LMFDB - Embedded newform 722.2.e.j.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			415.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	722.415
Dual form			722.2.e.j.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(2.00000 + 3.46410i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(2.00000 + 3.46410i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.87939 - 0.684040i) q^{13} +(0.694593 - 3.93923i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.59627 - 3.85673i) q^{17} +2.00000 q^{18} +(-3.06418 - 2.57115i) q^{21} +(2.81908 - 1.02606i) q^{22} +(-1.04189 - 5.90885i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(4.69846 + 1.71010i) q^{25} +(1.00000 + 1.73205i) q^{26} +(2.50000 - 4.33013i) q^{27} +(-3.06418 + 2.57115i) q^{28} +(-1.00000 - 1.73205i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.520945 - 2.95442i) q^{33} +(1.04189 + 5.90885i) q^{34} +(-1.53209 - 1.28558i) q^{36} -10.0000 q^{37} +2.00000 q^{39} +(-8.45723 + 3.07818i) q^{41} +(0.694593 + 3.93923i) q^{42} +(-0.694593 + 3.93923i) q^{43} +(-2.81908 - 1.02606i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(0.766044 - 0.642788i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-2.50000 - 4.33013i) q^{50} +(5.63816 + 2.05212i) q^{51} +(0.347296 - 1.96962i) q^{52} +(1.04189 + 5.90885i) q^{53} +(-4.69846 + 1.71010i) q^{54} +4.00000 q^{56} +(-6.89440 - 5.78509i) q^{59} +(-0.694593 - 3.93923i) q^{61} +(-0.347296 + 1.96962i) q^{62} +(-7.51754 - 2.73616i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.29813 + 1.92836i) q^{66} +(-5.36231 + 4.49951i) q^{67} +(3.00000 - 5.19615i) q^{68} +(3.00000 + 5.19615i) q^{69} +(-1.04189 + 5.90885i) q^{71} +(0.347296 + 1.96962i) q^{72} +(0.939693 - 0.342020i) q^{73} +(7.66044 + 6.42788i) q^{74} -5.00000 q^{75} -12.0000 q^{77} +(-1.53209 - 1.28558i) q^{78} +(3.75877 - 1.36808i) q^{79} +(0.173648 - 0.984808i) q^{81} +(8.45723 + 3.07818i) q^{82} +(-1.50000 - 2.59808i) q^{83} +(2.00000 - 3.46410i) q^{84} +(3.06418 - 2.57115i) q^{86} +(1.50000 + 2.59808i) q^{88} +(-5.63816 - 2.05212i) q^{89} +(-1.38919 - 7.87846i) q^{91} +(5.63816 - 2.05212i) q^{92} +(1.53209 + 1.28558i) q^{93} -1.00000 q^{96} +(13.0228 + 10.9274i) q^{97} +(8.45723 - 3.07818i) q^{98} +(-1.04189 - 5.90885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{7} + 3 q^{8}+O(q^{10}) $ 6 * q + 12 * q^7 + 3 * q^8	$ 6 q + 12 q^{7} + 3 q^{8} - 9 q^{11} - 3 q^{12} + 12 q^{18} + 6 q^{26} + 15 q^{27} - 6 q^{31} - 60 q^{37} + 12 q^{39} - 18 q^{46} - 27 q^{49} - 15 q^{50} + 24 q^{56} - 3 q^{64} + 18 q^{68} + 18 q^{69} - 30 q^{75} - 72 q^{77} - 9 q^{83} + 12 q^{84} + 9 q^{88} - 6 q^{96}+O(q^{100}) $ 6 * q + 12 * q^7 + 3 * q^8 - 9 * q^11 - 3 * q^12 + 12 * q^18 + 6 * q^26 + 15 * q^27 - 6 * q^31 - 60 * q^37 + 12 * q^39 - 18 * q^46 - 27 * q^49 - 15 * q^50 + 24 * q^56 - 3 * q^64 + 18 * q^68 + 18 * q^69 - 30 * q^75 - 72 * q^77 - 9 * q^83 + 12 * q^84 + 9 * q^88 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

Coefficient data

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

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

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

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i	−0.598725	−	0.800954i	$-0.704326\pi$
$3$	−0.939693	+	0.342020i	−0.542532	+	0.197465i	0.0561935	+	0.998420i	$0.482104\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$5$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$6$	0.939693	+	0.342020i	0.383628	+	0.139629i
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	0.944911	+	0.327327i	$0.106148\pi$
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−1.53209	+	1.28558i	−0.510696	+	0.428525i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	−1.87939	−	0.684040i	−0.521248	−	0.189719i	0.0679785	−	0.997687i	$-0.478345\pi$
$13$	−1.87939	−	0.684040i	−0.521248	−	0.189719i	−0.589226	+	0.807968i	$0.700567\pi$
$14$	0.694593	−	3.93923i	0.185638	−	1.05280i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−4.59627	−	3.85673i	−1.11476	−	0.935393i	−0.116431	−	0.993199i	$-0.537145\pi$
$17$	−4.59627	−	3.85673i	−1.11476	−	0.935393i	−0.998328	+	0.0578055i	$0.981590\pi$
$18$	2.00000			0.471405
$19$		0			0
$19$		0			0
$20$		0			0
$21$	−3.06418	−	2.57115i	−0.668658	−	0.561071i
$22$	2.81908	−	1.02606i	0.601029	−	0.218757i
$23$	−1.04189	−	5.90885i	−0.217249	−	1.23208i	−0.876961	−	0.480561i	$-0.840433\pi$
$23$	−1.04189	−	5.90885i	−0.217249	−	1.23208i	0.659712	−	0.751518i	$-0.270678\pi$
$24$	−0.173648	+	0.984808i	−0.0354458	+	0.201023i
$25$	4.69846	+	1.71010i	0.939693	+	0.342020i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	2.50000	−	4.33013i	0.481125	−	0.833333i
$28$	−3.06418	+	2.57115i	−0.579075	+	0.485902i
$29$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$29$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.520945	−	2.95442i	0.0906848	−	0.514299i
$34$	1.04189	+	5.90885i	0.178683	+	1.01336i
$35$		0			0
$36$	−1.53209	−	1.28558i	−0.255348	−	0.214263i
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$		0			0
$39$	2.00000			0.320256
$40$		0			0
$41$	−8.45723	+	3.07818i	−1.32080	+	0.480731i	−0.903714	−	0.428137i	$-0.859170\pi$
$41$	−8.45723	+	3.07818i	−1.32080	+	0.480731i	−0.417084	+	0.908868i	$0.636948\pi$
$42$	0.694593	+	3.93923i	0.107178	+	0.607837i
$43$	−0.694593	+	3.93923i	−0.105924	+	0.600727i	0.884923	+	0.465738i	$0.154211\pi$
$43$	−0.694593	+	3.93923i	−0.105924	+	0.600727i	−0.990847	+	0.134989i	$0.956900\pi$
$44$	−2.81908	−	1.02606i	−0.424992	−	0.154684i
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$47$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$48$	0.766044	−	0.642788i	0.110569	−	0.0927784i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	−2.50000	−	4.33013i	−0.353553	−	0.612372i
$51$	5.63816	+	2.05212i	0.789500	+	0.287354i
$52$	0.347296	−	1.96962i	0.0481613	−	0.273137i
$53$	1.04189	+	5.90885i	0.143114	+	0.811642i	0.968862	+	0.247602i	$0.0796426\pi$
$53$	1.04189	+	5.90885i	0.143114	+	0.811642i	−0.825747	+	0.564040i	$0.809246\pi$
$54$	−4.69846	+	1.71010i	−0.639380	+	0.232715i
$55$		0			0
$56$	4.00000			0.534522
$57$		0			0
$58$		0			0
$59$	−6.89440	−	5.78509i	−0.897574	−	0.753154i	0.0721404	−	0.997394i	$-0.477017\pi$
$59$	−6.89440	−	5.78509i	−0.897574	−	0.753154i	−0.969715	+	0.244240i	$0.921461\pi$
$60$		0			0
$61$	−0.694593	−	3.93923i	−0.0889335	−	0.504367i	−0.996438	−	0.0843252i	$-0.973127\pi$
$61$	−0.694593	−	3.93923i	−0.0889335	−	0.504367i	0.907505	−	0.420042i	$-0.137985\pi$
$62$	−0.347296	+	1.96962i	−0.0441067	+	0.250141i
$63$	−7.51754	−	2.73616i	−0.947121	−	0.344724i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−2.29813	+	1.92836i	−0.282881	+	0.237365i
$67$	−5.36231	+	4.49951i	−0.655111	+	0.549703i	−0.908617	−	0.417631i	$-0.862861\pi$
$67$	−5.36231	+	4.49951i	−0.655111	+	0.549703i	0.253506	+	0.967334i	$0.418416\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	3.00000	+	5.19615i	0.361158	+	0.625543i
$70$		0			0
$71$	−1.04189	+	5.90885i	−0.123649	+	0.701251i	0.858451	+	0.512895i	$0.171427\pi$
$71$	−1.04189	+	5.90885i	−0.123649	+	0.701251i	−0.982101	+	0.188356i	$0.939684\pi$
$72$	0.347296	+	1.96962i	0.0409293	+	0.232121i
$73$	0.939693	−	0.342020i	0.109983	−	0.0400304i	−0.286443	−	0.958097i	$-0.592473\pi$
$73$	0.939693	−	0.342020i	0.109983	−	0.0400304i	0.396425	+	0.918067i	$0.370251\pi$
$74$	7.66044	+	6.42788i	0.890509	+	0.747225i
$75$	−5.00000			−0.577350
$76$		0			0
$77$	−12.0000			−1.36753
$78$	−1.53209	−	1.28558i	−0.173475	−	0.145563i
$79$	3.75877	−	1.36808i	0.422895	−	0.153921i	−0.121802	−	0.992554i	$-0.538867\pi$
$79$	3.75877	−	1.36808i	0.422895	−	0.153921i	0.544696	+	0.838633i	$0.316645\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$	8.45723	+	3.07818i	0.933945	+	0.339928i
