LMFDB - Embedded newform 882.2.e.s.655.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(373,882)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("882.373"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,8,0,8,0,0,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.4
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.s.373.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +(1.67303 + 0.448288i) q^{3} +1.00000 q^{4} +(-1.93185 + 3.34607i) q^{5} +(1.67303 + 0.448288i) q^{6} +1.00000 q^{8} +(2.59808 + 1.50000i) q^{9} +(-1.93185 + 3.34607i) q^{10} +(1.86603 + 3.23205i) q^{11} +(1.67303 + 0.448288i) q^{12} +(-3.34607 - 5.79555i) q^{13} +(-4.73205 + 4.73205i) q^{15} +1.00000 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} +(0.732051 - 1.26795i) q^{23} +(1.67303 + 0.448288i) q^{24} +(-4.96410 - 8.59808i) q^{25} +(-3.34607 - 5.79555i) q^{26} +(3.67423 + 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-4.73205 + 4.73205i) q^{30} +1.79315 q^{31} +1.00000 q^{32} +(1.67303 + 6.24384i) q^{33} +(-2.70831 + 4.69093i) q^{34} +(2.59808 + 1.50000i) q^{36} +(-0.267949 - 0.464102i) q^{37} +(1.48356 + 2.56961i) q^{38} +(-3.00000 - 11.1962i) q^{39} +(-1.93185 + 3.34607i) q^{40} +(0.637756 + 1.10463i) q^{41} +(-1.86603 + 3.23205i) q^{43} +(1.86603 + 3.23205i) q^{44} +(-10.0382 + 5.79555i) q^{45} +(0.732051 - 1.26795i) q^{46} +10.5558 q^{47} +(1.67303 + 0.448288i) q^{48} +(-4.96410 - 8.59808i) q^{50} +(-6.63397 + 6.63397i) q^{51} +(-3.34607 - 5.79555i) q^{52} +(1.46410 - 2.53590i) q^{53} +(3.67423 + 3.67423i) q^{54} -14.4195 q^{55} +(1.33013 + 4.96410i) q^{57} +(2.00000 - 3.46410i) q^{58} -8.62398 q^{59} +(-4.73205 + 4.73205i) q^{60} +6.96953 q^{61} +1.79315 q^{62} +1.00000 q^{64} +25.8564 q^{65} +(1.67303 + 6.24384i) q^{66} +5.53590 q^{67} +(-2.70831 + 4.69093i) q^{68} +(1.79315 - 1.79315i) q^{69} +2.53590 q^{71} +(2.59808 + 1.50000i) q^{72} +(3.41542 - 5.91567i) q^{73} +(-0.267949 - 0.464102i) q^{74} +(-4.45069 - 16.6102i) q^{75} +(1.48356 + 2.56961i) q^{76} +(-3.00000 - 11.1962i) q^{78} -4.92820 q^{79} +(-1.93185 + 3.34607i) q^{80} +(4.50000 + 7.79423i) q^{81} +(0.637756 + 1.10463i) q^{82} +(8.95215 - 15.5056i) q^{83} +(-10.4641 - 18.1244i) q^{85} +(-1.86603 + 3.23205i) q^{86} +(4.89898 - 4.89898i) q^{87} +(1.86603 + 3.23205i) q^{88} +(-3.53553 - 6.12372i) q^{89} +(-10.0382 + 5.79555i) q^{90} +(0.732051 - 1.26795i) q^{92} +(3.00000 + 0.803848i) q^{93} +10.5558 q^{94} -11.4641 q^{95} +(1.67303 + 0.448288i) q^{96} +(2.94855 - 5.10703i) q^{97} +11.1962i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} + 8 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 24 q^{30} + 8 q^{32} - 16 q^{37} - 24 q^{39} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 12 q^{50}+ \cdots - 64 q^{95}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 + 8 * q^11 - 24 * q^15 + 8 * q^16 + 8 * q^22 - 8 * q^23 - 12 * q^25 + 16 * q^29 - 24 * q^30 + 8 * q^32 - 16 * q^37 - 24 * q^39 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 12 * q^50 - 60 * q^51 - 16 * q^53 - 24 * q^57 + 16 * q^58 - 24 * q^60 + 8 * q^64 + 96 * q^65 + 72 * q^67 + 48 * q^71 - 16 * q^74 - 24 * q^78 + 16 * q^79 + 36 * q^81 - 56 * q^85 - 8 * q^86 + 8 * q^88 - 8 * q^92 + 24 * q^93 - 64 * q^95

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	1.67303	+	0.448288i	0.965926	+	0.258819i
$3$	1.67303	+	0.448288i	0.965926	+	0.258819i
$4$	1.00000			0.500000
$5$	−1.93185	+	3.34607i	−0.863950	+	1.49641i	0.00413535	+	0.999991i	$0.498684\pi$
$5$	−1.93185	+	3.34607i	−0.863950	+	1.49641i	−0.868086	+	0.496414i	$0.834650\pi$
$6$	1.67303	+	0.448288i	0.683013	+	0.183013i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	2.59808	+	1.50000i	0.866025	+	0.500000i
$10$	−1.93185	+	3.34607i	−0.610905	+	1.05812i
$11$	1.86603	+	3.23205i	0.562628	+	0.974500i	0.997266	+	0.0738948i	$0.0235429\pi$
$11$	1.86603	+	3.23205i	0.562628	+	0.974500i	−0.434638	+	0.900605i	$0.643124\pi$
$12$	1.67303	+	0.448288i	0.482963	+	0.129410i
$13$	−3.34607	−	5.79555i	−0.928032	−	1.60740i	−0.786612	−	0.617448i	$-0.788167\pi$
$13$	−3.34607	−	5.79555i	−0.928032	−	1.60740i	−0.141420	−	0.989950i	$-0.545167\pi$
$14$		0			0
$15$	−4.73205	+	4.73205i	−1.22181	+	1.22181i
$16$	1.00000			0.250000
$17$	−2.70831	+	4.69093i	−0.656861	+	1.13772i	0.324562	+	0.945864i	$0.394783\pi$
$17$	−2.70831	+	4.69093i	−0.656861	+	1.13772i	−0.981424	+	0.191853i	$0.938550\pi$
$18$	2.59808	+	1.50000i	0.612372	+	0.353553i
$19$	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
$23$	0.732051	−	1.26795i	0.152643	−	0.264386i	−0.779555	−	0.626334i	$-0.784555\pi$
$23$	0.732051	−	1.26795i	0.152643	−	0.264386i	0.932198	+	0.361948i	$0.117888\pi$
$24$	1.67303	+	0.448288i	0.341506	+	0.0915064i
$25$	−4.96410	−	8.59808i	−0.992820	−	1.71962i
$26$	−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	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$	−4.73205	+	4.73205i	−0.863950	+	0.863950i
$31$	1.79315			0.322059			0.161030	−	0.986950i	$-0.448519\pi$
$31$	1.79315			0.322059			0.161030	+	0.986950i	$0.448519\pi$
$32$	1.00000			0.176777
$33$	1.67303	+	6.24384i	0.291238	+	1.08691i
$34$	−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	$0.847360\pi$
$38$	1.48356	+	2.56961i	0.240666	+	0.416845i
$39$	−3.00000	−	11.1962i	−0.480384	−	1.79282i
$40$	−1.93185	+	3.34607i	−0.305453	+	0.529059i
$41$	0.637756	+	1.10463i	0.0996008	+	0.172514i	0.911519	−	0.411257i	$-0.134910\pi$
$41$	0.637756	+	1.10463i	0.0996008	+	0.172514i	−0.811919	+	0.583771i	$0.801577\pi$
$42$		0			0
$43$	−1.86603	+	3.23205i	−0.284566	+	0.492883i	−0.972504	−	0.232887i	$-0.925183\pi$
$43$	−1.86603	+	3.23205i	−0.284566	+	0.492883i	0.687938	+	0.725770i	$0.258516\pi$
$44$	1.86603	+	3.23205i	0.281314	+	0.487250i
$45$	−10.0382	+	5.79555i	−1.49641	+	0.863950i
$46$	0.732051	−	1.26795i	0.107935	−	0.186949i
$47$	10.5558			1.53973			0.769863	−	0.638209i	$-0.220324\pi$
$47$	10.5558			1.53973			0.769863	+	0.638209i	$0.220324\pi$
$48$	1.67303	+	0.448288i	0.241481	+	0.0647048i
$49$		0			0
$50$	−4.96410	−	8.59808i	−0.702030	−	1.21595i
$51$	−6.63397	+	6.63397i	−0.928942	+	0.928942i
$52$	−3.34607	−	5.79555i	−0.464016	−	0.803699i
$53$	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	$0.102212\pi$
$54$	3.67423	+	3.67423i	0.500000	+	0.500000i
$55$	−14.4195			−1.94433
$56$		0			0
$57$	1.33013	+	4.96410i	0.176180	+	0.657511i
$58$	2.00000	−	3.46410i	0.262613	−	0.454859i
$59$	−8.62398			−1.12275			−0.561373	−	0.827563i	$-0.689727\pi$
$59$	−8.62398			−1.12275			−0.561373	+	0.827563i	$0.689727\pi$
$60$	−4.73205	+	4.73205i	−0.610905	+	0.610905i
$61$	6.96953			0.892357			0.446179	−	0.894944i	$-0.352785\pi$
$61$	6.96953			0.892357			0.446179	+	0.894944i	$0.352785\pi$
$62$	1.79315			0.227730
$63$		0			0
$64$	1.00000			0.125000
$65$	25.8564			3.20709
$66$	1.67303	+	6.24384i	0.205936	+	0.768564i
