LMFDB - Embedded newform 2646.2.h.t.361.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 882)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	2646.361
Dual form			2646.2.h.t.667.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.03528 q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.03528 q^{5} -1.00000 q^{8} +(-0.517638 + 0.896575i) q^{10} +0.267949 q^{11} +(0.896575 - 1.55291i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(3.41542 - 5.91567i) q^{17} +(2.19067 + 3.79435i) q^{19} +(0.517638 + 0.896575i) q^{20} +(0.133975 - 0.232051i) q^{22} -5.46410 q^{23} -3.92820 q^{25} +(-0.896575 - 1.55291i) q^{26} +(-2.00000 - 3.46410i) q^{29} +(3.34607 + 5.79555i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.41542 - 5.91567i) q^{34} +(-3.73205 - 6.46410i) q^{37} +4.38134 q^{38} +1.03528 q^{40} +(4.31199 - 7.46859i) q^{41} +(-0.133975 - 0.232051i) q^{43} +(-0.133975 - 0.232051i) q^{44} +(-2.73205 + 4.73205i) q^{46} +(-0.378937 + 0.656339i) q^{47} +(-1.96410 + 3.40192i) q^{50} -1.79315 q^{52} +(5.46410 - 9.46410i) q^{53} -0.277401 q^{55} -4.00000 q^{58} +(0.637756 + 1.10463i) q^{59} +(-6.31319 + 10.9348i) q^{61} +6.69213 q^{62} +1.00000 q^{64} +(-0.928203 + 1.60770i) q^{65} +(-6.23205 - 10.7942i) q^{67} -6.83083 q^{68} -9.46410 q^{71} +(2.70831 - 4.69093i) q^{73} -7.46410 q^{74} +(2.19067 - 3.79435i) q^{76} +(-4.46410 + 7.73205i) q^{79} +(0.517638 - 0.896575i) q^{80} +(-4.31199 - 7.46859i) q^{82} +(-3.29530 - 5.70762i) q^{83} +(-3.53590 + 6.12436i) q^{85} -0.267949 q^{86} -0.267949 q^{88} +(-3.53553 - 6.12372i) q^{89} +(2.73205 + 4.73205i) q^{92} +(0.378937 + 0.656339i) q^{94} +(-2.26795 - 3.92820i) q^{95} +(-9.07227 - 15.7136i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 16 q^{11} - 4 q^{16} + 8 q^{22} - 16 q^{23} + 24 q^{25} - 16 q^{29} + 4 q^{32} - 16 q^{37} - 8 q^{43} - 8 q^{44} - 8 q^{46} + 12 q^{50} + 16 q^{53} - 32 q^{58} + 8 q^{64} + 48 q^{65} - 36 q^{67} - 48 q^{71} - 32 q^{74} - 8 q^{79} - 56 q^{85} - 16 q^{86} - 16 q^{88} + 8 q^{92} - 32 q^{95}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 + 16 * q^11 - 4 * q^16 + 8 * q^22 - 16 * q^23 + 24 * q^25 - 16 * q^29 + 4 * q^32 - 16 * q^37 - 8 * q^43 - 8 * q^44 - 8 * q^46 + 12 * q^50 + 16 * q^53 - 32 * q^58 + 8 * q^64 + 48 * q^65 - 36 * q^67 - 48 * q^71 - 32 * q^74 - 8 * q^79 - 56 * q^85 - 16 * q^86 - 16 * q^88 + 8 * q^92 - 32 * q^95

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
$5$	−1.03528			−0.462990			−0.231495	−	0.972836i	$-0.574362\pi$
$5$	−1.03528			−0.462990			−0.231495	+	0.972836i	$0.574362\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.517638	+	0.896575i	−0.163692	+	0.283522i
$11$	0.267949			0.0807897			0.0403949	−	0.999184i	$-0.487138\pi$
$11$	0.267949			0.0807897			0.0403949	+	0.999184i	$0.487138\pi$
$12$		0			0
$13$	0.896575	−	1.55291i	0.248665	−	0.430701i	−0.714490	−	0.699645i	$-0.753341\pi$
$13$	0.896575	−	1.55291i	0.248665	−	0.430701i	0.963156	+	0.268944i	$0.0866747\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	3.41542	−	5.91567i	0.828360	−	1.43476i	−0.0709642	−	0.997479i	$-0.522608\pi$
$17$	3.41542	−	5.91567i	0.828360	−	1.43476i	0.899324	−	0.437283i	$-0.144059\pi$
$18$		0			0
$19$	2.19067	+	3.79435i	0.502574	+	0.870484i	0.999996	+	0.00297513i	$0.000947015\pi$
$19$	2.19067	+	3.79435i	0.502574	+	0.870484i	−0.497421	+	0.867509i	$0.665720\pi$
$20$	0.517638	+	0.896575i	0.115747	+	0.200480i
$21$		0			0
$22$	0.133975	−	0.232051i	0.0285635	−	0.0494734i
$23$	−5.46410			−1.13934			−0.569672	−	0.821872i	$-0.692930\pi$
$23$	−5.46410			−1.13934			−0.569672	+	0.821872i	$0.692930\pi$
$24$		0			0
$25$	−3.92820			−0.785641
$26$	−0.896575	−	1.55291i	−0.175833	−	0.304552i
$27$		0			0
$28$		0			0
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	0.618389	−	0.785872i	$-0.287786\pi$
$29$	−2.00000	−	3.46410i	−0.371391	−	0.643268i	−0.989780	+	0.142605i	$0.954452\pi$
$30$		0			0
$31$	3.34607	+	5.79555i	0.600971	+	1.04091i	0.992674	+	0.120821i	$0.0385526\pi$
$31$	3.34607	+	5.79555i	0.600971	+	1.04091i	−0.391703	+	0.920092i	$0.628114\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−3.41542	−	5.91567i	−0.585739	−	1.01453i
$35$		0			0
$36$		0			0
$37$	−3.73205	−	6.46410i	−0.613545	−	1.06269i	−0.990638	−	0.136516i	$-0.956409\pi$
$37$	−3.73205	−	6.46410i	−0.613545	−	1.06269i	0.377092	−	0.926176i	$-0.376924\pi$
$38$	4.38134			0.710747
$39$		0			0
$40$	1.03528			0.163692
$41$	4.31199	−	7.46859i	0.673420	−	1.16640i	−0.303508	−	0.952829i	$-0.598158\pi$
$41$	4.31199	−	7.46859i	0.673420	−	1.16640i	0.976928	−	0.213569i	$-0.0685087\pi$
$42$		0			0
$43$	−0.133975	−	0.232051i	−0.0204309	−	0.0353874i	0.855629	−	0.517589i	$-0.173170\pi$
$43$	−0.133975	−	0.232051i	−0.0204309	−	0.0353874i	−0.876060	+	0.482202i	$0.839837\pi$
$44$	−0.133975	−	0.232051i	−0.0201974	−	0.0349830i
$45$		0			0
$46$	−2.73205	+	4.73205i	−0.402819	+	0.697703i
$47$	−0.378937	+	0.656339i	−0.0552737	+	0.0957369i	−0.892338	−	0.451367i	$-0.850936\pi$
$47$	−0.378937	+	0.656339i	−0.0552737	+	0.0957369i	0.837065	+	0.547104i	$0.184270\pi$
$48$		0			0
$49$		0			0
$50$	−1.96410	+	3.40192i	−0.277766	+	0.481105i
$51$		0			0
$52$	−1.79315			−0.248665
$53$	5.46410	−	9.46410i	0.750552	−	1.29999i	−0.197003	−	0.980403i	$-0.563121\pi$
$53$	5.46410	−	9.46410i	0.750552	−	1.29999i	0.947555	−	0.319592i	$-0.103546\pi$
$54$		0			0
$55$	−0.277401			−0.0374048
$56$		0			0
$57$		0			0
$58$	−4.00000			−0.525226
$59$	0.637756	+	1.10463i	0.0830288	+	0.143810i	0.904550	−	0.426369i	$-0.140207\pi$
$59$	0.637756	+	1.10463i	0.0830288	+	0.143810i	−0.821521	+	0.570179i	$0.806874\pi$
$60$		0			0
$61$	−6.31319	+	10.9348i	−0.808322	+	1.40005i	0.105704	+	0.994398i	$0.466290\pi$
$61$	−6.31319	+	10.9348i	−0.808322	+	1.40005i	−0.914026	+	0.405656i	$0.867043\pi$
$62$	6.69213			0.849901
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.928203	+	1.60770i	−0.115129	+	0.199410i
$66$		0			0
$67$	−6.23205	−	10.7942i	−0.761366	−	1.31872i	−0.942146	−	0.335201i	$-0.891196\pi$
$67$	−6.23205	−	10.7942i	−0.761366	−	1.31872i	0.180780	−	0.983524i	$-0.442138\pi$
$68$	−6.83083			−0.828360
$69$		0			0
$70$		0			0
$71$	−9.46410			−1.12318			−0.561591	−	0.827415i	$-0.689811\pi$
$71$	−9.46410			−1.12318			−0.561591	+	0.827415i	$0.689811\pi$
$72$		0			0
$73$	2.70831	−	4.69093i	0.316984	−	0.549032i	−0.662874	−	0.748731i	$-0.730663\pi$
$73$	2.70831	−	4.69093i	0.316984	−	0.549032i	0.979857	+	0.199700i	$0.0639967\pi$
$74$	−7.46410			−0.867684
$75$		0			0
$76$	2.19067	−	3.79435i	0.251287	−	0.435242i
$77$		0			0
$78$		0			0
$79$	−4.46410	+	7.73205i	−0.502251	+	0.869924i	0.497746	+	0.867323i	$0.334161\pi$
$79$	−4.46410	+	7.73205i	−0.502251	+	0.869924i	−0.999997	+	0.00260080i	$0.999172\pi$
$80$	0.517638	−	0.896575i	0.0578737	−	0.100240i
$81$		0			0
