LMFDB - Embedded newform 1155.2.k.a.769.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(769,1155)]

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([0, 1, 1, 1]))

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

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

chi := DirichletCharacter("1155.769");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.k (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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			769.23
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.a.769.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.219070 q^{2} -1.00000 q^{3} -1.95201 q^{4} +(-1.49883 - 1.65937i) q^{5} +0.219070 q^{6} +(2.26343 - 1.37000i) q^{7} +0.865767 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.219070 q^{2} -1.00000 q^{3} -1.95201 q^{4} +(-1.49883 - 1.65937i) q^{5} +0.219070 q^{6} +(2.26343 - 1.37000i) q^{7} +0.865767 q^{8} +1.00000 q^{9} +(0.328349 + 0.363518i) q^{10} +(-3.31662 + 0.00596877i) q^{11} +1.95201 q^{12} -4.76056i q^{13} +(-0.495849 + 0.300126i) q^{14} +(1.49883 + 1.65937i) q^{15} +3.71435 q^{16} -1.75010i q^{17} -0.219070 q^{18} +3.98889 q^{19} +(2.92573 + 3.23910i) q^{20} +(-2.26343 + 1.37000i) q^{21} +(0.726572 - 0.00130758i) q^{22} -5.32653i q^{23} -0.865767 q^{24} +(-0.507009 + 4.97423i) q^{25} +1.04290i q^{26} -1.00000 q^{27} +(-4.41823 + 2.67425i) q^{28} +7.93087i q^{29} +(-0.328349 - 0.363518i) q^{30} +0.416788i q^{31} -2.54524 q^{32} +(3.31662 - 0.00596877i) q^{33} +0.383394i q^{34} +(-5.66583 - 1.70246i) q^{35} -1.95201 q^{36} -8.40684i q^{37} -0.873847 q^{38} +4.76056i q^{39} +(-1.29764 - 1.43663i) q^{40} -5.12766 q^{41} +(0.495849 - 0.300126i) q^{42} -10.5926 q^{43} +(6.47407 - 0.0116511i) q^{44} +(-1.49883 - 1.65937i) q^{45} +1.16688i q^{46} -1.02252 q^{47} -3.71435 q^{48} +(3.24621 - 6.20178i) q^{49} +(0.111070 - 1.08970i) q^{50} +1.75010i q^{51} +9.29265i q^{52} +4.16120i q^{53} +0.219070 q^{54} +(4.98096 + 5.49455i) q^{55} +(1.95960 - 1.18610i) q^{56} -3.98889 q^{57} -1.73742i q^{58} +1.47657i q^{59} +(-2.92573 - 3.23910i) q^{60} -7.08776 q^{61} -0.0913058i q^{62} +(2.26343 - 1.37000i) q^{63} -6.87112 q^{64} +(-7.89952 + 7.13527i) q^{65} +(-0.726572 + 0.00130758i) q^{66} +12.2899i q^{67} +3.41620i q^{68} +5.32653i q^{69} +(1.24121 + 0.372959i) q^{70} -5.14350 q^{71} +0.865767 q^{72} -14.7437i q^{73} +1.84169i q^{74} +(0.507009 - 4.97423i) q^{75} -7.78635 q^{76} +(-7.49875 + 4.55727i) q^{77} -1.04290i q^{78} +4.99740i q^{79} +(-5.56719 - 6.16348i) q^{80} +1.00000 q^{81} +1.12332 q^{82} +4.77780i q^{83} +(4.41823 - 2.67425i) q^{84} +(-2.90405 + 2.62310i) q^{85} +2.32051 q^{86} -7.93087i q^{87} +(-2.87142 + 0.00516756i) q^{88} +8.37576i q^{89} +(0.328349 + 0.363518i) q^{90} +(-6.52196 - 10.7752i) q^{91} +10.3974i q^{92} -0.416788i q^{93} +0.224004 q^{94} +(-5.97868 - 6.61904i) q^{95} +2.54524 q^{96} -8.91729 q^{97} +(-0.711148 + 1.35863i) q^{98} +(-3.31662 + 0.00596877i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9}+O(q^{10}) $ 48 * q - 48 * q^3 + 48 * q^4 + 4 * q^5 + 48 * q^9	$ 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9} - 48 q^{12} - 4 q^{15} + 40 q^{16} + 18 q^{20} + 20 q^{25} - 48 q^{27} + 48 q^{36} + 20 q^{38} - 16 q^{44} + 4 q^{45} - 8 q^{47} - 40 q^{48} + 24 q^{49} + 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} - 20 q^{75} + 32 q^{77} + 46 q^{80} + 48 q^{81} + 32 q^{82} - 16 q^{86} - 68 q^{97}+O(q^{100}) $ 48 * q - 48 * q^3 + 48 * q^4 + 4 * q^5 + 48 * q^9 - 48 * q^12 - 4 * q^15 + 40 * q^16 + 18 * q^20 + 20 * q^25 - 48 * q^27 + 48 * q^36 + 20 * q^38 - 16 * q^44 + 4 * q^45 - 8 * q^47 - 40 * q^48 + 24 * q^49 + 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 - 20 * q^75 + 32 * q^77 + 46 * q^80 + 48 * q^81 + 32 * q^82 - 16 * q^86 - 68 * q^97

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 $

$2$	−0.219070			−0.154906			−0.0774530	−	0.996996i	$-0.524679\pi$
$2$	−0.219070			−0.154906			−0.0774530	+	0.996996i	$0.524679\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−1.95201			−0.976004
$5$	−1.49883	−	1.65937i	−0.670298	−	0.742092i
$5$	−1.49883	−	1.65937i	−0.670298	−	0.742092i
$6$	0.219070			0.0894350
$7$	2.26343	−	1.37000i	0.855495	−	0.517811i
$7$	2.26343	−	1.37000i	0.855495	−	0.517811i
$8$	0.865767			0.306095
$9$	1.00000			0.333333
$10$	0.328349	+	0.363518i	0.103833	+	0.114955i
$11$	−3.31662	+	0.00596877i	−0.999998	+	0.00179965i
$11$	−3.31662	+	0.00596877i	−0.999998	+	0.00179965i
$12$	1.95201			0.563496
$13$		−	4.76056i		−	1.32034i	−0.751116	−	0.660171i	$-0.770484\pi$
$13$		−	4.76056i		−	1.32034i	0.751116	−	0.660171i	$-0.229516\pi$
$14$	−0.495849	+	0.300126i	−0.132521	+	0.0802120i
$15$	1.49883	+	1.65937i	0.386997	+	0.428447i
$16$	3.71435			0.928588
$17$		−	1.75010i		−	0.424461i	−0.977220	−	0.212230i	$-0.931927\pi$
$17$		−	1.75010i		−	0.424461i	0.977220	−	0.212230i	$-0.0680727\pi$
$18$	−0.219070			−0.0516353
$19$	3.98889			0.915115			0.457557	−	0.889180i	$-0.348724\pi$
$19$	3.98889			0.915115			0.457557	+	0.889180i	$0.348724\pi$
$20$	2.92573	+	3.23910i	0.654213	+	0.724285i
$21$	−2.26343	+	1.37000i	−0.493920	+	0.298958i
$22$	0.726572	−	0.00130758i	0.154906	−	0.000278777i
$23$		−	5.32653i		−	1.11066i	−0.831631	−	0.555329i	$-0.812592\pi$
$23$		−	5.32653i		−	1.11066i	0.831631	−	0.555329i	$-0.187408\pi$
$24$	−0.865767			−0.176724
$25$	−0.507009	+	4.97423i	−0.101402	+	0.994846i
$26$			1.04290i			0.204529i
$27$	−1.00000			−0.192450
$28$	−4.41823	+	2.67425i	−0.834967	+	0.505385i
$29$			7.93087i			1.47273i	0.676587	+	0.736363i	$0.263458\pi$
$29$			7.93087i			1.47273i	−0.676587	+	0.736363i	$0.736542\pi$
$30$	−0.328349	−	0.363518i	−0.0599481	−	0.0663690i
$31$			0.416788i			0.0748573i	0.999299	+	0.0374287i	$0.0119167\pi$
$31$			0.416788i			0.0748573i	−0.999299	+	0.0374287i	$0.988083\pi$
$32$	−2.54524			−0.449939
$33$	3.31662	−	0.00596877i	0.577349	−	0.00103903i
$34$			0.383394i			0.0657515i
$35$	−5.66583	−	1.70246i	−0.957700	−	0.287769i
$36$	−1.95201			−0.325335
$37$		−	8.40684i		−	1.38208i	−0.722819	−	0.691038i	$-0.757154\pi$
$37$		−	8.40684i		−	1.38208i	0.722819	−	0.691038i	$-0.242846\pi$
$38$	−0.873847			−0.141757
$39$			4.76056i			0.762299i
$40$	−1.29764	−	1.43663i	−0.205175	−	0.227151i
$41$	−5.12766			−0.800807			−0.400403	−	0.916339i	$-0.631130\pi$
$41$	−5.12766			−0.800807			−0.400403	+	0.916339i	$0.631130\pi$
$42$	0.495849	−	0.300126i	0.0765112	−	0.0463104i
$43$	−10.5926			−1.61535			−0.807676	−	0.589627i	$-0.799275\pi$
$43$	−10.5926			−1.61535			−0.807676	+	0.589627i	$0.799275\pi$
$44$	6.47407	−	0.0116511i	0.976003	−	0.00175647i
$45$	−1.49883	−	1.65937i	−0.223433	−	0.247364i
$46$			1.16688i			0.172048i
$47$	−1.02252			−0.149150			−0.0745751	−	0.997215i	$-0.523760\pi$
$47$	−1.02252			−0.149150			−0.0745751	+	0.997215i	$0.523760\pi$
$48$	−3.71435			−0.536121
$49$	3.24621	−	6.20178i	0.463744	−	0.885969i
$50$	0.111070	−	1.08970i	0.0157077	−	0.154108i
$51$			1.75010i			0.245063i
$52$			9.29265i			1.28866i
$53$			4.16120i			0.571585i	0.958292	+	0.285793i	$0.0922568\pi$
$53$			4.16120i			0.571585i	−0.958292	+	0.285793i	$0.907743\pi$
$54$	0.219070			0.0298117
$55$	4.98096	+	5.49455i	0.671632	+	0.740885i
$56$	1.95960	−	1.18610i	0.261863	−	0.158499i
$57$	−3.98889			−0.528342
$58$		−	1.73742i		−	0.228134i
$59$			1.47657i			0.192233i	0.995370	+	0.0961166i	$0.0306422\pi$
$59$			1.47657i			0.192233i	−0.995370	+	0.0961166i	$0.969358\pi$
$60$	−2.92573	−	3.23910i	−0.377710	−	0.418166i
$61$	−7.08776			−0.907495			−0.453747	−	0.891130i	$-0.649913\pi$
$61$	−7.08776			−0.907495			−0.453747	+	0.891130i	$0.649913\pi$
$62$		−	0.0913058i		−	0.0115958i
