LMFDB - Embedded newform 2240.2.bd.a.561.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2240,2,Mod(561,2240)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2240, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("2240.561");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2240 = 2^{6} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2240.bd (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:	$17.8864900528$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 560)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			561.10
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.448521 + 0.448521i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.59766i q^{9} +O(q^{10})$	\(q+(-0.448521 + 0.448521i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.59766i q^{9} +(1.28657 + 1.28657i) q^{11} +(-2.40412 + 2.40412i) q^{13} -0.634304 q^{15} +5.53380 q^{17} +(1.67235 - 1.67235i) q^{19} +(0.448521 + 0.448521i) q^{21} -0.722358i q^{23} +1.00000i q^{25} +(-2.51067 - 2.51067i) q^{27} +(-3.78126 + 3.78126i) q^{29} -3.07289 q^{31} -1.15410 q^{33} +(0.707107 - 0.707107i) q^{35} +(6.66136 + 6.66136i) q^{37} -2.15660i q^{39} +1.68834i q^{41} +(-4.96146 - 4.96146i) q^{43} +(-1.83682 + 1.83682i) q^{45} +2.72785 q^{47} -1.00000 q^{49} +(-2.48203 + 2.48203i) q^{51} +(-3.75198 - 3.75198i) q^{53} +1.81948i q^{55} +1.50016i q^{57} +(3.74801 + 3.74801i) q^{59} +(-5.14139 + 5.14139i) q^{61} +2.59766 q^{63} -3.39994 q^{65} +(-5.38226 + 5.38226i) q^{67} +(0.323993 + 0.323993i) q^{69} +5.68920i q^{71} +6.59094i q^{73} +(-0.448521 - 0.448521i) q^{75} +(1.28657 - 1.28657i) q^{77} -2.47325 q^{79} -5.54080 q^{81} +(-1.59485 + 1.59485i) q^{83} +(3.91299 + 3.91299i) q^{85} -3.39195i q^{87} -0.601875i q^{89} +(2.40412 + 2.40412i) q^{91} +(1.37825 - 1.37825i) q^{93} +2.36505 q^{95} +12.6823 q^{97} +(-3.34206 + 3.34206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q+O(q^{10}) $ 44 * q	$ 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) $ 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times$.

$n$	$897$	$1471$	$1541$	$1921$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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
$3$	−0.448521	+	0.448521i	−0.258954	+	0.258954i	−0.824628	−	0.565675i	$-0.808616\pi$
$3$	−0.448521	+	0.448521i	−0.258954	+	0.258954i	0.565675	+	0.824628i	$0.308616\pi$
$4$		0			0
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$5$	0.707107	+	0.707107i	0.316228	+	0.316228i
$6$		0			0
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$		0			0
$9$			2.59766i			0.865886i
$10$		0			0
$11$	1.28657	+	1.28657i	0.387914	+	0.387914i	0.873943	−	0.486029i	$-0.161555\pi$
$11$	1.28657	+	1.28657i	0.387914	+	0.387914i	−0.486029	+	0.873943i	$0.661555\pi$
$12$		0			0
$13$	−2.40412	+	2.40412i	−0.666783	+	0.666783i	−0.956970	−	0.290187i	$-0.906283\pi$
$13$	−2.40412	+	2.40412i	−0.666783	+	0.666783i	0.290187	+	0.956970i	$0.406283\pi$
$14$		0			0
$15$	−0.634304			−0.163777
$16$		0			0
$17$	5.53380			1.34214			0.671072	−	0.741392i	$-0.265834\pi$
$17$	5.53380			1.34214			0.671072	+	0.741392i	$0.265834\pi$
$18$		0			0
$19$	1.67235	−	1.67235i	0.383663	−	0.383663i	−0.488757	−	0.872420i	$-0.662550\pi$
$19$	1.67235	−	1.67235i	0.383663	−	0.383663i	0.872420	+	0.488757i	$0.162550\pi$
$20$		0			0
$21$	0.448521	+	0.448521i	0.0978753	+	0.0978753i
$22$		0			0
$23$		−	0.722358i		−	0.150622i	−0.997160	−	0.0753111i	$-0.976005\pi$
$23$		−	0.722358i		−	0.150622i	0.997160	−	0.0753111i	$-0.0239950\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−2.51067	−	2.51067i	−0.483178	−	0.483178i
$28$		0			0
$29$	−3.78126	+	3.78126i	−0.702163	+	0.702163i	−0.964874	−	0.262712i	$-0.915383\pi$
$29$	−3.78126	+	3.78126i	−0.702163	+	0.702163i	0.262712	+	0.964874i	$0.415383\pi$
$30$		0			0
$31$	−3.07289			−0.551907			−0.275953	−	0.961171i	$-0.588994\pi$
$31$	−3.07289			−0.551907			−0.275953	+	0.961171i	$0.588994\pi$
$32$		0			0
$33$	−1.15410			−0.200904
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	6.66136	+	6.66136i	1.09512	+	1.09512i	0.994973	+	0.100148i	$0.0319315\pi$
$37$	6.66136	+	6.66136i	1.09512	+	1.09512i	0.100148	+	0.994973i	$0.468068\pi$
$38$		0			0
$39$		−	2.15660i		−	0.345332i
$40$		0			0
$41$			1.68834i			0.263675i	0.991271	+	0.131837i	$0.0420876\pi$
$41$			1.68834i			0.263675i	−0.991271	+	0.131837i	$0.957912\pi$
$42$		0			0
$43$	−4.96146	−	4.96146i	−0.756615	−	0.756615i	0.219090	−	0.975705i	$-0.429691\pi$
$43$	−4.96146	−	4.96146i	−0.756615	−	0.756615i	−0.975705	+	0.219090i	$0.929691\pi$
$44$		0			0
$45$	−1.83682	+	1.83682i	−0.273817	+	0.273817i
$46$		0			0
$47$	2.72785			0.397898			0.198949	−	0.980010i	$-0.436247\pi$
$47$	2.72785			0.397898			0.198949	+	0.980010i	$0.436247\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−2.48203	+	2.48203i	−0.347553	+	0.347553i
$52$		0			0
$53$	−3.75198	−	3.75198i	−0.515374	−	0.515374i	0.400794	−	0.916168i	$-0.368734\pi$
$53$	−3.75198	−	3.75198i	−0.515374	−	0.515374i	−0.916168	+	0.400794i	$0.868734\pi$
$54$		0			0
$55$			1.81948i			0.245339i
$56$		0			0
$57$			1.50016i			0.198702i
$58$		0			0
$59$	3.74801	+	3.74801i	0.487949	+	0.487949i	0.907659	−	0.419709i	$-0.137868\pi$
$59$	3.74801	+	3.74801i	0.487949	+	0.487949i	−0.419709	+	0.907659i	$0.637868\pi$
$60$		0			0
$61$	−5.14139	+	5.14139i	−0.658287	+	0.658287i	−0.954975	−	0.296687i	$-0.904118\pi$
$61$	−5.14139	+	5.14139i	−0.658287	+	0.658287i	0.296687	+	0.954975i	$0.404118\pi$
$62$		0			0
$63$	2.59766			0.327274
$64$		0			0
$65$	−3.39994			−0.421711
$66$		0			0
$67$	−5.38226	+	5.38226i	−0.657548	+	0.657548i	−0.954799	−	0.297251i	$-0.903930\pi$
$67$	−5.38226	+	5.38226i	−0.657548	+	0.657548i	0.297251	+	0.954799i	$0.403930\pi$
$68$		0			0
$69$	0.323993	+	0.323993i	0.0390042	+	0.0390042i
$70$		0			0
$71$			5.68920i			0.675184i	0.941293	+	0.337592i	$0.109612\pi$
$71$			5.68920i			0.675184i	−0.941293	+	0.337592i	$0.890388\pi$
$72$		0			0
$73$			6.59094i			0.771411i	0.922622	+	0.385705i	$0.126042\pi$
$73$			6.59094i			0.771411i	−0.922622	+	0.385705i	$0.873958\pi$
$74$		0			0
$75$	−0.448521	−	0.448521i	−0.0517907	−	0.0517907i
