LMFDB - Embedded newform 1134.2.h.d.109.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(109,1134)] 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("1134.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1134, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-1,0,-1,0,0,5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$9.05503558921$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.109
Dual form			1134.2.h.d.541.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} -6.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +(3.00000 - 5.19615i) q^{22} -6.00000 q^{23} -5.00000 q^{25} +(-2.50000 - 4.33013i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(3.00000 + 5.19615i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(0.500000 + 0.866025i) q^{37} -4.00000 q^{38} +(-3.00000 + 5.19615i) q^{41} +(0.500000 + 0.866025i) q^{43} +(3.00000 + 5.19615i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(2.50000 - 4.33013i) q^{50} +5.00000 q^{52} +(-3.00000 + 5.19615i) q^{53} +(2.50000 + 0.866025i) q^{56} -6.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} -1.00000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{67} -6.00000 q^{68} -12.0000 q^{71} +(-1.00000 + 1.73205i) q^{73} -1.00000 q^{74} +(2.00000 - 3.46410i) q^{76} +(-15.0000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-3.00000 - 5.19615i) q^{82} +(3.00000 + 5.19615i) q^{83} -1.00000 q^{86} -6.00000 q^{88} +(-10.0000 + 8.66025i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-8.50000 - 14.7224i) q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 5 q^{7} + 2 q^{8} - 12 q^{11} - 5 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 6 q^{22} - 12 q^{23} - 10 q^{25} - 5 q^{26} - q^{28} + 6 q^{29} + q^{31} - q^{32} + 6 q^{34}+ \cdots - 13 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 5 * q^7 + 2 * q^8 - 12 * q^11 - 5 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 4 * q^19 + 6 * q^22 - 12 * q^23 - 10 * q^25 - 5 * q^26 - q^28 + 6 * q^29 + q^31 - q^32 + 6 * q^34 + q^37 - 8 * q^38 - 6 * q^41 + q^43 + 6 * q^44 + 6 * q^46 - 6 * q^47 + 11 * q^49 + 5 * q^50 + 10 * q^52 - 6 * q^53 + 5 * q^56 - 12 * q^58 - 6 * q^59 + q^61 - 2 * q^62 + 2 * q^64 + q^67 - 12 * q^68 - 24 * q^71 - 2 * q^73 - 2 * q^74 + 4 * q^76 - 30 * q^77 + q^79 - 6 * q^82 + 6 * q^83 - 2 * q^86 - 12 * q^88 - 20 * q^91 + 6 * q^92 - 6 * q^94 - 17 * q^97 - 13 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$		0			0
$11$	−6.00000			−1.80907			−0.904534	−	0.426401i	$-0.859781\pi$
$11$	−6.00000			−1.80907			−0.904534	+	0.426401i	$0.859781\pi$
$12$		0			0
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−2.00000	+	1.73205i	−0.534522	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	0.998899	−	0.0469020i	$-0.0149348\pi$
$19$	2.00000	+	3.46410i	0.458831	+	0.794719i	−0.540068	+	0.841621i	$0.681602\pi$
$20$		0			0
$21$		0			0
$22$	3.00000	−	5.19615i	0.639602	−	1.10782i
$23$	−6.00000			−1.25109			−0.625543	−	0.780189i	$-0.715123\pi$
$23$	−6.00000			−1.25109			−0.625543	+	0.780189i	$0.715123\pi$
$24$		0			0
$25$	−5.00000			−1.00000
$26$	−2.50000	−	4.33013i	−0.490290	−	0.849208i
$27$		0			0
$28$	−0.500000	−	2.59808i	−0.0944911	−	0.490990i
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	0.907428	−	0.420208i	$-0.138043\pi$
$31$	0.500000	+	0.866025i	0.0898027	+	0.155543i	−0.817625	+	0.575751i	$0.804710\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$		0			0
$36$		0			0
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	0.904194	−	0.427121i	$-0.140472\pi$
$37$	0.500000	+	0.866025i	0.0821995	+	0.142374i	−0.821995	+	0.569495i	$0.807139\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$		0			0
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	3.00000	+	5.19615i	0.452267	+	0.783349i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	−0.997503	−	0.0706177i	$-0.977503\pi$
$47$	−3.00000	+	5.19615i	−0.437595	+	0.757937i	0.559908	+	0.828554i	$0.310836\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	2.50000	−	4.33013i	0.353553	−	0.612372i
$51$		0			0
$52$	5.00000			0.693375
$53$	−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
$55$		0			0
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$		0			0
$58$	−6.00000			−0.787839
$59$	−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	$0.961054\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	−1.00000			−0.127000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	0.500000	+	0.866025i	0.0610847	+	0.105802i	0.894951	−	0.446165i	$-0.147211\pi$
$67$	0.500000	+	0.866025i	0.0610847	+	0.105802i	−0.833866	+	0.551967i	$0.813877\pi$
$68$	−6.00000			−0.727607
$69$		0			0
$70$		0			0
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−1.00000			−0.116248
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−15.0000	−	5.19615i	−1.70941	−	0.592157i
$78$		0			0
$79$	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	$0.148751\pi$
$80$		0			0
$81$		0			0
$82$	−3.00000	−	5.19615i	−0.331295	−	0.573819i
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$		0			0
$85$		0			0
$86$	−1.00000			−0.107833
$87$		0			0
$88$	−6.00000			−0.639602
$89$		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	+	8.66025i	−1.04828	+	0.907841i
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$		0			0
$96$		0			0
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	−0.868976	−	0.494854i	$-0.835222\pi$
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	0.00593185	−	0.999982i	$-0.498112\pi$
$98$	−6.50000	+	2.59808i	−0.656599	+	0.262445i
$99$		0			0
$100$	2.50000	+	4.33013i	0.250000	+	0.433013i
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$		0			0
$103$	−19.0000			−1.87213			−0.936063	−	0.351833i	$-0.885559\pi$