$63$	2.26343	−	1.37000i	0.285165	−	0.172604i
$64$	−6.87112			−0.858890
$65$	−7.89952	+	7.13527i	−0.979815	+	0.885022i
$66$	−0.726572	+	0.00130758i	−0.0894349	+	0.000160952i
$67$			12.2899i			1.50145i	0.660616	+	0.750724i	$0.270295\pi$
$67$			12.2899i			1.50145i	−0.660616	+	0.750724i	$0.729705\pi$
$68$			3.41620i			0.414275i
$69$			5.32653i			0.641239i
$70$	1.24121	+	0.372959i	0.148353	+	0.0445771i
$71$	−5.14350			−0.610422			−0.305211	−	0.952285i	$-0.598727\pi$
$71$	−5.14350			−0.610422			−0.305211	+	0.952285i	$0.598727\pi$
$72$	0.865767			0.102032
$73$		−	14.7437i		−	1.72562i	−0.505526	−	0.862812i	$-0.668701\pi$
$73$		−	14.7437i		−	1.72562i	0.505526	−	0.862812i	$-0.331299\pi$
$74$			1.84169i			0.214092i
$75$	0.507009	−	4.97423i	0.0585443	−	0.574374i
$76$	−7.78635			−0.893156
$77$	−7.49875	+	4.55727i	−0.854562	+	0.519349i
$78$		−	1.04290i		−	0.118085i
$79$			4.99740i			0.562252i	0.959671	+	0.281126i	$0.0907079\pi$
$79$			4.99740i			0.562252i	−0.959671	+	0.281126i	$0.909292\pi$
$80$	−5.56719	−	6.16348i	−0.622431	−	0.689098i
$81$	1.00000			0.111111
$82$	1.12332			0.124050
$83$			4.77780i			0.524432i	0.965009	+	0.262216i	$0.0844533\pi$
$83$			4.77780i			0.524432i	−0.965009	+	0.262216i	$0.915547\pi$
$84$	4.41823	−	2.67425i	0.482068	−	0.291784i
$85$	−2.90405	+	2.62310i	−0.314989	+	0.284515i
$86$	2.32051			0.250228
$87$		−	7.93087i		−	0.850279i
$88$	−2.87142	+	0.00516756i	−0.306094	+	0.000550864i
$89$			8.37576i			0.887828i	0.896069	+	0.443914i	$0.146410\pi$
$89$			8.37576i			0.887828i	−0.896069	+	0.443914i	$0.853590\pi$
$90$	0.328349	+	0.363518i	0.0346110	+	0.0383182i
$91$	−6.52196	−	10.7752i	−0.683687	−	1.12955i
$92$			10.3974i			1.08401i
$93$		−	0.416788i		−	0.0432189i
$94$	0.224004			0.0231043
$95$	−5.97868	−	6.61904i	−0.613399	−	0.679099i
$96$	2.54524			0.259772
$97$	−8.91729			−0.905414			−0.452707	−	0.891659i	$-0.649542\pi$
$97$	−8.91729			−0.905414			−0.452707	+	0.891659i	$0.649542\pi$
$98$	−0.711148	+	1.35863i	−0.0718368	+	0.137242i
$99$	−3.31662	+	0.00596877i	−0.333333	+	0.000599884i
$100$	0.989685	−	9.70973i	0.0989685	−	0.970973i
$101$	−15.5775			−1.55002			−0.775008	−	0.631951i	$-0.782254\pi$
$101$	−15.5775			−1.55002			−0.775008	+	0.631951i	$0.782254\pi$
$102$		−	0.383394i		−	0.0379617i
$103$	1.22728			0.120928			0.0604638	−	0.998170i	$-0.480742\pi$
$103$	1.22728			0.120928			0.0604638	+	0.998170i	$0.480742\pi$
$104$		−	4.12153i		−	0.404150i
$105$	5.66583	+	1.70246i	0.552928	+	0.166144i
$106$		−	0.911595i		−	0.0885420i
$107$	−2.52487			−0.244088			−0.122044	−	0.992525i	$-0.538945\pi$
$107$	−2.52487			−0.244088			−0.122044	+	0.992525i	$0.538945\pi$
$108$	1.95201			0.187832
$109$			19.4843i			1.86625i	0.359547	+	0.933127i	$0.382931\pi$
$109$			19.4843i			1.86625i	−0.359547	+	0.933127i	$0.617069\pi$
$110$	−1.09118	−	1.20369i	−0.104040	−	0.114767i
$111$			8.40684i			0.797942i
$112$	8.40717	−	5.08866i	0.794403	−	0.480833i
$113$			3.00342i			0.282538i	0.989971	+	0.141269i	$0.0451182\pi$
$113$			3.00342i			0.282538i	−0.989971	+	0.141269i	$0.954882\pi$
$114$	0.873847			0.0818433
$115$	−8.83868	+	7.98357i	−0.824211	+	0.744472i
$116$		−	15.4811i		−	1.43739i
$117$		−	4.76056i		−	0.440114i
$118$		−	0.323473i		−	0.0297781i
$119$	−2.39763	−	3.96122i	−0.219790	−	0.363124i
$120$	1.29764	+	1.43663i	0.118458	+	0.131145i
$121$	10.9999	−	0.0395923i	0.999994	−	0.00359930i
$122$	1.55272			0.140576
$123$	5.12766			0.462346
$124$		−	0.813573i		−	0.0730610i
$125$	9.01400	−	6.61421i	0.806237	−	0.591593i
$126$	−0.495849	+	0.300126i	−0.0441738	+	0.0267373i
$127$	16.2867			1.44521			0.722606	−	0.691260i	$-0.242944\pi$
$127$	16.2867			1.44521			0.722606	+	0.691260i	$0.242944\pi$
$128$	6.59573			0.582986
$129$	10.5926			0.932623
$130$	1.73055	−	1.56313i	0.151779	−	0.137095i
$131$	−20.6593			−1.80501			−0.902506	−	0.430678i	$-0.858274\pi$
$131$	−20.6593			−1.80501			−0.902506	+	0.430678i	$0.858274\pi$
$132$	−6.47407	+	0.0116511i	−0.563495	+	0.00101410i
$133$	9.02857	−	5.46478i	0.782876	−	0.473856i
$134$		−	2.69234i		−	0.232583i
$135$	1.49883	+	1.65937i	0.128999	+	0.142816i
$136$		−	1.51518i		−	0.129925i
$137$		−	16.2074i		−	1.38469i	−0.721566	−	0.692345i	$-0.756577\pi$
$137$		−	16.2074i		−	1.38469i	0.721566	−	0.692345i	$-0.243423\pi$
$138$		−	1.16688i		−	0.0993318i
$139$	17.7663			1.50692			0.753459	−	0.657495i	$-0.228384\pi$
$139$	17.7663			1.50692			0.753459	+	0.657495i	$0.228384\pi$
$140$	11.0597	+	3.32322i	0.934719	+	0.280864i
$141$	1.02252			0.0861119
$142$	1.12679			0.0945580
$143$	0.0284147	+	15.7890i	0.00237615	+	1.32034i
$144$	3.71435			0.309529
$145$	13.1602	−	11.8870i	1.09290	−	0.987165i
$146$			3.22991i			0.267309i
$147$	−3.24621	+	6.20178i	−0.267743	+	0.511515i
$148$			16.4102i			1.34891i
$149$		−	19.3124i		−	1.58214i	−0.611728	−	0.791068i	$-0.709525\pi$
$149$		−	19.3124i		−	1.58214i	0.611728	−	0.791068i	$-0.290475\pi$
$150$	−0.111070	+	1.08970i	−0.00906887	+	0.0889740i
$151$		−	15.0336i		−	1.22341i	−0.791084	−	0.611707i	$-0.790483\pi$
$151$		−	15.0336i		−	1.22341i	0.791084	−	0.611707i	$-0.209517\pi$
$152$	3.45345			0.280112
$153$		−	1.75010i		−	0.141487i
$154$	1.64275	−	0.998362i	0.132377	−	0.0804503i
$155$	0.691605	−	0.624695i	0.0555510	−	0.0501767i
$156$		−	9.29265i		−	0.744007i
$157$	9.76184			0.779080			0.389540	−	0.921010i	$-0.372634\pi$
$157$	9.76184			0.779080			0.389540	+	0.921010i	$0.372634\pi$
$158$		−	1.09478i		−	0.0870962i
$159$		−	4.16120i		−	0.330005i
$160$	3.81488	+	4.22349i	0.301593	+	0.333896i
$161$	−7.29734	−	12.0562i	−0.575111	−	0.950163i
$162$	−0.219070			−0.0172118
$163$		−	2.65834i		−	0.208217i	−0.994566	−	0.104108i	$-0.966801\pi$
$163$		−	2.65834i		−	0.208217i	0.994566	−	0.104108i	$-0.0331989\pi$
$164$	10.0092			0.781591
$165$	−4.98096	−	5.49455i	−0.387767	−	0.427750i
$166$		−	1.04667i		−	0.0812377i
$167$			12.3713i			0.957321i	0.878000	+	0.478661i	$0.158878\pi$
$167$			12.3713i			0.957321i	−0.878000	+	0.478661i	$0.841122\pi$
$168$	−1.95960	+	1.18610i	−0.151187	+	0.0915096i
$169$	−9.66291			−0.743301
$170$	0.636192	−	0.574643i	0.0487937	−	0.0440731i
$171$	3.98889			0.305038
$172$	20.6768			1.57659
$173$			5.30683i			0.403471i	0.979440	+	0.201735i	$0.0646581\pi$
$173$			5.30683i			0.403471i	−0.979440	+	0.201735i	$0.935342\pi$
$174$			1.73742i			0.131713i
$175$	5.66711	+	11.9534i	0.428393	+	0.903593i
$176$	−12.3191	+	0.0221701i	−0.928587	+	0.00167113i
$177$		−	1.47657i		−	0.110986i
$178$		−	1.83488i		−	0.137530i
$179$	6.03351			0.450966			0.225483	−	0.974247i	$-0.427604\pi$
$179$	6.03351			0.450966			0.225483	+	0.974247i	$0.427604\pi$
$180$	2.92573	+	3.23910i	0.218071	+	0.241428i
$181$			15.0417i			1.11804i	0.829153	+	0.559021i	$0.188823\pi$
$181$			15.0417i			1.11804i	−0.829153	+	0.559021i	$0.811177\pi$
$182$	1.42877	+	2.36052i	0.105907	+	0.174973i
$183$	7.08776			0.523942
$184$		−	4.61154i		−	0.339967i
$185$	−13.9500	+	12.6004i	−1.02563	+	0.926402i
$186$			0.0913058i			0.00669487i
$187$	0.0104459	+	5.80440i	0.000763881	+	0.424460i
$188$	1.99597			0.145571
$189$	−2.26343	+	1.37000i	−0.164640	+	0.0996527i
$190$	1.30975	+	1.45003i	0.0950192	+	0.105197i
$191$	18.7953			1.35998			0.679991	−	0.733220i	$-0.261984\pi$
$191$	18.7953			1.35998			0.679991	+	0.733220i	$0.261984\pi$
$192$	6.87112			0.495880
$193$	−1.81009			−0.130293			−0.0651467	−	0.997876i	$-0.520752\pi$
$193$	−1.81009			−0.130293			−0.0651467	+	0.997876i	$0.520752\pi$
$194$	1.95351			0.140254
$195$	7.89952	−	7.13527i	0.565696	−	0.510968i
$196$	−6.33663	+	12.1059i	−0.452616	+	0.864710i
$197$	−14.2265			−1.01360			−0.506799	−	0.862064i	$-0.669171\pi$
$197$	−14.2265			−1.01360			−0.506799	+	0.862064i	$0.669171\pi$
$198$	0.726572	−	0.00130758i	0.0516352	−	9.29256e-5i
