0.620665\pi$
$659$	−19.0000			−0.740135			−0.370067	+	0.929005i	$0.620665\pi$
$660$	3.00000	−	5.19615i	0.116775	−	0.202260i
$661$	6.00000	+	10.3923i	0.233373	+	0.404214i	0.958799	−	0.284087i	$-0.0916904\pi$
$661$	6.00000	+	10.3923i	0.233373	+	0.404214i	−0.725426	+	0.688301i	$0.758357\pi$
$662$	12.0000	+	20.7846i	0.466393	+	0.807817i
$663$	−13.5000	+	23.3827i	−0.524297	+	0.908108i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−2.00000	+	3.46410i	−0.0774403	+	0.134131i
$668$	3.00000	+	5.19615i	0.116073	+	0.201045i
$669$	−4.50000	−	7.79423i	−0.173980	−	0.301342i
$670$	−14.0000	+	24.2487i	−0.540867	+	0.936809i
$671$		0			0
$672$		0			0
$673$	12.0000			0.462566			0.231283	−	0.972887i	$-0.425708\pi$
$673$	12.0000			0.462566			0.231283	+	0.972887i	$0.425708\pi$
$674$	−24.0000	+	41.5692i	−0.924445	+	1.60119i
$675$	4.50000	+	7.79423i	0.173205	+	0.300000i
$676$	4.00000	+	6.92820i	0.153846	+	0.266469i
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	−0.939450	−	0.342687i	$-0.888663\pi$
$677$	−4.50000	+	7.79423i	−0.172949	+	0.299557i	0.766501	+	0.642244i	$0.221996\pi$
$678$	48.0000			1.84343
$679$		0			0
$680$		0			0
$681$	−4.50000	+	7.79423i	−0.172440	+	0.298675i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−4.00000	−	6.92820i	−0.153056	−	0.265100i	0.779294	−	0.626659i	$-0.215578\pi$
$683$	−4.00000	−	6.92820i	−0.153056	−	0.265100i	−0.932349	+	0.361559i	$0.882245\pi$
$684$	36.0000	−	62.3538i	1.37649	−	2.38416i
$685$	8.00000			0.305664
$686$		0			0
$687$	−18.0000			−0.686743
$688$	−12.0000	+	20.7846i	−0.457496	+	0.792406i
$689$	−15.0000	−	25.9808i	−0.571454	−	0.989788i
$690$	12.0000	+	20.7846i	0.456832	+	0.791257i
$691$	18.0000	−	31.1769i	0.684752	−	1.18603i	−0.288762	−	0.957401i	$-0.593244\pi$
$691$	18.0000	−	31.1769i	0.684752	−	1.18603i	0.973515	−	0.228625i	$-0.0734229\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−32.0000			−1.21470
$695$		0			0
$696$		0			0
$697$	9.00000	+	15.5885i	0.340899	+	0.590455i
$698$	30.0000	−	51.9615i	1.13552	−	1.96677i
$699$	24.0000			0.907763
$700$		0			0
$701$	47.0000			1.77517			0.887583	−	0.460648i	$-0.152383\pi$
$701$	47.0000			1.77517			0.887583	+	0.460648i	$0.152383\pi$
$702$	27.0000	−	46.7654i	1.01905	−	1.76505i
$703$		0			0
$704$	4.00000	+	6.92820i	0.150756	+	0.261116i
$705$	13.5000	−	23.3827i	0.508439	−	0.880643i
$706$	−6.00000			−0.225813
$707$		0			0
$708$	−36.0000			−1.35296
$709$	16.5000	−	28.5788i	0.619671	−	1.07330i	−0.369875	−	0.929081i	$-0.620600\pi$
$709$	16.5000	−	28.5788i	0.619671	−	1.07330i	0.989546	−	0.144219i	$-0.0460671\pi$
$710$	−8.00000	−	13.8564i	−0.300235	−	0.520022i
$711$	3.00000	+	5.19615i	0.112509	+	0.194871i
$712$		0			0
$713$	24.0000			0.898807
$714$		0			0
$715$	−3.00000			−0.112194
$716$	−4.00000	+	6.92820i	−0.149487	+	0.258919i
$717$	10.5000	+	18.1865i	0.392130	+	0.679189i