$76$		0			0
$77$	1.28657	−	1.28657i	0.146618	−	0.146618i
$78$		0			0
$79$	−2.47325			−0.278262			−0.139131	−	0.990274i	$-0.544431\pi$
$79$	−2.47325			−0.278262			−0.139131	+	0.990274i	$0.544431\pi$
$80$		0			0
$81$	−5.54080			−0.615644
$82$		0			0
$83$	−1.59485	+	1.59485i	−0.175058	+	0.175058i	−0.789197	−	0.614140i	$-0.789503\pi$
$83$	−1.59485	+	1.59485i	−0.175058	+	0.175058i	0.614140	+	0.789197i	$0.289503\pi$
$84$		0			0
$85$	3.91299	+	3.91299i	0.424423	+	0.424423i
$86$		0			0
$87$		−	3.39195i		−	0.363655i
$88$		0			0
$89$		−	0.601875i		−	0.0637986i	−0.999491	−	0.0318993i	$-0.989844\pi$
$89$		−	0.601875i		−	0.0637986i	0.999491	−	0.0318993i	$-0.0101556\pi$
$90$		0			0
$91$	2.40412	+	2.40412i	0.252020	+	0.252020i
$92$		0			0
$93$	1.37825	−	1.37825i	0.142918	−	0.142918i
$94$		0			0
$95$	2.36505			0.242649
$96$		0			0
$97$	12.6823			1.28769			0.643845	−	0.765156i	$-0.277338\pi$
$97$	12.6823			1.28769			0.643845	+	0.765156i	$0.277338\pi$
$98$		0			0
$99$	−3.34206	+	3.34206i	−0.335890	+	0.335890i
$100$		0			0
$101$	3.13851	+	3.13851i	0.312293	+	0.312293i	0.845797	−	0.533504i	$-0.179125\pi$
$101$	3.13851	+	3.13851i	0.312293	+	0.312293i	−0.533504	+	0.845797i	$0.679125\pi$
$102$		0			0
$103$		−	5.06857i		−	0.499421i	−0.968321	−	0.249711i	$-0.919665\pi$
$103$		−	5.06857i		−	0.499421i	0.968321	−	0.249711i	$-0.0803355\pi$
$104$		0			0
$105$			0.634304i			0.0619018i
$106$		0			0
$107$	10.9680	+	10.9680i	1.06031	+	1.06031i	0.998060	+	0.0622546i	$0.0198291\pi$
$107$	10.9680	+	10.9680i	1.06031	+	1.06031i	0.0622546	+	0.998060i	$0.480171\pi$
$108$		0			0
$109$	−7.22669	+	7.22669i	−0.692191	+	0.692191i	−0.962714	−	0.270523i	$-0.912803\pi$
$109$	−7.22669	+	7.22669i	−0.692191	+	0.692191i	0.270523	+	0.962714i	$0.412803\pi$
$110$		0			0
$111$	−5.97552			−0.567171
$112$		0			0
$113$	15.7255			1.47933			0.739667	−	0.672973i	$-0.234983\pi$
$113$	15.7255			1.47933			0.739667	+	0.672973i	$0.234983\pi$
$114$		0			0
$115$	0.510785	−	0.510785i	0.0476309	−	0.0476309i
$116$		0			0
$117$	−6.24508	−	6.24508i	−0.577358	−	0.577358i
$118$		0			0
$119$		−	5.53380i		−	0.507283i
$120$		0			0
$121$		−	7.68949i		−	0.699045i
$122$		0			0
$123$	−0.757256	−	0.757256i	−0.0682795	−	0.0682795i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−9.82265			−0.871619			−0.435810	−	0.900039i	$-0.643538\pi$
$127$	−9.82265			−0.871619			−0.435810	+	0.900039i	$0.643538\pi$
$128$		0			0
$129$	4.45063			0.391857
$130$		0			0
$131$	−14.1822	+	14.1822i	−1.23910	+	1.23910i	−0.278734	+	0.960368i	$0.589915\pi$
$131$	−14.1822	+	14.1822i	−1.23910	+	1.23910i	−0.960368	+	0.278734i	$0.910085\pi$
$132$		0			0
$133$	−1.67235	−	1.67235i	−0.145011	−	0.145011i
$134$		0			0
$135$		−	3.55062i		−	0.305589i
$136$		0			0
$137$		−	19.5141i		−	1.66720i	−0.552366	−	0.833601i	$-0.686275\pi$
$137$		−	19.5141i		−	1.66720i	0.552366	−	0.833601i	$-0.313725\pi$
$138$		0			0
$139$	14.7650	+	14.7650i	1.25235	+	1.25235i	0.954665	+	0.297682i	$0.0962137\pi$
$139$	14.7650	+	14.7650i	1.25235	+	1.25235i	0.297682	+	0.954665i	$0.403786\pi$
$140$		0			0
$141$	−1.22350	+	1.22350i	−0.103037	+	0.103037i
$142$		0			0
$143$	−6.18612			−0.517310
$144$		0			0
$145$	−5.34751			−0.444087
$146$		0			0
$147$	0.448521	−	0.448521i	0.0369934	−	0.0369934i
$148$		0			0
$149$	−4.60170	−	4.60170i	−0.376986	−	0.376986i	0.493028	−	0.870014i	$-0.335890\pi$
$149$	−4.60170	−	4.60170i	−0.376986	−	0.376986i	−0.870014	+	0.493028i	$0.835890\pi$
$150$		0			0
$151$			1.77062i			0.144091i	0.997401	+	0.0720453i	$0.0229526\pi$
$151$			1.77062i			0.144091i	−0.997401	+	0.0720453i	$0.977047\pi$
$152$		0			0
$153$			14.3749i			1.16214i
$154$		0			0
$155$	−2.17286	−	2.17286i	−0.174528	−	0.174528i
$156$		0			0
$157$	−4.62874	+	4.62874i	−0.369414	+	0.369414i	−0.867263	−	0.497850i	$-0.834123\pi$
$157$	−4.62874	+	4.62874i	−0.369414	+	0.369414i	0.497850	+	0.867263i	$0.334123\pi$
$158$		0			0
$159$	3.36568			0.266916
$160$		0			0
$161$	−0.722358			−0.0569298
$162$		0			0
$163$	−11.9314	+	11.9314i	−0.934541	+	0.934541i	−0.997985	−	0.0634446i	$-0.979791\pi$
$163$	−11.9314	+	11.9314i	−0.934541	+	0.934541i	0.0634446	+	0.997985i	$0.479791\pi$
$164$		0			0
$165$	−0.816075	−	0.816075i	−0.0635314	−	0.0635314i
$166$		0			0
$167$			18.1474i			1.40429i	0.712034	+	0.702145i	$0.247774\pi$
$167$			18.1474i			1.40429i	−0.712034	+	0.702145i	$0.752226\pi$
$168$		0			0
$169$			1.44041i			0.110801i
$170$		0			0
$171$	4.34418	+	4.34418i	0.332208	+	0.332208i
$172$		0			0
$173$	−9.96052	+	9.96052i	−0.757284	+	0.757284i	−0.975827	−	0.218543i	$-0.929870\pi$
$173$	−9.96052	+	9.96052i	−0.757284	+	0.757284i	0.218543	+	0.975827i	$0.429870\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	−3.36212			−0.252713
$178$		0			0
$179$	−0.221167	+	0.221167i	−0.0165308	+	0.0165308i	−0.715324	−	0.698793i	$-0.753721\pi$
$179$	−0.221167	+	0.221167i	−0.0165308	+	0.0165308i	0.698793	+	0.715324i	$0.253721\pi$
$180$		0			0
$181$	−6.15834	−	6.15834i	−0.457746	−	0.457746i	0.440169	−	0.897915i	$-0.354918\pi$
$181$	−6.15834	−	6.15834i	−0.457746	−	0.457746i	−0.897915	+	0.440169i	$0.854918\pi$
$182$		0			0
$183$		−	4.61204i		−	0.340932i
$184$		0			0
$185$			9.42058i			0.692615i
$186$		0			0
$187$	7.11960	+	7.11960i	0.520637	+	0.520637i
$188$		0			0
$189$	−2.51067	+	2.51067i	−0.182624	+	0.182624i
$190$		0			0
$191$	−24.7751			−1.79267			−0.896333	−	0.443382i	$-0.853779\pi$
$191$	−24.7751			−1.79267			−0.896333	+	0.443382i	$0.853779\pi$
$192$		0			0
$193$	7.10999			0.511788			0.255894	−	0.966705i	$-0.417630\pi$
$193$	7.10999			0.511788			0.255894	+	0.966705i	$0.417630\pi$
$194$		0			0
$195$	1.52494	−	1.52494i	0.109204	−	0.109204i
$196$		0			0
$197$	2.02901	+	2.02901i	0.144561	+	0.144561i	0.775683	−	0.631122i	$-0.217405\pi$
$197$	2.02901	+	2.02901i	0.144561	+	0.144561i	−0.631122	+	0.775683i	$0.717405\pi$
$198$		0			0
$199$		−	8.59661i		−	0.609397i	−0.952449	−	0.304699i	$-0.901444\pi$
$199$		−	8.59661i		−	0.609397i	0.952449	−	0.304699i	$-0.0985557\pi$
$200$		0			0
$201$		−	4.82812i		−	0.340549i
$202$		0			0
$203$	3.78126	+	3.78126i	0.265393	+	0.265393i
$204$		0			0
