LMFDB - Embedded newform 392.2.b.f.197.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [392,2,Mod(197,392)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("392.197"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(392, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	392.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [6,2,0,0,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$3.13013575923$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.1142512.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - x^{4} + 5x^{3} - 2x^{2} - 4x + 8 $ x^6 - x^5 - x^4 + 5x^3 - 2x^2 - 4*x + 8
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			197.1
Root			$1.17445 - 0.787829i$ of defining polynomial
Character	$\chi$	$=$	392.197
Dual form			392.2.b.f.197.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.933099 - 1.06270i) q^{2} +1.57566i q^{3} +(-0.258652 + 1.98320i) q^{4} -0.549738i q^{5} +(1.67445 - 1.47024i) q^{6} +(2.34889 - 1.57566i) q^{8} +0.517304 q^{9} +(-0.584205 + 0.512960i) q^{10} -2.39075i q^{11} +(-3.12485 - 0.407547i) q^{12} +3.96641i q^{13} +0.866198 q^{15} +(-3.86620 - 1.02592i) q^{16} +4.21509 q^{17} +(-0.482696 - 0.549738i) q^{18} +6.64154i q^{19} +(1.09024 + 0.142191i) q^{20} +(-2.54065 + 2.23081i) q^{22} -2.34889 q^{23} +(2.48270 + 3.70105i) q^{24} +4.69779 q^{25} +(4.21509 - 3.70105i) q^{26} +5.54207i q^{27} +8.21720i q^{29} +(-0.808249 - 0.920507i) q^{30} -0.866198 q^{31} +(2.51730 + 5.06588i) q^{32} +3.76700 q^{33} +(-3.93310 - 4.47937i) q^{34} +(-0.133802 + 1.02592i) q^{36} +0.265356i q^{37} +(7.05795 - 6.19722i) q^{38} -6.24970 q^{39} +(-0.866198 - 1.29128i) q^{40} +6.24970 q^{41} -5.35027i q^{43} +(4.74135 + 0.618373i) q^{44} -0.284382i q^{45} +(2.19175 + 2.49616i) q^{46} -2.59859 q^{47} +(1.61650 - 6.09180i) q^{48} +(-4.38350 - 4.99233i) q^{50} +6.64154i q^{51} +(-7.86620 - 1.02592i) q^{52} -10.8188i q^{53} +(5.88954 - 5.17130i) q^{54} -1.31429 q^{55} -10.4648 q^{57} +(8.73240 - 7.66746i) q^{58} +3.77461i q^{59} +(-0.224044 + 1.71785i) q^{60} -7.13675i q^{61} +(0.808249 + 0.920507i) q^{62} +(3.03461 - 7.40210i) q^{64} +2.18048 q^{65} +(-3.51499 - 4.00319i) q^{66} +2.67513i q^{67} +(-1.09024 + 8.35939i) q^{68} -3.70105i q^{69} +8.76700 q^{71} +(1.21509 - 0.815094i) q^{72} -4.66318 q^{73} +(0.281993 - 0.247604i) q^{74} +7.40210i q^{75} +(-13.1715 - 1.71785i) q^{76} +(5.83159 + 6.64154i) q^{78} +0.616498 q^{79} +(-0.563987 + 2.12540i) q^{80} -7.18048 q^{81} +(-5.83159 - 6.64154i) q^{82} +1.09948i q^{83} -2.31720i q^{85} +(-5.68571 + 4.99233i) q^{86} -12.9475 q^{87} +(-3.76700 - 5.61562i) q^{88} +6.39558 q^{89} +(-0.302212 + 0.265356i) q^{90} +(0.607546 - 4.65834i) q^{92} -1.36483i q^{93} +(2.42475 + 2.76152i) q^{94} +3.65111 q^{95} +(-7.98210 + 3.96641i) q^{96} -12.9475 q^{97} -1.23675i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 4 q^{6} + 2 q^{8} - 8 q^{10} - 2 q^{12} - 10 q^{15} - 8 q^{16} - 2 q^{17} - 6 q^{18} - 4 q^{20} + 6 q^{22} - 2 q^{23} + 18 q^{24} + 4 q^{25} - 2 q^{26} - 14 q^{30} + 10 q^{31} + 12 q^{32}+ \cdots - 20 q^{97}+O(q^{100}) $ 6 * q + 2 * q^2 + 4 * q^6 + 2 * q^8 - 8 * q^10 - 2 * q^12 - 10 * q^15 - 8 * q^16 - 2 * q^17 - 6 * q^18 - 4 * q^20 + 6 * q^22 - 2 * q^23 + 18 * q^24 + 4 * q^25 - 2 * q^26 - 14 * q^30 + 10 * q^31 + 12 * q^32 - 14 * q^33 - 16 * q^34 - 16 * q^36 + 18 * q^38 - 4 * q^39 + 10 * q^40 + 4 * q^41 + 30 * q^44 + 4 * q^46 + 30 * q^47 + 28 * q^48 - 8 * q^50 - 32 * q^52 + 2 * q^54 - 2 * q^55 - 2 * q^57 + 22 * q^58 - 6 * q^60 + 14 * q^62 + 12 * q^64 - 8 * q^65 - 38 * q^66 + 4 * q^68 + 16 * q^71 - 20 * q^72 - 10 * q^73 - 18 * q^74 - 26 * q^76 + 26 * q^78 + 22 * q^79 + 36 * q^80 - 22 * q^81 - 26 * q^82 - 40 * q^86 - 20 * q^87 + 14 * q^88 - 10 * q^89 - 26 * q^90 - 10 * q^92 + 42 * q^94 + 34 * q^95 + 16 * q^96 - 20 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.933099	−	1.06270i	−0.659801	−	0.751441i
$2$	−0.933099	−	1.06270i	−0.659801	−	0.751441i
$3$			1.57566i			0.909706i	0.890566	+	0.454853i	$0.150308\pi$
$3$			1.57566i			0.909706i	−0.890566	+	0.454853i	$0.849692\pi$
$4$	−0.258652	+	1.98320i	−0.129326	+	0.991602i
$5$		−	0.549738i		−	0.245850i	−0.992416	−	0.122925i	$-0.960773\pi$
$5$		−	0.549738i		−	0.245850i	0.992416	−	0.122925i	$-0.0392275\pi$
$6$	1.67445	−	1.47024i	0.683590	−	0.600225i
$7$		0			0
$7$		0			0
$8$	2.34889	−	1.57566i	0.830460	−	0.557079i
$9$	0.517304			0.172435
$10$	−0.584205	+	0.512960i	−0.184742	+	0.162212i
$11$		−	2.39075i		−	0.720839i	−0.932790	−	0.360419i	$-0.882634\pi$
$11$		−	2.39075i		−	0.720839i	0.932790	−	0.360419i	$-0.117366\pi$
$12$	−3.12485	−	0.407547i	−0.902067	−	0.117649i
$13$			3.96641i			1.10008i	0.835137	+	0.550042i	$0.185388\pi$
$13$			3.96641i			1.10008i	−0.835137	+	0.550042i	$0.814612\pi$
$14$		0			0
$15$	0.866198			0.223651
$16$	−3.86620	−	1.02592i	−0.966550	−	0.256480i
$17$	4.21509			1.02231			0.511155	−	0.859489i	$-0.329218\pi$
$17$	4.21509			1.02231			0.511155	+	0.859489i	$0.329218\pi$
$18$	−0.482696	−	0.549738i	−0.113773	−	0.129574i
$19$			6.64154i			1.52367i	0.647769	+	0.761837i	$0.275702\pi$
$19$			6.64154i			1.52367i	−0.647769	+	0.761837i	$0.724298\pi$
$20$	1.09024	+	0.142191i	0.243786	+	0.0317948i
$21$		0			0
$22$	−2.54065	+	2.23081i	−0.541667	+	0.475610i
$23$	−2.34889			−0.489778			−0.244889	−	0.969551i	$-0.578752\pi$
$23$	−2.34889			−0.489778			−0.244889	+	0.969551i	$0.578752\pi$
$24$	2.48270	+	3.70105i	0.506778	+	0.755474i
$25$	4.69779			0.939558
$26$	4.21509	−	3.70105i	0.826648	−	0.725836i
$27$			5.54207i			1.06657i
$28$		0			0
$29$			8.21720i			1.52590i	0.646460	+	0.762948i	$0.276249\pi$
$29$			8.21720i			1.52590i	−0.646460	+	0.762948i	$0.723751\pi$
$30$	−0.808249	−	0.920507i	−0.147565	−	0.168061i
