LMFDB - Embedded newform 1155.2.l.f.1121.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(1121,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1155.1121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.l (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1121.11
Character	$\chi$	$=$	1155.1121
Dual form			1155.2.l.f.1121.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.30517 q^{2} +(-0.259419 - 1.71251i) q^{3} -0.296539 q^{4} +1.00000i q^{5} +(0.338586 + 2.23512i) q^{6} +1.00000i q^{7} +2.99737 q^{8} +(-2.86540 + 0.888518i) q^{9} +O(q^{10})$	\(q-1.30517 q^{2} +(-0.259419 - 1.71251i) q^{3} -0.296539 q^{4} +1.00000i q^{5} +(0.338586 + 2.23512i) q^{6} +1.00000i q^{7} +2.99737 q^{8} +(-2.86540 + 0.888518i) q^{9} -1.30517i q^{10} +(3.24343 + 0.692934i) q^{11} +(0.0769280 + 0.507827i) q^{12} -1.36999i q^{13} -1.30517i q^{14} +(1.71251 - 0.259419i) q^{15} -3.31899 q^{16} -2.94453 q^{17} +(3.73983 - 1.15966i) q^{18} -4.15012i q^{19} -0.296539i q^{20} +(1.71251 - 0.259419i) q^{21} +(-4.23322 - 0.904395i) q^{22} +5.83432i q^{23} +(-0.777575 - 5.13303i) q^{24} -1.00000 q^{25} +1.78806i q^{26} +(2.26494 + 4.67654i) q^{27} -0.296539i q^{28} -2.33962 q^{29} +(-2.23512 + 0.338586i) q^{30} -7.48192 q^{31} -1.66290 q^{32} +(0.345250 - 5.73418i) q^{33} +3.84310 q^{34} -1.00000 q^{35} +(0.849704 - 0.263480i) q^{36} -7.95778 q^{37} +5.41660i q^{38} +(-2.34612 + 0.355402i) q^{39} +2.99737i q^{40} +6.55170 q^{41} +(-2.23512 + 0.338586i) q^{42} +4.00141i q^{43} +(-0.961804 - 0.205482i) q^{44} +(-0.888518 - 2.86540i) q^{45} -7.61476i q^{46} +4.08970i q^{47} +(0.861010 + 5.68381i) q^{48} -1.00000 q^{49} +1.30517 q^{50} +(0.763868 + 5.04254i) q^{51} +0.406255i q^{52} +4.31212i q^{53} +(-2.95613 - 6.10367i) q^{54} +(-0.692934 + 3.24343i) q^{55} +2.99737i q^{56} +(-7.10714 + 1.07662i) q^{57} +3.05359 q^{58} -2.85807i q^{59} +(-0.507827 + 0.0769280i) q^{60} +0.425904i q^{61} +9.76516 q^{62} +(-0.888518 - 2.86540i) q^{63} +8.80834 q^{64} +1.36999 q^{65} +(-0.450609 + 7.48406i) q^{66} +1.24059 q^{67} +0.873168 q^{68} +(9.99134 - 1.51353i) q^{69} +1.30517 q^{70} +3.21512i q^{71} +(-8.58866 + 2.66322i) q^{72} +7.14602i q^{73} +10.3862 q^{74} +(0.259419 + 1.71251i) q^{75} +1.23067i q^{76} +(-0.692934 + 3.24343i) q^{77} +(3.06208 - 0.463859i) q^{78} +11.0449i q^{79} -3.31899i q^{80} +(7.42107 - 5.09193i) q^{81} -8.55106 q^{82} +1.95574 q^{83} +(-0.507827 + 0.0769280i) q^{84} -2.94453i q^{85} -5.22250i q^{86} +(0.606942 + 4.00663i) q^{87} +(9.72175 + 2.07698i) q^{88} +9.13228i q^{89} +(1.15966 + 3.73983i) q^{90} +1.36999 q^{91} -1.73010i q^{92} +(1.94096 + 12.8129i) q^{93} -5.33775i q^{94} +4.15012 q^{95} +(0.431389 + 2.84774i) q^{96} -0.814080 q^{97} +1.30517 q^{98} +(-9.90942 + 0.896311i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	$ 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) $ 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.30517			−0.922892			−0.461446	−	0.887168i	$-0.652669\pi$
$2$	−1.30517			−0.922892			−0.461446	+	0.887168i	$0.652669\pi$
$3$	−0.259419	−	1.71251i	−0.149776	−	0.988720i
$3$	−0.259419	−	1.71251i	−0.149776	−	0.988720i
$4$	−0.296539			−0.148269
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	0.338586	+	2.23512i	0.138227	+	0.912482i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$	2.99737			1.05973
$9$	−2.86540	+	0.888518i	−0.955134	+	0.296173i
$10$		−	1.30517i		−	0.412730i
$11$	3.24343	+	0.692934i	0.977931	+	0.208928i
$11$	3.24343	+	0.692934i	0.977931	+	0.208928i
$12$	0.0769280	+	0.507827i	0.0222072	+	0.146597i
$13$		−	1.36999i		−	0.379967i	−0.981787	−	0.189983i	$-0.939157\pi$
$13$		−	1.36999i		−	0.379967i	0.981787	−	0.189983i	$-0.0608434\pi$
$14$		−	1.30517i		−	0.348821i
$15$	1.71251	−	0.259419i	0.442169	−	0.0669818i
$16$	−3.31899			−0.829747
$17$	−2.94453			−0.714153			−0.357077	−	0.934075i	$-0.616226\pi$
$17$	−2.94453			−0.714153			−0.357077	+	0.934075i	$0.616226\pi$
$18$	3.73983	−	1.15966i	0.881486	−	0.273336i
$19$		−	4.15012i		−	0.952103i	−0.879417	−	0.476051i	$-0.842068\pi$
$19$		−	4.15012i		−	0.952103i	0.879417	−	0.476051i	$-0.157932\pi$
$20$		−	0.296539i		−	0.0663081i
$21$	1.71251	−	0.259419i	0.373701	−	0.0566100i
$22$	−4.23322	−	0.904395i	−0.902525	−	0.192818i
$23$			5.83432i			1.21654i	0.793731	+	0.608269i	$0.208136\pi$
$23$			5.83432i			1.21654i	−0.793731	+	0.608269i	$0.791864\pi$
$24$	−0.777575	−	5.13303i	−0.158722	−	1.04778i
$25$	−1.00000			−0.200000
$26$			1.78806i			0.350668i
$27$	2.26494	+	4.67654i	0.435888	+	0.900001i
$28$		−	0.296539i		−	0.0560406i
$29$	−2.33962			−0.434456			−0.217228	−	0.976121i	$-0.569702\pi$
$29$	−2.33962			−0.434456			−0.217228	+	0.976121i	$0.569702\pi$
$30$	−2.23512	+	0.338586i	−0.408074	+	0.0618170i
$31$	−7.48192			−1.34379			−0.671897	−	0.740645i	$-0.734520\pi$
$31$	−7.48192			−1.34379			−0.671897	+	0.740645i	$0.734520\pi$
$32$	−1.66290			−0.293962
$33$	0.345250	−	5.73418i	0.0601004	−	0.998192i
$34$	3.84310			0.659087
$35$	−1.00000			−0.169031
$36$	0.849704	−	0.263480i	0.141617	−	0.0439134i
$37$	−7.95778			−1.30825			−0.654126	−	0.756386i	$-0.726963\pi$
$37$	−7.95778			−1.30825			−0.654126	+	0.756386i	$0.726963\pi$
$38$			5.41660i			0.878689i
$39$	−2.34612	+	0.355402i	−0.375681	+	0.0569098i
$40$			2.99737i			0.473925i
$41$	6.55170			1.02320			0.511602	−	0.859223i	$-0.329052\pi$
$41$	6.55170			1.02320			0.511602	+	0.859223i	$0.329052\pi$
$42$	−2.23512	+	0.338586i	−0.344886	+	0.0522449i
$43$			4.00141i			0.610209i	0.952319	+	0.305104i	$0.0986913\pi$
$43$			4.00141i			0.610209i	−0.952319	+	0.305104i	$0.901309\pi$
$44$	−0.961804	−	0.205482i	−0.144997	−	0.0309776i
$45$	−0.888518	−	2.86540i	−0.132452	−	0.427149i
$46$		−	7.61476i		−	1.12273i
$47$			4.08970i			0.596545i	0.954481	+	0.298272i	$0.0964104\pi$
$47$			4.08970i			0.596545i	−0.954481	+	0.298272i	$0.903590\pi$
$48$	0.861010	+	5.68381i	0.124276	+	0.820387i
$49$	−1.00000			−0.142857
$50$	1.30517			0.184578
$51$	0.763868	+	5.04254i	0.106963	+	0.706097i
$52$			0.406255i			0.0563374i
$53$			4.31212i			0.592315i	0.955139	+	0.296157i	$0.0957053\pi$
$53$			4.31212i			0.592315i	−0.955139	+	0.296157i	$0.904295\pi$
$54$	−2.95613	−	6.10367i	−0.402278	−	0.830604i
$55$	−0.692934	+	3.24343i	−0.0934352	+	0.437344i
$56$			2.99737i			0.400540i
$57$	−7.10714	+	1.07662i	−0.941363	+	0.142602i
$58$	3.05359			0.400956
$59$		−	2.85807i		−	0.372090i	−0.982541	−	0.186045i	$-0.940433\pi$
$59$		−	2.85807i		−	0.372090i	0.982541	−	0.186045i	$-0.0595670\pi$
$60$	−0.507827	+	0.0769280i	−0.0655602	+	0.00993136i
$61$			0.425904i			0.0545314i	0.999628	+	0.0272657i	$0.00868002\pi$
$61$			0.425904i			0.0545314i	−0.999628	+	0.0272657i	$0.991320\pi$
$62$	9.76516			1.24018
$63$	−0.888518	−	2.86540i	−0.111943	−	0.361007i
$64$	8.80834			1.10104
$65$	1.36999			0.169926
$66$	−0.450609	+	7.48406i	−0.0554662	+	0.921224i
$67$	1.24059			0.151563			0.0757813	−	0.997124i	$-0.475855\pi$
$67$	1.24059			0.151563			0.0757813	+	0.997124i	$0.475855\pi$
$68$	0.873168			0.105887
$69$	9.99134	−	1.51353i	1.20282	−	0.182208i
$70$	1.30517			0.155997
$71$			3.21512i			0.381564i	0.981632	+	0.190782i	$0.0611024\pi$
$71$			3.21512i			0.381564i	−0.981632	+	0.190782i	$0.938898\pi$
$72$	−8.58866	+	2.66322i	−1.01218	+	0.313863i
$73$			7.14602i			0.836378i	0.908360	+	0.418189i	$0.137335\pi$
$73$			7.14602i			0.836378i	−0.908360	+	0.418189i	$0.862665\pi$
$74$	10.3862			1.20738
$75$	0.259419	+	1.71251i	0.0299552	+	0.197744i
$76$			1.23067i			0.141168i
$77$	−0.692934	+	3.24343i	−0.0789672	+	0.369623i
$78$	3.06208	−	0.463859i	0.346713	−	0.0525216i
$79$			11.0449i			1.24265i	0.783554	+	0.621323i	$0.213405\pi$
