LMFDB - Embedded newform 2646.2.e.f.2125.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2646,2,Mod(1549,2646)] 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("2646.1549"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2646, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,2,0,2,-3,0,0,2,0,-3,-6,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			2125.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.2125
Dual form			2646.2.e.f.1549.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(3.00000 - 5.19615i) q^{17} +(3.50000 + 6.06218i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(3.00000 - 5.19615i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(3.00000 - 5.19615i) q^{34} +(-1.00000 - 1.73205i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +18.0000 q^{55} +(3.00000 - 5.19615i) q^{58} +5.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +8.00000 q^{67} +(3.00000 - 5.19615i) q^{68} -3.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +5.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 + 1.73205i) q^{86} +(-3.00000 - 5.19615i) q^{88} +(1.50000 - 2.59808i) q^{92} -21.0000 q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 2 q^{8} - 3 q^{10} - 6 q^{11} - 2 q^{13} + 2 q^{16} + 6 q^{17} + 7 q^{19} - 3 q^{20} - 6 q^{22} + 3 q^{23} - 4 q^{25} - 2 q^{26} + 6 q^{29} + 4 q^{31} + 2 q^{32} + 6 q^{34}+ \cdots - 2 q^{97}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 - 3 * q^5 + 2 * q^8 - 3 * q^10 - 6 * q^11 - 2 * q^13 + 2 * q^16 + 6 * q^17 + 7 * q^19 - 3 * q^20 - 6 * q^22 + 3 * q^23 - 4 * q^25 - 2 * q^26 + 6 * q^29 + 4 * q^31 + 2 * q^32 + 6 * q^34 - 2 * q^37 + 7 * q^38 - 3 * q^40 - 2 * q^43 - 6 * q^44 + 3 * q^46 - 4 * q^50 - 2 * q^52 + 6 * q^53 + 36 * q^55 + 6 * q^58 + 10 * q^61 + 4 * q^62 + 2 * q^64 + 12 * q^65 + 16 * q^67 + 6 * q^68 - 6 * q^71 - 2 * q^73 - 2 * q^74 + 7 * q^76 + 10 * q^79 - 3 * q^80 + 12 * q^83 + 18 * q^85 - 2 * q^86 - 6 * q^88 + 3 * q^92 - 42 * q^95 - 2 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	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
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	0.917663	+	0.397360i	$0.130073\pi$
$19$	3.50000	+	6.06218i	0.802955	+	1.39076i	−0.114708	+	0.993399i	$0.536593\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	−3.00000	−	5.19615i	−0.639602	−	1.10782i
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		0			0
$28$		0			0
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	−0.440652	−	0.897678i	$-0.645253\pi$
$29$	3.00000	−	5.19615i	0.557086	−	0.964901i	0.997738	−	0.0672232i	$-0.0214140\pi$
$30$		0			0
$31$	2.00000			0.359211			0.179605	−	0.983739i	$-0.442518\pi$
$31$	2.00000			0.359211			0.179605	+	0.983739i	$0.442518\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	3.00000	−	5.19615i	0.514496	−	0.891133i
$35$		0			0
$36$		0			0
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$	3.50000	+	6.06218i	0.567775	+	0.983415i
$39$		0			0
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$		0			0
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	−1.00000	−	1.73205i	−0.138675	−	0.240192i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	18.0000			2.42712
$56$		0			0
$57$		0			0
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	5.00000			0.640184			0.320092	−	0.947386i	$-0.396286\pi$
$61$	5.00000			0.640184			0.320092	+	0.947386i	$0.396286\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	6.00000			0.744208
$66$		0			0
$67$	8.00000			0.977356			0.488678	−	0.872464i	$-0.337479\pi$
$67$	8.00000			0.977356			0.488678	+	0.872464i	$0.337479\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$		0			0
$70$		0			0
$71$	−3.00000			−0.356034			−0.178017	−	0.984027i	$-0.556968\pi$
$71$	−3.00000			−0.356034			−0.178017	+	0.984027i	$0.556968\pi$
$72$		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	−	1.73205i	−0.116248	−	0.201347i
$75$		0			0
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$		0			0
$78$		0			0
$79$	5.00000			0.562544			0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000			0.562544			0.281272	+	0.959628i	$0.409244\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$		0			0
$82$		0			0
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	−0.322396	−	0.946605i	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$		0			0
$85$	9.00000	+	15.5885i	0.976187	+	1.69081i
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$		0			0
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$		0			0
$92$	1.50000	−	2.59808i	0.156386	−	0.270868i
$93$		0			0
$94$		0			0
$95$	−21.0000			−2.15455
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	0.998240	−	0.0592978i	$-0.0188862\pi$
$101$	4.50000	+	7.79423i	0.447767	+	0.775555i	−0.550474	+	0.834853i	$0.685553\pi$
$102$		0			0
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	−0.507300	−	0.861770i	$-0.669356\pi$
$103$	5.00000	−	8.66025i	0.492665	−	0.853320i	0.999964	+	0.00844953i	$0.00268960\pi$
$104$	−1.00000	−	1.73205i	−0.0980581	−	0.169842i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$		0			0
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	−0.520794	−	0.853682i	$-0.674364\pi$
$109$	5.00000	−	8.66025i	0.478913	−	0.829502i	0.999708	+	0.0241802i	$0.00769755\pi$
$110$	18.0000			1.71623
$111$		0			0
$112$		0			0
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	0.966496	+	0.256681i	$0.0826291\pi$
$113$	7.50000	+	12.9904i	0.705541	+	1.22203i	−0.260955	+	0.965351i	$0.584038\pi$
$114$		0			0
