LMFDB - Embedded newform 1764.2.b.k.1567.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1567,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("1764.1567");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1212153856.10
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{6} + 10x^{4} - 16x^{2} + 16 $ x^8 - 4x^6 + 10x^4 - 16*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 196)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.1
Root			$-1.07072 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.k.1567.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207107 - 1.39897i) q^{2} +(-1.91421 + 0.579471i) q^{4} -2.61313i q^{5} +(1.20711 + 2.55791i) q^{8} +O(q^{10})$	\(q+(-0.207107 - 1.39897i) q^{2} +(-1.91421 + 0.579471i) q^{4} -2.61313i q^{5} +(1.20711 + 2.55791i) q^{8} +(-3.65568 + 0.541196i) q^{10} +3.95687i q^{11} +1.08239i q^{13} +(3.32843 - 2.21846i) q^{16} -0.317025i q^{17} +5.16991 q^{19} +(1.51423 + 5.00208i) q^{20} +(5.53553 - 0.819496i) q^{22} +2.31788i q^{23} -1.82843 q^{25} +(1.51423 - 0.224171i) q^{26} +6.82843 q^{29} +6.05692 q^{31} +(-3.79289 - 4.19690i) q^{32} +(-0.443508 + 0.0656581i) q^{34} -4.00000 q^{37} +(-1.07072 - 7.23252i) q^{38} +(6.68414 - 3.15432i) q^{40} +2.29610i q^{41} -7.23486i q^{43} +(-2.29289 - 7.57430i) q^{44} +(3.24264 - 0.480049i) q^{46} +4.28289 q^{47} +(0.378680 + 2.55791i) q^{50} +(-0.627215 - 2.07193i) q^{52} -10.4853 q^{53} +10.3398 q^{55} +(-1.41421 - 9.55274i) q^{58} +11.2268 q^{59} +5.41196i q^{61} +(-1.25443 - 8.47343i) q^{62} +(-5.08579 + 6.17534i) q^{64} +2.82843 q^{65} +3.27798i q^{67} +(0.183707 + 0.606854i) q^{68} -14.0167i q^{73} +(0.828427 + 5.59587i) q^{74} +(-9.89630 + 2.99581i) q^{76} +7.91375i q^{79} +(-5.79712 - 8.69760i) q^{80} +(3.21217 - 0.475538i) q^{82} +9.45280 q^{83} -0.828427 q^{85} +(-10.1213 + 1.49839i) q^{86} +(-10.1213 + 4.77637i) q^{88} -5.99162i q^{89} +(-1.34315 - 4.43692i) q^{92} +(-0.887016 - 5.99162i) q^{94} -13.5096i q^{95} +9.23880i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8}+O(q^{10}) $ 8 * q + 4 * q^2 - 4 * q^4 + 4 * q^8	$ 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + 4 q^{16} + 16 q^{22} + 8 q^{25} + 32 q^{29} - 36 q^{32} - 32 q^{37} - 24 q^{44} - 8 q^{46} + 20 q^{50} - 16 q^{53} - 52 q^{64} - 16 q^{74} + 16 q^{85} - 64 q^{86} - 64 q^{88} - 56 q^{92}+O(q^{100}) $ 8 * q + 4 * q^2 - 4 * q^4 + 4 * q^8 + 4 * q^16 + 16 * q^22 + 8 * q^25 + 32 * q^29 - 36 * q^32 - 32 * q^37 - 24 * q^44 - 8 * q^46 + 20 * q^50 - 16 * q^53 - 52 * q^64 - 16 * q^74 + 16 * q^85 - 64 * q^86 - 64 * q^88 - 56 * q^92

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.207107	−	1.39897i	−0.146447	−	0.989219i
$2$	−0.207107	−	1.39897i	−0.146447	−	0.989219i
$3$		0			0
$3$		0			0
$4$	−1.91421	+	0.579471i	−0.957107	+	0.289735i
$5$		−	2.61313i		−	1.16863i	−0.811529	−	0.584313i	$-0.801364\pi$
$5$		−	2.61313i		−	1.16863i	0.811529	−	0.584313i	$-0.198636\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.20711	+	2.55791i	0.426777	+	0.904357i
$9$		0			0
$10$	−3.65568	+	0.541196i	−1.15603	+	0.171141i
$11$			3.95687i			1.19304i	0.802597	+	0.596521i	$0.203451\pi$
$11$			3.95687i			1.19304i	−0.802597	+	0.596521i	$0.796549\pi$
$12$		0			0
$13$			1.08239i			0.300202i	0.988671	+	0.150101i	$0.0479598\pi$
$13$			1.08239i			0.300202i	−0.988671	+	0.150101i	$0.952040\pi$
$14$		0			0
$15$		0			0
$16$	3.32843	−	2.21846i	0.832107	−	0.554615i
$17$		−	0.317025i		−	0.0768899i	−0.999261	−	0.0384450i	$-0.987760\pi$
$17$		−	0.317025i		−	0.0768899i	0.999261	−	0.0384450i	$-0.0122404\pi$
$18$		0			0
$19$	5.16991			1.18606			0.593029	−	0.805181i	$-0.297932\pi$
$19$	5.16991			1.18606			0.593029	+	0.805181i	$0.297932\pi$
$20$	1.51423	+	5.00208i	0.338592	+	1.11850i
$21$		0			0
$22$	5.53553	−	0.819496i	1.18018	−	0.174717i
$23$			2.31788i			0.483312i	0.970362	+	0.241656i	$0.0776906\pi$
$23$			2.31788i			0.483312i	−0.970362	+	0.241656i	$0.922309\pi$
$24$		0			0
$25$	−1.82843			−0.365685
$26$	1.51423	−	0.224171i	0.296965	−	0.0439635i
$27$		0			0
$28$		0			0
$29$	6.82843			1.26801			0.634004	−	0.773330i	$-0.281410\pi$
$29$	6.82843			1.26801			0.634004	+	0.773330i	$0.281410\pi$
$30$		0			0
$31$	6.05692			1.08786			0.543928	−	0.839132i	$-0.316937\pi$
$31$	6.05692			1.08786			0.543928	+	0.839132i	$0.316937\pi$
$32$	−3.79289	−	4.19690i	−0.670495	−	0.741914i
$33$		0			0
$34$	−0.443508	+	0.0656581i	−0.0760610	+	0.0112603i
$35$		0			0
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$	−1.07072	−	7.23252i	−0.173694	−	1.17327i
$39$		0			0
$40$	6.68414	−	3.15432i	1.05685	−	0.498742i
$41$			2.29610i			0.358591i	0.983795	+	0.179295i	$0.0573818\pi$
$41$			2.29610i			0.358591i	−0.983795	+	0.179295i	$0.942618\pi$
$42$		0			0
$43$		−	7.23486i		−	1.10331i	−0.834074	−	0.551653i	$-0.813997\pi$
$43$		−	7.23486i		−	1.10331i	0.834074	−	0.551653i	$-0.186003\pi$
$44$	−2.29289	−	7.57430i	−0.345667	−	1.14187i
$45$		0			0
$46$	3.24264	−	0.480049i	0.478101	−	0.0707794i
$47$	4.28289			0.624724			0.312362	−	0.949963i	$-0.398880\pi$
$47$	4.28289			0.624724			0.312362	+	0.949963i	$0.398880\pi$
$48$		0			0
$49$		0			0
$50$	0.378680	+	2.55791i	0.0535534	+	0.361743i
$51$		0			0
$52$	−0.627215	−	2.07193i	−0.0869790	−	0.287325i
$53$	−10.4853			−1.44026			−0.720132	−	0.693837i	$-0.755919\pi$
$53$	−10.4853			−1.44026			−0.720132	+	0.693837i	$0.755919\pi$
$54$		0			0
$55$	10.3398			1.39422
$56$		0			0
$57$		0			0
$58$	−1.41421	−	9.55274i	−0.185695	−	1.25434i
$59$	11.2268			1.46161			0.730804	−	0.682587i	$-0.239145\pi$
$59$	11.2268			1.46161			0.730804	+	0.682587i	$0.239145\pi$
$60$		0			0
$61$			5.41196i			0.692931i	0.938063	+	0.346465i	$0.112618\pi$
$61$			5.41196i			0.692931i	−0.938063	+	0.346465i	$0.887382\pi$
$62$	−1.25443	−	8.47343i	−0.159313	−	1.07613i
$63$		0			0
$64$	−5.08579	+	6.17534i	−0.635723	+	0.771917i
$65$	2.82843			0.350823
$66$		0			0
$67$			3.27798i			0.400469i	0.979748	+	0.200235i	$0.0641704\pi$
$67$			3.27798i			0.400469i	−0.979748	+	0.200235i	$0.935830\pi$
$68$	0.183707	+	0.606854i	0.0222777	+	0.0735919i
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$		−	14.0167i		−	1.64053i	−0.571983	−	0.820266i	$-0.693826\pi$
$73$		−	14.0167i		−	1.64053i	0.571983	−	0.820266i	$-0.306174\pi$
$74$	0.828427	+	5.59587i	0.0963027	+	0.650506i
$75$		0			0
