LMFDB - Embedded newform 2240.2.bd.a.561.5

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			561.5
Character	$\chi$	$=$	2240.561
Dual form			2240.2.bd.a.1681.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28029 + 1.28029i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} -0.278310i q^{9} +O(q^{10})$	\(q+(-1.28029 + 1.28029i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} -0.278310i q^{9} +(-2.22891 - 2.22891i) q^{11} +(0.755840 - 0.755840i) q^{13} -1.81061 q^{15} +0.805751 q^{17} +(1.00168 - 1.00168i) q^{19} +(1.28029 + 1.28029i) q^{21} +4.48666i q^{23} +1.00000i q^{25} +(-3.48457 - 3.48457i) q^{27} +(-0.0581885 + 0.0581885i) q^{29} -4.72963 q^{31} +5.70733 q^{33} +(0.707107 - 0.707107i) q^{35} +(-7.31260 - 7.31260i) q^{37} +1.93540i q^{39} -1.66826i q^{41} +(-2.71794 - 2.71794i) q^{43} +(0.196795 - 0.196795i) q^{45} -2.71262 q^{47} -1.00000 q^{49} +(-1.03160 + 1.03160i) q^{51} +(-7.19308 - 7.19308i) q^{53} -3.15216i q^{55} +2.56490i q^{57} +(-0.153744 - 0.153744i) q^{59} +(3.17084 - 3.17084i) q^{61} -0.278310 q^{63} +1.06892 q^{65} +(-2.38261 + 2.38261i) q^{67} +(-5.74425 - 5.74425i) q^{69} +1.61718i q^{71} -1.70069i q^{73} +(-1.28029 - 1.28029i) q^{75} +(-2.22891 + 2.22891i) q^{77} +15.8678 q^{79} +9.75747 q^{81} +(4.52351 - 4.52351i) q^{83} +(0.569752 + 0.569752i) q^{85} -0.148997i q^{87} -2.94054i q^{89} +(-0.755840 - 0.755840i) q^{91} +(6.05532 - 6.05532i) q^{93} +1.41659 q^{95} -13.0705 q^{97} +(-0.620329 + 0.620329i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.28029	+	1.28029i	−0.739179	+	0.739179i	−0.972419	−	0.233240i	$-0.925067\pi$
$3$	−1.28029	+	1.28029i	−0.739179	+	0.739179i	0.233240	+	0.972419i	$0.425067\pi$
$4$		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
$9$		−	0.278310i		−	0.0927701i
$10$		0			0
$11$	−2.22891	−	2.22891i	−0.672042	−	0.672042i	0.286144	−	0.958187i	$-0.407626\pi$
$11$	−2.22891	−	2.22891i	−0.672042	−	0.672042i	−0.958187	+	0.286144i	$0.907626\pi$
$12$		0			0
$13$	0.755840	−	0.755840i	0.209632	−	0.209632i	−0.594479	−	0.804111i	$-0.702642\pi$
$13$	0.755840	−	0.755840i	0.209632	−	0.209632i	0.804111	+	0.594479i	$0.202642\pi$
$14$		0			0
$15$	−1.81061			−0.467498
$16$		0			0
$17$	0.805751			0.195423			0.0977117	−	0.995215i	$-0.468848\pi$
$17$	0.805751			0.195423			0.0977117	+	0.995215i	$0.468848\pi$
$18$		0			0
$19$	1.00168	−	1.00168i	0.229802	−	0.229802i	−0.582808	−	0.812610i	$-0.698046\pi$
$19$	1.00168	−	1.00168i	0.229802	−	0.229802i	0.812610	+	0.582808i	$0.198046\pi$
$20$		0			0
$21$	1.28029	+	1.28029i	0.279383	+	0.279383i
$22$		0			0
$23$			4.48666i			0.935534i	0.883852	+	0.467767i	$0.154941\pi$
$23$			4.48666i			0.935534i	−0.883852	+	0.467767i	$0.845059\pi$
$24$		0			0
$25$			1.00000i			0.200000i
$26$		0			0
$27$	−3.48457	−	3.48457i	−0.670605	−	0.670605i
$28$		0			0
$29$	−0.0581885	+	0.0581885i	−0.0108053	+	0.0108053i	−0.712489	−	0.701683i	$-0.752432\pi$
$29$	−0.0581885	+	0.0581885i	−0.0108053	+	0.0108053i	0.701683	+	0.712489i	$0.252432\pi$
$30$		0			0
$31$	−4.72963			−0.849467			−0.424733	−	0.905319i	$-0.639632\pi$
$31$	−4.72963			−0.849467			−0.424733	+	0.905319i	$0.639632\pi$
$32$		0			0
$33$	5.70733			0.993518
$34$		0			0
$35$	0.707107	−	0.707107i	0.119523	−	0.119523i
$36$		0			0
$37$	−7.31260	−	7.31260i	−1.20218	−	1.20218i	−0.973501	−	0.228682i	$-0.926558\pi$
$37$	−7.31260	−	7.31260i	−1.20218	−	1.20218i	−0.228682	−	0.973501i	$-0.573442\pi$
$38$		0			0
$39$			1.93540i			0.309911i
$40$		0			0
$41$		−	1.66826i		−	0.260538i	−0.991479	−	0.130269i	$-0.958416\pi$
$41$		−	1.66826i		−	0.260538i	0.991479	−	0.130269i	$-0.0415841\pi$
$42$		0			0
$43$	−2.71794	−	2.71794i	−0.414481	−	0.414481i	0.468815	−	0.883296i	$-0.344681\pi$
$43$	−2.71794	−	2.71794i	−0.414481	−	0.414481i	−0.883296	+	0.468815i	$0.844681\pi$
$44$		0			0
$45$	0.196795	−	0.196795i	0.0293365	−	0.0293365i
$46$		0			0
$47$	−2.71262			−0.395677			−0.197838	−	0.980235i	$-0.563392\pi$
$47$	−2.71262			−0.395677			−0.197838	+	0.980235i	$0.563392\pi$
$48$		0			0
$49$	−1.00000			−0.142857
$50$		0			0
$51$	−1.03160	+	1.03160i	−0.144453	+	0.144453i
$52$		0			0
$53$	−7.19308	−	7.19308i	−0.988045	−	0.988045i	0.0118839	−	0.999929i	$-0.496217\pi$
$53$	−7.19308	−	7.19308i	−0.988045	−	0.988045i	−0.999929	+	0.0118839i	$0.996217\pi$
$54$		0			0
$55$		−	3.15216i		−	0.425037i
$56$		0			0
$57$			2.56490i			0.339729i
$58$		0			0
$59$	−0.153744	−	0.153744i	−0.0200157	−	0.0200157i	0.697028	−	0.717044i	$-0.254505\pi$
$59$	−0.153744	−	0.153744i	−0.0200157	−	0.0200157i	−0.717044	+	0.697028i	$0.754505\pi$
$60$		0			0
$61$	3.17084	−	3.17084i	0.405985	−	0.405985i	−0.474351	−	0.880336i	$-0.657317\pi$
$61$	3.17084	−	3.17084i	0.405985	−	0.405985i	0.880336	+	0.474351i	$0.157317\pi$
$62$		0			0
$63$	−0.278310			−0.0350638
$64$		0			0
$65$	1.06892			0.132583
$66$		0			0
$67$	−2.38261	+	2.38261i	−0.291083	+	0.291083i	−0.837508	−	0.546425i	$-0.815988\pi$
$67$	−2.38261	+	2.38261i	−0.291083	+	0.291083i	0.546425	+	0.837508i	$0.315988\pi$
$68$		0			0
$69$	−5.74425	−	5.74425i	−0.691527	−	0.691527i
$70$		0			0
$71$			1.61718i			0.191924i	0.995385	+	0.0959620i	$0.0305927\pi$
$71$			1.61718i			0.191924i	−0.995385	+	0.0959620i	$0.969407\pi$
$72$		0			0
$73$		−	1.70069i		−	0.199051i	−0.995035	−	0.0995253i	$-0.968268\pi$
$73$		−	1.70069i		−	0.199051i	0.995035	−	0.0995253i	$-0.0317324\pi$
$74$		0			0
$75$	−1.28029	−	1.28029i	−0.147836	−	0.147836i
$76$		0			0
$77$	−2.22891	+	2.22891i	−0.254008	+	0.254008i
$78$		0			0
$79$	15.8678			1.78527			0.892635	−	0.450781i	$-0.148854\pi$
$79$	15.8678			1.78527			0.892635	+	0.450781i	$0.148854\pi$
$80$		0			0
$81$	9.75747			1.08416
$82$		0			0
$83$	4.52351	−	4.52351i	0.496520	−	0.496520i	−0.413833	−	0.910353i	$-0.635810\pi$
$83$	4.52351	−	4.52351i	0.496520	−	0.496520i	0.910353	+	0.413833i	$0.135810\pi$
$84$		0			0
$85$	0.569752	+	0.569752i	0.0617983	+	0.0617983i
$86$		0			0
$87$		−	0.148997i		−	0.0159741i
$88$		0			0
$89$		−	2.94054i		−	0.311697i	−0.987781	−	0.155848i	$-0.950189\pi$
