LMFDB - Embedded newform 882.2.e.s.655.1

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)

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")

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);

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			655.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.s.373.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+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	$-0.501316\pi$
$5$	1.93185	−	3.34607i	0.863950	−	1.49641i	0.868086	−	0.496414i	$-0.165350\pi$
$6$	−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	$0.211833\pi$
$13$	3.34607	+	5.79555i	0.928032	+	1.60740i	0.141420	+	0.989950i	$0.454833\pi$
$14$		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	$-0.605217\pi$
$17$	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
$23$	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	$-0.551481\pi$
$31$	−1.79315			−0.322059			−0.161030	+	0.986950i	$0.551481\pi$
$32$	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	0.811919	−	0.583771i	$-0.198423\pi$
$41$	−0.637756	−	1.10463i	−0.0996008	−	0.172514i	−0.911519	+	0.411257i	$0.865090\pi$
$42$		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	$-0.779676\pi$
$47$	−10.5558			−1.53973			−0.769863	+	0.638209i	$0.779676\pi$
$48$	−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	$-0.310273\pi$
$59$	8.62398			1.12275			0.561373	+	0.827563i	$0.310273\pi$
$60$	−4.73205	+	4.73205i	−0.610905	+	0.610905i
$61$	−6.96953			−0.892357			−0.446179	−	0.894944i	$-0.647215\pi$
$61$	−6.96953			−0.892357			−0.446179	+	0.894944i	$0.647215\pi$
$62$	−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	−0.993694	−	0.112125i	$-0.964234\pi$
$73$	−3.41542	+	5.91567i	−0.399744	+	0.692377i	0.593950	+	0.804502i	$0.297568\pi$
$74$	−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	$0.607245\pi$
$83$	−8.95215	+	15.5056i	−0.982626	+	1.70196i	−0.652043	+	0.758182i	$0.726088\pi$
$84$		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	0.990292	−	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
$93$	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	−0.975994	−	0.217797i	$-0.930113\pi$
$97$	−2.94855	+	5.10703i	−0.299379	+	0.518540i	0.676615	+	0.736337i	$0.263446\pi$
$98$		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	0.961775	−	0.273842i	$-0.0882945\pi$
$101$	2.44949	+	4.24264i	0.243733	+	0.422159i	−0.718041	+	0.696000i	$0.754961\pi$
$102$	−6.63397	+	6.63397i	−0.656861	+	0.656861i
$103$	3.72500	−	6.45189i	0.367035	−	0.635724i	−0.622065	−	0.782965i	$-0.713706\pi$
$103$	3.72500	−	6.45189i	0.367035	−	0.635724i	0.989101	+	0.147241i	$0.0470394\pi$
$104$	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	−0.703541	−	0.710655i	$-0.748399\pi$
$131$	3.01790	−	5.22715i	0.263675	−	0.456698i	0.967216	+	0.253957i	$0.0817321\pi$
$132$	−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	$-0.922755\pi$
$139$	−8.17569	−	14.1607i	−0.693453	−	1.20110i	0.277246	−	0.960799i	$-0.410578\pi$
$140$		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	$-0.559041\pi$
$157$	−4.62158			−0.368842			−0.184421	+	0.982847i	$0.559041\pi$
$158$	−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	$0.137607\pi$
$167$	10.5558	+	18.2832i	0.816835	+	1.41480i	−0.0911679	+	0.995836i	$0.529060\pi$
$168$		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	$-0.521715\pi$
$173$	−1.79315			−0.136331			−0.0681654	+	0.997674i	$0.521715\pi$
$174$	−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	$-0.282765\pi$
$181$	16.9706			1.26141			0.630706	+	0.776022i	$0.282765\pi$
$182$		0			0
$183$	11.6603	+	3.12436i	0.861951	+	0.230959i
$184$	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	$0.384023\pi$
$199$	−8.90138	+	15.4176i	−0.631002	+	1.09293i	−0.987347	+	0.158574i	$0.949310\pi$