$205$	−1.19384	+	1.19384i	−0.0833812	+	0.0833812i
$206$		0			0
$207$	1.87644			0.130422
$208$		0			0
$209$	4.30317			0.297656
$210$		0			0
$211$	−9.74419	+	9.74419i	−0.670818	+	0.670818i	−0.957905	−	0.287087i	$-0.907313\pi$
$211$	−9.74419	+	9.74419i	−0.670818	+	0.670818i	0.287087	+	0.957905i	$0.407313\pi$
$212$		0			0
$213$	−2.55173	−	2.55173i	−0.174841	−	0.174841i
$214$		0			0
$215$		−	7.01656i		−	0.478525i
$216$		0			0
$217$			3.07289i			0.208601i
$218$		0			0
$219$	−2.95617	−	2.95617i	−0.199760	−	0.199760i
$220$		0			0
$221$	−13.3039	+	13.3039i	−0.894919	+	0.894919i
$222$		0			0
$223$	13.6474			0.913900			0.456950	−	0.889492i	$-0.348942\pi$
$223$	13.6474			0.913900			0.456950	+	0.889492i	$0.348942\pi$
$224$		0			0
$225$	−2.59766			−0.173177
$226$		0			0
$227$	20.0863	−	20.0863i	1.33317	−	1.33317i	0.430659	−	0.902515i	$-0.358281\pi$
$227$	20.0863	−	20.0863i	1.33317	−	1.33317i	0.902515	−	0.430659i	$-0.141719\pi$
$228$		0			0
$229$	−9.93824	−	9.93824i	−0.656738	−	0.656738i	0.297869	−	0.954607i	$-0.403724\pi$
$229$	−9.93824	−	9.93824i	−0.656738	−	0.656738i	−0.954607	+	0.297869i	$0.903724\pi$
$230$		0			0
$231$			1.15410i			0.0759345i
$232$		0			0
$233$		−	20.9258i		−	1.37090i	−0.728121	−	0.685449i	$-0.759606\pi$
$233$		−	20.9258i		−	1.37090i	0.728121	−	0.685449i	$-0.240394\pi$
$234$		0			0
$235$	1.92888	+	1.92888i	0.125826	+	0.125826i
$236$		0			0
$237$	1.10930	−	1.10930i	0.0720570	−	0.0720570i
$238$		0			0
$239$	1.92378			0.124439			0.0622196	−	0.998062i	$-0.480182\pi$
$239$	1.92378			0.124439			0.0622196	+	0.998062i	$0.480182\pi$
$240$		0			0
$241$	16.8157			1.08319			0.541597	−	0.840639i	$-0.317820\pi$
$241$	16.8157			1.08319			0.541597	+	0.840639i	$0.317820\pi$
$242$		0			0
$243$	10.0172	−	10.0172i	0.642601	−	0.642601i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$			8.04104i			0.511639i
$248$		0			0
$249$		−	1.43065i		−	0.0906638i
$250$		0			0
$251$	13.1554	+	13.1554i	0.830364	+	0.830364i	0.987566	−	0.157203i	$-0.0502475\pi$
$251$	13.1554	+	13.1554i	0.830364	+	0.830364i	−0.157203	+	0.987566i	$0.550248\pi$
$252$		0			0
$253$	0.929362	−	0.929362i	0.0584285	−	0.0584285i
$254$		0			0
$255$	−3.51012			−0.219812
$256$		0			0
$257$	−29.4134			−1.83476			−0.917379	−	0.398014i	$-0.869700\pi$
$257$	−29.4134			−1.83476			−0.917379	+	0.398014i	$0.869700\pi$
$258$		0			0
$259$	6.66136	−	6.66136i	0.413917	−	0.413917i
$260$		0			0
$261$	−9.82242	−	9.82242i	−0.607993	−	0.607993i
$262$		0			0
$263$		−	14.2063i		−	0.875997i	−0.898976	−	0.437998i	$-0.855688\pi$
$263$		−	14.2063i		−	0.875997i	0.898976	−	0.437998i	$-0.144312\pi$
$264$		0			0
$265$		−	5.30610i		−	0.325951i
$266$		0			0
$267$	0.269954	+	0.269954i	0.0165209	+	0.0165209i
$268$		0			0
$269$	0.103300	−	0.103300i	0.00629829	−	0.00629829i	−0.703951	−	0.710249i	$-0.748582\pi$
$269$	0.103300	−	0.103300i	0.00629829	−	0.00629829i	0.710249	+	0.703951i	$0.248582\pi$
$270$		0			0
$271$	9.24057			0.561325			0.280662	−	0.959807i	$-0.409446\pi$
$271$	9.24057			0.561325			0.280662	+	0.959807i	$0.409446\pi$
$272$		0			0
$273$	−2.15660			−0.130523
$274$		0			0
$275$	−1.28657	+	1.28657i	−0.0775829	+	0.0775829i
$276$		0			0
$277$	13.5564	+	13.5564i	0.814523	+	0.814523i	0.985308	−	0.170785i	$-0.0546304\pi$
$277$	13.5564	+	13.5564i	0.814523	+	0.814523i	−0.170785	+	0.985308i	$0.554630\pi$
$278$		0			0
$279$		−	7.98231i		−	0.477888i
$280$		0			0
$281$		−	17.0873i		−	1.01934i	−0.860370	−	0.509671i	$-0.829767\pi$
$281$		−	17.0873i		−	1.01934i	0.860370	−	0.509671i	$-0.170233\pi$
$282$		0			0
$283$	7.14539	+	7.14539i	0.424749	+	0.424749i	0.886835	−	0.462086i	$-0.152899\pi$
$283$	7.14539	+	7.14539i	0.424749	+	0.424749i	−0.462086	+	0.886835i	$0.652899\pi$
$284$		0			0
$285$	−1.06078	+	1.06078i	−0.0628350	+	0.0628350i
$286$		0			0
$287$	1.68834			0.0996596
$288$		0			0
$289$	13.6230			0.801351
$290$		0			0
$291$	−5.68827	+	5.68827i	−0.333452	+	0.333452i
$292$		0			0
$293$	18.4415	+	18.4415i	1.07736	+	1.07736i	0.996745	+	0.0806173i	$0.0256892\pi$
$293$	18.4415	+	18.4415i	1.07736	+	1.07736i	0.0806173	+	0.996745i	$0.474311\pi$
$294$		0			0
$295$			5.30049i			0.308606i
$296$		0			0
$297$		−	6.46028i		−	0.374864i
$298$		0			0
$299$	1.73664	+	1.73664i	0.100432	+	0.100432i
$300$		0			0
$301$	−4.96146	+	4.96146i	−0.285974	+	0.285974i
$302$		0			0
$303$	−2.81537			−0.161739
$304$		0			0
$305$	−7.27102			−0.416337
$306$		0			0
$307$	14.6795	−	14.6795i	0.837803	−	0.837803i	−0.150767	−	0.988569i	$-0.548174\pi$
$307$	14.6795	−	14.6795i	0.837803	−	0.837803i	0.988569	+	0.150767i	$0.0481742\pi$
$308$		0			0
$309$	2.27336	+	2.27336i	0.129327	+	0.129327i
$310$		0			0
$311$			2.18714i			0.124021i	0.998075	+	0.0620107i	$0.0197513\pi$
$311$			2.18714i			0.124021i	−0.998075	+	0.0620107i	$0.980249\pi$
$312$		0			0
$313$			24.2402i			1.37014i	0.728478	+	0.685070i	$0.240228\pi$
$313$			24.2402i			1.37014i	−0.728478	+	0.685070i	$0.759772\pi$
$314$		0			0
$315$	1.83682	+	1.83682i	0.103493	+	0.103493i
$316$		0			0
$317$	16.8209	−	16.8209i	0.944758	−	0.944758i	−0.0537943	−	0.998552i	$-0.517132\pi$
$317$	16.8209	−	16.8209i	0.944758	−	0.944758i	0.998552	+	0.0537943i	$0.0171315\pi$
$318$		0			0
$319$	−9.72969			−0.544758
$320$		0			0
$321$	−9.83874			−0.549145
$322$		0			0
$323$	9.25443	−	9.25443i	0.514930	−	0.514930i
$324$		0			0
$325$	−2.40412	−	2.40412i	−0.133357	−	0.133357i
$326$		0			0
$327$		−	6.48264i		−	0.358491i
$328$		0			0
$329$		−	2.72785i		−	0.150391i
$330$		0			0
$331$	−8.43266	−	8.43266i	−0.463501	−	0.463501i	0.436300	−	0.899801i	$-0.356289\pi$
$331$	−8.43266	−	8.43266i	−0.463501	−	0.463501i	−0.899801	+	0.436300i	$0.856289\pi$
$332$		0			0
$333$	−17.3039	+	17.3039i	−0.948249	+	0.948249i
$334$		0			0
$335$	−7.61167			−0.415870
$336$		0			0
$337$	35.9533			1.95850			0.979251	−	0.202650i	$-0.0649555\pi$
$337$	35.9533			1.95850			0.979251	+	0.202650i	$0.0649555\pi$
$338$		0			0
$339$	−7.05323	+	7.05323i	−0.383079	+	0.383079i
$340$		0			0
$341$	−3.95347	−	3.95347i	−0.214093	−	0.214093i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$			0.458195i			0.0246684i
$346$		0			0
$347$	−13.3660	−	13.3660i	−0.717524	−	0.717524i	0.250573	−	0.968098i	$-0.419381\pi$