$82$	−4.31199	−	7.46859i	−0.476180	−	0.824768i
$83$	−3.29530	−	5.70762i	−0.361706	−	0.626493i	0.626536	−	0.779393i	$-0.284472\pi$
$83$	−3.29530	−	5.70762i	−0.361706	−	0.626493i	−0.988242	+	0.152900i	$0.951139\pi$
$84$		0			0
$85$	−3.53590	+	6.12436i	−0.383522	+	0.664280i
$86$	−0.267949			−0.0288937
$87$		0			0
$88$	−0.267949			−0.0285635
$89$	−3.53553	−	6.12372i	−0.374766	−	0.649113i	0.615526	−	0.788116i	$-0.288944\pi$
$89$	−3.53553	−	6.12372i	−0.374766	−	0.649113i	−0.990292	+	0.139003i	$0.955610\pi$
$90$		0			0
$91$		0			0
$92$	2.73205	+	4.73205i	0.284836	+	0.493350i
$93$		0			0
$94$	0.378937	+	0.656339i	0.0390844	+	0.0676962i
$95$	−2.26795	−	3.92820i	−0.232687	−	0.403025i
$96$		0			0
$97$	−9.07227	−	15.7136i	−0.921149	−	1.59548i	−0.797640	−	0.603134i	$-0.793918\pi$
$97$	−9.07227	−	15.7136i	−0.921149	−	1.59548i	−0.123510	−	0.992343i	$-0.539415\pi$
$98$		0			0
$99$		0			0
$100$	1.96410	+	3.40192i	0.196410	+	0.340192i
$101$	−4.89898			−0.487467			−0.243733	−	0.969842i	$-0.578372\pi$
$101$	−4.89898			−0.487467			−0.243733	+	0.969842i	$0.578372\pi$
$102$		0			0
$103$	−12.3490			−1.21678			−0.608391	−	0.793638i	$-0.708185\pi$
$103$	−12.3490			−1.21678			−0.608391	+	0.793638i	$0.708185\pi$
$104$	−0.896575	+	1.55291i	−0.0879165	+	0.152276i
$105$		0			0
$106$	−5.46410	−	9.46410i	−0.530720	−	0.919235i
$107$	−8.69615	−	15.0622i	−0.840689	−	1.45612i	−0.889313	−	0.457299i	$-0.848817\pi$
$107$	−8.69615	−	15.0622i	−0.840689	−	1.45612i	0.0486244	−	0.998817i	$-0.484516\pi$
$108$		0			0
$109$	−2.46410	+	4.26795i	−0.236018	+	0.408795i	−0.959568	−	0.281477i	$-0.909176\pi$
$109$	−2.46410	+	4.26795i	−0.236018	+	0.408795i	0.723550	+	0.690272i	$0.242509\pi$
$110$	−0.138701	+	0.240237i	−0.0132246	+	0.0229057i
$111$		0			0
$112$		0			0
$113$	−3.46410	+	6.00000i	−0.325875	+	0.564433i	−0.981689	−	0.190490i	$-0.938992\pi$
$113$	−3.46410	+	6.00000i	−0.325875	+	0.564433i	0.655814	+	0.754923i	$0.272326\pi$
$114$		0			0
$115$	5.65685			0.527504
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$		0			0
$118$	1.27551			0.117420
$119$		0			0
$120$		0			0
$121$	−10.9282			−0.993473
$122$	6.31319	+	10.9348i	0.571570	+	0.989988i
$123$		0			0
$124$	3.34607	−	5.79555i	0.300486	−	0.520456i
$125$	9.24316			0.826733
$126$		0			0
$127$	13.4641			1.19475			0.597373	−	0.801964i	$-0.296211\pi$
$127$	13.4641			1.19475			0.597373	+	0.801964i	$0.296211\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	0.928203	+	1.60770i	0.0814088	+	0.141004i
$131$	10.9348			0.955375			0.477688	−	0.878530i	$-0.341475\pi$
$131$	10.9348			0.955375			0.477688	+	0.878530i	$0.341475\pi$
$132$		0			0
$133$		0			0
$134$	−12.4641			−1.07673
$135$		0			0
$136$	−3.41542	+	5.91567i	−0.292869	+	0.507265i
$137$	−8.66025			−0.739895			−0.369948	−	0.929053i	$-0.620624\pi$
$137$	−8.66025			−0.739895			−0.369948	+	0.929053i	$0.620624\pi$
$138$		0			0
$139$	0.397520	−	0.688524i	0.0337172	−	0.0583999i	−0.848674	−	0.528916i	$-0.822599\pi$
$139$	0.397520	−	0.688524i	0.0337172	−	0.0583999i	0.882392	+	0.470516i	$0.155932\pi$
$140$		0			0
$141$		0			0
$142$	−4.73205	+	8.19615i	−0.397105	+	0.687806i
$143$	0.240237	−	0.416102i	0.0200896	−	0.0347962i
$144$		0			0
$145$	2.07055	+	3.58630i	0.171950	+	0.297826i
$146$	−2.70831	−	4.69093i	−0.224141	−	0.388224i
$147$		0			0
$148$	−3.73205	+	6.46410i	−0.306773	+	0.531346i
$149$	−22.9282			−1.87835			−0.939176	−	0.343437i	$-0.888409\pi$
$149$	−22.9282			−1.87835			−0.939176	+	0.343437i	$0.888409\pi$
$150$		0			0
$151$	18.3923			1.49674			0.748372	−	0.663279i	$-0.230836\pi$
$151$	18.3923			1.49674			0.748372	+	0.663279i	$0.230836\pi$
$152$	−2.19067	−	3.79435i	−0.177687	−	0.307763i
$153$		0			0
$154$		0			0
$155$	−3.46410	−	6.00000i	−0.278243	−	0.481932i
$156$		0			0
$157$	4.76028	+	8.24504i	0.379912	+	0.658026i	0.991049	−	0.133498i	$-0.0426211\pi$
$157$	4.76028	+	8.24504i	0.379912	+	0.658026i	−0.611137	+	0.791524i	$0.709288\pi$
$158$	4.46410	+	7.73205i	0.355145	+	0.615129i
$159$		0			0
$160$	−0.517638	−	0.896575i	−0.0409229	−	0.0708805i
$161$		0			0
$162$		0			0
$163$	6.66025	+	11.5359i	0.521671	+	0.903561i	0.999682	+	0.0252074i	$0.00802461\pi$
$163$	6.66025	+	11.5359i	0.521671	+	0.903561i	−0.478011	+	0.878354i	$0.658642\pi$
$164$	−8.62398			−0.673420
$165$		0			0
$166$	−6.59059			−0.511529
$167$	−0.757875	+	1.31268i	−0.0586461	+	0.101578i	−0.893858	−	0.448350i	$-0.852012\pi$
$167$	−0.757875	+	1.31268i	−0.0586461	+	0.101578i	0.835212	+	0.549928i	$0.185345\pi$
$168$		0			0
$169$	4.89230	+	8.47372i	0.376331	+	0.651825i
$170$	3.53590	+	6.12436i	0.271191	+	0.469717i
$171$		0			0
$172$	−0.133975	+	0.232051i	−0.0102155	+	0.0176937i
$173$	−3.34607	+	5.79555i	−0.254397	+	0.440628i	−0.964731	−	0.263236i	$-0.915210\pi$
$173$	−3.34607	+	5.79555i	−0.254397	+	0.440628i	0.710335	+	0.703864i	$0.248544\pi$
$174$		0			0
$175$		0			0
$176$	−0.133975	+	0.232051i	−0.0100987	+	0.0174915i
$177$		0			0
$178$	−7.07107			−0.529999
$179$	2.53590	−	4.39230i	0.189542	−	0.328296i	−0.755556	−	0.655084i	$-0.772633\pi$
$179$	2.53590	−	4.39230i	0.189542	−	0.328296i	0.945098	+	0.326788i	$0.105966\pi$
$180$		0			0
$181$	16.9706			1.26141			0.630706	−	0.776022i	$-0.282765\pi$
$181$	16.9706			1.26141			0.630706	+	0.776022i	$0.282765\pi$
$182$		0			0
$183$		0			0
$184$	5.46410			0.402819
$185$	3.86370	+	6.69213i	0.284065	+	0.492015i
$186$		0			0
$187$	0.915158	−	1.58510i	0.0669230	−	0.115914i
$188$	0.757875			0.0552737
$189$		0			0
$190$	−4.53590			−0.329069
$191$	7.46410	−	12.9282i	0.540083	−	0.935452i	−0.458815	−	0.888532i	$-0.651726\pi$
$191$	7.46410	−	12.9282i	0.540083	−	0.935452i	0.998899	−	0.0469202i	$-0.0149407\pi$
$192$		0			0
$193$	−7.52628	−	13.0359i	−0.541753	−	0.938344i	−0.998804	−	0.0489035i	$-0.984427\pi$
$193$	−7.52628	−	13.0359i	−0.541753	−	0.938344i	0.457050	−	0.889441i	$-0.348906\pi$
$194$	−18.1445			−1.30270
$195$		0			0
$196$		0			0
$197$	16.9282			1.20608			0.603042	−	0.797709i	$-0.293955\pi$
$197$	16.9282			1.20608			0.603042	+	0.797709i	$0.293955\pi$
$198$		0			0
$199$	13.1440	−	22.7661i	0.931755	−	1.61385i	0.151435	−	0.988467i	$-0.451611\pi$
$199$	13.1440	−	22.7661i	0.931755	−	1.61385i	0.780320	−	0.625380i	$-0.215056\pi$
$200$	3.92820			0.277766
$201$		0			0
$202$	−2.44949	+	4.24264i	−0.172345	+	0.298511i
$203$		0			0
$204$		0			0
$205$	−4.46410	+	7.73205i	−0.311786	+	0.540030i
$206$	−6.17449	+	10.6945i	−0.430197	+	0.745124i
$207$		0			0
$208$	0.896575	+	1.55291i	0.0621663	+	0.107675i
$209$	0.586988	+	1.01669i	0.0406028	+	0.0703262i
$210$		0			0
$211$	−9.46410	+	16.3923i	−0.651536	+	1.12849i	0.331215	+	0.943555i	$0.392542\pi$
$211$	−9.46410	+	16.3923i	−0.651536	+	1.12849i	−0.982750	+	0.184937i	$0.940792\pi$
$212$	−10.9282			−0.750552
$213$		0			0
$214$	−17.3923			−1.18891
$215$	0.138701	+	0.240237i	0.00945931	+	0.0163840i