$718$	32.0000	+	55.4256i	1.19423	+	2.06847i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$	−24.0000			−0.894427
$721$		0			0
$722$	−34.0000			−1.26535
$723$	36.0000	−	62.3538i	1.33885	−	2.31896i
$724$	−6.00000	−	10.3923i	−0.222988	−	0.386227i
$725$	0.500000	+	0.866025i	0.0185695	+	0.0321634i
$726$	30.0000	−	51.9615i	1.11340	−	1.92847i
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−6.00000	+	10.3923i	−0.222070	+	0.384636i
$731$	9.00000	+	15.5885i	0.332877	+	0.576560i
$732$		0			0
$733$	7.50000	−	12.9904i	0.277019	−	0.479811i	−0.693624	−	0.720338i	$-0.743987\pi$
$733$	7.50000	−	12.9904i	0.277019	−	0.479811i	0.970642	+	0.240527i	$0.0773202\pi$
$734$	−66.0000			−2.43610
$735$		0			0
$736$	−32.0000			−1.17954
$737$	7.00000	−	12.1244i	0.257848	−	0.446606i
$738$	−36.0000	−	62.3538i	−1.32518	−	2.29528i
$739$	21.5000	+	37.2391i	0.790890	+	1.36986i	0.925416	+	0.378952i	$0.123715\pi$
$739$	21.5000	+	37.2391i	0.790890	+	1.36986i	−0.134526	+	0.990910i	$0.542951\pi$
$740$		0			0
$741$	−54.0000			−1.98374
$742$		0			0
$743$	−22.0000			−0.807102			−0.403551	−	0.914957i	$-0.632224\pi$
$743$	−22.0000			−0.807102			−0.403551	+	0.914957i	$0.632224\pi$
$744$		0			0
$745$	−5.00000	−	8.66025i	−0.183186	−	0.317287i
$746$	4.00000	+	6.92820i	0.146450	+	0.253660i
$747$	36.0000	−	62.3538i	1.31717	−	2.28141i
$748$	6.00000			0.219382
$749$		0			0
$750$	6.00000			0.219089
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	−0.969801	−	0.243898i	$-0.921574\pi$
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	0.696122	+	0.717923i	$0.254907\pi$
$752$	18.0000	+	31.1769i	0.656392	+	1.13691i
$753$	18.0000	+	31.1769i	0.655956	+	1.13615i
$754$	3.00000	−	5.19615i	0.109254	−	0.189233i
$755$	15.0000			0.545906
$756$		0			0
$757$	48.0000			1.74459			0.872295	−	0.488980i	$-0.162631\pi$
$757$	48.0000			1.74459			0.872295	+	0.488980i	$0.162631\pi$
$758$	−24.0000	+	41.5692i	−0.871719	+	1.50986i
$759$	−6.00000	−	10.3923i	−0.217786	−	0.377217i
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$	−12.0000			−0.434714
$763$		0			0
$764$	34.0000			1.23008
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$		0			0
$767$	9.00000	+	15.5885i	0.324971	+	0.562867i
$768$	24.0000	−	41.5692i	0.866025	−	1.50000i
$769$	−42.0000			−1.51456			−0.757279	−	0.653091i	$-0.773472\pi$
$769$	−42.0000			−1.51456			−0.757279	+	0.653091i	$0.773472\pi$
$770$		0			0
$771$	54.0000			1.94476
$772$	−12.0000	+	20.7846i	−0.431889	+	0.748054i
$773$	1.50000	+	2.59808i	0.0539513	+	0.0934463i	0.891740	−	0.452549i	$-0.149485\pi$
$773$	1.50000	+	2.59808i	0.0539513	+	0.0934463i	−0.837788	+	0.545995i	$0.816152\pi$
$774$	−36.0000	−	62.3538i	−1.29399	−	2.24126i
$775$	3.00000	−	5.19615i	0.107763	−	0.186651i
$776$		0			0
$777$		0			0
$778$	−26.0000			−0.932145
$779$	−18.0000	+	31.1769i	−0.644917	+	1.11703i
$780$	−9.00000	−	15.5885i	−0.322252	−	0.558156i
$781$	4.00000	+	6.92820i	0.143131	+	0.247911i
$782$	−12.0000	+	20.7846i	−0.429119	+	0.743256i