$347$	−13.3660	−	13.3660i	−0.717524	−	0.717524i	−0.968098	+	0.250573i	$0.919381\pi$
$348$		0			0
$349$	17.6571	−	17.6571i	0.945164	−	0.945164i	−0.0534090	−	0.998573i	$-0.517009\pi$
$349$	17.6571	−	17.6571i	0.945164	−	0.945164i	0.998573	+	0.0534090i	$0.0170087\pi$
$350$		0			0
$351$	12.0719			0.644350
$352$		0			0
$353$	−5.46978			−0.291127			−0.145563	−	0.989349i	$-0.546499\pi$
$353$	−5.46978			−0.291127			−0.145563	+	0.989349i	$0.546499\pi$
$354$		0			0
$355$	−4.02287	+	4.02287i	−0.213512	+	0.213512i
$356$		0			0
$357$	2.48203	+	2.48203i	0.131363	+	0.131363i
$358$		0			0
$359$		−	20.7591i		−	1.09563i	−0.836601	−	0.547813i	$-0.815461\pi$
$359$		−	20.7591i		−	1.09563i	0.836601	−	0.547813i	$-0.184539\pi$
$360$		0			0
$361$			13.4065i			0.705606i
$362$		0			0
$363$	3.44890	+	3.44890i	0.181020	+	0.181020i
$364$		0			0
$365$	−4.66050	+	4.66050i	−0.243941	+	0.243941i
$366$		0			0
$367$	29.7128			1.55100			0.775498	−	0.631350i	$-0.217499\pi$
$367$	29.7128			1.55100			0.775498	+	0.631350i	$0.217499\pi$
$368$		0			0
$369$	−4.38573			−0.228312
$370$		0			0
$371$	−3.75198	+	3.75198i	−0.194793	+	0.194793i
$372$		0			0
$373$	−3.82108	−	3.82108i	−0.197848	−	0.197848i	0.601229	−	0.799077i	$-0.294678\pi$
$373$	−3.82108	−	3.82108i	−0.197848	−	0.197848i	−0.799077	+	0.601229i	$0.794678\pi$
$374$		0			0
$375$		−	0.634304i		−	0.0327553i
$376$		0			0
$377$		−	18.1812i		−	0.936380i
$378$		0			0
$379$	4.59192	+	4.59192i	0.235871	+	0.235871i	0.815138	−	0.579267i	$-0.196661\pi$
$379$	4.59192	+	4.59192i	0.235871	+	0.235871i	−0.579267	+	0.815138i	$0.696661\pi$
$380$		0			0
$381$	4.40567	−	4.40567i	0.225709	−	0.225709i
$382$		0			0
$383$	−29.6564			−1.51537			−0.757686	−	0.652619i	$-0.773670\pi$
$383$	−29.6564			−1.51537			−0.757686	+	0.652619i	$0.773670\pi$
$384$		0			0
$385$	1.81948			0.0927293
$386$		0			0
$387$	12.8882	−	12.8882i	0.655142	−	0.655142i
$388$		0			0
$389$	−17.7518	−	17.7518i	−0.900051	−	0.900051i	0.0953887	−	0.995440i	$-0.469591\pi$
$389$	−17.7518	−	17.7518i	−0.900051	−	0.900051i	−0.995440	+	0.0953887i	$0.969591\pi$
$390$		0			0
$391$		−	3.99739i		−	0.202157i
$392$		0			0
$393$		−	12.7220i		−	0.641740i
$394$		0			0
$395$	−1.74885	−	1.74885i	−0.0879942	−	0.0879942i
$396$		0			0
$397$	19.7353	−	19.7353i	0.990484	−	0.990484i	−0.00947127	−	0.999955i	$-0.503015\pi$
$397$	19.7353	−	19.7353i	0.990484	−	0.990484i	0.999955	+	0.00947127i	$0.00301484\pi$
$398$		0			0
$399$	1.50016			0.0751022
$400$		0			0
$401$	22.3490			1.11606			0.558028	−	0.829822i	$-0.311558\pi$
$401$	22.3490			1.11606			0.558028	+	0.829822i	$0.311558\pi$
$402$		0			0
$403$	7.38759	−	7.38759i	0.368002	−	0.368002i
$404$		0			0
$405$	−3.91794	−	3.91794i	−0.194684	−	0.194684i
$406$		0			0
$407$			17.1406i			0.849626i
$408$		0			0
$409$		−	4.32271i		−	0.213744i	−0.994273	−	0.106872i	$-0.965916\pi$
$409$		−	4.32271i		−	0.213744i	0.994273	−	0.106872i	$-0.0340835\pi$
$410$		0			0
$411$	8.75249	+	8.75249i	0.431728	+	0.431728i
$412$		0			0
$413$	3.74801	−	3.74801i	0.184427	−	0.184427i
$414$		0			0
$415$	−2.25546			−0.110716
$416$		0			0
$417$	−13.2448			−0.648600
$418$		0			0
$419$	−26.1692	+	26.1692i	−1.27845	+	1.27845i	−0.336913	+	0.941536i	$0.609383\pi$
$419$	−26.1692	+	26.1692i	−1.27845	+	1.27845i	−0.941536	+	0.336913i	$0.890617\pi$
$420$		0			0
$421$	−19.0421	−	19.0421i	−0.928056	−	0.928056i	0.0695245	−	0.997580i	$-0.477852\pi$
$421$	−19.0421	−	19.0421i	−0.928056	−	0.928056i	−0.997580	+	0.0695245i	$0.977852\pi$
$422$		0			0
$423$			7.08602i			0.344534i
$424$		0			0
$425$			5.53380i			0.268429i
$426$		0			0
$427$	5.14139	+	5.14139i	0.248809	+	0.248809i
$428$		0			0
$429$	2.77461	−	2.77461i	0.133959	−	0.133959i
$430$		0			0
$431$	−31.5096			−1.51777			−0.758883	−	0.651227i	$-0.774255\pi$
$431$	−31.5096			−1.51777			−0.758883	+	0.651227i	$0.774255\pi$
$432$		0			0
$433$	14.0377			0.674609			0.337305	−	0.941396i	$-0.390485\pi$
$433$	14.0377			0.674609			0.337305	+	0.941396i	$0.390485\pi$
$434$		0			0
$435$	2.39847	−	2.39847i	0.114998	−	0.114998i
$436$		0			0
$437$	−1.20803	−	1.20803i	−0.0577881	−	0.0577881i
$438$		0			0
$439$		−	40.6062i		−	1.93803i	−0.247005	−	0.969014i	$-0.579446\pi$
$439$		−	40.6062i		−	1.93803i	0.247005	−	0.969014i	$-0.420554\pi$
$440$		0			0
$441$		−	2.59766i		−	0.123698i
$442$		0			0
$443$	2.68015	+	2.68015i	0.127338	+	0.127338i	0.767903	−	0.640566i	$-0.221300\pi$
$443$	2.68015	+	2.68015i	0.127338	+	0.127338i	−0.640566	+	0.767903i	$0.721300\pi$
$444$		0			0
$445$	0.425590	−	0.425590i	0.0201749	−	0.0201749i
$446$		0			0
$447$	4.12792			0.195244
$448$		0			0
$449$	26.5012			1.25067			0.625335	−	0.780357i	$-0.284962\pi$
$449$	26.5012			1.25067			0.625335	+	0.780357i	$0.284962\pi$
$450$		0			0
$451$	−2.17216	+	2.17216i	−0.102283	+	0.102283i
$452$		0			0
$453$	−0.794158	−	0.794158i	−0.0373128	−	0.0373128i
$454$		0			0
$455$			3.39994i			0.159392i
$456$		0			0
$457$		−	6.98569i		−	0.326777i	−0.986562	−	0.163388i	$-0.947758\pi$
$457$		−	6.98569i		−	0.326777i	0.986562	−	0.163388i	$-0.0522423\pi$
$458$		0			0
$459$	−13.8935	−	13.8935i	−0.648495	−	0.648495i
$460$		0			0
$461$	5.21061	−	5.21061i	0.242682	−	0.242682i	−0.575277	−	0.817959i	$-0.695106\pi$
$461$	5.21061	−	5.21061i	0.242682	−	0.242682i	0.817959	+	0.575277i	$0.195106\pi$
$462$		0			0
$463$	29.4515			1.36873			0.684364	−	0.729140i	$-0.260080\pi$
$463$	29.4515			1.36873			0.684364	+	0.729140i	$0.260080\pi$
$464$		0			0
$465$	1.94915			0.0903895
$466$		0			0
$467$	5.17260	−	5.17260i	0.239359	−	0.239359i	−0.577225	−	0.816585i	$-0.695865\pi$
$467$	5.17260	−	5.17260i	0.239359	−	0.239359i	0.816585	+	0.577225i	$0.195865\pi$
$468$		0			0
$469$	5.38226	+	5.38226i	0.248530	+	0.248530i
$470$		0			0
$471$		−	4.15218i		−	0.191322i
$472$		0			0
$473$		−	12.7665i		−	0.587004i
$474$		0			0
$475$	1.67235	+	1.67235i	0.0767325	+	0.0767325i
$476$		0			0
$477$	9.74636	−	9.74636i	0.446255	−	0.446255i
$478$		0			0
$479$	26.3995			1.20622			0.603111	−	0.797657i	$-0.293928\pi$
$479$	26.3995			1.20622			0.603111	+	0.797657i	$0.293928\pi$
$480$		0			0
$481$	−32.0294			−1.46042