$76$	−9.89630	+	2.99581i	−1.13518	+	0.343643i
$77$		0			0
$78$		0			0
$79$			7.91375i			0.890366i	0.895440	+	0.445183i	$0.146861\pi$
$79$			7.91375i			0.890366i	−0.895440	+	0.445183i	$0.853139\pi$
$80$	−5.79712	−	8.69760i	−0.648138	−	0.972421i
$81$		0			0
$82$	3.21217	−	0.475538i	0.354725	−	0.0525144i
$83$	9.45280			1.03758			0.518790	−	0.854902i	$-0.326383\pi$
$83$	9.45280			1.03758			0.518790	+	0.854902i	$0.326383\pi$
$84$		0			0
$85$	−0.828427			−0.0898555
$86$	−10.1213	+	1.49839i	−1.09141	+	0.161575i
$87$		0			0
$88$	−10.1213	+	4.77637i	−1.07894	+	0.509163i
$89$		−	5.99162i		−	0.635110i	−0.948240	−	0.317555i	$-0.897138\pi$
$89$		−	5.99162i		−	0.635110i	0.948240	−	0.317555i	$-0.102862\pi$
$90$		0			0
$91$		0			0
$92$	−1.34315	−	4.43692i	−0.140033	−	0.462581i
$93$		0			0
$94$	−0.887016	−	5.99162i	−0.0914887	−	0.617988i
$95$		−	13.5096i		−	1.38606i
$96$		0			0
$97$			9.23880i			0.938058i	0.883183	+	0.469029i	$0.155396\pi$
$97$			9.23880i			0.938058i	−0.883183	+	0.469029i	$0.844604\pi$
$98$		0			0
$99$		0			0
$100$	3.50000	−	1.05952i	0.350000	−	0.105952i
$101$		−	15.2304i		−	1.51548i	−0.652555	−	0.757741i	$-0.726303\pi$
$101$		−	15.2304i		−	1.51548i	0.652555	−	0.757741i	$-0.273697\pi$
$102$		0			0
$103$	−12.1138			−1.19361			−0.596806	−	0.802385i	$-0.703564\pi$
$103$	−12.1138			−1.19361			−0.596806	+	0.802385i	$0.703564\pi$
$104$	−2.76866	+	1.30656i	−0.271489	+	0.128119i
$105$		0			0
$106$	2.17157	+	14.6686i	0.210922	+	1.42474i
$107$			2.31788i			0.224078i	0.993704	+	0.112039i	$0.0357382\pi$
$107$			2.31788i			0.224078i	−0.993704	+	0.112039i	$0.964262\pi$
$108$		0			0
$109$	−5.65685			−0.541828			−0.270914	−	0.962604i	$-0.587326\pi$
$109$	−5.65685			−0.541828			−0.270914	+	0.962604i	$0.587326\pi$
$110$	−2.14144	−	14.4650i	−0.204179	−	1.37919i
$111$		0			0
$112$		0			0
$113$	4.24264			0.399114			0.199557	−	0.979886i	$-0.436050\pi$
$113$	4.24264			0.399114			0.199557	+	0.979886i	$0.436050\pi$
$114$		0			0
$115$	6.05692			0.564811
$116$	−13.0711	+	3.95687i	−1.21362	+	0.367387i
$117$		0			0
$118$	−2.32515	−	15.7060i	−0.214048	−	1.44585i
$119$		0			0
$120$		0			0
$121$	−4.65685			−0.423350
$122$	7.57115	−	1.12085i	0.685460	−	0.101477i
$123$		0			0
$124$	−11.5942	+	3.50981i	−1.04119	+	0.315190i
$125$		−	8.28772i		−	0.741276i
$126$		0			0
$127$		−	10.2316i		−	0.907911i	−0.891024	−	0.453955i	$-0.850013\pi$
$127$		−	10.2316i		−	0.907911i	0.891024	−	0.453955i	$-0.149987\pi$
$128$	9.69239	+	5.83589i	0.856694	+	0.515825i
$129$		0			0
$130$	−0.585786	−	3.95687i	−0.0513769	−	0.347041i
$131$	0.367414			0.0321011			0.0160505	−	0.999871i	$-0.494891\pi$
$131$	0.367414			0.0321011			0.0160505	+	0.999871i	$0.494891\pi$
$132$		0			0
$133$		0			0
$134$	4.58579	−	0.678892i	0.396152	−	0.0586474i
$135$		0			0
$136$	0.810922	−	0.382683i	0.0695360	−	0.0328148i
$137$	8.24264			0.704216			0.352108	−	0.935959i	$-0.385465\pi$
$137$	8.24264			0.704216			0.352108	+	0.935959i	$0.385465\pi$
$138$		0			0
$139$	22.8211			1.93566			0.967829	−	0.251610i	$-0.0809599\pi$
$139$	22.8211			1.93566			0.967829	+	0.251610i	$0.0809599\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−4.28289			−0.358153
$144$		0			0
$145$		−	17.8435i		−	1.48183i
$146$	−19.6089	+	2.90295i	−1.62284	+	0.240250i
$147$		0			0
$148$	7.65685	−	2.31788i	0.629390	−	0.190529i
$149$	−4.82843			−0.395560			−0.197780	−	0.980246i	$-0.563373\pi$
$149$	−4.82843			−0.395560			−0.197780	+	0.980246i	$0.563373\pi$
$150$		0			0
$151$		−	21.4234i		−	1.74341i	−0.490032	−	0.871704i	$-0.663015\pi$
$151$		−	21.4234i		−	1.74341i	0.490032	−	0.871704i	$-0.336985\pi$
$152$	6.24063	+	13.2241i	0.506182	+	1.07262i
$153$		0			0
$154$		0			0
$155$		−	15.8275i		−	1.27130i
$156$		0			0
$157$			19.1886i			1.53141i	0.643189	+	0.765707i	$0.277611\pi$
$157$			19.1886i			1.53141i	−0.643189	+	0.765707i	$0.722389\pi$
$158$	11.0711	−	1.63899i	0.880767	−	0.130391i
$159$		0			0
$160$	−10.9670	+	9.91131i	−0.867019	+	0.783558i
$161$		0			0
$162$		0			0
$163$			15.1486i			1.18653i	0.805007	+	0.593265i	$0.202161\pi$
$163$			15.1486i			1.18653i	−0.805007	+	0.593265i	$0.797839\pi$
$164$	−1.33052	−	4.39523i	−0.103896	−	0.343210i
$165$		0			0
$166$	−1.95774	−	13.2241i	−0.151950	−	1.02639i
$167$	7.83095			0.605977			0.302989	−	0.952994i	$-0.402016\pi$
$167$	7.83095			0.605977			0.302989	+	0.952994i	$0.402016\pi$
$168$		0			0
$169$	11.8284			0.909879
$170$	0.171573	+	1.15894i	0.0131590	+	0.0888868i
$171$		0			0
$172$	4.19239	+	13.8491i	0.319667	+	1.05598i
$173$		−	6.57128i		−	0.499605i	−0.968297	−	0.249802i	$-0.919634\pi$
$173$		−	6.57128i		−	0.499605i	0.968297	−	0.249802i	$-0.0803657\pi$
$174$		0			0
$175$		0			0
$176$	8.77817	+	13.1702i	0.661680	+	0.992739i
$177$		0			0
$178$	−8.38207	+	1.24090i	−0.628263	+	0.0930098i
$179$		−	13.5096i		−	1.00976i	−0.863191	−	0.504878i	$-0.831537\pi$
$179$		−	13.5096i		−	1.00976i	0.863191	−	0.504878i	$-0.168463\pi$
$180$		0			0
$181$		−	21.9874i		−	1.63431i	−0.576418	−	0.817155i	$-0.695550\pi$
$181$		−	21.9874i		−	1.63431i	0.576418	−	0.817155i	$-0.304450\pi$
$182$		0			0
$183$		0			0
$184$	−5.92893	+	2.79793i	−0.437087	+	0.206266i
$185$			10.4525i			0.768483i
$186$		0			0
$187$	1.25443			0.0917330
$188$	−8.19837	+	2.48181i	−0.597927	+	0.181005i
$189$		0			0
$190$	−18.8995	+	2.79793i	−1.37111	+	0.202983i
$191$			6.55596i			0.474373i	0.971464	+	0.237186i	$0.0762252\pi$
$191$			6.55596i			0.474373i	−0.971464	+	0.237186i	$0.923775\pi$
$192$		0			0
$193$	14.5858			1.04991			0.524954	−	0.851131i	$-0.324083\pi$
$193$	14.5858			1.04991			0.524954	+	0.851131i	$0.324083\pi$
$194$	12.9248	−	1.91342i	0.927944	−	0.137375i
$195$		0			0
$196$		0			0
$197$	−2.00000			−0.142494			−0.0712470	−	0.997459i	$-0.522698\pi$
$197$	−2.00000			−0.142494			−0.0712470	+	0.997459i	$0.522698\pi$
$198$		0			0
$199$	17.1316			1.21442			0.607212	−	0.794540i	$-0.292288\pi$
$199$	17.1316			1.21442			0.607212	+	0.794540i	$0.292288\pi$
$200$	−2.20711	−	4.67695i	−0.156066	−	0.330710i
$201$		0			0
$202$	−21.3068	+	3.15432i	−1.49914	+	0.221937i
$203$		0			0
$204$		0			0
$205$	6.00000			0.419058
$206$	2.50886	+	16.9469i	0.174800	+	1.18074i
$207$		0			0
$208$	2.40125	+	3.60266i	0.166496	+	0.249800i
$209$			20.4567i			1.41502i
$210$		0			0
$211$			14.4697i			0.996136i	0.867138	+	0.498068i	$0.165957\pi$
