LMFDB - Embedded newform 2646.2.h.t.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:	$8$
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			361.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	2646.361
Dual form			2646.2.h.t.667.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.86370 q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.86370 q^{5} -1.00000 q^{8} +(-1.93185 + 3.34607i) q^{10} +3.73205 q^{11} +(-3.34607 + 5.79555i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(2.70831 - 4.69093i) q^{17} +(1.48356 + 2.56961i) q^{19} +(1.93185 + 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +1.46410 q^{23} +9.92820 q^{25} +(3.34607 + 5.79555i) q^{26} +(-2.00000 - 3.46410i) q^{29} +(-0.896575 - 1.55291i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.70831 - 4.69093i) q^{34} +(-0.267949 - 0.464102i) q^{37} +2.96713 q^{38} +3.86370 q^{40} +(-0.637756 + 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +(-1.86603 - 3.23205i) q^{44} +(0.732051 - 1.26795i) q^{46} +(5.27792 - 9.14162i) q^{47} +(4.96410 - 8.59808i) q^{50} +6.69213 q^{52} +(-1.46410 + 2.53590i) q^{53} -14.4195 q^{55} -4.00000 q^{58} +(-4.31199 - 7.46859i) q^{59} +(-3.48477 + 6.03579i) q^{61} -1.79315 q^{62} +1.00000 q^{64} +(12.9282 - 22.3923i) q^{65} +(-2.76795 - 4.79423i) q^{67} -5.41662 q^{68} -2.53590 q^{71} +(3.41542 - 5.91567i) q^{73} -0.535898 q^{74} +(1.48356 - 2.56961i) q^{76} +(2.46410 - 4.26795i) q^{79} +(1.93185 - 3.34607i) q^{80} +(0.637756 + 1.10463i) q^{82} +(-8.95215 - 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} -3.73205 q^{86} -3.73205 q^{88} +(3.53553 + 6.12372i) q^{89} +(-0.732051 - 1.26795i) q^{92} +(-5.27792 - 9.14162i) q^{94} +(-5.73205 - 9.92820i) q^{95} +(2.94855 + 5.10703i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−3.86370			−1.72790			−0.863950	−	0.503577i	$-0.832017\pi$
$5$	−3.86370			−1.72790			−0.863950	+	0.503577i	$0.832017\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−1.93185	+	3.34607i	−0.610905	+	1.05812i
$11$	3.73205			1.12526			0.562628	−	0.826710i	$-0.309790\pi$
$11$	3.73205			1.12526			0.562628	+	0.826710i	$0.309790\pi$
$12$		0			0
$13$	−3.34607	+	5.79555i	−0.928032	+	1.60740i	−0.141420	+	0.989950i	$0.545167\pi$
$13$	−3.34607	+	5.79555i	−0.928032	+	1.60740i	−0.786612	+	0.617448i	$0.788167\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.70831	−	4.69093i	0.656861	−	1.13772i	−0.324562	−	0.945864i	$-0.605217\pi$
$17$	2.70831	−	4.69093i	0.656861	−	1.13772i	0.981424	−	0.191853i	$-0.0614497\pi$
$18$		0			0
$19$	1.48356	+	2.56961i	0.340353	+	0.589509i	0.984498	−	0.175395i	$-0.0561201\pi$
$19$	1.48356	+	2.56961i	0.340353	+	0.589509i	−0.644145	+	0.764903i	$0.722787\pi$
$20$	1.93185	+	3.34607i	0.431975	+	0.748203i
$21$		0			0
$22$	1.86603	−	3.23205i	0.397838	−	0.689076i
$23$	1.46410			0.305286			0.152643	−	0.988281i	$-0.451221\pi$
$23$	1.46410			0.305286			0.152643	+	0.988281i	$0.451221\pi$
$24$		0			0
$25$	9.92820			1.98564
$26$	3.34607	+	5.79555i	0.656217	+	1.13660i
$27$		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
$31$	−0.896575	−	1.55291i	−0.161030	−	0.278912i	0.774209	−	0.632931i	$-0.218148\pi$
$31$	−0.896575	−	1.55291i	−0.161030	−	0.278912i	−0.935238	+	0.354019i	$0.884815\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−2.70831	−	4.69093i	−0.464471	−	0.804488i
$35$		0			0
$36$		0			0
$37$	−0.267949	−	0.464102i	−0.0440506	−	0.0762978i	0.843159	−	0.537664i	$-0.180693\pi$
$37$	−0.267949	−	0.464102i	−0.0440506	−	0.0762978i	−0.887210	+	0.461366i	$0.847360\pi$
$38$	2.96713			0.481332
$39$		0			0
$40$	3.86370			0.610905
$41$	−0.637756	+	1.10463i	−0.0996008	+	0.172514i	−0.911519	−	0.411257i	$-0.865090\pi$
$41$	−0.637756	+	1.10463i	−0.0996008	+	0.172514i	0.811919	+	0.583771i	$0.198423\pi$
$42$		0			0
$43$	−1.86603	−	3.23205i	−0.284566	−	0.492883i	0.687938	−	0.725770i	$-0.258516\pi$
$43$	−1.86603	−	3.23205i	−0.284566	−	0.492883i	−0.972504	+	0.232887i	$0.925183\pi$
$44$	−1.86603	−	3.23205i	−0.281314	−	0.487250i
$45$		0			0
$46$	0.732051	−	1.26795i	0.107935	−	0.186949i
$47$	5.27792	−	9.14162i	0.769863	−	1.33344i	−0.167773	−	0.985826i	$-0.553658\pi$
$47$	5.27792	−	9.14162i	0.769863	−	1.33344i	0.937637	−	0.347617i	$-0.113009\pi$
$48$		0			0
$49$		0			0
$50$	4.96410	−	8.59808i	0.702030	−	1.21595i
$51$		0			0
$52$	6.69213			0.928032
$53$	−1.46410	+	2.53590i	−0.201110	+	0.348332i	−0.948886	−	0.315618i	$-0.897788\pi$
$53$	−1.46410	+	2.53590i	−0.201110	+	0.348332i	0.747776	+	0.663951i	$0.231121\pi$
$54$		0			0
$55$	−14.4195			−1.94433
$56$		0			0
$57$		0			0
$58$	−4.00000			−0.525226
$59$	−4.31199	−	7.46859i	−0.561373	−	0.972327i	−0.997377	−	0.0723823i	$-0.976940\pi$
$59$	−4.31199	−	7.46859i	−0.561373	−	0.972327i	0.436004	−	0.899945i	$-0.356394\pi$
$60$		0			0
$61$	−3.48477	+	6.03579i	−0.446179	+	0.772804i	−0.998133	−	0.0610700i	$-0.980549\pi$
$61$	−3.48477	+	6.03579i	−0.446179	+	0.772804i	0.551955	+	0.833874i	$0.313882\pi$
$62$	−1.79315			−0.227730
$63$		0			0
$64$	1.00000			0.125000
$65$	12.9282	−	22.3923i	1.60355	−	2.77742i
$66$		0			0
$67$	−2.76795	−	4.79423i	−0.338159	−	0.585708i	0.645928	−	0.763399i	$-0.276471\pi$
$67$	−2.76795	−	4.79423i	−0.338159	−	0.585708i	−0.984086	+	0.177690i	$0.943137\pi$
$68$	−5.41662			−0.656861
$69$		0			0
$70$		0			0
$71$	−2.53590			−0.300956			−0.150478	−	0.988613i	$-0.548081\pi$
$71$	−2.53590			−0.300956			−0.150478	+	0.988613i	$0.548081\pi$
$72$		0			0
$73$	3.41542	−	5.91567i	0.399744	−	0.692377i	−0.593950	−	0.804502i	$-0.702432\pi$
$73$	3.41542	−	5.91567i	0.399744	−	0.692377i	0.993694	+	0.112125i	$0.0357656\pi$
$74$	−0.535898			−0.0622969
$75$		0			0
$76$	1.48356	−	2.56961i	0.170176	−	0.294754i
$77$		0			0
$78$		0			0
$79$	2.46410	−	4.26795i	0.277233	−	0.480182i	−0.693463	−	0.720492i	$-0.743916\pi$
$79$	2.46410	−	4.26795i	0.277233	−	0.480182i	0.970696	+	0.240310i	$0.0772492\pi$
$80$	1.93185	−	3.34607i	0.215988	−	0.374101i
$81$		0			0
$82$	0.637756	+	1.10463i	0.0704284	+	0.121986i
$83$	−8.95215	−	15.5056i	−0.982626	−	1.70196i	−0.652043	−	0.758182i	$-0.726088\pi$
$83$	−8.95215	−	15.5056i	−0.982626	−	1.70196i	−0.330583	−	0.943777i	$-0.607245\pi$
$84$		0			0
$85$	−10.4641	+	18.1244i	−1.13499	+	1.96586i
$86$	−3.73205			−0.402437
$87$		0			0
$88$	−3.73205			−0.397838
$89$	3.53553	+	6.12372i	0.374766	+	0.649113i	0.990292	−	0.139003i	$-0.0443898\pi$
$89$	3.53553	+	6.12372i	0.374766	+	0.649113i	−0.615526	+	0.788116i	$0.711056\pi$
$90$		0			0
$91$		0			0
