LMFDB - Embedded newform 1764.2.b.k.1567.8

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			1567.8
Root			$-1.36145 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.k.1567.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.20711 + 0.736813i) q^{2} +(0.914214 + 1.77882i) q^{4} +1.08239i q^{5} +(-0.207107 + 2.82083i) q^{8} +O(q^{10})$	\(q+(1.20711 + 0.736813i) q^{2} +(0.914214 + 1.77882i) q^{4} +1.08239i q^{5} +(-0.207107 + 2.82083i) q^{8} +(-0.797521 + 1.30656i) q^{10} +2.08402i q^{11} +2.61313i q^{13} +(-2.32843 + 3.25245i) q^{16} -4.46088i q^{17} -1.12786 q^{19} +(-1.92538 + 0.989538i) q^{20} +(-1.53553 + 2.51564i) q^{22} +7.11529i q^{23} +3.82843 q^{25} +(-1.92538 + 3.15432i) q^{26} +1.17157 q^{29} -7.70154 q^{31} +(-5.20711 + 2.21044i) q^{32} +(3.28684 - 5.38476i) q^{34} -4.00000 q^{37} +(-1.36145 - 0.831025i) q^{38} +(-3.05325 - 0.224171i) q^{40} -5.54328i q^{41} +7.97852i q^{43} +(-3.70711 + 1.90524i) q^{44} +(-5.24264 + 8.58892i) q^{46} +5.44581 q^{47} +(4.62132 + 2.82083i) q^{50} +(-4.64829 + 2.38896i) q^{52} +6.48528 q^{53} -2.25573 q^{55} +(1.41421 + 0.863230i) q^{58} -8.82940 q^{59} +13.0656i q^{61} +(-9.29658 - 5.67459i) q^{62} +(-7.91421 - 1.16843i) q^{64} -2.82843 q^{65} -10.0625i q^{67} +(7.93513 - 4.07820i) q^{68} -7.97069i q^{73} +(-4.82843 - 2.94725i) q^{74} +(-1.03111 - 2.00627i) q^{76} +4.16804i q^{79} +(-3.52043 - 2.52027i) q^{80} +(4.08436 - 6.69133i) q^{82} +4.31795 q^{83} +4.82843 q^{85} +(-5.87868 + 9.63093i) q^{86} +(-5.87868 - 0.431615i) q^{88} +4.01254i q^{89} +(-12.6569 + 6.50490i) q^{92} +(6.57368 + 4.01254i) q^{94} -1.22079i q^{95} +3.82683i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	1.20711	+	0.736813i	0.853553	+	0.521005i
$2$	1.20711	+	0.736813i	0.853553	+	0.521005i
$3$		0			0
$3$		0			0
$4$	0.914214	+	1.77882i	0.457107	+	0.889412i
$5$			1.08239i			0.484061i	0.970269	+	0.242030i	$0.0778133\pi$
$5$			1.08239i			0.484061i	−0.970269	+	0.242030i	$0.922187\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−0.207107	+	2.82083i	−0.0732233	+	0.997316i
$9$		0			0
$10$	−0.797521	+	1.30656i	−0.252198	+	0.413171i
$11$			2.08402i			0.628356i	0.949364	+	0.314178i	$0.101729\pi$
$11$			2.08402i			0.628356i	−0.949364	+	0.314178i	$0.898271\pi$
$12$		0			0
$13$			2.61313i			0.724751i	0.932032	+	0.362375i	$0.118034\pi$
$13$			2.61313i			0.724751i	−0.932032	+	0.362375i	$0.881966\pi$
$14$		0			0
$15$		0			0
$16$	−2.32843	+	3.25245i	−0.582107	+	0.813112i
$17$		−	4.46088i		−	1.08192i	−0.841047	−	0.540962i	$-0.818060\pi$
$17$		−	4.46088i		−	1.08192i	0.841047	−	0.540962i	$-0.181940\pi$
$18$		0			0
$19$	−1.12786			−0.258750			−0.129375	−	0.991596i	$-0.541297\pi$
$19$	−1.12786			−0.258750			−0.129375	+	0.991596i	$0.541297\pi$
$20$	−1.92538	+	0.989538i	−0.430529	+	0.221267i
$21$		0			0
$22$	−1.53553	+	2.51564i	−0.327377	+	0.536336i
$23$			7.11529i			1.48364i	0.670598	+	0.741821i	$0.266037\pi$
$23$			7.11529i			1.48364i	−0.670598	+	0.741821i	$0.733963\pi$
$24$		0			0
$25$	3.82843			0.765685
$26$	−1.92538	+	3.15432i	−0.377599	+	0.618613i
$27$		0			0
$28$		0			0
$29$	1.17157			0.217556			0.108778	−	0.994066i	$-0.465306\pi$
$29$	1.17157			0.217556			0.108778	+	0.994066i	$0.465306\pi$
$30$		0			0
$31$	−7.70154			−1.38324			−0.691619	−	0.722263i	$-0.743102\pi$
$31$	−7.70154			−1.38324			−0.691619	+	0.722263i	$0.743102\pi$
$32$	−5.20711	+	2.21044i	−0.920495	+	0.390754i
$33$		0			0
$34$	3.28684	−	5.38476i	0.563688	−	0.923479i
$35$		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	$0.606644\pi$
$38$	−1.36145	−	0.831025i	−0.220857	−	0.134810i
$39$		0			0
$40$	−3.05325	−	0.224171i	−0.482761	−	0.0354445i
$41$		−	5.54328i		−	0.865714i	−0.901462	−	0.432857i	$-0.857505\pi$
$41$		−	5.54328i		−	0.865714i	0.901462	−	0.432857i	$-0.142495\pi$
$42$		0			0
$43$			7.97852i			1.21671i	0.793664	+	0.608357i	$0.208171\pi$
$43$			7.97852i			1.21671i	−0.793664	+	0.608357i	$0.791829\pi$
$44$	−3.70711	+	1.90524i	−0.558867	+	0.287226i
$45$		0			0
$46$	−5.24264	+	8.58892i	−0.772985	+	1.26637i
$47$	5.44581			0.794353			0.397177	−	0.917742i	$-0.369990\pi$
$47$	5.44581			0.794353			0.397177	+	0.917742i	$0.369990\pi$
$48$		0			0
$49$		0			0
$50$	4.62132	+	2.82083i	0.653553	+	0.398926i
$51$		0			0
$52$	−4.64829	+	2.38896i	−0.644602	+	0.331288i
$53$	6.48528			0.890822			0.445411	−	0.895326i	$-0.353058\pi$
$53$	6.48528			0.890822			0.445411	+	0.895326i	$0.353058\pi$
$54$		0			0
$55$	−2.25573			−0.304162
$56$		0			0
$57$		0			0
$58$	1.41421	+	0.863230i	0.185695	+	0.113348i
$59$	−8.82940			−1.14949			−0.574745	−	0.818332i	$-0.694899\pi$
$59$	−8.82940			−1.14949			−0.574745	+	0.818332i	$0.694899\pi$
$60$		0			0
$61$			13.0656i			1.67288i	0.548057	+	0.836441i	$0.315368\pi$
$61$			13.0656i			1.67288i	−0.548057	+	0.836441i	$0.684632\pi$
$62$	−9.29658	−	5.67459i	−1.18067	−	0.720674i
$63$		0			0
$64$	−7.91421	−	1.16843i	−0.989277	−	0.146053i
$65$	−2.82843			−0.350823
$66$		0			0
$67$		−	10.0625i		−	1.22934i	−0.788786	−	0.614668i	$-0.789290\pi$
$67$		−	10.0625i		−	1.22934i	0.788786	−	0.614668i	$-0.210710\pi$
$68$	7.93513	−	4.07820i	0.962276	−	0.494555i
$69$		0			0
$70$		0			0
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$		−	7.97069i		−	0.932899i	−0.884548	−	0.466450i	$-0.845533\pi$
$73$		−	7.97069i		−	0.932899i	0.884548	−	0.466450i	$-0.154467\pi$
$74$	−4.82843	−	2.94725i	−0.561293	−	0.342611i
$75$		0			0
$76$	−1.03111	−	2.00627i	−0.118276	−	0.230135i
$77$		0			0
$78$		0			0
$79$			4.16804i			0.468941i	0.972123	+	0.234471i	$0.0753357\pi$
$79$			4.16804i			0.468941i	−0.972123	+	0.234471i	$0.924664\pi$
$80$	−3.52043	−	2.52027i	−0.393596	−	0.281775i
$81$		0			0
$82$	4.08436	−	6.69133i	0.451042	−	0.738934i
$83$	4.31795			0.473956			0.236978	−	0.971515i	$-0.423843\pi$
$83$	4.31795			0.473956			0.236978	+	0.971515i	$0.423843\pi$
$84$		0			0
$85$	4.82843			0.523716
$86$	−5.87868	+	9.63093i	−0.633914	+	1.03853i
$87$		0			0
$88$	−5.87868	−	0.431615i	−0.626669	−	0.0460103i
$89$			4.01254i			0.425329i	0.977125	+	0.212664i	$0.0682141\pi$
$89$			4.01254i			0.425329i	−0.977125	+	0.212664i	$0.931786\pi$
