LMFDB - Embedded newform 80.3.p.c.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,3,Mod(17,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("80.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	80.p (of order $4$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17984211488$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 10)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	80.17
Dual form			80.3.p.c.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 2.00000i) q^{3} -5.00000i q^{5} +(-2.00000 - 2.00000i) q^{7} +1.00000i q^{9} +O(q^{10})$	\(q+(2.00000 - 2.00000i) q^{3} -5.00000i q^{5} +(-2.00000 - 2.00000i) q^{7} +1.00000i q^{9} +8.00000 q^{11} +(3.00000 - 3.00000i) q^{13} +(-10.0000 - 10.0000i) q^{15} +(7.00000 + 7.00000i) q^{17} +20.0000i q^{19} -8.00000 q^{21} +(2.00000 - 2.00000i) q^{23} -25.0000 q^{25} +(20.0000 + 20.0000i) q^{27} +40.0000i q^{29} -52.0000 q^{31} +(16.0000 - 16.0000i) q^{33} +(-10.0000 + 10.0000i) q^{35} +(-3.00000 - 3.00000i) q^{37} -12.0000i q^{39} -8.00000 q^{41} +(42.0000 - 42.0000i) q^{43} +5.00000 q^{45} +(18.0000 + 18.0000i) q^{47} -41.0000i q^{49} +28.0000 q^{51} +(53.0000 - 53.0000i) q^{53} -40.0000i q^{55} +(40.0000 + 40.0000i) q^{57} +20.0000i q^{59} -48.0000 q^{61} +(2.00000 - 2.00000i) q^{63} +(-15.0000 - 15.0000i) q^{65} +(-62.0000 - 62.0000i) q^{67} -8.00000i q^{69} +28.0000 q^{71} +(-47.0000 + 47.0000i) q^{73} +(-50.0000 + 50.0000i) q^{75} +(-16.0000 - 16.0000i) q^{77} +71.0000 q^{81} +(-18.0000 + 18.0000i) q^{83} +(35.0000 - 35.0000i) q^{85} +(80.0000 + 80.0000i) q^{87} +80.0000i q^{89} -12.0000 q^{91} +(-104.000 + 104.000i) q^{93} +100.000 q^{95} +(-63.0000 - 63.0000i) q^{97} +8.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{3} - 4 q^{7}+O(q^{10}) $ 2 * q + 4 * q^3 - 4 * q^7	$ 2 q + 4 q^{3} - 4 q^{7} + 16 q^{11} + 6 q^{13} - 20 q^{15} + 14 q^{17} - 16 q^{21} + 4 q^{23} - 50 q^{25} + 40 q^{27} - 104 q^{31} + 32 q^{33} - 20 q^{35} - 6 q^{37} - 16 q^{41} + 84 q^{43} + 10 q^{45} + 36 q^{47} + 56 q^{51} + 106 q^{53} + 80 q^{57} - 96 q^{61} + 4 q^{63} - 30 q^{65} - 124 q^{67} + 56 q^{71} - 94 q^{73} - 100 q^{75} - 32 q^{77} + 142 q^{81} - 36 q^{83} + 70 q^{85} + 160 q^{87} - 24 q^{91} - 208 q^{93} + 200 q^{95} - 126 q^{97}+O(q^{100}) $ 2 * q + 4 * q^3 - 4 * q^7 + 16 * q^11 + 6 * q^13 - 20 * q^15 + 14 * q^17 - 16 * q^21 + 4 * q^23 - 50 * q^25 + 40 * q^27 - 104 * q^31 + 32 * q^33 - 20 * q^35 - 6 * q^37 - 16 * q^41 + 84 * q^43 + 10 * q^45 + 36 * q^47 + 56 * q^51 + 106 * q^53 + 80 * q^57 - 96 * q^61 + 4 * q^63 - 30 * q^65 - 124 * q^67 + 56 * q^71 - 94 * q^73 - 100 * q^75 - 32 * q^77 + 142 * q^81 - 36 * q^83 + 70 * q^85 + 160 * q^87 - 24 * q^91 - 208 * q^93 + 200 * q^95 - 126 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.00000	−	2.00000i	0.666667	−	0.666667i	−0.290276	−	0.956943i	$-0.593747\pi$
$3$	2.00000	−	2.00000i	0.666667	−	0.666667i	0.956943	+	0.290276i	$0.0937472\pi$
$4$		0			0
$5$		−	5.00000i		−	1.00000i
$5$		−	5.00000i		−	1.00000i
$6$		0			0
$7$	−2.00000	−	2.00000i	−0.285714	−	0.285714i	0.549669	−	0.835383i	$-0.314754\pi$
$7$	−2.00000	−	2.00000i	−0.285714	−	0.285714i	−0.835383	+	0.549669i	$0.814754\pi$
$8$		0			0
$9$			1.00000i			0.111111i
$10$		0			0
$11$	8.00000			0.727273			0.363636	−	0.931541i	$-0.381535\pi$
$11$	8.00000			0.727273			0.363636	+	0.931541i	$0.381535\pi$
$12$		0			0
$13$	3.00000	−	3.00000i	0.230769	−	0.230769i	−0.582245	−	0.813014i	$-0.697825\pi$
$13$	3.00000	−	3.00000i	0.230769	−	0.230769i	0.813014	+	0.582245i	$0.197825\pi$
$14$		0			0
$15$	−10.0000	−	10.0000i	−0.666667	−	0.666667i
$16$		0			0
$17$	7.00000	+	7.00000i	0.411765	+	0.411765i	0.882353	−	0.470588i	$-0.155958\pi$
$17$	7.00000	+	7.00000i	0.411765	+	0.411765i	−0.470588	+	0.882353i	$0.655958\pi$
$18$		0			0
$19$			20.0000i			1.05263i	0.850289	+	0.526316i	$0.176427\pi$
$19$			20.0000i			1.05263i	−0.850289	+	0.526316i	$0.823573\pi$
$20$		0			0
$21$	−8.00000			−0.380952
$22$		0			0
$23$	2.00000	−	2.00000i	0.0869565	−	0.0869565i	−0.662291	−	0.749247i	$-0.730416\pi$
$23$	2.00000	−	2.00000i	0.0869565	−	0.0869565i	0.749247	+	0.662291i	$0.230416\pi$
$24$		0			0
$25$	−25.0000			−1.00000
$26$		0			0
$27$	20.0000	+	20.0000i	0.740741	+	0.740741i
$28$		0			0
$29$			40.0000i			1.37931i	0.724138	+	0.689655i	$0.242238\pi$
$29$			40.0000i			1.37931i	−0.724138	+	0.689655i	$0.757762\pi$
$30$		0			0
$31$	−52.0000			−1.67742			−0.838710	−	0.544579i	$-0.816690\pi$
$31$	−52.0000			−1.67742			−0.838710	+	0.544579i	$0.816690\pi$
$32$		0			0
$33$	16.0000	−	16.0000i	0.484848	−	0.484848i
$34$		0			0
$35$	−10.0000	+	10.0000i	−0.285714	+	0.285714i
$36$		0			0
$37$	−3.00000	−	3.00000i	−0.0810811	−	0.0810811i	0.665403	−	0.746484i	$-0.268260\pi$
$37$	−3.00000	−	3.00000i	−0.0810811	−	0.0810811i	−0.746484	+	0.665403i	$0.768260\pi$
$38$		0			0
$39$		−	12.0000i		−	0.307692i
$40$		0			0
$41$	−8.00000			−0.195122			−0.0975610	−	0.995230i	$-0.531104\pi$
$41$	−8.00000			−0.195122			−0.0975610	+	0.995230i	$0.531104\pi$
$42$		0			0
$43$	42.0000	−	42.0000i	0.976744	−	0.976744i	−0.0229915	−	0.999736i	$-0.507319\pi$
$43$	42.0000	−	42.0000i	0.976744	−	0.976744i	0.999736	+	0.0229915i	$0.00731906\pi$
$44$		0			0
$45$	5.00000			0.111111
$46$		0			0
$47$	18.0000	+	18.0000i	0.382979	+	0.382979i	0.872174	−	0.489195i	$-0.162710\pi$
$47$	18.0000	+	18.0000i	0.382979	+	0.382979i	−0.489195	+	0.872174i	$0.662710\pi$
$48$		0			0
$49$		−	41.0000i		−	0.836735i
$50$		0			0
$51$	28.0000			0.549020
$52$		0			0
$53$	53.0000	−	53.0000i	1.00000	−	1.00000i		−	1.00000i	$-0.5\pi$
$53$	53.0000	−	53.0000i	1.00000	−	1.00000i	1.00000			$0$
$54$		0			0
$55$		−	40.0000i		−	0.727273i
$56$		0			0
$57$	40.0000	+	40.0000i	0.701754	+	0.701754i
$58$		0			0
$59$			20.0000i			0.338983i	0.985532	+	0.169492i	$0.0542125\pi$
$59$			20.0000i			0.338983i	−0.985532	+	0.169492i	$0.945787\pi$
$60$		0			0
$61$	−48.0000			−0.786885			−0.393443	−	0.919349i	$-0.628716\pi$
$61$	−48.0000			−0.786885			−0.393443	+	0.919349i	$0.628716\pi$
$62$		0			0
$63$	2.00000	−	2.00000i	0.0317460	−	0.0317460i
$64$		0			0
$65$	−15.0000	−	15.0000i	−0.230769	−	0.230769i
$66$		0			0
$67$	−62.0000	−	62.0000i	−0.925373	−	0.925373i	0.0720294	−	0.997403i	$-0.477052\pi$
$67$	−62.0000	−	62.0000i	−0.925373	−	0.925373i	−0.997403	+	0.0720294i	$0.977052\pi$
$68$		0			0
$69$		−	8.00000i		−	0.115942i