$79$			11.0449i			1.24265i	−0.783554	+	0.621323i	$0.786595\pi$
$80$		−	3.31899i		−	0.371074i
$81$	7.42107	−	5.09193i	0.824563	−	0.565770i
$82$	−8.55106			−0.944307
$83$	1.95574			0.214670			0.107335	−	0.994223i	$-0.465768\pi$
$83$	1.95574			0.214670			0.107335	+	0.994223i	$0.465768\pi$
$84$	−0.507827	+	0.0769280i	−0.0554085	+	0.00839353i
$85$		−	2.94453i		−	0.319379i
$86$		−	5.22250i		−	0.563157i
$87$	0.606942	+	4.00663i	0.0650710	+	0.429555i
$88$	9.72175	+	2.07698i	1.03634	+	0.221407i
$89$			9.13228i			0.968020i	0.875063	+	0.484010i	$0.160820\pi$
$89$			9.13228i			0.968020i	−0.875063	+	0.484010i	$0.839180\pi$
$90$	1.15966	+	3.73983i	0.122239	+	0.394213i
$91$	1.36999			0.143614
$92$		−	1.73010i		−	0.180376i
$93$	1.94096	+	12.8129i	0.201268	+	1.32864i
$94$		−	5.33775i		−	0.550547i
$95$	4.15012			0.425793
$96$	0.431389	+	2.84774i	0.0440285	+	0.290646i
$97$	−0.814080			−0.0826573			−0.0413287	−	0.999146i	$-0.513159\pi$
$97$	−0.814080			−0.0826573			−0.0413287	+	0.999146i	$0.513159\pi$
$98$	1.30517			0.131842
$99$	−9.90942	+	0.896311i	−0.995934	+	0.0900827i
$100$	0.296539			0.0296539
$101$	14.2024			1.41320			0.706598	−	0.707615i	$-0.250229\pi$
$101$	14.2024			1.41320			0.706598	+	0.707615i	$0.250229\pi$
$102$	−0.996975	−	6.58136i	−0.0987153	−	0.651652i
$103$	−18.2071			−1.79400			−0.896998	−	0.442034i	$-0.854257\pi$
$103$	−18.2071			−1.79400			−0.896998	+	0.442034i	$0.854257\pi$
$104$		−	4.10636i		−	0.402662i
$105$	0.259419	+	1.71251i	0.0253167	+	0.167124i
$106$		−	5.62803i		−	0.546643i
$107$	3.20939			0.310263			0.155132	−	0.987894i	$-0.450420\pi$
$107$	3.20939			0.310263			0.155132	+	0.987894i	$0.450420\pi$
$108$	−0.671643	−	1.38678i	−0.0646289	−	0.133443i
$109$		−	6.76165i		−	0.647649i	−0.946117	−	0.323824i	$-0.895031\pi$
$109$		−	6.76165i		−	0.647649i	0.946117	−	0.323824i	$-0.104969\pi$
$110$	0.904395	−	4.23322i	0.0862307	−	0.403622i
$111$	2.06440	+	13.6278i	0.195945	+	1.29349i
$112$		−	3.31899i		−	0.313615i
$113$			4.97615i			0.468116i	0.972223	+	0.234058i	$0.0752006\pi$
$113$			4.97615i			0.468116i	−0.972223	+	0.234058i	$0.924799\pi$
$114$	9.27600	−	1.40517i	0.868777	−	0.131606i
$115$	−5.83432			−0.544053
$116$	0.693788			0.0644166
$117$	1.21726	+	3.92557i	0.112536	+	0.362919i
$118$			3.73026i			0.343399i
$119$		−	2.94453i		−	0.269925i
$120$	5.13303	−	0.777575i	0.468579	−	0.0709826i
$121$	10.0397	+	4.49497i	0.912699	+	0.408634i
$122$		−	0.555876i		−	0.0503266i
$123$	−1.69964	−	11.2199i	−0.153251	−	1.01166i
$124$	2.21868			0.199244
$125$		−	1.00000i		−	0.0894427i
$126$	1.15966	+	3.73983i	0.103311	+	0.333171i
$127$			7.27545i			0.645592i	0.946469	+	0.322796i	$0.104623\pi$
$127$			7.27545i			0.645592i	−0.946469	+	0.322796i	$0.895377\pi$
$128$	−8.17055			−0.722181
$129$	6.85246	−	1.03804i	0.603325	−	0.0913945i
$130$	−1.78806			−0.156824
$131$	8.15259			0.712295			0.356148	−	0.934430i	$-0.384090\pi$
$131$	8.15259			0.712295			0.356148	+	0.934430i	$0.384090\pi$
$132$	−0.102380	+	1.70041i	−0.00891105	+	0.148001i
$133$	4.15012			0.359861
$134$	−1.61918			−0.139876
$135$	−4.67654	+	2.26494i	−0.402493	+	0.194935i
$136$	−8.82583			−0.756809
$137$			18.0440i			1.54160i	0.637076	+	0.770801i	$0.280144\pi$
$137$			18.0440i			1.54160i	−0.637076	+	0.770801i	$0.719856\pi$
$138$	−13.0404	+	1.97542i	−1.11007	+	0.168159i
$139$			13.3038i			1.12841i	0.825635	+	0.564205i	$0.190817\pi$
$139$			13.3038i			1.12841i	−0.825635	+	0.564205i	$0.809183\pi$
$140$	0.296539			0.0250621
$141$	7.00367	−	1.06095i	0.589816	−	0.0893480i
$142$		−	4.19627i		−	0.352143i
$143$	0.949312	−	4.44346i	0.0793855	−	0.371581i
$144$	9.51023	−	2.94898i	0.792520	−	0.245748i
$145$		−	2.33962i		−	0.194295i
$146$		−	9.32675i		−	0.771887i
$147$	0.259419	+	1.71251i	0.0213966	+	0.141246i
$148$	2.35979			0.193974
$149$	−18.2500			−1.49510			−0.747551	−	0.664205i	$-0.768770\pi$
$149$	−18.2500			−1.49510			−0.747551	+	0.664205i	$0.768770\pi$
$150$	−0.338586	−	2.23512i	−0.0276454	−	0.182496i
$151$			13.7480i			1.11880i	0.828898	+	0.559400i	$0.188968\pi$
$151$			13.7480i			1.11880i	−0.828898	+	0.559400i	$0.811032\pi$
$152$		−	12.4394i		−	1.00897i
$153$	8.43726	−	2.61627i	0.682112	−	0.211513i
$154$	0.904395	−	4.23322i	0.0728782	−	0.341122i
$155$		−	7.48192i		−	0.600963i
$156$	0.695717	−	0.105390i	0.0557020	−	0.00843799i
$157$	−11.7618			−0.938697			−0.469348	−	0.883013i	$-0.655511\pi$
$157$	−11.7618			−0.938697			−0.469348	+	0.883013i	$0.655511\pi$
$158$		−	14.4154i		−	1.14683i
$159$	7.38456	−	1.11865i	0.585634	−	0.0887145i
$160$		−	1.66290i		−	0.131464i
$161$	−5.83432			−0.459808
$162$	−9.68574	+	6.64581i	−0.760983	+	0.522145i
$163$	−13.7254			−1.07506			−0.537529	−	0.843245i	$-0.680642\pi$
$163$	−13.7254			−1.07506			−0.537529	+	0.843245i	$0.680642\pi$
$164$	−1.94283			−0.151710
$165$	5.73418	+	0.345250i	0.446405	+	0.0268777i
$166$	−2.55256			−0.198117
$167$	−15.0317			−1.16318			−0.581592	−	0.813480i	$-0.697570\pi$
$167$	−15.0317			−1.16318			−0.581592	+	0.813480i	$0.697570\pi$
$168$	5.13303	−	0.777575i	0.396022	−	0.0599912i
$169$	11.1231			0.855625
$170$			3.84310i			0.294752i
$171$	3.68746	+	11.8918i	0.281987	+	0.909386i
$172$		−	1.18657i		−	0.0904753i
$173$	−9.46535			−0.719637			−0.359818	−	0.933022i	$-0.617161\pi$
$173$	−9.46535			−0.719637			−0.359818	+	0.933022i	$0.617161\pi$
$174$	−0.792161	−	5.22932i	−0.0600536	−	0.396433i
$175$		−	1.00000i		−	0.0755929i
$176$	−10.7649	−	2.29984i	−0.811435	−	0.173357i
$177$	−4.89449	+	0.741440i	−0.367892	+	0.0557300i
$178$		−	11.9191i		−	0.893378i
$179$			13.8510i			1.03527i	0.855600	+	0.517637i	$0.173188\pi$
$179$			13.8510i			1.03527i	−0.855600	+	0.517637i	$0.826812\pi$
$180$	0.263480	+	0.849704i	0.0196387	+	0.0633332i
$181$	−1.39661			−0.103809			−0.0519047	−	0.998652i	$-0.516529\pi$
$181$	−1.39661			−0.103809			−0.0519047	+	0.998652i	$0.516529\pi$
$182$	−1.78806			−0.132540
$183$	0.729366	−	0.110488i	0.0539163	−	0.00816749i
$184$			17.4876i			1.28920i
$185$		−	7.95778i		−	0.585068i
$186$	−2.53327	−	16.7230i	−0.185749	−	1.22619i
$187$	−9.55037	−	2.04036i	−0.698393	−	0.149206i
$188$		−	1.21276i		−	0.0884494i
$189$	−4.67654	+	2.26494i	−0.340168	+	0.164750i
$190$	−5.41660			−0.392962
$191$		−	18.4674i		−	1.33626i	−0.744046	−	0.668128i	$-0.767096\pi$
$191$		−	18.4674i		−	1.33626i	0.744046	−	0.668128i	$-0.232904\pi$
$192$	−2.28505	−	15.0844i	−0.164910	−	1.08862i
$193$			17.7871i			1.28034i	0.768231	+	0.640172i	$0.221137\pi$
$193$			17.7871i			1.28034i	−0.768231	+	0.640172i	$0.778863\pi$
$194$	1.06251			0.0762838
$195$	−0.355402	−	2.34612i	−0.0254508	−	0.168009i
$196$	0.296539			0.0211814
$197$	−16.7226			−1.19144			−0.595718	−	0.803194i	$-0.703132\pi$
$197$	−16.7226			−1.19144			−0.595718	+	0.803194i	$0.703132\pi$
$198$	12.9334	−	1.16984i	0.919140	−	0.0831366i
$199$	−18.5990			−1.31845			−0.659224	−	0.751947i	$-0.729115\pi$
$199$	−18.5990			−1.31845			−0.659224	+	0.751947i	$0.729115\pi$
$200$	−2.99737			−0.211946
$201$	−0.321834	−	2.12453i	−0.0227004	−	0.149853i
$202$	−18.5366			−1.30423
$203$		−	2.33962i		−	0.164209i
$204$	−0.226517	−	1.49531i	−0.0158593	−	0.104693i
$205$			6.55170i			0.457590i
$206$	23.7633			1.65567
$207$	−5.18390	−	16.7177i	−0.360306	−	1.16196i
$208$			4.54698i			0.315276i
$209$	2.87576	−	13.4606i	0.198921	−	0.931091i
$210$	−0.338586	−	2.23512i	−0.0233646	−	0.154238i
$211$		−	16.2283i		−	1.11721i	−0.829435	−	0.558603i	$-0.811338\pi$
$211$		−	16.2283i		−	1.11721i	0.829435	−	0.558603i	$-0.188662\pi$
$212$		−	1.27871i		−	0.0878222i
$213$	5.50593	−	0.834064i	0.377260	−	0.0571491i
$214$	−4.18879			−0.286340
