LMFDB - Embedded newform 735.2.q.c.214.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [735,2,Mod(79,735)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(735, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("735.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 735 = 3 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	735.q (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.86900454856$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			214.2
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	735.214
Dual form			735.2.q.c.79.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.448288 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-2.20711 - 0.358719i) q^{5} +0.517638 q^{6} -1.93185i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.448288 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-2.20711 - 0.358719i) q^{5} +0.517638 q^{6} -1.93185i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.08226 - 0.410432i) q^{10} +(-1.73205 + 3.00000i) q^{11} +(1.50000 - 0.866025i) q^{12} -4.00000i q^{13} +(1.73205 + 1.41421i) q^{15} +(-1.23205 - 2.13397i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-0.448288 - 0.258819i) q^{18} +(2.63896 + 4.57081i) q^{19} +(2.44949 - 3.00000i) q^{20} -1.79315i q^{22} +(-3.01790 + 1.74238i) q^{23} +(-0.965926 + 1.67303i) q^{24} +(4.74264 + 1.58346i) q^{25} +(1.03528 + 1.79315i) q^{26} -1.00000i q^{27} +4.92820 q^{29} +(-1.14248 - 0.185687i) q^{30} +(3.67423 - 6.36396i) q^{31} +(4.45069 + 2.56961i) q^{32} +(3.00000 - 1.73205i) q^{33} +2.07055 q^{34} -1.73205 q^{36} +(9.14162 - 5.27792i) q^{37} +(-2.36603 - 1.36603i) q^{38} +(-2.00000 + 3.46410i) q^{39} +(-0.692993 + 4.26380i) q^{40} +8.48528 q^{41} +(-3.00000 - 5.19615i) q^{44} +(-0.792893 - 2.09077i) q^{45} +(0.901924 - 1.56218i) q^{46} +(5.19615 - 3.00000i) q^{47} +2.46410i q^{48} +(-2.53590 + 0.517638i) q^{50} +(2.00000 + 3.46410i) q^{51} +(6.00000 + 3.46410i) q^{52} +(-6.36396 - 3.67423i) q^{53} +(0.258819 + 0.448288i) q^{54} +(4.89898 - 6.00000i) q^{55} -5.27792i q^{57} +(-2.20925 + 1.27551i) q^{58} +(-0.378937 + 0.656339i) q^{59} +(-3.62132 + 1.37333i) q^{60} +(-0.328169 - 0.568406i) q^{61} +3.80385i q^{62} +2.26795 q^{64} +(-1.43488 + 8.82843i) q^{65} +(-0.896575 + 1.55291i) q^{66} +(10.9348 + 6.31319i) q^{67} +(6.00000 - 3.46410i) q^{68} +3.48477 q^{69} -6.39230 q^{71} +(1.67303 - 0.965926i) q^{72} +(-2.53590 - 1.46410i) q^{73} +(-2.73205 + 4.73205i) q^{74} +(-3.31552 - 3.74264i) q^{75} -9.14162 q^{76} -2.07055i q^{78} +(-2.26795 - 3.92820i) q^{79} +(1.95377 + 5.15187i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.80385 + 2.19615i) q^{82} -6.00000i q^{83} +(6.92820 + 5.65685i) q^{85} +(-4.26795 - 2.46410i) q^{87} +(5.79555 + 3.34607i) q^{88} +(-7.72741 - 13.3843i) q^{89} +(0.896575 + 0.732051i) q^{90} -6.03579i q^{92} +(-6.36396 + 3.67423i) q^{93} +(-1.55291 + 2.68973i) q^{94} +(-4.18482 - 11.0349i) q^{95} +(-2.56961 - 4.45069i) q^{96} +18.9282i q^{97} -3.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 12 q^{5} + 4 q^{9}+O(q^{10}) $ 8 * q - 12 * q^5 + 4 * q^9	$ 8 q - 12 q^{5} + 4 q^{9} + 12 q^{10} + 12 q^{12} + 4 q^{16} + 4 q^{25} - 16 q^{29} + 4 q^{30} + 24 q^{33} - 12 q^{38} - 16 q^{39} - 12 q^{40} - 24 q^{44} - 12 q^{45} + 28 q^{46} - 48 q^{50} + 16 q^{51} + 48 q^{52} - 12 q^{60} + 32 q^{64} + 48 q^{68} + 32 q^{71} - 48 q^{73} - 8 q^{74} - 32 q^{79} - 12 q^{80} - 4 q^{81} - 72 q^{82} - 48 q^{87} + 16 q^{95}+O(q^{100}) $ 8 * q - 12 * q^5 + 4 * q^9 + 12 * q^10 + 12 * q^12 + 4 * q^16 + 4 * q^25 - 16 * q^29 + 4 * q^30 + 24 * q^33 - 12 * q^38 - 16 * q^39 - 12 * q^40 - 24 * q^44 - 12 * q^45 + 28 * q^46 - 48 * q^50 + 16 * q^51 + 48 * q^52 - 12 * q^60 + 32 * q^64 + 48 * q^68 + 32 * q^71 - 48 * q^73 - 8 * q^74 - 32 * q^79 - 12 * q^80 - 4 * q^81 - 72 * q^82 - 48 * q^87 + 16 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/735\mathbb{Z}\right)^\times$.

$n$	$346$	$442$	$491$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.448288	+	0.258819i	−0.316987	+	0.183013i	−0.650049	−	0.759892i	$-0.725252\pi$
$2$	−0.448288	+	0.258819i	−0.316987	+	0.183013i	0.333062	+	0.942905i	$0.391918\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.866025	+	1.50000i	−0.433013	+	0.750000i
$5$	−2.20711	−	0.358719i	−0.987048	−	0.160424i
$5$	−2.20711	−	0.358719i	−0.987048	−	0.160424i
$6$	0.517638			0.211325
$7$		0			0
$7$		0			0
$8$		−	1.93185i		−	0.683013i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	1.08226	−	0.410432i	0.342241	−	0.129790i
$11$	−1.73205	+	3.00000i	−0.522233	+	0.904534i	0.477432	+	0.878668i	$0.341568\pi$
$11$	−1.73205	+	3.00000i	−0.522233	+	0.904534i	−0.999665	+	0.0258656i	$0.991766\pi$
$12$	1.50000	−	0.866025i	0.433013	−	0.250000i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$		0			0
$15$	1.73205	+	1.41421i	0.447214	+	0.365148i
$16$	−1.23205	−	2.13397i	−0.308013	−	0.533494i
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	0.0171533	−	0.999853i	$-0.494540\pi$
$17$	−3.46410	−	2.00000i	−0.840168	−	0.485071i	−0.857321	+	0.514782i	$0.827873\pi$
$18$	−0.448288	−	0.258819i	−0.105662	−	0.0610042i
$19$	2.63896	+	4.57081i	0.605419	+	1.04862i	0.991985	+	0.126354i	$0.0403276\pi$
$19$	2.63896	+	4.57081i	0.605419	+	1.04862i	−0.386567	+	0.922261i	$0.626339\pi$
$20$	2.44949	−	3.00000i	0.547723	−	0.670820i
$21$		0			0
$22$		−	1.79315i		−	0.382301i
$23$	−3.01790	+	1.74238i	−0.629275	+	0.363312i	−0.780471	−	0.625192i	$-0.785021\pi$
$23$	−3.01790	+	1.74238i	−0.629275	+	0.363312i	0.151196	+	0.988504i	$0.451687\pi$
$24$	−0.965926	+	1.67303i	−0.197169	+	0.341506i
$25$	4.74264	+	1.58346i	0.948528	+	0.316693i
$26$	1.03528	+	1.79315i	0.203034	+	0.351666i
$27$		−	1.00000i		−	0.192450i
$28$		0			0
$29$	4.92820			0.915144			0.457572	−	0.889172i	$-0.348719\pi$
$29$	4.92820			0.915144			0.457572	+	0.889172i	$0.348719\pi$
$30$	−1.14248	−	0.185687i	−0.208588	−	0.0339016i
$31$	3.67423	−	6.36396i	0.659912	−	1.14300i	−0.320726	−	0.947172i	$-0.603927\pi$
$31$	3.67423	−	6.36396i	0.659912	−	1.14300i	0.980638	−	0.195829i	$-0.0627398\pi$
$32$	4.45069	+	2.56961i	0.786779	+	0.454247i
$33$	3.00000	−	1.73205i	0.522233	−	0.301511i
$34$	2.07055			0.355097
$35$		0			0
$36$	−1.73205			−0.288675
$37$	9.14162	−	5.27792i	1.50287	−	0.867684i	0.502879	−	0.864357i	$-0.332274\pi$
$37$	9.14162	−	5.27792i	1.50287	−	0.867684i	0.999994	−	0.00332716i	$-0.00105907\pi$
$38$	−2.36603	−	1.36603i	−0.383820	−	0.221599i
$39$	−2.00000	+	3.46410i	−0.320256	+	0.554700i
$40$	−0.692993	+	4.26380i	−0.109572	+	0.674166i
$41$	8.48528			1.32518			0.662589	−	0.748983i	$-0.269458\pi$
$41$	8.48528			1.32518			0.662589	+	0.748983i	$0.269458\pi$
$42$		0			0
$43$		0			0		1.00000			$0$
$43$		0			0		−1.00000			$\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$	−0.792893	−	2.09077i	−0.118198	−	0.311674i
$46$	0.901924	−	1.56218i	0.132981	−	0.230331i
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	−0.0706177	−	0.997503i	$-0.522497\pi$
$47$	5.19615	−	3.00000i	0.757937	−	0.437595i	0.828554	+	0.559908i	$0.189164\pi$
$48$			2.46410i			0.355662i
$49$		0			0
$50$	−2.53590	+	0.517638i	−0.358630	+	0.0732051i
$51$	2.00000	+	3.46410i	0.280056	+	0.485071i
$52$	6.00000	+	3.46410i	0.832050	+	0.480384i
$53$	−6.36396	−	3.67423i	−0.874157	−	0.504695i	−0.00542976	−	0.999985i	$-0.501728\pi$
$53$	−6.36396	−	3.67423i	−0.874157	−	0.504695i	−0.868728	+	0.495290i	$0.835062\pi$
$54$	0.258819	+	0.448288i	0.0352208	+	0.0610042i
$55$	4.89898	−	6.00000i	0.660578	−	0.809040i
$56$		0			0
$57$		−	5.27792i		−	0.699077i
$58$	−2.20925	+	1.27551i	−0.290089	+	0.167483i
$59$	−0.378937	+	0.656339i	−0.0493334	+	0.0854480i	−0.889638	−	0.456667i	$-0.849043\pi$
$59$	−0.378937	+	0.656339i	−0.0493334	+	0.0854480i	0.840304	+	0.542115i	$0.182376\pi$
$60$	−3.62132	+	1.37333i	−0.467510	+	0.177296i
$61$	−0.328169	−	0.568406i	−0.0420178	−	0.0727769i	0.844252	−	0.535947i	$-0.180045\pi$
$61$	−0.328169	−	0.568406i	−0.0420178	−	0.0727769i	−0.886269	+	0.463170i	$0.846712\pi$
$62$			3.80385i			0.483089i
$63$		0			0
$64$	2.26795			0.283494
$65$	−1.43488	+	8.82843i	−0.177975	+	1.09503i
$66$	−0.896575	+	1.55291i	−0.110361	+	0.191151i
$67$	10.9348	+	6.31319i	1.33589	+	0.771279i	0.986196	−	0.165583i	$-0.0529505\pi$