$216$		0			0
$217$		0			0
$218$	2.46410	+	4.26795i	0.166890	+	0.289062i
$219$		0			0
$220$	0.138701	+	0.240237i	0.00935120	+	0.0161968i
$221$	−6.12436	−	10.6077i	−0.411969	−	0.713551i
$222$		0			0
$223$	−3.58630	−	6.21166i	−0.240157	−	0.415963i	0.720602	−	0.693349i	$-0.243865\pi$
$223$	−3.58630	−	6.21166i	−0.240157	−	0.415963i	−0.960759	+	0.277385i	$0.910532\pi$
$224$		0			0
$225$		0			0
$226$	3.46410	+	6.00000i	0.230429	+	0.399114i
$227$	−27.6651			−1.83620			−0.918098	−	0.396352i	$-0.870276\pi$
$227$	−27.6651			−1.83620			−0.918098	+	0.396352i	$0.870276\pi$
$228$		0			0
$229$	−0.480473			−0.0317506			−0.0158753	−	0.999874i	$-0.505053\pi$
$229$	−0.480473			−0.0317506			−0.0158753	+	0.999874i	$0.505053\pi$
$230$	2.82843	−	4.89898i	0.186501	−	0.323029i
$231$		0			0
$232$	2.00000	+	3.46410i	0.131306	+	0.227429i
$233$	0.0621778	+	0.107695i	0.00407340	+	0.00705534i	0.868055	−	0.496468i	$-0.165370\pi$
$233$	0.0621778	+	0.107695i	0.00407340	+	0.00705534i	−0.863982	+	0.503524i	$0.832037\pi$
$234$		0			0
$235$	0.392305	−	0.679492i	0.0255911	−	0.0443252i
$236$	0.637756	−	1.10463i	0.0415144	−	0.0719051i
$237$		0			0
$238$		0			0
$239$	0.464102	−	0.803848i	0.0300202	−	0.0519966i	−0.850625	−	0.525773i	$-0.823776\pi$
$239$	0.464102	−	0.803848i	0.0300202	−	0.0519966i	0.880645	+	0.473776i	$0.157109\pi$
$240$		0			0
$241$	−6.27603			−0.404275			−0.202137	−	0.979357i	$-0.564789\pi$
$241$	−6.27603			−0.404275			−0.202137	+	0.979357i	$0.564789\pi$
$242$	−5.46410	+	9.46410i	−0.351246	+	0.608375i
$243$		0			0
$244$	12.6264			0.808322
$245$		0			0
$246$		0			0
$247$	7.85641			0.499891
$248$	−3.34607	−	5.79555i	−0.212475	−	0.368018i
$249$		0			0
$250$	4.62158	−	8.00481i	0.292294	−	0.506269i
$251$	0.795040			0.0501824			0.0250912	−	0.999685i	$-0.492012\pi$
$251$	0.795040			0.0501824			0.0250912	+	0.999685i	$0.492012\pi$
$252$		0			0
$253$	−1.46410			−0.0920473
$254$	6.73205	−	11.6603i	0.422406	−	0.731629i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.0382			0.626165			0.313083	−	0.949726i	$-0.398638\pi$
$257$	10.0382			0.626165			0.313083	+	0.949726i	$0.398638\pi$
$258$		0			0
$259$		0			0
$260$	1.85641			0.115129
$261$		0			0
$262$	5.46739	−	9.46979i	0.337776	−	0.585046i
$263$	8.53590			0.526346			0.263173	−	0.964749i	$-0.415231\pi$
$263$	8.53590			0.526346			0.263173	+	0.964749i	$0.415231\pi$
$264$		0			0
$265$	−5.65685	+	9.79796i	−0.347498	+	0.601884i
$266$		0			0
$267$		0			0
$268$	−6.23205	+	10.7942i	−0.380683	+	0.659362i
$269$	2.82843	−	4.89898i	0.172452	−	0.298696i	−0.766824	−	0.641857i	$-0.778164\pi$
$269$	2.82843	−	4.89898i	0.172452	−	0.298696i	0.939277	+	0.343161i	$0.111498\pi$
$270$		0			0
$271$	6.55343	+	11.3509i	0.398093	+	0.689516i	0.993491	−	0.113914i	$-0.0363390\pi$
$271$	6.55343	+	11.3509i	0.398093	+	0.689516i	−0.595398	+	0.803431i	$0.703006\pi$
$272$	3.41542	+	5.91567i	0.207090	+	0.358690i
$273$		0			0
$274$	−4.33013	+	7.50000i	−0.261593	+	0.453092i
$275$	−1.05256			−0.0634717
$276$		0			0
$277$	31.4641			1.89049			0.945247	−	0.326355i	$-0.105820\pi$
$277$	31.4641			1.89049			0.945247	+	0.326355i	$0.105820\pi$
$278$	−0.397520	−	0.688524i	−0.0238417	−	0.0412949i
$279$		0			0
$280$		0			0
$281$	8.92820	+	15.4641i	0.532612	+	0.922511i	0.999275	+	0.0380757i	$0.0121228\pi$
$281$	8.92820	+	15.4641i	0.532612	+	0.922511i	−0.466663	+	0.884435i	$0.654544\pi$
$282$		0			0
$283$	−7.53794	−	13.0561i	−0.448084	−	0.776104i	0.550177	−	0.835048i	$-0.314560\pi$
$283$	−7.53794	−	13.0561i	−0.448084	−	0.776104i	−0.998261	+	0.0589437i	$0.981227\pi$
$284$	4.73205	+	8.19615i	0.280796	+	0.486352i
$285$		0			0
$286$	−0.240237	−	0.416102i	−0.0142055	−	0.0246046i
$287$		0			0
$288$		0			0
$289$	−14.8301	−	25.6865i	−0.872360	−	1.51097i
$290$	4.14110			0.243174
$291$		0			0
$292$	−5.41662			−0.316984
$293$	4.62158	−	8.00481i	0.269995	−	0.467646i	−0.698865	−	0.715254i	$-0.746311\pi$
$293$	4.62158	−	8.00481i	0.269995	−	0.467646i	0.968860	+	0.247608i	$0.0796445\pi$
$294$		0			0
$295$	−0.660254	−	1.14359i	−0.0384415	−	0.0665826i
$296$	3.73205	+	6.46410i	0.216921	+	0.375718i
$297$		0			0
$298$	−11.4641	+	19.8564i	−0.664098	+	1.15025i
$299$	−4.89898	+	8.48528i	−0.283315	+	0.490716i
$300$		0			0
$301$		0			0
$302$	9.19615	−	15.9282i	0.529179	−	0.916565i
$303$		0			0
$304$	−4.38134			−0.251287
$305$	6.53590	−	11.3205i	0.374244	−	0.648210i
$306$		0			0
$307$	−1.17398			−0.0670024			−0.0335012	−	0.999439i	$-0.510666\pi$
$307$	−1.17398			−0.0670024			−0.0335012	+	0.999439i	$0.510666\pi$
$308$		0			0
$309$		0			0
$310$	−6.92820			−0.393496
$311$	3.72500	+	6.45189i	0.211226	+	0.365853i	0.952098	−	0.305792i	$-0.0989212\pi$
$311$	3.72500	+	6.45189i	0.211226	+	0.365853i	−0.740873	+	0.671645i	$0.765588\pi$
$312$		0			0
$313$	3.13801	−	5.43520i	0.177371	−	0.307216i	−0.763608	−	0.645680i	$-0.776574\pi$
$313$	3.13801	−	5.43520i	0.177371	−	0.307216i	0.940979	+	0.338464i	$0.109907\pi$
$314$	9.52056			0.537276
$315$		0			0
$316$	8.92820			0.502251
$317$	−13.0000	+	22.5167i	−0.730153	+	1.26466i	0.226665	+	0.973973i	$0.427218\pi$
$317$	−13.0000	+	22.5167i	−0.730153	+	1.26466i	−0.956818	+	0.290689i	$0.906116\pi$
$318$		0			0
$319$	−0.535898	−	0.928203i	−0.0300045	−	0.0519694i
$320$	−1.03528			−0.0578737
$321$		0			0
$322$		0			0
$323$	29.9282			1.66525
$324$		0			0
$325$	−3.52193	+	6.10016i	−0.195362	+	0.338376i
$326$	13.3205			0.737755
$327$		0			0
$328$	−4.31199	+	7.46859i	−0.238090	+	0.412384i
$329$		0			0
$330$		0			0
$331$	5.73205	−	9.92820i	0.315062	−	0.545703i	−0.664389	−	0.747387i	$-0.731308\pi$
$331$	5.73205	−	9.92820i	0.315062	−	0.545703i	0.979451	+	0.201684i	$0.0646413\pi$
$332$	−3.29530	+	5.70762i	−0.180853	+	0.313246i
$333$		0			0
$334$	0.757875	+	1.31268i	0.0414691	+	0.0718265i
$335$	6.45189	+	11.1750i	0.352505	+	0.610556i
$336$		0			0
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$	9.78461			0.532213
$339$		0			0
$340$	7.07180			0.383522
$341$	0.896575	+	1.55291i	0.0485523	+	0.0840950i
$342$		0			0
$343$		0			0
$344$	0.133975	+	0.232051i	0.00722343	+	0.0125113i
$345$		0			0
$346$	3.34607	+	5.79555i	0.179886	+	0.311571i
$347$	−4.79423	−	8.30385i	−0.257368	−	0.445774i	0.708168	−	0.706044i	$-0.249522\pi$
$347$	−4.79423	−	8.30385i	−0.257368	−	0.445774i	−0.965536	+	0.260270i	$0.916188\pi$
$348$		0			0
$349$	−4.00240	−	6.93237i	−0.214244	−	0.371081i	0.738795	−	0.673931i	$-0.235395\pi$
$349$	−4.00240	−	6.93237i	−0.214244	−	0.371081i	−0.953038	+	0.302850i	$0.902062\pi$
$350$		0			0
$351$		0			0
$352$	0.133975	+	0.232051i	0.00714087	+	0.0123683i
$353$	25.0125			1.33128			0.665641	−	0.746272i	$-0.268158\pi$
$353$	25.0125			1.33128			0.665641	+	0.746272i	$0.268158\pi$
$354$		0			0
$355$	9.79796			0.520022
$356$	−3.53553	+	6.12372i	−0.187383	+	0.324557i
$357$		0			0