$103$	−19.0000			−1.87213			−0.936063	+	0.351833i	$0.885559\pi$
$104$	−2.50000	+	4.33013i	−0.245145	+	0.424604i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	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
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000	+	1.73205i	−0.188982	+	0.163663i
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	−0.432670	−	0.901553i	$-0.642428\pi$
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	0.997102	−	0.0760733i	$-0.0242383\pi$
$114$		0			0
$115$		0			0
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$		0			0
$118$	6.00000			0.552345
$119$	12.0000	−	10.3923i	1.10004	−	0.952661i
$120$		0			0
$121$	25.0000			2.27273
$122$	0.500000	+	0.866025i	0.0452679	+	0.0784063i
$123$		0			0
$124$	0.500000	−	0.866025i	0.0449013	−	0.0777714i
$125$		0			0
$126$		0			0
$127$	−13.0000			−1.15356			−0.576782	−	0.816898i	$-0.695692\pi$
$127$	−13.0000			−1.15356			−0.576782	+	0.816898i	$0.695692\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$		0			0
$131$	12.0000			1.04844			0.524222	−	0.851581i	$-0.324356\pi$
$131$	12.0000			1.04844			0.524222	+	0.851581i	$0.324356\pi$
$132$		0			0
$133$	2.00000	+	10.3923i	0.173422	+	0.901127i
$134$	−1.00000			−0.0863868
$135$		0			0
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	6.00000			0.512615			0.256307	−	0.966595i	$-0.417494\pi$
$137$	6.00000			0.512615			0.256307	+	0.966595i	$0.417494\pi$
$138$		0			0
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$	3.50000	−	6.06218i	0.296866	−	0.514187i	0.975417	+	0.220366i	$0.0707252\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	15.0000	−	25.9808i	1.25436	−	2.17262i
$144$		0			0
$145$		0			0
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$		0			0
$151$	17.0000			1.38344			0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000			1.38344			0.691720	+	0.722166i	$0.256853\pi$
$152$	2.00000	+	3.46410i	0.162221	+	0.280976i
$153$		0			0
$154$	12.0000	−	10.3923i	0.966988	−	0.837436i
$155$		0			0
$156$		0			0
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.853646	+	0.520854i	$0.174386\pi$
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.0242497	+	0.999706i	$0.492280\pi$
$158$	0.500000	+	0.866025i	0.0397779	+	0.0688973i
$159$		0			0
$160$		0			0
$161$	−15.0000	−	5.19615i	−1.18217	−	0.409514i
$162$		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	$0.975100\pi$
$164$	6.00000			0.468521
$165$		0			0
$166$	−6.00000			−0.465690
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$		0			0
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	−12.5000	−	4.33013i	−0.944911	−	0.327327i
$176$	3.00000	−	5.19615i	0.226134	−	0.391675i
$177$		0			0
$178$		0			0
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−2.50000	−	12.9904i	−0.185312	−	0.962911i
$183$		0			0
$184$	−6.00000			−0.442326
$185$		0			0
$186$		0			0
$187$	−18.0000	+	31.1769i	−1.31629	+	2.27988i
$188$	6.00000			0.437595
$189$		0			0
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$	17.0000			1.22053
$195$		0			0
$196$	1.00000	−	6.92820i	0.0714286	−	0.494872i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$		0			0
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	−0.992434	−	0.122782i	$-0.960818\pi$
$199$	−5.50000	+	9.52628i	−0.389885	+	0.675300i	0.602549	+	0.798082i	$0.294152\pi$
$200$	−5.00000			−0.353553
$201$		0			0
$202$	6.00000	−	10.3923i	0.422159	−	0.731200i
$203$	3.00000	+	15.5885i	0.210559	+	1.09410i
$204$		0			0
$205$		0			0
$206$	9.50000	−	16.4545i	0.661896	−	1.14644i
$207$		0			0
$208$	−2.50000	−	4.33013i	−0.173344	−	0.300240i
$209$	−12.0000	−	20.7846i	−0.830057	−	1.43770i
$210$		0			0
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$	6.00000			0.412082
$213$		0			0
$214$	−18.0000			−1.23045
$215$		0			0
$216$		0			0
$217$	0.500000	+	2.59808i	0.0339422	+	0.176369i
$218$	−2.50000	−	4.33013i	−0.169321	−	0.293273i
$219$		0			0
$220$		0			0
$221$	15.0000	+	25.9808i	1.00901	+	1.74766i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	−0.500000	−	2.59808i	−0.0334077	−	0.173591i
$225$		0			0
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$	6.00000			0.398234			0.199117	−	0.979976i	$-0.436193\pi$
$227$	6.00000			0.398234			0.199117	+	0.979976i	$0.436193\pi$
$228$		0			0
$229$	5.00000			0.330409			0.165205	−	0.986259i	$-0.447172\pi$
$229$	5.00000			0.330409			0.165205	+	0.986259i	$0.447172\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	0.928312	+	0.371802i	$0.121260\pi$
$233$	12.0000	+	20.7846i	0.786146	+	1.36165i	−0.142166	+	0.989843i	$0.545407\pi$
$234$		0			0
$235$		0			0
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$		0			0
$238$	3.00000	+	15.5885i	0.194461	+	1.01045i
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	−0.157893	−	0.987456i	$-0.550470\pi$
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	0.934109	−	0.356988i	$-0.116196\pi$
$240$		0			0
$241$	17.0000			1.09507			0.547533	−	0.836784i	$-0.315567\pi$
$241$	17.0000			1.09507			0.547533	+	0.836784i	$0.315567\pi$
$242$	−12.5000	+	21.6506i	−0.803530	+	1.39176i
$243$		0			0
$244$	−1.00000			−0.0640184
$245$		0			0
$246$		0			0
$247$	−20.0000			−1.27257
$248$	0.500000	+	0.866025i	0.0317500	+	0.0549927i
$249$		0			0
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$	36.0000			2.26330
$254$	6.50000	−	11.2583i	0.407846	−	0.706410i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$		0			0
$259$	0.500000	+	2.59808i	0.0310685	+	0.161437i
$260$		0			0
$261$		0			0
$262$	−6.00000	+	10.3923i	−0.370681	+	0.642039i
$263$	−6.00000			−0.369976			−0.184988	−	0.982741i	$-0.559225\pi$
$263$	−6.00000			−0.369976			−0.184988	+	0.982741i	$0.559225\pi$
$264$		0			0
$265$		0			0
$266$	−10.0000	−	3.46410i	−0.613139	−	0.212398i