$31$	−0.866198			−0.155574			−0.0777869	−	0.996970i	$-0.524785\pi$
$31$	−0.866198			−0.155574			−0.0777869	+	0.996970i	$0.524785\pi$
$32$	2.51730	+	5.06588i	0.445001	+	0.895530i
$33$	3.76700			0.655751
$34$	−3.93310	−	4.47937i	−0.674521	−	0.768205i
$35$		0			0
$36$	−0.133802	+	1.02592i	−0.0223003	+	0.170987i
$37$			0.265356i			0.0436243i	0.999762	+	0.0218121i	$0.00694357\pi$
$37$			0.265356i			0.0436243i	−0.999762	+	0.0218121i	$0.993056\pi$
$38$	7.05795	−	6.19722i	1.14495	−	1.00532i
$39$	−6.24970			−1.00075
$40$	−0.866198	−	1.29128i	−0.136958	−	0.204169i
$41$	6.24970			0.976039			0.488020	−	0.872833i	$-0.337719\pi$
$41$	6.24970			0.976039			0.488020	+	0.872833i	$0.337719\pi$
$42$		0			0
$43$		−	5.35027i		−	0.815908i	−0.913003	−	0.407954i	$-0.866242\pi$
$43$		−	5.35027i		−	0.815908i	0.913003	−	0.407954i	$-0.133758\pi$
$44$	4.74135	+	0.618373i	0.714785	+	0.0932232i
$45$		−	0.284382i		−	0.0423931i
$46$	2.19175	+	2.49616i	0.323156	+	0.368039i
$47$	−2.59859			−0.379044			−0.189522	−	0.981876i	$-0.560694\pi$
$47$	−2.59859			−0.379044			−0.189522	+	0.981876i	$0.560694\pi$
$48$	1.61650	−	6.09180i	0.233321	−	0.879276i
$49$		0			0
$50$	−4.38350	−	4.99233i	−0.619921	−	0.706022i
$51$			6.64154i			0.930002i
$52$	−7.86620	−	1.02592i	−1.09085	−	0.142269i
$53$		−	10.8188i		−	1.48607i	−0.669251	−	0.743037i	$-0.733385\pi$
$53$		−	10.8188i		−	1.48607i	0.669251	−	0.743037i	$-0.266615\pi$
$54$	5.88954	−	5.17130i	0.801465	−	0.703724i
$55$	−1.31429			−0.177218
$56$		0			0
$57$	−10.4648			−1.38610
$58$	8.73240	−	7.66746i	1.14662	−	1.00679i
$59$			3.77461i			0.491412i	0.969344	+	0.245706i	$0.0790198\pi$
$59$			3.77461i			0.491412i	−0.969344	+	0.245706i	$0.920980\pi$
$60$	−0.224044	+	1.71785i	−0.0289239	+	0.221773i
$61$		−	7.13675i		−	0.913767i	−0.889527	−	0.456884i	$-0.848966\pi$
$61$		−	7.13675i		−	0.913767i	0.889527	−	0.456884i	$-0.151034\pi$
$62$	0.808249	+	0.920507i	0.102648	+	0.116904i
$63$		0			0
$64$	3.03461	−	7.40210i	0.379326	−	0.925263i
$65$	2.18048			0.270456
$66$	−3.51499	−	4.00319i	−0.432665	−	0.492758i
$67$			2.67513i			0.326819i	0.986558	+	0.163410i	$0.0522493\pi$
$67$			2.67513i			0.326819i	−0.986558	+	0.163410i	$0.947751\pi$
$68$	−1.09024	+	8.35939i	−0.132211	+	1.01372i
$69$		−	3.70105i		−	0.445554i
$70$		0			0
$71$	8.76700			1.04045			0.520226	−	0.854029i	$-0.325848\pi$
$71$	8.76700			1.04045			0.520226	+	0.854029i	$0.325848\pi$
$72$	1.21509	−	0.815094i	0.143200	−	0.0960597i
$73$	−4.66318			−0.545784			−0.272892	−	0.962045i	$-0.587980\pi$
$73$	−4.66318			−0.545784			−0.272892	+	0.962045i	$0.587980\pi$
$74$	0.281993	−	0.247604i	0.0327811	−	0.0287833i
$75$			7.40210i			0.854721i
$76$	−13.1715	−	1.71785i	−1.51088	−	0.197051i
$77$		0			0
$78$	5.83159	+	6.64154i	0.660298	+	0.752006i
$79$	0.616498			0.0693614			0.0346807	−	0.999398i	$-0.488959\pi$
$79$	0.616498			0.0693614			0.0346807	+	0.999398i	$0.488959\pi$
$80$	−0.563987	+	2.12540i	−0.0630556	+	0.237626i
$81$	−7.18048			−0.797832
$82$	−5.83159	−	6.64154i	−0.643991	−	0.733436i
$83$			1.09948i			0.120683i	0.998178	+	0.0603416i	$0.0192190\pi$
$83$			1.09948i			0.120683i	−0.998178	+	0.0603416i	$0.980781\pi$
$84$		0			0
$85$		−	2.31720i		−	0.251335i
$86$	−5.68571	+	4.99233i	−0.613106	+	0.538337i
$87$	−12.9475			−1.38812
$88$	−3.76700	−	5.61562i	−0.401564	−	0.598627i
$89$	6.39558			0.677930			0.338965	−	0.940799i	$-0.389923\pi$
$89$	6.39558			0.677930			0.338965	+	0.940799i	$0.389923\pi$
$90$	−0.302212	+	0.265356i	−0.0318559	+	0.0279710i
$91$		0			0
$92$	0.607546	−	4.65834i	0.0633411	−	0.485665i
$93$		−	1.36483i		−	0.141526i
$94$	2.42475	+	2.76152i	0.250094	+	0.284829i
$95$	3.65111			0.374596
$96$	−7.98210	+	3.96641i	−0.814669	+	0.404820i
$97$	−12.9475			−1.31462			−0.657309	−	0.753621i	$-0.728305\pi$
$97$	−12.9475			−1.31462			−0.657309	+	0.753621i	$0.728305\pi$
$98$		0			0
$99$		−	1.23675i		−	0.124298i
$100$	−1.21509	+	9.31667i	−0.121509	+	0.931667i
$101$		−	15.8847i		−	1.58058i	−0.612731	−	0.790291i	$-0.709929\pi$
$101$		−	15.8847i		−	1.58058i	0.612731	−	0.790291i	$-0.290071\pi$
$102$	7.05795	−	6.19722i	0.698841	−	0.613616i
$103$	−18.7791			−1.85036			−0.925179	−	0.379531i	$-0.876085\pi$
$103$	−18.7791			−1.85036			−0.925179	+	0.379531i	$0.876085\pi$
$104$	6.24970	+	9.31667i	0.612834	+	0.913575i
$105$		0			0
$106$	−11.4971	+	10.0950i	−1.11670	+	0.980512i
$107$		−	0.338912i		−	0.0327639i	−0.999866	−	0.0163819i	$-0.994785\pi$
$107$		−	0.338912i		−	0.0327639i	0.999866	−	0.0163819i	$-0.00521476\pi$
$108$	−10.9910	−	1.43347i	−1.05761	−	0.137935i
$109$			7.80473i			0.747558i	0.927518	+	0.373779i	$0.121938\pi$
$109$			7.80473i			0.747558i	−0.927518	+	0.373779i	$0.878062\pi$
$110$	1.22636	+	1.39669i	0.116929	+	0.133169i
$111$	−0.418110			−0.0396853
$112$		0			0
$113$	2.51730			0.236808			0.118404	−	0.992966i	$-0.462222\pi$
$113$	2.51730			0.236808			0.118404	+	0.992966i	$0.462222\pi$
$114$	9.76469	+	11.1209i	0.914547	+	1.04157i
$115$			1.29128i			0.120412i
$116$	−16.2964	−	2.12540i	−1.51308	−	0.197338i
$117$			2.05184i			0.189693i
$118$	4.01127	−	3.52208i	0.369267	−	0.324234i
$119$		0			0
$120$	2.03461	−	1.36483i	0.185733	−	0.124592i
$121$	5.28431			0.480392
$122$	−7.58420	+	6.65929i	−0.686642	+	0.602904i
$123$			9.84739i			0.887909i
$124$	0.224044	−	1.71785i	0.0201197	−	0.154267i
$125$		−	5.33124i		−	0.476841i
$126$		0			0
$127$	−5.30221			−0.470495			−0.235248	−	0.971935i	$-0.575590\pi$
$127$	−5.30221			−0.470495			−0.235248	+	0.971935i	$0.575590\pi$
$128$	−10.6978	+	3.68203i	−0.945560	+	0.325448i
$129$	8.43018			0.742236
$130$	−2.03461	−	2.31720i	−0.178447	−	0.203231i
$131$		−	10.0392i		−	0.877128i	−0.898700	−	0.438564i	$-0.855487\pi$
$131$		−	10.0392i		−	0.877128i	0.898700	−	0.438564i	$-0.144513\pi$
