LMFDB - Embedded newform 2646.2.h.e.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	2646.361
Dual form			2646.2.h.e.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +6.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(3.50000 + 6.06218i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-3.00000 + 5.19615i) q^{22} -3.00000 q^{23} +4.00000 q^{25} +(-1.00000 - 1.73205i) q^{26} +(3.00000 + 5.19615i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(-1.00000 - 1.73205i) q^{37} -7.00000 q^{38} +3.00000 q^{40} +(-1.00000 - 1.73205i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-2.00000 + 3.46410i) q^{50} +2.00000 q^{52} +(3.00000 - 5.19615i) q^{53} +18.0000 q^{55} -6.00000 q^{58} +(-2.50000 + 4.33013i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-4.00000 - 6.92820i) q^{67} -6.00000 q^{68} -3.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +2.00000 q^{74} +(3.50000 - 6.06218i) q^{76} +(-2.50000 + 4.33013i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(6.00000 + 10.3923i) q^{83} +(9.00000 - 15.5885i) q^{85} +2.00000 q^{86} +6.00000 q^{88} +(1.50000 + 2.59808i) q^{92} +(10.5000 + 18.1865i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 6 q^{5} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 6 * q^5 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 6 q^{5} + 2 q^{8} - 3 q^{10} + 12 q^{11} - 2 q^{13} - q^{16} + 6 q^{17} + 7 q^{19} - 3 q^{20} - 6 q^{22} - 6 q^{23} + 8 q^{25} - 2 q^{26} + 6 q^{29} - 2 q^{31} - q^{32} + 6 q^{34} - 2 q^{37} - 14 q^{38} + 6 q^{40} - 2 q^{43} - 6 q^{44} + 3 q^{46} - 4 q^{50} + 4 q^{52} + 6 q^{53} + 36 q^{55} - 12 q^{58} - 5 q^{61} + 4 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{67} - 12 q^{68} - 6 q^{71} - 2 q^{73} + 4 q^{74} + 7 q^{76} - 5 q^{79} - 3 q^{80} + 12 q^{83} + 18 q^{85} + 4 q^{86} + 12 q^{88} + 3 q^{92} + 21 q^{95} - 2 q^{97}+O(q^{100}) $ 2 * q - q^2 - q^4 + 6 * q^5 + 2 * q^8 - 3 * q^10 + 12 * q^11 - 2 * q^13 - q^16 + 6 * q^17 + 7 * q^19 - 3 * q^20 - 6 * q^22 - 6 * q^23 + 8 * q^25 - 2 * q^26 + 6 * q^29 - 2 * q^31 - q^32 + 6 * q^34 - 2 * q^37 - 14 * q^38 + 6 * q^40 - 2 * q^43 - 6 * q^44 + 3 * q^46 - 4 * q^50 + 4 * q^52 + 6 * q^53 + 36 * q^55 - 12 * q^58 - 5 * q^61 + 4 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^67 - 12 * q^68 - 6 * q^71 - 2 * q^73 + 4 * q^74 + 7 * q^76 - 5 * q^79 - 3 * q^80 + 12 * q^83 + 18 * q^85 + 4 * q^86 + 12 * q^88 + 3 * q^92 + 21 * q^95 - 2 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$		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
$11$	6.00000			1.80907			0.904534	−	0.426401i	$-0.140219\pi$
$11$	6.00000			1.80907			0.904534	+	0.426401i	$0.140219\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	−0.230285	−	0.973123i	$-0.573966\pi$
$17$	3.00000	−	5.19615i	0.727607	−	1.26025i	0.957892	−	0.287129i	$-0.0927008\pi$
$18$		0			0
$19$	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
$23$	−3.00000			−0.625543			−0.312772	−	0.949828i	$-0.601257\pi$
$23$	−3.00000			−0.625543			−0.312772	+	0.949828i	$0.601257\pi$
$24$		0			0
$25$	4.00000			0.800000
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		0			0
$28$		0			0
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	3.00000	+	5.19615i	0.514496	+	0.891133i
$35$		0			0
$36$		0			0
$37$	−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	$0.885902\pi$
$38$	−7.00000			−1.13555
$39$		0			0
$40$	3.00000			0.474342
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$		0			0
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$		0			0
$46$	1.50000	−	2.59808i	0.221163	−	0.383065i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$		0			0
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$		0			0
$52$	2.00000			0.277350
$53$	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
$58$	−6.00000			−0.787839
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−6.00000			−0.727607
$69$		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	$0.204008\pi$
$74$	2.00000			0.232495
$75$		0			0
$76$	3.50000	−	6.06218i	0.401478	−	0.695379i
$77$		0			0
$78$		0			0
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	−0.971698	−	0.236225i	$-0.924090\pi$
$79$	−2.50000	+	4.33013i	−0.281272	+	0.487177i	0.690426	+	0.723403i	$0.257423\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$		0			0
$82$		0			0
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	9.00000	−	15.5885i	0.976187	−	1.69081i
$86$	2.00000			0.215666
$87$		0			0
$88$	6.00000			0.639602
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$		0			0
