LMFDB - Embedded newform 882.2.h.q.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, 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("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.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:	$7.04280545828$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	882.67
Dual form			882.2.h.q.79.3

$q$-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} +(1.22474 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.86370 q^{5} +(-1.67303 + 0.448288i) q^{6} +1.00000 q^{8} +3.00000i q^{9} +(1.93185 - 3.34607i) q^{10} -3.73205 q^{11} +(0.448288 - 1.67303i) q^{12} +(3.34607 - 5.79555i) q^{13} +(-4.73205 - 4.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.70831 - 4.69093i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-1.48356 - 2.56961i) q^{19} +(1.93185 + 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} -1.46410 q^{23} +(1.22474 + 1.22474i) q^{24} +9.92820 q^{25} +(3.34607 + 5.79555i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 + 3.46410i) q^{29} +(6.46410 - 1.73205i) q^{30} +(0.896575 + 1.55291i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.57081 - 4.57081i) q^{33} +(2.70831 + 4.69093i) q^{34} +(2.59808 - 1.50000i) q^{36} +(-0.267949 - 0.464102i) q^{37} +2.96713 q^{38} +(11.1962 - 3.00000i) q^{39} -3.86370 q^{40} +(-0.637756 + 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +(1.86603 + 3.23205i) q^{44} -11.5911i q^{45} +(0.732051 - 1.26795i) q^{46} +(5.27792 - 9.14162i) q^{47} +(-1.67303 + 0.448288i) q^{48} +(-4.96410 + 8.59808i) q^{50} +(9.06218 - 2.42820i) q^{51} -6.69213 q^{52} +(1.46410 - 2.53590i) q^{53} +(-1.34486 - 5.01910i) q^{54} +14.4195 q^{55} +(1.33013 - 4.96410i) q^{57} -4.00000 q^{58} +(-4.31199 - 7.46859i) q^{59} +(-1.73205 + 6.46410i) q^{60} +(3.48477 - 6.03579i) q^{61} -1.79315 q^{62} +1.00000 q^{64} +(-12.9282 + 22.3923i) q^{65} +(6.24384 - 1.67303i) q^{66} +(-2.76795 - 4.79423i) q^{67} -5.41662 q^{68} +(-1.79315 - 1.79315i) q^{69} +2.53590 q^{71} +3.00000i q^{72} +(-3.41542 + 5.91567i) q^{73} +0.535898 q^{74} +(12.1595 + 12.1595i) q^{75} +(-1.48356 + 2.56961i) q^{76} +(-3.00000 + 11.1962i) q^{78} +(2.46410 - 4.26795i) q^{79} +(1.93185 - 3.34607i) q^{80} -9.00000 q^{81} +(-0.637756 - 1.10463i) q^{82} +(-8.95215 - 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +3.73205 q^{86} +(-1.79315 + 6.69213i) q^{87} -3.73205 q^{88} +(3.53553 + 6.12372i) q^{89} +(10.0382 + 5.79555i) q^{90} +(0.732051 + 1.26795i) q^{92} +(-0.803848 + 3.00000i) q^{93} +(5.27792 + 9.14162i) q^{94} +(5.73205 + 9.92820i) q^{95} +(0.448288 - 1.67303i) q^{96} +(-2.94855 - 5.10703i) q^{97} -11.1962i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} + 16 q^{23} + 24 q^{25} + 16 q^{29} + 24 q^{30} - 4 q^{32} - 16 q^{37} + 48 q^{39} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 12 q^{50}+ \cdots + 32 q^{95}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^11 - 24 * q^15 - 4 * q^16 + 8 * q^22 + 16 * q^23 + 24 * q^25 + 16 * q^29 + 24 * q^30 - 4 * q^32 - 16 * q^37 + 48 * q^39 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 12 * q^50 + 24 * q^51 - 16 * q^53 - 24 * q^57 - 32 * q^58 + 8 * q^64 - 48 * q^65 - 36 * q^67 + 48 * q^71 + 32 * q^74 - 24 * q^78 - 8 * q^79 - 72 * q^81 - 56 * q^85 + 16 * q^86 - 16 * q^88 - 8 * q^92 - 48 * q^93 + 32 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$3$	1.22474	+	1.22474i	0.707107	+	0.707107i
$4$	−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	$0.832017\pi$
$6$	−1.67303	+	0.448288i	−0.683013	+	0.183013i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$			3.00000i			1.00000i
$10$	1.93185	−	3.34607i	0.610905	−	1.05812i
$11$	−3.73205			−1.12526			−0.562628	−	0.826710i	$-0.690210\pi$
$11$	−3.73205			−1.12526			−0.562628	+	0.826710i	$0.690210\pi$
$12$	0.448288	−	1.67303i	0.129410	−	0.482963i
$13$	3.34607	−	5.79555i	0.928032	−	1.60740i	0.141420	−	0.989950i	$-0.454833\pi$
$13$	3.34607	−	5.79555i	0.928032	−	1.60740i	0.786612	−	0.617448i	$-0.211833\pi$
$14$		0			0
$15$	−4.73205	−	4.73205i	−1.22181	−	1.22181i
$16$	−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	$-0.0614497\pi$
$18$	−2.59808	−	1.50000i	−0.612372	−	0.353553i
$19$	−1.48356	−	2.56961i	−0.340353	−	0.589509i	0.644145	−	0.764903i	$-0.277213\pi$
$19$	−1.48356	−	2.56961i	−0.340353	−	0.589509i	−0.984498	+	0.175395i	$0.943880\pi$
$20$	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	$-0.548779\pi$
$23$	−1.46410			−0.305286			−0.152643	+	0.988281i	$0.548779\pi$
$24$	1.22474	+	1.22474i	0.250000	+	0.250000i
$25$	9.92820			1.98564
$26$	3.34607	+	5.79555i	0.656217	+	1.13660i
$27$	−3.67423	+	3.67423i	−0.707107	+	0.707107i
$28$		0			0
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	0.989780	−	0.142605i	$-0.0455477\pi$
$29$	2.00000	+	3.46410i	0.371391	+	0.643268i	−0.618389	+	0.785872i	$0.712214\pi$
$30$	6.46410	−	1.73205i	1.18018	−	0.316228i
$31$	0.896575	+	1.55291i	0.161030	+	0.278912i	0.935238	−	0.354019i	$-0.115185\pi$
$31$	0.896575	+	1.55291i	0.161030	+	0.278912i	−0.774209	+	0.632931i	$0.781852\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.57081	−	4.57081i	−0.795676	−	0.795676i
$34$	2.70831	+	4.69093i	0.464471	+	0.804488i
$35$		0			0
$36$	2.59808	−	1.50000i	0.433013	−	0.250000i
$37$	−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
$39$	11.1962	−	3.00000i	1.79282	−	0.480384i
$40$	−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
$45$		−	11.5911i		−	1.72790i
$46$	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	$-0.113009\pi$
$48$	−1.67303	+	0.448288i	−0.241481	+	0.0647048i
$49$		0			0
$50$	−4.96410	+	8.59808i	−0.702030	+	1.21595i
$51$	9.06218	−	2.42820i	1.26896	−	0.340016i
$52$	−6.69213			−0.928032
$53$	1.46410	−	2.53590i	0.201110	−	0.348332i	−0.747776	−	0.663951i	$-0.768879\pi$
$53$	1.46410	−	2.53590i	0.201110	−	0.348332i	0.948886	+	0.315618i	$0.102212\pi$
$54$	−1.34486	−	5.01910i	−0.183013	−	0.683013i
$55$	14.4195			1.94433
$56$		0			0
$57$	1.33013	−	4.96410i	0.176180	−	0.657511i
$58$	−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	$-0.356394\pi$
$60$	−1.73205	+	6.46410i	−0.223607	+	0.834512i