$89$		−	2.94054i		−	0.311697i	0.987781	−	0.155848i	$-0.0498111\pi$
$90$		0			0
$91$	−0.755840	−	0.755840i	−0.0792336	−	0.0792336i
$92$		0			0
$93$	6.05532	−	6.05532i	0.627907	−	0.627907i
$94$		0			0
$95$	1.41659			0.145339
$96$		0			0
$97$	−13.0705			−1.32711			−0.663556	−	0.748127i	$-0.730953\pi$
$97$	−13.0705			−1.32711			−0.663556	+	0.748127i	$0.730953\pi$
$98$		0			0
$99$	−0.620329	+	0.620329i	−0.0623454	+	0.0623454i
$100$		0			0
$101$	−8.02757	−	8.02757i	−0.798773	−	0.798773i	0.184129	−	0.982902i	$-0.441053\pi$
$101$	−8.02757	−	8.02757i	−0.798773	−	0.798773i	−0.982902	+	0.184129i	$0.941053\pi$
$102$		0			0
$103$		−	1.10995i		−	0.109366i	−0.998504	−	0.0546832i	$-0.982585\pi$
$103$		−	1.10995i		−	0.109366i	0.998504	−	0.0546832i	$-0.0174149\pi$
$104$		0			0
$105$			1.81061i			0.176697i
$106$		0			0
$107$	8.91230	+	8.91230i	0.861585	+	0.861585i	0.991522	−	0.129937i	$-0.0414777\pi$
$107$	8.91230	+	8.91230i	0.861585	+	0.861585i	−0.129937	+	0.991522i	$0.541478\pi$
$108$		0			0
$109$	3.58980	−	3.58980i	0.343840	−	0.343840i	−0.513969	−	0.857809i	$-0.671825\pi$
$109$	3.58980	−	3.58980i	0.343840	−	0.343840i	0.857809	+	0.513969i	$0.171825\pi$
$110$		0			0
$111$	18.7246			1.77726
$112$		0			0
$113$	14.0277			1.31962			0.659809	−	0.751434i	$-0.270637\pi$
$113$	14.0277			1.31962			0.659809	+	0.751434i	$0.270637\pi$
$114$		0			0
$115$	−3.17255	+	3.17255i	−0.295842	+	0.295842i
$116$		0			0
$117$	−0.210358	−	0.210358i	−0.0194476	−	0.0194476i
$118$		0			0
$119$		−	0.805751i		−	0.0738631i
$120$		0			0
$121$		−	1.06391i		−	0.0967186i
$122$		0			0
$123$	2.13586	+	2.13586i	0.192584	+	0.192584i
$124$		0			0
$125$	−0.707107	+	0.707107i	−0.0632456	+	0.0632456i
$126$		0			0
$127$	−16.6660			−1.47887			−0.739433	−	0.673230i	$-0.764906\pi$
$127$	−16.6660			−1.47887			−0.739433	+	0.673230i	$0.764906\pi$
$128$		0			0
$129$	6.95952			0.612751
$130$		0			0
$131$	7.43916	−	7.43916i	0.649962	−	0.649962i	−0.303021	−	0.952984i	$-0.597995\pi$
$131$	7.43916	−	7.43916i	0.649962	−	0.649962i	0.952984	+	0.303021i	$0.0979954\pi$
$132$		0			0
$133$	−1.00168	−	1.00168i	−0.0868569	−	0.0868569i
$134$		0			0
$135$		−	4.92792i		−	0.424128i
$136$		0			0
$137$		−	4.83668i		−	0.413225i	−0.978423	−	0.206613i	$-0.933756\pi$
$137$		−	4.83668i		−	0.413225i	0.978423	−	0.206613i	$-0.0662440\pi$
$138$		0			0
$139$	−12.0005	−	12.0005i	−1.01787	−	1.01787i	−0.999837	−	0.0180360i	$-0.994259\pi$
$139$	−12.0005	−	12.0005i	−1.01787	−	1.01787i	−0.0180360	−	0.999837i	$-0.505741\pi$
$140$		0			0
$141$	3.47296	−	3.47296i	0.292476	−	0.292476i
$142$		0			0
$143$	−3.36940			−0.281764
$144$		0			0
$145$	−0.0822909			−0.00683389
$146$		0			0
$147$	1.28029	−	1.28029i	0.105597	−	0.105597i
$148$		0			0
$149$	−1.84095	−	1.84095i	−0.150817	−	0.150817i	0.627666	−	0.778483i	$-0.284010\pi$
$149$	−1.84095	−	1.84095i	−0.150817	−	0.150817i	−0.778483	+	0.627666i	$0.784010\pi$
$150$		0			0
$151$		−	18.4210i		−	1.49908i	−0.661958	−	0.749541i	$-0.730274\pi$
$151$		−	18.4210i		−	1.49908i	0.661958	−	0.749541i	$-0.269726\pi$
$152$		0			0
$153$		−	0.224249i		−	0.0181294i
$154$		0			0
$155$	−3.34435	−	3.34435i	−0.268625	−	0.268625i
$156$		0			0
$157$	3.06675	−	3.06675i	0.244753	−	0.244753i	−0.574060	−	0.818813i	$-0.694632\pi$
$157$	3.06675	−	3.06675i	0.244753	−	0.244753i	0.818813	+	0.574060i	$0.194632\pi$
$158$		0			0
$159$	18.4185			1.46068
$160$		0			0
$161$	4.48666			0.353599
$162$		0			0
$163$	−14.4618	+	14.4618i	−1.13273	+	1.13273i	−0.143011	+	0.989721i	$0.545679\pi$
$163$	−14.4618	+	14.4618i	−1.13273	+	1.13273i	−0.989721	+	0.143011i	$0.954321\pi$
$164$		0			0
$165$	4.03569	+	4.03569i	0.314178	+	0.314178i
$166$		0			0
$167$		−	12.1545i		−	0.940547i	−0.882521	−	0.470274i	$-0.844155\pi$
$167$		−	12.1545i		−	0.940547i	0.882521	−	0.470274i	$-0.155845\pi$
$168$		0			0
$169$			11.8574i			0.912109i
$170$		0			0
$171$	−0.278779	−	0.278779i	−0.0213187	−	0.0213187i
$172$		0			0
$173$	11.6104	−	11.6104i	0.882726	−	0.882726i	−0.111085	−	0.993811i	$-0.535433\pi$
$173$	11.6104	−	11.6104i	0.882726	−	0.882726i	0.993811	+	0.111085i	$0.0354326\pi$
$174$		0			0
$175$	1.00000			0.0755929
$176$		0			0
$177$	0.393674			0.0295904
$178$		0			0
$179$	−4.97644	+	4.97644i	−0.371957	+	0.371957i	−0.868189	−	0.496233i	$-0.834716\pi$
$179$	−4.97644	+	4.97644i	−0.371957	+	0.371957i	0.496233	+	0.868189i	$0.334716\pi$
$180$		0			0
$181$	−14.8787	−	14.8787i	−1.10593	−	1.10593i	−0.993681	−	0.112245i	$-0.964196\pi$
$181$	−14.8787	−	14.8787i	−1.10593	−	1.10593i	−0.112245	−	0.993681i	$-0.535804\pi$
$182$		0			0
$183$			8.11923i			0.600191i
$184$		0			0
$185$		−	10.3416i		−	0.760328i
$186$		0			0
$187$	−1.79595	−	1.79595i	−0.131333	−	0.131333i
$188$		0			0
$189$	−3.48457	+	3.48457i	−0.253465	+	0.253465i
$190$		0			0
$191$	16.0788			1.16342			0.581710	−	0.813396i	$-0.302384\pi$
$191$	16.0788			1.16342			0.581710	+	0.813396i	$0.302384\pi$
$192$		0			0
$193$	21.6487			1.55831			0.779153	−	0.626834i	$-0.215650\pi$
$193$	21.6487			1.55831			0.779153	+	0.626834i	$0.215650\pi$
$194$		0			0
$195$	−1.36853	+	1.36853i	−0.0980026	+	0.0980026i
$196$		0			0
$197$	−11.3818	−	11.3818i	−0.810917	−	0.810917i	0.173854	−	0.984771i	$-0.444378\pi$
$197$	−11.3818	−	11.3818i	−0.810917	−	0.810917i	−0.984771	+	0.173854i	$0.944378\pi$
$198$		0			0
$199$		−	25.8868i		−	1.83507i	−0.397659	−	0.917533i	$-0.630177\pi$
$199$		−	25.8868i		−	1.83507i	0.397659	−	0.917533i	$-0.369823\pi$
$200$		0			0
$201$		−	6.10090i		−	0.430324i
$202$		0			0
$203$	0.0581885	+	0.0581885i	0.00408403	+	0.00408403i
$204$		0			0
$205$	1.17964	−	1.17964i	0.0823893	−	0.0823893i
$206$		0			0
$207$	1.24868			0.0867896
$208$		0			0
$209$	−4.46533			−0.308873
$210$		0			0
$211$	9.25199	−	9.25199i	0.636934	−	0.636934i	−0.312864	−	0.949798i	$-0.601289\pi$
$211$	9.25199	−	9.25199i	0.636934	−	0.636934i	0.949798	+	0.312864i	$0.101289\pi$
$212$		0			0
$213$	−2.07047	−	2.07047i	−0.141866	−	0.141866i
$214$		0			0
$215$		−	3.84374i		−	0.262141i