$783$	9.00000			0.321634
$784$		0			0
$785$	−18.0000			−0.642448
$786$	36.0000	−	62.3538i	1.28408	−	2.22409i
$787$	19.5000	+	33.7750i	0.695100	+	1.20395i	0.970147	+	0.242518i	$0.0779732\pi$
$787$	19.5000	+	33.7750i	0.695100	+	1.20395i	−0.275047	+	0.961431i	$0.588693\pi$
$788$	2.00000	+	3.46410i	0.0712470	+	0.123404i
$789$	−15.0000	+	25.9808i	−0.534014	+	0.924940i
$790$	2.00000			0.0711568
$791$		0			0
$792$		0			0
$793$		0			0
$794$	−9.00000	−	15.5885i	−0.319398	−	0.553214i
$795$	−15.0000	−	25.9808i	−0.531995	−	0.921443i
$796$	6.00000	−	10.3923i	0.212664	−	0.368345i
$797$	27.0000			0.956389			0.478195	−	0.878254i	$-0.341291\pi$
$797$	27.0000			0.956389			0.478195	+	0.878254i	$0.341291\pi$
$798$		0			0
$799$	27.0000			0.955191
$800$	−4.00000	+	6.92820i	−0.141421	+	0.244949i
$801$	36.0000	+	62.3538i	1.27200	+	2.20316i
$802$	−19.0000	−	32.9090i	−0.670913	−	1.16206i
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$	84.0000			2.96245
$805$		0			0
$806$	−36.0000			−1.26805
$807$	−36.0000	+	62.3538i	−1.26726	+	2.19496i
$808$		0			0
$809$	17.5000	+	30.3109i	0.615267	+	1.06567i	0.990338	+	0.138678i	$0.0442852\pi$
$809$	17.5000	+	30.3109i	0.615267	+	1.06567i	−0.375070	+	0.926996i	$0.622381\pi$
$810$	9.00000	−	15.5885i	0.316228	−	0.547723i
$811$	−48.0000			−1.68551			−0.842754	−	0.538299i	$-0.819067\pi$
$811$	−48.0000			−1.68551			−0.842754	+	0.538299i	$0.819067\pi$
$812$		0			0
$813$	72.0000			2.52515
$814$		0			0
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$	−18.0000	−	31.1769i	−0.630126	−	1.09141i
$817$	−18.0000	+	31.1769i	−0.629740	+	1.09074i
$818$	60.0000			2.09785
$819$		0			0
$820$	−12.0000			−0.419058
$821$	11.5000	−	19.9186i	0.401353	−	0.695163i	−0.592537	−	0.805543i	$-0.701873\pi$
$821$	11.5000	−	19.9186i	0.401353	−	0.695163i	0.993889	+	0.110380i	$0.0352068\pi$
$822$	−24.0000	−	41.5692i	−0.837096	−	1.44989i
$823$	−25.0000	−	43.3013i	−0.871445	−	1.50939i	−0.860502	−	0.509447i	$-0.829850\pi$
$823$	−25.0000	−	43.3013i	−0.871445	−	1.50939i	−0.0109433	−	0.999940i	$-0.503483\pi$
$824$		0			0
$825$	−3.00000			−0.104447
$826$		0			0
$827$	−16.0000			−0.556375			−0.278187	−	0.960527i	$-0.589734\pi$
$827$	−16.0000			−0.556375			−0.278187	+	0.960527i	$0.589734\pi$
$828$	24.0000	−	41.5692i	0.834058	−	1.44463i
$829$	3.00000	+	5.19615i	0.104194	+	0.180470i	0.913409	−	0.407044i	$-0.133440\pi$
$829$	3.00000	+	5.19615i	0.104194	+	0.180470i	−0.809214	+	0.587513i	$0.800107\pi$
$830$	−12.0000	−	20.7846i	−0.416526	−	0.721444i
$831$	−42.0000	+	72.7461i	−1.45696	+	2.52354i
$832$	24.0000			0.832050
$833$		0			0
$834$		0			0
$835$	1.50000	−	2.59808i	0.0519096	−	0.0899101i
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	−27.0000	−	46.7654i	−0.933257	−	1.61645i
$838$	6.00000	−	10.3923i	0.207267	−	0.358996i
$839$	24.0000			0.828572			0.414286	−	0.910147i	$-0.364031\pi$
