LMFDB - Embedded newform 1134.2.e.c.919.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(865,1134)] 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("1134.865"); 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([4, 4])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [2,-2,0,2,0,0,-1] 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:	$1$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			919.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.919
Dual form			1134.2.e.c.865.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{11} +(-2.50000 + 4.33013i) q^{13} +(0.500000 - 2.59808i) q^{14} +1.00000 q^{16} +(-3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(3.00000 - 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-0.500000 + 2.59808i) q^{28} +(-3.00000 - 5.19615i) q^{29} -1.00000 q^{31} -1.00000 q^{32} +(3.00000 + 5.19615i) q^{34} +(0.500000 - 0.866025i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(3.00000 - 5.19615i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{44} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(-6.50000 - 2.59808i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(-2.50000 + 4.33013i) q^{52} +(3.00000 + 5.19615i) q^{53} +(0.500000 - 2.59808i) q^{56} +(3.00000 + 5.19615i) q^{58} -6.00000 q^{59} -1.00000 q^{61} +1.00000 q^{62} +1.00000 q^{64} -1.00000 q^{67} +(-3.00000 - 5.19615i) q^{68} +12.0000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-12.0000 - 10.3923i) q^{77} -1.00000 q^{79} +(-3.00000 + 5.19615i) q^{82} +(-3.00000 - 5.19615i) q^{83} +(-0.500000 - 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{88} +(-10.0000 - 8.66025i) q^{91} +(-3.00000 - 5.19615i) q^{92} +6.00000 q^{94} +(-8.50000 - 14.7224i) q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + 2 q^{4} - q^{7} - 2 q^{8} - 6 q^{11} - 5 q^{13} + q^{14} + 2 q^{16} - 6 q^{17} + 4 q^{19} + 6 q^{22} - 6 q^{23} + 5 q^{25} + 5 q^{26} - q^{28} - 6 q^{29} - 2 q^{31} - 2 q^{32} + 6 q^{34}+ \cdots + 13 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 2 * q^4 - q^7 - 2 * q^8 - 6 * q^11 - 5 * q^13 + q^14 + 2 * q^16 - 6 * q^17 + 4 * q^19 + 6 * q^22 - 6 * q^23 + 5 * q^25 + 5 * q^26 - q^28 - 6 * q^29 - 2 * q^31 - 2 * q^32 + 6 * q^34 + q^37 - 4 * q^38 + 6 * q^41 + q^43 - 6 * q^44 + 6 * q^46 - 12 * q^47 - 13 * q^49 - 5 * q^50 - 5 * q^52 + 6 * q^53 + q^56 + 6 * q^58 - 12 * q^59 - 2 * q^61 + 2 * q^62 + 2 * q^64 - 2 * q^67 - 6 * q^68 + 24 * q^71 - 2 * q^73 - q^74 + 4 * q^76 - 24 * q^77 - 2 * q^79 - 6 * q^82 - 6 * q^83 - q^86 + 6 * q^88 - 20 * q^91 - 6 * q^92 + 12 * q^94 - 17 * q^97 + 13 * q^98

Character values

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

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

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 $

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$		0			0
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$7$	−0.500000	+	2.59808i	−0.188982	+	0.981981i
$8$	−1.00000			−0.353553
$9$		0			0
$10$		0			0
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.0829925	+	0.996550i	$0.526448\pi$
$11$	−3.00000	+	5.19615i	−0.904534	+	1.56670i	−0.821541	+	0.570149i	$0.806886\pi$
$12$		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	$0.922790\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	1.00000			0.250000
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$		0			0
$21$		0			0
$22$	3.00000	−	5.19615i	0.639602	−	1.10782i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$		0			0
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	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	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$		0			0
$31$	−1.00000			−0.179605			−0.0898027	−	0.995960i	$-0.528624\pi$
$31$	−1.00000			−0.179605			−0.0898027	+	0.995960i	$0.528624\pi$
$32$	−1.00000			−0.176777
$33$		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	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$		0			0
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		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
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$		0			0
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	−2.50000	+	4.33013i	−0.353553	+	0.612372i
$51$		0			0
$52$	−2.50000	+	4.33013i	−0.346688	+	0.600481i
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$		0			0
$58$	3.00000	+	5.19615i	0.393919	+	0.682288i
$59$	−6.00000			−0.781133			−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000			−0.781133			−0.390567	+	0.920575i	$0.627721\pi$
$60$		0			0
$61$	−1.00000			−0.128037			−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	−1.00000			−0.128037			−0.0640184	+	0.997949i	$0.520392\pi$
$62$	1.00000			0.127000
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−1.00000			−0.122169			−0.0610847	−	0.998133i	$-0.519456\pi$
$67$	−1.00000			−0.122169			−0.0610847	+	0.998133i	$0.519456\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$		0			0
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$	−12.0000	−	10.3923i	−1.36753	−	1.18431i