$358$	−2.53590	−	4.39230i	−0.134026	−	0.232141i
$359$	3.73205	+	6.46410i	0.196970	+	0.341162i	0.947545	−	0.319624i	$-0.103556\pi$
$359$	3.73205	+	6.46410i	0.196970	+	0.341162i	−0.750574	+	0.660786i	$0.770223\pi$
$360$		0			0
$361$	−0.0980762	+	0.169873i	−0.00516191	+	0.00894068i
$362$	8.48528	−	14.6969i	0.445976	−	0.772454i
$363$		0			0
$364$		0			0
$365$	−2.80385	+	4.85641i	−0.146760	+	0.254196i
$366$		0			0
$367$	−18.5606			−0.968858			−0.484429	−	0.874831i	$-0.660973\pi$
$367$	−18.5606			−0.968858			−0.484429	+	0.874831i	$0.660973\pi$
$368$	2.73205	−	4.73205i	0.142418	−	0.246675i
$369$		0			0
$370$	7.72741			0.401729
$371$		0			0
$372$		0			0
$373$	−10.7846			−0.558406			−0.279203	−	0.960232i	$-0.590070\pi$
$373$	−10.7846			−0.558406			−0.279203	+	0.960232i	$0.590070\pi$
$374$	−0.915158	−	1.58510i	−0.0473217	−	0.0819636i
$375$		0			0
$376$	0.378937	−	0.656339i	0.0195422	−	0.0338481i
$377$	−7.17260			−0.369408
$378$		0			0
$379$	13.5885			0.697992			0.348996	−	0.937124i	$-0.386523\pi$
$379$	13.5885			0.697992			0.348996	+	0.937124i	$0.386523\pi$
$380$	−2.26795	+	3.92820i	−0.116343	+	0.201513i
$381$		0			0
$382$	−7.46410	−	12.9282i	−0.381897	−	0.661464i
$383$	27.3233			1.39616			0.698078	−	0.716021i	$-0.254039\pi$
$383$	27.3233			1.39616			0.698078	+	0.716021i	$0.254039\pi$
$384$		0			0
$385$		0			0
$386$	−15.0526			−0.766155
$387$		0			0
$388$	−9.07227	+	15.7136i	−0.460575	+	0.797739i
$389$	−8.00000			−0.405616			−0.202808	−	0.979219i	$-0.565007\pi$
$389$	−8.00000			−0.405616			−0.202808	+	0.979219i	$0.565007\pi$
$390$		0			0
$391$	−18.6622	+	32.3238i	−0.943787	+	1.63469i
$392$		0			0
$393$		0			0
$394$	8.46410	−	14.6603i	0.426415	−	0.738573i
$395$	4.62158	−	8.00481i	0.232537	−	0.402766i
$396$		0			0
$397$	6.55343	+	11.3509i	0.328907	+	0.569684i	0.982295	−	0.187339i	$-0.0599863\pi$
$397$	6.55343	+	11.3509i	0.328907	+	0.569684i	−0.653388	+	0.757023i	$0.726653\pi$
$398$	−13.1440	−	22.7661i	−0.658850	−	1.14116i
$399$		0			0
$400$	1.96410	−	3.40192i	0.0982051	−	0.170096i
$401$	23.7846			1.18775			0.593873	−	0.804559i	$-0.297598\pi$
$401$	23.7846			1.18775			0.593873	+	0.804559i	$0.297598\pi$
$402$		0			0
$403$	12.0000			0.597763
$404$	2.44949	+	4.24264i	0.121867	+	0.211079i
$405$		0			0
$406$		0			0
$407$	−1.00000	−	1.73205i	−0.0495682	−	0.0858546i
$408$		0			0
$409$	2.24144	+	3.88229i	0.110832	+	0.191967i	0.916106	−	0.400936i	$-0.131315\pi$
$409$	2.24144	+	3.88229i	0.110832	+	0.191967i	−0.805274	+	0.592903i	$0.797982\pi$
$410$	4.46410	+	7.73205i	0.220466	+	0.381859i
$411$		0			0
$412$	6.17449	+	10.6945i	0.304195	+	0.526882i
$413$		0			0
$414$		0			0
$415$	3.41154	+	5.90897i	0.167466	+	0.290060i
$416$	1.79315			0.0879165
$417$		0			0
$418$	1.17398			0.0574211
$419$	−18.0938	+	31.3393i	−0.883939	+	1.53103i	−0.0370132	+	0.999315i	$0.511784\pi$
$419$	−18.0938	+	31.3393i	−0.883939	+	1.53103i	−0.846925	+	0.531712i	$0.821549\pi$
$420$		0			0
$421$	−3.80385	−	6.58846i	−0.185388	−	0.321102i	0.758319	−	0.651884i	$-0.226021\pi$
$421$	−3.80385	−	6.58846i	−0.185388	−	0.321102i	−0.943707	+	0.330782i	$0.892688\pi$
$422$	9.46410	+	16.3923i	0.460705	+	0.797965i
$423$		0			0
$424$	−5.46410	+	9.46410i	−0.265360	+	0.459617i
$425$	−13.4164	+	23.2380i	−0.650793	+	1.12721i
$426$		0			0
$427$		0			0
$428$	−8.69615	+	15.0622i	−0.420344	+	0.728058i
$429$		0			0
$430$	0.277401			0.0133775
$431$	−5.07180	+	8.78461i	−0.244300	+	0.423140i	−0.961935	−	0.273280i	$-0.911891\pi$
$431$	−5.07180	+	8.78461i	−0.244300	+	0.423140i	0.717635	+	0.696420i	$0.245225\pi$
$432$		0			0
$433$	19.8362			0.953265			0.476632	−	0.879103i	$-0.341857\pi$
$433$	19.8362			0.953265			0.476632	+	0.879103i	$0.341857\pi$
$434$		0			0
$435$		0			0
$436$	4.92820			0.236018
$437$	−11.9700	−	20.7327i	−0.572605	−	0.991781i
$438$		0			0
$439$	9.79796	−	16.9706i	0.467631	−	0.809961i	−0.531685	−	0.846942i	$-0.678441\pi$
$439$	9.79796	−	16.9706i	0.467631	−	0.809961i	0.999316	+	0.0369815i	$0.0117743\pi$
$440$	0.277401			0.0132246
$441$		0			0
$442$	−12.2487			−0.582612
$443$	8.16025	−	14.1340i	0.387705	−	0.671525i	−0.604435	−	0.796654i	$-0.706601\pi$
$443$	8.16025	−	14.1340i	0.387705	−	0.671525i	0.992140	+	0.125129i	$0.0399345\pi$
$444$		0			0
$445$	3.66025	+	6.33975i	0.173513	+	0.300533i
$446$	−7.17260			−0.339633
$447$		0			0
$448$		0			0
$449$	−23.7846			−1.12247			−0.561233	−	0.827658i	$-0.689673\pi$
$449$	−23.7846			−1.12247			−0.561233	+	0.827658i	$0.689673\pi$
$450$		0			0
$451$	1.15539	−	2.00120i	0.0544054	−	0.0942329i
$452$	6.92820			0.325875
$453$		0			0
$454$	−13.8325	+	23.9587i	−0.649194	+	1.12444i
$455$		0			0
$456$		0			0
$457$	15.5263	−	26.8923i	0.726289	−	1.25797i	−0.232153	−	0.972679i	$-0.574577\pi$
$457$	15.5263	−	26.8923i	0.726289	−	1.25797i	0.958441	−	0.285290i	$-0.0920898\pi$
$458$	−0.240237	+	0.416102i	−0.0112255	+	0.0194432i
$459$		0			0
$460$	−2.82843	−	4.89898i	−0.131876	−	0.228416i
$461$	5.51815	+	9.55772i	0.257006	+	0.445148i	0.965438	−	0.260631i	$-0.0839306\pi$
$461$	5.51815	+	9.55772i	0.257006	+	0.445148i	−0.708432	+	0.705779i	$0.750597\pi$
$462$		0			0
$463$	15.3205	−	26.5359i	0.712004	−	1.23323i	−0.252099	−	0.967701i	$-0.581121\pi$
$463$	15.3205	−	26.5359i	0.712004	−	1.23323i	0.964104	−	0.265526i	$-0.0855457\pi$
$464$	4.00000			0.185695
$465$		0			0
$466$	0.124356			0.00576066
$467$	−4.58939	−	7.94906i	−0.212372	−	0.367839i	0.740085	−	0.672514i	$-0.234785\pi$
$467$	−4.58939	−	7.94906i	−0.212372	−	0.367839i	−0.952456	+	0.304675i	$0.901452\pi$
$468$		0			0
$469$		0			0
$470$	−0.392305	−	0.679492i	−0.0180957	−	0.0313426i
$471$		0			0
$472$	−0.637756	−	1.10463i	−0.0293551	−	0.0508446i
$473$	−0.0358984	−	0.0621778i	−0.00165061	−	0.00285894i
$474$		0			0
$475$	−8.60540	−	14.9050i	−0.394843	−	0.683888i
$476$		0			0
$477$		0			0
$478$	−0.464102	−	0.803848i	−0.0212275	−	0.0367671i
$479$	−4.14110			−0.189212			−0.0946060	−	0.995515i	$-0.530159\pi$
$479$	−4.14110			−0.189212			−0.0946060	+	0.995515i	$0.530159\pi$
$480$		0			0
$481$	−13.3843			−0.610270
$482$	−3.13801	+	5.43520i	−0.142933	+	0.247567i
$483$		0			0
$484$	5.46410	+	9.46410i	0.248368	+	0.430186i
$485$	9.39230	+	16.2679i	0.426483	+	0.738690i
$486$		0			0
$487$	1.39230	−	2.41154i	0.0630914	−	0.109277i	−0.832754	−	0.553643i	$-0.813237\pi$
$487$	1.39230	−	2.41154i	0.0630914	−	0.109277i	0.895846	+	0.444365i	$0.146571\pi$
$488$	6.31319	−	10.9348i	0.285785	−	0.494994i
$489$		0			0
$490$		0			0
$491$	9.69615	−	16.7942i	0.437581	−	0.757913i	−0.559921	−	0.828546i	$-0.689169\pi$
$491$	9.69615	−	16.7942i	0.437581	−	0.757913i	0.997502	+	0.0706330i	$0.0225019\pi$
$492$		0			0
$493$	−27.3233			−1.23058
$494$	3.92820	−	6.80385i	0.176738	−	0.306120i
$495$		0			0
$496$	−6.69213			−0.300486
$497$		0			0
$498$		0			0
$499$	33.3923			1.49484			0.747422	−	0.664349i	$-0.231291\pi$