$839$	24.0000			0.828572			0.414286	+	0.910147i	$0.364031\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	1.00000	−	1.73205i	0.0344623	−	0.0596904i
$843$	−7.50000	−	12.9904i	−0.258314	−	0.447412i
$844$	−15.0000	−	25.9808i	−0.516321	−	0.894295i
$845$	2.00000	−	3.46410i	0.0688021	−	0.119169i
$846$	−108.000			−3.71312
$847$		0			0
$848$	40.0000			1.37361
$849$	−31.5000	+	54.5596i	−1.08108	+	1.87248i
$850$	3.00000	+	5.19615i	0.102899	+	0.178227i
$851$		0			0
$852$	−24.0000	+	41.5692i	−0.822226	+	1.42414i
$853$	−30.0000			−1.02718			−0.513590	−	0.858036i	$-0.671685\pi$
$853$	−30.0000			−1.02718			−0.513590	+	0.858036i	$0.671685\pi$
$854$		0			0
$855$	−36.0000			−1.23117
$856$		0			0
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.795843	+	0.605503i	$0.207028\pi$
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.126459	+	0.991972i	$0.459639\pi$
$858$	9.00000	+	15.5885i	0.307255	+	0.532181i
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	−0.745325	−	0.666701i	$-0.767706\pi$
$859$	6.00000	−	10.3923i	0.204717	−	0.354581i	0.950043	+	0.312120i	$0.101039\pi$
$860$	−12.0000			−0.409197
$861$		0			0
$862$	−10.0000			−0.340601
$863$	17.0000	−	29.4449i	0.578687	−	1.00231i	−0.416944	−	0.908932i	$-0.636899\pi$
$863$	17.0000	−	29.4449i	0.578687	−	1.00231i	0.995630	−	0.0933825i	$-0.0297679\pi$
$864$	36.0000	+	62.3538i	1.22474	+	2.12132i
$865$	−1.50000	−	2.59808i	−0.0510015	−	0.0883372i
$866$	30.0000	−	51.9615i	1.01944	−	1.76572i
$867$	24.0000			0.815083
$868$		0			0
$869$	−1.00000			−0.0339227
$870$	3.00000	−	5.19615i	0.101710	−	0.176166i
$871$	−21.0000	−	36.3731i	−0.711558	−	1.23245i
$872$		0			0
$873$	−45.0000	+	77.9423i	−1.52302	+	2.63795i
$874$	−48.0000			−1.62362
$875$		0			0
$876$	36.0000			1.21633
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	−12.0000	−	20.7846i	−0.404980	−	0.701447i
$879$	−13.5000	−	23.3827i	−0.455344	−	0.788678i
$880$	2.00000	−	3.46410i	0.0674200	−	0.116775i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$		0			0			−	1.00000i	$-0.5\pi$
$883$		0			0				1.00000i	$0.5\pi$
$884$	9.00000	−	15.5885i	0.302703	−	0.524297i
$885$	9.00000	+	15.5885i	0.302532	+	0.524000i
$886$	34.0000	+	58.8897i	1.14225	+	1.97844i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$		0			0
$889$		0			0
$890$	24.0000			0.804482
$891$	−4.50000	+	7.79423i	−0.150756	+	0.261116i
$892$	3.00000	+	5.19615i	0.100447	+	0.173980i
$893$	27.0000	+	46.7654i	0.903521	+	1.56494i
$894$	−30.0000	+	51.9615i	−1.00335	+	1.73785i
$895$	4.00000			0.133705
$896$		0			0
$897$	−36.0000			−1.20201
$898$	23.0000	−	39.8372i	0.767520	−	1.32938i
$899$	−3.00000	−	5.19615i	−0.100056	−	0.173301i
$900$	−6.00000	−	10.3923i	−0.200000	−	0.346410i
$901$	15.0000	−	25.9808i	0.499722	−	0.865545i
$902$	12.0000			0.399556
$903$		0			0
$904$		0			0
$905$	−3.00000	+	5.19615i	−0.0997234	+	0.172726i
$906$	−45.0000	−	77.9423i	−1.49502	−	2.58946i
