LMFDB - Embedded newform 1155.2.k.b.769.25

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			769.25
Character	$\chi$	$=$	1155.769
Dual form			1155.2.k.b.769.26

$q$-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} +(-1.11916 - 5.80926i) 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} +(-4.96115 - 5.51244i) 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} +(-0.245176 - 1.27263i) 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	$-0.475321\pi$
$2$	0.219070			0.154906			0.0774530	+	0.996996i	$0.475321\pi$
$3$	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	$-0.736542\pi$
$29$		−	7.93087i		−	1.47273i	0.676587	−	0.736363i	$-0.263458\pi$
$30$	0.328349	+	0.363518i	0.0599481	+	0.0663690i
$31$		−	0.416788i		−	0.0748573i	−0.999299	−	0.0374287i	$-0.988083\pi$
$31$		−	0.416788i		−	0.0748573i	0.999299	−	0.0374287i	$-0.0119167\pi$
$32$	2.54524			0.449939
$33$	−3.31662	−	0.00596877i	−0.577349	−	0.00103903i
$34$		−	0.383394i		−	0.0657515i
$35$	−1.11916	−	5.80926i	−0.189173	−	0.981944i
$36$	−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	$-0.200725\pi$
$43$	10.5926			1.61535			0.807676	+	0.589627i	$0.200725\pi$
$44$	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	$-0.476240\pi$
$47$	1.02252			0.149150			0.0745751	+	0.997215i	$0.476240\pi$
$48$	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
$55$	−4.96115	−	5.51244i	−0.668961	−	0.743297i
$56$	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	$-0.969358\pi$
$59$		−	1.47657i		−	0.192233i	0.995370	−	0.0961166i	$-0.0306422\pi$
$60$	−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
$70$	−0.245176	−	1.27263i	−0.0293041	−	0.152109i
$71$	−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	$-0.909292\pi$
$79$		−	4.99740i		−	0.562252i	0.959671	−	0.281126i	$-0.0907079\pi$
$80$	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	$-0.853590\pi$
$89$		−	8.37576i		−	0.887828i	0.896069	−	0.443914i	$-0.146410\pi$
$90$	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	$-0.350458\pi$
$97$	8.91729			0.905414			0.452707	+	0.891659i	$0.350458\pi$
$98$	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	$-0.519258\pi$
$103$	−1.22728			−0.120928			−0.0604638	+	0.998170i	$0.519258\pi$
$104$			4.12153i			0.404150i
$105$	−1.11916	−	5.80926i	−0.109219	−	0.566925i
$106$			0.911595i			0.0885420i
$107$	2.52487			0.244088			0.122044	−	0.992525i	$-0.461055\pi$
$107$	2.52487			0.244088			0.122044	+	0.992525i	$0.461055\pi$
$108$	−1.95201			−0.187832
$109$		−	19.4843i		−	1.86625i	−0.359547	−	0.933127i	$-0.617069\pi$
$109$		−	19.4843i		−	1.86625i	0.359547	−	0.933127i	$-0.382931\pi$
$110$	−1.08684	−	1.20761i	−0.103626	−	0.115141i
$111$		−	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	$-0.757056\pi$
$127$	−16.2867			−1.44521			−0.722606	+	0.691260i	$0.757056\pi$
$128$	−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	$0.228384\pi$
$140$	2.18462	+	11.3397i	0.184634	+	0.958381i
$141$	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	$0.290475\pi$
$149$			19.3124i			1.58214i	−0.611728	+	0.791068i	$0.709525\pi$
$150$	−0.111070	+	1.08970i	−0.00906887	+	0.0889740i
$151$			15.0336i			1.22341i	0.791084	+	0.611707i	$0.209517\pi$
$151$			15.0336i			1.22341i	−0.791084	+	0.611707i	$0.790483\pi$
$152$	−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	$-0.627366\pi$
$157$	−9.76184			−0.779080			−0.389540	+	0.921010i	$0.627366\pi$
$158$		−	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
$165$	−4.96115	−	5.51244i	−0.386225	−	0.429143i
$166$			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
$175$	7.96226	−	10.5642i	0.601890	−	0.798579i
$176$	−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	$-0.811177\pi$