$78$		0			0
$79$	−1.00000			−0.112509			−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000			−0.112509			−0.0562544	+	0.998416i	$0.517916\pi$
$80$		0			0
$81$		0			0
$82$	−3.00000	+	5.19615i	−0.331295	+	0.573819i
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	0.653079	−	0.757290i	$-0.273477\pi$
$83$	−3.00000	−	5.19615i	−0.329293	−	0.570352i	−0.982372	+	0.186938i	$0.940144\pi$
$84$		0			0
$85$		0			0
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$		0			0
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$		0			0
$91$	−10.0000	−	8.66025i	−1.04828	−	0.907841i
$92$	−3.00000	−	5.19615i	−0.312772	−	0.541736i
$93$		0			0
$94$	6.00000			0.618853
$95$		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
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	0.396236	+	0.918149i	$0.370316\pi$
$101$	−6.00000	+	10.3923i	−0.597022	+	1.03407i	−0.993258	+	0.115924i	$0.963017\pi$
$102$		0			0
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.772728	+	0.634738i	$0.218892\pi$
$103$	9.50000	+	16.4545i	0.936063	+	1.62131i	0.163335	+	0.986571i	$0.447775\pi$
$104$	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	−0.00813215	+	0.999967i	$0.502589\pi$
$107$	−9.00000	+	15.5885i	−0.870063	+	1.50699i	−0.861931	+	0.507026i	$0.830745\pi$
$108$		0			0
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	0.721102	−	0.692829i	$-0.243636\pi$
$109$	−2.50000	−	4.33013i	−0.239457	−	0.414751i	−0.960558	+	0.278078i	$0.910303\pi$
$110$		0			0
$111$		0			0
$112$	−0.500000	+	2.59808i	−0.0472456	+	0.245495i
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	0.432670	+	0.901553i	$0.357572\pi$
$113$	−6.00000	+	10.3923i	−0.564433	+	0.977626i	−0.997102	+	0.0760733i	$0.975762\pi$
$114$		0			0
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$		0			0
$118$	6.00000			0.552345
$119$	15.0000	−	5.19615i	1.37505	−	0.476331i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	1.00000			0.0905357
$123$		0			0
$124$	−1.00000			−0.0898027
$125$		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	$0.695692\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$		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
$133$	8.00000	+	6.92820i	0.693688	+	0.600751i
$134$	1.00000			0.0863868
$135$		0			0
$136$	3.00000	+	5.19615i	0.257248	+	0.445566i
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	−0.708942	−	0.705266i	$-0.750827\pi$
$137$	3.00000	−	5.19615i	0.256307	−	0.443937i	0.965250	+	0.261329i	$0.0841608\pi$
$138$		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
$142$	−12.0000			−1.00702
$143$	−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
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	0.999953	−	0.00974235i	$-0.00310113\pi$
$149$	6.00000	+	10.3923i	0.491539	+	0.851371i	−0.508413	+	0.861113i	$0.669768\pi$
$150$		0			0
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	0.279554	+	0.960130i	$0.409814\pi$
$151$	−8.50000	+	14.7224i	−0.691720	+	1.19809i	−0.971274	+	0.237964i	$0.923520\pi$
$152$	−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
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	1.00000			0.0795557
$159$		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	−0.996942	−	0.0781474i	$-0.975100\pi$
$163$	−5.50000	+	9.52628i	−0.430793	+	0.746156i	0.566149	+	0.824303i	$0.308433\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	9.00000	−	15.5885i	0.696441	−	1.20627i	−0.273252	−	0.961943i	$-0.588099\pi$
$167$	9.00000	−	15.5885i	0.696441	−	1.20627i	0.969693	−	0.244328i	$-0.0785675\pi$
$168$		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			−	1.00000i	$-0.5\pi$
$173$		0			0				1.00000i	$0.5\pi$
$174$		0			0
$175$	10.0000	+	8.66025i	0.755929	+	0.654654i
$176$	−3.00000	+	5.19615i	−0.226134	+	0.391675i
$177$		0			0
$178$		0			0
$179$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$179$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	10.0000	+	8.66025i	0.741249	+	0.641941i
$183$		0			0
$184$	3.00000	+	5.19615i	0.221163	+	0.383065i
$185$		0			0
$186$		0			0
$187$	36.0000			2.63258
$188$	−6.00000			−0.437595
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	−1.00000			−0.0719816			−0.0359908	−	0.999352i	$-0.511459\pi$
$193$	−1.00000			−0.0719816			−0.0359908	+	0.999352i	$0.511459\pi$
$194$	8.50000	+	14.7224i	0.610264	+	1.05701i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	0.602549	−	0.798082i	$-0.294152\pi$
$199$	−5.50000	−	9.52628i	−0.389885	−	0.675300i	−0.992434	+	0.122782i	$0.960818\pi$
$200$	−2.50000	+	4.33013i	−0.176777	+	0.306186i
$201$		0			0
$202$	6.00000	−	10.3923i	0.422159	−	0.731200i
$203$	15.0000	−	5.19615i	1.05279	−	0.364698i
$204$		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	$0.0189888\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$		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
$221$	30.0000			2.01802
$222$		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
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	−0.749125	−	0.662428i	$-0.769526\pi$