$907$	−12.0000	−	20.7846i	−0.398453	−	0.690142i	0.595082	−	0.803665i	$-0.297120\pi$
$907$	−12.0000	−	20.7846i	−0.398453	−	0.690142i	−0.993535	+	0.113523i	$0.963786\pi$
$908$	3.00000	−	5.19615i	0.0995585	−	0.172440i
$909$	108.000			3.58213
$910$		0			0
$911$	40.0000			1.32526			0.662630	−	0.748947i	$-0.269440\pi$
$911$	40.0000			1.32526			0.662630	+	0.748947i	$0.269440\pi$
$912$	36.0000	−	62.3538i	1.19208	−	2.06474i
$913$	6.00000	+	10.3923i	0.198571	+	0.343935i
$914$	6.00000	+	10.3923i	0.198462	+	0.343747i
$915$		0			0
$916$	12.0000			0.396491
$917$		0			0
$918$	54.0000			1.78227
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	−0.782210	−	0.623015i	$-0.785908\pi$
$919$	4.50000	−	7.79423i	0.148441	−	0.257108i	0.930652	+	0.365907i	$0.119241\pi$
$920$		0			0
$921$	4.50000	+	7.79423i	0.148280	+	0.256829i
$922$	−36.0000	+	62.3538i	−1.18560	+	2.05351i
$923$	24.0000			0.789970
$924$		0			0
$925$		0			0
$926$	−4.00000	+	6.92820i	−0.131448	+	0.227675i
$927$	−27.0000	−	46.7654i	−0.886796	−	1.53598i
$928$	4.00000	+	6.92820i	0.131306	+	0.227429i
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	−0.283178	−	0.959067i	$-0.591389\pi$
$929$	21.0000	−	36.3731i	0.688988	−	1.19336i	0.972166	−	0.234294i	$-0.0752779\pi$
$930$	−36.0000			−1.18049
$931$		0			0
$932$	−16.0000			−0.524097
$933$	9.00000	−	15.5885i	0.294647	−	0.510343i
$934$	15.0000	+	25.9808i	0.490815	+	0.850117i
$935$	−1.50000	−	2.59808i	−0.0490552	−	0.0849662i
$936$		0			0
$937$	27.0000			0.882052			0.441026	−	0.897494i	$-0.354615\pi$
$937$	27.0000			0.882052			0.441026	+	0.897494i	$0.354615\pi$
$938$		0			0
$939$	9.00000			0.293704
$940$	−9.00000	+	15.5885i	−0.293548	+	0.508439i
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	54.0000	+	93.5307i	1.75942	+	3.04740i
$943$	−12.0000	+	20.7846i	−0.390774	+	0.676840i
$944$	−24.0000			−0.781133
$945$		0			0
$946$	12.0000			0.390154
$947$	1.00000	−	1.73205i	0.0324956	−	0.0562841i	−0.849320	−	0.527878i	$-0.822988\pi$
$947$	1.00000	−	1.73205i	0.0324956	−	0.0562841i	0.881816	+	0.471594i	$0.156321\pi$
$948$	−3.00000	−	5.19615i	−0.0974355	−	0.168763i
$949$	−9.00000	−	15.5885i	−0.292152	−	0.506023i
$950$	−6.00000	+	10.3923i	−0.194666	+	0.337171i
$951$	66.0000			2.14020
$952$		0			0
$953$	−38.0000			−1.23094			−0.615470	−	0.788160i	$-0.711034\pi$
$953$	−38.0000			−1.23094			−0.615470	+	0.788160i	$0.711034\pi$
$954$	−60.0000	+	103.923i	−1.94257	+	3.36463i
$955$	−8.50000	−	14.7224i	−0.275054	−	0.476407i
$956$	−7.00000	−	12.1244i	−0.226396	−	0.392130i
$957$	−1.50000	+	2.59808i	−0.0484881	+	0.0839839i
$958$	−48.0000			−1.55081
$959$		0			0
$960$	24.0000			0.774597
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$	6.00000	+	10.3923i	0.193347	+	0.334887i
$964$	−24.0000	+	41.5692i	−0.772988	+	1.33885i
$965$	12.0000			0.386294
$966$		0			0
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$		0			0
$969$	−27.0000	−	46.7654i	−0.867365	−	1.50232i