$67$	10.9348	+	6.31319i	1.33589	+	0.771279i	0.349699	+	0.936862i	$0.386284\pi$
$68$	6.00000	−	3.46410i	0.727607	−	0.420084i
$69$	3.48477			0.419517
$70$		0			0
$71$	−6.39230			−0.758627			−0.379314	−	0.925268i	$-0.623840\pi$
$71$	−6.39230			−0.758627			−0.379314	+	0.925268i	$0.623840\pi$
$72$	1.67303	−	0.965926i	0.197169	−	0.113835i
$73$	−2.53590	−	1.46410i	−0.296804	−	0.171360i	0.344202	−	0.938896i	$-0.388149\pi$
$73$	−2.53590	−	1.46410i	−0.296804	−	0.171360i	−0.641006	+	0.767535i	$0.721483\pi$
$74$	−2.73205	+	4.73205i	−0.317594	+	0.550090i
$75$	−3.31552	−	3.74264i	−0.382843	−	0.432163i
$76$	−9.14162			−1.04862
$77$		0			0
$78$		−	2.07055i		−	0.234444i
$79$	−2.26795	−	3.92820i	−0.255164	−	0.441957i	0.709776	−	0.704428i	$-0.248796\pi$
$79$	−2.26795	−	3.92820i	−0.255164	−	0.441957i	−0.964940	+	0.262470i	$0.915463\pi$
$80$	1.95377	+	5.15187i	0.218438	+	0.575997i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.80385	+	2.19615i	−0.420065	+	0.242524i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$		0			0
$85$	6.92820	+	5.65685i	0.751469	+	0.613572i
$86$		0			0
$87$	−4.26795	−	2.46410i	−0.457572	−	0.264179i
$88$	5.79555	+	3.34607i	0.617808	+	0.356692i
$89$	−7.72741	−	13.3843i	−0.819103	−	1.41873i	−0.906344	−	0.422542i	$-0.861138\pi$
$89$	−7.72741	−	13.3843i	−0.819103	−	1.41873i	0.0872401	−	0.996187i	$-0.472195\pi$
$90$	0.896575	+	0.732051i	0.0945074	+	0.0771649i
$91$		0			0
$92$		−	6.03579i		−	0.629275i
$93$	−6.36396	+	3.67423i	−0.659912	+	0.381000i
$94$	−1.55291	+	2.68973i	−0.160171	+	0.277424i
$95$	−4.18482	−	11.0349i	−0.429354	−	1.13216i
$96$	−2.56961	−	4.45069i	−0.262260	−	0.454247i
$97$			18.9282i			1.92187i	0.276778	+	0.960934i	$0.410733\pi$
$97$			18.9282i			1.92187i	−0.276778	+	0.960934i	$0.589267\pi$
$98$		0			0
$99$	−3.46410			−0.348155
$100$	−6.48244	+	5.74264i	−0.648244	+	0.574264i
$101$	3.48477	−	6.03579i	0.346747	−	0.600584i	−0.638922	−	0.769271i	$-0.720620\pi$
$101$	3.48477	−	6.03579i	0.346747	−	0.600584i	0.985670	+	0.168687i	$0.0539529\pi$
$102$	−1.79315	−	1.03528i	−0.177548	−	0.102508i
$103$	−12.0000	+	6.92820i	−1.18240	+	0.682656i	−0.956567	−	0.291511i	$-0.905842\pi$
$103$	−12.0000	+	6.92820i	−1.18240	+	0.682656i	−0.225828	+	0.974167i	$0.572509\pi$
$104$	−7.72741			−0.757735
$105$		0			0
$106$	3.80385			0.369462
$107$	13.4722	−	7.77817i	1.30241	−	0.751945i	0.321590	−	0.946879i	$-0.395783\pi$
$107$	13.4722	−	7.77817i	1.30241	−	0.751945i	0.980816	+	0.194935i	$0.0624494\pi$
$108$	1.50000	+	0.866025i	0.144338	+	0.0833333i
$109$	7.92820	−	13.7321i	0.759384	−	1.31529i	−0.183781	−	0.982967i	$-0.558834\pi$
$109$	7.92820	−	13.7321i	0.759384	−	1.31529i	0.943165	−	0.332325i	$-0.107833\pi$
$110$	−0.643238	+	3.95768i	−0.0613304	+	0.377350i
$111$	−10.5558			−1.00192
$112$		0			0
$113$			5.27792i			0.496505i	0.968695	+	0.248252i	$0.0798562\pi$
$113$			5.27792i			0.496505i	−0.968695	+	0.248252i	$0.920144\pi$
$114$	1.36603	+	2.36603i	0.127940	+	0.221599i
$115$	7.28585	−	2.76305i	0.679409	−	0.257655i
$116$	−4.26795	+	7.39230i	−0.396269	+	0.686358i
$117$	3.46410	−	2.00000i	0.320256	−	0.184900i
$118$		−	0.392305i		−	0.0361146i
$119$		0			0
$120$	2.73205	−	3.34607i	0.249401	−	0.305453i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.294229	+	0.169873i	0.0266382	+	0.0153796i
$123$	−7.34847	−	4.24264i	−0.662589	−	0.382546i
$124$	6.36396	+	11.0227i	0.571501	+	0.989868i
$125$	−9.89949	−	5.19615i	−0.885438	−	0.464758i
$126$		0			0
$127$			2.82843i			0.250982i	0.992095	+	0.125491i	$0.0400507\pi$
$127$			2.82843i			0.250982i	−0.992095	+	0.125491i	$0.959949\pi$
$128$	−9.91808	+	5.72620i	−0.876642	+	0.506130i
$129$		0			0
$130$	−1.64173	−	4.32905i	−0.143989	−	0.379683i
$131$	2.82843	+	4.89898i	0.247121	+	0.428026i	0.962726	−	0.270479i	$-0.0871822\pi$
$131$	2.82843	+	4.89898i	0.247121	+	0.428026i	−0.715605	+	0.698505i	$0.753849\pi$
$132$			6.00000i			0.522233i
$133$		0			0
$134$	−6.53590			−0.564616
$135$	−0.358719	+	2.20711i	−0.0308737	+	0.189958i
$136$	−3.86370	+	6.69213i	−0.331310	+	0.573845i
$137$	−8.81345	−	5.08845i	−0.752984	−	0.434735i	0.0737871	−	0.997274i	$-0.476491\pi$
$137$	−8.81345	−	5.08845i	−0.752984	−	0.434735i	−0.826771	+	0.562539i	$0.809825\pi$
$138$	−1.56218	+	0.901924i	−0.132981	+	0.0767769i
$139$	0.378937			0.0321410			0.0160705	−	0.999871i	$-0.494884\pi$
$139$	0.378937			0.0321410			0.0160705	+	0.999871i	$0.494884\pi$
$140$		0			0
$141$	−6.00000			−0.505291
$142$	2.86559	−	1.65445i	0.240475	−	0.138838i
$143$	12.0000	+	6.92820i	1.00349	+	0.579365i
$144$	1.23205	−	2.13397i	0.102671	−	0.177831i
$145$	−10.8771	−	1.76784i	−0.903292	−	0.146811i
$146$	1.51575			0.125444
$147$		0			0
$148$			18.2832i			1.50287i
$149$	3.53590	+	6.12436i	0.289672	+	0.501727i	0.973731	−	0.227700i	$-0.0731204\pi$
$149$	3.53590	+	6.12436i	0.289672	+	0.501727i	−0.684059	+	0.729426i	$0.739787\pi$
$150$	2.45497	+	0.819661i	0.200448	+	0.0669251i
$151$	9.73205	−	16.8564i	0.791983	−	1.37175i	−0.132754	−	0.991149i	$-0.542382\pi$
$151$	9.73205	−	16.8564i	0.791983	−	1.37175i	0.924737	−	0.380606i	$-0.124285\pi$
$152$	8.83013	−	5.09808i	0.716218	−	0.413509i
$153$		−	4.00000i		−	0.323381i
$154$		0			0
$155$	−10.3923	+	12.7279i	−0.834730	+	1.02233i
$156$	−3.46410	−	6.00000i	−0.277350	−	0.480384i
$157$	−4.39230	−	2.53590i	−0.350544	−	0.202387i	0.314381	−	0.949297i	$-0.398203\pi$
$157$	−4.39230	−	2.53590i	−0.350544	−	0.202387i	−0.664925	+	0.746910i	$0.731536\pi$
$158$	2.03339	+	1.17398i	0.161768	+	0.0933966i
$159$	3.67423	+	6.36396i	0.291386	+	0.504695i
$160$	−8.90138	−	7.26795i	−0.703716	−	0.574582i
$161$		0			0
$162$		−	0.517638i		−	0.0406695i
$163$	19.4201	−	11.2122i	1.52110	−	0.878205i	0.521406	−	0.853309i	$-0.325408\pi$
$163$	19.4201	−	11.2122i	1.52110	−	0.878205i	0.999690	−	0.0248963i	$-0.00792556\pi$
$164$	−7.34847	+	12.7279i	−0.573819	+	0.993884i
$165$	−7.24264	+	2.74666i	−0.563839	+	0.213827i
$166$	1.55291	+	2.68973i	0.120530	+	0.208763i
$167$			18.9282i			1.46471i	0.680924	+	0.732354i	$0.261578\pi$
$167$			18.9282i			1.46471i	−0.680924	+	0.732354i	$0.738422\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$	−4.56993	−	0.742747i	−0.350498	−	0.0569661i
$171$	−2.63896	+	4.57081i	−0.201806	+	0.349539i
$172$		0			0
$173$	−13.8564	+	8.00000i	−1.05348	+	0.608229i	−0.923622	−	0.383304i	$-0.874786\pi$
$173$	−13.8564	+	8.00000i	−1.05348	+	0.608229i	−0.129861	+	0.991532i	$0.541453\pi$
$174$	2.55103			0.193393
$175$		0			0
$176$	8.53590			0.643418
$177$	0.656339	−	0.378937i	0.0493334	−	0.0284827i
$178$	6.92820	+	4.00000i	0.519291	+	0.299813i
$179$	5.19615	−	9.00000i	0.388379	−	0.672692i	−0.603853	−	0.797096i	$-0.706369\pi$
$179$	5.19615	−	9.00000i	0.388379	−	0.672692i	0.992232	+	0.124404i	$0.0397019\pi$
$180$	3.82282	+	0.621320i	0.284936	+	0.0463105i
$181$	−6.31319			−0.469256			−0.234628	−	0.972085i	$-0.575387\pi$
$181$	−6.31319			−0.469256			−0.234628	+	0.972085i	$0.575387\pi$
$182$		0			0
$183$			0.656339i			0.0485180i
$184$	3.36603	+	5.83013i	0.248147	+	0.429803i
$185$	−22.0698	+	8.36965i	−1.62261	+	0.615349i
$186$	1.90192	−	3.29423i	0.139456	−	0.241545i
$187$	12.0000	−	6.92820i	0.877527	−	0.506640i
$188$			10.3923i			0.757937i
$189$		0			0
$190$	4.73205	+	3.86370i	0.343299	+	0.280302i
$191$	3.73205	+	6.46410i	0.270042	+	0.467726i	0.968872	−	0.247561i	$-0.0796292\pi$
$191$	3.73205	+	6.46410i	0.270042	+	0.467726i	−0.698831	+	0.715287i	$0.746296\pi$
$192$	−1.96410	−	1.13397i	−0.141747	−	0.0818376i
$193$	−5.55532	−	3.20736i	−0.399881	−	0.230871i	0.286552	−	0.958065i	$-0.407491\pi$
$193$	−5.55532	−	3.20736i	−0.399881	−	0.230871i	−0.686432	+	0.727194i	$0.740824\pi$
$194$	−4.89898	−	8.48528i	−0.351726	−	0.609208i
$195$	5.65685	−	6.92820i	0.405096	−	0.496139i
$196$		0			0
$197$		−	22.8033i		−	1.62467i	−0.583193	−	0.812333i	$-0.698197\pi$
$197$		−	22.8033i		−	1.62467i	0.583193	−	0.812333i	$-0.301803\pi$
$198$	1.55291	−	0.896575i	0.110361	−	0.0637168i
$199$	4.05317	−	7.02030i	0.287322	−	0.497656i	−0.685848	−	0.727745i	$-0.740568\pi$
$199$	4.05317	−	7.02030i	0.287322	−	0.497656i	0.973170	+	0.230089i	$0.0739018\pi$
$200$	3.05902	−	9.16208i	0.216305	−	0.647857i
$201$	−6.31319	−	10.9348i	−0.445298	−	0.771279i
$202$			3.60770i			0.253837i
$203$		0			0
$204$	−6.92820			−0.485071