$227$	3.00000	−	5.19615i	0.199117	−	0.344881i	0.948242	+	0.317547i	$0.102859\pi$
$228$		0			0
$229$	−2.50000	−	4.33013i	−0.165205	−	0.286143i	0.771523	−	0.636201i	$-0.219495\pi$
$229$	−2.50000	−	4.33013i	−0.165205	−	0.286143i	−0.936728	+	0.350058i	$0.886162\pi$
$230$		0			0
$231$		0			0
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	0.142166	+	0.989843i	$0.454593\pi$
$233$	−12.0000	+	20.7846i	−0.786146	+	1.36165i	−0.928312	+	0.371802i	$0.878740\pi$
$234$		0			0
$235$		0			0
$236$	−6.00000			−0.390567
$237$		0			0
$238$	−15.0000	+	5.19615i	−0.972306	+	0.336817i
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$		0			0
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	0.450910	+	0.892570i	$0.351100\pi$
$241$	−8.50000	+	14.7224i	−0.547533	+	0.948355i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	12.5000	+	21.6506i	0.803530	+	1.39176i
$243$		0			0
$244$	−1.00000			−0.0640184
$245$		0			0
$246$		0			0
$247$	10.0000	+	17.3205i	0.636285	+	1.10208i
$248$	1.00000			0.0635001
$249$		0			0
$250$		0			0
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$	36.0000			2.26330
$254$	13.0000			0.815693
$255$		0			0
$256$	1.00000			0.0625000
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	2.00000	+	1.73205i	0.124274	+	0.107624i
$260$		0			0
$261$		0			0
$262$	−6.00000	−	10.3923i	−0.370681	−	0.642039i
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$		0			0
$265$		0			0
$266$	−8.00000	−	6.92820i	−0.490511	−	0.424795i
$267$		0			0
$268$	−1.00000			−0.0610847
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	−0.739921	−	0.672694i	$-0.765137\pi$
$271$	3.50000	−	6.06218i	0.212610	−	0.368251i	0.952531	+	0.304443i	$0.0984703\pi$
$272$	−3.00000	−	5.19615i	−0.181902	−	0.315063i
$273$		0			0
$274$	−3.00000	+	5.19615i	−0.181237	+	0.313911i
$275$	15.0000	+	25.9808i	0.904534	+	1.56670i
$276$		0			0
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$	−3.50000	+	6.06218i	−0.209916	+	0.363585i
$279$		0			0
$280$		0			0
$281$	−6.00000	−	10.3923i	−0.357930	−	0.619953i	0.629685	−	0.776851i	$-0.283184\pi$
$281$	−6.00000	−	10.3923i	−0.357930	−	0.619953i	−0.987615	+	0.156898i	$0.949851\pi$
$282$		0			0
$283$	−13.0000			−0.772770			−0.386385	−	0.922338i	$-0.626276\pi$
$283$	−13.0000			−0.772770			−0.386385	+	0.922338i	$0.626276\pi$
$284$	12.0000			0.712069
$285$		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
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$		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
$299$	30.0000			1.73494
$300$		0			0
$301$	−2.50000	+	0.866025i	−0.144098	+	0.0499169i
$302$	8.50000	−	14.7224i	0.489120	−	0.847181i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$		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	$0.338776\pi$
$308$	−12.0000	−	10.3923i	−0.683763	−	0.592157i
$309$		0			0
$310$		0			0
$311$	−12.0000			−0.680458			−0.340229	−	0.940343i	$-0.610505\pi$
$311$	−12.0000			−0.680458			−0.340229	+	0.940343i	$0.610505\pi$
$312$		0			0
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	22.0000			1.24153
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	18.0000			1.01098			0.505490	−	0.862832i	$-0.331312\pi$
$317$	18.0000			1.01098			0.505490	+	0.862832i	$0.331312\pi$
$318$		0			0
$319$	36.0000			2.01561
$320$		0			0
$321$		0			0
$322$	−15.0000	+	5.19615i	−0.835917	+	0.289570i
$323$	−24.0000			−1.33540
$324$		0			0
$325$	12.5000	+	21.6506i	0.693375	+	1.20096i
$326$	5.50000	−	9.52628i	0.304617	−	0.527612i
$327$		0			0
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	3.00000	−	15.5885i	0.165395	−	0.859419i
$330$		0			0
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	−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	$0.184015\pi$
$338$	6.00000	+	10.3923i	0.326357	+	0.565267i
$339$		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
$347$	−24.0000			−1.28839			−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000			−1.28839			−0.644194	+	0.764862i	$0.722807\pi$
$348$		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
$353$	18.0000	−	31.1769i	0.958043	−	1.65938i	0.230799	−	0.973002i	$-0.425866\pi$
$353$	18.0000	−	31.1769i	0.958043	−	1.65938i	0.727245	−	0.686378i	$-0.240800\pi$
$354$		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	$-0.883946\pi$
$359$	−3.00000	+	5.19615i	−0.158334	+	0.274242i	0.775934	+	0.630814i	$0.217279\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	10.0000			0.525588
$363$		0			0
$364$	−10.0000	−	8.66025i	−0.524142	−	0.453921i
$365$		0			0
$366$		0			0
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	−0.225750	−	0.974185i	$-0.572483\pi$
$367$	14.0000	−	24.2487i	0.730794	−	1.26577i	0.956544	−	0.291587i	$-0.0941834\pi$
$368$	−3.00000	−	5.19615i	−0.156386	−	0.270868i
$369$		0			0
$370$		0			0
$371$	−15.0000	+	5.19615i	−0.778761	+	0.269771i
$372$		0			0
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	−36.0000			−1.86152
$375$		0			0
$376$	6.00000			0.309426
$377$	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
