LMFDB - Embedded newform 3822.2.c.h.883.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3822,2,Mod(883,3822)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3822, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3822.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3822.c (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:	$30.5188236525$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(i, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9x^{2} + 16 $ x^4 + 9*x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			883.3
Root			$-2.56155i$ of defining polynomial
Character	$\chi$	$=$	3822.883
Dual form			3822.2.c.h.883.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.56155i q^{5} +1.00000i q^{6} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.56155i q^{5} +1.00000i q^{6} -1.00000i q^{8} +1.00000 q^{9} +3.56155 q^{10} +5.56155i q^{11} -1.00000 q^{12} +(-3.56155 + 0.561553i) q^{13} -3.56155i q^{15} +1.00000 q^{16} +6.68466 q^{17} +1.00000i q^{18} +1.56155i q^{19} +3.56155i q^{20} -5.56155 q^{22} -6.68466 q^{23} -1.00000i q^{24} -7.68466 q^{25} +(-0.561553 - 3.56155i) q^{26} +1.00000 q^{27} +1.56155 q^{29} +3.56155 q^{30} +6.24621i q^{31} +1.00000i q^{32} +5.56155i q^{33} +6.68466i q^{34} -1.00000 q^{36} +10.6847i q^{37} -1.56155 q^{38} +(-3.56155 + 0.561553i) q^{39} -3.56155 q^{40} -4.00000i q^{41} -6.43845 q^{43} -5.56155i q^{44} -3.56155i q^{45} -6.68466i q^{46} +10.2462i q^{47} +1.00000 q^{48} -7.68466i q^{50} +6.68466 q^{51} +(3.56155 - 0.561553i) q^{52} +4.87689 q^{53} +1.00000i q^{54} +19.8078 q^{55} +1.56155i q^{57} +1.56155i q^{58} -4.24621i q^{59} +3.56155i q^{60} +1.56155 q^{61} -6.24621 q^{62} -1.00000 q^{64} +(2.00000 + 12.6847i) q^{65} -5.56155 q^{66} -1.12311i q^{67} -6.68466 q^{68} -6.68466 q^{69} +9.36932i q^{71} -1.00000i q^{72} -11.5616i q^{73} -10.6847 q^{74} -7.68466 q^{75} -1.56155i q^{76} +(-0.561553 - 3.56155i) q^{78} +16.0000 q^{79} -3.56155i q^{80} +1.00000 q^{81} +4.00000 q^{82} +2.00000i q^{83} -23.8078i q^{85} -6.43845i q^{86} +1.56155 q^{87} +5.56155 q^{88} +8.00000i q^{89} +3.56155 q^{90} +6.68466 q^{92} +6.24621i q^{93} -10.2462 q^{94} +5.56155 q^{95} +1.00000i q^{96} -10.0000i q^{97} +5.56155i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9	$ 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9} + 6 q^{10} - 4 q^{12} - 6 q^{13} + 4 q^{16} + 2 q^{17} - 14 q^{22} - 2 q^{23} - 6 q^{25} + 6 q^{26} + 4 q^{27} - 2 q^{29} + 6 q^{30} - 4 q^{36} + 2 q^{38} - 6 q^{39} - 6 q^{40} - 34 q^{43} + 4 q^{48} + 2 q^{51} + 6 q^{52} + 36 q^{53} + 38 q^{55} - 2 q^{61} + 8 q^{62} - 4 q^{64} + 8 q^{65} - 14 q^{66} - 2 q^{68} - 2 q^{69} - 18 q^{74} - 6 q^{75} + 6 q^{78} + 64 q^{79} + 4 q^{81} + 16 q^{82} - 2 q^{87} + 14 q^{88} + 6 q^{90} + 2 q^{92} - 8 q^{94} + 14 q^{95}+O(q^{100}) $ 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9 + 6 * q^10 - 4 * q^12 - 6 * q^13 + 4 * q^16 + 2 * q^17 - 14 * q^22 - 2 * q^23 - 6 * q^25 + 6 * q^26 + 4 * q^27 - 2 * q^29 + 6 * q^30 - 4 * q^36 + 2 * q^38 - 6 * q^39 - 6 * q^40 - 34 * q^43 + 4 * q^48 + 2 * q^51 + 6 * q^52 + 36 * q^53 + 38 * q^55 - 2 * q^61 + 8 * q^62 - 4 * q^64 + 8 * q^65 - 14 * q^66 - 2 * q^68 - 2 * q^69 - 18 * q^74 - 6 * q^75 + 6 * q^78 + 64 * q^79 + 4 * q^81 + 16 * q^82 - 2 * q^87 + 14 * q^88 + 6 * q^90 + 2 * q^92 - 8 * q^94 + 14 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3822\mathbb{Z}\right)^\times$.

$n$	$1471$	$2549$	$3433$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$		−	3.56155i		−	1.59277i	−0.604787	−	0.796387i	$-0.706742\pi$
$5$		−	3.56155i		−	1.59277i	0.604787	−	0.796387i	$-0.293258\pi$
$6$			1.00000i			0.408248i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	3.56155			1.12626
$11$			5.56155i			1.67687i	0.545001	+	0.838436i	$0.316529\pi$
$11$			5.56155i			1.67687i	−0.545001	+	0.838436i	$0.683471\pi$
$12$	−1.00000			−0.288675
$13$	−3.56155	+	0.561553i	−0.987797	+	0.155747i
$13$	−3.56155	+	0.561553i	−0.987797	+	0.155747i
$14$		0			0
$15$		−	3.56155i		−	0.919589i
$16$	1.00000			0.250000
$17$	6.68466			1.62127			0.810634	−	0.585553i	$-0.199123\pi$
$17$	6.68466			1.62127			0.810634	+	0.585553i	$0.199123\pi$
$18$			1.00000i			0.235702i
$19$			1.56155i			0.358245i	0.983827	+	0.179122i	$0.0573258\pi$
$19$			1.56155i			0.358245i	−0.983827	+	0.179122i	$0.942674\pi$
$20$			3.56155i			0.796387i
$21$		0			0
$22$	−5.56155			−1.18573
$23$	−6.68466			−1.39385			−0.696924	−	0.717145i	$-0.745448\pi$
$23$	−6.68466			−1.39385			−0.696924	+	0.717145i	$0.745448\pi$
$24$		−	1.00000i		−	0.204124i
$25$	−7.68466			−1.53693
$26$	−0.561553	−	3.56155i	−0.110130	−	0.698478i
$27$	1.00000			0.192450
$28$		0			0
$29$	1.56155			0.289973			0.144987	−	0.989434i	$-0.453686\pi$
$29$	1.56155			0.289973			0.144987	+	0.989434i	$0.453686\pi$
$30$	3.56155			0.650248
$31$			6.24621i			1.12185i	0.827866	+	0.560926i	$0.189555\pi$
$31$			6.24621i			1.12185i	−0.827866	+	0.560926i	$0.810445\pi$
$32$			1.00000i			0.176777i
$33$			5.56155i			0.968142i
$34$			6.68466i			1.14641i
$35$		0			0
$36$	−1.00000			−0.166667
$37$			10.6847i			1.75655i	0.478159	+	0.878274i	$0.341304\pi$
$37$			10.6847i			1.75655i	−0.478159	+	0.878274i	$0.658696\pi$
$38$	−1.56155			−0.253317
$39$	−3.56155	+	0.561553i	−0.570305	+	0.0899204i
$40$	−3.56155			−0.563131
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$		0			0
$43$	−6.43845			−0.981854			−0.490927	−	0.871201i	$-0.663342\pi$
$43$	−6.43845			−0.981854			−0.490927	+	0.871201i	$0.663342\pi$
$44$		−	5.56155i		−	0.838436i
$45$		−	3.56155i		−	0.530925i
$46$		−	6.68466i		−	0.985599i
$47$			10.2462i			1.49456i	0.664507	+	0.747282i	$0.268641\pi$
$47$			10.2462i			1.49456i	−0.664507	+	0.747282i	$0.731359\pi$
$48$	1.00000			0.144338
$49$		0			0
$50$		−	7.68466i		−	1.08677i
$51$	6.68466			0.936039
$52$	3.56155	−	0.561553i	0.493899	−	0.0778734i
$53$	4.87689			0.669893			0.334946	−	0.942237i	$-0.391282\pi$
$53$	4.87689			0.669893			0.334946	+	0.942237i	$0.391282\pi$
$54$			1.00000i			0.136083i
$55$	19.8078			2.67088
$56$		0			0
$57$			1.56155i			0.206833i
$58$			1.56155i			0.205042i
$59$		−	4.24621i		−	0.552810i	−0.961041	−	0.276405i	$-0.910857\pi$
$59$		−	4.24621i		−	0.552810i	0.961041	−	0.276405i	$-0.0891431\pi$
$60$			3.56155i			0.459794i
$61$	1.56155			0.199936			0.0999682	−	0.994991i	$-0.468126\pi$
$61$	1.56155			0.199936			0.0999682	+	0.994991i	$0.468126\pi$
$62$	−6.24621			−0.793270