$115$	4.50000	+	7.79423i	0.419627	+	0.726816i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	5.00000			0.452679
$123$		0			0
$124$	2.00000			0.179605
$125$	−3.00000			−0.268328
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	6.00000			0.526235
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	−0.992865	−	0.119241i	$-0.961954\pi$
$131$	−4.50000	+	7.79423i	−0.393167	+	0.680985i	0.599699	+	0.800226i	$0.295287\pi$
$132$		0			0
$133$		0			0
$134$	8.00000			0.691095
$135$		0			0
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000			−0.251754
$143$	−6.00000	+	10.3923i	−0.501745	+	0.869048i
$144$		0			0
$145$	9.00000	+	15.5885i	0.747409	+	1.29455i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$		0			0
$148$	−1.00000	−	1.73205i	−0.0821995	−	0.142374i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−11.5000	−	19.9186i	−0.935857	−	1.62095i	−0.773099	−	0.634285i	$-0.781294\pi$
$151$	−11.5000	−	19.9186i	−0.935857	−	1.62095i	−0.162758	−	0.986666i	$-0.552039\pi$
$152$	3.50000	+	6.06218i	0.283887	+	0.491708i
$153$		0			0
$154$		0			0
$155$	−3.00000	+	5.19615i	−0.240966	+	0.417365i
$156$		0			0
$157$	−13.0000			−1.03751			−0.518756	−	0.854922i	$-0.673605\pi$
$157$	−13.0000			−1.03751			−0.518756	+	0.854922i	$0.673605\pi$
$158$	5.00000			0.397779
$159$		0			0
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$		0			0
$162$		0			0
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	0.824202	−	0.566296i	$-0.191624\pi$
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	−0.902528	+	0.430632i	$0.858291\pi$
$164$		0			0
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	9.00000	+	15.5885i	0.690268	+	1.19558i
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	6.00000			0.456172			0.228086	−	0.973641i	$-0.426753\pi$
$173$	6.00000			0.456172			0.228086	+	0.973641i	$0.426753\pi$
$174$		0			0
$175$		0			0
$176$	−3.00000	−	5.19615i	−0.226134	−	0.391675i
$177$		0			0
$178$		0			0
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	−0.304446	−	0.952529i	$-0.598471\pi$
$179$	9.00000	−	15.5885i	0.672692	−	1.16514i	0.977138	−	0.212607i	$-0.0681952\pi$
$180$		0			0
$181$	−25.0000			−1.85824			−0.929118	−	0.369784i	$-0.879432\pi$
$181$	−25.0000			−1.85824			−0.929118	+	0.369784i	$0.879432\pi$
$182$		0			0
$183$		0			0
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$	6.00000			0.441129
$186$		0			0
$187$	−36.0000			−2.63258
$188$		0			0
$189$		0			0
$190$	−21.0000			−1.52350
$191$	9.00000			0.651217			0.325609	−	0.945505i	$-0.394431\pi$
$191$	9.00000			0.651217			0.325609	+	0.945505i	$0.394431\pi$
$192$		0			0
$193$	17.0000			1.22369			0.611843	−	0.790979i	$-0.290428\pi$
$193$	17.0000			1.22369			0.611843	+	0.790979i	$0.290428\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$		0			0
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	−0.999990	−	0.00436292i	$-0.998611\pi$
$199$	−7.00000	+	12.1244i	−0.496217	+	0.859473i	0.503774	+	0.863836i	$0.331945\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$		0			0
$202$	4.50000	+	7.79423i	0.316619	+	0.548400i
$203$		0			0
$204$		0			0
$205$		0			0
$206$	5.00000	−	8.66025i	0.348367	−	0.603388i
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	21.0000	−	36.3731i	1.45260	−	2.51598i
$210$		0			0
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	0.694857	−	0.719148i	$-0.255467\pi$
$211$	−4.00000	−	6.92820i	−0.275371	−	0.476957i	−0.970229	+	0.242190i	$0.922134\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	−3.00000	−	5.19615i	−0.204598	−	0.354375i
$216$		0			0
$217$		0			0
$218$	5.00000	−	8.66025i	0.338643	−	0.586546i
$219$		0			0
$220$	18.0000			1.21356
$221$	−12.0000			−0.807207
$222$		0			0
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.167412	−	0.985887i	$-0.446459\pi$
$223$	14.0000	−	24.2487i	0.937509	−	1.62381i	0.770097	−	0.637927i	$-0.220208\pi$
$224$		0			0
$225$		0			0
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	0.502204	−	0.864749i	$-0.332523\pi$
$227$	−7.50000	−	12.9904i	−0.497792	−	0.862202i	−0.999997	+	0.00254715i	$0.999189\pi$
$228$		0			0
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	−0.849032	−	0.528341i	$-0.822814\pi$
$229$	0.500000	−	0.866025i	0.0330409	−	0.0572286i	0.882073	+	0.471113i	$0.156147\pi$
$230$	4.50000	+	7.79423i	0.296721	+	0.513936i
$231$		0			0
$232$	3.00000	−	5.19615i	0.196960	−	0.341144i
$233$	4.50000	+	7.79423i	0.294805	+	0.510617i	0.974939	−	0.222470i	$-0.0714120\pi$
$233$	4.50000	+	7.79423i	0.294805	+	0.510617i	−0.680135	+	0.733087i	$0.738079\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	0.514719	−	0.857359i	$-0.327896\pi$
$239$	−7.50000	−	12.9904i	−0.485135	−	0.840278i	−0.999854	+	0.0170808i	$0.994563\pi$
$240$		0			0
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$	−12.5000	+	21.6506i	−0.803530	+	1.39176i
$243$		0			0
$244$	5.00000			0.320092
$245$		0			0
$246$		0			0
$247$	7.00000	−	12.1244i	0.445399	−	0.771454i
$248$	2.00000			0.127000
$249$		0			0
$250$	−3.00000			−0.189737
$251$	−3.00000			−0.189358			−0.0946792	−	0.995508i	$-0.530183\pi$
$251$	−3.00000			−0.189358			−0.0946792	+	0.995508i	$0.530183\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$	17.0000			1.06667
$255$		0			0
$256$	1.00000			0.0625000
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	−0.435970	−	0.899961i	$-0.643595\pi$
$257$	9.00000	−	15.5885i	0.561405	−	0.972381i	0.997374	−	0.0724199i	$-0.0230722\pi$
$258$		0			0
$259$		0			0
$260$	6.00000			0.372104
$261$		0			0
$262$	−4.50000	+	7.79423i	−0.278011	+	0.481529i