$90$		0			0
$91$		0			0
$92$	−12.6569	+	6.50490i	−1.31957	+	0.678183i
$93$		0			0
$94$	6.57368	+	4.01254i	0.678023	+	0.413862i
$95$		−	1.22079i		−	0.125251i
$96$		0			0
$97$			3.82683i			0.388556i	0.980946	+	0.194278i	$0.0622364\pi$
$97$			3.82683i			0.388556i	−0.980946	+	0.194278i	$0.937764\pi$
$98$		0			0
$99$		0			0
$100$	3.50000	+	6.81010i	0.350000	+	0.681010i
$101$			0.185709i			0.0184788i	0.999957	+	0.00923938i	$0.00294103\pi$
$101$			0.185709i			0.0184788i	−0.999957	+	0.00923938i	$0.997059\pi$
$102$		0			0
$103$	15.4031			1.51771			0.758855	−	0.651259i	$-0.225759\pi$
$103$	15.4031			1.51771			0.758855	+	0.651259i	$0.225759\pi$
$104$	−7.37120	−	0.541196i	−0.722805	−	0.0530686i
$105$		0			0
$106$	7.82843	+	4.77844i	0.760364	+	0.464123i
$107$			7.11529i			0.687861i	0.938995	+	0.343931i	$0.111759\pi$
$107$			7.11529i			0.687861i	−0.938995	+	0.343931i	$0.888241\pi$
$108$		0			0
$109$	5.65685			0.541828			0.270914	−	0.962604i	$-0.412674\pi$
$109$	5.65685			0.541828			0.270914	+	0.962604i	$0.412674\pi$
$110$	−2.72291	−	1.66205i	−0.259619	−	0.158470i
$111$		0			0
$112$		0			0
$113$	−4.24264			−0.399114			−0.199557	−	0.979886i	$-0.563950\pi$
$113$	−4.24264			−0.399114			−0.199557	+	0.979886i	$0.563950\pi$
$114$		0			0
$115$	−7.70154			−0.718172
$116$	1.07107	+	2.08402i	0.0994461	+	0.193497i
$117$		0			0
$118$	−10.6580	−	6.50562i	−0.981151	−	0.598891i
$119$		0			0
$120$		0			0
$121$	6.65685			0.605169
$122$	−9.62692	+	15.7716i	−0.871581	+	1.42789i
$123$		0			0
$124$	−7.04085	−	13.6997i	−0.632287	−	1.23027i
$125$			9.55582i			0.854699i
$126$		0			0
$127$		−	11.2833i		−	1.00123i	−0.865669	−	0.500617i	$-0.833106\pi$
$127$		−	11.2833i		−	1.00123i	0.865669	−	0.500617i	$-0.166894\pi$
$128$	−8.69239	−	7.24171i	−0.768306	−	0.640083i
$129$		0			0
$130$	−3.41421	−	2.08402i	−0.299446	−	0.182781i
$131$	15.8703			1.38659			0.693295	−	0.720654i	$-0.256158\pi$
$131$	15.8703			1.38659			0.693295	+	0.720654i	$0.256158\pi$
$132$		0			0
$133$		0			0
$134$	7.41421	−	12.1466i	0.640490	−	1.04930i
$135$		0			0
$136$	12.5834	+	0.923880i	1.07902	+	0.0792220i
$137$	−0.242641			−0.0207302			−0.0103651	−	0.999946i	$-0.503299\pi$
$137$	−0.242641			−0.0207302			−0.0103651	+	0.999946i	$0.503299\pi$
$138$		0			0
$139$	−1.78855			−0.151703			−0.0758515	−	0.997119i	$-0.524167\pi$
$139$	−1.78855			−0.151703			−0.0758515	+	0.997119i	$0.524167\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−5.44581			−0.455402
$144$		0			0
$145$			1.26810i			0.105310i
$146$	5.87291	−	9.62148i	0.486045	−	0.796279i
$147$		0			0
$148$	−3.65685	−	7.11529i	−0.300592	−	0.584874i
$149$	0.828427			0.0678674			0.0339337	−	0.999424i	$-0.489196\pi$
$149$	0.828427			0.0678674			0.0339337	+	0.999424i	$0.489196\pi$
$150$		0			0
$151$		−	5.38883i		−	0.438537i	−0.975665	−	0.219269i	$-0.929633\pi$
$151$		−	5.38883i		−	0.438537i	0.975665	−	0.219269i	$-0.0703671\pi$
$152$	0.233588	−	3.18152i	0.0189465	−	0.258055i
$153$		0			0
$154$		0			0
$155$		−	8.33609i		−	0.669571i
$156$		0			0
$157$		−	20.1940i		−	1.61166i	−0.592147	−	0.805830i	$-0.701720\pi$
$157$		−	20.1940i		−	1.61166i	0.592147	−	0.805830i	$-0.298280\pi$
$158$	−3.07107	+	5.03127i	−0.244321	+	0.400267i
$159$		0			0
$160$	−2.39256	−	5.63613i	−0.189149	−	0.445575i
$161$		0			0
$162$		0			0
$163$		−	3.81048i		−	0.298460i	−0.988803	−	0.149230i	$-0.952321\pi$
$163$		−	3.81048i		−	0.298460i	0.988803	−	0.149230i	$-0.0476795\pi$
$164$	9.86051	−	5.06774i	0.769977	−	0.395724i
$165$		0			0
$166$	5.21222	+	3.18152i	0.404547	+	0.246934i
$167$	−20.8489			−1.61334			−0.806668	−	0.591005i	$-0.798731\pi$
$167$	−20.8489			−1.61334			−0.806668	+	0.591005i	$0.798731\pi$
$168$		0			0
$169$	6.17157			0.474736
$170$	5.82843	+	3.55765i	0.447020	+	0.272859i
$171$		0			0
$172$	−14.1924	+	7.29408i	−1.08216	+	0.556168i
$173$			21.0907i			1.60350i	0.597661	+	0.801749i	$0.296097\pi$
$173$			21.0907i			1.60350i	−0.597661	+	0.801749i	$0.703903\pi$
$174$		0			0
$175$		0			0
$176$	−6.77817	−	4.85249i	−0.510924	−	0.365770i
$177$		0			0
$178$	−2.95649	+	4.84357i	−0.221599	+	0.363041i
$179$		−	1.22079i		−	0.0912462i	−0.998959	−	0.0456231i	$-0.985473\pi$
$179$		−	1.22079i		−	0.0912462i	0.998959	−	0.0456231i	$-0.0145273\pi$
$180$		0			0
$181$			6.04601i			0.449397i	0.974428	+	0.224698i	$0.0721396\pi$
$181$			6.04601i			0.449397i	−0.974428	+	0.224698i	$0.927860\pi$
$182$		0			0
$183$		0			0
$184$	−20.0711	−	1.47363i	−1.47966	−	0.108637i
$185$		−	4.32957i		−	0.318316i
$186$		0			0
$187$	9.29658			0.679833
$188$	4.97863	+	9.68714i	0.363104	+	0.706507i
$189$		0			0
$190$	0.899495	−	1.47363i	0.0652562	−	0.106908i
$191$		−	20.1251i		−	1.45620i	−0.685471	−	0.728100i	$-0.740404\pi$
$191$		−	20.1251i		−	1.45620i	0.685471	−	0.728100i	$-0.259596\pi$
$192$		0			0
$193$	17.4142			1.25350			0.626751	−	0.779219i	$-0.284384\pi$
$193$	17.4142			1.25350			0.626751	+	0.779219i	$0.284384\pi$
$194$	−2.81966	+	4.61940i	−0.202440	+	0.331653i
$195$		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
$199$	21.7832			1.54417			0.772087	−	0.635517i	$-0.219213\pi$
$199$	21.7832			1.54417			0.772087	+	0.635517i	$0.219213\pi$
$200$	−0.792893	+	10.7994i	−0.0560660	+	0.763630i
$201$		0			0
$202$	−0.136833	+	0.224171i	−0.00962753	+	0.0157726i
$203$		0			0
$204$		0			0
$205$	6.00000			0.419058
$206$	18.5932	+	11.3492i	1.29545	+	0.790735i
$207$		0			0
$208$	−8.49906	−	6.08447i	−0.589304	−	0.421882i
$209$		−	2.35049i		−	0.162587i
$210$		0			0
$211$		−	15.9570i		−	1.09853i	−0.835649	−	0.549264i	$-0.814908\pi$
$211$		−	15.9570i		−	1.09853i	0.835649	−	0.549264i	$-0.185092\pi$
$212$	5.92893	+	11.5362i	0.407201	+	0.792308i
$213$		0			0
$214$	−5.24264	+	8.58892i	−0.358380	+	0.587127i
$215$	−8.63589			−0.588963
$216$		0			0
$217$		0			0
$218$	6.82843	+	4.16804i	0.462479	+	0.282295i
$219$		0			0
$220$	−2.06222	−	4.01254i	−0.139035	−	0.270526i
$221$	11.6569			0.784125
$222$		0			0
$223$	20.8489			1.39614			0.698072	−	0.716027i	$-0.254041\pi$
$223$	20.8489			1.39614			0.698072	+	0.716027i	$0.254041\pi$
$224$		0			0
$225$		0			0