$92$	1.50000	+	2.59808i	0.156386	+	0.270868i
$93$		0			0
$94$		0			0
$95$	10.5000	+	18.1865i	1.07728	+	1.86590i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$		0			0
$99$		0			0
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	−9.00000			−0.895533			−0.447767	−	0.894150i	$-0.647781\pi$
$101$	−9.00000			−0.895533			−0.447767	+	0.894150i	$0.647781\pi$
$102$		0			0
$103$	−10.0000			−0.985329			−0.492665	−	0.870219i	$-0.663977\pi$
$103$	−10.0000			−0.985329			−0.492665	+	0.870219i	$0.663977\pi$
$104$	−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	$0.00769755\pi$
$110$	−9.00000	+	15.5885i	−0.858116	+	1.48630i
$111$		0			0
$112$		0			0
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$		0			0
$115$	−9.00000			−0.839254
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$		0			0
$118$		0			0
$119$		0			0
$120$		0			0
$121$	25.0000			2.27273
$122$	−2.50000	−	4.33013i	−0.226339	−	0.392031i
$123$		0			0
$124$	−1.00000	+	1.73205i	−0.0898027	+	0.155543i
$125$	−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	$0.227999\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	9.00000			0.786334			0.393167	−	0.919467i	$-0.371379\pi$
$131$	9.00000			0.786334			0.393167	+	0.919467i	$0.371379\pi$
$132$		0			0
$133$		0			0
$134$	8.00000			0.691095
$135$		0			0
$136$	3.00000	−	5.19615i	0.257248	−	0.445566i
$137$	−6.00000			−0.512615			−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000			−0.512615			−0.256307	+	0.966595i	$0.582506\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		0			0
$142$	1.50000	−	2.59808i	0.125877	−	0.218026i
$143$	−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
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	23.0000			1.87171			0.935857	−	0.352381i	$-0.114628\pi$
$151$	23.0000			1.87171			0.935857	+	0.352381i	$0.114628\pi$
$152$	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
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	−2.50000	−	4.33013i	−0.198889	−	0.344486i
$159$		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
$166$	−12.0000			−0.931381
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		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
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		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
$184$	−3.00000			−0.221163
$185$	−3.00000	−	5.19615i	−0.220564	−	0.382029i
$186$		0			0
$187$	18.0000	−	31.1769i	1.31629	−	2.27988i
$188$		0			0
$189$		0			0
$190$	−21.0000			−1.52350
$191$	−4.50000	+	7.79423i	−0.325609	+	0.563971i	−0.981635	−	0.190767i	$-0.938902\pi$
$191$	−4.50000	+	7.79423i	−0.325609	+	0.563971i	0.656027	+	0.754738i	$0.272236\pi$
$192$		0			0
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	−0.990930	−	0.134382i	$-0.957095\pi$
$193$	−8.50000	−	14.7224i	−0.611843	−	1.05974i	0.379086	−	0.925361i	$-0.376238\pi$
$194$	2.00000			0.143592
$195$		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	$0.331945\pi$
$200$	4.00000			0.282843
$201$		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	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	−6.00000			−0.412082
$213$		0			0
$214$	12.0000			0.820303
$215$	−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
$220$	−9.00000	−	15.5885i	−0.606780	−	1.05097i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	14.0000	+	24.2487i	0.937509	+	1.62381i	0.770097	+	0.637927i	$0.220208\pi$
$223$	14.0000	+	24.2487i	0.937509	+	1.62381i	0.167412	+	0.985887i	$0.446459\pi$
$224$		0			0
$225$		0			0
$226$	7.50000	+	12.9904i	0.498893	+	0.864107i
$227$	15.0000			0.995585			0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000			0.995585			0.497792	+	0.867296i	$0.334144\pi$
$228$		0			0
$229$	−1.00000			−0.0660819			−0.0330409	−	0.999454i	$-0.510519\pi$
$229$	−1.00000			−0.0660819			−0.0330409	+	0.999454i	$0.510519\pi$
$230$	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	−0.999854	−	0.0170808i	$-0.994563\pi$
$239$	−7.50000	+	12.9904i	−0.485135	+	0.840278i	0.514719	+	0.857359i	$0.327896\pi$
$240$		0			0
$241$	8.00000			0.515325			0.257663	−	0.966235i	$-0.417048\pi$
$241$	8.00000			0.515325			0.257663	+	0.966235i	$0.417048\pi$
$242$	−12.5000	+	21.6506i	−0.803530	+	1.39176i
$243$		0			0
$244$	5.00000			0.320092
$245$		0			0
$246$		0			0
$247$	−14.0000			−0.890799
$248$	−1.00000	−	1.73205i	−0.0635001	−	0.109985i
$249$		0			0
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	−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
$254$	−8.50000	+	14.7224i	−0.533337	+	0.923768i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−18.0000			−1.12281			−0.561405	−	0.827541i	$-0.689739\pi$