$61$	3.48477	−	6.03579i	0.446179	−	0.772804i	−0.551955	−	0.833874i	$-0.686118\pi$
$61$	3.48477	−	6.03579i	0.446179	−	0.772804i	0.998133	+	0.0610700i	$0.0194513\pi$
$62$	−1.79315			−0.227730
$63$		0			0
$64$	1.00000			0.125000
$65$	−12.9282	+	22.3923i	−1.60355	+	2.77742i
$66$	6.24384	−	1.67303i	0.768564	−	0.205936i
$67$	−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
$69$	−1.79315	−	1.79315i	−0.215870	−	0.215870i
$70$		0			0
$71$	2.53590			0.300956			0.150478	−	0.988613i	$-0.451919\pi$
$71$	2.53590			0.300956			0.150478	+	0.988613i	$0.451919\pi$
$72$			3.00000i			0.353553i
$73$	−3.41542	+	5.91567i	−0.399744	+	0.692377i	−0.993694	−	0.112125i	$-0.964234\pi$
$73$	−3.41542	+	5.91567i	−0.399744	+	0.692377i	0.593950	+	0.804502i	$0.297568\pi$
$74$	0.535898			0.0622969
$75$	12.1595	+	12.1595i	1.40406	+	1.40406i
$76$	−1.48356	+	2.56961i	−0.170176	+	0.294754i
$77$		0			0
$78$	−3.00000	+	11.1962i	−0.339683	+	1.26771i
$79$	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
$81$	−9.00000			−1.00000
$82$	−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
$87$	−1.79315	+	6.69213i	−0.192246	+	0.717472i
$88$	−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	$0.711056\pi$
$90$	10.0382	+	5.79555i	1.05812	+	0.610905i
$91$		0			0
$92$	0.732051	+	1.26795i	0.0763216	+	0.132193i
$93$	−0.803848	+	3.00000i	−0.0833551	+	0.311086i
$94$	5.27792	+	9.14162i	0.544376	+	0.942886i
$95$	5.73205	+	9.92820i	0.588096	+	1.01861i
$96$	0.448288	−	1.67303i	0.0457532	−	0.170753i
$97$	−2.94855	−	5.10703i	−0.299379	−	0.518540i	0.676615	−	0.736337i	$-0.263446\pi$
$97$	−2.94855	−	5.10703i	−0.299379	−	0.518540i	−0.975994	+	0.217797i	$0.930113\pi$
$98$		0			0
$99$		−	11.1962i		−	1.12526i
$100$	−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	$0.578372\pi$
$102$	−2.42820	+	9.06218i	−0.240428	+	0.897289i
$103$	−7.45001			−0.734071			−0.367035	−	0.930207i	$-0.619627\pi$
$103$	−7.45001			−0.734071			−0.367035	+	0.930207i	$0.619627\pi$
$104$	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	0.772317	−	0.635237i	$-0.219098\pi$
$107$	−1.69615	−	2.93782i	−0.163973	−	0.284010i	−0.936290	+	0.351227i	$0.885764\pi$
$108$	5.01910	+	1.34486i	0.482963	+	0.129410i
$109$	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
$111$	0.240237	−	0.896575i	0.0228023	−	0.0850992i
$112$		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	$0.272326\pi$
$114$	3.63397	+	3.63397i	0.340353	+	0.340353i
$115$	5.65685			0.527504
$116$	2.00000	−	3.46410i	0.185695	−	0.321634i
$117$	17.3867	+	10.0382i	1.60740	+	0.928032i
$118$	8.62398			0.793902
$119$		0			0
$120$	−4.73205	−	4.73205i	−0.431975	−	0.431975i
$121$	2.92820			0.266200
$122$	3.48477	+	6.03579i	0.315496	+	0.546455i
$123$	−2.13397	+	0.571797i	−0.192414	+	0.0515572i
$124$	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
$129$	1.67303	−	6.24384i	0.147302	−	0.549740i
$130$	−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	$0.584935\pi$
$132$	−1.67303	+	6.24384i	−0.145619	+	0.543457i
$133$		0			0
$134$	5.53590			0.478229
$135$	14.1962	−	14.1962i	1.22181	−	1.22181i
$136$	2.70831	−	4.69093i	0.232236	−	0.402244i
$137$	−8.66025			−0.739895			−0.369948	−	0.929053i	$-0.620624\pi$
$137$	−8.66025			−0.739895			−0.369948	+	0.929053i	$0.620624\pi$
$138$	2.44949	−	0.656339i	0.208514	−	0.0558713i
$139$	−8.17569	+	14.1607i	−0.693453	+	1.20110i	0.277246	+	0.960799i	$0.410578\pi$
$139$	−8.17569	+	14.1607i	−0.693453	+	1.20110i	−0.970699	+	0.240297i	$0.922755\pi$
$140$		0			0
$141$	17.6603	−	4.73205i	1.48726	−	0.398511i
$142$	−1.26795	+	2.19615i	−0.106404	+	0.184297i
$143$	−12.4877	+	21.6293i	−1.04427	+	1.80873i
$144$	−2.59808	−	1.50000i	−0.216506	−	0.125000i
$145$	−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	$-0.378811\pi$
$149$	9.07180			0.743191			0.371595	+	0.928395i	$0.378811\pi$
$150$	−16.6102	+	4.45069i	−1.35622	+	0.363397i
$151$	−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
$153$	14.0728	+	8.12493i	1.13772	+	0.656861i
$154$		0			0
$155$	−3.46410	−	6.00000i	−0.278243	−	0.481932i
$156$	−8.19615	−	8.19615i	−0.656217	−	0.656217i
$157$	2.31079	+	4.00240i	0.184421	+	0.319427i	0.943381	−	0.331710i	$-0.107626\pi$
$157$	2.31079	+	4.00240i	0.184421	+	0.319427i	−0.758960	+	0.651137i	$0.774292\pi$
$158$	2.46410	+	4.26795i	0.196033	+	0.339540i
$159$	4.89898	−	1.31268i	0.388514	−	0.104102i
$160$	1.93185	+	3.34607i	0.152726	+	0.264530i
$161$		0			0
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	−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
$165$	17.6603	+	17.6603i	1.37485	+	1.37485i
$166$	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
$171$	7.70882	−	4.45069i	0.589509	−	0.340353i
$172$	−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	$0.144952\pi$
$174$	−4.89898	−	4.89898i	−0.371391	−	0.371391i
$175$		0			0
$176$	1.86603	−	3.23205i	0.140657	−	0.243625i
$177$	3.86603	−	14.4282i	0.290588	−	1.08449i
$178$	−7.07107			−0.529999
$179$	−9.46410	+	16.3923i	−0.707380	+	1.22522i	0.258446	+	0.966026i	$0.416790\pi$
$179$	−9.46410	+	16.3923i	−0.707380	+	1.22522i	−0.965826	+	0.259193i	$0.916544\pi$
$180$	−10.0382	+	5.79555i	−0.748203	+	0.431975i
$181$	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
$183$	11.6603	−	3.12436i	0.861951	−	0.230959i
$184$	−1.46410			−0.107935
$185$	1.03528	+	1.79315i	0.0761150	+	0.131835i
$186$	−2.19615	−	2.19615i	−0.161030	−	0.161030i
$187$	−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	−0.884762	−	0.466043i	$-0.845679\pi$
$191$	−0.535898	+	0.928203i	−0.0387762	+	0.0671624i	0.845986	+	0.533205i	$0.179013\pi$
$192$	1.22474	+	1.22474i	0.0883883	+	0.0883883i
$193$	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
$195$	−43.2586	+	11.5911i	−3.09781	+	0.830057i
$196$		0			0
$197$	−3.07180			−0.218856			−0.109428	−	0.993995i	$-0.534902\pi$
$197$	−3.07180			−0.218856			−0.109428	+	0.993995i	$0.534902\pi$
$198$	9.69615	+	5.59808i	0.689076	+	0.397838i
$199$	−8.90138	+	15.4176i	−0.631002	+	1.09293i	0.356345	+	0.934355i	$0.384023\pi$
$199$	−8.90138	+	15.4176i	−0.631002	+	1.09293i	−0.987347	+	0.158574i	$0.949310\pi$
$200$	9.92820			0.702030
$201$	2.48168	−	9.26174i	0.175044	−	0.653273i