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	0.771883	−	0.635764i	$-0.219315\pi$
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	−0.936530	+	0.350588i	$0.885982\pi$
$84$	2.00000	−	3.46410i	0.218218	−	0.377964i
$85$		0			0
$86$	3.06418	−	2.57115i	0.330419	−	0.277254i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−5.63816	−	2.05212i	−0.597643	−	0.217524i	0.0254445	−	0.999676i	$-0.491900\pi$
$89$	−5.63816	−	2.05212i	−0.597643	−	0.217524i	−0.623088	+	0.782152i	$0.714122\pi$
$90$		0			0
$91$	−1.38919	−	7.87846i	−0.145626	−	0.825887i
$92$	5.63816	−	2.05212i	0.587818	−	0.213948i
$93$	1.53209	+	1.28558i	0.158870	+	0.133308i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	13.0228	+	10.9274i	1.32226	+	1.10951i	0.985820	+	0.167803i	$0.0536674\pi$
$97$	13.0228	+	10.9274i	1.32226	+	1.10951i	0.336440	+	0.941705i	$0.390777\pi$
$98$	8.45723	−	3.07818i	0.854310	−	0.310943i
$99$	−1.04189	−	5.90885i	−0.104714	−	0.593861i
$100$	−0.868241	+	4.92404i	−0.0868241	+	0.492404i
$101$		0			0		0.342020	−	0.939693i	$-0.388889\pi$
$101$		0			0		−0.342020	+	0.939693i	$0.611111\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	−1.00000	+	1.73205i	−0.0985329	+	0.170664i	−0.911078	−	0.412235i	$-0.864748\pi$
$103$	−1.00000	+	1.73205i	−0.0985329	+	0.170664i	0.812545	+	0.582899i	$0.198082\pi$
$104$	−1.53209	+	1.28558i	−0.150234	+	0.126061i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	4.69846	+	1.71010i	0.452110	+	0.164555i
$109$	−2.77837	+	15.7569i	−0.266120	+	1.50924i	0.499708	+	0.866194i	$0.333441\pi$
$109$	−2.77837	+	15.7569i	−0.266120	+	1.50924i	−0.765828	+	0.643046i	$0.777671\pi$
$110$		0			0
$111$	9.39693	−	3.42020i	0.891917	−	0.324631i
$112$	−3.06418	−	2.57115i	−0.289538	−	0.242951i
$113$	15.0000			1.41108			0.705541	−	0.708669i	$-0.250704\pi$
$113$	15.0000			1.41108			0.705541	+	0.708669i	$0.250704\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.75877	−	1.36808i	0.347498	−	0.126479i
$118$	1.56283	+	8.86327i	0.143870	+	0.815930i
$119$	4.16756	−	23.6354i	0.382039	−	2.16665i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−2.00000	+	3.46410i	−0.181071	+	0.313625i
$123$	6.89440	−	5.78509i	0.621647	−	0.521624i
$124$	1.53209	−	1.28558i	0.137586	−	0.115448i
$125$		0			0
$126$	4.00000	+	6.92820i	0.356348	+	0.617213i
$127$	−1.87939	−	0.684040i	−0.166768	−	0.0606988i	0.257287	−	0.966335i	$-0.417172\pi$
$127$	−1.87939	−	0.684040i	−0.166768	−	0.0606988i	−0.424055	+	0.905636i	$0.639394\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−0.694593	−	3.93923i	−0.0611555	−	0.346830i
$130$		0			0
$131$	6.89440	+	5.78509i	0.602367	+	0.505446i	0.892205	−	0.451630i	$-0.149157\pi$
$131$	6.89440	+	5.78509i	0.602367	+	0.505446i	−0.289839	+	0.957075i	$0.593602\pi$
$132$	3.00000			0.261116
$133$		0			0
$134$	7.00000			0.604708
$135$		0			0
$136$	−5.63816	+	2.05212i	−0.483468	+	0.175968i
$137$	1.56283	+	8.86327i	0.133522	+	0.757240i	0.975878	+	0.218318i	$0.0700571\pi$
$137$	1.56283	+	8.86327i	0.133522	+	0.757240i	−0.842356	+	0.538922i	$0.818832\pi$
$138$	1.04189	−	5.90885i	0.0886915	−	0.502994i
$139$	−10.3366	−	3.76222i	−0.876741	−	0.319107i	−0.135847	−	0.990730i	$-0.543376\pi$
$139$	−10.3366	−	3.76222i	−0.876741	−	0.319107i	−0.740894	+	0.671622i	$0.765598\pi$
$140$		0			0
$141$		0			0
$142$	4.59627	−	3.85673i	0.385710	−	0.323649i
$143$	4.59627	−	3.85673i	0.384359	−	0.322516i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$		0			0
$146$	−0.939693	−	0.342020i	−0.0777695	−	0.0283058i
$147$	1.56283	−	8.86327i	0.128900	−	0.731030i
$148$	−1.73648	−	9.84808i	−0.142738	−	0.809507i
$149$	−16.9145	+	6.15636i	−1.38569	+	0.504349i	−0.923897	−	0.382641i	$-0.875015\pi$
$149$	−16.9145	+	6.15636i	−1.38569	+	0.504349i	−0.461790	+	0.886989i	$0.652793\pi$
$150$	3.83022	+	3.21394i	0.312736	+	0.262417i
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$		0			0
$153$	12.0000			0.970143
$154$	9.19253	+	7.71345i	0.740755	+	0.621568i
$155$		0			0
$156$	0.347296	+	1.96962i	0.0278060	+	0.157695i
$157$	−2.77837	+	15.7569i	−0.221738	+	1.25754i	0.647085	+	0.762418i	$0.275988\pi$
$157$	−2.77837	+	15.7569i	−0.221738	+	1.25754i	−0.868824	+	0.495122i	$0.835123\pi$
$158$	−3.75877	−	1.36808i	−0.299032	−	0.108839i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	18.3851	−	15.4269i	1.44895	−	1.21581i
$162$	−0.766044	+	0.642788i	−0.0601861	+	0.0505022i
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	−0.206518	−	0.978443i	$-0.566213\pi$
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	0.950615	−	0.310372i	$-0.100454\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$		0			0
$166$	−0.520945	+	2.95442i	−0.0404331	+	0.229308i
$167$	−4.16756	−	23.6354i	−0.322495	−	1.82896i	−0.526722	−	0.850038i	$-0.676579\pi$
$167$	−4.16756	−	23.6354i	−0.322495	−	1.82896i	0.204227	−	0.978924i	$-0.434532\pi$
$168$	−3.75877	+	1.36808i	−0.289995	+	0.105550i
$169$	−6.89440	−	5.78509i	−0.530338	−	0.445007i
$170$		0			0
$171$		0			0
$172$	−4.00000			−0.304997
$173$	4.59627	+	3.85673i	0.349448	+	0.293221i	0.800568	−	0.599242i	$-0.204531\pi$
$173$	4.59627	+	3.85673i	0.349448	+	0.293221i	−0.451121	+	0.892463i	$0.648976\pi$
$174$		0			0
$175$	3.47296	+	19.6962i	0.262531	+	1.48889i
$176$	0.520945	−	2.95442i	0.0392677	−	0.222698i
$177$	8.45723	+	3.07818i	0.635685	+	0.231370i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$		0			0
$181$	1.53209	−	1.28558i	0.113879	−	0.0955561i	−0.584070	−	0.811703i	$-0.698541\pi$
$181$	1.53209	−	1.28558i	0.113879	−	0.0955561i	0.697949	+	0.716147i	$0.254096\pi$
$182$	−4.00000	+	6.92820i	−0.296500	+	0.513553i
$183$	2.00000	+	3.46410i	0.147844	+	0.256074i
$184$	−5.63816	−	2.05212i	−0.415650	−	0.151284i
$185$		0			0
$186$	−0.347296	−	1.96962i	−0.0254650	−	0.144419i
$187$	16.9145	−	6.15636i	1.23691	−	0.450198i
$188$		0			0
$189$	20.0000			1.45479
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	0.766044	+	0.642788i	0.0552845	+	0.0463892i
$193$	−1.87939	+	0.684040i	−0.135281	+	0.0492383i	−0.408773	−	0.912636i	$-0.634043\pi$
$193$	−1.87939	+	0.684040i	−0.135281	+	0.0492383i	0.273492	+	0.961874i	$0.411821\pi$
$194$	−2.95202	−	16.7417i	−0.211943	−	1.20199i
$195$		0			0
$196$	−8.45723	−	3.07818i	−0.604088	−	0.219870i
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	−0.985160	−	0.171639i	$-0.945094\pi$
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	0.343937	−	0.938993i	$-0.388239\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	−7.66044	+	6.42788i	−0.543035	+	0.455660i	−0.872574	−	0.488482i	$-0.837551\pi$
$199$	−7.66044	+	6.42788i	−0.543035	+	0.455660i	0.329540	+	0.944142i	$0.393106\pi$
$200$	3.83022	−	3.21394i	0.270838	−	0.227260i
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$		0			0
$203$		0			0
$204$	−1.04189	+	5.90885i	−0.0729468	+	0.413702i
$205$		0			0
$206$	1.87939	−	0.684040i	0.130943	−	0.0476593i
$207$	9.19253	+	7.71345i	0.638925	+	0.536122i
$208$	2.00000			0.138675
$209$		0			0
$210$		0			0
$211$	15.3209	+	12.8558i	1.05473	+	0.885026i	0.993583	−	0.113102i	$-0.0360787\pi$
$211$	15.3209	+	12.8558i	1.05473	+	0.885026i	0.0611501	+	0.998129i	$0.480523\pi$
$212$	−5.63816	+	2.05212i	−0.387230	+	0.140940i
$213$	−1.04189	−	5.90885i	−0.0713891	−	0.404867i
$214$		0			0
$215$		0			0
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	4.00000	−	6.92820i	0.271538	−	0.470317i
$218$	12.2567	−	10.2846i	0.830129	−	0.696561i
$219$	−0.766044	+	0.642788i	−0.0517645	+	0.0434356i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$	−9.39693	−	3.42020i	−0.630680	−	0.229549i
$223$	2.43107	−	13.7873i	0.162797	−	0.923266i	−0.788510	−	0.615022i	$-0.789147\pi$
$223$	2.43107	−	13.7873i	0.162797	−	0.923266i	0.951307	−	0.308245i	$-0.0997416\pi$