$226$	−5.12132	−	3.12603i	−0.340665	−	0.207941i
$227$	18.1260			1.20306			0.601532	−	0.798849i	$-0.294557\pi$
$227$	18.1260			1.20306			0.601532	+	0.798849i	$0.294557\pi$
$228$		0			0
$229$			18.9259i			1.25066i	0.780360	+	0.625330i	$0.215036\pi$
$229$			18.9259i			1.25066i	−0.780360	+	0.625330i	$0.784964\pi$
$230$	−9.29658	−	5.67459i	−0.612998	−	0.374172i
$231$		0			0
$232$	−0.242641	+	3.30481i	−0.0159301	+	0.216972i
$233$	−7.75736			−0.508202			−0.254101	−	0.967178i	$-0.581779\pi$
$233$	−7.75736			−0.508202			−0.254101	+	0.967178i	$0.581779\pi$
$234$		0			0
$235$			5.89450i			0.384515i
$236$	−8.07196	−	15.7060i	−0.525440	−	1.02237i
$237$		0			0
$238$		0			0
$239$			11.2833i			0.729858i	0.931035	+	0.364929i	$0.118907\pi$
$239$			11.2833i			0.729858i	−0.931035	+	0.364929i	$0.881093\pi$
$240$		0			0
$241$			8.60474i			0.554280i	0.960830	+	0.277140i	$0.0893866\pi$
$241$			8.60474i			0.554280i	−0.960830	+	0.277140i	$0.910613\pi$
$242$	8.03553	+	4.90486i	0.516544	+	0.315296i
$243$		0			0
$244$	−23.2415	+	11.9448i	−1.48788	+	0.764686i
$245$		0			0
$246$		0			0
$247$		−	2.94725i		−	0.187529i
$248$	1.59504	−	21.7248i	0.101285	−	1.37952i
$249$		0			0
$250$	−7.04085	+	11.5349i	−0.445303	+	0.729531i
$251$	10.4244			0.657985			0.328993	−	0.944333i	$-0.393291\pi$
$251$	10.4244			0.657985			0.328993	+	0.944333i	$0.393291\pi$
$252$		0			0
$253$	−14.8284			−0.932255
$254$	8.31371	−	13.6202i	0.521648	−	0.854607i
$255$		0			0
$256$	−5.15685	−	15.1462i	−0.322303	−	0.946636i
$257$		−	9.42450i		−	0.587884i	−0.955823	−	0.293942i	$-0.905033\pi$
$257$		−	9.42450i		−	0.587884i	0.955823	−	0.293942i	$-0.0949673\pi$
$258$		0			0
$259$		0			0
$260$	−2.58579	−	5.03127i	−0.160364	−	0.312026i
$261$		0			0
$262$	19.1571	+	11.6934i	1.18353	+	0.722421i
$263$		−	21.8516i		−	1.34742i	−0.738994	−	0.673712i	$-0.764699\pi$
$263$		−	21.8516i		−	1.34742i	0.738994	−	0.673712i	$-0.235301\pi$
$264$		0			0
$265$			7.01962i			0.431212i
$266$		0			0
$267$		0			0
$268$	17.8995	−	9.19932i	1.09339	−	0.561938i
$269$		−	17.3952i		−	1.06060i	−0.847809	−	0.530302i	$-0.822079\pi$
$269$		−	17.3952i		−	1.06060i	0.847809	−	0.530302i	$-0.177921\pi$
$270$		0			0
$271$	−5.44581			−0.330809			−0.165405	−	0.986226i	$-0.552893\pi$
$271$	−5.44581			−0.330809			−0.165405	+	0.986226i	$0.552893\pi$
$272$	14.5088	+	10.3868i	0.879725	+	0.629795i
$273$		0			0
$274$	−0.292893	−	0.178781i	−0.0176943	−	0.0108005i
$275$			7.97852i			0.481123i
$276$		0			0
$277$	24.1421			1.45056			0.725280	−	0.688454i	$-0.241710\pi$
$277$	24.1421			1.45056			0.725280	+	0.688454i	$0.241710\pi$
$278$	−2.15897	−	1.31783i	−0.129487	−	0.0790381i
$279$		0			0
$280$		0			0
$281$	26.3848			1.57398			0.786992	−	0.616963i	$-0.211637\pi$
$281$	26.3848			1.57398			0.786992	+	0.616963i	$0.211637\pi$
$282$		0			0
$283$	−12.0195			−0.714484			−0.357242	−	0.934012i	$-0.616283\pi$
$283$	−12.0195			−0.714484			−0.357242	+	0.934012i	$0.616283\pi$
$284$		0			0
$285$		0			0
$286$	−6.57368	−	4.01254i	−0.388710	−	0.237267i
$287$		0			0
$288$		0			0
$289$	−2.89949			−0.170559
$290$	−0.934353	+	1.53073i	−0.0548671	+	0.0898878i
$291$		0			0
$292$	14.1785	−	7.28692i	0.829732	−	0.426435i
$293$			23.2555i			1.35860i	0.733860	+	0.679300i	$0.237717\pi$
$293$			23.2555i			1.35860i	−0.733860	+	0.679300i	$0.762283\pi$
$294$		0			0
$295$		−	9.55688i		−	0.556423i
$296$	0.828427	−	11.2833i	0.0481513	−	0.655831i
$297$		0			0
$298$	1.00000	+	0.610396i	0.0579284	+	0.0353593i
$299$	−18.5932			−1.07527
$300$		0			0
$301$		0			0
$302$	3.97056	−	6.50490i	0.228480	−	0.374315i
$303$		0			0
$304$	2.62615	−	3.66832i	0.150620	−	0.210393i
$305$	−14.1421			−0.809776
$306$		0			0
$307$	−10.4244			−0.594954			−0.297477	−	0.954729i	$-0.596145\pi$
$307$	−10.4244			−0.594954			−0.297477	+	0.954729i	$0.596145\pi$
$308$		0			0
$309$		0			0
$310$	6.14214	−	10.0625i	0.348850	−	0.571514i
$311$	−4.51146			−0.255821			−0.127911	−	0.991786i	$-0.540827\pi$
$311$	−4.51146			−0.255821			−0.127911	+	0.991786i	$0.540827\pi$
$312$		0			0
$313$		−	9.87285i		−	0.558046i	−0.960284	−	0.279023i	$-0.909989\pi$
$313$		−	9.87285i		−	0.558046i	0.960284	−	0.279023i	$-0.0900106\pi$
$314$	14.8792	−	24.3764i	0.839683	−	1.37564i
$315$		0			0
$316$	−7.41421	+	3.81048i	−0.417082	+	0.214356i
$317$	22.4853			1.26290			0.631450	−	0.775417i	$-0.282460\pi$
$317$	22.4853			1.26290			0.631450	+	0.775417i	$0.282460\pi$
$318$		0			0
$319$			2.44158i			0.136702i
$320$	1.26470	−	8.56628i	0.0706987	−	0.478870i
$321$		0			0
$322$		0			0
$323$			5.03127i			0.279948i
$324$		0			0
$325$			10.0042i			0.554931i
$326$	2.80761	−	4.59966i	0.155499	−	0.254751i
$327$		0			0
$328$	15.6367	+	1.14805i	0.863391	+	0.0633905i
$329$		0			0
$330$		0			0
$331$		−	3.81048i		−	0.209443i	−0.994502	−	0.104722i	$-0.966605\pi$
$331$		−	3.81048i		−	0.209443i	0.994502	−	0.104722i	$-0.0333951\pi$
$332$	3.94753	+	7.68087i	0.216649	+	0.421542i
$333$		0			0
$334$	−25.1668	−	15.3617i	−1.37707	−	0.840556i
$335$	10.8916			0.595073
$336$		0			0
$337$	5.17157			0.281714			0.140857	−	0.990030i	$-0.455014\pi$
$337$	5.17157			0.281714			0.140857	+	0.990030i	$0.455014\pi$
$338$	7.44975	+	4.54729i	0.405213	+	0.247340i
$339$		0			0
$340$	4.41421	+	8.58892i	0.239394	+	0.465800i
$341$		−	16.0502i		−	0.869166i
$342$		0			0
$343$		0			0
$344$	−22.5061	−	1.65241i	−1.21345	−	0.0890918i
$345$		0			0
$346$	−15.5399	+	25.4587i	−0.835431	+	1.36867i
$347$			2.08402i			0.111876i	0.998434	+	0.0559381i	$0.0178149\pi$
$347$			2.08402i			0.111876i	−0.998434	+	0.0559381i	$0.982185\pi$
$348$		0			0
$349$		−	5.67459i		−	0.303754i	−0.988399	−	0.151877i	$-0.951468\pi$
$349$		−	5.67459i		−	0.303754i	0.988399	−	0.151877i	$-0.0485318\pi$
$350$		0			0
$351$		0			0
$352$	−4.60660	−	10.8517i	−0.245533	−	0.578399i
$353$			27.9790i			1.48917i	0.667526	+	0.744586i	$0.267353\pi$
$353$			27.9790i			1.48917i	−0.667526	+	0.744586i	$0.732647\pi$
$354$		0			0
$355$		0			0
$356$	−7.13761	+	3.66832i	−0.378292	+	0.194421i
$357$		0			0
$358$	0.899495	−	1.47363i	0.0475398	−	0.0778835i
$359$		−	24.7988i		−	1.30883i	−0.756135	−	0.654415i	$-0.772915\pi$