$67$	5.53590			0.676318			0.338159	−	0.941089i	$-0.390196\pi$
$67$	5.53590			0.676318			0.338159	+	0.941089i	$0.390196\pi$
$68$	−2.70831	+	4.69093i	−0.328431	+	0.568859i
$69$	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	$0.451919\pi$
$72$	2.59808	+	1.50000i	0.306186	+	0.176777i
$73$	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	$0.0357656\pi$
$74$	−0.267949	−	0.464102i	−0.0311485	−	0.0539507i
$75$	−4.45069	−	16.6102i	−0.513922	−	1.91798i
$76$	1.48356	+	2.56961i	0.170176	+	0.294754i
$77$		0			0
$78$	−3.00000	−	11.1962i	−0.339683	−	1.26771i
$79$	−4.92820			−0.554466			−0.277233	−	0.960803i	$-0.589417\pi$
$79$	−4.92820			−0.554466			−0.277233	+	0.960803i	$0.589417\pi$
$80$	−1.93185	+	3.34607i	−0.215988	+	0.374101i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$	0.637756	+	1.10463i	0.0704284	+	0.121986i
$83$	8.95215	−	15.5056i	0.982626	−	1.70196i	0.330583	−	0.943777i	$-0.392755\pi$
$83$	8.95215	−	15.5056i	0.982626	−	1.70196i	0.652043	−	0.758182i	$-0.273912\pi$
$84$		0			0
$85$	−10.4641	−	18.1244i	−1.13499	−	1.96586i
$86$	−1.86603	+	3.23205i	−0.201219	+	0.348521i
$87$	4.89898	−	4.89898i	0.525226	−	0.525226i
$88$	1.86603	+	3.23205i	0.198919	+	0.344538i
$89$	−3.53553	−	6.12372i	−0.374766	−	0.649113i	0.615526	−	0.788116i	$-0.288944\pi$
$89$	−3.53553	−	6.12372i	−0.374766	−	0.649113i	−0.990292	+	0.139003i	$0.955610\pi$
$90$	−10.0382	+	5.79555i	−1.05812	+	0.610905i
$91$		0			0
$92$	0.732051	−	1.26795i	0.0763216	−	0.132193i
$93$	3.00000	+	0.803848i	0.311086	+	0.0833551i
$94$	10.5558			1.08875
$95$	−11.4641			−1.17619
$96$	1.67303	+	0.448288i	0.170753	+	0.0457532i
$97$	2.94855	−	5.10703i	0.299379	−	0.518540i	−0.676615	−	0.736337i	$-0.736554\pi$
$97$	2.94855	−	5.10703i	0.299379	−	0.518540i	0.975994	+	0.217797i	$0.0698870\pi$
$98$		0			0
$99$			11.1962i			1.12526i
$100$	−4.96410	−	8.59808i	−0.496410	−	0.859808i
$101$	−2.44949	−	4.24264i	−0.243733	−	0.422159i	0.718041	−	0.696000i	$-0.245039\pi$
$101$	−2.44949	−	4.24264i	−0.243733	−	0.422159i	−0.961775	+	0.273842i	$0.911706\pi$
$102$	−6.63397	+	6.63397i	−0.656861	+	0.656861i
$103$	−3.72500	+	6.45189i	−0.367035	+	0.635724i	−0.989101	−	0.147241i	$-0.952961\pi$
$103$	−3.72500	+	6.45189i	−0.367035	+	0.635724i	0.622065	+	0.782965i	$0.286294\pi$
$104$	−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	$0.885764\pi$
$108$	3.67423	+	3.67423i	0.353553	+	0.353553i
$109$	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	$0.0260317\pi$
$110$	−14.4195			−1.37485
$111$	−0.240237	−	0.896575i	−0.0228023	−	0.0850992i
$112$		0			0
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	0.655814	−	0.754923i	$-0.272326\pi$
$113$	−3.46410	−	6.00000i	−0.325875	−	0.564433i	−0.981689	+	0.190490i	$0.938992\pi$
$114$	1.33013	+	4.96410i	0.124578	+	0.464931i
$115$	2.82843	+	4.89898i	0.263752	+	0.456832i
$116$	2.00000	−	3.46410i	0.185695	−	0.321634i
$117$		−	20.0764i		−	1.85606i
$118$	−8.62398			−0.793902
$119$		0			0
$120$	−4.73205	+	4.73205i	−0.431975	+	0.431975i
$121$	−1.46410	+	2.53590i	−0.133100	+	0.230536i
$122$	6.96953			0.630992
$123$	0.571797	+	2.13397i	0.0515572	+	0.192414i
$124$	1.79315			0.161030
$125$	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	$0.406350\pi$
$128$	1.00000			0.0883883
$129$	−4.57081	+	4.57081i	−0.402437	+	0.402437i
$130$	25.8564			2.26776
$131$	−3.01790	+	5.22715i	−0.263675	+	0.456698i	−0.967216	−	0.253957i	$-0.918268\pi$
$131$	−3.01790	+	5.22715i	−0.263675	+	0.456698i	0.703541	+	0.710655i	$0.251601\pi$
$132$	1.67303	+	6.24384i	0.145619	+	0.543457i
$133$		0			0
$134$	5.53590			0.478229
$135$	−19.3923	+	5.19615i	−1.66902	+	0.447214i
$136$	−2.70831	+	4.69093i	−0.232236	+	0.402244i
$137$	4.33013	+	7.50000i	0.369948	+	0.640768i	0.989557	−	0.144142i	$-0.0460423\pi$
$137$	4.33013	+	7.50000i	0.369948	+	0.640768i	−0.619609	+	0.784910i	$0.712709\pi$
$138$	1.79315	−	1.79315i	0.152643	−	0.152643i
$139$	8.17569	+	14.1607i	0.693453	+	1.20110i	0.970699	+	0.240297i	$0.0772450\pi$
$139$	8.17569	+	14.1607i	0.693453	+	1.20110i	−0.277246	+	0.960799i	$0.589422\pi$
$140$		0			0
$141$	17.6603	+	4.73205i	1.48726	+	0.398511i
$142$	2.53590			0.212808
$143$	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
$149$	−4.53590	+	7.85641i	−0.371595	+	0.643622i	−0.989811	−	0.142386i	$-0.954522\pi$
$149$	−4.53590	+	7.85641i	−0.371595	+	0.643622i	0.618216	+	0.786008i	$0.287856\pi$
$150$	−4.45069	−	16.6102i	−0.363397	−	1.35622i
$151$	1.19615	+	2.07180i	0.0973415	+	0.168600i	0.910583	−	0.413325i	$-0.135633\pi$
$151$	1.19615	+	2.07180i	0.0973415	+	0.168600i	−0.813242	+	0.581926i	$0.802299\pi$
$152$	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
$156$	−3.00000	−	11.1962i	−0.240192	−	0.896410i
$157$	4.62158			0.368842			0.184421	−	0.982847i	$-0.440959\pi$
$157$	4.62158			0.368842			0.184421	+	0.982847i	$0.440959\pi$
$158$	−4.92820			−0.392067
$159$	3.58630	−	3.58630i	0.284412	−	0.284412i
$160$	−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	$-0.481185\pi$
$164$	0.637756	+	1.10463i	0.0498004	+	0.0862568i
$165$	−24.1244	−	6.46410i	−1.87808	−	0.503230i
$166$	8.95215	−	15.5056i	0.694822	−	1.20347i
$167$	−10.5558	−	18.2832i	−0.816835	−	1.41480i	−0.908003	−	0.418964i	$-0.862393\pi$
$167$	−10.5558	−	18.2832i	−0.816835	−	1.41480i	0.0911679	−	0.995836i	$-0.470940\pi$
$168$		0			0
$169$	−15.8923	+	27.5263i	−1.22248	+	2.11741i
$170$	−10.4641	−	18.1244i	−0.802560	−	1.39007i
$171$			8.90138i			0.680706i
$172$	−1.86603	+	3.23205i	−0.142283	+	0.246442i
$173$	1.79315			0.136331			0.0681654	−	0.997674i	$-0.478285\pi$
$173$	1.79315			0.136331			0.0681654	+	0.997674i	$0.478285\pi$
$174$	4.89898	−	4.89898i	0.371391	−	0.371391i
$175$		0			0
$176$	1.86603	+	3.23205i	0.140657	+	0.243625i
$177$	−14.4282	−	3.86603i	−1.08449	−	0.290588i
$178$	−3.53553	−	6.12372i	−0.264999	−	0.458993i
$179$	−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	$-0.717235\pi$
$181$	−16.9706			−1.26141			−0.630706	+	0.776022i	$0.717235\pi$
$182$		0			0
$183$	11.6603	+	3.12436i	0.861951	+	0.230959i
$184$	0.732051	−	1.26795i	0.0539675	−	0.0934745i
$185$	2.07055			0.152230
$186$	3.00000	+	0.803848i	0.219971	+	0.0589410i
$187$	−20.2151			−1.47827
$188$	10.5558			0.769863
$189$		0			0
$190$	−11.4641			−0.831693
$191$	1.07180			0.0775525			0.0387762	−	0.999248i	$-0.487654\pi$
$191$	1.07180			0.0775525			0.0387762	+	0.999248i	$0.487654\pi$
$192$	1.67303	+	0.448288i	0.120741	+	0.0323524i
$193$	−23.0526			−1.65936			−0.829680	−	0.558240i	$-0.811477\pi$
$193$	−23.0526			−1.65936			−0.829680	+	0.558240i	$0.811477\pi$
$194$	2.94855	−	5.10703i	0.211693	−	0.366663i
$195$	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	$0.534902\pi$
$198$			11.1962i			0.795676i
$199$	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	$-0.0506895\pi$
$200$	−4.96410	−	8.59808i	−0.351015	−	0.607976i
$201$	9.26174	+	2.48168i	0.653273	+	0.175044i
$202$	−2.44949	−	4.24264i	−0.172345	−	0.298511i