$63$		0			0
$64$	−1.00000			−0.125000
$65$	2.00000	+	12.6847i	0.248069	+	1.57334i
$66$	−5.56155			−0.684580
$67$		−	1.12311i		−	0.137209i	−0.997644	−	0.0686046i	$-0.978145\pi$
$67$		−	1.12311i		−	0.137209i	0.997644	−	0.0686046i	$-0.0218547\pi$
$68$	−6.68466			−0.810634
$69$	−6.68466			−0.804738
$70$		0			0
$71$			9.36932i			1.11193i	0.831205	+	0.555967i	$0.187652\pi$
$71$			9.36932i			1.11193i	−0.831205	+	0.555967i	$0.812348\pi$
$72$		−	1.00000i		−	0.117851i
$73$		−	11.5616i		−	1.35318i	−0.736361	−	0.676589i	$-0.763458\pi$
$73$		−	11.5616i		−	1.35318i	0.736361	−	0.676589i	$-0.236542\pi$
$74$	−10.6847			−1.24207
$75$	−7.68466			−0.887348
$76$		−	1.56155i		−	0.179122i
$77$		0			0
$78$	−0.561553	−	3.56155i	−0.0635833	−	0.403266i
$79$	16.0000			1.80014			0.900070	−	0.435745i	$-0.143515\pi$
$79$	16.0000			1.80014			0.900070	+	0.435745i	$0.143515\pi$
$80$		−	3.56155i		−	0.398194i
$81$	1.00000			0.111111
$82$	4.00000			0.441726
$83$			2.00000i			0.219529i	0.993958	+	0.109764i	$0.0350096\pi$
$83$			2.00000i			0.219529i	−0.993958	+	0.109764i	$0.964990\pi$
$84$		0			0
$85$		−	23.8078i		−	2.58231i
$86$		−	6.43845i		−	0.694276i
$87$	1.56155			0.167416
$88$	5.56155			0.592864
$89$			8.00000i			0.847998i	0.905663	+	0.423999i	$0.139374\pi$
$89$			8.00000i			0.847998i	−0.905663	+	0.423999i	$0.860626\pi$
$90$	3.56155			0.375421
$91$		0			0
$92$	6.68466			0.696924
$93$			6.24621i			0.647702i
$94$	−10.2462			−1.05682
$95$	5.56155			0.570603
$96$			1.00000i			0.102062i
$97$		−	10.0000i		−	1.01535i	−0.861550	−	0.507673i	$-0.830506\pi$
$97$		−	10.0000i		−	1.01535i	0.861550	−	0.507673i	$-0.169494\pi$
$98$		0			0
$99$			5.56155i			0.558957i
$100$	7.68466			0.768466
$101$	−6.00000			−0.597022			−0.298511	−	0.954406i	$-0.596490\pi$
$101$	−6.00000			−0.597022			−0.298511	+	0.954406i	$0.596490\pi$
$102$			6.68466i			0.661880i
$103$	−1.80776			−0.178124			−0.0890621	−	0.996026i	$-0.528387\pi$
$103$	−1.80776			−0.178124			−0.0890621	+	0.996026i	$0.528387\pi$
$104$	0.561553	+	3.56155i	0.0550648	+	0.349239i
$105$		0			0
$106$			4.87689i			0.473686i
$107$	−4.87689			−0.471467			−0.235734	−	0.971818i	$-0.575749\pi$
$107$	−4.87689			−0.471467			−0.235734	+	0.971818i	$0.575749\pi$
$108$	−1.00000			−0.0962250
$109$			12.9309i			1.23855i	0.785173	+	0.619276i	$0.212574\pi$
$109$			12.9309i			1.23855i	−0.785173	+	0.619276i	$0.787426\pi$
$110$			19.8078i			1.88860i
$111$			10.6847i			1.01414i
$112$		0			0
$113$	20.2462			1.90460			0.952302	−	0.305158i	$-0.0987093\pi$
$113$	20.2462			1.90460			0.952302	+	0.305158i	$0.0987093\pi$
$114$	−1.56155			−0.146253
$115$			23.8078i			2.22009i
$116$	−1.56155			−0.144987
$117$	−3.56155	+	0.561553i	−0.329266	+	0.0519156i
$118$	4.24621			0.390895
$119$		0			0
$120$	−3.56155			−0.325124
$121$	−19.9309			−1.81190
$122$			1.56155i			0.141376i
$123$		−	4.00000i		−	0.360668i
$124$		−	6.24621i		−	0.560926i
$125$			9.56155i			0.855211i
$126$		0			0
$127$	10.2462			0.909204			0.454602	−	0.890695i	$-0.349781\pi$
$127$	10.2462			0.909204			0.454602	+	0.890695i	$0.349781\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−6.43845			−0.566874
$130$	−12.6847	+	2.00000i	−1.11252	+	0.175412i
$131$	1.56155			0.136434			0.0682168	−	0.997671i	$-0.478269\pi$
$131$	1.56155			0.136434			0.0682168	+	0.997671i	$0.478269\pi$
$132$		−	5.56155i		−	0.484071i
$133$		0			0
$134$	1.12311			0.0970215
$135$		−	3.56155i		−	0.306530i
$136$		−	6.68466i		−	0.573205i
$137$			6.68466i			0.571109i	0.958362	+	0.285554i	$0.0921777\pi$
$137$			6.68466i			0.571109i	−0.958362	+	0.285554i	$0.907822\pi$
$138$		−	6.68466i		−	0.569036i
$139$	−10.2462			−0.869072			−0.434536	−	0.900654i	$-0.643088\pi$
$139$	−10.2462			−0.869072			−0.434536	+	0.900654i	$0.643088\pi$
$140$		0			0
$141$			10.2462i			0.862887i
$142$	−9.36932			−0.786256
$143$	−3.12311	−	19.8078i	−0.261167	−	1.65641i
$144$	1.00000			0.0833333
$145$		−	5.56155i		−	0.461862i
$146$	11.5616			0.956841
$147$		0			0
$148$		−	10.6847i		−	0.878274i
$149$			10.0000i			0.819232i	0.912258	+	0.409616i	$0.134337\pi$
$149$			10.0000i			0.819232i	−0.912258	+	0.409616i	$0.865663\pi$
$150$		−	7.68466i		−	0.627450i
$151$			16.6847i			1.35778i	0.734241	+	0.678889i	$0.237538\pi$
$151$			16.6847i			1.35778i	−0.734241	+	0.678889i	$0.762462\pi$
$152$	1.56155			0.126659
$153$	6.68466			0.540423
$154$		0			0
$155$	22.2462			1.78686
$156$	3.56155	−	0.561553i	0.285152	−	0.0449602i
$157$	11.8078			0.942362			0.471181	−	0.882037i	$-0.343828\pi$
$157$	11.8078			0.942362			0.471181	+	0.882037i	$0.343828\pi$
$158$			16.0000i			1.27289i
$159$	4.87689			0.386763
$160$	3.56155			0.281565
$161$		0			0
$162$			1.00000i			0.0785674i
$163$			9.12311i			0.714577i	0.933994	+	0.357288i	$0.116299\pi$
$163$			9.12311i			0.714577i	−0.933994	+	0.357288i	$0.883701\pi$
$164$			4.00000i			0.312348i
$165$	19.8078			1.54203
$166$	−2.00000			−0.155230
$167$			11.8078i			0.913712i	0.889541	+	0.456856i	$0.151025\pi$
$167$			11.8078i			0.913712i	−0.889541	+	0.456856i	$0.848975\pi$
$168$		0			0
$169$	12.3693	−	4.00000i	0.951486	−	0.307692i
$170$	23.8078			1.82597
$171$			1.56155i			0.119415i
$172$	6.43845			0.490927
$173$	3.75379			0.285395			0.142698	−	0.989766i	$-0.454422\pi$
$173$	3.75379			0.285395			0.142698	+	0.989766i	$0.454422\pi$
$174$			1.56155i			0.118381i
$175$		0			0
$176$			5.56155i			0.419218i
$177$		−	4.24621i		−	0.319165i
$178$	−8.00000			−0.599625
$179$	11.1231			0.831380			0.415690	−	0.909506i	$-0.363540\pi$
$179$	11.1231			0.831380			0.415690	+	0.909506i	$0.363540\pi$
$180$			3.56155i			0.265462i
$181$	13.3693			0.993733			0.496867	−	0.867827i	$-0.334484\pi$
$181$	13.3693			0.993733			0.496867	+	0.867827i	$0.334484\pi$
$182$		0			0
$183$	1.56155			0.115433
$184$			6.68466i			0.492800i
$185$	38.0540			2.79778
$186$	−6.24621			−0.457994
$187$			37.1771i			2.71866i
$188$		−	10.2462i		−	0.747282i
$189$		0			0
$190$			5.56155i			0.403477i
$191$	−24.0540			−1.74048			−0.870242	−	0.492624i	$-0.836038\pi$
$191$	−24.0540			−1.74048			−0.870242	+	0.492624i	$0.836038\pi$
$192$	−1.00000			−0.0721688
$193$		−	12.0000i		−	0.863779i	−0.901927	−	0.431889i	$-0.857847\pi$
$193$		−	12.0000i		−	0.863779i	0.901927	−	0.431889i	$-0.142153\pi$
$194$	10.0000			0.717958
$195$	2.00000	+	12.6847i	0.143223	+	0.908367i
$196$		0			0
$197$		−	6.00000i		−	0.427482i	−0.976890	−	0.213741i	$-0.931435\pi$
$197$		−	6.00000i		−	0.427482i	0.976890	−	0.213741i	$-0.0685649\pi$