$257$	−18.0000			−1.12281			−0.561405	+	0.827541i	$0.689739\pi$
$258$		0			0
$259$		0			0
$260$	6.00000			0.372104
$261$		0			0
$262$	−4.50000	+	7.79423i	−0.278011	+	0.481529i
$263$	21.0000			1.29492			0.647458	−	0.762101i	$-0.275832\pi$
$263$	21.0000			1.29492			0.647458	+	0.762101i	$0.275832\pi$
$264$		0			0
$265$	9.00000	−	15.5885i	0.552866	−	0.957591i
$266$		0			0
$267$		0			0
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	−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
$275$	24.0000			1.44725
$276$		0			0
$277$	−16.0000			−0.961347			−0.480673	−	0.876900i	$-0.659608\pi$
$277$	−16.0000			−0.961347			−0.480673	+	0.876900i	$0.659608\pi$
$278$	−2.50000	−	4.33013i	−0.149940	−	0.259704i
$279$		0			0
$280$		0			0
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	−0.916060	−	0.401042i	$-0.868648\pi$
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	0.110717	−	0.993852i	$-0.464685\pi$
$282$		0			0
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	0.997076	+	0.0764162i	$0.0243478\pi$
$283$	9.50000	+	16.4545i	0.564716	+	0.978117i	−0.432360	+	0.901701i	$0.642319\pi$
$284$	1.50000	+	2.59808i	0.0890086	+	0.154167i
$285$		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
$290$	−18.0000			−1.05700
$291$		0			0
$292$	2.00000			0.117041
$293$	−1.50000	+	2.59808i	−0.0876309	+	0.151781i	−0.906509	−	0.422186i	$-0.861263\pi$
$293$	−1.50000	+	2.59808i	−0.0876309	+	0.151781i	0.818878	+	0.573967i	$0.194596\pi$
$294$		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
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$		0			0
$302$	−11.5000	+	19.9186i	−0.661751	+	1.14619i
$303$		0			0
$304$	−7.00000			−0.401478
$305$	−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
$310$	6.00000			0.340777
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$	−13.0000			−0.733632
$315$		0			0
$316$	5.00000			0.281272
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	18.0000	+	31.1769i	1.00781	+	1.74557i
$320$	3.00000			0.167705
$321$		0			0
$322$		0			0
$323$	42.0000			2.33694
$324$		0			0
$325$	−4.00000	+	6.92820i	−0.221880	+	0.384308i
$326$	2.00000			0.110770
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	0.248590	+	0.968609i	$0.420033\pi$
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	−0.963135	+	0.269019i	$0.913301\pi$
$332$	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	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$	−9.00000			−0.489535
$339$		0			0
$340$	−18.0000			−0.976187
$341$	−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
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$		0			0
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	−0.969885	−	0.243563i	$-0.921684\pi$
$349$	−13.0000	−	22.5167i	−0.695874	−	1.20529i	0.274011	−	0.961727i	$-0.411649\pi$
$350$		0			0
$351$		0			0
$352$	−3.00000	−	5.19615i	−0.159901	−	0.276956i
$353$	18.0000			0.958043			0.479022	−	0.877803i	$-0.340992\pi$
$353$	18.0000			0.958043			0.479022	+	0.877803i	$0.340992\pi$
$354$		0			0
$355$	−9.00000			−0.477670
$356$		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
$362$	12.5000	−	21.6506i	0.656985	−	1.13793i
$363$		0			0
$364$		0			0
$365$	−3.00000	+	5.19615i	−0.157027	+	0.271979i
$366$		0			0
$367$	8.00000			0.417597			0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000			0.417597			0.208798	+	0.977959i	$0.433045\pi$
$368$	1.50000	−	2.59808i	0.0781929	−	0.135434i
$369$		0			0
$370$	6.00000			0.311925
$371$		0			0
$372$		0			0
$373$	14.0000			0.724893			0.362446	−	0.932005i	$-0.381942\pi$
$373$	14.0000			0.724893			0.362446	+	0.932005i	$0.381942\pi$
$374$	18.0000	+	31.1769i	0.930758	+	1.61212i
$375$		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	$0.483642\pi$
$380$	10.5000	−	18.1865i	0.538639	−	0.932949i
$381$		0			0
$382$	−4.50000	−	7.79423i	−0.230240	−	0.398787i
$383$	18.0000			0.919757			0.459879	−	0.887982i	$-0.347893\pi$
$383$	18.0000			0.919757			0.459879	+	0.887982i	$0.347893\pi$
$384$		0			0
$385$		0			0
$386$	17.0000			0.865277
$387$		0			0
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	−24.0000			−1.21685			−0.608424	−	0.793612i	$-0.708198\pi$
$389$	−24.0000			−1.21685			−0.608424	+	0.793612i	$0.708198\pi$
$390$		0			0
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$		0			0
$393$		0			0
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−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
$401$	−3.00000			−0.149813			−0.0749064	−	0.997191i	$-0.523866\pi$