$224$	0.694593	+	3.93923i	0.0464094	+	0.263201i
$225$	−9.39693	+	3.42020i	−0.626462	+	0.228013i
$226$	−11.4907	−	9.64181i	−0.764348	−	0.641364i
$227$	3.00000			0.199117			0.0995585	−	0.995032i	$-0.468257\pi$
$227$	3.00000			0.199117			0.0995585	+	0.995032i	$0.468257\pi$
$228$		0			0
$229$	−16.0000			−1.05731			−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000			−1.05731			−0.528655	+	0.848837i	$0.677303\pi$
$230$		0			0
$231$	11.2763	−	4.10424i	0.741927	−	0.270039i
$232$		0			0
$233$	0.520945	−	2.95442i	0.0341282	−	0.193551i	−0.962977	−	0.269583i	$-0.913114\pi$
$233$	0.520945	−	2.95442i	0.0341282	−	0.193551i	0.997105	+	0.0760324i	$0.0242252\pi$
$234$	−3.75877	−	1.36808i	−0.245719	−	0.0894342i
$235$		0			0
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	−3.06418	+	2.57115i	−0.199040	+	0.167014i
$238$	−18.3851	+	15.4269i	−1.19173	+	0.999978i
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$		0			0
$241$	−4.69846	−	1.71010i	−0.302655	−	0.110157i	0.186229	−	0.982506i	$-0.440373\pi$
$241$	−4.69846	−	1.71010i	−0.302655	−	0.110157i	−0.488883	+	0.872349i	$0.662596\pi$
$242$	0.347296	−	1.96962i	0.0223251	−	0.126612i
$243$	2.77837	+	15.7569i	0.178233	+	1.01081i
$244$	3.75877	−	1.36808i	0.240631	−	0.0875824i
$245$		0			0
$246$	−9.00000			−0.573819
$247$		0			0
$248$	−2.00000			−0.127000
$249$	2.29813	+	1.92836i	0.145638	+	0.122205i
$250$		0			0
$251$	−0.520945	−	2.95442i	−0.0328817	−	0.186482i	0.963943	−	0.266109i	$-0.0857381\pi$
$251$	−0.520945	−	2.95442i	−0.0328817	−	0.186482i	−0.996825	+	0.0796274i	$0.974627\pi$
$252$	1.38919	−	7.87846i	0.0875105	−	0.496296i
$253$	16.9145	+	6.15636i	1.06340	+	0.387047i
$254$	1.00000	+	1.73205i	0.0627456	+	0.108679i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	2.29813	−	1.92836i	0.143354	−	0.120288i	−0.568291	−	0.822828i	$-0.692395\pi$
$257$	2.29813	−	1.92836i	0.143354	−	0.120288i	0.711644	+	0.702540i	$0.247951\pi$
$258$	−2.00000	+	3.46410i	−0.124515	+	0.215666i
$259$	−20.0000	−	34.6410i	−1.24274	−	2.15249i
$260$		0			0
$261$		0			0
$262$	−1.56283	−	8.86327i	−0.0965522	−	0.547575i
$263$	11.2763	−	4.10424i	0.695327	−	0.253078i	0.0299127	−	0.999553i	$-0.490477\pi$
$263$	11.2763	−	4.10424i	0.695327	−	0.253078i	0.665414	+	0.746474i	$0.268255\pi$
$264$	−2.29813	−	1.92836i	−0.141440	−	0.118683i
$265$		0			0
$266$		0			0
$267$	6.00000			0.367194
$268$	−5.36231	−	4.49951i	−0.327555	−	0.274852i
$269$	−11.2763	+	4.10424i	−0.687529	+	0.250240i	−0.662077	−	0.749436i	$-0.730325\pi$
$269$	−11.2763	+	4.10424i	−0.687529	+	0.250240i	−0.0254521	+	0.999676i	$0.508103\pi$
$270$		0			0
$271$	−2.77837	+	15.7569i	−0.168774	+	0.957165i	0.776313	+	0.630347i	$0.217087\pi$
$271$	−2.77837	+	15.7569i	−0.168774	+	0.957165i	−0.945087	+	0.326818i	$0.894024\pi$
$272$	5.63816	+	2.05212i	0.341863	+	0.124428i
$273$	4.00000	+	6.92820i	0.242091	+	0.419314i
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$	−11.4907	+	9.64181i	−0.692913	+	0.581423i
$276$	−4.59627	+	3.85673i	−0.276663	+	0.232148i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	5.50000	+	9.52628i	0.329868	+	0.571348i
$279$	3.75877	+	1.36808i	0.225032	+	0.0819048i
$280$		0			0
$281$	4.68850	+	26.5898i	0.279693	+	1.58622i	0.723650	+	0.690167i	$0.242463\pi$
$281$	4.68850	+	26.5898i	0.279693	+	1.58622i	−0.443957	+	0.896048i	$0.646426\pi$
$282$		0			0
$283$	3.83022	+	3.21394i	0.227683	+	0.191049i	0.749492	−	0.662014i	$-0.230298\pi$
$283$	3.83022	+	3.21394i	0.227683	+	0.191049i	−0.521809	+	0.853063i	$0.674742\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−6.00000			−0.354787
$287$	−27.5776	−	23.1404i	−1.62785	−	1.36593i
$288$	−1.87939	+	0.684040i	−0.110744	+	0.0403075i
$289$	3.29932	+	18.7113i	0.194077	+	1.10067i
$290$		0			0
$291$	−15.9748	−	5.81434i	−0.936458	−	0.340843i
$292$	0.500000	+	0.866025i	0.0292603	+	0.0506803i
$293$	−12.0000	+	20.7846i	−0.701047	+	1.21425i	0.267052	+	0.963682i	$0.413951\pi$
$293$	−12.0000	+	20.7846i	−0.701047	+	1.21425i	−0.968099	+	0.250568i	$0.919383\pi$
$294$	−6.89440	+	5.78509i	−0.402090	+	0.337393i
$295$		0			0
$296$	−5.00000	+	8.66025i	−0.290619	+	0.503367i
$297$	7.50000	+	12.9904i	0.435194	+	0.753778i
$298$	16.9145	+	6.15636i	0.979829	+	0.356629i
$299$	−2.08378	+	11.8177i	−0.120508	+	0.683435i
$300$	−0.868241	−	4.92404i	−0.0501279	−	0.284290i
$301$	−15.0351	+	5.47232i	−0.866608	+	0.315419i
$302$	7.66044	+	6.42788i	0.440809	+	0.369883i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	−9.19253	−	7.71345i	−0.525502	−	0.440949i
$307$	6.57785	−	2.39414i	0.375418	−	0.136641i	−0.147418	−	0.989074i	$-0.547096\pi$
$307$	6.57785	−	2.39414i	0.375418	−	0.136641i	0.522836	+	0.852433i	$0.324874\pi$
$308$	−2.08378	−	11.8177i	−0.118734	−	0.673376i
$309$	0.347296	−	1.96962i	0.0197570	−	0.112048i
$310$		0			0
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$	1.00000	−	1.73205i	0.0566139	−	0.0980581i
$313$	−14.5548	+	12.2130i	−0.822688	+	0.690318i	−0.953600	−	0.301076i	$-0.902654\pi$
$313$	−14.5548	+	12.2130i	−0.822688	+	0.690318i	0.130912	+	0.991394i	$0.458210\pi$
$314$	12.2567	−	10.2846i	0.691686	−	0.580394i
$315$		0			0
$316$	2.00000	+	3.46410i	0.112509	+	0.194871i
$317$	16.9145	+	6.15636i	0.950011	+	0.345776i	0.770112	−	0.637909i	$-0.220201\pi$
$317$	16.9145	+	6.15636i	0.950011	+	0.345776i	0.179900	+	0.983685i	$0.442423\pi$
$318$	−1.04189	+	5.90885i	−0.0584262	+	0.331352i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	−24.0000			−1.33747
$323$		0			0
$324$	1.00000			0.0555556
$325$	−7.66044	−	6.42788i	−0.424925	−	0.356554i
$326$	−17.8542	+	6.49838i	−0.988850	+	0.359912i
$327$	−2.77837	−	15.7569i	−0.153644	−	0.871360i
$328$	−1.56283	+	8.86327i	−0.0862930	+	0.489392i
$329$		0			0
$330$		0			0
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	−0.926516	−	0.376254i	$-0.877212\pi$
$331$	−2.50000	+	4.33013i	−0.137412	+	0.238005i	0.789104	+	0.614260i	$0.210545\pi$
$332$	2.29813	−	1.92836i	0.126126	−	0.105833i
$333$	15.3209	−	12.8558i	0.839580	−	0.704491i
$334$	−12.0000	+	20.7846i	−0.656611	+	1.13728i
$335$		0			0
$336$	3.75877	+	1.36808i	0.205058	+	0.0746349i
$337$	1.91013	−	10.8329i	0.104051	−	0.590105i	−0.887544	−	0.460724i	$-0.847590\pi$
$337$	1.91013	−	10.8329i	0.104051	−	0.590105i	0.991595	−	0.129381i	$-0.0412990\pi$
$338$	1.56283	+	8.86327i	0.0850069	+	0.482098i
$339$	−14.0954	+	5.13030i	−0.765556	+	0.278640i
$340$		0			0
$341$	6.00000			0.324918
$342$		0			0
$343$	−8.00000			−0.431959
$344$	3.06418	+	2.57115i	0.165209	+	0.138627i
$345$		0			0
$346$	−1.04189	−	5.90885i	−0.0560123	−	0.317662i
$347$	−1.56283	+	8.86327i	−0.0838973	+	0.475805i	0.913692	+	0.406408i	$0.133219\pi$
$347$	−1.56283	+	8.86327i	−0.0838973	+	0.475805i	−0.997589	+	0.0693974i	$0.977892\pi$
$348$		0			0
$349$	2.00000	+	3.46410i	0.107058	+	0.185429i	0.914577	−	0.404412i	$-0.132524\pi$
$349$	2.00000	+	3.46410i	0.107058	+	0.185429i	−0.807519	+	0.589841i	$0.799190\pi$
$350$	10.0000	−	17.3205i	0.534522	−	0.925820i
$351$	−7.66044	+	6.42788i	−0.408884	+	0.343095i
$352$	−2.29813	+	1.92836i	−0.122491	+	0.102782i
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$	−4.50000	−	7.79423i	−0.239172	−	0.414259i
$355$		0			0
$356$	1.04189	−	5.90885i	0.0552200	−	0.313168i
$357$	4.16756	+	23.6354i	0.220570	+	1.25092i
$358$	8.45723	−	3.07818i	0.446979	−	0.162687i
$359$	−4.59627	−	3.85673i	−0.242582	−	0.203550i	0.513388	−	0.858156i	$-0.328390\pi$
$359$	−4.59627	−	3.85673i	−0.242582	−	0.203550i	−0.755970	+	0.654606i	$0.772834\pi$
$360$		0			0
$361$		0			0
$362$	−2.00000			−0.105118
$363$	−1.53209	−	1.28558i	−0.0804138	−	0.0674752i
$364$	7.51754	−	2.73616i	0.394026	−	0.143414i
$365$		0			0
$366$	0.694593	−	3.93923i	0.0363069	−	0.205907i