$132$	−0.974343	+	7.47074i	−0.0848057	+	0.650244i
$133$		0			0
$134$	2.84286	−	2.49616i	0.245585	−	0.215636i
$135$	3.04668			0.262217
$136$	9.90081	−	6.64154i	0.848987	−	0.569507i
$137$	3.24970			0.277641			0.138820	−	0.990318i	$-0.455669\pi$
$137$	3.24970			0.277641			0.138820	+	0.990318i	$0.455669\pi$
$138$	−3.93310	+	3.45345i	−0.334808	+	0.293977i
$139$		−	15.3349i		−	1.30069i	−0.759639	−	0.650346i	$-0.774624\pi$
$139$		−	15.3349i		−	1.30069i	0.759639	−	0.650346i	$-0.225376\pi$
$140$		0			0
$141$		−	4.09449i		−	0.344819i
$142$	−8.18048	−	9.31667i	−0.686491	−	0.781838i
$143$	9.48270			0.792983
$144$	−2.00000	−	0.530712i	−0.166667	−	0.0442260i
$145$	4.51730			0.375142
$146$	4.35121	+	4.95555i	0.360109	+	0.410124i
$147$		0			0
$148$	−0.526255	−	0.0686349i	−0.0432579	−	0.00564175i
$149$		−	7.38308i		−	0.604845i	−0.953174	−	0.302423i	$-0.902205\pi$
$149$		−	7.38308i		−	0.604845i	0.953174	−	0.302423i	$-0.0977954\pi$
$150$	7.86620	−	6.90690i	0.642272	−	0.563946i
$151$	8.33099			0.677966			0.338983	−	0.940792i	$-0.389917\pi$
$151$	8.33099			0.677966			0.338983	+	0.940792i	$0.389917\pi$
$152$	10.4648	+	15.6003i	0.848807	+	1.26535i
$153$	2.18048			0.176282
$154$		0			0
$155$			0.476182i			0.0382478i
$156$	1.61650	−	12.3944i	0.129423	−	0.992349i
$157$			7.13675i			0.569575i	0.958591	+	0.284787i	$0.0919230\pi$
$157$			7.13675i			0.569575i	−0.958591	+	0.284787i	$0.908077\pi$
$158$	−0.575253	−	0.655151i	−0.0457647	−	0.0521210i
$159$	17.0467			1.35189
$160$	2.78491	−	1.38386i	0.220166	−	0.109404i
$161$		0			0
$162$	6.70010	+	7.63068i	0.526410	+	0.599523i
$163$		−	7.30952i		−	0.572526i	−0.958151	−	0.286263i	$-0.907587\pi$
$163$		−	7.30952i		−	0.572526i	0.958151	−	0.286263i	$-0.0924131\pi$
$164$	−1.61650	+	12.3944i	−0.126227	+	0.967843i
$165$		−	2.07086i		−	0.161217i
$166$	1.16841	−	1.02592i	0.0906862	−	0.0796268i
$167$	−1.88873			−0.146154			−0.0730772	−	0.997326i	$-0.523282\pi$
$167$	−1.88873			−0.146154			−0.0730772	+	0.997326i	$0.523282\pi$
$168$		0			0
$169$	−2.73240			−0.210184
$170$	−2.46248	+	2.16217i	−0.188863	+	0.165831i
$171$			3.43570i			0.262734i
$172$	10.6107	+	1.38386i	0.809056	+	0.105518i
$173$		−	16.5526i		−	1.25847i	−0.777213	−	0.629237i	$-0.783367\pi$
$173$		−	16.5526i		−	1.25847i	0.777213	−	0.629237i	$-0.216633\pi$
$174$	12.0813	+	13.7593i	0.915880	+	1.04309i
$175$		0			0
$176$	−2.45272	+	9.24312i	−0.184881	+	0.696726i
$177$	−5.94749			−0.447041
$178$	−5.96771	−	6.79656i	−0.447299	−	0.509424i
$179$			5.54207i			0.414233i	0.978316	+	0.207117i	$0.0664080\pi$
$179$			5.54207i			0.414233i	−0.978316	+	0.207117i	$0.933592\pi$
$180$	0.563987	+	0.0735559i	0.0420371	+	0.00548253i
$181$		−	9.98466i		−	0.742154i	−0.928602	−	0.371077i	$-0.878989\pi$
$181$		−	9.98466i		−	0.742154i	0.928602	−	0.371077i	$-0.121011\pi$
$182$		0			0
$183$	11.2451			0.831259
$184$	−5.51730	+	3.70105i	−0.406741	+	0.272845i
$185$	0.145876			0.0107250
$186$	−1.45040	+	1.27352i	−0.106349	+	0.0933793i
$187$		−	10.0772i		−	0.736921i
$188$	0.672132	−	5.15354i	0.0490202	−	0.375861i
$189$		0			0
$190$	−3.40684	−	3.88002i	−0.247158	−	0.281486i
$191$	0.168410			0.0121857			0.00609285	−	0.999981i	$-0.498061\pi$
$191$	0.168410			0.0121857			0.00609285	+	0.999981i	$0.498061\pi$
$192$	11.6632	+	4.78150i	0.841718	+	0.345075i
$193$	7.51730			0.541107			0.270554	−	0.962705i	$-0.412793\pi$
$193$	7.51730			0.541107			0.270554	+	0.962705i	$0.412793\pi$
$194$	12.0813	+	13.7593i	0.867386	+	0.987858i
$195$			3.43570i			0.246035i
$196$		0			0
$197$			1.34581i			0.0958847i	0.998850	+	0.0479424i	$0.0152664\pi$
$197$			1.34581i			0.0958847i	−0.998850	+	0.0479424i	$0.984734\pi$
$198$	−1.31429	+	1.15401i	−0.0934022	+	0.0820116i
$199$	12.7612			0.904616			0.452308	−	0.891862i	$-0.350601\pi$
$199$	12.7612			0.904616			0.452308	+	0.891862i	$0.350601\pi$
$200$	11.0346	−	7.40210i	0.780265	−	0.523408i
$201$	−4.21509			−0.297310
$202$	−16.8806	+	14.8220i	−1.18771	+	1.04287i
$203$		0			0
$204$	−13.1715	−	1.71785i	−0.922192	−	0.120273i
$205$		−	3.43570i		−	0.239959i
$206$	17.5227	+	19.9565i	1.22087	+	1.39043i
$207$	−1.21509			−0.0844548
$208$	4.06922	−	15.3349i	0.282149	−	1.06329i
$209$	15.8783			1.09832
$210$		0			0
$211$		−	8.46353i		−	0.582653i	−0.956624	−	0.291327i	$-0.905903\pi$
$211$		−	8.46353i		−	0.582653i	0.956624	−	0.291327i	$-0.0940967\pi$
$212$	21.4558	+	2.79830i	1.47359	+	0.192188i
$213$			13.8138i			0.946506i
$214$	−0.360161	+	0.316239i	−0.0246201	+	0.0216176i
$215$	−2.94124			−0.200591
$216$	8.73240	+	13.0177i	0.594164	+	0.885744i
$217$		0			0
$218$	8.29407	−	7.28259i	0.561745	−	0.493239i
$219$		−	7.34757i		−	0.496503i
$220$	0.339943	−	2.60650i	0.0229189	−	0.175730i
$221$			16.7188i			1.12463i
$222$	0.390138	+	0.444325i	0.0261844	+	0.0298211i
$223$	5.80161			0.388505			0.194252	−	0.980952i	$-0.437772\pi$
$223$	5.80161			0.388505			0.194252	+	0.980952i	$0.437772\pi$
$224$		0			0
$225$	2.43018			0.162012
$226$	−2.34889	−	2.67513i	−0.156246	−	0.177947i
$227$		−	11.4230i		−	0.758174i	−0.925361	−	0.379087i	$-0.876238\pi$
$227$		−	11.4230i		−	0.758174i	0.925361	−	0.379087i	$-0.123762\pi$
$228$	2.70674	−	20.7538i	0.179258	−	1.37446i
$229$			18.5053i			1.22286i	0.791298	+	0.611431i	$0.209406\pi$
$229$			18.5053i			1.22286i	−0.791298	+	0.611431i	$0.790594\pi$
$230$	1.37224	−	1.20489i	0.0904825	−	0.0794480i
$231$		0			0
$232$	12.9475	+	19.3013i	0.850044	+	1.26719i
$233$	−11.0513			−0.723996			−0.361998	−	0.932179i	$-0.617905\pi$
$233$	−11.0513			−0.723996			−0.361998	+	0.932179i	$0.617905\pi$
$234$	2.18048	−	1.91457i	0.142543	−	0.125159i
$235$			1.42855i			0.0931880i
$236$	−7.48582	−	0.976310i	−0.487285	−	0.0635524i
$237$			0.971389i			0.0630985i
$238$		0			0
$239$	−22.6107			−1.46256			−0.731281	−	0.682076i	$-0.761077\pi$