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	0.779143	−	0.626846i	$-0.215654\pi$
$383$	−3.00000	−	5.19615i	−0.153293	−	0.265511i	−0.932436	+	0.361335i	$0.882321\pi$
$384$		0			0
$385$		0			0
$386$	1.00000			0.0508987
$387$		0			0
$388$	−8.50000	−	14.7224i	−0.431522	−	0.747418i
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	−0.672874	−	0.739758i	$-0.734940\pi$
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	0.977086	+	0.212847i	$0.0682735\pi$
$390$		0			0
$391$	−18.0000	+	31.1769i	−0.910299	+	1.57668i
$392$	6.50000	+	2.59808i	0.328300	+	0.131223i
$393$		0			0
$394$	12.0000			0.604551
$395$		0			0
$396$		0			0
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	−0.655534	−	0.755166i	$-0.727556\pi$
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	0.981760	+	0.190126i	$0.0608897\pi$
$398$	5.50000	+	9.52628i	0.275690	+	0.477509i
$399$		0			0
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$		0			0
$403$	2.50000	−	4.33013i	0.124534	−	0.215699i
$404$	−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
$409$	29.0000			1.43396			0.716979	−	0.697095i	$-0.245524\pi$
$409$	29.0000			1.43396			0.716979	+	0.697095i	$0.245524\pi$
$410$		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
$416$	2.50000	−	4.33013i	0.122573	−	0.212302i
$417$		0			0
$418$	−12.0000	−	20.7846i	−0.586939	−	1.01661i
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	−0.408481	−	0.912767i	$-0.633942\pi$
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	0.994720	−	0.102628i	$-0.0327251\pi$
$420$		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
$425$	−30.0000			−1.45521
$426$		0			0
$427$	0.500000	−	2.59808i	0.0241967	−	0.125730i
$428$	−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	$-0.0239399\pi$
$431$	9.00000	+	15.5885i	0.433515	+	0.750870i	−0.563658	+	0.826008i	$0.690607\pi$
$432$		0			0
$433$	−25.0000			−1.20142			−0.600712	−	0.799466i	$-0.705116\pi$
$433$	−25.0000			−1.20142			−0.600712	+	0.799466i	$0.705116\pi$
$434$	−0.500000	+	2.59808i	−0.0240008	+	0.124712i
$435$		0			0
$436$	−2.50000	−	4.33013i	−0.119728	−	0.207375i
$437$	−24.0000			−1.14808
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$		0			0
$442$	−30.0000			−1.42695
$443$	−24.0000			−1.14027			−0.570137	−	0.821549i	$-0.693110\pi$
$443$	−24.0000			−1.14027			−0.570137	+	0.821549i	$0.693110\pi$
$444$		0			0
$445$		0			0
$446$	4.00000	+	6.92820i	0.189405	+	0.328060i
$447$		0			0
$448$	−0.500000	+	2.59808i	−0.0236228	+	0.122748i
$449$	−24.0000			−1.13263			−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000			−1.13263			−0.566315	+	0.824189i	$0.691631\pi$
$450$		0			0
$451$	18.0000	+	31.1769i	0.847587	+	1.46806i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$		0			0
$454$	−3.00000	+	5.19615i	−0.140797	+	0.243868i
$455$		0			0
$456$		0			0
$457$	−19.0000			−0.888783			−0.444391	−	0.895833i	$-0.646580\pi$
$457$	−19.0000			−0.888783			−0.444391	+	0.895833i	$0.646580\pi$
$458$	2.50000	+	4.33013i	0.116817	+	0.202334i
$459$		0			0
$460$		0			0
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	0.576685	−	0.816967i	$-0.304346\pi$
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	−0.995856	+	0.0909401i	$0.971013\pi$
$462$		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	$0.226185\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$		0			0
$466$	12.0000	−	20.7846i	0.555889	−	0.962828i
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	−0.970799	−	0.239892i	$-0.922888\pi$
$467$	−6.00000	+	10.3923i	−0.277647	+	0.480899i	0.693153	+	0.720791i	$0.256221\pi$
$468$		0			0
$469$	0.500000	−	2.59808i	0.0230879	−	0.119968i
$470$		0			0
$471$		0			0
$472$	6.00000			0.276172
$473$	−6.00000			−0.275880
$474$		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
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	−0.969920	−	0.243426i	$-0.921729\pi$
$479$	−6.00000	+	10.3923i	−0.274147	+	0.474837i	0.695773	+	0.718262i	$0.255062\pi$
$480$		0			0
$481$	2.50000	+	4.33013i	0.113990	+	0.197437i
$482$	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	0.819181	+	0.573535i	$0.194428\pi$
$487$	20.0000	+	34.6410i	0.906287	+	1.56973i	0.0871056	+	0.996199i	$0.472238\pi$
$488$	1.00000			0.0452679
$489$		0			0
$490$		0			0
$491$	15.0000	−	25.9808i	0.676941	−	1.17250i	−0.298957	−	0.954267i	$-0.596639\pi$
$491$	15.0000	−	25.9808i	0.676941	−	1.17250i	0.975898	−	0.218229i	$-0.0700279\pi$
$492$		0			0
$493$	−18.0000	+	31.1769i	−0.810679	+	1.40414i
$494$	−10.0000	−	17.3205i	−0.449921	−	0.779287i
$495$		0			0
$496$	−1.00000			−0.0449013
$497$	−6.00000	+	31.1769i	−0.269137	+	1.39848i
$498$		0			0
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	0.997532	+	0.0702185i	$0.0223697\pi$
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	−0.437955	+	0.898997i	$0.644297\pi$
$500$		0			0
$501$		0			0
$502$	−18.0000			−0.803379
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$		0			0
$506$	−36.0000			−1.60040
$507$		0			0
$508$	−13.0000			−0.576782
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	5.00000	−	1.73205i	0.221187	−	0.0766214i