$401$	−3.00000			−0.149813			−0.0749064	+	0.997191i	$0.523866\pi$
$402$		0			0
$403$	4.00000			0.199254
$404$	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
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	−0.925256	−	0.379344i	$-0.876150\pi$
$409$	−16.0000	−	27.7128i	−0.791149	−	1.37031i	0.134107	−	0.990967i	$-0.457183\pi$
$410$		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
$416$	2.00000			0.0980581
$417$		0			0
$418$	−42.0000			−2.05429
$419$	7.50000	−	12.9904i	0.366399	−	0.634622i	−0.622601	−	0.782540i	$-0.713924\pi$
$419$	7.50000	−	12.9904i	0.366399	−	0.634622i	0.989000	+	0.147918i	$0.0472572\pi$
$420$		0			0
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	0.961761	−	0.273890i	$-0.0883103\pi$
$421$	5.00000	+	8.66025i	0.243685	+	0.422075i	−0.718076	+	0.695965i	$0.754977\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$		0			0
$424$	3.00000	−	5.19615i	0.145693	−	0.252347i
$425$	12.0000	−	20.7846i	0.582086	−	1.00820i
$426$		0			0
$427$		0			0
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	6.00000			0.289346
$431$	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
$436$	−10.0000			−0.478913
$437$	−10.5000	−	18.1865i	−0.502283	−	0.869980i
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	18.0000			0.858116
$441$		0			0
$442$	−12.0000			−0.570782
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	−0.569057	−	0.822298i	$-0.692691\pi$
$443$	9.00000	−	15.5885i	0.427603	−	0.740630i	0.996660	+	0.0816684i	$0.0260248\pi$
$444$		0			0
$445$		0			0
$446$	−28.0000			−1.32584
$447$		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
$452$	−15.0000			−0.705541
$453$		0			0
$454$	−7.50000	+	12.9904i	−0.351992	+	0.609669i
$455$		0			0
$456$		0			0
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	0.297217	+	0.954810i	$0.403942\pi$
$457$	−14.5000	+	25.1147i	−0.678281	+	1.17482i	−0.975498	+	0.220008i	$0.929392\pi$
$458$	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	−0.938386	−	0.345589i	$-0.887679\pi$
$461$	−16.5000	−	28.5788i	−0.768482	−	1.33105i	0.169904	−	0.985461i	$-0.445654\pi$
$462$		0			0
$463$	6.50000	−	11.2583i	0.302081	−	0.523219i	−0.674526	−	0.738251i	$-0.735652\pi$
$463$	6.50000	−	11.2583i	0.302081	−	0.523219i	0.976607	+	0.215032i	$0.0689855\pi$
$464$	−6.00000			−0.278543
$465$		0			0
$466$	−9.00000			−0.416917
$467$	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
$473$	−6.00000	−	10.3923i	−0.275880	−	0.477839i
$474$		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
$479$	6.00000			0.274147			0.137073	−	0.990561i	$-0.456230\pi$
$479$	6.00000			0.274147			0.137073	+	0.990561i	$0.456230\pi$
$480$		0			0
$481$	4.00000			0.182384
$482$	−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	$0.938467\pi$
$488$	−2.50000	+	4.33013i	−0.113170	+	0.196016i
$489$		0			0
$490$		0			0
$491$	9.00000	−	15.5885i	0.406164	−	0.703497i	−0.588292	−	0.808649i	$-0.700199\pi$
$491$	9.00000	−	15.5885i	0.406164	−	0.703497i	0.994456	+	0.105151i	$0.0335327\pi$
$492$		0			0
$493$	36.0000			1.62136
$494$	7.00000	−	12.1244i	0.314945	−	0.545501i
$495$		0			0
$496$	2.00000			0.0898027
$497$		0			0
$498$		0			0
$499$	32.0000			1.43252			0.716258	−	0.697835i	$-0.245853\pi$
$499$	32.0000			1.43252			0.716258	+	0.697835i	$0.245853\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$	1.50000	−	2.59808i	0.0669483	−	0.115958i
$503$	−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
$506$	9.00000	−	15.5885i	0.400099	−	0.692991i
$507$		0			0
$508$	−8.50000	−	14.7224i	−0.377127	−	0.653202i
$509$	−30.0000			−1.32973			−0.664863	−	0.746965i	$-0.731510\pi$
$509$	−30.0000			−1.32973			−0.664863	+	0.746965i	$0.731510\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	9.00000	−	15.5885i	0.396973	−	0.687577i
$515$	−30.0000			−1.32196
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	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
$527$	−12.0000			−0.522728
$528$		0			0
$529$	−14.0000			−0.608696
$530$	9.00000	+	15.5885i	0.390935	+	0.677119i
$531$		0			0
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−18.0000	−	31.1769i	−0.778208	−	1.34790i
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$		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	$-0.470961\pi$
$542$	−28.0000			−1.20270
$543$		0			0
$544$	−6.00000			−0.257248
$545$	15.0000	−	25.9808i	0.642529	−	1.11289i
$546$		0			0
$547$	−16.0000	−	27.7128i	−0.684111	−	1.18491i	−0.973715	−	0.227768i	$-0.926857\pi$
$547$	−16.0000	−	27.7128i	−0.684111	−	1.18491i	0.289605	−	0.957146i	$-0.406476\pi$
$548$	3.00000	+	5.19615i	0.128154	+	0.221969i