$367$	20.6732	+	7.52444i	1.07913	+	0.392773i	0.819585	−	0.572957i	$-0.194204\pi$
$367$	20.6732	+	7.52444i	1.07913	+	0.392773i	0.259549	+	0.965730i	$0.416426\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	9.00000	−	15.5885i	0.468521	−	0.811503i
$370$		0			0
$371$	−18.3851	+	15.4269i	−0.954505	+	0.800925i
$372$	−1.00000	+	1.73205i	−0.0518476	+	0.0898027i
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	−16.9145	−	6.15636i	−0.874626	−	0.318338i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−15.3209	−	12.8558i	−0.788021	−	0.661229i
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	−9.19253	−	7.71345i	−0.470331	−	0.394655i
$383$	33.8289	−	12.3127i	1.72858	−	0.629151i	0.730050	−	0.683394i	$-0.239497\pi$
$383$	33.8289	−	12.3127i	1.72858	−	0.629151i	0.998528	+	0.0542428i	$0.0172745\pi$
$384$	−0.173648	−	0.984808i	−0.00886145	−	0.0502558i
$385$		0			0
$386$	1.87939	+	0.684040i	0.0956582	+	0.0348167i
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	−8.50000	+	14.7224i	−0.431522	+	0.747418i
$389$	−27.5776	+	23.1404i	−1.39824	+	1.17326i	−0.436366	+	0.899769i	$0.643735\pi$
$389$	−27.5776	+	23.1404i	−1.39824	+	1.17326i	−0.961874	+	0.273493i	$0.911821\pi$
$390$		0			0
$391$	−18.0000	+	31.1769i	−0.910299	+	1.57668i
$392$	4.50000	+	7.79423i	0.227284	+	0.393668i
$393$	−8.45723	−	3.07818i	−0.426611	−	0.155274i
$394$	−3.12567	+	17.7265i	−0.157469	+	0.893050i
$395$		0			0
$396$	5.63816	−	2.05212i	0.283328	−	0.103123i
$397$	−7.66044	−	6.42788i	−0.384467	−	0.322606i	0.429986	−	0.902835i	$-0.358518\pi$
$397$	−7.66044	−	6.42788i	−0.384467	−	0.322606i	−0.814453	+	0.580230i	$0.802963\pi$
$398$	10.0000			0.501255
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−20.6832	−	17.3553i	−1.03287	−	0.866681i	−0.0416801	−	0.999131i	$-0.513271\pi$
$401$	−20.6832	−	17.3553i	−1.03287	−	0.866681i	−0.991190	+	0.132450i	$0.957715\pi$
$402$	−6.57785	+	2.39414i	−0.328073	+	0.119409i
$403$	0.694593	+	3.93923i	0.0346001	+	0.196227i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	15.0000	−	25.9808i	0.743522	−	1.28782i
$408$	4.59627	−	3.85673i	0.227549	−	0.190936i
$409$	3.83022	−	3.21394i	0.189392	−	0.158919i	−0.543161	−	0.839628i	$-0.682773\pi$
$409$	3.83022	−	3.21394i	0.189392	−	0.158919i	0.732554	+	0.680709i	$0.238328\pi$
$410$		0			0
$411$	−4.50000	−	7.79423i	−0.221969	−	0.384461i
$412$	−1.87939	−	0.684040i	−0.0925907	−	0.0337002i
$413$	6.25133	−	35.4531i	0.307608	−	1.74453i
$414$	−2.08378	−	11.8177i	−0.102412	−	0.580808i
$415$		0			0
$416$	−1.53209	−	1.28558i	−0.0751168	−	0.0630305i
$417$	11.0000			0.538672
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	9.39693	−	3.42020i	0.457978	−	0.166690i	−0.102721	−	0.994710i	$-0.532755\pi$
$421$	9.39693	−	3.42020i	0.457978	−	0.166690i	0.560699	+	0.828020i	$0.310533\pi$
$422$	−3.47296	−	19.6962i	−0.169061	−	0.958794i
$423$		0			0
$424$	5.63816	+	2.05212i	0.273813	+	0.0996598i
$425$	−15.0000	−	25.9808i	−0.727607	−	1.26025i
$426$	−3.00000	+	5.19615i	−0.145350	+	0.251754i
$427$	12.2567	−	10.2846i	0.593144	−	0.497707i
$428$		0			0
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$		0			0
$431$	28.1908	+	10.2606i	1.35790	+	0.494236i	0.915405	−	0.402534i	$-0.131871\pi$
$431$	28.1908	+	10.2606i	1.35790	+	0.494236i	0.442497	+	0.896770i	$0.354093\pi$
$432$	−0.868241	+	4.92404i	−0.0417733	+	0.236908i
$433$	4.51485	+	25.6050i	0.216970	+	1.23050i	0.877455	+	0.479659i	$0.159240\pi$
$433$	4.51485	+	25.6050i	0.216970	+	1.23050i	−0.660485	+	0.750839i	$0.729649\pi$
$434$	−7.51754	+	2.73616i	−0.360854	+	0.131340i
$435$		0			0
$436$	−16.0000			−0.766261
$437$		0			0
$438$	1.00000			0.0477818
$439$	10.7246	+	8.99903i	0.511858	+	0.429500i	0.861783	−	0.507278i	$-0.169348\pi$
$439$	10.7246	+	8.99903i	0.511858	+	0.429500i	−0.349924	+	0.936778i	$0.613793\pi$
$440$		0			0
$441$	−3.12567	−	17.7265i	−0.148841	−	0.844121i
$442$	2.08378	−	11.8177i	0.0991152	−	0.562110i
$443$	−8.45723	−	3.07818i	−0.401815	−	0.146249i	0.133204	−	0.991089i	$-0.457473\pi$
$443$	−8.45723	−	3.07818i	−0.401815	−	0.146249i	−0.535019	+	0.844840i	$0.679696\pi$
$444$	5.00000	+	8.66025i	0.237289	+	0.410997i
$445$		0			0
$446$	−10.7246	+	8.99903i	−0.507826	+	0.426116i
$447$	13.7888	−	11.5702i	0.652188	−	0.547251i
$448$	2.00000	−	3.46410i	0.0944911	−	0.163663i
$449$	−4.50000	−	7.79423i	−0.212368	−	0.367832i	0.740087	−	0.672511i	$-0.234784\pi$
$449$	−4.50000	−	7.79423i	−0.212368	−	0.367832i	−0.952455	+	0.304679i	$0.901451\pi$
$450$	9.39693	+	3.42020i	0.442975	+	0.161230i
$451$	4.68850	−	26.5898i	0.220773	−	1.25207i
$452$	2.60472	+	14.7721i	0.122516	+	0.694822i
$453$	9.39693	−	3.42020i	0.441506	−	0.160695i
$454$	−2.29813	−	1.92836i	−0.107857	−	0.0905026i
$455$		0			0
$456$		0			0
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$	12.2567	+	10.2846i	0.572718	+	0.480568i
$459$	−28.1908	+	10.2606i	−1.31583	+	0.478924i
$460$		0			0
$461$	1.04189	−	5.90885i	0.0485256	−	0.275202i	−0.950884	−	0.309546i	$-0.899823\pi$
$461$	1.04189	−	5.90885i	0.0485256	−	0.275202i	0.999410	+	0.0343436i	$0.0109340\pi$
$462$	−11.2763	−	4.10424i	−0.524621	−	0.190947i
$463$	17.0000	+	29.4449i	0.790057	+	1.36842i	0.925931	+	0.377693i	$0.123282\pi$
$463$	17.0000	+	29.4449i	0.790057	+	1.36842i	−0.135874	+	0.990726i	$0.543384\pi$
$464$		0			0
$465$		0			0
$466$	−2.29813	+	1.92836i	−0.106459	+	0.0893297i
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	−0.363892	−	0.931441i	$-0.618552\pi$
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	0.988598	−	0.150581i	$-0.0481143\pi$
$468$	2.00000	+	3.46410i	0.0924500	+	0.160128i
$469$	−26.3114	−	9.57656i	−1.21495	−	0.442205i
$470$		0			0
$471$	−2.77837	−	15.7569i	−0.128021	−	0.726041i
$472$	−8.45723	+	3.07818i	−0.389276	+	0.141685i
$473$	−9.19253	−	7.71345i	−0.422673	−	0.354665i
$474$	4.00000			0.183726
$475$		0			0
$476$	24.0000			1.10004
$477$	−9.19253	−	7.71345i	−0.420897	−	0.353175i
$478$	−11.2763	+	4.10424i	−0.515766	+	0.187724i
$479$	6.25133	+	35.4531i	0.285631	+	1.61989i	0.703024	+	0.711166i	$0.251833\pi$
$479$	6.25133	+	35.4531i	0.285631	+	1.61989i	−0.417393	+	0.908726i	$0.637056\pi$
$480$		0			0
$481$	18.7939	+	6.84040i	0.856926	+	0.311896i
$482$	2.50000	+	4.33013i	0.113872	+	0.197232i
$483$	−12.0000	+	20.7846i	−0.546019	+	0.945732i
$484$	−1.53209	+	1.28558i	−0.0696404	+	0.0584352i
$485$		0			0
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$	−3.75877	−	1.36808i	−0.170152	−	0.0619301i
$489$	−3.29932	+	18.7113i	−0.149200	+	0.846156i
$490$		0			0
$491$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$491$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$492$	6.89440	+	5.78509i	0.310824	+	0.260812i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	1.53209	+	1.28558i	0.0687928	+	0.0577240i
$497$	−22.5526	+	8.20848i	−1.01162	+	0.368201i
$498$	−0.520945	−	2.95442i	−0.0233441	−	0.132391i
$499$	−4.34120	+	24.6202i	−0.194339	+	1.10215i	0.719018	+	0.694991i	$0.244592\pi$
$499$	−4.34120	+	24.6202i	−0.194339	+	1.10215i	−0.913357	+	0.407160i	$0.866519\pi$
$500$		0			0
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$	−1.50000	+	2.59808i	−0.0669483	+	0.115958i
$503$	4.59627	−	3.85673i	0.204937	−	0.171963i	−0.534542	−	0.845142i	$-0.679516\pi$
$503$	4.59627	−	3.85673i	0.204937	−	0.171963i	0.739480	+	0.673179i	$0.235072\pi$
$504$	−6.12836	+	5.14230i	−0.272979	+	0.229056i
$505$		0			0
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	8.45723	+	3.07818i	0.375599	+	0.136707i
$508$	0.347296	−	1.96962i	0.0154088	−	0.0873876i
$509$	−4.16756	−	23.6354i	−0.184724	−	1.04762i	−0.926310	−	0.376762i	$-0.877037\pi$
$509$	−4.16756	−	23.6354i	−0.184724	−	1.04762i	0.741586	−	0.670858i	$-0.234074\pi$
$510$		0			0
$511$	3.06418	+	2.57115i	0.135551	+	0.113741i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−3.00000			−0.132324