$92$	−0.732051	−	1.26795i	−0.0763216	−	0.132193i
$93$		0			0
$94$	−5.27792	−	9.14162i	−0.544376	−	0.942886i
$95$	−5.73205	−	9.92820i	−0.588096	−	1.01861i
$96$		0			0
$97$	2.94855	+	5.10703i	0.299379	+	0.518540i	0.975994	−	0.217797i	$-0.0698870\pi$
$97$	2.94855	+	5.10703i	0.299379	+	0.518540i	−0.676615	+	0.736337i	$0.736554\pi$
$98$		0			0
$99$		0			0
$100$	−4.96410	−	8.59808i	−0.496410	−	0.859808i
$101$	−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
$103$	7.45001			0.734071			0.367035	−	0.930207i	$-0.380373\pi$
$103$	7.45001			0.734071			0.367035	+	0.930207i	$0.380373\pi$
$104$	3.34607	−	5.79555i	0.328109	−	0.568301i
$105$		0			0
$106$	1.46410	+	2.53590i	0.142206	+	0.246308i
$107$	1.69615	+	2.93782i	0.163973	+	0.284010i	0.936290	−	0.351227i	$-0.114236\pi$
$107$	1.69615	+	2.93782i	0.163973	+	0.284010i	−0.772317	+	0.635237i	$0.780902\pi$
$108$		0			0
$109$	4.46410	−	7.73205i	0.427583	−	0.740596i	−0.569074	−	0.822286i	$-0.692698\pi$
$109$	4.46410	−	7.73205i	0.427583	−	0.740596i	0.996658	+	0.0816899i	$0.0260317\pi$
$110$	−7.20977	+	12.4877i	−0.687424	+	1.19065i
$111$		0			0
$112$		0			0
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	−0.655814	−	0.754923i	$-0.727674\pi$
$113$	3.46410	−	6.00000i	0.325875	−	0.564433i	0.981689	+	0.190490i	$0.0610077\pi$
$114$		0			0
$115$	−5.65685			−0.527504
$116$	−2.00000	+	3.46410i	−0.185695	+	0.321634i
$117$		0			0
$118$	−8.62398			−0.793902
$119$		0			0
$120$		0			0
$121$	2.92820			0.266200
$122$	3.48477	+	6.03579i	0.315496	+	0.546455i
$123$		0			0
$124$	−0.896575	+	1.55291i	−0.0805149	+	0.139456i
$125$	−19.0411			−1.70309
$126$		0			0
$127$	6.53590			0.579967			0.289984	−	0.957032i	$-0.406350\pi$
$127$	6.53590			0.579967			0.289984	+	0.957032i	$0.406350\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−12.9282	−	22.3923i	−1.13388	−	1.96394i
$131$	−6.03579			−0.527350			−0.263675	−	0.964612i	$-0.584935\pi$
$131$	−6.03579			−0.527350			−0.263675	+	0.964612i	$0.584935\pi$
$132$		0			0
$133$		0			0
$134$	−5.53590			−0.478229
$135$		0			0
$136$	−2.70831	+	4.69093i	−0.232236	+	0.402244i
$137$	8.66025			0.739895			0.369948	−	0.929053i	$-0.379376\pi$
$137$	8.66025			0.739895			0.369948	+	0.929053i	$0.379376\pi$
$138$		0			0
$139$	8.17569	−	14.1607i	0.693453	−	1.20110i	−0.277246	−	0.960799i	$-0.589422\pi$
$139$	8.17569	−	14.1607i	0.693453	−	1.20110i	0.970699	−	0.240297i	$-0.0772450\pi$
$140$		0			0
$141$		0			0
$142$	−1.26795	+	2.19615i	−0.106404	+	0.184297i
$143$	−12.4877	+	21.6293i	−1.04427	+	1.80873i
$144$		0			0
$145$	7.72741	+	13.3843i	0.641726	+	1.11150i
$146$	−3.41542	−	5.91567i	−0.282662	−	0.489585i
$147$		0			0
$148$	−0.267949	+	0.464102i	−0.0220253	+	0.0381489i
$149$	−9.07180			−0.743191			−0.371595	−	0.928395i	$-0.621189\pi$
$149$	−9.07180			−0.743191			−0.371595	+	0.928395i	$0.621189\pi$
$150$		0			0
$151$	−2.39230			−0.194683			−0.0973415	−	0.995251i	$-0.531034\pi$
$151$	−2.39230			−0.194683			−0.0973415	+	0.995251i	$0.531034\pi$
$152$	−1.48356	−	2.56961i	−0.120333	−	0.208423i
$153$		0			0
$154$		0			0
$155$	3.46410	+	6.00000i	0.278243	+	0.481932i
$156$		0			0
$157$	−2.31079	−	4.00240i	−0.184421	−	0.319427i	0.758960	−	0.651137i	$-0.225708\pi$
$157$	−2.31079	−	4.00240i	−0.184421	−	0.319427i	−0.943381	+	0.331710i	$0.892374\pi$
$158$	−2.46410	−	4.26795i	−0.196033	−	0.339540i
$159$		0			0
$160$	−1.93185	−	3.34607i	−0.152726	−	0.264530i
$161$		0			0
$162$		0			0
$163$	−10.6603	−	18.4641i	−0.834976	−	1.44622i	−0.894050	−	0.447966i	$-0.852148\pi$
$163$	−10.6603	−	18.4641i	−0.834976	−	1.44622i	0.0590748	−	0.998254i	$-0.481185\pi$
$164$	1.27551			0.0996008
$165$		0			0
$166$	−17.9043			−1.38964
$167$	10.5558	−	18.2832i	0.816835	−	1.41480i	−0.0911679	−	0.995836i	$-0.529060\pi$
$167$	10.5558	−	18.2832i	0.816835	−	1.41480i	0.908003	−	0.418964i	$-0.137607\pi$
$168$		0			0
$169$	−15.8923	−	27.5263i	−1.22248	−	2.11741i
$170$	10.4641	+	18.1244i	0.802560	+	1.39007i
$171$		0			0
$172$	−1.86603	+	3.23205i	−0.142283	+	0.246442i
$173$	0.896575	−	1.55291i	0.0681654	−	0.118066i	−0.829928	−	0.557870i	$-0.811619\pi$
$173$	0.896575	−	1.55291i	0.0681654	−	0.118066i	0.898094	+	0.439804i	$0.144952\pi$
$174$		0			0
$175$		0			0
$176$	−1.86603	+	3.23205i	−0.140657	+	0.243625i
$177$		0			0
$178$	7.07107			0.529999
$179$	9.46410	−	16.3923i	0.707380	−	1.22522i	−0.258446	−	0.966026i	$-0.583210\pi$
$179$	9.46410	−	16.3923i	0.707380	−	1.22522i	0.965826	−	0.259193i	$-0.0834564\pi$
$180$		0			0
$181$	−16.9706			−1.26141			−0.630706	−	0.776022i	$-0.717235\pi$
$181$	−16.9706			−1.26141			−0.630706	+	0.776022i	$0.717235\pi$
$182$		0			0
$183$		0			0
$184$	−1.46410			−0.107935
$185$	1.03528	+	1.79315i	0.0761150	+	0.131835i
$186$		0			0
$187$	10.1075	−	17.5068i	0.739137	−	1.28022i
$188$	−10.5558			−0.769863
$189$		0			0
$190$	−11.4641			−0.831693
$191$	0.535898	−	0.928203i	0.0387762	−	0.0671624i	−0.845986	−	0.533205i	$-0.820987\pi$
$191$	0.535898	−	0.928203i	0.0387762	−	0.0671624i	0.884762	+	0.466043i	$0.154321\pi$
$192$		0			0
$193$	11.5263	+	19.9641i	0.829680	+	1.43705i	0.898290	+	0.439404i	$0.144810\pi$
$193$	11.5263	+	19.9641i	0.829680	+	1.43705i	−0.0686098	+	0.997644i	$0.521856\pi$
$194$	5.89709			0.423386
$195$		0			0
$196$		0			0
$197$	3.07180			0.218856			0.109428	−	0.993995i	$-0.465098\pi$
$197$	3.07180			0.218856			0.109428	+	0.993995i	$0.465098\pi$
$198$		0			0
$199$	8.90138	−	15.4176i	0.631002	−	1.09293i	−0.356345	−	0.934355i	$-0.615977\pi$
$199$	8.90138	−	15.4176i	0.631002	−	1.09293i	0.987347	−	0.158574i	$-0.0506895\pi$
$200$	−9.92820			−0.702030
$201$		0			0
$202$	−2.44949	+	4.24264i	−0.172345	+	0.298511i
$203$		0			0
$204$		0			0
$205$	2.46410	−	4.26795i	0.172100	−	0.298087i
$206$	3.72500	−	6.45189i	0.259533	−	0.449525i
$207$		0			0
$208$	−3.34607	−	5.79555i	−0.232008	−	0.401849i
$209$	5.53674	+	9.58991i	0.382984	+	0.663348i
$210$		0			0
$211$	−2.53590	+	4.39230i	−0.174578	+	0.302379i	−0.940015	−	0.341132i	$-0.889190\pi$
$211$	−2.53590	+	4.39230i	−0.174578	+	0.302379i	0.765437	+	0.643511i	$0.222523\pi$
$212$	2.92820			0.201110
$213$		0			0
$214$	3.39230			0.231893
$215$	7.20977	+	12.4877i	0.491702	+	0.851653i
$216$		0			0
$217$		0			0
$218$	−4.46410	−	7.73205i	−0.302347	−	0.523681i
$219$		0			0
$220$	7.20977	+	12.4877i	0.486082	+	0.841920i
$221$	18.1244	+	31.3923i	1.21918	+	2.11167i
$222$		0			0
$223$	13.3843	+	23.1822i	0.896276	+	1.55240i	0.832217	+	0.554450i	$0.187071\pi$
$223$	13.3843	+	23.1822i	0.896276	+	1.55240i	0.0640595	+	0.997946i	$0.479595\pi$