$202$	2.44949	−	4.24264i	0.172345	−	0.298511i
$203$		0			0
$204$	−6.63397	−	6.63397i	−0.464471	−	0.464471i
$205$	2.46410	−	4.26795i	0.172100	−	0.298087i
$206$	3.72500	−	6.45189i	0.259533	−	0.449525i
$207$		−	4.39230i		−	0.305286i
$208$	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
$213$	3.10583	+	3.10583i	0.212808	+	0.212808i
$214$	3.39230			0.231893
$215$	7.20977	+	12.4877i	0.491702	+	0.851653i
$216$	−3.67423	+	3.67423i	−0.250000	+	0.250000i
$217$		0			0
$218$	4.46410	+	7.73205i	0.302347	+	0.523681i
$219$	−11.4282	+	3.06218i	−0.772246	+	0.206923i
$220$	−7.20977	−	12.4877i	−0.486082	−	0.841920i
$221$	−18.1244	−	31.3923i	−1.21918	−	2.11167i
$222$	0.656339	+	0.656339i	0.0440506	+	0.0440506i
$223$	−13.3843	−	23.1822i	−0.896276	−	1.55240i	−0.832217	−	0.554450i	$-0.812929\pi$
$223$	−13.3843	−	23.1822i	−0.896276	−	1.55240i	−0.0640595	−	0.997946i	$-0.520405\pi$
$224$		0			0
$225$			29.7846i			1.98564i
$226$	−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	$0.386496\pi$
$228$	−4.96410	+	1.33013i	−0.328756	+	0.0880898i
$229$	−24.9754			−1.65042			−0.825209	−	0.564827i	$-0.808943\pi$
$229$	−24.9754			−1.65042			−0.825209	+	0.564827i	$0.808943\pi$
$230$	−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	$0.123367\pi$
$233$	12.0622	+	20.8923i	0.790220	+	1.36870i	−0.135611	+	0.990762i	$0.543300\pi$
$234$	−17.3867	+	10.0382i	−1.13660	+	0.656217i
$235$	−20.3923	+	35.3205i	−1.33025	+	2.30406i
$236$	−4.31199	+	7.46859i	−0.280687	+	0.486164i
$237$	8.24504	−	2.20925i	0.535573	−	0.143506i
$238$		0			0
$239$	6.46410	−	11.1962i	0.418128	−	0.724219i	−0.577623	−	0.816304i	$-0.696020\pi$
$239$	6.46410	−	11.1962i	0.418128	−	0.724219i	0.995751	+	0.0920846i	$0.0293530\pi$
$240$	6.46410	−	1.73205i	0.417256	−	0.111803i
$241$	−23.4225			−1.50877			−0.754387	−	0.656430i	$-0.772066\pi$
$241$	−23.4225			−1.50877			−0.754387	+	0.656430i	$0.772066\pi$
$242$	−1.46410	+	2.53590i	−0.0941160	+	0.163014i
$243$	−11.0227	−	11.0227i	−0.707107	−	0.707107i
$244$	−6.96953			−0.446179
$245$		0			0
$246$	0.571797	−	2.13397i	0.0364564	−	0.136057i
$247$	−19.8564			−1.26343
$248$	0.896575	+	1.55291i	0.0569326	+	0.0986102i
$249$	8.02628	−	29.9545i	0.508645	−	1.89829i
$250$	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
$255$	−35.0136	+	9.38186i	−2.19263	+	0.587515i
$256$	−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	$0.526735\pi$
$258$	4.57081	+	4.57081i	0.284566	+	0.284566i
$259$		0			0
$260$	25.8564			1.60355
$261$	−10.3923	+	6.00000i	−0.643268	+	0.371391i
$262$	3.01790	−	5.22715i	0.186446	−	0.322934i
$263$	−15.4641			−0.953557			−0.476779	−	0.879023i	$-0.658196\pi$
$263$	−15.4641			−0.953557			−0.476779	+	0.879023i	$0.658196\pi$
$264$	−4.57081	−	4.57081i	−0.281314	−	0.281314i
$265$	−5.65685	+	9.79796i	−0.347498	+	0.601884i
$266$		0			0
$267$	−3.16987	+	11.8301i	−0.193993	+	0.723992i
$268$	−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	$0.221836\pi$
$270$	5.19615	+	19.3923i	0.316228	+	1.18018i
$271$	9.00292	+	15.5935i	0.546888	+	0.947239i	0.998485	+	0.0550165i	$0.0175211\pi$
$271$	9.00292	+	15.5935i	0.546888	+	0.947239i	−0.451597	+	0.892222i	$0.649146\pi$
$272$	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
$276$	−0.656339	+	2.44949i	−0.0395070	+	0.147442i
$277$	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
$279$	−4.65874	+	2.68973i	−0.278912	+	0.161030i
$280$		0			0
$281$	4.92820	+	8.53590i	0.293992	+	0.509209i	0.974750	−	0.223299i	$-0.0716828\pi$
$281$	4.92820	+	8.53590i	0.293992	+	0.509209i	−0.680758	+	0.732508i	$0.738349\pi$
$282$	−4.73205	+	17.6603i	−0.281790	+	1.05165i
$283$	4.70951	+	8.15711i	0.279951	+	0.484890i	0.971372	−	0.237562i	$-0.0763483\pi$
$283$	4.70951	+	8.15711i	0.279951	+	0.484890i	−0.691421	+	0.722452i	$0.743015\pi$
$284$	−1.26795	−	2.19615i	−0.0752389	−	0.130318i
$285$	−5.13922	+	19.1798i	−0.304421	+	1.13611i
$286$	−12.4877	−	21.6293i	−0.738412	−	1.27897i
$287$		0			0
$288$	2.59808	−	1.50000i	0.153093	−	0.0883883i
$289$	−6.16987	−	10.6865i	−0.362934	−	0.628620i
$290$	15.4548			0.907538
$291$	2.64359	−	9.86603i	0.154970	−	0.578357i
$292$	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
$297$	13.7124	−	13.7124i	0.795676	−	0.795676i
$298$	−4.53590	+	7.85641i	−0.262758	+	0.455109i
$299$	−4.89898	+	8.48528i	−0.283315	+	0.490716i
$300$	4.45069	−	16.6102i	0.256961	−	0.958991i
$301$		0			0
$302$	1.19615	−	2.07180i	0.0688308	−	0.119219i
$303$	−6.00000	−	6.00000i	−0.344691	−	0.344691i
$304$	2.96713			0.170176
$305$	−13.4641	+	23.3205i	−0.770952	+	1.33533i
$306$	−14.0728	+	8.12493i	−0.804488	+	0.464471i
$307$	11.0735			0.631996			0.315998	−	0.948760i	$-0.397661\pi$
$307$	11.0735			0.631996			0.315998	+	0.948760i	$0.397661\pi$
$308$		0			0
$309$	−9.12436	−	9.12436i	−0.519066	−	0.519066i
$310$	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	$0.947194\pi$
$312$	11.1962	−	3.00000i	0.633857	−	0.169842i
$313$	11.7112	−	20.2844i	0.661958	−	1.14654i	−0.318143	−	0.948043i	$-0.603059\pi$
$313$	11.7112	−	20.2844i	0.661958	−	1.14654i	0.980101	−	0.198502i	$-0.0636075\pi$
$314$	−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	$-0.572782\pi$
$317$	13.0000	−	22.5167i	0.730153	−	1.26466i	0.956818	−	0.290689i	$-0.0938844\pi$
$318$	−1.31268	+	4.89898i	−0.0736113	+	0.274721i
$319$	−7.46410	−	12.9282i	−0.417909	−	0.723840i
$320$	−3.86370			−0.215988
$321$	1.52073	−	5.67544i	0.0848788	−	0.316772i
$322$		0			0
$323$	−16.0718			−0.894259
$324$	4.50000	+	7.79423i	0.250000	+	0.433013i
$325$	33.2204	−	57.5394i	1.84274	−	3.19171i
$326$	21.3205			1.18083
$327$	14.9372	−	4.00240i	0.826028	−	0.221333i
$328$	−0.637756	+	1.10463i	−0.0352142	+	0.0609928i
$329$		0			0
$330$	−24.1244	+	6.46410i	−1.32800	+	0.355837i
$331$	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
$333$	1.39230	−	0.803848i	0.0762978	−	0.0440506i
$334$	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
$339$	−11.5911	+	3.10583i	−0.629543	+	0.168685i
$340$	20.9282			1.13499
$341$	−3.34607	−	5.79555i	−0.181200	−	0.313847i
$342$			8.90138i			0.481332i
$343$		0			0
$344$	−1.86603	−	3.23205i	−0.100609	−	0.174261i
$345$	6.92820	+	6.92820i	0.373002	+	0.373002i
