LMFDB - Embedded newform 1064.2.q.a.305.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1064,2,Mod(305,1064)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1064, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 0]))

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

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

chi := DirichletCharacter("1064.305");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1064 = 2^{3} \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1064.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.49608277506$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			305.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1064.305
Dual form			1064.2.q.a.457.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +4.00000 q^{13} +2.00000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(4.00000 - 3.46410i) q^{21} +(3.50000 + 6.06218i) q^{23} +(2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +2.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(3.00000 + 5.19615i) q^{33} +(0.500000 + 2.59808i) q^{35} +(5.00000 + 8.66025i) q^{37} +(-4.00000 + 6.92820i) q^{39} +8.00000 q^{41} +7.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-3.00000 + 5.19615i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-7.00000 + 12.1244i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(0.500000 + 2.59808i) q^{63} +(-2.00000 - 3.46410i) q^{65} +(-7.00000 + 12.1244i) q^{67} -14.0000 q^{69} +8.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(4.00000 + 6.92820i) q^{75} +(-6.00000 + 5.19615i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} +17.0000 q^{83} +2.00000 q^{85} +(-2.00000 + 3.46410i) q^{87} +(-10.0000 - 3.46410i) q^{91} +(-6.00000 - 10.3923i) q^{93} +(-0.500000 + 0.866025i) q^{95} +12.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - q^{5} - 5 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 - q^5 - 5 * q^7 - q^9	$ 2 q - 2 q^{3} - q^{5} - 5 q^{7} - q^{9} + 3 q^{11} + 8 q^{13} + 4 q^{15} - 2 q^{17} - q^{19} + 8 q^{21} + 7 q^{23} + 4 q^{25} - 8 q^{27} + 4 q^{29} - 6 q^{31} + 6 q^{33} + q^{35} + 10 q^{37} - 8 q^{39} + 16 q^{41} + 14 q^{43} - q^{45} - 9 q^{47} + 11 q^{49} - 4 q^{51} - 6 q^{53} - 6 q^{55} + 4 q^{57} - 14 q^{59} - 5 q^{61} + q^{63} - 4 q^{65} - 14 q^{67} - 28 q^{69} + 16 q^{71} - q^{73} + 8 q^{75} - 12 q^{77} - 10 q^{79} + 11 q^{81} + 34 q^{83} + 4 q^{85} - 4 q^{87} - 20 q^{91} - 12 q^{93} - q^{95} + 24 q^{97} - 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - q^5 - 5 * q^7 - q^9 + 3 * q^11 + 8 * q^13 + 4 * q^15 - 2 * q^17 - q^19 + 8 * q^21 + 7 * q^23 + 4 * q^25 - 8 * q^27 + 4 * q^29 - 6 * q^31 + 6 * q^33 + q^35 + 10 * q^37 - 8 * q^39 + 16 * q^41 + 14 * q^43 - q^45 - 9 * q^47 + 11 * q^49 - 4 * q^51 - 6 * q^53 - 6 * q^55 + 4 * q^57 - 14 * q^59 - 5 * q^61 + q^63 - 4 * q^65 - 14 * q^67 - 28 * q^69 + 16 * q^71 - q^73 + 8 * q^75 - 12 * q^77 - 10 * q^79 + 11 * q^81 + 34 * q^83 + 4 * q^85 - 4 * q^87 - 20 * q^91 - 12 * q^93 - q^95 + 24 * q^97 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1064\mathbb{Z}\right)^\times$.

$n$	$533$	$799$	$913$	$1009$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$		0			0
$15$	2.00000			0.516398
$16$		0			0
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i
$20$		0			0
$21$	4.00000	−	3.46410i	0.872872	−	0.755929i
$22$		0			0
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	0.956967	+	0.290196i	$0.0937204\pi$
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	2.00000			0.371391			0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000			0.371391			0.185695	+	0.982607i	$0.440546\pi$
$30$		0			0
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$		0			0
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$		0			0
$35$	0.500000	+	2.59808i	0.0845154	+	0.439155i
$36$		0			0
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	0.904194	+	0.427121i	$0.140472\pi$
$37$	5.00000	+	8.66025i	0.821995	+	1.42374i	−0.0821995	+	0.996616i	$0.526194\pi$
$38$		0			0
$39$	−4.00000	+	6.92820i	−0.640513	+	1.10940i
$40$		0			0
$41$	8.00000			1.24939			0.624695	−	0.780869i	$-0.285223\pi$
$41$	8.00000			1.24939			0.624695	+	0.780869i	$0.285223\pi$
$42$		0			0
$43$	7.00000			1.06749			0.533745	−	0.845645i	$-0.320784\pi$
$43$	7.00000			1.06749			0.533745	+	0.845645i	$0.320784\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	−0.981543	−	0.191243i	$-0.938748\pi$
$47$	−4.50000	−	7.79423i	−0.656392	−	1.13691i	0.325150	−	0.945662i	$-0.394585\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$		0			0
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	−0.995117	−	0.0987002i	$-0.968532\pi$
$53$	−3.00000	+	5.19615i	−0.412082	+	0.713746i	0.583036	+	0.812447i	$0.301865\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.0991242	+	0.995075i	$0.531604\pi$
$59$	−7.00000	+	12.1244i	−0.911322	+	1.57846i	−0.812198	+	0.583382i	$0.801729\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$	0.500000	+	2.59808i	0.0629941	+	0.327327i
$64$		0			0
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$		0			0
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	0.0212861	+	0.999773i	$0.493224\pi$
$67$	−7.00000	+	12.1244i	−0.855186	+	1.48123i	−0.876472	+	0.481452i	$0.840109\pi$
$68$		0			0
$69$	−14.0000			−1.68540
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	−0.893801	−	0.448463i	$-0.851972\pi$
$73$	−0.500000	+	0.866025i	−0.0585206	+	0.101361i	0.835281	+	0.549823i	$0.185305\pi$
$74$		0			0
$75$	4.00000	+	6.92820i	0.461880	+	0.800000i
$76$		0			0
$77$	−6.00000	+	5.19615i	−0.683763	+	0.592157i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	17.0000			1.86599			0.932996	−	0.359886i	$-0.117184\pi$
$83$	17.0000			1.86599			0.932996	+	0.359886i	$0.117184\pi$
$84$		0			0