$239$	−22.6107			−1.46256			−0.731281	+	0.682076i	$0.761077\pi$
$240$	−3.34889	−	0.888650i	−0.216170	−	0.0573621i
$241$	−13.9296			−0.897284			−0.448642	−	0.893712i	$-0.648092\pi$
$241$	−13.9296			−0.897284			−0.448642	+	0.893712i	$0.648092\pi$
$242$	−4.93078	−	5.61562i	−0.316963	−	0.360986i
$243$			5.31221i			0.340779i
$244$	14.1536	+	1.84593i	0.906093	+	0.118174i
$245$		0			0
$246$	10.4648	−	9.18859i	0.667211	−	0.585843i
$247$	−26.3431			−1.67617
$248$	−2.03461	+	1.36483i	−0.129198	+	0.0866669i
$249$	−1.73240			−0.109786
$250$	−5.66550	+	4.97458i	−0.358317	+	0.314620i
$251$			0.706033i			0.0445644i	0.999752	+	0.0222822i	$0.00709323\pi$
$251$			0.706033i			0.0445644i	−0.999752	+	0.0222822i	$0.992907\pi$
$252$		0			0
$253$			5.61562i			0.353051i
$254$	4.94749	+	5.63465i	0.310433	+	0.353549i
$255$	3.65111			0.228641
$256$	13.8950	+	7.93282i	0.868436	+	0.495801i
$257$	−20.7837			−1.29645			−0.648226	−	0.761448i	$-0.724489\pi$
$257$	−20.7837			−1.29645			−0.648226	+	0.761448i	$0.724489\pi$
$258$	−7.86620	−	8.95874i	−0.489728	−	0.557747i
$259$		0			0
$260$	−0.563987	+	4.32435i	−0.0349770	+	0.268185i
$261$			4.25079i			0.263117i
$262$	−10.6686	+	9.36756i	−0.659109	+	0.578730i
$263$	−22.7791			−1.40462			−0.702309	−	0.711872i	$-0.747848\pi$
$263$	−22.7791			−1.40462			−0.702309	+	0.711872i	$0.747848\pi$
$264$	8.84830	−	5.93551i	0.544575	−	0.365305i
$265$	−5.94749			−0.365351
$266$		0			0
$267$			10.0772i			0.616717i
$268$	−5.30533	−	0.691928i	−0.324075	−	0.0422663i
$269$		−	2.99502i		−	0.182610i	−0.995823	−	0.0913048i	$-0.970896\pi$
$269$		−	2.99502i		−	0.182610i	0.995823	−	0.0913048i	$-0.0291037\pi$
$270$	−2.84286	−	3.23770i	−0.173011	−	0.197040i
$271$	25.1851			1.52989			0.764943	−	0.644098i	$-0.222767\pi$
$271$	25.1851			1.52989			0.764943	+	0.644098i	$0.222767\pi$
$272$	−16.2964	−	4.32435i	−0.988113	−	0.262202i
$273$		0			0
$274$	−3.03229	−	3.45345i	−0.183188	−	0.208630i
$275$		−	11.2312i		−	0.677269i
$276$	7.33994	+	0.957285i	0.441813	+	0.0576218i
$277$			9.44476i			0.567481i	0.958901	+	0.283740i	$0.0915754\pi$
$277$			9.44476i			0.567481i	−0.958901	+	0.283740i	$0.908425\pi$
$278$	−16.2964	+	14.3090i	−0.977392	+	0.858197i
$279$	−0.448088			−0.0268263
$280$		0			0
$281$	26.8425			1.60129			0.800644	−	0.599141i	$-0.204491\pi$
$281$	26.8425			1.60129			0.800644	+	0.599141i	$0.204491\pi$
$282$	−4.35121	+	3.82057i	−0.259111	+	0.227512i
$283$		−	12.9822i		−	0.771713i	−0.922559	−	0.385856i	$-0.873906\pi$
$283$		−	12.9822i		−	0.771713i	0.922559	−	0.385856i	$-0.126094\pi$
$284$	−2.26760	+	17.3868i	−0.134558	+	1.03171i
$285$			5.75289i			0.340772i
$286$	−8.84830	−	10.0772i	−0.523211	−	0.595880i
$287$		0			0
$288$	1.30221	+	2.62060i	0.0767336	+	0.154420i
$289$	0.767005			0.0451179
$290$	−4.21509	−	4.80053i	−0.247519	−	0.281897i
$291$		−	20.4008i		−	1.19592i
$292$	1.20614	−	9.24804i	0.0705841	−	0.541201i
$293$			9.56300i			0.558677i	0.960193	+	0.279338i	$0.0901151\pi$
$293$			9.56300i			0.558677i	−0.960193	+	0.279338i	$0.909885\pi$
$294$		0			0
$295$	2.07504			0.120814
$296$	0.418110	+	0.623294i	0.0243022	+	0.0362282i
$297$	13.2497			0.768826
$298$	−7.84598	+	6.88914i	−0.454505	+	0.399077i
$299$		−	9.31667i		−	0.538797i
$300$	−14.6799	−	1.91457i	−0.847544	−	0.110538i
$301$		0			0
$302$	−7.77364	−	8.85332i	−0.447323	−	0.509452i
$303$	25.0288			1.43787
$304$	6.81369	−	25.6775i	0.390792	−	1.47271i
$305$	−3.92334			−0.224650
$306$	−2.03461	−	2.31720i	−0.116311	−	0.132465i
$307$		−	12.2217i		−	0.697527i	−0.937211	−	0.348763i	$-0.886602\pi$
$307$		−	12.2217i		−	0.697527i	0.937211	−	0.348763i	$-0.113398\pi$
$308$		0			0
$309$		−	29.5894i		−	1.68328i
$310$	0.506037	−	0.444325i	0.0287410	−	0.0252360i
$311$	−31.8829			−1.80791			−0.903957	−	0.427624i	$-0.859351\pi$
$311$	−31.8829			−1.80791			−0.903957	+	0.427624i	$0.859351\pi$
$312$	−14.6799	+	9.84739i	−0.831085	+	0.557498i
$313$	−21.5236			−1.21658			−0.608291	−	0.793714i	$-0.708145\pi$
$313$	−21.5236			−1.21658			−0.608291	+	0.793714i	$0.708145\pi$
$314$	7.58420	−	6.65929i	0.428001	−	0.375806i
$315$		0			0
$316$	−0.159458	+	1.22264i	−0.00897023	+	0.0687789i
$317$			23.1495i			1.30021i	0.759846	+	0.650103i	$0.225274\pi$
$317$			23.1495i			1.30021i	−0.759846	+	0.650103i	$0.774726\pi$
$318$	−15.9062	−	18.1155i	−0.891978	−	1.01586i
$319$	19.6453			1.09992
$320$	−4.06922	−	1.66824i	−0.227476	−	0.0932574i
$321$	0.534009			0.0298055
$322$		0			0
$323$			27.9947i			1.55767i
$324$	1.85725	−	14.2404i	0.103180	−	0.791132i
$325$			18.6333i			1.03359i
$326$	−7.76781	+	6.82051i	−0.430219	+	0.377753i
$327$	−12.2976			−0.680058
$328$	14.6799	−	9.84739i	0.810561	−	0.543731i
$329$		0			0
$330$	−2.20070	+	1.93232i	−0.121145	+	0.106371i
$331$			29.5158i			1.62234i	0.584812	+	0.811169i	$0.301168\pi$
$331$			29.5158i			1.62234i	−0.584812	+	0.811169i	$0.698832\pi$
$332$	−2.18048	−	0.284382i	−0.119670	−	0.0156075i
$333$			0.137270i			0.00752234i
$334$	1.76237	+	2.00715i	0.0964328	+	0.109826i
$335$	1.47062			0.0803486
$336$		0			0
$337$	−3.28431			−0.178908			−0.0894538	−	0.995991i	$-0.528512\pi$
$337$	−3.28431			−0.178908			−0.0894538	+	0.995991i	$0.528512\pi$
$338$	2.54960	+	2.90371i	0.138680	+	0.157941i
$339$			3.96641i			0.215426i
$340$	4.59547	+	0.599347i	0.249224	+	0.0325042i
$341$			2.07086i			0.112144i
$342$	3.65111	−	3.20585i	0.197429	−	0.173352i
$343$		0			0
$344$	−8.43018	−	12.5672i	−0.454525	−	0.677578i
$345$	−2.03461			−0.109540
$346$	−17.5905	+	15.4453i	−0.945669	+	0.830342i
$347$		−	31.6767i		−	1.70050i	−0.526382	−	0.850248i	$-0.676452\pi$
$347$		−	31.6767i		−	1.70050i	0.526382	−	0.850248i	$-0.323548\pi$
$348$	3.34889	−	25.6775i	0.179520	−	1.37646i
$349$			28.4807i			1.52454i	0.647260	+	0.762269i	$0.275915\pi$