$224$		0			0
$225$		0			0
$226$	−3.46410	−	6.00000i	−0.230429	−	0.399114i
$227$	10.5187			0.698149			0.349074	−	0.937095i	$-0.386496\pi$
$227$	10.5187			0.698149			0.349074	+	0.937095i	$0.386496\pi$
$228$		0			0
$229$	24.9754			1.65042			0.825209	−	0.564827i	$-0.191057\pi$
$229$	24.9754			1.65042			0.825209	+	0.564827i	$0.191057\pi$
$230$	−2.82843	+	4.89898i	−0.186501	+	0.323029i
$231$		0			0
$232$	2.00000	+	3.46410i	0.131306	+	0.227429i
$233$	−12.0622	−	20.8923i	−0.790220	−	1.36870i	−0.925831	−	0.377938i	$-0.876633\pi$
$233$	−12.0622	−	20.8923i	−0.790220	−	1.36870i	0.135611	−	0.990762i	$-0.456700\pi$
$234$		0			0
$235$	−20.3923	+	35.3205i	−1.33025	+	2.30406i
$236$	−4.31199	+	7.46859i	−0.280687	+	0.486164i
$237$		0			0
$238$		0			0
$239$	−6.46410	+	11.1962i	−0.418128	+	0.724219i	−0.995751	−	0.0920846i	$-0.970647\pi$
$239$	−6.46410	+	11.1962i	−0.418128	+	0.724219i	0.577623	+	0.816304i	$0.303980\pi$
$240$		0			0
$241$	23.4225			1.50877			0.754387	−	0.656430i	$-0.227934\pi$
$241$	23.4225			1.50877			0.754387	+	0.656430i	$0.227934\pi$
$242$	1.46410	−	2.53590i	0.0941160	−	0.163014i
$243$		0			0
$244$	6.96953			0.446179
$245$		0			0
$246$		0			0
$247$	−19.8564			−1.26343
$248$	0.896575	+	1.55291i	0.0569326	+	0.0986102i
$249$		0			0
$250$	−9.52056	+	16.4901i	−0.602133	+	1.04292i
$251$	16.3514			1.03209			0.516045	−	0.856561i	$-0.327404\pi$
$251$	16.3514			1.03209			0.516045	+	0.856561i	$0.327404\pi$
$252$		0			0
$253$	5.46410			0.343525
$254$	3.26795	−	5.66025i	0.205049	−	0.355156i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−2.68973			−0.167781			−0.0838903	−	0.996475i	$-0.526735\pi$
$257$	−2.68973			−0.167781			−0.0838903	+	0.996475i	$0.526735\pi$
$258$		0			0
$259$		0			0
$260$	−25.8564			−1.60355
$261$		0			0
$262$	−3.01790	+	5.22715i	−0.186446	+	0.322934i
$263$	15.4641			0.953557			0.476779	−	0.879023i	$-0.341804\pi$
$263$	15.4641			0.953557			0.476779	+	0.879023i	$0.341804\pi$
$264$		0			0
$265$	5.65685	−	9.79796i	0.347498	−	0.601884i
$266$		0			0
$267$		0			0
$268$	−2.76795	+	4.79423i	−0.169079	+	0.292854i
$269$	−2.82843	+	4.89898i	−0.172452	+	0.298696i	−0.939277	−	0.343161i	$-0.888502\pi$
$269$	−2.82843	+	4.89898i	−0.172452	+	0.298696i	0.766824	+	0.641857i	$0.221836\pi$
$270$		0			0
$271$	−9.00292	−	15.5935i	−0.546888	−	0.947239i	−0.998485	−	0.0550165i	$-0.982479\pi$
$271$	−9.00292	−	15.5935i	−0.546888	−	0.947239i	0.451597	−	0.892222i	$-0.350854\pi$
$272$	2.70831	+	4.69093i	0.164215	+	0.284429i
$273$		0			0
$274$	4.33013	−	7.50000i	0.261593	−	0.453092i
$275$	37.0526			2.23435
$276$		0			0
$277$	24.5359			1.47422			0.737110	−	0.675773i	$-0.236190\pi$
$277$	24.5359			1.47422			0.737110	+	0.675773i	$0.236190\pi$
$278$	−8.17569	−	14.1607i	−0.490346	−	0.849303i
$279$		0			0
$280$		0			0
$281$	−4.92820	−	8.53590i	−0.293992	−	0.509209i	0.680758	−	0.732508i	$-0.261651\pi$
$281$	−4.92820	−	8.53590i	−0.293992	−	0.509209i	−0.974750	+	0.223299i	$0.928317\pi$
$282$		0			0
$283$	−4.70951	−	8.15711i	−0.279951	−	0.484890i	0.691421	−	0.722452i	$-0.256985\pi$
$283$	−4.70951	−	8.15711i	−0.279951	−	0.484890i	−0.971372	+	0.237562i	$0.923652\pi$
$284$	1.26795	+	2.19615i	0.0752389	+	0.130318i
$285$		0			0
$286$	12.4877	+	21.6293i	0.738412	+	1.27897i
$287$		0			0
$288$		0			0
$289$	−6.16987	−	10.6865i	−0.362934	−	0.628620i
$290$	15.4548			0.907538
$291$		0			0
$292$	−6.83083			−0.399744
$293$	−9.52056	+	16.4901i	−0.556197	+	0.963361i	0.441612	+	0.897206i	$0.354407\pi$
$293$	−9.52056	+	16.4901i	−0.556197	+	0.963361i	−0.997809	+	0.0661554i	$0.978927\pi$
$294$		0			0
$295$	16.6603	+	28.8564i	0.969997	+	1.68008i
$296$	0.267949	+	0.464102i	0.0155742	+	0.0269754i
$297$		0			0
$298$	−4.53590	+	7.85641i	−0.262758	+	0.455109i
$299$	−4.89898	+	8.48528i	−0.283315	+	0.490716i
$300$		0			0
$301$		0			0
$302$	−1.19615	+	2.07180i	−0.0688308	+	0.119219i
$303$		0			0
$304$	−2.96713			−0.170176
$305$	13.4641	−	23.3205i	0.770952	−	1.33533i
$306$		0			0
$307$	−11.0735			−0.631996			−0.315998	−	0.948760i	$-0.602339\pi$
$307$	−11.0735			−0.631996			−0.315998	+	0.948760i	$0.602339\pi$
$308$		0			0
$309$		0			0
$310$	6.92820			0.393496
$311$	−6.17449	−	10.6945i	−0.350123	−	0.606431i	0.636147	−	0.771568i	$-0.280527\pi$
$311$	−6.17449	−	10.6945i	−0.350123	−	0.606431i	−0.986271	+	0.165136i	$0.947194\pi$
$312$		0			0
$313$	−11.7112	+	20.2844i	−0.661958	+	1.14654i	0.318143	+	0.948043i	$0.396941\pi$
$313$	−11.7112	+	20.2844i	−0.661958	+	1.14654i	−0.980101	+	0.198502i	$0.936392\pi$
$314$	−4.62158			−0.260811
$315$		0			0
$316$	−4.92820			−0.277233
$317$	−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
$319$	−7.46410	−	12.9282i	−0.417909	−	0.723840i
$320$	−3.86370			−0.215988
$321$		0			0
$322$		0			0
$323$	16.0718			0.894259
$324$		0			0
$325$	−33.2204	+	57.5394i	−1.84274	+	3.19171i
$326$	−21.3205			−1.18083
$327$		0			0
$328$	0.637756	−	1.10463i	0.0352142	−	0.0609928i
$329$		0			0
$330$		0			0
$331$	2.26795	−	3.92820i	0.124658	−	0.215914i	−0.796941	−	0.604057i	$-0.793550\pi$
$331$	2.26795	−	3.92820i	0.124658	−	0.215914i	0.921599	+	0.388143i	$0.126883\pi$
$332$	−8.95215	+	15.5056i	−0.491313	+	0.850979i
$333$		0			0
$334$	−10.5558	−	18.2832i	−0.577590	−	1.00041i
$335$	10.6945	+	18.5235i	0.584305	+	1.01205i
$336$		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	$0.105605\pi$
$338$	−31.7846			−1.72885
$339$		0			0
$340$	20.9282			1.13499
$341$	−3.34607	−	5.79555i	−0.181200	−	0.313847i
$342$		0			0
$343$		0			0
$344$	1.86603	+	3.23205i	0.100609	+	0.174261i
$345$		0			0
$346$	−0.896575	−	1.55291i	−0.0482002	−	0.0834852i
$347$	10.7942	+	18.6962i	0.579465	+	1.00366i	0.995541	+	0.0943323i	$0.0300716\pi$
$347$	10.7942	+	18.6962i	0.579465	+	1.00366i	−0.416076	+	0.909330i	$0.636595\pi$
$348$		0			0
$349$	−8.24504	−	14.2808i	−0.441347	−	0.764436i	0.556443	−	0.830886i	$-0.312166\pi$
$349$	−8.24504	−	14.2808i	−0.441347	−	0.764436i	−0.997790	+	0.0664504i	$0.978833\pi$
$350$		0			0
$351$		0			0
$352$	1.86603	+	3.23205i	0.0994595	+	0.172269i
$353$	26.4267			1.40655			0.703277	−	0.710916i	$-0.251719\pi$
$353$	26.4267			1.40655			0.703277	+	0.710916i	$0.251719\pi$
$354$		0			0
$355$	9.79796			0.520022
$356$	3.53553	−	6.12372i	0.187383	−	0.324557i
$357$		0			0
$358$	−9.46410	−	16.3923i	−0.500193	−	0.866360i
$359$	0.267949	+	0.464102i	0.0141418	+	0.0244943i	0.873010	−	0.487703i	$-0.162165\pi$
$359$	0.267949	+	0.464102i	0.0141418	+	0.0244943i	−0.858868	+	0.512197i	$0.828832\pi$
$360$		0			0