$211$			14.4697i			0.996136i	−0.867138	+	0.498068i	$0.834043\pi$
$212$	20.0711	−	6.07591i	1.37849	−	0.417296i
$213$		0			0
$214$	3.24264	−	0.480049i	0.221662	−	0.0328155i
$215$	−18.9056			−1.28935
$216$		0			0
$217$		0			0
$218$	1.17157	+	7.91375i	0.0793489	+	0.535987i
$219$		0			0
$220$	−19.7926	+	5.99162i	−1.33442	+	0.403955i
$221$	0.343146			0.0230825
$222$		0			0
$223$	−7.83095			−0.524399			−0.262200	−	0.965014i	$-0.584448\pi$
$223$	−7.83095			−0.524399			−0.262200	+	0.965014i	$0.584448\pi$
$224$		0			0
$225$		0			0
$226$	−0.878680	−	5.93531i	−0.0584489	−	0.394811i
$227$	−9.97240			−0.661891			−0.330946	−	0.943650i	$-0.607368\pi$
$227$	−9.97240			−0.661891			−0.330946	+	0.943650i	$0.607368\pi$
$228$		0			0
$229$		−	1.34502i		−	0.0888817i	−0.999012	−	0.0444409i	$-0.985849\pi$
$229$		−	1.34502i		−	0.0888817i	0.999012	−	0.0444409i	$-0.0141506\pi$
$230$	−1.25443	−	8.47343i	−0.0827146	−	0.558721i
$231$		0			0
$232$	8.24264	+	17.4665i	0.541156	+	1.14673i
$233$	−16.2426			−1.06409			−0.532045	−	0.846716i	$-0.678576\pi$
$233$	−16.2426			−1.06409			−0.532045	+	0.846716i	$0.678576\pi$
$234$		0			0
$235$		−	11.1917i		−	0.730068i
$236$	−21.4905	+	6.50562i	−1.39892	+	0.423480i
$237$		0			0
$238$		0			0
$239$			10.2316i			0.661829i	0.943661	+	0.330915i	$0.107357\pi$
$239$			10.2316i			0.661829i	−0.943661	+	0.330915i	$0.892643\pi$
$240$		0			0
$241$			5.09494i			0.328194i	0.986444	+	0.164097i	$0.0524710\pi$
$241$			5.09494i			0.328194i	−0.986444	+	0.164097i	$0.947529\pi$
$242$	0.964466	+	6.51478i	0.0619982	+	0.418786i
$243$		0			0
$244$	−3.13607	−	10.3596i	−0.200767	−	0.663209i
$245$		0			0
$246$		0			0
$247$			5.59587i			0.356056i
$248$	7.31135	+	15.4930i	0.464271	+	0.983809i
$249$		0			0
$250$	−11.5942	+	1.71644i	−0.733284	+	0.108557i
$251$	−3.91548			−0.247143			−0.123571	−	0.992336i	$-0.539435\pi$
$251$	−3.91548			−0.247143			−0.123571	+	0.992336i	$0.539435\pi$
$252$		0			0
$253$	−9.17157			−0.576612
$254$	−14.3137	+	2.11904i	−0.898122	+	0.132960i
$255$		0			0
$256$	6.15685	−	14.7680i	0.384803	−	0.922999i
$257$			19.0572i			1.18876i	0.804185	+	0.594379i	$0.202602\pi$
$257$			19.0572i			1.18876i	−0.804185	+	0.594379i	$0.797398\pi$
$258$		0			0
$259$		0			0
$260$	−5.41421	+	1.63899i	−0.335775	+	0.101646i
$261$		0			0
$262$	−0.0760939	−	0.514000i	−0.00470110	−	0.0317550i
$263$			25.6614i			1.58235i	0.611588	+	0.791176i	$0.290531\pi$
$263$			25.6614i			1.58235i	−0.611588	+	0.791176i	$0.709469\pi$
$264$		0			0
$265$			27.3994i			1.68313i
$266$		0			0
$267$		0			0
$268$	−1.89949	−	6.27476i	−0.116030	−	0.383292i
$269$			5.04054i			0.307327i	0.988123	+	0.153664i	$0.0491072\pi$
$269$			5.04054i			0.307327i	−0.988123	+	0.153664i	$0.950893\pi$
$270$		0			0
$271$	−4.28289			−0.260167			−0.130084	−	0.991503i	$-0.541525\pi$
$271$	−4.28289			−0.260167			−0.130084	+	0.991503i	$0.541525\pi$
$272$	−0.703309	−	1.05520i	−0.0426443	−	0.0639806i
$273$		0			0
$274$	−1.70711	−	11.5312i	−0.103130	−	0.696624i
$275$		−	7.23486i		−	0.436278i
$276$		0			0
$277$	−4.14214			−0.248877			−0.124438	−	0.992227i	$-0.539713\pi$
$277$	−4.14214			−0.248877			−0.124438	+	0.992227i	$0.539713\pi$
$278$	−4.72640	−	31.9259i	−0.283470	−	1.91479i
$279$		0			0
$280$		0			0
$281$	−10.3848			−0.619504			−0.309752	−	0.950817i	$-0.600246\pi$
$281$	−10.3848			−0.619504			−0.309752	+	0.950817i	$0.600246\pi$
$282$		0			0
$283$	−3.39587			−0.201864			−0.100932	−	0.994893i	$-0.532182\pi$
$283$	−3.39587			−0.201864			−0.100932	+	0.994893i	$0.532182\pi$
$284$		0			0
$285$		0			0
$286$	0.887016	+	5.99162i	0.0524503	+	0.354292i
$287$		0			0
$288$		0			0
$289$	16.8995			0.994088
$290$	−24.9625	+	3.69552i	−1.46585	+	0.217008i
$291$		0			0
$292$	8.12227	+	26.8310i	0.475320	+	1.57016i
$293$		−	11.7975i		−	0.689219i	−0.938746	−	0.344609i	$-0.888011\pi$
$293$		−	11.7975i		−	0.689219i	0.938746	−	0.344609i	$-0.111989\pi$
$294$		0			0
$295$		−	29.3371i		−	1.70807i
$296$	−4.82843	−	10.2316i	−0.280647	−	0.594702i
$297$		0			0
$298$	1.00000	+	6.75481i	0.0579284	+	0.391295i
$299$	−2.50886			−0.145091
$300$		0			0
$301$		0			0
$302$	−29.9706	+	4.43692i	−1.72461	+	0.255316i
$303$		0			0
$304$	17.2077	−	11.4692i	0.986927	−	0.657806i
$305$	14.1421			0.809776
$306$		0			0
$307$	3.91548			0.223468			0.111734	−	0.993738i	$-0.464360\pi$
$307$	3.91548			0.223468			0.111734	+	0.993738i	$0.464360\pi$
$308$		0			0
$309$		0			0
$310$	−22.1421	+	3.27798i	−1.25759	+	0.186177i
$311$	20.6796			1.17263			0.586317	−	0.810082i	$-0.300577\pi$
$311$	20.6796			1.17263			0.586317	+	0.810082i	$0.300577\pi$
$312$		0			0
$313$			12.7486i			0.720594i	0.932838	+	0.360297i	$0.117325\pi$
$313$			12.7486i			0.720594i	−0.932838	+	0.360297i	$0.882675\pi$
$314$	26.8442	−	3.97408i	1.51490	−	0.224270i
$315$		0			0
$316$	−4.58579	−	15.1486i	−0.257971	−	0.852176i
$317$	5.51472			0.309737			0.154869	−	0.987935i	$-0.450505\pi$
$317$	5.51472			0.309737			0.154869	+	0.987935i	$0.450505\pi$
$318$		0			0
$319$			27.0192i			1.51279i
$320$	16.1369	+	13.2898i	0.902082	+	0.742922i
$321$		0			0
$322$		0			0
$323$		−	1.63899i		−	0.0911959i
$324$		0			0
$325$		−	1.97908i		−	0.109779i
$326$	21.1924	−	3.13738i	1.17374	−	0.173763i
$327$		0			0
$328$	−5.87321	+	2.77164i	−0.324294	+	0.153038i
$329$		0			0
$330$		0			0
$331$			15.1486i			0.832643i	0.909218	+	0.416321i	$0.136681\pi$
$331$			15.1486i			0.832643i	−0.909218	+	0.416321i	$0.863319\pi$
$332$	−18.0947	+	5.47762i	−0.993074	+	0.300623i
$333$		0			0
$334$	−1.62184	−	10.9552i	−0.0887433	−	0.599444i
$335$	8.56578			0.467999
$336$		0			0
$337$	10.8284			0.589862			0.294931	−	0.955519i	$-0.404703\pi$
$337$	10.8284			0.589862			0.294931	+	0.955519i	$0.404703\pi$
$338$	−2.44975	−	16.5476i	−0.133249	−	0.900069i
$339$		0			0
$340$	1.58579	−	0.480049i	0.0860013	−	0.0260343i
$341$			23.9665i			1.29786i
$342$		0			0
$343$		0			0
$344$	18.5061	−	8.73324i	0.997782	−	0.470865i
$345$		0			0
$346$	−9.19299	+	1.36096i	−0.494218	+	0.0731654i
$347$			3.95687i			0.212416i	0.994344	+	0.106208i	$0.0338710\pi$
$347$			3.95687i			0.212416i	−0.994344	+	0.106208i	$0.966129\pi$
$348$		0			0
$349$		−	8.47343i		−	0.453572i	−0.973945	−	0.226786i	$-0.927178\pi$
$349$		−	8.47343i		−	0.453572i	0.973945	−	0.226786i	$-0.0728218\pi$
$350$		0			0
$351$		0			0
$352$	16.6066	−	15.0080i	0.885135	−	0.799929i