$349$			28.4807i			1.52454i	−0.647260	+	0.762269i	$0.724085\pi$
$350$		0			0
$351$	−21.9821			−1.17332
$352$	12.1113	−	6.01825i	0.645533	−	0.320774i
$353$	−20.2392			−1.07723			−0.538613	−	0.842553i	$-0.681052\pi$
$353$	−20.2392			−1.07723			−0.538613	+	0.842553i	$0.681052\pi$
$354$	5.54960	+	6.32038i	0.294958	+	0.335925i
$355$		−	4.81955i		−	0.255795i
$356$	−1.65423	+	12.6837i	−0.0876740	+	0.672237i
$357$		0			0
$358$	5.88954	−	5.17130i	0.311272	−	0.273312i
$359$	25.1221			1.32590			0.662948	−	0.748665i	$-0.269305\pi$
$359$	25.1221			1.32590			0.662948	+	0.748665i	$0.269305\pi$
$360$	−0.448088	−	0.667982i	−0.0236163	−	0.0352058i
$361$	−25.1101			−1.32158
$362$	−10.6107	+	9.31667i	−0.557684	+	0.489674i
$363$			8.32626i			0.437015i
$364$		0			0
$365$			2.56353i			0.134181i
$366$	−10.4928	−	11.9501i	−0.548466	−	0.624642i
$367$	30.3823			1.58594			0.792972	−	0.609258i	$-0.208533\pi$
$367$	30.3823			1.58594			0.792972	+	0.609258i	$0.208533\pi$
$368$	9.08129	+	2.40978i	0.473395	+	0.125618i
$369$	3.23300			0.168303
$370$	−0.136117	−	0.155022i	−0.00707639	−	0.00805923i
$371$		0			0
$372$	2.70674	+	0.353016i	0.140338	+	0.0183031i
$373$		−	5.61562i		−	0.290766i	−0.989375	−	0.145383i	$-0.953559\pi$
$373$		−	5.61562i		−	0.290766i	0.989375	−	0.145383i	$-0.0464414\pi$
$374$	−10.7091	+	9.40306i	−0.553752	+	0.486221i
$375$	8.40021			0.433785
$376$	−6.10382	+	4.09449i	−0.314781	+	0.211157i
$377$	−32.5928			−1.67861
$378$		0			0
$379$		−	8.07009i		−	0.414533i	−0.978285	−	0.207266i	$-0.933543\pi$
$379$		−	8.07009i		−	0.414533i	0.978285	−	0.207266i	$-0.0664566\pi$
$380$	−0.944366	+	7.24089i	−0.0484449	+	0.371450i
$381$		−	8.35447i		−	0.428012i
$382$	−0.157143	−	0.178969i	−0.00804014	−	0.00915684i
$383$	25.6332			1.30980			0.654898	−	0.755718i	$-0.272712\pi$
$383$	25.6332			1.30980			0.654898	+	0.755718i	$0.272712\pi$
$384$	−5.80161	−	16.8560i	−0.296062	−	0.860182i
$385$		0			0
$386$	−7.01439	−	7.98862i	−0.357023	−	0.406610i
$387$		−	2.76771i		−	0.140691i
$388$	3.34889	−	25.6775i	0.170014	−	1.30358i
$389$		−	26.5471i		−	1.34599i	−0.739645	−	0.672997i	$-0.765007\pi$
$389$		−	26.5471i		−	1.34599i	0.739645	−	0.672997i	$-0.234993\pi$
$390$	3.65111	−	3.20585i	0.184881	−	0.162334i
$391$	−9.90081			−0.500705
$392$		0			0
$393$	15.8183			0.797929
$394$	1.43018	−	1.25577i	0.0720517	−	0.0632648i
$395$		−	0.338912i		−	0.0170525i
$396$	2.45272	+	0.319887i	0.123254	+	0.0160749i
$397$			34.0964i			1.71125i	0.517599	+	0.855624i	$0.326826\pi$
$397$			34.0964i			1.71125i	−0.517599	+	0.855624i	$0.673174\pi$
$398$	−11.9074	−	13.5613i	−0.596866	−	0.679765i
$399$		0			0
$400$	−18.1626	−	4.81955i	−0.908129	−	0.240978i
$401$	18.3535			0.916531			0.458266	−	0.888815i	$-0.348471\pi$
$401$	18.3535			0.916531			0.458266	+	0.888815i	$0.348471\pi$
$402$	3.93310	+	4.47937i	0.196165	+	0.223411i
$403$		−	3.43570i		−	0.171144i
$404$	31.5025	+	4.10860i	1.56731	+	0.204410i
$405$			3.94738i			0.196147i
$406$		0			0
$407$	0.634401			0.0314461
$408$	10.4648	+	15.6003i	0.518084	+	0.772329i
$409$	−11.7491			−0.580956			−0.290478	−	0.956882i	$-0.593814\pi$
$409$	−11.7491			−0.580956			−0.290478	+	0.956882i	$0.593814\pi$
$410$	−3.65111	+	3.20585i	−0.180315	+	0.158325i
$411$			5.12041i			0.252571i
$412$	4.85725	−	37.2427i	0.239299	−	1.83482i
$413$		0			0
$414$	1.13380	+	1.29128i	0.0557233	+	0.0634627i
$415$	0.604423			0.0296700
$416$	−20.0934	+	9.98466i	−0.985158	+	0.489538i
$417$	24.1626			1.18325
$418$	−14.8160	−	16.8738i	−0.724674	−	0.825325i
$419$			11.0841i			0.541495i	0.962650	+	0.270748i	$0.0872709\pi$
$419$			11.0841i			0.541495i	−0.962650	+	0.270748i	$0.912729\pi$
$420$		0			0
$421$			0.137270i			0.00669012i	0.999994	+	0.00334506i	$0.00106477\pi$
$421$			0.137270i			0.00669012i	−0.999994	+	0.00334506i	$0.998935\pi$
$422$	−8.99417	+	7.89731i	−0.437829	+	0.384435i
$423$	−1.34426			−0.0653603
$424$	−17.0467	−	25.4122i	−0.827860	−	1.23412i
$425$	19.8016			0.960519
$426$	14.6799	−	12.8896i	0.711243	−	0.624505i
$427$		0			0
$428$	0.672132	+	0.0876603i	0.0324887	+	0.00423722i
$429$			14.9415i			0.721381i
$430$	2.74447	+	3.12565i	0.132350	+	0.150732i
$431$	12.4602			0.600185			0.300092	−	0.953910i	$-0.402982\pi$
$431$	12.4602			0.600185			0.300092	+	0.953910i	$0.402982\pi$
$432$	5.68571	−	21.4267i	0.273554	−	1.03089i
$433$	14.1563			0.680310			0.340155	−	0.940369i	$-0.389520\pi$
$433$	14.1563			0.680310			0.340155	+	0.940369i	$0.389520\pi$
$434$		0			0
$435$			7.11772i			0.341269i
$436$	−15.4784	−	2.01871i	−0.741280	−	0.0966786i
$437$		−	15.6003i		−	0.746262i
$438$	−7.80825	+	6.85602i	−0.373093	+	0.327593i
$439$	5.45896			0.260542			0.130271	−	0.991478i	$-0.458415\pi$
$439$	5.45896			0.260542			0.130271	+	0.991478i	$0.458415\pi$
$440$	−3.08712	+	2.07086i	−0.147173	+	0.0987246i
$441$		0			0
$442$	17.7670	−	15.6003i	0.845090	−	0.742030i
$443$		−	33.3351i		−	1.58380i	−0.610651	−	0.791900i	$-0.709092\pi$
$443$		−	33.3351i		−	1.58380i	0.610651	−	0.791900i	$-0.290908\pi$
$444$	0.108145	−	0.829198i	0.00513234	−	0.0393520i
$445$		−	3.51589i		−	0.166669i
$446$	−5.41348	−	6.16536i	−0.256336	−	0.291938i
$447$	11.6332			0.550232
$448$		0			0
$449$	−26.9716			−1.27287			−0.636435	−	0.771330i	$-0.719592\pi$
$449$	−26.9716			−1.27287			−0.636435	+	0.771330i	$0.719592\pi$
$450$	−2.26760	−	2.58255i	−0.106896	−	0.121743i
$451$		−	14.9415i		−	0.703567i
$452$	−0.651106	+	4.99233i	−0.0306254	+	0.234819i
$453$			13.1268i			0.616750i
$454$	−12.1392	+	10.6588i	−0.569723	+	0.500244i
$455$		0			0
$456$	−24.5807	+	16.4889i	−1.15110	+	0.772165i
$457$	19.0934			0.893150			0.446575	−	0.894746i	$-0.352644\pi$
$457$	19.0934			0.893150			0.446575	+	0.894746i	$0.352644\pi$
$458$	19.6655	−	17.2672i	0.918908	−	0.806845i