$215$	−4.00141			−0.272894
$216$	6.78886	+	14.0173i	0.461923	+	0.953757i
$217$		−	7.48192i		−	0.507906i
$218$			8.82509i			0.597710i
$219$	12.2377	−	1.85382i	0.826944	−	0.125269i
$220$	0.205482	−	0.961804i	0.0138536	−	0.0648448i
$221$			4.03397i			0.271354i
$222$	−2.69439	−	17.7866i	−0.180836	−	1.19376i
$223$	3.72489			0.249437			0.124719	−	0.992192i	$-0.460197\pi$
$223$	3.72489			0.249437			0.124719	+	0.992192i	$0.460197\pi$
$224$		−	1.66290i		−	0.111107i
$225$	2.86540	−	0.888518i	0.191027	−	0.0592346i
$226$		−	6.49470i		−	0.432021i
$227$	6.32207			0.419610			0.209805	−	0.977743i	$-0.432717\pi$
$227$	6.32207			0.419610			0.209805	+	0.977743i	$0.432717\pi$
$228$	2.10754	−	0.319260i	0.139575	−	0.0211435i
$229$	26.2496			1.73463			0.867313	−	0.497764i	$-0.165845\pi$
$229$	26.2496			1.73463			0.867313	+	0.497764i	$0.165845\pi$
$230$	7.61476			0.502102
$231$	5.73418	+	0.345250i	0.377281	+	0.0227158i
$232$	−7.01269			−0.460406
$233$	−10.9742			−0.718942			−0.359471	−	0.933156i	$-0.617043\pi$
$233$	−10.9742			−0.718942			−0.359471	+	0.933156i	$0.617043\pi$
$234$	−1.58873	−	5.12353i	−0.103858	−	0.334935i
$235$	−4.08970			−0.266783
$236$			0.847530i			0.0551695i
$237$	18.9145	−	2.86526i	1.22863	−	0.186118i
$238$			3.84310i			0.249111i
$239$	−0.815925			−0.0527778			−0.0263889	−	0.999652i	$-0.508401\pi$
$239$	−0.815925			−0.0527778			−0.0263889	+	0.999652i	$0.508401\pi$
$240$	−5.68381	+	0.861010i	−0.366888	+	0.0555779i
$241$		−	11.1561i		−	0.718631i	−0.933216	−	0.359315i	$-0.883010\pi$
$241$		−	11.1561i		−	0.718631i	0.933216	−	0.359315i	$-0.116990\pi$
$242$	−13.1035	−	5.86668i	−0.842323	−	0.377125i
$243$	−10.6452	−	11.3877i	−0.682887	−	0.730524i
$244$		−	0.126297i		−	0.00808534i
$245$		−	1.00000i		−	0.0638877i
$246$	2.21831	+	14.6438i	0.141434	+	0.933655i
$247$	−5.68562			−0.361767
$248$	−22.4261			−1.42406
$249$	−0.507356	−	3.34922i	−0.0321524	−	0.212248i
$250$			1.30517i			0.0825460i
$251$		−	26.4923i		−	1.67218i	−0.548591	−	0.836091i	$-0.684836\pi$
$251$		−	26.4923i		−	1.67218i	0.548591	−	0.836091i	$-0.315164\pi$
$252$	0.263480	+	0.849704i	0.0165977	+	0.0535263i
$253$	−4.04280	+	18.9232i	−0.254168	+	1.18969i
$254$		−	9.49568i		−	0.595812i
$255$	−5.04254	+	0.763868i	−0.315776	+	0.0478353i
$256$	−6.95275			−0.434547
$257$			28.7699i			1.79462i	0.441404	+	0.897308i	$0.354481\pi$
$257$			28.7699i			1.79462i	−0.441404	+	0.897308i	$0.645519\pi$
$258$	−8.94360	+	1.35482i	−0.556805	+	0.0843473i
$259$		−	7.95778i		−	0.494473i
$260$	−0.406255			−0.0251949
$261$	6.70395	−	2.07879i	0.414964	−	0.128674i
$262$	−10.6405			−0.657372
$263$	21.4341			1.32168			0.660841	−	0.750526i	$-0.270200\pi$
$263$	21.4341			1.32168			0.660841	+	0.750526i	$0.270200\pi$
$264$	1.03484	−	17.1874i	0.0636901	−	1.05781i
$265$	−4.31212			−0.264891
$266$	−5.41660			−0.332113
$267$	15.6391	−	2.36909i	0.957100	−	0.144986i
$268$	−0.367884			−0.0224721
$269$			15.1220i			0.922008i	0.887398	+	0.461004i	$0.152511\pi$
$269$			15.1220i			0.922008i	−0.887398	+	0.461004i	$0.847489\pi$
$270$	6.10367	−	2.95613i	0.371457	−	0.179904i
$271$			0.939267i			0.0570564i	0.999593	+	0.0285282i	$0.00908204\pi$
$271$			0.939267i			0.0570564i	−0.999593	+	0.0285282i	$0.990918\pi$
$272$	9.77285			0.592566
$273$	−0.355402	−	2.34612i	−0.0215099	−	0.141994i
$274$		−	23.5504i		−	1.42273i
$275$	−3.24343	−	0.692934i	−0.195586	−	0.0417855i
$276$	−2.96282	+	0.448822i	−0.178341	+	0.0270159i
$277$			4.02831i			0.242037i	0.992650	+	0.121019i	$0.0386161\pi$
$277$			4.02831i			0.242037i	−0.992650	+	0.121019i	$0.961384\pi$
$278$		−	17.3636i		−	1.04140i
$279$	21.4387	−	6.64783i	1.28350	−	0.397995i
$280$	−2.99737			−0.179127
$281$	−0.439192			−0.0262000			−0.0131000	−	0.999914i	$-0.504170\pi$
$281$	−0.439192			−0.0262000			−0.0131000	+	0.999914i	$0.504170\pi$
$282$	−9.14096	+	1.38472i	−0.544337	+	0.0824586i
$283$		−	4.85184i		−	0.288412i	−0.989548	−	0.144206i	$-0.953937\pi$
$283$		−	4.85184i		−	0.288412i	0.989548	−	0.144206i	$-0.0460628\pi$
$284$		−	0.953408i		−	0.0565743i
$285$	−1.07662	−	7.10714i	−0.0637736	−	0.420990i
$286$	−1.23901	+	5.79946i	−0.0732643	+	0.342929i
$287$			6.55170i			0.386735i
$288$	4.76488	−	1.47752i	0.280774	−	0.0870636i
$289$	−8.32975			−0.489985
$290$			3.05359i			0.179313i
$291$	0.211188	+	1.39412i	0.0123801	+	0.0817250i
$292$		−	2.11907i		−	0.124009i
$293$	32.6690			1.90854			0.954272	−	0.298939i	$-0.0966328\pi$
$293$	32.6690			1.90854			0.954272	+	0.298939i	$0.0966328\pi$
$294$	−0.338586	−	2.23512i	−0.0197467	−	0.130355i
$295$	2.85807			0.166404
$296$	−23.8524			−1.38639
$297$	4.10564	+	16.7375i	0.238233	+	0.971208i
$298$	23.8193			1.37982
$299$	7.99295			0.462244
$300$	−0.0769280	−	0.507827i	−0.00444144	−	0.0293194i
$301$	−4.00141			−0.230637
$302$		−	17.9435i		−	1.03253i
$303$	−3.68439	−	24.3219i	−0.211663	−	1.39725i
$304$			13.7742i			0.790004i
$305$	−0.425904			−0.0243872
$306$	−11.0120	+	3.41467i	−0.629516	+	0.195203i
$307$		−	24.5078i		−	1.39873i	−0.714763	−	0.699367i	$-0.753465\pi$
$307$		−	24.5078i		−	1.39873i	0.714763	−	0.699367i	$-0.246535\pi$
$308$	0.205482	−	0.961804i	0.0117084	−	0.0548038i
$309$	4.72327	+	31.1799i	0.268697	+	1.77376i
$310$			9.76516i			0.554624i
$311$		−	9.24990i		−	0.524514i	−0.964998	−	0.262257i	$-0.915533\pi$
$311$		−	9.24990i		−	0.524514i	0.964998	−	0.262257i	$-0.0844668\pi$
$312$	−7.03220	+	1.06527i	−0.398120	+	0.0603090i
$313$	23.9410			1.35323			0.676614	−	0.736338i	$-0.263447\pi$
$313$	23.9410			1.35323			0.676614	+	0.736338i	$0.263447\pi$
$314$	15.3512			0.866316
$315$	2.86540	−	0.888518i	0.161447	−	0.0500623i
$316$		−	3.27524i		−	0.184247i
$317$		−	25.3173i		−	1.42196i	−0.703211	−	0.710981i	$-0.748251\pi$
$317$		−	25.3173i		−	1.42196i	0.703211	−	0.710981i	$-0.251749\pi$
$318$	−9.63808	+	1.46002i	−0.540477	+	0.0818739i
$319$	−7.58839	−	1.62120i	−0.424868	−	0.0907698i
$320$			8.80834i			0.492401i
$321$	−0.832578	−	5.49612i	−0.0464700	−	0.306764i
$322$	7.61476			0.424354
$323$			12.2201i			0.679947i
$324$	−2.20064	+	1.50995i	−0.122258	+	0.0838864i
$325$			1.36999i			0.0759933i
$326$	17.9140			0.992162
$327$	−11.5794	+	1.75410i	−0.640343	+	0.0970022i
$328$	19.6378			1.08432
$329$	−4.08970			−0.225473
$330$	−7.48406	−	0.450609i	−0.411984	−	0.0248052i
$331$	3.95859			0.217584			0.108792	−	0.994065i	$-0.465302\pi$
$331$	3.95859			0.217584			0.108792	+	0.994065i	$0.465302\pi$
$332$	−0.579952			−0.0318290
$333$	22.8023	−	7.07064i	1.24956	−	0.387469i
$334$	19.6188			1.07349
$335$			1.24059i			0.0677808i
$336$	−5.68381	+	0.861010i	−0.310077	+	0.0469719i
$337$		−	1.46445i		−	0.0797735i	−0.999204	−	0.0398867i	$-0.987300\pi$
$337$		−	1.46445i		−	0.0797735i	0.999204	−	0.0398867i	$-0.0126997\pi$
$338$	−14.5175			−0.789650
$339$	8.52172	−	1.29091i	0.462836	−	0.0701125i
$340$			0.873168i			0.0473542i
$341$	−24.2671	−	5.18448i	−1.31414	−	0.280755i
$342$	−4.81275	−	15.5207i	−0.260244	−	0.839266i
$343$		−	1.00000i		−	0.0539949i
$344$			11.9937i			0.646656i
$345$	1.51353	+	9.99134i	0.0814860	+	0.537916i
$346$	12.3539			0.664148
$347$	14.8483			0.797097			0.398549	−	0.917147i	$-0.369514\pi$
$347$	14.8483			0.797097			0.398549	+	0.917147i	$0.369514\pi$
$348$	−0.179982	−	1.18812i	−0.00964805	−	0.0636900i
$349$		−	30.0133i		−	1.60658i	−0.595591	−	0.803288i	$-0.703082\pi$
$349$		−	30.0133i		−	1.60658i	0.595591	−	0.803288i	$-0.296918\pi$
$350$			1.30517i			0.0697641i
$351$	6.40681	−	3.10294i	0.341970	−	0.165623i
$352$	−5.39351	−	1.15228i	−0.287475	−	0.0614168i
$353$			21.0466i			1.12020i	0.828425	+	0.560100i	$0.189237\pi$
$353$			21.0466i			1.12020i	−0.828425	+	0.560100i	$0.810763\pi$