$499$	33.3923			1.49484			0.747422	+	0.664349i	$0.231291\pi$
$500$	−4.62158	−	8.00481i	−0.206683	−	0.357986i
$501$		0			0
$502$	0.397520	−	0.688524i	0.0177422	−	0.0307303i
$503$	−12.3490			−0.550614			−0.275307	−	0.961356i	$-0.588780\pi$
$503$	−12.3490			−0.550614			−0.275307	+	0.961356i	$0.588780\pi$
$504$		0			0
$505$	5.07180			0.225692
$506$	−0.732051	+	1.26795i	−0.0325436	+	0.0563672i
$507$		0			0
$508$	−6.73205	−	11.6603i	−0.298686	−	0.517340i
$509$	21.5921			0.957055			0.478527	−	0.878073i	$-0.341171\pi$
$509$	21.5921			0.957055			0.478527	+	0.878073i	$0.341171\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	5.01910	−	8.69333i	0.221383	−	0.383446i
$515$	12.7846			0.563357
$516$		0			0
$517$	−0.101536	+	0.175865i	−0.00446555	+	0.00773455i
$518$		0			0
$519$		0			0
$520$	0.928203	−	1.60770i	0.0407044	−	0.0705021i
$521$	16.8876	−	29.2502i	0.739860	−	1.28147i	−0.212699	−	0.977118i	$-0.568225\pi$
$521$	16.8876	−	29.2502i	0.739860	−	1.28147i	0.952558	−	0.304357i	$-0.0984414\pi$
$522$		0			0
$523$	10.3664	+	17.9551i	0.453289	+	0.785120i	0.998588	−	0.0531215i	$-0.0169170\pi$
$523$	10.3664	+	17.9551i	0.453289	+	0.785120i	−0.545299	+	0.838242i	$0.683584\pi$
$524$	−5.46739	−	9.46979i	−0.238844	−	0.413690i
$525$		0			0
$526$	4.26795	−	7.39230i	0.186091	−	0.322320i
$527$	45.7128			1.99128
$528$		0			0
$529$	6.85641			0.298105
$530$	5.65685	+	9.79796i	0.245718	+	0.425596i
$531$		0			0
$532$		0			0
$533$	−7.73205	−	13.3923i	−0.334912	−	0.580085i
$534$		0			0
$535$	9.00292	+	15.5935i	0.389230	+	0.674166i
$536$	6.23205	+	10.7942i	0.269184	+	0.466240i
$537$		0			0
$538$	−2.82843	−	4.89898i	−0.121942	−	0.211210i
$539$		0			0
$540$		0			0
$541$	−7.66025	−	13.2679i	−0.329340	−	0.570434i	0.653041	−	0.757323i	$-0.273493\pi$
$541$	−7.66025	−	13.2679i	−0.329340	−	0.570434i	−0.982381	+	0.186889i	$0.940160\pi$
$542$	13.1069			0.562988
$543$		0			0
$544$	6.83083			0.292869
$545$	2.55103	−	4.41851i	0.109274	−	0.189268i
$546$		0			0
$547$	−17.1865	−	29.7679i	−0.734843	−	1.27279i	−0.954792	−	0.297274i	$-0.903922\pi$
$547$	−17.1865	−	29.7679i	−0.734843	−	1.27279i	0.219949	−	0.975511i	$-0.429411\pi$
$548$	4.33013	+	7.50000i	0.184974	+	0.320384i
$549$		0			0
$550$	−0.526279	+	0.911543i	−0.0224406	+	0.0388683i
$551$	8.76268	−	15.1774i	0.373303	−	0.646579i
$552$		0			0
$553$		0			0
$554$	15.7321	−	27.2487i	0.668391	−	1.15769i
$555$		0			0
$556$	−0.795040			−0.0337172
$557$	−3.46410	+	6.00000i	−0.146779	+	0.254228i	−0.930035	−	0.367471i	$-0.880224\pi$
$557$	−3.46410	+	6.00000i	−0.146779	+	0.254228i	0.783256	+	0.621699i	$0.213557\pi$
$558$		0			0
$559$	−0.480473			−0.0203219
$560$		0			0
$561$		0			0
$562$	17.8564			0.753227
$563$	9.12304	+	15.8016i	0.384490	+	0.665957i	0.991698	−	0.128586i	$-0.0410439\pi$
$563$	9.12304	+	15.8016i	0.384490	+	0.665957i	−0.607208	+	0.794543i	$0.707711\pi$
$564$		0			0
$565$	3.58630	−	6.21166i	0.150877	−	0.261326i
$566$	−15.0759			−0.633686
$567$		0			0
$568$	9.46410			0.397105
$569$	−12.8923	+	22.3301i	−0.540474	+	0.936128i	0.458403	+	0.888744i	$0.348422\pi$
$569$	−12.8923	+	22.3301i	−0.540474	+	0.936128i	−0.998877	+	0.0473833i	$0.984912\pi$
$570$		0			0
$571$	16.5263	+	28.6244i	0.691603	+	1.19789i	0.971312	+	0.237807i	$0.0764286\pi$
$571$	16.5263	+	28.6244i	0.691603	+	1.19789i	−0.279709	+	0.960085i	$0.590238\pi$
$572$	−0.480473			−0.0200896
$573$		0			0
$574$		0			0
$575$	21.4641			0.895115
$576$		0			0
$577$	−13.7446	+	23.8064i	−0.572196	+	0.991072i	0.424144	+	0.905595i	$0.360575\pi$
$577$	−13.7446	+	23.8064i	−0.572196	+	0.991072i	−0.996340	+	0.0854776i	$0.972758\pi$
$578$	−29.6603			−1.23370
$579$		0			0
$580$	2.07055	−	3.58630i	0.0859750	−	0.148913i
$581$		0			0
$582$		0			0
$583$	1.46410	−	2.53590i	0.0606369	−	0.105026i
$584$	−2.70831	+	4.69093i	−0.112071	+	0.194112i
$585$		0			0
$586$	−4.62158	−	8.00481i	−0.190916	−	0.330676i
$587$	20.9408	+	36.2705i	0.864319	+	1.49704i	0.867722	+	0.497049i	$0.165583\pi$
$587$	20.9408	+	36.2705i	0.864319	+	1.49704i	−0.00340370	+	0.999994i	$0.501083\pi$
$588$		0			0
$589$	−14.6603	+	25.3923i	−0.604065	+	1.04627i
$590$	−1.32051			−0.0543645
$591$		0			0
$592$	7.46410			0.306773
$593$	−8.43451	−	14.6090i	−0.346364	−	0.599920i	0.639237	−	0.769010i	$-0.279250\pi$
$593$	−8.43451	−	14.6090i	−0.346364	−	0.599920i	−0.985601	+	0.169090i	$0.945917\pi$
$594$		0			0
$595$		0			0
$596$	11.4641	+	19.8564i	0.469588	+	0.813350i
$597$		0			0
$598$	4.89898	+	8.48528i	0.200334	+	0.346989i
$599$	2.39230	+	4.14359i	0.0977469	+	0.169303i	0.910752	−	0.412954i	$-0.135503\pi$
$599$	2.39230	+	4.14359i	0.0977469	+	0.169303i	−0.813005	+	0.582257i	$0.802170\pi$
$600$		0			0
$601$	−1.67303	−	2.89778i	−0.0682444	−	0.118203i	0.829884	−	0.557936i	$-0.188406\pi$
$601$	−1.67303	−	2.89778i	−0.0682444	−	0.118203i	−0.898129	+	0.439733i	$0.855073\pi$
$602$		0			0
$603$		0			0
$604$	−9.19615	−	15.9282i	−0.374186	−	0.648109i
$605$	11.3137			0.459968
$606$		0			0
$607$	2.27362			0.0922836			0.0461418	−	0.998935i	$-0.485307\pi$
$607$	2.27362			0.0922836			0.0461418	+	0.998935i	$0.485307\pi$
$608$	−2.19067	+	3.79435i	−0.0888434	+	0.153881i
$609$		0			0
$610$	−6.53590	−	11.3205i	−0.264631	−	0.458354i
$611$	0.679492	+	1.17691i	0.0274893	+	0.0476129i
$612$		0			0
$613$	−12.4641	+	21.5885i	−0.503420	+	0.871950i	0.496572	+	0.867996i	$0.334592\pi$
$613$	−12.4641	+	21.5885i	−0.503420	+	0.871950i	−0.999992	+	0.00395396i	$0.998741\pi$
$614$	−0.586988	+	1.01669i	−0.0236889	+	0.0410304i
$615$		0			0
$616$		0			0
$617$	−1.57180	+	2.72243i	−0.0632782	+	0.109601i	−0.895929	−	0.444197i	$-0.853489\pi$
$617$	−1.57180	+	2.72243i	−0.0632782	+	0.109601i	0.832651	+	0.553798i	$0.186822\pi$
$618$		0			0
$619$	31.7047			1.27432			0.637159	−	0.770732i	$-0.280109\pi$
$619$	31.7047			1.27432			0.637159	+	0.770732i	$0.280109\pi$
$620$	−3.46410	+	6.00000i	−0.139122	+	0.240966i
$621$		0			0
$622$	7.45001			0.298718
$623$		0			0
$624$		0			0
$625$	10.0718			0.402872
$626$	−3.13801	−	5.43520i	−0.125420	−	0.217234i
$627$		0			0
$628$	4.76028	−	8.24504i	0.189956	−	0.329013i
$629$	−50.9860			−2.03295
$630$		0			0
$631$	−19.7128			−0.784755			−0.392377	−	0.919804i	$-0.628347\pi$
$631$	−19.7128			−0.784755			−0.392377	+	0.919804i	$0.628347\pi$
$632$	4.46410	−	7.73205i	0.177572	−	0.307564i
$633$		0			0
$634$	13.0000	+	22.5167i	0.516296	+	0.894251i
$635$	−13.9391			−0.553155
$636$		0			0
$637$		0			0
$638$	−1.07180			−0.0424328
$639$		0			0
$640$	−0.517638	+	0.896575i	−0.0204614	+	0.0354403i
$641$	−4.07180			−0.160826			−0.0804132	−	0.996762i	$-0.525624\pi$
$641$	−4.07180			−0.160826			−0.0804132	+	0.996762i	$0.525624\pi$
$642$		0			0
$643$	−22.4565	+	38.8959i	−0.885599	+	1.53390i	−0.0405737	+	0.999177i	$0.512919\pi$
$643$	−22.4565	+	38.8959i	−0.885599	+	1.53390i	−0.845025	+	0.534726i	$0.820415\pi$