$263$	−10.5000	−	18.1865i	−0.647458	−	1.12143i	−0.983728	−	0.179664i	$-0.942499\pi$
$263$	−10.5000	−	18.1865i	−0.647458	−	1.12143i	0.336270	−	0.941766i	$-0.390834\pi$
$264$		0			0
$265$	9.00000	+	15.5885i	0.552866	+	0.957591i
$266$		0			0
$267$		0			0
$268$	8.00000			0.488678
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	−0.969976	−	0.243201i	$-0.921803\pi$
$269$	−4.50000	+	7.79423i	−0.274370	+	0.475223i	0.695606	+	0.718423i	$0.255136\pi$
$270$		0			0
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	0.880812	+	0.473466i	$0.156997\pi$
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	3.00000	−	5.19615i	0.181902	−	0.315063i
$273$		0			0
$274$	3.00000	+	5.19615i	0.181237	+	0.313911i
$275$	−12.0000	+	20.7846i	−0.723627	+	1.25336i
$276$		0			0
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	0.999754	−	0.0221745i	$-0.00705893\pi$
$277$	8.00000	+	13.8564i	0.480673	+	0.832551i	−0.519081	+	0.854725i	$0.673726\pi$
$278$	−2.50000	−	4.33013i	−0.149940	−	0.259704i
$279$		0			0
$280$		0			0
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$		0			0
$283$	−19.0000			−1.12943			−0.564716	−	0.825285i	$-0.691014\pi$
$283$	−19.0000			−1.12943			−0.564716	+	0.825285i	$0.691014\pi$
$284$	−3.00000			−0.178017
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$		0			0
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$	9.00000	+	15.5885i	0.528498	+	0.915386i
$291$		0			0
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	0.818878	−	0.573967i	$-0.194596\pi$
$293$	−1.50000	−	2.59808i	−0.0876309	−	0.151781i	−0.906509	+	0.422186i	$0.861263\pi$
$294$		0			0
$295$		0			0
$296$	−1.00000	−	1.73205i	−0.0581238	−	0.100673i
$297$		0			0
$298$	−3.00000	+	5.19615i	−0.173785	+	0.301005i
$299$	−6.00000			−0.346989
$300$		0			0
$301$		0			0
$302$	−11.5000	−	19.9186i	−0.661751	−	1.14619i
$303$		0			0
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$	−7.50000	+	12.9904i	−0.429449	+	0.743827i
$306$		0			0
$307$	−25.0000			−1.42683			−0.713413	−	0.700744i	$-0.752851\pi$
$307$	−25.0000			−1.42683			−0.713413	+	0.700744i	$0.752851\pi$
$308$		0			0
$309$		0			0
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	−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
$313$	−10.0000			−0.565233			−0.282617	−	0.959233i	$-0.591202\pi$
$313$	−10.0000			−0.565233			−0.282617	+	0.959233i	$0.591202\pi$
$314$	−13.0000			−0.733632
$315$		0			0
$316$	5.00000			0.281272
$317$	−18.0000			−1.01098			−0.505490	−	0.862832i	$-0.668688\pi$
$317$	−18.0000			−1.01098			−0.505490	+	0.862832i	$0.668688\pi$
$318$		0			0
$319$	−36.0000			−2.01561
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$		0			0
$322$		0			0
$323$	42.0000			2.33694
$324$		0			0
$325$	−4.00000	+	6.92820i	−0.221880	+	0.384308i
$326$	−1.00000	−	1.73205i	−0.0553849	−	0.0959294i
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	26.0000			1.42909			0.714545	−	0.699590i	$-0.246634\pi$
$331$	26.0000			1.42909			0.714545	+	0.699590i	$0.246634\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$		0			0
$334$		0			0
$335$	−12.0000	+	20.7846i	−0.655630	+	1.13558i
$336$		0			0
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	0.992938	+	0.118633i	$0.0378512\pi$
$337$	11.0000	+	19.0526i	0.599208	+	1.03786i	−0.393730	+	0.919226i	$0.628816\pi$
$338$	4.50000	−	7.79423i	0.244768	−	0.423950i
$339$		0			0
$340$	9.00000	+	15.5885i	0.488094	+	0.845403i
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$		0			0
$343$		0			0
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$		0			0
$346$	6.00000			0.322562
$347$	24.0000			1.28839			0.644194	−	0.764862i	$-0.277193\pi$
$347$	24.0000			1.28839			0.644194	+	0.764862i	$0.277193\pi$
$348$		0			0
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$		0			0
$351$		0			0
$352$	−3.00000	−	5.19615i	−0.159901	−	0.276956i
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$		0			0
$355$	4.50000	−	7.79423i	0.238835	−	0.413675i
$356$		0			0
$357$		0			0
$358$	9.00000	−	15.5885i	0.475665	−	0.823876i
$359$	−1.50000	−	2.59808i	−0.0791670	−	0.137121i	0.823724	−	0.566991i	$-0.191893\pi$
$359$	−1.50000	−	2.59808i	−0.0791670	−	0.137121i	−0.902891	+	0.429870i	$0.858559\pi$
$360$		0			0
$361$	−15.0000	+	25.9808i	−0.789474	+	1.36741i
$362$	−25.0000			−1.31397
$363$		0			0
$364$		0			0
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$		0			0
$370$	6.00000			0.311925
$371$		0			0
$372$		0			0
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	−36.0000			−1.86152
$375$		0			0
$376$		0			0
$377$	−12.0000			−0.618031
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	−21.0000			−1.07728
$381$		0			0
$382$	9.00000			0.460480
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	−0.998954	−	0.0457244i	$-0.985440\pi$
$383$	−9.00000	+	15.5885i	−0.459879	+	0.796533i	0.539076	+	0.842257i	$0.318774\pi$
$384$		0			0
$385$		0			0
$386$	17.0000			0.865277
$387$		0			0
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	0.991500	+	0.130105i	$0.0415314\pi$
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	−0.383076	+	0.923717i	$0.625135\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$		0			0
$393$		0			0
$394$	−18.0000			−0.906827
$395$	−7.50000	+	12.9904i	−0.377366	+	0.653617i
$396$		0			0
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	−0.982526	−	0.186124i	$-0.940407\pi$
$397$	−13.0000	−	22.5167i	−0.652451	−	1.13008i	0.330075	−	0.943955i	$-0.392926\pi$
$398$	−7.00000	+	12.1244i	−0.350878	+	0.607739i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	4.50000	+	7.79423i	0.223883	+	0.387777i