$512$	−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
$518$	−2.00000	−	1.73205i	−0.0878750	−	0.0761019i
$519$		0			0
$520$		0			0
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.799370	−	0.600839i	$-0.794833\pi$
$521$	−21.0000	−	36.3731i	−0.920027	−	1.59353i	−0.120656	−	0.992694i	$-0.538500\pi$
$522$		0			0
$523$	−11.5000	+	19.9186i	−0.502860	+	0.870979i	0.497135	+	0.867673i	$0.334385\pi$
$523$	−11.5000	+	19.9186i	−0.502860	+	0.870979i	−0.999995	+	0.00330547i	$0.998948\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$		0			0
$526$	3.00000	−	5.19615i	0.130806	−	0.226563i
$527$	3.00000	+	5.19615i	0.130682	+	0.226348i
$528$		0			0
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		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
$536$	1.00000			0.0431934
$537$		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	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−3.50000	+	6.06218i	−0.150338	+	0.260393i
$543$		0			0
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$		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
$551$	−24.0000			−1.02243
$552$		0			0
$553$	0.500000	−	2.59808i	0.0212622	−	0.110481i
$554$	8.50000	−	14.7224i	0.361130	−	0.625496i
$555$		0			0
$556$	3.50000	−	6.06218i	0.148433	−	0.257094i
$557$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$557$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$558$		0			0
$559$	−5.00000			−0.211477
$560$		0			0
$561$		0			0
$562$	6.00000	+	10.3923i	0.253095	+	0.438373i
$563$	−42.0000			−1.77009			−0.885044	−	0.465506i	$-0.845872\pi$
$563$	−42.0000			−1.77009			−0.885044	+	0.465506i	$0.845872\pi$
$564$		0			0
$565$		0			0
$566$	13.0000			0.546431
$567$		0			0
$568$	−12.0000			−0.503509
$569$	−36.0000			−1.50920			−0.754599	−	0.656186i	$-0.772169\pi$
$569$	−36.0000			−1.50920			−0.754599	+	0.656186i	$0.772169\pi$
$570$		0			0
$571$	−16.0000			−0.669579			−0.334790	−	0.942293i	$-0.608665\pi$
$571$	−16.0000			−0.669579			−0.334790	+	0.942293i	$0.608665\pi$
$572$	−15.0000	−	25.9808i	−0.627182	−	1.08631i
$573$		0			0
$574$	−12.0000	−	10.3923i	−0.500870	−	0.433766i
$575$	−30.0000			−1.25109
$576$		0			0
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	0.520952	−	0.853586i	$-0.325577\pi$
$577$	−11.5000	−	19.9186i	−0.478751	−	0.829222i	−0.999703	+	0.0243645i	$0.992244\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$		0			0
$580$		0			0
$581$	15.0000	−	5.19615i	0.622305	−	0.215573i
$582$		0			0
$583$	−36.0000			−1.49097
$584$	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
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	0.213697	+	0.976900i	$0.431449\pi$
$593$	−18.0000	+	31.1769i	−0.739171	+	1.28028i	−0.952869	+	0.303383i	$0.901884\pi$
$594$		0			0
$595$		0			0
$596$	6.00000	+	10.3923i	0.245770	+	0.425685i
$597$		0			0
$598$	−30.0000			−1.22679
$599$	36.0000			1.47092			0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000			1.47092			0.735460	+	0.677568i	$0.236966\pi$
$600$		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
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	0.981454	−	0.191700i	$-0.0614000\pi$
$607$	8.00000	+	13.8564i	0.324710	+	0.562414i	−0.656744	+	0.754114i	$0.728067\pi$
$608$	−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	0.733316	−	0.679888i	$-0.237972\pi$
$613$	−5.50000	−	9.52628i	−0.222143	−	0.384763i	−0.955458	+	0.295126i	$0.904638\pi$
$614$	−17.0000			−0.686064
$615$		0			0
$616$	12.0000	+	10.3923i	0.483494	+	0.418718i
$617$	15.0000	−	25.9808i	0.603877	−	1.04595i	−0.388351	−	0.921512i	$-0.626955\pi$
$617$	15.0000	−	25.9808i	0.603877	−	1.04595i	0.992228	−	0.124434i	$-0.0397116\pi$
$618$		0			0
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	−0.497579	−	0.867419i	$-0.665777\pi$
$619$	12.5000	−	21.6506i	0.502417	−	0.870212i	0.999996	−	0.00279365i	$-0.000889247\pi$
$620$		0			0
$621$		0			0
$622$	12.0000			0.481156
$623$		0			0
$624$		0			0
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	22.0000			0.879297
$627$		0			0
$628$	−22.0000			−0.877896
$629$	−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	$0.544496\pi$
$632$	1.00000			0.0397779
$633$		0			0
$634$	−18.0000			−0.714871
$635$		0			0
$636$		0			0
$637$	27.5000	−	21.6506i	1.08959	−	0.857829i
$638$	−36.0000			−1.42525
$639$		0			0
$640$		0			0
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$		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	$0.00258453\pi$
$644$	15.0000	−	5.19615i	0.591083	−	0.204757i
$645$		0			0
$646$	24.0000			0.944267
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	0.959529	−	0.281609i	$-0.0908680\pi$
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	−0.723645	+	0.690172i	$0.757535\pi$
$648$		0			0
$649$	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
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		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
$661$	50.0000			1.94477			0.972387	−	0.233373i	$-0.0749763\pi$
$661$	50.0000			1.94477			0.972387	+	0.233373i	$0.0749763\pi$