$644$		0			0
$645$		0			0
$646$	14.9641	−	25.9186i	0.588755	−	1.01975i
$647$	−10.9348	+	18.9396i	−0.429890	+	0.744592i	−0.996863	−	0.0791447i	$-0.974781\pi$
$647$	−10.9348	+	18.9396i	−0.429890	+	0.744592i	0.566973	+	0.823736i	$0.308114\pi$
$648$		0			0
$649$	0.170886	+	0.295984i	0.00670787	+	0.0116184i
$650$	3.52193	+	6.10016i	0.138141	+	0.239268i
$651$		0			0
$652$	6.66025	−	11.5359i	0.260836	−	0.451781i
$653$	−6.00000			−0.234798			−0.117399	−	0.993085i	$-0.537456\pi$
$653$	−6.00000			−0.234798			−0.117399	+	0.993085i	$0.537456\pi$
$654$		0			0
$655$	−11.3205			−0.442329
$656$	4.31199	+	7.46859i	0.168355	+	0.291599i
$657$		0			0
$658$		0			0
$659$	−24.1244	−	41.7846i	−0.939751	−	1.62770i	−0.765934	−	0.642919i	$-0.777723\pi$
$659$	−24.1244	−	41.7846i	−0.939751	−	1.62770i	−0.173818	−	0.984778i	$-0.555610\pi$
$660$		0			0
$661$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$661$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$662$	−5.73205	−	9.92820i	−0.222782	−	0.385871i
$663$		0			0
$664$	3.29530	+	5.70762i	0.127882	+	0.221499i
$665$		0			0
$666$		0			0
$667$	10.9282	+	18.9282i	0.423142	+	0.732903i
$668$	1.51575			0.0586461
$669$		0			0
$670$	12.9038			0.498517
$671$	−1.69161	+	2.92996i	−0.0653041	+	0.113110i
$672$		0			0
$673$	−20.7846	−	36.0000i	−0.801188	−	1.38770i	−0.918835	−	0.394643i	$-0.870868\pi$
$673$	−20.7846	−	36.0000i	−0.801188	−	1.38770i	0.117647	−	0.993055i	$-0.462465\pi$
$674$	−3.50000	−	6.06218i	−0.134815	−	0.233506i
$675$		0			0
$676$	4.89230	−	8.47372i	0.188166	−	0.325912i
$677$	2.68973	−	4.65874i	0.103375	−	0.179050i	−0.809698	−	0.586846i	$-0.800369\pi$
$677$	2.68973	−	4.65874i	0.103375	−	0.179050i	0.913073	+	0.407796i	$0.133703\pi$
$678$		0			0
$679$		0			0
$680$	3.53590	−	6.12436i	0.135596	−	0.234858i
$681$		0			0
$682$	1.79315			0.0686633
$683$	−19.1603	+	33.1865i	−0.733147	+	1.26985i	0.222385	+	0.974959i	$0.428616\pi$
$683$	−19.1603	+	33.1865i	−0.733147	+	1.26985i	−0.955532	+	0.294888i	$0.904718\pi$
$684$		0			0
$685$	8.96575			0.342564
$686$		0			0
$687$		0			0
$688$	0.267949			0.0102155
$689$	−9.79796	−	16.9706i	−0.373273	−	0.646527i
$690$		0			0
$691$	12.1595	−	21.0609i	0.462570	−	0.801194i	−0.536518	−	0.843889i	$-0.680261\pi$
$691$	12.1595	−	21.0609i	0.462570	−	0.801194i	0.999088	+	0.0426942i	$0.0135941\pi$
$692$	6.69213			0.254397
$693$		0			0
$694$	−9.58846			−0.363973
$695$	−0.411543	+	0.712813i	−0.0156107	+	0.0270385i
$696$		0			0
$697$	−29.4545	−	51.0167i	−1.11567	−	1.93239i
$698$	−8.00481			−0.302986
$699$		0			0
$700$		0			0
$701$	20.7846			0.785024			0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$		0			0
$703$	16.3514	−	28.3214i	0.616704	−	1.06816i
$704$	0.267949			0.0100987
$705$		0			0
$706$	12.5063	−	21.6615i	0.470680	−	0.815241i
$707$		0			0
$708$		0			0
$709$	6.19615	−	10.7321i	0.232701	−	0.403051i	−0.725901	−	0.687799i	$-0.758577\pi$
$709$	6.19615	−	10.7321i	0.232701	−	0.403051i	0.958602	+	0.284749i	$0.0919102\pi$
$710$	4.89898	−	8.48528i	0.183855	−	0.318447i
$711$		0			0
$712$	3.53553	+	6.12372i	0.132500	+	0.229496i
$713$	−18.2832	−	31.6675i	−0.684713	−	1.18596i
$714$		0			0
$715$	−0.248711	+	0.430781i	−0.00930128	+	0.0161103i
$716$	−5.07180			−0.189542
$717$		0			0
$718$	7.46410			0.278558
$719$	24.8367	+	43.0184i	0.926251	+	1.60431i	0.789536	+	0.613704i	$0.210321\pi$
$719$	24.8367	+	43.0184i	0.926251	+	1.60431i	0.136716	+	0.990610i	$0.456345\pi$
$720$		0			0
$721$		0			0
$722$	0.0980762	+	0.169873i	0.00365002	+	0.00632202i
$723$		0			0
$724$	−8.48528	−	14.6969i	−0.315353	−	0.546207i
$725$	7.85641	+	13.6077i	0.291780	+	0.505377i
$726$		0			0
$727$	16.3514	+	28.3214i	0.606439	+	1.05038i	0.991822	+	0.127627i	$0.0407361\pi$
$727$	16.3514	+	28.3214i	0.606439	+	1.05038i	−0.385383	+	0.922757i	$0.625931\pi$
$728$		0			0
$729$		0			0
$730$	2.80385	+	4.85641i	0.103775	+	0.179744i
$731$	−1.83032			−0.0676967
$732$		0			0
$733$	−8.00481			−0.295664			−0.147832	−	0.989012i	$-0.547230\pi$
$733$	−8.00481			−0.295664			−0.147832	+	0.989012i	$0.547230\pi$
$734$	−9.28032	+	16.0740i	−0.342543	+	0.593302i
$735$		0			0
$736$	−2.73205	−	4.73205i	−0.100705	−	0.174426i
$737$	−1.66987	−	2.89230i	−0.0615106	−	0.106539i
$738$		0			0
$739$	−3.06218	+	5.30385i	−0.112644	+	0.195105i	−0.916836	−	0.399265i	$-0.869265\pi$
$739$	−3.06218	+	5.30385i	−0.112644	+	0.195105i	0.804191	+	0.594370i	$0.202599\pi$
$740$	3.86370	−	6.69213i	0.142033	−	0.246008i
$741$		0			0
$742$		0			0
$743$	−15.7846	+	27.3397i	−0.579081	+	1.00300i	0.416504	+	0.909134i	$0.363255\pi$
$743$	−15.7846	+	27.3397i	−0.579081	+	1.00300i	−0.995585	+	0.0938641i	$0.970078\pi$
$744$		0			0
$745$	23.7370			0.869657
$746$	−5.39230	+	9.33975i	−0.197426	+	0.341952i
$747$		0			0
$748$	−1.83032			−0.0669230
$749$		0			0
$750$		0			0
$751$	34.7846			1.26931			0.634654	−	0.772796i	$-0.281143\pi$
$751$	34.7846			1.26931			0.634654	+	0.772796i	$0.281143\pi$
$752$	−0.378937	−	0.656339i	−0.0138184	−	0.0239342i
$753$		0			0
$754$	−3.58630	+	6.21166i	−0.130605	+	0.226215i
$755$	−19.0411			−0.692977
$756$		0			0
$757$	19.3205			0.702216			0.351108	−	0.936335i	$-0.385805\pi$
$757$	19.3205			0.702216			0.351108	+	0.936335i	$0.385805\pi$
$758$	6.79423	−	11.7679i	0.246777	−	0.427431i
$759$		0			0
$760$	2.26795	+	3.92820i	0.0822672	+	0.142491i
$761$	−40.2543			−1.45922			−0.729609	−	0.683865i	$-0.760298\pi$
$761$	−40.2543			−1.45922			−0.729609	+	0.683865i	$0.760298\pi$
$762$		0			0
$763$		0			0
$764$	−14.9282			−0.540083
$765$		0			0
$766$	13.6617	−	23.6627i	0.493616	−	0.854968i
$767$	2.28719			0.0825855
$768$		0			0
$769$	19.0919	−	33.0681i	0.688471	−	1.19247i	−0.283862	−	0.958865i	$-0.591616\pi$
$769$	19.0919	−	33.0681i	0.688471	−	1.19247i	0.972332	−	0.233601i	$-0.0750511\pi$
$770$		0			0
$771$		0			0
$772$	−7.52628	+	13.0359i	−0.270877	+	0.469172i
$773$	−19.6975	+	34.1170i	−0.708468	+	1.22710i	0.256957	+	0.966423i	$0.417280\pi$
$773$	−19.6975	+	34.1170i	−0.708468	+	1.22710i	−0.965425	+	0.260680i	$0.916053\pi$
$774$		0			0
$775$	−13.1440	−	22.7661i	−0.472147	−	0.817783i
$776$	9.07227	+	15.7136i	0.325676	+	0.564087i
$777$		0			0
$778$	−4.00000	+	6.92820i	−0.143407	+	0.248388i
$779$	37.7846			1.35377
$780$		0			0
$781$	−2.53590			−0.0907416
$782$	18.6622	+	32.3238i	0.667358	+	1.15590i
$783$		0			0
$784$		0			0
$785$	−4.92820	−	8.53590i	−0.175895	−	0.304659i
$786$		0			0
$787$	3.57270	+	6.18810i	0.127353	+	0.220582i	0.922650	−	0.385638i	$-0.126019\pi$
$787$	3.57270	+	6.18810i	0.127353	+	0.220582i	−0.795297	+	0.606220i	$0.792685\pi$
$788$	−8.46410	−	14.6603i	−0.301521	−	0.522250i
$789$		0			0
$790$	−4.62158	−	8.00481i	−0.164428	−	0.284798i
$791$		0			0
$792$		0			0
$793$	11.3205	+	19.6077i	0.402003	+	0.696290i
$794$	13.1069			0.465145
$795$		0			0