$405$		0			0
$406$		0			0
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$		0			0
$409$	32.0000			1.58230			0.791149	−	0.611623i	$-0.209483\pi$
$409$	32.0000			1.58230			0.791149	+	0.611623i	$0.209483\pi$
$410$		0			0
$411$		0			0
$412$	5.00000	−	8.66025i	0.246332	−	0.426660i
$413$		0			0
$414$		0			0
$415$	18.0000	+	31.1769i	0.883585	+	1.53041i
$416$	−1.00000	−	1.73205i	−0.0490290	−	0.0849208i
$417$		0			0
$418$	21.0000	−	36.3731i	1.02714	−	1.77906i
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	0.989000	−	0.147918i	$-0.0472572\pi$
$419$	7.50000	+	12.9904i	0.366399	+	0.634622i	−0.622601	+	0.782540i	$0.713924\pi$
$420$		0			0
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	−0.718076	−	0.695965i	$-0.754977\pi$
$421$	5.00000	−	8.66025i	0.243685	−	0.422075i	0.961761	+	0.273890i	$0.0883103\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$		0			0
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	−24.0000			−1.16417
$426$		0			0
$427$		0			0
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$		0			0
$430$	−3.00000	−	5.19615i	−0.144673	−	0.250581i
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	−0.684564	−	0.728953i	$-0.740007\pi$
$431$	6.00000	−	10.3923i	0.289010	−	0.500580i	0.973574	+	0.228373i	$0.0733406\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	21.0000			1.00457
$438$		0			0
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$	18.0000			0.858116
$441$		0			0
$442$	−12.0000			−0.570782
$443$	−18.0000			−0.855206			−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000			−0.855206			−0.427603	+	0.903967i	$0.640642\pi$
$444$		0			0
$445$		0			0
$446$	14.0000	−	24.2487i	0.662919	−	1.14821i
$447$		0			0
$448$		0			0
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$		0			0
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$		0			0
$454$	−7.50000	−	12.9904i	−0.351992	−	0.609669i
$455$		0			0
$456$		0			0
$457$	29.0000			1.35656			0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000			1.35656			0.678281	+	0.734802i	$0.262725\pi$
$458$	0.500000	−	0.866025i	0.0233635	−	0.0404667i
$459$		0			0
$460$	4.50000	+	7.79423i	0.209814	+	0.363408i
$461$	−16.5000	+	28.5788i	−0.768482	+	1.33105i	0.169904	+	0.985461i	$0.445654\pi$
$461$	−16.5000	+	28.5788i	−0.768482	+	1.33105i	−0.938386	+	0.345589i	$0.887679\pi$
$462$		0			0
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	0.976607	−	0.215032i	$-0.0689855\pi$
$463$	6.50000	+	11.2583i	0.302081	+	0.523219i	−0.674526	+	0.738251i	$0.735652\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$		0			0
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	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			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$	12.0000			0.551761
$474$		0			0
$475$	14.0000	−	24.2487i	0.642364	−	1.11261i
$476$		0			0
$477$		0			0
$478$	−7.50000	−	12.9904i	−0.343042	−	0.594166i
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	0.789314	−	0.613990i	$-0.210436\pi$
$479$	−3.00000	−	5.19615i	−0.137073	−	0.237418i	−0.926388	+	0.376571i	$0.877103\pi$
$480$		0			0
$481$	−2.00000	+	3.46410i	−0.0911922	+	0.157949i
$482$	−4.00000	−	6.92820i	−0.182195	−	0.315571i
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	−3.00000	−	5.19615i	−0.136223	−	0.235945i
$486$		0			0
$487$	−14.5000	+	25.1147i	−0.657058	+	1.13806i	0.324316	+	0.945949i	$0.394866\pi$
$487$	−14.5000	+	25.1147i	−0.657058	+	1.13806i	−0.981374	+	0.192109i	$0.938467\pi$
$488$	5.00000			0.226339
$489$		0			0
$490$		0			0
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	0.994456	−	0.105151i	$-0.0335327\pi$
$491$	9.00000	+	15.5885i	0.406164	+	0.703497i	−0.588292	+	0.808649i	$0.700199\pi$
$492$		0			0
$493$	−18.0000	−	31.1769i	−0.810679	−	1.40414i
$494$	7.00000	−	12.1244i	0.314945	−	0.545501i
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$		0			0
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	0.246214	+	0.969216i	$0.420813\pi$
$499$	−16.0000	+	27.7128i	−0.716258	+	1.24060i	−0.962472	+	0.271380i	$0.912520\pi$
$500$	−3.00000			−0.134164
$501$		0			0
$502$	−3.00000			−0.133897
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$	−27.0000			−1.20148
$506$	−18.0000			−0.800198
$507$		0			0
$508$	17.0000			0.754253
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	9.00000	−	15.5885i	0.396973	−	0.687577i
$515$	15.0000	+	25.9808i	0.660979	+	1.14485i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	6.00000			0.263117
$521$	12.0000	−	20.7846i	0.525730	−	0.910590i	−0.473821	−	0.880621i	$-0.657126\pi$
$521$	12.0000	−	20.7846i	0.525730	−	0.910590i	0.999551	−	0.0299693i	$-0.00954094\pi$
$522$		0			0
$523$	6.50000	+	11.2583i	0.284225	+	0.492292i	0.972421	−	0.233233i	$-0.0749303\pi$
$523$	6.50000	+	11.2583i	0.284225	+	0.492292i	−0.688196	+	0.725525i	$0.741597\pi$
$524$	−4.50000	+	7.79423i	−0.196583	+	0.340492i
$525$		0			0
$526$	−10.5000	−	18.1865i	−0.457822	−	0.792971i
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$	9.00000	+	15.5885i	0.390935	+	0.677119i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	36.0000			1.55642
$536$	8.00000			0.345547
$537$		0			0
$538$	−4.50000	+	7.79423i	−0.194009	+	0.336033i
$539$		0			0
$540$		0			0
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	−0.907975	−	0.419025i	$-0.862372\pi$
$541$	−19.0000	−	32.9090i	−0.816874	−	1.41487i	0.0911008	−	0.995842i	$-0.470961\pi$
$542$	14.0000	+	24.2487i	0.601351	+	1.04157i
$543$		0			0
$544$	3.00000	−	5.19615i	0.128624	−	0.222783i