$85$	2.00000			0.216930
$86$		0			0
$87$	−2.00000	+	3.46410i	−0.214423	+	0.371391i
$88$		0			0
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−10.0000	−	3.46410i	−1.04828	−	0.363137i
$92$		0			0
$93$	−6.00000	−	10.3923i	−0.622171	−	1.07763i
$94$		0			0
$95$	−0.500000	+	0.866025i	−0.0512989	+	0.0888523i
$96$		0			0
$97$	12.0000			1.21842			0.609208	−	0.793011i	$-0.291488\pi$
$97$	12.0000			1.21842			0.609208	+	0.793011i	$0.291488\pi$
$98$		0			0
$99$	−3.00000			−0.301511
$100$		0			0
$101$	−5.50000	+	9.52628i	−0.547270	+	0.947900i	0.451190	+	0.892428i	$0.351000\pi$
$101$	−5.50000	+	9.52628i	−0.547270	+	0.947900i	−0.998460	+	0.0554722i	$0.982334\pi$
$102$		0			0
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$		0			0
$105$	−5.00000	−	1.73205i	−0.487950	−	0.169031i
$106$		0			0
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.861931	+	0.507026i	$0.169255\pi$
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.00813215	+	0.999967i	$0.497411\pi$
$108$		0			0
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	−0.173316	−	0.984866i	$-0.555448\pi$
$109$	8.00000	−	13.8564i	0.766261	−	1.32720i	0.939577	−	0.342337i	$-0.111218\pi$
$110$		0			0
$111$	−20.0000			−1.89832
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$	3.50000	−	6.06218i	0.326377	−	0.565301i
$116$		0			0
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$		0			0
$119$	4.00000	−	3.46410i	0.366679	−	0.317554i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	−8.00000	+	13.8564i	−0.721336	+	1.24939i
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	−7.00000	+	12.1244i	−0.616316	+	1.06749i
$130$		0			0
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$	0.500000	+	2.59808i	0.0433555	+	0.225282i
$134$		0			0
$135$	2.00000	+	3.46410i	0.172133	+	0.298142i
$136$		0			0
$137$	3.50000	−	6.06218i	0.299025	−	0.517927i	−0.676888	−	0.736086i	$-0.736672\pi$
$137$	3.50000	−	6.06218i	0.299025	−	0.517927i	0.975913	+	0.218159i	$0.0700052\pi$
$138$		0			0
$139$	9.00000			0.763370			0.381685	−	0.924292i	$-0.375344\pi$
$139$	9.00000			0.763370			0.381685	+	0.924292i	$0.375344\pi$
$140$		0			0
$141$	18.0000			1.51587
$142$		0			0
$143$	6.00000	−	10.3923i	0.501745	−	0.869048i
$144$		0			0
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$		0			0
$147$	−13.0000	+	5.19615i	−1.07222	+	0.428571i
$148$		0			0
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	−0.511636	−	0.859202i	$-0.670960\pi$
$151$	6.00000	−	10.3923i	0.488273	−	0.845714i	0.999909	+	0.0134886i	$0.00429367\pi$
$152$		0			0
$153$	2.00000			0.161690
$154$		0			0
$155$	6.00000			0.481932
$156$		0			0
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$		0			0
$159$	−6.00000	−	10.3923i	−0.475831	−	0.824163i
$160$		0			0
$161$	−3.50000	−	18.1865i	−0.275839	−	1.43330i
$162$		0			0
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	0.566149	−	0.824303i	$-0.308433\pi$
$163$	−5.50000	−	9.52628i	−0.430793	−	0.746156i	−0.996942	+	0.0781474i	$0.975100\pi$
$164$		0			0
$165$	3.00000	−	5.19615i	0.233550	−	0.404520i
$166$		0			0
$167$	−12.0000			−0.928588			−0.464294	−	0.885681i	$-0.653692\pi$
$167$	−12.0000			−0.928588			−0.464294	+	0.885681i	$0.653692\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$		0			0
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	0.998755	−	0.0498898i	$-0.0158870\pi$
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	−0.542583	+	0.840002i	$0.682554\pi$
$174$		0			0
$175$	−8.00000	+	6.92820i	−0.604743	+	0.523723i
$176$		0			0
$177$	−14.0000	−	24.2487i	−1.05230	−	1.82264i
$178$		0			0
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$		0			0
$181$	−16.0000			−1.18927			−0.594635	−	0.803996i	$-0.702704\pi$
$181$	−16.0000			−1.18927			−0.594635	+	0.803996i	$0.702704\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$		0			0
$185$	5.00000	−	8.66025i	0.367607	−	0.636715i
$186$		0			0
$187$	3.00000	+	5.19615i	0.219382	+	0.379980i
$188$		0			0
$189$	10.0000	+	3.46410i	0.727393	+	0.251976i
$190$		0			0
$191$	−6.50000	−	11.2583i	−0.470323	−	0.814624i	0.529101	−	0.848559i	$-0.322529\pi$
$191$	−6.50000	−	11.2583i	−0.470323	−	0.814624i	−0.999424	+	0.0339349i	$0.989196\pi$
$192$		0			0
$193$	12.0000	−	20.7846i	0.863779	−	1.49611i	−0.00447566	−	0.999990i	$-0.501425\pi$
$193$	12.0000	−	20.7846i	0.863779	−	1.49611i	0.868255	−	0.496119i	$-0.165242\pi$
$194$		0			0
$195$	8.00000			0.572892
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$		0			0
$199$	−0.500000	+	0.866025i	−0.0354441	+	0.0613909i	−0.883203	−	0.468990i	$-0.844618\pi$
$199$	−0.500000	+	0.866025i	−0.0354441	+	0.0613909i	0.847759	+	0.530381i	$0.177951\pi$
$200$		0			0
$201$	−14.0000	−	24.2487i	−0.987484	−	1.71037i
$202$		0			0
$203$	−5.00000	−	1.73205i	−0.350931	−	0.121566i
$204$		0			0
$205$	−4.00000	−	6.92820i	−0.279372	−	0.483887i
$206$		0			0
$207$	3.50000	−	6.06218i	0.243267	−	0.421350i
$208$		0			0
$209$	−3.00000			−0.207514
$210$		0			0
$211$	22.0000			1.51454			0.757271	−	0.653101i	$-0.226532\pi$
$211$	22.0000			1.51454			0.757271	+	0.653101i	$0.226532\pi$
$212$		0			0
$213$	−8.00000	+	13.8564i	−0.548151	+	0.949425i
$214$		0			0
$215$	−3.50000	−	6.06218i	−0.238698	−	0.413437i
$216$		0			0
$217$	12.0000	−	10.3923i	0.814613	−	0.705476i
$218$		0			0
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$		0			0
$221$	−4.00000	+	6.92820i	−0.269069	+	0.466041i
$222$		0			0
$223$	20.0000			1.33930			0.669650	−	0.742677i	$-0.266444\pi$
$223$	20.0000			1.33930			0.669650	+	0.742677i	$0.266444\pi$
$224$		0			0
$225$	−4.00000			−0.266667
$226$		0			0
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	−0.702202	−	0.711977i	$-0.747800\pi$
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	0.967692	+	0.252136i	$0.0811332\pi$
$228$		0			0