$459$			23.3603i			1.09037i
$460$	−2.56086	−	0.333991i	−0.119401	−	0.0155724i
$461$		−	18.9177i		−	0.881087i	−0.897731	−	0.440543i	$-0.854786\pi$
$461$		−	18.9177i		−	0.881087i	0.897731	−	0.440543i	$-0.145214\pi$
$462$		0			0
$463$	0.860370			0.0399848			0.0199924	−	0.999800i	$-0.493636\pi$
$463$	0.860370			0.0399848			0.0199924	+	0.999800i	$0.493636\pi$
$464$	8.43018	−	31.7693i	0.391362	−	1.47485i
$465$	−0.750299			−0.0347943
$466$	10.3120	+	11.7442i	0.477693	+	0.544040i
$467$		−	18.6879i		−	0.864772i	−0.901689	−	0.432386i	$-0.857672\pi$
$467$		−	18.6879i		−	0.864772i	0.901689	−	0.432386i	$-0.142328\pi$
$468$	−4.06922	−	0.530712i	−0.188100	−	0.0245322i
$469$		0			0
$470$	1.51811	−	1.33297i	0.0700253	−	0.0614855i
$471$	−11.2451			−0.518145
$472$	5.94749	+	8.86616i	0.273755	+	0.408098i
$473$	−12.7912			−0.588138
$474$	1.03229	−	0.906402i	0.0474148	−	0.0416324i
$475$			31.2006i			1.43158i
$476$		0			0
$477$		−	5.59660i		−	0.256251i
$478$	21.0980	+	24.0283i	0.965000	+	1.09903i
$479$	18.5473			0.847447			0.423723	−	0.905792i	$-0.360723\pi$
$479$	18.5473			0.847447			0.423723	+	0.905792i	$0.360723\pi$
$480$	2.18048	+	4.38806i	0.0995250	+	0.200287i
$481$	−1.05251			−0.0479904
$482$	12.9977	+	14.8029i	0.592028	+	0.674255i
$483$		0			0
$484$	−1.36680	+	10.4799i	−0.0621271	+	0.476357i
$485$			7.11772i			0.323199i
$486$	5.64528	−	4.95682i	0.256075	−	0.224846i
$487$	−22.9175			−1.03849			−0.519246	−	0.854625i	$-0.673787\pi$
$487$	−22.9175			−1.03849			−0.519246	+	0.854625i	$0.673787\pi$
$488$	−11.2451	−	16.7635i	−0.509040	−	0.758847i
$489$	11.5173			0.520830
$490$		0			0
$491$			24.7987i			1.11915i	0.828780	+	0.559575i	$0.189036\pi$
$491$			24.7987i			1.11915i	−0.828780	+	0.559575i	$0.810964\pi$
$492$	−19.5294	−	2.54705i	−0.880452	−	0.114830i
$493$			34.6363i			1.55994i
$494$	24.5807	+	27.9947i	1.10594	+	1.25954i
$495$	−0.679886			−0.0305586
$496$	3.34889	+	0.888650i	0.150370	+	0.0399016i
$497$		0			0
$498$	1.61650	+	1.84101i	0.0724370	+	0.0824978i
$499$			39.2260i			1.75599i	0.478665	+	0.877997i	$0.341121\pi$
$499$			39.2260i			1.75599i	−0.478665	+	0.877997i	$0.658879\pi$
$500$	10.5729	+	1.37894i	0.472836	+	0.0616679i
$501$		−	2.97599i		−	0.132958i
$502$	0.750299	−	0.658799i	0.0334875	−	0.0294036i
$503$	−7.59396			−0.338598			−0.169299	−	0.985565i	$-0.554150\pi$
$503$	−7.59396			−0.338598			−0.169299	+	0.985565i	$0.554150\pi$
$504$		0			0
$505$	−8.73240			−0.388587
$506$	5.96771	−	5.23993i	0.265297	−	0.232943i
$507$		−	4.30532i		−	0.191206i
$508$	1.37143	−	10.5154i	0.0608473	−	0.466544i
$509$		−	4.37888i		−	0.194090i	−0.995280	−	0.0970451i	$-0.969061\pi$
$509$		−	4.37888i		−	0.194090i	0.995280	−	0.0970451i	$-0.0309391\pi$
$510$	−3.40684	−	3.88002i	−0.150858	−	0.171810i
$511$		0			0
$512$	−4.53521	−	22.1683i	−0.200430	−	0.979708i
$513$	−36.8079			−1.62511
$514$	19.3933	+	22.0868i	0.855400	+	0.974207i
$515$			10.3236i			0.454911i
$516$	−2.18048	+	16.7188i	−0.0959905	+	0.736003i
$517$			6.21259i			0.273230i
$518$		0			0
$519$	26.0813			1.14484
$520$	5.12173	−	3.43570i	0.224603	−	0.150665i
$521$	10.7565			0.471253			0.235626	−	0.971844i	$-0.424286\pi$
$521$	10.7565			0.471253			0.235626	+	0.971844i	$0.424286\pi$
$522$	4.51730	−	3.96641i	0.197717	−	0.173605i
$523$			2.81240i			0.122978i	0.998108	+	0.0614889i	$0.0195849\pi$
$523$			2.81240i			0.122978i	−0.998108	+	0.0614889i	$0.980415\pi$
$524$	19.9098	+	2.59666i	0.869762	+	0.113435i
$525$		0			0
$526$	21.2551	+	24.2073i	0.926768	+	1.05549i
$527$	−3.65111			−0.159045
$528$	−14.5640	−	3.86464i	−0.633816	−	0.168187i
$529$	−17.4827			−0.760117
$530$	5.54960	+	6.32038i	0.241059	+	0.274540i
$531$			1.95262i			0.0847365i
$532$		0			0
$533$			24.7889i			1.07372i
$534$	10.7091	−	9.40306i	0.463426	−	0.406910i
$535$	−0.186313			−0.00805500
$536$	4.21509	+	6.28360i	0.182064	+	0.271410i
$537$	−8.73240			−0.376831
$538$	−3.18280	+	2.79465i	−0.137220	+	0.120486i
$539$		0			0
$540$	−0.788031	+	6.04219i	−0.0339114	+	0.260015i
$541$		−	31.2576i		−	1.34387i	−0.740610	−	0.671935i	$-0.765463\pi$
$541$		−	31.2576i		−	1.34387i	0.740610	−	0.671935i	$-0.234537\pi$
$542$	−23.5002	−	26.7642i	−1.00942	−	1.14962i
$543$	15.7324			0.675142
$544$	10.6107	+	21.3532i	0.454929	+	0.915510i
$545$	4.29055			0.183787
$546$		0			0
$547$		−	29.4711i		−	1.26010i	−0.776556	−	0.630048i	$-0.783035\pi$
$547$		−	29.4711i		−	1.26010i	0.776556	−	0.630048i	$-0.216965\pi$
$548$	−0.840542	+	6.44482i	−0.0359062	+	0.275309i
$549$		−	3.69187i		−	0.157565i
$550$	−11.9354	+	10.4799i	−0.508928	+	0.446863i
$551$	−54.5749			−2.32497
$552$	−5.83159	−	8.69338i	−0.248209	−	0.370015i
$553$		0			0
$554$	10.0369	−	8.81290i	0.426428	−	0.374424i
$555$			0.229851i			0.00975663i
$556$	30.4123	+	3.96641i	1.28977	+	0.168213i
$557$		−	22.3725i		−	0.947951i	−0.880538	−	0.473976i	$-0.842818\pi$
$557$		−	22.3725i		−	0.947951i	0.880538	−	0.473976i	$-0.157182\pi$
$558$	0.418110	+	0.476182i	0.0177000	+	0.0201584i
$559$	21.2213			0.897567
$560$		0			0
$561$	15.8783			0.670381
$562$	−25.0467	−	28.5254i	−1.05653	−	1.20327i
$563$			32.3926i			1.36519i	0.730799	+	0.682593i	$0.239148\pi$
$563$			32.3926i			1.36519i	−0.730799	+	0.682593i	$0.760852\pi$
$564$	8.12022	+	1.05905i	0.341923	+	0.0445940i
$565$		−	1.38386i		−	0.0582193i
$566$	−13.7962	+	12.1137i	−0.579896	+	0.509177i
$567$		0			0
$568$	20.5928	−	13.8138i	0.864053	−	0.579614i
$569$	−37.0576			−1.55353			−0.776767	−	0.629788i	$-0.783142\pi$
$569$	−37.0576			−1.55353			−0.776767	+	0.629788i	$0.783142\pi$
$570$	6.11358	−	5.36802i	0.256070	−	0.224842i
$571$		−	22.4362i		−	0.938924i	−0.882953	−	0.469462i	$-0.844448\pi$
$571$		−	22.4362i		−	0.938924i	0.882953	−	0.469462i	$-0.155552\pi$
$572$	−2.45272	+	18.8061i	−0.102553	+	0.786324i