$70$		0			0
$71$	28.0000			0.394366			0.197183	−	0.980367i	$-0.436821\pi$
$71$	28.0000			0.394366			0.197183	+	0.980367i	$0.436821\pi$
$72$		0			0
$73$	−47.0000	+	47.0000i	−0.643836	+	0.643836i	−0.951496	−	0.307661i	$-0.900454\pi$
$73$	−47.0000	+	47.0000i	−0.643836	+	0.643836i	0.307661	+	0.951496i	$0.400454\pi$
$74$		0			0
$75$	−50.0000	+	50.0000i	−0.666667	+	0.666667i
$76$		0			0
$77$	−16.0000	−	16.0000i	−0.207792	−	0.207792i
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$		0			0
$81$	71.0000			0.876543
$82$		0			0
$83$	−18.0000	+	18.0000i	−0.216867	+	0.216867i	−0.807177	−	0.590310i	$-0.799006\pi$
$83$	−18.0000	+	18.0000i	−0.216867	+	0.216867i	0.590310	+	0.807177i	$0.299006\pi$
$84$		0			0
$85$	35.0000	−	35.0000i	0.411765	−	0.411765i
$86$		0			0
$87$	80.0000	+	80.0000i	0.919540	+	0.919540i
$88$		0			0
$89$			80.0000i			0.898876i	0.893311	+	0.449438i	$0.148376\pi$
$89$			80.0000i			0.898876i	−0.893311	+	0.449438i	$0.851624\pi$
$90$		0			0
$91$	−12.0000			−0.131868
$92$		0			0
$93$	−104.000	+	104.000i	−1.11828	+	1.11828i
$94$		0			0
$95$	100.000			1.05263
$96$		0			0
$97$	−63.0000	−	63.0000i	−0.649485	−	0.649485i	0.303384	−	0.952868i	$-0.401884\pi$
$97$	−63.0000	−	63.0000i	−0.649485	−	0.649485i	−0.952868	+	0.303384i	$0.901884\pi$
$98$		0			0
$99$			8.00000i			0.0808081i
$100$		0			0
$101$	62.0000			0.613861			0.306931	−	0.951732i	$-0.400698\pi$
$101$	62.0000			0.613861			0.306931	+	0.951732i	$0.400698\pi$
$102$		0			0
$103$	−118.000	+	118.000i	−1.14563	+	1.14563i	−0.158229	+	0.987403i	$0.550578\pi$
$103$	−118.000	+	118.000i	−1.14563	+	1.14563i	−0.987403	+	0.158229i	$0.949422\pi$
$104$		0			0
$105$			40.0000i			0.380952i
$106$		0			0
$107$	−142.000	−	142.000i	−1.32710	−	1.32710i	−0.907886	−	0.419217i	$-0.862305\pi$
$107$	−142.000	−	142.000i	−1.32710	−	1.32710i	−0.419217	−	0.907886i	$-0.637695\pi$
$108$		0			0
$109$		−	10.0000i		−	0.0917431i	−0.998947	−	0.0458716i	$-0.985394\pi$
$109$		−	10.0000i		−	0.0917431i	0.998947	−	0.0458716i	$-0.0146065\pi$
$110$		0			0
$111$	−12.0000			−0.108108
$112$		0			0
$113$	23.0000	−	23.0000i	0.203540	−	0.203540i	−0.597975	−	0.801515i	$-0.704028\pi$
$113$	23.0000	−	23.0000i	0.203540	−	0.203540i	0.801515	+	0.597975i	$0.204028\pi$
$114$		0			0
$115$	−10.0000	−	10.0000i	−0.0869565	−	0.0869565i
$116$		0			0
$117$	3.00000	+	3.00000i	0.0256410	+	0.0256410i
$118$		0			0
$119$		−	28.0000i		−	0.235294i
$120$		0			0
$121$	−57.0000			−0.471074
$122$		0			0
$123$	−16.0000	+	16.0000i	−0.130081	+	0.130081i
$124$		0			0
$125$			125.000i			1.00000i
$126$		0			0
$127$	118.000	+	118.000i	0.929134	+	0.929134i	0.997650	−	0.0685161i	$-0.0218265\pi$
$127$	118.000	+	118.000i	0.929134	+	0.929134i	−0.0685161	+	0.997650i	$0.521826\pi$
$128$		0			0
$129$		−	168.000i		−	1.30233i
$130$		0			0
$131$	128.000			0.977099			0.488550	−	0.872536i	$-0.337526\pi$
$131$	128.000			0.977099			0.488550	+	0.872536i	$0.337526\pi$
$132$		0			0
$133$	40.0000	−	40.0000i	0.300752	−	0.300752i
$134$		0			0
$135$	100.000	−	100.000i	0.740741	−	0.740741i
$136$		0			0
$137$	−63.0000	−	63.0000i	−0.459854	−	0.459854i	0.438753	−	0.898607i	$-0.355420\pi$
$137$	−63.0000	−	63.0000i	−0.459854	−	0.459854i	−0.898607	+	0.438753i	$0.855420\pi$
$138$		0			0
$139$		−	140.000i		−	1.00719i	−0.863939	−	0.503597i	$-0.832010\pi$
$139$		−	140.000i		−	1.00719i	0.863939	−	0.503597i	$-0.167990\pi$
$140$		0			0
$141$	72.0000			0.510638
$142$		0			0
$143$	24.0000	−	24.0000i	0.167832	−	0.167832i
$144$		0			0
$145$	200.000			1.37931
$146$		0			0
$147$	−82.0000	−	82.0000i	−0.557823	−	0.557823i
$148$		0			0
$149$		−	150.000i		−	1.00671i	−0.864079	−	0.503356i	$-0.832099\pi$
$149$		−	150.000i		−	1.00671i	0.864079	−	0.503356i	$-0.167901\pi$
$150$		0			0
$151$	−52.0000			−0.344371			−0.172185	−	0.985065i	$-0.555083\pi$
$151$	−52.0000			−0.344371			−0.172185	+	0.985065i	$0.555083\pi$
$152$		0			0
$153$	−7.00000	+	7.00000i	−0.0457516	+	0.0457516i
$154$		0			0
$155$			260.000i			1.67742i
$156$		0			0
$157$	27.0000	+	27.0000i	0.171975	+	0.171975i	0.787846	−	0.615872i	$-0.211196\pi$
$157$	27.0000	+	27.0000i	0.171975	+	0.171975i	−0.615872	+	0.787846i	$0.711196\pi$
$158$		0			0
$159$		−	212.000i		−	1.33333i
$160$		0			0
$161$	−8.00000			−0.0496894
$162$		0			0
$163$	82.0000	−	82.0000i	0.503067	−	0.503067i	−0.409322	−	0.912390i	$-0.634235\pi$
$163$	82.0000	−	82.0000i	0.503067	−	0.503067i	0.912390	+	0.409322i	$0.134235\pi$
$164$		0			0
$165$	−80.0000	−	80.0000i	−0.484848	−	0.484848i
$166$		0			0
$167$	−62.0000	−	62.0000i	−0.371257	−	0.371257i	0.496678	−	0.867935i	$-0.334553\pi$
$167$	−62.0000	−	62.0000i	−0.371257	−	0.371257i	−0.867935	+	0.496678i	$0.834553\pi$
$168$		0			0
$169$			151.000i			0.893491i
$170$		0			0
$171$	−20.0000			−0.116959
$172$		0			0
$173$	−107.000	+	107.000i	−0.618497	+	0.618497i	−0.945146	−	0.326649i	$-0.894081\pi$
$173$	−107.000	+	107.000i	−0.618497	+	0.618497i	0.326649	+	0.945146i	$0.394081\pi$
$174$		0			0
$175$	50.0000	+	50.0000i	0.285714	+	0.285714i
$176$		0			0
$177$	40.0000	+	40.0000i	0.225989	+	0.225989i
$178$		0			0
$179$			220.000i			1.22905i	0.788897	+	0.614525i	$0.210652\pi$
$179$			220.000i			1.22905i	−0.788897	+	0.614525i	$0.789348\pi$
$180$		0			0
$181$	2.00000			0.0110497			0.00552486	−	0.999985i	$-0.498241\pi$
$181$	2.00000			0.0110497			0.00552486	+	0.999985i	$0.498241\pi$
$182$		0			0
$183$	−96.0000	+	96.0000i	−0.524590	+	0.524590i
$184$		0			0
$185$	−15.0000	+	15.0000i	−0.0810811	+	0.0810811i
$186$		0			0
$187$	56.0000	+	56.0000i	0.299465	+	0.299465i
$188$		0			0
$189$		−	80.0000i		−	0.423280i
$190$		0			0
$191$	−212.000			−1.10995			−0.554974	−	0.831868i	$-0.687272\pi$
$191$	−212.000			−1.10995			−0.554974	+	0.831868i	$0.687272\pi$
$192$		0			0
$193$	−57.0000	+	57.0000i	−0.295337	+	0.295337i	−0.839184	−	0.543847i	$-0.816967\pi$
$193$	−57.0000	+	57.0000i	−0.295337	+	0.295337i	0.543847	+	0.839184i	$0.316967\pi$
$194$		0			0
$195$	−60.0000			−0.307692
$196$		0			0
$197$	−3.00000	−	3.00000i	−0.0152284	−	0.0152284i	0.699452	−	0.714680i	$-0.253428\pi$
$197$	−3.00000	−	3.00000i	−0.0152284	−	0.0152284i	−0.714680	+	0.699452i	$0.753428\pi$
$198$		0			0
$199$			120.000i			0.603015i	0.953464	+	0.301508i	$0.0974898\pi$
$199$			120.000i			0.603015i	−0.953464	+	0.301508i	$0.902510\pi$
$200$		0			0
$201$	−248.000			−1.23383
$202$		0			0