$662$	−20.0000			−0.777322
$663$		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
$668$	9.00000	−	15.5885i	0.348220	−	0.603136i
$669$		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
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$		0			0
$679$	42.5000	−	14.7224i	1.63100	−	0.564995i
$680$		0			0
$681$		0			0
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	0.728101	−	0.685470i	$-0.240403\pi$
$683$	−6.00000	−	10.3923i	−0.229584	−	0.397650i	−0.957685	+	0.287819i	$0.907070\pi$
$684$		0			0
$685$		0			0
$686$	−10.0000	+	15.5885i	−0.381802	+	0.595170i
$687$		0			0
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	−30.0000			−1.14291
$690$		0			0
$691$	17.0000			0.646710			0.323355	−	0.946278i	$-0.395189\pi$
$691$	17.0000			0.646710			0.323355	+	0.946278i	$0.395189\pi$
$692$		0			0
$693$		0			0
$694$	24.0000			0.911028
$695$		0			0
$696$		0			0
$697$	−36.0000			−1.36360
$698$	−0.500000	−	0.866025i	−0.0189253	−	0.0327795i
$699$		0			0
$700$	10.0000	+	8.66025i	0.377964	+	0.327327i
$701$	48.0000			1.81293			0.906467	−	0.422276i	$-0.138769\pi$
$701$	48.0000			1.81293			0.906467	+	0.422276i	$0.138769\pi$
$702$		0			0
$703$	−2.00000	−	3.46410i	−0.0754314	−	0.130651i
$704$	−3.00000	+	5.19615i	−0.113067	+	0.195837i
$705$		0			0
$706$	−18.0000	+	31.1769i	−0.677439	+	1.17336i
$707$	−24.0000	−	20.7846i	−0.902613	−	0.781686i
$708$		0			0
$709$	17.0000			0.638448			0.319224	−	0.947679i	$-0.396578\pi$
$709$	17.0000			0.638448			0.319224	+	0.947679i	$0.396578\pi$
$710$		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
$718$	3.00000	−	5.19615i	0.111959	−	0.193919i
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	−0.955947	−	0.293538i	$-0.905167\pi$
$719$	−6.00000	+	10.3923i	−0.223762	+	0.387568i	0.732185	+	0.681106i	$0.238501\pi$
$720$		0			0
$721$	−47.5000	+	16.4545i	−1.76899	+	0.612797i
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$		0			0
$724$	−10.0000			−0.371647
$725$	−30.0000			−1.11417
$726$		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
$731$	3.00000	−	5.19615i	0.110959	−	0.192187i
$732$		0			0
$733$	−8.50000	−	14.7224i	−0.313955	−	0.543785i	0.665260	−	0.746612i	$-0.268321\pi$
$733$	−8.50000	−	14.7224i	−0.313955	−	0.543785i	−0.979215	+	0.202826i	$0.934987\pi$
$734$	−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	0.825877	+	0.563850i	$0.190680\pi$
$739$	24.5000	+	42.4352i	0.901247	+	1.56101i	0.0753699	+	0.997156i	$0.475986\pi$
$740$		0			0
$741$		0			0
$742$	15.0000	−	5.19615i	0.550667	−	0.190757i
$743$	−9.00000	+	15.5885i	−0.330178	+	0.571885i	−0.982547	−	0.186017i	$-0.940442\pi$
$743$	−9.00000	+	15.5885i	−0.330178	+	0.571885i	0.652369	+	0.757902i	$0.273775\pi$
$744$		0			0
$745$		0			0
$746$	13.0000	+	22.5167i	0.475964	+	0.824394i
$747$		0			0
$748$	36.0000			1.31629
$749$	−36.0000	−	31.1769i	−1.31541	−	1.13918i
$750$		0			0
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	0.974265	−	0.225407i	$-0.0723712\pi$
$751$	8.00000	+	13.8564i	0.291924	+	0.505627i	−0.682341	+	0.731034i	$0.739038\pi$
$752$	−6.00000			−0.218797
$753$		0			0
$754$	−30.0000			−1.09254
$755$		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	$0.323312\pi$
$758$	1.00000			0.0363216
$759$		0			0
$760$		0			0
$761$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$761$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$762$		0			0
$763$	12.5000	−	4.33013i	0.452530	−	0.156761i
$764$		0			0
$765$		0			0
$766$	3.00000	+	5.19615i	0.108394	+	0.187745i
$767$	15.0000	−	25.9808i	0.541619	−	0.938111i
$768$		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
$772$	−1.00000			−0.0359908
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	0.997012	−	0.0772449i	$-0.0246123\pi$
$773$	12.0000	+	20.7846i	0.431610	+	0.747570i	−0.565402	+	0.824815i	$0.691279\pi$
$774$		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
$779$	−12.0000	−	20.7846i	−0.429945	−	0.744686i
$780$		0			0
$781$	−36.0000	+	62.3538i	−1.28818	+	2.23120i
$782$	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
$787$	−31.0000			−1.10503			−0.552515	−	0.833503i	$-0.686332\pi$
$787$	−31.0000			−1.10503			−0.552515	+	0.833503i	$0.686332\pi$
$788$	−12.0000			−0.427482
$789$		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
$794$	−6.50000	+	11.2583i	−0.230676	+	0.399543i
$795$		0			0
$796$	−5.50000	−	9.52628i	−0.194942	−	0.337650i
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	−0.468004	−	0.883726i	$-0.655027\pi$
$797$	15.0000	−	25.9808i	0.531327	−	0.920286i	0.999331	−	0.0365596i	$-0.0116399\pi$
$798$		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
$803$	12.0000			0.423471
$804$		0			0
$805$		0			0
$806$	−2.50000	+	4.33013i	−0.0880587	+	0.152522i
$807$		0			0
$808$	6.00000	−	10.3923i	0.211079	−	0.365600i
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	0.999491	+	0.0319002i	$0.0101559\pi$
$809$	15.0000	+	25.9808i	0.527372	+	0.913435i	−0.472119	+	0.881535i	$0.656511\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	15.0000	−	5.19615i	0.526397	−	0.182349i
