LMFDB - Embedded newform 561.2.g.b.67.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [561,2,Mod(67,561)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(561, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("561.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 561 = 3 \cdot 11 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	561.g (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:	$4.47960755339$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 27x^{14} + 291x^{12} + 1585x^{10} + 4548x^{8} + 6536x^{6} + 4136x^{4} + 768x^{2} + 4 $ x^16 + 27x^14 + 291x^12 + 1585x^10 + 4548x^8 + 6536x^6 + 4136x^4 + 768*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			67.4
Root			$-2.49230i$ of defining polynomial
Character	$\chi$	$=$	561.67
Dual form			561.2.g.b.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.49230 q^{2} +1.00000i q^{3} +4.21156 q^{4} +2.17306i q^{5} -2.49230i q^{6} -2.46372i q^{7} -5.51186 q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-2.49230 q^{2} +1.00000i q^{3} +4.21156 q^{4} +2.17306i q^{5} -2.49230i q^{6} -2.46372i q^{7} -5.51186 q^{8} -1.00000 q^{9} -5.41591i q^{10} +1.00000i q^{11} +4.21156i q^{12} -1.16919 q^{13} +6.14032i q^{14} -2.17306 q^{15} +5.31409 q^{16} +(-3.84357 + 1.49230i) q^{17} +2.49230 q^{18} -4.88594 q^{19} +9.15196i q^{20} +2.46372 q^{21} -2.49230i q^{22} +1.25216i q^{23} -5.51186i q^{24} +0.277814 q^{25} +2.91397 q^{26} -1.00000i q^{27} -10.3761i q^{28} -2.57234i q^{29} +5.41591 q^{30} +8.05562i q^{31} -2.22058 q^{32} -1.00000 q^{33} +(9.57933 - 3.71926i) q^{34} +5.35381 q^{35} -4.21156 q^{36} -4.50608i q^{37} +12.1772 q^{38} -1.16919i q^{39} -11.9776i q^{40} +0.360915i q^{41} -6.14032 q^{42} -6.70304 q^{43} +4.21156i q^{44} -2.17306i q^{45} -3.12077i q^{46} -11.4420 q^{47} +5.31409i q^{48} +0.930091 q^{49} -0.692395 q^{50} +(-1.49230 - 3.84357i) q^{51} -4.92411 q^{52} -12.2611 q^{53} +2.49230i q^{54} -2.17306 q^{55} +13.5797i q^{56} -4.88594i q^{57} +6.41105i q^{58} -3.63942 q^{59} -9.15196 q^{60} -1.76690i q^{61} -20.0770i q^{62} +2.46372i q^{63} -5.09383 q^{64} -2.54072i q^{65} +2.49230 q^{66} +2.09079 q^{67} +(-16.1874 + 6.28490i) q^{68} -1.25216 q^{69} -13.3433 q^{70} -11.2231i q^{71} +5.51186 q^{72} -6.94305i q^{73} +11.2305i q^{74} +0.277814i q^{75} -20.5774 q^{76} +2.46372 q^{77} +2.91397i q^{78} +9.84882i q^{79} +11.5478i q^{80} +1.00000 q^{81} -0.899508i q^{82} -12.8475 q^{83} +10.3761 q^{84} +(-3.24285 - 8.35231i) q^{85} +16.7060 q^{86} +2.57234 q^{87} -5.51186i q^{88} +0.382289 q^{89} +5.41591i q^{90} +2.88056i q^{91} +5.27356i q^{92} -8.05562 q^{93} +28.5168 q^{94} -10.6174i q^{95} -2.22058i q^{96} +3.08407i q^{97} -2.31806 q^{98} -1.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 2 q^{2} + 22 q^{4} - 6 q^{8} - 16 q^{9}+O(q^{10}) $ 16 * q - 2 * q^2 + 22 * q^4 - 6 * q^8 - 16 * q^9	$ 16 q - 2 q^{2} + 22 q^{4} - 6 q^{8} - 16 q^{9} + 12 q^{13} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 2 q^{18} - 8 q^{19} + 2 q^{21} - 56 q^{25} - 8 q^{26} - 36 q^{30} - 34 q^{32} - 16 q^{33} + 30 q^{34} + 8 q^{35} - 22 q^{36} + 44 q^{38} - 12 q^{42} - 24 q^{43} + 18 q^{47} - 34 q^{49} + 30 q^{50} + 14 q^{51} + 28 q^{52} - 26 q^{53} - 4 q^{55} - 2 q^{59} - 12 q^{60} - 38 q^{64} + 2 q^{66} + 30 q^{67} + 42 q^{68} - 28 q^{69} + 88 q^{70} + 6 q^{72} - 84 q^{76} + 2 q^{77} + 16 q^{81} - 52 q^{83} + 24 q^{84} + 40 q^{85} - 52 q^{86} - 26 q^{87} + 78 q^{89} + 20 q^{93} - 16 q^{94} - 70 q^{98}+O(q^{100}) $ 16 * q - 2 * q^2 + 22 * q^4 - 6 * q^8 - 16 * q^9 + 12 * q^13 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 2 * q^18 - 8 * q^19 + 2 * q^21 - 56 * q^25 - 8 * q^26 - 36 * q^30 - 34 * q^32 - 16 * q^33 + 30 * q^34 + 8 * q^35 - 22 * q^36 + 44 * q^38 - 12 * q^42 - 24 * q^43 + 18 * q^47 - 34 * q^49 + 30 * q^50 + 14 * q^51 + 28 * q^52 - 26 * q^53 - 4 * q^55 - 2 * q^59 - 12 * q^60 - 38 * q^64 + 2 * q^66 + 30 * q^67 + 42 * q^68 - 28 * q^69 + 88 * q^70 + 6 * q^72 - 84 * q^76 + 2 * q^77 + 16 * q^81 - 52 * q^83 + 24 * q^84 + 40 * q^85 - 52 * q^86 - 26 * q^87 + 78 * q^89 + 20 * q^93 - 16 * q^94 - 70 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/561\mathbb{Z}\right)^\times$.

$n$	$188$	$409$	$496$
$\chi(n)$	$1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−2.49230			−1.76232			−0.881161	−	0.472817i	$-0.843237\pi$
$2$	−2.49230			−1.76232			−0.881161	+	0.472817i	$0.843237\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	4.21156			2.10578
$5$			2.17306i			0.971822i	0.874008	+	0.485911i	$0.161512\pi$
$5$			2.17306i			0.971822i	−0.874008	+	0.485911i	$0.838488\pi$
$6$		−	2.49230i		−	1.01748i
$7$		−	2.46372i		−	0.931198i	−0.884996	−	0.465599i	$-0.845839\pi$
$7$		−	2.46372i		−	0.931198i	0.884996	−	0.465599i	$-0.154161\pi$
$8$	−5.51186			−1.94874
$9$	−1.00000			−0.333333
$10$		−	5.41591i		−	1.71266i
$11$			1.00000i			0.301511i
$11$			1.00000i			0.301511i
$12$			4.21156i			1.21577i
$13$	−1.16919			−0.324275			−0.162138	−	0.986768i	$-0.551839\pi$
$13$	−1.16919			−0.324275			−0.162138	+	0.986768i	$0.551839\pi$
$14$			6.14032i			1.64107i
$15$	−2.17306			−0.561081
$16$	5.31409			1.32852
$17$	−3.84357	+	1.49230i	−0.932203	+	0.361936i
$17$	−3.84357	+	1.49230i	−0.932203	+	0.361936i
$18$	2.49230			0.587441
$19$	−4.88594			−1.12091			−0.560455	−	0.828185i	$-0.689374\pi$
$19$	−4.88594			−1.12091			−0.560455	+	0.828185i	$0.689374\pi$
$20$			9.15196i			2.04644i
$21$	2.46372			0.537627
$22$		−	2.49230i		−	0.531360i
$23$			1.25216i			0.261094i	0.991442	+	0.130547i	$0.0416734\pi$
$23$			1.25216i			0.261094i	−0.991442	+	0.130547i	$0.958327\pi$
$24$		−	5.51186i		−	1.12510i
$25$	0.277814			0.0555627
$26$	2.91397			0.571477
$27$		−	1.00000i		−	0.192450i
$28$		−	10.3761i		−	1.96090i
$29$		−	2.57234i		−	0.477672i	−0.971060	−	0.238836i	$-0.923234\pi$
$29$		−	2.57234i		−	0.477672i	0.971060	−	0.238836i	$-0.0767658\pi$
$30$	5.41591			0.988806
$31$			8.05562i			1.44683i	0.690413	+	0.723416i	$0.257429\pi$
$31$			8.05562i			1.44683i	−0.690413	+	0.723416i	$0.742571\pi$
$32$	−2.22058			−0.392546
$33$	−1.00000			−0.174078
$34$	9.57933	−	3.71926i	1.64284	−	0.637847i
$35$	5.35381			0.904958
$36$	−4.21156			−0.701926
$37$		−	4.50608i		−	0.740796i	−0.928873	−	0.370398i	$-0.879221\pi$
$37$		−	4.50608i		−	0.740796i	0.928873	−	0.370398i	$-0.120779\pi$
$38$	12.1772			1.97541
$39$		−	1.16919i		−	0.187220i
$40$		−	11.9776i		−	1.89382i
$41$			0.360915i			0.0563654i	0.999603	+	0.0281827i	$0.00897203\pi$
$41$			0.360915i			0.0563654i	−0.999603	+	0.0281827i	$0.991028\pi$
$42$	−6.14032			−0.947473
$43$	−6.70304			−1.02220			−0.511102	−	0.859520i	$-0.670762\pi$
$43$	−6.70304			−1.02220			−0.511102	+	0.859520i	$0.670762\pi$
$44$			4.21156i			0.634916i
$45$		−	2.17306i		−	0.323941i
$46$		−	3.12077i		−	0.460132i
$47$	−11.4420			−1.66898			−0.834491	−	0.551022i	$-0.814238\pi$