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	0.749714	−	0.661762i	$-0.230191\pi$
$229$	−3.00000	−	5.19615i	−0.198246	−	0.343371i	−0.947960	+	0.318390i	$0.896858\pi$
$230$		0			0
$231$	−3.00000	−	15.5885i	−0.197386	−	1.02565i
$232$		0			0
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−4.50000	+	7.79423i	−0.293548	+	0.508439i
$236$		0			0
$237$	20.0000			1.29914
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$		0			0
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$		0			0
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$		0			0
$249$	−17.0000	+	29.4449i	−1.07733	+	1.86599i
$250$		0			0
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$		0			0
$253$	21.0000			1.32026
$254$		0			0
$255$	−2.00000	+	3.46410i	−0.125245	+	0.216930i
$256$		0			0
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	0.666880	−	0.745165i	$-0.267629\pi$
$257$	−5.00000	−	8.66025i	−0.311891	−	0.540212i	−0.978772	+	0.204953i	$0.934296\pi$
$258$		0			0
$259$	−5.00000	−	25.9808i	−0.310685	−	1.61437i
$260$		0			0
$261$	−1.00000	−	1.73205i	−0.0618984	−	0.107211i
$262$		0			0
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$		0			0
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	0.543130	−	0.839649i	$-0.317239\pi$
$271$	−7.50000	−	12.9904i	−0.455593	−	0.789109i	−0.998722	+	0.0505395i	$0.983906\pi$
$272$		0			0
$273$	16.0000	−	13.8564i	0.968364	−	0.838628i
$274$		0			0
$275$	−6.00000	−	10.3923i	−0.361814	−	0.626680i
$276$		0			0
$277$	2.50000	−	4.33013i	0.150210	−	0.260172i	−0.781094	−	0.624413i	$-0.785338\pi$
$277$	2.50000	−	4.33013i	0.150210	−	0.260172i	0.931305	+	0.364241i	$0.118672\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	−10.0000			−0.596550			−0.298275	−	0.954480i	$-0.596411\pi$
$281$	−10.0000			−0.596550			−0.298275	+	0.954480i	$0.596411\pi$
$282$		0			0
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	−0.605575	−	0.795788i	$-0.707057\pi$
$283$	6.50000	−	11.2583i	0.386385	−	0.669238i	0.991960	+	0.126550i	$0.0403903\pi$
$284$		0			0
$285$	−1.00000	−	1.73205i	−0.0592349	−	0.102598i
$286$		0			0
$287$	−20.0000	−	6.92820i	−1.18056	−	0.408959i
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$		0			0
$291$	−12.0000	+	20.7846i	−0.703452	+	1.21842i
$292$		0			0
$293$	−24.0000			−1.40209			−0.701047	−	0.713115i	$-0.747284\pi$
$293$	−24.0000			−1.40209			−0.701047	+	0.713115i	$0.747284\pi$
$294$		0			0
$295$	14.0000			0.815112
$296$		0			0
$297$	−6.00000	+	10.3923i	−0.348155	+	0.603023i
$298$		0			0
$299$	14.0000	+	24.2487i	0.809641	+	1.40234i
$300$		0			0
$301$	−17.5000	−	6.06218i	−1.00868	−	0.349418i
$302$		0			0
$303$	−11.0000	−	19.0526i	−0.631933	−	1.09454i
$304$		0			0
$305$	−2.50000	+	4.33013i	−0.143150	+	0.247942i
$306$		0			0
$307$	−16.0000			−0.913168			−0.456584	−	0.889680i	$-0.650927\pi$
$307$	−16.0000			−0.913168			−0.456584	+	0.889680i	$0.650927\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$		0			0
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	0.749993	−	0.661445i	$-0.230057\pi$
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	−0.947825	+	0.318791i	$0.896723\pi$
$314$		0			0
$315$	2.00000	−	1.73205i	0.112687	−	0.0975900i
$316$		0			0
$317$	2.00000	+	3.46410i	0.112331	+	0.194563i	0.916710	−	0.399554i	$-0.130835\pi$
$317$	2.00000	+	3.46410i	0.112331	+	0.194563i	−0.804379	+	0.594117i	$0.797502\pi$
$318$		0			0
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$		0			0
$321$	−36.0000			−2.00932
$322$		0			0
$323$	2.00000			0.111283
$324$		0			0
$325$	8.00000	−	13.8564i	0.443760	−	0.768615i
$326$		0			0
$327$	16.0000	+	27.7128i	0.884802	+	1.53252i
$328$		0			0
$329$	4.50000	+	23.3827i	0.248093	+	1.28913i
$330$		0			0
$331$	−3.00000	−	5.19615i	−0.164895	−	0.285606i	0.771723	−	0.635959i	$-0.219395\pi$
$331$	−3.00000	−	5.19615i	−0.164895	−	0.285606i	−0.936618	+	0.350352i	$0.886062\pi$
$332$		0			0
$333$	5.00000	−	8.66025i	0.273998	−	0.474579i
$334$		0			0
$335$	14.0000			0.764902
$336$		0			0
$337$	28.0000			1.52526			0.762629	−	0.646837i	$-0.223908\pi$
$337$	28.0000			1.52526			0.762629	+	0.646837i	$0.223908\pi$
$338$		0			0
$339$	−2.00000	+	3.46410i	−0.108625	+	0.188144i
$340$		0			0
$341$	9.00000	+	15.5885i	0.487377	+	0.844162i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$		0			0
$345$	7.00000	+	12.1244i	0.376867	+	0.652753i
$346$		0			0
$347$	−6.50000	+	11.2583i	−0.348938	+	0.604379i	−0.986061	−	0.166383i	$-0.946791\pi$
$347$	−6.50000	+	11.2583i	−0.348938	+	0.604379i	0.637123	+	0.770762i	$0.280124\pi$
$348$		0			0
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−16.0000			−0.854017
$352$		0			0
$353$	−13.0000	+	22.5167i	−0.691920	+	1.19844i	0.279288	+	0.960207i	$0.409902\pi$
$353$	−13.0000	+	22.5167i	−0.691920	+	1.19844i	−0.971208	+	0.238233i	$0.923432\pi$
$354$		0			0
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$		0			0
$357$	2.00000	+	10.3923i	0.105851	+	0.550019i
$358$		0			0
$359$	12.5000	+	21.6506i	0.659725	+	1.14268i	0.980687	+	0.195585i	$0.0626605\pi$
$359$	12.5000	+	21.6506i	0.659725	+	1.14268i	−0.320962	+	0.947092i	$0.604006\pi$
$360$		0			0
$361$	−0.500000	+	0.866025i	−0.0263158	+	0.0455803i
$362$		0			0
$363$	−4.00000			−0.209946
$364$		0			0
$365$	1.00000			0.0523424
$366$		0			0
$367$	−6.00000	+	10.3923i	−0.313197	+	0.542474i	−0.979053	−	0.203607i	$-0.934733\pi$
$367$	−6.00000	+	10.3923i	−0.313197	+	0.542474i	0.665855	+	0.746081i	$0.268067\pi$
$368$		0			0
$369$	−4.00000	−	6.92820i	−0.208232	−	0.360668i
$370$		0			0
$371$	12.0000	−	10.3923i	0.623009	−	0.539542i
$372$		0			0
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$		0			0
$375$	9.00000	−	15.5885i	0.464758	−	0.804984i
$376$		0			0
$377$	8.00000			0.412021
$378$		0			0
$379$	18.0000			0.924598			0.462299	−	0.886724i	$-0.347025\pi$