$813$		0			0
$814$	−3.00000	−	5.19615i	−0.105150	−	0.182125i
$815$		0			0
$816$		0			0
$817$	4.00000			0.139942
$818$	−29.0000			−1.01396
$819$		0			0
$820$		0			0
$821$	6.00000			0.209401			0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000			0.209401			0.104701	+	0.994504i	$0.466612\pi$
$822$		0			0
$823$	−31.0000			−1.08059			−0.540296	−	0.841475i	$-0.681688\pi$
$823$	−31.0000			−1.08059			−0.540296	+	0.841475i	$0.681688\pi$
$824$	−9.50000	−	16.4545i	−0.330948	−	0.573219i
$825$		0			0
$826$	−3.00000	+	15.5885i	−0.104383	+	0.542392i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	0.718481	−	0.695546i	$-0.244838\pi$
$829$	−7.00000	−	12.1244i	−0.243120	−	0.421096i	−0.961601	+	0.274450i	$0.911504\pi$
$830$		0			0
$831$		0			0
$832$	−2.50000	+	4.33013i	−0.0866719	+	0.150120i
$833$	6.00000	+	41.5692i	0.207888	+	1.44029i
$834$		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	0.667803	−	0.744338i	$-0.267235\pi$
$839$	−9.00000	−	15.5885i	−0.310715	−	0.538173i	−0.978517	+	0.206165i	$0.933902\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	7.00000	+	12.1244i	0.241236	+	0.417833i
$843$		0			0
$844$	6.50000	−	11.2583i	0.223739	−	0.387528i
$845$		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
$850$	30.0000			1.02899
$851$	−6.00000			−0.205677
$852$		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
$857$	6.00000	−	10.3923i	0.204956	−	0.354994i	−0.745163	−	0.666883i	$-0.767628\pi$
$857$	6.00000	−	10.3923i	0.204956	−	0.354994i	0.950119	+	0.311888i	$0.100962\pi$
$858$		0			0
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	0.600387	−	0.799709i	$-0.295013\pi$
$859$	−11.5000	−	19.9186i	−0.392375	−	0.679613i	−0.992762	+	0.120096i	$0.961680\pi$
$860$		0			0
$861$		0			0
$862$	−9.00000	−	15.5885i	−0.306541	−	0.530945i
$863$	−18.0000	+	31.1769i	−0.612727	+	1.06127i	0.378052	+	0.925785i	$0.376594\pi$
$863$	−18.0000	+	31.1769i	−0.612727	+	1.06127i	−0.990779	+	0.135490i	$0.956739\pi$
$864$		0			0
$865$		0			0
$866$	25.0000			0.849535
$867$		0			0
$868$	0.500000	−	2.59808i	0.0169711	−	0.0881845i
$869$	3.00000	−	5.19615i	0.101768	−	0.176267i
$870$		0			0
$871$	2.50000	−	4.33013i	0.0847093	−	0.146721i
$872$	2.50000	+	4.33013i	0.0846607	+	0.146637i
$873$		0			0
$874$	24.0000			0.811812
$875$		0			0
$876$		0			0
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	0.954652	−	0.297724i	$-0.0962275\pi$
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	−0.735163	+	0.677891i	$0.762894\pi$
$878$	−8.00000			−0.269987
$879$		0			0
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	−40.0000			−1.34611			−0.673054	−	0.739594i	$-0.735018\pi$
$883$	−40.0000			−1.34611			−0.673054	+	0.739594i	$0.735018\pi$
$884$	30.0000			1.00901
$885$		0			0
$886$	24.0000			0.806296
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	0.976632	−	0.214919i	$-0.0689488\pi$
$887$	9.00000	+	15.5885i	0.302190	+	0.523409i	−0.674441	+	0.738328i	$0.735615\pi$
$888$		0			0
$889$	6.50000	−	33.7750i	0.218003	−	1.13278i
$890$		0			0
$891$		0			0
$892$	−4.00000	−	6.92820i	−0.133930	−	0.231973i
$893$	−12.0000	+	20.7846i	−0.401565	+	0.695530i
$894$		0			0
$895$		0			0
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		0			0
$898$	24.0000			0.800890
$899$	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
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	−0.376228	−	0.926527i	$-0.622779\pi$
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	0.990510	−	0.137441i	$-0.0438878\pi$
$908$	3.00000	−	5.19615i	0.0995585	−	0.172440i
$909$		0			0
$910$		0			0
$911$	3.00000	+	5.19615i	0.0993944	+	0.172156i	0.911434	−	0.411446i	$-0.134976\pi$
$911$	3.00000	+	5.19615i	0.0993944	+	0.172156i	−0.812040	+	0.583602i	$0.801643\pi$
$912$		0			0
$913$	36.0000			1.19143
$914$	19.0000			0.628464
$915$		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	0.0891245	−	0.996020i	$-0.471593\pi$
$919$	27.5000	−	47.6314i	0.907141	−	1.57121i	0.818017	−	0.575194i	$-0.195074\pi$
$920$		0			0
$921$		0			0
$922$	9.00000	+	15.5885i	0.296399	+	0.513378i
$923$	−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
$929$	48.0000			1.57483			0.787414	−	0.616424i	$-0.211419\pi$
$929$	48.0000			1.57483			0.787414	+	0.616424i	$0.211419\pi$
$930$		0			0
$931$	−22.0000	+	17.3205i	−0.721021	+	0.567657i
$932$	−12.0000	+	20.7846i	−0.393073	+	0.680823i
$933$		0			0
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$		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	$0.706575\pi$
$938$	−0.500000	+	2.59808i	−0.0163256	+	0.0848302i
$939$		0			0
$940$		0			0
$941$	18.0000			0.586783			0.293392	−	0.955992i	$-0.405216\pi$
$941$	18.0000			0.586783			0.293392	+	0.955992i	$0.405216\pi$
$942$		0			0
$943$	−36.0000			−1.17232
$944$	−6.00000			−0.195283
$945$		0			0
$946$	6.00000			0.195077
$947$	18.0000			0.584921			0.292461	−	0.956278i	$-0.405526\pi$
$947$	18.0000			0.584921			0.292461	+	0.956278i	$0.405526\pi$
$948$		0			0
$949$	10.0000			0.324614
$950$	10.0000	+	17.3205i	0.324443	+	0.561951i