$198$	−5.56155			−0.395242
$199$	−4.93087			−0.349540			−0.174770	−	0.984609i	$-0.555918\pi$
$199$	−4.93087			−0.349540			−0.174770	+	0.984609i	$0.555918\pi$
$200$			7.68466i			0.543387i
$201$		−	1.12311i		−	0.0792178i
$202$		−	6.00000i		−	0.422159i
$203$		0			0
$204$	−6.68466			−0.468020
$205$	−14.2462			−0.994999
$206$		−	1.80776i		−	0.125953i
$207$	−6.68466			−0.464616
$208$	−3.56155	+	0.561553i	−0.246949	+	0.0389367i
$209$	−8.68466			−0.600730
$210$		0			0
$211$	7.80776			0.537509			0.268754	−	0.963209i	$-0.413388\pi$
$211$	7.80776			0.537509			0.268754	+	0.963209i	$0.413388\pi$
$212$	−4.87689			−0.334946
$213$			9.36932i			0.641975i
$214$		−	4.87689i		−	0.333378i
$215$			22.9309i			1.56387i
$216$		−	1.00000i		−	0.0680414i
$217$		0			0
$218$	−12.9309			−0.875789
$219$		−	11.5616i		−	0.781257i
$220$	−19.8078			−1.33544
$221$	−23.8078	+	3.75379i	−1.60148	+	0.252507i
$222$	−10.6847			−0.717107
$223$			1.75379i			0.117442i	0.998274	+	0.0587212i	$0.0187023\pi$
$223$			1.75379i			0.117442i	−0.998274	+	0.0587212i	$0.981298\pi$
$224$		0			0
$225$	−7.68466			−0.512311
$226$			20.2462i			1.34676i
$227$			17.6155i			1.16918i	0.811328	+	0.584592i	$0.198745\pi$
$227$			17.6155i			1.16918i	−0.811328	+	0.584592i	$0.801255\pi$
$228$		−	1.56155i		−	0.103416i
$229$		−	2.00000i		−	0.132164i	−0.997814	−	0.0660819i	$-0.978950\pi$
$229$		−	2.00000i		−	0.132164i	0.997814	−	0.0660819i	$-0.0210498\pi$
$230$	−23.8078			−1.56984
$231$		0			0
$232$		−	1.56155i		−	0.102521i
$233$	2.00000			0.131024			0.0655122	−	0.997852i	$-0.479132\pi$
$233$	2.00000			0.131024			0.0655122	+	0.997852i	$0.479132\pi$
$234$	−0.561553	−	3.56155i	−0.0367099	−	0.232826i
$235$	36.4924			2.38050
$236$			4.24621i			0.276405i
$237$	16.0000			1.03931
$238$		0			0
$239$			14.2462i			0.921511i	0.887527	+	0.460755i	$0.152421\pi$
$239$			14.2462i			0.921511i	−0.887527	+	0.460755i	$0.847579\pi$
$240$		−	3.56155i		−	0.229897i
$241$		−	6.00000i		−	0.386494i	−0.981150	−	0.193247i	$-0.938098\pi$
$241$		−	6.00000i		−	0.386494i	0.981150	−	0.193247i	$-0.0619019\pi$
$242$		−	19.9309i		−	1.28120i
$243$	1.00000			0.0641500
$244$	−1.56155			−0.0999682
$245$		0			0
$246$	4.00000			0.255031
$247$	−0.876894	−	5.56155i	−0.0557955	−	0.353873i
$248$	6.24621			0.396635
$249$			2.00000i			0.126745i
$250$	−9.56155			−0.604726
$251$	−22.0540			−1.39203			−0.696017	−	0.718025i	$-0.745046\pi$
$251$	−22.0540			−1.39203			−0.696017	+	0.718025i	$0.745046\pi$
$252$		0			0
$253$		−	37.1771i		−	2.33730i
$254$			10.2462i			0.642904i
$255$		−	23.8078i		−	1.49090i
$256$	1.00000			0.0625000
$257$	26.0000			1.62184			0.810918	−	0.585160i	$-0.198968\pi$
$257$	26.0000			1.62184			0.810918	+	0.585160i	$0.198968\pi$
$258$		−	6.43845i		−	0.400840i
$259$		0			0
$260$	−2.00000	−	12.6847i	−0.124035	−	0.786669i
$261$	1.56155			0.0966577
$262$			1.56155i			0.0964731i
$263$	−23.3693			−1.44101			−0.720507	−	0.693448i	$-0.756091\pi$
$263$	−23.3693			−1.44101			−0.720507	+	0.693448i	$0.756091\pi$
$264$	5.56155			0.342290
$265$		−	17.3693i		−	1.06699i
$266$		0			0
$267$			8.00000i			0.489592i
$268$			1.12311i			0.0686046i
$269$	−31.3693			−1.91262			−0.956311	−	0.292353i	$-0.905562\pi$
$269$	−31.3693			−1.91262			−0.956311	+	0.292353i	$0.905562\pi$
$270$	3.56155			0.216749
$271$			8.00000i			0.485965i	0.970031	+	0.242983i	$0.0781258\pi$
$271$			8.00000i			0.485965i	−0.970031	+	0.242983i	$0.921874\pi$
$272$	6.68466			0.405317
$273$		0			0
$274$	−6.68466			−0.403835
$275$		−	42.7386i		−	2.57724i
$276$	6.68466			0.402369
$277$	−10.8769			−0.653529			−0.326765	−	0.945106i	$-0.605958\pi$
$277$	−10.8769			−0.653529			−0.326765	+	0.945106i	$0.605958\pi$
$278$		−	10.2462i		−	0.614527i
$279$			6.24621i			0.373951i
$280$		0			0
$281$			6.00000i			0.357930i	0.983855	+	0.178965i	$0.0572749\pi$
$281$			6.00000i			0.357930i	−0.983855	+	0.178965i	$0.942725\pi$
$282$	−10.2462			−0.610153
$283$	4.87689			0.289901			0.144951	−	0.989439i	$-0.453698\pi$
$283$	4.87689			0.289901			0.144951	+	0.989439i	$0.453698\pi$
$284$		−	9.36932i		−	0.555967i
$285$	5.56155			0.329438
$286$	19.8078	−	3.12311i	1.17126	−	0.184673i
$287$		0			0
$288$			1.00000i			0.0589256i
$289$	27.6847			1.62851
$290$	5.56155			0.326586
$291$		−	10.0000i		−	0.586210i
$292$			11.5616i			0.676589i
$293$			7.75379i			0.452981i	0.974013	+	0.226491i	$0.0727253\pi$
$293$			7.75379i			0.452981i	−0.974013	+	0.226491i	$0.927275\pi$
$294$		0			0
$295$	−15.1231			−0.880501
$296$	10.6847			0.621033
$297$			5.56155i			0.322714i
$298$	−10.0000			−0.579284
$299$	23.8078	−	3.75379i	1.37684	−	0.217087i
$300$	7.68466			0.443674
$301$		0			0
$302$	−16.6847			−0.960094
$303$	−6.00000			−0.344691
$304$			1.56155i			0.0895612i
$305$		−	5.56155i		−	0.318454i
$306$			6.68466i			0.382136i
$307$		−	26.2462i		−	1.49795i	−0.662598	−	0.748975i	$-0.730546\pi$
$307$		−	26.2462i		−	1.49795i	0.662598	−	0.748975i	$-0.269454\pi$
$308$		0			0
$309$	−1.80776			−0.102840
$310$			22.2462i			1.26350i
$311$	0.492423			0.0279227			0.0139614	−	0.999903i	$-0.495556\pi$
$311$	0.492423			0.0279227			0.0139614	+	0.999903i	$0.495556\pi$
$312$	0.561553	+	3.56155i	0.0317917	+	0.201633i
$313$	−32.2462			−1.82266			−0.911332	−	0.411673i	$-0.864945\pi$
$313$	−32.2462			−1.82266			−0.911332	+	0.411673i	$0.864945\pi$
$314$			11.8078i			0.666351i
$315$		0			0
$316$	−16.0000			−0.900070
$317$		−	3.36932i		−	0.189240i	−0.995513	−	0.0946198i	$-0.969836\pi$
$317$		−	3.36932i		−	0.189240i	0.995513	−	0.0946198i	$-0.0301636\pi$
$318$			4.87689i			0.273483i
$319$			8.68466i			0.486248i
$320$			3.56155i			0.199097i
$321$	−4.87689			−0.272202
$322$		0			0
$323$			10.4384i			0.580811i
$324$	−1.00000			−0.0555556
$325$	27.3693	−	4.31534i	1.51818	−	0.239372i
$326$	−9.12311			−0.505282
$327$			12.9309i			0.715079i
$328$	−4.00000			−0.220863
$329$		0			0
$330$			19.8078i			1.09038i
$331$		−	1.12311i		−	0.0617315i	−0.999524	−	0.0308657i	$-0.990174\pi$
$331$		−	1.12311i		−	0.0617315i	0.999524	−	0.0308657i	$-0.00982643\pi$
$332$		−	2.00000i		−	0.109764i
$333$			10.6847i			0.585516i
$334$	−11.8078			−0.646092
$335$	−4.00000			−0.218543
$336$		0			0
$337$	20.0540			1.09241			0.546205	−	0.837652i	$-0.316072\pi$
$337$	20.0540			1.09241			0.546205	+	0.837652i	$0.316072\pi$
$338$	4.00000	+	12.3693i	0.217571	+	0.672802i
$339$	20.2462			1.09962
$340$			23.8078i			1.29116i
$341$	−34.7386			−1.88120
$342$	−1.56155			−0.0844391