$361$	5.09808	−	8.83013i	0.268320	−	0.464744i
$362$	−8.48528	+	14.6969i	−0.445976	+	0.772454i
$363$		0			0
$364$		0			0
$365$	−13.1962	+	22.8564i	−0.690718	+	1.19636i
$366$		0			0
$367$	−15.7322			−0.821215			−0.410607	−	0.911812i	$-0.634683\pi$
$367$	−15.7322			−0.821215			−0.410607	+	0.911812i	$0.634683\pi$
$368$	−0.732051	+	1.26795i	−0.0381608	+	0.0660964i
$369$		0			0
$370$	2.07055			0.107643
$371$		0			0
$372$		0			0
$373$	30.7846			1.59397			0.796983	−	0.604001i	$-0.206428\pi$
$373$	30.7846			1.59397			0.796983	+	0.604001i	$0.206428\pi$
$374$	−10.1075	−	17.5068i	−0.522649	−	0.905254i
$375$		0			0
$376$	−5.27792	+	9.14162i	−0.272188	+	0.471443i
$377$	26.7685			1.37865
$378$		0			0
$379$	−17.5885			−0.903458			−0.451729	−	0.892155i	$-0.649193\pi$
$379$	−17.5885			−0.903458			−0.451729	+	0.892155i	$0.649193\pi$
$380$	−5.73205	+	9.92820i	−0.294048	+	0.509306i
$381$		0			0
$382$	−0.535898	−	0.928203i	−0.0274189	−	0.0474910i
$383$	21.6665			1.10710			0.553552	−	0.832814i	$-0.313272\pi$
$383$	21.6665			1.10710			0.553552	+	0.832814i	$0.313272\pi$
$384$		0			0
$385$		0			0
$386$	23.0526			1.17334
$387$		0			0
$388$	2.94855	−	5.10703i	0.149690	−	0.259270i
$389$	−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
$391$	3.96524	−	6.86800i	0.200531	−	0.347329i
$392$		0			0
$393$		0			0
$394$	1.53590	−	2.66025i	0.0773774	−	0.134022i
$395$	−9.52056	+	16.4901i	−0.479031	+	0.829706i
$396$		0			0
$397$	−9.00292	−	15.5935i	−0.451844	−	0.782616i	0.546657	−	0.837357i	$-0.315900\pi$
$397$	−9.00292	−	15.5935i	−0.451844	−	0.782616i	−0.998501	+	0.0547406i	$0.982567\pi$
$398$	−8.90138	−	15.4176i	−0.446186	−	0.772817i
$399$		0			0
$400$	−4.96410	+	8.59808i	−0.248205	+	0.429904i
$401$	−17.7846			−0.888121			−0.444061	−	0.895997i	$-0.646462\pi$
$401$	−17.7846			−0.888121			−0.444061	+	0.895997i	$0.646462\pi$
$402$		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
$409$	−8.36516	−	14.4889i	−0.413631	−	0.716429i	0.581653	−	0.813437i	$-0.302406\pi$
$409$	−8.36516	−	14.4889i	−0.413631	−	0.716429i	−0.995284	+	0.0970077i	$0.969073\pi$
$410$	−2.46410	−	4.26795i	−0.121693	−	0.210779i
$411$		0			0
$412$	−3.72500	−	6.45189i	−0.183518	−	0.317862i
$413$		0			0
$414$		0			0
$415$	34.5885	+	59.9090i	1.69788	+	2.94082i
$416$	−6.69213			−0.328109
$417$		0			0
$418$	11.0735			0.541621
$419$	−3.95164	+	6.84443i	−0.193050	+	0.334373i	−0.946260	−	0.323408i	$-0.895171\pi$
$419$	−3.95164	+	6.84443i	−0.193050	+	0.334373i	0.753209	+	0.657781i	$0.228505\pi$
$420$		0			0
$421$	−14.1962	−	24.5885i	−0.691878	−	1.19837i	−0.971222	−	0.238177i	$-0.923450\pi$
$421$	−14.1962	−	24.5885i	−0.691878	−	1.19837i	0.279344	−	0.960191i	$-0.409883\pi$
$422$	2.53590	+	4.39230i	0.123446	+	0.213814i
$423$		0			0
$424$	1.46410	−	2.53590i	0.0711031	−	0.123154i
$425$	26.8886	−	46.5725i	1.30429	−	2.25910i
$426$		0			0
$427$		0			0
$428$	1.69615	−	2.93782i	0.0819866	−	0.142005i
$429$		0			0
$430$	14.4195			0.695372
$431$	−18.9282	+	32.7846i	−0.911739	+	1.57918i	−0.100133	+	0.994974i	$0.531927\pi$
$431$	−18.9282	+	32.7846i	−0.911739	+	1.57918i	−0.811606	+	0.584205i	$0.801406\pi$
$432$		0			0
$433$	7.10823			0.341600			0.170800	−	0.985306i	$-0.445365\pi$
$433$	7.10823			0.341600			0.170800	+	0.985306i	$0.445365\pi$
$434$		0			0
$435$		0			0
$436$	−8.92820			−0.427583
$437$	2.17209	+	3.76217i	0.103905	+	0.179969i
$438$		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	$0.0117743\pi$
$440$	14.4195			0.687424
$441$		0			0
$442$	36.2487			1.72418
$443$	−9.16025	+	15.8660i	−0.435217	+	0.753818i	−0.997313	−	0.0732540i	$-0.976662\pi$
$443$	−9.16025	+	15.8660i	−0.435217	+	0.753818i	0.562097	+	0.827072i	$0.309995\pi$
$444$		0			0
$445$	−13.6603	−	23.6603i	−0.647558	−	1.12160i
$446$	26.7685			1.26753
$447$		0			0
$448$		0			0
$449$	17.7846			0.839308			0.419654	−	0.907684i	$-0.362151\pi$
$449$	17.7846			0.839308			0.419654	+	0.907684i	$0.362151\pi$
$450$		0			0
$451$	−2.38014	+	4.12252i	−0.112076	+	0.194122i
$452$	−6.92820			−0.325875
$453$		0			0
$454$	5.25933	−	9.10943i	0.246833	−	0.427527i
$455$		0			0
$456$		0			0
$457$	−3.52628	+	6.10770i	−0.164952	+	0.285706i	−0.936638	−	0.350298i	$-0.886080\pi$
$457$	−3.52628	+	6.10770i	−0.164952	+	0.285706i	0.771686	+	0.636004i	$0.219414\pi$
$458$	12.4877	−	21.6293i	0.583511	−	1.01067i
$459$		0			0
$460$	2.82843	+	4.89898i	0.131876	+	0.228416i
$461$	−12.8666	−	22.2856i	−0.599258	−	1.03795i	−0.992931	−	0.118695i	$-0.962129\pi$
$461$	−12.8666	−	22.2856i	−0.599258	−	1.03795i	0.393672	−	0.919251i	$-0.371204\pi$
$462$		0			0
$463$	−19.3205	+	33.4641i	−0.897900	+	1.55521i	−0.0677264	+	0.997704i	$0.521575\pi$
$463$	−19.3205	+	33.4641i	−0.897900	+	1.55521i	−0.830174	+	0.557505i	$0.811759\pi$
$464$	4.00000			0.185695
$465$		0			0
$466$	−24.1244			−1.11754
$467$	−13.7818	−	23.8707i	−0.637745	−	1.10461i	−0.985927	−	0.167179i	$-0.946534\pi$
$467$	−13.7818	−	23.8707i	−0.637745	−	1.10461i	0.348182	−	0.937427i	$-0.386799\pi$
$468$		0			0
$469$		0			0
$470$	20.3923	+	35.3205i	0.940627	+	1.62921i
$471$		0			0
$472$	4.31199	+	7.46859i	0.198475	+	0.343770i
$473$	−6.96410	−	12.0622i	−0.320210	−	0.554620i
$474$		0			0
$475$	14.7291	+	25.5116i	0.675819	+	1.17055i
$476$		0			0
$477$		0			0
$478$	6.46410	+	11.1962i	0.295661	+	0.512100i
$479$	−15.4548			−0.706148			−0.353074	−	0.935595i	$-0.614864\pi$
$479$	−15.4548			−0.706148			−0.353074	+	0.935595i	$0.614864\pi$
$480$		0			0
$481$	3.58630			0.163521
$482$	11.7112	−	20.2844i	0.533432	−	0.923931i
$483$		0			0
$484$	−1.46410	−	2.53590i	−0.0665501	−	0.115268i
$485$	−11.3923	−	19.7321i	−0.517298	−	0.895986i
$486$		0			0
$487$	−19.3923	+	33.5885i	−0.878749	+	1.52204i	−0.0260347	+	0.999661i	$0.508288\pi$
$487$	−19.3923	+	33.5885i	−0.878749	+	1.52204i	−0.852714	+	0.522377i	$0.825045\pi$
$488$	3.48477	−	6.03579i	0.157748	−	0.273227i
$489$		0			0
$490$		0			0
$491$	−0.696152	+	1.20577i	−0.0314169	+	0.0544157i	−0.881306	−	0.472545i	$-0.843335\pi$
$491$	−0.696152	+	1.20577i	−0.0314169	+	0.0544157i	0.849889	+	0.526961i	$0.176669\pi$
$492$		0			0
$493$	−21.6665			−0.975809
$494$	−9.92820	+	17.1962i	−0.446691	+	0.773691i
$495$		0			0
$496$	1.79315			0.0805149
$497$		0			0
$498$		0			0
$499$	12.6077			0.564398			0.282199	−	0.959356i	$-0.408936\pi$
$499$	12.6077			0.564398			0.282199	+	0.959356i	$0.408936\pi$
$500$	9.52056	+	16.4901i	0.425772	+	0.737459i
$501$		0			0
$502$	8.17569	−	14.1607i	0.364899	−	0.632024i
$503$	7.45001			0.332179			0.166090	−	0.986111i	$-0.446886\pi$