$346$	0.896575	+	1.55291i	0.0482002	+	0.0834852i
$347$	−10.7942	−	18.6962i	−0.579465	−	1.00366i	−0.995541	−	0.0943323i	$-0.969928\pi$
$347$	−10.7942	−	18.6962i	−0.579465	−	1.00366i	0.416076	−	0.909330i	$-0.363405\pi$
$348$	6.69213	−	1.79315i	0.358736	−	0.0961230i
$349$	8.24504	+	14.2808i	0.441347	+	0.764436i	0.997790	−	0.0664504i	$-0.0211674\pi$
$349$	8.24504	+	14.2808i	0.441347	+	0.764436i	−0.556443	+	0.830886i	$0.687834\pi$
$350$		0			0
$351$	9.00000	+	33.5885i	0.480384	+	1.79282i
$352$	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	$0.251719\pi$
$354$	10.5622	+	10.5622i	0.561373	+	0.561373i
$355$	−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	0.858868	−	0.512197i	$-0.171168\pi$
$359$	−0.267949	−	0.464102i	−0.0141418	−	0.0244943i	−0.873010	+	0.487703i	$0.837835\pi$
$360$		−	11.5911i		−	0.610905i
$361$	5.09808	−	8.83013i	0.268320	−	0.464744i
$362$	−8.48528	+	14.6969i	−0.445976	+	0.772454i
$363$	3.58630	+	3.58630i	0.188232	+	0.188232i
$364$		0			0
$365$	13.1962	−	22.8564i	0.690718	−	1.19636i
$366$	−3.12436	+	11.6603i	−0.163313	+	0.609491i
$367$	15.7322			0.821215			0.410607	−	0.911812i	$-0.365317\pi$
$367$	15.7322			0.821215			0.410607	+	0.911812i	$0.365317\pi$
$368$	0.732051	−	1.26795i	0.0381608	−	0.0660964i
$369$	−3.31388	−	1.91327i	−0.172514	−	0.0996008i
$370$	−2.07055			−0.107643
$371$		0			0
$372$	3.00000	−	0.803848i	0.155543	−	0.0416776i
$373$	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
$375$	−23.3205	−	23.3205i	−1.20427	−	1.20427i
$376$	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
$381$	8.00481	+	8.00481i	0.410099	+	0.410099i
$382$	−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	$0.313272\pi$
$384$	−1.67303	+	0.448288i	−0.0853766	+	0.0228766i
$385$		0			0
$386$	−23.0526			−1.17334
$387$	9.69615	−	5.59808i	0.492883	−	0.284566i
$388$	−2.94855	+	5.10703i	−0.149690	+	0.259270i
$389$	8.00000			0.405616			0.202808	−	0.979219i	$-0.434993\pi$
$389$	8.00000			0.405616			0.202808	+	0.979219i	$0.434993\pi$
$390$	11.5911	−	43.2586i	0.586939	−	2.19048i
$391$	−3.96524	+	6.86800i	−0.200531	+	0.347329i
$392$		0			0
$393$	−7.39230	−	7.39230i	−0.372892	−	0.372892i
$394$	1.53590	−	2.66025i	0.0773774	−	0.134022i
$395$	−9.52056	+	16.4901i	−0.479031	+	0.829706i
$396$	−9.69615	+	5.59808i	−0.487250	+	0.281314i
$397$	9.00292	+	15.5935i	0.451844	+	0.782616i	0.998501	−	0.0547406i	$-0.0174332\pi$
$397$	9.00292	+	15.5935i	0.451844	+	0.782616i	−0.546657	+	0.837357i	$0.684100\pi$
$398$	−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	$-0.353538\pi$
$401$	17.7846			0.888121			0.444061	+	0.895997i	$0.353538\pi$
$402$	6.78006	+	6.78006i	0.338159	+	0.338159i
$403$	12.0000			0.597763
$404$	2.44949	+	4.24264i	0.121867	+	0.211079i
$405$	34.7733			1.72790
$406$		0			0
$407$	1.00000	+	1.73205i	0.0495682	+	0.0858546i
$408$	9.06218	−	2.42820i	0.448645	−	0.120214i
$409$	8.36516	+	14.4889i	0.413631	+	0.716429i	0.995284	−	0.0970077i	$-0.0309271\pi$
$409$	8.36516	+	14.4889i	0.413631	+	0.716429i	−0.581653	+	0.813437i	$0.697594\pi$
$410$	2.46410	+	4.26795i	0.121693	+	0.210779i
$411$	−10.6066	−	10.6066i	−0.523185	−	0.523185i
$412$	3.72500	+	6.45189i	0.183518	+	0.317862i
$413$		0			0
$414$	3.80385	+	2.19615i	0.186949	+	0.107935i
$415$	34.5885	+	59.9090i	1.69788	+	2.94082i
$416$	−6.69213			−0.328109
$417$	−27.3564	+	7.33013i	−1.33965	+	0.358958i
$418$	−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
$423$	27.4249	+	15.8338i	1.33344	+	0.769863i
$424$	1.46410	−	2.53590i	0.0711031	−	0.123154i
$425$	26.8886	−	46.5725i	1.30429	−	2.25910i
$426$	−4.24264	+	1.13681i	−0.205557	+	0.0550787i
$427$		0			0
$428$	−1.69615	+	2.93782i	−0.0819866	+	0.142005i
$429$	−41.7846	+	11.1962i	−2.01738	+	0.540555i
$430$	−14.4195			−0.695372
$431$	18.9282	−	32.7846i	0.911739	−	1.57918i	0.100133	−	0.994974i	$-0.468073\pi$
$431$	18.9282	−	32.7846i	0.911739	−	1.57918i	0.811606	−	0.584205i	$-0.198594\pi$
$432$	−1.34486	−	5.01910i	−0.0647048	−	0.241481i
$433$	−7.10823			−0.341600			−0.170800	−	0.985306i	$-0.554635\pi$
$433$	−7.10823			−0.341600			−0.170800	+	0.985306i	$0.554635\pi$
$434$		0			0
$435$	6.92820	−	25.8564i	0.332182	−	1.23972i
$436$	−8.92820			−0.427583
$437$	2.17209	+	3.76217i	0.103905	+	0.179969i
$438$	3.06218	−	11.4282i	0.146317	−	0.546061i
$439$	−9.79796	+	16.9706i	−0.467631	+	0.809961i	−0.999316	−	0.0369815i	$-0.988226\pi$
$439$	−9.79796	+	16.9706i	−0.467631	+	0.809961i	0.531685	+	0.846942i	$0.321559\pi$
$440$	14.4195			0.687424
$441$		0			0
$442$	36.2487			1.72418
$443$	9.16025	−	15.8660i	0.435217	−	0.753818i	−0.562097	−	0.827072i	$-0.690005\pi$
$443$	9.16025	−	15.8660i	0.435217	−	0.753818i	0.997313	+	0.0732540i	$0.0233384\pi$
$444$	−0.896575	+	0.240237i	−0.0425496	+	0.0114011i
$445$	−13.6603	−	23.6603i	−0.647558	−	1.12160i
$446$	26.7685			1.26753
$447$	11.1106	+	11.1106i	0.525515	+	0.525515i
$448$		0			0
$449$	−17.7846			−0.839308			−0.419654	−	0.907684i	$-0.637849\pi$
$449$	−17.7846			−0.839308			−0.419654	+	0.907684i	$0.637849\pi$
$450$	−25.7942	−	14.8923i	−1.21595	−	0.702030i
$451$	2.38014	−	4.12252i	0.112076	−	0.194122i
$452$	6.92820			0.325875
$453$	−2.92996	−	2.92996i	−0.137662	−	0.137662i
$454$	−5.25933	+	9.10943i	−0.246833	+	0.427527i
$455$		0			0
$456$	1.33013	−	4.96410i	0.0622889	−	0.232465i
$457$	−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
$459$	7.28461	+	27.1865i	0.340016	+	1.26896i
$460$	−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
$465$	3.10583	−	11.5911i	0.144029	−	0.537525i
$466$	−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	$-0.386799\pi$
$468$		−	20.0764i		−	0.928032i
$469$		0			0
$470$	−20.3923	−	35.3205i	−0.940627	−	1.62921i
$471$	−2.07180	+	7.73205i	−0.0954634	+	0.356274i
$472$	−4.31199	−	7.46859i	−0.198475	−	0.343770i
$473$	6.96410	+	12.0622i	0.320210	+	0.554620i
$474$	−2.20925	+	8.24504i	−0.101474	+	0.378707i
$475$	−14.7291	−	25.5116i	−0.675819	−	1.17055i
$476$		0			0
$477$	7.60770	+	4.39230i	0.348332	+	0.201110i
$478$	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	$0.614864\pi$
$480$	−1.73205	+	6.46410i	−0.0790569	+	0.295045i
$481$	−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