$199$		−	7.65140i		−	0.542394i	−0.962524	−	0.271197i	$-0.912581\pi$
$199$		−	7.65140i		−	0.542394i	0.962524	−	0.271197i	$-0.0874194\pi$
$200$	−0.438951	+	4.30652i	−0.0310386	+	0.304517i
$201$		−	12.2899i		−	0.866861i
$202$	3.41256			0.240107
$203$	10.8653	+	17.9510i	0.762593	+	1.25991i
$204$		−	3.41620i		−	0.239182i
$205$	7.68550	+	8.50869i	0.536779	+	0.594272i
$206$	−0.268861			−0.0187324
$207$		−	5.32653i		−	0.370220i
$208$		−	17.6824i		−	1.22605i
$209$	−13.2296	+	0.0238088i	−0.915113	+	0.00164689i
$210$	−1.24121	−	0.372959i	−0.0856519	−	0.0257366i
$211$			2.11088i			0.145319i	0.997357	+	0.0726596i	$0.0231487\pi$
$211$			2.11088i			0.145319i	−0.997357	+	0.0726596i	$0.976851\pi$
$212$		−	8.12270i		−	0.557869i
$213$	5.14350			0.352427
$214$	0.553123			0.0378107
$215$	15.8765	+	17.5770i	1.08277	+	1.19874i
$216$	−0.865767			−0.0589080
$217$	0.570999	+	0.943369i	0.0387619	+	0.0640401i
$218$		−	4.26842i		−	0.289094i
$219$			14.7437i			0.996289i
$220$	−9.72287	−	10.7254i	−0.655516	−	0.723107i
$221$	−8.33143			−0.560433
$222$		−	1.84169i		−	0.123606i
$223$	−16.3707			−1.09626			−0.548131	−	0.836392i	$-0.684661\pi$
$223$	−16.3707			−1.09626			−0.548131	+	0.836392i	$0.684661\pi$
$224$	−5.76096	+	3.48697i	−0.384920	+	0.232983i
$225$	−0.507009	+	4.97423i	−0.0338006	+	0.331615i
$226$		−	0.657959i		−	0.0437668i
$227$			9.80413i			0.650723i	0.945590	+	0.325362i	$0.105486\pi$
$227$			9.80413i			0.650723i	−0.945590	+	0.325362i	$0.894514\pi$
$228$	7.78635			0.515664
$229$		−	8.04004i		−	0.531301i	−0.964069	−	0.265650i	$-0.914413\pi$
$229$		−	8.04004i		−	0.531301i	0.964069	−	0.265650i	$-0.0855867\pi$
$230$	1.93629	−	1.74896i	0.127675	−	0.115323i
$231$	7.49875	−	4.55727i	0.493382	−	0.299847i
$232$			6.86629i			0.450794i
$233$	−5.02365			−0.329110			−0.164555	−	0.986368i	$-0.552619\pi$
$233$	−5.02365			−0.329110			−0.164555	+	0.986368i	$0.552619\pi$
$234$			1.04290i			0.0681763i
$235$	1.53259	+	1.69674i	0.0999751	+	0.110683i
$236$		−	2.88228i		−	0.187620i
$237$		−	4.99740i		−	0.324616i
$238$	0.525249	+	0.867784i	0.0340468	+	0.0562501i
$239$			1.83401i			0.118632i	0.998239	+	0.0593162i	$0.0188920\pi$
$239$			1.83401i			0.118632i	−0.998239	+	0.0593162i	$0.981108\pi$
$240$	5.56719	+	6.16348i	0.359360	+	0.397851i
$241$	−16.4629			−1.06047			−0.530233	−	0.847852i	$-0.677896\pi$
$241$	−16.4629			−1.06047			−0.530233	+	0.847852i	$0.677896\pi$
$242$	−2.40976	+	0.00867348i	−0.154905	+	0.000557552i
$243$	−1.00000			−0.0641500
$244$	13.8354			0.885718
$245$	−15.1566	+	3.90877i	−0.968318	+	0.249722i
$246$	−1.12332			−0.0716202
$247$		−	18.9894i		−	1.20826i
$248$			0.360841i			0.0229134i
$249$		−	4.77780i		−	0.302781i
$250$	−1.97470	+	1.44898i	−0.124891	+	0.0916414i
$251$		−	29.2562i		−	1.84663i	−0.384040	−	0.923316i	$-0.625468\pi$
$251$		−	29.2562i		−	1.84663i	0.384040	−	0.923316i	$-0.374532\pi$
$252$	−4.41823	+	2.67425i	−0.278322	+	0.168462i
$253$	0.0317928	+	17.6661i	0.00199880	+	1.11066i
$254$	−3.56793			−0.223872
$255$	2.90405	−	2.62310i	0.181859	−	0.164265i
$256$	12.2973			0.768582
$257$	−13.1186			−0.818316			−0.409158	−	0.912463i	$-0.634178\pi$
$257$	−13.1186			−0.818316			−0.409158	+	0.912463i	$0.634178\pi$
$258$	−2.32051			−0.144469
$259$	−11.5174	−	19.0283i	−0.715653	−	1.18236i
$260$	15.4199	−	13.9281i	0.956303	−	0.863785i
$261$			7.93087i			0.490909i
$262$	4.52584			0.279607
$263$	−7.58284			−0.467578			−0.233789	−	0.972287i	$-0.575113\pi$
$263$	−7.58284			−0.467578			−0.233789	+	0.972287i	$0.575113\pi$
$264$	2.87142	−	0.00516756i	0.176724	−	0.000318041i
$265$	6.90497	−	6.23694i	0.424169	−	0.383132i
$266$	−1.97789	+	1.19717i	−0.121272	+	0.0734032i
$267$		−	8.37576i		−	0.512588i
$268$		−	23.9899i		−	1.46542i
$269$			24.5700i			1.49806i	0.662535	+	0.749031i	$0.269480\pi$
$269$			24.5700i			1.49806i	−0.662535	+	0.749031i	$0.730520\pi$
$270$	−0.328349	−	0.363518i	−0.0199827	−	0.0221230i
$271$	15.0926			0.916810			0.458405	−	0.888743i	$-0.348421\pi$
$271$	15.0926			0.916810			0.458405	+	0.888743i	$0.348421\pi$
$272$		−	6.50048i		−	0.394149i
$273$	6.52196	+	10.7752i	0.394727	+	0.652143i
$274$			3.55056i			0.214497i
$275$	1.65186	−	16.5006i	0.0996112	−	0.995026i
$276$		−	10.3974i		−	0.625852i
$277$	−5.23707			−0.314665			−0.157332	−	0.987546i	$-0.550289\pi$
$277$	−5.23707			−0.314665			−0.157332	+	0.987546i	$0.550289\pi$
$278$	−3.89207			−0.233431
$279$			0.416788i			0.0249524i
$280$	−4.90529	−	1.47394i	−0.293147	−	0.0880846i
$281$		−	19.5161i		−	1.16423i	−0.813105	−	0.582117i	$-0.802224\pi$
$281$		−	19.5161i		−	1.16423i	0.813105	−	0.582117i	$-0.197776\pi$
$282$	−0.224004			−0.0133393
$283$			14.0410i			0.834650i	0.908757	+	0.417325i	$0.137032\pi$
$283$			14.0410i			0.834650i	−0.908757	+	0.417325i	$0.862968\pi$
$284$	10.0402			0.595774
$285$	5.97868	+	6.61904i	0.354146	+	0.392078i
$286$	−0.00622480	−	3.45889i	−0.000368080	−	0.204528i
$287$	−11.6061	+	7.02489i	−0.685086	+	0.414666i
$288$	−2.54524			−0.149980
$289$	13.9372			0.819833
$290$	−2.88302	+	2.60410i	−0.169296	+	0.152918i
$291$	8.91729			0.522741
$292$			28.7799i			1.68422i
$293$			15.9012i			0.928957i	0.885584	+	0.464478i	$0.153758\pi$
$293$			15.9012i			0.928957i	−0.885584	+	0.464478i	$0.846242\pi$
$294$	0.711148	−	1.35863i	0.0414750	−	0.0792367i
$295$	2.45018	−	2.21313i	0.142655	−	0.128854i
$296$		−	7.27836i		−	0.423046i
$297$	3.31662	−	0.00596877i	0.192450	−	0.000346343i
$298$			4.23078i			0.245082i
$299$	−25.3573			−1.46645
$300$	−0.989685	+	9.70973i	−0.0571395	+	0.560592i
$301$	−23.9755	+	14.5118i	−1.38193	+	0.836446i
$302$			3.29341i			0.189514i
$303$	15.5775			0.894903
$304$	14.8162			0.849765
$305$	10.6234	+	11.7612i	0.608292	+	0.673445i
$306$			0.383394i			0.0219172i
$307$		−	15.3444i		−	0.875754i	−0.899035	−	0.437877i	$-0.855731\pi$
$307$		−	15.3444i		−	0.875754i	0.899035	−	0.437877i	$-0.144269\pi$
$308$	14.6376	−	8.89583i	0.834056	−	0.506887i
$309$	−1.22728			−0.0698176
$310$	−0.151510	+	0.136852i	−0.00860519	+	0.00777267i
$311$			29.9189i			1.69655i	0.529558	+	0.848274i	$0.322358\pi$
$311$			29.9189i			1.69655i	−0.529558	+	0.848274i	$0.677642\pi$
$312$			4.12153i			0.233336i
$313$	12.8166			0.724440			0.362220	−	0.932093i	$-0.382019\pi$
$313$	12.8166			0.724440			0.362220	+	0.932093i	$0.382019\pi$
$314$	−2.13853			−0.120684
$315$	−5.66583	−	1.70246i	−0.319233	−	0.0959230i
$316$		−	9.75497i		−	0.548760i
$317$		−	0.0935753i		−	0.00525571i	−0.999997	−	0.00262786i	$-0.999164\pi$
$317$		−	0.0935753i		−	0.00525571i	0.999997	−	0.00262786i	$-0.000836474\pi$
$318$			0.911595i			0.0511197i
$319$	−0.0473375	−	26.3037i	−0.00265039	−	1.47272i
$320$	10.2987	+	11.4017i	0.575712	+	0.637376i
$321$	2.52487			0.140924
$322$	1.59863	+	2.64116i	0.0890881	+	0.147186i
$323$		−	6.98095i		−	0.388430i
$324$	−1.95201			−0.108445
$325$	23.6801	+	2.41364i	1.31354	+	0.133885i
$326$			0.582362i			0.0322540i
$327$		−	19.4843i		−	1.07748i
$328$	−4.43936			−0.245123
$329$	−2.31441	+	1.40085i	−0.127597	+	0.0772316i
$330$	1.09118	+	1.20369i	0.0600674	+	0.0662610i
$331$	2.60137			0.142984			0.0714922	−	0.997441i	$-0.477224\pi$
$331$	2.60137			0.142984			0.0714922	+	0.997441i	$0.477224\pi$
$332$		−	9.32631i		−	0.511848i
$333$		−	8.40684i		−	0.460692i
$334$		−	2.71019i		−	0.148295i
$335$	20.3934	−	18.4205i	1.11421	−	1.00642i
$336$	−8.40717	+	5.08866i	−0.458649	+	0.277609i
$337$	9.63959			0.525102			0.262551	−	0.964918i	$-0.415436\pi$
$337$	9.63959			0.525102			0.262551	+	0.964918i	$0.415436\pi$
$338$	2.11686			0.115142
$339$		−	3.00342i		−	0.163123i
$340$	5.66874	−	5.12031i	0.307431	−	0.277688i
$341$	−0.00248771	−	1.38233i	−0.000134717	−	0.0748572i
$342$	−0.873847			−0.0472522