$796$	−26.2880			−0.931755
$797$	18.9396	−	32.8043i	0.670874	−	1.16199i	−0.306782	−	0.951780i	$-0.599252\pi$
$797$	18.9396	−	32.8043i	0.670874	−	1.16199i	0.977657	−	0.210209i	$-0.0674143\pi$
$798$		0			0
$799$	2.58846	+	4.48334i	0.0915730	+	0.158609i
$800$	−1.96410	−	3.40192i	−0.0694415	−	0.120276i
$801$		0			0
$802$	11.8923	−	20.5981i	0.419932	−	0.727343i
$803$	0.725689	−	1.25693i	0.0256090	−	0.0443561i
$804$		0			0
$805$		0			0
$806$	6.00000	−	10.3923i	0.211341	−	0.366053i
$807$		0			0
$808$	4.89898			0.172345
$809$	−14.8660	+	25.7487i	−0.522662	+	0.905276i	0.476991	+	0.878908i	$0.341728\pi$
$809$	−14.8660	+	25.7487i	−0.522662	+	0.905276i	−0.999652	+	0.0263681i	$0.991606\pi$
$810$		0			0
$811$	24.9110			0.874744			0.437372	−	0.899281i	$-0.355909\pi$
$811$	24.9110			0.874744			0.437372	+	0.899281i	$0.355909\pi$
$812$		0			0
$813$		0			0
$814$	−2.00000			−0.0701000
$815$	−6.89520	−	11.9428i	−0.241528	−	0.418339i
$816$		0			0
$817$	0.586988	−	1.01669i	0.0205361	−	0.0355696i
$818$	4.48288			0.156740
$819$		0			0
$820$	8.92820			0.311786
$821$	5.19615	−	9.00000i	0.181347	−	0.314102i	−0.760993	−	0.648761i	$-0.775288\pi$
$821$	5.19615	−	9.00000i	0.181347	−	0.314102i	0.942339	+	0.334659i	$0.108621\pi$
$822$		0			0
$823$	5.39230	+	9.33975i	0.187964	+	0.325563i	0.944571	−	0.328306i	$-0.106478\pi$
$823$	5.39230	+	9.33975i	0.187964	+	0.325563i	−0.756607	+	0.653870i	$0.773145\pi$
$824$	12.3490			0.430197
$825$		0			0
$826$		0			0
$827$	12.0000			0.417281			0.208640	−	0.977992i	$-0.433096\pi$
$827$	12.0000			0.417281			0.208640	+	0.977992i	$0.433096\pi$
$828$		0			0
$829$	3.96524	−	6.86800i	0.137718	−	0.238535i	−0.788914	−	0.614503i	$-0.789356\pi$
$829$	3.96524	−	6.86800i	0.137718	−	0.238535i	0.926633	+	0.375968i	$0.122690\pi$
$830$	6.82309			0.236833
$831$		0			0
$832$	0.896575	−	1.55291i	0.0310832	−	0.0538376i
$833$		0			0
$834$		0			0
$835$	0.784610	−	1.35898i	0.0271525	−	0.0470296i
$836$	0.586988	−	1.01669i	0.0203014	−	0.0351631i
$837$		0			0
$838$	18.0938	+	31.3393i	0.625039	+	1.08260i
$839$	−11.3137	−	19.5959i	−0.390593	−	0.676526i	0.601935	−	0.798545i	$-0.294397\pi$
$839$	−11.3137	−	19.5959i	−0.390593	−	0.676526i	−0.992528	+	0.122019i	$0.961063\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	−7.60770			−0.262178
$843$		0			0
$844$	18.9282			0.651536
$845$	−5.06489	−	8.77264i	−0.174237	−	0.301788i
$846$		0			0
$847$		0			0
$848$	5.46410	+	9.46410i	0.187638	+	0.324999i
$849$		0			0
$850$	13.4164	+	23.2380i	0.460180	+	0.797056i
$851$	20.3923	+	35.3205i	0.699039	+	1.21077i
$852$		0			0
$853$	16.4901	+	28.5617i	0.564610	+	0.977933i	0.997086	+	0.0762876i	$0.0243067\pi$
$853$	16.4901	+	28.5617i	0.564610	+	0.977933i	−0.432476	+	0.901645i	$0.642360\pi$
$854$		0			0
$855$		0			0
$856$	8.69615	+	15.0622i	0.297228	+	0.514815i
$857$	−11.2122			−0.383001			−0.191500	−	0.981493i	$-0.561335\pi$
$857$	−11.2122			−0.383001			−0.191500	+	0.981493i	$0.561335\pi$
$858$		0			0
$859$	41.6042			1.41952			0.709758	−	0.704446i	$-0.248804\pi$
$859$	41.6042			1.41952			0.709758	+	0.704446i	$0.248804\pi$
$860$	0.138701	−	0.240237i	0.00472965	−	0.00819200i
$861$		0			0
$862$	5.07180	+	8.78461i	0.172746	+	0.299205i
$863$	−27.0526	−	46.8564i	−0.920880	−	1.59501i	−0.798057	−	0.602582i	$-0.794139\pi$
$863$	−27.0526	−	46.8564i	−0.920880	−	1.59501i	−0.122823	−	0.992429i	$-0.539195\pi$
$864$		0			0
$865$	3.46410	−	6.00000i	0.117783	−	0.204006i
$866$	9.91808	−	17.1786i	0.337030	−	0.583753i
$867$		0			0
$868$		0			0
$869$	−1.19615	+	2.07180i	−0.0405767	+	0.0702809i
$870$		0			0
$871$	−22.3500			−0.757301
$872$	2.46410	−	4.26795i	0.0834450	−	0.144531i
$873$		0			0
$874$	−23.9401			−0.809786
$875$		0			0
$876$		0			0
$877$	−29.1769			−0.985234			−0.492617	−	0.870246i	$-0.663960\pi$
$877$	−29.1769			−0.985234			−0.492617	+	0.870246i	$0.663960\pi$
$878$	−9.79796	−	16.9706i	−0.330665	−	0.572729i
$879$		0			0
$880$	0.138701	−	0.240237i	0.00467560	−	0.00809838i
$881$	−12.7279			−0.428815			−0.214407	−	0.976744i	$-0.568782\pi$
$881$	−12.7279			−0.428815			−0.214407	+	0.976744i	$0.568782\pi$
$882$		0			0
$883$	14.4641			0.486756			0.243378	−	0.969932i	$-0.421744\pi$
$883$	14.4641			0.486756			0.243378	+	0.969932i	$0.421744\pi$
$884$	−6.12436	+	10.6077i	−0.205984	+	0.356775i
$885$		0			0
$886$	−8.16025	−	14.1340i	−0.274149	−	0.474840i
$887$	53.2596			1.78828			0.894142	−	0.447784i	$-0.147787\pi$
$887$	53.2596			1.78828			0.894142	+	0.447784i	$0.147787\pi$
$888$		0			0
$889$		0			0
$890$	7.32051			0.245384
$891$		0			0
$892$	−3.58630	+	6.21166i	−0.120078	+	0.207982i
$893$	−3.32051			−0.111117
$894$		0			0
$895$	−2.62536	+	4.54725i	−0.0877559	+	0.151998i
$896$		0			0
$897$		0			0
$898$	−11.8923	+	20.5981i	−0.396851	+	0.687367i
$899$	13.3843	−	23.1822i	0.446390	−	0.773170i
$900$		0			0
$901$	−37.3244	−	64.6477i	−1.24345	−	2.15373i
$902$	−1.15539	−	2.00120i	−0.0384704	−	0.0666327i
$903$		0			0
$904$	3.46410	−	6.00000i	0.115214	−	0.199557i
$905$	−17.5692			−0.584021
$906$		0			0
$907$	−5.24871			−0.174281			−0.0871403	−	0.996196i	$-0.527773\pi$
$907$	−5.24871			−0.174281			−0.0871403	+	0.996196i	$0.527773\pi$
$908$	13.8325	+	23.9587i	0.459049	+	0.795097i
$909$		0			0
$910$		0			0
$911$	−16.5359	−	28.6410i	−0.547859	−	0.948919i	−0.998421	−	0.0561742i	$-0.982110\pi$
$911$	−16.5359	−	28.6410i	−0.547859	−	0.948919i	0.450562	−	0.892745i	$-0.351224\pi$
$912$		0			0
$913$	−0.882972	−	1.52935i	−0.0292221	−	0.0506142i
$914$	−15.5263	−	26.8923i	−0.513564	−	0.889518i
$915$		0			0
$916$	0.240237	+	0.416102i	0.00793764	+	0.0137484i
$917$		0			0
$918$		0			0
$919$	−4.53590	−	7.85641i	−0.149625	−	0.259159i	0.781464	−	0.623951i	$-0.214473\pi$
$919$	−4.53590	−	7.85641i	−0.149625	−	0.259159i	−0.931089	+	0.364792i	$0.881140\pi$
$920$	−5.65685			−0.186501
$921$		0			0
$922$	11.0363			0.363461
$923$	−8.48528	+	14.6969i	−0.279296	+	0.483756i
$924$		0			0
$925$	14.6603	+	25.3923i	0.482026	+	0.834894i
$926$	−15.3205	−	26.5359i	−0.503463	−	0.872024i
$927$		0			0
$928$	2.00000	−	3.46410i	0.0656532	−	0.113715i
$929$	−15.4040	+	26.6806i	−0.505390	+	0.875362i	0.494590	+	0.869126i	$0.335318\pi$
$929$	−15.4040	+	26.6806i	−0.505390	+	0.875362i	−0.999981	+	0.00623544i	$0.998015\pi$
$930$		0			0
$931$		0			0
$932$	0.0621778	−	0.107695i	0.00203670	−	0.00352767i
$933$		0			0
$934$	−9.17878			−0.300339
$935$	−0.947441	+	1.64102i	−0.0309846	+	0.0536670i
$936$		0			0
$937$	9.89949			0.323402			0.161701	−	0.986840i	$-0.448302\pi$
$937$	9.89949			0.323402			0.161701	+	0.986840i	$0.448302\pi$
$938$		0			0
$939$		0			0
$940$	−0.784610			−0.0255911
$941$	23.9401	+	41.4655i	0.780425	+	1.35174i	0.931694	+	0.363243i	$0.118330\pi$
$941$	23.9401	+	41.4655i	0.780425	+	1.35174i	−0.151270	+	0.988493i	$0.548336\pi$
$942$		0			0
$943$	−23.5612	+	40.8091i	−0.767257	+	1.32893i