$203$		0			0
$204$	−6.63397	+	6.63397i	−0.464471	+	0.464471i
$205$	−4.92820			−0.344201
$206$	−3.72500	+	6.45189i	−0.259533	+	0.449525i
$207$	3.80385	−	2.19615i	0.264386	−	0.152643i
$208$	−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	0.765437	−	0.643511i	$-0.222523\pi$
$211$	−2.53590	−	4.39230i	−0.174578	−	0.302379i	−0.940015	+	0.341132i	$0.889190\pi$
$212$	1.46410	−	2.53590i	0.100555	−	0.174166i
$213$	4.24264	+	1.13681i	0.290701	+	0.0778931i
$214$	−1.69615	−	2.93782i	−0.115947	−	0.200825i
$215$	−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
$219$	8.36603	−	8.36603i	0.565324	−	0.565324i
$220$	−14.4195			−0.972165
$221$	36.2487			2.43835
$222$	−0.240237	−	0.896575i	−0.0161236	−	0.0601742i
$223$	13.3843	−	23.1822i	0.896276	−	1.55240i	0.0640595	−	0.997946i	$-0.479595\pi$
$223$	13.3843	−	23.1822i	0.896276	−	1.55240i	0.832217	−	0.554450i	$-0.187071\pi$
$224$		0			0
$225$		−	29.7846i		−	1.98564i
$226$	−3.46410	−	6.00000i	−0.230429	−	0.399114i
$227$	5.25933	+	9.10943i	0.349074	+	0.604614i	0.986085	−	0.166240i	$-0.0531627\pi$
$227$	5.25933	+	9.10943i	0.349074	+	0.604614i	−0.637011	+	0.770855i	$0.719829\pi$
$228$	1.33013	+	4.96410i	0.0880898	+	0.328756i
$229$	−12.4877	+	21.6293i	−0.825209	+	1.42930i	0.0765496	+	0.997066i	$0.475610\pi$
$229$	−12.4877	+	21.6293i	−0.825209	+	1.42930i	−0.901759	+	0.432239i	$0.857724\pi$
$230$	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	$0.543300\pi$
$234$		−	20.0764i		−	1.31243i
$235$	−20.3923	+	35.3205i	−1.33025	+	2.30406i
$236$	−8.62398			−0.561373
$237$	−8.24504	−	2.20925i	−0.535573	−	0.143506i
$238$		0			0
$239$	6.46410	+	11.1962i	0.418128	+	0.724219i	0.995751	−	0.0920846i	$-0.0293530\pi$
$239$	6.46410	+	11.1962i	0.418128	+	0.724219i	−0.577623	+	0.816304i	$0.696020\pi$
$240$	−4.73205	+	4.73205i	−0.305453	+	0.305453i
$241$	−11.7112	−	20.2844i	−0.754387	−	1.30664i	−0.945679	−	0.325103i	$-0.894601\pi$
$241$	−11.7112	−	20.2844i	−0.754387	−	1.30664i	0.191292	−	0.981533i	$-0.438732\pi$
$242$	−1.46410	+	2.53590i	−0.0941160	+	0.163014i
$243$	4.03459	+	15.0573i	0.258819	+	0.965926i
$244$	6.96953			0.446179
$245$		0			0
$246$	0.571797	+	2.13397i	0.0364564	+	0.136057i
$247$	9.92820	−	17.1962i	0.631716	−	1.09416i
$248$	1.79315			0.113865
$249$	21.9282	−	21.9282i	1.38964	−	1.38964i
$250$	19.0411			1.20427
$251$	−16.3514			−1.03209			−0.516045	−	0.856561i	$-0.672596\pi$
$251$	−16.3514			−1.03209			−0.516045	+	0.856561i	$0.672596\pi$
$252$		0			0
$253$	5.46410			0.343525
$254$	6.53590			0.410099
$255$	−9.38186	−	35.0136i	−0.587515	−	2.19263i
$256$	1.00000			0.0625000
$257$	−1.34486	+	2.32937i	−0.0838903	+	0.145302i	−0.904918	−	0.425586i	$-0.860068\pi$
$257$	−1.34486	+	2.32937i	−0.0838903	+	0.145302i	0.821028	+	0.570889i	$0.193401\pi$
$258$	−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
$263$	7.73205	+	13.3923i	0.476779	+	0.825805i	0.999646	−	0.0266092i	$-0.00847098\pi$
$263$	7.73205	+	13.3923i	0.476779	+	0.825805i	−0.522867	+	0.852414i	$0.675138\pi$
$264$	1.67303	+	6.24384i	0.102968	+	0.384282i
$265$	5.65685	+	9.79796i	0.347498	+	0.601884i
$266$		0			0
$267$	−3.16987	−	11.8301i	−0.193993	−	0.723992i
$268$	5.53590			0.338159
$269$	2.82843	−	4.89898i	0.172452	−	0.298696i	−0.766824	−	0.641857i	$-0.778164\pi$
$269$	2.82843	−	4.89898i	0.172452	−	0.298696i	0.939277	+	0.343161i	$0.111498\pi$
$270$	−19.3923	+	5.19615i	−1.18018	+	0.316228i
$271$	−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
$275$	18.5263	−	32.0885i	1.11718	−	1.93501i
$276$	1.79315	−	1.79315i	0.107935	−	0.107935i
$277$	−12.2679	−	21.2487i	−0.737110	−	1.27671i	−0.953792	−	0.300469i	$-0.902857\pi$
$277$	−12.2679	−	21.2487i	−0.737110	−	1.27671i	0.216682	−	0.976242i	$-0.430477\pi$
$278$	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	−0.680758	−	0.732508i	$-0.738349\pi$
$281$	4.92820	−	8.53590i	0.293992	−	0.509209i	0.974750	+	0.223299i	$0.0716828\pi$
$282$	17.6603	+	4.73205i	1.05165	+	0.281790i
$283$	9.41902			0.559903			0.279951	−	0.960014i	$-0.409682\pi$
$283$	9.41902			0.559903			0.279951	+	0.960014i	$0.409682\pi$
$284$	2.53590			0.150478
$285$	−19.1798	−	5.13922i	−1.13611	−	0.304421i
$286$	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
$290$	7.72741	+	13.3843i	0.453769	+	0.785951i
$291$	7.22243	−	7.22243i	0.423386	−	0.423386i
$292$	3.41542	−	5.91567i	0.199872	−	0.346189i
$293$	9.52056	+	16.4901i	0.556197	+	0.963361i	0.997809	+	0.0661554i	$0.0210733\pi$
$293$	9.52056	+	16.4901i	0.556197	+	0.963361i	−0.441612	+	0.897206i	$0.645593\pi$
$294$		0			0
$295$	16.6603	−	28.8564i	0.969997	−	1.68008i
$296$	−0.267949	−	0.464102i	−0.0155742	−	0.0269754i
$297$	−5.01910	+	18.7315i	−0.291238	+	1.08691i
$298$	−4.53590	+	7.85641i	−0.262758	+	0.455109i
$299$	−9.79796			−0.566631
$300$	−4.45069	−	16.6102i	−0.256961	−	0.958991i
$301$		0			0
$302$	1.19615	+	2.07180i	0.0688308	+	0.119219i
$303$	−2.19615	−	8.19615i	−0.126166	−	0.470857i
$304$	1.48356	+	2.56961i	0.0850882	+	0.147377i
$305$	−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	$-0.602339\pi$
$307$	−11.0735			−0.631996			−0.315998	+	0.948760i	$0.602339\pi$
$308$		0			0
$309$	−9.12436	+	9.12436i	−0.519066	+	0.519066i
$310$	−3.46410	+	6.00000i	−0.196748	+	0.340777i
$311$	−12.3490			−0.700247			−0.350123	−	0.936704i	$-0.613860\pi$
$311$	−12.3490			−0.700247			−0.350123	+	0.936704i	$0.613860\pi$
$312$	−3.00000	−	11.1962i	−0.169842	−	0.633857i
$313$	23.4225			1.32392			0.661958	−	0.749541i	$-0.269726\pi$
$313$	23.4225			1.32392			0.661958	+	0.749541i	$0.269726\pi$
$314$	4.62158			0.260811
$315$		0			0
$316$	−4.92820			−0.277233
$317$	−26.0000			−1.46031			−0.730153	−	0.683284i	$-0.760551\pi$
$317$	−26.0000			−1.46031			−0.730153	+	0.683284i	$0.760551\pi$
$318$	3.58630	−	3.58630i	0.201110	−	0.201110i
$319$	14.9282			0.835819
$320$	−1.93185	+	3.34607i	−0.107994	+	0.187051i
$321$	−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
$326$	−10.6603	−	18.4641i	−0.590417	−	1.02263i
$327$	10.9348	−	10.9348i	0.604694	−	0.604694i
$328$	0.637756	+	1.10463i	0.0352142	+	0.0609928i
$329$		0			0
$330$	−24.1244	−	6.46410i	−1.32800	−	0.355837i
$331$	−4.53590			−0.249316			−0.124658	−	0.992200i	$-0.539783\pi$
$331$	−4.53590			−0.249316			−0.124658	+	0.992200i	$0.539783\pi$
$332$	8.95215	−	15.5056i	0.491313	−	0.850979i
$333$		−	1.60770i		−	0.0881012i
$334$	−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	0.945468	−	0.325714i	$-0.105605\pi$
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	−0.754811	+	0.655942i	$0.772271\pi$
$338$	−15.8923	+	27.5263i	−0.864427	+	1.49723i
$339$	−3.10583	−	11.5911i	−0.168685	−	0.629543i
$340$	−10.4641	−	18.1244i	−0.567496	−	0.982931i
$341$	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
$345$	2.53590	+	9.46410i	0.136528	+	0.509530i
$346$	1.79315			0.0964004
$347$	21.5885			1.15893			0.579465	−	0.814997i	$-0.303262\pi$