$343$	−1.14887	−	18.4846i	−0.0620332	−	0.998074i
$344$	−9.17069			−0.494451
$345$	8.83868	−	7.98357i	0.475859	−	0.429821i
$346$		−	1.16257i		−	0.0625000i
$347$	4.68884			0.251710			0.125855	−	0.992049i	$-0.459833\pi$
$347$	4.68884			0.251710			0.125855	+	0.992049i	$0.459833\pi$
$348$			15.4811i			0.829875i
$349$	−22.7013			−1.21517			−0.607586	−	0.794254i	$-0.707862\pi$
$349$	−22.7013			−1.21517			−0.607586	+	0.794254i	$0.707862\pi$
$350$	−1.24149	−	2.61863i	−0.0663606	−	0.139972i
$351$			4.76056i			0.254100i
$352$	8.44159	−	0.0151919i	0.449938	−	0.000809733i
$353$	−12.5022			−0.665427			−0.332713	−	0.943028i	$-0.607964\pi$
$353$	−12.5022			−0.665427			−0.332713	+	0.943028i	$0.607964\pi$
$354$			0.323473i			0.0171924i
$355$	7.70924	+	8.53497i	0.409164	+	0.452989i
$356$		−	16.3495i		−	0.866524i
$357$	2.39763	+	3.96122i	0.126896	+	0.209650i
$358$	−1.32176			−0.0698573
$359$		−	17.7385i		−	0.936201i	−0.883675	−	0.468100i	$-0.844939\pi$
$359$		−	17.7385i		−	0.936201i	0.883675	−	0.468100i	$-0.155061\pi$
$360$	−1.29764	−	1.43663i	−0.0683916	−	0.0757169i
$361$	−3.08874			−0.162565
$362$		−	3.29519i		−	0.173192i
$363$	−10.9999	+	0.0395923i	−0.577347	+	0.00207805i
$364$	12.7309	+	21.0332i	0.667281	+	1.10244i
$365$	−24.4653	+	22.0984i	−1.28057	+	1.15668i
$366$	−1.55272			−0.0811618
$367$	7.93121			0.414006			0.207003	−	0.978340i	$-0.433629\pi$
$367$	7.93121			0.414006			0.207003	+	0.978340i	$0.433629\pi$
$368$		−	19.7846i		−	1.03134i
$369$	−5.12766			−0.266936
$370$	3.05604	−	2.76038i	0.158876	−	0.143505i
$371$	5.70084	+	9.41858i	0.295973	+	0.488988i
$372$			0.813573i			0.0421818i
$373$	−24.8316			−1.28573			−0.642865	−	0.765979i	$-0.722255\pi$
$373$	−24.8316			−1.28573			−0.642865	+	0.765979i	$0.722255\pi$
$374$	−0.00228839	−	1.27157i	−0.000118330	−	0.0657514i
$375$	−9.01400	+	6.61421i	−0.465481	+	0.341557i
$376$	−0.885266			−0.0456541
$377$	37.7554			1.94450
$378$	0.495849	−	0.300126i	0.0255037	−	0.0154368i
$379$	−14.0392			−0.721146			−0.360573	−	0.932731i	$-0.617419\pi$
$379$	−14.0392			−0.721146			−0.360573	+	0.932731i	$0.617419\pi$
$380$	11.6704	+	12.9204i	0.598680	+	0.662804i
$381$	−16.2867			−0.834393
$382$	−4.11749			−0.210669
$383$	3.60704			0.184311			0.0921556	−	0.995745i	$-0.470624\pi$
$383$	3.60704			0.184311			0.0921556	+	0.995745i	$0.470624\pi$
$384$	−6.59573			−0.336587
$385$	18.8016	+	5.61261i	0.958216	+	0.286045i
$386$	0.396537			0.0201832
$387$	−10.5926			−0.538450
$388$	17.4066			0.883688
$389$	16.4302			0.833042			0.416521	−	0.909126i	$-0.363249\pi$
$389$	16.4302			0.833042			0.416521	+	0.909126i	$0.363249\pi$
$390$	−1.73055	+	1.56313i	−0.0876298	+	0.0791519i
$391$	−9.32194			−0.471431
$392$	2.81046	−	5.36930i	0.141950	−	0.271191i
$393$	20.6593			1.04212
$394$	3.11661			0.157013
$395$	8.29253	−	7.49027i	0.417243	−	0.376876i
$396$	6.47407	−	0.0116511i	0.325334	−	0.000585489i
$397$	−22.2690			−1.11765			−0.558825	−	0.829285i	$-0.688748\pi$
$397$	−22.2690			−1.11765			−0.558825	+	0.829285i	$0.688748\pi$
$398$			1.67619i			0.0840200i
$399$	−9.02857	+	5.46478i	−0.451994	+	0.273581i
$400$	−1.88321	+	18.4760i	−0.0941604	+	0.923802i
$401$	15.4955			0.773808			0.386904	−	0.922120i	$-0.373544\pi$
$401$	15.4955			0.773808			0.386904	+	0.922120i	$0.373544\pi$
$402$			2.69234i			0.134282i
$403$	1.98414			0.0988372
$404$	30.4074			1.51282
$405$	−1.49883	−	1.65937i	−0.0744775	−	0.0824547i
$406$	−2.38026	−	3.93252i	−0.118130	−	0.195168i
$407$	0.0501784	+	27.8823i	0.00248725	+	1.38207i
$408$			1.51518i			0.0750124i
$409$	−27.9722			−1.38314			−0.691568	−	0.722311i	$-0.743080\pi$
$409$	−27.9722			−1.38314			−0.691568	+	0.722311i	$0.743080\pi$
$410$	−1.68366	−	1.86400i	−0.0831503	−	0.0920564i
$411$			16.2074i			0.799452i
$412$	−2.39566			−0.118026
$413$	2.02290	+	3.34211i	0.0995404	+	0.164455i
$414$			1.16688i			0.0573492i
$415$	7.92814	−	7.16112i	0.389177	−	0.351526i
$416$			12.1168i			0.594073i
$417$	−17.7663			−0.870019
$418$	2.89822	−	0.00521579i	0.141757	−	0.000255113i
$419$		−	39.1953i		−	1.91482i	−0.288740	−	0.957408i	$-0.593236\pi$
$419$		−	39.1953i		−	1.91482i	0.288740	−	0.957408i	$-0.406764\pi$
$420$	−11.0597	−	3.32322i	−0.539660	−	0.162157i
$421$	2.18571			0.106525			0.0532625	−	0.998581i	$-0.483038\pi$
$421$	2.18571			0.106525			0.0532625	+	0.998581i	$0.483038\pi$
$422$		−	0.462431i		−	0.0225108i
$423$	−1.02252			−0.0497167
$424$			3.60263i			0.174959i
$425$	8.70538	+	0.887314i	0.422273	+	0.0430410i
$426$	−1.12679			−0.0545931
$427$	−16.0426	+	9.71022i	−0.776357	+	0.469910i
$428$	4.92856			0.238231
$429$	−0.0284147	−	15.7890i	−0.00137187	−	0.762298i
$430$	−3.47806	−	3.85059i	−0.167727	−	0.185692i
$431$			12.4815i			0.601214i	0.953748	+	0.300607i	$0.0971892\pi$
$431$			12.4815i			0.601214i	−0.953748	+	0.300607i	$0.902811\pi$
$432$	−3.71435			−0.178707
$433$	−39.1498			−1.88142			−0.940711	−	0.339210i	$-0.889840\pi$
$433$	−39.1498			−1.88142			−0.940711	+	0.339210i	$0.889840\pi$
$434$	−0.125089	−	0.206664i	−0.00600445	−	0.00992019i
$435$	−13.1602	+	11.8870i	−0.630985	+	0.569940i
$436$		−	38.0334i		−	1.82147i
$437$		−	21.2470i		−	1.01638i
$438$		−	3.22991i		−	0.154331i
$439$	9.40386			0.448822			0.224411	−	0.974495i	$-0.427954\pi$
$439$	9.40386			0.448822			0.224411	+	0.974495i	$0.427954\pi$
$440$	4.31235	+	4.75700i	0.205583	+	0.226781i
$441$	3.24621	−	6.20178i	0.154581	−	0.295323i
$442$	1.82517			0.0868144
$443$		−	25.4918i		−	1.21115i	−0.795787	−	0.605576i	$-0.792943\pi$
$443$		−	25.4918i		−	1.21115i	0.795787	−	0.605576i	$-0.207057\pi$
$444$		−	16.4102i		−	0.778794i
$445$	13.8985	−	12.5538i	0.658850	−	0.595109i
$446$	3.58633			0.169818
$447$			19.3124i			0.913447i
$448$	−15.5523	+	9.41342i	−0.734776	+	0.444742i
$449$	−16.8178			−0.793680			−0.396840	−	0.917888i	$-0.629893\pi$
$449$	−16.8178			−0.793680			−0.396840	+	0.917888i	$0.629893\pi$
$450$	0.111070	−	1.08970i	0.00523591	−	0.0513692i
$451$	17.0065	−	0.0306058i	0.800805	−	0.00144117i
$452$		−	5.86270i		−	0.275758i
$453$			15.0336i			0.706339i
$454$		−	2.14779i		−	0.100801i
$455$	−8.10468	+	26.9725i	−0.379953	+	1.26449i
$456$	−3.45345			−0.161723
$457$	−7.02926			−0.328815			−0.164408	−	0.986392i	$-0.552571\pi$
$457$	−7.02926			−0.328815			−0.164408	+	0.986392i	$0.552571\pi$
$458$			1.76133i			0.0823017i
$459$			1.75010i			0.0816875i
$460$	17.2532	−	15.5840i	0.804433	−	0.726608i
$461$	−16.0285			−0.746520			−0.373260	−	0.927727i	$-0.621760\pi$
$461$	−16.0285			−0.746520			−0.373260	+	0.927727i	$0.621760\pi$
$462$	−1.64275	+	0.998362i	−0.0764278	+	0.0464480i
$463$		−	24.3558i		−	1.13191i	−0.824437	−	0.565954i	$-0.808508\pi$
$463$		−	24.3558i		−	1.13191i	0.824437	−	0.565954i	$-0.191492\pi$
$464$			29.4580i			1.36756i
$465$	−0.691605	+	0.624695i	−0.0320724	+	0.0289695i
$466$	1.10053			0.0509811
$467$	−33.4675			−1.54869			−0.774346	−	0.632762i	$-0.781921\pi$
$467$	−33.4675			−1.54869			−0.774346	+	0.632762i	$0.781921\pi$
$468$			9.29265i			0.429553i
$469$	16.8371	+	27.8172i	0.777465	+	1.28448i
$470$	−0.335744	−	0.371705i	−0.0154867	−	0.0171455i
$471$	−9.76184			−0.449802
$472$			1.27837i			0.0588416i
$473$	35.1315	−	0.0632245i	1.61535	−	0.00290707i
$474$			1.09478i			0.0502850i
$475$	−2.02240	+	19.8417i	−0.0927942	+	0.910398i
$476$	4.68019	+	7.73233i	0.214516	+	0.354411i
$477$			4.16120i			0.190528i
$478$		−	0.401778i		−	0.0183769i
$479$	−6.33570			−0.289485			−0.144743	−	0.989469i	$-0.546235\pi$
$479$	−6.33570			−0.289485			−0.144743	+	0.989469i	$0.546235\pi$
$480$	−3.81488	−	4.22349i	−0.174125	−	0.192775i
$481$	−40.0212			−1.82481
$482$	3.60652			0.164273
$483$	7.29734	+	12.0562i	0.332040	+	0.548577i
$484$	−21.4720	+	0.0772844i	−0.975998	+	0.00351293i