$549$		0			0
$550$	−12.0000	+	20.7846i	−0.511682	+	0.886259i
$551$	−21.0000	+	36.3731i	−0.894630	+	1.54954i
$552$		0			0
$553$		0			0
$554$	8.00000	−	13.8564i	0.339887	−	0.588702i
$555$		0			0
$556$	5.00000			0.212047
$557$	−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
$562$	27.0000			1.13893
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	−0.970048	−	0.242912i	$-0.921897\pi$
$563$	−16.5000	−	28.5788i	−0.695392	−	1.20445i	0.274656	−	0.961542i	$-0.411436\pi$
$564$		0			0
$565$	22.5000	−	38.9711i	0.946582	−	1.63953i
$566$	−19.0000			−0.798630
$567$		0			0
$568$	−3.00000			−0.125877
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	12.0000			0.501745
$573$		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	$0.140133\pi$
$578$	19.0000			0.790296
$579$		0			0
$580$	9.00000	−	15.5885i	0.373705	−	0.647275i
$581$		0			0
$582$		0			0
$583$	18.0000	−	31.1769i	0.745484	−	1.29122i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$		0			0
$586$	−1.50000	−	2.59808i	−0.0619644	−	0.107326i
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	0.833408	−	0.552658i	$-0.186386\pi$
$587$	−1.50000	−	2.59808i	−0.0619116	−	0.107234i	−0.895320	+	0.445424i	$0.853053\pi$
$588$		0			0
$589$	7.00000	−	12.1244i	0.288430	−	0.499575i
$590$		0			0
$591$		0			0
$592$	2.00000			0.0821995
$593$		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
$598$	3.00000	+	5.19615i	0.122679	+	0.212486i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	−7.00000	−	12.1244i	−0.285536	−	0.494563i	0.687203	−	0.726465i	$-0.258838\pi$
$601$	−7.00000	−	12.1244i	−0.285536	−	0.494563i	−0.972739	+	0.231903i	$0.925505\pi$
$602$		0			0
$603$		0			0
$604$	−11.5000	−	19.9186i	−0.467928	−	0.810476i
$605$	75.0000			3.04918
$606$		0			0
$607$	−22.0000			−0.892952			−0.446476	−	0.894795i	$-0.647321\pi$
$607$	−22.0000			−0.892952			−0.446476	+	0.894795i	$0.647321\pi$
$608$	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	$0.218319\pi$
$614$	12.5000	−	21.6506i	0.504459	−	0.873749i
$615$		0			0
$616$		0			0
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	−0.0398207	−	0.999207i	$-0.512679\pi$
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	0.885249	−	0.465118i	$-0.153988\pi$
$618$		0			0
$619$	−7.00000			−0.281354			−0.140677	−	0.990056i	$-0.544928\pi$
$619$	−7.00000			−0.281354			−0.140677	+	0.990056i	$0.544928\pi$
$620$	−3.00000	+	5.19615i	−0.120483	+	0.208683i
$621$		0			0
$622$	−12.0000			−0.481156
$623$		0			0
$624$		0			0
$625$	−29.0000			−1.16000
$626$	5.00000	+	8.66025i	0.199840	+	0.346133i
$627$		0			0
$628$	6.50000	−	11.2583i	0.259378	−	0.449256i
$629$	−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	$0.544496\pi$
$632$	−2.50000	+	4.33013i	−0.0994447	+	0.172243i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	51.0000			2.02387
$636$		0			0
$637$		0			0
$638$	−36.0000			−1.42525
$639$		0			0
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	−27.0000			−1.06644			−0.533218	−	0.845978i	$-0.679017\pi$
$641$	−27.0000			−1.06644			−0.533218	+	0.845978i	$0.679017\pi$
$642$		0			0
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	−0.823891	−	0.566748i	$-0.808201\pi$
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	0.902764	+	0.430137i	$0.141535\pi$
$644$		0			0
$645$		0			0
$646$	−21.0000	+	36.3731i	−0.826234	+	1.43108i
$647$		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
$653$	36.0000			1.40879			0.704394	−	0.709809i	$-0.251219\pi$
$653$	36.0000			1.40879			0.704394	+	0.709809i	$0.251219\pi$
$654$		0			0
$655$	27.0000			1.05498
$656$		0			0
$657$		0			0
$658$		0			0
$659$	21.0000	+	36.3731i	0.818044	+	1.41689i	0.907122	+	0.420869i	$0.138275\pi$
$659$	21.0000	+	36.3731i	0.818044	+	1.41689i	−0.0890776	+	0.996025i	$0.528392\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$	−13.0000	−	22.5167i	−0.505259	−	0.875135i
$663$		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
$670$	24.0000			0.927201
$671$	−15.0000	+	25.9808i	−0.579069	+	1.00298i
$672$		0			0
$673$	18.5000	+	32.0429i	0.713123	+	1.23516i	0.963679	+	0.267063i	$0.0860531\pi$
$673$	18.5000	+	32.0429i	0.713123	+	1.23516i	−0.250557	+	0.968102i	$0.580614\pi$
$674$	11.0000	+	19.0526i	0.423704	+	0.733877i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$		0			0
$679$		0			0
$680$	9.00000	−	15.5885i	0.345134	−	0.597790i
$681$		0			0
$682$	12.0000			0.459504
$683$	−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
$688$	2.00000			0.0762493
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−23.5000	+	40.7032i	−0.893982	+	1.54842i	−0.0589228	+	0.998263i	$0.518767\pi$