$482$		0			0
$483$	0.323993	−	0.323993i	0.0147422	−	0.0147422i
$484$		0			0
$485$	8.96773	+	8.96773i	0.407204	+	0.407204i
$486$		0			0
$487$		−	26.0852i		−	1.18204i	−0.806659	−	0.591018i	$-0.798726\pi$
$487$		−	26.0852i		−	1.18204i	0.806659	−	0.591018i	$-0.201274\pi$
$488$		0			0
$489$		−	10.7030i		−	0.484006i
$490$		0			0
$491$	−20.4375	−	20.4375i	−0.922333	−	0.922333i	0.0748607	−	0.997194i	$-0.476149\pi$
$491$	−20.4375	−	20.4375i	−0.922333	−	0.922333i	−0.997194	+	0.0748607i	$0.976149\pi$
$492$		0			0
$493$	−20.9248	+	20.9248i	−0.942403	+	0.942403i
$494$		0			0
$495$	−4.72639			−0.212435
$496$		0			0
$497$	5.68920			0.255196
$498$		0			0
$499$	−8.05328	+	8.05328i	−0.360514	+	0.360514i	−0.864002	−	0.503488i	$-0.832050\pi$
$499$	−8.05328	+	8.05328i	−0.360514	+	0.360514i	0.503488	+	0.864002i	$0.332050\pi$
$500$		0			0
$501$	−8.13950	−	8.13950i	−0.363646	−	0.363646i
$502$		0			0
$503$		−	42.4626i		−	1.89332i	−0.322241	−	0.946658i	$-0.604436\pi$
$503$		−	42.4626i		−	1.89332i	0.322241	−	0.946658i	$-0.395564\pi$
$504$		0			0
$505$			4.43852i			0.197512i
$506$		0			0
$507$	−0.646053	−	0.646053i	−0.0286922	−	0.0286922i
$508$		0			0
$509$	20.5652	−	20.5652i	0.911536	−	0.911536i	−0.0848570	−	0.996393i	$-0.527043\pi$
$509$	20.5652	−	20.5652i	0.911536	−	0.911536i	0.996393	+	0.0848570i	$0.0270433\pi$
$510$		0			0
$511$	6.59094			0.291566
$512$		0			0
$513$	−8.39741			−0.370755
$514$		0			0
$515$	3.58402	−	3.58402i	0.157931	−	0.157931i
$516$		0			0
$517$	3.50956	+	3.50956i	0.154350	+	0.154350i
$518$		0			0
$519$		−	8.93500i		−	0.392203i
$520$		0			0
$521$			8.58015i			0.375903i	0.982178	+	0.187952i	$0.0601848\pi$
$521$			8.58015i			0.375903i	−0.982178	+	0.187952i	$0.939815\pi$
$522$		0			0
$523$	−12.7735	−	12.7735i	−0.558545	−	0.558545i	0.370348	−	0.928893i	$-0.379238\pi$
$523$	−12.7735	−	12.7735i	−0.558545	−	0.558545i	−0.928893	+	0.370348i	$0.879238\pi$
$524$		0			0
$525$	−0.448521	+	0.448521i	−0.0195751	+	0.0195751i
$526$		0			0
$527$	−17.0047			−0.740739
$528$		0			0
$529$	22.4782			0.977313
$530$		0			0
$531$	−9.73605	+	9.73605i	−0.422508	+	0.422508i
$532$		0			0
$533$	−4.05898	−	4.05898i	−0.175814	−	0.175814i
$534$		0			0
$535$			15.5111i			0.670602i
$536$		0			0
$537$		−	0.198396i		−	0.00856144i
$538$		0			0
$539$	−1.28657	−	1.28657i	−0.0554164	−	0.0554164i
$540$		0			0
$541$	10.3095	−	10.3095i	0.443241	−	0.443241i	−0.449858	−	0.893100i	$-0.648526\pi$
$541$	10.3095	−	10.3095i	0.443241	−	0.443241i	0.893100	+	0.449858i	$0.148526\pi$
$542$		0			0
$543$	5.52429			0.237070
$544$		0			0
$545$	−10.2201			−0.437780
$546$		0			0
$547$	20.3462	−	20.3462i	0.869943	−	0.869943i	−0.122523	−	0.992466i	$-0.539099\pi$
$547$	20.3462	−	20.3462i	0.869943	−	0.869943i	0.992466	+	0.122523i	$0.0390985\pi$
$548$		0			0
$549$	−13.3556	−	13.3556i	−0.570002	−	0.570002i
$550$		0			0
$551$			12.6472i			0.538787i
$552$		0			0
$553$			2.47325i			0.105173i
$554$		0			0
$555$	−4.22533	−	4.22533i	−0.179355	−	0.179355i
$556$		0			0
$557$	3.16772	−	3.16772i	0.134221	−	0.134221i	−0.636805	−	0.771025i	$-0.719744\pi$
$557$	3.16772	−	3.16772i	0.134221	−	0.134221i	0.771025	+	0.636805i	$0.219744\pi$
$558$		0			0
$559$	23.8559			1.00900
$560$		0			0
$561$	−6.38658			−0.269642
$562$		0			0
$563$	17.7883	−	17.7883i	0.749686	−	0.749686i	−0.224734	−	0.974420i	$-0.572151\pi$
$563$	17.7883	−	17.7883i	0.749686	−	0.749686i	0.974420	+	0.224734i	$0.0721514\pi$
$564$		0			0
$565$	11.1196	+	11.1196i	0.467806	+	0.467806i
$566$		0			0
$567$			5.54080i			0.232692i
$568$		0			0
$569$			20.5923i			0.863274i	0.902047	+	0.431637i	$0.142064\pi$
$569$			20.5923i			0.863274i	−0.902047	+	0.431637i	$0.857936\pi$
$570$		0			0
$571$	−25.1558	−	25.1558i	−1.05274	−	1.05274i	−0.998530	−	0.0542067i	$-0.982737\pi$
$571$	−25.1558	−	25.1558i	−1.05274	−	1.05274i	−0.0542067	−	0.998530i	$-0.517263\pi$
$572$		0			0
$573$	11.1122	−	11.1122i	0.464217	−	0.464217i
$574$		0			0
$575$	0.722358			0.0301244
$576$		0			0
$577$	−11.8610			−0.493782			−0.246891	−	0.969043i	$-0.579409\pi$
$577$	−11.8610			−0.493782			−0.246891	+	0.969043i	$0.579409\pi$
$578$		0			0
$579$	−3.18898	+	3.18898i	−0.132529	+	0.132529i
$580$		0			0
$581$	1.59485	+	1.59485i	0.0661657	+	0.0661657i
$582$		0			0
$583$		−	9.65434i		−	0.399842i
$584$		0			0
$585$		−	8.83188i		−	0.365153i
$586$		0			0
$587$	−12.2824	−	12.2824i	−0.506949	−	0.506949i	0.406640	−	0.913588i	$-0.366700\pi$
$587$	−12.2824	−	12.2824i	−0.506949	−	0.506949i	−0.913588	+	0.406640i	$0.866700\pi$
$588$		0			0
$589$	−5.13893	+	5.13893i	−0.211746	+	0.211746i
$590$		0			0
$591$	−1.82011			−0.0748692
$592$		0			0
$593$	18.7346			0.769340			0.384670	−	0.923054i	$-0.374315\pi$
$593$	18.7346			0.769340			0.384670	+	0.923054i	$0.374315\pi$
$594$		0			0
$595$	3.91299	−	3.91299i	0.160417	−	0.160417i
$596$		0			0
$597$	3.85576	+	3.85576i	0.157806	+	0.157806i
$598$		0			0
$599$			27.2142i			1.11194i	0.831202	+	0.555971i	$0.187653\pi$
$599$			27.2142i			1.11194i	−0.831202	+	0.555971i	$0.812347\pi$
$600$		0			0
$601$			33.3637i			1.36093i	0.732779	+	0.680467i	$0.238223\pi$
$601$			33.3637i			1.36093i	−0.732779	+	0.680467i	$0.761777\pi$
$602$		0			0
$603$	−13.9813	−	13.9813i	−0.569362	−	0.569362i
$604$		0			0
$605$	5.43729	−	5.43729i	0.221057	−	0.221057i
$606$		0			0
$607$	−0.703571			−0.0285570			−0.0142785	−	0.999898i	$-0.504545\pi$
$607$	−0.703571			−0.0285570			−0.0142785	+	0.999898i	$0.504545\pi$
$608$		0			0
$609$	−3.39195			−0.137449
$610$		0			0
$611$	−6.55808	+	6.55808i	−0.265311	+	0.265311i
$612$		0			0
$613$	−25.7430	−	25.7430i	−1.03975	−	1.03975i	−0.999177	−	0.0405719i	$-0.987082\pi$
$613$	−25.7430	−	25.7430i	−1.03975	−	1.03975i	−0.0405719	−	0.999177i	$-0.512918\pi$
$614$		0			0
$615$		−	1.07092i		−	0.0431838i
$616$		0			0
$617$		−	4.23064i		−	0.170319i	−0.996367	−	0.0851595i	$-0.972860\pi$
$617$		−	4.23064i		−	0.170319i	0.996367	−	0.0851595i	$-0.0271400\pi$
$618$		0			0
$619$	20.3749	+	20.3749i	0.818937	+	0.818937i	0.985954	−	0.167017i	$-0.0534136\pi$
$619$	20.3749	+	20.3749i	0.818937	+	0.818937i	−0.167017	+	0.985954i	$0.553414\pi$
$620$		0			0
$621$	−1.81360	+	1.81360i	−0.0727773	+	0.0727773i