$47$	−11.4420			−1.66898			−0.834491	+	0.551022i	$0.814238\pi$
$48$			5.31409i			0.767022i
$49$	0.930091			0.132870
$50$	−0.692395			−0.0979194
$51$	−1.49230	−	3.84357i	−0.208964	−	0.538208i
$52$	−4.92411			−0.682851
$53$	−12.2611			−1.68419			−0.842094	−	0.539330i	$-0.818678\pi$
$53$	−12.2611			−1.68419			−0.842094	+	0.539330i	$0.818678\pi$
$54$			2.49230i			0.339159i
$55$	−2.17306			−0.293015
$56$			13.5797i			1.81466i
$57$		−	4.88594i		−	0.647158i
$58$			6.41105i			0.841812i
$59$	−3.63942			−0.473812			−0.236906	−	0.971533i	$-0.576133\pi$
$59$	−3.63942			−0.473812			−0.236906	+	0.971533i	$0.576133\pi$
$60$	−9.15196			−1.18151
$61$		−	1.76690i		−	0.226229i	−0.993582	−	0.113114i	$-0.963917\pi$
$61$		−	1.76690i		−	0.226229i	0.993582	−	0.113114i	$-0.0360826\pi$
$62$		−	20.0770i		−	2.54978i
$63$			2.46372i			0.310399i
$64$	−5.09383			−0.636728
$65$		−	2.54072i		−	0.315138i
$66$	2.49230			0.306781
$67$	2.09079			0.255431			0.127715	−	0.991811i	$-0.459236\pi$
$67$	2.09079			0.255431			0.127715	+	0.991811i	$0.459236\pi$
$68$	−16.1874	+	6.28490i	−1.96301	+	0.762156i
$69$	−1.25216			−0.150743
$70$	−13.3433			−1.59483
$71$		−	11.2231i		−	1.33193i	−0.745981	−	0.665967i	$-0.768019\pi$
$71$		−	11.2231i		−	1.33193i	0.745981	−	0.665967i	$-0.231981\pi$
$72$	5.51186			0.649579
$73$		−	6.94305i		−	0.812622i	−0.913735	−	0.406311i	$-0.866815\pi$
$73$		−	6.94305i		−	0.812622i	0.913735	−	0.406311i	$-0.133185\pi$
$74$			11.2305i			1.30552i
$75$			0.277814i			0.0320792i
$76$	−20.5774			−2.36039
$77$	2.46372			0.280767
$78$			2.91397i			0.329942i
$79$			9.84882i			1.10808i	0.832490	+	0.554040i	$0.186914\pi$
$79$			9.84882i			1.10808i	−0.832490	+	0.554040i	$0.813086\pi$
$80$			11.5478i			1.29109i
$81$	1.00000			0.111111
$82$		−	0.899508i		−	0.0993340i
$83$	−12.8475			−1.41020			−0.705098	−	0.709110i	$-0.749097\pi$
$83$	−12.8475			−1.41020			−0.705098	+	0.709110i	$0.749097\pi$
$84$	10.3761			1.13212
$85$	−3.24285	−	8.35231i	−0.351737	−	0.905935i
$86$	16.7060			1.80145
$87$	2.57234			0.275784
$88$		−	5.51186i		−	0.587566i
$89$	0.382289			0.0405225			0.0202613	−	0.999795i	$-0.493550\pi$
$89$	0.382289			0.0405225			0.0202613	+	0.999795i	$0.493550\pi$
$90$			5.41591i			0.570887i
$91$			2.88056i			0.301964i
$92$			5.27356i			0.549806i
$93$	−8.05562			−0.835329
$94$	28.5168			2.94128
$95$		−	10.6174i		−	1.08933i
$96$		−	2.22058i		−	0.226637i
$97$			3.08407i			0.313140i	0.987667	+	0.156570i	$0.0500437\pi$
$97$			3.08407i			0.313140i	−0.987667	+	0.156570i	$0.949956\pi$
$98$	−2.31806			−0.234160
$99$		−	1.00000i		−	0.100504i
$100$	1.17003			0.117003
$101$	14.7352			1.46621			0.733105	−	0.680115i	$-0.238070\pi$
$101$	14.7352			1.46621			0.733105	+	0.680115i	$0.238070\pi$
$102$	3.71926	+	9.57933i	0.368261	+	0.948495i
$103$	−7.14160			−0.703682			−0.351841	−	0.936060i	$-0.614444\pi$
$103$	−7.14160			−0.703682			−0.351841	+	0.936060i	$0.614444\pi$
$104$	6.44441			0.631926
$105$			5.35381i			0.522478i
$106$	30.5583			2.96808
$107$		−	13.0437i		−	1.26098i	−0.776198	−	0.630489i	$-0.782854\pi$
$107$		−	13.0437i		−	1.26098i	0.776198	−	0.630489i	$-0.217146\pi$
$108$		−	4.21156i		−	0.405257i
$109$			12.0663i			1.15574i	0.816128	+	0.577871i	$0.196116\pi$
$109$			12.0663i			1.15574i	−0.816128	+	0.577871i	$0.803884\pi$
$110$	5.41591			0.516387
$111$	4.50608			0.427698
$112$		−	13.0924i		−	1.23712i
$113$		−	12.2114i		−	1.14876i	−0.818590	−	0.574378i	$-0.805244\pi$
$113$		−	12.2114i		−	1.14876i	0.818590	−	0.574378i	$-0.194756\pi$
$114$			12.1772i			1.14050i
$115$	−2.72103			−0.253737
$116$		−	10.8336i		−	1.00587i
$117$	1.16919			0.108092
$118$	9.07053			0.835010
$119$	3.67661	+	9.46948i	0.337034	+	0.868066i
$120$	11.9776			1.09340
$121$	−1.00000			−0.0909091
$122$			4.40365i			0.398688i
$123$	−0.360915			−0.0325426
$124$			33.9267i			3.04671i
$125$			11.4690i			1.02582i
$126$		−	6.14032i		−	0.547024i
$127$	9.08945			0.806559			0.403279	−	0.915077i	$-0.367870\pi$
$127$	9.08945			0.806559			0.403279	+	0.915077i	$0.367870\pi$
$128$	17.1365			1.51467
$129$		−	6.70304i		−	0.590169i
$130$			6.33223i			0.555374i
$131$			18.6298i			1.62769i	0.581079	+	0.813847i	$0.302631\pi$
$131$			18.6298i			1.62769i	−0.581079	+	0.813847i	$0.697369\pi$
$132$	−4.21156			−0.366569
$133$			12.0376i			1.04379i
$134$	−5.21087			−0.450151
$135$	2.17306			0.187027
$136$	21.1852	−	8.22534i	1.81662	−	0.705317i
$137$	−0.528456			−0.0451491			−0.0225745	−	0.999745i	$-0.507186\pi$
$137$	−0.528456			−0.0451491			−0.0225745	+	0.999745i	$0.507186\pi$
$138$	3.12077			0.265657
$139$		−	10.8443i		−	0.919801i	−0.887970	−	0.459900i	$-0.847885\pi$
$139$		−	10.8443i		−	0.919801i	0.887970	−	0.459900i	$-0.152115\pi$
$140$	22.5478			1.90564
$141$		−	11.4420i		−	0.963587i
$142$			27.9713i			2.34730i
$143$		−	1.16919i		−	0.0977726i
$144$	−5.31409			−0.442840
$145$	5.58985			0.464212
$146$			17.3042i			1.43210i
$147$			0.930091i			0.0767126i
$148$		−	18.9776i		−	1.55995i
$149$	−5.01956			−0.411218			−0.205609	−	0.978634i	$-0.565918\pi$
$149$	−5.01956			−0.411218			−0.205609	+	0.978634i	$0.565918\pi$
$150$		−	0.692395i		−	0.0565338i
$151$	−9.67446			−0.787296			−0.393648	−	0.919261i	$-0.628787\pi$
$151$	−9.67446			−0.787296			−0.393648	+	0.919261i	$0.628787\pi$
$152$	26.9306			2.18436
$153$	3.84357	−	1.49230i	0.310734	−	0.120645i
$154$	−6.14032			−0.494801
$155$	−17.5053			−1.40606
$156$		−	4.92411i		−	0.394244i
$157$	15.4750			1.23504			0.617518	−	0.786557i	$-0.288138\pi$
$157$	15.4750			1.23504			0.617518	+	0.786557i	$0.288138\pi$
$158$		−	24.5462i		−	1.95279i
$159$		−	12.2611i		−	0.972367i
$160$		−	4.82545i		−	0.381485i
$161$	3.08498			0.243130
$162$	−2.49230			−0.195814
$163$			1.04064i			0.0815093i	0.999169	+	0.0407547i	$0.0129762\pi$
$163$			1.04064i			0.0815093i	−0.999169	+	0.0407547i	$0.987024\pi$
$164$			1.52001i			0.118693i
$165$		−	2.17306i		−	0.169172i
$166$	32.0198			2.48522
$167$		−	17.3378i		−	1.34164i	−0.741621	−	0.670819i	$-0.765943\pi$
$167$		−	17.3378i		−	1.34164i	0.741621	−	0.670819i	$-0.234057\pi$
$168$	−13.5797			−1.04769
$169$	−11.6330			−0.894846
$170$	8.08216	+	20.8165i	0.619874	+	1.59655i
$171$	4.88594			0.373637
$172$	−28.2302			−2.15253
$173$			17.3731i			1.32085i	0.750892	+	0.660425i	$0.229624\pi$
$173$			17.3731i			1.32085i	−0.750892	+	0.660425i	$0.770376\pi$
$174$	−6.41105			−0.486020
$175$		−	0.684455i		−	0.0517399i
$176$			5.31409i			0.400564i
$177$		−	3.63942i		−	0.273556i
$178$	−0.952777			−0.0714137
$179$	4.96915			0.371412			0.185706	−	0.982605i	$-0.440543\pi$
$179$	4.96915			0.371412			0.185706	+	0.982605i	$0.440543\pi$
$180$		−	9.15196i		−	0.682147i
$181$			14.6179i			1.08654i	0.839559	+	0.543269i	$0.182814\pi$
$181$			14.6179i			1.08654i	−0.839559	+	0.543269i	$0.817186\pi$
$182$		−	7.17921i		−	0.532158i
$183$	1.76690			0.130613
$184$		−	6.90175i		−	0.508803i