$347$	21.5885			1.15893			0.579465	+	0.814997i	$0.303262\pi$
$348$	4.89898	−	4.89898i	0.262613	−	0.262613i
$349$	−8.24504	+	14.2808i	−0.441347	+	0.764436i	−0.997790	−	0.0664504i	$-0.978833\pi$
$349$	−8.24504	+	14.2808i	−0.441347	+	0.764436i	0.556443	+	0.830886i	$0.312166\pi$
$350$		0			0
$351$	9.00000	−	33.5885i	0.480384	−	1.79282i
$352$	1.86603	+	3.23205i	0.0994595	+	0.172269i
$353$	13.2134	+	22.8862i	0.703277	+	1.21811i	0.967310	+	0.253598i	$0.0816139\pi$
$353$	13.2134	+	22.8862i	0.703277	+	1.21811i	−0.264033	+	0.964514i	$0.585053\pi$
$354$	−14.4282	−	3.86603i	−0.766850	−	0.205477i
$355$	−4.89898	+	8.48528i	−0.260011	+	0.450352i
$356$	−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	$0.837835\pi$
$360$	−10.0382	+	5.79555i	−0.529059	+	0.305453i
$361$	5.09808	−	8.83013i	0.268320	−	0.464744i
$362$	−16.9706			−0.891953
$363$	−3.58630	+	3.58630i	−0.188232	+	0.188232i
$364$		0			0
$365$	13.1962	+	22.8564i	0.690718	+	1.19636i
$366$	11.6603	+	3.12436i	0.609491	+	0.163313i
$367$	7.86611	+	13.6245i	0.410607	+	0.711193i	0.994956	−	0.100310i	$-0.0319833\pi$
$367$	7.86611	+	13.6245i	0.410607	+	0.711193i	−0.584349	+	0.811503i	$0.698650\pi$
$368$	0.732051	−	1.26795i	0.0381608	−	0.0660964i
$369$			3.82654i			0.199202i
$370$	2.07055			0.107643
$371$		0			0
$372$	3.00000	+	0.803848i	0.155543	+	0.0416776i
$373$	−15.3923	+	26.6603i	−0.796983	+	1.38042i	0.124589	+	0.992208i	$0.460239\pi$
$373$	−15.3923	+	26.6603i	−0.796983	+	1.38042i	−0.921572	+	0.388207i	$0.873095\pi$
$374$	−20.2151			−1.04530
$375$	31.8564	+	8.53590i	1.64506	+	0.440792i
$376$	10.5558			0.544376
$377$	−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	$0.649193\pi$
$380$	−11.4641			−0.588096
$381$	10.9348	+	2.92996i	0.560205	+	0.150107i
$382$	1.07180			0.0548379
$383$	10.8332	−	18.7637i	0.553552	−	0.958781i	−0.444462	−	0.895798i	$-0.646605\pi$
$383$	10.8332	−	18.7637i	0.553552	−	0.958781i	0.998015	−	0.0629833i	$-0.0200615\pi$
$384$	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
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	0.746624	−	0.665246i	$-0.231673\pi$
$389$	−4.00000	−	6.92820i	−0.202808	−	0.351274i	−0.949432	+	0.313972i	$0.898340\pi$
$390$	43.2586	+	11.5911i	2.19048	+	0.586939i
$391$	3.96524	+	6.86800i	0.200531	+	0.347329i
$392$		0			0
$393$	−7.39230	+	7.39230i	−0.372892	+	0.372892i
$394$	−3.07180			−0.154755
$395$	9.52056	−	16.4901i	0.479031	−	0.829706i
$396$			11.1962i			0.562628i
$397$	−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
$401$	−8.89230	+	15.4019i	−0.444061	+	0.769135i	−0.997986	−	0.0634307i	$-0.979796\pi$
$401$	−8.89230	+	15.4019i	−0.444061	+	0.769135i	0.553926	+	0.832566i	$0.313129\pi$
$402$	9.26174	+	2.48168i	0.461934	+	0.123775i
$403$	−6.00000	−	10.3923i	−0.298881	−	0.517678i
$404$	−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
$408$	−6.63397	+	6.63397i	−0.328431	+	0.328431i
$409$	16.7303			0.827261			0.413631	−	0.910445i	$-0.364260\pi$
$409$	16.7303			0.827261			0.413631	+	0.910445i	$0.364260\pi$
$410$	−4.92820			−0.243387
$411$	3.88229	+	14.4889i	0.191499	+	0.714684i
$412$	−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
$416$	−3.34607	−	5.79555i	−0.164054	−	0.284150i
$417$	7.33013	+	27.3564i	0.358958	+	1.33965i
$418$	−5.53674	+	9.58991i	−0.270811	+	0.469058i
$419$	3.95164	+	6.84443i	0.193050	+	0.334373i	0.946260	−	0.323408i	$-0.104829\pi$
$419$	3.95164	+	6.84443i	0.193050	+	0.334373i	−0.753209	+	0.657781i	$0.771495\pi$
$420$		0			0
$421$	−14.1962	+	24.5885i	−0.691878	+	1.19837i	0.279344	+	0.960191i	$0.409883\pi$
$421$	−14.1962	+	24.5885i	−0.691878	+	1.19837i	−0.971222	+	0.238177i	$0.923450\pi$
$422$	−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
$425$	53.7773			2.60858
$426$	4.24264	+	1.13681i	0.205557	+	0.0550787i
$427$		0			0
$428$	−1.69615	−	2.93782i	−0.0819866	−	0.142005i
$429$	30.5885	−	30.5885i	1.47682	−	1.47682i
$430$	−7.20977	−	12.4877i	−0.347686	−	0.602210i
$431$	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	$-0.198594\pi$
$432$	3.67423	+	3.67423i	0.176777	+	0.176777i
$433$	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
$435$	6.92820	+	25.8564i	0.332182	+	1.23972i
$436$	4.46410	−	7.73205i	0.213792	−	0.370298i
$437$	4.34418			0.207810
$438$	8.36603	−	8.36603i	0.399744	−	0.399744i
$439$	−19.5959			−0.935262			−0.467631	−	0.883924i	$-0.654892\pi$
$439$	−19.5959			−0.935262			−0.467631	+	0.883924i	$0.654892\pi$
$440$	−14.4195			−0.687424
$441$		0			0
$442$	36.2487			1.72418
$443$	−18.3205			−0.870434			−0.435217	−	0.900326i	$-0.643328\pi$
$443$	−18.3205			−0.870434			−0.435217	+	0.900326i	$0.643328\pi$
$444$	−0.240237	−	0.896575i	−0.0114011	−	0.0425496i
$445$	27.3205			1.29512
$446$	13.3843	−	23.1822i	0.633763	−	1.09771i
$447$	−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	$0.637849\pi$
$450$		−	29.7846i		−	1.40406i
$451$	−2.38014	+	4.12252i	−0.112076	+	0.194122i
$452$	−3.46410	−	6.00000i	−0.162938	−	0.282216i
$453$	1.07244	+	4.00240i	0.0503877	+	0.188049i
$454$	5.25933	+	9.10943i	0.246833	+	0.427527i
$455$		0			0
$456$	1.33013	+	4.96410i	0.0622889	+	0.232465i
$457$	7.05256			0.329905			0.164952	−	0.986302i	$-0.447253\pi$
$457$	7.05256			0.329905			0.164952	+	0.986302i	$0.447253\pi$
$458$	−12.4877	+	21.6293i	−0.583511	+	1.01067i
$459$	−27.1865	+	7.28461i	−1.26896	+	0.340016i
$460$	2.82843	+	4.89898i	0.131876	+	0.228416i
$461$	12.8666	−	22.2856i	0.599258	−	1.03795i	−0.393672	−	0.919251i	$-0.628796\pi$
$461$	12.8666	−	22.2856i	0.599258	−	1.03795i	0.992931	−	0.118695i	$-0.0378711\pi$
$462$		0			0
$463$	−19.3205	−	33.4641i	−0.897900	−	1.55521i	−0.830174	−	0.557505i	$-0.811759\pi$
$463$	−19.3205	−	33.4641i	−0.897900	−	1.55521i	−0.0677264	−	0.997704i	$-0.521575\pi$
$464$	2.00000	−	3.46410i	0.0928477	−	0.160817i
$465$	−8.48528	+	8.48528i	−0.393496	+	0.393496i
$466$	12.0622	+	20.8923i	0.558770	+	0.967817i
$467$	13.7818	+	23.8707i	0.637745	+	1.10461i	0.985927	+	0.167179i	$0.0534659\pi$
$467$	13.7818	+	23.8707i	0.637745	+	1.10461i	−0.348182	+	0.937427i	$0.613201\pi$
$468$		−	20.0764i		−	0.928032i
$469$		0			0
$470$	−20.3923	+	35.3205i	−0.940627	+	1.62921i
$471$	7.73205	+	2.07180i	0.356274	+	0.0954634i
$472$	−8.62398			−0.396951
$473$	−13.9282			−0.640419
$474$	−8.24504	−	2.20925i	−0.378707	−	0.101474i
$475$	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
$479$	−7.72741	−	13.3843i	−0.353074	−	0.611542i	0.633712	−	0.773569i	$-0.281530\pi$
$479$	−7.72741	−	13.3843i	−0.353074	−	0.611542i	−0.986786	+	0.162026i	$0.948197\pi$
$480$	−4.73205	+	4.73205i	−0.215988	+	0.215988i
$481$	−1.79315	+	3.10583i	−0.0817606	+	0.141614i
$482$	−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
$486$	4.03459	+	15.0573i	0.183013	+	0.683013i
$487$	−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	$0.825045\pi$
$488$	6.96953			0.315496
$489$	−9.55772	−	35.6699i	−0.432215	−	1.61305i
$490$		0			0