$503$	7.45001			0.332179			0.166090	+	0.986111i	$0.446886\pi$
$504$		0			0
$505$	18.9282			0.842294
$506$	2.73205	−	4.73205i	0.121454	−	0.210365i
$507$		0			0
$508$	−3.26795	−	5.66025i	−0.144992	−	0.251133i
$509$	−26.4911			−1.17420			−0.587099	−	0.809515i	$-0.699730\pi$
$509$	−26.4911			−1.17420			−0.587099	+	0.809515i	$0.699730\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−1.34486	+	2.32937i	−0.0593194	+	0.102744i
$515$	−28.7846			−1.26840
$516$		0			0
$517$	19.6975	−	34.1170i	0.866293	−	1.50046i
$518$		0			0
$519$		0			0
$520$	−12.9282	+	22.3923i	−0.566939	+	0.981968i
$521$	16.1805	−	28.0255i	0.708881	−	1.22782i	−0.256392	−	0.966573i	$-0.582534\pi$
$521$	16.1805	−	28.0255i	0.708881	−	1.22782i	0.965273	−	0.261244i	$-0.0841329\pi$
$522$		0			0
$523$	1.88108	+	3.25813i	0.0822540	+	0.142468i	0.904218	−	0.427072i	$-0.140455\pi$
$523$	1.88108	+	3.25813i	0.0822540	+	0.142468i	−0.821964	+	0.569540i	$0.807121\pi$
$524$	3.01790	+	5.22715i	0.131837	+	0.228349i
$525$		0			0
$526$	7.73205	−	13.3923i	0.337133	−	0.583932i
$527$	−9.71281			−0.423097
$528$		0			0
$529$	−20.8564			−0.906800
$530$	−5.65685	−	9.79796i	−0.245718	−	0.425596i
$531$		0			0
$532$		0			0
$533$	−4.26795	−	7.39230i	−0.184865	−	0.320196i
$534$		0			0
$535$	−6.55343	−	11.3509i	−0.283329	−	0.490741i
$536$	2.76795	+	4.79423i	0.119557	+	0.207079i
$537$		0			0
$538$	2.82843	+	4.89898i	0.121942	+	0.211210i
$539$		0			0
$540$		0			0
$541$	9.66025	+	16.7321i	0.415327	+	0.719367i	0.995463	−	0.0951526i	$-0.0303339\pi$
$541$	9.66025	+	16.7321i	0.415327	+	0.719367i	−0.580136	+	0.814520i	$0.697001\pi$
$542$	−18.0058			−0.773417
$543$		0			0
$544$	5.41662			0.232236
$545$	−17.2480	+	29.8744i	−0.738822	+	1.27968i
$546$		0			0
$547$	19.1865	+	33.2321i	0.820357	+	1.42090i	0.905417	+	0.424524i	$0.139559\pi$
$547$	19.1865	+	33.2321i	0.820357	+	1.42090i	−0.0850597	+	0.996376i	$0.527108\pi$
$548$	−4.33013	−	7.50000i	−0.184974	−	0.320384i
$549$		0			0
$550$	18.5263	−	32.0885i	0.789963	−	1.36826i
$551$	5.93426	−	10.2784i	0.252808	−	0.437876i
$552$		0			0
$553$		0			0
$554$	12.2679	−	21.2487i	0.521215	−	0.902771i
$555$		0			0
$556$	−16.3514			−0.693453
$557$	3.46410	−	6.00000i	0.146779	−	0.254228i	−0.783256	−	0.621699i	$-0.786443\pi$
$557$	3.46410	−	6.00000i	0.146779	−	0.254228i	0.930035	+	0.367471i	$0.119776\pi$
$558$		0			0
$559$	24.9754			1.05635
$560$		0			0
$561$		0			0
$562$	−9.85641			−0.415767
$563$	−12.7973	−	22.1655i	−0.539341	−	0.934166i	−0.998940	−	0.0460390i	$-0.985340\pi$
$563$	−12.7973	−	22.1655i	−0.539341	−	0.934166i	0.459599	−	0.888127i	$-0.347993\pi$
$564$		0			0
$565$	−13.3843	+	23.1822i	−0.563080	+	0.975283i
$566$	−9.41902			−0.395911
$567$		0			0
$568$	2.53590			0.106404
$569$	7.89230	−	13.6699i	0.330863	−	0.573071i	−0.651819	−	0.758375i	$-0.725994\pi$
$569$	7.89230	−	13.6699i	0.330863	−	0.573071i	0.982681	+	0.185304i	$0.0593270\pi$
$570$		0			0
$571$	−2.52628	−	4.37564i	−0.105722	−	0.183115i	0.808311	−	0.588755i	$-0.200382\pi$
$571$	−2.52628	−	4.37564i	−0.105722	−	0.183115i	−0.914033	+	0.405640i	$0.867049\pi$
$572$	24.9754			1.04427
$573$		0			0
$574$		0			0
$575$	14.5359			0.606189
$576$		0			0
$577$	22.3178	−	38.6556i	0.929103	−	1.60925i	0.144278	−	0.989537i	$-0.453914\pi$
$577$	22.3178	−	38.6556i	0.929103	−	1.60925i	0.784825	−	0.619717i	$-0.212753\pi$
$578$	−12.3397			−0.513266
$579$		0			0
$580$	7.72741	−	13.3843i	0.320863	−	0.555751i
$581$		0			0
$582$		0			0
$583$	−5.46410	+	9.46410i	−0.226300	+	0.391963i
$584$	−3.41542	+	5.91567i	−0.141331	+	0.244792i
$585$		0			0
$586$	9.52056	+	16.4901i	0.393291	+	0.681199i
$587$	14.5768	+	25.2478i	0.601650	+	1.04209i	0.992571	+	0.121664i	$0.0388230\pi$
$587$	14.5768	+	25.2478i	0.601650	+	1.04209i	−0.390922	+	0.920424i	$0.627844\pi$
$588$		0			0
$589$	2.66025	−	4.60770i	0.109614	−	0.189857i
$590$	33.3205			1.37178
$591$		0			0
$592$	0.535898			0.0220253
$593$	−1.36345	−	2.36156i	−0.0559900	−	0.0969775i	0.836672	−	0.547704i	$-0.184498\pi$
$593$	−1.36345	−	2.36156i	−0.0559900	−	0.0969775i	−0.892662	+	0.450727i	$0.851165\pi$
$594$		0			0
$595$		0			0
$596$	4.53590	+	7.85641i	0.185798	+	0.321811i
$597$		0			0
$598$	4.89898	+	8.48528i	0.200334	+	0.346989i
$599$	−18.3923	−	31.8564i	−0.751489	−	1.30162i	−0.947101	−	0.320936i	$-0.896003\pi$
$599$	−18.3923	−	31.8564i	−0.751489	−	1.30162i	0.195612	−	0.980681i	$-0.437331\pi$
$600$		0			0
$601$	0.448288	+	0.776457i	0.0182860	+	0.0316723i	0.875024	−	0.484080i	$-0.160846\pi$
$601$	0.448288	+	0.776457i	0.0182860	+	0.0316723i	−0.856738	+	0.515753i	$0.827512\pi$
$602$		0			0
$603$		0			0
$604$	1.19615	+	2.07180i	0.0486708	+	0.0843002i
$605$	−11.3137			−0.459968
$606$		0			0
$607$	−31.6675			−1.28534			−0.642672	−	0.766141i	$-0.722174\pi$
$607$	−31.6675			−1.28534			−0.642672	+	0.766141i	$0.722174\pi$
$608$	−1.48356	+	2.56961i	−0.0601665	+	0.104211i
$609$		0			0
$610$	−13.4641	−	23.3205i	−0.545146	−	0.944220i
$611$	35.3205	+	61.1769i	1.42891	+	2.47495i
$612$		0			0
$613$	−5.53590	+	9.58846i	−0.223593	+	0.387274i	−0.955896	−	0.293704i	$-0.905112\pi$
$613$	−5.53590	+	9.58846i	−0.223593	+	0.387274i	0.732304	+	0.680978i	$0.238445\pi$
$614$	−5.53674	+	9.58991i	−0.223444	+	0.387017i
$615$		0			0
$616$		0			0
$617$	−15.4282	+	26.7224i	−0.621116	+	1.07580i	0.368162	+	0.929762i	$0.379987\pi$
$617$	−15.4282	+	26.7224i	−0.621116	+	1.07580i	−0.989278	+	0.146043i	$0.953346\pi$
$618$		0			0
$619$	24.6336			0.990108			0.495054	−	0.868862i	$-0.335148\pi$
$619$	24.6336			0.990108			0.495054	+	0.868862i	$0.335148\pi$
$620$	3.46410	−	6.00000i	0.139122	−	0.240966i
$621$		0			0
$622$	−12.3490			−0.495149
$623$		0			0
$624$		0			0
$625$	23.9282			0.957128
$626$	11.7112	+	20.2844i	0.468075	+	0.810729i
$627$		0			0
$628$	−2.31079	+	4.00240i	−0.0922105	+	0.159713i
$629$	−2.90276			−0.115740
$630$		0			0
$631$	35.7128			1.42170			0.710852	−	0.703341i	$-0.248309\pi$
$631$	35.7128			1.42170			0.710852	+	0.703341i	$0.248309\pi$
$632$	−2.46410	+	4.26795i	−0.0980167	+	0.169770i
$633$		0			0
$634$	13.0000	+	22.5167i	0.516296	+	0.894251i
$635$	−25.2528			−1.00213
$636$		0			0
$637$		0			0
$638$	−14.9282			−0.591013
$639$		0			0
$640$	−1.93185	+	3.34607i	−0.0763631	+	0.132265i
$641$	−17.9282			−0.708121			−0.354061	−	0.935222i	$-0.615199\pi$
$641$	−17.9282			−0.708121			−0.354061	+	0.935222i	$0.615199\pi$
$642$		0			0
$643$	6.53485	−	11.3187i	0.257709	−	0.446365i	−0.707919	−	0.706294i	$-0.750366\pi$
$643$	6.53485	−	11.3187i	0.257709	−	0.446365i	0.965628	+	0.259929i	$0.0836990\pi$