$203$	80.0000	−	80.0000i	0.394089	−	0.394089i
$204$		0			0
$205$			40.0000i			0.195122i
$206$		0			0
$207$	2.00000	+	2.00000i	0.00966184	+	0.00966184i
$208$		0			0
$209$			160.000i			0.765550i
$210$		0			0
$211$	328.000			1.55450			0.777251	−	0.629190i	$-0.216613\pi$
$211$	328.000			1.55450			0.777251	+	0.629190i	$0.216613\pi$
$212$		0			0
$213$	56.0000	−	56.0000i	0.262911	−	0.262911i
$214$		0			0
$215$	−210.000	−	210.000i	−0.976744	−	0.976744i
$216$		0			0
$217$	104.000	+	104.000i	0.479263	+	0.479263i
$218$		0			0
$219$			188.000i			0.858447i
$220$		0			0
$221$	42.0000			0.190045
$222$		0			0
$223$	−138.000	+	138.000i	−0.618834	+	0.618834i	−0.945232	−	0.326398i	$-0.894165\pi$
$223$	−138.000	+	138.000i	−0.618834	+	0.618834i	0.326398	+	0.945232i	$0.394165\pi$
$224$		0			0
$225$		−	25.0000i		−	0.111111i
$226$		0			0
$227$	−2.00000	−	2.00000i	−0.00881057	−	0.00881057i	0.702688	−	0.711498i	$-0.251983\pi$
$227$	−2.00000	−	2.00000i	−0.00881057	−	0.00881057i	−0.711498	+	0.702688i	$0.751983\pi$
$228$		0			0
$229$			120.000i			0.524017i	0.965066	+	0.262009i	$0.0843849\pi$
$229$			120.000i			0.524017i	−0.965066	+	0.262009i	$0.915615\pi$
$230$		0			0
$231$	−64.0000			−0.277056
$232$		0			0
$233$	183.000	−	183.000i	0.785408	−	0.785408i	−0.195330	−	0.980738i	$-0.562578\pi$
$233$	183.000	−	183.000i	0.785408	−	0.785408i	0.980738	+	0.195330i	$0.0625777\pi$
$234$		0			0
$235$	90.0000	−	90.0000i	0.382979	−	0.382979i
$236$		0			0
$237$		0			0
$238$		0			0
$239$		−	120.000i		−	0.502092i	−0.967975	−	0.251046i	$-0.919225\pi$
$239$		−	120.000i		−	0.502092i	0.967975	−	0.251046i	$-0.0807746\pi$
$240$		0			0
$241$	232.000			0.962656			0.481328	−	0.876541i	$-0.340155\pi$
$241$	232.000			0.962656			0.481328	+	0.876541i	$0.340155\pi$
$242$		0			0
$243$	−38.0000	+	38.0000i	−0.156379	+	0.156379i
$244$		0			0
$245$	−205.000			−0.836735
$246$		0			0
$247$	60.0000	+	60.0000i	0.242915	+	0.242915i
$248$		0			0
$249$			72.0000i			0.289157i
$250$		0			0
$251$	48.0000			0.191235			0.0956175	−	0.995418i	$-0.469517\pi$
$251$	48.0000			0.191235			0.0956175	+	0.995418i	$0.469517\pi$
$252$		0			0
$253$	16.0000	−	16.0000i	0.0632411	−	0.0632411i
$254$		0			0
$255$		−	140.000i		−	0.549020i
$256$		0			0
$257$	−313.000	−	313.000i	−1.21790	−	1.21790i	−0.968366	−	0.249532i	$-0.919723\pi$
$257$	−313.000	−	313.000i	−1.21790	−	1.21790i	−0.249532	−	0.968366i	$-0.580277\pi$
$258$		0			0
$259$			12.0000i			0.0463320i
$260$		0			0
$261$	−40.0000			−0.153257
$262$		0			0
$263$	262.000	−	262.000i	0.996198	−	0.996198i	−0.00379508	−	0.999993i	$-0.501208\pi$
$263$	262.000	−	262.000i	0.996198	−	0.996198i	0.999993	+	0.00379508i	$0.00120801\pi$
$264$		0			0
$265$	−265.000	−	265.000i	−1.00000	−	1.00000i
$266$		0			0
$267$	160.000	+	160.000i	0.599251	+	0.599251i
$268$		0			0
$269$			10.0000i			0.0371747i	0.999827	+	0.0185874i	$0.00591688\pi$
$269$			10.0000i			0.0371747i	−0.999827	+	0.0185874i	$0.994083\pi$
$270$		0			0
$271$	−252.000			−0.929889			−0.464945	−	0.885340i	$-0.653926\pi$
$271$	−252.000			−0.929889			−0.464945	+	0.885340i	$0.653926\pi$
$272$		0			0
$273$	−24.0000	+	24.0000i	−0.0879121	+	0.0879121i
$274$		0			0
$275$	−200.000			−0.727273
$276$		0			0
$277$	267.000	+	267.000i	0.963899	+	0.963899i	0.999371	−	0.0354718i	$-0.0112934\pi$
$277$	267.000	+	267.000i	0.963899	+	0.963899i	−0.0354718	+	0.999371i	$0.511293\pi$
$278$		0			0
$279$		−	52.0000i		−	0.186380i
$280$		0			0
$281$	312.000			1.11032			0.555160	−	0.831743i	$-0.312657\pi$
$281$	312.000			1.11032			0.555160	+	0.831743i	$0.312657\pi$
$282$		0			0
$283$	262.000	−	262.000i	0.925795	−	0.925795i	−0.0716358	−	0.997431i	$-0.522822\pi$
$283$	262.000	−	262.000i	0.925795	−	0.925795i	0.997431	+	0.0716358i	$0.0228219\pi$
$284$		0			0
$285$	200.000	−	200.000i	0.701754	−	0.701754i
$286$		0			0
$287$	16.0000	+	16.0000i	0.0557491	+	0.0557491i
$288$		0			0
$289$		−	191.000i		−	0.660900i
$290$		0			0
$291$	−252.000			−0.865979
$292$		0			0
$293$	243.000	−	243.000i	0.829352	−	0.829352i	−0.158075	−	0.987427i	$-0.550529\pi$
$293$	243.000	−	243.000i	0.829352	−	0.829352i	0.987427	+	0.158075i	$0.0505289\pi$
$294$		0			0
$295$	100.000			0.338983
$296$		0			0
$297$	160.000	+	160.000i	0.538721	+	0.538721i
$298$		0			0
$299$		−	12.0000i		−	0.0401338i
$300$		0			0
$301$	−168.000			−0.558140
$302$		0			0
$303$	124.000	−	124.000i	0.409241	−	0.409241i
$304$		0			0
$305$			240.000i			0.786885i
$306$		0			0
$307$	18.0000	+	18.0000i	0.0586319	+	0.0586319i	0.735815	−	0.677183i	$-0.236799\pi$
$307$	18.0000	+	18.0000i	0.0586319	+	0.0586319i	−0.677183	+	0.735815i	$0.736799\pi$
$308$		0			0
$309$			472.000i			1.52751i
$310$		0			0
$311$	388.000			1.24759			0.623794	−	0.781589i	$-0.285590\pi$
$311$	388.000			1.24759			0.623794	+	0.781589i	$0.285590\pi$
$312$		0			0
$313$	183.000	−	183.000i	0.584665	−	0.584665i	−0.351517	−	0.936182i	$-0.614334\pi$
$313$	183.000	−	183.000i	0.584665	−	0.584665i	0.936182	+	0.351517i	$0.114334\pi$
$314$		0			0
$315$	−10.0000	−	10.0000i	−0.0317460	−	0.0317460i
$316$		0			0
$317$	−213.000	−	213.000i	−0.671924	−	0.671924i	0.286235	−	0.958159i	$-0.407596\pi$
$317$	−213.000	−	213.000i	−0.671924	−	0.671924i	−0.958159	+	0.286235i	$0.907596\pi$
$318$		0			0
$319$			320.000i			1.00313i
$320$		0			0
$321$	−568.000			−1.76947
$322$		0			0
$323$	−140.000	+	140.000i	−0.433437	+	0.433437i
$324$		0			0
$325$	−75.0000	+	75.0000i	−0.230769	+	0.230769i
$326$		0			0
$327$	−20.0000	−	20.0000i	−0.0611621	−	0.0611621i
$328$		0			0
$329$		−	72.0000i		−	0.218845i
$330$		0			0
$331$	−232.000			−0.700906			−0.350453	−	0.936580i	$-0.613972\pi$
$331$	−232.000			−0.700906			−0.350453	+	0.936580i	$0.613972\pi$
$332$		0			0
$333$	3.00000	−	3.00000i	0.00900901	−	0.00900901i
$334$		0			0
$335$	−310.000	+	310.000i	−0.925373	+	0.925373i
$336$		0			0
$337$	417.000	+	417.000i	1.23739	+	1.23739i	0.961064	+	0.276324i	$0.0891164\pi$
$337$	417.000	+	417.000i	1.23739	+	1.23739i	0.276324	+	0.961064i	$0.410884\pi$
$338$		0			0
$339$		−	92.0000i		−	0.271386i
$340$		0			0
$341$	−416.000			−1.21994
$342$		0			0
$343$	−180.000	+	180.000i	−0.524781	+	0.524781i
$344$		0			0
$345$	−40.0000			−0.115942
$346$		0			0
$347$	−202.000	−	202.000i	−0.582133	−	0.582133i	0.353356	−	0.935489i	$-0.385040\pi$
$347$	−202.000	−	202.000i	−0.582133	−	0.582133i	−0.935489	+	0.353356i	$0.885040\pi$