$359$		−	24.7988i		−	1.30883i	0.756135	−	0.654415i	$-0.227085\pi$
$360$		0			0
$361$	−17.7279			−0.933049
$362$	−4.45478	+	7.29818i	−0.234138	+	0.383584i
$363$		0			0
$364$		0			0
$365$	8.62742			0.451580
$366$		0			0
$367$	−16.3374			−0.852807			−0.426404	−	0.904533i	$-0.640220\pi$
$367$	−16.3374			−0.852807			−0.426404	+	0.904533i	$0.640220\pi$
$368$	−23.1421	−	16.5674i	−1.20637	−	0.863638i
$369$		0			0
$370$	3.19008	−	5.22625i	0.165844	−	0.271700i
$371$		0			0
$372$		0			0
$373$	8.14214			0.421584			0.210792	−	0.977531i	$-0.432396\pi$
$373$	8.14214			0.421584			0.210792	+	0.977531i	$0.432396\pi$
$374$	11.2220	+	6.84984i	0.580274	+	0.354197i
$375$		0			0
$376$	−1.12786	+	15.3617i	−0.0581652	+	0.792221i
$377$			3.06147i			0.157674i
$378$		0			0
$379$			23.9356i			1.22949i	0.788727	+	0.614744i	$0.210741\pi$
$379$			23.9356i			1.22949i	−0.788727	+	0.614744i	$0.789259\pi$
$380$	2.17157	−	1.11606i	0.111399	−	0.0572529i
$381$		0			0
$382$	14.8284	−	24.2931i	0.758688	−	1.24294i
$383$	−6.76719			−0.345787			−0.172894	−	0.984941i	$-0.555312\pi$
$383$	−6.76719			−0.345787			−0.172894	+	0.984941i	$0.555312\pi$
$384$		0			0
$385$		0			0
$386$	21.0208	+	12.8310i	1.06993	+	0.653082i
$387$		0			0
$388$	−6.80726	+	3.49854i	−0.345586	+	0.177612i
$389$	14.1421			0.717035			0.358517	−	0.933523i	$-0.383282\pi$
$389$	14.1421			0.717035			0.358517	+	0.933523i	$0.383282\pi$
$390$		0			0
$391$	31.7405			1.60519
$392$		0			0
$393$		0			0
$394$	−2.41421	−	1.47363i	−0.121626	−	0.0742402i
$395$	−4.51146			−0.226996
$396$		0			0
$397$		−	12.8030i		−	0.642564i	−0.946984	−	0.321282i	$-0.895886\pi$
$397$		−	12.8030i		−	0.642564i	0.946984	−	0.321282i	$-0.104114\pi$
$398$	26.2947	+	16.0502i	1.31803	+	0.804523i
$399$		0			0
$400$	−8.91421	+	12.4518i	−0.445711	+	0.622588i
$401$	7.17157			0.358131			0.179066	−	0.983837i	$-0.442693\pi$
$401$	7.17157			0.358131			0.179066	+	0.983837i	$0.442693\pi$
$402$		0			0
$403$		−	20.1251i		−	1.00250i
$404$	−0.330344	+	0.169778i	−0.0164352	+	0.00844676i
$405$		0			0
$406$		0			0
$407$		−	8.33609i		−	0.413204i
$408$		0			0
$409$		−	7.25972i		−	0.358970i	−0.983761	−	0.179485i	$-0.942557\pi$
$409$		−	7.25972i		−	0.358970i	0.983761	−	0.179485i	$-0.0574431\pi$
$410$	7.24264	+	4.42088i	0.357689	+	0.218332i
$411$		0			0
$412$	14.0817	+	27.3994i	0.693756	+	1.34987i
$413$		0			0
$414$		0			0
$415$			4.67371i			0.229423i
$416$	−5.77615	−	13.6068i	−0.283199	−	0.667130i
$417$		0			0
$418$	1.73187	−	2.83730i	0.0847087	−	0.138777i
$419$	16.5309			0.807589			0.403795	−	0.914850i	$-0.367691\pi$
$419$	16.5309			0.807589			0.403795	+	0.914850i	$0.367691\pi$
$420$		0			0
$421$	6.48528			0.316073			0.158037	−	0.987433i	$-0.449484\pi$
$421$	6.48528			0.316073			0.158037	+	0.987433i	$0.449484\pi$
$422$	11.7574	−	19.2619i	0.572339	−	0.937653i
$423$		0			0
$424$	−1.34315	+	18.2939i	−0.0652289	+	0.888431i
$425$		−	17.0782i		−	0.828413i
$426$		0			0
$427$		0			0
$428$	−12.6569	+	6.50490i	−0.611792	+	0.314426i
$429$		0			0
$430$	−10.4244	−	6.36304i	−0.502711	−	0.306853i
$431$		−	17.1778i		−	0.827427i	−0.910407	−	0.413714i	$-0.864231\pi$
$431$		−	17.1778i		−	0.827427i	0.910407	−	0.413714i	$-0.135769\pi$
$432$		0			0
$433$		−	15.1760i		−	0.729313i	−0.931142	−	0.364657i	$-0.881186\pi$
$433$		−	15.1760i		−	0.729313i	0.931142	−	0.364657i	$-0.118814\pi$
$434$		0			0
$435$		0			0
$436$	5.17157	+	10.0625i	0.247673	+	0.481909i
$437$		−	8.02509i		−	0.383892i
$438$		0			0
$439$	−17.6588			−0.842809			−0.421404	−	0.906873i	$-0.638463\pi$
$439$	−17.6588			−0.842809			−0.421404	+	0.906873i	$0.638463\pi$
$440$	0.467177	−	6.36304i	0.0222718	−	0.303346i
$441$		0			0
$442$	14.0711	+	8.58892i	0.669292	+	0.408533i
$443$		−	26.7347i		−	1.27020i	−0.772428	−	0.635102i	$-0.780958\pi$
$443$		−	26.7347i		−	1.27020i	0.772428	−	0.635102i	$-0.219042\pi$
$444$		0			0
$445$	−4.34315			−0.205885
$446$	25.1668	+	15.3617i	1.19168	+	0.727399i
$447$		0			0
$448$		0			0
$449$	−40.2843			−1.90113			−0.950566	−	0.310522i	$-0.899496\pi$
$449$	−40.2843			−1.90113			−0.950566	+	0.310522i	$0.899496\pi$
$450$		0			0
$451$	11.5523			0.543977
$452$	−3.87868	−	7.54691i	−0.182438	−	0.354977i
$453$		0			0
$454$	21.8800	+	13.3555i	1.02688	+	0.626803i
$455$		0			0
$456$		0			0
$457$	−24.7279			−1.15672			−0.578362	−	0.815780i	$-0.696308\pi$
$457$	−24.7279			−1.15672			−0.578362	+	0.815780i	$0.696308\pi$
$458$	−13.9449	+	22.8456i	−0.651601	+	1.06751i
$459$		0			0
$460$	−7.04085	−	13.6997i	−0.328281	−	0.638751i
$461$		−	27.4763i		−	1.27970i	−0.768501	−	0.639849i	$-0.778997\pi$
$461$		−	27.4763i		−	1.27970i	0.768501	−	0.639849i	$-0.221003\pi$
$462$		0			0
$463$			6.60963i			0.307175i	0.988135	+	0.153588i	$0.0490828\pi$
$463$			6.60963i			0.307175i	−0.988135	+	0.153588i	$0.950917\pi$
$464$	−2.72792	+	3.81048i	−0.126641	+	0.176897i
$465$		0			0
$466$	−9.36396	−	5.71572i	−0.433777	−	0.264776i
$467$	−7.50803			−0.347430			−0.173715	−	0.984796i	$-0.555577\pi$
$467$	−7.50803			−0.347430			−0.173715	+	0.984796i	$0.555577\pi$
$468$		0			0
$469$		0			0
$470$	−4.34315	+	7.11529i	−0.200334	+	0.328204i
$471$		0			0
$472$	1.82863	−	24.9063i	0.0841695	−	1.14640i
$473$	−16.6274			−0.764529
$474$		0			0
$475$	−4.31795			−0.198121
$476$		0			0
$477$		0			0
$478$	−8.31371	+	13.6202i	−0.380260	+	0.622973i
$479$	19.9145			0.909918			0.454959	−	0.890512i	$-0.349654\pi$
$479$	19.9145			0.909918			0.454959	+	0.890512i	$0.349654\pi$
$480$		0			0
$481$		−	10.4525i		−	0.476593i
$482$	−6.34009	+	10.3868i	−0.288783	+	0.473108i
$483$		0			0
$484$	6.08579	+	11.8414i	0.276627	+	0.538244i
$485$	−4.14214			−0.188085
$486$		0			0
$487$			39.7445i			1.80100i	0.434860	+	0.900498i	$0.356798\pi$
$487$			39.7445i			1.80100i	−0.434860	+	0.900498i	$0.643202\pi$
$488$	−36.8560	−	2.70598i	−1.66839	−	0.122494i
$489$		0			0
$490$		0			0
$491$		−	15.9570i		−	0.720132i	−0.932927	−	0.360066i	$-0.882754\pi$
$491$		−	15.9570i		−	0.720132i	0.932927	−	0.360066i	$-0.117246\pi$
$492$		0			0
$493$		−	5.22625i		−	0.235379i
$494$	2.17157	−	3.55765i	0.0977037	−	0.160066i
$495$		0			0