$216$		0			0
$217$			4.72963i			0.321068i
$218$		0			0
$219$	2.17738	+	2.17738i	0.147134	+	0.147134i
$220$		0			0
$221$	0.609019	−	0.609019i	0.0409671	−	0.0409671i
$222$		0			0
$223$	−20.1128			−1.34685			−0.673425	−	0.739255i	$-0.735178\pi$
$223$	−20.1128			−1.34685			−0.673425	+	0.739255i	$0.735178\pi$
$224$		0			0
$225$	0.278310			0.0185540
$226$		0			0
$227$	−9.25163	+	9.25163i	−0.614052	+	0.614052i	−0.943999	−	0.329947i	$-0.892969\pi$
$227$	−9.25163	+	9.25163i	−0.614052	+	0.614052i	0.329947	+	0.943999i	$0.392969\pi$
$228$		0			0
$229$	20.7546	+	20.7546i	1.37150	+	1.37150i	0.858219	+	0.513284i	$0.171571\pi$
$229$	20.7546	+	20.7546i	1.37150	+	1.37150i	0.513284	+	0.858219i	$0.328429\pi$
$230$		0			0
$231$		−	5.70733i		−	0.375515i
$232$		0			0
$233$			19.9887i			1.30950i	0.755845	+	0.654751i	$0.227226\pi$
$233$			19.9887i			1.30950i	−0.755845	+	0.654751i	$0.772774\pi$
$234$		0			0
$235$	−1.91811	−	1.91811i	−0.125124	−	0.125124i
$236$		0			0
$237$	−20.3155	+	20.3155i	−1.31963	+	1.31963i
$238$		0			0
$239$	24.2947			1.57149			0.785746	−	0.618549i	$-0.212279\pi$
$239$	24.2947			1.57149			0.785746	+	0.618549i	$0.212279\pi$
$240$		0			0
$241$	2.13694			0.137652			0.0688262	−	0.997629i	$-0.478075\pi$
$241$	2.13694			0.137652			0.0688262	+	0.997629i	$0.478075\pi$
$242$		0			0
$243$	−2.03875	+	2.03875i	−0.130786	+	0.130786i
$244$		0			0
$245$	−0.707107	−	0.707107i	−0.0451754	−	0.0451754i
$246$		0			0
$247$		−	1.51422i		−	0.0963478i
$248$		0			0
$249$			11.5829i			0.734034i
$250$		0			0
$251$	−2.25569	−	2.25569i	−0.142378	−	0.142378i	0.632325	−	0.774703i	$-0.282101\pi$
$251$	−2.25569	−	2.25569i	−0.142378	−	0.142378i	−0.774703	+	0.632325i	$0.782101\pi$
$252$		0			0
$253$	10.0004	−	10.0004i	0.628718	−	0.628718i
$254$		0			0
$255$	−1.45890			−0.0913600
$256$		0			0
$257$	−28.0927			−1.75238			−0.876188	−	0.481969i	$-0.839922\pi$
$257$	−28.0927			−1.75238			−0.876188	+	0.481969i	$0.839922\pi$
$258$		0			0
$259$	−7.31260	+	7.31260i	−0.454383	+	0.454383i
$260$		0			0
$261$	0.0161944	+	0.0161944i	0.00100241	+	0.00100241i
$262$		0			0
$263$		−	11.8279i		−	0.729339i	−0.931137	−	0.364670i	$-0.881182\pi$
$263$		−	11.8279i		−	0.729339i	0.931137	−	0.364670i	$-0.118818\pi$
$264$		0			0
$265$		−	10.1726i		−	0.624895i
$266$		0			0
$267$	3.76476	+	3.76476i	0.230400	+	0.230400i
$268$		0			0
$269$	−14.5788	+	14.5788i	−0.888887	+	0.888887i	−0.994416	−	0.105529i	$-0.966346\pi$
$269$	−14.5788	+	14.5788i	−0.888887	+	0.888887i	0.105529	+	0.994416i	$0.466346\pi$
$270$		0			0
$271$	20.1581			1.22452			0.612260	−	0.790657i	$-0.290261\pi$
$271$	20.1581			1.22452			0.612260	+	0.790657i	$0.290261\pi$
$272$		0			0
$273$	1.93540			0.117136
$274$		0			0
$275$	2.22891	−	2.22891i	0.134408	−	0.134408i
$276$		0			0
$277$	4.07943	+	4.07943i	0.245109	+	0.245109i	0.818960	−	0.573851i	$-0.194551\pi$
$277$	4.07943	+	4.07943i	0.245109	+	0.245109i	−0.573851	+	0.818960i	$0.694551\pi$
$278$		0			0
$279$			1.31630i			0.0788051i
$280$		0			0
$281$			6.75695i			0.403086i	0.979480	+	0.201543i	$0.0645955\pi$
$281$			6.75695i			0.403086i	−0.979480	+	0.201543i	$0.935404\pi$
$282$		0			0
$283$	−16.9193	−	16.9193i	−1.00575	−	1.00575i	−0.999983	−	0.00576414i	$-0.998165\pi$
$283$	−16.9193	−	16.9193i	−1.00575	−	1.00575i	−0.00576414	−	0.999983i	$-0.501835\pi$
$284$		0			0
$285$	−1.81366	+	1.81366i	−0.107432	+	0.107432i
$286$		0			0
$287$	−1.66826			−0.0984741
$288$		0			0
$289$	−16.3508			−0.961810
$290$		0			0
$291$	16.7341	−	16.7341i	0.980972	−	0.980972i
$292$		0			0
$293$	−6.61686	−	6.61686i	−0.386561	−	0.386561i	0.486898	−	0.873459i	$-0.338128\pi$
$293$	−6.61686	−	6.61686i	−0.386561	−	0.386561i	−0.873459	+	0.486898i	$0.838128\pi$
$294$		0			0
$295$		−	0.217426i		−	0.0126591i
$296$		0			0
$297$			15.5336i			0.901350i
$298$		0			0
$299$	3.39120	+	3.39120i	0.196118	+	0.196118i
$300$		0			0
$301$	−2.71794	+	2.71794i	−0.156659	+	0.156659i
$302$		0			0
$303$	20.5553			1.18087
$304$		0			0
$305$	4.48425			0.256767
$306$		0			0
$307$	−10.2767	+	10.2767i	−0.586521	+	0.586521i	−0.936687	−	0.350166i	$-0.886125\pi$
$307$	−10.2767	+	10.2767i	−0.586521	+	0.586521i	0.350166	+	0.936687i	$0.386125\pi$
$308$		0			0
$309$	1.42106	+	1.42106i	0.0808413	+	0.0808413i
$310$		0			0
$311$		−	1.82679i		−	0.103588i	−0.998658	−	0.0517938i	$-0.983506\pi$
$311$		−	1.82679i		−	0.103588i	0.998658	−	0.0517938i	$-0.0164939\pi$
$312$		0			0
$313$			20.0503i			1.13331i	0.823955	+	0.566655i	$0.191763\pi$
$313$			20.0503i			1.13331i	−0.823955	+	0.566655i	$0.808237\pi$
$314$		0			0
$315$	−0.196795	−	0.196795i	−0.0110881	−	0.0110881i
$316$		0			0
$317$	−20.2513	+	20.2513i	−1.13743	+	1.13743i	−0.148519	+	0.988910i	$0.547451\pi$
$317$	−20.2513	+	20.2513i	−1.13743	+	1.13743i	−0.988910	+	0.148519i	$0.952549\pi$
$318$		0			0
$319$	0.259394			0.0145233
$320$		0			0
$321$	−22.8207			−1.27373
$322$		0			0
$323$	0.807107	−	0.807107i	0.0449087	−	0.0449087i
$324$		0			0
$325$	0.755840	+	0.755840i	0.0419265	+	0.0419265i
$326$		0			0
$327$			9.19201i			0.508319i
$328$		0			0
$329$			2.71262i			0.149552i
$330$		0			0
$331$	14.1733	+	14.1733i	0.779038	+	0.779038i	0.979667	−	0.200630i	$-0.0642988\pi$
$331$	14.1733	+	14.1733i	0.779038	+	0.779038i	−0.200630	+	0.979667i	$0.564299\pi$
$332$		0			0
$333$	−2.03517	+	2.03517i	−0.111527	+	0.111527i
$334$		0			0
$335$	−3.36953			−0.184097
$336$		0			0
$337$	1.99463			0.108654			0.0543272	−	0.998523i	$-0.482699\pi$
$337$	1.99463			0.108654			0.0543272	+	0.998523i	$0.482699\pi$
$338$		0			0
$339$	−17.9596	+	17.9596i	−0.975433	+	0.975433i
$340$		0			0
$341$	10.5419	+	10.5419i	0.570877	+	0.570877i
$342$		0			0
$343$			1.00000i			0.0539949i
$344$		0			0
$345$		−	8.12360i		−	0.437360i
$346$		0			0
$347$	14.0205	+	14.0205i	0.752657	+	0.752657i	0.974974	−	0.222317i	$-0.0713620\pi$
$347$	14.0205	+	14.0205i	0.752657	+	0.752657i	−0.222317	+	0.974974i	$0.571362\pi$
$348$		0			0
$349$	20.3320	−	20.3320i	1.08834	−	1.08834i	0.0926456	−	0.995699i	$-0.470468\pi$