$348$		0			0
$349$		−	440.000i		−	1.26074i	−0.776293	−	0.630372i	$-0.782902\pi$
$349$		−	440.000i		−	1.26074i	0.776293	−	0.630372i	$-0.217098\pi$
$350$		0			0
$351$	120.000			0.341880
$352$		0			0
$353$	−447.000	+	447.000i	−1.26629	+	1.26629i	−0.318298	+	0.947991i	$0.603111\pi$
$353$	−447.000	+	447.000i	−1.26629	+	1.26629i	−0.947991	+	0.318298i	$0.896889\pi$
$354$		0			0
$355$		−	140.000i		−	0.394366i
$356$		0			0
$357$	−56.0000	−	56.0000i	−0.156863	−	0.156863i
$358$		0			0
$359$			400.000i			1.11421i	0.830443	+	0.557103i	$0.188087\pi$
$359$			400.000i			1.11421i	−0.830443	+	0.557103i	$0.811913\pi$
$360$		0			0
$361$	−39.0000			−0.108033
$362$		0			0
$363$	−114.000	+	114.000i	−0.314050	+	0.314050i
$364$		0			0
$365$	235.000	+	235.000i	0.643836	+	0.643836i
$366$		0			0
$367$	118.000	+	118.000i	0.321526	+	0.321526i	0.849352	−	0.527826i	$-0.176993\pi$
$367$	118.000	+	118.000i	0.321526	+	0.321526i	−0.527826	+	0.849352i	$0.676993\pi$
$368$		0			0
$369$		−	8.00000i		−	0.0216802i
$370$		0			0
$371$	−212.000			−0.571429
$372$		0			0
$373$	−107.000	+	107.000i	−0.286863	+	0.286863i	−0.835839	−	0.548975i	$-0.815018\pi$
$373$	−107.000	+	107.000i	−0.286863	+	0.286863i	0.548975	+	0.835839i	$0.315018\pi$
$374$		0			0
$375$	250.000	+	250.000i	0.666667	+	0.666667i
$376$		0			0
$377$	120.000	+	120.000i	0.318302	+	0.318302i
$378$		0			0
$379$		−	340.000i		−	0.897098i	−0.893758	−	0.448549i	$-0.851941\pi$
$379$		−	340.000i		−	0.897098i	0.893758	−	0.448549i	$-0.148059\pi$
$380$		0			0
$381$	472.000			1.23885
$382$		0			0
$383$	342.000	−	342.000i	0.892950	−	0.892950i	−0.101849	−	0.994800i	$-0.532476\pi$
$383$	342.000	−	342.000i	0.892950	−	0.892950i	0.994800	+	0.101849i	$0.0324760\pi$
$384$		0			0
$385$	−80.0000	+	80.0000i	−0.207792	+	0.207792i
$386$		0			0
$387$	42.0000	+	42.0000i	0.108527	+	0.108527i
$388$		0			0
$389$			390.000i			1.00257i	0.865282	+	0.501285i	$0.167139\pi$
$389$			390.000i			1.00257i	−0.865282	+	0.501285i	$0.832861\pi$
$390$		0			0
$391$	28.0000			0.0716113
$392$		0			0
$393$	256.000	−	256.000i	0.651399	−	0.651399i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−323.000	−	323.000i	−0.813602	−	0.813602i	0.171570	−	0.985172i	$-0.445116\pi$
$397$	−323.000	−	323.000i	−0.813602	−	0.813602i	−0.985172	+	0.171570i	$0.945116\pi$
$398$		0			0
$399$		−	160.000i		−	0.401003i
$400$		0			0
$401$	642.000			1.60100			0.800499	−	0.599334i	$-0.204568\pi$
$401$	642.000			1.60100			0.800499	+	0.599334i	$0.204568\pi$
$402$		0			0
$403$	−156.000	+	156.000i	−0.387097	+	0.387097i
$404$		0			0
$405$		−	355.000i		−	0.876543i
$406$		0			0
$407$	−24.0000	−	24.0000i	−0.0589681	−	0.0589681i
$408$		0			0
$409$		−	150.000i		−	0.366748i	−0.983043	−	0.183374i	$-0.941298\pi$
$409$		−	150.000i		−	0.366748i	0.983043	−	0.183374i	$-0.0587020\pi$
$410$		0			0
$411$	−252.000			−0.613139
$412$		0			0
$413$	40.0000	−	40.0000i	0.0968523	−	0.0968523i
$414$		0			0
$415$	90.0000	+	90.0000i	0.216867	+	0.216867i
$416$		0			0
$417$	−280.000	−	280.000i	−0.671463	−	0.671463i
$418$		0			0
$419$		−	300.000i		−	0.715990i	−0.933723	−	0.357995i	$-0.883460\pi$
$419$		−	300.000i		−	0.715990i	0.933723	−	0.357995i	$-0.116540\pi$
$420$		0			0
$421$	−208.000			−0.494062			−0.247031	−	0.969008i	$-0.579455\pi$
$421$	−208.000			−0.494062			−0.247031	+	0.969008i	$0.579455\pi$
$422$		0			0
$423$	−18.0000	+	18.0000i	−0.0425532	+	0.0425532i
$424$		0			0
$425$	−175.000	−	175.000i	−0.411765	−	0.411765i
$426$		0			0
$427$	96.0000	+	96.0000i	0.224824	+	0.224824i
$428$		0			0
$429$		−	96.0000i		−	0.223776i
$430$		0			0
$431$	788.000			1.82831			0.914153	−	0.405369i	$-0.132857\pi$
$431$	788.000			1.82831			0.914153	+	0.405369i	$0.132857\pi$
$432$		0			0
$433$	−367.000	+	367.000i	−0.847575	+	0.847575i	−0.989830	−	0.142255i	$-0.954565\pi$
$433$	−367.000	+	367.000i	−0.847575	+	0.847575i	0.142255	+	0.989830i	$0.454565\pi$
$434$		0			0
$435$	400.000	−	400.000i	0.919540	−	0.919540i
$436$		0			0
$437$	40.0000	+	40.0000i	0.0915332	+	0.0915332i
$438$		0			0
$439$		−	560.000i		−	1.27563i	−0.770191	−	0.637813i	$-0.779839\pi$
$439$		−	560.000i		−	1.27563i	0.770191	−	0.637813i	$-0.220161\pi$
$440$		0			0
$441$	41.0000			0.0929705
$442$		0			0
$443$	−378.000	+	378.000i	−0.853273	+	0.853273i	−0.990535	−	0.137262i	$-0.956170\pi$
$443$	−378.000	+	378.000i	−0.853273	+	0.853273i	0.137262	+	0.990535i	$0.456170\pi$
$444$		0			0
$445$	400.000			0.898876
$446$		0			0
$447$	−300.000	−	300.000i	−0.671141	−	0.671141i
$448$		0			0
$449$		−	410.000i		−	0.913140i	−0.889687	−	0.456570i	$-0.849078\pi$
$449$		−	410.000i		−	0.913140i	0.889687	−	0.456570i	$-0.150922\pi$
$450$		0			0
$451$	−64.0000			−0.141907
$452$		0			0
$453$	−104.000	+	104.000i	−0.229581	+	0.229581i
$454$		0			0
$455$			60.0000i			0.131868i
$456$		0			0
$457$	−393.000	−	393.000i	−0.859956	−	0.859956i	0.131376	−	0.991333i	$-0.458060\pi$
$457$	−393.000	−	393.000i	−0.859956	−	0.859956i	−0.991333	+	0.131376i	$0.958060\pi$
$458$		0			0
$459$			280.000i			0.610022i
$460$		0			0
$461$	622.000			1.34924			0.674620	−	0.738165i	$-0.264307\pi$
$461$	622.000			1.34924			0.674620	+	0.738165i	$0.264307\pi$
$462$		0			0
$463$	−278.000	+	278.000i	−0.600432	+	0.600432i	−0.940427	−	0.339995i	$-0.889575\pi$
$463$	−278.000	+	278.000i	−0.600432	+	0.600432i	0.339995	+	0.940427i	$0.389575\pi$
$464$		0			0
$465$	520.000	+	520.000i	1.11828	+	1.11828i
$466$		0			0
$467$	38.0000	+	38.0000i	0.0813704	+	0.0813704i	0.746621	−	0.665250i	$-0.231675\pi$
$467$	38.0000	+	38.0000i	0.0813704	+	0.0813704i	−0.665250	+	0.746621i	$0.731675\pi$
$468$		0			0
$469$			248.000i			0.528785i
$470$		0			0
$471$	108.000			0.229299
$472$		0			0
$473$	336.000	−	336.000i	0.710359	−	0.710359i
$474$		0			0
$475$		−	500.000i		−	1.05263i
$476$		0			0
$477$	53.0000	+	53.0000i	0.111111	+	0.111111i
$478$		0			0
$479$			440.000i			0.918580i	0.888286	+	0.459290i	$0.151896\pi$
$479$			440.000i			0.918580i	−0.888286	+	0.459290i	$0.848104\pi$
$480$		0			0
$481$	−18.0000			−0.0374220
$482$		0			0
$483$	−16.0000	+	16.0000i	−0.0331263	+	0.0331263i
$484$		0			0
$485$	−315.000	+	315.000i	−0.649485	+	0.649485i
$486$		0			0
$487$	−522.000	−	522.000i	−1.07187	−	1.07187i	−0.997209	−	0.0746595i	$-0.976213\pi$
$487$	−522.000	−	522.000i	−1.07187	−	1.07187i	−0.0746595	−	0.997209i	$-0.523787\pi$
$488$		0			0