$379$	18.0000			0.924598			0.462299	+	0.886724i	$0.347025\pi$
$380$		0			0
$381$	−8.00000	+	13.8564i	−0.409852	+	0.709885i
$382$		0			0
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	0.671027	−	0.741433i	$-0.265853\pi$
$383$	−6.00000	−	10.3923i	−0.306586	−	0.531022i	−0.977613	+	0.210411i	$0.932520\pi$
$384$		0			0
$385$	7.50000	+	2.59808i	0.382235	+	0.132410i
$386$		0			0
$387$	−3.50000	−	6.06218i	−0.177915	−	0.308158i
$388$		0			0
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	−0.932002	−	0.362454i	$-0.881939\pi$
$389$	−3.00000	+	5.19615i	−0.152106	+	0.263455i	0.779895	+	0.625910i	$0.215272\pi$
$390$		0			0
$391$	−14.0000			−0.708010
$392$		0			0
$393$	−24.0000			−1.21064
$394$		0			0
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$		0			0
$397$	3.00000	+	5.19615i	0.150566	+	0.260787i	0.931436	−	0.363906i	$-0.118557\pi$
$397$	3.00000	+	5.19615i	0.150566	+	0.260787i	−0.780870	+	0.624694i	$0.785224\pi$
$398$		0			0
$399$	−5.00000	−	1.73205i	−0.250313	−	0.0867110i
$400$		0			0
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$	−12.0000	+	20.7846i	−0.597763	+	1.03536i
$404$		0			0
$405$	−11.0000			−0.546594
$406$		0			0
$407$	30.0000			1.48704
$408$		0			0
$409$	17.0000	−	29.4449i	0.840596	−	1.45595i	−0.0487958	−	0.998809i	$-0.515538\pi$
$409$	17.0000	−	29.4449i	0.840596	−	1.45595i	0.889392	−	0.457146i	$-0.151128\pi$
$410$		0			0
$411$	7.00000	+	12.1244i	0.345285	+	0.598050i
$412$		0			0
$413$	28.0000	−	24.2487i	1.37779	−	1.19320i
$414$		0			0
$415$	−8.50000	−	14.7224i	−0.417249	−	0.722696i
$416$		0			0
$417$	−9.00000	+	15.5885i	−0.440732	+	0.763370i
$418$		0			0
$419$	−23.0000			−1.12362			−0.561812	−	0.827265i	$-0.689895\pi$
$419$	−23.0000			−1.12362			−0.561812	+	0.827265i	$0.689895\pi$
$420$		0			0
$421$	−8.00000			−0.389896			−0.194948	−	0.980814i	$-0.562454\pi$
$421$	−8.00000			−0.389896			−0.194948	+	0.980814i	$0.562454\pi$
$422$		0			0
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$		0			0
$425$	4.00000	+	6.92820i	0.194029	+	0.336067i
$426$		0			0
$427$	2.50000	+	12.9904i	0.120983	+	0.628649i
$428$		0			0
$429$	12.0000	+	20.7846i	0.579365	+	1.00349i
$430$		0			0
$431$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$431$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$	4.00000			0.191785
$436$		0			0
$437$	3.50000	−	6.06218i	0.167428	−	0.289993i
$438$		0			0
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	−0.989401	−	0.145210i	$-0.953614\pi$
$439$	−13.0000	−	22.5167i	−0.620456	−	1.07466i	0.368945	−	0.929451i	$-0.379719\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	6.00000			0.283790
$448$		0			0
$449$	−32.0000			−1.51017			−0.755087	−	0.655625i	$-0.772405\pi$
$449$	−32.0000			−1.51017			−0.755087	+	0.655625i	$0.772405\pi$
$450$		0			0
$451$	12.0000	−	20.7846i	0.565058	−	0.978709i
$452$		0			0
$453$	12.0000	+	20.7846i	0.563809	+	0.976546i
$454$		0			0
$455$	2.00000	+	10.3923i	0.0937614	+	0.487199i
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$		0			0
$459$	4.00000	−	6.92820i	0.186704	−	0.323381i
$460$		0			0
$461$	7.00000			0.326023			0.163011	−	0.986624i	$-0.447879\pi$
$461$	7.00000			0.326023			0.163011	+	0.986624i	$0.447879\pi$
$462$		0			0
$463$	33.0000			1.53364			0.766820	−	0.641862i	$-0.221838\pi$
$463$	33.0000			1.53364			0.766820	+	0.641862i	$0.221838\pi$
$464$		0			0
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$		0			0
$467$	14.5000	+	25.1147i	0.670980	+	1.16217i	0.977627	+	0.210348i	$0.0674597\pi$
$467$	14.5000	+	25.1147i	0.670980	+	1.16217i	−0.306647	+	0.951823i	$0.599207\pi$
$468$		0			0
$469$	28.0000	−	24.2487i	1.29292	−	1.11970i
$470$		0			0
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$		0			0
$473$	10.5000	−	18.1865i	0.482791	−	0.836218i
$474$		0			0
$475$	−4.00000			−0.183533
$476$		0			0
$477$	6.00000			0.274721
$478$		0			0
$479$	−3.50000	+	6.06218i	−0.159919	+	0.276988i	−0.934839	−	0.355071i	$-0.884457\pi$
$479$	−3.50000	+	6.06218i	−0.159919	+	0.276988i	0.774920	+	0.632059i	$0.217790\pi$
$480$		0			0
$481$	20.0000	+	34.6410i	0.911922	+	1.57949i
$482$		0			0
$483$	35.0000	+	12.1244i	1.59256	+	0.551677i
$484$		0			0
$485$	−6.00000	−	10.3923i	−0.272446	−	0.471890i
$486$		0			0
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	−0.842479	−	0.538730i	$-0.818904\pi$
$487$	1.00000	−	1.73205i	0.0453143	−	0.0784867i	0.887793	+	0.460243i	$0.152238\pi$
$488$		0			0
$489$	22.0000			0.994874
$490$		0			0
$491$	−27.0000			−1.21849			−0.609246	−	0.792981i	$-0.708528\pi$
$491$	−27.0000			−1.21849			−0.609246	+	0.792981i	$0.708528\pi$
$492$		0			0
$493$	−2.00000	+	3.46410i	−0.0900755	+	0.156015i
$494$		0			0
$495$	1.50000	+	2.59808i	0.0674200	+	0.116775i
$496$		0			0
$497$	−20.0000	−	6.92820i	−0.897123	−	0.310772i
$498$		0			0
$499$	−6.50000	−	11.2583i	−0.290980	−	0.503992i	0.683062	−	0.730361i	$-0.260648\pi$
$499$	−6.50000	−	11.2583i	−0.290980	−	0.503992i	−0.974042	+	0.226369i	$0.927315\pi$
$500$		0			0
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$		0			0
$503$	9.00000			0.401290			0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000			0.401290			0.200645	+	0.979664i	$0.435696\pi$
$504$		0			0
$505$	11.0000			0.489494
$506$		0			0
$507$	−3.00000	+	5.19615i	−0.133235	+	0.230769i
$508$		0			0
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	2.00000	−	1.73205i	0.0884748	−	0.0766214i
$512$		0			0
$513$	2.00000	+	3.46410i	0.0883022	+	0.152944i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−27.0000			−1.18746
$518$		0			0
$519$	−24.0000			−1.05348
$520$		0			0
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	−0.954519	−	0.298150i	$-0.903630\pi$
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	0.735465	+	0.677563i	$0.236964\pi$
$522$		0			0