$185$	9.79199			0.719921
$186$	20.0770			1.47212
$187$	−1.49230	−	3.84357i	−0.109128	−	0.281070i
$188$	−48.1885			−3.51450
$189$	−2.46372			−0.179209
$190$			26.4618i			1.91974i
$191$	22.2674			1.61121			0.805606	−	0.592452i	$-0.201840\pi$
$191$	22.2674			1.61121			0.805606	+	0.592452i	$0.201840\pi$
$192$		−	5.09383i		−	0.367615i
$193$			15.1822i			1.09284i	0.837511	+	0.546421i	$0.184010\pi$
$193$			15.1822i			1.09284i	−0.837511	+	0.546421i	$0.815990\pi$
$194$		−	7.68644i		−	0.551854i
$195$	2.54072			0.181945
$196$	3.91713			0.279795
$197$			5.72137i			0.407631i	0.979009	+	0.203815i	$0.0653342\pi$
$197$			5.72137i			0.407631i	−0.979009	+	0.203815i	$0.934666\pi$
$198$			2.49230i			0.177120i
$199$		−	2.29581i		−	0.162746i	−0.996684	−	0.0813728i	$-0.974070\pi$
$199$		−	2.29581i		−	0.162746i	0.996684	−	0.0813728i	$-0.0259304\pi$
$200$	−1.53127			−0.108277
$201$			2.09079i			0.147473i
$202$	−36.7246			−2.58393
$203$	−6.33753			−0.444807
$204$	−6.28490	−	16.1874i	−0.440031	−	1.13335i
$205$	−0.784289			−0.0547772
$206$	17.7990			1.24011
$207$		−	1.25216i		−	0.0870314i
$208$	−6.21318			−0.430806
$209$		−	4.88594i		−	0.337967i
$210$		−	13.3433i		−	0.920774i
$211$			12.3687i			0.851497i	0.904841	+	0.425749i	$0.139989\pi$
$211$			12.3687i			0.851497i	−0.904841	+	0.425749i	$0.860011\pi$
$212$	−51.6382			−3.54653
$213$	11.2231			0.768992
$214$			32.5087i			2.22225i
$215$		−	14.5661i		−	0.993399i
$216$			5.51186i			0.375034i
$217$	19.8468			1.34729
$218$		−	30.0728i		−	2.03679i
$219$	6.94305			0.469168
$220$	−9.15196			−0.617025
$221$	4.49387	−	1.74478i	0.302290	−	0.117367i
$222$	−11.2305			−0.753742
$223$	−19.0369			−1.27481			−0.637404	−	0.770530i	$-0.719992\pi$
$223$	−19.0369			−1.27481			−0.637404	+	0.770530i	$0.719992\pi$
$224$			5.47088i			0.365538i
$225$	−0.277814			−0.0185209
$226$			30.4346i			2.02448i
$227$			24.2887i			1.61210i	0.591847	+	0.806050i	$0.298399\pi$
$227$			24.2887i			1.61210i	−0.591847	+	0.806050i	$0.701601\pi$
$228$		−	20.5774i		−	1.36277i
$229$	0.0162373			0.00107299			0.000536496	−	1.00000i	$-0.499829\pi$
$229$	0.0162373			0.00107299			0.000536496		1.00000i	$0.499829\pi$
$230$	6.78161			0.447166
$231$			2.46372i			0.162101i
$232$			14.1784i			0.930856i
$233$		−	2.89854i		−	0.189889i	−0.995483	−	0.0949447i	$-0.969733\pi$
$233$		−	2.89854i		−	0.189889i	0.995483	−	0.0949447i	$-0.0302674\pi$
$234$	−2.91397			−0.190492
$235$		−	24.8641i		−	1.62195i
$236$	−15.3276			−0.997743
$237$	−9.84882			−0.639750
$238$	−9.16320	−	23.6008i	−0.593962	−	1.52981i
$239$	−14.5492			−0.941107			−0.470553	−	0.882371i	$-0.655946\pi$
$239$	−14.5492			−0.941107			−0.470553	+	0.882371i	$0.655946\pi$
$240$	−11.5478			−0.745409
$241$			4.30109i			0.277057i	0.990358	+	0.138529i	$0.0442373\pi$
$241$			4.30109i			0.277057i	−0.990358	+	0.138529i	$0.955763\pi$
$242$	2.49230			0.160211
$243$			1.00000i			0.0641500i
$244$		−	7.44141i		−	0.476387i
$245$			2.02114i			0.129126i
$246$	0.899508			0.0573505
$247$	5.71259			0.363483
$248$		−	44.4014i		−	2.81949i
$249$		−	12.8475i		−	0.814177i
$250$		−	28.5842i		−	1.80782i
$251$	7.78251			0.491228			0.245614	−	0.969368i	$-0.421010\pi$
$251$	7.78251			0.491228			0.245614	+	0.969368i	$0.421010\pi$
$252$			10.3761i			0.653632i
$253$	−1.25216			−0.0787228
$254$	−22.6536			−1.42142
$255$	8.35231	−	3.24285i	0.523042	−	0.203075i
$256$	−32.5216			−2.03260
$257$	11.1017			0.692507			0.346253	−	0.938141i	$-0.387454\pi$
$257$	11.1017			0.692507			0.346253	+	0.938141i	$0.387454\pi$
$258$			16.7060i			1.04007i
$259$	−11.1017			−0.689827
$260$		−	10.7004i		−	0.663609i
$261$			2.57234i			0.159224i
$262$		−	46.4311i		−	2.86852i
$263$	−21.2656			−1.31129			−0.655646	−	0.755069i	$-0.727603\pi$
$263$	−21.2656			−1.31129			−0.655646	+	0.755069i	$0.727603\pi$
$264$	5.51186			0.339231
$265$		−	26.6441i		−	1.63673i
$266$		−	30.0012i		−	1.83949i
$267$			0.382289i			0.0233957i
$268$	8.80547			0.537880
$269$			30.7627i			1.87563i	0.347130	+	0.937817i	$0.387156\pi$
$269$			30.7627i			1.87563i	−0.347130	+	0.937817i	$0.612844\pi$
$270$	−5.41591			−0.329602
$271$	−18.6513			−1.13299			−0.566493	−	0.824066i	$-0.691700\pi$
$271$	−18.6513			−1.13299			−0.566493	+	0.824066i	$0.691700\pi$
$272$	−20.4251	+	7.93021i	−1.23845	+	0.480839i
$273$	−2.88056			−0.174339
$274$	1.31707			0.0795672
$275$			0.277814i			0.0167528i
$276$	−5.27356			−0.317431
$277$			5.87638i			0.353077i	0.984294	+	0.176539i	$0.0564901\pi$
$277$			5.87638i			0.353077i	−0.984294	+	0.176539i	$0.943510\pi$
$278$			27.0272i			1.62099i
$279$		−	8.05562i		−	0.482277i
$280$	−29.5094			−1.76352
$281$	11.3488			0.677016			0.338508	−	0.940964i	$-0.390078\pi$
$281$	11.3488			0.677016			0.338508	+	0.940964i	$0.390078\pi$
$282$			28.5168i			1.69815i
$283$			16.1346i			0.959102i	0.877514	+	0.479551i	$0.159201\pi$
$283$			16.1346i			0.959102i	−0.877514	+	0.479551i	$0.840799\pi$
$284$		−	47.2666i		−	2.80476i
$285$	10.6174			0.628922
$286$			2.91397i			0.172307i
$287$	0.889193			0.0524874
$288$	2.22058			0.130849
$289$	12.5461	−	11.4715i	0.738005	−	0.674795i
$290$	−13.9316			−0.818091
$291$	−3.08407			−0.180792
$292$		−	29.2410i		−	1.71120i
$293$	16.7239			0.977023			0.488511	−	0.872558i	$-0.337540\pi$
$293$	16.7239			0.977023			0.488511	+	0.872558i	$0.337540\pi$
$294$		−	2.31806i		−	0.135192i
$295$		−	7.90868i		−	0.460461i
$296$			24.8369i			1.44361i
$297$	1.00000			0.0580259
$298$	12.5102			0.724699
$299$		−	1.46402i		−	0.0846663i
$300$			1.17003i			0.0675516i
$301$			16.5144i			0.951874i
$302$	24.1116			1.38747
$303$			14.7352i			0.846517i
$304$	−25.9643			−1.48915
$305$	3.83958			0.219854
$306$	−9.57933	+	3.71926i	−0.547614	+	0.212616i
$307$	−15.2687			−0.871432			−0.435716	−	0.900084i	$-0.643505\pi$
$307$	−15.2687			−0.871432			−0.435716	+	0.900084i	$0.643505\pi$
$308$	10.3761			0.591232
$309$		−	7.14160i		−	0.406271i
$310$	43.6285			2.47793
$311$		−	17.8996i		−	1.01499i	−0.861654	−	0.507496i	$-0.830571\pi$
$311$		−	17.8996i		−	1.01499i	0.861654	−	0.507496i	$-0.169429\pi$
$312$			6.44441i			0.364843i
$313$			16.3886i			0.926340i	0.886269	+	0.463170i	$0.153288\pi$
$313$			16.3886i			0.926340i	−0.886269	+	0.463170i	$0.846712\pi$
$314$	−38.5682			−2.17653
$315$	−5.35381			−0.301653
$316$			41.4789i			2.33337i
$317$			31.5448i			1.77173i	0.463939	+	0.885867i	$0.346436\pi$
$317$			31.5448i			1.77173i	−0.463939	+	0.885867i	$0.653564\pi$
$318$			30.5583i			1.71362i
$319$	2.57234			0.144023
$320$		−	11.0692i		−	0.618786i
$321$	13.0437			0.728026
$322$	−7.68869			−0.428474
$323$	18.7794	−	7.29128i	1.04492	−	0.405698i
$324$	4.21156			0.233975
$325$	−0.324817			−0.0180176
$326$		−	2.59359i		−	0.143646i
$327$	−12.0663			−0.667268
$328$		−	1.98931i		−	0.109841i
$329$			28.1898i			1.55415i
$330$			5.41591i			0.298136i
$331$	27.9726			1.53751			0.768757	−	0.639541i	$-0.220876\pi$