$496$	17.9325	−	25.0489i	0.805192	−	1.12473i
$497$		0			0
$498$		0			0
$499$		−	18.3986i		−	0.823636i	−0.911266	−	0.411818i	$-0.864894\pi$
$499$		−	18.3986i		−	0.823636i	0.911266	−	0.411818i	$-0.135106\pi$
$500$	−16.9981	+	8.73606i	−0.760179	+	0.390689i
$501$		0			0
$502$	12.5834	+	7.68087i	0.561625	+	0.342814i
$503$	20.8489			0.929606			0.464803	−	0.885414i	$-0.346125\pi$
$503$	20.8489			0.929606			0.464803	+	0.885414i	$0.346125\pi$
$504$		0			0
$505$	−0.201010			−0.00894483
$506$	−17.8995	−	10.9258i	−0.795730	−	0.485710i
$507$		0			0
$508$	20.0711	−	10.3154i	0.890510	−	0.457671i
$509$			21.0907i			0.934830i	0.884038	+	0.467415i	$0.154815\pi$
$509$			21.0907i			0.934830i	−0.884038	+	0.467415i	$0.845185\pi$
$510$		0			0
$511$		0			0
$512$	4.93503	−	22.0827i	0.218100	−	0.975927i
$513$		0			0
$514$	6.94410	−	11.3764i	0.306291	−	0.501791i
$515$			16.6722i			0.734664i
$516$		0			0
$517$			11.3492i			0.499137i
$518$		0			0
$519$		0			0
$520$	0.585786	−	7.97852i	0.0256884	−	0.349881i
$521$			17.9749i			0.787493i	0.919219	+	0.393746i	$0.128821\pi$
$521$			17.9749i			0.787493i	−0.919219	+	0.393746i	$0.871179\pi$
$522$		0			0
$523$	−36.7191			−1.60562			−0.802808	−	0.596238i	$-0.796662\pi$
$523$	−36.7191			−1.60562			−0.802808	+	0.596238i	$0.796662\pi$
$524$	14.5088	+	28.2304i	0.633820	+	1.23325i
$525$		0			0
$526$	16.1005	−	26.3772i	0.702015	−	1.15010i
$527$			34.3557i			1.49656i
$528$		0			0
$529$	−27.6274			−1.20119
$530$	−5.17214	+	8.47343i	−0.224664	+	0.368062i
$531$		0			0
$532$		0			0
$533$	14.4853			0.627427
$534$		0			0
$535$	−7.70154			−0.332967
$536$	28.3848	+	2.08402i	1.22604	+	0.0900160i
$537$		0			0
$538$	12.8170	−	20.9979i	0.552580	−	0.905282i
$539$		0			0
$540$		0			0
$541$	22.6863			0.975360			0.487680	−	0.873023i	$-0.337843\pi$
$541$	22.6863			0.975360			0.487680	+	0.873023i	$0.337843\pi$
$542$	−6.57368	−	4.01254i	−0.282364	−	0.172353i
$543$		0			0
$544$	9.86051	+	23.2283i	0.422766	+	0.995905i
$545$			6.12293i			0.262278i
$546$		0			0
$547$			14.5882i			0.623744i	0.950124	+	0.311872i	$0.100956\pi$
$547$			14.5882i			0.623744i	−0.950124	+	0.311872i	$0.899044\pi$
$548$	−0.221825	−	0.431615i	−0.00947591	−	0.0184377i
$549$		0			0
$550$	−5.87868	+	9.63093i	−0.250668	+	0.410664i
$551$	−1.32138			−0.0562925
$552$		0			0
$553$		0			0
$554$	29.1421	+	17.7882i	1.23813	+	0.755750i
$555$		0			0
$556$	−1.63512	−	3.18152i	−0.0693445	−	0.134926i
$557$	8.34315			0.353510			0.176755	−	0.984255i	$-0.443440\pi$
$557$	8.34315			0.353510			0.176755	+	0.984255i	$0.443440\pi$
$558$		0			0
$559$	−20.8489			−0.881814
$560$		0			0
$561$		0			0
$562$	31.8492	+	19.4406i	1.34348	+	0.820054i
$563$	−11.3588			−0.478716			−0.239358	−	0.970931i	$-0.576937\pi$
$563$	−11.3588			−0.478716			−0.239358	+	0.970931i	$0.576937\pi$
$564$		0			0
$565$		−	4.59220i		−	0.193195i
$566$	−14.5088	−	8.85611i	−0.609850	−	0.372250i
$567$		0			0
$568$		0			0
$569$	−13.1716			−0.552181			−0.276091	−	0.961132i	$-0.589039\pi$
$569$	−13.1716			−0.552181			−0.276091	+	0.961132i	$0.589039\pi$
$570$		0			0
$571$		−	40.6077i		−	1.69938i	−0.527282	−	0.849691i	$-0.676789\pi$
$571$		−	40.6077i		−	1.69938i	0.527282	−	0.849691i	$-0.323211\pi$
$572$	−4.97863	−	9.68714i	−0.208167	−	0.405040i
$573$		0			0
$574$		0			0
$575$			27.2404i			1.13600i
$576$		0			0
$577$			38.6172i			1.60766i	0.594862	+	0.803828i	$0.297207\pi$
$577$			38.6172i			1.60766i	−0.594862	+	0.803828i	$0.702793\pi$
$578$	−3.50000	−	2.13639i	−0.145581	−	0.0888619i
$579$		0			0
$580$	−2.25573	+	1.15932i	−0.0936640	+	0.0481380i
$581$		0			0
$582$		0			0
$583$			13.5155i			0.559753i
$584$	22.4840	+	1.65078i	0.930395	+	0.0683100i
$585$		0			0
$586$	−17.1350	+	28.0719i	−0.707838	+	1.15964i
$587$	−1.78855			−0.0738214			−0.0369107	−	0.999319i	$-0.511752\pi$
$587$	−1.78855			−0.0738214			−0.0369107	+	0.999319i	$0.511752\pi$
$588$		0			0
$589$	8.68629			0.357912
$590$	7.04163	−	11.5362i	0.289899	−	0.474937i
$591$		0			0
$592$	9.31371	−	13.0098i	0.382791	−	0.534699i
$593$		−	34.9986i		−	1.43722i	−0.695412	−	0.718611i	$-0.744778\pi$
$593$		−	34.9986i		−	1.43722i	0.695412	−	0.718611i	$-0.255222\pi$
$594$		0			0
$595$		0			0
$596$	0.757359	+	1.47363i	0.0310226	+	0.0603621i
$597$		0			0
$598$	−22.4439	−	13.6997i	−0.917801	−	0.560222i
$599$			41.9766i			1.71512i	0.514385	+	0.857560i	$0.328020\pi$
$599$			41.9766i			1.71512i	−0.514385	+	0.857560i	$0.671980\pi$
$600$		0			0
$601$			6.25425i			0.255116i	0.991831	+	0.127558i	$0.0407139\pi$
$601$			6.25425i			0.255116i	−0.991831	+	0.127558i	$0.959286\pi$
$602$		0			0
$603$		0			0
$604$	9.58579	−	4.92655i	0.390040	−	0.200458i
$605$			7.20533i			0.292938i
$606$		0			0
$607$	15.4031			0.625192			0.312596	−	0.949886i	$-0.398801\pi$
$607$	15.4031			0.625192			0.312596	+	0.949886i	$0.398801\pi$
$608$	5.87291	−	2.49307i	0.238178	−	0.101108i
$609$		0			0
$610$	−17.0711	−	10.4201i	−0.691187	−	0.421898i
$611$			14.2306i			0.575708i
$612$		0			0
$613$	−31.3137			−1.26475			−0.632374	−	0.774663i	$-0.717920\pi$
$613$	−31.3137			−1.26475			−0.632374	+	0.774663i	$0.717920\pi$
$614$	−12.5834	−	7.68087i	−0.507825	−	0.309974i
$615$		0			0
$616$		0			0
$617$	−15.4558			−0.622229			−0.311114	−	0.950372i	$-0.600702\pi$
$617$	−15.4558			−0.622229			−0.311114	+	0.950372i	$0.600702\pi$
$618$		0			0
$619$	44.4207			1.78542			0.892709	−	0.450634i	$-0.148802\pi$
$619$	44.4207			1.78542			0.892709	+	0.450634i	$0.148802\pi$
$620$	14.8284	−	7.62096i	0.595524	−	0.306065i
$621$		0			0
$622$	−5.44581	−	3.32410i	−0.218357	−	0.133284i
$623$		0			0
$624$		0			0
$625$	8.79899			0.351960
$626$	7.27444	−	11.9176i	0.290745	−	0.476322i
$627$		0			0
$628$	35.9216	−	18.4617i	1.43343	−	0.736700i
$629$			17.8435i			0.711469i
$630$		0			0
$631$			22.5667i			0.898365i	0.893440	+	0.449183i	$0.148285\pi$
$631$			22.5667i			0.898365i	−0.893440	+	0.449183i	$0.851715\pi$
$632$	−11.7574	−	0.863230i	−0.467683	−	0.0343374i
$633$		0			0
$634$	27.1421	+	16.5674i	1.07795	+	0.657977i
$635$	12.2130			0.484658
$636$		0			0
$637$		0			0
$638$	−1.79899	+	2.94725i	−0.0712227	+	0.116683i
$639$		0			0