$491$	0.696152	+	1.20577i	0.0314169	+	0.0544157i	0.881306	−	0.472545i	$-0.156665\pi$
$491$	0.696152	+	1.20577i	0.0314169	+	0.0544157i	−0.849889	+	0.526961i	$0.823331\pi$
$492$	0.571797	+	2.13397i	0.0257786	+	0.0962070i
$493$	10.8332	+	18.7637i	0.487904	+	0.845075i
$494$	9.92820	−	17.1962i	0.446691	−	0.773691i
$495$	−37.4631	−	21.6293i	−1.68384	−	0.972165i
$496$	1.79315			0.0805149
$497$		0			0
$498$	21.9282	−	21.9282i	0.982626	−	0.982626i
$499$	−6.30385	+	10.9186i	−0.282199	+	0.488783i	−0.971926	−	0.235286i	$-0.924397\pi$
$499$	−6.30385	+	10.9186i	−0.282199	+	0.488783i	0.689727	+	0.724069i	$0.257731\pi$
$500$	19.0411			0.851545
$501$	−9.46410	−	35.3205i	−0.422825	−	1.57800i
$502$	−16.3514			−0.729798
$503$	−7.45001			−0.332179			−0.166090	−	0.986111i	$-0.553114\pi$
$503$	−7.45001			−0.332179			−0.166090	+	0.986111i	$0.553114\pi$
$504$		0			0
$505$	18.9282			0.842294
$506$	5.46410			0.242909
$507$	−38.9280	+	38.9280i	−1.72885	+	1.72885i
$508$	6.53590			0.289984
$509$	−13.2456	+	22.9420i	−0.587099	+	1.01689i	0.407511	+	0.913200i	$0.366397\pi$
$509$	−13.2456	+	22.9420i	−0.587099	+	1.01689i	−0.994610	+	0.103685i	$0.966937\pi$
$510$	−9.38186	−	35.0136i	−0.415436	−	1.55043i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−3.99038	+	14.8923i	−0.176180	+	0.657511i
$514$	−1.34486	+	2.32937i	−0.0593194	+	0.102744i
$515$	−14.3923	−	24.9282i	−0.634201	−	1.09847i
$516$	−4.57081	+	4.57081i	−0.201219	+	0.201219i
$517$	19.6975	+	34.1170i	0.866293	+	1.50046i
$518$		0			0
$519$	3.00000	+	0.803848i	0.131685	+	0.0352850i
$520$	25.8564			1.13388
$521$	−16.1805	+	28.0255i	−0.708881	+	1.22782i	0.256392	+	0.966573i	$0.417466\pi$
$521$	−16.1805	+	28.0255i	−0.708881	+	1.22782i	−0.965273	+	0.261244i	$0.915867\pi$
$522$	10.3923	−	6.00000i	0.454859	−	0.262613i
$523$	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
$527$	−4.85641	+	8.41154i	−0.211548	+	0.366413i
$528$	1.67303	+	6.24384i	0.0728094	+	0.271728i
$529$	10.4282	+	18.0622i	0.453400	+	0.785312i
$530$	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
$534$	−3.16987	−	11.8301i	−0.137174	−	0.511940i
$535$	13.1069			0.566659
$536$	5.53590			0.239114
$537$	−23.1822	+	23.1822i	−1.00039	+	1.00039i
$538$	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	$0.697001\pi$
$542$	−9.00292	−	15.5935i	−0.386709	−	0.669799i
$543$	−28.3923	−	7.60770i	−1.21843	−	0.326477i
$544$	−2.70831	+	4.69093i	−0.116118	+	0.201122i
$545$	17.2480	+	29.8744i	0.738822	+	1.27968i
$546$		0			0
$547$	19.1865	−	33.2321i	0.820357	−	1.42090i	−0.0850597	−	0.996376i	$-0.527108\pi$
$547$	19.1865	−	33.2321i	0.820357	−	1.42090i	0.905417	−	0.424524i	$-0.139559\pi$
$548$	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
$551$	11.8685			0.505616
$552$	1.79315	−	1.79315i	0.0763216	−	0.0763216i
$553$		0			0
$554$	−12.2679	−	21.2487i	−0.521215	−	0.902771i
$555$	3.46410	+	0.928203i	0.147043	+	0.0394000i
$556$	8.17569	+	14.1607i	0.346727	+	0.600548i
$557$	−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	$0.213557\pi$
$558$	4.65874	+	2.68973i	0.197220	+	0.113865i
$559$	24.9754			1.05635
$560$		0			0
$561$	−33.8205	−	9.06218i	−1.42790	−	0.382605i
$562$	4.92820	−	8.53590i	0.207884	−	0.360065i
$563$	−25.5945			−1.07868			−0.539341	−	0.842088i	$-0.681327\pi$
$563$	−25.5945			−1.07868			−0.539341	+	0.842088i	$0.681327\pi$
$564$	17.6603	+	4.73205i	0.743631	+	0.199255i
$565$	26.7685			1.12616
$566$	9.41902			0.395911
$567$		0			0
$568$	2.53590			0.106404
$569$	15.7846			0.661725			0.330863	−	0.943679i	$-0.392660\pi$
$569$	15.7846			0.661725			0.330863	+	0.943679i	$0.392660\pi$
$570$	−19.1798	−	5.13922i	−0.803354	−	0.215258i
$571$	5.05256			0.211443			0.105722	−	0.994396i	$-0.466285\pi$
$571$	5.05256			0.211443			0.105722	+	0.994396i	$0.466285\pi$
$572$	12.4877	−	21.6293i	0.522136	−	0.904367i
$573$	1.79315	+	0.480473i	0.0749100	+	0.0200721i
$574$		0			0
$575$	−14.5359			−0.606189
$576$	2.59808	+	1.50000i	0.108253	+	0.0625000i
$577$	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	$-0.212753\pi$
$578$	−6.16987	−	10.6865i	−0.256633	−	0.444501i
$579$	−38.5677	−	10.3342i	−1.60282	−	0.429474i
$580$	7.72741	+	13.3843i	0.320863	+	0.555751i
$581$		0			0
$582$	7.22243	−	7.22243i	0.299379	−	0.299379i
$583$	10.9282			0.452600
$584$	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	0.390922	+	0.920424i	$0.372156\pi$
$587$	−14.5768	+	25.2478i	−0.601650	+	1.04209i	−0.992571	+	0.121664i	$0.961177\pi$
$588$		0			0
$589$	2.66025	+	4.60770i	0.109614	+	0.189857i
$590$	16.6603	−	28.8564i	0.685892	−	1.18800i
$591$	−5.13922	−	1.37705i	−0.211399	−	0.0566442i
$592$	−0.267949	−	0.464102i	−0.0110126	−	0.0190745i
$593$	1.36345	+	2.36156i	0.0559900	+	0.0969775i	0.892662	−	0.450727i	$-0.148835\pi$
$593$	1.36345	+	2.36156i	0.0559900	+	0.0969775i	−0.836672	+	0.547704i	$0.815502\pi$
$594$	−5.01910	+	18.7315i	−0.205936	+	0.768564i
$595$		0			0
$596$	−4.53590	+	7.85641i	−0.185798	+	0.321811i
$597$	21.8038	−	21.8038i	0.892372	−	0.892372i
$598$	−9.79796			−0.400668
$599$	−36.7846			−1.50298			−0.751489	−	0.659745i	$-0.770664\pi$
$599$	−36.7846			−1.50298			−0.751489	+	0.659745i	$0.770664\pi$
$600$	−4.45069	−	16.6102i	−0.181699	−	0.678109i
$601$	0.448288	−	0.776457i	0.0182860	−	0.0316723i	−0.856738	−	0.515753i	$-0.827512\pi$
$601$	0.448288	−	0.776457i	0.0182860	−	0.0316723i	0.875024	+	0.484080i	$0.160846\pi$
$602$		0			0
$603$	14.3827	+	8.30385i	0.585708	+	0.338159i
$604$	1.19615	+	2.07180i	0.0486708	+	0.0843002i
$605$	−5.65685	−	9.79796i	−0.229984	−	0.398344i
$606$	−2.19615	−	8.19615i	−0.0892126	−	0.332946i
$607$	15.8338	−	27.4249i	0.642672	−	1.11314i	−0.342162	−	0.939641i	$-0.611159\pi$
$607$	15.8338	−	27.4249i	0.642672	−	1.11314i	0.984834	−	0.173500i	$-0.0555076\pi$
$608$	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
$612$	−14.0728	+	8.12493i	−0.568859	+	0.328431i
$613$	−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	$0.238445\pi$
$614$	−11.0735			−0.446889
$615$	−8.24504	−	2.20925i	−0.332472	−	0.0890857i
$616$		0			0
$617$	15.4282	+	26.7224i	0.621116	+	1.07580i	0.989278	+	0.146043i	$0.0466538\pi$
$617$	15.4282	+	26.7224i	0.621116	+	1.07580i	−0.368162	+	0.929762i	$0.620013\pi$
$618$	−9.12436	+	9.12436i	−0.367035	+	0.367035i
$619$	−12.3168	−	21.3333i	−0.495054	−	0.857459i	0.504930	−	0.863160i	$-0.331518\pi$
$619$	−12.3168	−	21.3333i	−0.495054	−	0.857459i	−0.999984	+	0.00570182i	$0.998185\pi$
$620$	−3.46410	+	6.00000i	−0.139122	+	0.240966i
$621$	7.34847	−	1.96902i	0.294884	−	0.0790139i
$622$	−12.3490			−0.495149
$623$		0			0
$624$	−3.00000	−	11.1962i	−0.120096	−	0.448205i
$625$	−11.9641	+	20.7224i	−0.478564	+	0.828897i
$626$	23.4225			0.936150
$627$	−13.5622	+	13.5622i	−0.541621	+	0.541621i
$628$	4.62158			0.184421
$629$	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	$0.248309\pi$
$632$	−4.92820			−0.196033
$633$	−2.27362	−	8.48528i	−0.0903685	−	0.337260i