$343$		0			0
$344$			6.43845i			0.347138i
$345$			23.8078i			1.28177i
$346$			3.75379i			0.201805i
$347$	−24.4924			−1.31482			−0.657411	−	0.753532i	$-0.728348\pi$
$347$	−24.4924			−1.31482			−0.657411	+	0.753532i	$0.728348\pi$
$348$	−1.56155			−0.0837080
$349$		−	3.36932i		−	0.180355i	−0.995926	−	0.0901777i	$-0.971256\pi$
$349$		−	3.36932i		−	0.180355i	0.995926	−	0.0901777i	$-0.0287435\pi$
$350$		0			0
$351$	−3.56155	+	0.561553i	−0.190102	+	0.0299735i
$352$	−5.56155			−0.296432
$353$			18.2462i			0.971148i	0.874196	+	0.485574i	$0.161389\pi$
$353$			18.2462i			0.971148i	−0.874196	+	0.485574i	$0.838611\pi$
$354$	4.24621			0.225684
$355$	33.3693			1.77106
$356$		−	8.00000i		−	0.423999i
$357$		0			0
$358$			11.1231i			0.587874i
$359$			23.6155i			1.24638i	0.782071	+	0.623190i	$0.214164\pi$
$359$			23.6155i			1.24638i	−0.782071	+	0.623190i	$0.785836\pi$
$360$	−3.56155			−0.187710
$361$	16.5616			0.871661
$362$			13.3693i			0.702676i
$363$	−19.9309			−1.04610
$364$		0			0
$365$	−41.1771			−2.15531
$366$			1.56155i			0.0816237i
$367$	−0.630683			−0.0329214			−0.0164607	−	0.999865i	$-0.505240\pi$
$367$	−0.630683			−0.0329214			−0.0164607	+	0.999865i	$0.505240\pi$
$368$	−6.68466			−0.348462
$369$		−	4.00000i		−	0.208232i
$370$			38.0540i			1.97833i
$371$		0			0
$372$		−	6.24621i		−	0.323851i
$373$	−6.00000			−0.310668			−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000			−0.310668			−0.155334	+	0.987862i	$0.549645\pi$
$374$	−37.1771			−1.92238
$375$			9.56155i			0.493756i
$376$	10.2462			0.528408
$377$	−5.56155	+	0.876894i	−0.286435	+	0.0451624i
$378$		0			0
$379$		−	18.8769i		−	0.969641i	−0.874614	−	0.484820i	$-0.838885\pi$
$379$		−	18.8769i		−	0.969641i	0.874614	−	0.484820i	$-0.161115\pi$
$380$	−5.56155			−0.285302
$381$	10.2462			0.524929
$382$		−	24.0540i		−	1.23071i
$383$		−	17.5616i		−	0.897353i	−0.893694	−	0.448677i	$-0.851895\pi$
$383$		−	17.5616i		−	0.897353i	0.893694	−	0.448677i	$-0.148105\pi$
$384$		−	1.00000i		−	0.0510310i
$385$		0			0
$386$	12.0000			0.610784
$387$	−6.43845			−0.327285
$388$			10.0000i			0.507673i
$389$	27.1231			1.37520			0.687598	−	0.726092i	$-0.258665\pi$
$389$	27.1231			1.37520			0.687598	+	0.726092i	$0.258665\pi$
$390$	−12.6847	+	2.00000i	−0.642313	+	0.101274i
$391$	−44.6847			−2.25980
$392$		0			0
$393$	1.56155			0.0787699
$394$	6.00000			0.302276
$395$		−	56.9848i		−	2.86722i
$396$		−	5.56155i		−	0.279479i
$397$		−	15.3693i		−	0.771364i	−0.922632	−	0.385682i	$-0.873966\pi$
$397$		−	15.3693i		−	0.771364i	0.922632	−	0.385682i	$-0.126034\pi$
$398$		−	4.93087i		−	0.247162i
$399$		0			0
$400$	−7.68466			−0.384233
$401$		−	30.9848i		−	1.54731i	−0.633608	−	0.773655i	$-0.718427\pi$
$401$		−	30.9848i		−	1.54731i	0.633608	−	0.773655i	$-0.281573\pi$
$402$	1.12311			0.0560154
$403$	−3.50758	−	22.2462i	−0.174725	−	1.10816i
$404$	6.00000			0.298511
$405$		−	3.56155i		−	0.176975i
$406$		0			0
$407$	−59.4233			−2.94550
$408$		−	6.68466i		−	0.330940i
$409$		−	13.8078i		−	0.682750i	−0.939927	−	0.341375i	$-0.889107\pi$
$409$		−	13.8078i		−	0.682750i	0.939927	−	0.341375i	$-0.110893\pi$
$410$		−	14.2462i		−	0.703570i
$411$			6.68466i			0.329730i
$412$	1.80776			0.0890621
$413$		0			0
$414$		−	6.68466i		−	0.328533i
$415$	7.12311			0.349660
$416$	−0.561553	−	3.56155i	−0.0275324	−	0.174619i
$417$	−10.2462			−0.501759
$418$		−	8.68466i		−	0.424781i
$419$	20.6847			1.01051			0.505256	−	0.862970i	$-0.331398\pi$
$419$	20.6847			1.01051			0.505256	+	0.862970i	$0.331398\pi$
$420$		0			0
$421$		−	10.0000i		−	0.487370i	−0.969854	−	0.243685i	$-0.921644\pi$
$421$		−	10.0000i		−	0.487370i	0.969854	−	0.243685i	$-0.0783563\pi$
$422$			7.80776i			0.380076i
$423$			10.2462i			0.498188i
$424$		−	4.87689i		−	0.236843i
$425$	−51.3693			−2.49178
$426$	−9.36932			−0.453945
$427$		0			0
$428$	4.87689			0.235734
$429$	−3.12311	−	19.8078i	−0.150785	−	0.956328i
$430$	−22.9309			−1.10582
$431$			29.8617i			1.43839i	0.694809	+	0.719195i	$0.255489\pi$
$431$			29.8617i			1.43839i	−0.694809	+	0.719195i	$0.744511\pi$
$432$	1.00000			0.0481125
$433$	−23.3693			−1.12306			−0.561529	−	0.827457i	$-0.689787\pi$
$433$	−23.3693			−1.12306			−0.561529	+	0.827457i	$0.689787\pi$
$434$		0			0
$435$		−	5.56155i		−	0.266656i
$436$		−	12.9309i		−	0.619276i
$437$		−	10.4384i		−	0.499339i
$438$	11.5616			0.552432
$439$	8.93087			0.426247			0.213124	−	0.977025i	$-0.431636\pi$
$439$	8.93087			0.426247			0.213124	+	0.977025i	$0.431636\pi$
$440$		−	19.8078i		−	0.944298i
$441$		0			0
$442$	−3.75379	−	23.8078i	−0.178550	−	1.13242i
$443$	6.63068			0.315033			0.157517	−	0.987516i	$-0.449651\pi$
$443$	6.63068			0.315033			0.157517	+	0.987516i	$0.449651\pi$
$444$		−	10.6847i		−	0.507071i
$445$	28.4924			1.35067
$446$	−1.75379			−0.0830443
$447$			10.0000i			0.472984i
$448$		0			0
$449$		−	9.31534i		−	0.439618i	−0.975543	−	0.219809i	$-0.929457\pi$
$449$		−	9.31534i		−	0.439618i	0.975543	−	0.219809i	$-0.0705434\pi$
$450$		−	7.68466i		−	0.362258i
$451$	22.2462			1.04753
$452$	−20.2462			−0.952302
$453$			16.6847i			0.783914i
$454$	−17.6155			−0.826738
$455$		0			0
$456$	1.56155			0.0731264
$457$		−	16.0000i		−	0.748448i	−0.927338	−	0.374224i	$-0.877909\pi$
$457$		−	16.0000i		−	0.748448i	0.927338	−	0.374224i	$-0.122091\pi$
$458$	2.00000			0.0934539
$459$	6.68466			0.312013
$460$		−	23.8078i		−	1.11004i
$461$		−	36.9309i		−	1.72004i	−0.510259	−	0.860021i	$-0.670450\pi$
$461$		−	36.9309i		−	1.72004i	0.510259	−	0.860021i	$-0.329550\pi$
$462$		0			0
$463$		−	30.5464i		−	1.41961i	−0.704397	−	0.709806i	$-0.748783\pi$
$463$		−	30.5464i		−	1.41961i	0.704397	−	0.709806i	$-0.251217\pi$
$464$	1.56155			0.0724933
$465$	22.2462			1.03164
$466$			2.00000i			0.0926482i
$467$	−1.56155			−0.0722600			−0.0361300	−	0.999347i	$-0.511503\pi$
$467$	−1.56155			−0.0722600			−0.0361300	+	0.999347i	$0.511503\pi$
$468$	3.56155	−	0.561553i	0.164633	−	0.0259578i
$469$		0			0
$470$			36.4924i			1.68327i
$471$	11.8078			0.544073
$472$	−4.24621			−0.195448
$473$		−	35.8078i		−	1.64644i
$474$			16.0000i			0.734904i
$475$		−	12.0000i		−	0.550598i
$476$		0			0
$477$	4.87689			0.223298
$478$	−14.2462			−0.651607
$479$		−	12.3002i		−	0.562010i	−0.959706	−	0.281005i	$-0.909332\pi$
$479$		−	12.3002i		−	0.562010i	0.959706	−	0.281005i	$-0.0906677\pi$
$480$	3.56155			0.162562
$481$	−6.00000	−	38.0540i	−0.273576	−	1.73511i
$482$	6.00000			0.273293
$483$		0			0
$484$	19.9309			0.905949