$349$	20.3320	−	20.3320i	1.08834	−	1.08834i	0.995699	−	0.0926456i	$-0.0295323\pi$
$350$		0			0
$351$	−5.26755			−0.281161
$352$		0			0
$353$	−11.0734			−0.589379			−0.294690	−	0.955593i	$-0.595216\pi$
$353$	−11.0734			−0.589379			−0.294690	+	0.955593i	$0.595216\pi$
$354$		0			0
$355$	−1.14352	+	1.14352i	−0.0606917	+	0.0606917i
$356$		0			0
$357$	1.03160	+	1.03160i	0.0545980	+	0.0545980i
$358$		0			0
$359$		−	17.7068i		−	0.934529i	−0.884118	−	0.467265i	$-0.845240\pi$
$359$		−	17.7068i		−	0.934529i	0.884118	−	0.467265i	$-0.154760\pi$
$360$		0			0
$361$			16.9933i			0.894382i
$362$		0			0
$363$	1.36211	+	1.36211i	0.0714924	+	0.0714924i
$364$		0			0
$365$	1.20257	−	1.20257i	0.0629453	−	0.0629453i
$366$		0			0
$367$	−29.5032			−1.54006			−0.770028	−	0.638010i	$-0.779758\pi$
$367$	−29.5032			−1.54006			−0.770028	+	0.638010i	$0.779758\pi$
$368$		0			0
$369$	−0.464293			−0.0241701
$370$		0			0
$371$	−7.19308	+	7.19308i	−0.373446	+	0.373446i
$372$		0			0
$373$	−4.07867	−	4.07867i	−0.211185	−	0.211185i	0.593586	−	0.804771i	$-0.297712\pi$
$373$	−4.07867	−	4.07867i	−0.211185	−	0.211185i	−0.804771	+	0.593586i	$0.797712\pi$
$374$		0			0
$375$		−	1.81061i		−	0.0934995i
$376$		0			0
$377$			0.0879623i			0.00453029i
$378$		0			0
$379$	−5.01908	−	5.01908i	−0.257813	−	0.257813i	0.566351	−	0.824164i	$-0.308355\pi$
$379$	−5.01908	−	5.01908i	−0.257813	−	0.257813i	−0.824164	+	0.566351i	$0.808355\pi$
$380$		0			0
$381$	21.3374	−	21.3374i	1.09315	−	1.09315i
$382$		0			0
$383$	−10.0609			−0.514088			−0.257044	−	0.966400i	$-0.582748\pi$
$383$	−10.0609			−0.514088			−0.257044	+	0.966400i	$0.582748\pi$
$384$		0			0
$385$	−3.15216			−0.160649
$386$		0			0
$387$	−0.756429	+	0.756429i	−0.0384515	+	0.0384515i
$388$		0			0
$389$	−3.40872	−	3.40872i	−0.172829	−	0.172829i	0.615392	−	0.788221i	$-0.288998\pi$
$389$	−3.40872	−	3.40872i	−0.172829	−	0.172829i	−0.788221	+	0.615392i	$0.788998\pi$
$390$		0			0
$391$			3.61514i			0.182825i
$392$		0			0
$393$			19.0486i			0.960876i
$394$		0			0
$395$	11.2202	+	11.2202i	0.564552	+	0.564552i
$396$		0			0
$397$	−17.8188	+	17.8188i	−0.894301	+	0.894301i	−0.994925	−	0.100624i	$-0.967916\pi$
$397$	−17.8188	+	17.8188i	−0.894301	+	0.894301i	0.100624	+	0.994925i	$0.467916\pi$
$398$		0			0
$399$	2.56490			0.128406
$400$		0			0
$401$	19.0095			0.949288			0.474644	−	0.880178i	$-0.342577\pi$
$401$	19.0095			0.949288			0.474644	+	0.880178i	$0.342577\pi$
$402$		0			0
$403$	−3.57484	+	3.57484i	−0.178076	+	0.178076i
$404$		0			0
$405$	6.89958	+	6.89958i	0.342843	+	0.342843i
$406$		0			0
$407$			32.5983i			1.61584i
$408$		0			0
$409$			39.2985i			1.94318i	0.236663	+	0.971592i	$0.423946\pi$
$409$			39.2985i			1.94318i	−0.236663	+	0.971592i	$0.576054\pi$
$410$		0			0
$411$	6.19238	+	6.19238i	0.305447	+	0.305447i
$412$		0			0
$413$	−0.153744	+	0.153744i	−0.00756523	+	0.00756523i
$414$		0			0
$415$	6.39721			0.314027
$416$		0			0
$417$	30.7285			1.50478
$418$		0			0
$419$	−28.7053	+	28.7053i	−1.40234	+	1.40234i	−0.609754	+	0.792591i	$0.708732\pi$
$419$	−28.7053	+	28.7053i	−1.40234	+	1.40234i	−0.792591	+	0.609754i	$0.791268\pi$
$420$		0			0
$421$	−15.2329	−	15.2329i	−0.742404	−	0.742404i	0.230636	−	0.973040i	$-0.425919\pi$
$421$	−15.2329	−	15.2329i	−0.742404	−	0.742404i	−0.973040	+	0.230636i	$0.925919\pi$
$422$		0			0
$423$			0.754951i			0.0367070i
$424$		0			0
$425$			0.805751i			0.0390847i
$426$		0			0
$427$	−3.17084	−	3.17084i	−0.153448	−	0.153448i
$428$		0			0
$429$	4.31383	−	4.31383i	0.208274	−	0.208274i
$430$		0			0
$431$	4.21616			0.203085			0.101543	−	0.994831i	$-0.467622\pi$
$431$	4.21616			0.203085			0.101543	+	0.994831i	$0.467622\pi$
$432$		0			0
$433$	−23.5263			−1.13060			−0.565302	−	0.824884i	$-0.691240\pi$
$433$	−23.5263			−1.13060			−0.565302	+	0.824884i	$0.691240\pi$
$434$		0			0
$435$	0.105357	−	0.105357i	0.00505146	−	0.00505146i
$436$		0			0
$437$	4.49421	+	4.49421i	0.214987	+	0.214987i
$438$		0			0
$439$			14.9845i			0.715170i	0.933881	+	0.357585i	$0.116400\pi$
$439$			14.9845i			0.715170i	−0.933881	+	0.357585i	$0.883600\pi$
$440$		0			0
$441$			0.278310i			0.0132529i
$442$		0			0
$443$	15.5887	+	15.5887i	0.740644	+	0.740644i	0.972702	−	0.232058i	$-0.0745460\pi$
$443$	15.5887	+	15.5887i	0.740644	+	0.740644i	−0.232058	+	0.972702i	$0.574546\pi$
$444$		0			0
$445$	2.07928	−	2.07928i	0.0985672	−	0.0985672i
$446$		0			0
$447$	4.71392			0.222961
$448$		0			0
$449$	−23.8125			−1.12378			−0.561891	−	0.827211i	$-0.689926\pi$
$449$	−23.8125			−1.12378			−0.561891	+	0.827211i	$0.689926\pi$
$450$		0			0
$451$	−3.71840	+	3.71840i	−0.175092	+	0.175092i
$452$		0			0
$453$	23.5843	+	23.5843i	1.10809	+	1.10809i
$454$		0			0
$455$		−	1.06892i		−	0.0501117i
$456$		0			0
$457$		−	15.6350i		−	0.731374i	−0.930738	−	0.365687i	$-0.880834\pi$
$457$		−	15.6350i		−	0.731374i	0.930738	−	0.365687i	$-0.119166\pi$
$458$		0			0
$459$	−2.80769	−	2.80769i	−0.131052	−	0.131052i
$460$		0			0
$461$	−0.243499	+	0.243499i	−0.0113409	+	0.0113409i	−0.712754	−	0.701414i	$-0.752553\pi$
$461$	−0.243499	+	0.243499i	−0.0113409	+	0.0113409i	0.701414	+	0.712754i	$0.252553\pi$
$462$		0			0
$463$	−31.8764			−1.48142			−0.740710	−	0.671825i	$-0.765511\pi$
$463$	−31.8764			−1.48142			−0.740710	+	0.671825i	$0.765511\pi$
$464$		0			0
$465$	8.56352			0.397124
$466$		0			0
$467$	13.7167	−	13.7167i	0.634731	−	0.634731i	−0.314520	−	0.949251i	$-0.601843\pi$
$467$	13.7167	−	13.7167i	0.634731	−	0.634731i	0.949251	+	0.314520i	$0.101843\pi$
$468$		0			0
$469$	2.38261	+	2.38261i	0.110019	+	0.110019i
$470$		0			0
$471$			7.85269i			0.361833i
$472$		0			0
$473$			12.1161i			0.557098i
$474$		0			0
$475$	1.00168	+	1.00168i	0.0459604	+	0.0459604i
$476$		0			0
$477$	−2.00191	+	2.00191i	−0.0916611	+	0.0916611i
$478$		0			0
$479$	−21.0543			−0.961994			−0.480997	−	0.876722i	$-0.659725\pi$
$479$	−21.0543			−0.961994			−0.480997	+	0.876722i	$0.659725\pi$
$480$		0			0
$481$	−11.0543			−0.504033
$482$		0			0
$483$	−5.74425	+	5.74425i	−0.261372	+	0.261372i