$200$	−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	$0.520405\pi$
$223$	−13.3843	+	23.1822i	−0.896276	+	1.55240i	−0.832217	+	0.554450i	$0.812929\pi$
$224$		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	0.637011	−	0.770855i	$-0.280171\pi$
$227$	−5.25933	−	9.10943i	−0.349074	−	0.604614i	−0.986085	+	0.166240i	$0.946837\pi$
$228$	1.33013	+	4.96410i	0.0880898	+	0.328756i
$229$	12.4877	−	21.6293i	0.825209	−	1.42930i	−0.0765496	−	0.997066i	$-0.524390\pi$
$229$	12.4877	−	21.6293i	0.825209	−	1.42930i	0.901759	−	0.432239i	$-0.142276\pi$
$230$	−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	$0.105399\pi$
$241$	11.7112	+	20.2844i	0.754387	+	1.30664i	−0.191292	+	0.981533i	$0.561268\pi$
$242$	−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	$-0.327404\pi$
$251$	16.3514			1.03209			0.516045	+	0.856561i	$0.327404\pi$
$252$		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	−0.821028	−	0.570889i	$-0.806599\pi$
$257$	1.34486	−	2.32937i	0.0838903	−	0.145302i	0.904918	+	0.425586i	$0.139932\pi$
$258$	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	−0.939277	−	0.343161i	$-0.888502\pi$
$269$	−2.82843	+	4.89898i	−0.172452	+	0.298696i	0.766824	+	0.641857i	$0.221836\pi$
$270$	−19.3923	+	5.19615i	−1.18018	+	0.316228i
$271$	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
$275$	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	$-0.590318\pi$
$283$	−9.41902			−0.559903			−0.279951	+	0.960014i	$0.590318\pi$
$284$	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	$-0.978927\pi$
$293$	−9.52056	−	16.4901i	−0.556197	−	0.963361i	0.441612	−	0.897206i	$-0.354407\pi$
$294$		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	$-0.397661\pi$
$307$	11.0735			0.631996			0.315998	+	0.948760i	$0.397661\pi$
$308$		0			0
$309$	−9.12436	+	9.12436i	−0.519066	+	0.519066i
$310$	−3.46410	+	6.00000i	−0.196748	+	0.340777i
$311$	12.3490			0.700247			0.350123	−	0.936704i	$-0.386140\pi$
$311$	12.3490			0.700247			0.350123	+	0.936704i	$0.386140\pi$
$312$	−3.00000	−	11.1962i	−0.169842	−	0.633857i
$313$	−23.4225			−1.32392			−0.661958	−	0.749541i	$-0.730274\pi$
$313$	−23.4225			−1.32392			−0.661958	+	0.749541i	$0.730274\pi$
$314$	−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	−0.556443	−	0.830886i	$-0.687834\pi$
$349$	8.24504	−	14.2808i	0.441347	−	0.764436i	0.997790	+	0.0664504i	$0.0211674\pi$
$350$		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	$-0.918386\pi$
$353$	−13.2134	−	22.8862i	−0.703277	−	1.21811i	0.264033	−	0.964514i	$-0.414947\pi$
$354$	−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	0.584349	−	0.811503i	$-0.301350\pi$
$367$	−7.86611	−	13.6245i	−0.410607	−	0.711193i	−0.994956	+	0.100310i	$0.968017\pi$
$368$	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	$0.353395\pi$
$383$	−10.8332	+	18.7637i	−0.553552	+	0.958781i	−0.998015	+	0.0629833i	$0.979939\pi$
$384$	−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	0.998501	−	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
$401$	−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	$-0.635740\pi$
$409$	−16.7303			−0.827261			−0.413631	+	0.910445i	$0.635740\pi$
$410$	−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	0.753209	−	0.657781i	$-0.228505\pi$
$419$	−3.95164	−	6.84443i	−0.193050	−	0.334373i	−0.946260	+	0.323408i	$0.895171\pi$
$420$		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	$-0.554635\pi$
$433$	−7.10823			−0.341600			−0.170800	+	0.985306i	$0.554635\pi$
$434$		0			0
$435$	6.92820	+	25.8564i	0.332182	+	1.23972i
$436$	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	$-0.345108\pi$
$439$	19.5959			0.935262			0.467631	+	0.883924i	$0.345108\pi$
$440$	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	$0.371204\pi$