$545$	15.0000	+	25.9808i	0.642529	+	1.11289i
$546$		0			0
$547$	−16.0000	+	27.7128i	−0.684111	+	1.18491i	0.289605	+	0.957146i	$0.406476\pi$
$547$	−16.0000	+	27.7128i	−0.684111	+	1.18491i	−0.973715	+	0.227768i	$0.926857\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$		0			0
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$	42.0000			1.78926
$552$		0			0
$553$		0			0
$554$	8.00000	+	13.8564i	0.339887	+	0.588702i
$555$		0			0
$556$	−2.50000	−	4.33013i	−0.106024	−	0.183638i
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	0.491496	+	0.870880i	$0.336450\pi$
$557$	−12.0000	+	20.7846i	−0.508456	+	0.880672i	−0.999952	+	0.00979220i	$0.996883\pi$
$558$		0			0
$559$	4.00000			0.169182
$560$		0			0
$561$		0			0
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	33.0000			1.39078			0.695392	−	0.718631i	$-0.255231\pi$
$563$	33.0000			1.39078			0.695392	+	0.718631i	$0.255231\pi$
$564$		0			0
$565$	−45.0000			−1.89316
$566$	−19.0000			−0.798630
$567$		0			0
$568$	−3.00000			−0.125877
$569$	18.0000			0.754599			0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000			0.754599			0.377300	+	0.926091i	$0.376853\pi$
$570$		0			0
$571$	32.0000			1.33916			0.669579	−	0.742741i	$-0.266474\pi$
$571$	32.0000			1.33916			0.669579	+	0.742741i	$0.266474\pi$
$572$	−6.00000	+	10.3923i	−0.250873	+	0.434524i
$573$		0			0
$574$		0			0
$575$	−12.0000			−0.500435
$576$		0			0
$577$	2.00000	−	3.46410i	0.0832611	−	0.144212i	−0.821388	−	0.570370i	$-0.806800\pi$
$577$	2.00000	−	3.46410i	0.0832611	−	0.144212i	0.904649	+	0.426158i	$0.140133\pi$
$578$	−9.50000	−	16.4545i	−0.395148	−	0.684416i
$579$		0			0
$580$	9.00000	+	15.5885i	0.373705	+	0.647275i
$581$		0			0
$582$		0			0
$583$	−36.0000			−1.49097
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−1.50000	−	2.59808i	−0.0619644	−	0.107326i
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	−0.895320	−	0.445424i	$-0.853053\pi$
$587$	−1.50000	+	2.59808i	−0.0619116	+	0.107234i	0.833408	+	0.552658i	$0.186386\pi$
$588$		0			0
$589$	7.00000	+	12.1244i	0.288430	+	0.499575i
$590$		0			0
$591$		0			0
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$	−6.00000			−0.245358
$599$	24.0000			0.980613			0.490307	−	0.871550i	$-0.336885\pi$
$599$	24.0000			0.980613			0.490307	+	0.871550i	$0.336885\pi$
$600$		0			0
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	−0.972739	−	0.231903i	$-0.925505\pi$
$601$	−7.00000	+	12.1244i	−0.285536	+	0.494563i	0.687203	+	0.726465i	$0.258838\pi$
$602$		0			0
$603$		0			0
$604$	−11.5000	−	19.9186i	−0.467928	−	0.810476i
$605$	−37.5000	−	64.9519i	−1.52459	−	2.64067i
$606$		0			0
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	−0.551678	−	0.834058i	$-0.686012\pi$
$607$	11.0000	−	19.0526i	0.446476	−	0.773320i	0.998154	+	0.0607380i	$0.0193454\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$		0			0
$610$	−7.50000	+	12.9904i	−0.303666	+	0.525965i
$611$		0			0
$612$		0			0
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	−0.935428	−	0.353518i	$-0.884985\pi$
$613$	−4.00000	+	6.92820i	−0.161558	+	0.279827i	0.773869	+	0.633345i	$0.218319\pi$
$614$	−25.0000			−1.00892
$615$		0			0
$616$		0			0
$617$	21.0000	+	36.3731i	0.845428	+	1.46432i	0.885249	+	0.465118i	$0.153988\pi$
$617$	21.0000	+	36.3731i	0.845428	+	1.46432i	−0.0398207	+	0.999207i	$0.512679\pi$
$618$		0			0
$619$	3.50000	+	6.06218i	0.140677	+	0.243659i	0.927752	−	0.373198i	$-0.121739\pi$
$619$	3.50000	+	6.06218i	0.140677	+	0.243659i	−0.787075	+	0.616858i	$0.788405\pi$
$620$	−3.00000	+	5.19615i	−0.120483	+	0.208683i
$621$		0			0
$622$	−12.0000			−0.481156
$623$		0			0
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−10.0000			−0.399680
$627$		0			0
$628$	−13.0000			−0.518756
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	5.00000			0.198889
$633$		0			0
$634$	−18.0000			−0.714871
$635$	−25.5000	+	44.1673i	−1.01194	+	1.75273i
$636$		0			0
$637$		0			0
$638$	−36.0000			−1.42525
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	0.999247	+	0.0387913i	$0.0123508\pi$
$641$	13.5000	+	23.3827i	0.533218	+	0.923561i	−0.466029	+	0.884769i	$0.654316\pi$
$642$		0			0
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	0.902764	−	0.430137i	$-0.141535\pi$
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	−0.823891	+	0.566748i	$0.808201\pi$
$644$		0			0
$645$		0			0
$646$	42.0000			1.65247
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$		0			0
$649$		0			0
$650$	−4.00000	+	6.92820i	−0.156893	+	0.271746i
$651$		0			0
$652$	−1.00000	−	1.73205i	−0.0391630	−	0.0678323i
$653$	−18.0000	+	31.1769i	−0.704394	+	1.22005i	0.262515	+	0.964928i	$0.415448\pi$
$653$	−18.0000	+	31.1769i	−0.704394	+	1.22005i	−0.966910	+	0.255119i	$0.917885\pi$
$654$		0			0
$655$	−13.5000	−	23.3827i	−0.527489	−	0.913637i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.0000	−	36.3731i	0.818044	−	1.41689i	−0.0890776	−	0.996025i	$-0.528392\pi$
$659$	21.0000	−	36.3731i	0.818044	−	1.41689i	0.907122	−	0.420869i	$-0.138275\pi$
$660$		0			0
$661$	5.00000			0.194477			0.0972387	−	0.995261i	$-0.468999\pi$
$661$	5.00000			0.194477			0.0972387	+	0.995261i	$0.468999\pi$
$662$	26.0000			1.01052
$663$		0			0
$664$	6.00000	−	10.3923i	0.232845	−	0.403300i
$665$		0			0
$666$		0			0
$667$	−9.00000	−	15.5885i	−0.348481	−	0.603587i
$668$		0			0
$669$		0			0
$670$	−12.0000	+	20.7846i	−0.463600	+	0.802980i
$671$	−15.0000	−	25.9808i	−0.579069	−	1.00298i
$672$		0			0
$673$	18.5000	−	32.0429i	0.713123	−	1.23516i	−0.250557	−	0.968102i	$-0.580614\pi$