$944$	−1.27551			−0.0415144
$945$		0			0
$946$	−0.0717968			−0.00233431
$947$	−9.06218	+	15.6962i	−0.294481	+	0.510056i	−0.974864	−	0.222800i	$-0.928480\pi$
$947$	−9.06218	+	15.6962i	−0.294481	+	0.510056i	0.680383	+	0.732857i	$0.261814\pi$
$948$		0			0
$949$	−4.85641	−	8.41154i	−0.157646	−	0.273050i
$950$	−17.2108			−0.558392
$951$		0			0
$952$		0			0
$953$	−19.0000			−0.615470			−0.307735	−	0.951472i	$-0.599571\pi$
$953$	−19.0000			−0.615470			−0.307735	+	0.951472i	$0.599571\pi$
$954$		0			0
$955$	−7.72741	+	13.3843i	−0.250053	+	0.433105i
$956$	−0.928203			−0.0300202
$957$		0			0
$958$	−2.07055	+	3.58630i	−0.0668965	+	0.115868i
$959$		0			0
$960$		0			0
$961$	−6.89230	+	11.9378i	−0.222332	+	0.385091i
$962$	−6.69213	+	11.5911i	−0.215763	+	0.373712i
$963$		0			0
$964$	3.13801	+	5.43520i	0.101069	+	0.175056i
$965$	7.79178	+	13.4958i	0.250826	+	0.434444i
$966$		0			0
$967$	23.7846	−	41.1962i	0.764861	−	1.32478i	−0.175458	−	0.984487i	$-0.556141\pi$
$967$	23.7846	−	41.1962i	0.764861	−	1.32478i	0.940320	−	0.340292i	$-0.110526\pi$
$968$	10.9282			0.351246
$969$		0			0
$970$	18.7846			0.603137
$971$	−15.6443	−	27.0967i	−0.502049	−	0.869574i	−0.999997	−	0.00236748i	$-0.999246\pi$
$971$	−15.6443	−	27.0967i	−0.502049	−	0.869574i	0.497948	−	0.867207i	$-0.334087\pi$
$972$		0			0
$973$		0			0
$974$	−1.39230	−	2.41154i	−0.0446123	−	0.0772708i
$975$		0			0
$976$	−6.31319	−	10.9348i	−0.202080	−	0.350013i
$977$	0.990381	+	1.71539i	0.0316851	+	0.0548802i	0.881433	−	0.472309i	$-0.156579\pi$
$977$	0.990381	+	1.71539i	0.0316851	+	0.0548802i	−0.849748	+	0.527189i	$0.823246\pi$
$978$		0			0
$979$	−0.947343	−	1.64085i	−0.0302772	−	0.0524417i
$980$		0			0
$981$		0			0
$982$	−9.69615	−	16.7942i	−0.309417	−	0.535925i
$983$	12.6264			0.402719			0.201360	−	0.979517i	$-0.435464\pi$
$983$	12.6264			0.402719			0.201360	+	0.979517i	$0.435464\pi$
$984$		0			0
$985$	−17.5254			−0.558405
$986$	−13.6617	+	23.6627i	−0.435076	+	0.753574i
$987$		0			0
$988$	−3.92820	−	6.80385i	−0.124973	−	0.216459i
$989$	0.732051	+	1.26795i	0.0232779	+	0.0403184i
$990$		0			0
$991$	−25.1244	+	43.5167i	−0.798101	+	1.38235i	0.122750	+	0.992438i	$0.460829\pi$
$991$	−25.1244	+	43.5167i	−0.798101	+	1.38235i	−0.920851	+	0.389915i	$0.872505\pi$
$992$	−3.34607	+	5.79555i	−0.106238	+	0.184009i
$993$		0			0
$994$		0			0
$995$	−13.6077	+	23.5692i	−0.431393	+	0.747194i
$996$		0			0
$997$	37.6018			1.19086			0.595430	−	0.803407i	$-0.296982\pi$
$997$	37.6018			1.19086			0.595430	+	0.803407i	$0.296982\pi$
$998$	16.6962	−	28.9186i	0.528507	−	0.915402i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.t.361.2		8
3.2	odd	2		882.2.h.q.67.2		8
7.2	even	3		2646.2.e.q.1549.3		8
7.3	odd	6		2646.2.f.r.1765.2		8
7.4	even	3		2646.2.f.r.1765.3		8
7.5	odd	6		2646.2.e.q.1549.2		8
7.6	odd	2	inner	2646.2.h.t.361.3		8
9.2	odd	6		882.2.e.s.655.2		8
9.7	even	3		2646.2.e.q.2125.3		8
21.2	odd	6		882.2.e.s.373.2		8
21.5	even	6		882.2.e.s.373.3		8
21.11	odd	6		882.2.f.q.589.4	yes	8
21.17	even	6		882.2.f.q.589.1	yes	8
21.20	even	2		882.2.h.q.67.3		8
63.2	odd	6		882.2.h.q.79.1		8
63.4	even	3		7938.2.a.ci.1.2		4
63.11	odd	6		882.2.f.q.295.4	yes	8
63.16	even	3	inner	2646.2.h.t.667.2		8
63.20	even	6		882.2.e.s.655.3		8
63.25	even	3		2646.2.f.r.883.3		8
63.31	odd	6		7938.2.a.ci.1.3		4
63.32	odd	6		7938.2.a.cp.1.3		4
63.34	odd	6		2646.2.e.q.2125.2		8
63.38	even	6		882.2.f.q.295.1	✓	8
63.47	even	6		882.2.h.q.79.4		8
63.52	odd	6		2646.2.f.r.883.2		8
63.59	even	6		7938.2.a.cp.1.2		4
63.61	odd	6	inner	2646.2.h.t.667.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.2		8	21.2	odd	6
882.2.e.s.373.3		8	21.5	even	6
882.2.e.s.655.2		8	9.2	odd	6
882.2.e.s.655.3		8	63.20	even	6
882.2.f.q.295.1	✓	8	63.38	even	6
882.2.f.q.295.4	yes	8	63.11	odd	6
882.2.f.q.589.1	yes	8	21.17	even	6
882.2.f.q.589.4	yes	8	21.11	odd	6
882.2.h.q.67.2		8	3.2	odd	2
882.2.h.q.67.3		8	21.20	even	2
882.2.h.q.79.1		8	63.2	odd	6
882.2.h.q.79.4		8	63.47	even	6
2646.2.e.q.1549.2		8	7.5	odd	6
2646.2.e.q.1549.3		8	7.2	even	3
2646.2.e.q.2125.2		8	63.34	odd	6
2646.2.e.q.2125.3		8	9.7	even	3
2646.2.f.r.883.2		8	63.52	odd	6
2646.2.f.r.883.3		8	63.25	even	3
2646.2.f.r.1765.2		8	7.3	odd	6
2646.2.f.r.1765.3		8	7.4	even	3
2646.2.h.t.361.2		8	1.1	even	1	trivial
2646.2.h.t.361.3		8	7.6	odd	2	inner
2646.2.h.t.667.2		8	63.16	even	3	inner
2646.2.h.t.667.3		8	63.61	odd	6	inner
7938.2.a.ci.1.2		4	63.4	even	3
7938.2.a.ci.1.3		4	63.31	odd	6
7938.2.a.cp.1.2		4	63.59	even	6
7938.2.a.cp.1.3		4	63.32	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.03528 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -1.03528 q^{5} -1.00000 q^{8} +(-0.517638 + 0.896575i) q^{10} +0.267949 q^{11} +(0.896575 - 1.55291i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(3.41542 - 5.91567i) q^{17} +(2.19067 + 3.79435i) q^{19} +(0.517638 + 0.896575i) q^{20} +(0.133975 - 0.232051i) q^{22} -5.46410 q^{23} -3.92820 q^{25} +(-0.896575 - 1.55291i) q^{26} +(-2.00000 - 3.46410i) q^{29} +(3.34607 + 5.79555i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-3.41542 - 5.91567i) q^{34} +(-3.73205 - 6.46410i) q^{37} +4.38134 q^{38} +1.03528 q^{40} +(4.31199 - 7.46859i) q^{41} +(-0.133975 - 0.232051i) q^{43} +(-0.133975 - 0.232051i) q^{44} +(-2.73205 + 4.73205i) q^{46} +(-0.378937 + 0.656339i) q^{47} +(-1.96410 + 3.40192i) q^{50} -1.79315 q^{52} +(5.46410 - 9.46410i) q^{53} -0.277401 q^{55} -4.00000 q^{58} +(0.637756 + 1.10463i) q^{59} +(-6.31319 + 10.9348i) q^{61} +6.69213 q^{62} +1.00000 q^{64} +(-0.928203 + 1.60770i) q^{65} +(-6.23205 - 10.7942i) q^{67} -6.83083 q^{68} -9.46410 q^{71} +(2.70831 - 4.69093i) q^{73} -7.46410 q^{74} +(2.19067 - 3.79435i) q^{76} +(-4.46410 + 7.73205i) q^{79} +(0.517638 - 0.896575i) q^{80} +(-4.31199 - 7.46859i) q^{82} +(-3.29530 - 5.70762i) q^{83} +(-3.53590 + 6.12436i) q^{85} -0.267949 q^{86} -0.267949 q^{88} +(-3.53553 - 6.12372i) q^{89} +(2.73205 + 4.73205i) q^{92} +(0.378937 + 0.656339i) q^{94} +(-2.26795 - 3.92820i) q^{95} +(-9.07227 - 15.7136i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8} + 16 q^{11} - 4 q^{16} + 8 q^{22} - 16 q^{23} + 24 q^{25} - 16 q^{29} + 4 q^{32} - 16 q^{37} - 8 q^{43} - 8 q^{44} - 8 q^{46} + 12 q^{50} + 16 q^{53} - 32 q^{58} + 8 q^{64} + 48 q^{65} - 36 q^{67} - 48 q^{71} - 32 q^{74} - 8 q^{79} - 56 q^{85} - 16 q^{86} - 16 q^{88} + 8 q^{92} - 32 q^{95}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 - 8 * q^8 + 16 * q^11 - 4 * q^16 + 8 * q^22 - 16 * q^23 + 24 * q^25 - 16 * q^29 + 4 * q^32 - 16 * q^37 - 8 * q^43 - 8 * q^44 - 8 * q^46 + 12 * q^50 + 16 * q^53 - 32 * q^58 + 8 * q^64 + 48 * q^65 - 36 * q^67 - 48 * q^71 - 32 * q^74 - 8 * q^79 - 56 * q^85 - 16 * q^86 - 16 * q^88 + 8 * q^92 - 32 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more