$353$			10.0586i			0.535363i	0.963507	+	0.267681i	$0.0862575\pi$
$353$			10.0586i			0.535363i	−0.963507	+	0.267681i	$0.913743\pi$
$354$		0			0
$355$		0			0
$356$	3.47197	+	11.4692i	0.184014	+	0.607868i
$357$		0			0
$358$	−18.8995	+	2.79793i	−0.998869	+	0.147875i
$359$			31.2573i			1.64970i	0.565353	+	0.824849i	$0.308740\pi$
$359$			31.2573i			1.64970i	−0.565353	+	0.824849i	$0.691260\pi$
$360$		0			0
$361$	7.72792			0.406733
$362$	−30.7596	+	4.55374i	−1.61669	+	0.239339i
$363$		0			0
$364$		0			0
$365$	−36.6274			−1.91717
$366$		0			0
$367$	−12.8487			−0.670695			−0.335348	−	0.942094i	$-0.608854\pi$
$367$	−12.8487			−0.670695			−0.335348	+	0.942094i	$0.608854\pi$
$368$	5.14214	+	7.71491i	0.268052	+	0.402167i
$369$		0			0
$370$	14.6227	−	2.16478i	0.760198	−	0.112542i
$371$		0			0
$372$		0			0
$373$	−20.1421			−1.04292			−0.521460	−	0.853276i	$-0.674612\pi$
$373$	−20.1421			−1.04292			−0.521460	+	0.853276i	$0.674612\pi$
$374$	−0.259801	−	1.75490i	−0.0134340	−	0.0907440i
$375$		0			0
$376$	5.16991	+	10.9552i	0.266618	+	0.564973i
$377$			7.39104i			0.380658i
$378$		0			0
$379$		−	21.7046i		−	1.11489i	−0.830214	−	0.557444i	$-0.811782\pi$
$379$		−	21.7046i		−	1.11489i	0.830214	−	0.557444i	$-0.188218\pi$
$380$	7.82843	+	25.8603i	0.401590	+	1.32660i
$381$		0			0
$382$	9.17157	−	1.35778i	0.469258	−	0.0694703i
$383$	31.0194			1.58502			0.792509	−	0.609860i	$-0.208774\pi$
$383$	31.0194			1.58502			0.792509	+	0.609860i	$0.208774\pi$
$384$		0			0
$385$		0			0
$386$	−3.02082	−	20.4050i	−0.153755	−	1.03859i
$387$		0			0
$388$	−5.35361	−	17.6850i	−0.271788	−	0.897821i
$389$	−14.1421			−0.717035			−0.358517	−	0.933523i	$-0.616718\pi$
$389$	−14.1421			−0.717035			−0.358517	+	0.933523i	$0.616718\pi$
$390$		0			0
$391$	0.734828			0.0371618
$392$		0			0
$393$		0			0
$394$	0.414214	+	2.79793i	0.0208678	+	0.140958i
$395$	20.6796			1.04050
$396$		0			0
$397$			16.1271i			0.809396i	0.914450	+	0.404698i	$0.132623\pi$
$397$			16.1271i			0.809396i	−0.914450	+	0.404698i	$0.867377\pi$
$398$	−3.54806	−	23.9665i	−0.177848	−	1.20133i
$399$		0			0
$400$	−6.08579	+	4.05630i	−0.304289	+	0.202815i
$401$	12.8284			0.640621			0.320311	−	0.947313i	$-0.396213\pi$
$401$	12.8284			0.640621			0.320311	+	0.947313i	$0.396213\pi$
$402$		0			0
$403$			6.55596i			0.326576i
$404$	8.82558	+	29.1543i	0.439089	+	1.45048i
$405$		0			0
$406$		0			0
$407$		−	15.8275i		−	0.784540i
$408$		0			0
$409$			13.8310i			0.683899i	0.939718	+	0.341949i	$0.111087\pi$
$409$			13.8310i			0.683899i	−0.939718	+	0.341949i	$0.888913\pi$
$410$	−1.24264	−	8.39380i	−0.0613696	−	0.414540i
$411$		0			0
$412$	23.1885	−	7.01962i	1.14241	−	0.345832i
$413$		0			0
$414$		0			0
$415$		−	24.7013i		−	1.21254i
$416$	4.54269	−	4.10540i	0.222724	−	0.201284i
$417$		0			0
$418$	28.6182	−	4.23671i	1.39976	−	0.207224i
$419$	−17.2837			−0.844366			−0.422183	−	0.906511i	$-0.638736\pi$
$419$	−17.2837			−0.844366			−0.422183	+	0.906511i	$0.638736\pi$
$420$		0			0
$421$	−10.4853			−0.511021			−0.255511	−	0.966806i	$-0.582244\pi$
$421$	−10.4853			−0.511021			−0.255511	+	0.966806i	$0.582244\pi$
$422$	20.2426	−	2.99678i	0.985396	−	0.145881i
$423$		0			0
$424$	−12.6569	−	26.8204i	−0.614671	−	1.30251i
$425$			0.579658i			0.0281175i
$426$		0			0
$427$		0			0
$428$	−1.34315	−	4.43692i	−0.0649234	−	0.214467i
$429$		0			0
$430$	3.91548	+	26.4483i	0.188821	+	1.27545i
$431$			0.960099i			0.0462463i	0.999733	+	0.0231232i	$0.00736099\pi$
$431$			0.960099i			0.0462463i	−0.999733	+	0.0231232i	$0.992639\pi$
$432$		0			0
$433$		−	26.1857i		−	1.25840i	−0.777243	−	0.629201i	$-0.783382\pi$
$433$		−	26.1857i		−	1.25840i	0.777243	−	0.629201i	$-0.216618\pi$
$434$		0			0
$435$		0			0
$436$	10.8284	−	3.27798i	0.518588	−	0.156987i
$437$			11.9832i			0.573236i
$438$		0			0
$439$	22.4537			1.07165			0.535827	−	0.844328i	$-0.320000\pi$
$439$	22.4537			1.07165			0.535827	+	0.844328i	$0.320000\pi$
$440$	12.4813	+	26.4483i	0.595021	+	1.26087i
$441$		0			0
$442$	−0.0710678	−	0.480049i	−0.00338035	−	0.0228336i
$443$		−	28.3770i		−	1.34823i	−0.738625	−	0.674116i	$-0.764525\pi$
$443$		−	28.3770i		−	1.34823i	0.738625	−	0.674116i	$-0.235475\pi$
$444$		0			0
$445$	−15.6569			−0.742206
$446$	1.62184	+	10.9552i	0.0767965	+	0.518746i
$447$		0			0
$448$		0			0
$449$	16.2843			0.768502			0.384251	−	0.923229i	$-0.374460\pi$
$449$	16.2843			0.768502			0.384251	+	0.923229i	$0.374460\pi$
$450$		0			0
$451$	−9.08538			−0.427814
$452$	−8.12132	+	2.45849i	−0.381995	+	0.115637i
$453$		0			0
$454$	2.06535	+	13.9510i	0.0969317	+	0.654755i
$455$		0			0
$456$		0			0
$457$	0.727922			0.0340508			0.0170254	−	0.999855i	$-0.494580\pi$
$457$	0.727922			0.0340508			0.0170254	+	0.999855i	$0.494580\pi$
$458$	−1.88164	+	0.278564i	−0.0879235	+	0.0130164i
$459$		0			0
$460$	−11.5942	+	3.50981i	−0.540584	+	0.163646i
$461$		−	29.7499i		−	1.38559i	−0.721135	−	0.692794i	$-0.756379\pi$
$461$		−	29.7499i		−	1.38559i	0.721135	−	0.692794i	$-0.243621\pi$
$462$		0			0
$463$			34.9330i			1.62347i	0.584024	+	0.811737i	$0.301477\pi$
$463$			34.9330i			1.62347i	−0.584024	+	0.811737i	$0.698523\pi$
$464$	22.7279	−	15.1486i	1.05512	−	0.703256i
$465$		0			0
$466$	3.36396	+	22.7229i	0.155832	+	1.05262i
$467$	−24.0755			−1.11408			−0.557041	−	0.830485i	$-0.688063\pi$
$467$	−24.0755			−1.11408			−0.557041	+	0.830485i	$0.688063\pi$
$468$		0			0
$469$		0			0
$470$	−15.6569	+	2.31788i	−0.722197	+	0.106916i
$471$		0			0
$472$	13.5520	+	28.7172i	0.623780	+	1.32182i
$473$	28.6274			1.31629
$474$		0			0
$475$	−9.45280			−0.433724
$476$		0			0
$477$		0			0
$478$	14.3137	−	2.11904i	0.654694	−	0.0969226i
$479$	−32.7935			−1.49837			−0.749186	−	0.662360i	$-0.769555\pi$
$479$	−32.7935			−1.49837			−0.749186	+	0.662360i	$0.769555\pi$
$480$		0			0
$481$		−	4.32957i		−	0.197411i
$482$	7.12764	−	1.05520i	0.324655	−	0.0480628i
$483$		0			0
$484$	8.91421	−	2.69851i	0.405192	−	0.122660i
$485$	24.1421			1.09624
$486$		0			0
$487$			19.5032i			0.883773i	0.897071	+	0.441886i	$0.145691\pi$
$487$			19.5032i			0.883773i	−0.897071	+	0.441886i	$0.854309\pi$
$488$	−13.8433	+	6.53281i	−0.626657	+	0.295727i
$489$		0			0
$490$		0			0
$491$			14.4697i			0.653009i	0.945196	+	0.326504i	$0.105871\pi$
$491$			14.4697i			0.653009i	−0.945196	+	0.326504i	$0.894129\pi$
$492$		0			0