$622$		0			0
$623$	−0.601875			−0.0241136
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	−1.93006	+	1.93006i	−0.0770793	+	0.0770793i
$628$		0			0
$629$	36.8626	+	36.8626i	1.46981	+	1.46981i
$630$		0			0
$631$			48.3673i			1.92547i	0.270442	+	0.962736i	$0.412830\pi$
$631$			48.3673i			1.92547i	−0.270442	+	0.962736i	$0.587170\pi$
$632$		0			0
$633$		−	8.74095i		−	0.347422i
$634$		0			0
$635$	−6.94566	−	6.94566i	−0.275630	−	0.275630i
$636$		0			0
$637$	2.40412	−	2.40412i	0.0952547	−	0.0952547i
$638$		0			0
$639$	−14.7786			−0.584632
$640$		0			0
$641$	−44.1494			−1.74380			−0.871899	−	0.489685i	$-0.837112\pi$
$641$	−44.1494			−1.74380			−0.871899	+	0.489685i	$0.837112\pi$
$642$		0			0
$643$	3.09230	−	3.09230i	0.121948	−	0.121948i	−0.643499	−	0.765447i	$-0.722518\pi$
$643$	3.09230	−	3.09230i	0.121948	−	0.121948i	0.765447	+	0.643499i	$0.222518\pi$
$644$		0			0
$645$	3.14707	+	3.14707i	0.123916	+	0.123916i
$646$		0			0
$647$			22.6950i			0.892231i	0.894975	+	0.446115i	$0.147193\pi$
$647$			22.6950i			0.892231i	−0.894975	+	0.446115i	$0.852807\pi$
$648$		0			0
$649$			9.64413i			0.378565i
$650$		0			0
$651$	−1.37825	−	1.37825i	−0.0540181	−	0.0540181i
$652$		0			0
$653$	−4.46385	+	4.46385i	−0.174684	+	0.174684i	−0.789034	−	0.614350i	$-0.789418\pi$
$653$	−4.46385	+	4.46385i	−0.174684	+	0.174684i	0.614350	+	0.789034i	$0.289418\pi$
$654$		0			0
$655$	−20.0566			−0.783677
$656$		0			0
$657$	−17.1210			−0.667954
$658$		0			0
$659$	3.48471	−	3.48471i	0.135745	−	0.135745i	−0.635969	−	0.771714i	$-0.719400\pi$
$659$	3.48471	−	3.48471i	0.135745	−	0.135745i	0.771714	+	0.635969i	$0.219400\pi$
$660$		0			0
$661$	34.4140	+	34.4140i	1.33855	+	1.33855i	0.897468	+	0.441080i	$0.145405\pi$
$661$	34.4140	+	34.4140i	1.33855	+	1.33855i	0.441080	+	0.897468i	$0.354595\pi$
$662$		0			0
$663$		−	11.9342i		−	0.463485i
$664$		0			0
$665$		−	2.36505i		−	0.0917129i
$666$		0			0
$667$	2.73143	+	2.73143i	0.105761	+	0.105761i
$668$		0			0
$669$	−6.12116	+	6.12116i	−0.236658	+	0.236658i
$670$		0			0
$671$	−13.2295			−0.510718
$672$		0			0
$673$	16.3886			0.631735			0.315867	−	0.948803i	$-0.397705\pi$
$673$	16.3886			0.631735			0.315867	+	0.948803i	$0.397705\pi$
$674$		0			0
$675$	2.51067	−	2.51067i	0.0966356	−	0.0966356i
$676$		0			0
$677$	11.3071	+	11.3071i	0.434565	+	0.434565i	0.890178	−	0.455613i	$-0.150580\pi$
$677$	11.3071	+	11.3071i	0.434565	+	0.434565i	−0.455613	+	0.890178i	$0.650580\pi$
$678$		0			0
$679$		−	12.6823i		−	0.486701i
$680$		0			0
$681$			18.0182i			0.690460i
$682$		0			0
$683$	6.99710	+	6.99710i	0.267737	+	0.267737i	0.828188	−	0.560451i	$-0.189372\pi$
$683$	6.99710	+	6.99710i	0.267737	+	0.267737i	−0.560451	+	0.828188i	$0.689372\pi$
$684$		0			0
$685$	13.7986	−	13.7986i	0.527216	−	0.527216i
$686$		0			0
$687$	8.91502			0.340129
$688$		0			0
$689$	18.0404			0.687285
$690$		0			0
$691$	15.8586	−	15.8586i	0.603290	−	0.603290i	−0.337894	−	0.941184i	$-0.609715\pi$
$691$	15.8586	−	15.8586i	0.603290	−	0.603290i	0.941184	+	0.337894i	$0.109715\pi$
$692$		0			0
$693$	3.34206	+	3.34206i	0.126954	+	0.126954i
$694$		0			0
$695$			20.8808i			0.792054i
$696$		0			0
$697$			9.34295i			0.353889i
$698$		0			0
$699$	9.38568	+	9.38568i	0.354999	+	0.354999i
$700$		0			0
$701$	−30.1315	+	30.1315i	−1.13805	+	1.13805i	−0.149253	+	0.988799i	$0.547687\pi$
$701$	−30.1315	+	30.1315i	−1.13805	+	1.13805i	−0.988799	+	0.149253i	$0.952313\pi$
$702$		0			0
$703$	22.2802			0.840313
$704$		0			0
$705$	−1.73029			−0.0651664
$706$		0			0
$707$	3.13851	−	3.13851i	0.118036	−	0.118036i
$708$		0			0
$709$	−23.5195	−	23.5195i	−0.883295	−	0.883295i	0.110573	−	0.993868i	$-0.464731\pi$
$709$	−23.5195	−	23.5195i	−0.883295	−	0.883295i	−0.993868	+	0.110573i	$0.964731\pi$
$710$		0			0
$711$		−	6.42465i		−	0.240943i
$712$		0			0
$713$			2.21973i			0.0831294i
$714$		0			0
$715$	−4.37425	−	4.37425i	−0.163588	−	0.163588i
$716$		0			0
$717$	−0.862857	+	0.862857i	−0.0322240	+	0.0322240i
$718$		0			0
$719$	9.27413			0.345867			0.172933	−	0.984934i	$-0.444675\pi$
$719$	9.27413			0.345867			0.172933	+	0.984934i	$0.444675\pi$
$720$		0			0
$721$	−5.06857			−0.188763
$722$		0			0
$723$	−7.54218	+	7.54218i	−0.280497	+	0.280497i
$724$		0			0
$725$	−3.78126	−	3.78126i	−0.140433	−	0.140433i
$726$		0			0
$727$		−	31.5849i		−	1.17142i	−0.810520	−	0.585710i	$-0.800816\pi$
$727$		−	31.5849i		−	1.17142i	0.810520	−	0.585710i	$-0.199184\pi$
$728$		0			0
$729$		−	7.63658i		−	0.282836i
$730$		0			0
$731$	−27.4557	−	27.4557i	−1.01549	−	1.01549i
$732$		0			0
$733$	12.0673	−	12.0673i	0.445717	−	0.445717i	−0.448211	−	0.893928i	$-0.647939\pi$
$733$	12.0673	−	12.0673i	0.445717	−	0.445717i	0.893928	+	0.448211i	$0.147939\pi$
$734$		0			0
$735$	0.634304			0.0233967
$736$		0			0
$737$	−13.8493			−0.510145
$738$		0			0
$739$	5.80617	−	5.80617i	0.213584	−	0.213584i	−0.592204	−	0.805788i	$-0.701742\pi$
$739$	5.80617	−	5.80617i	0.213584	−	0.213584i	0.805788	+	0.592204i	$0.201742\pi$
$740$		0			0
$741$	−3.60658	−	3.60658i	−0.132491	−	0.132491i
$742$		0			0
$743$			8.10865i			0.297478i	0.988877	+	0.148739i	$0.0475214\pi$
$743$			8.10865i			0.297478i	−0.988877	+	0.148739i	$0.952479\pi$
$744$		0			0
$745$		−	6.50778i		−	0.238427i
$746$		0			0
$747$	−4.14289	−	4.14289i	−0.151580	−	0.151580i
$748$		0			0
$749$	10.9680	−	10.9680i	0.400761	−	0.400761i
$750$		0			0
$751$	−7.87287			−0.287285			−0.143643	−	0.989630i	$-0.545882\pi$
$751$	−7.87287			−0.287285			−0.143643	+	0.989630i	$0.545882\pi$
$752$		0			0
$753$	−11.8010			−0.430052
$754$		0			0
$755$	−1.25201	+	1.25201i	−0.0455655	+	0.0455655i
$756$		0			0
$757$	17.7048	+	17.7048i	0.643492	+	0.643492i	0.951412	−	0.307921i	$-0.0996331\pi$
$757$	17.7048	+	17.7048i	0.643492	+	0.643492i	−0.307921	+	0.951412i	$0.599633\pi$
$758$		0			0
$759$			0.833677i			0.0302606i
$760$		0			0
$761$		−	15.7220i		−	0.569921i	−0.958539	−	0.284960i	$-0.908020\pi$
$761$		−	15.7220i		−	0.569921i	0.958539	−	0.284960i	$-0.0919805\pi$
$762$		0			0
$763$	7.22669	+	7.22669i	0.261624	+	0.261624i
$764$		0			0
$765$	−10.1646	+	10.1646i	−0.367502	+	0.367502i
$766$		0			0