$489$		−	328.000i		−	0.670757i
$490$		0			0
$491$	328.000			0.668024			0.334012	−	0.942569i	$-0.391597\pi$
$491$	328.000			0.668024			0.334012	+	0.942569i	$0.391597\pi$
$492$		0			0
$493$	−280.000	+	280.000i	−0.567951	+	0.567951i
$494$		0			0
$495$	40.0000			0.0808081
$496$		0			0
$497$	−56.0000	−	56.0000i	−0.112676	−	0.112676i
$498$		0			0
$499$		−	380.000i		−	0.761523i	−0.924673	−	0.380762i	$-0.875662\pi$
$499$		−	380.000i		−	0.761523i	0.924673	−	0.380762i	$-0.124338\pi$
$500$		0			0
$501$	−248.000			−0.495010
$502$		0			0
$503$	42.0000	−	42.0000i	0.0834990	−	0.0834990i	−0.664124	−	0.747623i	$-0.731195\pi$
$503$	42.0000	−	42.0000i	0.0834990	−	0.0834990i	0.747623	+	0.664124i	$0.231195\pi$
$504$		0			0
$505$		−	310.000i		−	0.613861i
$506$		0			0
$507$	302.000	+	302.000i	0.595661	+	0.595661i
$508$		0			0
$509$		−	440.000i		−	0.864440i	−0.901768	−	0.432220i	$-0.857730\pi$
$509$		−	440.000i		−	0.864440i	0.901768	−	0.432220i	$-0.142270\pi$
$510$		0			0
$511$	188.000			0.367906
$512$		0			0
$513$	−400.000	+	400.000i	−0.779727	+	0.779727i
$514$		0			0
$515$	590.000	+	590.000i	1.14563	+	1.14563i
$516$		0			0
$517$	144.000	+	144.000i	0.278530	+	0.278530i
$518$		0			0
$519$			428.000i			0.824663i
$520$		0			0
$521$	−258.000			−0.495202			−0.247601	−	0.968862i	$-0.579642\pi$
$521$	−258.000			−0.495202			−0.247601	+	0.968862i	$0.579642\pi$
$522$		0			0
$523$	−258.000	+	258.000i	−0.493308	+	0.493308i	−0.909347	−	0.416039i	$-0.863418\pi$
$523$	−258.000	+	258.000i	−0.493308	+	0.493308i	0.416039	+	0.909347i	$0.363418\pi$
$524$		0			0
$525$	200.000			0.380952
$526$		0			0
$527$	−364.000	−	364.000i	−0.690702	−	0.690702i
$528$		0			0
$529$			521.000i			0.984877i
$530$		0			0
$531$	−20.0000			−0.0376648
$532$		0			0
$533$	−24.0000	+	24.0000i	−0.0450281	+	0.0450281i
$534$		0			0
$535$	−710.000	+	710.000i	−1.32710	+	1.32710i
$536$		0			0
$537$	440.000	+	440.000i	0.819367	+	0.819367i
$538$		0			0
$539$		−	328.000i		−	0.608534i
$540$		0			0
$541$	−338.000			−0.624769			−0.312384	−	0.949956i	$-0.601128\pi$
$541$	−338.000			−0.624769			−0.312384	+	0.949956i	$0.601128\pi$
$542$		0			0
$543$	4.00000	−	4.00000i	0.00736648	−	0.00736648i
$544$		0			0
$545$	−50.0000			−0.0917431
$546$		0			0
$547$	558.000	+	558.000i	1.02011	+	1.02011i	0.999794	+	0.0203161i	$0.00646725\pi$
$547$	558.000	+	558.000i	1.02011	+	1.02011i	0.0203161	+	0.999794i	$0.493533\pi$
$548$		0			0
$549$		−	48.0000i		−	0.0874317i
$550$		0			0
$551$	−800.000			−1.45191
$552$		0			0
$553$		0			0
$554$		0			0
$555$			60.0000i			0.108108i
$556$		0			0
$557$	−3.00000	−	3.00000i	−0.00538600	−	0.00538600i	0.704409	−	0.709795i	$-0.251212\pi$
$557$	−3.00000	−	3.00000i	−0.00538600	−	0.00538600i	−0.709795	+	0.704409i	$0.751212\pi$
$558$		0			0
$559$		−	252.000i		−	0.450805i
$560$		0			0
$561$	224.000			0.399287
$562$		0			0
$563$	42.0000	−	42.0000i	0.0746004	−	0.0746004i	−0.668822	−	0.743422i	$-0.733201\pi$
$563$	42.0000	−	42.0000i	0.0746004	−	0.0746004i	0.743422	+	0.668822i	$0.233201\pi$
$564$		0			0
$565$	−115.000	−	115.000i	−0.203540	−	0.203540i
$566$		0			0
$567$	−142.000	−	142.000i	−0.250441	−	0.250441i
$568$		0			0
$569$			950.000i			1.66960i	0.550557	+	0.834798i	$0.314416\pi$
$569$			950.000i			1.66960i	−0.550557	+	0.834798i	$0.685584\pi$
$570$		0			0
$571$	−392.000			−0.686515			−0.343257	−	0.939241i	$-0.611530\pi$
$571$	−392.000			−0.686515			−0.343257	+	0.939241i	$0.611530\pi$
$572$		0			0
$573$	−424.000	+	424.000i	−0.739965	+	0.739965i
$574$		0			0
$575$	−50.0000	+	50.0000i	−0.0869565	+	0.0869565i
$576$		0			0
$577$	−473.000	−	473.000i	−0.819757	−	0.819757i	0.166315	−	0.986073i	$-0.446813\pi$
$577$	−473.000	−	473.000i	−0.819757	−	0.819757i	−0.986073	+	0.166315i	$0.946813\pi$
$578$		0			0
$579$			228.000i			0.393782i
$580$		0			0
$581$	72.0000			0.123924
$582$		0			0
$583$	424.000	−	424.000i	0.727273	−	0.727273i
$584$		0			0
$585$	15.0000	−	15.0000i	0.0256410	−	0.0256410i
$586$		0			0
$587$	198.000	+	198.000i	0.337308	+	0.337308i	0.855353	−	0.518045i	$-0.173340\pi$
$587$	198.000	+	198.000i	0.337308	+	0.337308i	−0.518045	+	0.855353i	$0.673340\pi$
$588$		0			0
$589$		−	1040.00i		−	1.76570i
$590$		0			0
$591$	−12.0000			−0.0203046
$592$		0			0
$593$	−47.0000	+	47.0000i	−0.0792580	+	0.0792580i	−0.745624	−	0.666366i	$-0.767849\pi$
$593$	−47.0000	+	47.0000i	−0.0792580	+	0.0792580i	0.666366	+	0.745624i	$0.267849\pi$
$594$		0			0
$595$	−140.000			−0.235294
$596$		0			0
$597$	240.000	+	240.000i	0.402010	+	0.402010i
$598$		0			0
$599$		−	520.000i		−	0.868114i	−0.900886	−	0.434057i	$-0.857082\pi$
$599$		−	520.000i		−	0.868114i	0.900886	−	0.434057i	$-0.142918\pi$
$600$		0			0
$601$	−328.000			−0.545757			−0.272879	−	0.962048i	$-0.587976\pi$
$601$	−328.000			−0.545757			−0.272879	+	0.962048i	$0.587976\pi$
$602$		0			0
$603$	62.0000	−	62.0000i	0.102819	−	0.102819i
$604$		0			0
$605$			285.000i			0.471074i
$606$		0			0
$607$	−462.000	−	462.000i	−0.761120	−	0.761120i	0.215405	−	0.976525i	$-0.430893\pi$
$607$	−462.000	−	462.000i	−0.761120	−	0.761120i	−0.976525	+	0.215405i	$0.930893\pi$
$608$		0			0
$609$		−	320.000i		−	0.525452i
$610$		0			0
$611$	108.000			0.176759
$612$		0			0
$613$	723.000	−	723.000i	1.17945	−	1.17945i	0.199560	−	0.979886i	$-0.436049\pi$
$613$	723.000	−	723.000i	1.17945	−	1.17945i	0.979886	−	0.199560i	$-0.0639512\pi$
$614$		0			0
$615$	80.0000	+	80.0000i	0.130081	+	0.130081i
$616$		0			0
$617$	327.000	+	327.000i	0.529984	+	0.529984i	0.920567	−	0.390584i	$-0.127727\pi$
$617$	327.000	+	327.000i	0.529984	+	0.529984i	−0.390584	+	0.920567i	$0.627727\pi$
$618$		0			0
$619$			660.000i			1.06624i	0.846041	+	0.533118i	$0.178980\pi$
$619$			660.000i			1.06624i	−0.846041	+	0.533118i	$0.821020\pi$
$620$		0			0
$621$	80.0000			0.128824
$622$		0			0
$623$	160.000	−	160.000i	0.256822	−	0.256822i
$624$		0			0
$625$	625.000			1.00000
$626$		0			0
$627$	320.000	+	320.000i	0.510367	+	0.510367i
$628$		0			0
$629$		−	42.0000i		−	0.0667727i
$630$		0			0
$631$	548.000			0.868463			0.434231	−	0.900801i	$-0.357020\pi$
$631$	548.000			0.868463			0.434231	+	0.900801i	$0.357020\pi$
$632$		0			0
$633$	656.000	−	656.000i	1.03633	−	1.03633i
$634$		0			0
$635$	590.000	−	590.000i	0.929134	−	0.929134i
$636$		0			0
$637$	−123.000	−	123.000i	−0.193093	−	0.193093i
$638$		0			0
$639$			28.0000i			0.0438185i
$640$		0			0