$331$	27.9726			1.53751			0.768757	+	0.639541i	$0.220876\pi$
$332$	−54.1080			−2.96956
$333$			4.50608i			0.246932i
$334$			43.2110i			2.36440i
$335$			4.54341i			0.248233i
$336$	13.0924			0.714250
$337$			11.3053i			0.615841i	0.951412	+	0.307921i	$0.0996332\pi$
$337$			11.3053i			0.615841i	−0.951412	+	0.307921i	$0.900367\pi$
$338$	28.9929			1.57701
$339$	12.2114			0.663234
$340$	−13.6575	−	35.1762i	−0.740680	−	1.90770i
$341$	−8.05562			−0.436236
$342$	−12.1772			−0.658468
$343$		−	19.5375i		−	1.05493i
$344$	36.9462			1.99200
$345$		−	2.72103i		−	0.146495i
$346$		−	43.2989i		−	2.32776i
$347$			3.35792i			0.180262i	0.995930	+	0.0901312i	$0.0287286\pi$
$347$			3.35792i			0.180262i	−0.995930	+	0.0901312i	$0.971271\pi$
$348$	10.8336			0.580740
$349$	−27.6667			−1.48097			−0.740483	−	0.672075i	$-0.765403\pi$
$349$	−27.6667			−1.48097			−0.740483	+	0.672075i	$0.765403\pi$
$350$			1.70587i			0.0911824i
$351$			1.16919i			0.0624068i
$352$		−	2.22058i		−	0.118357i
$353$	8.35039			0.444446			0.222223	−	0.974996i	$-0.428669\pi$
$353$	8.35039			0.444446			0.222223	+	0.974996i	$0.428669\pi$
$354$			9.07053i			0.482093i
$355$	24.3884			1.29440
$356$	1.61003			0.0853314
$357$	−9.46948	+	3.67661i	−0.501178	+	0.194587i
$358$	−12.3846			−0.654547
$359$	2.49303			0.131577			0.0657885	−	0.997834i	$-0.479044\pi$
$359$	2.49303			0.131577			0.0657885	+	0.997834i	$0.479044\pi$
$360$			11.9776i			0.631274i
$361$	4.87237			0.256441
$362$		−	36.4321i		−	1.91483i
$363$		−	1.00000i		−	0.0524864i
$364$			12.1316i			0.635870i
$365$	15.0877			0.789724
$366$	−4.40365			−0.230182
$367$		−	0.611578i		−	0.0319241i	−0.999873	−	0.0159621i	$-0.994919\pi$
$367$		−	0.611578i		−	0.0319241i	0.999873	−	0.0159621i	$-0.00508110\pi$
$368$			6.65410i			0.346869i
$369$		−	0.360915i		−	0.0187885i
$370$	−24.4046			−1.26873
$371$			30.2079i			1.56831i
$372$	−33.9267			−1.75902
$373$	14.4426			0.747811			0.373905	−	0.927467i	$-0.378018\pi$
$373$	14.4426			0.747811			0.373905	+	0.927467i	$0.378018\pi$
$374$	3.71926	+	9.57933i	0.192318	+	0.495335i
$375$	−11.4690			−0.592257
$376$	63.0665			3.25240
$377$			3.00756i			0.154897i
$378$	6.14032			0.315824
$379$			36.8637i			1.89356i	0.321882	+	0.946780i	$0.395685\pi$
$379$			36.8637i			1.89356i	−0.321882	+	0.946780i	$0.604315\pi$
$380$		−	44.7159i		−	2.29388i
$381$			9.08945i			0.465667i
$382$	−55.4970			−2.83947
$383$	33.8273			1.72849			0.864247	−	0.503067i	$-0.167795\pi$
$383$	33.8273			1.72849			0.864247	+	0.503067i	$0.167795\pi$
$384$			17.1365i			0.874493i
$385$			5.35381i			0.272855i
$386$		−	37.8387i		−	1.92594i
$387$	6.70304			0.340734
$388$			12.9887i			0.659404i
$389$	−22.7700			−1.15448			−0.577242	−	0.816573i	$-0.695871\pi$
$389$	−22.7700			−1.15448			−0.577242	+	0.816573i	$0.695871\pi$
$390$	−6.33223			−0.320645
$391$	−1.86860	−	4.81278i	−0.0944993	−	0.243393i
$392$	−5.12653			−0.258929
$393$	−18.6298			−0.939750
$394$		−	14.2594i		−	0.718376i
$395$	−21.4021			−1.07686
$396$		−	4.21156i		−	0.211639i
$397$		−	30.5518i		−	1.53335i	−0.642034	−	0.766676i	$-0.721909\pi$
$397$		−	30.5518i		−	1.53335i	0.642034	−	0.766676i	$-0.278091\pi$
$398$			5.72184i			0.286810i
$399$	−12.0376			−0.602632
$400$	1.47633			0.0738163
$401$		−	10.4877i		−	0.523732i	−0.965104	−	0.261866i	$-0.915662\pi$
$401$		−	10.4877i		−	0.523732i	0.965104	−	0.261866i	$-0.0843379\pi$
$402$		−	5.21087i		−	0.259895i
$403$		−	9.41855i		−	0.469171i
$404$	62.0582			3.08751
$405$			2.17306i			0.107980i
$406$	15.7950			0.783893
$407$	4.50608			0.223358
$408$	8.22534	+	21.1852i	0.407215	+	1.04882i
$409$	−3.62681			−0.179334			−0.0896672	−	0.995972i	$-0.528580\pi$
$409$	−3.62681			−0.179334			−0.0896672	+	0.995972i	$0.528580\pi$
$410$	1.95468			0.0965350
$411$		−	0.528456i		−	0.0260668i
$412$	−30.0772			−1.48180
$413$			8.96651i			0.441213i
$414$			3.12077i			0.153377i
$415$		−	27.9184i		−	1.37046i
$416$	2.59628			0.127293
$417$	10.8443			0.531047
$418$			12.1772i			0.595607i
$419$		−	35.3148i		−	1.72524i	−0.505853	−	0.862620i	$-0.668822\pi$
$419$		−	35.3148i		−	1.72524i	0.505853	−	0.862620i	$-0.331178\pi$
$420$			22.5478i			1.10022i
$421$	18.3897			0.896261			0.448131	−	0.893968i	$-0.352090\pi$
$421$	18.3897			0.896261			0.448131	+	0.893968i	$0.352090\pi$
$422$		−	30.8265i		−	1.50061i
$423$	11.4420			0.556327
$424$	67.5813			3.28204
$425$	−1.06780	+	0.414581i	−0.0517958	+	0.0201101i
$426$	−27.9713			−1.35521
$427$	−4.35315			−0.210664
$428$		−	54.9341i		−	2.65534i
$429$	1.16919			0.0564490
$430$			36.3031i			1.75069i
$431$		−	29.1330i		−	1.40329i	−0.712528	−	0.701644i	$-0.752450\pi$
$431$		−	29.1330i		−	1.40329i	0.712528	−	0.701644i	$-0.247550\pi$
$432$		−	5.31409i		−	0.255674i
$433$	39.0053			1.87448			0.937239	−	0.348689i	$-0.113373\pi$
$433$	39.0053			1.87448			0.937239	+	0.348689i	$0.113373\pi$
$434$	−49.4641			−2.37435
$435$			5.58985i			0.268013i
$436$			50.8179i			2.43374i
$437$		−	6.11799i		−	0.292663i
$438$	−17.3042			−0.826824
$439$		−	37.3994i		−	1.78498i	−0.451070	−	0.892489i	$-0.648957\pi$
$439$		−	37.3994i		−	1.78498i	0.451070	−	0.892489i	$-0.351043\pi$
$440$	11.9776			0.571009
$441$	−0.930091			−0.0442900
$442$	−11.2001	+	4.34852i	−0.532733	+	0.206838i
$443$	13.3303			0.633344			0.316672	−	0.948535i	$-0.397435\pi$
$443$	13.3303			0.633344			0.316672	+	0.948535i	$0.397435\pi$
$444$	18.9776			0.900638
$445$			0.830736i			0.0393806i
$446$	47.4457			2.24662
$447$		−	5.01956i		−	0.237417i
$448$			12.5498i			0.592920i
$449$		−	11.0850i		−	0.523135i	−0.965185	−	0.261568i	$-0.915761\pi$
$449$		−	11.0850i		−	0.523135i	0.965185	−	0.261568i	$-0.0842394\pi$
$450$	0.692395			0.0326398
$451$	−0.360915			−0.0169948
$452$		−	51.4292i		−	2.41902i
$453$		−	9.67446i		−	0.454546i
$454$		−	60.5348i		−	2.84104i
$455$	−6.25962			−0.293455
$456$			26.9306i			1.26114i
$457$	−10.1154			−0.473177			−0.236588	−	0.971610i	$-0.576029\pi$
$457$	−10.1154			−0.473177			−0.236588	+	0.971610i	$0.576029\pi$
$458$	−0.0404683			−0.00189096
$459$	1.49230	+	3.84357i	0.0696546	+	0.179403i
$460$	−11.4597			−0.534314
$461$	−28.3509			−1.32043			−0.660217	−	0.751075i	$-0.729536\pi$
$461$	−28.3509			−1.32043			−0.660217	+	0.751075i	$0.729536\pi$
$462$		−	6.14032i		−	0.285674i
$463$	−30.1816			−1.40266			−0.701329	−	0.712838i	$-0.747409\pi$
$463$	−30.1816			−1.40266			−0.701329	+	0.712838i	$0.747409\pi$
$464$		−	13.6696i		−	0.634597i
$465$		−	17.5053i		−	0.811790i
$466$			7.22402i			0.334646i
$467$	12.5433			0.580437			0.290218	−	0.956960i	$-0.406272\pi$
$467$	12.5433			0.580437			0.290218	+	0.956960i	$0.406272\pi$
$468$	4.92411			0.227617
$469$		−	5.15112i		−	0.237856i
$470$			61.9687i			2.85840i
$471$			15.4750i			0.713048i
$472$	20.0600			0.923335
$473$		−	6.70304i		−	0.308206i
$474$	24.5462			1.12745
$475$	−1.35738			−0.0622809
$476$	15.4842	+	39.8812i	0.709718	+	1.82795i