$673$	18.5000	−	32.0429i	0.713123	−	1.23516i	0.963679	−	0.267063i	$-0.0860531\pi$
$674$	11.0000	+	19.0526i	0.423704	+	0.733877i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−42.0000			−1.61419			−0.807096	−	0.590421i	$-0.798962\pi$
$677$	−42.0000			−1.61419			−0.807096	+	0.590421i	$0.798962\pi$
$678$		0			0
$679$		0			0
$680$	9.00000	+	15.5885i	0.345134	+	0.597790i
$681$		0			0
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−3.00000	+	5.19615i	−0.114792	+	0.198825i	−0.917697	−	0.397282i	$-0.869953\pi$
$683$	−3.00000	+	5.19615i	−0.114792	+	0.198825i	0.802905	+	0.596107i	$0.203287\pi$
$684$		0			0
$685$	−18.0000			−0.687745
$686$		0			0
$687$		0			0
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	−12.0000			−0.457164
$690$		0			0
$691$	47.0000			1.78796			0.893982	−	0.448103i	$-0.147900\pi$
$691$	47.0000			1.78796			0.893982	+	0.448103i	$0.147900\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	24.0000			0.911028
$695$	15.0000			0.568982
$696$		0			0
$697$		0			0
$698$	−13.0000	+	22.5167i	−0.492057	+	0.852268i
$699$		0			0
$700$		0			0
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	7.00000	−	12.1244i	0.264010	−	0.457279i
$704$	−3.00000	−	5.19615i	−0.113067	−	0.195837i
$705$		0			0
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$		0			0
$708$		0			0
$709$	−52.0000			−1.95290			−0.976450	−	0.215742i	$-0.930783\pi$
$709$	−52.0000			−1.95290			−0.976450	+	0.215742i	$0.930783\pi$
$710$	4.50000	−	7.79423i	0.168882	−	0.292512i
$711$		0			0
$712$		0			0
$713$	3.00000	−	5.19615i	0.112351	−	0.194597i
$714$		0			0
$715$	−18.0000	−	31.1769i	−0.673162	−	1.16595i
$716$	9.00000	−	15.5885i	0.336346	−	0.582568i
$717$		0			0
$718$	−1.50000	−	2.59808i	−0.0559795	−	0.0969593i
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	−0.977539	−	0.210752i	$-0.932409\pi$
$719$	−18.0000	−	31.1769i	−0.671287	−	1.16270i	0.306253	−	0.951950i	$-0.400925\pi$
$720$		0			0
$721$		0			0
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$		0			0
$724$	−25.0000			−0.929118
$725$	−24.0000			−0.891338
$726$		0			0
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$		0			0
$729$		0			0
$730$	−3.00000	−	5.19615i	−0.111035	−	0.192318i
$731$	6.00000	+	10.3923i	0.221918	+	0.384373i
$732$		0			0
$733$	−14.5000	+	25.1147i	−0.535570	+	0.927634i	0.463566	+	0.886062i	$0.346570\pi$
$733$	−14.5000	+	25.1147i	−0.535570	+	0.927634i	−0.999136	+	0.0415715i	$0.986764\pi$
$734$	−4.00000	−	6.92820i	−0.147643	−	0.255725i
$735$		0			0
$736$	1.50000	−	2.59808i	0.0552907	−	0.0957664i
$737$	−24.0000	−	41.5692i	−0.884051	−	1.53122i
$738$		0			0
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	−0.999688	−	0.0249776i	$-0.992049\pi$
$739$	−13.0000	+	22.5167i	−0.478213	+	0.828289i	0.521475	+	0.853266i	$0.325382\pi$
$740$	6.00000			0.220564
$741$		0			0
$742$		0			0
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$		0			0
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$	−7.00000	+	12.1244i	−0.256288	+	0.443904i
$747$		0			0
$748$	−36.0000			−1.31629
$749$		0			0
$750$		0			0
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$		0			0
$753$		0			0
$754$	−12.0000			−0.437014
$755$	69.0000			2.51117
$756$		0			0
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	2.00000			0.0726433
$759$		0			0
$760$	−21.0000			−0.761750
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	0.180957	+	0.983491i	$0.442080\pi$
$761$	−21.0000	+	36.3731i	−0.761249	+	1.31852i	−0.942207	+	0.335032i	$0.891253\pi$
$762$		0			0
$763$		0			0
$764$	9.00000			0.325609
$765$		0			0
$766$	−9.00000	+	15.5885i	−0.325183	+	0.563234i
$767$		0			0
$768$		0			0
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	0.711767	−	0.702416i	$-0.247895\pi$
$769$	−7.00000	−	12.1244i	−0.252426	−	0.437215i	−0.964193	+	0.265200i	$0.914562\pi$
$770$		0			0
$771$		0			0
$772$	17.0000			0.611843
$773$	−25.5000	+	44.1673i	−0.917171	+	1.58859i	−0.113480	+	0.993540i	$0.536200\pi$
$773$	−25.5000	+	44.1673i	−0.917171	+	1.58859i	−0.803691	+	0.595047i	$0.797133\pi$
$774$		0			0
$775$	−4.00000	−	6.92820i	−0.143684	−	0.248868i
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$		0			0
$778$	12.0000	+	20.7846i	0.430221	+	0.745164i
$779$		0			0
$780$		0			0
$781$	9.00000	+	15.5885i	0.322045	+	0.557799i
$782$	−9.00000	−	15.5885i	−0.321839	−	0.557442i
$783$		0			0
$784$		0			0
$785$	19.5000	−	33.7750i	0.695985	−	1.20548i
$786$		0			0
$787$	20.0000			0.712923			0.356462	−	0.934310i	$-0.383983\pi$
$787$	20.0000			0.712923			0.356462	+	0.934310i	$0.383983\pi$
$788$	−18.0000			−0.641223
$789$		0			0
$790$	−7.50000	+	12.9904i	−0.266838	+	0.462177i
$791$		0			0
$792$		0			0
$793$	−5.00000	−	8.66025i	−0.177555	−	0.307535i
$794$	−13.0000	−	22.5167i	−0.461353	−	0.799086i
$795$		0			0
$796$	−7.00000	+	12.1244i	−0.248108	+	0.429736i
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	0.891368	−	0.453279i	$-0.149746\pi$
$797$	1.50000	+	2.59808i	0.0531327	+	0.0920286i	−0.838236	+	0.545308i	$0.816413\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	1.50000	−	2.59808i	0.0529668	−	0.0917413i
$803$	12.0000			0.423471
$804$		0			0
$805$		0			0
$806$	−2.00000	−	3.46410i	−0.0704470	−	0.122018i
$807$		0			0
$808$	4.50000	+	7.79423i	0.158309	+	0.274200i
$809$	−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	$0.590639\pi$
$812$		0			0
$813$		0			0
$814$	−6.00000	+	10.3923i	−0.210300	+	0.364250i
$815$	6.00000			0.210171
$816$		0			0
$817$	−14.0000			−0.489798
$818$	32.0000			1.11885
$819$		0			0
$820$		0			0