$267$		0			0
$268$	0.500000	−	0.866025i	0.0305424	−	0.0529009i
$269$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$269$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$270$		0			0
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	0.952531	−	0.304443i	$-0.0984703\pi$
$271$	3.50000	+	6.06218i	0.212610	+	0.368251i	−0.739921	+	0.672694i	$0.765137\pi$
$272$	3.00000	+	5.19615i	0.181902	+	0.315063i
$273$		0			0
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	30.0000			1.80907
$276$		0			0
$277$	17.0000			1.02143			0.510716	−	0.859750i	$-0.329381\pi$
$277$	17.0000			1.02143			0.510716	+	0.859750i	$0.329381\pi$
$278$	3.50000	+	6.06218i	0.209916	+	0.363585i
$279$		0			0
$280$		0			0
$281$	6.00000	+	10.3923i	0.357930	+	0.619953i	0.987615	−	0.156898i	$-0.0501493\pi$
$281$	6.00000	+	10.3923i	0.357930	+	0.619953i	−0.629685	+	0.776851i	$0.716816\pi$
$282$		0			0
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	0.991960	−	0.126550i	$-0.0403903\pi$
$283$	6.50000	+	11.2583i	0.386385	+	0.669238i	−0.605575	+	0.795788i	$0.707057\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	15.0000	+	25.9808i	0.886969	+	1.53627i
$287$	−12.0000	+	10.3923i	−0.708338	+	0.613438i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$		0			0
$292$	2.00000			0.117041
$293$	9.00000	−	15.5885i	0.525786	−	0.910687i	−0.473763	−	0.880652i	$-0.657105\pi$
$293$	9.00000	−	15.5885i	0.525786	−	0.910687i	0.999549	−	0.0300351i	$-0.00956192\pi$
$294$		0			0
$295$		0			0
$296$	0.500000	+	0.866025i	0.0290619	+	0.0503367i
$297$		0			0
$298$	−6.00000	+	10.3923i	−0.347571	+	0.602010i
$299$	15.0000	−	25.9808i	0.867472	−	1.50251i
$300$		0			0
$301$	0.500000	+	2.59808i	0.0288195	+	0.149751i
$302$	−8.50000	+	14.7224i	−0.489120	+	0.847181i
$303$		0			0
$304$	−4.00000			−0.229416
$305$		0			0
$306$		0			0
$307$	17.0000			0.970241			0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000			0.970241			0.485121	+	0.874447i	$0.338776\pi$
$308$	3.00000	+	15.5885i	0.170941	+	0.888235i
$309$		0			0
$310$		0			0
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	0.644246	−	0.764818i	$-0.277171\pi$
$311$	−6.00000	−	10.3923i	−0.340229	−	0.589294i	−0.984475	+	0.175525i	$0.943838\pi$
$312$		0			0
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	−0.367402	−	0.930062i	$-0.619753\pi$
$313$	11.0000	−	19.0526i	0.621757	−	1.07691i	0.989158	−	0.146852i	$-0.0469141\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	−18.0000	−	31.1769i	−1.00781	−	1.74557i
$320$		0			0
$321$		0			0
$322$	12.0000	−	10.3923i	0.668734	−	0.579141i
$323$	24.0000			1.33540
$324$		0			0
$325$	12.5000	−	21.6506i	0.693375	−	1.20096i
$326$	11.0000			0.609234
$327$		0			0
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	−12.0000	+	10.3923i	−0.661581	+	0.572946i
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$		0			0
$334$	−9.00000	−	15.5885i	−0.492458	−	0.852962i
$335$		0			0
$336$		0			0
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	−0.891976	−	0.452082i	$-0.850681\pi$
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	0.837503	+	0.546433i	$0.184015\pi$
$338$	12.0000			0.652714
$339$		0			0
$340$		0			0
$341$	−3.00000	−	5.19615i	−0.162459	−	0.281387i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$		0			0
$346$		0			0
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$		0			0
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	0.879097	−	0.476642i	$-0.158146\pi$
$349$	0.500000	+	0.866025i	0.0267644	+	0.0463573i	−0.852333	+	0.523000i	$0.824813\pi$
$350$	10.0000	−	8.66025i	0.534522	−	0.462910i
$351$		0			0
$352$	3.00000	+	5.19615i	0.159901	+	0.276956i
$353$	36.0000			1.91609			0.958043	−	0.286623i	$-0.0925328\pi$
$353$	36.0000			1.91609			0.958043	+	0.286623i	$0.0925328\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$		0			0
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	5.00000	−	8.66025i	0.262794	−	0.455173i
$363$		0			0
$364$	12.5000	+	4.33013i	0.655178	+	0.226960i
$365$		0			0
$366$		0			0
$367$	−28.0000			−1.46159			−0.730794	−	0.682598i	$-0.760850\pi$
$367$	−28.0000			−1.46159			−0.730794	+	0.682598i	$0.760850\pi$
$368$	3.00000	−	5.19615i	0.156386	−	0.270868i
$369$		0			0
$370$		0			0
$371$	−12.0000	+	10.3923i	−0.623009	+	0.539542i
$372$		0			0
$373$	26.0000			1.34623			0.673114	−	0.739538i	$-0.264956\pi$
$373$	26.0000			1.34623			0.673114	+	0.739538i	$0.264956\pi$
$374$	−18.0000	−	31.1769i	−0.930758	−	1.61212i
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	−30.0000			−1.54508
$378$		0			0
$379$	−1.00000			−0.0513665			−0.0256833	−	0.999670i	$-0.508176\pi$
$379$	−1.00000			−0.0513665			−0.0256833	+	0.999670i	$0.508176\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−6.00000			−0.306586			−0.153293	−	0.988181i	$-0.548988\pi$
$383$	−6.00000			−0.306586			−0.153293	+	0.988181i	$0.548988\pi$
$384$		0			0
$385$		0			0
$386$	−1.00000			−0.0508987
$387$		0			0
$388$	−8.50000	+	14.7224i	−0.431522	+	0.747418i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$	−18.0000	+	31.1769i	−0.910299	+	1.57668i
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$		0			0
$394$	−6.00000	+	10.3923i	−0.302276	+	0.523557i
$395$		0			0
$396$		0			0
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	0.981760	−	0.190126i	$-0.0608897\pi$
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	−0.655534	+	0.755166i	$0.727556\pi$
$398$	−5.50000	−	9.52628i	−0.275690	−	0.477509i
$399$		0			0
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	6.00000			0.299626			0.149813	−	0.988714i	$-0.452133\pi$
$401$	6.00000			0.299626			0.149813	+	0.988714i	$0.452133\pi$
$402$		0			0
$403$	−5.00000			−0.249068
$404$	6.00000	+	10.3923i	0.298511	+	0.517036i