$354$	6.38813	−	0.967703i	0.339525	−	0.0514328i
$355$	−3.21512			−0.170641
$356$		−	2.70808i		−	0.143528i
$357$	−5.04254	+	0.763868i	−0.266880	+	0.0404282i
$358$		−	18.0779i		−	0.955447i
$359$	−26.4226			−1.39453			−0.697266	−	0.716812i	$-0.745601\pi$
$359$	−26.4226			−1.39453			−0.697266	+	0.716812i	$0.745601\pi$
$360$	−2.66322	−	8.58866i	−0.140364	−	0.452662i
$361$	1.77650			0.0934999
$362$	1.82281			0.0958049
$363$	5.09320	−	18.3592i	0.267324	−	0.963607i
$364$	−0.406255			−0.0212936
$365$	−7.14602			−0.374040
$366$	−0.951945	+	0.144205i	−0.0497589	+	0.00753771i
$367$	−21.0720			−1.09995			−0.549974	−	0.835182i	$-0.685362\pi$
$367$	−21.0720			−1.09995			−0.549974	+	0.835182i	$0.685362\pi$
$368$		−	19.3640i		−	1.00942i
$369$	−18.7733	+	5.82130i	−0.977297	+	0.303045i
$370$			10.3862i			0.539955i
$371$	−4.31212			−0.223874
$372$	−0.575569	−	3.79952i	−0.0298419	−	0.196996i
$373$		−	33.6869i		−	1.74424i	−0.489289	−	0.872122i	$-0.662744\pi$
$373$		−	33.6869i		−	1.74424i	0.489289	−	0.872122i	$-0.337256\pi$
$374$	12.4648	+	2.66302i	0.644541	+	0.137701i
$375$	−1.71251	+	0.259419i	−0.0884338	+	0.0133964i
$376$			12.2583i			0.632176i
$377$			3.20525i			0.165079i
$378$	6.10367	−	2.95613i	0.313939	−	0.152047i
$379$	21.9850			1.12929			0.564646	−	0.825333i	$-0.309013\pi$
$379$	21.9850			1.12929			0.564646	+	0.825333i	$0.309013\pi$
$380$	−1.23067			−0.0631322
$381$	12.4593	−	1.88739i	0.638310	−	0.0966941i
$382$			24.1031i			1.23322i
$383$		−	25.6079i		−	1.30850i	−0.756276	−	0.654252i	$-0.772983\pi$
$383$		−	25.6079i		−	1.30850i	0.756276	−	0.654252i	$-0.227017\pi$
$384$	2.11960	+	13.9922i	0.108165	+	0.714035i
$385$	−3.24343	−	0.692934i	−0.165301	−	0.0353152i
$386$		−	23.2152i		−	1.18162i
$387$	−3.55532	−	11.4656i	−0.180727	−	0.582831i
$388$	0.241407			0.0122556
$389$			24.4192i			1.23810i	0.785351	+	0.619050i	$0.212482\pi$
$389$			24.4192i			1.23810i	−0.785351	+	0.619050i	$0.787518\pi$
$390$	0.463859	+	3.06208i	0.0234884	+	0.155055i
$391$		−	17.1793i		−	0.868795i
$392$	−2.99737			−0.151390
$393$	−2.11494	−	13.9614i	−0.106685	−	0.704261i
$394$	21.8258			1.09957
$395$	−11.0449			−0.555728
$396$	2.93853	−	0.265791i	0.147667	−	0.0133565i
$397$	−24.1132			−1.21021			−0.605103	−	0.796148i	$-0.706868\pi$
$397$	−24.1132			−1.21021			−0.605103	+	0.796148i	$0.706868\pi$
$398$	24.2748			1.21679
$399$	−1.07662	−	7.10714i	−0.0538985	−	0.355802i
$400$	3.31899			0.165949
$401$			6.54697i			0.326940i	0.986548	+	0.163470i	$0.0522687\pi$
$401$			6.54697i			0.326940i	−0.986548	+	0.163470i	$0.947731\pi$
$402$	0.420047	+	2.77287i	0.0209500	+	0.138298i
$403$			10.2502i			0.510597i
$404$	−4.21158			−0.209534
$405$	5.09193	+	7.42107i	0.253020	+	0.368756i
$406$			3.05359i			0.151547i
$407$	−25.8105	−	5.51422i	−1.27938	−	0.273330i
$408$	2.28959	+	15.1144i	0.113352	+	0.748272i
$409$			4.99093i			0.246785i	0.992358	+	0.123393i	$0.0393775\pi$
$409$			4.99093i			0.246785i	−0.992358	+	0.123393i	$0.960623\pi$
$410$		−	8.55106i		−	0.422307i
$411$	30.9006	−	4.68096i	1.52421	−	0.230895i
$412$	5.39911			0.265995
$413$	2.85807			0.140637
$414$	6.76585	+	21.8193i	0.332523	+	1.07236i
$415$			1.95574i			0.0960033i
$416$			2.27816i			0.111696i
$417$	22.7829	−	3.45125i	1.11568	−	0.169009i
$418$	−3.75335	+	17.5684i	−0.183582	+	0.859297i
$419$			9.00836i			0.440087i	0.975490	+	0.220044i	$0.0706199\pi$
$419$			9.00836i			0.440087i	−0.975490	+	0.220044i	$0.929380\pi$
$420$	−0.0769280	−	0.507827i	−0.00375370	−	0.0247794i
$421$	−7.26752			−0.354197			−0.177099	−	0.984193i	$-0.556671\pi$
$421$	−7.26752			−0.354197			−0.177099	+	0.984193i	$0.556671\pi$
$422$			21.1807i			1.03106i
$423$	−3.63378	−	11.7187i	−0.176680	−	0.569780i
$424$			12.9250i			0.627693i
$425$	2.94453			0.142831
$426$	−7.18616	+	1.08859i	−0.348171	+	0.0527425i
$427$	−0.425904			−0.0206109
$428$	−0.951709			−0.0460026
$429$	−7.85576	−	0.472989i	−0.379280	−	0.0228361i
$430$	5.22250			0.251851
$431$	−35.6761			−1.71846			−0.859229	−	0.511591i	$-0.829056\pi$
$431$	−35.6761			−1.71846			−0.859229	+	0.511591i	$0.829056\pi$
$432$	−7.51731	−	15.5214i	−0.361677	−	0.746773i
$433$	6.58535			0.316472			0.158236	−	0.987401i	$-0.449419\pi$
$433$	6.58535			0.316472			0.158236	+	0.987401i	$0.449419\pi$
$434$			9.76516i			0.468743i
$435$	−4.00663	+	0.606942i	−0.192103	+	0.0291006i
$436$			2.00509i			0.0960266i
$437$	24.2131			1.15827
$438$	−15.9722	+	2.41954i	−0.763180	+	0.115610i
$439$		−	32.6233i		−	1.55702i	−0.627630	−	0.778512i	$-0.715975\pi$
$439$		−	32.6233i		−	1.55702i	0.627630	−	0.778512i	$-0.284025\pi$
$440$	−2.07698	+	9.72175i	−0.0990161	+	0.463466i
$441$	2.86540	−	0.888518i	0.136448	−	0.0423104i
$442$		−	5.26501i		−	0.250431i
$443$			2.03036i			0.0964652i	0.998836	+	0.0482326i	$0.0153589\pi$
$443$			2.03036i			0.0964652i	−0.998836	+	0.0482326i	$0.984641\pi$
$444$	−0.612176	−	4.04118i	−0.0290526	−	0.191786i
$445$	−9.13228			−0.432912
$446$	−4.86161			−0.230204
$447$	4.73441	+	31.2534i	0.223930	+	1.47824i
$448$			8.80834i			0.416155i
$449$			37.2713i			1.75894i	0.475951	+	0.879472i	$0.342104\pi$
$449$			37.2713i			1.75894i	−0.475951	+	0.879472i	$0.657896\pi$
$450$	−3.73983	+	1.15966i	−0.176297	+	0.0546671i
$451$	21.2500	+	4.53990i	1.00062	+	0.213775i
$452$		−	1.47562i		−	0.0694074i
$453$	23.5437	−	3.56651i	1.10618	−	0.167569i
$454$	−8.25135			−0.387255
$455$			1.36999i			0.0642261i
$456$	−21.3027	+	3.22703i	−0.997590	+	0.151120i
$457$			23.3833i			1.09382i	0.837191	+	0.546911i	$0.184196\pi$
$457$			23.3833i			1.09382i	−0.837191	+	0.546911i	$0.815804\pi$
$458$	−34.2602			−1.60087
$459$	−6.66918	−	13.7702i	−0.311291	−	0.642738i
$460$	1.73010			0.0806664
$461$	3.58071			0.166770			0.0833852	−	0.996517i	$-0.473427\pi$
$461$	3.58071			0.166770			0.0833852	+	0.996517i	$0.473427\pi$
$462$	−7.48406	−	0.450609i	−0.348190	−	0.0209642i
$463$	−12.8088			−0.595275			−0.297637	−	0.954679i	$-0.596199\pi$
$463$	−12.8088			−0.595275			−0.297637	+	0.954679i	$0.596199\pi$
$464$	7.76516			0.360488
$465$	−12.8129	+	1.94096i	−0.594184	+	0.0900097i
$466$	14.3231			0.663506
$467$			37.4993i			1.73526i	0.497211	+	0.867630i	$0.334357\pi$
$467$			37.4993i			1.73526i	−0.497211	+	0.867630i	$0.665643\pi$
$468$	−0.360965	−	1.16408i	−0.0166856	−	0.0538098i
$469$			1.24059i			0.0572852i
$470$	5.33775			0.246212
$471$	3.05125	+	20.1423i	0.140594	+	0.928108i
$472$		−	8.56670i		−	0.394314i
$473$	−2.77271	+	12.9783i	−0.127489	+	0.596742i
$474$	−24.6866	+	3.73964i	−1.13389	+	0.171767i
$475$			4.15012i			0.190421i
$476$			0.873168i			0.0400216i
$477$	−3.83140	−	12.3560i	−0.175428	−	0.565740i
$478$	1.06492			0.0487082
$479$	−8.01329			−0.366137			−0.183068	−	0.983100i	$-0.558603\pi$
$479$	−8.01329			−0.366137			−0.183068	+	0.983100i	$0.558603\pi$
$480$	−2.84774	+	0.431389i	−0.129981	+	0.0196901i
$481$			10.9021i			0.497092i
$482$			14.5606i			0.663219i
$483$	1.51353	+	9.99134i	0.0688682	+	0.454622i
$484$	−2.97716	−	1.33293i	−0.135325	−	0.0605879i
$485$		−	0.814080i		−	0.0369655i
$486$	13.8937	+	14.8629i	0.630232	+	0.674195i
$487$	13.5242			0.612840			0.306420	−	0.951896i	$-0.400869\pi$
$487$	13.5242			0.612840			0.306420	+	0.951896i	$0.400869\pi$
$488$			1.27659i			0.0577885i
$489$	3.56064	+	23.5050i	0.161018	+	1.06293i
$490$			1.30517i			0.0589614i
$491$	−17.9932			−0.812023			−0.406011	−	0.913868i	$-0.633081\pi$
$491$	−17.9932			−0.812023			−0.406011	+	0.913868i	$0.633081\pi$
$492$	0.504009	+	3.32713i	0.0227225	+	0.149999i
$493$	6.88907			0.310268
$494$	7.42068			0.333872
$495$	−0.896311	−	9.90942i	−0.0402862	−	0.445395i
$496$	24.8324			1.11501
$497$	−3.21512			−0.144218