$515$		0			0
$516$	3.75877	−	1.36808i	0.165471	−	0.0602264i
$517$		0			0
$518$	−6.94593	+	39.3923i	−0.305187	+	1.73080i
$519$	−5.63816	−	2.05212i	−0.247488	−	0.0900781i
$520$		0			0
$521$	−4.50000	+	7.79423i	−0.197149	+	0.341471i	−0.947603	−	0.319451i	$-0.896501\pi$
$521$	−4.50000	+	7.79423i	−0.197149	+	0.341471i	0.750454	+	0.660922i	$0.229835\pi$
$522$		0			0
$523$	−21.4492	+	17.9981i	−0.937910	+	0.787000i	−0.977220	−	0.212227i	$-0.931928\pi$
$523$	−21.4492	+	17.9981i	−0.937910	+	0.787000i	0.0393104	+	0.999227i	$0.487484\pi$
$524$	−4.50000	+	7.79423i	−0.196583	+	0.340492i
$525$	−10.0000	−	17.3205i	−0.436436	−	0.755929i
$526$	−11.2763	−	4.10424i	−0.491671	−	0.178953i
$527$	−2.08378	+	11.8177i	−0.0907708	+	0.514787i
$528$	0.520945	+	2.95442i	0.0226712	+	0.128575i
$529$	−12.2160	+	4.44626i	−0.531131	+	0.193316i
$530$		0			0
$531$	18.0000			0.781133
$532$		0			0
$533$	18.0000			0.779667
$534$	−4.59627	−	3.85673i	−0.198900	−	0.166897i
$535$		0			0
$536$	1.21554	+	6.89365i	0.0525032	+	0.297761i
$537$	1.56283	−	8.86327i	0.0674412	−	0.382478i
$538$	11.2763	+	4.10424i	0.486156	+	0.176946i
$539$	−13.5000	−	23.3827i	−0.581486	−	1.00716i
$540$		0			0
$541$	33.7060	−	28.2827i	1.44913	−	1.21597i	0.515922	−	0.856636i	$-0.327449\pi$
$541$	33.7060	−	28.2827i	1.44913	−	1.21597i	0.933210	−	0.359331i	$-0.116995\pi$
$542$	12.2567	−	10.2846i	0.526471	−	0.441761i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	−3.00000	−	5.19615i	−0.128624	−	0.222783i
$545$		0			0
$546$	1.38919	−	7.87846i	0.0594516	−	0.337167i
$547$	−0.694593	−	3.93923i	−0.0296986	−	0.168429i	0.966351	−	0.257227i	$-0.0828087\pi$
$547$	−0.694593	−	3.93923i	−0.0296986	−	0.168429i	−0.996050	+	0.0887974i	$0.971698\pi$
$548$	−8.45723	+	3.07818i	−0.361275	+	0.131493i
$549$	6.12836	+	5.14230i	0.261552	+	0.219468i
$550$	15.0000			0.639602
$551$		0			0
$552$	6.00000			0.255377
$553$	12.2567	+	10.2846i	0.521208	+	0.437346i
$554$	7.51754	−	2.73616i	0.319390	−	0.116248i
$555$		0			0
$556$	1.91013	−	10.8329i	0.0810076	−	0.459417i
$557$	−22.5526	−	8.20848i	−0.955585	−	0.347805i	−0.183283	−	0.983060i	$-0.558673\pi$
$557$	−22.5526	−	8.20848i	−0.955585	−	0.347805i	−0.772302	+	0.635256i	$0.780895\pi$
$558$	−2.00000	−	3.46410i	−0.0846668	−	0.146647i
$559$	4.00000	−	6.92820i	0.169182	−	0.293032i
$560$		0			0
$561$	−13.7888	+	11.5702i	−0.582164	+	0.488493i
$562$	13.5000	−	23.3827i	0.569463	−	0.986339i
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	0.997876	−	0.0651433i	$-0.0207504\pi$
$563$	10.5000	+	18.1865i	0.442522	+	0.766471i	−0.555354	+	0.831614i	$0.687417\pi$
$564$		0			0
$565$		0			0
$566$	−0.868241	−	4.92404i	−0.0364949	−	0.206973i
$567$	3.75877	−	1.36808i	0.157854	−	0.0574540i
$568$	4.59627	+	3.85673i	0.192855	+	0.161825i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	4.59627	+	3.85673i	0.192180	+	0.161258i
$573$	−11.2763	+	4.10424i	−0.471075	+	0.171457i
$574$	6.25133	+	35.4531i	0.260926	+	1.47978i
$575$	5.20945	−	29.5442i	0.217249	−	1.23208i
$576$	1.87939	+	0.684040i	0.0783077	+	0.0285017i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	9.50000	−	16.4545i	0.395148	−	0.684416i
$579$	1.53209	−	1.28558i	0.0636714	−	0.0534267i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	8.50000	+	14.7224i	0.352336	+	0.610264i
$583$	−16.9145	−	6.15636i	−0.700526	−	0.254970i
$584$	0.173648	−	0.984808i	0.00718561	−	0.0407516i
$585$		0			0
$586$	22.5526	−	8.20848i	0.931640	−	0.339089i
$587$	−9.19253	−	7.71345i	−0.379416	−	0.318368i	0.433057	−	0.901367i	$-0.357435\pi$
$587$	−9.19253	−	7.71345i	−0.379416	−	0.318368i	−0.812473	+	0.582998i	$0.801879\pi$
$588$	9.00000			0.371154
$589$		0			0
$590$		0			0
$591$	13.7888	+	11.5702i	0.567195	+	0.475933i
$592$	9.39693	−	3.42020i	0.386211	−	0.140569i
$593$	−3.64661	−	20.6810i	−0.149748	−	0.849265i	−0.963431	−	0.267956i	$-0.913652\pi$
$593$	−3.64661	−	20.6810i	−0.149748	−	0.849265i	0.813683	−	0.581309i	$-0.197459\pi$
$594$	2.60472	−	14.7721i	0.106873	−	0.606107i
$595$		0			0
$596$	−9.00000	−	15.5885i	−0.368654	−	0.638528i
$597$	5.00000	−	8.66025i	0.204636	−	0.354441i
$598$	9.19253	−	7.71345i	0.375911	−	0.315426i
$599$	−4.59627	+	3.85673i	−0.187798	+	0.157582i	−0.731840	−	0.681477i	$-0.761338\pi$
$599$	−4.59627	+	3.85673i	−0.187798	+	0.157582i	0.544041	+	0.839059i	$0.316894\pi$
$600$	−2.50000	+	4.33013i	−0.102062	+	0.176777i
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	0.967600	−	0.252486i	$-0.0812483\pi$
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	−0.702460	+	0.711723i	$0.747915\pi$
$602$	15.0351	+	5.47232i	0.612784	+	0.223035i
$603$	2.43107	−	13.7873i	0.0990010	−	0.561463i
$604$	−1.73648	−	9.84808i	−0.0706564	−	0.400713i
$605$		0			0
$606$		0			0
$607$	20.0000			0.811775			0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000			0.811775			0.405887	+	0.913923i	$0.366962\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	2.08378	+	11.8177i	0.0842317	+	0.477702i
$613$	0.347296	−	1.96962i	0.0140272	−	0.0795520i	−0.976991	−	0.213282i	$-0.931585\pi$
$613$	0.347296	−	1.96962i	0.0140272	−	0.0795520i	0.991018	+	0.133730i	$0.0426956\pi$
$614$	−6.57785	−	2.39414i	−0.265460	−	0.0966197i
$615$		0			0
$616$	−6.00000	+	10.3923i	−0.241747	+	0.418718i
$617$	2.29813	−	1.92836i	0.0925194	−	0.0776330i	−0.595355	−	0.803463i	$-0.702989\pi$
$617$	2.29813	−	1.92836i	0.0925194	−	0.0776330i	0.687874	+	0.725830i	$0.258544\pi$
$618$	−1.53209	+	1.28558i	−0.0616297	+	0.0517134i
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$620$		0			0
$621$	−28.1908	−	10.2606i	−1.13126	−	0.411744i
$622$	5.20945	−	29.5442i	0.208880	−	1.18462i
$623$	−4.16756	−	23.6354i	−0.166970	−	0.946932i
$624$	−1.87939	+	0.684040i	−0.0752356	+	0.0273835i
$625$	19.1511	+	16.0697i	0.766044	+	0.642788i
$626$	19.0000			0.759393
$627$		0			0
$628$	−16.0000			−0.638470
$629$	45.9627	+	38.5673i	1.83265	+	1.53778i
$630$		0			0
$631$	−4.86215	−	27.5746i	−0.193559	−	1.09773i	−0.914456	−	0.404686i	$-0.867381\pi$
$631$	−4.86215	−	27.5746i	−0.193559	−	1.09773i	0.720897	−	0.693042i	$-0.243730\pi$
$632$	0.694593	−	3.93923i	0.0276294	−	0.156694i
$633$	−18.7939	−	6.84040i	−0.746989	−	0.271882i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$	4.59627	−	3.85673i	0.182254	−	0.152929i
$637$	13.7888	−	11.5702i	0.546332	−	0.458427i
$638$		0			0
$639$	−6.00000	−	10.3923i	−0.237356	−	0.411113i
$640$		0			0
$641$	−6.77228	+	38.4075i	−0.267489	+	1.51701i	0.494364	+	0.869255i	$0.335401\pi$
$641$	−6.77228	+	38.4075i	−0.267489	+	1.51701i	−0.761853	+	0.647750i	$0.775710\pi$
$642$		0			0
$643$	40.4068	−	14.7069i	1.59349	−	0.579982i	0.615407	−	0.788209i	$-0.288991\pi$
$643$	40.4068	−	14.7069i	1.59349	−	0.579982i	0.978081	+	0.208227i	$0.0667693\pi$
$644$	18.3851	+	15.4269i	0.724473	+	0.607905i
$645$		0			0
$646$		0			0
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	−0.766044	−	0.642788i	−0.0300931	−	0.0252511i
$649$	25.3717	−	9.23454i	0.995926	−	0.362488i
$650$	1.73648	+	9.84808i	0.0681104	+	0.386273i
$651$	−1.38919	+	7.87846i	−0.0544465	+	0.308781i
$652$	17.8542	+	6.49838i	0.699223	+	0.254496i
$653$	6.00000	+	10.3923i	0.234798	+	0.406682i	0.959214	−	0.282681i	$-0.0912238\pi$
$653$	6.00000	+	10.3923i	0.234798	+	0.406682i	−0.724416	+	0.689363i	$0.757890\pi$
$654$	−8.00000	+	13.8564i	−0.312825	+	0.541828i
$655$		0			0
$656$	6.89440	−	5.78509i	0.269181	−	0.225870i
$657$	−1.00000	+	1.73205i	−0.0390137	+	0.0675737i
$658$		0			0
$659$	−33.8289	−	12.3127i	−1.31779	−	0.479636i	−0.415039	−	0.909804i	$-0.636232\pi$
$659$	−33.8289	−	12.3127i	−1.31779	−	0.479636i	−0.902749	+	0.430168i	$0.858454\pi$
$660$		0			0
$661$	−6.94593	−	39.3923i	−0.270165	−	1.53218i	−0.753912	−	0.656975i	$-0.771836\pi$