$181$		−	15.0417i		−	1.11804i	0.829153	−	0.559021i	$-0.188823\pi$
$182$	−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	$-0.479248\pi$
$193$	1.81009			0.130293			0.0651467	+	0.997876i	$0.479248\pi$
$194$	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	$-0.330829\pi$
$197$	14.2265			1.01360			0.506799	+	0.862064i	$0.330829\pi$
$198$	−0.726572	−	0.00130758i	−0.0516352	−	9.29256e-5i
$199$			7.65140i			0.542394i	0.962524	+	0.271197i	$0.0874194\pi$
$199$			7.65140i			0.542394i	−0.962524	+	0.271197i	$0.912581\pi$
$200$	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
$210$	−0.245176	−	1.27263i	−0.0169187	−	0.0878202i
$211$		−	2.11088i		−	0.145319i	−0.997357	−	0.0726596i	$-0.976851\pi$
$211$		−	2.11088i		−	0.145319i	0.997357	−	0.0726596i	$-0.0231487\pi$
$212$		−	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
$220$	9.68420	+	10.7603i	0.652909	+	0.725461i
$221$	−8.33143			−0.560433
$222$		−	1.84169i		−	0.123606i
$223$	16.3707			1.09626			0.548131	−	0.836392i	$-0.315339\pi$
$223$	16.3707			1.09626			0.548131	+	0.836392i	$0.315339\pi$
$224$	−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	$0.0855867\pi$
$229$			8.04004i			0.531301i	−0.964069	+	0.265650i	$0.914413\pi$
$230$	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	$-0.447381\pi$
$233$	5.02365			0.329110			0.164555	+	0.986368i	$0.447381\pi$
$234$		−	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	$-0.981108\pi$
$239$		−	1.83401i		−	0.118632i	0.998239	−	0.0593162i	$-0.0188920\pi$
$240$	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
$245$	−5.42552	+	14.6821i	−0.346624	+	0.938004i
$246$	−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	$0.374532\pi$
$251$			29.2562i			1.84663i	−0.384040	+	0.923316i	$0.625468\pi$
$252$	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	$-0.365822\pi$
$257$	13.1186			0.818316			0.409158	+	0.912463i	$0.365822\pi$
$258$	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	$-0.424887\pi$
$263$	7.58284			0.467578			0.233789	+	0.972287i	$0.424887\pi$
$264$	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	$-0.730520\pi$
$269$		−	24.5700i		−	1.49806i	0.662535	−	0.749031i	$-0.269480\pi$
$270$	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
$275$	1.71124	−	16.4946i	0.103192	−	0.994661i
$276$			10.3974i			0.625852i
$277$	5.23707			0.314665			0.157332	−	0.987546i	$-0.449711\pi$
$277$	5.23707			0.314665			0.157332	+	0.987546i	$0.449711\pi$
$278$	3.89207			0.233431
$279$		−	0.416788i		−	0.0249524i
$280$	0.968936	+	5.02946i	0.0579050	+	0.300568i
$281$			19.5161i			1.16423i	0.813105	+	0.582117i	$0.197776\pi$
$281$			19.5161i			1.16423i	−0.813105	+	0.582117i	$0.802224\pi$
$282$	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	$-0.677642\pi$
$311$		−	29.9189i		−	1.69655i	0.529558	−	0.848274i	$-0.322358\pi$
$312$			4.12153i			0.233336i
$313$	−12.8166			−0.724440			−0.362220	−	0.932093i	$-0.617981\pi$
$313$	−12.8166			−0.724440			−0.362220	+	0.932093i	$0.617981\pi$
$314$	−2.13853			−0.120684
$315$	−1.11916	−	5.80926i	−0.0630578	−	0.327315i
$316$			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
$330$	−1.08684	−	1.20761i	−0.0598286	−	0.0664768i
$331$	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	$-0.584564\pi$
$337$	−9.63959			−0.525102			−0.262551	+	0.964918i	$0.584564\pi$
$338$	−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	$-0.540167\pi$
$347$	−4.68884			−0.251710			−0.125855	+	0.992049i	$0.540167\pi$
$348$			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	$0.707862\pi$
$350$	1.74429	−	2.31430i	0.0932364	−	0.123705i
$351$		−	4.76056i		−	0.254100i
$352$	−8.44159	−	0.0151919i	−0.449938	−	0.000809733i