$641$	−568.000			−0.886115			−0.443058	−	0.896493i	$-0.646106\pi$
$641$	−568.000			−0.886115			−0.443058	+	0.896493i	$0.646106\pi$
$642$		0			0
$643$	342.000	−	342.000i	0.531882	−	0.531882i	−0.389250	−	0.921132i	$-0.627266\pi$
$643$	342.000	−	342.000i	0.531882	−	0.531882i	0.921132	+	0.389250i	$0.127266\pi$
$644$		0			0
$645$	−840.000			−1.30233
$646$		0			0
$647$	118.000	+	118.000i	0.182380	+	0.182380i	0.792392	−	0.610012i	$-0.208835\pi$
$647$	118.000	+	118.000i	0.182380	+	0.182380i	−0.610012	+	0.792392i	$0.708835\pi$
$648$		0			0
$649$			160.000i			0.246533i
$650$		0			0
$651$	416.000			0.639017
$652$		0			0
$653$	453.000	−	453.000i	0.693721	−	0.693721i	−0.269327	−	0.963049i	$-0.586801\pi$
$653$	453.000	−	453.000i	0.693721	−	0.693721i	0.963049	+	0.269327i	$0.0868014\pi$
$654$		0			0
$655$		−	640.000i		−	0.977099i
$656$		0			0
$657$	−47.0000	−	47.0000i	−0.0715373	−	0.0715373i
$658$		0			0
$659$		−	140.000i		−	0.212443i	−0.994342	−	0.106222i	$-0.966125\pi$
$659$		−	140.000i		−	0.212443i	0.994342	−	0.106222i	$-0.0338753\pi$
$660$		0			0
$661$	512.000			0.774584			0.387292	−	0.921957i	$-0.373411\pi$
$661$	512.000			0.774584			0.387292	+	0.921957i	$0.373411\pi$
$662$		0			0
$663$	84.0000	−	84.0000i	0.126697	−	0.126697i
$664$		0			0
$665$	−200.000	−	200.000i	−0.300752	−	0.300752i
$666$		0			0
$667$	80.0000	+	80.0000i	0.119940	+	0.119940i
$668$		0			0
$669$			552.000i			0.825112i
$670$		0			0
$671$	−384.000			−0.572280
$672$		0			0
$673$	193.000	−	193.000i	0.286776	−	0.286776i	−0.549028	−	0.835804i	$-0.685002\pi$
$673$	193.000	−	193.000i	0.286776	−	0.286776i	0.835804	+	0.549028i	$0.185002\pi$
$674$		0			0
$675$	−500.000	−	500.000i	−0.740741	−	0.740741i
$676$		0			0
$677$	157.000	+	157.000i	0.231905	+	0.231905i	0.813488	−	0.581582i	$-0.197566\pi$
$677$	157.000	+	157.000i	0.231905	+	0.231905i	−0.581582	+	0.813488i	$0.697566\pi$
$678$		0			0
$679$			252.000i			0.371134i
$680$		0			0
$681$	−8.00000			−0.0117474
$682$		0			0
$683$	−438.000	+	438.000i	−0.641288	+	0.641288i	−0.950872	−	0.309584i	$-0.899810\pi$
$683$	−438.000	+	438.000i	−0.641288	+	0.641288i	0.309584	+	0.950872i	$0.399810\pi$
$684$		0			0
$685$	−315.000	+	315.000i	−0.459854	+	0.459854i
$686$		0			0
$687$	240.000	+	240.000i	0.349345	+	0.349345i
$688$		0			0
$689$		−	318.000i		−	0.461538i
$690$		0			0
$691$	−1032.00			−1.49349			−0.746744	−	0.665112i	$-0.768384\pi$
$691$	−1032.00			−1.49349			−0.746744	+	0.665112i	$0.768384\pi$
$692$		0			0
$693$	16.0000	−	16.0000i	0.0230880	−	0.0230880i
$694$		0			0
$695$	−700.000			−1.00719
$696$		0			0
$697$	−56.0000	−	56.0000i	−0.0803443	−	0.0803443i
$698$		0			0
$699$		−	732.000i		−	1.04721i
$700$		0			0
$701$	−128.000			−0.182596			−0.0912981	−	0.995824i	$-0.529102\pi$
$701$	−128.000			−0.182596			−0.0912981	+	0.995824i	$0.529102\pi$
$702$		0			0
$703$	60.0000	−	60.0000i	0.0853485	−	0.0853485i
$704$		0			0
$705$		−	360.000i		−	0.510638i
$706$		0			0
$707$	−124.000	−	124.000i	−0.175389	−	0.175389i
$708$		0			0
$709$			760.000i			1.07193i	0.844239	+	0.535966i	$0.180053\pi$
$709$			760.000i			1.07193i	−0.844239	+	0.535966i	$0.819947\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−104.000	+	104.000i	−0.145863	+	0.145863i
$714$		0			0
$715$	−120.000	−	120.000i	−0.167832	−	0.167832i
$716$		0			0
$717$	−240.000	−	240.000i	−0.334728	−	0.334728i
$718$		0			0
$719$			1160.00i			1.61335i	0.590994	+	0.806676i	$0.298736\pi$
$719$			1160.00i			1.61335i	−0.590994	+	0.806676i	$0.701264\pi$
$720$		0			0
$721$	472.000			0.654646
$722$		0			0
$723$	464.000	−	464.000i	0.641770	−	0.641770i
$724$		0			0
$725$		−	1000.00i		−	1.37931i
$726$		0			0
$727$	558.000	+	558.000i	0.767538	+	0.767538i	0.977672	−	0.210135i	$-0.0673902\pi$
$727$	558.000	+	558.000i	0.767538	+	0.767538i	−0.210135	+	0.977672i	$0.567390\pi$
$728$		0			0
$729$			791.000i			1.08505i
$730$		0			0
$731$	588.000			0.804378
$732$		0			0
$733$	−827.000	+	827.000i	−1.12824	+	1.12824i	−0.137777	+	0.990463i	$0.543996\pi$
$733$	−827.000	+	827.000i	−1.12824	+	1.12824i	−0.990463	+	0.137777i	$0.956004\pi$
$734$		0			0
$735$	−410.000	+	410.000i	−0.557823	+	0.557823i
$736$		0			0
$737$	−496.000	−	496.000i	−0.672999	−	0.672999i
$738$		0			0
$739$			700.000i			0.947226i	0.880733	+	0.473613i	$0.157050\pi$
$739$			700.000i			0.947226i	−0.880733	+	0.473613i	$0.842950\pi$
$740$		0			0
$741$	240.000			0.323887
$742$		0			0
$743$	382.000	−	382.000i	0.514132	−	0.514132i	−0.401658	−	0.915790i	$-0.631566\pi$
$743$	382.000	−	382.000i	0.514132	−	0.514132i	0.915790	+	0.401658i	$0.131566\pi$
$744$		0			0
$745$	−750.000			−1.00671
$746$		0			0
$747$	−18.0000	−	18.0000i	−0.0240964	−	0.0240964i
$748$		0			0
$749$			568.000i			0.758344i
$750$		0			0
$751$	588.000			0.782956			0.391478	−	0.920187i	$-0.371964\pi$
$751$	588.000			0.782956			0.391478	+	0.920187i	$0.371964\pi$
$752$		0			0
$753$	96.0000	−	96.0000i	0.127490	−	0.127490i
$754$		0			0
$755$			260.000i			0.344371i
$756$		0			0
$757$	987.000	+	987.000i	1.30383	+	1.30383i	0.925788	+	0.378043i	$0.123403\pi$
$757$	987.000	+	987.000i	1.30383	+	1.30383i	0.378043	+	0.925788i	$0.376597\pi$
$758$		0			0
$759$		−	64.0000i		−	0.0843215i
$760$		0			0
$761$	−158.000			−0.207622			−0.103811	−	0.994597i	$-0.533104\pi$
$761$	−158.000			−0.207622			−0.103811	+	0.994597i	$0.533104\pi$
$762$		0			0
$763$	−20.0000	+	20.0000i	−0.0262123	+	0.0262123i
$764$		0			0
$765$	35.0000	+	35.0000i	0.0457516	+	0.0457516i
$766$		0			0
$767$	60.0000	+	60.0000i	0.0782269	+	0.0782269i
$768$		0			0
$769$			80.0000i			0.104031i	0.998646	+	0.0520156i	$0.0165646\pi$
$769$			80.0000i			0.104031i	−0.998646	+	0.0520156i	$0.983435\pi$
$770$		0			0
$771$	−1252.00			−1.62387
$772$		0			0
$773$	243.000	−	243.000i	0.314360	−	0.314360i	−0.532236	−	0.846596i	$-0.678648\pi$
$773$	243.000	−	243.000i	0.314360	−	0.314360i	0.846596	+	0.532236i	$0.178648\pi$
$774$		0			0
$775$	1300.00			1.67742
$776$		0			0
$777$	24.0000	+	24.0000i	0.0308880	+	0.0308880i
$778$		0			0
$779$		−	160.000i		−	0.205392i
$780$		0			0
$781$	224.000			0.286812
$782$		0			0
$783$	−800.000	+	800.000i	−1.02171	+	1.02171i
$784$		0			0
$785$	135.000	−	135.000i	0.171975	−	0.171975i
$786$		0			0
$787$	−262.000	−	262.000i	−0.332910	−	0.332910i	0.520781	−	0.853690i	$-0.325641\pi$
$787$	−262.000	−	262.000i	−0.332910	−	0.332910i	−0.853690	+	0.520781i	$0.825641\pi$