$691$	−23.5000	+	40.7032i	−0.893982	+	1.54842i	−0.835059	+	0.550160i	$0.814567\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	24.0000			0.911028
$695$	−7.50000	+	12.9904i	−0.284491	+	0.492753i
$696$		0			0
$697$		0			0
$698$	26.0000			0.984115
$699$		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
$704$	6.00000			0.226134
$705$		0			0
$706$	−9.00000	+	15.5885i	−0.338719	+	0.586679i
$707$		0			0
$708$		0			0
$709$	26.0000	−	45.0333i	0.976450	−	1.69126i	0.301388	−	0.953502i	$-0.402550\pi$
$709$	26.0000	−	45.0333i	0.976450	−	1.69126i	0.675063	−	0.737760i	$-0.264116\pi$
$710$	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
$716$	−18.0000			−0.672692
$717$		0			0
$718$	3.00000			0.111959
$719$	−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
$724$	12.5000	+	21.6506i	0.464559	+	0.804640i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$		0			0
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	0.782267	−	0.622944i	$-0.214063\pi$
$727$	−4.00000	−	6.92820i	−0.148352	−	0.256953i	−0.930618	+	0.365991i	$0.880730\pi$
$728$		0			0
$729$		0			0
$730$	−3.00000	−	5.19615i	−0.111035	−	0.192318i
$731$	−12.0000			−0.443836
$732$		0			0
$733$	29.0000			1.07114			0.535570	−	0.844491i	$-0.320097\pi$
$733$	29.0000			1.07114			0.535570	+	0.844491i	$0.320097\pi$
$734$	−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	$0.325382\pi$
$740$	−3.00000	+	5.19615i	−0.110282	+	0.191014i
$741$		0			0
$742$		0			0
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$		0			0
$745$	18.0000			0.659469
$746$	−7.00000	+	12.1244i	−0.256288	+	0.443904i
$747$		0			0
$748$	−36.0000			−1.31629
$749$		0			0
$750$		0			0
$751$	−31.0000			−1.13121			−0.565603	−	0.824678i	$-0.691357\pi$
$751$	−31.0000			−1.13121			−0.565603	+	0.824678i	$0.691357\pi$
$752$		0			0
$753$		0			0
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$	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	$0.343354\pi$
$758$	−1.00000	+	1.73205i	−0.0363216	+	0.0629109i
$759$		0			0
$760$	10.5000	+	18.1865i	0.380875	+	0.659695i
$761$	42.0000			1.52250			0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000			1.52250			0.761249	+	0.648459i	$0.224586\pi$
$762$		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	−0.964193	−	0.265200i	$-0.914562\pi$
$769$	−7.00000	+	12.1244i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$770$		0			0
$771$		0			0
$772$	−8.50000	+	14.7224i	−0.305922	+	0.529872i
$773$	−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
$781$	−18.0000			−0.644091
$782$	−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
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	0.630905	−	0.775860i	$-0.282684\pi$
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	−0.987367	+	0.158450i	$0.949350\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$		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
$794$	26.0000			0.922705
$795$		0			0
$796$	14.0000			0.496217
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	−0.838236	−	0.545308i	$-0.816413\pi$
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	0.891368	+	0.453279i	$0.149746\pi$
$798$		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
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$		0			0
$805$		0			0
$806$	−2.00000	+	3.46410i	−0.0704470	+	0.122018i
$807$		0			0
$808$	−9.00000			−0.316619
$809$	−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
$814$	12.0000			0.420600
$815$	−3.00000	−	5.19615i	−0.105085	−	0.182013i
$816$		0			0
$817$	7.00000	−	12.1244i	0.244899	−	0.424178i
$818$	32.0000			1.11885
$819$		0			0
$820$		0			0
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	−0.995819	−	0.0913446i	$-0.970884\pi$
$821$	−12.0000	+	20.7846i	−0.418803	+	0.725388i	0.577016	+	0.816733i	$0.304217\pi$
$822$		0			0
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	0.787850	−	0.615867i	$-0.211194\pi$
$823$	−4.00000	−	6.92820i	−0.139431	−	0.241502i	−0.927281	+	0.374365i	$0.877861\pi$
$824$	−10.0000			−0.348367
$825$		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	$-0.0343769\pi$
$830$	−36.0000			−1.24958
$831$		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	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$		0			0
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−10.0000			−0.344623
$843$		0			0
$844$	8.00000			0.275371
$845$	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
$850$	12.0000	+	20.7846i	0.411597	+	0.712906i
$851$	3.00000	+	5.19615i	0.102839	+	0.178122i
$852$		0			0