$493$		−	2.16478i		−	0.0974970i
$494$	7.82843	−	1.15894i	0.352218	−	0.0521433i
$495$		0			0
$496$	20.1600	−	13.4370i	0.905212	−	0.603341i
$497$		0			0
$498$		0			0
$499$		−	12.5495i		−	0.561793i	−0.959738	−	0.280897i	$-0.909368\pi$
$499$		−	12.5495i		−	0.561793i	0.959738	−	0.280897i	$-0.0906318\pi$
$500$	4.80249	+	15.8645i	0.214774	+	0.709480i
$501$		0			0
$502$	0.810922	+	5.47762i	0.0361932	+	0.244478i
$503$	−7.83095			−0.349165			−0.174582	−	0.984643i	$-0.555858\pi$
$503$	−7.83095			−0.349165			−0.174582	+	0.984643i	$0.555858\pi$
$504$		0			0
$505$	−39.7990			−1.77103
$506$	1.89949	+	12.8307i	0.0844428	+	0.570395i
$507$		0			0
$508$	5.92893	+	19.5855i	0.263054	+	0.868967i
$509$		−	6.57128i		−	0.291267i	−0.989339	−	0.145633i	$-0.953478\pi$
$509$		−	6.57128i		−	0.291267i	0.989339	−	0.145633i	$-0.0465220\pi$
$510$		0			0
$511$		0			0
$512$	−21.9350	−	5.55468i	−0.969400	−	0.245485i
$513$		0			0
$514$	26.6604	−	3.94689i	1.17594	−	0.174090i
$515$			31.6550i			1.39489i
$516$		0			0
$517$			16.9469i			0.745322i
$518$		0			0
$519$		0			0
$520$	3.41421	+	7.23486i	0.149723	+	0.317269i
$521$			12.0376i			0.527378i	0.964608	+	0.263689i	$0.0849393\pi$
$521$			12.0376i			0.527378i	−0.964608	+	0.263689i	$0.915061\pi$
$522$		0			0
$523$	7.46354			0.326358			0.163179	−	0.986597i	$-0.447825\pi$
$523$	7.46354			0.326358			0.163179	+	0.986597i	$0.447825\pi$
$524$	−0.703309	+	0.212906i	−0.0307242	+	0.00930083i
$525$		0			0
$526$	35.8995	−	5.31466i	1.56529	−	0.231730i
$527$		−	1.92020i		−	0.0836451i
$528$		0			0
$529$	17.6274			0.766409
$530$	38.3308	−	5.67459i	1.66498	−	0.246489i
$531$		0			0
$532$		0			0
$533$	−2.48528			−0.107649
$534$		0			0
$535$	6.05692			0.261864
$536$	−8.38478	+	3.95687i	−0.362167	+	0.170911i
$537$		0			0
$538$	7.05155	−	1.04393i	0.304014	−	0.0450070i
$539$		0			0
$540$		0			0
$541$	45.3137			1.94819			0.974094	−	0.226142i	$-0.0726115\pi$
$541$	45.3137			1.94819			0.974094	+	0.226142i	$0.0726115\pi$
$542$	0.887016	+	5.99162i	0.0381006	+	0.257362i
$543$		0			0
$544$	−1.33052	+	1.20244i	−0.0570457	+	0.0515543i
$545$			14.7821i			0.633194i
$546$		0			0
$547$			27.6981i			1.18429i	0.805833	+	0.592143i	$0.201718\pi$
$547$			27.6981i			1.18429i	−0.805833	+	0.592143i	$0.798282\pi$
$548$	−15.7782	+	4.77637i	−0.674010	+	0.204036i
$549$		0			0
$550$	−10.1213	+	1.49839i	−0.431575	+	0.0638915i
$551$	35.3023			1.50393
$552$		0			0
$553$		0			0
$554$	0.857864	+	5.79471i	0.0364472	+	0.246194i
$555$		0			0
$556$	−43.6844	+	13.2241i	−1.85263	+	0.560829i
$557$	19.6569			0.832888			0.416444	−	0.909161i	$-0.363276\pi$
$557$	19.6569			0.832888			0.416444	+	0.909161i	$0.363276\pi$
$558$		0			0
$559$	7.83095			0.331214
$560$		0			0
$561$		0			0
$562$	2.15076	+	14.5280i	0.0907242	+	0.612825i
$563$	−21.0470			−0.887027			−0.443513	−	0.896268i	$-0.646268\pi$
$563$	−21.0470			−0.887027			−0.443513	+	0.896268i	$0.646268\pi$
$564$		0			0
$565$		−	11.0866i		−	0.466415i
$566$	0.703309	+	4.75071i	0.0295623	+	0.199687i
$567$		0			0
$568$		0			0
$569$	−18.8284			−0.789329			−0.394664	−	0.918825i	$-0.629139\pi$
$569$	−18.8284			−0.789329			−0.394664	+	0.918825i	$0.629139\pi$
$570$		0			0
$571$		−	9.95043i		−	0.416412i	−0.978085	−	0.208206i	$-0.933237\pi$
$571$		−	9.95043i		−	0.416412i	0.978085	−	0.208206i	$-0.0667625\pi$
$572$	8.19837	−	2.48181i	0.342791	−	0.103770i
$573$		0			0
$574$		0			0
$575$		−	4.23808i		−	0.176740i
$576$		0			0
$577$		−	0.842290i		−	0.0350650i	−0.999846	−	0.0175325i	$-0.994419\pi$
$577$		−	0.842290i		−	0.0350650i	0.999846	−	0.0175325i	$-0.00558105\pi$
$578$	−3.50000	−	23.6418i	−0.145581	−	0.983370i
$579$		0			0
$580$	10.3398	+	34.1563i	0.429337	+	1.41827i
$581$		0			0
$582$		0			0
$583$		−	41.4889i		−	1.71830i
$584$	35.8534	−	16.9197i	1.48363	−	0.700141i
$585$		0			0
$586$	−16.5043	+	2.44335i	−0.681788	+	0.100934i
$587$	22.8211			0.941926			0.470963	−	0.882153i	$-0.343906\pi$
$587$	22.8211			0.941926			0.470963	+	0.882153i	$0.343906\pi$
$588$		0			0
$589$	31.3137			1.29026
$590$	−41.0416	+	6.07591i	−1.68966	+	0.250141i
$591$		0			0
$592$	−13.3137	+	8.87385i	−0.547190	+	0.364713i
$593$		−	37.4579i		−	1.53821i	−0.639121	−	0.769106i	$-0.720702\pi$
$593$		−	37.4579i		−	1.53821i	0.639121	−	0.769106i	$-0.279298\pi$
$594$		0			0
$595$		0			0
$596$	9.24264	−	2.79793i	0.378593	−	0.114608i
$597$		0			0
$598$	0.519602	+	3.50981i	0.0212481	+	0.143527i
$599$		−	32.2174i		−	1.31637i	−0.752857	−	0.658184i	$-0.771325\pi$
$599$		−	32.2174i		−	1.31637i	0.752857	−	0.658184i	$-0.228675\pi$
$600$		0			0
$601$			25.5516i			1.04227i	0.853474	+	0.521136i	$0.174491\pi$
$601$			25.5516i			1.04227i	−0.853474	+	0.521136i	$0.825509\pi$
$602$		0			0
$603$		0			0
$604$	12.4142	+	41.0089i	0.505127	+	1.66863i
$605$			12.1689i			0.494738i
$606$		0			0
$607$	−12.1138			−0.491686			−0.245843	−	0.969310i	$-0.579065\pi$
$607$	−12.1138			−0.491686			−0.245843	+	0.969310i	$0.579065\pi$
$608$	−19.6089	−	21.6976i	−0.795246	−	0.879953i
$609$		0			0
$610$	−2.92893	−	19.7844i	−0.118589	−	0.801046i
$611$			4.63577i			0.187543i
$612$		0			0
$613$	−8.68629			−0.350836			−0.175418	−	0.984494i	$-0.556128\pi$
$613$	−8.68629			−0.350836			−0.175418	+	0.984494i	$0.556128\pi$
$614$	−0.810922	−	5.47762i	−0.0327261	−	0.221059i
$615$		0			0
$616$		0			0
$617$	35.4558			1.42740			0.713699	−	0.700452i	$-0.247018\pi$
$617$	35.4558			1.42740			0.713699	+	0.700452i	$0.247018\pi$
$618$		0			0
$619$	−13.5205			−0.543433			−0.271717	−	0.962377i	$-0.587591\pi$
$619$	−13.5205			−0.543433			−0.271717	+	0.962377i	$0.587591\pi$
$620$	9.17157	+	30.2972i	0.368339	+	1.21677i
$621$		0			0
$622$	−4.28289	−	28.9301i	−0.171728	−	1.15999i
$623$		0			0
$624$		0			0
$625$	−30.7990			−1.23196
$626$	17.8349	−	2.64032i	0.712825	−	0.105529i
$627$		0			0
$628$	−11.1192	−	36.7310i	−0.443705	−	1.46573i
$629$			1.26810i			0.0505625i
$630$		0			0
$631$			20.4633i			0.814630i	0.913288	+	0.407315i	$0.133535\pi$
$631$			20.4633i			0.814630i	−0.913288	+	0.407315i	$0.866465\pi$
$632$	−20.2426	+	9.55274i	−0.805209	+	0.379988i
$633$		0			0
$634$	−1.14214	−	7.71491i	−0.0453600	−	0.306398i
$635$	−26.7365			−1.06101
$636$		0			0
$637$		0			0
$638$	37.7990	−	5.59587i	1.49648	−	0.221542i
$639$		0			0
$640$	15.2499	−	25.3274i	0.602806	−	1.00115i
$641$	−49.4558			−1.95339			−0.976694	−	0.214636i	$-0.931144\pi$