$573$			0.265356i			0.0110854i
$574$		0			0
$575$	−11.0346			−0.460175
$576$	1.56982	−	3.82914i	0.0654090	−	0.159547i
$577$	−9.56862			−0.398347			−0.199173	−	0.979964i	$-0.563826\pi$
$577$	−9.56862			−0.398347			−0.199173	+	0.979964i	$0.563826\pi$
$578$	−0.715691	−	0.815094i	−0.0297688	−	0.0339034i
$579$			11.8447i			0.492249i
$580$	−1.16841	+	8.95874i	−0.0485156	+	0.371991i
$581$		0			0
$582$	−21.6799	+	19.0360i	−0.898660	+	0.789067i
$583$	−25.8650			−1.07122
$584$	−10.9533	+	7.34757i	−0.453251	+	0.304045i
$585$	1.12797			0.0466360
$586$	10.1626	−	8.92323i	0.419812	−	0.368615i
$587$		−	23.6894i		−	0.977766i	−0.872349	−	0.488883i	$-0.837405\pi$
$587$		−	23.6894i		−	0.977766i	0.872349	−	0.488883i	$-0.162595\pi$
$588$		0			0
$589$		−	5.75289i		−	0.237044i
$590$	−1.93622	−	2.20514i	−0.0797130	−	0.0907844i
$591$	−2.12053			−0.0872269
$592$	0.272234	−	1.02592i	0.0111888	−	0.0421650i
$593$	7.44809			0.305856			0.152928	−	0.988237i	$-0.451130\pi$
$593$	7.44809			0.305856			0.152928	+	0.988237i	$0.451130\pi$
$594$	−12.3633	−	14.0804i	−0.507272	−	0.577727i
$595$		0			0
$596$	14.6422	+	1.90965i	0.599766	+	0.0782222i
$597$			20.1072i			0.822935i
$598$	−9.90081	+	8.69338i	−0.404874	+	0.355499i
$599$	1.67525			0.0684491			0.0342245	−	0.999414i	$-0.489104\pi$
$599$	1.67525			0.0684491			0.0342245	+	0.999414i	$0.489104\pi$
$600$	11.6632	+	17.3868i	0.476147	+	0.709812i
$601$	8.27385			0.337497			0.168749	−	0.985659i	$-0.446027\pi$
$601$	8.27385			0.337497			0.168749	+	0.985659i	$0.446027\pi$
$602$		0			0
$603$			1.38386i			0.0563550i
$604$	−2.15483	+	16.5221i	−0.0876787	+	0.672273i
$605$		−	2.90498i		−	0.118104i
$606$	−23.3543	−	26.5980i	−0.948705	−	1.08047i
$607$	26.5294			1.07679			0.538397	−	0.842691i	$-0.319030\pi$
$607$	26.5294			1.07679			0.538397	+	0.842691i	$0.319030\pi$
$608$	−33.6453	+	16.7188i	−1.36450	+	0.678036i
$609$		0			0
$610$	3.66087	+	4.16932i	0.148224	+	0.168811i
$611$		−	10.3071i		−	0.416980i
$612$	−0.563987	+	4.32435i	−0.0227978	+	0.174801i
$613$			31.6032i			1.27644i	0.769854	+	0.638220i	$0.220329\pi$
$613$			31.6032i			1.27644i	−0.769854	+	0.638220i	$0.779671\pi$
$614$	−12.9879	+	11.4040i	−0.524150	+	0.460229i
$615$	5.41348			0.218293
$616$		0			0
$617$	10.1113			0.407064			0.203532	−	0.979068i	$-0.434758\pi$
$617$	10.1113			0.407064			0.203532	+	0.979068i	$0.434758\pi$
$618$	−31.4446	+	27.6098i	−1.26489	+	1.11063i
$619$			5.53222i			0.222359i	0.993800	+	0.111179i	$0.0354628\pi$
$619$			5.53222i			0.222359i	−0.993800	+	0.111179i	$0.964537\pi$
$620$	−0.944366	−	0.123165i	−0.0379266	−	0.00494644i
$621$		−	13.0177i		−	0.522383i
$622$	29.7499	+	33.8819i	1.19286	+	1.35854i
$623$		0			0
$624$	24.1626	+	6.41169i	0.967277	+	0.256673i
$625$	20.5582			0.822326
$626$	20.0836	+	22.8730i	0.802702	+	0.914190i
$627$			25.0187i			0.999151i
$628$	−14.1536	−	1.84593i	−0.564791	−	0.0736608i
$629$			1.11850i			0.0445975i
$630$		0			0
$631$	35.5582			1.41555			0.707774	−	0.706439i	$-0.249700\pi$
$631$	35.5582			1.41555			0.707774	+	0.706439i	$0.249700\pi$
$632$	1.44809	−	0.971389i	0.0576018	−	0.0386398i
$633$	13.3356			0.530043
$634$	24.6009	−	21.6008i	0.977027	−	0.857876i
$635$			2.91483i			0.115671i
$636$	−4.40916	+	33.8071i	−0.174835	+	1.34054i
$637$		0			0
$638$	−18.3310	−	20.8770i	−0.725731	−	0.826528i
$639$	4.53521			0.179410
$640$	2.02415	+	5.88098i	0.0800115	+	0.232466i
$641$	9.46599			0.373884			0.186942	−	0.982371i	$-0.440142\pi$
$641$	9.46599			0.373884			0.186942	+	0.982371i	$0.440142\pi$
$642$	−0.498284	−	0.567490i	−0.0196657	−	0.0223971i
$643$		−	13.0085i		−	0.513007i	−0.966543	−	0.256503i	$-0.917430\pi$
$643$		−	13.0085i		−	0.513007i	0.966543	−	0.256503i	$-0.0825705\pi$
$644$		0			0
$645$		−	4.63439i		−	0.182479i
$646$	29.7499	−	26.1218i	1.17049	−	1.02775i
$647$	−27.5219			−1.08200			−0.540999	−	0.841023i	$-0.681954\pi$
$647$	−27.5219			−1.08200			−0.540999	+	0.841023i	$0.681954\pi$
$648$	−16.8662	+	11.3140i	−0.662567	+	0.444455i
$649$	9.02415			0.354229
$650$	19.8016	−	17.3868i	0.776683	−	0.681965i
$651$		0			0
$652$	14.4963	+	1.89062i	0.567718	+	0.0740425i
$653$		−	35.1479i		−	1.37545i	−0.725974	−	0.687723i	$-0.758611\pi$
$653$		−	35.1479i		−	1.37545i	0.725974	−	0.687723i	$-0.241389\pi$
$654$	11.4749	+	13.0686i	0.448703	+	0.511023i
$655$	−5.51892			−0.215642
$656$	−24.1626	−	6.41169i	−0.943390	−	0.250334i
$657$	−2.41228			−0.0941121
$658$		0			0
$659$		−	3.86719i		−	0.150644i	−0.997159	−	0.0753222i	$-0.976001\pi$
$659$		−	3.86719i		−	0.150644i	0.997159	−	0.0753222i	$-0.0239985\pi$
$660$	4.10695	+	0.535633i	0.159863	+	0.0208495i
$661$		−	16.6617i		−	0.648065i	−0.946046	−	0.324033i	$-0.894961\pi$
$661$		−	16.6617i		−	0.648065i	0.946046	−	0.324033i	$-0.105039\pi$
$662$	31.3664	−	27.5412i	1.21909	−	1.07042i
$663$	−26.3431			−1.02308
$664$	1.73240	+	2.58255i	0.0672300	+	0.100222i
$665$		0			0
$666$	0.145876	−	0.128086i	0.00565259	−	0.00496325i
$667$		−	19.3013i		−	0.747350i
$668$	0.488524	−	3.74574i	0.0189016	−	0.144927i
$669$			9.14135i			0.353425i
$670$	−1.37224	−	1.56283i	−0.0530141	−	0.0603772i
$671$	−17.0622			−0.658679
$672$		0			0
$673$	−3.95795			−0.152568			−0.0762838	−	0.997086i	$-0.524306\pi$
$673$	−3.95795			−0.152568			−0.0762838	+	0.997086i	$0.524306\pi$
$674$	3.06459	+	3.49023i	0.118043	+	0.134439i
$675$			26.0355i			1.00211i
$676$	0.706740	−	5.41890i	0.0271823	−	0.208419i
$677$		−	41.2042i		−	1.58361i	−0.610776	−	0.791804i	$-0.709142\pi$
$677$		−	41.2042i		−	1.58361i	0.610776	−	0.791804i	$-0.290858\pi$
$678$	4.21509	−	3.70105i	0.161880	−	0.142138i
$679$		0			0
$680$	−3.65111	−	5.44285i	−0.140014	−	0.208724i
$681$	17.9988			0.689716
$682$	2.20070	−	1.93232i	0.0842693	−	0.0739924i
$683$			33.0986i			1.26648i	0.773954	+	0.633242i	$0.218276\pi$