$477$	12.2611			0.561396
$478$	36.2609			1.65853
$479$			33.7149i			1.54047i	0.637759	+	0.770236i	$0.279862\pi$
$479$			33.7149i			1.54047i	−0.637759	+	0.770236i	$0.720138\pi$
$480$	4.82545			0.220251
$481$			5.26847i			0.240222i
$482$		−	10.7196i		−	0.488264i
$483$			3.08498i			0.140371i
$484$	−4.21156			−0.191434
$485$	−6.70188			−0.304317
$486$		−	2.49230i		−	0.113053i
$487$			7.96912i			0.361115i	0.983564	+	0.180558i	$0.0577902\pi$
$487$			7.96912i			0.361115i	−0.983564	+	0.180558i	$0.942210\pi$
$488$			9.73891i			0.440860i
$489$	−1.04064			−0.0470594
$490$		−	5.03729i		−	0.227562i
$491$	25.5849			1.15463			0.577316	−	0.816521i	$-0.304100\pi$
$491$	25.5849			1.15463			0.577316	+	0.816521i	$0.304100\pi$
$492$	−1.52001			−0.0685275
$493$	3.83870	+	9.88698i	0.172887	+	0.445287i
$494$	−14.2375			−0.640575
$495$	2.17306			0.0976717
$496$			42.8082i			1.92215i
$497$	−27.6505			−1.24029
$498$			32.0198i			1.43484i
$499$		−	3.60127i		−	0.161215i	−0.996746	−	0.0806074i	$-0.974314\pi$
$499$		−	3.60127i		−	0.161215i	0.996746	−	0.0806074i	$-0.0256860\pi$
$500$			48.3023i			2.16015i
$501$	17.3378			0.774595
$502$	−19.3963			−0.865701
$503$			25.8760i			1.15375i	0.816832	+	0.576876i	$0.195728\pi$
$503$			25.8760i			1.15375i	−0.816832	+	0.576876i	$0.804272\pi$
$504$		−	13.5797i		−	0.604886i
$505$			32.0205i			1.42489i
$506$	3.12077			0.138735
$507$		−	11.6330i		−	0.516639i
$508$	38.2807			1.69843
$509$	−18.1150			−0.802933			−0.401467	−	0.915874i	$-0.631499\pi$
$509$	−18.1150			−0.802933			−0.401467	+	0.915874i	$0.631499\pi$
$510$	−20.8165	+	8.08216i	−0.921768	+	0.357884i
$511$	−17.1057			−0.756712
$512$	46.7806			2.06743
$513$			4.88594i			0.215719i
$514$	−27.6688			−1.22042
$515$		−	15.5191i		−	0.683854i
$516$		−	28.2302i		−	1.24277i
$517$		−	11.4420i		−	0.503217i
$518$	27.6688			1.21570
$519$	−17.3731			−0.762594
$520$			14.0041i			0.614120i
$521$			10.8997i			0.477524i	0.971078	+	0.238762i	$0.0767416\pi$
$521$			10.8997i			0.477524i	−0.971078	+	0.238762i	$0.923258\pi$
$522$		−	6.41105i		−	0.280604i
$523$	18.0935			0.791174			0.395587	−	0.918429i	$-0.370541\pi$
$523$	18.0935			0.791174			0.395587	+	0.918429i	$0.370541\pi$
$524$			78.4605i			3.42756i
$525$	0.684455			0.0298721
$526$	53.0002			2.31092
$527$	−12.0214	−	30.9623i	−0.523660	−	1.34874i
$528$	−5.31409			−0.231266
$529$	21.4321			0.931830
$530$			66.4050i			2.88445i
$531$	3.63942			0.157937
$532$			50.6969i			2.19799i
$533$		−	0.421978i		−	0.0182779i
$534$		−	0.952777i		−	0.0412307i
$535$	28.3446			1.22545
$536$	−11.5241			−0.497767
$537$			4.96915i			0.214435i
$538$		−	76.6698i		−	3.30547i
$539$			0.930091i			0.0400619i
$540$	9.15196			0.393838
$541$		−	34.0965i		−	1.46592i	−0.680271	−	0.732961i	$-0.738138\pi$
$541$		−	34.0965i		−	1.46592i	0.680271	−	0.732961i	$-0.261862\pi$
$542$	46.4846			1.99669
$543$	−14.6179			−0.627313
$544$	8.53495	−	3.31377i	0.365933	−	0.142077i
$545$	−26.2208			−1.12318
$546$	7.17921			0.307242
$547$		−	28.1313i		−	1.20281i	−0.798945	−	0.601404i	$-0.794608\pi$
$547$		−	28.1313i		−	1.20281i	0.798945	−	0.601404i	$-0.205392\pi$
$548$	−2.22562			−0.0950739
$549$			1.76690i			0.0754096i
$550$		−	0.692395i		−	0.0295238i
$551$			12.5683i			0.535428i
$552$	6.90175			0.293758
$553$	24.2647			1.03184
$554$		−	14.6457i		−	0.622236i
$555$			9.79199i			0.415647i
$556$		−	45.6713i		−	1.93690i
$557$	1.54307			0.0653822			0.0326911	−	0.999466i	$-0.489592\pi$
$557$	1.54307			0.0653822			0.0326911	+	0.999466i	$0.489592\pi$
$558$			20.0770i			0.849928i
$559$	7.83713			0.331475
$560$	28.4506			1.20226
$561$	3.84357	−	1.49230i	0.162276	−	0.0630049i
$562$	−28.2847			−1.19312
$563$	−38.7420			−1.63278			−0.816390	−	0.577500i	$-0.804028\pi$
$563$	−38.7420			−1.63278			−0.816390	+	0.577500i	$0.804028\pi$
$564$		−	48.1885i		−	2.02910i
$565$	26.5362			1.11639
$566$		−	40.2122i		−	1.69025i
$567$		−	2.46372i		−	0.103466i
$568$			61.8600i			2.59559i
$569$	40.0767			1.68010			0.840052	−	0.542507i	$-0.182525\pi$
$569$	40.0767			1.68010			0.840052	+	0.542507i	$0.182525\pi$
$570$	−26.4618			−1.10836
$571$			30.6869i			1.28421i	0.766617	+	0.642104i	$0.221938\pi$
$571$			30.6869i			1.28421i	−0.766617	+	0.642104i	$0.778062\pi$
$572$		−	4.92411i		−	0.205887i
$573$			22.2674i			0.930233i
$574$	−2.21613			−0.0924997
$575$			0.347868i			0.0145071i
$576$	5.09383			0.212243
$577$	−3.32245			−0.138316			−0.0691578	−	0.997606i	$-0.522031\pi$
$577$	−3.32245			−0.138316			−0.0691578	+	0.997606i	$0.522031\pi$
$578$	−31.2686	+	28.5905i	−1.30060	+	1.18921i
$579$	−15.1822			−0.630952
$580$	23.5420			0.977527
$581$			31.6526i			1.31317i
$582$	7.68644			0.318613
$583$		−	12.2611i		−	0.507802i
$584$			38.2691i			1.58359i
$585$			2.54072i			0.105046i
$586$	−41.6811			−1.72183
$587$	−40.0937			−1.65484			−0.827422	−	0.561581i	$-0.810193\pi$
$587$	−40.0937			−1.65484			−0.827422	+	0.561581i	$0.810193\pi$
$588$			3.91713i			0.161540i
$589$		−	39.3592i		−	1.62177i
$590$			19.7108i			0.811481i
$591$	−5.72137			−0.235346
$592$		−	23.9457i		−	0.984163i
$593$	8.44784			0.346911			0.173456	−	0.984842i	$-0.444507\pi$
$593$	8.44784			0.346911			0.173456	+	0.984842i	$0.444507\pi$
$594$	−2.49230			−0.102260
$595$	−20.5777	+	7.98948i	−0.843605	+	0.327537i
$596$	−21.1401			−0.865934
$597$	2.29581			0.0939612
$598$			3.64877i			0.149209i
$599$	−41.4590			−1.69397			−0.846984	−	0.531619i	$-0.821584\pi$
$599$	−41.4590			−1.69397			−0.846984	+	0.531619i	$0.821584\pi$
$600$		−	1.53127i		−	0.0625138i
$601$		−	23.8221i		−	0.971724i	−0.874036	−	0.485862i	$-0.838506\pi$
$601$		−	23.8221i		−	0.971724i	0.874036	−	0.485862i	$-0.161494\pi$
$602$		−	41.1588i		−	1.67751i
$603$	−2.09079			−0.0851435
$604$	−40.7445			−1.65787
$605$		−	2.17306i		−	0.0883474i
$606$		−	36.7246i		−	1.49183i
$607$			39.1248i			1.58803i	0.607901	+	0.794013i	$0.292012\pi$
$607$			39.1248i			1.58803i	−0.607901	+	0.794013i	$0.707988\pi$
$608$	10.8496			0.440010
$609$		−	6.33753i		−	0.256810i
$610$	−9.56939			−0.387453
$611$	13.3778			0.541209
$612$	16.1874	−	6.28490i	0.654337	−	0.254052i
$613$	12.4063			0.501085			0.250543	−	0.968106i	$-0.419391\pi$
$613$	12.4063			0.501085			0.250543	+	0.968106i	$0.419391\pi$
$614$	38.0542			1.53574
$615$		−	0.784289i		−	0.0316256i
$616$	−13.5797			−0.547140
$617$			19.3261i			0.778038i	0.921230	+	0.389019i	$0.127186\pi$
$617$			19.3261i			0.778038i	−0.921230	+	0.389019i	$0.872814\pi$
$618$			17.7990i			0.715981i
$619$		−	28.4522i		−	1.14359i	−0.820397	−	0.571795i	$-0.806247\pi$
$619$		−	28.4522i		−	1.14359i	0.820397	−	0.571795i	$-0.193753\pi$
$620$	−73.7247			−2.96085
$621$	1.25216			0.0502476
$622$			44.6111i			1.78874i
$623$		−	0.941851i		−	0.0377345i
$624$		−	6.21318i		−	0.248726i
$625$	−23.5338			−0.941350
$626$		−	40.8454i		−	1.63251i
$627$	4.88594			0.195126
$628$	65.1736			2.60071