$767$	−18.0213			−0.650713
$768$		0			0
$769$	28.9860			1.04526			0.522631	−	0.852559i	$-0.324950\pi$
$769$	28.9860			1.04526			0.522631	+	0.852559i	$0.324950\pi$
$770$		0			0
$771$	13.1925	−	13.1925i	0.475118	−	0.475118i
$772$		0			0
$773$	1.12906	+	1.12906i	0.0406094	+	0.0406094i	0.727120	−	0.686511i	$-0.240858\pi$
$773$	1.12906	+	1.12906i	0.0406094	+	0.0406094i	−0.686511	+	0.727120i	$0.740858\pi$
$774$		0			0
$775$		−	3.07289i		−	0.110381i
$776$		0			0
$777$			5.97552i			0.214370i
$778$		0			0
$779$	2.82349	+	2.82349i	0.101162	+	0.101162i
$780$		0			0
$781$	−7.31954	+	7.31954i	−0.261914	+	0.261914i
$782$		0			0
$783$	18.9870			0.678539
$784$		0			0
$785$	−6.54603			−0.233638
$786$		0			0
$787$	19.2451	−	19.2451i	0.686014	−	0.686014i	−0.275334	−	0.961349i	$-0.588789\pi$
$787$	19.2451	−	19.2451i	0.686014	−	0.686014i	0.961349	+	0.275334i	$0.0887886\pi$
$788$		0			0
$789$	6.37182	+	6.37182i	0.226843	+	0.226843i
$790$		0			0
$791$		−	15.7255i		−	0.559135i
$792$		0			0
$793$		−	24.7210i		−	0.877870i
$794$		0			0
$795$	2.37990	+	2.37990i	0.0844062	+	0.0844062i
$796$		0			0
$797$	29.9016	−	29.9016i	1.05917	−	1.05917i	0.0610324	−	0.998136i	$-0.480561\pi$
$797$	29.9016	−	29.9016i	1.05917	−	1.05917i	0.998136	−	0.0610324i	$-0.0194393\pi$
$798$		0			0
$799$	15.0954			0.534036
$800$		0			0
$801$	1.56347			0.0552424
$802$		0			0
$803$	−8.47968	+	8.47968i	−0.299241	+	0.299241i
$804$		0			0
$805$	−0.510785	−	0.510785i	−0.0180028	−	0.0180028i
$806$		0			0
$807$			0.0926641i			0.00326193i
$808$		0			0
$809$		−	23.5752i		−	0.828859i	−0.910081	−	0.414429i	$-0.863981\pi$
$809$		−	23.5752i		−	0.828859i	0.910081	−	0.414429i	$-0.136019\pi$
$810$		0			0
$811$	32.7019	+	32.7019i	1.14832	+	1.14832i	0.986883	+	0.161438i	$0.0516131\pi$
$811$	32.7019	+	32.7019i	1.14832	+	1.14832i	0.161438	+	0.986883i	$0.448387\pi$
$812$		0			0
$813$	−4.14459	+	4.14459i	−0.145357	+	0.145357i
$814$		0			0
$815$	−16.8736			−0.591055
$816$		0			0
$817$	−16.5945			−0.580570
$818$		0			0
$819$	−6.24508	+	6.24508i	−0.218221	+	0.218221i
$820$		0			0
$821$	26.9046	+	26.9046i	0.938978	+	0.938978i	0.998242	−	0.0592639i	$-0.0188754\pi$
$821$	26.9046	+	26.9046i	0.938978	+	0.938978i	−0.0592639	+	0.998242i	$0.518875\pi$
$822$		0			0
$823$			22.4116i			0.781221i	0.920556	+	0.390610i	$0.127736\pi$
$823$			22.4116i			0.781221i	−0.920556	+	0.390610i	$0.872264\pi$
$824$		0			0
$825$		−	1.15410i		−	0.0401808i
$826$		0			0
$827$	−26.5996	−	26.5996i	−0.924957	−	0.924957i	0.0724172	−	0.997374i	$-0.476929\pi$
$827$	−26.5996	−	26.5996i	−0.924957	−	0.924957i	−0.997374	+	0.0724172i	$0.976929\pi$
$828$		0			0
$829$	−8.01933	+	8.01933i	−0.278523	+	0.278523i	−0.832519	−	0.553996i	$-0.813102\pi$
$829$	−8.01933	+	8.01933i	−0.278523	+	0.278523i	0.553996	+	0.832519i	$0.313102\pi$
$830$		0			0
$831$	−12.1606			−0.421848
$832$		0			0
$833$	−5.53380			−0.191735
$834$		0			0
$835$	−12.8322	+	12.8322i	−0.444075	+	0.444075i
$836$		0			0
$837$	7.71500	+	7.71500i	0.266669	+	0.266669i
$838$		0			0
$839$			29.3075i			1.01181i	0.862590	+	0.505903i	$0.168841\pi$
$839$			29.3075i			1.01181i	−0.862590	+	0.505903i	$0.831159\pi$
$840$		0			0
$841$			0.404116i			0.0139350i
$842$		0			0
$843$	7.66400	+	7.66400i	0.263962	+	0.263962i
$844$		0			0
$845$	−1.01852	+	1.01852i	−0.0350382	+	0.0350382i
$846$		0			0
$847$	−7.68949			−0.264214
$848$		0			0
$849$	−6.40972			−0.219981
$850$		0			0
$851$	4.81189	−	4.81189i	0.164949	−	0.164949i
$852$		0			0
$853$	7.06486	+	7.06486i	0.241896	+	0.241896i	0.817634	−	0.575738i	$-0.195285\pi$
$853$	7.06486	+	7.06486i	0.241896	+	0.241896i	−0.575738	+	0.817634i	$0.695285\pi$
$854$		0			0
$855$			6.14360i			0.210107i
$856$		0			0
$857$		−	16.8956i		−	0.577143i	−0.957458	−	0.288572i	$-0.906820\pi$
$857$		−	16.8956i		−	0.577143i	0.957458	−	0.288572i	$-0.0931803\pi$
$858$		0			0
$859$	4.62017	+	4.62017i	0.157638	+	0.157638i	0.781519	−	0.623881i	$-0.214445\pi$
$859$	4.62017	+	4.62017i	0.157638	+	0.157638i	−0.623881	+	0.781519i	$0.714445\pi$
$860$		0			0
$861$	−0.757256	+	0.757256i	−0.0258072	+	0.0258072i
$862$		0			0
$863$	1.75149			0.0596214			0.0298107	−	0.999556i	$-0.490510\pi$
$863$	1.75149			0.0596214			0.0298107	+	0.999556i	$0.490510\pi$
$864$		0			0
$865$	−14.0863			−0.478948
$866$		0			0
$867$	−6.11018	+	6.11018i	−0.207513	+	0.207513i
$868$		0			0
$869$	−3.18200	−	3.18200i	−0.107942	−	0.107942i
$870$		0			0
$871$		−	25.8792i		−	0.876884i
$872$		0			0
$873$			32.9442i			1.11499i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	10.9355	−	10.9355i	0.369267	−	0.369267i	−0.497943	−	0.867210i	$-0.665911\pi$
$877$	10.9355	−	10.9355i	0.369267	−	0.369267i	0.867210	+	0.497943i	$0.165911\pi$
$878$		0			0
$879$	−16.5428			−0.557974
$880$		0			0
$881$	8.14000			0.274243			0.137122	−	0.990554i	$-0.456215\pi$
$881$	8.14000			0.274243			0.137122	+	0.990554i	$0.456215\pi$
$882$		0			0
$883$	−16.7247	+	16.7247i	−0.562831	+	0.562831i	−0.930111	−	0.367280i	$-0.880289\pi$
$883$	−16.7247	+	16.7247i	−0.562831	+	0.562831i	0.367280	+	0.930111i	$0.380289\pi$
$884$		0			0
$885$	−2.37738	−	2.37738i	−0.0799147	−	0.0799147i
$886$		0			0
$887$			50.4191i			1.69291i	0.532461	+	0.846454i	$0.321267\pi$
$887$			50.4191i			1.69291i	−0.532461	+	0.846454i	$0.678733\pi$
$888$		0			0
$889$			9.82265i			0.329441i
$890$		0			0
$891$	−7.12861	−	7.12861i	−0.238817	−	0.238817i
$892$		0			0
$893$	4.56191	−	4.56191i	0.152658	−	0.152658i
$894$		0			0
$895$	−0.312778			−0.0104550
$896$		0			0
$897$	−1.55784			−0.0520146
$898$		0			0
$899$	11.6194	−	11.6194i	0.387528	−	0.387528i
$900$		0			0
$901$	−20.7627	−	20.7627i	−0.691706	−	0.691706i
$902$		0			0
$903$		−	4.45063i		−	0.148108i
$904$		0			0
$905$		−	8.70920i		−	0.289504i
$906$		0			0
$907$	−38.2378	−	38.2378i	−1.26966	−	1.26966i	−0.946261	−	0.323403i	$-0.895173\pi$
$907$	−38.2378	−	38.2378i	−1.26966	−	1.26966i	−0.323403	−	0.946261i	$-0.604827\pi$
$908$		0			0
$909$	−8.15277	+	8.15277i	−0.270410	+	0.270410i
$910$		0			0
$911$	47.1124			1.56090			0.780451	−	0.625216i	$-0.214989\pi$
$911$	47.1124			1.56090			0.780451	+	0.625216i	$0.214989\pi$
$912$		0			0