$644$		0			0
$645$		0			0
$646$	8.03590	−	13.9186i	0.316168	−	0.547619i
$647$	6.03579	−	10.4543i	0.237291	−	0.411001i	−0.722645	−	0.691220i	$-0.757074\pi$
$647$	6.03579	−	10.4543i	0.237291	−	0.411001i	0.959936	+	0.280219i	$0.0904070\pi$
$648$		0			0
$649$	−16.0926	−	27.8731i	−0.631689	−	1.09412i
$650$	33.2204	+	57.5394i	1.30301	+	2.25688i
$651$		0			0
$652$	−10.6603	+	18.4641i	−0.417488	+	0.723110i
$653$	−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
$655$	23.3205			0.911208
$656$	−0.637756	−	1.10463i	−0.0249002	−	0.0431284i
$657$		0			0
$658$		0			0
$659$	0.124356	+	0.215390i	0.00484421	+	0.00839042i	0.868437	−	0.495799i	$-0.165125\pi$
$659$	0.124356	+	0.215390i	0.00484421	+	0.00839042i	−0.863593	+	0.504189i	$0.831791\pi$
$660$		0			0
$661$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$661$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$662$	−2.26795	−	3.92820i	−0.0881463	−	0.152674i
$663$		0			0
$664$	8.95215	+	15.5056i	0.347411	+	0.601733i
$665$		0			0
$666$		0			0
$667$	−2.92820	−	5.07180i	−0.113380	−	0.196381i
$668$	−21.1117			−0.816835
$669$		0			0
$670$	21.3891			0.826332
$671$	−13.0053	+	22.5259i	−0.502065	+	0.869602i
$672$		0			0
$673$	20.7846	+	36.0000i	0.801188	+	1.38770i	0.918835	+	0.394643i	$0.129132\pi$
$673$	20.7846	+	36.0000i	0.801188	+	1.38770i	−0.117647	+	0.993055i	$0.537535\pi$
$674$	−3.50000	−	6.06218i	−0.134815	−	0.233506i
$675$		0			0
$676$	−15.8923	+	27.5263i	−0.611242	+	1.05870i
$677$	−10.0382	+	17.3867i	−0.385799	+	0.668224i	−0.991880	−	0.127179i	$-0.959408\pi$
$677$	−10.0382	+	17.3867i	−0.385799	+	0.668224i	0.606081	+	0.795403i	$0.292741\pi$
$678$		0			0
$679$		0			0
$680$	10.4641	−	18.1244i	0.401280	−	0.695037i
$681$		0			0
$682$	−6.69213			−0.256255
$683$	−1.83975	+	3.18653i	−0.0703959	+	0.121929i	−0.899075	−	0.437795i	$-0.855760\pi$
$683$	−1.83975	+	3.18653i	−0.0703959	+	0.121929i	0.828679	+	0.559724i	$0.189093\pi$
$684$		0			0
$685$	−33.4607			−1.27847
$686$		0			0
$687$		0			0
$688$	3.73205			0.142283
$689$	−9.79796	−	16.9706i	−0.373273	−	0.646527i
$690$		0			0
$691$	−4.81105	+	8.33298i	−0.183021	+	0.317001i	−0.942908	−	0.333054i	$-0.891921\pi$
$691$	−4.81105	+	8.33298i	−0.183021	+	0.317001i	0.759887	+	0.650055i	$0.225254\pi$
$692$	−1.79315			−0.0681654
$693$		0			0
$694$	21.5885			0.819487
$695$	−31.5885	+	54.7128i	−1.19822	+	2.07538i
$696$		0			0
$697$	3.45448	+	5.98334i	0.130848	+	0.226635i
$698$	−16.4901			−0.624159
$699$		0			0
$700$		0			0
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$		0			0
$703$	0.795040	−	1.37705i	0.0299855	−	0.0519364i
$704$	3.73205			0.140657
$705$		0			0
$706$	13.2134	−	22.8862i	0.497292	−	0.861335i
$707$		0			0
$708$		0			0
$709$	−4.19615	+	7.26795i	−0.157590	+	0.272954i	−0.933999	−	0.357276i	$-0.883706\pi$
$709$	−4.19615	+	7.26795i	−0.157590	+	0.272954i	0.776409	+	0.630229i	$0.217039\pi$
$710$	4.89898	−	8.48528i	0.183855	−	0.318447i
$711$		0			0
$712$	−3.53553	−	6.12372i	−0.132500	−	0.229496i
$713$	−1.31268	−	2.27362i	−0.0491602	−	0.0851479i
$714$		0			0
$715$	48.2487	−	83.5692i	1.80440	−	3.12531i
$716$	−18.9282			−0.707380
$717$		0			0
$718$	0.535898			0.0199996
$719$	−7.69024	−	13.3199i	−0.286798	−	0.496748i	0.686246	−	0.727370i	$-0.259257\pi$
$719$	−7.69024	−	13.3199i	−0.286798	−	0.496748i	−0.973044	+	0.230622i	$0.925924\pi$
$720$		0			0
$721$		0			0
$722$	−5.09808	−	8.83013i	−0.189731	−	0.328623i
$723$		0			0
$724$	8.48528	+	14.6969i	0.315353	+	0.546207i
$725$	−19.8564	−	34.3923i	−0.737448	−	1.27730i
$726$		0			0
$727$	0.795040	+	1.37705i	0.0294864	+	0.0510719i	0.880392	−	0.474247i	$-0.157279\pi$
$727$	0.795040	+	1.37705i	0.0294864	+	0.0510719i	−0.850906	+	0.525319i	$0.823946\pi$
$728$		0			0
$729$		0			0
$730$	13.1962	+	22.8564i	0.488412	+	0.845954i
$731$	−20.2151			−0.747682
$732$		0			0
$733$	−16.4901			−0.609075			−0.304538	−	0.952500i	$-0.598502\pi$
$733$	−16.4901			−0.609075			−0.304538	+	0.952500i	$0.598502\pi$
$734$	−7.86611	+	13.6245i	−0.290343	+	0.502889i
$735$		0			0
$736$	0.732051	+	1.26795i	0.0269838	+	0.0467372i
$737$	−10.3301	−	17.8923i	−0.380515	−	0.659072i
$738$		0			0
$739$	9.06218	−	15.6962i	0.333358	−	0.577392i	−0.649810	−	0.760096i	$-0.725152\pi$
$739$	9.06218	−	15.6962i	0.333358	−	0.577392i	0.983168	+	0.182704i	$0.0584850\pi$
$740$	1.03528	−	1.79315i	0.0380575	−	0.0659175i
$741$		0			0
$742$		0			0
$743$	25.7846	−	44.6603i	0.945946	−	1.63843i	0.192099	−	0.981376i	$-0.438471\pi$
$743$	25.7846	−	44.6603i	0.945946	−	1.63843i	0.753847	−	0.657050i	$-0.228196\pi$
$744$		0			0
$745$	35.0507			1.28416
$746$	15.3923	−	26.6603i	0.563552	−	0.976101i
$747$		0			0
$748$	−20.2151			−0.739137
$749$		0			0
$750$		0			0
$751$	−6.78461			−0.247574			−0.123787	−	0.992309i	$-0.539504\pi$
$751$	−6.78461			−0.247574			−0.123787	+	0.992309i	$0.539504\pi$
$752$	5.27792	+	9.14162i	0.192466	+	0.333361i
$753$		0			0
$754$	13.3843	−	23.1822i	0.487426	−	0.844247i
$755$	9.24316			0.336393
$756$		0			0
$757$	−15.3205			−0.556833			−0.278417	−	0.960460i	$-0.589810\pi$
$757$	−15.3205			−0.556833			−0.278417	+	0.960460i	$0.589810\pi$
$758$	−8.79423	+	15.2321i	−0.319421	+	0.553253i
$759$		0			0
$760$	5.73205	+	9.92820i	0.207923	+	0.360134i
$761$	30.4564			1.10404			0.552021	−	0.833830i	$-0.313857\pi$
$761$	30.4564			1.10404			0.552021	+	0.833830i	$0.313857\pi$
$762$		0			0
$763$		0			0
$764$	−1.07180			−0.0387762
$765$		0			0
$766$	10.8332	−	18.7637i	0.391421	−	0.677961i
$767$	57.7128			2.08389
$768$		0			0
$769$	−19.0919	+	33.0681i	−0.688471	+	1.19247i	0.283862	+	0.958865i	$0.408384\pi$
$769$	−19.0919	+	33.0681i	−0.688471	+	1.19247i	−0.972332	+	0.233601i	$0.924949\pi$
$770$		0			0
$771$		0			0
$772$	11.5263	−	19.9641i	0.414840	−	0.718524i
$773$	0.101536	−	0.175865i	0.00365199	−	0.00632544i	−0.864194	−	0.503159i	$-0.832171\pi$
$773$	0.101536	−	0.175865i	0.00365199	−	0.00632544i	0.867846	+	0.496834i	$0.165504\pi$
$774$		0			0
$775$	−8.90138	−	15.4176i	−0.319747	−	0.553818i
$776$	−2.94855	−	5.10703i	−0.105847	−	0.183332i
$777$		0			0
$778$	−4.00000	+	6.92820i	−0.143407	+	0.248388i
$779$	−3.78461			−0.135598
$780$		0			0
$781$	−9.46410			−0.338652
$782$	−3.96524	−	6.86800i	−0.141797	−	0.245599i
$783$		0			0
$784$		0			0
$785$	8.92820	+	15.4641i	0.318661	+	0.551937i
$786$		0			0
$787$	23.3717	+	40.4810i	0.833111	+	1.44299i	0.895559	+	0.444942i	$0.146776\pi$
$787$	23.3717	+	40.4810i	0.833111	+	1.44299i	−0.0624487	+	0.998048i	$0.519891\pi$
$788$	−1.53590	−	2.66025i	−0.0547141	−	0.0947676i