$498$	0.662184	+	4.37129i	0.0296732	+	0.195882i
$499$	−30.9780			−1.38677			−0.693384	−	0.720568i	$-0.743881\pi$
$499$	−30.9780			−1.38677			−0.693384	+	0.720568i	$0.743881\pi$
$500$			0.296539i			0.0132616i
$501$	3.89950	+	25.7419i	0.174217	+	1.15006i
$502$			34.5769i			1.54324i
$503$	3.97684			0.177319			0.0886594	−	0.996062i	$-0.471742\pi$
$503$	3.97684			0.177319			0.0886594	+	0.996062i	$0.471742\pi$
$504$	−2.66322	−	8.58866i	−0.118629	−	0.382570i
$505$			14.2024i			0.632000i
$506$	5.27653	−	24.6979i	0.234570	−	1.09796i
$507$	−2.88556	−	19.0485i	−0.128152	−	0.845974i
$508$		−	2.15746i		−	0.0957216i
$509$			1.09049i			0.0483350i	0.999708	+	0.0241675i	$0.00769351\pi$
$509$			1.09049i			0.0483350i	−0.999708	+	0.0241675i	$0.992306\pi$
$510$	6.58136	−	0.996975i	0.291428	−	0.0441468i
$511$	−7.14602			−0.316121
$512$	25.4156			1.12322
$513$	19.4082	−	9.39978i	0.856894	−	0.415010i
$514$		−	37.5495i		−	1.65624i
$515$		−	18.2071i		−	0.802300i
$516$	−2.03202	+	0.307820i	−0.0894548	+	0.0135510i
$517$	−2.83390	+	13.2647i	−0.124635	+	0.583380i
$518$			10.3862i			0.456345i
$519$	2.45549	+	16.2095i	0.107784	+	0.711519i
$520$	4.10636			0.180076
$521$			3.79621i			0.166315i	0.996536	+	0.0831574i	$0.0265004\pi$
$521$			3.79621i			0.166315i	−0.996536	+	0.0831574i	$0.973500\pi$
$522$	−8.74977	+	2.71317i	−0.382967	+	0.118752i
$523$			25.5285i			1.11628i	0.829746	+	0.558141i	$0.188485\pi$
$523$			25.5285i			1.11628i	−0.829746	+	0.558141i	$0.811515\pi$
$524$	−2.41756			−0.105612
$525$	−1.71251	+	0.259419i	−0.0747402	+	0.0113220i
$526$	−27.9751			−1.21977
$527$	22.0307			0.959674
$528$	−1.14588	+	19.0317i	−0.0498681	+	0.828247i
$529$	−11.0392			−0.479967
$530$	5.62803			0.244466
$531$	2.53945	+	8.18953i	0.110203	+	0.355396i
$532$	−1.23067			−0.0533564
$533$		−	8.97575i		−	0.388783i
$534$	−20.4117	+	3.09206i	−0.883301	+	0.133806i
$535$			3.20939i			0.138754i
$536$	3.71851			0.160615
$537$	23.7201	−	3.59323i	1.02360	−	0.155059i
$538$		−	19.7368i		−	0.850914i
$539$	−3.24343	−	0.692934i	−0.139704	−	0.0298468i
$540$	1.38678	−	0.671643i	0.0596774	−	0.0289029i
$541$		−	36.6469i		−	1.57557i	−0.615949	−	0.787786i	$-0.711227\pi$
$541$		−	36.6469i		−	1.57557i	0.615949	−	0.787786i	$-0.288773\pi$
$542$		−	1.22590i		−	0.0526569i
$543$	0.362308	+	2.39172i	0.0155481	+	0.102638i
$544$	4.89646			0.209934
$545$	6.76165			0.289637
$546$	0.463859	+	3.06208i	0.0198513	+	0.131045i
$547$		−	20.4657i		−	0.875051i	−0.899206	−	0.437526i	$-0.855855\pi$
$547$		−	20.4657i		−	0.875051i	0.899206	−	0.437526i	$-0.144145\pi$
$548$		−	5.35074i		−	0.228572i
$549$	−0.378423	−	1.22039i	−0.0161507	−	0.0520848i
$550$	4.23322	+	0.904395i	0.180505	+	0.0385635i
$551$			9.70969i			0.413647i
$552$	29.9477	−	4.53662i	1.27466	−	0.193091i
$553$	−11.0449			−0.469676
$554$		−	5.25761i		−	0.223375i
$555$	−13.6278	+	2.06440i	−0.578468	+	0.0876291i
$556$		−	3.94508i		−	0.167309i
$557$	−14.2650			−0.604428			−0.302214	−	0.953240i	$-0.597726\pi$
$557$	−14.2650			−0.604428			−0.302214	+	0.953240i	$0.597726\pi$
$558$	−27.9811	+	8.67652i	−1.18454	+	0.367307i
$559$	5.48188			0.231859
$560$	3.31899			0.140253
$561$	−1.01660	+	16.8845i	−0.0429209	+	0.712862i
$562$	0.573218			0.0241798
$563$	9.07818			0.382599			0.191300	−	0.981532i	$-0.438730\pi$
$563$	9.07818			0.382599			0.191300	+	0.981532i	$0.438730\pi$
$564$	−2.07686	+	0.314613i	−0.0874517	+	0.0132476i
$565$	−4.97615			−0.209348
$566$			6.33246i			0.266173i
$567$	5.09193	+	7.42107i	0.213841	+	0.311656i
$568$			9.63689i			0.404355i
$569$	19.3007			0.809127			0.404564	−	0.914510i	$-0.367423\pi$
$569$	19.3007			0.809127			0.404564	+	0.914510i	$0.367423\pi$
$570$	1.40517	+	9.27600i	0.0588562	+	0.388529i
$571$		−	8.06079i		−	0.337333i	−0.985673	−	0.168667i	$-0.946054\pi$
$571$		−	8.06079i		−	0.337333i	0.985673	−	0.168667i	$-0.0539462\pi$
$572$	−0.281508	+	1.31766i	−0.0117704	+	0.0550941i
$573$	−31.6257	+	4.79081i	−1.32118	+	0.200139i
$574$		−	8.55106i		−	0.356914i
$575$		−	5.83432i		−	0.243308i
$576$	−25.2394	+	7.82637i	−1.05164	+	0.326099i
$577$	35.4891			1.47743			0.738715	−	0.674018i	$-0.235433\pi$
$577$	35.4891			1.47743			0.738715	+	0.674018i	$0.235433\pi$
$578$	10.8717			0.452204
$579$	30.4607	−	4.61432i	1.26590	−	0.191765i
$580$			0.693788i			0.0288080i
$581$			1.95574i			0.0811376i
$582$	−0.275636	−	1.81956i	−0.0114255	−	0.0754233i
$583$	−2.98801	+	13.9861i	−0.123751	+	0.579243i
$584$			21.4192i			0.886335i
$585$	−3.92557	+	1.21726i	−0.162302	+	0.0503275i
$586$	−42.6385			−1.76138
$587$			4.73774i			0.195548i	0.995209	+	0.0977738i	$0.0311722\pi$
$587$			4.73774i			0.195548i	−0.995209	+	0.0977738i	$0.968828\pi$
$588$	−0.0769280	−	0.507827i	−0.00317246	−	0.0209424i
$589$			31.0509i			1.27943i
$590$	−3.73026			−0.153573
$591$	4.33817	+	28.6377i	0.178448	+	1.17800i
$592$	26.4118			1.08552
$593$	−28.2871			−1.16161			−0.580806	−	0.814042i	$-0.697263\pi$
$593$	−28.2871			−1.16161			−0.580806	+	0.814042i	$0.697263\pi$
$594$	−5.35855	−	21.8452i	−0.219864	−	0.896320i
$595$	2.94453			0.120714
$596$	5.41185			0.221678
$597$	4.82494	+	31.8510i	0.197472	+	1.30358i
$598$	−10.4321			−0.426602
$599$		−	32.5143i		−	1.32850i	−0.747512	−	0.664248i	$-0.768752\pi$
$599$		−	32.5143i		−	1.32850i	0.747512	−	0.664248i	$-0.231248\pi$
$600$	0.777575	+	5.13303i	0.0317444	+	0.209555i
$601$		−	10.0679i		−	0.410678i	−0.978691	−	0.205339i	$-0.934170\pi$
$601$		−	10.0679i		−	0.410678i	0.978691	−	0.205339i	$-0.0658297\pi$
$602$	5.22250			0.212853
$603$	−3.55480	+	1.10229i	−0.144763	+	0.0448887i
$604$		−	4.07683i		−	0.165884i
$605$	−4.49497	+	10.0397i	−0.182746	+	0.408171i
$606$	4.80874	+	31.7441i	0.195342	+	1.28952i
$607$		−	1.88309i		−	0.0764322i	−0.999269	−	0.0382161i	$-0.987832\pi$
$607$		−	1.88309i		−	0.0764322i	0.999269	−	0.0382161i	$-0.0121675\pi$
$608$			6.90124i			0.279882i
$609$	−4.00663	+	0.606942i	−0.162357	+	0.0245945i
$610$	0.555876			0.0225068
$611$	5.60285			0.226667
$612$	−2.50198	+	0.775825i	−0.101136	+	0.0313609i
$613$			42.8352i			1.73010i	0.501688	+	0.865049i	$0.332713\pi$
$613$			42.8352i			1.73010i	−0.501688	+	0.865049i	$0.667287\pi$
$614$			31.9868i			1.29088i
$615$	11.2199	−	1.69964i	0.452429	−	0.0685360i
$616$	−2.07698	+	9.72175i	−0.0836838	+	0.391701i
$617$		−	33.2892i		−	1.34017i	−0.742283	−	0.670087i	$-0.766257\pi$
$617$		−	33.2892i		−	1.34017i	0.742283	−	0.670087i	$-0.233743\pi$
$618$	−6.16465	−	40.6949i	−0.247979	−	1.63699i
$619$	1.90091			0.0764040			0.0382020	−	0.999270i	$-0.487837\pi$
$619$	1.90091			0.0764040			0.0382020	+	0.999270i	$0.487837\pi$
$620$			2.21868i			0.0891044i
$621$	−27.2844	+	13.2144i	−1.09489	+	0.530275i
$622$			12.0727i			0.484070i
$623$	−9.13228			−0.365877
$624$	7.78675	−	1.17957i	0.311720	−	0.0472207i
$625$	1.00000			0.0400000
$626$	−31.2471			−1.24888
$627$	−23.7975	−	1.43283i	−0.950382	−	0.0572217i
$628$	3.48784			0.139180
$629$	23.4319			0.934292
$630$	−3.73983	+	1.15966i	−0.148998	+	0.0462022i
$631$	2.93688			0.116915			0.0584577	−	0.998290i	$-0.481382\pi$
$631$	2.93688			0.116915			0.0584577	+	0.998290i	$0.481382\pi$
$632$			33.1056i			1.31687i
$633$	−27.7913	+	4.20995i	−1.10460	+	0.167330i
$634$			33.0433i			1.31232i
$635$	−7.27545			−0.288718
$636$	−2.18981	+	0.331722i	−0.0868316	+	0.0131537i
$637$			1.36999i			0.0542809i
$638$	9.90411	+	2.11594i	0.392108	+	0.0837708i
$639$	−2.85669	−	9.21261i	−0.113009	−	0.364445i
$640$		−	8.17055i		−	0.322969i
$641$		−	0.929667i		−	0.0367196i	−0.999831	−	0.0183598i	$-0.994156\pi$
$641$		−	0.929667i		−	0.0367196i	0.999831	−	0.0183598i	$-0.00584444\pi$
$642$	1.08665	+	7.17336i	0.0428868	+	0.283110i