$353$	12.5022			0.665427			0.332713	−	0.943028i	$-0.392036\pi$
$353$	12.5022			0.665427			0.332713	+	0.943028i	$0.392036\pi$
$354$		−	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	$0.155061\pi$
$359$			17.7385i			0.936201i	−0.883675	+	0.468100i	$0.844939\pi$
$360$	−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	$-0.566371\pi$
$367$	−7.93121			−0.414006			−0.207003	+	0.978340i	$0.566371\pi$
$368$		−	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	$-0.277745\pi$
$373$	24.8316			1.28573			0.642865	+	0.765979i	$0.277745\pi$
$374$	−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	$-0.529376\pi$
$383$	−3.60704			−0.184311			−0.0921556	+	0.995745i	$0.529376\pi$
$384$	−6.59573			−0.336587
$385$	3.67717	+	19.2738i	0.187406	+	0.982283i
$386$	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	$-0.311252\pi$
$397$	22.2690			1.11765			0.558825	+	0.829285i	$0.311252\pi$
$398$			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	$0.406764\pi$
$419$			39.1953i			1.91482i	−0.288740	+	0.957408i	$0.593236\pi$
$420$	2.18462	+	11.3397i	0.106598	+	0.553322i
$421$	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	$-0.902811\pi$
$431$		−	12.4815i		−	0.601214i	0.953748	−	0.300607i	$-0.0971892\pi$
$432$	3.71435			0.178707
$433$	39.1498			1.88142			0.940711	−	0.339210i	$-0.110160\pi$
$433$	39.1498			1.88142			0.940711	+	0.339210i	$0.110160\pi$
$434$	−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	$0.427954\pi$
$440$	4.29520	+	4.77249i	0.204766	+	0.227520i
$441$	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
$455$	−27.6553	+	5.32785i	−1.29650	+	0.249773i
$456$	−3.45345			−0.161723
$457$	7.02926			0.328815			0.164408	−	0.986392i	$-0.447429\pi$
$457$	7.02926			0.328815			0.164408	+	0.986392i	$0.447429\pi$
$458$			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	$-0.218079\pi$
$467$	33.4675			1.54869			0.774346	+	0.632762i	$0.218079\pi$
$468$			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
$490$	−1.18857	+	3.21641i	−0.0536941	+	0.145302i
$491$			26.5710i			1.19913i	0.800326	+	0.599565i	$0.204660\pi$
$491$			26.5710i			1.19913i	−0.800326	+	0.599565i	$0.795340\pi$
$492$	10.0092			0.451252
$493$	−13.8798			−0.625114
$494$		−	4.16000i		−	0.187167i
$495$	−4.96115	−	5.51244i	−0.222987	−	0.247766i
$496$		−	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	$0.171463\pi$
$509$			23.1473i			1.02598i	−0.858393	+	0.512992i	$0.828537\pi$
$510$	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	$0.241336\pi$
$521$			31.3896i			1.37520i	−0.726089	+	0.687601i	$0.758664\pi$
$522$		−	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
$525$	7.96226	−	10.5642i	0.347502	−	0.461060i
$526$	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	$-0.757549\pi$
$541$		−	32.1045i		−	1.38028i	0.723677	−	0.690139i	$-0.242451\pi$
$542$	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	$-0.237729\pi$
$547$	34.3259			1.46767			0.733834	+	0.679329i	$0.237729\pi$
$548$			31.6370i			1.35146i
$549$	−7.08776			−0.302498
$550$	0.374883	−	3.61347i	0.0159850	−	0.154079i
$551$		−	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	$-0.440762\pi$
$557$	8.73363			0.370056			0.185028	+	0.982733i	$0.440762\pi$
$558$		−	0.0913058i		−	0.00386528i
$559$		−	50.4265i		−	2.13281i
$560$	−4.15697	−	21.5776i	−0.175664	−	0.911821i
$561$	−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	$-0.753395\pi$
$569$		−	33.3725i		−	1.39905i	0.714608	−	0.699525i	$-0.246605\pi$
$570$	1.30975	+	1.45003i	0.0548594	+	0.0607353i
$571$		−	20.4207i		−	0.854579i	−0.904115	−	0.427289i	$-0.859469\pi$
$571$		−	20.4207i		−	0.854579i	0.904115	−	0.427289i	$-0.140531\pi$
$572$	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	$-0.699565\pi$