$970$	15.0000	+	25.9808i	0.481621	+	0.834192i
$971$	−9.00000	+	15.5885i	−0.288824	+	0.500257i	−0.973529	−	0.228562i	$-0.926597\pi$
$971$	−9.00000	+	15.5885i	−0.288824	+	0.500257i	0.684706	+	0.728820i	$0.259931\pi$
$972$		0			0
$973$		0			0
$974$	−72.0000			−2.30703
$975$	−4.50000	+	7.79423i	−0.144115	+	0.249615i
$976$		0			0
$977$	−17.0000	−	29.4449i	−0.543878	−	0.942025i	−0.998677	−	0.0514302i	$-0.983622\pi$
$977$	−17.0000	−	29.4449i	−0.543878	−	0.942025i	0.454798	−	0.890594i	$-0.349711\pi$
$978$	−48.0000	+	83.1384i	−1.53487	+	2.65847i
$979$	−12.0000			−0.383522
$980$		0			0
$981$	−90.0000			−2.87348
$982$	23.0000	−	39.8372i	0.733959	−	1.27126i
$983$	22.5000	+	38.9711i	0.717639	+	1.24299i	0.961933	+	0.273285i	$0.0881103\pi$
$983$	22.5000	+	38.9711i	0.717639	+	1.24299i	−0.244294	+	0.969701i	$0.578556\pi$
$984$		0			0
$985$	1.00000	−	1.73205i	0.0318626	−	0.0551877i
$986$	6.00000			0.191079
$987$		0			0
$988$	36.0000			1.14531
$989$	−12.0000	+	20.7846i	−0.381578	+	0.660912i
$990$	6.00000	+	10.3923i	0.190693	+	0.330289i
$991$	18.0000	+	31.1769i	0.571789	+	0.990367i	0.996382	+	0.0849833i	$0.0270837\pi$
$991$	18.0000	+	31.1769i	0.571789	+	0.990367i	−0.424594	+	0.905384i	$0.639583\pi$
$992$	24.0000	−	41.5692i	0.762001	−	1.31982i
$993$	−36.0000			−1.14243
$994$		0			0
$995$	−6.00000			−0.190213
$996$	−36.0000	+	62.3538i	−1.14070	+	1.97576i
$997$	−1.50000	−	2.59808i	−0.0475055	−	0.0822819i	0.841295	−	0.540576i	$-0.181794\pi$
$997$	−1.50000	−	2.59808i	−0.0475055	−	0.0822819i	−0.888800	+	0.458295i	$0.848460\pi$
$998$	−27.0000	−	46.7654i	−0.854670	−	1.48033i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.e.d.226.1		2
7.2	even	3		245.2.a.a.1.1	✓	1
7.3	odd	6		245.2.e.c.116.1		2
7.4	even	3	inner	245.2.e.d.116.1		2
7.5	odd	6		245.2.a.b.1.1	yes	1
7.6	odd	2		245.2.e.c.226.1		2
21.2	odd	6		2205.2.a.j.1.1		1
21.5	even	6		2205.2.a.l.1.1		1
28.19	even	6		3920.2.a.a.1.1		1
28.23	odd	6		3920.2.a.bj.1.1		1
35.2	odd	12		1225.2.b.b.99.1		2
35.9	even	6		1225.2.a.j.1.1		1
35.12	even	12		1225.2.b.a.99.1		2
35.19	odd	6		1225.2.a.h.1.1		1
35.23	odd	12		1225.2.b.b.99.2		2
35.33	even	12		1225.2.b.a.99.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.a.a.1.1	✓	1	7.2	even	3
245.2.a.b.1.1	yes	1	7.5	odd	6
245.2.e.c.116.1		2	7.3	odd	6
245.2.e.c.226.1		2	7.6	odd	2
245.2.e.d.116.1		2	7.4	even	3	inner
245.2.e.d.226.1		2	1.1	even	1	trivial
1225.2.a.h.1.1		1	35.19	odd	6
1225.2.a.j.1.1		1	35.9	even	6
1225.2.b.a.99.1		2	35.12	even	12
1225.2.b.a.99.2		2	35.33	even	12
1225.2.b.b.99.1		2	35.2	odd	12
1225.2.b.b.99.2		2	35.23	odd	12
2205.2.a.j.1.1		1	21.2	odd	6
2205.2.a.l.1.1		1	21.5	even	6
3920.2.a.a.1.1		1	28.19	even	6