$643$	−13.0808			−0.515858			−0.257929	−	0.966164i	$-0.583040\pi$
$643$	−13.0808			−0.515858			−0.257929	+	0.966164i	$0.583040\pi$
$644$	1.73010			0.0681756
$645$	1.03804	+	6.85246i	0.0408729	+	0.269815i
$646$		−	15.9493i		−	0.627518i
$647$			8.61972i			0.338876i	0.985541	+	0.169438i	$0.0541953\pi$
$647$			8.61972i			0.338876i	−0.985541	+	0.169438i	$0.945805\pi$
$648$	22.2437	−	15.2624i	0.873814	−	0.599563i
$649$	1.98046	−	9.26997i	0.0777398	−	0.363878i
$650$		−	1.78806i		−	0.0701337i
$651$	−12.8129	+	1.94096i	−0.502177	+	0.0760721i
$652$	4.07012			0.159398
$653$		−	18.7709i		−	0.734561i	−0.930110	−	0.367281i	$-0.880289\pi$
$653$		−	18.7709i		−	0.734561i	0.930110	−	0.367281i	$-0.119711\pi$
$654$	15.1131	−	2.28940i	0.590968	−	0.0895226i
$655$			8.15259i			0.318548i
$656$	−21.7450			−0.849000
$657$	−6.34937	−	20.4762i	−0.247713	−	0.798854i
$658$	5.33775			0.208087
$659$	−7.21970			−0.281239			−0.140620	−	0.990064i	$-0.544909\pi$
$659$	−7.21970			−0.281239			−0.140620	+	0.990064i	$0.544909\pi$
$660$	−1.70041	−	0.102380i	−0.0661883	−	0.00398514i
$661$	42.4264			1.65019			0.825097	−	0.564991i	$-0.191120\pi$
$661$	42.4264			1.65019			0.825097	+	0.564991i	$0.191120\pi$
$662$	−5.16662			−0.200806
$663$	6.90823	−	1.04649i	0.268293	−	0.0406423i
$664$	5.86206			0.227492
$665$			4.15012i			0.160935i
$666$	−29.7608	+	9.22836i	−1.15321	+	0.357592i
$667$		−	13.6501i		−	0.528533i
$668$	4.45747			0.172465
$669$	−0.966309	−	6.37893i	−0.0373597	−	0.246624i
$670$		−	1.61918i		−	0.0625544i
$671$	−0.295123	+	1.38139i	−0.0113931	+	0.0533280i
$672$	−2.84774	+	0.431389i	−0.109854	+	0.0166412i
$673$		−	19.5105i		−	0.752074i	−0.926605	−	0.376037i	$-0.877287\pi$
$673$		−	19.5105i		−	0.752074i	0.926605	−	0.376037i	$-0.122713\pi$
$674$			1.91135i			0.0736223i
$675$	−2.26494	−	4.67654i	−0.0871776	−	0.180000i
$676$	−3.29844			−0.126863
$677$	35.9848			1.38301			0.691504	−	0.722372i	$-0.256948\pi$
$677$	35.9848			1.38301			0.691504	+	0.722372i	$0.256948\pi$
$678$	−11.1223	+	1.68485i	−0.427148	+	0.0647063i
$679$		−	0.814080i		−	0.0312415i
$680$		−	8.82583i		−	0.338455i
$681$	−1.64007	−	10.8266i	−0.0628475	−	0.414877i
$682$	31.6726	+	6.76661i	1.21281	+	0.259107i
$683$			23.8903i			0.914138i	0.889431	+	0.457069i	$0.151101\pi$
$683$			23.8903i			0.914138i	−0.889431	+	0.457069i	$0.848899\pi$
$684$	−1.09348	−	3.52637i	−0.0418101	−	0.134834i
$685$	−18.0440			−0.689425
$686$			1.30517i			0.0498315i
$687$	−6.80967	−	44.9529i	−0.259805	−	1.71506i
$688$		−	13.2806i		−	0.506319i
$689$	5.90755			0.225060
$690$	−1.97542	−	13.0404i	−0.0752028	−	0.496438i
$691$	33.1419			1.26078			0.630390	−	0.776279i	$-0.282895\pi$
$691$	33.1419			1.26078			0.630390	+	0.776279i	$0.282895\pi$
$692$	2.80684			0.106700
$693$	−0.896311	−	9.90942i	−0.0340481	−	0.376428i
$694$	−19.3795			−0.735635
$695$	−13.3038			−0.504640
$696$	1.81923	+	12.0093i	0.0689577	+	0.455212i
$697$	−19.2917			−0.730724
$698$			39.1724i			1.48270i
$699$	2.84691	+	18.7934i	0.107680	+	0.710832i
$700$			0.296539i			0.0112081i
$701$	−51.9015			−1.96029			−0.980146	−	0.198276i	$-0.936466\pi$
$701$	−51.9015			−1.96029			−0.980146	+	0.198276i	$0.936466\pi$
$702$	−8.36196	+	4.04986i	−0.315602	+	0.152852i
$703$			33.0258i			1.24559i
$704$	28.5692	+	6.10360i	1.07674	+	0.230038i
$705$	1.06095	+	7.00367i	0.0399576	+	0.263774i
$706$		−	27.4694i		−	1.03382i
$707$			14.2024i			0.534138i
$708$	1.45141	−	0.219866i	0.0545472	−	0.00826306i
$709$	44.6965			1.67861			0.839307	−	0.543658i	$-0.182961\pi$
$709$	44.6965			1.67861			0.839307	+	0.543658i	$0.182961\pi$
$710$	4.19627			0.157483
$711$	−9.81358	−	31.6480i	−0.368038	−	1.18689i
$712$			27.3728i			1.02584i
$713$		−	43.6519i		−	1.63478i
$714$	6.58136	−	0.996975i	0.246301	−	0.0373109i
$715$	4.44346	+	0.949312i	0.166176	+	0.0355023i
$716$		−	4.10737i		−	0.153500i
$717$	0.211667	+	1.39728i	0.00790484	+	0.0521824i
$718$	34.4859			1.28700
$719$		−	33.4909i		−	1.24900i	−0.781025	−	0.624500i	$-0.785303\pi$
$719$		−	33.4909i		−	1.24900i	0.781025	−	0.624500i	$-0.214697\pi$
$720$	2.94898	+	9.51023i	0.109902	+	0.354426i
$721$		−	18.2071i		−	0.678067i
$722$	−2.31863			−0.0862903
$723$	−19.1051	+	2.89412i	−0.710524	+	0.107634i
$724$	0.414150			0.0153918
$725$	2.33962			0.0868912
$726$	−6.64748	+	23.9618i	−0.246711	+	0.889305i
$727$	−8.43995			−0.313020			−0.156510	−	0.987676i	$-0.550024\pi$
$727$	−8.43995			−0.313020			−0.156510	+	0.987676i	$0.550024\pi$
$728$	4.10636			0.152192
$729$	−16.7401	+	21.1842i	−0.620003	+	0.784599i
$730$	9.32675			0.345199
$731$		−	11.7823i		−	0.435782i
$732$	−0.216285	+	0.0327639i	−0.00799414	+	0.00121099i
$733$			5.50171i			0.203210i	0.994825	+	0.101605i	$0.0323978\pi$
$733$			5.50171i			0.203210i	−0.994825	+	0.101605i	$0.967602\pi$
$734$	27.5024			1.01513
$735$	−1.71251	+	0.259419i	−0.0631670	+	0.00956883i
$736$		−	9.70189i		−	0.357617i
$737$	4.02378	+	0.859649i	0.148218	+	0.0316656i
$738$	24.5022	−	7.59777i	0.901940	−	0.279678i
$739$		−	8.23267i		−	0.302843i	−0.988469	−	0.151422i	$-0.951615\pi$
$739$		−	8.23267i		−	0.302843i	0.988469	−	0.151422i	$-0.0483852\pi$
$740$			2.35979i			0.0867477i
$741$	1.47496	+	9.73670i	0.0541840	+	0.357687i
$742$	5.62803			0.206612
$743$	37.3360			1.36973			0.684863	−	0.728672i	$-0.259862\pi$
$743$	37.3360			1.36973			0.684863	+	0.728672i	$0.259862\pi$
$744$	5.81776	+	38.4049i	0.213289	+	1.40799i
$745$		−	18.2500i		−	0.668630i
$746$			43.9671i			1.60975i
$747$	−5.60397	+	1.73771i	−0.205039	+	0.0635794i
$748$	2.83206	+	0.605048i	0.103550	+	0.0221227i
$749$			3.20939i			0.117269i
$750$	2.23512	−	0.338586i	0.0816149	−	0.0123634i
$751$	−19.7445			−0.720486			−0.360243	−	0.932858i	$-0.617306\pi$
$751$	−19.7445			−0.720486			−0.360243	+	0.932858i	$0.617306\pi$
$752$		−	13.5737i		−	0.494981i
$753$	−45.3685	+	6.87263i	−1.65332	+	0.250452i
$754$		−	4.18339i		−	0.152350i
$755$	−13.7480			−0.500343
$756$	1.38678	−	0.671643i	0.0504366	−	0.0244274i
$757$	−16.1892			−0.588408			−0.294204	−	0.955743i	$-0.595054\pi$
$757$	−16.1892			−0.588408			−0.294204	+	0.955743i	$0.595054\pi$
$758$	−28.6941			−1.04222
$759$	33.4550	+	2.01430i	1.21434	+	0.0731144i
$760$	12.4394			0.451226
$761$	45.8379			1.66162			0.830812	−	0.556553i	$-0.187876\pi$
$761$	45.8379			1.66162			0.830812	+	0.556553i	$0.187876\pi$
$762$	−16.2615	+	2.46336i	−0.589091	+	0.0892383i
$763$	6.76165			0.244788
$764$			5.47631i			0.198126i
$765$	2.61627	+	8.43726i	0.0945914	+	0.305050i
$766$			33.4226i			1.20761i
$767$	−3.91553			−0.141382
$768$	1.80368	+	11.9067i	0.0650846	+	0.429645i
$769$			30.3905i			1.09591i	0.836509	+	0.547954i	$0.184593\pi$
$769$			30.3905i			1.09591i	−0.836509	+	0.547954i	$0.815407\pi$
$770$	4.23322	+	0.904395i	0.152555	+	0.0325921i
$771$	49.2688	−	7.46347i	1.77437	−	0.268790i
$772$		−	5.27457i		−	0.189836i
$773$			21.1779i			0.761718i	0.924633	+	0.380859i	$0.124372\pi$
$773$			21.1779i			0.761718i	−0.924633	+	0.380859i	$0.875628\pi$
$774$	4.64029	+	14.9646i	0.166792	+	0.537891i
$775$	7.48192			0.268759
$776$	−2.44010			−0.0875944
$777$	−13.6278	+	2.06440i	−0.488895	+	0.0740601i
$778$		−	31.8711i		−	1.14263i
$779$		−	27.1903i		−	0.974195i
$780$	0.105390	+	0.695717i	0.00377358	+	0.0249107i
$781$	−2.22787	+	10.4280i	−0.0797193	+	0.373144i
$782$			22.4219i			0.801804i
$783$	−5.29909	−	10.9413i	−0.189374	−	0.391011i
$784$	3.31899			0.118535
$785$		−	11.7618i		−	0.419798i
$786$	2.76035	+	18.2220i	0.0984584	+	0.649957i
$787$		−	8.70200i		−	0.310193i	−0.987899	−	0.155096i	$-0.950431\pi$
$787$		−	8.70200i		−	0.310193i	0.987899	−	0.155096i	$-0.0495688\pi$
$788$	4.95890			0.176654
$789$	−5.56042	−	36.7062i	−0.197956	−	1.30677i