$405$		0			0
$406$	−15.0000	−	5.19615i	−0.744438	−	0.257881i
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$		0			0
$409$	−14.5000	−	25.1147i	−0.716979	−	1.24184i	−0.962191	−	0.272374i	$-0.912191\pi$
$409$	−14.5000	−	25.1147i	−0.716979	−	1.24184i	0.245212	−	0.969469i	$-0.421142\pi$
$410$		0			0
$411$		0			0
$412$	9.50000	+	16.4545i	0.468031	+	0.810654i
$413$	−3.00000	−	15.5885i	−0.147620	−	0.767058i
$414$		0			0
$415$		0			0
$416$	5.00000			0.245145
$417$		0			0
$418$	24.0000			1.17388
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	0.408481	+	0.912767i	$0.366058\pi$
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	−0.994720	+	0.102628i	$0.967275\pi$
$420$		0			0
$421$	−7.00000	−	12.1244i	−0.341159	−	0.590905i	0.643489	−	0.765455i	$-0.277486\pi$
$421$	−7.00000	−	12.1244i	−0.341159	−	0.590905i	−0.984648	+	0.174550i	$0.944153\pi$
$422$	6.50000	+	11.2583i	0.316415	+	0.548047i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−15.0000	+	25.9808i	−0.727607	+	1.26025i
$426$		0			0
$427$	2.00000	−	1.73205i	0.0967868	−	0.0838198i
$428$	9.00000	−	15.5885i	0.435031	−	0.753497i
$429$		0			0
$430$		0			0
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	−0.997173	−	0.0751385i	$-0.976060\pi$
$431$	−9.00000	+	15.5885i	−0.433515	+	0.750870i	0.563658	+	0.826008i	$0.309393\pi$
$432$		0			0
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$	−2.50000	−	0.866025i	−0.120004	−	0.0415705i
$435$		0			0
$436$	5.00000			0.239457
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$		0			0
$441$		0			0
$442$	−30.0000			−1.42695
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	0.426414	+	0.904528i	$0.359777\pi$
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	−0.996551	+	0.0829786i	$0.973557\pi$
$444$		0			0
$445$		0			0
$446$	8.00000			0.378811
$447$		0			0
$448$	2.50000	+	0.866025i	0.118114	+	0.0409159i
$449$	24.0000			1.13263			0.566315	−	0.824189i	$-0.308369\pi$
$449$	24.0000			1.13263			0.566315	+	0.824189i	$0.308369\pi$
$450$		0			0
$451$	18.0000	−	31.1769i	0.847587	−	1.46806i
$452$	−12.0000			−0.564433
$453$		0			0
$454$	−3.00000	+	5.19615i	−0.140797	+	0.243868i
$455$		0			0
$456$		0			0
$457$	9.50000	−	16.4545i	0.444391	−	0.769708i	−0.553618	−	0.832771i	$-0.686753\pi$
$457$	9.50000	−	16.4545i	0.444391	−	0.769708i	0.998010	+	0.0630623i	$0.0200867\pi$
$458$	−2.50000	+	4.33013i	−0.116817	+	0.202334i
$459$		0			0
$460$		0			0
$461$	9.00000	+	15.5885i	0.419172	+	0.726027i	0.995856	−	0.0909401i	$-0.0289872\pi$
$461$	9.00000	+	15.5885i	0.419172	+	0.726027i	−0.576685	+	0.816967i	$0.695654\pi$
$462$		0			0
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	−0.943878	−	0.330294i	$-0.892852\pi$
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	0.757982	+	0.652275i	$0.226185\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	−24.0000			−1.11178
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	0.970799	−	0.239892i	$-0.0771121\pi$
$467$	6.00000	+	10.3923i	0.277647	+	0.480899i	−0.693153	+	0.720791i	$0.743779\pi$
$468$		0			0
$469$	0.500000	+	2.59808i	0.0230879	+	0.119968i
$470$		0			0
$471$		0			0
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−3.00000	−	5.19615i	−0.137940	−	0.238919i
$474$		0			0
$475$	−10.0000	−	17.3205i	−0.458831	−	0.794719i
$476$	−15.0000	−	5.19615i	−0.687524	−	0.238165i
$477$		0			0
$478$	12.0000	+	20.7846i	0.548867	+	0.950666i
$479$	−12.0000			−0.548294			−0.274147	−	0.961688i	$-0.588395\pi$
$479$	−12.0000			−0.548294			−0.274147	+	0.961688i	$0.588395\pi$
$480$		0			0
$481$	−5.00000			−0.227980
$482$	−8.50000	+	14.7224i	−0.387164	+	0.670588i
$483$		0			0
$484$	−12.5000	−	21.6506i	−0.568182	−	0.984120i
$485$		0			0
$486$		0			0
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.0871056	−	0.996199i	$-0.472238\pi$
$487$	20.0000	−	34.6410i	0.906287	−	1.56973i	0.819181	−	0.573535i	$-0.194428\pi$
$488$	0.500000	−	0.866025i	0.0226339	−	0.0392031i
$489$		0			0
$490$		0			0
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	0.298957	+	0.954267i	$0.403361\pi$
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	−0.975898	+	0.218229i	$0.929972\pi$
$492$		0			0
$493$	36.0000			1.62136
$494$	10.0000	−	17.3205i	0.449921	−	0.779287i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	−30.0000	−	10.3923i	−1.34568	−	0.466159i
$498$		0			0
$499$	−25.0000			−1.11915			−0.559577	−	0.828778i	$-0.689036\pi$
$499$	−25.0000			−1.11915			−0.559577	+	0.828778i	$0.689036\pi$
$500$		0			0
$501$		0			0
$502$	9.00000	−	15.5885i	0.401690	−	0.695747i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		0			0
$505$		0			0
$506$	−18.0000	+	31.1769i	−0.800198	+	1.38598i
$507$		0			0
$508$	6.50000	+	11.2583i	0.288391	+	0.499508i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$		0			0
$511$	−4.00000	+	3.46410i	−0.176950	+	0.153243i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.00000	+	5.19615i	−0.132324	+	0.229192i
$515$		0			0
$516$		0			0
$517$	18.0000	−	31.1769i	0.791639	−	1.37116i
$518$	−2.50000	−	0.866025i	−0.109844	−	0.0380510i
$519$		0			0
$520$		0			0
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.799370	−	0.600839i	$-0.205167\pi$
$522$		0			0
$523$	−11.5000	−	19.9186i	−0.502860	−	0.870979i	−0.999995	−	0.00330547i	$-0.998948\pi$
$523$	−11.5000	−	19.9186i	−0.502860	−	0.870979i	0.497135	−	0.867673i	$-0.334385\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		0			0
$526$	3.00000	−	5.19615i	0.130806	−	0.226563i
$527$	6.00000			0.261364
$528$		0			0
$529$	13.0000			0.565217
$530$		0			0
$531$		0			0
$532$	8.00000	−	6.92820i	0.346844	−	0.300376i
$533$	−15.0000	−	25.9808i	−0.649722	−	1.12535i
$534$		0			0
$535$		0			0
$536$	0.500000	+	0.866025i	0.0215967	+	0.0374066i
$537$		0			0
$538$		0			0