$853$	−17.5000	−	30.3109i	−0.599189	−	1.03783i	−0.992941	−	0.118609i	$-0.962157\pi$
$853$	−17.5000	−	30.3109i	−0.599189	−	1.03783i	0.393753	−	0.919216i	$-0.371177\pi$
$854$		0			0
$855$		0			0
$856$	−6.00000	−	10.3923i	−0.205076	−	0.355202i
$857$	−54.0000			−1.84460			−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000			−1.84460			−0.922302	+	0.386469i	$0.873695\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−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
$866$	−7.00000	+	12.1244i	−0.237870	+	0.412002i
$867$		0			0
$868$		0			0
$869$	−15.0000	+	25.9808i	−0.508840	+	0.881337i
$870$		0			0
$871$	16.0000			0.542139
$872$	5.00000	−	8.66025i	0.169321	−	0.293273i
$873$		0			0
$874$	21.0000			0.710336
$875$		0			0
$876$		0			0
$877$	−22.0000			−0.742887			−0.371444	−	0.928456i	$-0.621137\pi$
$877$	−22.0000			−0.742887			−0.371444	+	0.928456i	$0.621137\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$		0			0
$880$	−9.00000	+	15.5885i	−0.303390	+	0.525487i
$881$		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	$0.693869\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	9.00000	+	15.5885i	0.302361	+	0.523704i
$887$	−24.0000			−0.805841			−0.402921	−	0.915235i	$-0.632005\pi$
$887$	−24.0000			−0.805841			−0.402921	+	0.915235i	$0.632005\pi$
$888$		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
$898$	16.5000	−	28.5788i	0.550612	−	0.953688i
$899$	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
$905$	−75.0000			−2.49308
$906$		0			0
$907$	32.0000			1.06254			0.531271	−	0.847202i	$-0.321714\pi$
$907$	32.0000			1.06254			0.531271	+	0.847202i	$0.321714\pi$
$908$	−7.50000	−	12.9904i	−0.248896	−	0.431101i
$909$		0			0
$910$		0			0
$911$	7.50000	+	12.9904i	0.248486	+	0.430391i	0.963106	−	0.269122i	$-0.0867336\pi$
$911$	7.50000	+	12.9904i	0.248486	+	0.430391i	−0.714620	+	0.699513i	$0.753400\pi$
$912$		0			0
$913$	36.0000	+	62.3538i	1.19143	+	2.06361i
$914$	−14.5000	−	25.1147i	−0.479617	−	0.830722i
$915$		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	$0.891405\pi$
$920$	−9.00000			−0.296721
$921$		0			0
$922$	33.0000			1.08680
$923$	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		−0.866025	−	0.500000i	$-0.833333\pi$
$929$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$930$		0			0
$931$		0			0
$932$	4.50000	−	7.79423i	0.147402	−	0.255308i
$933$		0			0
$934$	−12.0000			−0.392652
$935$	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
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	0.984858	−	0.173365i	$-0.0554641\pi$
$941$	10.5000	+	18.1865i	0.342290	+	0.592864i	−0.642567	+	0.766229i	$0.722131\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$	12.0000			0.390154
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	−0.992442	−	0.122714i	$-0.960840\pi$
$947$	−12.0000	+	20.7846i	−0.389948	+	0.675409i	0.602494	+	0.798123i	$0.294174\pi$
$948$		0			0
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$	−28.0000			−0.908440
$951$		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
$956$	15.0000			0.485135
$957$		0			0
$958$	−3.00000	+	5.19615i	−0.0969256	+	0.167880i
$959$		0			0
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−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	−0.969715	−	0.244238i	$-0.921462\pi$
$967$	−8.50000	+	14.7224i	−0.273342	+	0.473441i	0.696374	+	0.717679i	$0.254796\pi$
$968$	25.0000			0.803530
$969$		0			0
$970$	6.00000			0.192648
$971$	−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
$976$	−2.50000	−	4.33013i	−0.0800230	−	0.138604i
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	0.910017	−	0.414572i	$-0.136069\pi$
$977$	3.00000	+	5.19615i	0.0959785	+	0.166240i	−0.814038	+	0.580812i	$0.802735\pi$
$978$		0			0
$979$		0			0
$980$		0			0
$981$		0			0
$982$	9.00000	+	15.5885i	0.287202	+	0.497448i
$983$	−18.0000			−0.574111			−0.287055	−	0.957914i	$-0.592676\pi$
$983$	−18.0000			−0.574111			−0.287055	+	0.957914i	$0.592676\pi$
$984$		0			0
$985$	−54.0000			−1.72058
$986$	−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	$-0.0524655\pi$
$992$	−1.00000	+	1.73205i	−0.0317500	+	0.0549927i
$993$		0			0
$994$		0			0
$995$	−21.0000	+	36.3731i	−0.665745	+	1.15310i
$996$		0			0
$997$	−55.0000			−1.74187			−0.870934	−	0.491400i	$-0.836485\pi$
$997$	−55.0000			−1.74187			−0.870934	+	0.491400i	$0.836485\pi$
$998$	−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.h.e.361.1		2
3.2	odd	2		882.2.h.j.67.1		2
7.2	even	3		2646.2.e.f.1549.1		2
7.3	odd	6		2646.2.f.c.1765.1		2
7.4	even	3		378.2.f.a.253.1		2
7.5	odd	6		2646.2.e.j.1549.1		2