$788$		0			0
$789$		−	1048.00i		−	1.32826i
$790$		0			0
$791$	−92.0000			−0.116308
$792$		0			0
$793$	−144.000	+	144.000i	−0.181589	+	0.181589i
$794$		0			0
$795$	−1060.00			−1.33333
$796$		0			0
$797$	267.000	+	267.000i	0.335006	+	0.335006i	0.854484	−	0.519478i	$-0.173873\pi$
$797$	267.000	+	267.000i	0.335006	+	0.335006i	−0.519478	+	0.854484i	$0.673873\pi$
$798$		0			0
$799$			252.000i			0.315394i
$800$		0			0
$801$	−80.0000			−0.0998752
$802$		0			0
$803$	−376.000	+	376.000i	−0.468244	+	0.468244i
$804$		0			0
$805$			40.0000i			0.0496894i
$806$		0			0
$807$	20.0000	+	20.0000i	0.0247831	+	0.0247831i
$808$		0			0
$809$			560.000i			0.692213i	0.938195	+	0.346106i	$0.112496\pi$
$809$			560.000i			0.692213i	−0.938195	+	0.346106i	$0.887504\pi$
$810$		0			0
$811$	208.000			0.256473			0.128237	−	0.991744i	$-0.459068\pi$
$811$	208.000			0.256473			0.128237	+	0.991744i	$0.459068\pi$
$812$		0			0
$813$	−504.000	+	504.000i	−0.619926	+	0.619926i
$814$		0			0
$815$	−410.000	−	410.000i	−0.503067	−	0.503067i
$816$		0			0
$817$	840.000	+	840.000i	1.02815	+	1.02815i
$818$		0			0
$819$		−	12.0000i		−	0.0146520i
$820$		0			0
$821$	−1568.00			−1.90987			−0.954933	−	0.296821i	$-0.904073\pi$
$821$	−1568.00			−1.90987			−0.954933	+	0.296821i	$0.904073\pi$
$822$		0			0
$823$	562.000	−	562.000i	0.682868	−	0.682868i	−0.277778	−	0.960645i	$-0.589598\pi$
$823$	562.000	−	562.000i	0.682868	−	0.682868i	0.960645	+	0.277778i	$0.0895979\pi$
$824$		0			0
$825$	−400.000	+	400.000i	−0.484848	+	0.484848i
$826$		0			0
$827$	−762.000	−	762.000i	−0.921403	−	0.921403i	0.0757260	−	0.997129i	$-0.475873\pi$
$827$	−762.000	−	762.000i	−0.921403	−	0.921403i	−0.997129	+	0.0757260i	$0.975873\pi$
$828$		0			0
$829$			170.000i			0.205066i	0.994730	+	0.102533i	$0.0326948\pi$
$829$			170.000i			0.205066i	−0.994730	+	0.102533i	$0.967305\pi$
$830$		0			0
$831$	1068.00			1.28520
$832$		0			0
$833$	287.000	−	287.000i	0.344538	−	0.344538i
$834$		0			0
$835$	−310.000	+	310.000i	−0.371257	+	0.371257i
$836$		0			0
$837$	−1040.00	−	1040.00i	−1.24253	−	1.24253i
$838$		0			0
$839$			280.000i			0.333731i	0.985980	+	0.166865i	$0.0533645\pi$
$839$			280.000i			0.333731i	−0.985980	+	0.166865i	$0.946635\pi$
$840$		0			0
$841$	−759.000			−0.902497
$842$		0			0
$843$	624.000	−	624.000i	0.740214	−	0.740214i
$844$		0			0
$845$	755.000			0.893491
$846$		0			0
$847$	114.000	+	114.000i	0.134593	+	0.134593i
$848$		0			0
$849$		−	1048.00i		−	1.23439i
$850$		0			0
$851$	−12.0000			−0.0141011
$852$		0			0
$853$	1123.00	−	1123.00i	1.31653	−	1.31653i	0.400026	−	0.916504i	$-0.369001\pi$
$853$	1123.00	−	1123.00i	1.31653	−	1.31653i	0.916504	−	0.400026i	$-0.130999\pi$
$854$		0			0
$855$			100.000i			0.116959i
$856$		0			0
$857$	417.000	+	417.000i	0.486581	+	0.486581i	0.907226	−	0.420644i	$-0.138196\pi$
$857$	417.000	+	417.000i	0.486581	+	0.486581i	−0.420644	+	0.907226i	$0.638196\pi$
$858$		0			0
$859$			1300.00i			1.51339i	0.653769	+	0.756694i	$0.273187\pi$
$859$			1300.00i			1.51339i	−0.653769	+	0.756694i	$0.726813\pi$
$860$		0			0
$861$	64.0000			0.0743322
$862$		0			0
$863$	242.000	−	242.000i	0.280417	−	0.280417i	−0.552858	−	0.833275i	$-0.686463\pi$
$863$	242.000	−	242.000i	0.280417	−	0.280417i	0.833275	+	0.552858i	$0.186463\pi$
$864$		0			0
$865$	535.000	+	535.000i	0.618497	+	0.618497i
$866$		0			0
$867$	−382.000	−	382.000i	−0.440600	−	0.440600i
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−372.000			−0.427095
$872$		0			0
$873$	63.0000	−	63.0000i	0.0721649	−	0.0721649i
$874$		0			0
$875$	250.000	−	250.000i	0.285714	−	0.285714i
$876$		0			0
$877$	−453.000	−	453.000i	−0.516534	−	0.516534i	0.399987	−	0.916521i	$-0.369015\pi$
$877$	−453.000	−	453.000i	−0.516534	−	0.516534i	−0.916521	+	0.399987i	$0.869015\pi$
$878$		0			0
$879$		−	972.000i		−	1.10580i
$880$		0			0
$881$	712.000			0.808173			0.404086	−	0.914721i	$-0.367590\pi$
$881$	712.000			0.808173			0.404086	+	0.914721i	$0.367590\pi$
$882$		0			0
$883$	−118.000	+	118.000i	−0.133635	+	0.133635i	−0.770760	−	0.637125i	$-0.780123\pi$
$883$	−118.000	+	118.000i	−0.133635	+	0.133635i	0.637125	+	0.770760i	$0.280123\pi$
$884$		0			0
$885$	200.000	−	200.000i	0.225989	−	0.225989i
$886$		0			0
$887$	1158.00	+	1158.00i	1.30552	+	1.30552i	0.924611	+	0.380914i	$0.124390\pi$
$887$	1158.00	+	1158.00i	1.30552	+	1.30552i	0.380914	+	0.924611i	$0.375610\pi$
$888$		0			0
$889$		−	472.000i		−	0.530934i
$890$		0			0
$891$	568.000			0.637486
$892$		0			0
$893$	−360.000	+	360.000i	−0.403135	+	0.403135i
$894$		0			0
$895$	1100.00			1.22905
$896$		0			0
$897$	−24.0000	−	24.0000i	−0.0267559	−	0.0267559i
$898$		0			0
$899$		−	2080.00i		−	2.31368i
$900$		0			0
$901$	742.000			0.823529
$902$		0			0
$903$	−336.000	+	336.000i	−0.372093	+	0.372093i
$904$		0			0
$905$		−	10.0000i		−	0.0110497i
$906$		0			0
$907$	−142.000	−	142.000i	−0.156560	−	0.156560i	0.624480	−	0.781040i	$-0.285311\pi$
$907$	−142.000	−	142.000i	−0.156560	−	0.156560i	−0.781040	+	0.624480i	$0.785311\pi$
$908$		0			0
$909$			62.0000i			0.0682068i
$910$		0			0
$911$	−1172.00			−1.28650			−0.643249	−	0.765657i	$-0.722414\pi$
$911$	−1172.00			−1.28650			−0.643249	+	0.765657i	$0.722414\pi$
$912$		0			0
$913$	−144.000	+	144.000i	−0.157722	+	0.157722i
$914$		0			0
$915$	480.000	+	480.000i	0.524590	+	0.524590i
$916$		0			0
$917$	−256.000	−	256.000i	−0.279171	−	0.279171i
$918$		0			0
$919$		−	920.000i		−	1.00109i	−0.865711	−	0.500544i	$-0.833133\pi$
$919$		−	920.000i		−	1.00109i	0.865711	−	0.500544i	$-0.166867\pi$
$920$		0			0
$921$	72.0000			0.0781759
$922$		0			0
$923$	84.0000	−	84.0000i	0.0910076	−	0.0910076i
$924$		0			0
$925$	75.0000	+	75.0000i	0.0810811	+	0.0810811i
$926$		0			0
$927$	−118.000	−	118.000i	−0.127292	−	0.127292i
$928$		0			0
$929$		−	1190.00i		−	1.28095i	−0.767980	−	0.640474i	$-0.778738\pi$
$929$		−	1190.00i		−	1.28095i	0.767980	−	0.640474i	$-0.221262\pi$
$930$		0			0
$931$	820.000			0.880773
$932$		0			0
$933$	776.000	−	776.000i	0.831726	−	0.831726i
$934$		0			0
$935$	280.000	−	280.000i	0.299465	−	0.299465i
$936$		0			0
$937$	−233.000	−	233.000i	−0.248666	−	0.248666i	0.571757	−	0.820423i	$-0.306262\pi$
$937$	−233.000	−	233.000i	−0.248666	−	0.248666i	−0.820423	+	0.571757i	$0.806262\pi$
$938$		0			0
$939$		−	732.000i		−	0.779553i
$940$		0			0
$941$	−78.0000			−0.0828905			−0.0414453	−	0.999141i	$-0.513196\pi$