$484$		0			0
$485$	−9.24226	−	9.24226i	−0.419670	−	0.419670i
$486$		0			0
$487$			11.4018i			0.516664i	0.966056	+	0.258332i	$0.0831728\pi$
$487$			11.4018i			0.516664i	−0.966056	+	0.258332i	$0.916827\pi$
$488$		0			0
$489$		−	37.0306i		−	1.67458i
$490$		0			0
$491$	15.9747	+	15.9747i	0.720927	+	0.720927i	0.968794	−	0.247867i	$-0.0797297\pi$
$491$	15.9747	+	15.9747i	0.720927	+	0.720927i	−0.247867	+	0.968794i	$0.579730\pi$
$492$		0			0
$493$	−0.0468854	+	0.0468854i	−0.00211161	+	0.00211161i
$494$		0			0
$495$	−0.877278			−0.0394307
$496$		0			0
$497$	1.61718			0.0725405
$498$		0			0
$499$	−6.27270	+	6.27270i	−0.280805	+	0.280805i	−0.833430	−	0.552625i	$-0.813626\pi$
$499$	−6.27270	+	6.27270i	−0.280805	+	0.280805i	0.552625	+	0.833430i	$0.313626\pi$
$500$		0			0
$501$	15.5614	+	15.5614i	0.695232	+	0.695232i
$502$		0			0
$503$			3.59037i			0.160087i	0.996791	+	0.0800434i	$0.0255059\pi$
$503$			3.59037i			0.160087i	−0.996791	+	0.0800434i	$0.974494\pi$
$504$		0			0
$505$		−	11.3527i		−	0.505188i
$506$		0			0
$507$	−15.1810	−	15.1810i	−0.674211	−	0.674211i
$508$		0			0
$509$	3.40927	−	3.40927i	0.151113	−	0.151113i	−0.627502	−	0.778615i	$-0.715922\pi$
$509$	3.40927	−	3.40927i	0.151113	−	0.151113i	0.778615	+	0.627502i	$0.215922\pi$
$510$		0			0
$511$	−1.70069			−0.0752340
$512$		0			0
$513$	−6.98086			−0.308212
$514$		0			0
$515$	0.784851	−	0.784851i	0.0345847	−	0.0345847i
$516$		0			0
$517$	6.04620	+	6.04620i	0.265911	+	0.265911i
$518$		0			0
$519$			29.7296i			1.30498i
$520$		0			0
$521$		−	7.25314i		−	0.317766i	−0.987297	−	0.158883i	$-0.949211\pi$
$521$		−	7.25314i		−	0.317766i	0.987297	−	0.158883i	$-0.0507892\pi$
$522$		0			0
$523$	−24.3995	−	24.3995i	−1.06692	−	1.06692i	−0.997594	−	0.0693224i	$-0.977916\pi$
$523$	−24.3995	−	24.3995i	−1.06692	−	1.06692i	−0.0693224	−	0.997594i	$-0.522084\pi$
$524$		0			0
$525$	−1.28029	+	1.28029i	−0.0558767	+	0.0558767i
$526$		0			0
$527$	−3.81091			−0.166006
$528$		0			0
$529$	2.86986			0.124776
$530$		0			0
$531$	−0.0427884	+	0.0427884i	−0.00185686	+	0.00185686i
$532$		0			0
$533$	−1.26094	−	1.26094i	−0.0546172	−	0.0546172i
$534$		0			0
$535$			12.6039i			0.544914i
$536$		0			0
$537$		−	12.7426i		−	0.549885i
$538$		0			0
$539$	2.22891	+	2.22891i	0.0960060	+	0.0960060i
$540$		0			0
$541$	−2.07554	+	2.07554i	−0.0892344	+	0.0892344i	−0.750315	−	0.661081i	$-0.770098\pi$
$541$	−2.07554	+	2.07554i	−0.0892344	+	0.0892344i	0.661081	+	0.750315i	$0.270098\pi$
$542$		0			0
$543$	38.0983			1.63495
$544$		0			0
$545$	5.07674			0.217464
$546$		0			0
$547$	−7.13186	+	7.13186i	−0.304937	+	0.304937i	−0.842942	−	0.538005i	$-0.819178\pi$
$547$	−7.13186	+	7.13186i	−0.304937	+	0.304937i	0.538005	+	0.842942i	$0.319178\pi$
$548$		0			0
$549$	−0.882479	−	0.882479i	−0.0376633	−	0.0376633i
$550$		0			0
$551$			0.116573i			0.00496617i
$552$		0			0
$553$		−	15.8678i		−	0.674768i
$554$		0			0
$555$	13.2403	+	13.2403i	0.562018	+	0.562018i
$556$		0			0
$557$	0.181907	−	0.181907i	0.00770763	−	0.00770763i	−0.703242	−	0.710950i	$-0.748265\pi$
$557$	0.181907	−	0.181907i	0.00770763	−	0.00770763i	0.710950	+	0.703242i	$0.248265\pi$
$558$		0			0
$559$	−4.10865			−0.173777
$560$		0			0
$561$	4.59869			0.194157
$562$		0			0
$563$	24.5594	−	24.5594i	1.03505	−	1.03505i	0.0356908	−	0.999363i	$-0.488637\pi$
$563$	24.5594	−	24.5594i	1.03505	−	1.03505i	0.999363	−	0.0356908i	$-0.0113631\pi$
$564$		0			0
$565$	9.91910	+	9.91910i	0.417300	+	0.417300i
$566$		0			0
$567$		−	9.75747i		−	0.409775i
$568$		0			0
$569$		−	15.1936i		−	0.636951i	−0.947931	−	0.318475i	$-0.896829\pi$
$569$		−	15.1936i		−	0.636951i	0.947931	−	0.318475i	$-0.103171\pi$
$570$		0			0
$571$	−2.34108	−	2.34108i	−0.0979710	−	0.0979710i	0.656422	−	0.754393i	$-0.272069\pi$
$571$	−2.34108	−	2.34108i	−0.0979710	−	0.0979710i	−0.754393	+	0.656422i	$0.772069\pi$
$572$		0			0
$573$	−20.5856	+	20.5856i	−0.859975	+	0.859975i
$574$		0			0
$575$	−4.48666			−0.187107
$576$		0			0
$577$	9.43346			0.392720			0.196360	−	0.980532i	$-0.437088\pi$
$577$	9.43346			0.392720			0.196360	+	0.980532i	$0.437088\pi$
$578$		0			0
$579$	−27.7167	+	27.7167i	−1.15187	+	1.15187i
$580$		0			0
$581$	−4.52351	−	4.52351i	−0.187667	−	0.187667i
$582$		0			0
$583$			32.0655i			1.32802i
$584$		0			0
$585$		−	0.297491i		−	0.0122997i
$586$		0			0
$587$	26.2760	+	26.2760i	1.08453	+	1.08453i	0.996081	+	0.0884455i	$0.0281899\pi$
$587$	26.2760	+	26.2760i	1.08453	+	1.08453i	0.0884455	+	0.996081i	$0.471810\pi$
$588$		0			0
$589$	−4.73759	+	4.73759i	−0.195209	+	0.195209i
$590$		0			0
$591$	29.1440			1.19883
$592$		0			0
$593$	32.0643			1.31672			0.658361	−	0.752702i	$-0.271250\pi$
$593$	32.0643			1.31672			0.658361	+	0.752702i	$0.271250\pi$
$594$		0			0
$595$	0.569752	−	0.569752i	0.0233576	−	0.0233576i
$596$		0			0
$597$	33.1427	+	33.1427i	1.35644	+	1.35644i
$598$		0			0
$599$			16.8990i			0.690474i	0.938516	+	0.345237i	$0.112201\pi$
$599$			16.8990i			0.690474i	−0.938516	+	0.345237i	$0.887799\pi$
$600$		0			0
$601$			8.61332i			0.351345i	0.984449	+	0.175672i	$0.0562099\pi$
$601$			8.61332i			0.351345i	−0.984449	+	0.175672i	$0.943790\pi$
$602$		0			0
$603$	0.663106	+	0.663106i	0.0270038	+	0.0270038i
$604$		0			0
$605$	0.752294	−	0.752294i	0.0305851	−	0.0305851i
$606$		0			0
$607$	−9.40889			−0.381895			−0.190948	−	0.981600i	$-0.561156\pi$
$607$	−9.40889			−0.381895			−0.190948	+	0.981600i	$0.561156\pi$
$608$		0			0
$609$	−0.148997			−0.00603765
$610$		0			0
$611$	−2.05031	+	2.05031i	−0.0829466	+	0.0829466i
$612$		0			0
$613$	−28.2463	−	28.2463i	−1.14086	−	1.14086i	−0.988294	−	0.152562i	$-0.951248\pi$
$613$	−28.2463	−	28.2463i	−1.14086	−	1.14086i	−0.152562	−	0.988294i	$-0.548752\pi$
$614$		0			0
$615$			3.02056i			0.121801i
$616$		0			0
$617$		−	27.4121i		−	1.10357i	−0.833987	−	0.551784i	$-0.813947\pi$
$617$		−	27.4121i		−	1.10357i	0.833987	−	0.551784i	$-0.186053\pi$
$618$		0			0
$619$	−1.57549	−	1.57549i	−0.0633241	−	0.0633241i	0.674736	−	0.738060i	$-0.264258\pi$