$640$	7.83837	−	9.40857i	0.309839	−	0.371907i
$641$	1.45584			0.0575024			0.0287512	−	0.999587i	$-0.490847\pi$
$641$	1.45584			0.0575024			0.0287512	+	0.999587i	$0.490847\pi$
$642$		0			0
$643$	−6.84734			−0.270033			−0.135016	−	0.990843i	$-0.543109\pi$
$643$	−6.84734			−0.270033			−0.135016	+	0.990843i	$0.543109\pi$
$644$		0			0
$645$		0			0
$646$	−3.70711	+	6.07328i	−0.145854	+	0.238950i
$647$	−9.57025			−0.376245			−0.188123	−	0.982146i	$-0.560240\pi$
$647$	−9.57025			−0.376245			−0.188123	+	0.982146i	$0.560240\pi$
$648$		0			0
$649$		−	18.4007i		−	0.722289i
$650$	−7.37120	+	12.0761i	−0.289122	+	0.473663i
$651$		0			0
$652$	6.77817	−	3.48359i	0.265454	−	0.136428i
$653$	−15.7990			−0.618262			−0.309131	−	0.951019i	$-0.600038\pi$
$653$	−15.7990			−0.618262			−0.309131	+	0.951019i	$0.600038\pi$
$654$		0			0
$655$			17.1778i			0.671194i
$656$	18.0292	+	12.9071i	0.703923	+	0.503938i
$657$		0			0
$658$		0			0
$659$		−	30.5452i		−	1.18987i	−0.803773	−	0.594936i	$-0.797177\pi$
$659$		−	30.5452i		−	1.18987i	0.803773	−	0.594936i	$-0.202823\pi$
$660$		0			0
$661$			12.5404i			0.487764i	0.969805	+	0.243882i	$0.0784209\pi$
$661$			12.5404i			0.487764i	−0.969805	+	0.243882i	$0.921579\pi$
$662$	2.80761	−	4.59966i	0.109121	−	0.178771i
$663$		0			0
$664$	−0.894276	+	12.1802i	−0.0347046	+	0.472684i
$665$		0			0
$666$		0			0
$667$			8.33609i			0.322775i
$668$	−19.0603	−	37.0865i	−0.737467	−	1.43492i
$669$		0			0
$670$	13.1474	+	8.02509i	0.507926	+	0.310036i
$671$	−27.2291			−1.05117
$672$		0			0
$673$	−26.3848			−1.01706			−0.508529	−	0.861045i	$-0.669811\pi$
$673$	−26.3848			−1.01706			−0.508529	+	0.861045i	$0.669811\pi$
$674$	6.24264	+	3.81048i	0.240458	+	0.146774i
$675$		0			0
$676$	5.64214	+	10.9781i	0.217005	+	0.422236i
$677$			40.0936i			1.54092i	0.637488	+	0.770461i	$0.279974\pi$
$677$			40.0936i			1.54092i	−0.637488	+	0.770461i	$0.720026\pi$
$678$		0			0
$679$		0			0
$680$	−1.00000	+	13.6202i	−0.0383482	+	0.522311i
$681$		0			0
$682$	11.8260	−	19.3743i	0.452840	−	0.741879i
$683$			41.9766i			1.60619i	0.595850	+	0.803096i	$0.296815\pi$
$683$			41.9766i			1.60619i	−0.595850	+	0.803096i	$0.703185\pi$
$684$		0			0
$685$		−	0.262632i		−	0.0100347i
$686$		0			0
$687$		0			0
$688$	−25.9497	−	18.5774i	−0.989325	−	0.708257i
$689$			16.9469i			0.645624i
$690$		0			0
$691$	4.97863			0.189396			0.0946981	−	0.995506i	$-0.469811\pi$
$691$	4.97863			0.189396			0.0946981	+	0.995506i	$0.469811\pi$
$692$	−37.5167	+	19.2814i	−1.42617	+	0.732970i
$693$		0			0
$694$	−1.53553	+	2.51564i	−0.0582881	+	0.0954923i
$695$		−	1.93591i		−	0.0734334i
$696$		0			0
$697$	−24.7279			−0.936637
$698$	4.18111	−	6.84984i	0.158257	−	0.259270i
$699$		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
$703$	4.51146			0.170153
$704$	2.43503	−	16.4934i	0.0917736	−	0.621618i
$705$		0			0
$706$	−20.6153	+	33.7737i	−0.775867	+	1.27109i
$707$		0			0
$708$		0			0
$709$	−1.37258			−0.0515484			−0.0257742	−	0.999668i	$-0.508205\pi$
$709$	−1.37258			−0.0515484			−0.0257742	+	0.999668i	$0.508205\pi$
$710$		0			0
$711$		0			0
$712$	−11.3187	−	0.831025i	−0.424187	−	0.0311440i
$713$		−	54.7987i		−	2.05223i
$714$		0			0
$715$		−	5.89450i		−	0.220442i
$716$	2.17157	−	1.11606i	0.0811555	−	0.0417093i
$717$		0			0
$718$	18.2721	−	29.9348i	0.681908	−	1.11716i
$719$	−11.8260			−0.441034			−0.220517	−	0.975383i	$-0.570775\pi$
$719$	−11.8260			−0.441034			−0.220517	+	0.975383i	$0.570775\pi$
$720$		0			0
$721$		0			0
$722$	−21.3995	−	13.0622i	−0.796407	−	0.486123i
$723$		0			0
$724$	−10.7548	+	5.52735i	−0.399699	+	0.205422i
$725$	4.48528			0.166579
$726$		0			0
$727$	−38.1207			−1.41382			−0.706909	−	0.707305i	$-0.749911\pi$
$727$	−38.1207			−1.41382			−0.706909	+	0.707305i	$0.749911\pi$
$728$		0			0
$729$		0			0
$730$	10.4142	+	6.35679i	0.385447	+	0.235275i
$731$	35.5913			1.31639
$732$		0			0
$733$			2.35049i			0.0868175i	0.999057	+	0.0434087i	$0.0138218\pi$
$733$			2.35049i			0.0868175i	−0.999057	+	0.0434087i	$0.986178\pi$
$734$	−19.7210	−	12.0376i	−0.727916	−	0.444317i
$735$		0			0
$736$	−15.7279	−	37.0501i	−0.579739	−	1.36568i
$737$	20.9706			0.772461
$738$		0			0
$739$			52.3968i			1.92745i	0.266905	+	0.963723i	$0.413999\pi$
$739$			52.3968i			1.92745i	−0.266905	+	0.963723i	$0.586001\pi$
$740$	7.70154	−	3.95815i	0.283114	−	0.145505i
$741$		0			0
$742$		0			0
$743$			17.8930i			0.656429i	0.944603	+	0.328215i	$0.106447\pi$
$743$			17.8930i			0.656429i	−0.944603	+	0.328215i	$0.893553\pi$
$744$		0			0
$745$			0.896683i			0.0328519i
$746$	9.82843	+	5.99923i	0.359844	+	0.219647i
$747$		0			0
$748$	8.49906	+	16.5370i	0.310756	+	0.604652i
$749$		0			0
$750$		0			0
$751$		−	13.7249i		−	0.500829i	−0.968139	−	0.250415i	$-0.919433\pi$
$751$		−	13.7249i		−	0.500829i	0.968139	−	0.250415i	$-0.0805670\pi$
$752$	−12.6802	+	17.7122i	−0.462398	+	0.645898i
$753$		0			0
$754$	−2.25573	+	3.69552i	−0.0821488	+	0.134583i
$755$	5.83283			0.212279
$756$		0			0
$757$	12.2843			0.446479			0.223240	−	0.974764i	$-0.428337\pi$
$757$	12.2843			0.446479			0.223240	+	0.974764i	$0.428337\pi$
$758$	−17.6360	+	28.8928i	−0.640570	+	1.04943i
$759$		0			0
$760$	3.44365	+	0.252834i	0.124914	+	0.00917126i
$761$		−	25.9999i		−	0.942497i	−0.882000	−	0.471249i	$-0.843803\pi$
$761$		−	25.9999i		−	0.942497i	0.882000	−	0.471249i	$-0.156197\pi$
$762$		0			0
$763$		0			0
$764$	35.7990	−	18.3986i	1.29516	−	0.665639i
$765$		0			0
$766$	−8.16872	−	4.98615i	−0.295148	−	0.180157i
$767$		−	23.0723i		−	0.833094i
$768$		0			0
$769$		−	46.1940i		−	1.66580i	−0.553425	−	0.832899i	$-0.686680\pi$
$769$		−	46.1940i		−	1.66580i	0.553425	−	0.832899i	$-0.313320\pi$
$770$		0			0
$771$		0			0
$772$	15.9203	+	30.9768i	0.572985	+	1.11488i
$773$		−	52.9735i		−	1.90532i	−0.304031	−	0.952662i	$-0.598333\pi$
$773$		−	52.9735i		−	1.90532i	0.304031	−	0.952662i	$-0.401667\pi$
$774$		0			0
$775$	−29.4848			−1.05912
$776$	−10.7949	−	0.792563i	−0.387513	−	0.0284514i
$777$		0			0
$778$	17.0711	+	10.4201i	0.612027	+	0.373579i
$779$			6.25206i			0.224003i
$780$		0			0
$781$		0			0
$782$	38.3142	+	23.3868i	1.37011	+	0.836311i