$539$	−33.0000	−	25.9808i	−1.42141	−	1.11907i
$540$		0			0
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	−7.00000			−0.300676
$543$		0			0
$544$	−6.00000			−0.257248
$545$		0			0
$546$		0			0
$547$	18.5000	+	32.0429i	0.791003	+	1.37006i	0.925347	+	0.379122i	$0.123774\pi$
$547$	18.5000	+	32.0429i	0.791003	+	1.37006i	−0.134344	+	0.990935i	$0.542893\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$		0			0
$550$	−15.0000	+	25.9808i	−0.639602	+	1.10782i
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$		0			0
$553$	2.00000	−	1.73205i	0.0850487	−	0.0736543i
$554$	−8.50000	+	14.7224i	−0.361130	+	0.625496i
$555$		0			0
$556$	−7.00000			−0.296866
$557$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$557$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$		0			0
$562$	−12.0000			−0.506189
$563$	−21.0000	−	36.3731i	−0.885044	−	1.53294i	−0.845663	−	0.533718i	$-0.820794\pi$
$563$	−21.0000	−	36.3731i	−0.885044	−	1.53294i	−0.0393818	−	0.999224i	$-0.512539\pi$
$564$		0			0
$565$		0			0
$566$	−13.0000			−0.546431
$567$		0			0
$568$	−12.0000			−0.503509
$569$	−18.0000	+	31.1769i	−0.754599	+	1.30700i	0.190974	+	0.981595i	$0.438835\pi$
$569$	−18.0000	+	31.1769i	−0.754599	+	1.30700i	−0.945573	+	0.325409i	$0.894498\pi$
$570$		0			0
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	0.983444	−	0.181210i	$-0.0580014\pi$
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	−0.648655	+	0.761083i	$0.724668\pi$
$572$	−30.0000			−1.25436
$573$		0			0
$574$	−3.00000	−	15.5885i	−0.125218	−	0.650650i
$575$	30.0000			1.25109
$576$		0			0
$577$	−11.5000	+	19.9186i	−0.478751	+	0.829222i	−0.999703	−	0.0243645i	$-0.992244\pi$
$577$	−11.5000	+	19.9186i	−0.478751	+	0.829222i	0.520952	+	0.853586i	$0.325577\pi$
$578$	19.0000			0.790296
$579$		0			0
$580$		0			0
$581$	3.00000	+	15.5885i	0.124461	+	0.646718i
$582$		0			0
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	9.00000	+	15.5885i	0.371787	+	0.643953i
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$		0			0
$592$	−1.00000			−0.0410997
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	0.952869	+	0.303383i	$0.0981160\pi$
$593$	18.0000	+	31.1769i	0.739171	+	1.28028i	−0.213697	+	0.976900i	$0.568551\pi$
$594$		0			0
$595$		0			0
$596$	−6.00000	−	10.3923i	−0.245770	−	0.425685i
$597$		0			0
$598$	15.0000	+	25.9808i	0.613396	+	1.06243i
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	0.954521	+	0.298143i	$0.0963673\pi$
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	−0.219061	+	0.975711i	$0.570299\pi$
$600$		0			0
$601$	−23.5000	−	40.7032i	−0.958585	−	1.66032i	−0.725942	−	0.687756i	$-0.758596\pi$
$601$	−23.5000	−	40.7032i	−0.958585	−	1.66032i	−0.232643	−	0.972562i	$-0.574737\pi$
$602$	−2.50000	−	0.866025i	−0.101892	−	0.0352966i
$603$		0			0
$604$	−8.50000	−	14.7224i	−0.345860	−	0.599047i
$605$		0			0
$606$		0			0
$607$	−16.0000			−0.649420			−0.324710	−	0.945814i	$-0.605267\pi$
$607$	−16.0000			−0.649420			−0.324710	+	0.945814i	$0.605267\pi$
$608$	2.00000	−	3.46410i	0.0811107	−	0.140488i
$609$		0			0
$610$		0			0
$611$	−15.0000	−	25.9808i	−0.606835	−	1.05107i
$612$		0			0
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	−0.955458	−	0.295126i	$-0.904638\pi$
$613$	−5.50000	+	9.52628i	−0.222143	+	0.384763i	0.733316	+	0.679888i	$0.237972\pi$
$614$	−8.50000	+	14.7224i	−0.343032	+	0.594149i
$615$		0			0
$616$	−15.0000	−	5.19615i	−0.604367	−	0.209359i
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	0.388351	+	0.921512i	$0.373045\pi$
$617$	−15.0000	+	25.9808i	−0.603877	+	1.04595i	−0.992228	+	0.124434i	$0.960288\pi$
$618$		0			0
$619$	−25.0000			−1.00483			−0.502417	−	0.864625i	$-0.667556\pi$
$619$	−25.0000			−1.00483			−0.502417	+	0.864625i	$0.667556\pi$
$620$		0			0
$621$		0			0
$622$	12.0000			0.481156
$623$		0			0
$624$		0			0
$625$	25.0000			1.00000
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$		0			0
$628$	11.0000	−	19.0526i	0.438948	−	0.760280i
$629$	6.00000			0.239236
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	0.500000	−	0.866025i	0.0198889	−	0.0344486i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$		0			0
$636$		0			0
$637$	−32.5000	+	12.9904i	−1.28770	+	0.514698i
$638$	36.0000			1.42525
$639$		0			0
$640$		0			0
$641$	−18.0000			−0.710957			−0.355479	−	0.934684i	$-0.615682\pi$
$641$	−18.0000			−0.710957			−0.355479	+	0.934684i	$0.615682\pi$
$642$		0			0
$643$	12.5000	−	21.6506i	0.492952	−	0.853818i	−0.507015	−	0.861937i	$-0.669251\pi$
$643$	12.5000	−	21.6506i	0.492952	−	0.853818i	0.999967	+	0.00811944i	$0.00258453\pi$
$644$	3.00000	+	15.5885i	0.118217	+	0.614271i
$645$		0			0
$646$	−12.0000	+	20.7846i	−0.472134	+	0.817760i
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	−0.959529	−	0.281609i	$-0.909132\pi$
$647$	−6.00000	+	10.3923i	−0.235884	+	0.408564i	0.723645	+	0.690172i	$0.242465\pi$
$648$		0			0
$649$	18.0000	+	31.1769i	0.706562	+	1.22380i
$650$	12.5000	+	21.6506i	0.490290	+	0.849208i
$651$		0			0
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	18.0000			0.704394			0.352197	−	0.935926i	$-0.385435\pi$
$653$	18.0000			0.704394			0.352197	+	0.935926i	$0.385435\pi$
$654$		0			0
$655$		0			0
$656$	−3.00000	−	5.19615i	−0.117130	−	0.202876i
$657$		0			0
$658$	−3.00000	−	15.5885i	−0.116952	−	0.607701i
$659$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$659$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$660$		0			0
$661$	−25.0000	−	43.3013i	−0.972387	−	1.68422i	−0.688301	−	0.725426i	$-0.741643\pi$
$661$	−25.0000	−	43.3013i	−0.972387	−	1.68422i	−0.284087	−	0.958799i	$-0.591690\pi$
$662$	−10.0000	−	17.3205i	−0.388661	−	0.673181i
$663$		0			0
$664$	3.00000	+	5.19615i	0.116423	+	0.201650i
$665$		0			0
$666$		0			0