$641$	−49.4558			−1.95339			−0.976694	+	0.214636i	$0.931144\pi$
$642$		0			0
$643$	−41.7267			−1.64554			−0.822769	−	0.568375i	$-0.807572\pi$
$643$	−41.7267			−1.64554			−0.822769	+	0.568375i	$0.807572\pi$
$644$		0			0
$645$		0			0
$646$	−2.29289	+	0.339446i	−0.0902127	+	0.0133553i
$647$	−43.8681			−1.72463			−0.862317	−	0.506370i	$-0.830987\pi$
$647$	−43.8681			−1.72463			−0.862317	+	0.506370i	$0.830987\pi$
$648$		0			0
$649$			44.4231i			1.74376i
$650$	−2.76866	+	0.409880i	−0.108596	+	0.0160768i
$651$		0			0
$652$	−8.77817	−	28.9977i	−0.343780	−	1.13564i
$653$	23.7990			0.931326			0.465663	−	0.884962i	$-0.345816\pi$
$653$	23.7990			0.931326			0.465663	+	0.884962i	$0.345816\pi$
$654$		0			0
$655$		−	0.960099i		−	0.0375142i
$656$	5.09381	+	7.64240i	0.198880	+	0.298386i
$657$		0			0
$658$		0			0
$659$		−	13.2284i		−	0.515306i	−0.966238	−	0.257653i	$-0.917051\pi$
$659$		−	13.2284i		−	0.515306i	0.966238	−	0.257653i	$-0.0829491\pi$
$660$		0			0
$661$		−	37.6662i		−	1.46504i	−0.680744	−	0.732522i	$-0.738343\pi$
$661$		−	37.6662i		−	1.46504i	0.680744	−	0.732522i	$-0.261657\pi$
$662$	21.1924	−	3.13738i	0.823666	−	0.121938i
$663$		0			0
$664$	11.4105	+	24.1794i	0.442815	+	0.938342i
$665$		0			0
$666$		0			0
$667$			15.8275i			0.612843i
$668$	−14.9901	+	4.53781i	−0.579985	+	0.175573i
$669$		0			0
$670$	−1.77403	−	11.9832i	−0.0685368	−	0.462953i
$671$	−21.4144			−0.826696
$672$		0			0
$673$	10.3848			0.400304			0.200152	−	0.979765i	$-0.435856\pi$
$673$	10.3848			0.400304			0.200152	+	0.979765i	$0.435856\pi$
$674$	−2.24264	−	15.1486i	−0.0863833	−	0.583502i
$675$		0			0
$676$	−22.6421	+	6.85423i	−0.870851	+	0.263624i
$677$			28.8532i			1.10892i	0.832211	+	0.554459i	$0.187075\pi$
$677$			28.8532i			1.10892i	−0.832211	+	0.554459i	$0.812925\pi$
$678$		0			0
$679$		0			0
$680$	−1.00000	−	2.11904i	−0.0383482	−	0.0812615i
$681$		0			0
$682$	33.5283	−	4.96362i	1.28386	−	0.190067i
$683$		−	32.2174i		−	1.23276i	−0.787447	−	0.616382i	$-0.788598\pi$
$683$		−	32.2174i		−	1.23276i	0.787447	−	0.616382i	$-0.211402\pi$
$684$		0			0
$685$		−	21.5391i		−	0.822965i
$686$		0			0
$687$		0			0
$688$	−16.0503	−	24.0807i	−0.611910	−	0.918068i
$689$		−	11.3492i		−	0.432370i
$690$		0			0
$691$	−8.19837			−0.311881			−0.155940	−	0.987766i	$-0.549841\pi$
$691$	−8.19837			−0.311881			−0.155940	+	0.987766i	$0.549841\pi$
$692$	3.80786	+	12.5788i	0.144753	+	0.478175i
$693$		0			0
$694$	5.53553	−	0.819496i	0.210126	−	0.0311076i
$695$		−	59.6343i		−	2.26206i
$696$		0			0
$697$	0.727922			0.0275720
$698$	−11.8540	+	1.75490i	−0.448682	+	0.0664241i
$699$		0			0
$700$		0			0
$701$	−16.0000			−0.604312			−0.302156	−	0.953259i	$-0.597706\pi$
$701$	−16.0000			−0.604312			−0.302156	+	0.953259i	$0.597706\pi$
$702$		0			0
$703$	−20.6796			−0.779947
$704$	−24.4350	−	20.1238i	−0.920930	−	0.758445i
$705$		0			0
$706$	14.0716	−	2.08319i	0.529591	−	0.0784021i
$707$		0			0
$708$		0			0
$709$	−46.6274			−1.75113			−0.875565	−	0.483101i	$-0.839510\pi$
$709$	−46.6274			−1.75113			−0.875565	+	0.483101i	$0.839510\pi$
$710$		0			0
$711$		0			0
$712$	15.3260	−	7.23252i	0.574366	−	0.271050i
$713$			14.0392i			0.525774i
$714$		0			0
$715$			11.1917i			0.418547i
$716$	7.82843	+	25.8603i	0.292562	+	0.966444i
$717$		0			0
$718$	43.7279	−	6.47360i	1.63191	−	0.241593i
$719$	−33.5283			−1.25039			−0.625197	−	0.780467i	$-0.714981\pi$
$719$	−33.5283			−1.25039			−0.625197	+	0.780467i	$0.714981\pi$
$720$		0			0
$721$		0			0
$722$	−1.60051	−	10.8111i	−0.0595646	−	0.402348i
$723$		0			0
$724$	12.7411	+	42.0886i	0.473518	+	1.56421i
$725$	−12.4853			−0.463692
$726$		0			0
$727$	−29.9802			−1.11191			−0.555953	−	0.831214i	$-0.687646\pi$
$727$	−29.9802			−1.11191			−0.555953	+	0.831214i	$0.687646\pi$
$728$		0			0
$729$		0			0
$730$	7.58579	+	51.2405i	0.280763	+	1.89650i
$731$	−2.29363			−0.0848331
$732$		0			0
$733$		−	20.4567i		−	0.755584i	−0.925890	−	0.377792i	$-0.876683\pi$
$733$		−	20.4567i		−	0.755584i	0.925890	−	0.377792i	$-0.123317\pi$
$734$	2.66105	+	17.9749i	0.0982210	+	0.663464i
$735$		0			0
$736$	9.72792	−	8.79148i	0.358576	−	0.324058i
$737$	−12.9706			−0.477777
$738$		0			0
$739$		−	12.4330i		−	0.457357i	−0.973502	−	0.228678i	$-0.926560\pi$
$739$		−	12.4330i		−	0.457357i	0.973502	−	0.228678i	$-0.0734404\pi$
$740$	−6.05692	−	20.0083i	−0.222657	−	0.735521i
$741$		0			0
$742$		0			0
$743$			45.1646i			1.65693i	0.560042	+	0.828464i	$0.310785\pi$
$743$			45.1646i			1.65693i	−0.560042	+	0.828464i	$0.689215\pi$
$744$		0			0
$745$			12.6173i			0.462262i
$746$	4.17157	+	28.1782i	0.152732	+	1.03168i
$747$		0			0
$748$	−2.40125	+	0.726905i	−0.0877982	+	0.0265783i
$749$		0			0
$750$		0			0
$751$		−	37.2509i		−	1.35930i	−0.733535	−	0.679652i	$-0.762131\pi$
$751$		−	37.2509i		−	1.35930i	0.733535	−	0.679652i	$-0.237869\pi$
$752$	14.2553	−	9.50143i	0.519837	−	0.346481i
$753$		0			0
$754$	10.3398	−	1.53073i	0.376554	−	0.0557460i
$755$	−55.9819			−2.03739
$756$		0			0
$757$	−44.2843			−1.60954			−0.804770	−	0.593587i	$-0.797711\pi$
$757$	−44.2843			−1.60954			−0.804770	+	0.593587i	$0.797711\pi$
$758$	−30.3640	+	4.49516i	−1.10287	+	0.163272i
$759$		0			0
$760$	34.5563	−	16.3075i	1.25349	−	0.591537i
$761$		−	0.0543929i		−	0.00197174i	−1.00000		0.000985871i	$-0.999686\pi$
$761$		−	0.0543929i		−	0.00197174i	1.00000		0.000985871i	$-0.000313813\pi$
$762$		0			0
$763$		0			0
$764$	−3.79899	−	12.5495i	−0.137443	−	0.454026i
$765$		0			0
$766$	−6.42433	−	43.3951i	−0.232121	−	1.56793i
$767$			12.1518i			0.438777i
$768$		0			0
$769$			19.1342i			0.689996i	0.938603	+	0.344998i	$0.112120\pi$
$769$			19.1342i			0.689996i	−0.938603	+	0.344998i	$0.887880\pi$
$770$		0			0
$771$		0			0
$772$	−27.9203	+	8.45204i	−1.00487	+	0.304195i
$773$		−	49.4955i		−	1.78023i	−0.455735	−	0.890116i	$-0.650624\pi$
$773$		−	49.4955i		−	1.78023i	0.455735	−	0.890116i	$-0.349376\pi$
$774$		0			0
$775$	−11.0746			−0.397813
$776$	−23.6320	+	11.1522i	−0.848339	+	0.400341i
$777$		0			0
$778$	2.92893	+	19.7844i	0.105007	+	0.709304i
$779$			11.8706i			0.425309i
$780$		0			0
$781$		0			0
$782$	−0.152188	−	1.02800i	−0.00544222	−	0.0367612i
$783$		0			0
$784$		0			0
$785$	50.1421			1.78965
$786$		0			0
$787$	−41.2071			−1.46887			−0.734436	−	0.678677i	$-0.762553\pi$
$787$	−41.2071			−1.46887			−0.734436	+	0.678677i	$0.762553\pi$