$205$	−18.7279	−	3.04384i	−1.30801	−	0.212591i
$206$	3.58630	−	6.21166i	0.249869	−	0.432787i
$207$	−3.01790	−	1.74238i	−0.209758	−	0.121104i
$208$	−8.53590	+	4.92820i	−0.591858	+	0.341709i
$209$	−18.2832			−1.26468
$210$		0			0
$211$	−26.9282			−1.85381			−0.926907	−	0.375291i	$-0.877543\pi$
$211$	−26.9282			−1.85381			−0.926907	+	0.375291i	$0.877543\pi$
$212$	11.0227	−	6.36396i	0.757042	−	0.437079i
$213$	5.53590	+	3.19615i	0.379314	+	0.218997i
$214$	−4.02628	+	6.97372i	−0.275231	+	0.476714i
$215$		0			0
$216$	−1.93185			−0.131446
$217$		0			0
$218$			8.20788i			0.555908i
$219$	1.46410	+	2.53590i	0.0989348	+	0.171360i
$220$	4.75736	+	12.5446i	0.320741	+	0.845758i
$221$	−8.00000	+	13.8564i	−0.538138	+	0.932083i
$222$	4.73205	−	2.73205i	0.317594	−	0.183363i
$223$		−	8.00000i		−	0.535720i	−0.963458	−	0.267860i	$-0.913684\pi$
$223$		−	8.00000i		−	0.535720i	0.963458	−	0.267860i	$-0.0863164\pi$
$224$		0			0
$225$	1.00000	+	4.89898i	0.0666667	+	0.326599i
$226$	−1.36603	−	2.36603i	−0.0908667	−	0.157386i
$227$	−3.46410	−	2.00000i	−0.229920	−	0.132745i	0.380615	−	0.924734i	$-0.375712\pi$
$227$	−3.46410	−	2.00000i	−0.229920	−	0.132745i	−0.610535	+	0.791989i	$0.709046\pi$
$228$	7.91688	+	4.57081i	0.524308	+	0.302709i
$229$	−6.74290	−	11.6790i	−0.445583	−	0.771773i	0.552509	−	0.833507i	$-0.313670\pi$
$229$	−6.74290	−	11.6790i	−0.445583	−	0.771773i	−0.998093	+	0.0617338i	$0.980337\pi$
$230$	−2.55103	+	3.12436i	−0.168210	+	0.206014i
$231$		0			0
$232$		−	9.52056i		−	0.625055i
$233$	4.57081	−	2.63896i	0.299444	−	0.172884i	−0.342749	−	0.939427i	$-0.611358\pi$
$233$	4.57081	−	2.63896i	0.299444	−	0.172884i	0.642193	+	0.766543i	$0.278025\pi$
$234$	−1.03528	+	1.79315i	−0.0676781	+	0.117222i
$235$	−12.5446	+	4.75736i	−0.818321	+	0.310336i
$236$	−0.656339	−	1.13681i	−0.0427240	−	0.0740002i
$237$			4.53590i			0.294638i
$238$		0			0
$239$	8.53590			0.552141			0.276071	−	0.961137i	$-0.410968\pi$
$239$	8.53590			0.552141			0.276071	+	0.961137i	$0.410968\pi$
$240$	0.883921	−	5.43854i	0.0570569	−	0.351056i
$241$	−7.02030	+	12.1595i	−0.452217	+	0.783263i	−0.998523	−	0.0543223i	$-0.982700\pi$
$241$	−7.02030	+	12.1595i	−0.452217	+	0.783263i	0.546306	+	0.837586i	$0.316034\pi$
$242$	0.448288	+	0.258819i	0.0288170	+	0.0166375i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	1.13681			0.0727769
$245$		0			0
$246$	4.39230			0.280043
$247$	18.2832	−	10.5558i	1.16333	−	0.671652i
$248$	−12.2942	−	7.09808i	−0.780684	−	0.450728i
$249$	−3.00000	+	5.19615i	−0.190117	+	0.329293i
$250$	5.78269	−	0.232806i	0.365729	−	0.0147240i
$251$	20.3538			1.28472			0.642360	−	0.766403i	$-0.277955\pi$
$251$	20.3538			1.28472			0.642360	+	0.766403i	$0.277955\pi$
$252$		0			0
$253$		−	12.0716i		−	0.758934i
$254$	−0.732051	−	1.26795i	−0.0459330	−	0.0795582i
$255$	−3.17157	−	8.36308i	−0.198612	−	0.523716i
$256$	0.696152	−	1.20577i	0.0435095	−	0.0753607i
$257$	−3.00000	+	1.73205i	−0.187135	+	0.108042i	−0.590641	−	0.806935i	$-0.701125\pi$
$257$	−3.00000	+	1.73205i	−0.187135	+	0.108042i	0.403506	+	0.914977i	$0.367792\pi$
$258$		0			0
$259$		0			0
$260$	−12.0000	−	9.79796i	−0.744208	−	0.607644i
$261$	2.46410	+	4.26795i	0.152524	+	0.264179i
$262$	−2.53590	−	1.46410i	−0.156668	−	0.0904525i
$263$	6.60420	+	3.81294i	0.407232	+	0.235116i	0.689600	−	0.724191i	$-0.257786\pi$
$263$	6.60420	+	3.81294i	0.407232	+	0.235116i	−0.282368	+	0.959306i	$0.591120\pi$
$264$	−3.34607	−	5.79555i	−0.205936	−	0.356692i
$265$	12.7279	+	10.3923i	0.781870	+	0.638394i
$266$		0			0
$267$			15.4548i			0.945819i
$268$	−18.9396	+	10.9348i	−1.15692	+	0.667947i
$269$	15.4548	−	26.7685i	0.942297	−	1.63211i	0.181221	−	0.983442i	$-0.441995\pi$
$269$	15.4548	−	26.7685i	0.942297	−	1.63211i	0.761076	−	0.648663i	$-0.224672\pi$
$270$	−0.410432	−	1.08226i	−0.0249781	−	0.0658644i
$271$	0.845807	+	1.46498i	0.0513791	+	0.0889913i	0.890571	−	0.454844i	$-0.150305\pi$
$271$	0.845807	+	1.46498i	0.0513791	+	0.0889913i	−0.839192	+	0.543835i	$0.816972\pi$
$272$			9.85641i			0.597632i
$273$		0			0
$274$	5.26795			0.318248
$275$	−12.9649	+	11.4853i	−0.781812	+	0.692589i
$276$	−3.01790	+	5.22715i	−0.181656	+	0.314637i
$277$	9.79796	+	5.65685i	0.588702	+	0.339887i	0.764584	−	0.644524i	$-0.222944\pi$
$277$	9.79796	+	5.65685i	0.588702	+	0.339887i	−0.175882	+	0.984411i	$0.556278\pi$
$278$	−0.169873	+	0.0980762i	−0.0101883	+	0.00588222i
$279$	7.34847			0.439941
$280$		0			0
$281$	27.8564			1.66177			0.830887	−	0.556441i	$-0.187834\pi$
$281$	27.8564			1.66177			0.830887	+	0.556441i	$0.187834\pi$
$282$	2.68973	−	1.55291i	0.160171	−	0.0924747i
$283$	1.85641	+	1.07180i	0.110352	+	0.0637117i	0.554160	−	0.832410i	$-0.313040\pi$
$283$	1.85641	+	1.07180i	0.110352	+	0.0637117i	−0.443808	+	0.896122i	$0.646373\pi$
$284$	5.53590	−	9.58846i	0.328495	−	0.568970i
$285$	−1.89329	+	11.6489i	−0.112149	+	0.690023i
$286$	−7.17260			−0.424125
$287$		0			0
$288$			5.13922i			0.302831i
$289$	−0.500000	−	0.866025i	−0.0294118	−	0.0509427i
$290$	5.33361	−	2.02269i	0.313200	−	0.118777i
$291$	9.46410	−	16.3923i	0.554795	−	0.960934i
$292$	4.39230	−	2.53590i	0.257040	−	0.148402i
$293$		−	11.4641i		−	0.669740i	−0.942264	−	0.334870i	$-0.891308\pi$
$293$		−	11.4641i		−	0.669740i	0.942264	−	0.334870i	$-0.108692\pi$
$294$		0			0
$295$	1.07180	−	1.31268i	0.0624024	−	0.0764270i
$296$	−10.1962	−	17.6603i	−0.592639	−	1.02648i
$297$	3.00000	+	1.73205i	0.174078	+	0.100504i
$298$	−3.17020	−	1.83032i	−0.183645	−	0.106027i
$299$	6.96953	+	12.0716i	0.403058	+	0.698118i
$300$	8.48528	−	1.73205i	0.489898	−	0.100000i
$301$		0			0
$302$			10.0754i			0.579772i
$303$	−6.03579	+	3.48477i	−0.346747	+	0.200195i
$304$	6.50266	−	11.2629i	0.372953	−	0.645974i
$305$	0.520407	+	1.37225i	0.0297984	+	0.0785750i
$306$	1.03528	+	1.79315i	0.0591828	+	0.102508i
$307$		−	4.00000i		−	0.228292i	−0.993464	−	0.114146i	$-0.963587\pi$
$307$		−	4.00000i		−	0.228292i	0.993464	−	0.114146i	$-0.0364132\pi$
$308$		0			0
$309$	13.8564			0.788263
$310$	1.36451	−	8.39550i	0.0774992	−	0.476832i
$311$	−2.07055	+	3.58630i	−0.117410	+	0.203361i	−0.918741	−	0.394861i	$-0.870793\pi$
$311$	−2.07055	+	3.58630i	−0.117410	+	0.203361i	0.801330	+	0.598222i	$0.204126\pi$
$312$	6.69213	+	3.86370i	0.378867	+	0.218739i
$313$	2.53590	−	1.46410i	0.143337	−	0.0827559i	−0.426616	−	0.904433i	$-0.640294\pi$
$313$	2.53590	−	1.46410i	0.143337	−	0.0827559i	0.569954	+	0.821677i	$0.306961\pi$
$314$	2.62536			0.148157
$315$		0			0
$316$	7.85641			0.441957
$317$	−4.09034	+	2.36156i	−0.229736	+	0.132638i	−0.610450	−	0.792055i	$-0.709012\pi$
$317$	−4.09034	+	2.36156i	−0.229736	+	0.132638i	0.380714	+	0.924693i	$0.375678\pi$
$318$	−3.29423	−	1.90192i	−0.184731	−	0.106655i
$319$	−8.53590	+	14.7846i	−0.477919	+	0.827779i
$320$	−5.00561	−	0.813558i	−0.279822	−	0.0454792i
$321$	−15.5563			−0.868271
$322$		0			0
$323$		−	21.1117i		−	1.17468i
$324$	−0.866025	−	1.50000i	−0.0481125	−	0.0833333i
$325$	6.33386	−	18.9706i	0.351339	−	1.05230i
$326$	−5.80385	+	10.0526i	−0.321445	+	0.556760i
$327$	−13.7321	+	7.92820i	−0.759384	+	0.438431i
$328$		−	16.3923i		−	0.905114i
$329$		0			0
$330$	2.53590	−	3.10583i	0.139597	−	0.170970i
$331$	4.39230	+	7.60770i	0.241423	+	0.418157i	0.961120	−	0.276132i	$-0.0890526\pi$
$331$	4.39230	+	7.60770i	0.241423	+	0.418157i	−0.719697	+	0.694288i	$0.755719\pi$
$332$	9.00000	+	5.19615i	0.493939	+	0.285176i
$333$	9.14162	+	5.27792i	0.500958	+	0.289228i
$334$	−4.89898	−	8.48528i	−0.268060	−	0.464294i
$335$	−21.8695	−	17.8564i	−1.19486	−	0.975600i
$336$		0			0
$337$		−	17.7284i		−	0.965730i	−0.875695	−	0.482865i	$-0.839596\pi$
$337$		−	17.7284i		−	0.965730i	0.875695	−	0.482865i	$-0.160404\pi$
$338$	1.34486	−	0.776457i	0.0731509	−	0.0422337i
$339$	2.63896	−	4.57081i	0.143329	−	0.248252i
$340$	−14.4853	+	5.49333i	−0.785575	+	0.297917i
$341$	12.7279	+	22.0454i	0.689256	+	1.19383i
$342$		−	2.73205i		−	0.147732i
$343$		0			0
$344$		0			0
$345$	−7.69125	−	1.25005i	−0.414083	−	0.0673006i
$346$	4.14110	−	7.17260i	0.222627	−	0.385602i
$347$	26.8565	+	15.5056i	1.44173	+	0.832383i	0.997965	−	0.0637601i	$-0.0203092\pi$
$347$	26.8565	+	15.5056i	1.44173	+	0.832383i	0.443765	+	0.896143i	$0.353643\pi$
$348$	7.39230	−	4.26795i	0.396269	−	0.228786i