$634$	−26.0000			−1.03259
$635$	−12.6264	+	21.8695i	−0.501063	+	0.867866i
$636$	3.58630	−	3.58630i	0.142206	−	0.142206i
$637$		0			0
$638$	14.9282			0.591013
$639$	6.58846	+	3.80385i	0.260635	+	0.150478i
$640$	−1.93185	+	3.34607i	−0.0763631	+	0.132265i
$641$	−8.96410	−	15.5263i	−0.354061	−	0.613251i	0.632896	−	0.774237i	$-0.281866\pi$
$641$	−8.96410	−	15.5263i	−0.354061	−	0.613251i	−0.986957	+	0.160986i	$0.948533\pi$
$642$	−1.52073	−	5.67544i	−0.0600184	−	0.223992i
$643$	6.53485	+	11.3187i	0.257709	+	0.446365i	0.965628	−	0.259929i	$-0.0836990\pi$
$643$	6.53485	+	11.3187i	0.257709	+	0.446365i	−0.707919	+	0.706294i	$0.750366\pi$
$644$		0			0
$645$	−6.46410	−	24.1244i	−0.254524	−	0.949896i
$646$	−16.0718			−0.632336
$647$	−6.03579	+	10.4543i	−0.237291	+	0.411001i	−0.959936	−	0.280219i	$-0.909593\pi$
$647$	−6.03579	+	10.4543i	−0.237291	+	0.411001i	0.722645	+	0.691220i	$0.242926\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	−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
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	−0.918736	−	0.394872i	$-0.870789\pi$
$653$	−3.00000	+	5.19615i	−0.117399	+	0.203341i	0.801337	+	0.598213i	$0.204122\pi$
$654$	10.9348	−	10.9348i	0.427583	−	0.427583i
$655$	−11.6603	−	20.1962i	−0.455604	−	0.789129i
$656$	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	−0.868437	−	0.495799i	$-0.834875\pi$
$659$	−0.124356	+	0.215390i	−0.00484421	+	0.00839042i	0.863593	+	0.504189i	$0.168209\pi$
$660$	−24.1244	−	6.46410i	−0.939039	−	0.251615i
$661$		0			0			−	1.00000i	$-0.5\pi$
$661$		0			0				1.00000i	$0.5\pi$
$662$	−4.53590			−0.176293
$663$	60.6453	+	16.2499i	2.35527	+	0.631092i
$664$	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
$668$	−10.5558	−	18.2832i	−0.408417	−	0.707400i
$669$	32.7846	−	32.7846i	1.26753	−	1.26753i
$670$	−10.6945	+	18.5235i	−0.413166	+	0.715624i
$671$	13.0053	+	22.5259i	0.502065	+	0.869602i
$672$		0			0
$673$	20.7846	−	36.0000i	0.801188	−	1.38770i	−0.117647	−	0.993055i	$-0.537535\pi$
$673$	20.7846	−	36.0000i	0.801188	−	1.38770i	0.918835	−	0.394643i	$-0.129132\pi$
$674$	3.50000	+	6.06218i	0.134815	+	0.233506i
$675$	13.3521	−	49.8306i	0.513922	−	1.91798i
$676$	−15.8923	+	27.5263i	−0.611242	+	1.05870i
$677$	−20.0764			−0.771598			−0.385799	−	0.922583i	$-0.626074\pi$
$677$	−20.0764			−0.771598			−0.385799	+	0.922583i	$0.626074\pi$
$678$	−3.10583	−	11.5911i	−0.119279	−	0.445154i
$679$		0			0
$680$	−10.4641	−	18.1244i	−0.401280	−	0.695037i
$681$	4.71539	+	17.5981i	0.180694	+	0.674360i
$682$	3.34607	+	5.79555i	0.128127	+	0.221923i
$683$	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	$0.144240\pi$
$684$			8.90138i			0.340353i
$685$	−33.4607			−1.27847
$686$		0			0
$687$	−30.5885	+	30.5885i	−1.16702	+	1.16702i
$688$	−1.86603	+	3.23205i	−0.0711416	+	0.123221i
$689$	−19.5959			−0.746545
$690$	2.53590	+	9.46410i	0.0965400	+	0.360292i
$691$	9.62209			0.366042			0.183021	−	0.983109i	$-0.441412\pi$
$691$	9.62209			0.366042			0.183021	+	0.983109i	$0.441412\pi$
$692$	1.79315			0.0681654
$693$		0			0
$694$	21.5885			0.819487
$695$	−63.1769			−2.39644
$696$	4.89898	−	4.89898i	0.185695	−	0.185695i
$697$	−6.90897			−0.261696
$698$	−8.24504	+	14.2808i	−0.312080	+	0.540538i
$699$	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	$0.371606\pi$
$702$	9.00000	−	33.5885i	0.339683	−	1.26771i
$703$	0.795040	−	1.37705i	0.0299855	−	0.0519364i
$704$	1.86603	+	3.23205i	0.0703285	+	0.121812i
$705$	−49.9507	+	49.9507i	−1.88125	+	1.88125i
$706$	13.2134	+	22.8862i	0.497292	+	0.861335i
$707$		0			0
$708$	−14.4282	−	3.86603i	−0.542245	−	0.145294i
$709$	8.39230			0.315180			0.157590	−	0.987505i	$-0.449628\pi$
$709$	8.39230			0.315180			0.157590	+	0.987505i	$0.449628\pi$
$710$	−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
$716$	−9.46410	+	16.3923i	−0.353690	+	0.612609i
$717$	5.79555	+	21.6293i	0.216439	+	0.807761i
$718$	−0.267949	−	0.464102i	−0.00999978	−	0.0173201i
$719$	7.69024	+	13.3199i	0.286798	+	0.496748i	0.973044	−	0.230622i	$-0.0740759\pi$
$719$	7.69024	+	13.3199i	0.286798	+	0.496748i	−0.686246	+	0.727370i	$0.740743\pi$
$720$	−10.0382	+	5.79555i	−0.374101	+	0.215988i
$721$		0			0
$722$	5.09808	−	8.83013i	0.189731	−	0.328623i
$723$	−10.5000	−	39.1865i	−0.390499	−	1.45736i
$724$	−16.9706			−0.630706
$725$	−39.7128			−1.47490
$726$	−3.58630	+	3.58630i	−0.133100	+	0.133100i
$727$	0.795040	−	1.37705i	0.0294864	−	0.0510719i	−0.850906	−	0.525319i	$-0.823946\pi$
$727$	0.795040	−	1.37705i	0.0294864	−	0.0510719i	0.880392	+	0.474247i	$0.157279\pi$
$728$		0			0
$729$			27.0000i			1.00000i
$730$	13.1962	+	22.8564i	0.488412	+	0.845954i
$731$	−10.1075	−	17.5068i	−0.373841	−	0.647512i
$732$	11.6603	+	3.12436i	0.430975	+	0.115480i
$733$	8.24504	−	14.2808i	0.304538	−	0.527475i	−0.672621	−	0.739988i	$-0.734831\pi$
$733$	8.24504	−	14.2808i	0.304538	−	0.527475i	0.977158	+	0.212513i	$0.0681647\pi$
$734$	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
$738$			3.82654i			0.140857i
$739$	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	$0.0584850\pi$
$740$	2.07055			0.0761150
$741$	24.3190	−	24.3190i	0.893382	−	0.893382i
$742$		0			0
$743$	−25.7846	−	44.6603i	−0.945946	−	1.63843i	−0.753847	−	0.657050i	$-0.771804\pi$
$743$	−25.7846	−	44.6603i	−0.945946	−	1.63843i	−0.192099	−	0.981376i	$-0.561529\pi$
$744$	3.00000	+	0.803848i	0.109985	+	0.0294705i
$745$	−17.5254	−	30.3548i	−0.642080	−	1.11211i
$746$	−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
$751$	3.39230	−	5.87564i	0.123787	−	0.214405i	−0.797471	−	0.603357i	$-0.793829\pi$
$751$	3.39230	−	5.87564i	0.123787	−	0.214405i	0.921258	+	0.388952i	$0.127163\pi$
$752$	10.5558			0.384932
$753$	−27.3564	−	7.33013i	−0.996923	−	0.267125i
$754$	−26.7685			−0.974852
$755$	−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	$0.589810\pi$
$758$	−17.5885			−0.638842
$759$	9.14162	+	2.44949i	0.331820	+	0.0889108i
$760$	−11.4641			−0.415847
$761$	15.2282	−	26.3760i	0.552021	−	0.956129i	−0.446108	−	0.894979i	$-0.647190\pi$
$761$	15.2282	−	26.3760i	0.552021	−	0.956129i	0.998129	−	0.0611492i	$-0.0194765\pi$
$762$	10.9348	+	2.92996i	0.396125	+	0.106141i
$763$		0			0
$764$	1.07180			0.0387762
$765$		−	62.7846i		−	2.26998i
$766$	10.8332	−	18.7637i	0.391421	−	0.677961i
$767$	28.8564	+	49.9808i	1.04194	+	1.80470i
$768$	1.67303	+	0.448288i	0.0603704	+	0.0161762i
$769$	−19.0919	−	33.0681i	−0.688471	−	1.19247i	−0.972332	−	0.233601i	$-0.924949\pi$
$769$	−19.0919	−	33.0681i	−0.688471	−	1.19247i	0.283862	−	0.958865i	$-0.408384\pi$
$770$		0			0
$771$	−3.29423	+	3.29423i	−0.118639	+	0.118639i
$772$	−23.0526			−0.829680
$773$	−0.101536	+	0.175865i	−0.00365199	+	0.00632544i	−0.867846	−	0.496834i	$-0.834496\pi$
$773$	−0.101536	+	0.175865i	−0.00365199	+	0.00632544i	0.864194	+	0.503159i	$0.167829\pi$
$774$	−9.69615	+	5.59808i	−0.348521	+	0.201219i
$775$	−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