$523$	20.0000	+	34.6410i	0.874539	+	1.51475i	0.857253	+	0.514895i	$0.172169\pi$
$523$	20.0000	+	34.6410i	0.874539	+	1.51475i	0.0172859	+	0.999851i	$0.494497\pi$
$524$		0			0
$525$	−4.00000	−	20.7846i	−0.174574	−	0.907115i
$526$		0			0
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$		0			0
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$		0			0
$531$	14.0000			0.607548
$532$		0			0
$533$	32.0000			1.38607
$534$		0			0
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$		0			0
$537$	18.0000	+	31.1769i	0.776757	+	1.34538i
$538$		0			0
$539$	19.5000	−	7.79423i	0.839924	−	0.335721i
$540$		0			0
$541$	−16.5000	−	28.5788i	−0.709390	−	1.22870i	−0.965084	−	0.261942i	$-0.915637\pi$
$541$	−16.5000	−	28.5788i	−0.709390	−	1.22870i	0.255693	−	0.966758i	$-0.417696\pi$
$542$		0			0
$543$	16.0000	−	27.7128i	0.686626	−	1.18927i
$544$		0			0
$545$	−16.0000			−0.685365
$546$		0			0
$547$	−34.0000			−1.45374			−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000			−1.45374			−0.726868	+	0.686778i	$0.759025\pi$
$548$		0			0
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$		0			0
$551$	−1.00000	−	1.73205i	−0.0426014	−	0.0737878i
$552$		0			0
$553$	5.00000	+	25.9808i	0.212622	+	1.10481i
$554$		0			0
$555$	10.0000	+	17.3205i	0.424476	+	0.735215i
$556$		0			0
$557$	−17.5000	+	30.3109i	−0.741499	+	1.28431i	0.210314	+	0.977634i	$0.432551\pi$
$557$	−17.5000	+	30.3109i	−0.741499	+	1.28431i	−0.951813	+	0.306680i	$0.900782\pi$
$558$		0			0
$559$	28.0000			1.18427
$560$		0			0
$561$	−12.0000			−0.506640
$562$		0			0
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	−1.00000	−	1.73205i	−0.0420703	−	0.0728679i
$566$		0			0
$567$	−22.0000	+	19.0526i	−0.923913	+	0.800132i
$568$		0			0
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	−10.5000	+	18.1865i	−0.439411	+	0.761083i	−0.997644	−	0.0686016i	$-0.978146\pi$
$571$	−10.5000	+	18.1865i	−0.439411	+	0.761083i	0.558233	+	0.829684i	$0.311480\pi$
$572$		0			0
$573$	26.0000			1.08617
$574$		0			0
$575$	28.0000			1.16768
$576$		0			0
$577$	2.50000	−	4.33013i	0.104076	−	0.180266i	−0.809284	−	0.587417i	$-0.800145\pi$
$577$	2.50000	−	4.33013i	0.104076	−	0.180266i	0.913360	+	0.407152i	$0.133478\pi$
$578$		0			0
$579$	24.0000	+	41.5692i	0.997406	+	1.72756i
$580$		0			0
$581$	−42.5000	−	14.7224i	−1.76320	−	0.610789i
$582$		0			0
$583$	9.00000	+	15.5885i	0.372742	+	0.645608i
$584$		0			0
$585$	−2.00000	+	3.46410i	−0.0826898	+	0.143223i
$586$		0			0
$587$	36.0000			1.48588			0.742940	−	0.669359i	$-0.233431\pi$
$587$	36.0000			1.48588			0.742940	+	0.669359i	$0.233431\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$		0			0
$593$	−5.50000	−	9.52628i	−0.225858	−	0.391197i	0.730719	−	0.682679i	$-0.239185\pi$
$593$	−5.50000	−	9.52628i	−0.225858	−	0.391197i	−0.956576	+	0.291481i	$0.905852\pi$
$594$		0			0
$595$	−5.00000	−	1.73205i	−0.204980	−	0.0710072i
$596$		0			0
$597$	−1.00000	−	1.73205i	−0.0409273	−	0.0708881i
$598$		0			0
$599$	−4.00000	+	6.92820i	−0.163436	+	0.283079i	−0.936099	−	0.351738i	$-0.885591\pi$
$599$	−4.00000	+	6.92820i	−0.163436	+	0.283079i	0.772663	+	0.634816i	$0.218924\pi$
$600$		0			0
$601$	−6.00000			−0.244745			−0.122373	−	0.992484i	$-0.539050\pi$
$601$	−6.00000			−0.244745			−0.122373	+	0.992484i	$0.539050\pi$
$602$		0			0
$603$	14.0000			0.570124
$604$		0			0
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$		0			0
$609$	8.00000	−	6.92820i	0.324176	−	0.280745i
$610$		0			0
$611$	−18.0000	−	31.1769i	−0.728202	−	1.26128i
$612$		0			0
$613$	−9.00000	+	15.5885i	−0.363507	+	0.629612i	−0.988535	−	0.150990i	$-0.951754\pi$
$613$	−9.00000	+	15.5885i	−0.363507	+	0.629612i	0.625029	+	0.780602i	$0.285087\pi$
$614$		0			0
$615$	16.0000			0.645182
$616$		0			0
$617$	5.00000			0.201292			0.100646	−	0.994922i	$-0.467909\pi$
$617$	5.00000			0.201292			0.100646	+	0.994922i	$0.467909\pi$
$618$		0			0
$619$	21.5000	−	37.2391i	0.864158	−	1.49677i	−0.00372288	−	0.999993i	$-0.501185\pi$
$619$	21.5000	−	37.2391i	0.864158	−	1.49677i	0.867881	−	0.496772i	$-0.165482\pi$
$620$		0			0
$621$	−14.0000	−	24.2487i	−0.561801	−	0.973067i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$		0			0
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$		0			0
$629$	−20.0000			−0.797452
$630$		0			0
$631$	25.0000			0.995234			0.497617	−	0.867397i	$-0.334208\pi$
$631$	25.0000			0.995234			0.497617	+	0.867397i	$0.334208\pi$
$632$		0			0
$633$	−22.0000	+	38.1051i	−0.874421	+	1.51454i
$634$		0			0
$635$	−4.00000	−	6.92820i	−0.158735	−	0.274937i
$636$		0			0
$637$	22.0000	+	17.3205i	0.871672	+	0.686264i
$638$		0			0
$639$	−4.00000	−	6.92820i	−0.158238	−	0.274075i
$640$		0			0
$641$	5.00000	−	8.66025i	0.197488	−	0.342059i	−0.750225	−	0.661182i	$-0.770055\pi$
$641$	5.00000	−	8.66025i	0.197488	−	0.342059i	0.947713	+	0.319123i	$0.103388\pi$
$642$		0			0
$643$	36.0000			1.41970			0.709851	−	0.704352i	$-0.248762\pi$
$643$	36.0000			1.41970			0.709851	+	0.704352i	$0.248762\pi$
$644$		0			0
$645$	14.0000			0.551249
$646$		0			0
$647$	3.50000	−	6.06218i	0.137599	−	0.238329i	−0.788988	−	0.614408i	$-0.789395\pi$
$647$	3.50000	−	6.06218i	0.137599	−	0.238329i	0.926587	+	0.376080i	$0.122728\pi$
$648$		0			0
$649$	21.0000	+	36.3731i	0.824322	+	1.42777i
$650$		0			0
$651$	6.00000	+	31.1769i	0.235159	+	1.22192i
$652$		0			0
$653$	7.00000	+	12.1244i	0.273931	+	0.474463i	0.969865	−	0.243643i	$-0.0783426\pi$
$653$	7.00000	+	12.1244i	0.273931	+	0.474463i	−0.695934	+	0.718106i	$0.745009\pi$
$654$		0			0
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$		0			0
$657$	1.00000			0.0390137
$658$		0			0
$659$	6.00000			0.233727			0.116863	−	0.993148i	$-0.462716\pi$
$659$	6.00000			0.233727			0.116863	+	0.993148i	$0.462716\pi$
$660$		0			0
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	−0.978615	−	0.205702i	$-0.934052\pi$