$349$	17.6269			0.943546			0.471773	−	0.881720i	$-0.343614\pi$
$349$	17.6269			0.943546			0.471773	+	0.881720i	$0.343614\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	−15.4176	+	8.90138i	−0.821763	+	0.474445i
$353$	9.92820	+	5.73205i	0.528425	+	0.305086i	0.740375	−	0.672194i	$-0.234648\pi$
$353$	9.92820	+	5.73205i	0.528425	+	0.305086i	−0.211950	+	0.977281i	$0.567981\pi$
$354$	−0.196152	+	0.339746i	−0.0104254	+	0.0180573i
$355$	14.1085	+	2.29304i	0.748801	+	0.121702i
$356$	26.7685			1.41873
$357$		0			0
$358$			5.37945i			0.284313i
$359$	7.73205	+	13.3923i	0.408082	+	0.706819i	0.994675	−	0.103063i	$-0.0328644\pi$
$359$	7.73205	+	13.3923i	0.408082	+	0.706819i	−0.586593	+	0.809882i	$0.699531\pi$
$360$	−4.03906	+	1.53175i	−0.212877	+	0.0807304i
$361$	−4.42820	+	7.66987i	−0.233063	+	0.403678i
$362$	2.83013	−	1.63397i	0.148748	−	0.0858798i
$363$			1.00000i			0.0524864i
$364$		0			0
$365$	5.07180	+	4.14110i	0.265470	+	0.216755i
$366$	−0.169873	−	0.294229i	−0.00887940	−	0.0153796i
$367$	−3.46410	−	2.00000i	−0.180825	−	0.104399i	0.406855	−	0.913493i	$-0.366625\pi$
$367$	−3.46410	−	2.00000i	−0.180825	−	0.104399i	−0.587680	+	0.809093i	$0.699959\pi$
$368$	7.43640	+	4.29341i	0.387649	+	0.223809i
$369$	4.24264	+	7.34847i	0.220863	+	0.382546i
$370$	7.72741	−	9.46410i	0.401729	−	0.492015i
$371$		0			0
$372$		−	12.7279i		−	0.659912i
$373$	−6.21166	+	3.58630i	−0.321627	+	0.185692i	−0.652118	−	0.758118i	$-0.726119\pi$
$373$	−6.21166	+	3.58630i	−0.321627	+	0.185692i	0.330490	+	0.943809i	$0.392786\pi$
$374$	−3.58630	+	6.21166i	−0.185443	+	0.321197i
$375$	5.97514	+	9.44975i	0.308555	+	0.487983i
$376$	−5.79555	−	10.0382i	−0.298883	−	0.517680i
$377$		−	19.7128i		−	1.01526i
$378$		0			0
$379$	−11.4641			−0.588871			−0.294436	−	0.955671i	$-0.595132\pi$
$379$	−11.4641			−0.588871			−0.294436	+	0.955671i	$0.595132\pi$
$380$	20.1765	+	3.27928i	1.03503	+	0.168223i
$381$	1.41421	−	2.44949i	0.0724524	−	0.125491i
$382$	−3.34607	−	1.93185i	−0.171200	−	0.0988421i
$383$	20.6603	−	11.9282i	1.05569	−	0.609503i	0.131453	−	0.991322i	$-0.458036\pi$
$383$	20.6603	−	11.9282i	1.05569	−	0.609503i	0.924237	+	0.381820i	$0.124702\pi$
$384$	11.4524			0.584428
$385$		0			0
$386$	3.32051			0.169009
$387$		0			0
$388$	−28.3923	−	16.3923i	−1.44140	−	0.832193i
$389$	5.53590	−	9.58846i	0.280681	−	0.486154i	−0.690872	−	0.722978i	$-0.742773\pi$
$389$	5.53590	−	9.58846i	0.280681	−	0.486154i	0.971553	+	0.236823i	$0.0761063\pi$
$390$	−0.742747	+	4.56993i	−0.0376105	+	0.231407i
$391$	13.9391			0.704929
$392$		0			0
$393$		−	5.65685i		−	0.285351i
$394$	5.90192	+	10.2224i	0.297335	+	0.514999i
$395$	3.59648	+	9.48352i	0.180959	+	0.477168i
$396$	3.00000	−	5.19615i	0.150756	−	0.261116i
$397$	20.5359	−	11.8564i	1.03067	−	0.595056i	0.113491	−	0.993539i	$-0.463797\pi$
$397$	20.5359	−	11.8564i	1.03067	−	0.595056i	0.917176	+	0.398483i	$0.130463\pi$
$398$			4.19615i			0.210334i
$399$		0			0
$400$	−2.46410	−	12.0716i	−0.123205	−	0.603579i
$401$	−1.00000	−	1.73205i	−0.0499376	−	0.0864945i	0.839976	−	0.542623i	$-0.182569\pi$
$401$	−1.00000	−	1.73205i	−0.0499376	−	0.0864945i	−0.889914	+	0.456129i	$0.849236\pi$
$402$	5.66025	+	3.26795i	0.282308	+	0.162990i
$403$	−25.4558	−	14.6969i	−1.26805	−	0.732107i
$404$	6.03579	+	10.4543i	0.300292	+	0.520121i
$405$	1.41421	−	1.73205i	0.0702728	−	0.0860663i
$406$		0			0
$407$			36.5665i			1.81253i
$408$	6.69213	−	3.86370i	0.331310	−	0.191282i
$409$	−5.70762	+	9.88589i	−0.282224	+	0.488826i	−0.971932	−	0.235261i	$-0.924405\pi$
$409$	−5.70762	+	9.88589i	−0.282224	+	0.488826i	0.689708	+	0.724087i	$0.257739\pi$
$410$	9.18330	−	3.48263i	0.453531	−	0.171995i
$411$	5.08845	+	8.81345i	0.250995	+	0.434735i
$412$		−	24.0000i		−	1.18240i
$413$		0			0
$414$	1.80385			0.0886543
$415$	−2.15232	+	13.2426i	−0.105653	+	0.650056i
$416$	10.2784	−	17.8028i	0.503942	−	0.872852i
$417$	−0.328169	−	0.189469i	−0.0160705	−	0.00927832i
$418$	8.19615	−	4.73205i	0.400887	−	0.231452i
$419$	21.1117			1.03137			0.515686	−	0.856778i	$-0.327537\pi$
$419$	21.1117			1.03137			0.515686	+	0.856778i	$0.327537\pi$
$420$		0			0
$421$	12.7846			0.623084			0.311542	−	0.950232i	$-0.399155\pi$
$421$	12.7846			0.623084			0.311542	+	0.950232i	$0.399155\pi$
$422$	12.0716	−	6.96953i	0.587635	−	0.339272i
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$	−7.09808	+	12.2942i	−0.344713	+	0.597061i
$425$	−13.2621	−	14.9706i	−0.643304	−	0.726179i
$426$	−3.30890			−0.160317
$427$		0			0
$428$			26.9444i			1.30241i
$429$	−6.92820	−	12.0000i	−0.334497	−	0.579365i
$430$		0			0
$431$	−18.6603	+	32.3205i	−0.898833	+	1.55682i	−0.0698447	+	0.997558i	$0.522250\pi$
$431$	−18.6603	+	32.3205i	−0.898833	+	1.55682i	−0.828988	+	0.559266i	$0.811083\pi$
$432$	−2.13397	+	1.23205i	−0.102671	+	0.0592771i
$433$			17.8564i			0.858124i	0.903275	+	0.429062i	$0.141156\pi$
$433$			17.8564i			0.858124i	−0.903275	+	0.429062i	$0.858844\pi$
$434$		0			0
$435$	8.53590	+	6.96953i	0.409265	+	0.334163i
$436$	13.7321	+	23.7846i	0.657646	+	1.13908i
$437$	−15.9282	−	9.19615i	−0.761949	−	0.439912i
$438$	−1.31268	−	0.757875i	−0.0627222	−	0.0362127i
$439$	6.50266	+	11.2629i	0.310355	+	0.537551i	0.978439	−	0.206535i	$-0.0662187\pi$
$439$	6.50266	+	11.2629i	0.310355	+	0.537551i	−0.668084	+	0.744086i	$0.732885\pi$
$440$	−11.5911	−	9.46410i	−0.552584	−	0.451183i
$441$		0			0
$442$		−	8.28221i		−	0.393945i
$443$	−10.8468	+	6.26243i	−0.515349	+	0.297537i	−0.735030	−	0.678035i	$-0.762832\pi$
$443$	−10.8468	+	6.26243i	−0.515349	+	0.297537i	0.219681	+	0.975572i	$0.429498\pi$
$444$	9.14162	−	15.8338i	0.433842	−	0.751437i
$445$	12.2540	+	32.3125i	0.580896	+	1.53176i
$446$	2.07055	+	3.58630i	0.0980435	+	0.169816i
$447$		−	7.07180i		−	0.334485i
$448$		0			0
$449$	−35.8564			−1.69217			−0.846084	−	0.533049i	$-0.821046\pi$
$449$	−35.8564			−1.69217			−0.846084	+	0.533049i	$0.821046\pi$
$450$	−1.71624	−	1.93733i	−0.0809042	−	0.0913268i
$451$	−14.6969	+	25.4558i	−0.692052	+	1.19867i
$452$	−7.91688	−	4.57081i	−0.372378	−	0.214993i
$453$	−16.8564	+	9.73205i	−0.791983	+	0.457252i
$454$	2.07055			0.0971758
$455$		0			0
$456$	−10.1962			−0.477479
$457$	−18.9396	+	10.9348i	−0.885956	+	0.511507i	−0.872618	−	0.488404i	$-0.837579\pi$
$457$	−18.9396	+	10.9348i	−0.885956	+	0.511507i	−0.0133385	+	0.999911i	$0.504246\pi$
$458$	6.04552	+	3.49038i	0.282488	+	0.163095i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$	−2.16516	+	13.3216i	−0.100951	+	0.621125i
$461$	32.4254			1.51020			0.755100	−	0.655609i	$-0.227588\pi$
$461$	32.4254			1.51020			0.755100	+	0.655609i	$0.227588\pi$
$462$		0			0
$463$		−	22.4243i		−	1.04215i	−0.853512	−	0.521074i	$-0.825532\pi$
$463$		−	22.4243i		−	1.04215i	0.853512	−	0.521074i	$-0.174468\pi$
$464$	−6.07180	−	10.5167i	−0.281876	−	0.488224i
$465$	15.3640	−	5.82655i	0.712487	−	0.270200i
$466$	−1.36603	+	2.36603i	−0.0632799	+	0.109604i
$467$	−8.53590	+	4.92820i	−0.394994	+	0.228050i	−0.684322	−	0.729180i	$-0.739902\pi$
$467$	−8.53590	+	4.92820i	−0.394994	+	0.228050i	0.289328	+	0.957230i	$0.406568\pi$
$468$			6.92820i			0.320256i
$469$		0			0
$470$	4.39230	−	5.37945i	0.202602	−	0.248136i
$471$	2.53590	+	4.39230i	0.116848	+	0.202387i
$472$	1.26795	+	0.732051i	0.0583621	+	0.0336954i
$473$		0			0
$474$	−1.17398	−	2.03339i	−0.0539225	−	0.0933966i
$475$	5.27792	+	25.8564i	0.242167	+	1.18637i
$476$		0			0
$477$		−	7.34847i		−	0.336463i
$478$	−3.82654	+	2.20925i	−0.175022	+	0.101049i
$479$	−12.6264	+	21.8695i	−0.576914	+	0.999245i	0.418916	+	0.908025i	$0.362410\pi$
$479$	−12.6264	+	21.8695i	−0.576914	+	0.999245i	−0.995831	+	0.0912201i	$0.970923\pi$
$480$	4.07485	+	10.7449i	0.185991	+	0.490436i
$481$	−21.1117	−	36.5665i	−0.962609	−	1.66729i
$482$		−	7.26795i		−	0.331046i
$483$		0			0
$484$	1.73205			0.0787296
$485$	6.78991	−	41.7766i	0.308314	−	1.89698i
$486$	−0.258819	+	0.448288i	−0.0117403	+	0.0203347i
$487$	−13.3843	−	7.72741i	−0.606499	−	0.350162i	0.165095	−	0.986278i	$-0.447207\pi$
$487$	−13.3843	−	7.72741i	−0.606499	−	0.350162i	−0.771594	+	0.636115i	$0.780540\pi$
$488$	−1.09808	+	0.633975i	−0.0497076	+	0.0286987i
$489$	−22.4243			−1.01406
$490$		0			0
$491$	41.3205			1.86477			0.932384	−	0.361469i	$-0.117725\pi$
$491$	41.3205			1.86477			0.932384	+	0.361469i	$0.117725\pi$