$485$	13.3655	+	14.7971i	0.606897	+	0.671901i
$486$	0.219070			0.00993722
$487$		−	1.38135i		−	0.0625949i	−0.999510	−	0.0312974i	$-0.990036\pi$
$487$		−	1.38135i		−	0.0625949i	0.999510	−	0.0312974i	$-0.00996391\pi$
$488$	−6.13635			−0.277779
$489$			2.65834i			0.120214i
$490$	3.32035	−	0.856295i	0.149998	−	0.0386835i
$491$		−	26.5710i		−	1.19913i	−0.800326	−	0.599565i	$-0.795340\pi$
$491$		−	26.5710i		−	1.19913i	0.800326	−	0.599565i	$-0.204660\pi$
$492$	−10.0092			−0.451252
$493$	13.8798			0.625114
$494$			4.16000i			0.187167i
$495$	4.98096	+	5.49455i	0.223877	+	0.246962i
$496$			1.54810i			0.0695116i
$497$	−11.6419	+	7.04659i	−0.522213	+	0.316083i
$498$			1.04667i			0.0469026i
$499$	21.9537			0.982781			0.491391	−	0.870939i	$-0.336489\pi$
$499$	21.9537			0.982781			0.491391	+	0.870939i	$0.336489\pi$
$500$	−17.5954	+	12.9110i	−0.786890	+	0.577398i
$501$		−	12.3713i		−	0.552710i
$502$			6.40915i			0.286054i
$503$		−	34.3973i		−	1.53370i	−0.641827	−	0.766849i	$-0.721823\pi$
$503$		−	34.3973i		−	1.53370i	0.641827	−	0.766849i	$-0.278177\pi$
$504$	1.95960	−	1.18610i	0.0872876	−	0.0528331i
$505$	23.3480	+	25.8488i	1.03897	+	1.15026i
$506$	−0.00696486	−	3.87011i	−0.000309626	−	0.172047i
$507$	9.66291			0.429145
$508$	−31.7918			−1.41053
$509$		−	23.1473i		−	1.02598i	−0.858393	−	0.512992i	$-0.828537\pi$
$509$		−	23.1473i		−	1.02598i	0.858393	−	0.512992i	$-0.171463\pi$
$510$	−0.636192	+	0.574643i	−0.0281710	+	0.0254456i
$511$	−20.1989	−	33.3714i	−0.893546	−	1.47626i
$512$	−15.8854			−0.702044
$513$	−3.98889			−0.176114
$514$	2.87390			0.126762
$515$	−1.83949	−	2.03651i	−0.0810575	−	0.0897394i
$516$	−20.6768			−0.910244
$517$	3.39132	−	0.00610320i	0.149150	−	0.000268418i
$518$	2.52311	+	4.16853i	0.110859	+	0.183154i
$519$		−	5.30683i		−	0.232944i
$520$	−6.83914	+	6.17749i	−0.299916	+	0.270901i
$521$		−	31.3896i		−	1.37520i	−0.726089	−	0.687601i	$-0.758664\pi$
$521$		−	31.3896i		−	1.37520i	0.726089	−	0.687601i	$-0.241336\pi$
$522$		−	1.73742i		−	0.0760447i
$523$		−	29.0877i		−	1.27192i	−0.771723	−	0.635959i	$-0.780605\pi$
$523$		−	29.0877i		−	1.27192i	0.771723	−	0.635959i	$-0.219395\pi$
$524$	40.3271			1.76170
$525$	−5.66711	−	11.9534i	−0.247333	−	0.521689i
$526$	1.66117			0.0724307
$527$	0.729419			0.0317740
$528$	12.3191	−	0.0221701i	0.536120	−	0.000964830i
$529$	−5.37194			−0.233563
$530$	−1.51267	+	1.36633i	−0.0657063	+	0.0593495i
$531$			1.47657i			0.0640778i
$532$	−17.6238	+	10.6673i	−0.764090	+	0.462486i
$533$			24.4105i			1.05734i
$534$			1.83488i			0.0794029i
$535$	3.78435	+	4.18969i	0.163612	+	0.181136i
$536$			10.6402i			0.459585i
$537$	−6.03351			−0.260365
$538$		−	5.38256i		−	0.232059i
$539$	−10.7294	+	20.5883i	−0.462149	+	0.886802i
$540$	−2.92573	−	3.23910i	−0.125903	−	0.139389i
$541$			32.1045i			1.38028i	0.723677	+	0.690139i	$0.242451\pi$
$541$			32.1045i			1.38028i	−0.723677	+	0.690139i	$0.757549\pi$
$542$	−3.30634			−0.142019
$543$		−	15.0417i		−	0.645502i
$544$			4.45441i			0.190981i
$545$	32.3316	−	29.2036i	1.38493	−	1.25095i
$546$	−1.42877	−	2.36052i	−0.0611455	−	0.101021i
$547$	−34.3259			−1.46767			−0.733834	−	0.679329i	$-0.762271\pi$
$547$	−34.3259			−1.46767			−0.733834	+	0.679329i	$0.762271\pi$
$548$			31.6370i			1.35146i
$549$	−7.08776			−0.302498
$550$	−0.361874	+	3.61480i	−0.0154304	+	0.154136i
$551$			31.6354i			1.34771i
$552$			4.61154i			0.196280i
$553$	6.84643	+	11.3113i	0.291140	+	0.481004i
$554$	1.14728			0.0487435
$555$	13.9500	−	12.6004i	0.592146	−	0.534858i
$556$	−34.6800			−1.47076
$557$	−8.73363			−0.370056			−0.185028	−	0.982733i	$-0.559238\pi$
$557$	−8.73363			−0.370056			−0.185028	+	0.982733i	$0.559238\pi$
$558$		−	0.0913058i		−	0.00386528i
$559$			50.4265i			2.13281i
$560$	−21.0449	−	6.32355i	−0.889309	−	0.267219i
$561$	−0.0104459	−	5.80440i	−0.000441027	−	0.245062i
$562$			4.27540i			0.180347i
$563$			3.77704i			0.159183i	0.996828	+	0.0795917i	$0.0253617\pi$
$563$			3.77704i			0.159183i	−0.996828	+	0.0795917i	$0.974638\pi$
$564$	−1.99597			−0.0840456
$565$	4.98378	−	4.50162i	0.209669	−	0.189384i
$566$		−	3.07596i		−	0.129292i
$567$	2.26343	−	1.37000i	0.0950550	−	0.0575345i
$568$	−4.45308			−0.186847
$569$			33.3725i			1.39905i	0.714608	+	0.699525i	$0.246605\pi$
$569$			33.3725i			1.39905i	−0.714608	+	0.699525i	$0.753395\pi$
$570$	−1.30975	−	1.45003i	−0.0548594	−	0.0607353i
$571$			20.4207i			0.854579i	0.904115	+	0.427289i	$0.140531\pi$
$571$			20.4207i			0.854579i	−0.904115	+	0.427289i	$0.859469\pi$
$572$	−0.0554656	−	30.8202i	−0.00231914	−	1.28866i
$573$	−18.7953			−0.785186
$574$	2.54255	−	1.53894i	0.106124	−	0.0642343i
$575$	26.4954	+	2.70060i	1.10493	+	0.112623i
$576$	−6.87112			−0.286297
$577$	28.1851			1.17336			0.586680	−	0.809819i	$-0.300435\pi$
$577$	28.1851			1.17336			0.586680	+	0.809819i	$0.300435\pi$
$578$	−3.05322			−0.126997
$579$	1.81009			0.0752249
$580$	−25.6889	+	23.2036i	−1.06667	+	0.963477i
$581$	6.54558	+	10.8142i	0.271557	+	0.448649i
$582$	−1.95351			−0.0809757
$583$	−0.0248372	−	13.8011i	−0.00102865	−	0.571584i
$584$		−	12.7646i		−	0.528204i
$585$	−7.89952	+	7.13527i	−0.326605	+	0.295007i
$586$		−	3.48347i		−	0.143901i
$587$	46.9856			1.93930			0.969651	−	0.244492i	$-0.0786213\pi$
$587$	46.9856			1.93930			0.969651	+	0.244492i	$0.0786213\pi$
$588$	6.33663	−	12.1059i	0.261318	−	0.499240i
$589$			1.66252i			0.0685030i
$590$	−0.536761	+	0.484831i	−0.0220981	+	0.0199602i
$591$	14.2265			0.585201
$592$		−	31.2260i		−	1.28338i
$593$		−	9.05085i		−	0.371674i	−0.982581	−	0.185837i	$-0.940500\pi$
$593$		−	9.05085i		−	0.371674i	0.982581	−	0.185837i	$-0.0594996\pi$
$594$	−0.726572	+	0.00130758i	−0.0298116	+	5.36506e-5i
$595$	−2.97948	+	9.91575i	−0.122147	+	0.406506i
$596$			37.6980i			1.54417i
$597$			7.65140i			0.313151i
$598$	5.55502			0.227162
$599$	30.1385			1.23143			0.615713	−	0.787971i	$-0.288868\pi$
$599$	30.1385			1.23143			0.615713	+	0.787971i	$0.288868\pi$
$600$	0.438951	−	4.30652i	0.0179201	−	0.175813i
$601$	−4.88298			−0.199181			−0.0995905	−	0.995029i	$-0.531753\pi$
$601$	−4.88298			−0.199181			−0.0995905	+	0.995029i	$0.531753\pi$
$602$	5.25232	−	3.17910i	0.214068	−	0.129570i
$603$			12.2899i			0.500482i
$604$			29.3457i			1.19406i
$605$	−16.5527	−	18.1936i	−0.672964	−	0.739675i
$606$	−3.41256			−0.138626
$607$		−	0.685604i		−	0.0278278i	−0.999903	−	0.0139139i	$-0.995571\pi$
$607$		−	0.685604i		−	0.0278278i	0.999903	−	0.0139139i	$-0.00442908\pi$
$608$	−10.1527			−0.411746
$609$	−10.8653	−	17.9510i	−0.440283	−	0.727409i
$610$	−2.32726	−	2.57653i	−0.0942280	−	0.104321i
$611$			4.86778i			0.196929i
$612$			3.41620i			0.138092i
$613$	−32.2070			−1.30083			−0.650414	−	0.759580i	$-0.725404\pi$
$613$	−32.2070			−1.30083			−0.650414	+	0.759580i	$0.725404\pi$
$614$			3.36151i			0.135659i
$615$	−7.68550	−	8.50869i	−0.309909	−	0.343103i
$616$	−6.49217	+	3.94554i	−0.261577	+	0.158970i
$617$		−	28.7997i		−	1.15943i	−0.814819	−	0.579716i	$-0.803163\pi$
$617$		−	28.7997i		−	1.15943i	0.814819	−	0.579716i	$-0.196837\pi$
$618$	0.268861			0.0108152
$619$			18.4418i			0.741239i	0.928785	+	0.370619i	$0.120855\pi$
$619$			18.4418i			0.741239i	−0.928785	+	0.370619i	$0.879145\pi$
$620$	−1.35002	+	1.21941i	−0.0542180	+	0.0489727i
$621$			5.32653i			0.213746i
$622$		−	6.55435i		−	0.262805i
$623$	11.4748	+	18.9579i	0.459727	+	0.759533i
$624$			17.6824i			0.707862i
$625$	−24.4859	−	5.04395i	−0.979435	−	0.201758i
$626$	−2.80774			−0.112220
$627$	13.2296	−	0.0238088i	0.528341	−	0.000950831i
$628$	−19.0552			−0.760385
$629$	−14.7128			−0.586637
$630$	1.24121	+	0.372959i	0.0494511	+	0.0148590i
$631$	21.1920			0.843641			0.421821	−	0.906679i	$-0.361391\pi$