$661$	−8.00000	+	13.8564i	−0.311164	+	0.538952i	0.667451	+	0.744654i	$0.267385\pi$
$662$		0			0
$663$	−8.00000	−	13.8564i	−0.310694	−	0.538138i
$664$		0			0
$665$	2.00000	−	1.73205i	0.0775567	−	0.0671660i
$666$		0			0
$667$	7.00000	+	12.1244i	0.271041	+	0.469457i
$668$		0			0
$669$	−20.0000	+	34.6410i	−0.773245	+	1.33930i
$670$		0			0
$671$	−15.0000			−0.579069
$672$		0			0
$673$	−50.0000			−1.92736			−0.963679	−	0.267063i	$-0.913947\pi$
$673$	−50.0000			−1.92736			−0.963679	+	0.267063i	$0.913947\pi$
$674$		0			0
$675$	−8.00000	+	13.8564i	−0.307920	+	0.533333i
$676$		0			0
$677$	16.0000	+	27.7128i	0.614930	+	1.06509i	0.990397	+	0.138254i	$0.0441491\pi$
$677$	16.0000	+	27.7128i	0.614930	+	1.06509i	−0.375467	+	0.926836i	$0.622518\pi$
$678$		0			0
$679$	−30.0000	−	10.3923i	−1.15129	−	0.398820i
$680$		0			0
$681$	8.00000	+	13.8564i	0.306561	+	0.530979i
$682$		0			0
$683$	7.00000	−	12.1244i	0.267848	−	0.463926i	−0.700458	−	0.713693i	$-0.747021\pi$
$683$	7.00000	−	12.1244i	0.267848	−	0.463926i	0.968306	+	0.249768i	$0.0803543\pi$
$684$		0			0
$685$	−7.00000			−0.267456
$686$		0			0
$687$	12.0000			0.457829
$688$		0			0
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	0.610704	−	0.791859i	$-0.290887\pi$
$691$	−10.0000	−	17.3205i	−0.380418	−	0.658903i	−0.991122	+	0.132956i	$0.957553\pi$
$692$		0			0
$693$	7.50000	+	2.59808i	0.284901	+	0.0986928i
$694$		0			0
$695$	−4.50000	−	7.79423i	−0.170695	−	0.295652i
$696$		0			0
$697$	−8.00000	+	13.8564i	−0.303022	+	0.524849i
$698$		0			0
$699$	−12.0000			−0.453882
$700$		0			0
$701$	−33.0000			−1.24639			−0.623196	−	0.782065i	$-0.714166\pi$
$701$	−33.0000			−1.24639			−0.623196	+	0.782065i	$0.714166\pi$
$702$		0			0
$703$	5.00000	−	8.66025i	0.188579	−	0.326628i
$704$		0			0
$705$	−9.00000	−	15.5885i	−0.338960	−	0.587095i
$706$		0			0
$707$	22.0000	−	19.0526i	0.827395	−	0.716545i
$708$		0			0
$709$	6.50000	+	11.2583i	0.244113	+	0.422815i	0.961882	−	0.273466i	$-0.0881700\pi$
$709$	6.50000	+	11.2583i	0.244113	+	0.422815i	−0.717769	+	0.696281i	$0.754837\pi$
$710$		0			0
$711$	−5.00000	+	8.66025i	−0.187515	+	0.324785i
$712$		0			0
$713$	−42.0000			−1.57291
$714$		0			0
$715$	−12.0000			−0.448775
$716$		0			0
$717$	24.0000	−	41.5692i	0.896296	−	1.55243i
$718$		0			0
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	0.930923	−	0.365216i	$-0.119005\pi$
$719$	4.00000	+	6.92820i	0.149175	+	0.258378i	−0.781748	+	0.623595i	$0.785672\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	−10.0000	−	17.3205i	−0.371904	−	0.644157i
$724$		0			0
$725$	4.00000	−	6.92820i	0.148556	−	0.257307i
$726$		0			0
$727$	−49.0000			−1.81731			−0.908655	−	0.417548i	$-0.862889\pi$
$727$	−49.0000			−1.81731			−0.908655	+	0.417548i	$0.862889\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−7.00000	+	12.1244i	−0.258904	+	0.448435i
$732$		0			0
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	0.965854	−	0.259087i	$-0.0834217\pi$
$733$	7.00000	+	12.1244i	0.258551	+	0.447823i	−0.707303	+	0.706910i	$0.750088\pi$
$734$		0			0
$735$	11.0000	+	8.66025i	0.405741	+	0.319438i
$736$		0			0
$737$	21.0000	+	36.3731i	0.773545	+	1.33982i
$738$		0			0
$739$	−14.0000	+	24.2487i	−0.514998	+	0.892003i	0.484850	+	0.874597i	$0.338874\pi$
$739$	−14.0000	+	24.2487i	−0.514998	+	0.892003i	−0.999849	+	0.0174060i	$0.994459\pi$
$740$		0			0
$741$	8.00000			0.293887
$742$		0			0
$743$	6.00000			0.220119			0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000			0.220119			0.110059	+	0.993925i	$0.464896\pi$
$744$		0			0
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$		0			0
$747$	−8.50000	−	14.7224i	−0.310999	−	0.538666i
$748$		0			0
$749$	−9.00000	−	46.7654i	−0.328853	−	1.70877i
$750$		0			0
$751$	−15.0000	−	25.9808i	−0.547358	−	0.948051i	−0.998454	−	0.0555764i	$-0.982300\pi$
$751$	−15.0000	−	25.9808i	−0.547358	−	0.948051i	0.451097	−	0.892475i	$-0.351033\pi$
$752$		0			0
$753$	15.0000	−	25.9808i	0.546630	−	0.946792i
$754$		0			0
$755$	−12.0000			−0.436725
$756$		0			0
$757$	−23.0000			−0.835949			−0.417975	−	0.908459i	$-0.637260\pi$
$757$	−23.0000			−0.835949			−0.417975	+	0.908459i	$0.637260\pi$
$758$		0			0
$759$	−21.0000	+	36.3731i	−0.762252	+	1.32026i
$760$		0			0
$761$	−10.5000	−	18.1865i	−0.380625	−	0.659261i	0.610527	−	0.791995i	$-0.290958\pi$
$761$	−10.5000	−	18.1865i	−0.380625	−	0.659261i	−0.991152	+	0.132734i	$0.957624\pi$
$762$		0			0
$763$	−32.0000	+	27.7128i	−1.15848	+	1.00327i
$764$		0			0
$765$	−1.00000	−	1.73205i	−0.0361551	−	0.0626224i
$766$		0			0
$767$	−28.0000	+	48.4974i	−1.01102	+	1.75114i
$768$		0			0
$769$	15.0000			0.540914			0.270457	−	0.962732i	$-0.412825\pi$
$769$	15.0000			0.540914			0.270457	+	0.962732i	$0.412825\pi$
$770$		0			0
$771$	20.0000			0.720282
$772$		0			0
$773$	−11.0000	+	19.0526i	−0.395643	+	0.685273i	−0.993183	−	0.116566i	$-0.962811\pi$
$773$	−11.0000	+	19.0526i	−0.395643	+	0.685273i	0.597540	+	0.801839i	$0.296145\pi$
$774$		0			0
$775$	12.0000	+	20.7846i	0.431053	+	0.746605i
$776$		0			0
$777$	50.0000	+	17.3205i	1.79374	+	0.621370i
$778$		0			0
$779$	−4.00000	−	6.92820i	−0.143315	−	0.248229i
$780$		0			0
$781$	12.0000	−	20.7846i	0.429394	−	0.743732i
$782$		0			0
$783$	−8.00000			−0.285897
$784$		0			0
$785$	7.00000			0.249841
$786$		0			0
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	−0.500953	−	0.865474i	$-0.667017\pi$
$787$	14.0000	−	24.2487i	0.499046	−	0.864373i	0.999999	+	0.00110111i	$0.000350496\pi$
$788$		0			0
$789$	−16.0000	−	27.7128i	−0.569615	−	0.986602i
$790$		0			0
$791$	−5.00000	−	1.73205i	−0.177780	−	0.0615846i
$792$		0			0
$793$	−10.0000	−	17.3205i	−0.355110	−	0.615069i
$794$		0			0
$795$	−6.00000	+	10.3923i	−0.212798	+	0.368577i
$796$		0			0
$797$	−42.0000			−1.48772			−0.743858	−	0.668338i	$-0.767006\pi$