$485$	−35.6155			−1.61722
$486$			1.00000i			0.0453609i
$487$		−	13.7538i		−	0.623244i	−0.950206	−	0.311622i	$-0.899128\pi$
$487$		−	13.7538i		−	0.623244i	0.950206	−	0.311622i	$-0.100872\pi$
$488$		−	1.56155i		−	0.0706882i
$489$			9.12311i			0.412561i
$490$		0			0
$491$	−10.2462			−0.462405			−0.231203	−	0.972906i	$-0.574266\pi$
$491$	−10.2462			−0.462405			−0.231203	+	0.972906i	$0.574266\pi$
$492$			4.00000i			0.180334i
$493$	10.4384			0.470124
$494$	5.56155	−	0.876894i	0.250226	−	0.0394533i
$495$	19.8078			0.890293
$496$			6.24621i			0.280463i
$497$		0			0
$498$	−2.00000			−0.0896221
$499$		−	1.50758i		−	0.0674884i	−0.999431	−	0.0337442i	$-0.989257\pi$
$499$		−	1.50758i		−	0.0674884i	0.999431	−	0.0337442i	$-0.0107432\pi$
$500$		−	9.56155i		−	0.427606i
$501$			11.8078i			0.527532i
$502$		−	22.0540i		−	0.984317i
$503$	−35.6155			−1.58802			−0.794009	−	0.607906i	$-0.792010\pi$
$503$	−35.6155			−1.58802			−0.794009	+	0.607906i	$0.792010\pi$
$504$		0			0
$505$			21.3693i			0.950922i
$506$	37.1771			1.65272
$507$	12.3693	−	4.00000i	0.549341	−	0.177646i
$508$	−10.2462			−0.454602
$509$		−	2.68466i		−	0.118995i	−0.998228	−	0.0594977i	$-0.981050\pi$
$509$		−	2.68466i		−	0.118995i	0.998228	−	0.0594977i	$-0.0189499\pi$
$510$	23.8078			1.05423
$511$		0			0
$512$			1.00000i			0.0441942i
$513$			1.56155i			0.0689442i
$514$			26.0000i			1.14681i
$515$			6.43845i			0.283712i
$516$	6.43845			0.283437
$517$	−56.9848			−2.50619
$518$		0			0
$519$	3.75379			0.164773
$520$	12.6847	−	2.00000i	0.556259	−	0.0877058i
$521$	−8.05398			−0.352851			−0.176426	−	0.984314i	$-0.556453\pi$
$521$	−8.05398			−0.352851			−0.176426	+	0.984314i	$0.556453\pi$
$522$			1.56155i			0.0683473i
$523$	8.49242			0.371348			0.185674	−	0.982611i	$-0.440553\pi$
$523$	8.49242			0.371348			0.185674	+	0.982611i	$0.440553\pi$
$524$	−1.56155			−0.0682168
$525$		0			0
$526$		−	23.3693i		−	1.01895i
$527$			41.7538i			1.81882i
$528$			5.56155i			0.242036i
$529$	21.6847			0.942811
$530$	17.3693			0.754475
$531$		−	4.24621i		−	0.184270i
$532$		0			0
$533$	2.24621	+	14.2462i	0.0972942	+	0.617072i
$534$	−8.00000			−0.346194
$535$			17.3693i			0.750941i
$536$	−1.12311			−0.0485108
$537$	11.1231			0.479997
$538$		−	31.3693i		−	1.35243i
$539$		0			0
$540$			3.56155i			0.153265i
$541$		−	6.19224i		−	0.266225i	−0.991101	−	0.133113i	$-0.957503\pi$
$541$		−	6.19224i		−	0.266225i	0.991101	−	0.133113i	$-0.0424972\pi$
$542$	−8.00000			−0.343629
$543$	13.3693			0.573732
$544$			6.68466i			0.286602i
$545$	46.0540			1.97274
$546$		0			0
$547$	28.9848			1.23930			0.619651	−	0.784877i	$-0.287274\pi$
$547$	28.9848			1.23930			0.619651	+	0.784877i	$0.287274\pi$
$548$		−	6.68466i		−	0.285554i
$549$	1.56155			0.0666455
$550$	42.7386			1.82238
$551$			2.43845i			0.103881i
$552$			6.68466i			0.284518i
$553$		0			0
$554$		−	10.8769i		−	0.462115i
$555$	38.0540			1.61530
$556$	10.2462			0.434536
$557$			16.2462i			0.688374i	0.938901	+	0.344187i	$0.111845\pi$
$557$			16.2462i			0.688374i	−0.938901	+	0.344187i	$0.888155\pi$
$558$	−6.24621			−0.264423
$559$	22.9309	−	3.61553i	0.969872	−	0.152921i
$560$		0			0
$561$			37.1771i			1.56962i
$562$	−6.00000			−0.253095
$563$	−38.0540			−1.60378			−0.801892	−	0.597469i	$-0.796173\pi$
$563$	−38.0540			−1.60378			−0.801892	+	0.597469i	$0.796173\pi$
$564$		−	10.2462i		−	0.431443i
$565$		−	72.1080i		−	3.03360i
$566$			4.87689i			0.204991i
$567$		0			0
$568$	9.36932			0.393128
$569$	−18.0000			−0.754599			−0.377300	−	0.926091i	$-0.623147\pi$
$569$	−18.0000			−0.754599			−0.377300	+	0.926091i	$0.623147\pi$
$570$			5.56155i			0.232948i
$571$	−18.2462			−0.763580			−0.381790	−	0.924249i	$-0.624692\pi$
$571$	−18.2462			−0.763580			−0.381790	+	0.924249i	$0.624692\pi$
$572$	3.12311	+	19.8078i	0.130584	+	0.828204i
$573$	−24.0540			−1.00487
$574$		0			0
$575$	51.3693			2.14225
$576$	−1.00000			−0.0416667
$577$		−	7.75379i		−	0.322794i	−0.986890	−	0.161397i	$-0.948400\pi$
$577$		−	7.75379i		−	0.322794i	0.986890	−	0.161397i	$-0.0516000\pi$
$578$			27.6847i			1.15153i
$579$		−	12.0000i		−	0.498703i
$580$			5.56155i			0.230931i
$581$		0			0
$582$	10.0000			0.414513
$583$			27.1231i			1.12332i
$584$	−11.5616			−0.478420
$585$	2.00000	+	12.6847i	0.0826898	+	0.524446i
$586$	−7.75379			−0.320306
$587$			37.1231i			1.53223i	0.642701	+	0.766117i	$0.277814\pi$
$587$			37.1231i			1.53223i	−0.642701	+	0.766117i	$0.722186\pi$
$588$		0			0
$589$	−9.75379			−0.401898
$590$		−	15.1231i		−	0.622608i
$591$		−	6.00000i		−	0.246807i
$592$			10.6847i			0.439137i
$593$			28.0000i			1.14982i	0.818216	+	0.574911i	$0.194963\pi$
$593$			28.0000i			1.14982i	−0.818216	+	0.574911i	$0.805037\pi$
$594$	−5.56155			−0.228193
$595$		0			0
$596$		−	10.0000i		−	0.409616i
$597$	−4.93087			−0.201807
$598$	3.75379	+	23.8078i	0.153504	+	0.973572i
$599$	30.3002			1.23803			0.619016	−	0.785378i	$-0.287532\pi$
$599$	30.3002			1.23803			0.619016	+	0.785378i	$0.287532\pi$
$600$			7.68466i			0.313725i
$601$	31.8617			1.29967			0.649834	−	0.760076i	$-0.274839\pi$
$601$	31.8617			1.29967			0.649834	+	0.760076i	$0.274839\pi$
$602$		0			0
$603$		−	1.12311i		−	0.0457364i
$604$		−	16.6847i		−	0.678889i
$605$			70.9848i			2.88594i
$606$		−	6.00000i		−	0.243733i
$607$	28.5464			1.15866			0.579331	−	0.815092i	$-0.303314\pi$
$607$	28.5464			1.15866			0.579331	+	0.815092i	$0.303314\pi$
$608$	−1.56155			−0.0633293
$609$		0			0
$610$	5.56155			0.225181
$611$	−5.75379	−	36.4924i	−0.232773	−	1.47633i
$612$	−6.68466			−0.270211
$613$		−	1.80776i		−	0.0730149i	−0.999333	−	0.0365075i	$-0.988377\pi$
$613$		−	1.80776i		−	0.0730149i	0.999333	−	0.0365075i	$-0.0116233\pi$
$614$	26.2462			1.05921
$615$	−14.2462			−0.574463
$616$		0			0
$617$			6.19224i			0.249290i	0.992201	+	0.124645i	$0.0397792\pi$
$617$			6.19224i			0.249290i	−0.992201	+	0.124645i	$0.960221\pi$
$618$		−	1.80776i		−	0.0727189i
$619$			30.9309i			1.24322i	0.783328	+	0.621608i	$0.213520\pi$
$619$			30.9309i			1.24322i	−0.783328	+	0.621608i	$0.786480\pi$
$620$	−22.2462			−0.893429
$621$	−6.68466			−0.268246
$622$			0.492423i			0.0197443i
$623$		0			0
$624$	−3.56155	+	0.561553i	−0.142576	+	0.0224801i
$625$	−4.36932			−0.174773
$626$		−	32.2462i		−	1.28882i
$627$	−8.68466			−0.346832
$628$	−11.8078			−0.471181
$629$			71.4233i			2.84783i
$630$		0			0
$631$			12.6847i			0.504968i	0.967601	+	0.252484i	$0.0812476\pi$
$631$			12.6847i			0.504968i	−0.967601	+	0.252484i	$0.918752\pi$