$788$	3.82843	−	1.15894i	0.136382	−	0.0412856i
$789$		0			0
$790$	−4.28289	−	28.9301i	−0.152378	−	1.02929i
$791$		0			0
$792$		0			0
$793$	−5.85786			−0.208019
$794$	22.5613	−	3.34003i	0.800669	−	0.118533i
$795$		0			0
$796$	−32.7935	+	9.92724i	−1.16233	+	0.351862i
$797$		−	20.1940i		−	0.715309i	−0.933854	−	0.357655i	$-0.883576\pi$
$797$		−	20.1940i		−	0.715309i	0.933854	−	0.357655i	$-0.116424\pi$
$798$		0			0
$799$		−	1.35778i		−	0.0480350i
$800$	6.93503	+	7.67372i	0.245190	+	0.271307i
$801$		0			0
$802$	−2.65685	−	17.9465i	−0.0938168	−	0.633714i
$803$	55.4623			1.95722
$804$		0			0
$805$		0			0
$806$	9.17157	−	1.35778i	0.323055	−	0.0478259i
$807$		0			0
$808$	38.9580	−	18.3847i	1.37054	−	0.646773i
$809$	0.0416306			0.00146365			0.000731826	−	1.00000i	$-0.499767\pi$
$809$	0.0416306			0.00146365			0.000731826		1.00000i	$0.499767\pi$
$810$		0			0
$811$	−39.4330			−1.38468			−0.692340	−	0.721571i	$-0.743420\pi$
$811$	−39.4330			−1.38468			−0.692340	+	0.721571i	$0.743420\pi$
$812$		0			0
$813$		0			0
$814$	−22.1421	+	3.27798i	−0.776081	+	0.114893i
$815$	39.5852			1.38661
$816$		0			0
$817$		−	37.4035i		−	1.30858i
$818$	19.3491	−	2.86449i	0.676525	−	0.100155i
$819$		0			0
$820$	−11.4853	+	3.47682i	−0.401083	+	0.121416i
$821$	18.0000			0.628204			0.314102	−	0.949389i	$-0.398297\pi$
$821$	18.0000			0.628204			0.314102	+	0.949389i	$0.398297\pi$
$822$		0			0
$823$		−	17.1853i		−	0.599041i	−0.954090	−	0.299521i	$-0.903173\pi$
$823$		−	17.1853i		−	0.599041i	0.954090	−	0.299521i	$-0.0968267\pi$
$824$	−14.6227	−	30.9861i	−0.509406	−	1.07945i
$825$		0			0
$826$		0			0
$827$			45.1646i			1.57053i	0.619162	+	0.785264i	$0.287473\pi$
$827$			45.1646i			1.57053i	−0.619162	+	0.785264i	$0.712527\pi$
$828$		0			0
$829$		−	47.2220i		−	1.64009i	−0.572301	−	0.820044i	$-0.693949\pi$
$829$		−	47.2220i		−	1.64009i	0.572301	−	0.820044i	$-0.306051\pi$
$830$	−34.5563	+	5.11582i	−1.19947	+	0.177573i
$831$		0			0
$832$	−6.68414	−	5.50482i	−0.231731	−	0.190845i
$833$		0			0
$834$		0			0
$835$		−	20.4633i		−	0.708160i
$836$	−11.8540	−	39.1584i	−0.409981	−	1.35432i
$837$		0			0
$838$	3.57958	+	24.1794i	0.123655	+	0.835263i
$839$	42.3984			1.46376			0.731878	−	0.681435i	$-0.238644\pi$
$839$	42.3984			1.46376			0.731878	+	0.681435i	$0.238644\pi$
$840$		0			0
$841$	17.6274			0.607842
$842$	2.17157	+	14.6686i	0.0748373	+	0.505512i
$843$		0			0
$844$	−8.38478	−	27.6981i	−0.288616	−	0.953409i
$845$		−	30.9092i		−	1.06331i
$846$		0			0
$847$		0			0
$848$	−34.8995	+	23.2612i	−1.19845	+	0.798793i
$849$		0			0
$850$	0.810922	−	0.120051i	0.0278144	−	0.00411772i
$851$		−	9.27153i		−	0.317824i
$852$		0			0
$853$		−	38.3002i		−	1.31137i	−0.755033	−	0.655687i	$-0.772379\pi$
$853$		−	38.3002i		−	1.31137i	0.755033	−	0.655687i	$-0.227621\pi$
$854$		0			0
$855$		0			0
$856$	−5.92893	+	2.79793i	−0.202647	+	0.0956314i
$857$		−	3.45542i		−	0.118035i	−0.998257	−	0.0590174i	$-0.981203\pi$
$857$		−	3.45542i		−	0.118035i	0.998257	−	0.0590174i	$-0.0187967\pi$
$858$		0			0
$859$	−2.66105			−0.0907937			−0.0453969	−	0.998969i	$-0.514455\pi$
$859$	−2.66105			−0.0907937			−0.0453969	+	0.998969i	$0.514455\pi$
$860$	36.1893	−	10.9552i	1.23405	−	0.373571i
$861$		0			0
$862$	1.34315	−	0.198843i	0.0457477	−	0.00677262i
$863$			12.5495i			0.427190i	0.976922	+	0.213595i	$0.0685174\pi$
$863$			12.5495i			0.427190i	−0.976922	+	0.213595i	$0.931483\pi$
$864$		0			0
$865$	−17.1716			−0.583851
$866$	−36.6328	+	5.42323i	−1.24483	+	0.184289i
$867$		0			0
$868$		0			0
$869$	−31.3137			−1.06224
$870$		0			0
$871$	−3.54806			−0.120221
$872$	−6.82843	−	14.4697i	−0.231240	−	0.490006i
$873$		0			0
$874$	16.7641	−	2.48181i	0.567056	−	0.0839485i
$875$		0			0
$876$		0			0
$877$	30.4264			1.02743			0.513713	−	0.857962i	$-0.328269\pi$
$877$	30.4264			1.02743			0.513713	+	0.857962i	$0.328269\pi$
$878$	−4.65030	−	31.4119i	−0.156940	−	1.06010i
$879$		0			0
$880$	34.4153	−	22.9385i	1.16014	−	0.773256i
$881$			26.1857i			0.882217i	0.897454	+	0.441109i	$0.145415\pi$
$881$			26.1857i			0.882217i	−0.897454	+	0.441109i	$0.854585\pi$
$882$		0			0
$883$			24.7013i			0.831266i	0.909532	+	0.415633i	$0.136440\pi$
$883$			24.7013i			0.831266i	−0.909532	+	0.415633i	$0.863560\pi$
$884$	−0.656854	+	0.198843i	−0.0220924	+	0.00668781i
$885$		0			0
$886$	−39.6985	+	5.87707i	−1.33370	+	0.197444i
$887$	−22.4537			−0.753920			−0.376960	−	0.926230i	$-0.623031\pi$
$887$	−22.4537			−0.753920			−0.376960	+	0.926230i	$0.623031\pi$
$888$		0			0
$889$		0			0
$890$	3.24264	+	21.9034i	0.108694	+	0.734204i
$891$		0			0
$892$	14.9901	−	4.53781i	0.501906	−	0.151937i
$893$	22.1421			0.740958
$894$		0			0
$895$	−35.3023			−1.18003
$896$		0			0
$897$		0			0
$898$	−3.37258	−	22.7811i	−0.112545	−	0.760217i
$899$	41.3592			1.37941
$900$		0			0
$901$			3.32410i			0.110742i
$902$	1.88164	+	12.7101i	0.0626519	+	0.423201i
$903$		0			0
$904$	5.12132	+	10.8523i	0.170333	+	0.360942i
$905$	−57.4558			−1.90990
$906$		0			0
$907$			33.9729i			1.12805i	0.825757	+	0.564025i	$0.190748\pi$
$907$			33.9729i			1.12805i	−0.825757	+	0.564025i	$0.809252\pi$
$908$	19.0893	−	5.77871i	0.633501	−	0.191773i
$909$		0			0
$910$		0			0
$911$			18.7078i			0.619817i	0.950766	+	0.309908i	$0.100298\pi$
$911$			18.7078i			0.619817i	−0.950766	+	0.309908i	$0.899702\pi$
$912$		0			0
$913$			37.4035i			1.23788i
$914$	−0.150758	−	1.01834i	−0.00498662	−	0.0336836i
$915$		0			0
$916$	0.779403	+	2.57466i	0.0257522	+	0.0850693i
$917$		0			0
$918$		0			0
$919$			48.8403i			1.61109i	0.592533	+	0.805546i	$0.298128\pi$
$919$			48.8403i			1.61109i	−0.592533	+	0.805546i	$0.701872\pi$
$920$	7.31135	+	15.4930i	0.241048	+	0.510791i
$921$		0			0
$922$	−41.6190	+	6.16140i	−1.37065	+	0.202915i
$923$		0			0
$924$		0			0
$925$	7.31371			0.240473
$926$	48.8701	−	7.23486i	1.60597	−	0.237752i
$927$		0			0
$928$	−25.8995	−	28.6582i	−0.850193	−	0.940752i
$929$		−	29.8812i		−	0.980369i	−0.871619	−	0.490185i	$-0.836929\pi$
$929$		−	29.8812i		−	0.980369i	0.871619	−	0.490185i	$-0.163071\pi$
$930$		0			0
$931$		0			0
$932$	31.0919	−	9.41214i	1.01845	−	0.308305i
$933$		0			0
$934$	4.98620	+	33.6808i	0.163153	+	1.10207i
$935$		−	3.27798i		−	0.107201i
$936$		0			0
$937$		−	29.8042i		−	0.973662i	−0.873496	−	0.486831i	$-0.838153\pi$