$631$	21.1920			0.843641			0.421821	+	0.906679i	$0.361391\pi$
$632$			4.32659i			0.172102i
$633$		−	2.11088i		−	0.0839000i
$634$			0.0204996i			0.000814141i
$635$	−24.4110	−	27.0257i	−0.968722	−	1.07248i
$636$			8.12270i			0.322086i
$637$	−29.5240	−	15.4538i	−1.16978	−	0.612301i
$638$	0.0103702	+	5.76235i	0.000410562	+	0.228134i
$639$	−5.14350			−0.203474
$640$	−9.88589	−	10.9448i	−0.390774	−	0.432629i
$641$	−25.4119			−1.00371			−0.501855	−	0.864952i	$-0.667349\pi$
$641$	−25.4119			−1.00371			−0.501855	+	0.864952i	$0.667349\pi$
$642$	−0.553123			−0.0218300
$643$	−12.1435			−0.478893			−0.239447	−	0.970910i	$-0.576966\pi$
$643$	−12.1435			−0.478893			−0.239447	+	0.970910i	$0.576966\pi$
$644$	14.2445	+	23.5338i	0.561311	+	0.927363i
$645$	−15.8765	−	17.5770i	−0.625135	−	0.692093i
$646$			1.52932i			0.0601702i
$647$	13.9580			0.548745			0.274373	−	0.961623i	$-0.411530\pi$
$647$	13.9580			0.548745			0.274373	+	0.961623i	$0.411530\pi$
$648$	0.865767			0.0340105
$649$	−0.00881331	−	4.89723i	−0.000345953	−	0.192233i
$650$	−5.18760	−	0.528757i	−0.203475	−	0.0207396i
$651$	−0.570999	−	0.943369i	−0.0223792	−	0.0369736i
$652$			5.18909i			0.203221i
$653$		−	25.7898i		−	1.00923i	−0.863344	−	0.504616i	$-0.831634\pi$
$653$		−	25.7898i		−	1.00923i	0.863344	−	0.504616i	$-0.168366\pi$
$654$			4.26842i			0.166908i
$655$	30.9648	+	34.2814i	1.20990	+	1.33948i
$656$	−19.0460			−0.743620
$657$		−	14.7437i		−	0.575208i
$658$	0.507017	−	0.306885i	0.0197656	−	0.0119636i
$659$		−	5.42636i		−	0.211381i	−0.994399	−	0.105690i	$-0.966295\pi$
$659$		−	5.42636i		−	0.211381i	0.994399	−	0.105690i	$-0.0337053\pi$
$660$	9.72287	+	10.7254i	0.378462	+	0.417486i
$661$		−	36.7560i		−	1.42964i	−0.699307	−	0.714821i	$-0.746508\pi$
$661$		−	36.7560i		−	1.42964i	0.699307	−	0.714821i	$-0.253492\pi$
$662$	−0.569883			−0.0221491
$663$	8.33143			0.323566
$664$			4.13647i			0.160526i
$665$	−22.6004	−	6.79095i	−0.876405	−	0.263342i
$666$			1.84169i			0.0713639i
$667$	42.2440			1.63570
$668$		−	24.1489i		−	0.934350i
$669$	16.3707			0.632928
$670$	−4.46759	+	4.03537i	−0.172598	+	0.155900i
$671$	23.5074	−	0.0423052i	0.907493	−	0.00163317i
$672$	5.76096	−	3.48697i	0.222234	−	0.134513i
$673$	−33.7245			−1.29998			−0.649991	−	0.759942i	$-0.725228\pi$
$673$	−33.7245			−1.29998			−0.649991	+	0.759942i	$0.725228\pi$
$674$	−2.11175			−0.0813414
$675$	0.507009	−	4.97423i	0.0195148	−	0.191458i
$676$	18.8621			0.725465
$677$		−	22.1771i		−	0.852334i	−0.904644	−	0.426167i	$-0.859864\pi$
$677$		−	22.1771i		−	0.852334i	0.904644	−	0.426167i	$-0.140136\pi$
$678$			0.657959i			0.0252688i
$679$	−20.1837	+	12.2167i	−0.774577	+	0.468833i
$680$	−2.51424	+	2.27099i	−0.0964165	+	0.0870886i
$681$		−	9.80413i		−	0.375695i
$682$	0.000544983		0.302827i	2.08685e−5		0.0115958i
$683$		−	5.37195i		−	0.205552i	−0.994705	−	0.102776i	$-0.967228\pi$
$683$		−	5.37195i		−	0.205552i	0.994705	−	0.102776i	$-0.0327725\pi$
$684$	−7.78635			−0.297719
$685$	−26.8940	+	24.2921i	−1.02757	+	0.928155i
$686$	0.251683	+	4.04942i	0.00960932	+	0.154608i
$687$			8.04004i			0.306747i
$688$	−39.3445			−1.50000
$689$	19.8096			0.754687
$690$	−1.93629	+	1.74896i	−0.0737133	+	0.0665819i
$691$		−	14.5410i		−	0.553167i	−0.960990	−	0.276584i	$-0.910798\pi$
$691$		−	14.5410i		−	0.553167i	0.960990	−	0.276584i	$-0.0892023\pi$
$692$		−	10.3590i		−	0.393789i
$693$	−7.49875	+	4.55727i	−0.284854	+	0.173116i
$694$	−1.02719			−0.0389914
$695$	−26.6287	−	29.4808i	−1.01008	−	1.11827i
$696$		−	6.86629i		−	0.260266i
$697$			8.97391i			0.339911i
$698$	4.97317			0.188237
$699$	5.02365			0.190012
$700$	−11.0622	−	23.3331i	−0.418113	−	0.881910i
$701$			22.9952i			0.868517i	0.900788	+	0.434258i	$0.142990\pi$
$701$			22.9952i			0.868517i	−0.900788	+	0.434258i	$0.857010\pi$
$702$		−	1.04290i		−	0.0393616i
$703$		−	33.5340i		−	1.26476i
$704$	22.7889	−	0.0410121i	0.858889	−	0.00154570i
$705$	−1.53259	−	1.69674i	−0.0577206	−	0.0639030i
$706$	2.73887			0.103079
$707$	−35.2585	+	21.3411i	−1.32603	+	0.802615i
$708$			2.88228i			0.108323i
$709$	11.8461			0.444890			0.222445	−	0.974945i	$-0.428596\pi$
$709$	11.8461			0.444890			0.222445	+	0.974945i	$0.428596\pi$
$710$	−1.68887	−	1.86976i	−0.0633820	−	0.0701707i
$711$			4.99740i			0.187417i
$712$			7.25145i			0.271760i
$713$	2.22003			0.0831409
$714$	−0.525249	−	0.867784i	−0.0196569	−	0.0324760i
$715$	26.1571	−	23.7121i	0.978221	−	0.886784i
$716$	−11.7775			−0.440145
$717$		−	1.83401i		−	0.0684925i
$718$			3.88597i			0.145023i
$719$			27.9271i			1.04151i	0.853708	+	0.520753i	$0.174349\pi$
$719$			27.9271i			1.04151i	−0.853708	+	0.520753i	$0.825651\pi$
$720$	−5.56719	−	6.16348i	−0.207477	−	0.229699i
$721$	2.77786	−	1.68137i	0.103453	−	0.0626176i
$722$	0.676651			0.0251823
$723$	16.4629			0.612260
$724$		−	29.3616i		−	1.09121i
$725$	−39.4500	−	4.02102i	−1.46513	−	0.149337i
$726$	2.40976	−	0.00867348i	0.0894344	−	0.000321903i
$727$	38.8892			1.44232			0.721161	−	0.692767i	$-0.243609\pi$
$727$	38.8892			1.44232			0.721161	+	0.692767i	$0.243609\pi$
$728$	−5.64649	−	9.32879i	−0.209273	−	0.345748i
$729$	1.00000			0.0370370
$730$	5.35961	−	4.84109i	0.198368	−	0.179177i
$731$			18.5380i			0.685653i
$732$	−13.8354			−0.511370
$733$		−	12.2498i		−	0.452458i	−0.974074	−	0.226229i	$-0.927360\pi$
$733$		−	12.2498i		−	0.452458i	0.974074	−	0.226229i	$-0.0726398\pi$
$734$	−1.73749			−0.0641320
$735$	15.1566	−	3.90877i	0.559058	−	0.144177i
$736$			13.5573i			0.499728i
$737$	−0.0733554	−	40.7608i	−0.00270208	−	1.50144i
$738$	1.12332			0.0413499
$739$		−	12.3392i		−	0.453903i	−0.973906	−	0.226952i	$-0.927124\pi$
$739$		−	12.3392i		−	0.453903i	0.973906	−	0.226952i	$-0.0728759\pi$
$740$	27.2306	−	24.5961i	1.00102	−	0.904172i
$741$			18.9894i			0.697591i
$742$	−1.24888	−	2.06333i	−0.0458480	−	0.0757472i
$743$	37.7653			1.38547			0.692737	−	0.721191i	$-0.256405\pi$
$743$	37.7653			1.38547			0.692737	+	0.721191i	$0.256405\pi$
$744$		−	0.360841i		−	0.0132291i
$745$	−32.0464	+	28.9461i	−1.17409	+	1.06050i
$746$	5.43986			0.199167
$747$			4.77780i			0.174811i
$748$	−0.0203905	−	11.3302i	−0.000745551	−	0.414275i
$749$	−5.71486	+	3.45906i	−0.208816	+	0.126391i
$750$	1.97470	−	1.44898i	0.0721058	−	0.0529092i
$751$	10.2252			0.373124			0.186562	−	0.982443i	$-0.440266\pi$
$751$	10.2252			0.373124			0.186562	+	0.982443i	$0.440266\pi$
$752$	−3.79801			−0.138499
$753$			29.2562i			1.06615i
$754$	−8.27107			−0.301215
$755$	−24.9462	+	22.5328i	−0.907887	+	0.820052i
$756$	4.41823	−	2.67425i	0.160689	−	0.0972615i
$757$			0.670498i			0.0243696i	0.999926	+	0.0121848i	$0.00387865\pi$
$757$			0.670498i			0.0243696i	−0.999926	+	0.0121848i	$0.996121\pi$
$758$	3.07557			0.111710
$759$	−0.0317928	−	17.6661i	−0.00115401	−	0.641238i
$760$	−5.17614	−	5.73055i	−0.187758	−	0.207869i
$761$	46.2002			1.67476			0.837378	−	0.546624i	$-0.184087\pi$
$761$	46.2002			1.67476			0.837378	+	0.546624i	$0.184087\pi$
$762$	3.56793			0.129253
$763$	26.6934	+	44.1012i	0.966366	+	1.59657i
$764$	−36.6886			−1.32735
$765$	−2.90405	+	2.62310i	−0.104996	+	0.0948384i
$766$	−0.790195			−0.0285509
$767$	7.02931			0.253814
$768$	−12.2973			−0.443741
$769$	0.657059			0.0236942			0.0118471	−	0.999930i	$-0.496229\pi$
$769$	0.657059			0.0236942			0.0118471	+	0.999930i	$0.496229\pi$
$770$	−4.11886	−	1.22956i	−0.148433	−	0.0443101i
$771$	13.1186			0.472455
$772$	3.53332			0.127167
$773$	2.59489			0.0933316			0.0466658	−	0.998911i	$-0.485140\pi$
$773$	2.59489			0.0933316			0.0466658	+	0.998911i	$0.485140\pi$
$774$	2.32051			0.0834092
$775$	−2.07320	−	0.211315i	−0.0744715	−	0.00759066i
$776$	−7.72030			−0.277143
$777$	11.5174	+	19.0283i	0.413183	+	0.682635i