$632$		−	16.0000i		−	0.636446i
$633$	7.80776			0.310331
$634$	3.36932			0.133813
$635$		−	36.4924i		−	1.44816i
$636$	−4.87689			−0.193381
$637$		0			0
$638$	−8.68466			−0.343829
$639$			9.36932i			0.370644i
$640$	−3.56155			−0.140783
$641$	30.1080			1.18919			0.594596	−	0.804024i	$-0.297312\pi$
$641$	30.1080			1.18919			0.594596	+	0.804024i	$0.297312\pi$
$642$		−	4.87689i		−	0.192476i
$643$			0.192236i			0.00758105i	0.999993	+	0.00379052i	$0.00120656\pi$
$643$			0.192236i			0.00758105i	−0.999993	+	0.00379052i	$0.998793\pi$
$644$		0			0
$645$			22.9309i			0.902902i
$646$	−10.4384			−0.410695
$647$	−10.6307			−0.417935			−0.208968	−	0.977923i	$-0.567010\pi$
$647$	−10.6307			−0.417935			−0.208968	+	0.977923i	$0.567010\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	23.6155			0.926991
$650$	4.31534	+	27.3693i	0.169262	+	1.07351i
$651$		0			0
$652$		−	9.12311i		−	0.357288i
$653$	−29.5616			−1.15683			−0.578416	−	0.815742i	$-0.696329\pi$
$653$	−29.5616			−1.15683			−0.578416	+	0.815742i	$0.696329\pi$
$654$	−12.9309			−0.505637
$655$		−	5.56155i		−	0.217308i
$656$		−	4.00000i		−	0.156174i
$657$		−	11.5616i		−	0.451059i
$658$		0			0
$659$	12.8769			0.501613			0.250806	−	0.968037i	$-0.419304\pi$
$659$	12.8769			0.501613			0.250806	+	0.968037i	$0.419304\pi$
$660$	−19.8078			−0.771016
$661$			44.7386i			1.74013i	0.492936	+	0.870066i	$0.335924\pi$
$661$			44.7386i			1.74013i	−0.492936	+	0.870066i	$0.664076\pi$
$662$	1.12311			0.0436507
$663$	−23.8078	+	3.75379i	−0.924617	+	0.145785i
$664$	2.00000			0.0776151
$665$		0			0
$666$	−10.6847			−0.414022
$667$	−10.4384			−0.404178
$668$		−	11.8078i		−	0.456856i
$669$			1.75379i			0.0678054i
$670$		−	4.00000i		−	0.154533i
$671$			8.68466i			0.335268i
$672$		0			0
$673$	37.8078			1.45738			0.728691	−	0.684843i	$-0.240129\pi$
$673$	37.8078			1.45738			0.728691	+	0.684843i	$0.240129\pi$
$674$			20.0540i			0.772450i
$675$	−7.68466			−0.295783
$676$	−12.3693	+	4.00000i	−0.475743	+	0.153846i
$677$	−31.3693			−1.20562			−0.602810	−	0.797884i	$-0.705952\pi$
$677$	−31.3693			−1.20562			−0.602810	+	0.797884i	$0.705952\pi$
$678$			20.2462i			0.777551i
$679$		0			0
$680$	−23.8078			−0.912986
$681$			17.6155i			0.675029i
$682$		−	34.7386i		−	1.33021i
$683$			0.684658i			0.0261977i	0.999914	+	0.0130989i	$0.00416962\pi$
$683$			0.684658i			0.0261977i	−0.999914	+	0.0130989i	$0.995830\pi$
$684$		−	1.56155i		−	0.0597075i
$685$	23.8078			0.909648
$686$		0			0
$687$		−	2.00000i		−	0.0763048i
$688$	−6.43845			−0.245463
$689$	−17.3693	+	2.73863i	−0.661718	+	0.104334i
$690$	−23.8078			−0.906346
$691$		−	36.4924i		−	1.38824i	−0.719861	−	0.694119i	$-0.755794\pi$
$691$		−	36.4924i		−	1.38824i	0.719861	−	0.694119i	$-0.244206\pi$
$692$	−3.75379			−0.142698
$693$		0			0
$694$		−	24.4924i		−	0.929720i
$695$			36.4924i			1.38424i
$696$		−	1.56155i		−	0.0591905i
$697$		−	26.7386i		−	1.01280i
$698$	3.36932			0.127531
$699$	2.00000			0.0756469
$700$		0			0
$701$	−3.61553			−0.136557			−0.0682783	−	0.997666i	$-0.521751\pi$
$701$	−3.61553			−0.136557			−0.0682783	+	0.997666i	$0.521751\pi$
$702$	−0.561553	−	3.56155i	−0.0211944	−	0.134422i
$703$	−16.6847			−0.629274
$704$		−	5.56155i		−	0.209609i
$705$	36.4924			1.37438
$706$	−18.2462			−0.686705
$707$		0			0
$708$			4.24621i			0.159582i
$709$			31.7538i			1.19254i	0.802784	+	0.596269i	$0.203351\pi$
$709$			31.7538i			1.19254i	−0.802784	+	0.596269i	$0.796649\pi$
$710$			33.3693i			1.25233i
$711$	16.0000			0.600047
$712$	8.00000			0.299813
$713$		−	41.7538i		−	1.56369i
$714$		0			0
$715$	−70.5464	+	11.1231i	−2.63829	+	0.415981i
$716$	−11.1231			−0.415690
$717$			14.2462i			0.532035i
$718$	−23.6155			−0.881324
$719$	−13.7538			−0.512930			−0.256465	−	0.966554i	$-0.582558\pi$
$719$	−13.7538			−0.512930			−0.256465	+	0.966554i	$0.582558\pi$
$720$		−	3.56155i		−	0.132731i
$721$		0			0
$722$			16.5616i			0.616357i
$723$		−	6.00000i		−	0.223142i
$724$	−13.3693			−0.496867
$725$	−12.0000			−0.445669
$726$		−	19.9309i		−	0.739704i
$727$	48.9309			1.81475			0.907373	−	0.420327i	$-0.138085\pi$
$727$	48.9309			1.81475			0.907373	+	0.420327i	$0.138085\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		−	41.1771i		−	1.52403i
$731$	−43.0388			−1.59185
$732$	−1.56155			−0.0577167
$733$			22.8769i			0.844977i	0.906368	+	0.422489i	$0.138843\pi$
$733$			22.8769i			0.844977i	−0.906368	+	0.422489i	$0.861157\pi$
$734$		−	0.630683i		−	0.0232789i
$735$		0			0
$736$		−	6.68466i		−	0.246400i
$737$	6.24621			0.230082
$738$	4.00000			0.147242
$739$		−	17.6155i		−	0.647998i	−0.946057	−	0.323999i	$-0.894973\pi$
$739$		−	17.6155i		−	0.647998i	0.946057	−	0.323999i	$-0.105027\pi$
$740$	−38.0540			−1.39889
$741$	−0.876894	−	5.56155i	−0.0322135	−	0.204309i
$742$		0			0
$743$		−	16.0000i		−	0.586983i	−0.955962	−	0.293492i	$-0.905183\pi$
$743$		−	16.0000i		−	0.586983i	0.955962	−	0.293492i	$-0.0948173\pi$
$744$	6.24621			0.228997
$745$	35.6155			1.30485
$746$		−	6.00000i		−	0.219676i
$747$			2.00000i			0.0731762i
$748$		−	37.1771i		−	1.35933i
$749$		0			0
$750$	−9.56155			−0.349139
$751$	2.24621			0.0819654			0.0409827	−	0.999160i	$-0.486951\pi$
$751$	2.24621			0.0819654			0.0409827	+	0.999160i	$0.486951\pi$
$752$			10.2462i			0.373641i
$753$	−22.0540			−0.803692
$754$	−0.876894	−	5.56155i	−0.0319346	−	0.202540i
$755$	59.4233			2.16264
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	18.8769			0.685640
$759$		−	37.1771i		−	1.34944i
$760$		−	5.56155i		−	0.201739i
$761$			39.1231i			1.41821i	0.705102	+	0.709106i	$0.250901\pi$
$761$			39.1231i			1.41821i	−0.705102	+	0.709106i	$0.749099\pi$
$762$			10.2462i			0.371181i
$763$		0			0
$764$	24.0540			0.870242
$765$		−	23.8078i		−	0.860772i
$766$	17.5616			0.634525
$767$	2.38447	+	15.1231i	0.0860983	+	0.546064i
$768$	1.00000			0.0360844
$769$			8.43845i			0.304298i	0.988358	+	0.152149i	$0.0486194\pi$
$769$			8.43845i			0.304298i	−0.988358	+	0.152149i	$0.951381\pi$
$770$		0			0
$771$	26.0000			0.936367
$772$			12.0000i			0.431889i
$773$		−	12.9309i		−	0.465091i	−0.972586	−	0.232546i	$-0.925295\pi$
$773$		−	12.9309i		−	0.465091i	0.972586	−	0.232546i	$-0.0747055\pi$
$774$		−	6.43845i		−	0.231425i
$775$		−	48.0000i		−	1.72421i
$776$	−10.0000			−0.358979
$777$		0			0
$778$			27.1231i			0.972410i
$779$	6.24621			0.223794
$780$	−2.00000	−	12.6847i	−0.0716115	−	0.454184i
$781$	−52.1080			−1.86457
$782$		−	44.6847i		−	1.59792i