7.6	odd	2		2646.2.h.a.361.1		2
9.2	odd	6		882.2.e.b.655.1		2
9.7	even	3		2646.2.e.f.2125.1		2
21.2	odd	6		882.2.e.b.373.1		2
21.5	even	6		882.2.e.d.373.1		2
21.11	odd	6		126.2.f.a.85.1	yes	2
21.17	even	6		882.2.f.h.589.1		2
21.20	even	2		882.2.h.f.67.1		2
28.11	odd	6		3024.2.r.a.1009.1		2
63.2	odd	6		882.2.h.j.79.1		2
63.4	even	3		1134.2.a.h.1.1		1
63.11	odd	6		126.2.f.a.43.1	✓	2
63.16	even	3	inner	2646.2.h.e.667.1		2
63.20	even	6		882.2.e.d.655.1		2
63.25	even	3		378.2.f.a.127.1		2
63.31	odd	6		7938.2.a.u.1.1		1
63.32	odd	6		1134.2.a.a.1.1		1
63.34	odd	6		2646.2.e.j.2125.1		2
63.38	even	6		882.2.f.h.295.1		2
63.47	even	6		882.2.h.f.79.1		2
63.52	odd	6		2646.2.f.c.883.1		2
63.59	even	6		7938.2.a.l.1.1		1
63.61	odd	6		2646.2.h.a.667.1		2
84.11	even	6		1008.2.r.d.337.1		2
252.11	even	6		1008.2.r.d.673.1		2
252.67	odd	6		9072.2.a.w.1.1		1
252.95	even	6		9072.2.a.c.1.1		1
252.151	odd	6		3024.2.r.a.2017.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.a.43.1	✓	2	63.11	odd	6
126.2.f.a.85.1	yes	2	21.11	odd	6
378.2.f.a.127.1		2	63.25	even	3
378.2.f.a.253.1		2	7.4	even	3
882.2.e.b.373.1		2	21.2	odd	6
882.2.e.b.655.1		2	9.2	odd	6
882.2.e.d.373.1		2	21.5	even	6
882.2.e.d.655.1		2	63.20	even	6
882.2.f.h.295.1		2	63.38	even	6
882.2.f.h.589.1		2	21.17	even	6
882.2.h.f.67.1		2	21.20	even	2
882.2.h.f.79.1		2	63.47	even	6
882.2.h.j.67.1		2	3.2	odd	2
882.2.h.j.79.1		2	63.2	odd	6
1008.2.r.d.337.1		2	84.11	even	6
1008.2.r.d.673.1		2	252.11	even	6
1134.2.a.a.1.1		1	63.32	odd	6
1134.2.a.h.1.1		1	63.4	even	3
2646.2.e.f.1549.1		2	7.2	even	3
2646.2.e.f.2125.1		2	9.7	even	3
2646.2.e.j.1549.1		2	7.5	odd	6
2646.2.e.j.2125.1		2	63.34	odd	6
2646.2.f.c.883.1		2	63.52	odd	6
2646.2.f.c.1765.1		2	7.3	odd	6
2646.2.h.a.361.1		2	7.6	odd	2
2646.2.h.a.667.1		2	63.61	odd	6
2646.2.h.e.361.1		2	1.1	even	1	trivial
2646.2.h.e.667.1		2	63.16	even	3	inner
3024.2.r.a.1009.1		2	28.11	odd	6
3024.2.r.a.2017.1		2	252.151	odd	6
7938.2.a.l.1.1		1	63.59	even	6
7938.2.a.u.1.1		1	63.31	odd	6
9072.2.a.c.1.1		1	252.95	even	6
9072.2.a.w.1.1		1	252.67	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +1.00000 q^{8} +(-1.50000 + 2.59808i) q^{10} +6.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(3.00000 - 5.19615i) q^{17} +(3.50000 + 6.06218i) q^{19} +(-1.50000 - 2.59808i) q^{20} +(-3.00000 + 5.19615i) q^{22} -3.00000 q^{23} +4.00000 q^{25} +(-1.00000 - 1.73205i) q^{26} +(3.00000 + 5.19615i) q^{29} +(-1.00000 - 1.73205i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{34} +(-1.00000 - 1.73205i) q^{37} -7.00000 q^{38} +3.00000 q^{40} +(-1.00000 - 1.73205i) q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.50000 - 2.59808i) q^{46} +(-2.00000 + 3.46410i) q^{50} +2.00000 q^{52} +(3.00000 - 5.19615i) q^{53} +18.0000 q^{55} -6.00000 q^{58} +(-2.50000 + 4.33013i) q^{61} +2.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(-4.00000 - 6.92820i) q^{67} -6.00000 q^{68} -3.00000 q^{71} +(-1.00000 + 1.73205i) q^{73} +2.00000 q^{74} +(3.50000 - 6.06218i) q^{76} +(-2.50000 + 4.33013i) q^{79} +(-1.50000 + 2.59808i) q^{80} +(6.00000 + 10.3923i) q^{83} +(9.00000 - 15.5885i) q^{85} +2.00000 q^{86} +6.00000 q^{88} +(1.50000 + 2.59808i) q^{92} +(10.5000 + 18.1865i) q^{95} +(-1.00000 - 1.73205i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 6 q^{5} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 6 * q^5 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 6 q^{5} + 2 q^{8} - 3 q^{10} + 12 q^{11} - 2 q^{13} - q^{16} + 6 q^{17} + 7 q^{19} - 3 q^{20} - 6 q^{22} - 6 q^{23} + 8 q^{25} - 2 q^{26} + 6 q^{29} - 2 q^{31} - q^{32} + 6 q^{34} - 2 q^{37} - 14 q^{38} + 6 q^{40} - 2 q^{43} - 6 q^{44} + 3 q^{46} - 4 q^{50} + 4 q^{52} + 6 q^{53} + 36 q^{55} - 12 q^{58} - 5 q^{61} + 4 q^{62} + 2 q^{64} - 6 q^{65} - 8 q^{67} - 12 q^{68} - 6 q^{71} - 2 q^{73} + 4 q^{74} + 7 q^{76} - 5 q^{79} - 3 q^{80} + 12 q^{83} + 18 q^{85} + 4 q^{86} + 12 q^{88} + 3 q^{92} + 21 q^{95} - 2 q^{97}+O(q^{100}) \) 2 * q - q^2 - q^4 + 6 * q^5 + 2 * q^8 - 3 * q^10 + 12 * q^11 - 2 * q^13 - q^16 + 6 * q^17 + 7 * q^19 - 3 * q^20 - 6 * q^22 - 6 * q^23 + 8 * q^25 - 2 * q^26 + 6 * q^29 - 2 * q^31 - q^32 + 6 * q^34 - 2 * q^37 - 14 * q^38 + 6 * q^40 - 2 * q^43 - 6 * q^44 + 3 * q^46 - 4 * q^50 + 4 * q^52 + 6 * q^53 + 36 * q^55 - 12 * q^58 - 5 * q^61 + 4 * q^62 + 2 * q^64 - 6 * q^65 - 8 * q^67 - 12 * q^68 - 6 * q^71 - 2 * q^73 + 4 * q^74 + 7 * q^76 - 5 * q^79 - 3 * q^80 + 12 * q^83 + 18 * q^85 + 4 * q^86 + 12 * q^88 + 3 * q^92 + 21 * q^95 - 2 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more