$619$	−1.57549	−	1.57549i	−0.0633241	−	0.0633241i	−0.738060	+	0.674736i	$0.764258\pi$
$620$		0			0
$621$	15.6341	−	15.6341i	0.627374	−	0.627374i
$622$		0			0
$623$	−2.94054			−0.117810
$624$		0			0
$625$	−1.00000			−0.0400000
$626$		0			0
$627$	5.71693	−	5.71693i	0.228312	−	0.228312i
$628$		0			0
$629$	−5.89213	−	5.89213i	−0.234935	−	0.234935i
$630$		0			0
$631$			8.93549i			0.355716i	0.984056	+	0.177858i	$0.0569168\pi$
$631$			8.93549i			0.355716i	−0.984056	+	0.177858i	$0.943083\pi$
$632$		0			0
$633$			23.6906i			0.941615i
$634$		0			0
$635$	−11.7846	−	11.7846i	−0.467658	−	0.467658i
$636$		0			0
$637$	−0.755840	+	0.755840i	−0.0299475	+	0.0299475i
$638$		0			0
$639$	0.450078			0.0178048
$640$		0			0
$641$	29.8424			1.17870			0.589351	−	0.807877i	$-0.299383\pi$
$641$	29.8424			1.17870			0.589351	+	0.807877i	$0.299383\pi$
$642$		0			0
$643$	−5.57031	+	5.57031i	−0.219671	+	0.219671i	−0.808360	−	0.588689i	$-0.799644\pi$
$643$	−5.57031	+	5.57031i	−0.219671	+	0.219671i	0.588689	+	0.808360i	$0.299644\pi$
$644$		0			0
$645$	4.92112	+	4.92112i	0.193769	+	0.193769i
$646$		0			0
$647$		−	25.2784i		−	0.993795i	−0.867809	−	0.496898i	$-0.834472\pi$
$647$		−	25.2784i		−	0.993795i	0.867809	−	0.496898i	$-0.165528\pi$
$648$		0			0
$649$			0.685362i			0.0269028i
$650$		0			0
$651$	−6.05532	−	6.05532i	−0.237327	−	0.237327i
$652$		0			0
$653$	−8.16666	+	8.16666i	−0.319586	+	0.319586i	−0.848608	−	0.529022i	$-0.822559\pi$
$653$	−8.16666	+	8.16666i	−0.319586	+	0.319586i	0.529022	+	0.848608i	$0.322559\pi$
$654$		0			0
$655$	10.5206			0.411072
$656$		0			0
$657$	−0.473319			−0.0184659
$658$		0			0
$659$	21.2377	−	21.2377i	0.827303	−	0.827303i	−0.159840	−	0.987143i	$-0.551098\pi$
$659$	21.2377	−	21.2377i	0.827303	−	0.827303i	0.987143	+	0.159840i	$0.0510977\pi$
$660$		0			0
$661$	−14.4061	−	14.4061i	−0.560333	−	0.560333i	0.369069	−	0.929402i	$-0.379677\pi$
$661$	−14.4061	−	14.4061i	−0.560333	−	0.560333i	−0.929402	+	0.369069i	$0.879677\pi$
$662$		0			0
$663$			1.55945i			0.0605640i
$664$		0			0
$665$		−	1.41659i		−	0.0549331i
$666$		0			0
$667$	−0.261072	−	0.261072i	−0.0101087	−	0.0101087i
$668$		0			0
$669$	25.7503	−	25.7503i	0.995563	−	0.995563i
$670$		0			0
$671$	−14.1351			−0.545678
$672$		0			0
$673$	−19.4428			−0.749465			−0.374732	−	0.927133i	$-0.622265\pi$
$673$	−19.4428			−0.749465			−0.374732	+	0.927133i	$0.622265\pi$
$674$		0			0
$675$	3.48457	−	3.48457i	0.134121	−	0.134121i
$676$		0			0
$677$	29.5302	+	29.5302i	1.13494	+	1.13494i	0.989344	+	0.145594i	$0.0465094\pi$
$677$	29.5302	+	29.5302i	1.13494	+	1.13494i	0.145594	+	0.989344i	$0.453491\pi$
$678$		0			0
$679$			13.0705i			0.501601i
$680$		0			0
$681$		−	23.6896i		−	0.907789i
$682$		0			0
$683$	16.5736	+	16.5736i	0.634172	+	0.634172i	0.949112	−	0.314940i	$-0.101984\pi$
$683$	16.5736	+	16.5736i	0.634172	+	0.634172i	−0.314940	+	0.949112i	$0.601984\pi$
$684$		0			0
$685$	3.42005	−	3.42005i	0.130673	−	0.130673i
$686$		0			0
$687$	−53.1440			−2.02757
$688$		0			0
$689$	−10.8736			−0.414253
$690$		0			0
$691$	13.6441	−	13.6441i	0.519046	−	0.519046i	−0.398237	−	0.917283i	$-0.630378\pi$
$691$	13.6441	−	13.6441i	0.519046	−	0.519046i	0.917283	+	0.398237i	$0.130378\pi$
$692$		0			0
$693$	0.620329	+	0.620329i	0.0235644	+	0.0235644i
$694$		0			0
$695$		−	16.9713i		−	0.643760i
$696$		0			0
$697$		−	1.34420i		−	0.0509152i
$698$		0			0
$699$	−25.5914	−	25.5914i	−0.967955	−	0.967955i
$700$		0			0
$701$	−8.26656	+	8.26656i	−0.312224	+	0.312224i	−0.845771	−	0.533547i	$-0.820859\pi$
$701$	−8.26656	+	8.26656i	−0.312224	+	0.312224i	0.533547	+	0.845771i	$0.320859\pi$
$702$		0			0
$703$	−14.6498			−0.552528
$704$		0			0
$705$	4.91150			0.184978
$706$		0			0
$707$	−8.02757	+	8.02757i	−0.301908	+	0.301908i
$708$		0			0
$709$	−15.6244	−	15.6244i	−0.586786	−	0.586786i	0.349974	−	0.936760i	$-0.386191\pi$
$709$	−15.6244	−	15.6244i	−0.586786	−	0.586786i	−0.936760	+	0.349974i	$0.886191\pi$
$710$		0			0
$711$		−	4.41618i		−	0.165620i
$712$		0			0
$713$		−	21.2203i		−	0.794705i
$714$		0			0
$715$	−2.38253	−	2.38253i	−0.0891015	−	0.0891015i
$716$		0			0
$717$	−31.1044	+	31.1044i	−1.16161	+	1.16161i
$718$		0			0
$719$	20.7843			0.775125			0.387563	−	0.921843i	$-0.373317\pi$
$719$	20.7843			0.775125			0.387563	+	0.921843i	$0.373317\pi$
$720$		0			0
$721$	−1.10995			−0.0413366
$722$		0			0
$723$	−2.73591	+	2.73591i	−0.101750	+	0.101750i
$724$		0			0
$725$	−0.0581885	−	0.0581885i	−0.00216106	−	0.00216106i
$726$		0			0
$727$			50.9962i			1.89134i	0.325124	+	0.945671i	$0.394594\pi$
$727$			50.9962i			1.89134i	−0.325124	+	0.945671i	$0.605406\pi$
$728$		0			0
$729$			24.0520i			0.890816i
$730$		0			0
$731$	−2.18998	−	2.18998i	−0.0809994	−	0.0809994i
$732$		0			0
$733$	37.5556	−	37.5556i	1.38715	−	1.38715i	0.555891	−	0.831255i	$-0.312377\pi$
$733$	37.5556	−	37.5556i	1.38715	−	1.38715i	0.831255	−	0.555891i	$-0.187623\pi$
$734$		0			0
$735$	1.81061			0.0667854
$736$		0			0
$737$	10.6213			0.391240
$738$		0			0
$739$	−6.74839	+	6.74839i	−0.248243	+	0.248243i	−0.820249	−	0.572006i	$-0.806165\pi$
$739$	−6.74839	+	6.74839i	−0.248243	+	0.248243i	0.572006	+	0.820249i	$0.306165\pi$
$740$		0			0
$741$	1.93865	+	1.93865i	0.0712182	+	0.0712182i
$742$		0			0
$743$			17.1716i			0.629964i	0.949098	+	0.314982i	$0.101998\pi$
$743$			17.1716i			0.629964i	−0.949098	+	0.314982i	$0.898002\pi$
$744$		0			0
$745$		−	2.60350i		−	0.0953847i
$746$		0			0
$747$	−1.25894	−	1.25894i	−0.0460622	−	0.0460622i
$748$		0			0
$749$	8.91230	−	8.91230i	0.325648	−	0.325648i
$750$		0			0
$751$	−9.40072			−0.343037			−0.171519	−	0.985181i	$-0.554867\pi$
$751$	−9.40072			−0.343037			−0.171519	+	0.985181i	$0.554867\pi$
$752$		0			0
$753$	5.77590			0.210486
$754$		0			0
$755$	13.0256	−	13.0256i	0.474051	−	0.474051i
$756$		0			0
$757$	−25.9738	−	25.9738i	−0.944032	−	0.944032i	0.0544824	−	0.998515i	$-0.482649\pi$
$757$	−25.9738	−	25.9738i	−0.944032	−	0.944032i	−0.998515	+	0.0544824i	$0.982649\pi$
$758$		0			0
$759$			25.6069i			0.929470i
$760$		0			0