$667$	−18.0000	−	31.1769i	−0.696963	−	1.20717i
$668$	18.0000			0.696441
$669$		0			0
$670$		0			0
$671$	−3.00000	+	5.19615i	−0.115814	+	0.200595i
$672$		0			0
$673$	17.0000	+	29.4449i	0.655302	+	1.13502i	0.981818	+	0.189824i	$0.0607919\pi$
$673$	17.0000	+	29.4449i	0.655302	+	1.13502i	−0.326516	+	0.945192i	$0.605875\pi$
$674$	−1.00000	−	1.73205i	−0.0385186	−	0.0667161i
$675$		0			0
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	−0.727386	−	0.686229i	$-0.759265\pi$
$677$	6.00000	−	10.3923i	0.230599	−	0.399409i	0.957984	+	0.286820i	$0.0925982\pi$
$678$		0			0
$679$	−8.50000	−	44.1673i	−0.326200	−	1.69499i
$680$		0			0
$681$		0			0
$682$	6.00000			0.229752
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	−0.728101	−	0.685470i	$-0.759597\pi$
$683$	6.00000	−	10.3923i	0.229584	−	0.397650i	0.957685	+	0.287819i	$0.0929302\pi$
$684$		0			0
$685$		0			0
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$		0			0
$688$	−1.00000			−0.0381246
$689$	−15.0000	−	25.9808i	−0.571454	−	0.989788i
$690$		0			0
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	−0.981178	−	0.193105i	$-0.938144\pi$
$691$	−8.50000	+	14.7224i	−0.323355	+	0.560068i	0.657823	+	0.753173i	$0.271478\pi$
$692$		0			0
$693$		0			0
$694$	24.0000			0.911028
$695$		0			0
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$	−1.00000			−0.0378506
$699$		0			0
$700$	2.50000	+	12.9904i	0.0944911	+	0.490990i
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$		0			0
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$	−6.00000			−0.226134
$705$		0			0
$706$	−18.0000	+	31.1769i	−0.677439	+	1.17336i
$707$	−30.0000	−	10.3923i	−1.12827	−	0.390843i
$708$		0			0
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	−0.980326	−	0.197383i	$-0.936756\pi$
$709$	−8.50000	+	14.7224i	−0.319224	+	0.552913i	0.661102	+	0.750296i	$0.270089\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−3.00000	−	5.19615i	−0.112351	−	0.194597i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$	−6.00000			−0.223918
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	0.955947	−	0.293538i	$-0.0948328\pi$
$719$	6.00000	+	10.3923i	0.223762	+	0.387568i	−0.732185	+	0.681106i	$0.761499\pi$
$720$		0			0
$721$	−47.5000	−	16.4545i	−1.76899	−	0.612797i
$722$	1.50000	+	2.59808i	0.0558242	+	0.0966904i
$723$		0			0
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	−15.0000	−	25.9808i	−0.557086	−	0.964901i
$726$		0			0
$727$	−2.50000	−	4.33013i	−0.0927199	−	0.160596i	0.815935	−	0.578144i	$-0.196223\pi$
$727$	−2.50000	−	4.33013i	−0.0927199	−	0.160596i	−0.908655	+	0.417548i	$0.862889\pi$
$728$	−10.0000	+	8.66025i	−0.370625	+	0.320970i
$729$		0			0
$730$		0			0
$731$	6.00000			0.221918
$732$		0			0
$733$	17.0000			0.627909			0.313955	−	0.949438i	$-0.398346\pi$
$733$	17.0000			0.627909			0.313955	+	0.949438i	$0.398346\pi$
$734$	14.0000	−	24.2487i	0.516749	−	0.895036i
$735$		0			0
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	−3.00000	−	5.19615i	−0.110506	−	0.191403i
$738$		0			0
$739$	24.5000	−	42.4352i	0.901247	−	1.56101i	0.0753699	−	0.997156i	$-0.475986\pi$
$739$	24.5000	−	42.4352i	0.901247	−	1.56101i	0.825877	−	0.563850i	$-0.190680\pi$
$740$		0			0
$741$		0			0
$742$	−3.00000	−	15.5885i	−0.110133	−	0.572270i
$743$	9.00000	−	15.5885i	0.330178	−	0.571885i	−0.652369	−	0.757902i	$-0.726225\pi$
$743$	9.00000	−	15.5885i	0.330178	−	0.571885i	0.982547	+	0.186017i	$0.0595579\pi$
$744$		0			0
$745$		0			0
$746$	−13.0000	+	22.5167i	−0.475964	+	0.824394i
$747$		0			0
$748$	36.0000			1.31629
$749$	9.00000	+	46.7654i	0.328853	+	1.70877i
$750$		0			0
$751$	−16.0000			−0.583848			−0.291924	−	0.956441i	$-0.594295\pi$
$751$	−16.0000			−0.583848			−0.291924	+	0.956441i	$0.594295\pi$
$752$	−3.00000	−	5.19615i	−0.109399	−	0.189484i
$753$		0			0
$754$	15.0000	−	25.9808i	0.546268	−	0.946164i
$755$		0			0
$756$		0			0
$757$	29.0000			1.05402			0.527011	−	0.849858i	$-0.323312\pi$
$757$	29.0000			1.05402			0.527011	+	0.849858i	$0.323312\pi$
$758$	0.500000	−	0.866025i	0.0181608	−	0.0314555i
$759$		0			0
$760$		0			0
$761$		0			0			−	1.00000i	$-0.5\pi$
$761$		0			0				1.00000i	$0.5\pi$
$762$		0			0
$763$	−10.0000	+	8.66025i	−0.362024	+	0.313522i
$764$		0			0
$765$		0			0
$766$	3.00000	−	5.19615i	0.108394	−	0.187745i
$767$	30.0000			1.08324
$768$		0			0
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	−0.761680	−	0.647954i	$-0.775625\pi$
$769$	5.00000	−	8.66025i	0.180305	−	0.312297i	0.941984	+	0.335657i	$0.108958\pi$
$770$		0			0
$771$		0			0
$772$	0.500000	−	0.866025i	0.0179954	−	0.0311689i
$773$	−12.0000	+	20.7846i	−0.431610	+	0.747570i	−0.997012	−	0.0772449i	$-0.975388\pi$
$773$	−12.0000	+	20.7846i	−0.431610	+	0.747570i	0.565402	+	0.824815i	$0.308721\pi$
$774$		0			0
$775$	−2.50000	−	4.33013i	−0.0898027	−	0.155543i
$776$	−8.50000	−	14.7224i	−0.305132	−	0.528505i
$777$		0			0
$778$	−6.00000	+	10.3923i	−0.215110	+	0.372582i
$779$	−24.0000			−0.859889
$780$		0			0
$781$	72.0000			2.57636
$782$	−18.0000	−	31.1769i	−0.643679	−	1.11488i
$783$		0			0
$784$	−6.50000	+	2.59808i	−0.232143	+	0.0927884i
$785$		0			0
$786$		0			0
$787$	15.5000	+	26.8468i	0.552515	+	0.956985i	0.998092	+	0.0617409i	$0.0196653\pi$
$787$	15.5000	+	26.8468i	0.552515	+	0.956985i	−0.445577	+	0.895244i	$0.647001\pi$
$788$	−6.00000	−	10.3923i	−0.213741	−	0.370211i
$789$		0			0
$790$		0			0
$791$	24.0000	−	20.7846i	0.853342	−	0.739016i
$792$		0			0
$793$	2.50000	+	4.33013i	0.0887776	+	0.153767i
$794$	−13.0000			−0.461353
$795$		0			0
$796$	11.0000			0.389885
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	0.468004	+	0.883726i	$0.344973\pi$
$797$	−15.0000	+	25.9808i	−0.531327	+	0.920286i	−0.999331	+	0.0365596i	$0.988360\pi$
$798$		0			0