$486$	15.0573	−	4.03459i	0.683013	−	0.183013i
$487$	−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
$489$	9.55772	−	35.6699i	0.432215	−	1.61305i
$490$		0			0
$491$	0.696152	−	1.20577i	0.0314169	−	0.0544157i	−0.849889	−	0.526961i	$-0.823331\pi$
$491$	0.696152	−	1.20577i	0.0314169	−	0.0544157i	0.881306	+	0.472545i	$0.156665\pi$
$492$	1.56218	+	1.56218i	0.0704284	+	0.0704284i
$493$	21.6665			0.975809
$494$	9.92820	−	17.1962i	0.446691	−	0.773691i
$495$			43.2586i			1.94433i
$496$	−1.79315			−0.0805149
$497$		0			0
$498$	21.9282	+	21.9282i	0.982626	+	0.982626i
$499$	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
$501$	35.3205	−	9.46410i	1.57800	−	0.422825i
$502$	−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
$507$	14.2487	−	53.1767i	0.632805	−	2.36166i
$508$	−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	$0.699730\pi$
$510$	9.38186	−	35.0136i	0.415436	−	1.55043i
$511$		0			0
$512$	1.00000			0.0441942
$513$	14.8923	+	3.99038i	0.657511	+	0.176180i
$514$	1.34486	−	2.32937i	0.0593194	−	0.102744i
$515$	28.7846			1.26840
$516$	−6.24384	+	1.67303i	−0.274870	+	0.0736512i
$517$	−19.6975	+	34.1170i	−0.866293	+	1.50046i
$518$		0			0
$519$	3.00000	−	0.803848i	0.131685	−	0.0352850i
$520$	−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	$-0.0841329\pi$
$522$		−	12.0000i		−	0.525226i
$523$	−1.88108	−	3.25813i	−0.0822540	−	0.142468i	0.821964	−	0.569540i	$-0.192879\pi$
$523$	−1.88108	−	3.25813i	−0.0822540	−	0.142468i	−0.904218	+	0.427072i	$0.859545\pi$
$524$	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
$528$	6.24384	−	1.67303i	0.271728	−	0.0728094i
$529$	−20.8564			−0.906800
$530$	−5.65685	−	9.79796i	−0.245718	−	0.425596i
$531$	22.4058	−	12.9360i	0.972327	−	0.561373i
$532$		0			0
$533$	4.26795	+	7.39230i	0.184865	+	0.320196i
$534$	−8.66025	−	8.66025i	−0.374766	−	0.374766i
$535$	6.55343	+	11.3509i	0.283329	+	0.490741i
$536$	−2.76795	−	4.79423i	−0.119557	−	0.207079i
$537$	−31.6675	+	8.48528i	−1.36655	+	0.366167i
$538$	−2.82843	−	4.89898i	−0.121942	−	0.211210i
$539$		0			0
$540$	−19.3923	−	5.19615i	−0.834512	−	0.223607i
$541$	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
$543$	20.7846	+	20.7846i	0.891953	+	0.891953i
$544$	−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
$549$	18.1074	+	10.4543i	0.772804	+	0.446179i
$550$	18.5263	−	32.0885i	0.789963	−	1.36826i
$551$	5.93426	−	10.2784i	0.252808	−	0.437876i
$552$	−1.79315	−	1.79315i	−0.0763216	−	0.0763216i
$553$		0			0
$554$	−12.2679	+	21.2487i	−0.521215	+	0.902771i
$555$	−0.928203	+	3.46410i	−0.0394000	+	0.147043i
$556$	16.3514			0.693453
$557$	−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	$0.213557\pi$
$558$		−	5.37945i		−	0.227730i
$559$	−24.9754			−1.05635
$560$		0			0
$561$	−33.8205	+	9.06218i	−1.42790	+	0.382605i
$562$	−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	$-0.347993\pi$
$564$	−12.9282	−	12.9282i	−0.544376	−	0.544376i
$565$	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	−0.982681	−	0.185304i	$-0.940673\pi$
$569$	−7.89230	+	13.6699i	−0.330863	+	0.573071i	0.651819	+	0.758375i	$0.274006\pi$
$570$	−14.0406	−	14.0406i	−0.588096	−	0.588096i
$571$	−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
$573$	−1.79315	+	0.480473i	−0.0749100	+	0.0200721i
$574$		0			0
$575$	−14.5359			−0.606189
$576$			3.00000i			0.125000i
$577$	−22.3178	+	38.6556i	−0.929103	+	1.60925i	−0.144278	+	0.989537i	$0.546086\pi$
$577$	−22.3178	+	38.6556i	−0.929103	+	1.60925i	−0.784825	+	0.619717i	$0.787247\pi$
$578$	12.3397			0.513266
$579$	−10.3342	+	38.5677i	−0.429474	+	1.60282i
$580$	−7.72741	+	13.3843i	−0.320863	+	0.555751i
$581$		0			0
$582$	7.22243	+	7.22243i	0.299379	+	0.299379i
$583$	−5.46410	+	9.46410i	−0.226300	+	0.391963i
$584$	−3.41542	+	5.91567i	−0.141331	+	0.244792i
$585$	−67.1769	−	38.7846i	−2.77742	−	1.60355i
$586$	−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
$591$	−3.76217	−	3.76217i	−0.154755	−	0.154755i
$592$	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	$0.851165\pi$
$594$	5.01910	+	18.7315i	0.205936	+	0.768564i
$595$		0			0
$596$	−4.53590	−	7.85641i	−0.185798	−	0.321811i
$597$	−29.7846	+	7.98076i	−1.21900	+	0.326631i
$598$	−4.89898	−	8.48528i	−0.200334	−	0.346989i
$599$	18.3923	+	31.8564i	0.751489	+	1.30162i	0.947101	+	0.320936i	$0.103997\pi$
$599$	18.3923	+	31.8564i	0.751489	+	1.30162i	−0.195612	+	0.980681i	$0.562669\pi$
$600$	12.1595	+	12.1595i	0.496410	+	0.496410i
$601$	−0.448288	−	0.776457i	−0.0182860	−	0.0316723i	0.856738	−	0.515753i	$-0.172488\pi$
$601$	−0.448288	−	0.776457i	−0.0182860	−	0.0316723i	−0.875024	+	0.484080i	$0.839154\pi$
$602$		0			0
$603$	14.3827	−	8.30385i	0.585708	−	0.338159i
$604$	1.19615	+	2.07180i	0.0486708	+	0.0843002i
$605$	−11.3137			−0.459968
$606$	8.19615	−	2.19615i	0.332946	−	0.0892126i
$607$	31.6675			1.28534			0.642672	−	0.766141i	$-0.277826\pi$
$607$	31.6675			1.28534			0.642672	+	0.766141i	$0.277826\pi$
$608$	−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
$612$		−	16.2499i		−	0.656861i
$613$	−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
$615$	8.24504	−	2.20925i	0.332472	−	0.0890857i
$616$		0			0
$617$	15.4282	−	26.7224i	0.621116	−	1.07580i	−0.368162	−	0.929762i	$-0.620013\pi$
$617$	15.4282	−	26.7224i	0.621116	−	1.07580i	0.989278	−	0.146043i	$-0.0466538\pi$
$618$	12.4641	−	3.33975i	0.501380	−	0.134344i
$619$	−24.6336			−0.990108			−0.495054	−	0.868862i	$-0.664852\pi$
$619$	−24.6336			−0.990108			−0.495054	+	0.868862i	$0.664852\pi$
$620$	−3.46410	+	6.00000i	−0.139122	+	0.240966i
$621$	5.37945	−	5.37945i	0.215870	−	0.215870i
$622$	12.3490			0.495149
$623$		0			0
$624$	−3.00000	+	11.1962i	−0.120096	+	0.448205i
$625$	23.9282			0.957128
$626$	11.7112	+	20.2844i	0.468075	+	0.810729i
$627$	−4.96410	+	18.5263i	−0.198247	+	0.739868i
$628$	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
$633$	−8.48528	+	2.27362i	−0.337260	+	0.0903685i
$634$	13.0000	+	22.5167i	0.516296	+	0.894251i
$635$	−25.2528			−1.00213
$636$	−3.58630	−	3.58630i	−0.142206	−	0.142206i
$637$		0			0
$638$	14.9282			0.591013
$639$			7.60770i			0.300956i
$640$	1.93185	−	3.34607i	0.0763631	−	0.132265i