$661$	−6.94593	−	39.3923i	−0.270165	−	1.53218i	0.483747	−	0.875208i	$-0.339276\pi$
$662$	4.69846	−	1.71010i	0.182611	−	0.0664650i
$663$	−9.19253	−	7.71345i	−0.357008	−	0.299566i
$664$	−3.00000			−0.116423
$665$		0			0
$666$	−20.0000			−0.774984
$667$		0			0
$668$	22.5526	−	8.20848i	0.872587	−	0.317596i
$669$	2.43107	+	13.7873i	0.0939908	+	0.533048i
$670$		0			0
$671$	11.2763	+	4.10424i	0.435317	+	0.158442i
$672$	−2.00000	−	3.46410i	−0.0771517	−	0.133631i
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	−0.968818	−	0.247774i	$-0.920301\pi$
$673$	−7.00000	+	12.1244i	−0.269830	+	0.467360i	0.698988	+	0.715134i	$0.253634\pi$
$674$	−8.42649	+	7.07066i	−0.324576	+	0.272352i
$675$	19.1511	−	16.0697i	0.737127	−	0.618523i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	0.914867	+	0.403755i	$0.132295\pi$
$677$	21.0000	+	36.3731i	0.807096	+	1.39793i	−0.107772	+	0.994176i	$0.534372\pi$
$678$	14.0954	+	5.13030i	0.541330	+	0.197028i
$679$	−11.8081	+	66.9669i	−0.453152	+	2.56995i
$680$		0			0
$681$	−2.81908	+	1.02606i	−0.108027	+	0.0393187i
$682$	−4.59627	−	3.85673i	−0.176000	−	0.147682i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$		0			0
$686$	6.12836	+	5.14230i	0.233982	+	0.196334i
$687$	15.0351	−	5.47232i	0.573624	−	0.208782i
$688$	−0.694593	−	3.93923i	−0.0264811	−	0.150182i
$689$	2.08378	−	11.8177i	0.0793856	−	0.450218i
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	−3.00000	+	5.19615i	−0.114043	+	0.197528i
$693$	18.3851	−	15.4269i	0.698391	−	0.586020i
$694$	6.89440	−	5.78509i	0.261708	−	0.219599i
$695$		0			0
$696$		0			0
$697$	50.7434	+	18.4691i	1.92204	+	0.699567i
$698$	0.694593	−	3.93923i	0.0262907	−	0.149102i
$699$	0.520945	+	2.95442i	0.0197039	+	0.111747i
$700$	−18.7939	+	6.84040i	−0.710341	+	0.258543i
$701$	−18.3851	−	15.4269i	−0.694394	−	0.582666i	0.225778	−	0.974179i	$-0.427507\pi$
$701$	−18.3851	−	15.4269i	−0.694394	−	0.582666i	−0.920173	+	0.391513i	$0.871952\pi$
$702$	10.0000			0.377426
$703$		0			0
$704$	3.00000			0.113067
$705$		0			0
$706$	2.81908	−	1.02606i	0.106097	−	0.0386163i
$707$		0			0
$708$	−1.56283	+	8.86327i	−0.0587349	+	0.333102i
$709$	−13.1557	−	4.78828i	−0.494073	−	0.179828i	0.0829535	−	0.996553i	$-0.473565\pi$
$709$	−13.1557	−	4.78828i	−0.494073	−	0.179828i	−0.577026	+	0.816726i	$0.695787\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	−4.59627	+	3.85673i	−0.172252	+	0.144537i
$713$	−9.19253	+	7.71345i	−0.344263	+	0.288871i
$714$	12.0000	−	20.7846i	0.449089	−	0.777844i
$715$		0			0
$716$	−8.45723	−	3.07818i	−0.316062	−	0.115037i
$717$	−2.08378	+	11.8177i	−0.0778201	+	0.441340i
$718$	1.04189	+	5.90885i	0.0388830	+	0.220516i
$719$	−28.1908	+	10.2606i	−1.05134	+	0.382656i	−0.809168	−	0.587578i	$-0.800082\pi$
$719$	−28.1908	+	10.2606i	−1.05134	+	0.382656i	−0.242171	+	0.970234i	$0.577859\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$		0			0
$723$	5.00000			0.185952
$724$	1.53209	+	1.28558i	0.0569396	+	0.0477780i
$725$		0			0
$726$	0.347296	+	1.96962i	0.0128894	+	0.0730993i
$727$	5.55674	−	31.5138i	0.206088	−	1.16878i	−0.689630	−	0.724162i	$-0.742227\pi$
$727$	5.55674	−	31.5138i	0.206088	−	1.16878i	0.895718	−	0.444622i	$-0.146662\pi$
$728$	−7.51754	−	2.73616i	−0.278619	−	0.101409i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$		0			0
$731$	18.3851	−	15.4269i	0.679996	−	0.570585i
$732$	−3.06418	+	2.57115i	−0.113255	+	0.0950325i
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	−11.0000	−	19.0526i	−0.406017	−	0.703243i
$735$		0			0
$736$	1.04189	−	5.90885i	0.0384045	−	0.217803i
$737$	−3.64661	−	20.6810i	−0.134325	−	0.761793i
$738$	−16.9145	+	6.15636i	−0.622630	+	0.226619i
$739$	26.8116	+	22.4976i	0.986279	+	0.827586i	0.985025	−	0.172413i	$-0.0551563\pi$
$739$	26.8116	+	22.4976i	0.986279	+	0.827586i	0.00125424	+	0.999999i	$0.499601\pi$
$740$		0			0
$741$		0			0
$742$	24.0000			0.881068
$743$	−13.7888	−	11.5702i	−0.505862	−	0.424469i	0.353808	−	0.935318i	$-0.384887\pi$
$743$	−13.7888	−	11.5702i	−0.505862	−	0.424469i	−0.859670	+	0.510849i	$0.829331\pi$
$744$	1.87939	−	0.684040i	0.0689016	−	0.0250781i
$745$		0			0
$746$	0.694593	−	3.93923i	0.0254308	−	0.144225i
$747$	5.63816	+	2.05212i	0.206289	+	0.0750832i
$748$	9.00000	+	15.5885i	0.329073	+	0.569970i
$749$		0			0
$750$		0			0
$751$	29.1097	−	24.4259i	1.06223	−	0.891315i	0.0679018	−	0.997692i	$-0.478370\pi$
$751$	29.1097	−	24.4259i	1.06223	−	0.891315i	0.994326	+	0.106377i	$0.0339251\pi$
$752$		0			0
$753$	1.50000	+	2.59808i	0.0546630	+	0.0946792i
$754$		0			0
$755$		0			0
$756$	3.47296	+	19.6962i	0.126310	+	0.716342i
$757$	9.39693	−	3.42020i	0.341537	−	0.124309i	−0.165557	−	0.986200i	$-0.552942\pi$
$757$	9.39693	−	3.42020i	0.341537	−	0.124309i	0.507094	+	0.861891i	$0.330720\pi$
$758$	21.4492	+	17.9981i	0.779072	+	0.653719i
$759$	−18.0000			−0.653359
$760$		0			0
$761$	−39.0000			−1.41375			−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000			−1.41375			−0.706874	+	0.707339i	$0.749895\pi$
$762$	−1.53209	−	1.28558i	−0.0555017	−	0.0465715i
$763$	−60.1403	+	21.8893i	−2.17723	+	0.792445i
$764$	2.08378	+	11.8177i	0.0753884	+	0.427549i
$765$		0			0
$766$	−33.8289	−	12.3127i	−1.22229	−	0.444877i
$767$	9.00000	+	15.5885i	0.324971	+	0.562867i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	1.53209	−	1.28558i	0.0552485	−	0.0463590i	−0.614745	−	0.788726i	$-0.710741\pi$
$769$	1.53209	−	1.28558i	0.0552485	−	0.0463590i	0.669994	+	0.742367i	$0.266297\pi$
$770$		0			0
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$	−1.00000	−	1.73205i	−0.0359908	−	0.0623379i
$773$	45.1052	+	16.4170i	1.62232	+	0.590477i	0.983823	−	0.179144i	$-0.0573329\pi$
$773$	45.1052	+	16.4170i	1.62232	+	0.590477i	0.638500	+	0.769622i	$0.279555\pi$
$774$	−1.38919	+	7.87846i	−0.0499332	+	0.283185i
$775$	−1.73648	−	9.84808i	−0.0623763	−	0.353753i
$776$	15.9748	−	5.81434i	0.573461	−	0.208723i
$777$	30.6418	+	25.7115i	1.09927	+	0.922395i
$778$	36.0000			1.29066
$779$		0			0
$780$		0			0
$781$	−13.7888	−	11.5702i	−0.493402	−	0.414013i
$782$	33.8289	−	12.3127i	1.20972	−	0.440302i
$783$		0			0
$784$	1.56283	−	8.86327i	0.0558155	−	0.316545i
$785$		0			0
$786$	4.50000	+	7.79423i	0.160510	+	0.278011i
$787$	3.50000	−	6.06218i	0.124762	−	0.216093i	−0.796878	−	0.604140i	$-0.793517\pi$
$787$	3.50000	−	6.06218i	0.124762	−	0.216093i	0.921640	+	0.388047i	$0.126850\pi$
$788$	13.7888	−	11.5702i	0.491206	−	0.412170i
$789$	−9.19253	+	7.71345i	−0.327263	+	0.274606i
$790$		0			0
$791$	30.0000	+	51.9615i	1.06668	+	1.84754i
$792$	−5.63816	−	2.05212i	−0.200343	−	0.0729189i
$793$	−1.38919	+	7.87846i	−0.0493314	+	0.279772i
$794$	1.73648	+	9.84808i	0.0616254	+	0.349495i
$795$		0			0
$796$	−7.66044	−	6.42788i	−0.271517	−	0.227830i
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$		0			0
$799$		0			0
$800$	3.83022	+	3.21394i	0.135419	+	0.113630i
$801$	11.2763	−	4.10424i	0.398429	−	0.145016i
$802$	4.68850	+	26.5898i	0.165557	+	0.938919i
$803$	−0.520945	+	2.95442i	−0.0183837	+	0.104259i
$804$	6.57785	+	2.39414i	0.231983	+	0.0844348i
$805$		0			0
$806$	2.00000	−	3.46410i	0.0704470	−	0.122018i
$807$	9.19253	−	7.71345i	0.323592	−	0.271526i
$808$		0			0
$809$	−22.5000	+	38.9711i	−0.791058	+	1.37015i	0.134255	+	0.990947i	$0.457136\pi$
$809$	−22.5000	+	38.9711i	−0.791058	+	1.37015i	−0.925312	+	0.379206i	$0.876197\pi$
$810$		0			0
$811$	15.0351	+	5.47232i	0.527953	+	0.192159i	0.592224	−	0.805773i	$-0.298250\pi$
$811$	15.0351	+	5.47232i	0.527953	+	0.192159i	−0.0642710	+	0.997932i	$0.520472\pi$
$812$		0			0
$813$	−2.77837	−	15.7569i	−0.0974417	−	0.552619i
$814$	−28.1908	+	10.2606i	−0.988086	+	0.359634i
$815$		0			0
$816$	−6.00000			−0.210042
$817$		0			0
$818$	−5.00000			−0.174821
$819$	12.2567	+	10.2846i	0.428284	+	0.359373i