$783$	1.56155			0.0558053
$784$		0			0
$785$		−	42.0540i		−	1.50097i
$786$			1.56155i			0.0556987i
$787$		−	17.0691i		−	0.608449i	−0.952600	−	0.304224i	$-0.901603\pi$
$787$		−	17.0691i		−	0.608449i	0.952600	−	0.304224i	$-0.0983973\pi$
$788$			6.00000i			0.213741i
$789$	−23.3693			−0.831970
$790$	56.9848			2.02743
$791$		0			0
$792$	5.56155			0.197621
$793$	−5.56155	+	0.876894i	−0.197497	+	0.0311394i
$794$	15.3693			0.545437
$795$		−	17.3693i		−	0.616026i
$796$	4.93087			0.174770
$797$	−3.75379			−0.132966			−0.0664830	−	0.997788i	$-0.521178\pi$
$797$	−3.75379			−0.132966			−0.0664830	+	0.997788i	$0.521178\pi$
$798$		0			0
$799$			68.4924i			2.42309i
$800$		−	7.68466i		−	0.271694i
$801$			8.00000i			0.282666i
$802$	30.9848			1.09411
$803$	64.3002			2.26910
$804$			1.12311i			0.0396089i
$805$		0			0
$806$	22.2462	−	3.50758i	0.783589	−	0.123549i
$807$	−31.3693			−1.10425
$808$			6.00000i			0.211079i
$809$	−55.3693			−1.94668			−0.973341	−	0.229364i	$-0.926335\pi$
$809$	−55.3693			−1.94668			−0.973341	+	0.229364i	$0.926335\pi$
$810$	3.56155			0.125140
$811$			2.05398i			0.0721248i	0.999350	+	0.0360624i	$0.0114815\pi$
$811$			2.05398i			0.0721248i	−0.999350	+	0.0360624i	$0.988518\pi$
$812$		0			0
$813$			8.00000i			0.280572i
$814$		−	59.4233i		−	2.08279i
$815$	32.4924			1.13816
$816$	6.68466			0.234010
$817$		−	10.0540i		−	0.351744i
$818$	13.8078			0.482777
$819$		0			0
$820$	14.2462			0.497499
$821$		−	30.8769i		−	1.07761i	−0.842430	−	0.538806i	$-0.818876\pi$
$821$		−	30.8769i		−	1.07761i	0.842430	−	0.538806i	$-0.181124\pi$
$822$	−6.68466			−0.233154
$823$	−30.7386			−1.07148			−0.535741	−	0.844383i	$-0.679968\pi$
$823$	−30.7386			−1.07148			−0.535741	+	0.844383i	$0.679968\pi$
$824$			1.80776i			0.0629764i
$825$		−	42.7386i		−	1.48797i
$826$		0			0
$827$			22.0540i			0.766892i	0.923563	+	0.383446i	$0.125263\pi$
$827$			22.0540i			0.766892i	−0.923563	+	0.383446i	$0.874737\pi$
$828$	6.68466			0.232308
$829$	−42.0540			−1.46059			−0.730297	−	0.683129i	$-0.760619\pi$
$829$	−42.0540			−1.46059			−0.730297	+	0.683129i	$0.760619\pi$
$830$			7.12311i			0.247247i
$831$	−10.8769			−0.377315
$832$	3.56155	−	0.561553i	0.123475	−	0.0194683i
$833$		0			0
$834$		−	10.2462i		−	0.354797i
$835$	42.0540			1.45534
$836$	8.68466			0.300365
$837$			6.24621i			0.215901i
$838$			20.6847i			0.714540i
$839$		−	25.7538i		−	0.889120i	−0.895749	−	0.444560i	$-0.853360\pi$
$839$		−	25.7538i		−	0.889120i	0.895749	−	0.444560i	$-0.146640\pi$
$840$		0			0
$841$	−26.5616			−0.915916
$842$	10.0000			0.344623
$843$			6.00000i			0.206651i
$844$	−7.80776			−0.268754
$845$	−14.2462	−	44.0540i	−0.490085	−	1.51550i
$846$	−10.2462			−0.352272
$847$		0			0
$848$	4.87689			0.167473
$849$	4.87689			0.167375
$850$		−	51.3693i		−	1.76195i
$851$		−	71.4233i		−	2.44836i
$852$		−	9.36932i		−	0.320988i
$853$		−	10.8769i		−	0.372418i	−0.982510	−	0.186209i	$-0.940380\pi$
$853$		−	10.8769i		−	0.372418i	0.982510	−	0.186209i	$-0.0596201\pi$
$854$		0			0
$855$	5.56155			0.190201
$856$			4.87689i			0.166689i
$857$	38.0000			1.29806			0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000			1.29806			0.649028	+	0.760765i	$0.275176\pi$
$858$	19.8078	−	3.12311i	0.676226	−	0.106621i
$859$	−0.384472			−0.0131180			−0.00655901	−	0.999978i	$-0.502088\pi$
$859$	−0.384472			−0.0131180			−0.00655901	+	0.999978i	$0.502088\pi$
$860$		−	22.9309i		−	0.781936i
$861$		0			0
$862$	−29.8617			−1.01709
$863$		−	42.7386i		−	1.45484i	−0.686192	−	0.727420i	$-0.740719\pi$
$863$		−	42.7386i		−	1.45484i	0.686192	−	0.727420i	$-0.259281\pi$
$864$			1.00000i			0.0340207i
$865$		−	13.3693i		−	0.454570i
$866$		−	23.3693i		−	0.794122i
$867$	27.6847			0.940220
$868$		0			0
$869$			88.9848i			3.01860i
$870$	5.56155			0.188554
$871$	0.630683	+	4.00000i	0.0213699	+	0.135535i
$872$	12.9309			0.437895
$873$		−	10.0000i		−	0.338449i
$874$	10.4384			0.353086
$875$		0			0
$876$			11.5616i			0.390629i
$877$		−	22.9848i		−	0.776143i	−0.921629	−	0.388072i	$-0.873141\pi$
$877$		−	22.9848i		−	0.776143i	0.921629	−	0.388072i	$-0.126859\pi$
$878$			8.93087i			0.301402i
$879$			7.75379i			0.261529i
$880$	19.8078			0.667720
$881$	−14.3002			−0.481786			−0.240893	−	0.970552i	$-0.577440\pi$
$881$	−14.3002			−0.481786			−0.240893	+	0.970552i	$0.577440\pi$
$882$		0			0
$883$	−14.4384			−0.485892			−0.242946	−	0.970040i	$-0.578114\pi$
$883$	−14.4384			−0.485892			−0.242946	+	0.970040i	$0.578114\pi$
$884$	23.8078	−	3.75379i	0.800742	−	0.126254i
$885$	−15.1231			−0.508358
$886$			6.63068i			0.222762i
$887$	37.8617			1.27127			0.635636	−	0.771989i	$-0.280738\pi$
$887$	37.8617			1.27127			0.635636	+	0.771989i	$0.280738\pi$
$888$	10.6847			0.358554
$889$		0			0
$890$			28.4924i			0.955068i
$891$			5.56155i			0.186319i
$892$		−	1.75379i		−	0.0587212i
$893$	−16.0000			−0.535420
$894$	−10.0000			−0.334450
$895$		−	39.6155i		−	1.32420i
$896$		0			0
$897$	23.8078	−	3.75379i	0.794918	−	0.125335i
$898$	9.31534			0.310857
$899$			9.75379i			0.325307i
$900$	7.68466			0.256155
$901$	32.6004			1.08608
$902$			22.2462i			0.740718i
$903$		0			0
$904$		−	20.2462i		−	0.673379i
$905$		−	47.6155i		−	1.58279i
$906$	−16.6847			−0.554311
$907$	−24.4924			−0.813258			−0.406629	−	0.913593i	$-0.633296\pi$
$907$	−24.4924			−0.813258			−0.406629	+	0.913593i	$0.633296\pi$
$908$		−	17.6155i		−	0.584592i
$909$	−6.00000			−0.199007
$910$		0			0
$911$	−4.43845			−0.147052			−0.0735262	−	0.997293i	$-0.523425\pi$
$911$	−4.43845			−0.147052			−0.0735262	+	0.997293i	$0.523425\pi$
$912$			1.56155i			0.0517082i
$913$	−11.1231			−0.368121
$914$	16.0000			0.529233
$915$		−	5.56155i		−	0.183859i
$916$			2.00000i			0.0660819i
$917$		0			0
$918$			6.68466i			0.220627i
$919$	−17.8617			−0.589204			−0.294602	−	0.955620i	$-0.595187\pi$
$919$	−17.8617			−0.589204			−0.294602	+	0.955620i	$0.595187\pi$
$920$	23.8078			0.784919
$921$		−	26.2462i		−	0.864842i
$922$	36.9309			1.21625
$923$	−5.26137	−	33.3693i	−0.173180	−	1.09836i
$924$		0			0
$925$		−	82.1080i		−	2.69969i
$926$	30.5464			1.00382
$927$	−1.80776			−0.0593748
$928$			1.56155i			0.0512605i
$929$			40.8769i			1.34113i	0.741852	+	0.670564i	$0.233948\pi$
$929$			40.8769i			1.34113i	−0.741852	+	0.670564i	$0.766052\pi$
$930$			22.2462i			0.729482i
$931$		0			0
$932$	−2.00000			−0.0655122
$933$	0.492423			0.0161212
$934$		−	1.56155i		−	0.0510956i
$935$	132.408			4.33021
$936$	0.561553	+	3.56155i	0.0183549	+	0.116413i