$492$	12.7279	−	7.34847i	0.573819	−	0.331295i
$493$	−17.0718	−	9.85641i	−0.768875	−	0.443910i
$494$	−5.46410	+	9.46410i	−0.245842	+	0.425810i
$495$	7.64564	+	1.24264i	0.343646	+	0.0558525i
$496$	−18.1074			−0.813045
$497$		0			0
$498$		−	3.10583i		−	0.139176i
$499$	−16.1244	−	27.9282i	−0.721825	−	1.25024i	−0.960267	−	0.279081i	$-0.909970\pi$
$499$	−16.1244	−	27.9282i	−0.721825	−	1.25024i	0.238442	−	0.971157i	$-0.423363\pi$
$500$	16.3674	−	10.3492i	0.731974	−	0.462832i
$501$	9.46410	−	16.3923i	0.422825	−	0.732354i
$502$	−9.12436	+	5.26795i	−0.407240	+	0.235120i
$503$		−	23.8564i		−	1.06370i	−0.846837	−	0.531852i	$-0.821496\pi$
$503$		−	23.8564i		−	1.06370i	0.846837	−	0.531852i	$-0.178504\pi$
$504$		0			0
$505$	−9.85641	+	12.0716i	−0.438604	+	0.537178i
$506$	3.12436	+	5.41154i	0.138895	+	0.240572i
$507$	2.59808	+	1.50000i	0.115385	+	0.0666173i
$508$	−4.24264	−	2.44949i	−0.188237	−	0.108679i
$509$	−1.51575	−	2.62536i	−0.0671844	−	0.116367i	0.830476	−	0.557054i	$-0.188068\pi$
$509$	−1.51575	−	2.62536i	−0.0671844	−	0.116367i	−0.897661	+	0.440687i	$0.854735\pi$
$510$	3.58630	+	2.92820i	0.158804	+	0.129663i
$511$		0			0
$512$		−	22.1841i		−	0.980408i
$513$	4.57081	−	2.63896i	0.201806	−	0.116513i
$514$	0.896575	−	1.55291i	0.0395462	−	0.0684961i
$515$	28.9706	−	10.9867i	1.27660	−	0.484130i
$516$		0			0
$517$			20.7846i			0.914106i
$518$		0			0
$519$	16.0000			0.702322
$520$	17.0552	+	2.77197i	0.747921	+	0.121559i
$521$	14.1421	−	24.4949i	0.619578	−	1.07314i	−0.369984	−	0.929038i	$-0.620637\pi$
$521$	14.1421	−	24.4949i	0.619578	−	1.07314i	0.989563	−	0.144103i	$-0.0460297\pi$
$522$	−2.20925	−	1.27551i	−0.0966964	−	0.0558277i
$523$	37.8564	−	21.8564i	1.65535	−	0.955714i	0.680524	−	0.732726i	$-0.261752\pi$
$523$	37.8564	−	21.8564i	1.65535	−	0.955714i	0.974821	−	0.222988i	$-0.0715811\pi$
$524$	−9.79796			−0.428026
$525$		0			0
$526$	−3.94744			−0.172117
$527$	−25.4558	+	14.6969i	−1.10887	+	0.640209i
$528$	−7.39230	−	4.26795i	−0.321709	−	0.185739i
$529$	−5.42820	+	9.40192i	−0.236009	+	0.408779i
$530$	−8.39550	−	1.36451i	−0.364677	−	0.0592707i
$531$	−0.757875			−0.0328890
$532$		0			0
$533$		−	33.9411i		−	1.47015i
$534$	−4.00000	−	6.92820i	−0.173097	−	0.299813i
$535$	−32.5248	+	12.3345i	−1.40617	+	0.533268i
$536$	12.1962	−	21.1244i	0.526794	−	0.912433i
$537$	−9.00000	+	5.19615i	−0.388379	+	0.224231i
$538$			16.0000i			0.689809i
$539$		0			0
$540$	−3.00000	−	2.44949i	−0.129099	−	0.105409i
$541$	−13.3205	−	23.0718i	−0.572693	−	0.991934i	−0.996288	−	0.0860822i	$-0.972565\pi$
$541$	−13.3205	−	23.0718i	−0.572693	−	0.991934i	0.423595	−	0.905852i	$-0.360768\pi$
$542$	−0.758330	−	0.437822i	−0.0325731	−	0.0188061i
$543$	5.46739	+	3.15660i	0.234628	+	0.135463i
$544$	−10.2784	−	17.8028i	−0.440684	−	0.763287i
$545$	−22.4243	+	27.4641i	−0.960553	+	1.17643i
$546$		0			0
$547$			10.0010i			0.427613i	0.976876	+	0.213807i	$0.0685862\pi$
$547$			10.0010i			0.427613i	−0.976876	+	0.213807i	$0.931414\pi$
$548$	15.2653	−	8.81345i	0.652103	−	0.376492i
$549$	0.328169	−	0.568406i	0.0140059	−	0.0242590i
$550$	2.83939	−	8.50427i	0.121072	−	0.362623i
$551$	13.0053	+	22.5259i	0.554045	+	0.959635i
$552$		−	6.73205i		−	0.286535i
$553$		0			0
$554$	−5.85641			−0.248815
$555$	23.2979	+	3.78658i	0.988939	+	0.160731i
$556$	−0.328169	+	0.568406i	−0.0139175	+	0.0241058i
$557$	−7.67664	−	4.43211i	−0.325270	−	0.187795i	0.328469	−	0.944515i	$-0.393467\pi$
$557$	−7.67664	−	4.43211i	−0.325270	−	0.187795i	−0.653739	+	0.756720i	$0.726801\pi$
$558$	−3.29423	+	1.90192i	−0.139456	+	0.0805149i
$559$		0			0
$560$		0			0
$561$	−13.8564			−0.585018
$562$	−12.4877	+	7.20977i	−0.526761	+	0.304126i
$563$	3.58846	+	2.07180i	0.151235	+	0.0873158i	0.573708	−	0.819060i	$-0.305504\pi$
$563$	3.58846	+	2.07180i	0.151235	+	0.0873158i	−0.422473	+	0.906376i	$0.638838\pi$
$564$	5.19615	−	9.00000i	0.218797	−	0.378968i
$565$	1.89329	−	11.6489i	0.0796514	−	0.490074i
$566$	−1.10961			−0.0466402
$567$		0			0
$568$			12.3490i			0.518152i
$569$	−7.92820	−	13.7321i	−0.332368	−	0.575678i	0.650608	−	0.759414i	$-0.274514\pi$
$569$	−7.92820	−	13.7321i	−0.332368	−	0.575678i	−0.982976	+	0.183736i	$0.941181\pi$
$570$	−2.16622	−	5.71209i	−0.0907332	−	0.239253i
$571$	7.85641	−	13.6077i	0.328780	−	0.569464i	−0.653490	−	0.756935i	$-0.726696\pi$
$571$	7.85641	−	13.6077i	0.328780	−	0.569464i	0.982270	+	0.187471i	$0.0600291\pi$
$572$	−20.7846	+	12.0000i	−0.869048	+	0.501745i
$573$		−	7.46410i		−	0.311817i
$574$		0			0
$575$	−17.0718	+	3.48477i	−0.711943	+	0.145325i
$576$	1.13397	+	1.96410i	0.0472489	+	0.0818376i
$577$	−3.46410	−	2.00000i	−0.144212	−	0.0832611i	0.426158	−	0.904649i	$-0.359867\pi$
$577$	−3.46410	−	2.00000i	−0.144212	−	0.0832611i	−0.570370	+	0.821388i	$0.693200\pi$
$578$	0.448288	+	0.258819i	0.0186463	+	0.0107655i
$579$	3.20736	+	5.55532i	0.133294	+	0.230871i
$580$	12.0716	−	14.7846i	0.501245	−	0.613898i
$581$		0			0
$582$			9.79796i			0.406138i
$583$	22.0454	−	12.7279i	0.913027	−	0.527137i
$584$	−2.82843	+	4.89898i	−0.117041	+	0.202721i
$585$	−8.36308	+	3.17157i	−0.345771	+	0.131128i
$586$	2.96713	+	5.13922i	0.122571	+	0.212299i
$587$		−	4.14359i		−	0.171024i	−0.996337	−	0.0855122i	$-0.972747\pi$
$587$		−	4.14359i		−	0.171024i	0.996337	−	0.0855122i	$-0.0272527\pi$
$588$		0			0
$589$	38.7846			1.59809
$590$	−0.140727	+	0.865859i	−0.00579365	+	0.0356468i
$591$	−11.4016	+	19.7482i	−0.469001	+	0.812333i
$592$	−22.5259	−	13.0053i	−0.925808	−	0.534516i
$593$	−21.9282	+	12.6603i	−0.900483	+	0.519894i	−0.877357	−	0.479838i	$-0.840695\pi$
$593$	−21.9282	+	12.6603i	−0.900483	+	0.519894i	−0.0231264	+	0.999733i	$0.507362\pi$
$594$	−1.79315			−0.0735739
$595$		0			0
$596$	−12.2487			−0.501727
$597$	−7.02030	+	4.05317i	−0.287322	+	0.165885i
$598$	−6.24871	−	3.60770i	−0.255529	−	0.147530i
$599$	14.6603	−	25.3923i	0.599002	−	1.03750i	−0.393967	−	0.919125i	$-0.628898\pi$
$599$	14.6603	−	25.3923i	0.599002	−	1.03750i	0.992969	−	0.118377i	$-0.0377691\pi$
$600$	−7.23023	+	6.40508i	−0.295173	+	0.261486i
$601$	−25.1512			−1.02594			−0.512970	−	0.858406i	$-0.671455\pi$
$601$	−25.1512			−1.02594			−0.512970	+	0.858406i	$0.671455\pi$
$602$		0			0
$603$			12.6264i			0.514186i
$604$	16.8564	+	29.1962i	0.685877	+	1.18797i
$605$	0.792893	+	2.09077i	0.0322357	+	0.0850019i
$606$	1.80385	−	3.12436i	0.0732763	−	0.126918i
$607$	−10.3923	+	6.00000i	−0.421811	+	0.243532i	−0.695852	−	0.718186i	$-0.744973\pi$
$607$	−10.3923	+	6.00000i	−0.421811	+	0.243532i	0.274041	+	0.961718i	$0.411640\pi$
$608$			27.1244i			1.10004i
$609$		0			0
$610$	−0.588457	−	0.480473i	−0.0238259	−	0.0194538i
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$	6.00000	+	3.46410i	0.242536	+	0.140028i
$613$	8.48528	+	4.89898i	0.342717	+	0.197868i	0.661473	−	0.749969i	$-0.269932\pi$
$613$	8.48528	+	4.89898i	0.342717	+	0.197868i	−0.318756	+	0.947837i	$0.603265\pi$
$614$	1.03528	+	1.79315i	0.0417803	+	0.0723657i
$615$	14.6969	+	12.0000i	0.592638	+	0.483887i
$616$		0			0
$617$			27.1475i			1.09292i	0.837487	+	0.546458i	$0.184024\pi$
$617$			27.1475i			1.09292i	−0.837487	+	0.546458i	$0.815976\pi$
$618$	−6.21166	+	3.58630i	−0.249869	+	0.144262i
$619$	−10.3664	+	17.9551i	−0.416659	+	0.721675i	−0.995601	−	0.0936937i	$-0.970133\pi$
$619$	−10.3664	+	17.9551i	−0.416659	+	0.721675i	0.578942	+	0.815369i	$0.303466\pi$
$620$	−10.0919	−	26.6112i	−0.405300	−	1.06873i
$621$	1.74238	+	3.01790i	0.0699194	+	0.121104i
$622$		−	2.14359i		−	0.0859503i
$623$		0			0
$624$	9.85641			0.394572
$625$	19.9853	+	15.0196i	0.799411	+	0.600784i
$626$	−0.757875	+	1.31268i	−0.0302908	+	0.0524651i
$627$	15.8338	+	9.14162i	0.632339	+	0.365081i
$628$	7.60770	−	4.39230i	0.303580	−	0.175272i
$629$	−42.2233			−1.68355
$630$		0			0
$631$	−25.3205			−1.00799			−0.503997	−	0.863706i	$-0.668138\pi$
$631$	−25.3205			−1.00799			−0.503997	+	0.863706i	$0.668138\pi$
$632$	−7.58871	+	4.38134i	−0.301863	+	0.174280i
$633$	23.3205	+	13.4641i	0.926907	+	0.535150i
$634$	1.22243	−	2.11731i	0.0485490	−	0.0840893i
$635$	1.01461	−	6.24264i	0.0402636	−	0.247732i
$636$	−12.7279			−0.504695
$637$		0			0
$638$		−	8.83701i		−	0.349861i
$639$	−3.19615	−	5.53590i	−0.126438	−	0.218997i
$640$	23.9444	−	9.08054i	0.946484	−	0.358940i
$641$	−5.00000	+	8.66025i	−0.197488	+	0.342059i	−0.947713	−	0.319123i	$-0.896612\pi$