3920.2.a.bj.1.1		1	28.23	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-1.00000 - 1.73205i) q^{4} +(-0.500000 + 0.866025i) q^{5} +6.00000 q^{6} +(-3.00000 + 5.19615i) q^{9} +(1.00000 + 1.73205i) q^{10} +(-0.500000 - 0.866025i) q^{11} +(3.00000 - 5.19615i) q^{12} -3.00000 q^{13} -3.00000 q^{15} +(2.00000 - 3.46410i) q^{16} +(-1.50000 - 2.59808i) q^{17} +(6.00000 + 10.3923i) q^{18} +(3.00000 - 5.19615i) q^{19} +2.00000 q^{20} -2.00000 q^{22} +(2.00000 - 3.46410i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} -9.00000 q^{27} -1.00000 q^{29} +(-3.00000 + 5.19615i) q^{30} +(3.00000 + 5.19615i) q^{31} +(-4.00000 - 6.92820i) q^{32} +(1.50000 - 2.59808i) q^{33} -6.00000 q^{34} +12.0000 q^{36} +(-6.00000 - 10.3923i) q^{38} +(-4.50000 - 7.79423i) q^{39} -6.00000 q^{41} -6.00000 q^{43} +(-1.00000 + 1.73205i) q^{44} +(-3.00000 - 5.19615i) q^{45} +(-4.00000 - 6.92820i) q^{46} +(-4.50000 + 7.79423i) q^{47} +12.0000 q^{48} -2.00000 q^{50} +(4.50000 - 7.79423i) q^{51} +(3.00000 + 5.19615i) q^{52} +(5.00000 + 8.66025i) q^{53} +(-9.00000 + 15.5885i) q^{54} +1.00000 q^{55} +18.0000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(3.00000 + 5.19615i) q^{60} +12.0000 q^{62} -8.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-3.00000 - 5.19615i) q^{66} +(7.00000 + 12.1244i) q^{67} +(-3.00000 + 5.19615i) q^{68} +12.0000 q^{69} -8.00000 q^{71} +(3.00000 + 5.19615i) q^{73} +(1.50000 - 2.59808i) q^{75} -12.0000 q^{76} -18.0000 q^{78} +(0.500000 - 0.866025i) q^{79} +(2.00000 + 3.46410i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-6.00000 + 10.3923i) q^{82} -12.0000 q^{83} +3.00000 q^{85} +(-6.00000 + 10.3923i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(6.00000 - 10.3923i) q^{89} -12.0000 q^{90} -8.00000 q^{92} +(-9.00000 + 15.5885i) q^{93} +(9.00000 + 15.5885i) q^{94} +(3.00000 + 5.19615i) q^{95} +(12.0000 - 20.7846i) q^{96} +15.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 3 q^{3} - 2 q^{4} - q^{5} + 12 q^{6} - 6 q^{9} + 2 q^{10} - q^{11} + 6 q^{12} - 6 q^{13} - 6 q^{15} + 4 q^{16} - 3 q^{17} + 12 q^{18} + 6 q^{19} + 4 q^{20} - 4 q^{22} + 4 q^{23} - q^{25}+ \cdots + 12 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 3 * q^3 - 2 * q^4 - q^5 + 12 * q^6 - 6 * q^9 + 2 * q^10 - q^11 + 6 * q^12 - 6 * q^13 - 6 * q^15 + 4 * q^16 - 3 * q^17 + 12 * q^18 + 6 * q^19 + 4 * q^20 - 4 * q^22 + 4 * q^23 - q^25 - 6 * q^26 - 18 * q^27 - 2 * q^29 - 6 * q^30 + 6 * q^31 - 8 * q^32 + 3 * q^33 - 12 * q^34 + 24 * q^36 - 12 * q^38 - 9 * q^39 - 12 * q^41 - 12 * q^43 - 2 * q^44 - 6 * q^45 - 8 * q^46 - 9 * q^47 + 24 * q^48 - 4 * q^50 + 9 * q^51 + 6 * q^52 + 10 * q^53 - 18 * q^54 + 2 * q^55 + 36 * q^57 - 2 * q^58 - 6 * q^59 + 6 * q^60 + 24 * q^62 - 16 * q^64 + 3 * q^65 - 6 * q^66 + 14 * q^67 - 6 * q^68 + 24 * q^69 - 16 * q^71 + 6 * q^73 + 3 * q^75 - 24 * q^76 - 36 * q^78 + q^79 + 4 * q^80 - 9 * q^81 - 12 * q^82 - 24 * q^83 + 6 * q^85 - 12 * q^86 - 3 * q^87 + 12 * q^89 - 24 * q^90 - 16 * q^92 - 18 * q^93 + 18 * q^94 + 6 * q^95 + 24 * q^96 + 30 * q^97 + 12 * q^99

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