$461$	−12.8666	+	22.2856i	−0.599258	+	1.03795i	−0.992931	+	0.118695i	$0.962129\pi$
$462$		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	$-0.946534\pi$
$467$	−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
$471$	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	0.986786	−	0.162026i	$-0.0518030\pi$
$479$	7.72741	+	13.3843i	0.353074	+	0.611542i	−0.633712	+	0.773569i	$0.718470\pi$
$480$	−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	$-0.446886\pi$
$503$	7.45001			0.332179			0.166090	+	0.986111i	$0.446886\pi$
$504$		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	$-0.633603\pi$
$509$	13.2456	−	22.9420i	0.587099	−	1.01689i	0.994610	−	0.103685i	$-0.0330635\pi$
$510$	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	$-0.582534\pi$
$521$	16.1805	−	28.0255i	0.708881	−	1.22782i	0.965273	−	0.261244i	$-0.0841329\pi$
$522$	10.3923	−	6.00000i	0.454859	−	0.262613i
$523$	−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
$527$	−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	$-0.318673\pi$
$563$	25.5945			1.07868			0.539341	+	0.842088i	$0.318673\pi$
$564$	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	$0.546086\pi$
$577$	−22.3178	+	38.6556i	−0.929103	+	1.60925i	−0.784825	+	0.619717i	$0.787247\pi$
$578$	−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	$-0.627844\pi$
$587$	14.5768	−	25.2478i	0.601650	−	1.04209i	0.992571	−	0.121664i	$-0.0388230\pi$
$588$		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	0.836672	−	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
$597$	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	−0.875024	−	0.484080i	$-0.839154\pi$
$601$	−0.448288	+	0.776457i	−0.0182860	+	0.0316723i	0.856738	+	0.515753i	$0.172488\pi$
$602$		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	$0.388841\pi$
$607$	−15.8338	+	27.4249i	−0.642672	+	1.11314i	−0.984834	+	0.173500i	$0.944492\pi$
$608$	−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	0.999984	−	0.00570182i	$-0.00181496\pi$
$619$	12.3168	+	21.3333i	0.495054	+	0.857459i	−0.504930	+	0.863160i	$0.668482\pi$
$620$	−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	0.707919	−	0.706294i	$-0.249634\pi$
$643$	−6.53485	−	11.3187i	−0.257709	−	0.446365i	−0.965628	+	0.259929i	$0.916301\pi$
$644$		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	−0.722645	−	0.691220i	$-0.757074\pi$
$647$	6.03579	−	10.4543i	0.237291	−	0.411001i	0.959936	+	0.280219i	$0.0904070\pi$
$648$	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	$-0.373926\pi$
$677$	20.0764			0.771598			0.385799	+	0.922583i	$0.373926\pi$
$678$	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	$-0.558588\pi$
$691$	−9.62209			−0.366042			−0.183021	+	0.983109i	$0.558588\pi$
$692$	−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	0.686246	−	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
$723$	−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	−0.880392	−	0.474247i	$-0.842721\pi$
$727$	−0.795040	+	1.37705i	−0.0294864	+	0.0510719i	0.850906	+	0.525319i	$0.176054\pi$
$728$		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	−0.977158	−	0.212513i	$-0.931835\pi$
$733$	−8.24504	+	14.2808i	−0.304538	+	0.527475i	0.672621	+	0.739988i	$0.265169\pi$
$734$	−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	$0.352810\pi$
$761$	−15.2282	+	26.3760i	−0.552021	+	0.956129i	−0.998129	+	0.0611492i	$0.980523\pi$
$762$	−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	$0.0750511\pi$
$769$	19.0919	+	33.0681i	0.688471	+	1.19247i	−0.283862	+	0.958865i	$0.591616\pi$
$770$		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	−0.864194	−	0.503159i	$-0.832171\pi$
$773$	0.101536	−	0.175865i	0.00365199	−	0.00632544i	0.867846	+	0.496834i	$0.165504\pi$
$774$	−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	$-0.186558\pi$