$641$	−5.00000	+	8.66025i	−0.197488	+	0.342059i	0.750225	+	0.661182i	$0.229945\pi$
$642$	6.97372	−	4.02628i	0.275231	−	0.158905i
$643$			4.00000i			0.157745i	0.996885	+	0.0788723i	$0.0251319\pi$
$643$			4.00000i			0.157745i	−0.996885	+	0.0788723i	$0.974868\pi$
$644$		0			0
$645$		0			0
$646$	5.46410	+	9.46410i	0.214982	+	0.372360i
$647$	37.1769	+	21.4641i	1.46158	+	0.843841i	0.999084	−	0.0427831i	$-0.0136224\pi$
$647$	37.1769	+	21.4641i	1.46158	+	0.843841i	0.462491	+	0.886624i	$0.346956\pi$
$648$	1.67303	+	0.965926i	0.0657229	+	0.0379452i
$649$	−1.31268	−	2.27362i	−0.0515271	−	0.0892476i
$650$	2.07055	+	10.1436i	0.0812137	+	0.397864i
$651$		0			0
$652$			38.8401i			1.52110i
$653$	3.43400	−	1.98262i	0.134383	−	0.0775859i	−0.431301	−	0.902208i	$-0.641945\pi$
$653$	3.43400	−	1.98262i	0.134383	−	0.0775859i	0.565684	+	0.824622i	$0.308612\pi$
$654$	4.10394	−	7.10823i	0.160477	−	0.277954i
$655$	−4.48528	−	11.8272i	−0.175254	−	0.462126i
$656$	−10.4543	−	18.1074i	−0.408172	−	0.706974i
$657$		−	2.92820i		−	0.114240i
$658$		0			0
$659$	−10.3923			−0.404827			−0.202413	−	0.979300i	$-0.564878\pi$
$659$	−10.3923			−0.404827			−0.202413	+	0.979300i	$0.564878\pi$
$660$	2.15232	−	13.2426i	0.0837788	−	0.515469i
$661$	−6.74290	+	11.6790i	−0.262268	+	0.454262i	−0.966844	−	0.255366i	$-0.917804\pi$
$661$	−6.74290	+	11.6790i	−0.262268	+	0.454262i	0.704576	+	0.709629i	$0.251137\pi$
$662$	−3.93803	−	2.27362i	−0.153056	−	0.0883669i
$663$	13.8564	−	8.00000i	0.538138	−	0.310694i
$664$	−11.5911			−0.449822
$665$		0			0
$666$	−5.46410			−0.211730
$667$	−14.8728	+	8.58682i	−0.575877	+	0.332483i
$668$	−28.3923	−	16.3923i	−1.09853	−	0.634237i
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$	14.4254	+	2.34455i	0.557303	+	0.0905780i
$671$	2.27362			0.0877723
$672$		0			0
$673$		−	21.8695i		−	0.843009i	−0.906826	−	0.421504i	$-0.861502\pi$
$673$		−	21.8695i		−	0.843009i	0.906826	−	0.421504i	$-0.138498\pi$
$674$	4.58846	+	7.94744i	0.176741	+	0.306124i
$675$	1.58346	−	4.74264i	0.0609476	−	0.182544i
$676$	2.59808	−	4.50000i	0.0999260	−	0.173077i
$677$	−20.0718	+	11.5885i	−0.771422	+	0.445381i	−0.833382	−	0.552698i	$-0.813598\pi$
$677$	−20.0718	+	11.5885i	−0.771422	+	0.445381i	0.0619598	+	0.998079i	$0.480265\pi$
$678$			2.73205i			0.104924i
$679$		0			0
$680$	10.9282	−	13.3843i	0.419077	−	0.513263i
$681$	2.00000	+	3.46410i	0.0766402	+	0.132745i
$682$	−11.4115	−	6.58846i	−0.436971	−	0.252285i
$683$	−36.6544	−	21.1624i	−1.40254	−	0.809758i	−0.407889	−	0.913031i	$-0.633735\pi$
$683$	−36.6544	−	21.1624i	−1.40254	−	0.809758i	−0.994653	+	0.103273i	$0.967068\pi$
$684$	−4.57081	−	7.91688i	−0.174769	−	0.302709i
$685$	17.6269	+	14.3923i	0.673489	+	0.549902i
$686$		0			0
$687$			13.4858i			0.514515i
$688$		0			0
$689$	−14.6969	+	25.4558i	−0.559909	+	0.969790i
$690$	3.77143	−	1.43026i	0.143576	−	0.0544490i
$691$	−5.46739	−	9.46979i	−0.207989	−	0.360248i	0.743092	−	0.669189i	$-0.233359\pi$
$691$	−5.46739	−	9.46979i	−0.207989	−	0.360248i	−0.951081	+	0.308942i	$0.900025\pi$
$692$		−	27.7128i		−	1.05348i
$693$		0			0
$694$	−16.0526			−0.609347
$695$	−0.836355	−	0.135932i	−0.0317248	−	0.00515620i
$696$	−4.76028	+	8.24504i	−0.180438	+	0.312528i
$697$	−29.3939	−	16.9706i	−1.11337	−	0.642806i
$698$	−7.90192	+	4.56218i	−0.299092	+	0.172681i
$699$	−5.27792			−0.199629
$700$		0			0
$701$	−11.0718			−0.418176			−0.209088	−	0.977897i	$-0.567050\pi$
$701$	−11.0718			−0.418176			−0.209088	+	0.977897i	$0.567050\pi$
$702$	1.79315	−	1.03528i	0.0676781	−	0.0390740i
$703$	48.2487	+	27.8564i	1.81973	+	1.05062i
$704$	−3.92820	+	6.80385i	−0.148050	+	0.256430i
$705$	13.2426	+	2.15232i	0.498747	+	0.0810609i
$706$	−5.93426			−0.223339
$707$		0			0
$708$			1.31268i			0.0493334i
$709$	−5.46410	−	9.46410i	−0.205209	−	0.355432i	0.744991	−	0.667075i	$-0.232454\pi$
$709$	−5.46410	−	9.46410i	−0.205209	−	0.355432i	−0.950199	+	0.311643i	$0.899121\pi$
$710$	−6.91815	+	2.62360i	−0.259634	+	0.0984621i
$711$	2.26795	−	3.92820i	0.0850547	−	0.147319i
$712$	−25.8564	+	14.9282i	−0.969010	+	0.559458i
$713$			25.6077i			0.959016i
$714$		0			0
$715$	−24.0000	−	19.5959i	−0.897549	−	0.732846i
$716$	9.00000	+	15.5885i	0.336346	+	0.582568i
$717$	−7.39230	−	4.26795i	−0.276071	−	0.159389i
$718$	−6.93237	−	4.00240i	−0.258714	−	0.149368i
$719$	7.34847	+	12.7279i	0.274052	+	0.474671i	0.969895	−	0.243522i	$-0.0783027\pi$
$719$	7.34847	+	12.7279i	0.274052	+	0.474671i	−0.695844	+	0.718193i	$0.744969\pi$
$720$	−3.48477	+	4.26795i	−0.129870	+	0.159057i
$721$		0			0
$722$		−	4.58441i		−	0.170614i
$723$	12.1595	−	7.02030i	0.452217	−	0.261088i
$724$	5.46739	−	9.46979i	0.203194	−	0.351942i
$725$	23.3727	+	7.80363i	0.868040	+	0.289820i
$726$	−0.258819	−	0.448288i	−0.00960568	−	0.0166375i
$727$		−	23.7128i		−	0.879460i	−0.898130	−	0.439730i	$-0.855074\pi$
$727$		−	23.7128i		−	0.879460i	0.898130	−	0.439730i	$-0.144926\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$	−3.34542	−	0.543729i	−0.123820	−	0.0201243i
$731$		0			0
$732$	−0.984508	−	0.568406i	−0.0363885	−	0.0210089i
$733$	−15.4641	+	8.92820i	−0.571180	+	0.329771i	−0.757620	−	0.652696i	$-0.773638\pi$
$733$	−15.4641	+	8.92820i	−0.571180	+	0.329771i	0.186441	+	0.982466i	$0.440305\pi$
$734$	2.07055			0.0764255
$735$		0			0
$736$	−17.9090			−0.660133
$737$	−37.8792	+	21.8695i	−1.39530	+	0.805575i
$738$	−3.80385	−	2.19615i	−0.140022	−	0.0808415i
$739$	−12.9282	+	22.3923i	−0.475572	+	0.823714i	−0.999608	−	0.0279814i	$-0.991092\pi$
$739$	−12.9282	+	22.3923i	−0.475572	+	0.823714i	0.524037	+	0.851696i	$0.324425\pi$
$740$	6.55855	−	40.3531i	0.241097	−	1.48341i
$741$	−21.1117			−0.775556
$742$		0			0
$743$			51.1619i			1.87695i	0.345351	+	0.938474i	$0.387760\pi$
$743$			51.1619i			1.87695i	−0.345351	+	0.938474i	$0.612240\pi$
$744$	7.09808	+	12.2942i	0.260228	+	0.450728i
$745$	−5.60718	−	14.7855i	−0.205431	−	0.541699i
$746$	1.85641	−	3.21539i	0.0679679	−	0.117724i
$747$	5.19615	−	3.00000i	0.190117	−	0.109764i
$748$			24.0000i			0.877527i
$749$		0			0
$750$	−5.12436	−	2.68973i	−0.187115	−	0.0982149i
$751$	18.3923	+	31.8564i	0.671145	+	1.16246i	0.977580	+	0.210565i	$0.0675304\pi$
$751$	18.3923	+	31.8564i	0.671145	+	1.16246i	−0.306435	+	0.951892i	$0.599136\pi$
$752$	−12.8038	−	7.39230i	−0.466908	−	0.269570i
$753$	−17.6269	−	10.1769i	−0.642360	−	0.370867i
$754$	5.10205	+	8.83701i	0.185806	+	0.321825i
$755$	−27.5264	+	33.7128i	−1.00179	+	1.22693i
$756$		0			0
$757$			34.2929i			1.24640i	0.782064	+	0.623198i	$0.214167\pi$
$757$			34.2929i			1.24640i	−0.782064	+	0.623198i	$0.785833\pi$
$758$	5.13922	−	2.96713i	0.186665	−	0.107771i
$759$	−6.03579	+	10.4543i	−0.219085	+	0.379467i
$760$	−21.3178	+	8.08446i	−0.773278	+	0.293254i
$761$	−9.04008	−	15.6579i	−0.327703	−	0.567598i	0.654353	−	0.756189i	$-0.272941\pi$
$761$	−9.04008	−	15.6579i	−0.327703	−	0.567598i	−0.982056	+	0.188591i	$0.939608\pi$
$762$			1.46410i			0.0530388i
$763$		0			0
$764$	−12.9282			−0.467726
$765$	−1.43488	+	8.82843i	−0.0518781	+	0.319192i
$766$	−6.17449	+	10.6945i	−0.223093	+	0.386409i
$767$	2.62536	+	1.51575i	0.0947961	+	0.0547305i
$768$	−1.20577	+	0.696152i	−0.0435095	+	0.0251202i
$769$	−39.2934			−1.41696			−0.708478	−	0.705733i	$-0.750618\pi$
$769$	−39.2934			−1.41696			−0.708478	+	0.705733i	$0.750618\pi$
$770$		0			0
$771$	3.46410			0.124757
$772$	9.62209	−	5.55532i	0.346307	−	0.199940i
$773$	32.7846	+	18.9282i	1.17918	+	0.680800i	0.955825	−	0.293937i	$-0.0949655\pi$
$773$	32.7846	+	18.9282i	1.17918	+	0.680800i	0.223356	+	0.974737i	$0.428299\pi$
$774$		0			0
$775$	27.5027	−	24.3640i	0.987925	−	0.875179i
$776$	36.5665			1.31266
$777$		0			0
$778$			5.73118i			0.205473i
$779$	22.3923	+	38.7846i	0.802288	+	1.38960i
$780$	5.49333	+	14.4853i	0.196693	+	0.518656i
$781$	11.0718	−	19.1769i	0.396180	−	0.686204i
$782$	−6.24871	+	3.60770i	−0.223453	+	0.129011i
$783$		−	4.92820i		−	0.176120i
$784$		0			0
$785$	8.78461	+	7.17260i	0.313536	+	0.256001i
$786$	1.46410	+	2.53590i	0.0522228	+	0.0904525i
$787$	39.7128	+	22.9282i	1.41561	+	0.817302i	0.995909	−	0.0903608i	$-0.0288020\pi$
$787$	39.7128	+	22.9282i	1.41561	+	0.817302i	0.419700	+	0.907663i	$0.362135\pi$
$788$	34.2049	+	19.7482i	1.21850	+	0.703501i