$761$		−	27.5184i		−	0.997542i	−0.866734	−	0.498771i	$-0.833785\pi$
$761$		−	27.5184i		−	0.997542i	0.866734	−	0.498771i	$-0.166215\pi$
$762$		0			0
$763$	−3.58980	−	3.58980i	−0.129959	−	0.129959i
$764$		0			0
$765$	0.158568	−	0.158568i	0.00573304	−	0.00573304i
$766$		0			0
$767$	−0.232411			−0.00839188
$768$		0			0
$769$	−34.6525			−1.24960			−0.624800	−	0.780785i	$-0.714820\pi$
$769$	−34.6525			−1.24960			−0.624800	+	0.780785i	$0.714820\pi$
$770$		0			0
$771$	35.9670	−	35.9670i	1.29532	−	1.29532i
$772$		0			0
$773$	−22.1926	−	22.1926i	−0.798212	−	0.798212i	0.184602	−	0.982813i	$-0.440901\pi$
$773$	−22.1926	−	22.1926i	−0.798212	−	0.798212i	−0.982813	+	0.184602i	$0.940901\pi$
$774$		0			0
$775$		−	4.72963i		−	0.169893i
$776$		0			0
$777$		−	18.7246i		−	0.671740i
$778$		0			0
$779$	−1.67106	−	1.67106i	−0.0598721	−	0.0598721i
$780$		0			0
$781$	3.60455	−	3.60455i	0.128981	−	0.128981i
$782$		0			0
$783$	0.405523			0.0144922
$784$		0			0
$785$	4.33704			0.154796
$786$		0			0
$787$	19.6511	−	19.6511i	0.700488	−	0.700488i	−0.264027	−	0.964515i	$-0.585051\pi$
$787$	19.6511	−	19.6511i	0.700488	−	0.700488i	0.964515	+	0.264027i	$0.0850510\pi$
$788$		0			0
$789$	15.1432	+	15.1432i	0.539112	+	0.539112i
$790$		0			0
$791$		−	14.0277i		−	0.498768i
$792$		0			0
$793$		−	4.79330i		−	0.170215i
$794$		0			0
$795$	13.0239	+	13.0239i	0.461909	+	0.461909i
$796$		0			0
$797$	0.760916	−	0.760916i	0.0269530	−	0.0269530i	−0.693502	−	0.720455i	$-0.743933\pi$
$797$	0.760916	−	0.760916i	0.0269530	−	0.0269530i	0.720455	+	0.693502i	$0.243933\pi$
$798$		0			0
$799$	−2.18570			−0.0773245
$800$		0			0
$801$	−0.818383			−0.0289161
$802$		0			0
$803$	−3.79068	+	3.79068i	−0.133770	+	0.133770i
$804$		0			0
$805$	3.17255	+	3.17255i	0.111818	+	0.111818i
$806$		0			0
$807$		−	37.3304i		−	1.31409i
$808$		0			0
$809$			10.6974i			0.376102i	0.982159	+	0.188051i	$0.0602171\pi$
$809$			10.6974i			0.376102i	−0.982159	+	0.188051i	$0.939783\pi$
$810$		0			0
$811$	−18.2823	−	18.2823i	−0.641977	−	0.641977i	0.309064	−	0.951041i	$-0.399984\pi$
$811$	−18.2823	−	18.2823i	−0.641977	−	0.641977i	−0.951041	+	0.309064i	$0.899984\pi$
$812$		0			0
$813$	−25.8084	+	25.8084i	−0.905139	+	0.905139i
$814$		0			0
$815$	−20.4520			−0.716403
$816$		0			0
$817$	−5.44502			−0.190497
$818$		0			0
$819$	−0.210358	+	0.210358i	−0.00735051	+	0.00735051i
$820$		0			0
$821$	19.6136	+	19.6136i	0.684521	+	0.684521i	0.961015	−	0.276495i	$-0.0891729\pi$
$821$	19.6136	+	19.6136i	0.684521	+	0.684521i	−0.276495	+	0.961015i	$0.589173\pi$
$822$		0			0
$823$		−	17.0719i		−	0.595090i	−0.954708	−	0.297545i	$-0.903832\pi$
$823$		−	17.0719i		−	0.595090i	0.954708	−	0.297545i	$-0.0961679\pi$
$824$		0			0
$825$			5.70733i			0.198704i
$826$		0			0
$827$	13.4725	+	13.4725i	0.468485	+	0.468485i	0.901423	−	0.432939i	$-0.142523\pi$
$827$	13.4725	+	13.4725i	0.468485	+	0.468485i	−0.432939	+	0.901423i	$0.642523\pi$
$828$		0			0
$829$	−24.9790	+	24.9790i	−0.867556	+	0.867556i	−0.992201	−	0.124645i	$-0.960221\pi$
$829$	−24.9790	+	24.9790i	−0.867556	+	0.867556i	0.124645	+	0.992201i	$0.460221\pi$
$830$		0			0
$831$	−10.4458			−0.362359
$832$		0			0
$833$	−0.805751			−0.0279176
$834$		0			0
$835$	8.59456	−	8.59456i	0.297427	−	0.297427i
$836$		0			0
$837$	16.4807	+	16.4807i	0.569656	+	0.569656i
$838$		0			0
$839$			0.431110i			0.0148836i	0.999972	+	0.00744178i	$0.00236881\pi$
$839$			0.431110i			0.0148836i	−0.999972	+	0.00744178i	$0.997631\pi$
$840$		0			0
$841$			28.9932i			0.999766i
$842$		0			0
$843$	−8.65088	−	8.65088i	−0.297952	−	0.297952i
$844$		0			0
$845$	−8.38446	+	8.38446i	−0.288434	+	0.288434i
$846$		0			0
$847$	−1.06391			−0.0365562
$848$		0			0
$849$	43.3234			1.48685
$850$		0			0
$851$	32.8092	−	32.8092i	1.12468	−	1.12468i
$852$		0			0
$853$	34.5024	+	34.5024i	1.18134	+	1.18134i	0.979397	+	0.201943i	$0.0647254\pi$
$853$	34.5024	+	34.5024i	1.18134	+	1.18134i	0.201943	+	0.979397i	$0.435275\pi$
$854$		0			0
$855$		−	0.394253i		−	0.0134832i
$856$		0			0
$857$			16.7259i			0.571346i	0.958327	+	0.285673i	$0.0922172\pi$
$857$			16.7259i			0.571346i	−0.958327	+	0.285673i	$0.907783\pi$
$858$		0			0
$859$	−12.2290	−	12.2290i	−0.417248	−	0.417248i	0.467006	−	0.884254i	$-0.345333\pi$
$859$	−12.2290	−	12.2290i	−0.417248	−	0.417248i	−0.884254	+	0.467006i	$0.845333\pi$
$860$		0			0
$861$	2.13586	−	2.13586i	0.0727899	−	0.0727899i
$862$		0			0
$863$	12.9352			0.440320			0.220160	−	0.975464i	$-0.429342\pi$
$863$	12.9352			0.440320			0.220160	+	0.975464i	$0.429342\pi$
$864$		0			0
$865$	16.4196			0.558285
$866$		0			0
$867$	20.9338	−	20.9338i	0.710949	−	0.710949i
$868$		0			0
$869$	−35.3680	−	35.3680i	−1.19978	−	1.19978i
$870$		0			0
$871$			3.60175i			0.122041i
$872$		0			0
$873$			3.63766i			0.123116i
$874$		0			0
$875$	0.707107	+	0.707107i	0.0239046	+	0.0239046i
$876$		0			0
$877$	−13.0399	+	13.0399i	−0.440328	+	0.440328i	−0.892122	−	0.451794i	$-0.850784\pi$
$877$	−13.0399	+	13.0399i	−0.440328	+	0.440328i	0.451794	+	0.892122i	$0.350784\pi$
$878$		0			0
$879$	16.9431			0.571475
$880$		0			0
$881$	46.0111			1.55015			0.775076	−	0.631868i	$-0.217711\pi$
$881$	46.0111			1.55015			0.775076	+	0.631868i	$0.217711\pi$
$882$		0			0
$883$	34.4773	−	34.4773i	1.16025	−	1.16025i	0.175832	−	0.984420i	$-0.443738\pi$
$883$	34.4773	−	34.4773i	1.16025	−	1.16025i	0.984420	−	0.175832i	$-0.0562617\pi$
$884$		0			0
$885$	0.278370	+	0.278370i	0.00935730	+	0.00935730i
$886$		0			0
$887$		−	26.1611i		−	0.878404i	−0.898388	−	0.439202i	$-0.855261\pi$
$887$		−	26.1611i		−	0.878404i	0.898388	−	0.439202i	$-0.144739\pi$
$888$		0			0
$889$			16.6660i			0.558959i
$890$		0			0
$891$	−21.7485	−	21.7485i	−0.728604	−	0.728604i
$892$		0			0
$893$	−2.71719	+	2.71719i	−0.0909272	+	0.0909272i
$894$		0			0
$895$	−7.03775			−0.235246
$896$		0			0
$897$	−8.68347			−0.289933
$898$		0			0
$899$	0.275210	−	0.275210i	0.00917876	−	0.00917876i
$900$		0			0
$901$	−5.79583	−	5.79583i	−0.193087	−	0.193087i
$902$		0			0
$903$		−	6.95952i		−	0.231598i