$821$	24.0000			0.837606			0.418803	−	0.908077i	$-0.362450\pi$
$821$	24.0000			0.837606			0.418803	+	0.908077i	$0.362450\pi$
$822$		0			0
$823$	8.00000			0.278862			0.139431	−	0.990232i	$-0.455473\pi$
$823$	8.00000			0.278862			0.139431	+	0.990232i	$0.455473\pi$
$824$	5.00000	−	8.66025i	0.174183	−	0.301694i
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$	18.0000	+	31.1769i	0.624789	+	1.08217i
$831$		0			0
$832$	−1.00000	−	1.73205i	−0.0346688	−	0.0600481i
$833$		0			0
$834$		0			0
$835$		0			0
$836$	21.0000	−	36.3731i	0.726300	−	1.25799i
$837$		0			0
$838$	7.50000	+	12.9904i	0.259083	+	0.448745i
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	5.00000	−	8.66025i	0.172311	−	0.298452i
$843$		0			0
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	13.5000	+	23.3827i	0.464414	+	0.804389i
$846$		0			0
$847$		0			0
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	−24.0000			−0.823193
$851$	−6.00000			−0.205677
$852$		0			0
$853$	−17.5000	+	30.3109i	−0.599189	+	1.03783i	0.393753	+	0.919216i	$0.371177\pi$
$853$	−17.5000	+	30.3109i	−0.599189	+	1.03783i	−0.992941	+	0.118609i	$0.962157\pi$
$854$		0			0
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.795843	+	0.605503i	$0.207028\pi$
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.126459	+	0.991972i	$0.459639\pi$
$858$		0			0
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$	−3.00000	−	5.19615i	−0.102299	−	0.177187i
$861$		0			0
$862$	6.00000	−	10.3923i	0.204361	−	0.353963i
$863$	4.50000	+	7.79423i	0.153182	+	0.265319i	0.932395	−	0.361440i	$-0.117715\pi$
$863$	4.50000	+	7.79423i	0.153182	+	0.265319i	−0.779214	+	0.626758i	$0.784381\pi$
$864$		0			0
$865$	−9.00000	+	15.5885i	−0.306009	+	0.530023i
$866$	14.0000			0.475739
$867$		0			0
$868$		0			0
$869$	−15.0000	−	25.9808i	−0.508840	−	0.881337i
$870$		0			0
$871$	−8.00000	−	13.8564i	−0.271070	−	0.469506i
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$		0			0
$874$	21.0000			0.710336
$875$		0			0
$876$		0			0
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	8.00000			0.269987
$879$		0			0
$880$	18.0000			0.606780
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	−12.0000			−0.403604
$885$		0			0
$886$	−18.0000			−0.604722
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$		0			0
$892$	14.0000	−	24.2487i	0.468755	−	0.811907i
$893$		0			0
$894$		0			0
$895$	27.0000	+	46.7654i	0.902510	+	1.56319i
$896$		0			0
$897$		0			0
$898$	−33.0000			−1.10122
$899$	6.00000	−	10.3923i	0.200111	−	0.346603i
$900$		0			0
$901$	−18.0000	−	31.1769i	−0.599667	−	1.03865i
$902$		0			0
$903$		0			0
$904$	7.50000	+	12.9904i	0.249446	+	0.432054i
$905$	37.5000	−	64.9519i	1.24654	−	2.15907i
$906$		0			0
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	−0.999334	−	0.0364935i	$-0.988381\pi$
$907$	−16.0000	−	27.7128i	−0.531271	−	0.920189i	0.468063	−	0.883695i	$-0.344952\pi$
$908$	−7.50000	−	12.9904i	−0.248896	−	0.431101i
$909$		0			0
$910$		0			0
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	−0.714620	−	0.699513i	$-0.753400\pi$
$911$	7.50000	−	12.9904i	0.248486	−	0.430391i	0.963106	+	0.269122i	$0.0867336\pi$
$912$		0			0
$913$	−72.0000			−2.38285
$914$	29.0000			0.959235
$915$		0			0
$916$	0.500000	−	0.866025i	0.0165205	−	0.0286143i
$917$		0			0
$918$		0			0
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	0.760939	−	0.648824i	$-0.224739\pi$
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	−0.942367	+	0.334581i	$0.891405\pi$
$920$	4.50000	+	7.79423i	0.148361	+	0.256968i
$921$		0			0
$922$	−16.5000	+	28.5788i	−0.543399	+	0.941194i
$923$	3.00000	+	5.19615i	0.0987462	+	0.171033i
$924$		0			0
$925$	−4.00000	+	6.92820i	−0.131519	+	0.227798i
$926$	6.50000	+	11.2583i	0.213603	+	0.369972i
$927$		0			0
$928$	3.00000	−	5.19615i	0.0984798	−	0.170572i
$929$		0			0			−	1.00000i	$-0.5\pi$
$929$		0			0				1.00000i	$0.5\pi$
$930$		0			0
$931$		0			0
$932$	4.50000	+	7.79423i	0.147402	+	0.255308i
$933$		0			0
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$	54.0000	−	93.5307i	1.76599	−	3.05878i
$936$		0			0
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−21.0000			−0.684580			−0.342290	−	0.939594i	$-0.611203\pi$
$941$	−21.0000			−0.684580			−0.342290	+	0.939594i	$0.611203\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	12.0000			0.390154
$947$	24.0000			0.779895			0.389948	−	0.920837i	$-0.372493\pi$
$947$	24.0000			0.779895			0.389948	+	0.920837i	$0.372493\pi$
$948$		0			0
$949$	4.00000			0.129845
$950$	14.0000	−	24.2487i	0.454220	−	0.786732i
$951$		0			0
$952$		0			0
$953$	−42.0000			−1.36051			−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000			−1.36051			−0.680257	+	0.732974i	$0.738132\pi$
$954$		0			0
$955$	−13.5000	+	23.3827i	−0.436850	+	0.756646i
$956$	−7.50000	−	12.9904i	−0.242567	−	0.420139i
$957$		0			0
$958$	−3.00000	−	5.19615i	−0.0969256	−	0.167880i
$959$		0			0
$960$		0			0
$961$	−27.0000			−0.870968
$962$	−2.00000	+	3.46410i	−0.0644826	+	0.111687i
$963$		0			0
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$	−25.5000	+	44.1673i	−0.820874	+	1.42180i
$966$		0			0
$967$	−8.50000	−	14.7224i	−0.273342	−	0.473441i	0.696374	−	0.717679i	$-0.254796\pi$
$967$	−8.50000	−	14.7224i	−0.273342	−	0.473441i	−0.969715	+	0.244238i	$0.921462\pi$
$968$	−12.5000	+	21.6506i	−0.401765	+	0.695878i
$969$		0			0
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	0.720224	−	0.693742i	$-0.244039\pi$
$971$	−7.50000	−	12.9904i	−0.240686	−	0.416881i	−0.960910	+	0.276861i	$0.910706\pi$
$972$		0			0
$973$		0			0