$789$	−3.81294	−	6.60420i	−0.135744	−	0.235116i
$790$	−4.06678	−	3.32051i	−0.144689	−	0.118138i
$791$		0			0
$792$			6.69213i			0.237795i
$793$	−2.27362	+	1.31268i	−0.0807388	+	0.0466145i
$794$	−6.13733	+	10.6302i	−0.217806	+	0.377250i
$795$	−5.82655	−	15.3640i	−0.206646	−	0.544904i
$796$	7.02030	+	12.1595i	0.248828	+	0.430983i
$797$		−	10.1436i		−	0.359305i	−0.983730	−	0.179652i	$-0.942503\pi$
$797$		−	10.1436i		−	0.359305i	0.983730	−	0.179652i	$-0.0574973\pi$
$798$		0			0
$799$	−24.0000			−0.849059
$800$	17.0391	+	19.2342i	0.602425	+	0.680033i
$801$	7.72741	−	13.3843i	0.273034	−	0.472910i
$802$	0.896575	+	0.517638i	0.0316592	+	0.0182784i
$803$	8.78461	−	5.07180i	0.310002	−	0.178980i
$804$	21.8695			0.771279
$805$		0			0
$806$	15.2154			0.535939
$807$	−26.7685	+	15.4548i	−0.942297	+	0.544035i
$808$	−11.6603	−	6.73205i	−0.410206	−	0.236833i
$809$	10.8564	−	18.8038i	0.381691	−	0.661108i	−0.609613	−	0.792699i	$-0.708675\pi$
$809$	10.8564	−	18.8038i	0.381691	−	0.661108i	0.991304	+	0.131591i	$0.0420085\pi$
$810$	−0.185687	+	1.14248i	−0.00652437	+	0.0401427i
$811$	−25.6317			−0.900051			−0.450026	−	0.893016i	$-0.648585\pi$
$811$	−25.6317			−0.900051			−0.450026	+	0.893016i	$0.648585\pi$
$812$		0			0
$813$		−	1.69161i		−	0.0593275i
$814$	−9.46410	−	16.3923i	−0.331717	−	0.574550i
$815$	−46.8842	+	17.7801i	−1.64228	+	0.622810i
$816$	4.92820	−	8.53590i	0.172522	−	0.298816i
$817$		0			0
$818$		−	5.90897i		−	0.206602i
$819$		0			0
$820$	20.7846	−	25.4558i	0.725830	−	0.888957i
$821$	−9.39230	−	16.2679i	−0.327794	−	0.567755i	0.654280	−	0.756252i	$-0.272972\pi$
$821$	−9.39230	−	16.2679i	−0.327794	−	0.567755i	−0.982074	+	0.188497i	$0.939638\pi$
$822$	−4.56218	−	2.63397i	−0.159124	−	0.0918704i
$823$	26.5927	+	15.3533i	0.926962	+	0.535182i	0.885849	−	0.463973i	$-0.153577\pi$
$823$	26.5927	+	15.3533i	0.926962	+	0.535182i	0.0411123	+	0.999155i	$0.486910\pi$
$824$	13.3843	+	23.1822i	0.466263	+	0.807591i
$825$	16.9706	−	3.46410i	0.590839	−	0.120605i
$826$		0			0
$827$		−	8.18067i		−	0.284470i	−0.989833	−	0.142235i	$-0.954571\pi$
$827$		−	8.18067i		−	0.284470i	0.989833	−	0.142235i	$-0.0454289\pi$
$828$	5.22715	−	3.01790i	0.181656	−	0.104879i
$829$	−3.25813	+	5.64325i	−0.113160	+	0.195998i	−0.917043	−	0.398789i	$-0.869430\pi$
$829$	−3.25813	+	5.64325i	−0.113160	+	0.195998i	0.803883	+	0.594788i	$0.202764\pi$
$830$	−2.46259	−	6.49357i	−0.0854778	−	0.225395i
$831$	−5.65685	−	9.79796i	−0.196234	−	0.339887i
$832$		−	9.07180i		−	0.314508i
$833$		0			0
$834$	0.196152			0.00679220
$835$	6.78991	−	41.7766i	0.234975	−	1.44574i
$836$	15.8338	−	27.4249i	0.547622	−	0.948509i
$837$	−6.36396	−	3.67423i	−0.219971	−	0.127000i
$838$	−9.46410	+	5.46410i	−0.326932	+	0.188754i
$839$	20.3538			0.702691			0.351345	−	0.936246i	$-0.385724\pi$
$839$	20.3538			0.702691			0.351345	+	0.936246i	$0.385724\pi$
$840$		0			0
$841$	−4.71281			−0.162511
$842$	−5.73118	+	3.30890i	−0.197510	+	0.114032i
$843$	−24.1244	−	13.9282i	−0.830887	−	0.479713i
$844$	23.3205	−	40.3923i	0.802725	−	1.39036i
$845$	6.62132	+	1.07616i	0.227780	+	0.0370210i
$846$	−3.10583			−0.106781
$847$		0			0
$848$			18.1074i			0.621810i
$849$	−1.07180	−	1.85641i	−0.0367840	−	0.0637117i
$850$	9.81989	+	3.27865i	0.336819	+	0.112457i
$851$	−18.3923	+	31.8564i	−0.630480	+	1.09202i
$852$	−9.58846	+	5.53590i	−0.328495	+	0.189657i
$853$		−	13.0718i		−	0.447570i	−0.974639	−	0.223785i	$-0.928159\pi$
$853$		−	13.0718i		−	0.447570i	0.974639	−	0.223785i	$-0.0718413\pi$
$854$		0			0
$855$	7.46410	−	9.14162i	0.255267	−	0.312637i
$856$	−15.0263	−	26.0263i	−0.513588	−	0.889560i
$857$	8.53590	+	4.92820i	0.291581	+	0.168344i	0.638655	−	0.769494i	$-0.279491\pi$
$857$	8.53590	+	4.92820i	0.291581	+	0.168344i	−0.347074	+	0.937838i	$0.612825\pi$
$858$	6.21166	+	3.58630i	0.212062	+	0.122434i
$859$	−1.70522	−	2.95352i	−0.0581813	−	0.100773i	0.835468	−	0.549539i	$-0.185197\pi$
$859$	−1.70522	−	2.95352i	−0.0581813	−	0.100773i	−0.893649	+	0.448767i	$0.851863\pi$
$860$		0			0
$861$		0			0
$862$		−	19.3185i		−	0.657991i
$863$	13.7768	−	7.95404i	0.468968	−	0.270759i	−0.246840	−	0.969056i	$-0.579392\pi$
$863$	13.7768	−	7.95404i	0.468968	−	0.270759i	0.715808	+	0.698298i	$0.246059\pi$
$864$	2.56961	−	4.45069i	0.0874198	−	0.151416i
$865$	33.4523	−	12.6863i	1.13741	−	0.431347i
$866$	−4.62158	−	8.00481i	−0.157048	−	0.272014i
$867$			1.00000i			0.0339618i
$868$		0			0
$869$	15.7128			0.533021
$870$	−5.63039	−	0.915103i	−0.190888	−	0.0310249i
$871$	25.2528	−	43.7391i	0.855658	−	1.48204i
$872$	−26.5283	−	15.3161i	−0.898361	−	0.518669i
$873$	−16.3923	+	9.46410i	−0.554795	+	0.320311i
$874$	9.52056			0.322038
$875$		0			0
$876$	−5.07180			−0.171360
$877$	−29.3939	+	16.9706i	−0.992561	+	0.573055i	−0.906039	−	0.423195i	$-0.860909\pi$
$877$	−29.3939	+	16.9706i	−0.992561	+	0.573055i	−0.0865220	+	0.996250i	$0.527575\pi$
$878$	−5.83013	−	3.36603i	−0.196757	−	0.113598i
$879$	−5.73205	+	9.92820i	−0.193337	+	0.334870i
$880$	−18.8396	−	3.06199i	−0.635084	−	0.103220i
$881$	−29.5969			−0.997147			−0.498573	−	0.866848i	$-0.666143\pi$
$881$	−29.5969			−0.997147			−0.498573	+	0.866848i	$0.666143\pi$
$882$		0			0
$883$		−	29.3939i		−	0.989183i	−0.869126	−	0.494591i	$-0.835318\pi$
$883$		−	29.3939i		−	0.989183i	0.869126	−	0.494591i	$-0.164682\pi$
$884$	−13.8564	−	24.0000i	−0.466041	−	0.807207i
$885$	−1.58454	+	0.600914i	−0.0532638	+	0.0201995i
$886$	3.24167	−	5.61474i	0.108906	−	0.188631i
$887$	11.8756	−	6.85641i	0.398745	−	0.230216i	−0.287197	−	0.957871i	$-0.592724\pi$
$887$	11.8756	−	6.85641i	0.398745	−	0.230216i	0.685942	+	0.727656i	$0.259390\pi$
$888$			20.3923i			0.684321i
$889$		0			0
$890$	−13.8564	−	11.3137i	−0.464468	−	0.379236i
$891$	−1.73205	−	3.00000i	−0.0580259	−	0.100504i
$892$	12.0000	+	6.92820i	0.401790	+	0.231973i
$893$	27.4249	+	15.8338i	0.917738	+	0.529856i
$894$	1.83032	+	3.17020i	0.0612149	+	0.106027i
$895$	−14.6969	+	18.0000i	−0.491264	+	0.601674i
$896$		0			0
$897$		−	13.9391i		−	0.465412i
$898$	16.0740	−	9.28032i	0.536396	−	0.309688i
$899$	18.1074	−	31.3629i	0.603915	−	1.04601i
$900$	−8.21449	−	2.74264i	−0.273816	−	0.0914214i
$901$	14.6969	+	25.4558i	0.489626	+	0.848057i
$902$		−	15.2154i		−	0.506617i
$903$		0			0
$904$	10.1962			0.339119
$905$	13.9339	+	2.26467i	0.463178	+	0.0752800i
$906$	5.03768	−	8.72552i	0.167366	−	0.289886i
$907$	−5.85993	−	3.38323i	−0.194576	−	0.112338i	0.399547	−	0.916713i	$-0.369167\pi$
$907$	−5.85993	−	3.38323i	−0.194576	−	0.112338i	−0.594123	+	0.804374i	$0.702501\pi$
$908$	6.00000	−	3.46410i	0.199117	−	0.114960i
$909$	6.96953			0.231165
$910$		0			0
$911$	9.60770			0.318317			0.159159	−	0.987253i	$-0.449122\pi$
$911$	9.60770			0.318317			0.159159	+	0.987253i	$0.449122\pi$
$912$	−11.2629	+	6.50266i	−0.372953	+	0.215325i
$913$	18.0000	+	10.3923i	0.595713	+	0.343935i
$914$	5.66025	−	9.80385i	0.187225	−	0.324282i
$915$	0.235442	−	1.44861i	0.00778346	−	0.0478896i
$916$	23.3581			0.771773
$917$		0			0
$918$		−	2.07055i		−	0.0683384i
$919$	−4.53590	−	7.85641i	−0.149625	−	0.259159i	0.781464	−	0.623951i	$-0.214473\pi$
$919$	−4.53590	−	7.85641i	−0.149625	−	0.259159i	−0.931089	+	0.364792i	$0.881140\pi$
$920$	−5.33780	−	14.0752i	−0.175982	−	0.464045i
$921$	−2.00000	+	3.46410i	−0.0659022	+	0.114146i
$922$	−14.5359	+	8.39230i	−0.478714	+	0.276386i
$923$			25.5692i			0.841621i
$924$		0			0
$925$	51.7128	−	10.5558i	1.70031	−	0.347074i
$926$	5.80385	+	10.0526i	0.190726	+	0.330348i
$927$	−12.0000	−	6.92820i	−0.394132	−	0.227552i
$928$	21.9339	+	12.6636i	0.720016	+	0.415701i
$929$	−9.04008	−	15.6579i	−0.296596	−	0.513719i	0.678759	−	0.734361i	$-0.262518\pi$
$929$	−9.04008	−	15.6579i	−0.296596	−	0.513719i	−0.975355	+	0.220642i	$0.929185\pi$
$930$	−5.37945	+	6.58846i	−0.176399	+	0.216044i
$931$		0			0
$932$			9.14162i			0.299444i
$933$	3.58630	−	2.07055i	0.117410	−	0.0677868i
$934$	2.55103	−	4.41851i	0.0834721	−	0.144578i
$935$	−28.9706	+	10.9867i	−0.947439	+	0.359302i
$936$	−3.86370	−	6.69213i	−0.126289	−	0.218739i
$937$		−	16.7846i		−	0.548329i	−0.961683	−	0.274165i	$-0.911599\pi$
$937$		−	16.7846i		−	0.548329i	0.961683	−	0.274165i	$-0.0884013\pi$
$938$		0			0
$939$	−2.92820			−0.0955583
$940$	3.72792	−	22.9369i	0.121591	−	0.748120i