$629$	6.72442	+	17.3195i	0.268120	+	0.690572i
$630$	13.3433			0.531609
$631$	−32.7357			−1.30319			−0.651594	−	0.758568i	$-0.725899\pi$
$631$	−32.7357			−1.30319			−0.651594	+	0.758568i	$0.725899\pi$
$632$		−	54.2853i		−	2.15935i
$633$	−12.3687			−0.491612
$634$		−	78.6192i		−	3.12237i
$635$			19.7519i			0.783831i
$636$		−	51.6382i		−	2.04759i
$637$	−1.08745			−0.0430865
$638$	−6.41105			−0.253816
$639$			11.2231i			0.443978i
$640$			37.2386i			1.47199i
$641$		−	27.9023i		−	1.10207i	−0.834481	−	0.551036i	$-0.814233\pi$
$641$		−	27.9023i		−	1.10207i	0.834481	−	0.551036i	$-0.185767\pi$
$642$	−32.5087			−1.28302
$643$			27.3963i			1.08040i	0.841535	+	0.540202i	$0.181652\pi$
$643$			27.3963i			1.08040i	−0.841535	+	0.540202i	$0.818348\pi$
$644$	12.9926			0.511978
$645$	14.5661			0.573539
$646$	−46.8040	+	18.1720i	−1.84148	+	0.714970i
$647$	−17.5963			−0.691781			−0.345890	−	0.938275i	$-0.612423\pi$
$647$	−17.5963			−0.691781			−0.345890	+	0.938275i	$0.612423\pi$
$648$	−5.51186			−0.216526
$649$		−	3.63942i		−	0.142860i
$650$	0.809541			0.0317528
$651$			19.8468i			0.777856i
$652$			4.38272i			0.171641i
$653$			3.55890i			0.139270i	0.997573	+	0.0696352i	$0.0221835\pi$
$653$			3.55890i			0.139270i	−0.997573	+	0.0696352i	$0.977816\pi$
$654$	30.0728			1.17594
$655$	−40.4837			−1.58183
$656$			1.91793i			0.0748827i
$657$			6.94305i			0.270874i
$658$		−	70.2574i		−	2.73892i
$659$	−20.1999			−0.786878			−0.393439	−	0.919351i	$-0.628715\pi$
$659$	−20.1999			−0.786878			−0.393439	+	0.919351i	$0.628715\pi$
$660$		−	9.15196i		−	0.356239i
$661$	11.9976			0.466654			0.233327	−	0.972398i	$-0.425039\pi$
$661$	11.9976			0.466654			0.233327	+	0.972398i	$0.425039\pi$
$662$	−69.7161			−2.70959
$663$	1.74478	+	4.49387i	0.0677617	+	0.174527i
$664$	70.8136			2.74810
$665$	−26.1584			−1.01438
$666$		−	11.2305i		−	0.435173i
$667$	3.22099			0.124717
$668$		−	73.0191i		−	2.82519i
$669$		−	19.0369i		−	0.736010i
$670$		−	11.3235i		−	0.437466i
$671$	1.76690			0.0682105
$672$	−5.47088			−0.211044
$673$		−	30.8862i		−	1.19058i	−0.803513	−	0.595288i	$-0.797038\pi$
$673$		−	30.8862i		−	1.19058i	0.803513	−	0.595288i	$-0.202962\pi$
$674$		−	28.1763i		−	1.08531i
$675$		−	0.277814i		−	0.0106931i
$676$	−48.9930			−1.88435
$677$			39.2716i			1.50933i	0.656111	+	0.754665i	$0.272200\pi$
$677$			39.2716i			1.50933i	−0.656111	+	0.754665i	$0.727800\pi$
$678$	−30.4346			−1.16883
$679$	7.59829			0.291596
$680$	17.8741	+	46.0367i	0.685442	+	1.76543i
$681$	−24.2887			−0.930747
$682$	20.0770			0.768788
$683$			20.4844i			0.783812i	0.920005	+	0.391906i	$0.128184\pi$
$683$			20.4844i			0.783812i	−0.920005	+	0.391906i	$0.871816\pi$
$684$	20.5774			0.786796
$685$		−	1.14837i		−	0.0438769i
$686$			48.6933i			1.85912i
$687$			0.0162373i			0.000619493i
$688$	−35.6205			−1.35802
$689$	14.3355			0.546140
$690$			6.78161i			0.258171i
$691$			28.3145i			1.07714i	0.842582	+	0.538568i	$0.181034\pi$
$691$			28.3145i			1.07714i	−0.842582	+	0.538568i	$0.818966\pi$
$692$			73.1677i			2.78142i
$693$	−2.46372			−0.0935889
$694$		−	8.36894i		−	0.317680i
$695$	23.5653			0.893882
$696$	−14.1784			−0.537430
$697$	−0.538593	−	1.38720i	−0.0204007	−	0.0525440i
$698$	68.9538			2.60994
$699$	2.89854			0.109633
$700$		−	2.88262i		−	0.108953i
$701$	27.5094			1.03901			0.519507	−	0.854466i	$-0.326116\pi$
$701$	27.5094			1.03901			0.519507	+	0.854466i	$0.326116\pi$
$702$		−	2.91397i		−	0.109981i
$703$			22.0164i			0.830366i
$704$		−	5.09383i		−	0.191981i
$705$	24.8641			0.936435
$706$	−20.8117			−0.783258
$707$		−	36.3035i		−	1.36533i
$708$		−	15.3276i		−	0.576047i
$709$		−	51.6726i		−	1.94061i	−0.241892	−	0.970303i	$-0.577768\pi$
$709$		−	51.6726i		−	1.94061i	0.241892	−	0.970303i	$-0.422232\pi$
$710$	−60.7832			−2.28115
$711$		−	9.84882i		−	0.369360i
$712$	−2.10712			−0.0789676
$713$	−10.0870			−0.377759
$714$	23.6008	−	9.16320i	0.883237	−	0.342924i
$715$	2.54072			0.0950175
$716$	20.9278			0.782110
$717$		−	14.5492i		−	0.543348i
$718$	−6.21337			−0.231881
$719$			27.8188i			1.03747i	0.854936	+	0.518733i	$0.173596\pi$
$719$			27.8188i			1.03747i	−0.854936	+	0.518733i	$0.826404\pi$
$720$		−	11.5478i		−	0.430362i
$721$			17.5949i			0.655268i
$722$	−12.1434			−0.451931
$723$	−4.30109			−0.159959
$724$			61.5640i			2.28801i
$725$		−	0.714632i		−	0.0265408i
$726$			2.49230i			0.0924979i
$727$	0.0811307			0.00300897			0.00150449	−	0.999999i	$-0.499521\pi$
$727$	0.0811307			0.00300897			0.00150449	+	0.999999i	$0.499521\pi$
$728$		−	15.8772i		−	0.588449i
$729$	−1.00000			−0.0370370
$730$	−37.6029			−1.39175
$731$	25.7636	−	10.0029i	0.952901	−	0.369972i
$732$	7.44141			0.275042
$733$	−37.1675			−1.37281			−0.686406	−	0.727218i	$-0.740813\pi$
$733$	−37.1675			−1.37281			−0.686406	+	0.727218i	$0.740813\pi$
$734$			1.52424i			0.0562606i
$735$	−2.02114			−0.0745510
$736$		−	2.78053i		−	0.102492i
$737$			2.09079i			0.0770152i
$738$			0.899508i			0.0331113i
$739$	−37.4457			−1.37746			−0.688730	−	0.725018i	$-0.741832\pi$
$739$	−37.4457			−1.37746			−0.688730	+	0.725018i	$0.741832\pi$
$740$	41.2395			1.51599
$741$			5.71259i			0.209857i
$742$		−	75.2870i		−	2.76387i
$743$			14.4261i			0.529241i	0.964353	+	0.264621i	$0.0852467\pi$
$743$			14.4261i			0.529241i	−0.964353	+	0.264621i	$0.914753\pi$
$744$	44.4014			1.62783
$745$		−	10.9078i		−	0.399631i
$746$	−35.9953			−1.31788
$747$	12.8475			0.470066
$748$	−6.28490	−	16.1874i	−0.229799	−	0.591870i
$749$	−32.1359			−1.17422
$750$	28.5842			1.04375
$751$		−	30.5053i		−	1.11316i	−0.830796	−	0.556578i	$-0.812114\pi$
$751$		−	30.5053i		−	1.11316i	0.830796	−	0.556578i	$-0.187886\pi$
$752$	−60.8036			−2.21728
$753$			7.78251i			0.283610i
$754$		−	7.49573i		−	0.272978i
$755$		−	21.0232i		−	0.765112i
$756$	−10.3761			−0.377375
$757$	−15.7346			−0.571883			−0.285941	−	0.958247i	$-0.592306\pi$
$757$	−15.7346			−0.571883			−0.285941	+	0.958247i	$0.592306\pi$
$758$		−	91.8753i		−	3.33706i
$759$		−	1.25216i		−	0.0454507i
$760$			58.5217i			2.12281i
$761$	−14.0029			−0.507606			−0.253803	−	0.967256i	$-0.581682\pi$
$761$	−14.0029			−0.507606			−0.253803	+	0.967256i	$0.581682\pi$
$762$		−	22.6536i		−	0.820655i
$763$	29.7280			1.07622
$764$	93.7803			3.39285
$765$	3.24285	+	8.35231i	0.117246	+	0.301978i
$766$	−84.3078			−3.04616
$767$	4.25518			0.153646
$768$		−	32.5216i		−	1.17352i
$769$	19.9053			0.717802			0.358901	−	0.933376i	$-0.383151\pi$
$769$	19.9053			0.717802			0.358901	+	0.933376i	$0.383151\pi$
$770$		−	13.3433i		−	0.480859i
$771$			11.1017i			0.399819i
$772$			63.9408i			2.30128i
$773$	18.7886			0.675779			0.337890	−	0.941186i	$-0.390287\pi$
$773$	18.7886			0.675779			0.337890	+	0.941186i	$0.390287\pi$
$774$	−16.7060			−0.600484
$775$			2.23796i			0.0803899i
$776$		−	16.9990i		−	0.610228i
$777$		−	11.1017i		−	0.398272i
$778$	56.7497			2.03457
$779$		−	1.76341i		−	0.0631806i