$790$	14.4154			0.512877
$791$	−4.97615			−0.176931
$792$	−29.7022	+	2.68657i	−1.05542	+	0.0954633i
$793$	0.583484			0.0207201
$794$	31.4717			1.11689
$795$	1.11865	+	7.38456i	0.0396743	+	0.261903i
$796$	5.51533			0.195486
$797$			43.8328i			1.55264i	0.630340	+	0.776319i	$0.282915\pi$
$797$			43.8328i			1.55264i	−0.630340	+	0.776319i	$0.717085\pi$
$798$	1.40517	+	9.27600i	0.0497425	+	0.328367i
$799$		−	12.0423i		−	0.426024i
$800$	1.66290			0.0587925
$801$	−8.11420	−	26.1677i	−0.286701	−	0.924589i
$802$		−	8.54489i		−	0.301731i
$803$	−4.95172	+	23.1776i	−0.174742	+	0.817920i
$804$	0.0954363	+	0.630006i	0.00336578	+	0.0222186i
$805$		−	5.83432i		−	0.205633i
$806$		−	13.3782i		−	0.471226i
$807$	25.8967	−	3.92295i	0.911607	−	0.138094i
$808$	42.5699			1.49760
$809$	3.36377			0.118264			0.0591319	−	0.998250i	$-0.481167\pi$
$809$	3.36377			0.118264			0.0591319	+	0.998250i	$0.481167\pi$
$810$	−6.64581	−	9.68574i	−0.233510	−	0.340322i
$811$		−	17.5612i		−	0.616657i	−0.951280	−	0.308328i	$-0.900230\pi$
$811$		−	17.5612i		−	0.616657i	0.951280	−	0.308328i	$-0.0997695\pi$
$812$			0.693788i			0.0243472i
$813$	1.60851	−	0.243664i	0.0564128	−	0.00854568i
$814$	33.6870	+	7.19698i	1.18073	+	0.252254i
$815$		−	13.7254i		−	0.480780i
$816$	−2.53527	−	16.7361i	−0.0887521	−	0.585882i
$817$	16.6063			0.580981
$818$		−	6.51399i		−	0.227756i
$819$	−3.92557	+	1.21726i	−0.137171	+	0.0425345i
$820$		−	1.94283i		−	0.0678467i
$821$	−15.2514			−0.532278			−0.266139	−	0.963935i	$-0.585748\pi$
$821$	−15.2514			−0.532278			−0.266139	+	0.963935i	$0.585748\pi$
$822$	−40.3304	+	6.10943i	−1.40668	+	0.213091i
$823$	−52.2341			−1.82076			−0.910382	−	0.413768i	$-0.864213\pi$
$823$	−52.2341			−1.82076			−0.910382	+	0.413768i	$0.864213\pi$
$824$	−54.5733			−1.90115
$825$	−0.345250	+	5.73418i	−0.0120201	+	0.199638i
$826$	−3.73026			−0.129792
$827$	−15.5865			−0.541994			−0.270997	−	0.962580i	$-0.587353\pi$
$827$	−15.5865			−0.541994			−0.270997	+	0.962580i	$0.587353\pi$
$828$	1.53723	+	4.95744i	0.0534223	+	0.172283i
$829$	−29.6495			−1.02977			−0.514885	−	0.857259i	$-0.672165\pi$
$829$	−29.6495			−1.02977			−0.514885	+	0.857259i	$0.672165\pi$
$830$		−	2.55256i		−	0.0886007i
$831$	6.89853	−	1.04502i	0.239307	−	0.0362514i
$832$		−	12.0673i		−	0.418359i
$833$	2.94453			0.102022
$834$	−29.7354	+	4.50446i	−1.02965	+	0.155977i
$835$		−	15.0317i		−	0.520192i
$836$	−0.852775	+	3.99160i	−0.0294938	+	0.138052i
$837$	−16.9461	−	34.9895i	−0.585743	−	1.20942i
$838$		−	11.7574i		−	0.406153i
$839$		−	30.7530i		−	1.06171i	−0.847462	−	0.530856i	$-0.821871\pi$
$839$		−	30.7530i		−	1.06171i	0.847462	−	0.530856i	$-0.178129\pi$
$840$	0.777575	+	5.13303i	0.0268289	+	0.177106i
$841$	−23.5262			−0.811248
$842$	9.48533			0.326886
$843$	0.113935	+	0.752121i	0.00392412	+	0.0259044i
$844$			4.81234i			0.165647i
$845$			11.1231i			0.382647i
$846$	4.74269	+	15.2948i	0.163057	+	0.525846i
$847$	−4.49497	+	10.0397i	−0.154449	+	0.344968i
$848$		−	14.3119i		−	0.491471i
$849$	−8.30884	+	1.25866i	−0.285159	+	0.0431971i
$850$	−3.84310			−0.131817
$851$		−	46.4282i		−	1.59154i
$852$	−1.63272	+	0.247332i	−0.0559362	+	0.00847347i
$853$		−	12.9363i		−	0.442930i	−0.975168	−	0.221465i	$-0.928916\pi$
$853$		−	12.9363i		−	0.442930i	0.975168	−	0.221465i	$-0.0710838\pi$
$854$	0.555876			0.0190217
$855$	−11.8918	+	3.68746i	−0.406690	+	0.126108i
$856$	9.61972			0.328795
$857$	55.9293			1.91051			0.955253	−	0.295788i	$-0.0955823\pi$
$857$	55.9293			1.91051			0.955253	+	0.295788i	$0.0955823\pi$
$858$	10.2531	+	0.617330i	0.350034	+	0.0210753i
$859$	9.79941			0.334352			0.167176	−	0.985927i	$-0.446535\pi$
$859$	9.79941			0.334352			0.167176	+	0.985927i	$0.446535\pi$
$860$	1.18657			0.0404618
$861$	11.2199	−	1.69964i	0.382372	−	0.0579235i
$862$	46.5633			1.58595
$863$		−	23.6121i		−	0.803767i	−0.915691	−	0.401883i	$-0.868356\pi$
$863$		−	23.6121i		−	0.803767i	0.915691	−	0.401883i	$-0.131644\pi$
$864$	−3.76637	−	7.77663i	−0.128135	−	0.264566i
$865$		−	9.46535i		−	0.321831i
$866$	−8.59498			−0.292069
$867$	2.16090	+	14.2648i	0.0733880	+	0.484458i
$868$			2.21868i			0.0753070i
$869$	−7.65338	+	35.8233i	−0.259623	+	1.21522i
$870$	5.22932	−	0.792161i	0.177290	−	0.0268568i
$871$		−	1.69960i		−	0.0575887i
$872$		−	20.2672i		−	0.686333i
$873$	2.33267	−	0.723325i	0.0789489	−	0.0244809i
$874$	−31.6022			−1.06896
$875$	1.00000			0.0338062
$876$	−3.62894	+	0.549729i	−0.122611	+	0.0185736i
$877$		−	41.7228i		−	1.40888i	−0.709765	−	0.704439i	$-0.751199\pi$
$877$		−	41.7228i		−	1.40888i	0.709765	−	0.704439i	$-0.248801\pi$
$878$			42.5788i			1.43696i
$879$	−8.47498	−	55.9461i	−0.285854	−	1.88702i
$880$	2.29984	−	10.7649i	0.0775276	−	0.362885i
$881$		−	25.6365i		−	0.863715i	−0.901942	−	0.431857i	$-0.857858\pi$
$881$		−	25.6365i		−	0.863715i	0.901942	−	0.431857i	$-0.142142\pi$
$882$	−3.73983	+	1.15966i	−0.125927	+	0.0390479i
$883$	−15.2069			−0.511752			−0.255876	−	0.966710i	$-0.582364\pi$
$883$	−15.2069			−0.511752			−0.255876	+	0.966710i	$0.582364\pi$
$884$		−	1.19623i		−	0.0402336i
$885$	−0.741440	−	4.89449i	−0.0249232	−	0.164526i
$886$		−	2.64996i		−	0.0890271i
$887$	38.5488			1.29434			0.647171	−	0.762345i	$-0.275952\pi$
$887$	38.5488			1.29434			0.647171	+	0.762345i	$0.275952\pi$
$888$	6.18778	+	40.8476i	0.207648	+	1.37075i
$889$	−7.27545			−0.244011
$890$	11.9191			0.399531
$891$	27.5981	−	11.3730i	0.924571	−	0.381010i
$892$	−1.10458			−0.0369839
$893$	16.9728			0.567972
$894$	−6.17920	−	40.7909i	−0.206663	−	1.36425i
$895$	−13.8510			−0.462989
$896$		−	8.17055i		−	0.272959i
$897$	−2.07353	−	13.6880i	−0.0692330	−	0.457030i
$898$		−	48.6453i		−	1.62332i
$899$	17.5048			0.583819
$900$	−0.849704	+	0.263480i	−0.0283235	+	0.00878268i
$901$		−	12.6972i		−	0.423004i
$902$	−27.7348	−	5.92532i	−0.923467	−	0.197292i
$903$	1.03804	+	6.85246i	0.0345439	+	0.228036i
$904$			14.9153i			0.496077i
$905$		−	1.39661i		−	0.0464250i
$906$	−30.7285	+	4.65489i	−1.02089	+	0.154648i
$907$	44.6404			1.48226			0.741130	−	0.671362i	$-0.234290\pi$
$907$	44.6404			1.48226			0.741130	+	0.671362i	$0.234290\pi$
$908$	−1.87474			−0.0622154
$909$	−40.6957	+	12.6191i	−1.34979	+	0.418550i
$910$		−	1.78806i		−	0.0592738i
$911$			44.6677i			1.47991i	0.672659	+	0.739953i	$0.265152\pi$
$911$			44.6677i			1.47991i	−0.672659	+	0.739953i	$0.734848\pi$
$912$	23.5885	−	3.57329i	0.781093	−	0.118324i
$913$	6.34329	+	1.35520i	0.209932	+	0.0448504i
$914$		−	30.5191i		−	1.00948i
$915$	0.110488	+	0.729366i	0.00365261	+	0.0241121i
$916$	−7.78404			−0.257192
$917$			8.15259i			0.269222i
$918$	8.70440	+	17.9724i	0.287288	+	0.593178i
$919$			57.7113i			1.90372i	0.306535	+	0.951859i	$0.400830\pi$
$919$			57.7113i			1.90372i	−0.306535	+	0.951859i	$0.599170\pi$
$920$	−17.4876			−0.576549
$921$	−41.9699	+	6.35780i	−1.38296	+	0.209497i
$922$	−4.67343			−0.153911
$923$	4.40468			0.144982
$924$	−1.70041	−	0.102380i	−0.0559393	−	0.00336806i
$925$	7.95778			0.261650
$926$	16.7176			0.549375
$927$	52.1706	−	16.1773i	1.71351	−	0.531333i
$928$	3.89055			0.127714
$929$		−	52.7358i		−	1.73021i	−0.501594	−	0.865103i	$-0.667253\pi$
$929$		−	52.7358i		−	1.73021i	0.501594	−	0.865103i	$-0.332747\pi$
$930$	16.7230	−	2.53327i	0.548368	−	0.0830693i
$931$			4.15012i			0.136015i
$932$	3.25427			0.106597
$933$	−15.8406	+	2.39960i	−0.518597	+	0.0785595i
$934$		−	48.9428i		−	1.60146i
$935$	2.04036	−	9.55037i	0.0667271	−	0.312331i
$936$	3.64858	+	11.7664i	0.119257	+	0.384596i
$937$		−	34.9190i		−	1.14075i	−0.821383	−	0.570377i	$-0.806797\pi$
$937$		−	34.9190i		−	1.14075i	0.821383	−	0.570377i	$-0.193203\pi$