$797$	−42.0000			−1.48772			−0.743858	+	0.668338i	$0.767006\pi$
$798$		0			0
$799$	18.0000			0.636794
$800$		0			0
$801$		0			0
$802$		0			0
$803$	1.50000	+	2.59808i	0.0529339	+	0.0916841i
$804$		0			0
$805$	−14.0000	+	12.1244i	−0.493435	+	0.427327i
$806$		0			0
$807$	−24.0000	−	41.5692i	−0.844840	−	1.46331i
$808$		0			0
$809$	20.5000	−	35.5070i	0.720742	−	1.24836i	−0.239961	−	0.970782i	$-0.577135\pi$
$809$	20.5000	−	35.5070i	0.720742	−	1.24836i	0.960703	−	0.277579i	$-0.0895319\pi$
$810$		0			0
$811$	42.0000			1.47482			0.737410	−	0.675446i	$-0.236049\pi$
$811$	42.0000			1.47482			0.737410	+	0.675446i	$0.236049\pi$
$812$		0			0
$813$	30.0000			1.05215
$814$		0			0
$815$	−5.50000	+	9.52628i	−0.192657	+	0.333691i
$816$		0			0
$817$	−3.50000	−	6.06218i	−0.122449	−	0.212089i
$818$		0			0
$819$	2.00000	+	10.3923i	0.0698857	+	0.363137i
$820$		0			0
$821$	−15.5000	−	26.8468i	−0.540954	−	0.936959i	−0.998850	−	0.0479535i	$-0.984730\pi$
$821$	−15.5000	−	26.8468i	−0.540954	−	0.936959i	0.457896	−	0.889006i	$-0.348603\pi$
$822$		0			0
$823$	−11.5000	+	19.9186i	−0.400865	+	0.694318i	−0.993831	−	0.110910i	$-0.964624\pi$
$823$	−11.5000	+	19.9186i	−0.400865	+	0.694318i	0.592966	+	0.805228i	$0.297957\pi$
$824$		0			0
$825$	24.0000			0.835573
$826$		0			0
$827$	8.00000			0.278187			0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000			0.278187			0.139094	+	0.990279i	$0.455581\pi$
$828$		0			0
$829$	−2.00000	+	3.46410i	−0.0694629	+	0.120313i	−0.898665	−	0.438636i	$-0.855462\pi$
$829$	−2.00000	+	3.46410i	−0.0694629	+	0.120313i	0.829202	+	0.558949i	$0.188795\pi$
$830$		0			0
$831$	5.00000	+	8.66025i	0.173448	+	0.300421i
$832$		0			0
$833$	−13.0000	+	5.19615i	−0.450423	+	0.180036i
$834$		0			0
$835$	6.00000	+	10.3923i	0.207639	+	0.359641i
$836$		0			0
$837$	12.0000	−	20.7846i	0.414781	−	0.718421i
$838$		0			0
$839$	54.0000			1.86429			0.932144	−	0.362089i	$-0.117936\pi$
$839$	54.0000			1.86429			0.932144	+	0.362089i	$0.117936\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$		0			0
$843$	10.0000	−	17.3205i	0.344418	−	0.596550i
$844$		0			0
$845$	−1.50000	−	2.59808i	−0.0516016	−	0.0893765i
$846$		0			0
$847$	−1.00000	−	5.19615i	−0.0343604	−	0.178542i
$848$		0			0
$849$	13.0000	+	22.5167i	0.446159	+	0.772770i
$850$		0			0
$851$	−35.0000	+	60.6218i	−1.19978	+	2.07809i
$852$		0			0
$853$	37.0000			1.26686			0.633428	−	0.773802i	$-0.281647\pi$
$853$	37.0000			1.26686			0.633428	+	0.773802i	$0.281647\pi$
$854$		0			0
$855$	1.00000			0.0341993
$856$		0			0
$857$	16.0000	−	27.7128i	0.546550	−	0.946652i	−0.451958	−	0.892039i	$-0.649274\pi$
$857$	16.0000	−	27.7128i	0.546550	−	0.946652i	0.998508	−	0.0546125i	$-0.0173923\pi$
$858$		0			0
$859$	8.50000	+	14.7224i	0.290016	+	0.502323i	0.973813	−	0.227349i	$-0.0730059\pi$
$859$	8.50000	+	14.7224i	0.290016	+	0.502323i	−0.683797	+	0.729672i	$0.739673\pi$
$860$		0			0
$861$	32.0000	−	27.7128i	1.09056	−	0.944450i
$862$		0			0
$863$	15.0000	+	25.9808i	0.510606	+	0.884395i	0.999924	+	0.0122903i	$0.00391222\pi$
$863$	15.0000	+	25.9808i	0.510606	+	0.884395i	−0.489319	+	0.872105i	$0.662754\pi$
$864$		0			0
$865$	6.00000	−	10.3923i	0.204006	−	0.353349i
$866$		0			0
$867$	−26.0000			−0.883006
$868$		0			0
$869$	−30.0000			−1.01768
$870$		0			0
$871$	−28.0000	+	48.4974i	−0.948744	+	1.64327i
$872$		0			0
$873$	−6.00000	−	10.3923i	−0.203069	−	0.351726i
$874$		0			0
$875$	22.5000	+	7.79423i	0.760639	+	0.263493i
$876$		0			0
$877$	4.00000	+	6.92820i	0.135070	+	0.233949i	0.925624	−	0.378444i	$-0.123541\pi$
$877$	4.00000	+	6.92820i	0.135070	+	0.233949i	−0.790554	+	0.612392i	$0.790207\pi$
$878$		0			0
$879$	24.0000	−	41.5692i	0.809500	−	1.40209i
$880$		0			0
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	−36.0000			−1.21150			−0.605748	−	0.795656i	$-0.707126\pi$
$883$	−36.0000			−1.21150			−0.605748	+	0.795656i	$0.707126\pi$
$884$		0			0
$885$	−14.0000	+	24.2487i	−0.470605	+	0.815112i
$886$		0			0
$887$	−16.0000	−	27.7128i	−0.537227	−	0.930505i	−0.999052	−	0.0435339i	$-0.986138\pi$
$887$	−16.0000	−	27.7128i	−0.537227	−	0.930505i	0.461825	−	0.886971i	$-0.347195\pi$
$888$		0			0
$889$	−20.0000	−	6.92820i	−0.670778	−	0.232364i
$890$		0			0
$891$	−16.5000	−	28.5788i	−0.552771	−	0.957427i
$892$		0			0
$893$	−4.50000	+	7.79423i	−0.150587	+	0.260824i
$894$		0			0
$895$	−18.0000			−0.601674
$896$		0			0
$897$	−56.0000			−1.86979
$898$		0			0
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$		0			0
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$		0			0
$903$	28.0000	−	24.2487i	0.931782	−	0.806947i
$904$		0			0
$905$	8.00000	+	13.8564i	0.265929	+	0.460603i
$906$		0			0
$907$	19.0000	−	32.9090i	0.630885	−	1.09272i	−0.356487	−	0.934300i	$-0.616025\pi$
$907$	19.0000	−	32.9090i	0.630885	−	1.09272i	0.987371	−	0.158424i	$-0.0506412\pi$
$908$		0			0
$909$	11.0000			0.364847
$910$		0			0
$911$	−58.0000			−1.92163			−0.960813	−	0.277198i	$-0.910594\pi$
$911$	−58.0000			−1.92163			−0.960813	+	0.277198i	$0.910594\pi$
$912$		0			0
$913$	25.5000	−	44.1673i	0.843927	−	1.46172i
$914$		0			0
$915$	−5.00000	−	8.66025i	−0.165295	−	0.286299i
$916$		0			0
$917$	−6.00000	−	31.1769i	−0.198137	−	1.02955i
$918$		0			0
$919$	−19.5000	−	33.7750i	−0.643246	−	1.11413i	−0.984704	−	0.174237i	$-0.944254\pi$
$919$	−19.5000	−	33.7750i	−0.643246	−	1.11413i	0.341458	−	0.939897i	$-0.389079\pi$
$920$		0			0
$921$	16.0000	−	27.7128i	0.527218	−	0.913168i
$922$		0			0
$923$	32.0000			1.05329
$924$		0			0
$925$	40.0000			1.31519
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−25.5000	−	44.1673i	−0.836628	−	1.44908i	−0.892698	−	0.450655i	$-0.851190\pi$
$929$	−25.5000	−	44.1673i	−0.836628	−	1.44908i	0.0560703	−	0.998427i	$-0.482143\pi$
$930$		0			0
$931$	1.00000	−	6.92820i	0.0327737	−	0.227063i