$778$	−3.59936			−0.129043
$779$	−20.4537			−0.732830
$780$	−15.4199	+	13.9281i	−0.552122	+	0.498706i
$781$	17.0590	−	0.0307004i	0.610421	−	0.00109855i
$782$	2.04216			0.0730275
$783$		−	7.93087i		−	0.283426i
$784$	12.0576	−	23.0356i	0.430627	−	0.822700i
$785$	−14.6314	−	16.1985i	−0.522216	−	0.578149i
$786$	−4.52584			−0.161431
$787$			29.5992i			1.05510i	0.849525	+	0.527549i	$0.176889\pi$
$787$			29.5992i			1.05510i	−0.849525	+	0.527549i	$0.823111\pi$
$788$	27.7703			0.989277
$789$	7.58284			0.269956
$790$	−1.81665	+	1.64089i	−0.0646334	+	0.0583804i
$791$	4.11468	+	6.79802i	0.146301	+	0.241710i
$792$	−2.87142	+	0.00516756i	−0.102031	+	0.000183621i
$793$			33.7417i			1.19820i
$794$	4.87848			0.173131
$795$	−6.90497	+	6.23694i	−0.244894	+	0.221201i
$796$			14.9356i			0.529378i
$797$	18.3391			0.649603			0.324801	−	0.945782i	$-0.394703\pi$
$797$	18.3391			0.649603			0.324801	+	0.945782i	$0.394703\pi$
$798$	1.97789	−	1.19717i	0.0700165	−	0.0423793i
$799$			1.78951i			0.0633084i
$800$	1.29046	−	12.6606i	0.0456246	−	0.447620i
$801$			8.37576i			0.295943i
$802$	−3.39460			−0.119868
$803$	0.0880019	+	48.8993i	0.00310552	+	1.72562i
$804$			23.9899i			0.846060i
$805$	−9.06823	+	30.1792i	−0.319613	+	1.06368i
$806$	−0.434666			−0.0153105
$807$		−	24.5700i		−	0.864906i
$808$	−13.4865			−0.474452
$809$		−	19.7647i		−	0.694890i	−0.937700	−	0.347445i	$-0.887049\pi$
$809$		−	19.7647i		−	0.694890i	0.937700	−	0.347445i	$-0.112951\pi$
$810$	0.328349	+	0.363518i	0.0115370	+	0.0127727i
$811$	20.7871			0.729935			0.364967	−	0.931020i	$-0.381080\pi$
$811$	20.7871			0.729935			0.364967	+	0.931020i	$0.381080\pi$
$812$	−21.2091	−	35.0404i	−0.744294	−	1.22968i
$813$	−15.0926			−0.529320
$814$	−0.0109926	−	6.10817i	−0.000385290	−	0.214091i
$815$	−4.41116	+	3.98440i	−0.154516	+	0.139567i
$816$			6.50048i			0.227562i
$817$	−42.2526			−1.47823
$818$	6.12787			0.214256
$819$	−6.52196	−	10.7752i	−0.227896	−	0.376515i
$820$	−15.0022	−	16.6090i	−0.523898	−	0.580012i
$821$			4.20073i			0.146607i	0.997310	+	0.0733033i	$0.0233541\pi$
$821$			4.20073i			0.146607i	−0.997310	+	0.0733033i	$0.976646\pi$
$822$		−	3.55056i		−	0.123840i
$823$			0.993153i			0.0346191i	0.999850	+	0.0173096i	$0.00551008\pi$
$823$			0.993153i			0.0346191i	−0.999850	+	0.0173096i	$0.994490\pi$
$824$	1.06254			0.0370153
$825$	−1.65186	+	16.5006i	−0.0575105	+	0.574479i
$826$	−0.443157	−	0.732157i	−0.0154194	−	0.0254750i
$827$	45.7635			1.59135			0.795676	−	0.605722i	$-0.207116\pi$
$827$	45.7635			1.59135			0.795676	+	0.605722i	$0.207116\pi$
$828$			10.3974i			0.361336i
$829$		−	12.6023i		−	0.437697i	−0.975759	−	0.218848i	$-0.929770\pi$
$829$		−	12.6023i		−	0.437697i	0.975759	−	0.218848i	$-0.0702300\pi$
$830$	−1.73682	+	1.56879i	−0.0602858	+	0.0544534i
$831$	5.23707			0.181672
$832$			32.7104i			1.13403i
$833$	−10.8537	−	5.68118i	−0.376059	−	0.196841i
$834$	3.89207			0.134771
$835$	20.5286	−	18.5425i	0.710421	−	0.641690i
$836$	25.8244	−	0.0464749i	0.893154	−	0.00160737i
$837$		−	0.416788i		−	0.0144063i
$838$			8.58652i			0.296616i
$839$		−	42.7111i		−	1.47455i	−0.675592	−	0.737276i	$-0.736112\pi$
$839$		−	42.7111i		−	1.47455i	0.675592	−	0.737276i	$-0.263888\pi$
$840$	4.90529	+	1.47394i	0.169249	+	0.0508557i
$841$	−33.8987			−1.16892
$842$	−0.478824			−0.0165014
$843$			19.5161i			0.672171i
$844$		−	4.12046i		−	0.141832i
$845$	14.4831	+	16.0343i	0.498233	+	0.551598i
$846$	0.224004			0.00770142
$847$	24.8433	−	15.1595i	0.853626	−	0.520886i
$848$			15.4562i			0.530767i
$849$		−	14.0410i		−	0.481885i
$850$	−1.90709	−	0.194384i	−0.0654126	−	0.00666732i
$851$	−44.7793			−1.53501
$852$	−10.0402			−0.343970
$853$			33.1450i			1.13486i	0.823421	+	0.567431i	$0.192063\pi$
$853$			33.1450i			1.13486i	−0.823421	+	0.567431i	$0.807937\pi$
$854$	3.51446	−	2.12722i	0.120262	−	0.0727919i
$855$	−5.97868	−	6.61904i	−0.204466	−	0.226366i
$856$	−2.18595			−0.0747141
$857$			13.9133i			0.475268i	0.971355	+	0.237634i	$0.0763718\pi$
$857$			13.9133i			0.475268i	−0.971355	+	0.237634i	$0.923628\pi$
$858$	0.00622480	+	3.45889i	0.000212511	+	0.118085i
$859$			54.9993i			1.87655i	0.345886	+	0.938277i	$0.387578\pi$
$859$			54.9993i			1.87655i	−0.345886	+	0.938277i	$0.612422\pi$
$860$	−30.9910	−	34.3104i	−1.05678	−	1.16997i
$861$	11.6061	−	7.02489i	0.395535	−	0.239408i
$862$		−	2.73433i		−	0.0931316i
$863$		−	0.856611i		−	0.0291594i	−0.999894	−	0.0145797i	$-0.995359\pi$
$863$		−	0.856611i		−	0.0291594i	0.999894	−	0.0145797i	$-0.00464102\pi$
$864$	2.54524			0.0865908
$865$	8.80598	−	7.95404i	0.299412	−	0.270445i
$866$	8.57656			0.291443
$867$	−13.9372			−0.473331
$868$	−1.11459	−	1.84146i	−0.0378318	−	0.0625034i
$869$	−0.0298283	−	16.5745i	−0.00101186	−	0.562251i
$870$	2.88302	−	2.60410i	0.0977434	−	0.0882871i
$871$	58.5067			1.98242
$872$			16.8688i			0.571251i
$873$	−8.91729			−0.301805
$874$			4.65458i			0.157443i
$875$	11.3411	−	27.3200i	0.383398	−	0.923583i
$876$		−	28.7799i		−	0.972382i
$877$	−44.0077			−1.48603			−0.743017	−	0.669272i	$-0.766606\pi$
$877$	−44.0077			−1.48603			−0.743017	+	0.669272i	$0.766606\pi$
$878$	−2.06010			−0.0695252
$879$		−	15.9012i		−	0.536333i
$880$	18.5010	+	20.4087i	0.623670	+	0.687977i
$881$		−	3.83174i		−	0.129094i	−0.997915	−	0.0645472i	$-0.979440\pi$
$881$		−	3.83174i		−	0.129094i	0.997915	−	0.0645472i	$-0.0205603\pi$
$882$	−0.711148	+	1.35863i	−0.0239456	+	0.0457473i
$883$		−	45.6823i		−	1.53733i	−0.639651	−	0.768665i	$-0.720921\pi$
$883$		−	45.6823i		−	1.53733i	0.639651	−	0.768665i	$-0.279079\pi$
$884$	16.2630			0.546985
$885$	−2.45018	+	2.21313i	−0.0823618	+	0.0743936i
$886$			5.58450i			0.187615i
$887$			40.4637i			1.35864i	0.733844	+	0.679319i	$0.237725\pi$
$887$			40.4637i			1.35864i	−0.733844	+	0.679319i	$0.762275\pi$
$888$			7.27836i			0.244246i
$889$	36.8638	−	22.3128i	1.23637	−	0.748346i
$890$	−3.04474	+	2.75017i	−0.102060	+	0.0921860i
$891$	−3.31662	+	0.00596877i	−0.111111	+	0.000199961i
$892$	31.9557			1.06996
$893$	−4.07873			−0.136490
$894$		−	4.23078i		−	0.141498i
$895$	−9.04322	−	10.0118i	−0.302281	−	0.334658i
$896$	14.9290	−	9.03614i	0.498742	−	0.301876i
$897$	25.3573			0.846654
$898$	3.68427			0.122946
$899$	−3.30549			−0.110244
$900$	0.989685	−	9.70973i	0.0329895	−	0.323658i
$901$	7.28250			0.242615
$902$	−3.72562	+	0.00670482i	−0.124050	+	0.000223246i
$903$	23.9755	−	14.5118i	0.797855	−	0.482922i
$904$			2.60026i			0.0864834i
$905$	24.9598	−	22.5450i	0.829691	−	0.749422i
$906$		−	3.29341i		−	0.109416i
$907$			15.3807i			0.510708i	0.966848	+	0.255354i	$0.0821921\pi$
$907$			15.3807i			0.510708i	−0.966848	+	0.255354i	$0.917808\pi$
$908$		−	19.1377i		−	0.635108i
$909$	−15.5775			−0.516672
$910$	1.77549	−	5.90887i	0.0588570	−	0.195877i
$911$	35.4906			1.17586			0.587928	−	0.808913i	$-0.299944\pi$
$911$	35.4906			1.17586			0.587928	+	0.808913i	$0.299944\pi$
$912$	−14.8162			−0.490612
$913$	−0.0285176	−	15.8462i	−0.000943795	−	0.524431i
$914$	1.53990			0.0509354
$915$	−10.6234	−	11.7612i	−0.351197	−	0.388813i
$916$			15.6942i			0.518552i
$917$	−46.7608	+	28.3032i	−1.54418	+	0.934654i
$918$		−	0.383394i		−	0.0126539i
$919$		−	24.5333i		−	0.809277i	−0.914477	−	0.404639i	$-0.867397\pi$
$919$		−	24.5333i		−	0.809277i	0.914477	−	0.404639i	$-0.132603\pi$
$920$	−7.65224	+	6.91191i	−0.252287	+	0.227879i
$921$			15.3444i			0.505617i
$922$	3.51136			0.115640
$923$			24.4859i			0.805965i
$924$	−14.6376	+	8.89583i	−0.481542	+	0.292651i
$925$	41.8175	+	4.26234i	1.37495	+	0.140145i
$926$			5.33562i			0.175339i
$927$	1.22728			0.0403092
$928$		−	20.1860i		−	0.662636i
$929$		−	8.88182i		−	0.291403i	−0.989329	−	0.145701i	$-0.953456\pi$