$904$		0			0
$905$		−	21.0417i		−	0.699448i
$906$		0			0
$907$	40.5336	+	40.5336i	1.34590	+	1.34590i	0.890068	+	0.455827i	$0.150656\pi$
$907$	40.5336	+	40.5336i	1.34590	+	1.34590i	0.455827	+	0.890068i	$0.349344\pi$
$908$		0			0
$909$	−2.23415	+	2.23415i	−0.0741022	+	0.0741022i
$910$		0			0
$911$	−19.3325			−0.640515			−0.320258	−	0.947330i	$-0.603770\pi$
$911$	−19.3325			−0.640515			−0.320258	+	0.947330i	$0.603770\pi$
$912$		0			0
$913$	−20.1650			−0.667365
$914$		0			0
$915$	−5.74116	+	5.74116i	−0.189797	+	0.189797i
$916$		0			0
$917$	−7.43916	−	7.43916i	−0.245663	−	0.245663i
$918$		0			0
$919$		−	26.1172i		−	0.861527i	−0.902465	−	0.430763i	$-0.858244\pi$
$919$		−	26.1172i		−	0.861527i	0.902465	−	0.430763i	$-0.141756\pi$
$920$		0			0
$921$		−	26.3144i		−	0.867088i
$922$		0			0
$923$	1.22233	+	1.22233i	0.0402335	+	0.0402335i
$924$		0			0
$925$	7.31260	−	7.31260i	0.240437	−	0.240437i
$926$		0			0
$927$	−0.308910			−0.0101459
$928$		0			0
$929$	−13.6349			−0.447346			−0.223673	−	0.974664i	$-0.571805\pi$
$929$	−13.6349			−0.447346			−0.223673	+	0.974664i	$0.571805\pi$
$930$		0			0
$931$	−1.00168	+	1.00168i	−0.0328288	+	0.0328288i
$932$		0			0
$933$	2.33883	+	2.33883i	0.0765698	+	0.0765698i
$934$		0			0
$935$		−	2.53986i		−	0.0830621i
$936$		0			0
$937$			10.4918i			0.342751i	0.985206	+	0.171376i	$0.0548211\pi$
$937$			10.4918i			0.342751i	−0.985206	+	0.171376i	$0.945179\pi$
$938$		0			0
$939$	−25.6703	−	25.6703i	−0.837718	−	0.837718i
$940$		0			0
$941$	4.40033	−	4.40033i	0.143447	−	0.143447i	−0.631737	−	0.775183i	$-0.717658\pi$
$941$	4.40033	−	4.40033i	0.143447	−	0.143447i	0.775183	+	0.631737i	$0.217658\pi$
$942$		0			0
$943$	7.48491			0.243742
$944$		0			0
$945$	−4.92792			−0.160305
$946$		0			0
$947$	15.4408	−	15.4408i	0.501758	−	0.501758i	−0.410226	−	0.911984i	$-0.634550\pi$
$947$	15.4408	−	15.4408i	0.501758	−	0.501758i	0.911984	+	0.410226i	$0.134550\pi$
$948$		0			0
$949$	−1.28545	−	1.28545i	−0.0417274	−	0.0417274i
$950$		0			0
$951$		−	51.8554i		−	1.68153i
$952$		0			0
$953$			42.4788i			1.37602i	0.725699	+	0.688012i	$0.241516\pi$
$953$			42.4788i			1.37602i	−0.725699	+	0.688012i	$0.758484\pi$
$954$		0			0
$955$	11.3694	+	11.3694i	0.367906	+	0.367906i
$956$		0			0
$957$	−0.332101	+	0.332101i	−0.0107353	+	0.0107353i
$958$		0			0
$959$	−4.83668			−0.156185
$960$		0			0
$961$	−8.63061			−0.278407
$962$		0			0
$963$	2.48039	−	2.48039i	0.0799293	−	0.0799293i
$964$		0			0
$965$	15.3079	+	15.3079i	0.492780	+	0.492780i
$966$		0			0
$967$		−	0.295998i		−	0.00951867i	−0.999989	−	0.00475933i	$-0.998485\pi$
$967$		−	0.295998i		−	0.00951867i	0.999989	−	0.00475933i	$-0.00151495\pi$
$968$		0			0
$969$			2.06667i			0.0663910i
$970$		0			0
$971$	20.3831	+	20.3831i	0.654124	+	0.654124i	0.953983	−	0.299859i	$-0.0969397\pi$
$971$	20.3831	+	20.3831i	0.654124	+	0.654124i	−0.299859	+	0.953983i	$0.596940\pi$
$972$		0			0
$973$	−12.0005	+	12.0005i	−0.384720	+	0.384720i
$974$		0			0
$975$	−1.93540			−0.0619823
$976$		0			0
$977$	8.69777			0.278266			0.139133	−	0.990274i	$-0.455568\pi$
$977$	8.69777			0.278266			0.139133	+	0.990274i	$0.455568\pi$
$978$		0			0
$979$	−6.55421	+	6.55421i	−0.209473	+	0.209473i
$980$		0			0
$981$	−0.999078	−	0.999078i	−0.0318981	−	0.0318981i
$982$		0			0
$983$			2.44840i			0.0780917i	0.999237	+	0.0390459i	$0.0124318\pi$
$983$			2.44840i			0.0780917i	−0.999237	+	0.0390459i	$0.987568\pi$
$984$		0			0
$985$		−	16.0962i		−	0.512869i
$986$		0			0
$987$	−3.47296	−	3.47296i	−0.110545	−	0.110545i
$988$		0			0
$989$	12.1945	−	12.1945i	0.387761	−	0.387761i
$990$		0			0
$991$	−27.7558			−0.881694			−0.440847	−	0.897582i	$-0.645322\pi$
$991$	−27.7558			−0.881694			−0.440847	+	0.897582i	$0.645322\pi$
$992$		0			0
$993$	−36.2921			−1.15170
$994$		0			0
$995$	18.3047	−	18.3047i	0.580299	−	0.580299i
$996$		0			0
$997$	13.6885	+	13.6885i	0.433520	+	0.433520i	0.889824	−	0.456304i	$-0.150827\pi$
$997$	13.6885	+	13.6885i	0.433520	+	0.433520i	−0.456304	+	0.889824i	$0.650827\pi$
$998$		0			0
$999$			50.9624i			1.61238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2240.2.bd.a.561.5		44
4.3	odd	2		560.2.bd.a.421.15	yes	44
16.3	odd	4		560.2.bd.a.141.15	✓	44
16.13	even	4	inner	2240.2.bd.a.1681.5		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
560.2.bd.a.141.15	✓	44	16.3	odd	4
560.2.bd.a.421.15	yes	44	4.3	odd	2
2240.2.bd.a.561.5		44	1.1	even	1	trivial
2240.2.bd.a.1681.5		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)

\(f(q)\)	\(=\)	\(q+(-1.28029 + 1.28029i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} -0.278310i q^{9} +O(q^{10})\)	\(q+(-1.28029 + 1.28029i) q^{3} +(0.707107 + 0.707107i) q^{5} -1.00000i q^{7} -0.278310i q^{9} +(-2.22891 - 2.22891i) q^{11} +(0.755840 - 0.755840i) q^{13} -1.81061 q^{15} +0.805751 q^{17} +(1.00168 - 1.00168i) q^{19} +(1.28029 + 1.28029i) q^{21} +4.48666i q^{23} +1.00000i q^{25} +(-3.48457 - 3.48457i) q^{27} +(-0.0581885 + 0.0581885i) q^{29} -4.72963 q^{31} +5.70733 q^{33} +(0.707107 - 0.707107i) q^{35} +(-7.31260 - 7.31260i) q^{37} +1.93540i q^{39} -1.66826i q^{41} +(-2.71794 - 2.71794i) q^{43} +(0.196795 - 0.196795i) q^{45} -2.71262 q^{47} -1.00000 q^{49} +(-1.03160 + 1.03160i) q^{51} +(-7.19308 - 7.19308i) q^{53} -3.15216i q^{55} +2.56490i q^{57} +(-0.153744 - 0.153744i) q^{59} +(3.17084 - 3.17084i) q^{61} -0.278310 q^{63} +1.06892 q^{65} +(-2.38261 + 2.38261i) q^{67} +(-5.74425 - 5.74425i) q^{69} +1.61718i q^{71} -1.70069i q^{73} +(-1.28029 - 1.28029i) q^{75} +(-2.22891 + 2.22891i) q^{77} +15.8678 q^{79} +9.75747 q^{81} +(4.52351 - 4.52351i) q^{83} +(0.569752 + 0.569752i) q^{85} -0.148997i q^{87} -2.94054i q^{89} +(-0.755840 - 0.755840i) q^{91} +(6.05532 - 6.05532i) q^{93} +1.41659 q^{95} -13.0705 q^{97} +(-0.620329 + 0.620329i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q+O(q^{10}) \) 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

L-functions

Modular forms

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