$641$	17.9282			0.708121			0.354061	−	0.935222i	$-0.384801\pi$
$641$	17.9282			0.708121			0.354061	+	0.935222i	$0.384801\pi$
$642$	4.15471	+	4.15471i	0.163973	+	0.163973i
$643$	−6.53485	+	11.3187i	−0.257709	+	0.446365i	−0.965628	−	0.259929i	$-0.916301\pi$
$643$	−6.53485	+	11.3187i	−0.257709	+	0.446365i	0.707919	+	0.706294i	$0.249634\pi$
$644$		0			0
$645$	−6.46410	+	24.1244i	−0.254524	+	0.949896i
$646$	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	$0.0904070\pi$
$648$	−9.00000			−0.353553
$649$	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	$-0.462544\pi$
$653$	6.00000			0.234798			0.117399	+	0.993085i	$0.462544\pi$
$654$	−4.00240	+	14.9372i	−0.156506	+	0.584090i
$655$	23.3205			0.911208
$656$	−0.637756	−	1.10463i	−0.0249002	−	0.0431284i
$657$	−17.7470	−	10.2462i	−0.692377	−	0.399744i
$658$		0			0
$659$	−0.124356	−	0.215390i	−0.00484421	−	0.00839042i	0.863593	−	0.504189i	$-0.168209\pi$
$659$	−0.124356	−	0.215390i	−0.00484421	−	0.00839042i	−0.868437	+	0.495799i	$0.834875\pi$
$660$	6.46410	−	24.1244i	0.251615	−	0.939039i
$661$		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
$663$	16.2499	−	60.6453i	0.631092	−	2.35527i
$664$	−8.95215	−	15.5056i	−0.347411	−	0.601733i
$665$		0			0
$666$			1.60770i			0.0622969i
$667$	−2.92820	−	5.07180i	−0.113380	−	0.196381i
$668$	−21.1117			−0.816835
$669$	12.0000	−	44.7846i	0.463947	−	1.73147i
$670$	−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
$675$	−36.4785	+	36.4785i	−1.40406	+	1.40406i
$676$	−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	$0.292741\pi$
$678$	3.10583	−	11.5911i	0.119279	−	0.445154i
$679$		0			0
$680$	−10.4641	+	18.1244i	−0.401280	+	0.695037i
$681$	12.8827	+	12.8827i	0.493666	+	0.493666i
$682$	6.69213			0.256255
$683$	1.83975	−	3.18653i	0.0703959	−	0.121929i	−0.828679	−	0.559724i	$-0.810907\pi$
$683$	1.83975	−	3.18653i	0.0703959	−	0.121929i	0.899075	+	0.437795i	$0.144240\pi$
$684$	−7.70882	−	4.45069i	−0.294754	−	0.170176i
$685$	33.4607			1.27847
$686$		0			0
$687$	−30.5885	−	30.5885i	−1.16702	−	1.16702i
$688$	3.73205			0.142283
$689$	−9.79796	−	16.9706i	−0.373273	−	0.646527i
$690$	−9.46410	+	2.53590i	−0.360292	+	0.0965400i
$691$	4.81105	−	8.33298i	0.183021	−	0.317001i	−0.759887	−	0.650055i	$-0.774746\pi$
$691$	4.81105	−	8.33298i	0.183021	−	0.317001i	0.942908	+	0.333054i	$0.108079\pi$
$692$	−1.79315			−0.0681654
$693$		0			0
$694$	21.5885			0.819487
$695$	31.5885	−	54.7128i	1.19822	−	2.07538i
$696$	−1.79315	+	6.69213i	−0.0679692	+	0.253665i
$697$	3.45448	+	5.98334i	0.130848	+	0.226635i
$698$	−16.4901			−0.624159
$699$	−10.8147	+	40.3608i	−0.409048	+	1.52659i
$700$		0			0
$701$	20.7846			0.785024			0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$	−33.5885	−	9.00000i	−1.26771	−	0.339683i
$703$	−0.795040	+	1.37705i	−0.0299855	+	0.0519364i
$704$	−3.73205			−0.140657
$705$	−68.2340	+	18.2832i	−2.56984	+	0.688587i
$706$	−13.2134	+	22.8862i	−0.497292	+	0.861335i
$707$		0			0
$708$	−14.4282	+	3.86603i	−0.542245	+	0.145294i
$709$	−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
$711$	12.8038	+	7.39230i	0.480182	+	0.277233i
$712$	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
$717$	21.6293	−	5.79555i	0.807761	−	0.216439i
$718$	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	$0.925924\pi$
$720$	10.0382	+	5.79555i	0.374101	+	0.215988i
$721$		0			0
$722$	5.09808	+	8.83013i	0.189731	+	0.328623i
$723$	−28.6865	−	28.6865i	−1.06686	−	1.06686i
$724$	−8.48528	−	14.6969i	−0.315353	−	0.546207i
$725$	19.8564	+	34.3923i	0.737448	+	1.27730i
$726$	−4.89898	+	1.31268i	−0.181818	+	0.0487180i
$727$	−0.795040	−	1.37705i	−0.0294864	−	0.0510719i	0.850906	−	0.525319i	$-0.176054\pi$
$727$	−0.795040	−	1.37705i	−0.0294864	−	0.0510719i	−0.880392	+	0.474247i	$0.842721\pi$
$728$		0			0
$729$		−	27.0000i		−	1.00000i
$730$	13.1962	+	22.8564i	0.488412	+	0.845954i
$731$	−20.2151			−0.747682
$732$	−8.53590	−	8.53590i	−0.315496	−	0.315496i
$733$	16.4901			0.609075			0.304538	−	0.952500i	$-0.401498\pi$
$733$	16.4901			0.609075			0.304538	+	0.952500i	$0.401498\pi$
$734$	−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
$738$	3.31388	−	1.91327i	0.121986	−	0.0704284i
$739$	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
$741$	−24.3190	−	24.3190i	−0.893382	−	0.893382i
$742$		0			0
$743$	−25.7846	+	44.6603i	−0.945946	+	1.63843i	−0.192099	+	0.981376i	$0.561529\pi$
$743$	−25.7846	+	44.6603i	−0.945946	+	1.63843i	−0.753847	+	0.657050i	$0.771804\pi$
$744$	−0.803848	+	3.00000i	−0.0294705	+	0.109985i
$745$	−35.0507			−1.28416
$746$	−15.3923	+	26.6603i	−0.563552	+	0.976101i
$747$	46.5167	−	26.8565i	1.70196	−	0.982626i
$748$	20.2151			0.739137
$749$		0			0
$750$	31.8564	−	8.53590i	1.16323	−	0.311687i
$751$	−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
$753$	20.0263	+	20.0263i	0.729798	+	0.729798i
$754$	−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
$759$	6.69213	+	6.69213i	0.242909	+	0.242909i
$760$	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	$0.313857\pi$
$762$	−10.9348	+	2.92996i	−0.396125	+	0.106141i
$763$		0			0
$764$	1.07180			0.0387762
$765$	−54.3731	−	31.3923i	−1.96586	−	1.13499i
$766$	−10.8332	+	18.7637i	−0.391421	+	0.677961i
$767$	−57.7128			−2.08389
$768$	0.448288	−	1.67303i	0.0161762	−	0.0603704i
$769$	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
$771$	−3.29423	−	3.29423i	−0.118639	−	0.118639i
$772$	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	$0.165504\pi$
$774$			11.1962i			0.402437i
$775$	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
$780$	31.6675	+	31.6675i	1.13388	+	1.13388i
$781$	−9.46410			−0.338652
$782$	−3.96524	−	6.86800i	−0.141797	−	0.245599i
$783$	−20.0764	−	5.37945i	−0.717472	−	0.192246i
$784$		0			0
$785$	−8.92820	−	15.4641i	−0.318661	−	0.551937i
$786$	10.0981	−	2.70577i	0.360186	−	0.0965117i
$787$	−23.3717	−	40.4810i	−0.833111	−	1.44299i	−0.895559	−	0.444942i	$-0.853224\pi$
$787$	−23.3717	−	40.4810i	−0.833111	−	1.44299i	0.0624487	−	0.998048i	$-0.480109\pi$
$788$	1.53590	+	2.66025i	0.0547141	+	0.0947676i
$789$	−18.9396	−	18.9396i	−0.674267	−	0.674267i
$790$	−9.52056	−	16.4901i	−0.338726	−	0.586691i