$937$	19.8617			0.648855			0.324427	−	0.945911i	$-0.394828\pi$
$937$	19.8617			0.648855			0.324427	+	0.945911i	$0.394828\pi$
$938$		0			0
$939$	−32.2462			−1.05232
$940$	−36.4924			−1.19025
$941$			26.4924i			0.863628i	0.901963	+	0.431814i	$0.142126\pi$
$941$			26.4924i			0.863628i	−0.901963	+	0.431814i	$0.857874\pi$
$942$			11.8078i			0.384718i
$943$			26.7386i			0.870730i
$944$		−	4.24621i		−	0.138202i
$945$		0			0
$946$	35.8078			1.16421
$947$			27.8078i			0.903631i	0.892111	+	0.451815i	$0.149223\pi$
$947$			27.8078i			0.903631i	−0.892111	+	0.451815i	$0.850777\pi$
$948$	−16.0000			−0.519656
$949$	6.49242	+	41.1771i	0.210753	+	1.33666i
$950$	12.0000			0.389331
$951$		−	3.36932i		−	0.109258i
$952$		0			0
$953$	0.738634			0.0239267			0.0119633	−	0.999928i	$-0.496192\pi$
$953$	0.738634			0.0239267			0.0119633	+	0.999928i	$0.496192\pi$
$954$			4.87689i			0.157895i
$955$			85.6695i			2.77220i
$956$		−	14.2462i		−	0.460755i
$957$			8.68466i			0.280735i
$958$	12.3002			0.397401
$959$		0			0
$960$			3.56155i			0.114949i
$961$	−8.01515			−0.258553
$962$	38.0540	−	6.00000i	1.22691	−	0.193448i
$963$	−4.87689			−0.157156
$964$			6.00000i			0.193247i
$965$	−42.7386			−1.37581
$966$		0			0
$967$			2.93087i			0.0942504i	0.998889	+	0.0471252i	$0.0150060\pi$
$967$			2.93087i			0.0942504i	−0.998889	+	0.0471252i	$0.984994\pi$
$968$			19.9309i			0.640602i
$969$			10.4384i			0.335331i
$970$		−	35.6155i		−	1.14355i
$971$	−4.00000			−0.128366			−0.0641831	−	0.997938i	$-0.520444\pi$
$971$	−4.00000			−0.128366			−0.0641831	+	0.997938i	$0.520444\pi$
$972$	−1.00000			−0.0320750
$973$		0			0
$974$	13.7538			0.440700
$975$	27.3693	−	4.31534i	0.876520	−	0.138202i
$976$	1.56155			0.0499841
$977$		−	46.7926i		−	1.49703i	−0.663119	−	0.748514i	$-0.730768\pi$
$977$		−	46.7926i		−	1.49703i	0.663119	−	0.748514i	$-0.269232\pi$
$978$	−9.12311			−0.291725
$979$	−44.4924			−1.42198
$980$		0			0
$981$			12.9309i			0.412851i
$982$		−	10.2462i		−	0.326970i
$983$			2.43845i			0.0777744i	0.999244	+	0.0388872i	$0.0123813\pi$
$983$			2.43845i			0.0777744i	−0.999244	+	0.0388872i	$0.987619\pi$
$984$	−4.00000			−0.127515
$985$	−21.3693			−0.680883
$986$			10.4384i			0.332428i
$987$		0			0
$988$	0.876894	+	5.56155i	0.0278977	+	0.176937i
$989$	43.0388			1.36855
$990$			19.8078i			0.629532i
$991$	−30.2462			−0.960803			−0.480401	−	0.877049i	$-0.659509\pi$
$991$	−30.2462			−0.960803			−0.480401	+	0.877049i	$0.659509\pi$
$992$	−6.24621			−0.198317
$993$		−	1.12311i		−	0.0356407i
$994$		0			0
$995$			17.5616i			0.556739i
$996$		−	2.00000i		−	0.0633724i
$997$	34.6307			1.09676			0.548382	−	0.836228i	$-0.315244\pi$
$997$	34.6307			1.09676			0.548382	+	0.836228i	$0.315244\pi$
$998$	1.50758			0.0477215
$999$			10.6847i			0.338048i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3822.2.c.h.883.3		4
7.6	odd	2		546.2.c.e.337.4	yes	4
13.12	even	2	inner	3822.2.c.h.883.2		4
21.20	even	2		1638.2.c.h.883.1		4
28.27	even	2		4368.2.h.n.337.4		4
91.34	even	4		7098.2.a.bg.1.1		2
91.83	even	4		7098.2.a.bv.1.2		2
91.90	odd	2		546.2.c.e.337.1	✓	4
273.272	even	2		1638.2.c.h.883.4		4
364.363	even	2		4368.2.h.n.337.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.c.e.337.1	✓	4	91.90	odd	2
546.2.c.e.337.4	yes	4	7.6	odd	2
1638.2.c.h.883.1		4	21.20	even	2
1638.2.c.h.883.4		4	273.272	even	2
3822.2.c.h.883.2		4	13.12	even	2	inner
3822.2.c.h.883.3		4	1.1	even	1	trivial
4368.2.h.n.337.1		4	364.363	even	2
4368.2.h.n.337.4		4	28.27	even	2
7098.2.a.bg.1.1		2	91.34	even	4
7098.2.a.bv.1.2		2	91.83	even	4

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:	\( N \)	\(=\)	\( 3822 = 2 \cdot 3 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3822.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.56155i q^{5} +1.00000i q^{6} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} -3.56155i q^{5} +1.00000i q^{6} -1.00000i q^{8} +1.00000 q^{9} +3.56155 q^{10} +5.56155i q^{11} -1.00000 q^{12} +(-3.56155 + 0.561553i) q^{13} -3.56155i q^{15} +1.00000 q^{16} +6.68466 q^{17} +1.00000i q^{18} +1.56155i q^{19} +3.56155i q^{20} -5.56155 q^{22} -6.68466 q^{23} -1.00000i q^{24} -7.68466 q^{25} +(-0.561553 - 3.56155i) q^{26} +1.00000 q^{27} +1.56155 q^{29} +3.56155 q^{30} +6.24621i q^{31} +1.00000i q^{32} +5.56155i q^{33} +6.68466i q^{34} -1.00000 q^{36} +10.6847i q^{37} -1.56155 q^{38} +(-3.56155 + 0.561553i) q^{39} -3.56155 q^{40} -4.00000i q^{41} -6.43845 q^{43} -5.56155i q^{44} -3.56155i q^{45} -6.68466i q^{46} +10.2462i q^{47} +1.00000 q^{48} -7.68466i q^{50} +6.68466 q^{51} +(3.56155 - 0.561553i) q^{52} +4.87689 q^{53} +1.00000i q^{54} +19.8078 q^{55} +1.56155i q^{57} +1.56155i q^{58} -4.24621i q^{59} +3.56155i q^{60} +1.56155 q^{61} -6.24621 q^{62} -1.00000 q^{64} +(2.00000 + 12.6847i) q^{65} -5.56155 q^{66} -1.12311i q^{67} -6.68466 q^{68} -6.68466 q^{69} +9.36932i q^{71} -1.00000i q^{72} -11.5616i q^{73} -10.6847 q^{74} -7.68466 q^{75} -1.56155i q^{76} +(-0.561553 - 3.56155i) q^{78} +16.0000 q^{79} -3.56155i q^{80} +1.00000 q^{81} +4.00000 q^{82} +2.00000i q^{83} -23.8078i q^{85} -6.43845i q^{86} +1.56155 q^{87} +5.56155 q^{88} +8.00000i q^{89} +3.56155 q^{90} +6.68466 q^{92} +6.24621i q^{93} -10.2462 q^{94} +5.56155 q^{95} +1.00000i q^{96} -10.0000i q^{97} +5.56155i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9	\( 4 q + 4 q^{3} - 4 q^{4} + 4 q^{9} + 6 q^{10} - 4 q^{12} - 6 q^{13} + 4 q^{16} + 2 q^{17} - 14 q^{22} - 2 q^{23} - 6 q^{25} + 6 q^{26} + 4 q^{27} - 2 q^{29} + 6 q^{30} - 4 q^{36} + 2 q^{38} - 6 q^{39} - 6 q^{40} - 34 q^{43} + 4 q^{48} + 2 q^{51} + 6 q^{52} + 36 q^{53} + 38 q^{55} - 2 q^{61} + 8 q^{62} - 4 q^{64} + 8 q^{65} - 14 q^{66} - 2 q^{68} - 2 q^{69} - 18 q^{74} - 6 q^{75} + 6 q^{78} + 64 q^{79} + 4 q^{81} + 16 q^{82} - 2 q^{87} + 14 q^{88} + 6 q^{90} + 2 q^{92} - 8 q^{94} + 14 q^{95}+O(q^{100}) \) 4 * q + 4 * q^3 - 4 * q^4 + 4 * q^9 + 6 * q^10 - 4 * q^12 - 6 * q^13 + 4 * q^16 + 2 * q^17 - 14 * q^22 - 2 * q^23 - 6 * q^25 + 6 * q^26 + 4 * q^27 - 2 * q^29 + 6 * q^30 - 4 * q^36 + 2 * q^38 - 6 * q^39 - 6 * q^40 - 34 * q^43 + 4 * q^48 + 2 * q^51 + 6 * q^52 + 36 * q^53 + 38 * q^55 - 2 * q^61 + 8 * q^62 - 4 * q^64 + 8 * q^65 - 14 * q^66 - 2 * q^68 - 2 * q^69 - 18 * q^74 - 6 * q^75 + 6 * q^78 + 64 * q^79 + 4 * q^81 + 16 * q^82 - 2 * q^87 + 14 * q^88 + 6 * q^90 + 2 * q^92 - 8 * q^94 + 14 * q^95

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