$937$		−	29.8042i		−	0.973662i	0.873496	−	0.486831i	$-0.161847\pi$
$938$		0			0
$939$		0			0
$940$	6.48528	+	21.4234i	0.211527	+	0.698753i
$941$		−	24.7862i		−	0.808008i	−0.914757	−	0.404004i	$-0.867618\pi$
$941$		−	24.7862i		−	0.808008i	0.914757	−	0.404004i	$-0.132382\pi$
$942$		0			0
$943$	−5.32209			−0.173311
$944$	37.3677	−	24.9063i	1.21621	−	0.810631i
$945$		0			0
$946$	−5.92893	−	40.0488i	−0.192766	−	1.30210i
$947$		−	9.15505i		−	0.297499i	−0.988875	−	0.148750i	$-0.952475\pi$
$947$		−	9.15505i		−	0.297499i	0.988875	−	0.148750i	$-0.0475249\pi$
$948$		0			0
$949$	15.1716			0.492490
$950$	1.95774	+	13.2241i	0.0635174	+	0.429048i
$951$		0			0
$952$		0			0
$953$	−26.3431			−0.853338			−0.426669	−	0.904408i	$-0.640313\pi$
$953$	−26.3431			−0.853338			−0.426669	+	0.904408i	$0.640313\pi$
$954$		0			0
$955$	17.1316			0.554364
$956$	−5.92893	−	19.5855i	−0.191755	−	0.633441i
$957$		0			0
$958$	6.79175	+	45.8770i	0.219431	+	1.48222i
$959$		0			0
$960$		0			0
$961$	5.68629			0.183429
$962$	−6.05692	+	0.896683i	−0.195283	+	0.0289102i
$963$		0			0
$964$	−2.95237	−	9.75279i	−0.0950893	−	0.314116i
$965$		−	38.1145i		−	1.22695i
$966$		0			0
$967$		−	45.1646i		−	1.45240i	−0.687486	−	0.726198i	$-0.741286\pi$
$967$		−	45.1646i		−	1.45240i	0.687486	−	0.726198i	$-0.258714\pi$
$968$	−5.62132	−	11.9118i	−0.180676	−	0.382860i
$969$		0			0
$970$	−5.00000	−	33.7740i	−0.160540	−	1.08442i
$971$	−13.0009			−0.417217			−0.208609	−	0.977999i	$-0.566894\pi$
$971$	−13.0009			−0.417217			−0.208609	+	0.977999i	$0.566894\pi$
$972$		0			0
$973$		0			0
$974$	27.2843	−	4.03924i	0.874244	−	0.129426i
$975$		0			0
$976$	12.0062	+	18.0133i	0.384310	+	0.576592i
$977$	−17.6152			−0.563561			−0.281780	−	0.959479i	$-0.590925\pi$
$977$	−17.6152			−0.563561			−0.281780	+	0.959479i	$0.590925\pi$
$978$		0			0
$979$	23.7081			0.757714
$980$		0			0
$981$		0			0
$982$	20.2426	−	2.99678i	0.645969	−	0.0956310i
$983$	9.60498			0.306351			0.153176	−	0.988199i	$-0.451050\pi$
$983$	9.60498			0.306351			0.153176	+	0.988199i	$0.451050\pi$
$984$		0			0
$985$			5.22625i			0.166522i
$986$	−3.02846	+	0.448342i	−0.0964458	+	0.0142781i
$987$		0			0
$988$	−3.24264	−	10.7117i	−0.103162	−	0.340784i
$989$	16.7696			0.533241
$990$		0			0
$991$		−	25.6614i		−	0.815163i	−0.913169	−	0.407581i	$-0.866372\pi$
$991$		−	25.6614i		−	0.815163i	0.913169	−	0.407581i	$-0.133628\pi$
$992$	−22.9733	−	25.4203i	−0.729402	−	0.807095i
$993$		0			0
$994$		0			0
$995$		−	44.7669i		−	1.41921i
$996$		0			0
$997$		−	30.9092i		−	0.978903i	−0.872030	−	0.489452i	$-0.837197\pi$
$997$		−	30.9092i		−	0.978903i	0.872030	−	0.489452i	$-0.162803\pi$
$998$	−17.5563	+	2.59909i	−0.555737	+	0.0822727i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.k.1567.1		8
3.2	odd	2		196.2.d.c.195.8	yes	8
4.3	odd	2	inner	1764.2.b.k.1567.3		8
7.6	odd	2	inner	1764.2.b.k.1567.2		8
12.11	even	2		196.2.d.c.195.5	✓	8
21.2	odd	6		196.2.f.d.31.5		16
21.5	even	6		196.2.f.d.31.6		16
21.11	odd	6		196.2.f.d.19.1		16
21.17	even	6		196.2.f.d.19.2		16
21.20	even	2		196.2.d.c.195.7	yes	8
24.5	odd	2		3136.2.f.i.3135.3		8
24.11	even	2		3136.2.f.i.3135.5		8
28.27	even	2	inner	1764.2.b.k.1567.4		8
84.11	even	6		196.2.f.d.19.6		16
84.23	even	6		196.2.f.d.31.2		16
84.47	odd	6		196.2.f.d.31.1		16
84.59	odd	6		196.2.f.d.19.5		16
84.83	odd	2		196.2.d.c.195.6	yes	8
168.83	odd	2		3136.2.f.i.3135.4		8
168.125	even	2		3136.2.f.i.3135.6		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.d.c.195.5	✓	8	12.11	even	2
196.2.d.c.195.6	yes	8	84.83	odd	2
196.2.d.c.195.7	yes	8	21.20	even	2
196.2.d.c.195.8	yes	8	3.2	odd	2
196.2.f.d.19.1		16	21.11	odd	6
196.2.f.d.19.2		16	21.17	even	6
196.2.f.d.19.5		16	84.59	odd	6
196.2.f.d.19.6		16	84.11	even	6
196.2.f.d.31.1		16	84.47	odd	6
196.2.f.d.31.2		16	84.23	even	6
196.2.f.d.31.5		16	21.2	odd	6
196.2.f.d.31.6		16	21.5	even	6
1764.2.b.k.1567.1		8	1.1	even	1	trivial
1764.2.b.k.1567.2		8	7.6	odd	2	inner
1764.2.b.k.1567.3		8	4.3	odd	2	inner
1764.2.b.k.1567.4		8	28.27	even	2	inner
3136.2.f.i.3135.3		8	24.5	odd	2
3136.2.f.i.3135.4		8	168.83	odd	2
3136.2.f.i.3135.5		8	24.11	even	2
3136.2.f.i.3135.6		8	168.125	even	2

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:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 - 1.39897i) q^{2} +(-1.91421 + 0.579471i) q^{4} -2.61313i q^{5} +(1.20711 + 2.55791i) q^{8} +O(q^{10})\)	\(q+(-0.207107 - 1.39897i) q^{2} +(-1.91421 + 0.579471i) q^{4} -2.61313i q^{5} +(1.20711 + 2.55791i) q^{8} +(-3.65568 + 0.541196i) q^{10} +3.95687i q^{11} +1.08239i q^{13} +(3.32843 - 2.21846i) q^{16} -0.317025i q^{17} +5.16991 q^{19} +(1.51423 + 5.00208i) q^{20} +(5.53553 - 0.819496i) q^{22} +2.31788i q^{23} -1.82843 q^{25} +(1.51423 - 0.224171i) q^{26} +6.82843 q^{29} +6.05692 q^{31} +(-3.79289 - 4.19690i) q^{32} +(-0.443508 + 0.0656581i) q^{34} -4.00000 q^{37} +(-1.07072 - 7.23252i) q^{38} +(6.68414 - 3.15432i) q^{40} +2.29610i q^{41} -7.23486i q^{43} +(-2.29289 - 7.57430i) q^{44} +(3.24264 - 0.480049i) q^{46} +4.28289 q^{47} +(0.378680 + 2.55791i) q^{50} +(-0.627215 - 2.07193i) q^{52} -10.4853 q^{53} +10.3398 q^{55} +(-1.41421 - 9.55274i) q^{58} +11.2268 q^{59} +5.41196i q^{61} +(-1.25443 - 8.47343i) q^{62} +(-5.08579 + 6.17534i) q^{64} +2.82843 q^{65} +3.27798i q^{67} +(0.183707 + 0.606854i) q^{68} -14.0167i q^{73} +(0.828427 + 5.59587i) q^{74} +(-9.89630 + 2.99581i) q^{76} +7.91375i q^{79} +(-5.79712 - 8.69760i) q^{80} +(3.21217 - 0.475538i) q^{82} +9.45280 q^{83} -0.828427 q^{85} +(-10.1213 + 1.49839i) q^{86} +(-10.1213 + 4.77637i) q^{88} -5.99162i q^{89} +(-1.34315 - 4.43692i) q^{92} +(-0.887016 - 5.99162i) q^{94} -13.5096i q^{95} +9.23880i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8}+O(q^{10}) \) 8 * q + 4 * q^2 - 4 * q^4 + 4 * q^8	\( 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8} + 4 q^{16} + 16 q^{22} + 8 q^{25} + 32 q^{29} - 36 q^{32} - 32 q^{37} - 24 q^{44} - 8 q^{46} + 20 q^{50} - 16 q^{53} - 52 q^{64} - 16 q^{74} + 16 q^{85} - 64 q^{86} - 64 q^{88} - 56 q^{92}+O(q^{100}) \) 8 * q + 4 * q^2 - 4 * q^4 + 4 * q^8 + 4 * q^16 + 16 * q^22 + 8 * q^25 + 32 * q^29 - 36 * q^32 - 32 * q^37 - 24 * q^44 - 8 * q^46 + 20 * q^50 - 16 * q^53 - 52 * q^64 - 16 * q^74 + 16 * q^85 - 64 * q^86 - 64 * q^88 - 56 * q^92

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