$941$	−78.0000			−0.0828905			−0.0414453	+	0.999141i	$0.513196\pi$
$942$		0			0
$943$	−16.0000	+	16.0000i	−0.0169671	+	0.0169671i
$944$		0			0
$945$	−400.000			−0.423280
$946$		0			0
$947$	−62.0000	−	62.0000i	−0.0654699	−	0.0654699i	0.673614	−	0.739084i	$-0.264741\pi$
$947$	−62.0000	−	62.0000i	−0.0654699	−	0.0654699i	−0.739084	+	0.673614i	$0.764741\pi$
$948$		0			0
$949$			282.000i			0.297155i
$950$		0			0
$951$	−852.000			−0.895899
$952$		0			0
$953$	−1017.00	+	1017.00i	−1.06716	+	1.06716i	−0.0695800	+	0.997576i	$0.522166\pi$
$953$	−1017.00	+	1017.00i	−1.06716	+	1.06716i	−0.997576	+	0.0695800i	$0.977834\pi$
$954$		0			0
$955$			1060.00i			1.10995i
$956$		0			0
$957$	640.000	+	640.000i	0.668757	+	0.668757i
$958$		0			0
$959$			252.000i			0.262774i
$960$		0			0
$961$	1743.00			1.81374
$962$		0			0
$963$	142.000	−	142.000i	0.147456	−	0.147456i
$964$		0			0
$965$	285.000	+	285.000i	0.295337	+	0.295337i
$966$		0			0
$967$	−502.000	−	502.000i	−0.519131	−	0.519131i	0.398177	−	0.917309i	$-0.369643\pi$
$967$	−502.000	−	502.000i	−0.519131	−	0.519131i	−0.917309	+	0.398177i	$0.869643\pi$
$968$		0			0
$969$			560.000i			0.577915i
$970$		0			0
$971$	−992.000			−1.02163			−0.510814	−	0.859691i	$-0.670656\pi$
$971$	−992.000			−1.02163			−0.510814	+	0.859691i	$0.670656\pi$
$972$		0			0
$973$	−280.000	+	280.000i	−0.287770	+	0.287770i
$974$		0			0
$975$			300.000i			0.307692i
$976$		0			0
$977$	−783.000	−	783.000i	−0.801433	−	0.801433i	0.181887	−	0.983320i	$-0.441780\pi$
$977$	−783.000	−	783.000i	−0.801433	−	0.801433i	−0.983320	+	0.181887i	$0.941780\pi$
$978$		0			0
$979$			640.000i			0.653728i
$980$		0			0
$981$	10.0000			0.0101937
$982$		0			0
$983$	−1058.00	+	1058.00i	−1.07630	+	1.07630i	−0.0794589	+	0.996838i	$0.525319\pi$
$983$	−1058.00	+	1058.00i	−1.07630	+	1.07630i	−0.996838	+	0.0794589i	$0.974681\pi$
$984$		0			0
$985$	−15.0000	+	15.0000i	−0.0152284	+	0.0152284i
$986$		0			0
$987$	−144.000	−	144.000i	−0.145897	−	0.145897i
$988$		0			0
$989$		−	168.000i		−	0.169869i
$990$		0			0
$991$	68.0000			0.0686176			0.0343088	−	0.999411i	$-0.489077\pi$
$991$	68.0000			0.0686176			0.0343088	+	0.999411i	$0.489077\pi$
$992$		0			0
$993$	−464.000	+	464.000i	−0.467271	+	0.467271i
$994$		0			0
$995$	600.000			0.603015
$996$		0			0
$997$	−773.000	−	773.000i	−0.775326	−	0.775326i	0.203706	−	0.979032i	$-0.434701\pi$
$997$	−773.000	−	773.000i	−0.775326	−	0.775326i	−0.979032	+	0.203706i	$0.934701\pi$
$998$		0			0
$999$		−	120.000i		−	0.120120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.3.p.c.17.1		2
3.2	odd	2		720.3.bh.c.577.1		2
4.3	odd	2		10.3.c.a.7.1	yes	2
5.2	odd	4		400.3.p.b.193.1		2
5.3	odd	4	inner	80.3.p.c.33.1		2
5.4	even	2		400.3.p.b.257.1		2
8.3	odd	2		320.3.p.h.257.1		2
8.5	even	2		320.3.p.a.257.1		2
12.11	even	2		90.3.g.b.37.1		2
15.8	even	4		720.3.bh.c.433.1		2
20.3	even	4		10.3.c.a.3.1	✓	2
20.7	even	4		50.3.c.c.43.1		2
20.19	odd	2		50.3.c.c.7.1		2
28.27	even	2		490.3.f.b.197.1		2
40.3	even	4		320.3.p.h.193.1		2
40.13	odd	4		320.3.p.a.193.1		2
60.23	odd	4		90.3.g.b.73.1		2
60.47	odd	4		450.3.g.b.343.1		2
60.59	even	2		450.3.g.b.307.1		2
140.83	odd	4		490.3.f.b.393.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.3.c.a.3.1	✓	2	20.3	even	4
10.3.c.a.7.1	yes	2	4.3	odd	2
50.3.c.c.7.1		2	20.19	odd	2
50.3.c.c.43.1		2	20.7	even	4
80.3.p.c.17.1		2	1.1	even	1	trivial
80.3.p.c.33.1		2	5.3	odd	4	inner
90.3.g.b.37.1		2	12.11	even	2
90.3.g.b.73.1		2	60.23	odd	4
320.3.p.a.193.1		2	40.13	odd	4
320.3.p.a.257.1		2	8.5	even	2
320.3.p.h.193.1		2	40.3	even	4
320.3.p.h.257.1		2	8.3	odd	2
400.3.p.b.193.1		2	5.2	odd	4
400.3.p.b.257.1		2	5.4	even	2
450.3.g.b.307.1		2	60.59	even	2
450.3.g.b.343.1		2	60.47	odd	4
490.3.f.b.197.1		2	28.27	even	2
490.3.f.b.393.1		2	140.83	odd	4
720.3.bh.c.433.1		2	15.8	even	4
720.3.bh.c.577.1		2	3.2	odd	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:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	80.p (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 2.00000i) q^{3} -5.00000i q^{5} +(-2.00000 - 2.00000i) q^{7} +1.00000i q^{9} +O(q^{10})\)	\(q+(2.00000 - 2.00000i) q^{3} -5.00000i q^{5} +(-2.00000 - 2.00000i) q^{7} +1.00000i q^{9} +8.00000 q^{11} +(3.00000 - 3.00000i) q^{13} +(-10.0000 - 10.0000i) q^{15} +(7.00000 + 7.00000i) q^{17} +20.0000i q^{19} -8.00000 q^{21} +(2.00000 - 2.00000i) q^{23} -25.0000 q^{25} +(20.0000 + 20.0000i) q^{27} +40.0000i q^{29} -52.0000 q^{31} +(16.0000 - 16.0000i) q^{33} +(-10.0000 + 10.0000i) q^{35} +(-3.00000 - 3.00000i) q^{37} -12.0000i q^{39} -8.00000 q^{41} +(42.0000 - 42.0000i) q^{43} +5.00000 q^{45} +(18.0000 + 18.0000i) q^{47} -41.0000i q^{49} +28.0000 q^{51} +(53.0000 - 53.0000i) q^{53} -40.0000i q^{55} +(40.0000 + 40.0000i) q^{57} +20.0000i q^{59} -48.0000 q^{61} +(2.00000 - 2.00000i) q^{63} +(-15.0000 - 15.0000i) q^{65} +(-62.0000 - 62.0000i) q^{67} -8.00000i q^{69} +28.0000 q^{71} +(-47.0000 + 47.0000i) q^{73} +(-50.0000 + 50.0000i) q^{75} +(-16.0000 - 16.0000i) q^{77} +71.0000 q^{81} +(-18.0000 + 18.0000i) q^{83} +(35.0000 - 35.0000i) q^{85} +(80.0000 + 80.0000i) q^{87} +80.0000i q^{89} -12.0000 q^{91} +(-104.000 + 104.000i) q^{93} +100.000 q^{95} +(-63.0000 - 63.0000i) q^{97} +8.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{3} - 4 q^{7}+O(q^{10}) \) 2 * q + 4 * q^3 - 4 * q^7	\( 2 q + 4 q^{3} - 4 q^{7} + 16 q^{11} + 6 q^{13} - 20 q^{15} + 14 q^{17} - 16 q^{21} + 4 q^{23} - 50 q^{25} + 40 q^{27} - 104 q^{31} + 32 q^{33} - 20 q^{35} - 6 q^{37} - 16 q^{41} + 84 q^{43} + 10 q^{45} + 36 q^{47} + 56 q^{51} + 106 q^{53} + 80 q^{57} - 96 q^{61} + 4 q^{63} - 30 q^{65} - 124 q^{67} + 56 q^{71} - 94 q^{73} - 100 q^{75} - 32 q^{77} + 142 q^{81} - 36 q^{83} + 70 q^{85} + 160 q^{87} - 24 q^{91} - 208 q^{93} + 200 q^{95} - 126 q^{97}+O(q^{100}) \) 2 * q + 4 * q^3 - 4 * q^7 + 16 * q^11 + 6 * q^13 - 20 * q^15 + 14 * q^17 - 16 * q^21 + 4 * q^23 - 50 * q^25 + 40 * q^27 - 104 * q^31 + 32 * q^33 - 20 * q^35 - 6 * q^37 - 16 * q^41 + 84 * q^43 + 10 * q^45 + 36 * q^47 + 56 * q^51 + 106 * q^53 + 80 * q^57 - 96 * q^61 + 4 * q^63 - 30 * q^65 - 124 * q^67 + 56 * q^71 - 94 * q^73 - 100 * q^75 - 32 * q^77 + 142 * q^81 - 36 * q^83 + 70 * q^85 + 160 * q^87 - 24 * q^91 - 208 * q^93 + 200 * q^95 - 126 * q^97

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