$799$	18.0000	+	31.1769i	0.636794	+	1.10296i
$800$	2.50000	+	4.33013i	0.0883883	+	0.153093i
$801$		0			0
$802$	−3.00000	+	5.19615i	−0.105934	+	0.183483i
$803$	6.00000	−	10.3923i	0.211735	−	0.366736i
$804$		0			0
$805$		0			0
$806$	2.50000	−	4.33013i	0.0880587	−	0.152522i
$807$		0			0
$808$	−12.0000			−0.422159
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	0.472119	+	0.881535i	$0.343489\pi$
$809$	−15.0000	+	25.9808i	−0.527372	+	0.913435i	−0.999491	+	0.0319002i	$0.989844\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	12.0000	−	10.3923i	0.421117	−	0.364698i
$813$		0			0
$814$	6.00000			0.210300
$815$		0			0
$816$		0			0
$817$	−2.00000	+	3.46410i	−0.0699711	+	0.121194i
$818$	29.0000			1.01396
$819$		0			0
$820$		0			0
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$		0			0
$823$	15.5000	+	26.8468i	0.540296	+	0.935820i	0.998887	+	0.0471726i	$0.0150211\pi$
$823$	15.5000	+	26.8468i	0.540296	+	0.935820i	−0.458591	+	0.888648i	$0.651646\pi$
$824$	−19.0000			−0.661896
$825$		0			0
$826$	15.0000	+	5.19615i	0.521917	+	0.180797i
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	−0.961601	−	0.274450i	$-0.911504\pi$
$829$	−7.00000	+	12.1244i	−0.243120	+	0.421096i	0.718481	+	0.695546i	$0.244838\pi$
$830$		0			0
$831$		0			0
$832$	−2.50000	+	4.33013i	−0.0866719	+	0.150120i
$833$	39.0000	−	15.5885i	1.35127	−	0.540108i
$834$		0			0
$835$		0			0
$836$	−12.0000	+	20.7846i	−0.415029	+	0.718851i
$837$		0			0
$838$	−12.0000	−	20.7846i	−0.414533	−	0.717992i
$839$	9.00000	+	15.5885i	0.310715	+	0.538173i	0.978517	−	0.206165i	$-0.0660984\pi$
$839$	9.00000	+	15.5885i	0.310715	+	0.538173i	−0.667803	+	0.744338i	$0.732765\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	14.0000			0.482472
$843$		0			0
$844$	−13.0000			−0.447478
$845$		0			0
$846$		0			0
$847$	62.5000	+	21.6506i	2.14753	+	0.743925i
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$		0			0
$850$	−15.0000	−	25.9808i	−0.514496	−	0.891133i
$851$	−3.00000	−	5.19615i	−0.102839	−	0.178122i
$852$		0			0
$853$	23.0000	+	39.8372i	0.787505	+	1.36400i	0.927491	+	0.373845i	$0.121961\pi$
$853$	23.0000	+	39.8372i	0.787505	+	1.36400i	−0.139986	+	0.990153i	$0.544706\pi$
$854$	0.500000	+	2.59808i	0.0171096	+	0.0889043i
$855$		0			0
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	12.0000			0.409912			0.204956	−	0.978771i	$-0.434295\pi$
$857$	12.0000			0.409912			0.204956	+	0.978771i	$0.434295\pi$
$858$		0			0
$859$	23.0000			0.784750			0.392375	−	0.919805i	$-0.371654\pi$
$859$	23.0000			0.784750			0.392375	+	0.919805i	$0.371654\pi$
$860$		0			0
$861$		0			0
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$	18.0000	+	31.1769i	0.612727	+	1.06127i	0.990779	+	0.135490i	$0.0432609\pi$
$863$	18.0000	+	31.1769i	0.612727	+	1.06127i	−0.378052	+	0.925785i	$0.623406\pi$
$864$		0			0
$865$		0			0
$866$	12.5000	−	21.6506i	0.424767	−	0.735719i
$867$		0			0
$868$	2.00000	−	1.73205i	0.0678844	−	0.0587896i
$869$	−3.00000	+	5.19615i	−0.101768	+	0.176267i
$870$		0			0
$871$	−5.00000			−0.169419
$872$	−2.50000	+	4.33013i	−0.0846607	+	0.146637i
$873$		0			0
$874$	24.0000			0.811812
$875$		0			0
$876$		0			0
$877$	−13.0000			−0.438979			−0.219489	−	0.975615i	$-0.570439\pi$
$877$	−13.0000			−0.438979			−0.219489	+	0.975615i	$0.570439\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$		0			0
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$	15.0000	−	25.9808i	0.504505	−	0.873828i
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	18.0000			0.604381			0.302190	−	0.953248i	$-0.402282\pi$
$887$	18.0000			0.604381			0.302190	+	0.953248i	$0.402282\pi$
$888$		0			0
$889$	−32.5000	−	11.2583i	−1.09002	−	0.377592i
$890$		0			0
$891$		0			0
$892$	−4.00000	+	6.92820i	−0.133930	+	0.231973i
$893$	−24.0000			−0.803129
$894$		0			0
$895$		0			0
$896$	−2.00000	+	1.73205i	−0.0668153	+	0.0578638i
$897$		0			0
$898$	−12.0000	+	20.7846i	−0.400445	+	0.693591i
$899$	−3.00000	+	5.19615i	−0.100056	+	0.173301i
$900$		0			0
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$	18.0000	+	31.1769i	0.599334	+	1.03808i
$903$		0			0
$904$	6.00000	−	10.3923i	0.199557	−	0.345643i
$905$		0			0
$906$		0			0
$907$	−37.0000			−1.22856			−0.614282	−	0.789086i	$-0.710554\pi$
$907$	−37.0000			−1.22856			−0.614282	+	0.789086i	$0.710554\pi$
$908$	−3.00000	−	5.19615i	−0.0995585	−	0.172440i
$909$		0			0
$910$		0			0
$911$	−3.00000	−	5.19615i	−0.0993944	−	0.172156i	0.812040	−	0.583602i	$-0.198357\pi$
$911$	−3.00000	−	5.19615i	−0.0993944	−	0.172156i	−0.911434	+	0.411446i	$0.865024\pi$
$912$		0			0
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$	9.50000	+	16.4545i	0.314232	+	0.544266i
$915$		0			0
$916$	−2.50000	−	4.33013i	−0.0826023	−	0.143071i
$917$	30.0000	+	10.3923i	0.990687	+	0.343184i
$918$		0			0
$919$	27.5000	+	47.6314i	0.907141	+	1.57121i	0.818017	+	0.575194i	$0.195074\pi$
$919$	27.5000	+	47.6314i	0.907141	+	1.57121i	0.0891245	+	0.996020i	$0.471593\pi$
$920$		0			0
$921$		0			0
$922$	−18.0000			−0.592798
$923$	30.0000	−	51.9615i	0.987462	−	1.71033i
$924$		0			0
$925$	−2.50000	−	4.33013i	−0.0821995	−	0.142374i
$926$	−4.00000	−	6.92820i	−0.131448	−	0.227675i
$927$		0			0
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$	24.0000	−	41.5692i	0.787414	−	1.36384i	−0.140132	−	0.990133i	$-0.544753\pi$
$929$	24.0000	−	41.5692i	0.787414	−	1.36384i	0.927546	−	0.373709i	$-0.121914\pi$
$930$		0			0
$931$	−4.00000	+	27.7128i	−0.131095	+	0.908251i
$932$	12.0000	−	20.7846i	0.393073	−	0.680823i
$933$		0			0
$934$	−12.0000			−0.392652
$935$		0			0
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	−2.50000	−	0.866025i	−0.0816279	−	0.0282767i
$939$		0			0
$940$		0			0
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	0.974609	−	0.223912i	$-0.0718827\pi$