$791$		0			0
$792$		−	11.1962i		−	0.397838i
$793$	−23.3205	−	40.3923i	−0.828136	−	1.43437i
$794$	−18.0058			−0.639003
$795$	−18.9282	+	5.07180i	−0.671314	+	0.179878i
$796$	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
$801$	−18.3712	+	10.6066i	−0.649113	+	0.374766i
$802$	−8.89230	+	15.4019i	−0.313998	+	0.543861i
$803$	12.7465	−	22.0776i	0.449814	−	0.779101i
$804$	−9.26174	+	2.48168i	−0.326636	+	0.0875219i
$805$		0			0
$806$	−6.00000	+	10.3923i	−0.211341	+	0.366053i
$807$	−9.46410	+	2.53590i	−0.333152	+	0.0892679i
$808$	−4.89898			−0.172345
$809$	13.1340	−	22.7487i	0.461766	−	0.799802i	−0.537283	−	0.843402i	$-0.680549\pi$
$809$	13.1340	−	22.7487i	0.461766	−	0.799802i	0.999049	+	0.0435999i	$0.0138827\pi$
$810$	−17.3867	+	30.1146i	−0.610905	+	1.05812i
$811$	−46.1242			−1.61964			−0.809820	−	0.586679i	$-0.800435\pi$
$811$	−46.1242			−1.61964			−0.809820	+	0.586679i	$0.800435\pi$
$812$		0			0
$813$	−8.07180	+	30.1244i	−0.283090	+	1.05651i
$814$	−2.00000			−0.0701000
$815$	41.1881	+	71.3398i	1.44275	+	2.49892i
$816$	−2.42820	+	9.06218i	−0.0850041	+	0.317240i
$817$	−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	−0.760993	−	0.648761i	$-0.775288\pi$
$821$	5.19615	−	9.00000i	0.181347	−	0.314102i	0.942339	+	0.334659i	$0.108621\pi$
$822$	14.4889	−	3.88229i	0.505358	−	0.135410i
$823$	−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
$825$	−45.3799	−	45.3799i	−1.57993	−	1.57993i
$826$		0			0
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−3.80385	+	2.19615i	−0.132193	+	0.0763216i
$829$	18.6622	−	32.3238i	0.648164	−	1.12265i	−0.335397	−	0.942077i	$-0.608870\pi$
$829$	18.6622	−	32.3238i	0.648164	−	1.12265i	0.983561	−	0.180576i	$-0.0577963\pi$
$830$	−69.1769			−2.40117
$831$	30.0502	+	30.0502i	1.04243	+	1.04243i
$832$	3.34607	−	5.79555i	0.116004	−	0.200925i
$833$		0			0
$834$	7.33013	−	27.3564i	0.253822	−	0.947275i
$835$	−40.7846	+	70.6410i	−1.41141	+	2.44463i
$836$	5.53674	−	9.58991i	0.191492	−	0.331674i
$837$	−9.00000	−	2.41154i	−0.311086	−	0.0833551i
$838$	−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
$843$	−4.41851	+	16.4901i	−0.152181	+	0.567949i
$844$	5.07180			0.174578
$845$	61.4032	+	106.353i	2.11233	+	3.65867i
$846$	−27.4249	+	15.8338i	−0.942886	+	0.544376i
$847$		0			0
$848$	1.46410	+	2.53590i	0.0502775	+	0.0870831i
$849$	−4.22243	+	15.7583i	−0.144913	+	0.540824i
$850$	26.8886	+	46.5725i	0.922273	+	1.59742i
$851$	0.392305	+	0.679492i	0.0134480	+	0.0232927i
$852$	1.13681	−	4.24264i	0.0389465	−	0.145350i
$853$	−8.00481	−	13.8647i	−0.274079	−	0.474719i	0.695823	−	0.718213i	$-0.255040\pi$
$853$	−8.00481	−	13.8647i	−0.274079	−	0.474719i	−0.969902	+	0.243494i	$0.921706\pi$
$854$		0			0
$855$	−29.7846	+	17.1962i	−1.01861	+	0.588096i
$856$	−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	$0.545737\pi$
$858$	11.1962	−	41.7846i	0.382230	−	1.42650i
$859$	−14.7341			−0.502721			−0.251361	−	0.967894i	$-0.580878\pi$
$859$	−14.7341			−0.502721			−0.251361	+	0.967894i	$0.580878\pi$
$860$	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	0.614277	−	0.789090i	$-0.289448\pi$
$863$	−11.0526	−	19.1436i	−0.376233	−	0.651656i	−0.990511	+	0.137435i	$0.956114\pi$
$864$	5.01910	+	1.34486i	0.170753	+	0.0457532i
$865$	−3.46410	+	6.00000i	−0.117783	+	0.204006i
$866$	3.55412	−	6.15591i	0.120774	−	0.209186i
$867$	5.53176	−	20.6448i	0.187868	−	0.701134i
$868$		0			0
$869$	−9.19615	+	15.9282i	−0.311958	+	0.540327i
$870$	18.9282	+	18.9282i	0.641726	+	0.641726i
$871$	−37.0470			−1.25529
$872$	4.46410	−	7.73205i	0.151174	−	0.261840i
$873$	15.3211	−	8.84564i	0.518540	−	0.299379i
$874$	−4.34418			−0.146944
$875$		0			0
$876$	8.36603	+	8.36603i	0.282662	+	0.282662i
$877$	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
$879$	−31.8564	+	8.53590i	−1.07449	+	0.287909i
$880$	−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
$885$	−14.9372	+	55.7463i	−0.502108	+	1.87389i
$886$	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	$0.660421\pi$
$888$	0.240237	−	0.896575i	0.00806181	−	0.0300871i
$889$		0			0
$890$	27.3205			0.915786
$891$	33.5885			1.12526
$892$	−13.3843	+	23.1822i	−0.448138	+	0.776198i
$893$	−31.3205			−1.04810
$894$	−15.1774	+	4.06678i	−0.507609	+	0.136013i
$895$	36.5665	−	63.3350i	1.22228	−	2.11706i
$896$		0			0
$897$	−16.3923	+	4.39230i	−0.547323	+	0.146655i
$898$	8.89230	−	15.4019i	0.296740	−	0.513969i
$899$	−3.58630	+	6.21166i	−0.119610	+	0.207170i
$900$	25.7942	−	14.8923i	0.859808	−	0.496410i
$901$	−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
$906$	4.00240	−	1.07244i	0.132971	−	0.0356295i
$907$	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
$909$		−	14.6969i		−	0.487467i
$910$		0			0
$911$	23.4641	+	40.6410i	0.777400	+	1.34650i	0.933435	+	0.358745i	$0.116795\pi$
$911$	23.4641	+	40.6410i	0.777400	+	1.34650i	−0.156035	+	0.987752i	$0.549871\pi$
$912$	3.63397	+	3.63397i	0.120333	+	0.120333i
$913$	33.4099	+	57.8676i	1.10571	+	1.91514i
$914$	−3.52628	−	6.10770i	−0.116639	−	0.202025i
$915$	−45.0518	+	12.0716i	−1.48937	+	0.399074i
$916$	12.4877	+	21.6293i	0.412605	+	0.714652i
$917$		0			0
$918$	−27.1865	−	7.28461i	−0.897289	−	0.240428i
$919$	−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
$921$	13.5622	+	13.5622i	0.446889	+	0.446889i
$922$	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
$927$		−	22.3500i		−	0.734071i
$928$	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	$0.318456\pi$
$930$	8.48528	+	8.48528i	0.278243	+	0.278243i
$931$		0			0
$932$	12.0622	−	20.8923i	0.395110	−	0.684350i
$933$	5.53590	−	20.6603i	0.181237	−	0.676386i
$934$	27.5636			0.901907
$935$	39.0526	−	67.6410i	1.27716	−	2.21210i
$936$	17.3867	+	10.0382i	0.568301	+	0.328109i
$937$	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
$939$	39.1865	−	10.5000i	1.27880	−	0.342655i
$940$	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	$0.878563\pi$
$942$	−5.66025	−	5.66025i	−0.184421	−	0.184421i
$943$	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	−0.911481	−	0.411342i	$-0.865060\pi$
$947$	−3.06218	+	5.30385i	−0.0995074	+	0.172352i	0.811973	+	0.583694i	$0.198393\pi$
$948$	−6.03579	−	6.03579i	−0.196033	−	0.196033i