$951$		0			0
$952$	−15.0000	+	5.19615i	−0.486153	+	0.168408i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		0			0
$956$	−12.0000	+	20.7846i	−0.388108	+	0.672222i
$957$		0			0
$958$	6.00000	−	10.3923i	0.193851	−	0.335760i
$959$	12.0000	+	10.3923i	0.387500	+	0.335585i
$960$		0			0
$961$	−30.0000			−0.967742
$962$	−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	$0.976405\pi$
$968$	12.5000	+	21.6506i	0.401765	+	0.695878i
$969$		0			0
$970$		0			0
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	−0.418101	−	0.908401i	$-0.637304\pi$
$971$	18.0000	−	31.1769i	0.577647	−	1.00051i	0.995748	−	0.0921142i	$-0.0293625\pi$
$972$		0			0
$973$	14.0000	+	12.1244i	0.448819	+	0.388689i
$974$	−20.0000	−	34.6410i	−0.640841	−	1.10997i
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	6.00000			0.191957			0.0959785	−	0.995383i	$-0.469402\pi$
$977$	6.00000			0.191957			0.0959785	+	0.995383i	$0.469402\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	−15.0000	+	25.9808i	−0.478669	+	0.829079i
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$		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	0.823583	−	0.567196i	$-0.191972\pi$
$991$	−2.50000	−	4.33013i	−0.0794151	−	0.137551i	−0.902998	+	0.429645i	$0.858639\pi$
$992$	1.00000			0.0317500
$993$		0			0
$994$	6.00000	−	31.1769i	0.190308	−	0.988872i
$995$		0			0
$996$		0			0
$997$	−11.5000	+	19.9186i	−0.364209	+	0.630828i	−0.988649	−	0.150245i	$-0.951994\pi$
$997$	−11.5000	+	19.9186i	−0.364209	+	0.630828i	0.624440	+	0.781073i	$0.285327\pi$
$998$	−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.e.c.919.1		2
3.2	odd	2		1134.2.e.m.919.1		2
7.4	even	3		1134.2.h.n.109.1		2
9.2	odd	6		1134.2.h.d.541.1		2
9.4	even	3		378.2.g.e.163.1	yes	2
9.5	odd	6		378.2.g.b.163.1	yes	2
9.7	even	3		1134.2.h.n.541.1		2
21.11	odd	6		1134.2.h.d.109.1		2
63.4	even	3		378.2.g.e.109.1	yes	2
63.5	even	6		2646.2.a.w.1.1		1
63.11	odd	6		1134.2.e.m.865.1		2
63.23	odd	6		2646.2.a.x.1.1		1
63.25	even	3	inner	1134.2.e.c.865.1		2
63.32	odd	6		378.2.g.b.109.1	✓	2
63.40	odd	6		2646.2.a.g.1.1		1
63.58	even	3		2646.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.g.b.109.1	✓	2	63.32	odd	6
378.2.g.b.163.1	yes	2	9.5	odd	6
378.2.g.e.109.1	yes	2	63.4	even	3
378.2.g.e.163.1	yes	2	9.4	even	3
1134.2.e.c.865.1		2	63.25	even	3	inner
1134.2.e.c.919.1		2	1.1	even	1	trivial
1134.2.e.m.865.1		2	63.11	odd	6
1134.2.e.m.919.1		2	3.2	odd	2
1134.2.h.d.109.1		2	21.11	odd	6
1134.2.h.d.541.1		2	9.2	odd	6
1134.2.h.n.109.1		2	7.4	even	3
1134.2.h.n.541.1		2	9.7	even	3
2646.2.a.g.1.1		1	63.40	odd	6
2646.2.a.h.1.1		1	63.58	even	3
2646.2.a.w.1.1		1	63.5	even	6
2646.2.a.x.1.1		1	63.23	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-0.500000 + 2.59808i) q^{7} -1.00000 q^{8} +(-3.00000 + 5.19615i) q^{11} +(-2.50000 + 4.33013i) q^{13} +(0.500000 - 2.59808i) q^{14} +1.00000 q^{16} +(-3.00000 - 5.19615i) q^{17} +(2.00000 - 3.46410i) q^{19} +(3.00000 - 5.19615i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(2.50000 - 4.33013i) q^{25} +(2.50000 - 4.33013i) q^{26} +(-0.500000 + 2.59808i) q^{28} +(-3.00000 - 5.19615i) q^{29} -1.00000 q^{31} -1.00000 q^{32} +(3.00000 + 5.19615i) q^{34} +(0.500000 - 0.866025i) q^{37} +(-2.00000 + 3.46410i) q^{38} +(3.00000 - 5.19615i) q^{41} +(0.500000 + 0.866025i) q^{43} +(-3.00000 + 5.19615i) q^{44} +(3.00000 + 5.19615i) q^{46} -6.00000 q^{47} +(-6.50000 - 2.59808i) q^{49} +(-2.50000 + 4.33013i) q^{50} +(-2.50000 + 4.33013i) q^{52} +(3.00000 + 5.19615i) q^{53} +(0.500000 - 2.59808i) q^{56} +(3.00000 + 5.19615i) q^{58} -6.00000 q^{59} -1.00000 q^{61} +1.00000 q^{62} +1.00000 q^{64} -1.00000 q^{67} +(-3.00000 - 5.19615i) q^{68} +12.0000 q^{71} +(-1.00000 - 1.73205i) q^{73} +(-0.500000 + 0.866025i) q^{74} +(2.00000 - 3.46410i) q^{76} +(-12.0000 - 10.3923i) q^{77} -1.00000 q^{79} +(-3.00000 + 5.19615i) q^{82} +(-3.00000 - 5.19615i) q^{83} +(-0.500000 - 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{88} +(-10.0000 - 8.66025i) q^{91} +(-3.00000 - 5.19615i) q^{92} +6.00000 q^{94} +(-8.50000 - 14.7224i) q^{97} +(6.50000 + 2.59808i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 2 q^{4} - q^{7} - 2 q^{8} - 6 q^{11} - 5 q^{13} + q^{14} + 2 q^{16} - 6 q^{17} + 4 q^{19} + 6 q^{22} - 6 q^{23} + 5 q^{25} + 5 q^{26} - q^{28} - 6 q^{29} - 2 q^{31} - 2 q^{32} + 6 q^{34}+ \cdots + 13 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 2 * q^4 - q^7 - 2 * q^8 - 6 * q^11 - 5 * q^13 + q^14 + 2 * q^16 - 6 * q^17 + 4 * q^19 + 6 * q^22 - 6 * q^23 + 5 * q^25 + 5 * q^26 - q^28 - 6 * q^29 - 2 * q^31 - 2 * q^32 + 6 * q^34 + q^37 - 4 * q^38 + 6 * q^41 + q^43 - 6 * q^44 + 6 * q^46 - 12 * q^47 - 13 * q^49 - 5 * q^50 - 5 * q^52 + 6 * q^53 + q^56 + 6 * q^58 - 12 * q^59 - 2 * q^61 + 2 * q^62 + 2 * q^64 - 2 * q^67 - 6 * q^68 + 24 * q^71 - 2 * q^73 - q^74 + 4 * q^76 - 24 * q^77 - 2 * q^79 - 6 * q^82 - 6 * q^83 - q^86 + 6 * q^88 - 20 * q^91 - 6 * q^92 + 12 * q^94 - 17 * q^97 + 13 * q^98

Introduction

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