$577$	−28.1851			−1.17336			−0.586680	+	0.809819i	$0.699565\pi$
$578$	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	$-0.921379\pi$
$587$	−46.9856			−1.93930			−0.969651	+	0.244492i	$0.921379\pi$
$588$	−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
$595$	−10.1668	+	1.95865i	−0.416797	+	0.0802966i
$596$		−	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
$605$	16.4213	+	18.3123i	0.667622	+	0.744500i
$606$	−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	$-0.274596\pi$
$613$	32.2070			1.30083			0.650414	+	0.759580i	$0.274596\pi$
$614$		−	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	$-0.879145\pi$
$619$		−	18.4418i		−	0.741239i	0.928785	−	0.370619i	$-0.120855\pi$
$620$	−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
$630$	−0.245176	−	1.27263i	−0.00976803	−	0.0507030i
$631$	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	$-0.423034\pi$
$643$	12.1435			0.478893			0.239447	+	0.970910i	$0.423034\pi$
$644$	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	$-0.588470\pi$
$647$	−13.9580			−0.548745			−0.274373	+	0.961623i	$0.588470\pi$
$648$	−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	$0.0337053\pi$
$659$			5.42636i			0.211381i	−0.994399	+	0.105690i	$0.966295\pi$
$660$	9.68420	+	10.7603i	0.376957	+	0.418845i
$661$			36.7560i			1.42964i	0.699307	+	0.714821i	$0.253492\pi$
$661$			36.7560i			1.42964i	−0.699307	+	0.714821i	$0.746508\pi$
$662$	0.569883			0.0221491
$663$	−8.33143			−0.323566
$664$		−	4.13647i		−	0.160526i
$665$	−4.46423	−	23.1725i	−0.173115	−	0.898591i
$666$		−	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	$-0.274772\pi$
$673$	33.7245			1.29998			0.649991	+	0.759942i	$0.274772\pi$
$674$	−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	$0.0892023\pi$
$691$			14.5410i			0.553167i	−0.960990	+	0.276584i	$0.910798\pi$
$692$		−	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
$700$	−15.5424	+	20.6214i	−0.587447	+	0.779416i
$701$		−	22.9952i		−	0.868517i	−0.900788	−	0.434258i	$-0.857010\pi$
$701$		−	22.9952i		−	0.868517i	0.900788	−	0.434258i	$-0.142990\pi$
$702$		−	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
$715$	−26.2423	+	23.6178i	−0.981406	+	0.883257i
$716$	−11.7775			−0.440145
$717$		−	1.83401i		−	0.0684925i
$718$			3.88597i			0.145023i
$719$		−	27.9271i		−	1.04151i	−0.853708	−	0.520753i	$-0.825651\pi$
$719$		−	27.9271i		−	1.04151i	0.853708	−	0.520753i	$-0.174349\pi$
$720$	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	$-0.756391\pi$
$727$	−38.8892			−1.44232			−0.721161	+	0.692767i	$0.756391\pi$
$728$	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
$735$	−5.42552	+	14.6821i	−0.200123	+	0.541557i
$736$		−	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	$0.0728759\pi$
$739$			12.3392i			0.453903i	−0.973906	+	0.226952i	$0.927124\pi$
$740$	−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	$-0.743595\pi$
$743$	−37.7653			−1.38547			−0.692737	+	0.721191i	$0.743595\pi$
$744$			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	$0.496229\pi$
$770$	0.805558	+	4.22231i	0.0290303	+	0.152161i
$771$	13.1186			0.472455
$772$	−3.53332			−0.127167
$773$	−2.59489			−0.0933316			−0.0466658	−	0.998911i	$-0.514860\pi$
$773$	−2.59489			−0.0933316			−0.0466658	+	0.998911i	$0.514860\pi$
$774$	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	$-0.605297\pi$
$797$	−18.3391			−0.649603			−0.324801	+	0.945782i	$0.605297\pi$
$798$	−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
$805$	−30.9432	+	5.96127i	−1.09060	+	0.210107i
$806$	−0.434666			−0.0153105
$807$		−	24.5700i		−	0.864906i
$808$	13.4865			0.474452
$809$			19.7647i			0.694890i	0.937700	+	0.347445i	$0.112951\pi$