$913$	−4.10377			−0.135815
$914$		0			0
$915$	3.26121	−	3.26121i	0.107812	−	0.107812i
$916$		0			0
$917$	14.1822	+	14.1822i	0.468337	+	0.468337i
$918$		0			0
$919$			4.09584i			0.135109i	0.997716	+	0.0675546i	$0.0215197\pi$
$919$			4.09584i			0.135109i	−0.997716	+	0.0675546i	$0.978480\pi$
$920$		0			0
$921$			13.1681i			0.433904i
$922$		0			0
$923$	−13.6775	−	13.6775i	−0.450201	−	0.450201i
$924$		0			0
$925$	−6.66136	+	6.66136i	−0.219024	+	0.219024i
$926$		0			0
$927$	13.1664			0.432442
$928$		0			0
$929$	−28.9007			−0.948200			−0.474100	−	0.880471i	$-0.657227\pi$
$929$	−28.9007			−0.948200			−0.474100	+	0.880471i	$0.657227\pi$
$930$		0			0
$931$	−1.67235	+	1.67235i	−0.0548089	+	0.0548089i
$932$		0			0
$933$	−0.980979	−	0.980979i	−0.0321158	−	0.0321158i
$934$		0			0
$935$			10.0686i			0.329280i
$936$		0			0
$937$		−	29.0968i		−	0.950551i	−0.879837	−	0.475276i	$-0.842348\pi$
$937$		−	29.0968i		−	0.950551i	0.879837	−	0.475276i	$-0.157652\pi$
$938$		0			0
$939$	−10.8723	−	10.8723i	−0.354803	−	0.354803i
$940$		0			0
$941$	−15.2957	+	15.2957i	−0.498624	+	0.498624i	−0.911010	−	0.412385i	$-0.864696\pi$
$941$	−15.2957	+	15.2957i	−0.498624	+	0.498624i	0.412385	+	0.911010i	$0.364696\pi$
$942$		0			0
$943$	1.21959			0.0397152
$944$		0			0
$945$	−3.55062			−0.115502
$946$		0			0
$947$	−0.311233	+	0.311233i	−0.0101137	+	0.0101137i	−0.712146	−	0.702032i	$-0.752276\pi$
$947$	−0.311233	+	0.311233i	−0.0101137	+	0.0101137i	0.702032	+	0.712146i	$0.252276\pi$
$948$		0			0
$949$	−15.8454	−	15.8454i	−0.514364	−	0.514364i
$950$		0			0
$951$			15.0891i			0.489297i
$952$		0			0
$953$			16.6099i			0.538046i	0.963134	+	0.269023i	$0.0867008\pi$
$953$			16.6099i			0.538046i	−0.963134	+	0.269023i	$0.913299\pi$
$954$		0			0
$955$	−17.5187	−	17.5187i	−0.566891	−	0.566891i
$956$		0			0
$957$	4.36397	−	4.36397i	0.141067	−	0.141067i
$958$		0			0
$959$	−19.5141			−0.630143
$960$		0			0
$961$	−21.5574			−0.695399
$962$		0			0
$963$	−28.4911	+	28.4911i	−0.918112	+	0.918112i
$964$		0			0
$965$	5.02752	+	5.02752i	0.161842	+	0.161842i
$966$		0			0
$967$			56.4753i			1.81612i	0.418836	+	0.908062i	$0.362438\pi$
$967$			56.4753i			1.81612i	−0.418836	+	0.908062i	$0.637562\pi$
$968$		0			0
$969$			8.30161i			0.266686i
$970$		0			0
$971$	−24.5481	−	24.5481i	−0.787787	−	0.787787i	0.193344	−	0.981131i	$-0.438067\pi$
$971$	−24.5481	−	24.5481i	−0.787787	−	0.787787i	−0.981131	+	0.193344i	$0.938067\pi$
$972$		0			0
$973$	14.7650	−	14.7650i	0.473343	−	0.473343i
$974$		0			0
$975$	2.15660			0.0690664
$976$		0			0
$977$	−43.1830			−1.38155			−0.690773	−	0.723072i	$-0.742730\pi$
$977$	−43.1830			−1.38155			−0.690773	+	0.723072i	$0.742730\pi$
$978$		0			0
$979$	0.774353	−	0.774353i	0.0247484	−	0.0247484i
$980$		0			0
$981$	−18.7725	−	18.7725i	−0.599358	−	0.599358i
$982$		0			0
$983$			32.5513i			1.03823i	0.854705	+	0.519113i	$0.173738\pi$
$983$			32.5513i			1.03823i	−0.854705	+	0.519113i	$0.826262\pi$
$984$		0			0
$985$			2.86945i			0.0914284i
$986$		0			0
$987$	1.22350	+	1.22350i	0.0389444	+	0.0389444i
$988$		0			0
$989$	−3.58395	+	3.58395i	−0.113963	+	0.113963i
$990$		0			0
$991$	44.1290			1.40180			0.700902	−	0.713257i	$-0.252781\pi$
$991$	44.1290			1.40180			0.700902	+	0.713257i	$0.252781\pi$
$992$		0			0
$993$	7.56445			0.240051
$994$		0			0
$995$	6.07872	−	6.07872i	0.192708	−	0.192708i
$996$		0			0
$997$	19.1102	+	19.1102i	0.605227	+	0.605227i	0.941695	−	0.336468i	$-0.109232\pi$
$997$	19.1102	+	19.1102i	0.605227	+	0.605227i	−0.336468	+	0.941695i	$0.609232\pi$
$998$		0			0
$999$		−	33.4489i		−	1.05828i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.10		44
4.3	odd	2		560.2.bd.a.421.6	yes	44
16.3	odd	4		560.2.bd.a.141.6	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.10		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.6	✓	44	16.3	odd	4
560.2.bd.a.421.6	yes	44	4.3	odd	2
2240.2.bd.a.561.10		44	1.1	even	1	trivial
2240.2.bd.a.1681.10		44	16.13	even	4	inner

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:	\( N \)	\(=\)	\( 2240 = 2^{6} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2240.bd (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.448521 + 0.448521i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.59766i q^{9} +O(q^{10})\)	\(q+(-0.448521 + 0.448521i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} +2.59766i q^{9} +(1.28657 + 1.28657i) q^{11} +(-2.40412 + 2.40412i) q^{13} -0.634304 q^{15} +5.53380 q^{17} +(1.67235 - 1.67235i) q^{19} +(0.448521 + 0.448521i) q^{21} -0.722358i q^{23} +1.00000i q^{25} +(-2.51067 - 2.51067i) q^{27} +(-3.78126 + 3.78126i) q^{29} -3.07289 q^{31} -1.15410 q^{33} +(0.707107 - 0.707107i) q^{35} +(6.66136 + 6.66136i) q^{37} -2.15660i q^{39} +1.68834i q^{41} +(-4.96146 - 4.96146i) q^{43} +(-1.83682 + 1.83682i) q^{45} +2.72785 q^{47} -1.00000 q^{49} +(-2.48203 + 2.48203i) q^{51} +(-3.75198 - 3.75198i) q^{53} +1.81948i q^{55} +1.50016i q^{57} +(3.74801 + 3.74801i) q^{59} +(-5.14139 + 5.14139i) q^{61} +2.59766 q^{63} -3.39994 q^{65} +(-5.38226 + 5.38226i) q^{67} +(0.323993 + 0.323993i) q^{69} +5.68920i q^{71} +6.59094i q^{73} +(-0.448521 - 0.448521i) q^{75} +(1.28657 - 1.28657i) q^{77} -2.47325 q^{79} -5.54080 q^{81} +(-1.59485 + 1.59485i) q^{83} +(3.91299 + 3.91299i) q^{85} -3.39195i q^{87} -0.601875i q^{89} +(2.40412 + 2.40412i) q^{91} +(1.37825 - 1.37825i) q^{93} +2.36505 q^{95} +12.6823 q^{97} +(-3.34206 + 3.34206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 44 * q	\( 44 q - 12 q^{11} - 8 q^{15} - 8 q^{19} + 24 q^{27} + 12 q^{29} + 28 q^{37} + 44 q^{43} - 44 q^{49} + 8 q^{51} - 12 q^{53} - 24 q^{59} - 16 q^{61} - 28 q^{63} - 40 q^{65} + 28 q^{67} + 40 q^{69} - 12 q^{77} + 16 q^{79} + 20 q^{81} + 16 q^{85} + 88 q^{93} + 32 q^{95} - 28 q^{99}+O(q^{100}) \) 44 * q - 12 * q^11 - 8 * q^15 - 8 * q^19 + 24 * q^27 + 12 * q^29 + 28 * q^37 + 44 * q^43 - 44 * q^49 + 8 * q^51 - 12 * q^53 - 24 * q^59 - 16 * q^61 - 28 * q^63 - 40 * q^65 + 28 * q^67 + 40 * q^69 - 12 * q^77 + 16 * q^79 + 20 * q^81 + 16 * q^85 + 88 * q^93 + 32 * q^95 - 28 * q^99

Introduction

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