$929$		−	8.88182i		−	0.291403i	0.989329	−	0.145701i	$-0.0465439\pi$
$930$	0.151510	−	0.136852i	0.00496821	−	0.00448755i
$931$	12.9488	−	24.7382i	0.424379	−	0.810763i
$932$	9.80620			0.321213
$933$		−	29.9189i		−	0.979502i
$934$	7.33173			0.239902
$935$	9.61599	−	8.71716i	0.314476	−	0.285081i
$936$		−	4.12153i		−	0.134717i
$937$		−	14.8334i		−	0.484587i	−0.970203	−	0.242294i	$-0.922100\pi$
$937$		−	14.8334i		−	0.484587i	0.970203	−	0.242294i	$-0.0778997\pi$
$938$	−3.68851	−	6.09393i	−0.120434	−	0.198974i
$939$	−12.8166			−0.418255
$940$	−2.99163	−	3.31205i	−0.0975761	−	0.108027i
$941$	9.65898			0.314874			0.157437	−	0.987529i	$-0.449677\pi$
$941$	9.65898			0.314874			0.157437	+	0.987529i	$0.449677\pi$
$942$	2.13853			0.0696770
$943$			27.3127i			0.889423i
$944$			5.48451i			0.178506i
$945$	5.66583	+	1.70246i	0.184309	+	0.0553812i
$946$	−7.69626	+	0.0138506i	−0.250227	+	0.000450322i
$947$			21.8372i			0.709613i	0.934940	+	0.354806i	$0.115453\pi$
$947$			21.8372i			0.709613i	−0.934940	+	0.354806i	$0.884547\pi$
$948$			9.75497i			0.316827i
$949$	−70.1884			−2.27841
$950$	0.443048	−	4.34672i	0.0143744	−	0.141026i
$951$			0.0935753i			0.00303439i
$952$	−2.07579	−	3.42949i	−0.0672767	−	0.111150i
$953$	−8.84782			−0.286609			−0.143304	−	0.989679i	$-0.545773\pi$
$953$	−8.84782			−0.286609			−0.143304	+	0.989679i	$0.545773\pi$
$954$		−	0.911595i		−	0.0295140i
$955$	−28.1710	−	31.1884i	−0.911593	−	1.00923i
$956$		−	3.58001i		−	0.115786i
$957$	0.0473375	+	26.3037i	0.00153020	+	0.850277i
$958$	1.38796			0.0448430
$959$	−22.2041	−	36.6843i	−0.717008	−	1.18460i
$960$	−10.2987	−	11.4017i	−0.332388	−	0.367989i
$961$	30.8263			0.994396
$962$	8.76746			0.282674
$963$	−2.52487			−0.0813627
$964$	32.1356			1.03502
$965$	2.71303	+	3.00361i	0.0873354	+	0.0966897i
$966$	−1.59863	−	2.64116i	−0.0514351	−	0.0849779i
$967$	13.5577			0.435987			0.217994	−	0.975950i	$-0.430049\pi$
$967$	13.5577			0.435987			0.217994	+	0.975950i	$0.430049\pi$
$968$	9.52338	−	0.0342777i	0.306093	−	0.00110173i
$969$			6.98095i			0.224260i
$970$	−2.92799	−	3.24160i	−0.0940120	−	0.104081i
$971$		−	33.7112i		−	1.08184i	−0.841073	−	0.540921i	$-0.818076\pi$
$971$		−	33.7112i		−	1.08184i	0.841073	−	0.540921i	$-0.181924\pi$
$972$	1.95201			0.0626107
$973$	40.2127	−	24.3398i	1.28916	−	0.780298i
$974$			0.302612i			0.00969632i
$975$	−23.6801	−	2.41364i	−0.758370	−	0.0772985i
$976$	−26.3264			−0.842689
$977$			47.1128i			1.50727i	0.657293	+	0.753635i	$0.271701\pi$
$977$			47.1128i			1.50727i	−0.657293	+	0.753635i	$0.728299\pi$
$978$		−	0.582362i		−	0.0186219i
$979$	−0.0499929	−	27.7792i	−0.00159778	−	0.887827i
$980$	29.5857	−	7.62995i	0.945082	−	0.243730i
$981$			19.4843i			0.622085i
$982$			5.82091i			0.185753i
$983$	−18.7123			−0.596831			−0.298416	−	0.954436i	$-0.596458\pi$
$983$	−18.7123			−0.596831			−0.298416	+	0.954436i	$0.596458\pi$
$984$	4.43936			0.141522
$985$	21.3232	+	23.6071i	0.679413	+	0.752184i
$986$	−3.04065			−0.0968339
$987$	2.31441	−	1.40085i	0.0736683	−	0.0445897i
$988$			37.0674i			1.17927i
$989$			56.4216i			1.79410i
$990$	−1.09118	−	1.20369i	−0.0346800	−	0.0382558i
$991$	0.578234			0.0183682			0.00918411	−	0.999958i	$-0.497077\pi$
$991$	0.578234			0.0183682			0.00918411	+	0.999958i	$0.497077\pi$
$992$		−	1.06082i		−	0.0336812i
$993$	−2.60137			−0.0825521
$994$	2.55040	−	1.54370i	0.0808939	−	0.0489631i
$995$	−12.6965	+	11.4682i	−0.402506	+	0.363565i
$996$			9.32631i			0.295516i
$997$			1.90956i			0.0604763i	0.999543	+	0.0302381i	$0.00962657\pi$
$997$			1.90956i			0.0604763i	−0.999543	+	0.0302381i	$0.990373\pi$
$998$	−4.80940			−0.152239
$999$			8.40684i			0.265981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.k.a.769.23	✓	48
5.4	even	2		1155.2.k.b.769.26	yes	48
7.6	odd	2		1155.2.k.b.769.24	yes	48
11.10	odd	2	inner	1155.2.k.a.769.26	yes	48
35.34	odd	2	inner	1155.2.k.a.769.25	yes	48
55.54	odd	2		1155.2.k.b.769.23	yes	48
77.76	even	2		1155.2.k.b.769.25	yes	48
385.384	even	2	inner	1155.2.k.a.769.24	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.k.a.769.23	✓	48	1.1	even	1	trivial
1155.2.k.a.769.24	yes	48	385.384	even	2	inner
1155.2.k.a.769.25	yes	48	35.34	odd	2	inner
1155.2.k.a.769.26	yes	48	11.10	odd	2	inner
1155.2.k.b.769.23	yes	48	55.54	odd	2
1155.2.k.b.769.24	yes	48	7.6	odd	2
1155.2.k.b.769.25	yes	48	77.76	even	2
1155.2.k.b.769.26	yes	48	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.219070 q^{2} -1.00000 q^{3} -1.95201 q^{4} +(-1.49883 - 1.65937i) q^{5} +0.219070 q^{6} +(2.26343 - 1.37000i) q^{7} +0.865767 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.219070 q^{2} -1.00000 q^{3} -1.95201 q^{4} +(-1.49883 - 1.65937i) q^{5} +0.219070 q^{6} +(2.26343 - 1.37000i) q^{7} +0.865767 q^{8} +1.00000 q^{9} +(0.328349 + 0.363518i) q^{10} +(-3.31662 + 0.00596877i) q^{11} +1.95201 q^{12} -4.76056i q^{13} +(-0.495849 + 0.300126i) q^{14} +(1.49883 + 1.65937i) q^{15} +3.71435 q^{16} -1.75010i q^{17} -0.219070 q^{18} +3.98889 q^{19} +(2.92573 + 3.23910i) q^{20} +(-2.26343 + 1.37000i) q^{21} +(0.726572 - 0.00130758i) q^{22} -5.32653i q^{23} -0.865767 q^{24} +(-0.507009 + 4.97423i) q^{25} +1.04290i q^{26} -1.00000 q^{27} +(-4.41823 + 2.67425i) q^{28} +7.93087i q^{29} +(-0.328349 - 0.363518i) q^{30} +0.416788i q^{31} -2.54524 q^{32} +(3.31662 - 0.00596877i) q^{33} +0.383394i q^{34} +(-5.66583 - 1.70246i) q^{35} -1.95201 q^{36} -8.40684i q^{37} -0.873847 q^{38} +4.76056i q^{39} +(-1.29764 - 1.43663i) q^{40} -5.12766 q^{41} +(0.495849 - 0.300126i) q^{42} -10.5926 q^{43} +(6.47407 - 0.0116511i) q^{44} +(-1.49883 - 1.65937i) q^{45} +1.16688i q^{46} -1.02252 q^{47} -3.71435 q^{48} +(3.24621 - 6.20178i) q^{49} +(0.111070 - 1.08970i) q^{50} +1.75010i q^{51} +9.29265i q^{52} +4.16120i q^{53} +0.219070 q^{54} +(4.98096 + 5.49455i) q^{55} +(1.95960 - 1.18610i) q^{56} -3.98889 q^{57} -1.73742i q^{58} +1.47657i q^{59} +(-2.92573 - 3.23910i) q^{60} -7.08776 q^{61} -0.0913058i q^{62} +(2.26343 - 1.37000i) q^{63} -6.87112 q^{64} +(-7.89952 + 7.13527i) q^{65} +(-0.726572 + 0.00130758i) q^{66} +12.2899i q^{67} +3.41620i q^{68} +5.32653i q^{69} +(1.24121 + 0.372959i) q^{70} -5.14350 q^{71} +0.865767 q^{72} -14.7437i q^{73} +1.84169i q^{74} +(0.507009 - 4.97423i) q^{75} -7.78635 q^{76} +(-7.49875 + 4.55727i) q^{77} -1.04290i q^{78} +4.99740i q^{79} +(-5.56719 - 6.16348i) q^{80} +1.00000 q^{81} +1.12332 q^{82} +4.77780i q^{83} +(4.41823 - 2.67425i) q^{84} +(-2.90405 + 2.62310i) q^{85} +2.32051 q^{86} -7.93087i q^{87} +(-2.87142 + 0.00516756i) q^{88} +8.37576i q^{89} +(0.328349 + 0.363518i) q^{90} +(-6.52196 - 10.7752i) q^{91} +10.3974i q^{92} -0.416788i q^{93} +0.224004 q^{94} +(-5.97868 - 6.61904i) q^{95} +2.54524 q^{96} -8.91729 q^{97} +(-0.711148 + 1.35863i) q^{98} +(-3.31662 + 0.00596877i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9}+O(q^{10}) \) 48 * q - 48 * q^3 + 48 * q^4 + 4 * q^5 + 48 * q^9	\( 48 q - 48 q^{3} + 48 q^{4} + 4 q^{5} + 48 q^{9} - 48 q^{12} - 4 q^{15} + 40 q^{16} + 18 q^{20} + 20 q^{25} - 48 q^{27} + 48 q^{36} + 20 q^{38} - 16 q^{44} + 4 q^{45} - 8 q^{47} - 40 q^{48} + 24 q^{49} + 8 q^{55} - 8 q^{56} - 18 q^{60} - 4 q^{64} - 14 q^{70} - 32 q^{71} - 20 q^{75} + 32 q^{77} + 46 q^{80} + 48 q^{81} + 32 q^{82} - 16 q^{86} - 68 q^{97}+O(q^{100}) \) 48 * q - 48 * q^3 + 48 * q^4 + 4 * q^5 + 48 * q^9 - 48 * q^12 - 4 * q^15 + 40 * q^16 + 18 * q^20 + 20 * q^25 - 48 * q^27 + 48 * q^36 + 20 * q^38 - 16 * q^44 + 4 * q^45 - 8 * q^47 - 40 * q^48 + 24 * q^49 + 8 * q^55 - 8 * q^56 - 18 * q^60 - 4 * q^64 - 14 * q^70 - 32 * q^71 - 20 * q^75 + 32 * q^77 + 46 * q^80 + 48 * q^81 + 32 * q^82 - 16 * q^86 - 68 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more