$779$	−1.89230	+	3.27757i	−0.0677989	+	0.117431i
$780$	43.2586	+	11.5911i	1.54891	+	0.415028i
$781$	4.73205	+	8.19615i	0.169326	+	0.293281i
$782$	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
$786$	−7.39230	+	7.39230i	−0.263675	+	0.263675i
$787$	−46.7434			−1.66622			−0.833111	−	0.553106i	$-0.813442\pi$
$787$	−46.7434			−1.66622			−0.833111	+	0.553106i	$0.813442\pi$
$788$	−3.07180			−0.109428
$789$	6.93237	+	25.8719i	0.246799	+	0.921066i
$790$	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
$794$	−9.00292	−	15.5935i	−0.319502	−	0.553393i
$795$	5.07180	+	18.9282i	0.179878	+	0.671314i
$796$	8.90138	−	15.4176i	0.315501	−	0.546464i
$797$	−10.4543	−	18.1074i	−0.370310	−	0.641396i	0.619303	−	0.785152i	$-0.287415\pi$
$797$	−10.4543	−	18.1074i	−0.370310	−	0.641396i	−0.989613	+	0.143756i	$0.954082\pi$
$798$		0			0
$799$	−28.5885	+	49.5167i	−1.01139	+	1.75177i
$800$	−4.96410	−	8.59808i	−0.175507	−	0.303988i
$801$		−	21.2132i		−	0.749532i
$802$	−8.89230	+	15.4019i	−0.313998	+	0.543861i
$803$	25.4930			0.899629
$804$	9.26174	+	2.48168i	0.326636	+	0.0875219i
$805$		0			0
$806$	−6.00000	−	10.3923i	−0.211341	−	0.366053i
$807$	6.92820	−	6.92820i	0.243884	−	0.243884i
$808$	−2.44949	−	4.24264i	−0.0861727	−	0.149256i
$809$	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	$0.0138827\pi$
$810$	−34.7733			−1.22181
$811$	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
$813$	−8.07180	−	30.1244i	−0.283090	−	1.05651i
$814$	1.00000	−	1.73205i	0.0350500	−	0.0607083i
$815$	82.3761			2.88551
$816$	−6.63397	+	6.63397i	−0.232236	+	0.232236i
$817$	−11.0735			−0.387412
$818$	16.7303			0.584962
$819$		0			0
$820$	−4.92820			−0.172100
$821$	−10.3923			−0.362694			−0.181347	−	0.983419i	$-0.558046\pi$
$821$	−10.3923			−0.362694			−0.181347	+	0.983419i	$0.558046\pi$
$822$	3.88229	+	14.4889i	0.135410	+	0.505358i
$823$	30.7846			1.07308			0.536542	−	0.843874i	$-0.319730\pi$
$823$	30.7846			1.07308			0.536542	+	0.843874i	$0.319730\pi$
$824$	−3.72500	+	6.45189i	−0.129767	+	0.224762i
$825$	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	$0.391130\pi$
$829$	−18.6622	+	32.3238i	−0.648164	+	1.12265i	−0.983561	+	0.180576i	$0.942204\pi$
$830$	34.5885	+	59.9090i	1.20058	+	2.07947i
$831$	−10.9991	−	41.0494i	−0.381556	−	1.42399i
$832$	−3.34607	−	5.79555i	−0.116004	−	0.200925i
$833$		0			0
$834$	7.33013	+	27.3564i	0.253822	+	0.947275i
$835$	81.5692			2.82282
$836$	−5.53674	+	9.58991i	−0.191492	+	0.331674i
$837$	6.58846	+	6.58846i	0.227730	+	0.227730i
$838$	3.95164	+	6.84443i	0.136507	+	0.236437i
$839$	−11.3137	+	19.5959i	−0.390593	+	0.676526i	−0.992528	−	0.122019i	$-0.961063\pi$
$839$	−11.3137	+	19.5959i	−0.390593	+	0.676526i	0.601935	+	0.798545i	$0.294397\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−14.1962	+	24.5885i	−0.489232	+	0.847374i
$843$	12.0716	−	12.0716i	0.415767	−	0.415767i
$844$	−2.53590	−	4.39230i	−0.0872892	−	0.151189i
$845$	−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
$849$	15.7583	+	4.22243i	0.540824	+	0.144913i
$850$	53.7773			1.84455
$851$	−0.784610			−0.0268961
$852$	4.24264	+	1.13681i	0.145350	+	0.0389465i
$853$	8.00481	−	13.8647i	0.274079	−	0.474719i	−0.695823	−	0.718213i	$-0.744960\pi$
$853$	8.00481	−	13.8647i	0.274079	−	0.474719i	0.969902	+	0.243494i	$0.0782936\pi$
$854$		0			0
$855$	−29.7846	−	17.1962i	−1.01861	−	0.588096i
$856$	−1.69615	−	2.93782i	−0.0579733	−	0.100413i
$857$	−4.19187	−	7.26054i	−0.143192	−	0.248015i	0.785505	−	0.618855i	$-0.212403\pi$
$857$	−4.19187	−	7.26054i	−0.143192	−	0.248015i	−0.928697	+	0.370840i	$0.879070\pi$
$858$	30.5885	−	30.5885i	1.04427	−	1.04427i
$859$	−7.36705	+	12.7601i	−0.251361	+	0.435369i	−0.963901	−	0.266262i	$-0.914211\pi$
$859$	−7.36705	+	12.7601i	−0.251361	+	0.435369i	0.712540	+	0.701631i	$0.247545\pi$
$860$	−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	$0.956114\pi$
$864$	3.67423	+	3.67423i	0.125000	+	0.125000i
$865$	−3.46410	+	6.00000i	−0.117783	+	0.204006i
$866$	7.10823			0.241548
$867$	−5.53176	−	20.6448i	−0.187868	−	0.701134i
$868$		0			0
$869$	−9.19615	−	15.9282i	−0.311958	−	0.540327i
$870$	6.92820	+	25.8564i	0.234888	+	0.876614i
$871$	−18.5235	−	32.0836i	−0.627644	−	1.08711i
$872$	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
$877$	−16.5885	+	28.7321i	−0.560152	+	0.970212i	0.437330	+	0.899301i	$0.355924\pi$
$877$	−16.5885	+	28.7321i	−0.560152	+	0.970212i	−0.997483	+	0.0709114i	$0.977409\pi$
$878$	−19.5959			−0.661330
$879$	8.53590	+	31.8564i	0.287909	+	1.07449i
$880$	−14.4195			−0.486082
$881$	−12.7279			−0.428815			−0.214407	−	0.976744i	$-0.568782\pi$
$881$	−12.7279			−0.428815			−0.214407	+	0.976744i	$0.568782\pi$
$882$		0			0
$883$	7.53590			0.253603			0.126802	−	0.991928i	$-0.459529\pi$
$883$	7.53590			0.253603			0.126802	+	0.991928i	$0.459529\pi$
$884$	36.2487			1.21918
$885$	40.8091	−	40.8091i	1.37178	−	1.37178i
$886$	−18.3205			−0.615490
$887$	−14.3824	+	24.9110i	−0.482913	+	0.836430i	−0.999808	−	0.0196195i	$-0.993755\pi$
$887$	−14.3824	+	24.9110i	−0.482913	+	0.836430i	0.516895	+	0.856049i	$0.327088\pi$
$888$	−0.240237	−	0.896575i	−0.00806181	−	0.0300871i
$889$		0			0
$890$	27.3205			0.915786
$891$	−16.7942	+	29.0885i	−0.562628	+	0.974500i
$892$	13.3843	−	23.1822i	0.448138	−	0.776198i
$893$	15.6603	+	27.1244i	0.524050	+	0.907682i
$894$	−11.1106	+	11.1106i	−0.371595	+	0.371595i
$895$	−36.5665	−	63.3350i	−1.22228	−	2.11706i
$896$		0			0
$897$	−16.3923	−	4.39230i	−0.547323	−	0.146655i
$898$	−17.7846			−0.593480
$899$	3.58630	−	6.21166i	0.119610	−	0.207170i
$900$		−	29.7846i		−	0.992820i
$901$	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
$905$	32.7846	−	56.7846i	1.08980	−	1.88758i
$906$	1.07244	+	4.00240i	0.0356295	+	0.132971i
$907$	−21.6244	−	37.4545i	−0.718025	−	1.24366i	−0.961781	−	0.273819i	$-0.911713\pi$
$907$	−21.6244	−	37.4545i	−0.718025	−	1.24366i	0.243756	−	0.969837i	$-0.421620\pi$
$908$	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	−0.156035	−	0.987752i	$-0.549871\pi$
$911$	23.4641	−	40.6410i	0.777400	−	1.34650i	0.933435	−	0.358745i	$-0.116795\pi$
$912$	1.33013	+	4.96410i	0.0440449	+	0.164378i
$913$	66.8198			2.21141
$914$	7.05256			0.233278
$915$	−32.9802	+	32.9802i	−1.09029	+	1.09029i
$916$	−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	$0.956778\pi$
$920$	2.82843	+	4.89898i	0.0932505	+	0.161515i
$921$	−18.5263	−	4.96410i	−0.610462	−	0.163573i
$922$	12.8666	−	22.2856i	0.423740	−	0.733939i
$923$	−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
$927$	−19.3557	+	11.1750i	−0.635724	+	0.367035i
$928$	2.00000	−	3.46410i	0.0656532	−	0.113715i
$929$	−27.9797			−0.917983			−0.458991	−	0.888441i	$-0.651789\pi$
$929$	−27.9797			−0.917983			−0.458991	+	0.888441i	$0.651789\pi$
$930$	−8.48528	+	8.48528i	−0.278243	+	0.278243i
$931$		0			0
$932$	12.0622	+	20.8923i	0.395110	+	0.684350i