$787$	46.7434			1.66622			0.833111	+	0.553106i	$0.186558\pi$
$788$	−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	0.989613	−	0.143756i	$-0.0459181\pi$
$797$	10.4543	+	18.1074i	0.370310	+	0.641396i	−0.619303	+	0.785152i	$0.712585\pi$
$798$		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	$-0.800435\pi$
$811$	−46.1242			−1.61964			−0.809820	+	0.586679i	$0.800435\pi$
$812$		0			0
$813$	−8.07180	−	30.1244i	−0.283090	−	1.05651i
$814$	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	$-0.608870\pi$
$829$	18.6622	−	32.3238i	0.648164	−	1.12265i	0.983561	−	0.180576i	$-0.0577963\pi$
$830$	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	−0.601935	−	0.798545i	$-0.705603\pi$
$839$	11.3137	−	19.5959i	0.390593	−	0.676526i	0.992528	+	0.122019i	$0.0389368\pi$
$840$		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	−0.969902	−	0.243494i	$-0.921706\pi$
$853$	−8.00481	+	13.8647i	−0.274079	+	0.474719i	0.695823	+	0.718213i	$0.255040\pi$
$854$		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	0.928697	−	0.370840i	$-0.120930\pi$
$857$	4.19187	+	7.26054i	0.143192	+	0.248015i	−0.785505	+	0.618855i	$0.787597\pi$
$858$	30.5885	−	30.5885i	1.04427	−	1.04427i
$859$	7.36705	−	12.7601i	0.251361	−	0.435369i	−0.712540	−	0.701631i	$-0.752455\pi$
$859$	7.36705	−	12.7601i	0.251361	−	0.435369i	0.963901	+	0.266262i	$0.0857887\pi$
$860$	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	$-0.431218\pi$
$881$	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	$0.459529\pi$
$884$	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	−0.516895	−	0.856049i	$-0.672912\pi$
$887$	14.3824	−	24.9110i	0.482913	−	0.836430i	0.999808	+	0.0196195i	$0.00624547\pi$
$888$	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	$-0.348211\pi$
$929$	27.9797			0.917983			0.458991	+	0.888441i	$0.348211\pi$
$930$	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	$-0.448302\pi$
$937$	9.89949			0.323402			0.161701	+	0.986840i	$0.448302\pi$
$938$		0			0
$939$	39.1865	+	10.5000i	1.27880	+	0.342655i
$940$	−20.3923	+	35.3205i	−0.665124	+	1.15203i
$941$	8.68835			0.283232			0.141616	−	0.989922i	$-0.454770\pi$
$941$	8.68835			0.283232			0.141616	+	0.989922i	$0.454770\pi$
$942$	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	0.840915	−	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
$975$	−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	0.805086	−	0.593158i	$-0.202119\pi$
$983$	−3.48477	−	6.03579i	−0.111147	−	0.192512i	−0.916233	+	0.400646i	$0.868786\pi$
$984$	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	0.912819	−	0.408365i	$-0.133901\pi$
$997$	3.24453	+	5.61969i	0.102755	+	0.177977i	−0.810064	+	0.586342i	$0.800567\pi$
$998$	−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.655.1		8
3.2	odd	2		2646.2.e.q.2125.1		8
7.2	even	3		882.2.h.q.79.3		8
7.3	odd	6		882.2.f.q.295.2	✓	8
7.4	even	3		882.2.f.q.295.3	yes	8
7.5	odd	6		882.2.h.q.79.2		8
7.6	odd	2	inner	882.2.e.s.655.4		8
9.4	even	3		882.2.h.q.67.4		8
9.5	odd	6		2646.2.h.t.361.4		8
21.2	odd	6		2646.2.h.t.667.4		8
21.5	even	6		2646.2.h.t.667.1		8
21.11	odd	6		2646.2.f.r.883.1		8
21.17	even	6		2646.2.f.r.883.4		8
21.20	even	2		2646.2.e.q.2125.4		8
63.4	even	3		882.2.f.q.589.3	yes	8
63.5	even	6		2646.2.e.q.1549.4		8
63.11	odd	6		7938.2.a.ci.1.4		4
63.13	odd	6		882.2.h.q.67.1		8
63.23	odd	6		2646.2.e.q.1549.1		8
63.25	even	3		7938.2.a.cp.1.1		4
63.31	odd	6		882.2.f.q.589.2	yes	8
63.32	odd	6		2646.2.f.r.1765.1		8
63.38	even	6		7938.2.a.ci.1.1		4
63.40	odd	6	inner	882.2.e.s.373.4		8
63.41	even	6		2646.2.h.t.361.1		8
63.52	odd	6		7938.2.a.cp.1.4		4
63.58	even	3	inner	882.2.e.s.373.1		8
63.59	even	6		2646.2.f.r.1765.4		8

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

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