$949$	22.8564	+	39.5885i	0.741950	+	1.28510i
$950$	29.4582			0.955752
$951$	43.4988	−	11.6555i	1.41055	−	0.377955i
$952$		0			0
$953$	19.0000			0.615470			0.307735	−	0.951472i	$-0.400429\pi$
$953$	19.0000			0.615470			0.307735	+	0.951472i	$0.400429\pi$
$954$	−7.60770	+	4.39230i	−0.246308	+	0.142206i
$955$	2.07055	−	3.58630i	0.0670015	−	0.116050i
$956$	−12.9282			−0.418128
$957$	6.69213	−	24.9754i	0.216326	−	0.807339i
$958$	7.72741	−	13.3843i	0.249661	−	0.432426i
$959$		0			0
$960$	−4.73205	−	4.73205i	−0.152726	−	0.152726i
$961$	13.8923	−	24.0622i	0.448139	−	0.776199i
$962$	1.79315	−	3.10583i	0.0578135	−	0.100136i
$963$	8.81347	−	5.08846i	0.284010	−	0.163973i
$964$	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
$969$	−19.6839	−	19.6839i	−0.632336	−	0.632336i
$970$	−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	$0.848684\pi$
$972$	−4.03459	+	15.0573i	−0.129410	+	0.482963i
$973$		0			0
$974$	−19.3923	−	33.5885i	−0.621370	−	1.07624i
$975$	111.158	−	29.7846i	3.55989	−	0.953871i
$976$	3.48477	+	6.03579i	0.111545	+	0.193201i
$977$	24.9904	+	43.2846i	0.799513	+	1.38480i	0.919934	+	0.392074i	$0.128242\pi$
$977$	24.9904	+	43.2846i	0.799513	+	1.38480i	−0.120420	+	0.992723i	$0.538424\pi$
$978$	26.1122	+	26.1122i	0.834976	+	0.834976i
$979$	−13.1948	−	22.8541i	−0.421707	−	0.730419i
$980$		0			0
$981$	23.1962	+	13.3923i	0.740596	+	0.427583i
$982$	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	$0.464548\pi$
$984$	−2.13397	+	0.571797i	−0.0680286	+	0.0182282i
$985$	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
$990$	−37.4631	−	21.6293i	−1.19065	−	0.687424i
$991$	−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
$993$	7.58871	−	2.03339i	0.240820	−	0.0645276i
$994$		0			0
$995$	34.3923	−	59.5692i	1.09031	−	1.88847i
$996$	−29.9545	+	8.02628i	−0.949144	+	0.254322i
$997$	−6.48906			−0.205511			−0.102755	−	0.994707i	$-0.532766\pi$
$997$	−6.48906			−0.205511			−0.102755	+	0.994707i	$0.532766\pi$
$998$	−6.30385	+	10.9186i	−0.199545	+	0.345622i
$999$	2.68973	+	0.720710i	0.0850992	+	0.0228023i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.1		8	7.2	even	3
882.2.e.s.373.4		8	7.5	odd	6
882.2.e.s.655.1		8	9.7	even	3
882.2.e.s.655.4		8	63.34	odd	6
882.2.f.q.295.2	✓	8	63.52	odd	6
882.2.f.q.295.3	yes	8	63.25	even	3
882.2.f.q.589.2	yes	8	7.3	odd	6
882.2.f.q.589.3	yes	8	7.4	even	3
882.2.h.q.67.1		8	7.6	odd	2	inner
882.2.h.q.67.4		8	1.1	even	1	trivial
882.2.h.q.79.2		8	63.61	odd	6	inner
882.2.h.q.79.3		8	63.16	even	3	inner
2646.2.e.q.1549.1		8	21.2	odd	6
2646.2.e.q.1549.4		8	21.5	even	6
2646.2.e.q.2125.1		8	9.2	odd	6
2646.2.e.q.2125.4		8	63.20	even	6
2646.2.f.r.883.1		8	63.11	odd	6
2646.2.f.r.883.4		8	63.38	even	6
2646.2.f.r.1765.1		8	21.11	odd	6
2646.2.f.r.1765.4		8	21.17	even	6
2646.2.h.t.361.1		8	21.20	even	2
2646.2.h.t.361.4		8	3.2	odd	2
2646.2.h.t.667.1		8	63.47	even	6
2646.2.h.t.667.4		8	63.2	odd	6
7938.2.a.ci.1.1		4	63.59	even	6
7938.2.a.ci.1.4		4	63.32	odd	6
7938.2.a.cp.1.1		4	63.4	even	3
7938.2.a.cp.1.4		4	63.31	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.22474 + 1.22474i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.86370 q^{5} +(-1.67303 + 0.448288i) q^{6} +1.00000 q^{8} +3.00000i q^{9} +(1.93185 - 3.34607i) q^{10} -3.73205 q^{11} +(0.448288 - 1.67303i) q^{12} +(3.34607 - 5.79555i) q^{13} +(-4.73205 - 4.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.70831 - 4.69093i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(-1.48356 - 2.56961i) q^{19} +(1.93185 + 3.34607i) q^{20} +(1.86603 - 3.23205i) q^{22} -1.46410 q^{23} +(1.22474 + 1.22474i) q^{24} +9.92820 q^{25} +(3.34607 + 5.79555i) q^{26} +(-3.67423 + 3.67423i) q^{27} +(2.00000 + 3.46410i) q^{29} +(6.46410 - 1.73205i) q^{30} +(0.896575 + 1.55291i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-4.57081 - 4.57081i) q^{33} +(2.70831 + 4.69093i) q^{34} +(2.59808 - 1.50000i) q^{36} +(-0.267949 - 0.464102i) q^{37} +2.96713 q^{38} +(11.1962 - 3.00000i) q^{39} -3.86370 q^{40} +(-0.637756 + 1.10463i) q^{41} +(-1.86603 - 3.23205i) q^{43} +(1.86603 + 3.23205i) q^{44} -11.5911i q^{45} +(0.732051 - 1.26795i) q^{46} +(5.27792 - 9.14162i) q^{47} +(-1.67303 + 0.448288i) q^{48} +(-4.96410 + 8.59808i) q^{50} +(9.06218 - 2.42820i) q^{51} -6.69213 q^{52} +(1.46410 - 2.53590i) q^{53} +(-1.34486 - 5.01910i) q^{54} +14.4195 q^{55} +(1.33013 - 4.96410i) q^{57} -4.00000 q^{58} +(-4.31199 - 7.46859i) q^{59} +(-1.73205 + 6.46410i) q^{60} +(3.48477 - 6.03579i) q^{61} -1.79315 q^{62} +1.00000 q^{64} +(-12.9282 + 22.3923i) q^{65} +(6.24384 - 1.67303i) q^{66} +(-2.76795 - 4.79423i) q^{67} -5.41662 q^{68} +(-1.79315 - 1.79315i) q^{69} +2.53590 q^{71} +3.00000i q^{72} +(-3.41542 + 5.91567i) q^{73} +0.535898 q^{74} +(12.1595 + 12.1595i) q^{75} +(-1.48356 + 2.56961i) q^{76} +(-3.00000 + 11.1962i) q^{78} +(2.46410 - 4.26795i) q^{79} +(1.93185 - 3.34607i) q^{80} -9.00000 q^{81} +(-0.637756 - 1.10463i) q^{82} +(-8.95215 - 15.5056i) q^{83} +(-10.4641 + 18.1244i) q^{85} +3.73205 q^{86} +(-1.79315 + 6.69213i) q^{87} -3.73205 q^{88} +(3.53553 + 6.12372i) q^{89} +(10.0382 + 5.79555i) q^{90} +(0.732051 + 1.26795i) q^{92} +(-0.803848 + 3.00000i) q^{93} +(5.27792 + 9.14162i) q^{94} +(5.73205 + 9.92820i) q^{95} +(0.448288 - 1.67303i) q^{96} +(-2.94855 - 5.10703i) q^{97} -11.1962i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{4} + 8 q^{8} - 16 q^{11} - 24 q^{15} - 4 q^{16} + 8 q^{22} + 16 q^{23} + 24 q^{25} + 16 q^{29} + 24 q^{30} - 4 q^{32} - 16 q^{37} + 48 q^{39} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 12 q^{50}+ \cdots + 32 q^{95}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^4 + 8 * q^8 - 16 * q^11 - 24 * q^15 - 4 * q^16 + 8 * q^22 + 16 * q^23 + 24 * q^25 + 16 * q^29 + 24 * q^30 - 4 * q^32 - 16 * q^37 + 48 * q^39 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 12 * q^50 + 24 * q^51 - 16 * q^53 - 24 * q^57 - 32 * q^58 + 8 * q^64 - 48 * q^65 - 36 * q^67 + 48 * q^71 + 32 * q^74 - 24 * q^78 - 8 * q^79 - 72 * q^81 - 56 * q^85 + 16 * q^86 - 16 * q^88 - 8 * q^92 - 48 * q^93 + 32 * q^95

Introduction

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