$974$	−14.5000	+	25.1147i	−0.464610	+	0.804728i
$975$		0			0
$976$	5.00000			0.160046
$977$	−6.00000			−0.191957			−0.0959785	−	0.995383i	$-0.530598\pi$
$977$	−6.00000			−0.191957			−0.0959785	+	0.995383i	$0.530598\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	9.00000	+	15.5885i	0.287202	+	0.497448i
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	0.973106	−	0.230360i	$-0.0739903\pi$
$983$	9.00000	+	15.5885i	0.287055	+	0.497195i	−0.686050	+	0.727554i	$0.740657\pi$
$984$		0			0
$985$	27.0000	−	46.7654i	0.860292	−	1.49007i
$986$	−18.0000	−	31.1769i	−0.573237	−	0.992875i
$987$		0			0
$988$	7.00000	−	12.1244i	0.222700	−	0.385727i
$989$	3.00000	+	5.19615i	0.0953945	+	0.165228i
$990$		0			0
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$	2.00000			0.0635001
$993$		0			0
$994$		0			0
$995$	−21.0000	−	36.3731i	−0.665745	−	1.15310i
$996$		0			0
$997$	27.5000	+	47.6314i	0.870934	+	1.50850i	0.861032	+	0.508551i	$0.169818\pi$
$997$	27.5000	+	47.6314i	0.870934	+	1.50850i	0.00990158	+	0.999951i	$0.496848\pi$
$998$	−16.0000	+	27.7128i	−0.506471	+	0.877234i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.f.2125.1		2
3.2	odd	2		882.2.e.b.655.1		2
7.2	even	3		2646.2.h.e.667.1		2
7.3	odd	6		2646.2.f.c.883.1		2
7.4	even	3		378.2.f.a.127.1		2
7.5	odd	6		2646.2.h.a.667.1		2
7.6	odd	2		2646.2.e.j.2125.1		2
9.4	even	3		2646.2.h.e.361.1		2
9.5	odd	6		882.2.h.j.67.1		2
21.2	odd	6		882.2.h.j.79.1		2
21.5	even	6		882.2.h.f.79.1		2
21.11	odd	6		126.2.f.a.43.1	✓	2
21.17	even	6		882.2.f.h.295.1		2
21.20	even	2		882.2.e.d.655.1		2
28.11	odd	6		3024.2.r.a.2017.1		2
63.4	even	3		378.2.f.a.253.1		2
63.5	even	6		882.2.e.d.373.1		2
63.11	odd	6		1134.2.a.a.1.1		1
63.13	odd	6		2646.2.h.a.361.1		2
63.23	odd	6		882.2.e.b.373.1		2
63.25	even	3		1134.2.a.h.1.1		1
63.31	odd	6		2646.2.f.c.1765.1		2
63.32	odd	6		126.2.f.a.85.1	yes	2
63.38	even	6		7938.2.a.l.1.1		1
63.40	odd	6		2646.2.e.j.1549.1		2
63.41	even	6		882.2.h.f.67.1		2
63.52	odd	6		7938.2.a.u.1.1		1
63.58	even	3	inner	2646.2.e.f.1549.1		2
63.59	even	6		882.2.f.h.589.1		2
84.11	even	6		1008.2.r.d.673.1		2
252.11	even	6		9072.2.a.c.1.1		1
252.67	odd	6		3024.2.r.a.1009.1		2
252.95	even	6		1008.2.r.d.337.1		2
252.151	odd	6		9072.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.a.43.1	✓	2	21.11	odd	6
126.2.f.a.85.1	yes	2	63.32	odd	6
378.2.f.a.127.1		2	7.4	even	3
378.2.f.a.253.1		2	63.4	even	3
882.2.e.b.373.1		2	63.23	odd	6
882.2.e.b.655.1		2	3.2	odd	2
882.2.e.d.373.1		2	63.5	even	6
882.2.e.d.655.1		2	21.20	even	2
882.2.f.h.295.1		2	21.17	even	6
882.2.f.h.589.1		2	63.59	even	6
882.2.h.f.67.1		2	63.41	even	6
882.2.h.f.79.1		2	21.5	even	6
882.2.h.j.67.1		2	9.5	odd	6
882.2.h.j.79.1		2	21.2	odd	6
1008.2.r.d.337.1		2	252.95	even	6
1008.2.r.d.673.1		2	84.11	even	6
1134.2.a.a.1.1		1	63.11	odd	6
1134.2.a.h.1.1		1	63.25	even	3
2646.2.e.f.1549.1		2	63.58	even	3	inner
2646.2.e.f.2125.1		2	1.1	even	1	trivial
2646.2.e.j.1549.1		2	63.40	odd	6
2646.2.e.j.2125.1		2	7.6	odd	2
2646.2.f.c.883.1		2	7.3	odd	6
2646.2.f.c.1765.1		2	63.31	odd	6
2646.2.h.a.361.1		2	63.13	odd	6
2646.2.h.a.667.1		2	7.5	odd	6
2646.2.h.e.361.1		2	9.4	even	3
2646.2.h.e.667.1		2	7.2	even	3
3024.2.r.a.1009.1		2	252.67	odd	6
3024.2.r.a.2017.1		2	28.11	odd	6
7938.2.a.l.1.1		1	63.38	even	6
7938.2.a.u.1.1		1	63.52	odd	6
9072.2.a.c.1.1		1	252.11	even	6
9072.2.a.w.1.1		1	252.151	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-1.50000 + 2.59808i) q^{5} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +(-3.00000 - 5.19615i) q^{11} +(-1.00000 - 1.73205i) q^{13} +1.00000 q^{16} +(3.00000 - 5.19615i) q^{17} +(3.50000 + 6.06218i) q^{19} +(-1.50000 + 2.59808i) q^{20} +(-3.00000 - 5.19615i) q^{22} +(1.50000 - 2.59808i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(3.00000 - 5.19615i) q^{29} +2.00000 q^{31} +1.00000 q^{32} +(3.00000 - 5.19615i) q^{34} +(-1.00000 - 1.73205i) q^{37} +(3.50000 + 6.06218i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-1.00000 + 1.73205i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-2.00000 - 3.46410i) q^{50} +(-1.00000 - 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +18.0000 q^{55} +(3.00000 - 5.19615i) q^{58} +5.00000 q^{61} +2.00000 q^{62} +1.00000 q^{64} +6.00000 q^{65} +8.00000 q^{67} +(3.00000 - 5.19615i) q^{68} -3.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +(-1.00000 - 1.73205i) q^{74} +(3.50000 + 6.06218i) q^{76} +5.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(6.00000 - 10.3923i) q^{83} +(9.00000 + 15.5885i) q^{85} +(-1.00000 + 1.73205i) q^{86} +(-3.00000 - 5.19615i) q^{88} +(1.50000 - 2.59808i) q^{92} -21.0000 q^{95} +(-1.00000 + 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} - 3 q^{5} + 2 q^{8} - 3 q^{10} - 6 q^{11} - 2 q^{13} + 2 q^{16} + 6 q^{17} + 7 q^{19} - 3 q^{20} - 6 q^{22} + 3 q^{23} - 4 q^{25} - 2 q^{26} + 6 q^{29} + 4 q^{31} + 2 q^{32} + 6 q^{34}+ \cdots - 2 q^{97}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 - 3 * q^5 + 2 * q^8 - 3 * q^10 - 6 * q^11 - 2 * q^13 + 2 * q^16 + 6 * q^17 + 7 * q^19 - 3 * q^20 - 6 * q^22 + 3 * q^23 - 4 * q^25 - 2 * q^26 + 6 * q^29 + 4 * q^31 + 2 * q^32 + 6 * q^34 - 2 * q^37 + 7 * q^38 - 3 * q^40 - 2 * q^43 - 6 * q^44 + 3 * q^46 - 4 * q^50 - 2 * q^52 + 6 * q^53 + 36 * q^55 + 6 * q^58 + 10 * q^61 + 4 * q^62 + 2 * q^64 + 12 * q^65 + 16 * q^67 + 6 * q^68 - 6 * q^71 - 2 * q^73 - 2 * q^74 + 7 * q^76 + 10 * q^79 - 3 * q^80 + 12 * q^83 + 18 * q^85 - 2 * q^86 - 6 * q^88 + 3 * q^92 - 42 * q^95 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more