$789$		0			0
$790$	9.52056	+	16.4901i	0.338726	+	0.586691i
$791$		0			0
$792$		0			0
$793$	−23.3205	−	40.3923i	−0.828136	−	1.43437i
$794$	−18.0058			−0.639003
$795$		0			0
$796$	−17.8028			−0.631002
$797$	10.4543	−	18.1074i	0.370310	−	0.641396i	−0.619303	−	0.785152i	$-0.712585\pi$
$797$	10.4543	−	18.1074i	0.370310	−	0.641396i	0.989613	+	0.143756i	$0.0459181\pi$
$798$		0			0
$799$	−28.5885	−	49.5167i	−1.01139	−	1.75177i
$800$	4.96410	+	8.59808i	0.175507	+	0.303988i
$801$		0			0
$802$	−8.89230	+	15.4019i	−0.313998	+	0.543861i
$803$	12.7465	−	22.0776i	0.449814	−	0.779101i
$804$		0			0
$805$		0			0
$806$	6.00000	−	10.3923i	0.211341	−	0.366053i
$807$		0			0
$808$	4.89898			0.172345
$809$	−13.1340	+	22.7487i	−0.461766	+	0.799802i	−0.999049	−	0.0435999i	$-0.986117\pi$
$809$	−13.1340	+	22.7487i	−0.461766	+	0.799802i	0.537283	+	0.843402i	$0.319451\pi$
$810$		0			0
$811$	46.1242			1.61964			0.809820	−	0.586679i	$-0.199565\pi$
$811$	46.1242			1.61964			0.809820	+	0.586679i	$0.199565\pi$
$812$		0			0
$813$		0			0
$814$	−2.00000			−0.0701000
$815$	41.1881	+	71.3398i	1.44275	+	2.49892i
$816$		0			0
$817$	5.53674	−	9.58991i	0.193706	−	0.335508i
$818$	−16.7303			−0.584962
$819$		0			0
$820$	−4.92820			−0.172100
$821$	−5.19615	+	9.00000i	−0.181347	+	0.314102i	−0.942339	−	0.334659i	$-0.891379\pi$
$821$	−5.19615	+	9.00000i	−0.181347	+	0.314102i	0.760993	+	0.648761i	$0.224712\pi$
$822$		0			0
$823$	−15.3923	−	26.6603i	−0.536542	−	0.929318i	−0.999087	−	0.0427222i	$-0.986397\pi$
$823$	−15.3923	−	26.6603i	−0.536542	−	0.929318i	0.462545	−	0.886596i	$-0.346936\pi$
$824$	−7.45001			−0.259533
$825$		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
$829$	−18.6622	+	32.3238i	−0.648164	+	1.12265i	0.335397	+	0.942077i	$0.391130\pi$
$829$	−18.6622	+	32.3238i	−0.648164	+	1.12265i	−0.983561	+	0.180576i	$0.942204\pi$
$830$	69.1769			2.40117
$831$		0			0
$832$	−3.34607	+	5.79555i	−0.116004	+	0.200925i
$833$		0			0
$834$		0			0
$835$	−40.7846	+	70.6410i	−1.41141	+	2.44463i
$836$	5.53674	−	9.58991i	0.191492	−	0.331674i
$837$		0			0
$838$	3.95164	+	6.84443i	0.136507	+	0.236437i
$839$	11.3137	+	19.5959i	0.390593	+	0.676526i	0.992528	−	0.122019i	$-0.0389368\pi$
$839$	11.3137	+	19.5959i	0.390593	+	0.676526i	−0.601935	+	0.798545i	$0.705603\pi$
$840$		0			0
$841$	6.50000	−	11.2583i	0.224138	−	0.388218i
$842$	−28.3923			−0.978463
$843$		0			0
$844$	5.07180			0.174578
$845$	61.4032	+	106.353i	2.11233	+	3.65867i
$846$		0			0
$847$		0			0
$848$	−1.46410	−	2.53590i	−0.0502775	−	0.0870831i
$849$		0			0
$850$	−26.8886	−	46.5725i	−0.922273	−	1.59742i
$851$	−0.392305	−	0.679492i	−0.0134480	−	0.0232927i
$852$		0			0
$853$	8.00481	+	13.8647i	0.274079	+	0.474719i	0.969902	−	0.243494i	$-0.0782936\pi$
$853$	8.00481	+	13.8647i	0.274079	+	0.474719i	−0.695823	+	0.718213i	$0.744960\pi$
$854$		0			0
$855$		0			0
$856$	−1.69615	−	2.93782i	−0.0579733	−	0.100413i
$857$	−8.38375			−0.286383			−0.143192	−	0.989695i	$-0.545737\pi$
$857$	−8.38375			−0.286383			−0.143192	+	0.989695i	$0.545737\pi$
$858$		0			0
$859$	14.7341			0.502721			0.251361	−	0.967894i	$-0.419122\pi$
$859$	14.7341			0.502721			0.251361	+	0.967894i	$0.419122\pi$
$860$	7.20977	−	12.4877i	0.245851	−	0.425827i
$861$		0			0
$862$	18.9282	+	32.7846i	0.644697	+	1.11665i
$863$	11.0526	+	19.1436i	0.376233	+	0.651656i	0.990511	−	0.137435i	$-0.0438857\pi$
$863$	11.0526	+	19.1436i	0.376233	+	0.651656i	−0.614277	+	0.789090i	$0.710552\pi$
$864$		0			0
$865$	−3.46410	+	6.00000i	−0.117783	+	0.204006i
$866$	3.55412	−	6.15591i	0.120774	−	0.209186i
$867$		0			0
$868$		0			0
$869$	9.19615	−	15.9282i	0.311958	−	0.540327i
$870$		0			0
$871$	37.0470			1.25529
$872$	−4.46410	+	7.73205i	−0.151174	+	0.261840i
$873$		0			0
$874$	4.34418			0.146944
$875$		0			0
$876$		0			0
$877$	33.1769			1.12030			0.560152	−	0.828390i	$-0.310743\pi$
$877$	33.1769			1.12030			0.560152	+	0.828390i	$0.310743\pi$
$878$	−9.79796	−	16.9706i	−0.330665	−	0.572729i
$879$		0			0
$880$	7.20977	−	12.4877i	0.243041	−	0.420960i
$881$	12.7279			0.428815			0.214407	−	0.976744i	$-0.431218\pi$
$881$	12.7279			0.428815			0.214407	+	0.976744i	$0.431218\pi$
$882$		0			0
$883$	7.53590			0.253603			0.126802	−	0.991928i	$-0.459529\pi$
$883$	7.53590			0.253603			0.126802	+	0.991928i	$0.459529\pi$
$884$	18.1244	−	31.3923i	0.609588	−	1.05584i
$885$		0			0
$886$	9.16025	+	15.8660i	0.307745	+	0.533030i
$887$	−28.7647			−0.965826			−0.482913	−	0.875668i	$-0.660421\pi$
$887$	−28.7647			−0.965826			−0.482913	+	0.875668i	$0.660421\pi$
$888$		0			0
$889$		0			0
$890$	−27.3205			−0.915786
$891$		0			0
$892$	13.3843	−	23.1822i	0.448138	−	0.776198i
$893$	31.3205			1.04810
$894$		0			0
$895$	−36.5665	+	63.3350i	−1.22228	+	2.11706i
$896$		0			0
$897$		0			0
$898$	8.89230	−	15.4019i	0.296740	−	0.513969i
$899$	−3.58630	+	6.21166i	−0.119610	+	0.207170i
$900$		0			0
$901$	7.93048	+	13.7360i	0.264203	+	0.457612i
$902$	2.38014	+	4.12252i	0.0792500	+	0.137265i
$903$		0			0
$904$	−3.46410	+	6.00000i	−0.115214	+	0.199557i
$905$	65.5692			2.17959
$906$		0			0
$907$	43.2487			1.43605			0.718025	−	0.696017i	$-0.245046\pi$
$907$	43.2487			1.43605			0.718025	+	0.696017i	$0.245046\pi$
$908$	−5.25933	−	9.10943i	−0.174537	−	0.302307i
$909$		0			0
$910$		0			0
$911$	−23.4641	−	40.6410i	−0.777400	−	1.34650i	−0.933435	−	0.358745i	$-0.883205\pi$
$911$	−23.4641	−	40.6410i	−0.777400	−	1.34650i	0.156035	−	0.987752i	$-0.450129\pi$
$912$		0			0
$913$	−33.4099	−	57.8676i	−1.10571	−	1.91514i
$914$	3.52628	+	6.10770i	0.116639	+	0.202025i
$915$		0			0
$916$	−12.4877	−	21.6293i	−0.412605	−	0.714652i
$917$		0			0
$918$		0			0
$919$	−11.4641	−	19.8564i	−0.378166	−	0.655002i	0.612630	−	0.790370i	$-0.290112\pi$
$919$	−11.4641	−	19.8564i	−0.378166	−	0.655002i	−0.990795	+	0.135368i	$0.956778\pi$
$920$	5.65685			0.186501
$921$		0			0
$922$	−25.7332			−0.847479
$923$	8.48528	−	14.6969i	0.279296	−	0.483756i
$924$		0			0
$925$	−2.66025	−	4.60770i	−0.0874686	−	0.151500i
$926$	19.3205	+	33.4641i	0.634911	+	1.09970i
$927$		0			0
$928$	2.00000	−	3.46410i	0.0656532	−	0.113715i
$929$	−13.9898	+	24.2311i	−0.458991	+	0.794997i	−0.998908	−	0.0467220i	$-0.985122\pi$
$929$	−13.9898	+	24.2311i	−0.458991	+	0.794997i	0.539916	+	0.841719i	$0.318456\pi$
$930$		0			0
$931$		0			0
$932$	−12.0622	+	20.8923i	−0.395110	+	0.684350i
$933$		0			0
$934$	−27.5636			−0.901907
$935$	−39.0526	+	67.6410i	−1.27716	+	2.21210i
$936$		0			0
$937$	−9.89949			−0.323402			−0.161701	−	0.986840i	$-0.551698\pi$