$780$	10.7004			0.383135
$781$	11.2231			0.401593
$782$	4.65712	+	11.9949i	0.166538	+	0.428936i
$783$	−2.57234			−0.0919280
$784$	4.94258			0.176521
$785$			33.6280i			1.20023i
$786$	46.4311			1.65614
$787$			14.4342i			0.514525i	0.966342	+	0.257263i	$0.0828206\pi$
$787$			14.4342i			0.514525i	−0.966342	+	0.257263i	$0.917179\pi$
$788$			24.0959i			0.858380i
$789$		−	21.2656i		−	0.757074i
$790$	53.3404			1.89777
$791$	−30.0856			−1.06972
$792$			5.51186i			0.195855i
$793$			2.06585i			0.0733603i
$794$			76.1443i			2.70226i
$795$	26.6441			0.944967
$796$		−	9.66893i		−	0.342706i
$797$	13.2002			0.467574			0.233787	−	0.972288i	$-0.424888\pi$
$797$	13.2002			0.467574			0.233787	+	0.972288i	$0.424888\pi$
$798$	30.0012			1.06203
$799$	43.9780	−	17.0748i	1.55583	−	0.604064i
$800$	−0.616907			−0.0218110
$801$	−0.382289			−0.0135075
$802$			26.1386i			0.922985i
$803$	6.94305			0.245015
$804$			8.80547i			0.310545i
$805$			6.70384i			0.236279i
$806$			23.4738i			0.826831i
$807$	−30.7627			−1.08290
$808$	−81.2185			−2.85726
$809$		−	38.9591i		−	1.36973i	−0.728671	−	0.684864i	$-0.759861\pi$
$809$		−	38.9591i		−	1.36973i	0.728671	−	0.684864i	$-0.240139\pi$
$810$		−	5.41591i		−	0.190296i
$811$			38.3560i			1.34686i	0.739250	+	0.673431i	$0.235180\pi$
$811$			38.3560i			1.34686i	−0.739250	+	0.673431i	$0.764820\pi$
$812$	−26.6908			−0.936665
$813$		−	18.6513i		−	0.654130i
$814$	−11.2305			−0.393629
$815$	−2.26138			−0.0792125
$816$	−7.93021	−	20.4251i	−0.277613	−	0.715020i
$817$	32.7506			1.14580
$818$	9.03911			0.316045
$819$		−	2.88056i		−	0.100655i
$820$	−3.30308			−0.115348
$821$		−	11.0804i		−	0.386710i	−0.981129	−	0.193355i	$-0.938063\pi$
$821$		−	11.0804i		−	0.386710i	0.981129	−	0.193355i	$-0.0619369\pi$
$822$			1.31707i			0.0459381i
$823$		−	22.5520i		−	0.786115i	−0.919514	−	0.393057i	$-0.871417\pi$
$823$		−	22.5520i		−	0.786115i	0.919514	−	0.393057i	$-0.128583\pi$
$824$	39.3635			1.37129
$825$	−0.277814			−0.00967223
$826$		−	22.3472i		−	0.777560i
$827$		−	42.6634i		−	1.48355i	−0.670648	−	0.741775i	$-0.733984\pi$
$827$		−	42.6634i		−	1.48355i	0.670648	−	0.741775i	$-0.266016\pi$
$828$		−	5.27356i		−	0.183269i
$829$	15.0823			0.523828			0.261914	−	0.965091i	$-0.415646\pi$
$829$	15.0823			0.523828			0.261914	+	0.965091i	$0.415646\pi$
$830$			69.5810i			2.41519i
$831$	−5.87638			−0.203849
$832$	5.95565			0.206475
$833$	−3.57487	+	1.38797i	−0.123862	+	0.0480904i
$834$	−27.0272			−0.935876
$835$	37.6760			1.30383
$836$		−	20.5774i		−	0.711684i
$837$	8.05562			0.278443
$838$			88.0150i			3.04043i
$839$		−	39.7959i		−	1.37391i	−0.726701	−	0.686954i	$-0.758947\pi$
$839$		−	39.7959i		−	1.37391i	0.726701	−	0.686954i	$-0.241053\pi$
$840$		−	29.5094i		−	1.01817i
$841$	22.3831			0.771830
$842$	−45.8327			−1.57950
$843$			11.3488i			0.390875i
$844$			52.0915i			1.79306i
$845$		−	25.2792i		−	0.869630i
$846$	−28.5168			−0.980428
$847$			2.46372i			0.0846544i
$848$	−65.1564			−2.23748
$849$	−16.1346			−0.553738
$850$	2.66127	−	1.03326i	0.0912808	−	0.0354405i
$851$	5.64235			0.193417
$852$	47.2666			1.61933
$853$		−	7.36095i		−	0.252034i	−0.992028	−	0.126017i	$-0.959781\pi$
$853$		−	7.36095i		−	0.252034i	0.992028	−	0.126017i	$-0.0402194\pi$
$854$	10.8494			0.371257
$855$			10.6174i			0.363108i
$856$			71.8948i			2.45731i
$857$			23.7530i			0.811386i	0.914009	+	0.405693i	$0.132970\pi$
$857$			23.7530i			0.811386i	−0.914009	+	0.405693i	$0.867030\pi$
$858$	−2.91397			−0.0994814
$859$	−22.2891			−0.760494			−0.380247	−	0.924885i	$-0.624161\pi$
$859$	−22.2891			−0.760494			−0.380247	+	0.924885i	$0.624161\pi$
$860$		−	61.3459i		−	2.09188i
$861$			0.889193i			0.0303036i
$862$			72.6082i			2.47304i
$863$	33.3324			1.13465			0.567323	−	0.823495i	$-0.307979\pi$
$863$	33.3324			1.13465			0.567323	+	0.823495i	$0.307979\pi$
$864$			2.22058i			0.0755456i
$865$	−37.7527			−1.28363
$866$	−97.2130			−3.30343
$867$	11.4715	+	12.5461i	0.389593	+	0.426087i
$868$	83.5858			2.83709
$869$	−9.84882			−0.334098
$870$		−	13.9316i		−	0.472325i
$871$	−2.44453			−0.0828298
$872$		−	66.5077i		−	2.25224i
$873$		−	3.08407i		−	0.104380i
$874$			15.2479i			0.515767i
$875$	28.2564			0.955240
$876$	29.2410			0.987963
$877$			29.8884i			1.00926i	0.863336	+	0.504629i	$0.168371\pi$
$877$			29.8884i			1.00926i	−0.863336	+	0.504629i	$0.831629\pi$
$878$			93.2106i			3.14570i
$879$			16.7239i			0.564084i
$880$	−11.5478			−0.389277
$881$		−	46.4237i		−	1.56406i	−0.623244	−	0.782028i	$-0.714186\pi$
$881$		−	46.4237i		−	1.56406i	0.623244	−	0.782028i	$-0.285814\pi$
$882$	2.31806			0.0780533
$883$	−29.5880			−0.995717			−0.497858	−	0.867258i	$-0.665880\pi$
$883$	−29.5880			−0.995717			−0.497858	+	0.867258i	$0.665880\pi$
$884$	18.9262	−	7.34824i	0.636556	−	0.247148i
$885$	7.90868			0.265847
$886$	−33.2232			−1.11616
$887$		−	16.0077i		−	0.537487i	−0.963212	−	0.268744i	$-0.913392\pi$
$887$		−	16.0077i		−	0.537487i	0.963212	−	0.268744i	$-0.0866084\pi$
$888$	−24.8369			−0.833471
$889$		−	22.3939i		−	0.751066i
$890$		−	2.07044i		−	0.0694014i
$891$			1.00000i			0.0335013i
$892$	−80.1751			−2.68446
$893$	55.9047			1.87078
$894$			12.5102i			0.418405i
$895$			10.7983i			0.360946i
$896$		−	42.2195i		−	1.41045i
$897$	1.46402			0.0488821
$898$			27.6272i			0.921932i
$899$	20.7218			0.691111
$900$	−1.17003			−0.0390009
$901$	47.1263	−	18.2972i	1.57001	−	0.609568i
$902$	0.899508			0.0299503
$903$	−16.5144			−0.549565
$904$			67.3077i			2.23862i
$905$	−31.7655			−1.05592
$906$			24.1116i			0.801056i
$907$			19.1916i			0.637248i	0.947881	+	0.318624i	$0.103221\pi$
$907$			19.1916i			0.637248i	−0.947881	+	0.318624i	$0.896779\pi$
$908$			102.293i			3.39473i
$909$	−14.7352			−0.488737
$910$	15.6008			0.517163
$911$			1.47434i			0.0488471i	0.999702	+	0.0244236i	$0.00777503\pi$
$911$			1.47434i			0.0488471i	−0.999702	+	0.0244236i	$0.992225\pi$
$912$		−	25.9643i		−	0.859763i
$913$		−	12.8475i		−	0.425190i
$914$	25.2105			0.833890
$915$			3.83958i			0.126933i
$916$	0.0683844			0.00225948
$917$	45.8986			1.51571
$918$	−3.71926	−	9.57933i	−0.122754	−	0.316165i
$919$	28.0769			0.926171			0.463085	−	0.886314i	$-0.346742\pi$
$919$	28.0769			0.926171			0.463085	+	0.886314i	$0.346742\pi$
$920$	14.9979			0.494466
$921$		−	15.2687i		−	0.503121i
$922$	70.6590			2.32703
$923$			13.1219i			0.431913i
$924$			10.3761i			0.341348i
$925$		−	1.25185i		−	0.0411606i
$926$	75.2215			2.47193
$927$	7.14160			0.234561
$928$			5.71209i			0.187508i
$929$			32.8862i			1.07896i	0.841998	+	0.539481i	$0.181379\pi$
$929$			32.8862i			1.07896i	−0.841998	+	0.539481i	$0.818621\pi$
$930$			43.6285i			1.43064i
$931$	−4.54437			−0.148936
$932$		−	12.2073i		−	0.399865i
$933$	17.8996			0.586006
$934$	−31.2618			−1.02292
$935$	8.35231	−	3.24285i	0.273150	−	0.106053i
$936$	−6.44441			−0.210642
$937$	40.7780			1.33216			0.666080	−	0.745880i	$-0.267971\pi$