$933$	−20.6603	−	5.53590i	−0.676386	−	0.181237i
$934$	13.7818	+	23.8707i	0.450954	+	0.781075i
$935$	39.0526	−	67.6410i	1.27716	−	2.21210i
$936$		−	20.0764i		−	0.656217i
$937$	−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
$939$	39.1865	+	10.5000i	1.27880	+	0.342655i
$940$	−20.3923	+	35.3205i	−0.665124	+	1.15203i
$941$	−8.68835			−0.283232			−0.141616	−	0.989922i	$-0.545230\pi$
$941$	−8.68835			−0.283232			−0.141616	+	0.989922i	$0.545230\pi$
$942$	7.73205	+	2.07180i	0.251924	+	0.0675028i
$943$	1.86748			0.0608135
$944$	−8.62398			−0.280687
$945$		0			0
$946$	−13.9282			−0.452845
$947$	6.12436			0.199015			0.0995074	−	0.995037i	$-0.468273\pi$
$947$	6.12436			0.199015			0.0995074	+	0.995037i	$0.468273\pi$
$948$	−8.24504	−	2.20925i	−0.267787	−	0.0717532i
$949$	−45.7128			−1.48390
$950$	14.7291	−	25.5116i	0.477876	−	0.827705i
$951$	−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
$956$	6.46410	+	11.1962i	0.209064	+	0.362109i
$957$	24.9754	+	6.69213i	0.807339	+	0.216326i
$958$	−7.72741	−	13.3843i	−0.249661	−	0.432426i
$959$		0			0
$960$	−4.73205	+	4.73205i	−0.152726	+	0.152726i
$961$	−27.7846			−0.896278
$962$	−1.79315	+	3.10583i	−0.0578135	+	0.100136i
$963$		−	10.1769i		−	0.327946i
$964$	−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	−0.996369	−	0.0851359i	$-0.972868\pi$
$967$	−17.7846	−	30.8038i	−0.571914	−	0.990585i	0.424455	−	0.905449i	$-0.360466\pi$
$968$	−1.46410	+	2.53590i	−0.0470580	+	0.0815069i
$969$	−26.8886	−	7.20479i	−0.863788	−	0.231451i
$970$	11.3923	+	19.7321i	0.365785	+	0.633558i
$971$	1.50215	+	2.60179i	0.0482062	+	0.0834955i	0.889122	−	0.457671i	$-0.151316\pi$
$971$	1.50215	+	2.60179i	0.0482062	+	0.0834955i	−0.840915	+	0.541166i	$0.817983\pi$
$972$	4.03459	+	15.0573i	0.129410	+	0.482963i
$973$		0			0
$974$	−19.3923	+	33.5885i	−0.621370	+	1.07624i
$975$	−81.3731	+	81.3731i	−2.60602	+	2.60602i
$976$	6.96953			0.223089
$977$	−49.9808			−1.59903			−0.799513	−	0.600649i	$-0.794909\pi$
$977$	−49.9808			−1.59903			−0.799513	+	0.600649i	$0.794909\pi$
$978$	−9.55772	−	35.6699i	−0.305622	−	1.14060i
$979$	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
$983$	3.48477	+	6.03579i	0.111147	+	0.192512i	0.916233	−	0.400646i	$-0.131214\pi$
$983$	3.48477	+	6.03579i	0.111147	+	0.192512i	−0.805086	+	0.593158i	$0.797881\pi$
$984$	0.571797	+	2.13397i	0.0182282	+	0.0680286i
$985$	5.93426	−	10.2784i	0.189081	−	0.327498i
$986$	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	$0.175522\pi$
$992$	1.79315			0.0569326
$993$	−7.58871	−	2.03339i	−0.240820	−	0.0645276i
$994$		0			0
$995$	34.3923	+	59.5692i	1.09031	+	1.88847i
$996$	21.9282	−	21.9282i	0.694822	−	0.694822i
$997$	−3.24453	−	5.61969i	−0.102755	−	0.177977i	0.810064	−	0.586342i	$-0.199433\pi$
$997$	−3.24453	−	5.61969i	−0.102755	−	0.177977i	−0.912819	+	0.408365i	$0.866099\pi$
$998$	−6.30385	+	10.9186i	−0.199545	+	0.345622i
$999$	0.720710	−	2.68973i	0.0228023	−	0.0850992i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.e.s.373.1		8	63.40	odd	6	inner
882.2.e.s.373.4		8	63.58	even	3	inner
882.2.e.s.655.1		8	7.6	odd	2	inner
882.2.e.s.655.4		8	1.1	even	1	trivial
882.2.f.q.295.2	✓	8	7.4	even	3
882.2.f.q.295.3	yes	8	7.3	odd	6
882.2.f.q.589.2	yes	8	63.4	even	3
882.2.f.q.589.3	yes	8	63.31	odd	6
882.2.h.q.67.1		8	9.4	even	3
882.2.h.q.67.4		8	63.13	odd	6
882.2.h.q.79.2		8	7.2	even	3
882.2.h.q.79.3		8	7.5	odd	6
2646.2.e.q.1549.1		8	63.5	even	6
2646.2.e.q.1549.4		8	63.23	odd	6
2646.2.e.q.2125.1		8	21.20	even	2
2646.2.e.q.2125.4		8	3.2	odd	2
2646.2.f.r.883.1		8	21.17	even	6
2646.2.f.r.883.4		8	21.11	odd	6
2646.2.f.r.1765.1		8	63.59	even	6
2646.2.f.r.1765.4		8	63.32	odd	6
2646.2.h.t.361.1		8	9.5	odd	6
2646.2.h.t.361.4		8	63.41	even	6
2646.2.h.t.667.1		8	21.2	odd	6
2646.2.h.t.667.4		8	21.5	even	6
7938.2.a.ci.1.1		4	63.11	odd	6
7938.2.a.ci.1.4		4	63.38	even	6
7938.2.a.cp.1.1		4	63.52	odd	6
7938.2.a.cp.1.4		4	63.25	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(1.67303 + 0.448288i) q^{3} +1.00000 q^{4} +(-1.93185 + 3.34607i) q^{5} +(1.67303 + 0.448288i) q^{6} +1.00000 q^{8} +(2.59808 + 1.50000i) q^{9} +(-1.93185 + 3.34607i) q^{10} +(1.86603 + 3.23205i) q^{11} +(1.67303 + 0.448288i) q^{12} +(-3.34607 - 5.79555i) q^{13} +(-4.73205 + 4.73205i) q^{15} +1.00000 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} +(0.732051 - 1.26795i) q^{23} +(1.67303 + 0.448288i) q^{24} +(-4.96410 - 8.59808i) q^{25} +(-3.34607 - 5.79555i) q^{26} +(3.67423 + 3.67423i) q^{27} +(2.00000 - 3.46410i) q^{29} +(-4.73205 + 4.73205i) q^{30} +1.79315 q^{31} +1.00000 q^{32} +(1.67303 + 6.24384i) q^{33} +(-2.70831 + 4.69093i) q^{34} +(2.59808 + 1.50000i) q^{36} +(-0.267949 - 0.464102i) q^{37} +(1.48356 + 2.56961i) q^{38} +(-3.00000 - 11.1962i) q^{39} +(-1.93185 + 3.34607i) q^{40} +(0.637756 + 1.10463i) q^{41} +(-1.86603 + 3.23205i) q^{43} +(1.86603 + 3.23205i) q^{44} +(-10.0382 + 5.79555i) q^{45} +(0.732051 - 1.26795i) q^{46} +10.5558 q^{47} +(1.67303 + 0.448288i) q^{48} +(-4.96410 - 8.59808i) q^{50} +(-6.63397 + 6.63397i) q^{51} +(-3.34607 - 5.79555i) q^{52} +(1.46410 - 2.53590i) q^{53} +(3.67423 + 3.67423i) q^{54} -14.4195 q^{55} +(1.33013 + 4.96410i) q^{57} +(2.00000 - 3.46410i) q^{58} -8.62398 q^{59} +(-4.73205 + 4.73205i) q^{60} +6.96953 q^{61} +1.79315 q^{62} +1.00000 q^{64} +25.8564 q^{65} +(1.67303 + 6.24384i) q^{66} +5.53590 q^{67} +(-2.70831 + 4.69093i) q^{68} +(1.79315 - 1.79315i) q^{69} +2.53590 q^{71} +(2.59808 + 1.50000i) q^{72} +(3.41542 - 5.91567i) q^{73} +(-0.267949 - 0.464102i) q^{74} +(-4.45069 - 16.6102i) q^{75} +(1.48356 + 2.56961i) q^{76} +(-3.00000 - 11.1962i) q^{78} -4.92820 q^{79} +(-1.93185 + 3.34607i) q^{80} +(4.50000 + 7.79423i) q^{81} +(0.637756 + 1.10463i) q^{82} +(8.95215 - 15.5056i) q^{83} +(-10.4641 - 18.1244i) q^{85} +(-1.86603 + 3.23205i) q^{86} +(4.89898 - 4.89898i) q^{87} +(1.86603 + 3.23205i) q^{88} +(-3.53553 - 6.12372i) q^{89} +(-10.0382 + 5.79555i) q^{90} +(0.732051 - 1.26795i) q^{92} +(3.00000 + 0.803848i) q^{93} +10.5558 q^{94} -11.4641 q^{95} +(1.67303 + 0.448288i) q^{96} +(2.94855 - 5.10703i) q^{97} +11.1962i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{4} + 8 q^{8} + 8 q^{11} - 24 q^{15} + 8 q^{16} + 8 q^{22} - 8 q^{23} - 12 q^{25} + 16 q^{29} - 24 q^{30} + 8 q^{32} - 16 q^{37} - 24 q^{39} - 8 q^{43} + 8 q^{44} - 8 q^{46} - 12 q^{50}+ \cdots - 64 q^{95}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^4 + 8 * q^8 + 8 * q^11 - 24 * q^15 + 8 * q^16 + 8 * q^22 - 8 * q^23 - 12 * q^25 + 16 * q^29 - 24 * q^30 + 8 * q^32 - 16 * q^37 - 24 * q^39 - 8 * q^43 + 8 * q^44 - 8 * q^46 - 12 * q^50 - 60 * q^51 - 16 * q^53 - 24 * q^57 + 16 * q^58 - 24 * q^60 + 8 * q^64 + 96 * q^65 + 72 * q^67 + 48 * q^71 - 16 * q^74 - 24 * q^78 + 16 * q^79 + 36 * q^81 - 56 * q^85 - 8 * q^86 + 8 * q^88 - 8 * q^92 + 24 * q^93 - 64 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more