$932$		0			0
$933$	24.0000	+	41.5692i	0.785725	+	1.36092i
$934$		0			0
$935$	3.00000	−	5.19615i	0.0981105	−	0.169932i
$936$		0			0
$937$	−7.00000			−0.228680			−0.114340	−	0.993442i	$-0.536475\pi$
$937$	−7.00000			−0.228680			−0.114340	+	0.993442i	$0.536475\pi$
$938$		0			0
$939$	14.0000			0.456873
$940$		0			0
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	28.0000	+	48.4974i	0.911805	+	1.57929i
$944$		0			0
$945$	−2.00000	−	10.3923i	−0.0650600	−	0.338062i
$946$		0			0
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	0.994885	+	0.101012i	$0.0322080\pi$
$947$	18.0000	+	31.1769i	0.584921	+	1.01311i	−0.409964	+	0.912102i	$0.634459\pi$
$948$		0			0
$949$	−2.00000	+	3.46410i	−0.0649227	+	0.112449i
$950$		0			0
$951$	−8.00000			−0.259418
$952$		0			0
$953$	46.0000			1.49009			0.745043	−	0.667016i	$-0.232429\pi$
$953$	46.0000			1.49009			0.745043	+	0.667016i	$0.232429\pi$
$954$		0			0
$955$	−6.50000	+	11.2583i	−0.210335	+	0.364311i
$956$		0			0
$957$	6.00000	+	10.3923i	0.193952	+	0.335936i
$958$		0			0
$959$	−14.0000	+	12.1244i	−0.452084	+	0.391516i
$960$		0			0
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$		0			0
$963$	9.00000	−	15.5885i	0.290021	−	0.502331i
$964$		0			0
$965$	−24.0000			−0.772587
$966$		0			0
$967$	−48.0000			−1.54358			−0.771788	−	0.635880i	$-0.780637\pi$
$967$	−48.0000			−1.54358			−0.771788	+	0.635880i	$0.780637\pi$
$968$		0			0
$969$	−2.00000	+	3.46410i	−0.0642493	+	0.111283i
$970$		0			0
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	0.910140	−	0.414301i	$-0.135974\pi$
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	−0.813865	+	0.581054i	$0.802641\pi$
$972$		0			0
$973$	−22.5000	−	7.79423i	−0.721317	−	0.249871i
$974$		0			0
$975$	16.0000	+	27.7128i	0.512410	+	0.887520i
$976$		0			0
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$	−16.0000			−0.510841
$982$		0			0
$983$	−4.00000	+	6.92820i	−0.127580	+	0.220975i	−0.922739	−	0.385426i	$-0.874054\pi$
$983$	−4.00000	+	6.92820i	−0.127580	+	0.220975i	0.795158	+	0.606402i	$0.207388\pi$
$984$		0			0
$985$	1.50000	+	2.59808i	0.0477940	+	0.0827816i
$986$		0			0
$987$	−45.0000	−	15.5885i	−1.43237	−	0.496186i
$988$		0			0
$989$	24.5000	+	42.4352i	0.779055	+	1.34936i
$990$		0			0
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	−0.388723	−	0.921355i	$-0.627084\pi$
$991$	19.0000	−	32.9090i	0.603555	−	1.04539i	0.992278	−	0.124033i	$-0.0395829\pi$
$992$		0			0
$993$	12.0000			0.380808
$994$		0			0
$995$	1.00000			0.0317021
$996$		0			0
$997$	31.0000	−	53.6936i	0.981780	−	1.70049i	0.326326	−	0.945257i	$-0.394189\pi$
$997$	31.0000	−	53.6936i	0.981780	−	1.70049i	0.655454	−	0.755235i	$-0.272477\pi$
$998$		0			0
$999$	−20.0000	−	34.6410i	−0.632772	−	1.09599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1064.2.q.a.305.1	✓	2
7.2	even	3	inner	1064.2.q.a.457.1	yes	2
7.3	odd	6		7448.2.a.a.1.1		1
7.4	even	3		7448.2.a.t.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1064.2.q.a.305.1	✓	2	1.1	even	1	trivial
1064.2.q.a.457.1	yes	2	7.2	even	3	inner
7448.2.a.a.1.1		1	7.3	odd	6
7448.2.a.t.1.1		1	7.4	even	3

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:	\( N \)	\(=\)	\( 1064 = 2^{3} \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1064.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(1.50000 - 2.59808i) q^{11} +4.00000 q^{13} +2.00000 q^{15} +(-1.00000 + 1.73205i) q^{17} +(-0.500000 - 0.866025i) q^{19} +(4.00000 - 3.46410i) q^{21} +(3.50000 + 6.06218i) q^{23} +(2.00000 - 3.46410i) q^{25} -4.00000 q^{27} +2.00000 q^{29} +(-3.00000 + 5.19615i) q^{31} +(3.00000 + 5.19615i) q^{33} +(0.500000 + 2.59808i) q^{35} +(5.00000 + 8.66025i) q^{37} +(-4.00000 + 6.92820i) q^{39} +8.00000 q^{41} +7.00000 q^{43} +(-0.500000 + 0.866025i) q^{45} +(-4.50000 - 7.79423i) q^{47} +(5.50000 + 4.33013i) q^{49} +(-2.00000 - 3.46410i) q^{51} +(-3.00000 + 5.19615i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-7.00000 + 12.1244i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(0.500000 + 2.59808i) q^{63} +(-2.00000 - 3.46410i) q^{65} +(-7.00000 + 12.1244i) q^{67} -14.0000 q^{69} +8.00000 q^{71} +(-0.500000 + 0.866025i) q^{73} +(4.00000 + 6.92820i) q^{75} +(-6.00000 + 5.19615i) q^{77} +(-5.00000 - 8.66025i) q^{79} +(5.50000 - 9.52628i) q^{81} +17.0000 q^{83} +2.00000 q^{85} +(-2.00000 + 3.46410i) q^{87} +(-10.0000 - 3.46410i) q^{91} +(-6.00000 - 10.3923i) q^{93} +(-0.500000 + 0.866025i) q^{95} +12.0000 q^{97} -3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - q^{5} - 5 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 - q^5 - 5 * q^7 - q^9	\( 2 q - 2 q^{3} - q^{5} - 5 q^{7} - q^{9} + 3 q^{11} + 8 q^{13} + 4 q^{15} - 2 q^{17} - q^{19} + 8 q^{21} + 7 q^{23} + 4 q^{25} - 8 q^{27} + 4 q^{29} - 6 q^{31} + 6 q^{33} + q^{35} + 10 q^{37} - 8 q^{39} + 16 q^{41} + 14 q^{43} - q^{45} - 9 q^{47} + 11 q^{49} - 4 q^{51} - 6 q^{53} - 6 q^{55} + 4 q^{57} - 14 q^{59} - 5 q^{61} + q^{63} - 4 q^{65} - 14 q^{67} - 28 q^{69} + 16 q^{71} - q^{73} + 8 q^{75} - 12 q^{77} - 10 q^{79} + 11 q^{81} + 34 q^{83} + 4 q^{85} - 4 q^{87} - 20 q^{91} - 12 q^{93} - q^{95} + 24 q^{97} - 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - q^5 - 5 * q^7 - q^9 + 3 * q^11 + 8 * q^13 + 4 * q^15 - 2 * q^17 - q^19 + 8 * q^21 + 7 * q^23 + 4 * q^25 - 8 * q^27 + 4 * q^29 - 6 * q^31 + 6 * q^33 + q^35 + 10 * q^37 - 8 * q^39 + 16 * q^41 + 14 * q^43 - q^45 - 9 * q^47 + 11 * q^49 - 4 * q^51 - 6 * q^53 - 6 * q^55 + 4 * q^57 - 14 * q^59 - 5 * q^61 + q^63 - 4 * q^65 - 14 * q^67 - 28 * q^69 + 16 * q^71 - q^73 + 8 * q^75 - 12 * q^77 - 10 * q^79 + 11 * q^81 + 34 * q^83 + 4 * q^85 - 4 * q^87 - 20 * q^91 - 12 * q^93 - q^95 + 24 * q^97 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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