$820$		0			0
$821$	3.12567	+	17.7265i	0.109087	+	0.618660i	0.989509	+	0.144471i	$0.0461479\pi$
$821$	3.12567	+	17.7265i	0.109087	+	0.618660i	−0.880423	+	0.474190i	$0.842741\pi$
$822$	−1.56283	+	8.86327i	−0.0545101	+	0.309142i
$823$	−13.1557	−	4.78828i	−0.458579	−	0.166909i	0.102393	−	0.994744i	$-0.467350\pi$
$823$	−13.1557	−	4.78828i	−0.458579	−	0.166909i	−0.560972	+	0.827835i	$0.689572\pi$
$824$	1.00000	+	1.73205i	0.0348367	+	0.0603388i
$825$	7.50000	−	12.9904i	0.261116	−	0.452267i
$826$	−27.5776	+	23.1404i	−0.959547	+	0.805156i
$827$	−29.8757	+	25.0687i	−1.03888	+	0.871725i	−0.991881	−	0.127170i	$-0.959411\pi$
$827$	−29.8757	+	25.0687i	−1.03888	+	0.871725i	−0.0470001	+	0.998895i	$0.514966\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	−22.0000	−	38.1051i	−0.764092	−	1.32345i	−0.940726	−	0.339169i	$-0.889854\pi$
$829$	−22.0000	−	38.1051i	−0.764092	−	1.32345i	0.176634	−	0.984277i	$-0.443479\pi$
$830$		0			0
$831$	1.38919	−	7.87846i	0.0481903	−	0.273301i
$832$	0.347296	+	1.96962i	0.0120403	+	0.0682841i
$833$	50.7434	−	18.4691i	1.75815	−	0.639916i
$834$	−8.42649	−	7.07066i	−0.291785	−	0.244837i
$835$		0			0
$836$		0			0
$837$	−10.0000			−0.345651
$838$	9.19253	+	7.71345i	0.317551	+	0.266457i
$839$	11.2763	−	4.10424i	0.389302	−	0.141694i	−0.139951	−	0.990158i	$-0.544695\pi$
$839$	11.2763	−	4.10424i	0.389302	−	0.141694i	0.529253	+	0.848464i	$0.322472\pi$
$840$		0			0
$841$	−5.03580	+	28.5594i	−0.173648	+	0.984808i
$842$	−9.39693	−	3.42020i	−0.323839	−	0.117868i
$843$	−13.5000	−	23.3827i	−0.464965	−	0.805342i
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$		0			0
$846$		0			0
$847$	−4.00000	+	6.92820i	−0.137442	+	0.238056i
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$	−4.69846	−	1.71010i	−0.161251	−	0.0586905i
$850$	−5.20945	+	29.5442i	−0.178683	+	1.01336i
$851$	10.4189	+	59.0885i	0.357155	+	2.02553i
$852$	5.63816	−	2.05212i	0.193160	−	0.0703045i
$853$	−16.8530	−	14.1413i	−0.577035	−	0.484190i	0.306937	−	0.951730i	$-0.400696\pi$
$853$	−16.8530	−	14.1413i	−0.577035	−	0.484190i	−0.883972	+	0.467540i	$0.845140\pi$
$854$	−16.0000			−0.547509
$855$		0			0
$856$		0			0
$857$	−2.29813	−	1.92836i	−0.0785027	−	0.0658716i	0.602692	−	0.797974i	$-0.294095\pi$
$857$	−2.29813	−	1.92836i	−0.0785027	−	0.0658716i	−0.681195	+	0.732102i	$0.738539\pi$
$858$	5.63816	−	2.05212i	0.192483	−	0.0700583i
$859$	−7.46687	−	42.3467i	−0.254766	−	1.44485i	−0.796672	−	0.604412i	$-0.793408\pi$
$859$	−7.46687	−	42.3467i	−0.254766	−	1.44485i	0.541905	−	0.840440i	$-0.317703\pi$
$860$		0			0
$861$	33.8289	+	12.3127i	1.15289	+	0.419617i
$862$	−15.0000	−	25.9808i	−0.510902	−	0.884908i
$863$	−9.00000	+	15.5885i	−0.306364	+	0.530637i	−0.977564	−	0.210639i	$-0.932446\pi$
$863$	−9.00000	+	15.5885i	−0.306364	+	0.530637i	0.671200	+	0.741276i	$0.265779\pi$
$864$	3.83022	−	3.21394i	0.130307	−	0.109340i
$865$		0			0
$866$	13.0000	−	22.5167i	0.441758	−	0.765147i
$867$	−9.50000	−	16.4545i	−0.322637	−	0.558824i
$868$	7.51754	+	2.73616i	0.255162	+	0.0928714i
$869$	−2.08378	+	11.8177i	−0.0706873	+	0.400888i
$870$		0			0
$871$	13.1557	−	4.78828i	0.445764	−	0.162245i
$872$	12.2567	+	10.2846i	0.415065	+	0.348281i
$873$	−34.0000			−1.15073
$874$		0			0
$875$		0			0
$876$	−0.766044	−	0.642788i	−0.0258822	−	0.0217178i
$877$	−18.7939	+	6.84040i	−0.634623	+	0.230984i	−0.639242	−	0.769005i	$-0.720752\pi$
$877$	−18.7939	+	6.84040i	−0.634623	+	0.230984i	0.00461905	+	0.999989i	$0.498530\pi$
$878$	−2.43107	−	13.7873i	−0.0820448	−	0.465299i
$879$	4.16756	−	23.6354i	0.140568	−	0.797202i
$880$		0			0
$881$	4.50000	+	7.79423i	0.151609	+	0.262594i	0.931819	−	0.362923i	$-0.118221\pi$
$881$	4.50000	+	7.79423i	0.151609	+	0.262594i	−0.780210	+	0.625517i	$0.784888\pi$
$882$	−9.00000	+	15.5885i	−0.303046	+	0.524891i
$883$	−14.5548	+	12.2130i	−0.489810	+	0.410999i	−0.853958	−	0.520342i	$-0.825805\pi$
$883$	−14.5548	+	12.2130i	−0.489810	+	0.410999i	0.364149	+	0.931341i	$0.381360\pi$
$884$	−9.19253	+	7.71345i	−0.309178	+	0.259431i
$885$		0			0
$886$	4.50000	+	7.79423i	0.151180	+	0.261852i
$887$	−45.1052	−	16.4170i	−1.51449	−	0.551228i	−0.554722	−	0.832036i	$-0.687175\pi$
$887$	−45.1052	−	16.4170i	−1.51449	−	0.551228i	−0.959764	+	0.280808i	$0.909398\pi$
$888$	1.73648	−	9.84808i	0.0582725	−	0.330480i
$889$	−1.38919	−	7.87846i	−0.0465918	−	0.264235i
$890$		0			0
$891$	2.29813	+	1.92836i	0.0769904	+	0.0646026i
$892$	14.0000			0.468755
$893$		0			0
$894$	−18.0000			−0.602010
$895$		0			0
$896$	−3.75877	+	1.36808i	−0.125572	+	0.0457044i
$897$	−2.08378	−	11.8177i	−0.0695753	−	0.394581i
$898$	−1.56283	+	8.86327i	−0.0521524	+	0.295771i
$899$		0			0
$900$	−5.00000	−	8.66025i	−0.166667	−	0.288675i
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$	−20.6832	+	17.3553i	−0.688675	+	0.577867i
$903$	12.2567	−	10.2846i	0.407878	−	0.342250i
$904$	7.50000	−	12.9904i	0.249446	−	0.432054i
$905$		0			0
$906$	−9.39693	−	3.42020i	−0.312192	−	0.113629i
$907$	2.95202	−	16.7417i	0.0980202	−	0.555900i	−0.895760	−	0.444538i	$-0.853368\pi$
$907$	2.95202	−	16.7417i	0.0980202	−	0.555900i	0.993780	−	0.111362i	$-0.0355212\pi$
$908$	0.520945	+	2.95442i	0.0172882	+	0.0980460i
$909$		0			0
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$		0			0
$913$	9.00000			0.297857
$914$	−3.83022	−	3.21394i	−0.126692	−	0.106308i
$915$		0			0
$916$	−2.77837	−	15.7569i	−0.0918000	−	0.520623i
$917$	−6.25133	+	35.4531i	−0.206437	+	1.17076i
$918$	28.1908	+	10.2606i	0.930434	+	0.338650i
$919$	5.00000	+	8.66025i	0.164935	+	0.285675i	0.936632	−	0.350315i	$-0.113925\pi$
$919$	5.00000	+	8.66025i	0.164935	+	0.285675i	−0.771697	+	0.635990i	$0.780592\pi$
$920$		0			0
$921$	−5.36231	+	4.49951i	−0.176694	+	0.148264i
$922$	−4.59627	+	3.85673i	−0.151370	+	0.127014i
$923$	6.00000	−	10.3923i	0.197492	−	0.342067i
$924$	6.00000	+	10.3923i	0.197386	+	0.341882i
$925$	−46.9846	−	17.1010i	−1.54485	−	0.562278i
$926$	5.90404	−	33.4835i	0.194019	−	1.10033i
$927$	−0.694593	−	3.93923i	−0.0228134	−	0.129381i
$928$		0			0
$929$	−2.29813	−	1.92836i	−0.0753993	−	0.0632675i	0.604309	−	0.796750i	$-0.293449\pi$
$929$	−2.29813	−	1.92836i	−0.0753993	−	0.0632675i	−0.679708	+	0.733482i	$0.737894\pi$
$930$		0			0
$931$		0			0
$932$	3.00000			0.0982683
$933$	−22.9813	−	19.2836i	−0.752375	−	0.631318i
$934$	−25.3717	+	9.23454i	−0.830187	+	0.302164i
$935$		0			0
$936$	0.694593	−	3.93923i	0.0227035	−	0.128758i
$937$	−32.8892	−	11.9707i	−1.07444	−	0.391066i	−0.256608	−	0.966516i	$-0.582605\pi$
$937$	−32.8892	−	11.9707i	−1.07444	−	0.391066i	−0.817837	+	0.575450i	$0.804827\pi$
$938$	14.0000	+	24.2487i	0.457116	+	0.791748i
$939$	9.50000	−	16.4545i	0.310021	−	0.536972i
$940$		0			0
$941$	−32.1739	+	26.9971i	−1.04884	+	0.880080i	−0.992971	−	0.118359i	$-0.962237\pi$
$941$	−32.1739	+	26.9971i	−1.04884	+	0.880080i	−0.0558672	+	0.998438i	$0.517792\pi$
$942$	−8.00000	+	13.8564i	−0.260654	+	0.451466i
$943$	27.0000	+	46.7654i	0.879241	+	1.52289i
$944$	8.45723	+	3.07818i	0.275260	+	0.100186i
$945$		0			0
$946$	2.08378	+	11.8177i	0.0677495	+	0.384226i
$947$	−56.3816	+	20.5212i	−1.83215	+	0.666850i	−0.839882	+	0.542768i	$0.817376\pi$
$947$	−56.3816	+	20.5212i	−1.83215	+	0.666850i	−0.992272	+	0.124081i	$0.960402\pi$
$948$	−3.06418	−	2.57115i	−0.0995199	−	0.0835071i
$949$	−2.00000			−0.0649227
$950$		0			0
$951$	−18.0000			−0.583690
$952$	−18.3851	−	15.4269i	−0.595863	−	0.499989i
$953$	14.0954	−	5.13030i	0.456594	−	0.166187i	−0.103476	−	0.994632i	$-0.532996\pi$
$953$	14.0954	−	5.13030i	0.456594	−	0.166187i	0.560070	+	0.828445i	$0.310774\pi$
$954$	2.08378	+	11.8177i	0.0674648	+	0.382612i
$955$		0			0
$956$	11.2763	+	4.10424i	0.364702	+	0.132741i
$957$		0			0
$958$	18.0000	−	31.1769i	0.581554	−	1.00728i