$783$		0			0
$784$		0			0
$785$	21.8579			0.780141
$786$		0			0
$787$	−29.2913			−1.04412			−0.522061	−	0.852908i	$-0.674836\pi$
$787$	−29.2913			−1.04412			−0.522061	+	0.852908i	$0.674836\pi$
$788$	−1.82843	−	3.55765i	−0.0651350	−	0.126736i
$789$		0			0
$790$	−5.44581	−	3.32410i	−0.193753	−	0.118266i
$791$		0			0
$792$		0			0
$793$	−34.1421			−1.21242
$794$	9.43341	−	15.4546i	0.334779	−	0.548463i
$795$		0			0
$796$	19.9145	+	38.7485i	0.705852	+	1.37341i
$797$		−	19.1886i		−	0.679694i	−0.940481	−	0.339847i	$-0.889625\pi$
$797$		−	19.1886i		−	0.679694i	0.940481	−	0.339847i	$-0.110375\pi$
$798$		0			0
$799$		−	24.2931i		−	0.859429i
$800$	−19.9350	+	8.46250i	−0.704810	+	0.299195i
$801$		0			0
$802$	8.65685	+	5.28411i	0.305684	+	0.186588i
$803$	16.6111			0.586193
$804$		0			0
$805$		0			0
$806$	14.8284	−	24.2931i	0.522309	−	0.855689i
$807$		0			0
$808$	−0.523855	−	0.0384616i	−0.0184291	−	0.00135308i
$809$	−48.0416			−1.68905			−0.844527	−	0.535513i	$-0.820118\pi$
$809$	−48.0416			−1.68905			−0.844527	+	0.535513i	$0.820118\pi$
$810$		0			0
$811$	−42.4386			−1.49022			−0.745111	−	0.666941i	$-0.767603\pi$
$811$	−42.4386			−1.49022			−0.745111	+	0.666941i	$0.767603\pi$
$812$		0			0
$813$		0			0
$814$	6.14214	−	10.0625i	0.215282	−	0.352692i
$815$	4.12444			0.144473
$816$		0			0
$817$		−	8.99869i		−	0.314824i
$818$	5.34906	−	8.76326i	0.187025	−	0.306400i
$819$		0			0
$820$	5.48528	+	10.6729i	0.191554	+	0.372715i
$821$	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
$823$		−	32.6292i		−	1.13738i	−0.822551	−	0.568692i	$-0.807450\pi$
$823$		−	32.6292i		−	1.13738i	0.822551	−	0.568692i	$-0.192550\pi$
$824$	−3.19008	+	43.4495i	−0.111132	+	1.51364i
$825$		0			0
$826$		0			0
$827$			17.8930i			0.622199i	0.950377	+	0.311100i	$0.100697\pi$
$827$			17.8930i			0.622199i	−0.950377	+	0.311100i	$0.899303\pi$
$828$		0			0
$829$			4.25265i			0.147700i	0.997269	+	0.0738502i	$0.0235287\pi$
$829$			4.25265i			0.147700i	−0.997269	+	0.0738502i	$0.976471\pi$
$830$	−3.44365	+	5.64167i	−0.119531	+	0.195825i
$831$		0			0
$832$	3.05325	−	20.6808i	0.105852	−	0.716979i
$833$		0			0
$834$		0			0
$835$		−	22.5667i		−	0.780952i
$836$	4.18111	−	2.14885i	0.144607	−	0.0743196i
$837$		0			0
$838$	19.9546	+	12.1802i	0.689321	+	0.420758i
$839$	−53.9108			−1.86121			−0.930603	−	0.366029i	$-0.880717\pi$
$839$	−53.9108			−1.86121			−0.930603	+	0.366029i	$0.880717\pi$
$840$		0			0
$841$	−27.6274			−0.952670
$842$	7.82843	+	4.77844i	0.269785	+	0.164676i
$843$		0			0
$844$	28.3848	−	14.5882i	0.977044	−	0.502145i
$845$			6.68006i			0.229801i
$846$		0			0
$847$		0			0
$848$	−15.1005	+	21.0930i	−0.518553	+	0.724338i
$849$		0			0
$850$	12.5834	−	20.6152i	0.431608	−	0.707095i
$851$		−	28.4612i		−	0.975637i
$852$		0			0
$853$			3.61859i			0.123898i	0.998079	+	0.0619492i	$0.0197317\pi$
$853$			3.61859i			0.123898i	−0.998079	+	0.0619492i	$0.980268\pi$
$854$		0			0
$855$		0			0
$856$	−20.0711	−	1.47363i	−0.686015	−	0.0503675i
$857$			39.6996i			1.35611i	0.735010	+	0.678057i	$0.237178\pi$
$857$			39.6996i			1.35611i	−0.735010	+	0.678057i	$0.762822\pi$
$858$		0			0
$859$	19.7210			0.672873			0.336436	−	0.941706i	$-0.390778\pi$
$859$	19.7210			0.672873			0.336436	+	0.941706i	$0.390778\pi$
$860$	−7.89505	−	15.3617i	−0.269219	−	0.523831i
$861$		0			0
$862$	12.6569	−	20.7355i	0.431094	−	0.706254i
$863$			18.3986i			0.626297i	0.949704	+	0.313148i	$0.101384\pi$
$863$			18.3986i			0.626297i	−0.949704	+	0.313148i	$0.898616\pi$
$864$		0			0
$865$	−22.8284			−0.776190
$866$	11.1819	−	18.3191i	0.379976	−	0.622508i
$867$		0			0
$868$		0			0
$869$	−8.68629			−0.294662
$870$		0			0
$871$	26.2947			0.890962
$872$	−1.17157	+	15.9570i	−0.0396745	+	0.540374i
$873$		0			0
$874$	5.91299	−	9.68714i	0.200010	−	0.327672i
$875$		0			0
$876$		0			0
$877$	−54.4264			−1.83785			−0.918925	−	0.394433i	$-0.870941\pi$
$877$	−54.4264			−1.83785			−0.918925	+	0.394433i	$0.870941\pi$
$878$	−21.3161	−	13.0112i	−0.719382	−	0.439108i
$879$		0			0
$880$	5.25230	−	7.33664i	0.177055	−	0.247318i
$881$			15.1760i			0.511293i	0.966770	+	0.255647i	$0.0822883\pi$
$881$			15.1760i			0.511293i	−0.966770	+	0.255647i	$0.917712\pi$
$882$		0			0
$883$		−	4.67371i		−	0.157283i	−0.996903	−	0.0786415i	$-0.974942\pi$
$883$		−	4.67371i		−	0.157283i	0.996903	−	0.0786415i	$-0.0250582\pi$
$884$	10.6569	+	20.7355i	0.358429	+	0.697410i
$885$		0			0
$886$	19.6985	−	32.2717i	0.661784	−	1.08419i
$887$	17.6588			0.592925			0.296462	−	0.955045i	$-0.404193\pi$
$887$	17.6588			0.592925			0.296462	+	0.955045i	$0.404193\pi$
$888$		0			0
$889$		0			0
$890$	−5.24264	−	3.20009i	−0.175734	−	0.107267i
$891$		0			0
$892$	19.0603	+	37.0865i	0.638187	+	1.24175i
$893$	−6.14214			−0.205539
$894$		0			0
$895$	1.32138			0.0441687
$896$		0			0
$897$		0			0
$898$	−48.6274	−	29.6820i	−1.62272	−	0.990500i
$899$	−9.02291			−0.300931
$900$		0			0
$901$		−	28.9301i		−	0.963801i
$902$	13.9449	+	8.51189i	0.464313	+	0.283415i
$903$		0			0
$904$	0.878680	−	11.9678i	0.0292245	−	0.398043i
$905$	−6.54416			−0.217535
$906$		0			0
$907$			23.7875i			0.789850i	0.918713	+	0.394925i	$0.129229\pi$
$907$			23.7875i			0.789850i	−0.918713	+	0.394925i	$0.870771\pi$
$908$	16.5710	+	32.2429i	0.549929	+	1.07002i
$909$		0			0
$910$		0			0
$911$		−	43.1974i		−	1.43119i	−0.698513	−	0.715597i	$-0.746155\pi$
$911$		−	43.1974i		−	1.43119i	0.698513	−	0.715597i	$-0.253845\pi$
$912$		0			0
$913$			8.99869i			0.297813i
$914$	−29.8492	−	18.2199i	−0.987325	−	0.602659i
$915$		0			0
$916$	−33.6659	+	17.3023i	−1.11235	+	0.571686i
$917$		0			0
$918$		0			0
$919$			49.3014i			1.62630i	0.582052	+	0.813151i	$0.302250\pi$
$919$			49.3014i			1.62630i	−0.582052	+	0.813151i	$0.697750\pi$
$920$	1.59504	−	21.7248i	0.0525869	−	0.716244i
$921$		0			0
$922$	20.2449	−	33.1668i	0.666730	−	1.09229i
$923$		0			0
$924$		0			0
$925$	−15.3137			−0.503512
$926$	−4.87006	+	7.97852i	−0.160040	+	0.262191i
$927$		0			0
$928$	−6.10051	+	2.58969i	−0.200259	+	0.0850107i
$929$		−	16.7068i		−	0.548131i	−0.961711	−	0.274065i	$-0.911632\pi$