$941$	9.00000	+	15.5885i	0.293392	+	0.508169i	−0.681218	+	0.732081i	$0.738549\pi$
$942$		0			0
$943$	18.0000	−	31.1769i	0.586161	−	1.01526i
$944$	6.00000			0.195283
$945$		0			0
$946$	6.00000			0.195077
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	−0.681930	−	0.731417i	$-0.738859\pi$
$947$	9.00000	−	15.5885i	0.292461	−	0.506557i	0.974391	+	0.224860i	$0.0721926\pi$
$948$		0			0
$949$	−5.00000	−	8.66025i	−0.162307	−	0.281124i
$950$	20.0000			0.648886
$951$		0			0
$952$	12.0000	−	10.3923i	0.388922	−	0.336817i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$		0			0
$955$		0			0
$956$	−24.0000			−0.776215
$957$		0			0
$958$	6.00000	−	10.3923i	0.193851	−	0.335760i
$959$	15.0000	+	5.19615i	0.484375	+	0.167793i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$	2.50000	−	4.33013i	0.0806032	−	0.139609i
$963$		0			0
$964$	−8.50000	−	14.7224i	−0.273767	−	0.474178i
$965$		0			0
$966$		0			0
$967$	−17.5000	+	30.3109i	−0.562762	+	0.974732i	0.434492	+	0.900676i	$0.356928\pi$
$967$	−17.5000	+	30.3109i	−0.562762	+	0.974732i	−0.997254	+	0.0740568i	$0.976405\pi$
$968$	25.0000			0.803530
$969$		0			0
$970$		0			0
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	−0.995748	−	0.0921142i	$-0.970638\pi$
$971$	−18.0000	−	31.1769i	−0.577647	−	1.00051i	0.418101	−	0.908401i	$-0.362696\pi$
$972$		0			0
$973$	14.0000	−	12.1244i	0.448819	−	0.388689i
$974$	20.0000	+	34.6410i	0.640841	+	1.10997i
$975$		0			0
$976$	0.500000	+	0.866025i	0.0160046	+	0.0277208i
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−15.0000	−	25.9808i	−0.478669	−	0.829079i
$983$	24.0000			0.765481			0.382741	−	0.923856i	$-0.374980\pi$
$983$	24.0000			0.765481			0.382741	+	0.923856i	$0.374980\pi$
$984$		0			0
$985$		0			0
$986$	−18.0000	+	31.1769i	−0.573237	+	0.992875i
$987$		0			0
$988$	10.0000	+	17.3205i	0.318142	+	0.551039i
$989$	−3.00000	−	5.19615i	−0.0953945	−	0.165228i
$990$		0			0
$991$	−2.50000	+	4.33013i	−0.0794151	+	0.137551i	−0.902998	−	0.429645i	$-0.858639\pi$
$991$	−2.50000	+	4.33013i	−0.0794151	+	0.137551i	0.823583	+	0.567196i	$0.191972\pi$
$992$	0.500000	−	0.866025i	0.0158750	−	0.0274963i
$993$		0			0
$994$	24.0000	−	20.7846i	0.761234	−	0.659248i
$995$		0			0
$996$		0			0
$997$	23.0000			0.728417			0.364209	−	0.931317i	$-0.381339\pi$
$997$	23.0000			0.728417			0.364209	+	0.931317i	$0.381339\pi$
$998$	12.5000	−	21.6506i	0.395681	−	0.685339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.d.109.1		2
3.2	odd	2		1134.2.h.n.109.1		2
7.2	even	3		1134.2.e.m.919.1		2
9.2	odd	6		1134.2.e.c.865.1		2
9.4	even	3		378.2.g.b.109.1	✓	2
9.5	odd	6		378.2.g.e.109.1	yes	2
9.7	even	3		1134.2.e.m.865.1		2
21.2	odd	6		1134.2.e.c.919.1		2
63.2	odd	6		1134.2.h.n.541.1		2
63.4	even	3		2646.2.a.x.1.1		1
63.16	even	3	inner	1134.2.h.d.541.1		2
63.23	odd	6		378.2.g.e.163.1	yes	2
63.31	odd	6		2646.2.a.w.1.1		1
63.32	odd	6		2646.2.a.h.1.1		1
63.58	even	3		378.2.g.b.163.1	yes	2
63.59	even	6		2646.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.b.109.1	✓	2	9.4	even	3
378.2.g.b.163.1	yes	2	63.58	even	3
378.2.g.e.109.1	yes	2	9.5	odd	6
378.2.g.e.163.1	yes	2	63.23	odd	6
1134.2.e.c.865.1		2	9.2	odd	6
1134.2.e.c.919.1		2	21.2	odd	6
1134.2.e.m.865.1		2	9.7	even	3
1134.2.e.m.919.1		2	7.2	even	3
1134.2.h.d.109.1		2	1.1	even	1	trivial
1134.2.h.d.541.1		2	63.16	even	3	inner
1134.2.h.n.109.1		2	3.2	odd	2
1134.2.h.n.541.1		2	63.2	odd	6
2646.2.a.g.1.1		1	63.59	even	6
2646.2.a.h.1.1		1	63.32	odd	6
2646.2.a.w.1.1		1	63.31	odd	6
2646.2.a.x.1.1		1	63.4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(2.50000 + 0.866025i) q^{7} +1.00000 q^{8} -6.00000 q^{11} +(-2.50000 + 4.33013i) q^{13} +(-2.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(2.00000 + 3.46410i) q^{19} +(3.00000 - 5.19615i) q^{22} -6.00000 q^{23} -5.00000 q^{25} +(-2.50000 - 4.33013i) q^{26} +(-0.500000 - 2.59808i) q^{28} +(3.00000 + 5.19615i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(0.500000 + 0.866025i) q^{37} -4.00000 q^{38} +(-3.00000 + 5.19615i) q^{41} +(0.500000 + 0.866025i) q^{43} +(3.00000 + 5.19615i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-3.00000 + 5.19615i) q^{47} +(5.50000 + 4.33013i) q^{49} +(2.50000 - 4.33013i) q^{50} +5.00000 q^{52} +(-3.00000 + 5.19615i) q^{53} +(2.50000 + 0.866025i) q^{56} -6.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} -1.00000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{67} -6.00000 q^{68} -12.0000 q^{71} +(-1.00000 + 1.73205i) q^{73} -1.00000 q^{74} +(2.00000 - 3.46410i) q^{76} +(-15.0000 - 5.19615i) q^{77} +(0.500000 - 0.866025i) q^{79} +(-3.00000 - 5.19615i) q^{82} +(3.00000 + 5.19615i) q^{83} -1.00000 q^{86} -6.00000 q^{88} +(-10.0000 + 8.66025i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(-8.50000 - 14.7224i) q^{97} +(-6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 5 q^{7} + 2 q^{8} - 12 q^{11} - 5 q^{13} - 4 q^{14} - q^{16} + 6 q^{17} + 4 q^{19} + 6 q^{22} - 12 q^{23} - 10 q^{25} - 5 q^{26} - q^{28} + 6 q^{29} + q^{31} - q^{32} + 6 q^{34}+ \cdots - 13 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 5 * q^7 + 2 * q^8 - 12 * q^11 - 5 * q^13 - 4 * q^14 - q^16 + 6 * q^17 + 4 * q^19 + 6 * q^22 - 12 * q^23 - 10 * q^25 - 5 * q^26 - q^28 + 6 * q^29 + q^31 - q^32 + 6 * q^34 + q^37 - 8 * q^38 - 6 * q^41 + q^43 + 6 * q^44 + 6 * q^46 - 6 * q^47 + 11 * q^49 + 5 * q^50 + 10 * q^52 - 6 * q^53 + 5 * q^56 - 12 * q^58 - 6 * q^59 + q^61 - 2 * q^62 + 2 * q^64 + q^67 - 12 * q^68 - 24 * q^71 - 2 * q^73 - 2 * q^74 + 4 * q^76 - 30 * q^77 + q^79 - 6 * q^82 + 6 * q^83 - 2 * q^86 - 12 * q^88 - 20 * q^91 + 6 * q^92 - 6 * q^94 - 17 * q^97 - 13 * q^98

Introduction

L-functions

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