$959$	−27.5776	+	23.1404i	−0.890527	+	0.747241i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	−10.0000	−	17.3205i	−0.322413	−	0.558436i
$963$		0			0
$964$	0.868241	−	4.92404i	0.0279642	−	0.158593i
$965$		0			0
$966$	22.5526	−	8.20848i	0.725619	−	0.264104i
$967$	−26.0455	−	21.8548i	−0.837567	−	0.702802i	0.119448	−	0.992840i	$-0.461888\pi$
$967$	−26.0455	−	21.8548i	−0.837567	−	0.702802i	−0.957015	+	0.290038i	$0.906332\pi$
$968$	2.00000			0.0642824
$969$		0			0
$970$		0			0
$971$	16.0869	+	13.4985i	0.516254	+	0.433189i	0.863324	−	0.504651i	$-0.168379\pi$
$971$	16.0869	+	13.4985i	0.516254	+	0.433189i	−0.347069	+	0.937839i	$0.612823\pi$
$972$	−15.0351	+	5.47232i	−0.482250	+	0.175525i
$973$	−7.64052	−	43.3315i	−0.244944	−	1.38915i
$974$	−0.347296	+	1.96962i	−0.0111281	+	0.0631106i
$975$	9.39693	+	3.42020i	0.300942	+	0.109534i
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	−16.5000	+	28.5788i	−0.527882	+	0.914318i	0.471590	+	0.881818i	$0.343680\pi$
$977$	−16.5000	+	28.5788i	−0.527882	+	0.914318i	−0.999472	+	0.0325001i	$0.989653\pi$
$978$	14.5548	−	12.2130i	0.465413	−	0.390528i
$979$	13.7888	−	11.5702i	0.440692	−	0.369784i
$980$		0			0
$981$	−16.0000	−	27.7128i	−0.510841	−	0.884802i
$982$		0			0
$983$	4.16756	−	23.6354i	0.132924	−	0.753852i	−0.843358	−	0.537352i	$-0.819425\pi$
$983$	4.16756	−	23.6354i	0.132924	−	0.753852i	0.976283	−	0.216500i	$-0.0694641\pi$
$984$	−1.56283	−	8.86327i	−0.0498213	−	0.282551i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	24.0000			0.763156
$990$		0			0
$991$	−7.51754	+	2.73616i	−0.238803	+	0.0869170i	−0.458649	−	0.888617i	$-0.651667\pi$
$991$	−7.51754	+	2.73616i	−0.238803	+	0.0869170i	0.219847	+	0.975534i	$0.429444\pi$
$992$	−0.347296	−	1.96962i	−0.0110267	−	0.0625354i
$993$	0.868241	−	4.92404i	0.0275528	−	0.156260i
$994$	22.5526	+	8.20848i	0.715326	+	0.260357i
$995$		0			0
$996$	−1.50000	+	2.59808i	−0.0475293	+	0.0823232i
$997$	−3.06418	+	2.57115i	−0.0970435	+	0.0814292i	−0.690019	−	0.723792i	$-0.742398\pi$
$997$	−3.06418	+	2.57115i	−0.0970435	+	0.0814292i	0.592975	+	0.805221i	$0.297953\pi$
$998$	19.1511	−	16.0697i	0.606218	−	0.508677i
$999$	−25.0000	+	43.3013i	−0.790965	+	1.36999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.j.415.1		6
19.2	odd	18		722.2.c.b.653.1		2
19.3	odd	18		722.2.c.b.429.1		2
19.4	even	9	inner	722.2.e.j.389.1		6
19.5	even	9		722.2.a.c.1.1		1
19.6	even	9	inner	722.2.e.j.595.1		6
19.7	even	3	inner	722.2.e.j.423.1		6
19.8	odd	6		722.2.e.i.245.1		6
19.9	even	9	inner	722.2.e.j.99.1		6
19.10	odd	18		722.2.e.i.99.1		6
19.11	even	3	inner	722.2.e.j.245.1		6
19.12	odd	6		722.2.e.i.423.1		6
19.13	odd	18		722.2.e.i.595.1		6
19.14	odd	18		722.2.a.d.1.1		1
19.15	odd	18		722.2.e.i.389.1		6
19.16	even	9		38.2.c.a.11.1	yes	2
19.17	even	9		38.2.c.a.7.1	✓	2
19.18	odd	2		722.2.e.i.415.1		6
57.5	odd	18		6498.2.a.s.1.1		1
57.14	even	18		6498.2.a.e.1.1		1
57.17	odd	18		342.2.g.b.235.1		2
57.35	odd	18		342.2.g.b.163.1		2
76.35	odd	18		304.2.i.c.49.1		2
76.43	odd	18		5776.2.a.g.1.1		1
76.55	odd	18		304.2.i.c.273.1		2
76.71	even	18		5776.2.a.n.1.1		1
95.17	odd	36		950.2.j.e.349.1		4
95.54	even	18		950.2.e.d.201.1		2
95.73	odd	36		950.2.j.e.49.1		4
95.74	even	18		950.2.e.d.501.1		2
95.92	odd	36		950.2.j.e.49.2		4
95.93	odd	36		950.2.j.e.349.2		4
152.35	odd	18		1216.2.i.d.961.1		2
152.93	even	18		1216.2.i.h.577.1		2
152.131	odd	18		1216.2.i.d.577.1		2
152.149	even	18		1216.2.i.h.961.1		2
228.35	even	18		2736.2.s.m.1873.1		2
228.131	even	18		2736.2.s.m.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.a.7.1	✓	2	19.17	even	9
38.2.c.a.11.1	yes	2	19.16	even	9
304.2.i.c.49.1		2	76.35	odd	18
304.2.i.c.273.1		2	76.55	odd	18
342.2.g.b.163.1		2	57.35	odd	18
342.2.g.b.235.1		2	57.17	odd	18
722.2.a.c.1.1		1	19.5	even	9
722.2.a.d.1.1		1	19.14	odd	18
722.2.c.b.429.1		2	19.3	odd	18
722.2.c.b.653.1		2	19.2	odd	18
722.2.e.i.99.1		6	19.10	odd	18
722.2.e.i.245.1		6	19.8	odd	6
722.2.e.i.389.1		6	19.15	odd	18
722.2.e.i.415.1		6	19.18	odd	2
722.2.e.i.423.1		6	19.12	odd	6
722.2.e.i.595.1		6	19.13	odd	18
722.2.e.j.99.1		6	19.9	even	9	inner
722.2.e.j.245.1		6	19.11	even	3	inner
722.2.e.j.389.1		6	19.4	even	9	inner
722.2.e.j.415.1		6	1.1	even	1	trivial
722.2.e.j.423.1		6	19.7	even	3	inner
722.2.e.j.595.1		6	19.6	even	9	inner
950.2.e.d.201.1		2	95.54	even	18
950.2.e.d.501.1		2	95.74	even	18
950.2.j.e.49.1		4	95.73	odd	36
950.2.j.e.49.2		4	95.92	odd	36
950.2.j.e.349.1		4	95.17	odd	36
950.2.j.e.349.2		4	95.93	odd	36
1216.2.i.d.577.1		2	152.131	odd	18
1216.2.i.d.961.1		2	152.35	odd	18
1216.2.i.h.577.1		2	152.93	even	18
1216.2.i.h.961.1		2	152.149	even	18
2736.2.s.m.577.1		2	228.131	even	18
2736.2.s.m.1873.1		2	228.35	even	18
5776.2.a.g.1.1		1	76.43	odd	18
5776.2.a.n.1.1		1	76.71	even	18
6498.2.a.e.1.1		1	57.14	even	18
6498.2.a.s.1.1		1	57.5	odd	18

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(2.00000 + 3.46410i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.939693 + 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(2.00000 + 3.46410i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-1.87939 - 0.684040i) q^{13} +(0.694593 - 3.93923i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(-4.59627 - 3.85673i) q^{17} +2.00000 q^{18} +(-3.06418 - 2.57115i) q^{21} +(2.81908 - 1.02606i) q^{22} +(-1.04189 - 5.90885i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(4.69846 + 1.71010i) q^{25} +(1.00000 + 1.73205i) q^{26} +(2.50000 - 4.33013i) q^{27} +(-3.06418 + 2.57115i) q^{28} +(-1.00000 - 1.73205i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.520945 - 2.95442i) q^{33} +(1.04189 + 5.90885i) q^{34} +(-1.53209 - 1.28558i) q^{36} -10.0000 q^{37} +2.00000 q^{39} +(-8.45723 + 3.07818i) q^{41} +(0.694593 + 3.93923i) q^{42} +(-0.694593 + 3.93923i) q^{43} +(-2.81908 - 1.02606i) q^{44} +(-3.00000 + 5.19615i) q^{46} +(0.766044 - 0.642788i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(-2.50000 - 4.33013i) q^{50} +(5.63816 + 2.05212i) q^{51} +(0.347296 - 1.96962i) q^{52} +(1.04189 + 5.90885i) q^{53} +(-4.69846 + 1.71010i) q^{54} +4.00000 q^{56} +(-6.89440 - 5.78509i) q^{59} +(-0.694593 - 3.93923i) q^{61} +(-0.347296 + 1.96962i) q^{62} +(-7.51754 - 2.73616i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.29813 + 1.92836i) q^{66} +(-5.36231 + 4.49951i) q^{67} +(3.00000 - 5.19615i) q^{68} +(3.00000 + 5.19615i) q^{69} +(-1.04189 + 5.90885i) q^{71} +(0.347296 + 1.96962i) q^{72} +(0.939693 - 0.342020i) q^{73} +(7.66044 + 6.42788i) q^{74} -5.00000 q^{75} -12.0000 q^{77} +(-1.53209 - 1.28558i) q^{78} +(3.75877 - 1.36808i) q^{79} +(0.173648 - 0.984808i) q^{81} +(8.45723 + 3.07818i) q^{82} +(-1.50000 - 2.59808i) q^{83} +(2.00000 - 3.46410i) q^{84} +(3.06418 - 2.57115i) q^{86} +(1.50000 + 2.59808i) q^{88} +(-5.63816 - 2.05212i) q^{89} +(-1.38919 - 7.87846i) q^{91} +(5.63816 - 2.05212i) q^{92} +(1.53209 + 1.28558i) q^{93} -1.00000 q^{96} +(13.0228 + 10.9274i) q^{97} +(8.45723 - 3.07818i) q^{98} +(-1.04189 - 5.90885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{7} + 3 q^{8}+O(q^{10}) \) 6 * q + 12 * q^7 + 3 * q^8	\( 6 q + 12 q^{7} + 3 q^{8} - 9 q^{11} - 3 q^{12} + 12 q^{18} + 6 q^{26} + 15 q^{27} - 6 q^{31} - 60 q^{37} + 12 q^{39} - 18 q^{46} - 27 q^{49} - 15 q^{50} + 24 q^{56} - 3 q^{64} + 18 q^{68} + 18 q^{69} - 30 q^{75} - 72 q^{77} - 9 q^{83} + 12 q^{84} + 9 q^{88} - 6 q^{96}+O(q^{100}) \) 6 * q + 12 * q^7 + 3 * q^8 - 9 * q^11 - 3 * q^12 + 12 * q^18 + 6 * q^26 + 15 * q^27 - 6 * q^31 - 60 * q^37 + 12 * q^39 - 18 * q^46 - 27 * q^49 - 15 * q^50 + 24 * q^56 - 3 * q^64 + 18 * q^68 + 18 * q^69 - 30 * q^75 - 72 * q^77 - 9 * q^83 + 12 * q^84 + 9 * q^88 - 6 * q^96

Introduction

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