$929$		−	16.7068i		−	0.548131i	0.961711	−	0.274065i	$-0.0883685\pi$
$930$		0			0
$931$		0			0
$932$	−7.09188	−	13.7990i	−0.232302	−	0.452000i
$933$		0			0
$934$	−9.06299	−	5.53201i	−0.296550	−	0.181013i
$935$			10.0625i			0.329080i
$936$		0			0
$937$		−	53.4762i		−	1.74699i	−0.486831	−	0.873496i	$-0.661847\pi$
$937$		−	53.4762i		−	1.74699i	0.486831	−	0.873496i	$-0.338153\pi$
$938$		0			0
$939$		0			0
$940$	−10.4853	+	5.38883i	−0.341992	+	0.175764i
$941$		−	8.10201i		−	0.264118i	−0.991242	−	0.132059i	$-0.957841\pi$
$941$		−	8.10201i		−	0.264118i	0.991242	−	0.132059i	$-0.0421588\pi$
$942$		0			0
$943$	39.4421			1.28441
$944$	20.5586	−	28.7172i	0.669126	−	0.934665i
$945$		0			0
$946$	−20.0711	−	12.2513i	−0.652567	−	0.398324i
$947$			42.3342i			1.37568i	0.725864	+	0.687838i	$0.241440\pi$
$947$			42.3342i			1.37568i	−0.725864	+	0.687838i	$0.758560\pi$
$948$		0			0
$949$	20.8284			0.676119
$950$	−5.21222	−	3.18152i	−0.169107	−	0.103222i
$951$		0			0
$952$		0			0
$953$	−37.6569			−1.21983			−0.609913	−	0.792469i	$-0.708795\pi$
$953$	−37.6569			−1.21983			−0.609913	+	0.792469i	$0.708795\pi$
$954$		0			0
$955$	21.7832			0.704889
$956$	−20.0711	+	10.3154i	−0.649145	+	0.333623i
$957$		0			0
$958$	24.0390	+	14.6733i	0.776664	+	0.474072i
$959$		0			0
$960$		0			0
$961$	28.3137			0.913345
$962$	7.70154	−	12.6173i	0.248308	−	0.406798i
$963$		0			0
$964$	−15.3063	+	7.86657i	−0.492983	+	0.253365i
$965$			18.8490i			0.606771i
$966$		0			0
$967$		−	17.8930i		−	0.575399i	−0.957721	−	0.287699i	$-0.907110\pi$
$967$		−	17.8930i		−	0.575399i	0.957721	−	0.287699i	$-0.0928904\pi$
$968$	−1.37868	+	18.7779i	−0.0443124	+	0.603544i
$969$		0			0
$970$	−5.00000	−	3.05198i	−0.160540	−	0.0979931i
$971$	21.9768			0.705268			0.352634	−	0.935761i	$-0.385286\pi$
$971$	21.9768			0.705268			0.352634	+	0.935761i	$0.385286\pi$
$972$		0			0
$973$		0			0
$974$	−29.2843	+	47.9759i	−0.938329	+	1.53725i
$975$		0			0
$976$	−42.4953	−	30.4224i	−1.36024	−	0.973796i
$977$	−54.3848			−1.73992			−0.869962	−	0.493120i	$-0.835857\pi$
$977$	−54.3848			−1.73992			−0.869962	+	0.493120i	$0.835857\pi$
$978$		0			0
$979$	−8.36223			−0.267258
$980$		0			0
$981$		0			0
$982$	11.7574	−	19.2619i	0.375192	−	0.614671i
$983$	−33.9962			−1.08431			−0.542156	−	0.840278i	$-0.682392\pi$
$983$	−33.9962			−1.08431			−0.542156	+	0.840278i	$0.682392\pi$
$984$		0			0
$985$		−	2.16478i		−	0.0689758i
$986$	3.85077	−	6.30864i	0.122633	−	0.200908i
$987$		0			0
$988$	5.24264	−	2.69442i	0.166791	−	0.0857208i
$989$	−56.7696			−1.80517
$990$		0			0
$991$			21.8516i			0.694137i	0.937840	+	0.347069i	$0.112823\pi$
$991$			21.8516i			0.694137i	−0.937840	+	0.347069i	$0.887177\pi$
$992$	40.1027	−	17.0238i	1.27326	−	0.540506i
$993$		0			0
$994$		0			0
$995$			23.5780i			0.747473i
$996$		0			0
$997$			6.68006i			0.211560i	0.994390	+	0.105780i	$0.0337339\pi$
$997$			6.68006i			0.211560i	−0.994390	+	0.105780i	$0.966266\pi$
$998$	13.5563	−	22.2091i	0.429119	−	0.703017i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.k.1567.8		8
3.2	odd	2		196.2.d.c.195.2	yes	8
4.3	odd	2	inner	1764.2.b.k.1567.6		8
7.6	odd	2	inner	1764.2.b.k.1567.7		8
12.11	even	2		196.2.d.c.195.3	yes	8
21.2	odd	6		196.2.f.d.31.3		16
21.5	even	6		196.2.f.d.31.4		16
21.11	odd	6		196.2.f.d.19.7		16
21.17	even	6		196.2.f.d.19.8		16
21.20	even	2		196.2.d.c.195.1	✓	8
24.5	odd	2		3136.2.f.i.3135.2		8
24.11	even	2		3136.2.f.i.3135.8		8
28.27	even	2	inner	1764.2.b.k.1567.5		8
84.11	even	6		196.2.f.d.19.4		16
84.23	even	6		196.2.f.d.31.8		16
84.47	odd	6		196.2.f.d.31.7		16
84.59	odd	6		196.2.f.d.19.3		16
84.83	odd	2		196.2.d.c.195.4	yes	8
168.83	odd	2		3136.2.f.i.3135.1		8
168.125	even	2		3136.2.f.i.3135.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.d.c.195.1	✓	8	21.20	even	2
196.2.d.c.195.2	yes	8	3.2	odd	2
196.2.d.c.195.3	yes	8	12.11	even	2
196.2.d.c.195.4	yes	8	84.83	odd	2
196.2.f.d.19.3		16	84.59	odd	6
196.2.f.d.19.4		16	84.11	even	6
196.2.f.d.19.7		16	21.11	odd	6
196.2.f.d.19.8		16	21.17	even	6
196.2.f.d.31.3		16	21.2	odd	6
196.2.f.d.31.4		16	21.5	even	6
196.2.f.d.31.7		16	84.47	odd	6
196.2.f.d.31.8		16	84.23	even	6
1764.2.b.k.1567.5		8	28.27	even	2	inner
1764.2.b.k.1567.6		8	4.3	odd	2	inner
1764.2.b.k.1567.7		8	7.6	odd	2	inner
1764.2.b.k.1567.8		8	1.1	even	1	trivial
3136.2.f.i.3135.1		8	168.83	odd	2
3136.2.f.i.3135.2		8	24.5	odd	2
3136.2.f.i.3135.7		8	168.125	even	2
3136.2.f.i.3135.8		8	24.11	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)

\(f(q)\)	\(=\)	\(q+(1.20711 + 0.736813i) q^{2} +(0.914214 + 1.77882i) q^{4} +1.08239i q^{5} +(-0.207107 + 2.82083i) q^{8} +O(q^{10})\)	\(q+(1.20711 + 0.736813i) q^{2} +(0.914214 + 1.77882i) q^{4} +1.08239i q^{5} +(-0.207107 + 2.82083i) q^{8} +(-0.797521 + 1.30656i) q^{10} +2.08402i q^{11} +2.61313i q^{13} +(-2.32843 + 3.25245i) q^{16} -4.46088i q^{17} -1.12786 q^{19} +(-1.92538 + 0.989538i) q^{20} +(-1.53553 + 2.51564i) q^{22} +7.11529i q^{23} +3.82843 q^{25} +(-1.92538 + 3.15432i) q^{26} +1.17157 q^{29} -7.70154 q^{31} +(-5.20711 + 2.21044i) q^{32} +(3.28684 - 5.38476i) q^{34} -4.00000 q^{37} +(-1.36145 - 0.831025i) q^{38} +(-3.05325 - 0.224171i) q^{40} -5.54328i q^{41} +7.97852i q^{43} +(-3.70711 + 1.90524i) q^{44} +(-5.24264 + 8.58892i) q^{46} +5.44581 q^{47} +(4.62132 + 2.82083i) q^{50} +(-4.64829 + 2.38896i) q^{52} +6.48528 q^{53} -2.25573 q^{55} +(1.41421 + 0.863230i) q^{58} -8.82940 q^{59} +13.0656i q^{61} +(-9.29658 - 5.67459i) q^{62} +(-7.91421 - 1.16843i) q^{64} -2.82843 q^{65} -10.0625i q^{67} +(7.93513 - 4.07820i) q^{68} -7.97069i q^{73} +(-4.82843 - 2.94725i) q^{74} +(-1.03111 - 2.00627i) q^{76} +4.16804i q^{79} +(-3.52043 - 2.52027i) q^{80} +(4.08436 - 6.69133i) q^{82} +4.31795 q^{83} +4.82843 q^{85} +(-5.87868 + 9.63093i) q^{86} +(-5.87868 - 0.431615i) q^{88} +4.01254i q^{89} +(-12.6569 + 6.50490i) q^{92} +(6.57368 + 4.01254i) q^{94} -1.22079i q^{95} +3.82683i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 4 q^{4} + 4 q^{8}+O(q^{10}) \) 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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