$941$	−0.101536	+	0.175865i	−0.00330998	+	0.00573305i	−0.867676	−	0.497131i	$-0.834387\pi$
$941$	−0.101536	+	0.175865i	−0.00330998	+	0.00573305i	0.864366	+	0.502864i	$0.167720\pi$
$942$	−2.27362	−	1.31268i	−0.0740787	−	0.0427693i
$943$	−25.6077	+	14.7846i	−0.833901	+	0.481453i
$944$	1.86748			0.0607813
$945$		0			0
$946$		0			0
$947$	15.9217	−	9.19239i	0.517385	−	0.298712i	−0.218479	−	0.975842i	$-0.570110\pi$
$947$	15.9217	−	9.19239i	0.517385	−	0.298712i	0.735864	+	0.677129i	$0.236776\pi$
$948$	−6.80385	−	3.92820i	−0.220979	−	0.127582i
$949$	−5.85641	+	10.1436i	−0.190107	+	0.329275i
$950$	−9.05816	−	10.2251i	−0.293885	−	0.331746i
$951$	4.72311			0.153157
$952$		0			0
$953$		−	53.9160i		−	1.74651i	−0.487264	−	0.873255i	$-0.662005\pi$
$953$		−	53.9160i		−	1.74651i	0.487264	−	0.873255i	$-0.337995\pi$
$954$	1.90192	+	3.29423i	0.0615771	+	0.106655i
$955$	−5.91824	−	15.6057i	−0.191510	−	0.504989i
$956$	−7.39230	+	12.8038i	−0.239084	+	0.414106i
$957$	14.7846	−	8.53590i	0.477919	−	0.275926i
$958$		−	13.0718i		−	0.422331i
$959$		0			0
$960$	3.92820	+	3.20736i	0.126782	+	0.103517i
$961$	−11.5000	−	19.9186i	−0.370968	−	0.642535i
$962$	18.9282	+	10.9282i	0.610270	+	0.352339i
$963$	13.4722	+	7.77817i	0.434135	+	0.250648i
$964$	−12.1595	−	21.0609i	−0.391632	−	0.678326i
$965$	11.1106	+	9.07180i	0.357664	+	0.292031i
$966$		0			0
$967$			10.0010i			0.321611i	0.986986	+	0.160806i	$0.0514093\pi$
$967$			10.0010i			0.321611i	−0.986986	+	0.160806i	$0.948591\pi$
$968$	−1.67303	+	0.965926i	−0.0537733	+	0.0310460i
$969$	−10.5558	+	18.2832i	−0.339102	+	0.587342i
$970$	7.76874	+	20.4853i	0.249439	+	0.657743i
$971$	5.83272	+	10.1026i	0.187181	+	0.324207i	0.944309	−	0.329059i	$-0.106732\pi$
$971$	5.83272	+	10.1026i	0.187181	+	0.324207i	−0.757128	+	0.653266i	$0.773398\pi$
$972$			1.73205i			0.0555556i
$973$		0			0
$974$	8.00000			0.256337
$975$	−14.9706	+	13.2621i	−0.479442	+	0.424726i
$976$	−0.808643	+	1.40061i	−0.0258840	+	0.0448324i
$977$	−39.5200	−	22.8169i	−1.26436	−	0.729977i	−0.290443	−	0.956892i	$-0.593803\pi$
$977$	−39.5200	−	22.8169i	−1.26436	−	0.729977i	−0.973914	+	0.226916i	$0.927136\pi$
$978$	10.0526	−	5.80385i	0.321445	−	0.185587i
$979$	53.5370			1.71105
$980$		0			0
$981$	15.8564			0.506256
$982$	−18.5235	+	10.6945i	−0.591108	+	0.341276i
$983$	−21.4641	−	12.3923i	−0.684599	−	0.395253i	0.116987	−	0.993133i	$-0.462676\pi$
$983$	−21.4641	−	12.3923i	−0.684599	−	0.395253i	−0.801585	+	0.597880i	$0.796010\pi$
$984$	−8.19615	+	14.1962i	−0.261284	+	0.452557i
$985$	−8.17998	+	50.3293i	−0.260636	+	1.60362i
$986$	10.2041			0.324965
$987$		0			0
$988$			36.5665i			1.16333i
$989$		0			0
$990$	−3.74907	+	1.42178i	−0.119153	+	0.0451870i
$991$	−6.39230	+	11.0718i	−0.203058	+	0.351707i	−0.949512	−	0.313730i	$-0.898421\pi$
$991$	−6.39230	+	11.0718i	−0.203058	+	0.351707i	0.746454	+	0.665437i	$0.231755\pi$
$992$	32.7058	−	18.8827i	1.03841	−	0.599526i
$993$		−	8.78461i		−	0.278771i
$994$		0			0
$995$	−11.4641	+	14.0406i	−0.363436	+	0.445117i
$996$	−5.19615	−	9.00000i	−0.164646	−	0.285176i
$997$	−36.2487	−	20.9282i	−1.14801	−	0.662803i	−0.199607	−	0.979876i	$-0.563967\pi$
$997$	−36.2487	−	20.9282i	−1.14801	−	0.662803i	−0.948401	+	0.317073i	$0.897300\pi$
$998$	14.4567	+	8.34658i	0.457619	+	0.264206i
$999$	−5.27792	−	9.14162i	−0.166986	−	0.289228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	735.2.q.c.214.2		8
5.4	even	2		735.2.q.d.214.3		8
7.2	even	3		735.2.q.d.79.3		8
7.3	odd	6		735.2.d.f.589.3	✓	8
7.4	even	3		735.2.d.f.589.4	yes	8
7.5	odd	6	inner	735.2.q.c.79.3		8
7.6	odd	2		735.2.q.d.214.2		8
21.11	odd	6		2205.2.d.t.1324.5		8
21.17	even	6		2205.2.d.t.1324.6		8
35.3	even	12		3675.2.a.bu.1.2		4
35.4	even	6		735.2.d.f.589.5	yes	8
35.9	even	6	inner	735.2.q.c.79.2		8
35.17	even	12		3675.2.a.bs.1.3		4
35.18	odd	12		3675.2.a.bs.1.2		4
35.19	odd	6		735.2.q.d.79.2		8
35.24	odd	6		735.2.d.f.589.6	yes	8
35.32	odd	12		3675.2.a.bu.1.3		4
35.34	odd	2	inner	735.2.q.c.214.3		8
105.59	even	6		2205.2.d.t.1324.4		8
105.74	odd	6		2205.2.d.t.1324.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
735.2.d.f.589.3	✓	8	7.3	odd	6
735.2.d.f.589.4	yes	8	7.4	even	3
735.2.d.f.589.5	yes	8	35.4	even	6
735.2.d.f.589.6	yes	8	35.24	odd	6
735.2.q.c.79.2		8	35.9	even	6	inner
735.2.q.c.79.3		8	7.5	odd	6	inner
735.2.q.c.214.2		8	1.1	even	1	trivial
735.2.q.c.214.3		8	35.34	odd	2	inner
735.2.q.d.79.2		8	35.19	odd	6
735.2.q.d.79.3		8	7.2	even	3
735.2.q.d.214.2		8	7.6	odd	2
735.2.q.d.214.3		8	5.4	even	2
2205.2.d.t.1324.3		8	105.74	odd	6
2205.2.d.t.1324.4		8	105.59	even	6
2205.2.d.t.1324.5		8	21.11	odd	6
2205.2.d.t.1324.6		8	21.17	even	6
3675.2.a.bs.1.2		4	35.18	odd	12
3675.2.a.bs.1.3		4	35.17	even	12
3675.2.a.bu.1.2		4	35.3	even	12
3675.2.a.bu.1.3		4	35.32	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 735 = 3 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	735.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.448288 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-2.20711 - 0.358719i) q^{5} +0.517638 q^{6} -1.93185i q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.448288 + 0.258819i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 1.50000i) q^{4} +(-2.20711 - 0.358719i) q^{5} +0.517638 q^{6} -1.93185i q^{8} +(0.500000 + 0.866025i) q^{9} +(1.08226 - 0.410432i) q^{10} +(-1.73205 + 3.00000i) q^{11} +(1.50000 - 0.866025i) q^{12} -4.00000i q^{13} +(1.73205 + 1.41421i) q^{15} +(-1.23205 - 2.13397i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-0.448288 - 0.258819i) q^{18} +(2.63896 + 4.57081i) q^{19} +(2.44949 - 3.00000i) q^{20} -1.79315i q^{22} +(-3.01790 + 1.74238i) q^{23} +(-0.965926 + 1.67303i) q^{24} +(4.74264 + 1.58346i) q^{25} +(1.03528 + 1.79315i) q^{26} -1.00000i q^{27} +4.92820 q^{29} +(-1.14248 - 0.185687i) q^{30} +(3.67423 - 6.36396i) q^{31} +(4.45069 + 2.56961i) q^{32} +(3.00000 - 1.73205i) q^{33} +2.07055 q^{34} -1.73205 q^{36} +(9.14162 - 5.27792i) q^{37} +(-2.36603 - 1.36603i) q^{38} +(-2.00000 + 3.46410i) q^{39} +(-0.692993 + 4.26380i) q^{40} +8.48528 q^{41} +(-3.00000 - 5.19615i) q^{44} +(-0.792893 - 2.09077i) q^{45} +(0.901924 - 1.56218i) q^{46} +(5.19615 - 3.00000i) q^{47} +2.46410i q^{48} +(-2.53590 + 0.517638i) q^{50} +(2.00000 + 3.46410i) q^{51} +(6.00000 + 3.46410i) q^{52} +(-6.36396 - 3.67423i) q^{53} +(0.258819 + 0.448288i) q^{54} +(4.89898 - 6.00000i) q^{55} -5.27792i q^{57} +(-2.20925 + 1.27551i) q^{58} +(-0.378937 + 0.656339i) q^{59} +(-3.62132 + 1.37333i) q^{60} +(-0.328169 - 0.568406i) q^{61} +3.80385i q^{62} +2.26795 q^{64} +(-1.43488 + 8.82843i) q^{65} +(-0.896575 + 1.55291i) q^{66} +(10.9348 + 6.31319i) q^{67} +(6.00000 - 3.46410i) q^{68} +3.48477 q^{69} -6.39230 q^{71} +(1.67303 - 0.965926i) q^{72} +(-2.53590 - 1.46410i) q^{73} +(-2.73205 + 4.73205i) q^{74} +(-3.31552 - 3.74264i) q^{75} -9.14162 q^{76} -2.07055i q^{78} +(-2.26795 - 3.92820i) q^{79} +(1.95377 + 5.15187i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-3.80385 + 2.19615i) q^{82} -6.00000i q^{83} +(6.92820 + 5.65685i) q^{85} +(-4.26795 - 2.46410i) q^{87} +(5.79555 + 3.34607i) q^{88} +(-7.72741 - 13.3843i) q^{89} +(0.896575 + 0.732051i) q^{90} -6.03579i q^{92} +(-6.36396 + 3.67423i) q^{93} +(-1.55291 + 2.68973i) q^{94} +(-4.18482 - 11.0349i) q^{95} +(-2.56961 - 4.45069i) q^{96} +18.9282i q^{97} -3.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 12 q^{5} + 4 q^{9}+O(q^{10}) \) 8 * q - 12 * q^5 + 4 * q^9	\( 8 q - 12 q^{5} + 4 q^{9} + 12 q^{10} + 12 q^{12} + 4 q^{16} + 4 q^{25} - 16 q^{29} + 4 q^{30} + 24 q^{33} - 12 q^{38} - 16 q^{39} - 12 q^{40} - 24 q^{44} - 12 q^{45} + 28 q^{46} - 48 q^{50} + 16 q^{51} + 48 q^{52} - 12 q^{60} + 32 q^{64} + 48 q^{68} + 32 q^{71} - 48 q^{73} - 8 q^{74} - 32 q^{79} - 12 q^{80} - 4 q^{81} - 72 q^{82} - 48 q^{87} + 16 q^{95}+O(q^{100}) \) 8 * q - 12 * q^5 + 4 * q^9 + 12 * q^10 + 12 * q^12 + 4 * q^16 + 4 * q^25 - 16 * q^29 + 4 * q^30 + 24 * q^33 - 12 * q^38 - 16 * q^39 - 12 * q^40 - 24 * q^44 - 12 * q^45 + 28 * q^46 - 48 * q^50 + 16 * q^51 + 48 * q^52 - 12 * q^60 + 32 * q^64 + 48 * q^68 + 32 * q^71 - 48 * q^73 - 8 * q^74 - 32 * q^79 - 12 * q^80 - 4 * q^81 - 72 * q^82 - 48 * q^87 + 16 * q^95

Introduction

L-functions

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