$937$	−9.89949			−0.323402			−0.161701	+	0.986840i	$0.551698\pi$
$938$		0			0
$939$		0			0
$940$	40.7846			1.33025
$941$	−4.34418	−	7.52433i	−0.141616	−	0.245286i	0.786489	−	0.617604i	$-0.211897\pi$
$941$	−4.34418	−	7.52433i	−0.141616	−	0.245286i	−0.928105	+	0.372318i	$0.878563\pi$
$942$		0			0
$943$	−0.933740	+	1.61729i	−0.0304068	+	0.0526661i
$944$	8.62398			0.280687
$945$		0			0
$946$	−13.9282			−0.452845
$947$	3.06218	−	5.30385i	0.0995074	−	0.172352i	−0.811973	−	0.583694i	$-0.801607\pi$
$947$	3.06218	−	5.30385i	0.0995074	−	0.172352i	0.911481	+	0.411342i	$0.134940\pi$
$948$		0			0
$949$	22.8564	+	39.5885i	0.741950	+	1.28510i
$950$	29.4582			0.955752
$951$		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
$955$	−2.07055	+	3.58630i	−0.0670015	+	0.116050i
$956$	12.9282			0.418128
$957$		0			0
$958$	−7.72741	+	13.3843i	−0.249661	+	0.432426i
$959$		0			0
$960$		0			0
$961$	13.8923	−	24.0622i	0.448139	−	0.776199i
$962$	1.79315	−	3.10583i	0.0578135	−	0.100136i
$963$		0			0
$964$	−11.7112	−	20.2844i	−0.377193	−	0.653318i
$965$	−44.5341	−	77.1354i	−1.43360	−	2.48308i
$966$		0			0
$967$	−17.7846	+	30.8038i	−0.571914	+	0.990585i	0.424455	+	0.905449i	$0.360466\pi$
$967$	−17.7846	+	30.8038i	−0.571914	+	0.990585i	−0.996369	+	0.0851359i	$0.972868\pi$
$968$	−2.92820			−0.0941160
$969$		0			0
$970$	−22.7846			−0.731570
$971$	−1.50215	−	2.60179i	−0.0482062	−	0.0834955i	0.840915	−	0.541166i	$-0.182017\pi$
$971$	−1.50215	−	2.60179i	−0.0482062	−	0.0834955i	−0.889122	+	0.457671i	$0.848684\pi$
$972$		0			0
$973$		0			0
$974$	19.3923	+	33.5885i	0.621370	+	1.07624i
$975$		0			0
$976$	−3.48477	−	6.03579i	−0.111545	−	0.193201i
$977$	−24.9904	−	43.2846i	−0.799513	−	1.38480i	−0.919934	−	0.392074i	$-0.871758\pi$
$977$	−24.9904	−	43.2846i	−0.799513	−	1.38480i	0.120420	−	0.992723i	$-0.461576\pi$
$978$		0			0
$979$	13.1948	+	22.8541i	0.421707	+	0.730419i
$980$		0			0
$981$		0			0
$982$	0.696152	+	1.20577i	0.0222151	+	0.0384777i
$983$	6.96953			0.222294			0.111147	−	0.993804i	$-0.464548\pi$
$983$	6.96953			0.222294			0.111147	+	0.993804i	$0.464548\pi$
$984$		0			0
$985$	−11.8685			−0.378162
$986$	−10.8332	+	18.7637i	−0.345000	+	0.597558i
$987$		0			0
$988$	9.92820	+	17.1962i	0.315858	+	0.547082i
$989$	−2.73205	−	4.73205i	−0.0868742	−	0.150470i
$990$		0			0
$991$	−0.875644	+	1.51666i	−0.0278158	+	0.0481783i	−0.879598	−	0.475717i	$-0.842189\pi$
$991$	−0.875644	+	1.51666i	−0.0278158	+	0.0481783i	0.851782	+	0.523896i	$0.175522\pi$
$992$	0.896575	−	1.55291i	0.0284663	−	0.0493051i
$993$		0			0
$994$		0			0
$995$	−34.3923	+	59.5692i	−1.09031	+	1.88847i
$996$		0			0
$997$	6.48906			0.205511			0.102755	−	0.994707i	$-0.467234\pi$
$997$	6.48906			0.205511			0.102755	+	0.994707i	$0.467234\pi$
$998$	6.30385	−	10.9186i	0.199545	−	0.345622i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.t.361.1		8
3.2	odd	2		882.2.h.q.67.1		8
7.2	even	3		2646.2.e.q.1549.4		8
7.3	odd	6		2646.2.f.r.1765.1		8
7.4	even	3		2646.2.f.r.1765.4		8
7.5	odd	6		2646.2.e.q.1549.1		8
7.6	odd	2	inner	2646.2.h.t.361.4		8
9.2	odd	6		882.2.e.s.655.4		8
9.7	even	3		2646.2.e.q.2125.4		8
21.2	odd	6		882.2.e.s.373.4		8
21.5	even	6		882.2.e.s.373.1		8
21.11	odd	6		882.2.f.q.589.2	yes	8
21.17	even	6		882.2.f.q.589.3	yes	8
21.20	even	2		882.2.h.q.67.4		8
63.2	odd	6		882.2.h.q.79.2		8
63.4	even	3		7938.2.a.ci.1.1		4
63.11	odd	6		882.2.f.q.295.2	✓	8
63.16	even	3	inner	2646.2.h.t.667.1		8
63.20	even	6		882.2.e.s.655.1		8
63.25	even	3		2646.2.f.r.883.4		8
63.31	odd	6		7938.2.a.ci.1.4		4
63.32	odd	6		7938.2.a.cp.1.4		4
63.34	odd	6		2646.2.e.q.2125.1		8
63.38	even	6		882.2.f.q.295.3	yes	8
63.47	even	6		882.2.h.q.79.3		8
63.52	odd	6		2646.2.f.r.883.1		8
63.59	even	6		7938.2.a.cp.1.1		4
63.61	odd	6	inner	2646.2.h.t.667.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.1		8	21.5	even	6
882.2.e.s.373.4		8	21.2	odd	6
882.2.e.s.655.1		8	63.20	even	6
882.2.e.s.655.4		8	9.2	odd	6
882.2.f.q.295.2	✓	8	63.11	odd	6
882.2.f.q.295.3	yes	8	63.38	even	6
882.2.f.q.589.2	yes	8	21.11	odd	6
882.2.f.q.589.3	yes	8	21.17	even	6
882.2.h.q.67.1		8	3.2	odd	2
882.2.h.q.67.4		8	21.20	even	2
882.2.h.q.79.2		8	63.2	odd	6
882.2.h.q.79.3		8	63.47	even	6
2646.2.e.q.1549.1		8	7.5	odd	6
2646.2.e.q.1549.4		8	7.2	even	3
2646.2.e.q.2125.1		8	63.34	odd	6
2646.2.e.q.2125.4		8	9.7	even	3
2646.2.f.r.883.1		8	63.52	odd	6
2646.2.f.r.883.4		8	63.25	even	3
2646.2.f.r.1765.1		8	7.3	odd	6
2646.2.f.r.1765.4		8	7.4	even	3
2646.2.h.t.361.1		8	1.1	even	1	trivial
2646.2.h.t.361.4		8	7.6	odd	2	inner
2646.2.h.t.667.1		8	63.16	even	3	inner
2646.2.h.t.667.4		8	63.61	odd	6	inner
7938.2.a.ci.1.1		4	63.4	even	3
7938.2.a.ci.1.4		4	63.31	odd	6
7938.2.a.cp.1.1		4	63.59	even	6
7938.2.a.cp.1.4		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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.86370 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} -3.86370 q^{5} -1.00000 q^{8} +(-1.93185 + 3.34607i) q^{10} +3.73205 q^{11} +(-3.34607 + 5.79555i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(2.70831 - 4.69093i) q^{17} +(1.48356 + 2.56961i) q^{19} +(1.93185 + 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} +1.46410 q^{23} +9.92820 q^{25} +(3.34607 + 5.79555i) q^{26} +(-2.00000 - 3.46410i) q^{29} +(-0.896575 - 1.55291i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-2.70831 - 4.69093i) q^{34} +(-0.267949 - 0.464102i) q^{37} +2.96713 q^{38} +3.86370 q^{40} +(-0.637756 + 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +(-1.86603 - 3.23205i) q^{44} +(0.732051 - 1.26795i) q^{46} +(5.27792 - 9.14162i) q^{47} +(4.96410 - 8.59808i) q^{50} +6.69213 q^{52} +(-1.46410 + 2.53590i) q^{53} -14.4195 q^{55} -4.00000 q^{58} +(-4.31199 - 7.46859i) q^{59} +(-3.48477 + 6.03579i) q^{61} -1.79315 q^{62} +1.00000 q^{64} +(12.9282 - 22.3923i) q^{65} +(-2.76795 - 4.79423i) q^{67} -5.41662 q^{68} -2.53590 q^{71} +(3.41542 - 5.91567i) q^{73} -0.535898 q^{74} +(1.48356 - 2.56961i) q^{76} +(2.46410 - 4.26795i) q^{79} +(1.93185 - 3.34607i) q^{80} +(0.637756 + 1.10463i) q^{82} +(-8.95215 - 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} -3.73205 q^{86} -3.73205 q^{88} +(3.53553 + 6.12372i) q^{89} +(-0.732051 - 1.26795i) q^{92} +(-5.27792 - 9.14162i) q^{94} +(-5.73205 - 9.92820i) q^{95} +(2.94855 + 5.10703i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} - 8 q^{8}+O(q^{10}) \) 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

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