$809$			19.7647i			0.694890i	−0.937700	+	0.347445i	$0.887049\pi$
$810$	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	$-0.976646\pi$
$821$		−	4.20073i		−	0.146607i	0.997310	−	0.0733033i	$-0.0233541\pi$
$822$		−	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
$825$	1.71124	−	16.4946i	0.0595779	−	0.574268i
$826$	−0.443157	+	0.732157i	−0.0154194	+	0.0254750i
$827$	−45.7635			−1.59135			−0.795676	−	0.605722i	$-0.792884\pi$
$827$	−45.7635			−1.59135			−0.795676	+	0.605722i	$0.792884\pi$
$828$			10.3974i			0.361336i
$829$			12.6023i			0.437697i	0.975759	+	0.218848i	$0.0702300\pi$
$829$			12.6023i			0.437697i	−0.975759	+	0.218848i	$0.929770\pi$
$830$	−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	$0.263888\pi$
$839$			42.7111i			1.47455i	−0.675592	+	0.737276i	$0.736112\pi$
$840$	0.968936	+	5.02946i	0.0334315	+	0.173533i
$841$	−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	$-0.612422\pi$
$859$		−	54.9993i		−	1.87655i	0.345886	−	0.938277i	$-0.387578\pi$
$860$	−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
$875$	29.4640	−	2.62164i	0.996065	−	0.0886275i
$876$			28.7799i			0.972382i
$877$	44.0077			1.48603			0.743017	−	0.669272i	$-0.233394\pi$
$877$	44.0077			1.48603			0.743017	+	0.669272i	$0.233394\pi$
$878$	2.06010			0.0695252
$879$			15.9012i			0.536333i
$880$	−18.4275	−	20.4751i	−0.621189	−	0.690217i
$881$			3.83174i			0.129094i	0.997915	+	0.0645472i	$0.0205603\pi$
$881$			3.83174i			0.129094i	−0.997915	+	0.0645472i	$0.979440\pi$
$882$	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
$910$	−6.05845	+	1.16717i	−0.200836	+	0.0386914i
$911$	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	$0.132603\pi$
$919$			24.5333i			0.809277i	−0.914477	+	0.404639i	$0.867397\pi$
$920$	−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	$0.0465439\pi$
$929$			8.88182i			0.291403i	−0.989329	+	0.145701i	$0.953456\pi$
$930$	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
$935$	−9.64730	+	8.68249i	−0.315501	+	0.283948i
$936$			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
$945$	−1.11916	−	5.80926i	−0.0364064	−	0.188975i
$946$	−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	$-0.454227\pi$
$953$	8.84782			0.286609			0.143304	+	0.989679i	$0.454227\pi$
$954$			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	$-0.569951\pi$
$967$	−13.5577			−0.435987			−0.217994	+	0.975950i	$0.569951\pi$
$968$	−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	$0.181924\pi$
$971$			33.7112i			1.08184i	−0.841073	+	0.540921i	$0.818076\pi$
$972$	−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
$980$	10.5907	−	28.6596i	0.338306	−	0.915496i
$981$		−	19.4843i		−	0.622085i
$982$			5.82091i			0.185753i
$983$	18.7123			0.596831			0.298416	−	0.954436i	$-0.403542\pi$
$983$	18.7123			0.596831			0.298416	+	0.954436i	$0.403542\pi$
$984$	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
$990$	−1.08684	−	1.20761i	−0.0345420	−	0.0383804i
$991$	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.b.769.25	yes	48
5.4	even	2		1155.2.k.a.769.24	yes	48
7.6	odd	2		1155.2.k.a.769.26	yes	48
11.10	odd	2	inner	1155.2.k.b.769.24	yes	48
35.34	odd	2	inner	1155.2.k.b.769.23	yes	48
55.54	odd	2		1155.2.k.a.769.25	yes	48
77.76	even	2		1155.2.k.a.769.23	✓	48
385.384	even	2	inner	1155.2.k.b.769.26	yes	48

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.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} +(-1.11916 - 5.80926i) 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} +(-4.96115 - 5.51244i) 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} +(-0.245176 - 1.27263i) 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

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