$937$	40.7780			1.33216			0.666080	+	0.745880i	$0.267971\pi$
$938$			12.8381i			0.419180i
$939$	−16.3886			−0.534823
$940$		−	104.716i		−	3.41547i
$941$		−	7.41252i		−	0.241641i	−0.992674	−	0.120821i	$-0.961447\pi$
$941$		−	7.41252i		−	0.241641i	0.992674	−	0.120821i	$-0.0385526\pi$
$942$		−	38.5682i		−	1.25662i
$943$	−0.451924			−0.0147167
$944$	−19.3402			−0.629470
$945$		−	5.35381i		−	0.174159i
$946$			16.7060i			0.543158i
$947$		−	14.3045i		−	0.464833i	−0.972616	−	0.232416i	$-0.925337\pi$
$947$		−	14.3045i		−	0.464833i	0.972616	−	0.232416i	$-0.0746632\pi$
$948$	−41.4789			−1.34717
$949$			8.11774i			0.263513i
$950$	3.38300			0.109759
$951$	−31.5448			−1.02291
$952$	−20.2649	−	52.1944i	−0.656790	−	1.69163i
$953$	18.9313			0.613244			0.306622	−	0.951831i	$-0.400801\pi$
$953$	18.9313			0.613244			0.306622	+	0.951831i	$0.400801\pi$
$954$	−30.5583			−0.989361
$955$			48.3883i			1.56581i
$956$	−61.2746			−1.98176
$957$			2.57234i			0.0831520i
$958$		−	84.0276i		−	2.71481i
$959$			1.30197i			0.0420427i
$960$	11.0692			0.357256
$961$	−33.8930			−1.09332
$962$		−	13.1306i		−	0.423348i
$963$			13.0437i			0.420326i
$964$			18.1143i			0.583421i
$965$	−32.9919			−1.06205
$966$		−	7.68869i		−	0.247380i
$967$	−27.9784			−0.899724			−0.449862	−	0.893098i	$-0.648527\pi$
$967$	−27.9784			−0.899724			−0.449862	+	0.893098i	$0.648527\pi$
$968$	5.51186			0.177158
$969$	7.29128	+	18.7794i	0.234230	+	0.603283i
$970$	16.7031			0.536304
$971$	−2.98377			−0.0957538			−0.0478769	−	0.998853i	$-0.515246\pi$
$971$	−2.98377			−0.0957538			−0.0478769	+	0.998853i	$0.515246\pi$
$972$			4.21156i			0.135086i
$973$	−26.7173			−0.856517
$974$		−	19.8614i		−	0.636401i
$975$		−	0.324817i		−	0.0104025i
$976$		−	9.38947i		−	0.300550i
$977$	−1.42540			−0.0456025			−0.0228013	−	0.999740i	$-0.507258\pi$
$977$	−1.42540			−0.0456025			−0.0228013	+	0.999740i	$0.507258\pi$
$978$	2.59359			0.0829339
$979$			0.382289i			0.0122180i
$980$			8.51215i			0.271911i
$981$		−	12.0663i		−	0.385247i
$982$	−63.7653			−2.03483
$983$		−	27.7494i		−	0.885070i	−0.896751	−	0.442535i	$-0.854079\pi$
$983$		−	27.7494i		−	0.885070i	0.896751	−	0.442535i	$-0.145921\pi$
$984$	1.98931			0.0634169
$985$	−12.4329			−0.396144
$986$	−9.56720	−	24.6413i	−0.304682	−	0.784739i
$987$	−28.1898			−0.897291
$988$	24.0589			0.765415
$989$		−	8.39330i		−	0.266891i
$990$	−5.41591			−0.172129
$991$			17.6481i			0.560609i	0.959911	+	0.280305i	$0.0904355\pi$
$991$			17.6481i			0.560609i	−0.959911	+	0.280305i	$0.909564\pi$
$992$		−	17.8881i		−	0.567949i
$993$			27.9726i			0.887684i
$994$	68.9133			2.18580
$995$	4.98893			0.158160
$996$		−	54.1080i		−	1.71448i
$997$			2.84413i			0.0900744i	0.998985	+	0.0450372i	$0.0143406\pi$
$997$			2.84413i			0.0900744i	−0.998985	+	0.0450372i	$0.985659\pi$
$998$			8.97544i			0.284112i
$999$	−4.50608			−0.142566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	561.2.g.b.67.4	yes	16
3.2	odd	2		1683.2.g.c.1189.13		16
17.4	even	4		9537.2.a.bn.1.7		8
17.13	even	4		9537.2.a.bm.1.7		8
17.16	even	2	inner	561.2.g.b.67.3	✓	16
51.50	odd	2		1683.2.g.c.1189.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
561.2.g.b.67.3	✓	16	17.16	even	2	inner
561.2.g.b.67.4	yes	16	1.1	even	1	trivial
1683.2.g.c.1189.13		16	3.2	odd	2
1683.2.g.c.1189.14		16	51.50	odd	2
9537.2.a.bm.1.7		8	17.13	even	4
9537.2.a.bn.1.7		8	17.4	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 561 = 3 \cdot 11 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	561.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.49230 q^{2} +1.00000i q^{3} +4.21156 q^{4} +2.17306i q^{5} -2.49230i q^{6} -2.46372i q^{7} -5.51186 q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-2.49230 q^{2} +1.00000i q^{3} +4.21156 q^{4} +2.17306i q^{5} -2.49230i q^{6} -2.46372i q^{7} -5.51186 q^{8} -1.00000 q^{9} -5.41591i q^{10} +1.00000i q^{11} +4.21156i q^{12} -1.16919 q^{13} +6.14032i q^{14} -2.17306 q^{15} +5.31409 q^{16} +(-3.84357 + 1.49230i) q^{17} +2.49230 q^{18} -4.88594 q^{19} +9.15196i q^{20} +2.46372 q^{21} -2.49230i q^{22} +1.25216i q^{23} -5.51186i q^{24} +0.277814 q^{25} +2.91397 q^{26} -1.00000i q^{27} -10.3761i q^{28} -2.57234i q^{29} +5.41591 q^{30} +8.05562i q^{31} -2.22058 q^{32} -1.00000 q^{33} +(9.57933 - 3.71926i) q^{34} +5.35381 q^{35} -4.21156 q^{36} -4.50608i q^{37} +12.1772 q^{38} -1.16919i q^{39} -11.9776i q^{40} +0.360915i q^{41} -6.14032 q^{42} -6.70304 q^{43} +4.21156i q^{44} -2.17306i q^{45} -3.12077i q^{46} -11.4420 q^{47} +5.31409i q^{48} +0.930091 q^{49} -0.692395 q^{50} +(-1.49230 - 3.84357i) q^{51} -4.92411 q^{52} -12.2611 q^{53} +2.49230i q^{54} -2.17306 q^{55} +13.5797i q^{56} -4.88594i q^{57} +6.41105i q^{58} -3.63942 q^{59} -9.15196 q^{60} -1.76690i q^{61} -20.0770i q^{62} +2.46372i q^{63} -5.09383 q^{64} -2.54072i q^{65} +2.49230 q^{66} +2.09079 q^{67} +(-16.1874 + 6.28490i) q^{68} -1.25216 q^{69} -13.3433 q^{70} -11.2231i q^{71} +5.51186 q^{72} -6.94305i q^{73} +11.2305i q^{74} +0.277814i q^{75} -20.5774 q^{76} +2.46372 q^{77} +2.91397i q^{78} +9.84882i q^{79} +11.5478i q^{80} +1.00000 q^{81} -0.899508i q^{82} -12.8475 q^{83} +10.3761 q^{84} +(-3.24285 - 8.35231i) q^{85} +16.7060 q^{86} +2.57234 q^{87} -5.51186i q^{88} +0.382289 q^{89} +5.41591i q^{90} +2.88056i q^{91} +5.27356i q^{92} -8.05562 q^{93} +28.5168 q^{94} -10.6174i q^{95} -2.22058i q^{96} +3.08407i q^{97} -2.31806 q^{98} -1.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 2 q^{2} + 22 q^{4} - 6 q^{8} - 16 q^{9}+O(q^{10}) \) 16 * q - 2 * q^2 + 22 * q^4 - 6 * q^8 - 16 * q^9	\( 16 q - 2 q^{2} + 22 q^{4} - 6 q^{8} - 16 q^{9} + 12 q^{13} - 4 q^{15} + 34 q^{16} - 6 q^{17} + 2 q^{18} - 8 q^{19} + 2 q^{21} - 56 q^{25} - 8 q^{26} - 36 q^{30} - 34 q^{32} - 16 q^{33} + 30 q^{34} + 8 q^{35} - 22 q^{36} + 44 q^{38} - 12 q^{42} - 24 q^{43} + 18 q^{47} - 34 q^{49} + 30 q^{50} + 14 q^{51} + 28 q^{52} - 26 q^{53} - 4 q^{55} - 2 q^{59} - 12 q^{60} - 38 q^{64} + 2 q^{66} + 30 q^{67} + 42 q^{68} - 28 q^{69} + 88 q^{70} + 6 q^{72} - 84 q^{76} + 2 q^{77} + 16 q^{81} - 52 q^{83} + 24 q^{84} + 40 q^{85} - 52 q^{86} - 26 q^{87} + 78 q^{89} + 20 q^{93} - 16 q^{94} - 70 q^{98}+O(q^{100}) \) 16 * q - 2 * q^2 + 22 * q^4 - 6 * q^8 - 16 * q^9 + 12 * q^13 - 4 * q^15 + 34 * q^16 - 6 * q^17 + 2 * q^18 - 8 * q^19 + 2 * q^21 - 56 * q^25 - 8 * q^26 - 36 * q^30 - 34 * q^32 - 16 * q^33 + 30 * q^34 + 8 * q^35 - 22 * q^36 + 44 * q^38 - 12 * q^42 - 24 * q^43 + 18 * q^47 - 34 * q^49 + 30 * q^50 + 14 * q^51 + 28 * q^52 - 26 * q^53 - 4 * q^55 - 2 * q^59 - 12 * q^60 - 38 * q^64 + 2 * q^66 + 30 * q^67 + 42 * q^68 - 28 * q^69 + 88 * q^70 + 6 * q^72 - 84 * q^76 + 2 * q^77 + 16 * q^81 - 52 * q^83 + 24 * q^84 + 40 * q^85 - 52 * q^86 - 26 * q^87 + 78 * q^89 + 20 * q^93 - 16 * q^94 - 70 * q^98

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