$938$		−	1.61918i		−	0.0528681i
$939$	−6.21077	−	40.9994i	−0.202681	−	1.33796i
$940$	1.21276			0.0395558
$941$	40.4719			1.31935			0.659673	−	0.751553i	$-0.270695\pi$
$941$	40.4719			1.31935			0.659673	+	0.751553i	$0.270695\pi$
$942$	−3.98239	−	26.2891i	−0.129753	−	0.856544i
$943$			38.2247i			1.24477i
$944$			9.48591i			0.308740i
$945$	−2.26494	−	4.67654i	−0.0736785	−	0.152128i
$946$	3.61885	−	16.9388i	0.117659	−	0.550729i
$947$		−	0.984183i		−	0.0319817i	−0.999872	−	0.0159908i	$-0.994910\pi$
$947$		−	0.984183i		−	0.0319817i	0.999872	−	0.0159908i	$-0.00509026\pi$
$948$	−5.60889	+	0.849660i	−0.182168	+	0.0275957i
$949$	9.78997			0.317796
$950$		−	5.41660i		−	0.175738i
$951$	−43.3563	+	6.56781i	−1.40592	+	0.212976i
$952$		−	8.82583i		−	0.286047i
$953$	14.0671			0.455678			0.227839	−	0.973699i	$-0.426834\pi$
$953$	14.0671			0.455678			0.227839	+	0.973699i	$0.426834\pi$
$954$	5.00061	+	16.1266i	0.161901	+	0.522118i
$955$	18.4674			0.597592
$956$	0.241953			0.00782533
$957$	−0.807754	+	13.4158i	−0.0261110	+	0.433671i
$958$	10.4587			0.337905
$959$	−18.0440			−0.582671
$960$	15.0844	−	2.28505i	0.486847	−	0.0737498i
$961$	24.9792			0.805780
$962$		−	14.2290i		−	0.458762i
$963$	−9.19619	+	2.85160i	−0.296343	+	0.0918915i
$964$			3.30823i			0.106551i
$965$	−17.7871			−0.572588
$966$	−1.97542	−	13.0404i	−0.0635580	−	0.419567i
$967$		−	41.4502i		−	1.33295i	−0.745528	−	0.666475i	$-0.767802\pi$
$967$		−	41.4502i		−	1.33295i	0.745528	−	0.666475i	$-0.232198\pi$
$968$	30.0926	+	13.4731i	0.967213	+	0.433041i
$969$	20.9272	−	3.17014i	0.672278	−	0.101840i
$970$			1.06251i			0.0341152i
$971$		−	59.7042i		−	1.91600i	−0.286772	−	0.957999i	$-0.592582\pi$
$971$		−	59.7042i		−	1.91600i	0.286772	−	0.957999i	$-0.407418\pi$
$972$	3.15671	+	3.37691i	0.101251	+	0.108314i
$973$	−13.3038			−0.426499
$974$	−17.6513			−0.565586
$975$	2.34612	−	0.355402i	0.0751361	−	0.0113820i
$976$		−	1.41357i		−	0.0452473i
$977$		−	18.9219i		−	0.605367i	−0.953091	−	0.302683i	$-0.902118\pi$
$977$		−	18.9219i		−	0.605367i	0.953091	−	0.302683i	$-0.0978824\pi$
$978$	−4.64723	−	30.6779i	−0.148602	−	0.980971i
$979$	−6.32807	+	29.6199i	−0.202246	+	0.946657i
$980$			0.296539i			0.00947259i
$981$	6.00785	+	19.3749i	0.191816	+	0.618592i
$982$	23.4842			0.749410
$983$			11.5359i			0.367939i	0.982932	+	0.183970i	$0.0588948\pi$
$983$			11.5359i			0.367939i	−0.982932	+	0.183970i	$0.941105\pi$
$984$	−5.09444	−	33.6301i	−0.162405	−	1.07209i
$985$		−	16.7226i		−	0.532826i
$986$	−8.99139			−0.286344
$987$	1.06095	+	7.00367i	0.0337704	+	0.222929i
$988$	1.68601			0.0536391
$989$	−23.3455			−0.742342
$990$	1.16984	+	12.9334i	0.0371798	+	0.411052i
$991$	−33.9048			−1.07702			−0.538511	−	0.842619i	$-0.681013\pi$
$991$	−33.9048			−1.07702			−0.538511	+	0.842619i	$0.681013\pi$
$992$	12.4417			0.395025
$993$	−1.02693	−	6.77914i	−0.0325888	−	0.215129i
$994$	4.19627			0.133097
$995$		−	18.5990i		−	0.589628i
$996$	0.150451	+	0.993175i	0.00476721	+	0.0314700i
$997$			5.88467i			0.186369i	0.995649	+	0.0931846i	$0.0297047\pi$
$997$			5.88467i			0.186369i	−0.995649	+	0.0931846i	$0.970295\pi$
$998$	40.4315			1.27984
$999$	−18.0239	−	37.2149i	−0.570251	−	1.17743i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.l.f.1121.11	yes	40
3.2	odd	2		1155.2.l.e.1121.30	yes	40
11.10	odd	2		1155.2.l.e.1121.29	✓	40
33.32	even	2	inner	1155.2.l.f.1121.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.l.e.1121.29	✓	40	11.10	odd	2
1155.2.l.e.1121.30	yes	40	3.2	odd	2
1155.2.l.f.1121.11	yes	40	1.1	even	1	trivial
1155.2.l.f.1121.12	yes	40	33.32	even	2	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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.30517 q^{2} +(-0.259419 - 1.71251i) q^{3} -0.296539 q^{4} +1.00000i q^{5} +(0.338586 + 2.23512i) q^{6} +1.00000i q^{7} +2.99737 q^{8} +(-2.86540 + 0.888518i) q^{9} +O(q^{10})\)	\(q-1.30517 q^{2} +(-0.259419 - 1.71251i) q^{3} -0.296539 q^{4} +1.00000i q^{5} +(0.338586 + 2.23512i) q^{6} +1.00000i q^{7} +2.99737 q^{8} +(-2.86540 + 0.888518i) q^{9} -1.30517i q^{10} +(3.24343 + 0.692934i) q^{11} +(0.0769280 + 0.507827i) q^{12} -1.36999i q^{13} -1.30517i q^{14} +(1.71251 - 0.259419i) q^{15} -3.31899 q^{16} -2.94453 q^{17} +(3.73983 - 1.15966i) q^{18} -4.15012i q^{19} -0.296539i q^{20} +(1.71251 - 0.259419i) q^{21} +(-4.23322 - 0.904395i) q^{22} +5.83432i q^{23} +(-0.777575 - 5.13303i) q^{24} -1.00000 q^{25} +1.78806i q^{26} +(2.26494 + 4.67654i) q^{27} -0.296539i q^{28} -2.33962 q^{29} +(-2.23512 + 0.338586i) q^{30} -7.48192 q^{31} -1.66290 q^{32} +(0.345250 - 5.73418i) q^{33} +3.84310 q^{34} -1.00000 q^{35} +(0.849704 - 0.263480i) q^{36} -7.95778 q^{37} +5.41660i q^{38} +(-2.34612 + 0.355402i) q^{39} +2.99737i q^{40} +6.55170 q^{41} +(-2.23512 + 0.338586i) q^{42} +4.00141i q^{43} +(-0.961804 - 0.205482i) q^{44} +(-0.888518 - 2.86540i) q^{45} -7.61476i q^{46} +4.08970i q^{47} +(0.861010 + 5.68381i) q^{48} -1.00000 q^{49} +1.30517 q^{50} +(0.763868 + 5.04254i) q^{51} +0.406255i q^{52} +4.31212i q^{53} +(-2.95613 - 6.10367i) q^{54} +(-0.692934 + 3.24343i) q^{55} +2.99737i q^{56} +(-7.10714 + 1.07662i) q^{57} +3.05359 q^{58} -2.85807i q^{59} +(-0.507827 + 0.0769280i) q^{60} +0.425904i q^{61} +9.76516 q^{62} +(-0.888518 - 2.86540i) q^{63} +8.80834 q^{64} +1.36999 q^{65} +(-0.450609 + 7.48406i) q^{66} +1.24059 q^{67} +0.873168 q^{68} +(9.99134 - 1.51353i) q^{69} +1.30517 q^{70} +3.21512i q^{71} +(-8.58866 + 2.66322i) q^{72} +7.14602i q^{73} +10.3862 q^{74} +(0.259419 + 1.71251i) q^{75} +1.23067i q^{76} +(-0.692934 + 3.24343i) q^{77} +(3.06208 - 0.463859i) q^{78} +11.0449i q^{79} -3.31899i q^{80} +(7.42107 - 5.09193i) q^{81} -8.55106 q^{82} +1.95574 q^{83} +(-0.507827 + 0.0769280i) q^{84} -2.94453i q^{85} -5.22250i q^{86} +(0.606942 + 4.00663i) q^{87} +(9.72175 + 2.07698i) q^{88} +9.13228i q^{89} +(1.15966 + 3.73983i) q^{90} +1.36999 q^{91} -1.73010i q^{92} +(1.94096 + 12.8129i) q^{93} -5.33775i q^{94} +4.15012 q^{95} +(0.431389 + 2.84774i) q^{96} -0.814080 q^{97} +1.30517 q^{98} +(-9.90942 + 0.896311i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9	\( 40 q + 4 q^{2} - 4 q^{3} + 44 q^{4} + 4 q^{6} + 12 q^{8} - 2 q^{9} + 6 q^{11} + 8 q^{12} + 2 q^{15} + 68 q^{16} - 40 q^{18} + 2 q^{21} - 4 q^{22} + 12 q^{24} - 40 q^{25} + 32 q^{27} + 24 q^{29} - 8 q^{31} - 52 q^{32} + 28 q^{33} + 32 q^{34} - 40 q^{35} - 48 q^{37} - 66 q^{39} + 16 q^{41} - 32 q^{44} + 32 q^{48} - 40 q^{49} - 4 q^{50} + 14 q^{51} + 72 q^{54} + 8 q^{55} + 24 q^{57} - 80 q^{58} + 24 q^{60} - 48 q^{62} + 76 q^{64} - 4 q^{65} - 48 q^{67} + 32 q^{68} - 20 q^{69} - 4 q^{70} - 128 q^{72} + 4 q^{75} + 8 q^{77} - 28 q^{78} + 50 q^{81} - 32 q^{82} + 24 q^{83} + 24 q^{84} + 32 q^{87} - 16 q^{88} - 8 q^{90} - 4 q^{91} - 20 q^{93} + 12 q^{95} - 12 q^{96} + 100 q^{97} - 4 q^{98} + 56 q^{99}+O(q^{100}) \) 40 * q + 4 * q^2 - 4 * q^3 + 44 * q^4 + 4 * q^6 + 12 * q^8 - 2 * q^9 + 6 * q^11 + 8 * q^12 + 2 * q^15 + 68 * q^16 - 40 * q^18 + 2 * q^21 - 4 * q^22 + 12 * q^24 - 40 * q^25 + 32 * q^27 + 24 * q^29 - 8 * q^31 - 52 * q^32 + 28 * q^33 + 32 * q^34 - 40 * q^35 - 48 * q^37 - 66 * q^39 + 16 * q^41 - 32 * q^44 + 32 * q^48 - 40 * q^49 - 4 * q^50 + 14 * q^51 + 72 * q^54 + 8 * q^55 + 24 * q^57 - 80 * q^58 + 24 * q^60 - 48 * q^62 + 76 * q^64 - 4 * q^65 - 48 * q^67 + 32 * q^68 - 20 * q^69 - 4 * q^70 - 128 * q^72 + 4 * q^75 + 8 * q^77 - 28 * q^78 + 50 * q^81 - 32 * q^82 + 24 * q^83 + 24 * q^84 + 32 * q^87 - 16 * q^88 - 8 * q^90 - 4 * q^91 - 20 * q^93 + 12 * q^95 - 12 * q^96 + 100 * q^97 - 4 * q^98 + 56 * q^99

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