$683$			33.0986i			1.26648i	−0.773954	+	0.633242i	$0.781724\pi$
$684$	−6.81369	−	0.888650i	−0.260528	−	0.0339784i
$685$		−	1.78648i		−	0.0682580i
$686$		0			0
$687$	−29.1580			−1.11245
$688$	−5.48894	+	20.6852i	−0.209264	+	0.788615i
$689$	42.9117			1.63480
$690$	1.89849	+	2.16217i	0.0722743	+	0.0823125i
$691$			14.8968i			0.566701i	0.959016	+	0.283350i	$0.0914459\pi$
$691$			14.8968i			0.566701i	−0.959016	+	0.283350i	$0.908554\pi$
$692$	32.8273	+	4.28137i	1.24791	+	0.162753i
$693$		0			0
$694$	−33.6628	+	29.5575i	−1.27782	+	1.12199i
$695$	−8.43018			−0.319775
$696$	−30.4123	+	20.4008i	−1.15277	+	0.773291i
$697$	26.3431			0.997815
$698$	30.2664	−	26.5753i	1.14560	−	1.00589i
$699$		−	17.4131i		−	0.658623i
$700$		0			0
$701$		−	32.5746i		−	1.23032i	−0.788401	−	0.615162i	$-0.789090\pi$
$701$		−	32.5746i		−	1.23032i	0.788401	−	0.615162i	$-0.210910\pi$
$702$	20.5115	+	23.3603i	0.774156	+	0.881678i
$703$	−1.76237			−0.0664692
$704$	−17.6966	−	7.25499i	−0.666965	−	0.273433i
$705$	−2.25090			−0.0847737
$706$	18.8852	+	21.5082i	0.710755	+	0.809471i
$707$		0			0
$708$	1.53833	−	11.7951i	0.0578140	−	0.443286i
$709$		−	11.4966i		−	0.431764i	−0.976419	−	0.215882i	$-0.930737\pi$
$709$		−	11.4966i		−	0.431764i	0.976419	−	0.215882i	$-0.0692626\pi$
$710$	−5.12173	+	4.49712i	−0.192215	+	0.168774i
$711$	0.318917			0.0119603
$712$	15.0225	−	10.0772i	0.562993	−	0.377660i
$713$	2.03461			0.0761967
$714$		0			0
$715$		−	5.21300i		−	0.194955i
$716$	−10.9910	−	1.43347i	−0.410755	−	0.0535712i
$717$		−	35.6267i		−	1.33050i
$718$	−23.4415	−	26.6972i	−0.874827	−	0.996332i
$719$	26.9775			1.00609			0.503045	−	0.864260i	$-0.332213\pi$
$719$	26.9775			1.00609			0.503045	+	0.864260i	$0.332213\pi$
$720$	−0.291753	+	1.09948i	−0.0108730	+	0.0409750i
$721$		0			0
$722$	23.4302	+	26.6844i	0.871981	+	0.993091i
$723$		−	21.9483i		−	0.816264i
$724$	19.8016	+	2.58255i	0.735921	+	0.0959798i
$725$			38.6027i			1.43367i
$726$	8.84830	−	7.76923i	0.328391	−	0.288343i
$727$	27.0230			1.00223			0.501113	−	0.865382i	$-0.332924\pi$
$727$	27.0230			1.00223			0.501113	+	0.865382i	$0.332924\pi$
$728$		0			0
$729$	−29.9117			−1.10784
$730$	2.72425	−	2.39202i	0.100829	−	0.0885328i
$731$		−	22.5519i		−	0.834111i
$732$	−2.90856	+	22.3013i	−0.107503	+	0.824279i
$733$		−	20.6760i		−	0.763686i	−0.924227	−	0.381843i	$-0.875290\pi$
$733$		−	20.6760i		−	0.763686i	0.924227	−	0.381843i	$-0.124710\pi$
$734$	−28.3497	−	32.2872i	−1.04641	−	1.19174i
$735$		0			0
$736$	−5.91288	−	11.8992i	−0.217952	−	0.438611i
$737$	6.39558			0.235584
$738$	−3.01671	−	3.43570i	−0.111046	−	0.126470i
$739$		−	10.7452i		−	0.395269i	−0.980276	−	0.197635i	$-0.936674\pi$
$739$		−	10.7452i		−	0.395269i	0.980276	−	0.197635i	$-0.0633260\pi$
$740$	−0.0377312	+	0.289302i	−0.00138703	+	0.0106350i
$741$		−	41.5076i		−	1.52482i
$742$		0			0
$743$	11.8708			0.435498			0.217749	−	0.976005i	$-0.430129\pi$
$743$	11.8708			0.435498			0.217749	+	0.976005i	$0.430129\pi$
$744$	−2.15051	−	3.20585i	−0.0788414	−	0.117532i
$745$	−4.05876			−0.148701
$746$	−5.96771	+	5.23993i	−0.218493	+	0.191848i
$747$			0.568763i			0.0208100i
$748$	19.9852	+	2.60650i	0.730732	+	0.0953030i
$749$		0			0
$750$	−7.83823	−	8.92688i	−0.286212	−	0.325964i
$751$	17.0646			0.622696			0.311348	−	0.950296i	$-0.399220\pi$
$751$	17.0646			0.622696			0.311348	+	0.950296i	$0.399220\pi$
$752$	10.0467	+	2.66595i	0.366365	+	0.0972172i
$753$	−1.11247			−0.0405405
$754$	30.4123	+	34.6363i	1.10755	+	1.26138i
$755$		−	4.57986i		−	0.166678i
$756$		0			0
$757$			46.3272i			1.68379i	0.539641	+	0.841895i	$0.318560\pi$
$757$			46.3272i			1.68379i	−0.539641	+	0.841895i	$0.681440\pi$
$758$	−8.57606	+	7.53019i	−0.311497	+	0.273509i
$759$	−8.84830			−0.321173
$760$	8.57606	−	5.75289i	0.311086	−	0.208679i
$761$	14.6095			0.529593			0.264796	−	0.964304i	$-0.414695\pi$
$761$	14.6095			0.529593			0.264796	+	0.964304i	$0.414695\pi$
$762$	−8.87827	+	7.79555i	−0.321626	+	0.282403i
$763$		0			0
$764$	−0.0435595	+	0.333991i	−0.00157593	+	0.0120834i
$765$		−	1.19869i		−	0.0433389i
$766$	−23.9183	−	27.2403i	−0.864204	−	0.984234i
$767$	−14.9716			−0.540595
$768$	−12.4994	+	21.8937i	−0.451033	+	0.790022i
$769$	−49.3177			−1.77844			−0.889221	−	0.457477i	$-0.848753\pi$
$769$	−49.3177			−1.77844			−0.889221	+	0.457477i	$0.848753\pi$
$770$		0			0
$771$		−	32.7480i		−	1.17939i
$772$	−1.94437	+	14.9083i	−0.0699793	+	0.536563i
$773$			1.04240i			0.0374925i	0.999824	+	0.0187462i	$0.00596747\pi$
$773$			1.04240i			0.0374925i	−0.999824	+	0.0187462i	$0.994033\pi$
$774$	−2.94124	+	2.58255i	−0.105721	+	0.0928279i
$775$	−4.06922			−0.146171
$776$	−30.4123	+	20.4008i	−1.09174	+	0.732346i
$777$		0			0
$778$	−28.2116	+	24.7711i	−1.01143	+	0.888087i
$779$			41.5076i			1.48717i
$780$	−6.81369	−	0.888650i	−0.243969	−	0.0318188i
$781$		−	20.9597i		−	0.749998i
$782$	9.23843	+	10.5216i	0.330366	+	0.376250i
$783$	−45.5403			−1.62748
$784$		0			0
$785$	3.92334			0.140030
$786$	−14.7601	−	16.8101i	−0.526474	−	0.599596i
$787$		−	40.2874i		−	1.43609i	−0.695997	−	0.718045i	$-0.745037\pi$
$787$		−	40.2874i		−	1.43609i	0.695997	−	0.718045i	$-0.254963\pi$
$788$	−2.66901	−	0.348096i	−0.0950795	−	0.0124004i
$789$		−	35.8920i		−	1.27779i
$790$	−0.360161	+	0.316239i	−0.0128140	+	0.0112513i
$791$		0			0
$792$	−1.94869	−	2.90498i	−0.0692436	−	0.103224i
$793$	28.3073			1.00522
$794$	36.2341	−	31.8153i	1.28590	−	1.12908i
$795$		−	9.37120i		−	0.332362i
$796$	−3.30070	+	25.3080i	−0.116990	+	0.897019i
$797$		−	32.2902i		−	1.14378i	−0.820331	−	0.571889i	$-0.806211\pi$
$797$		−	32.2902i		−	1.14378i	0.820331	−	0.571889i	$-0.193789\pi$
$798$		0			0
$799$	−10.9533			−0.387501
$800$	11.8258	+	23.7985i	0.418104	+	0.841402i
$801$	3.30846			0.116899
$802$	−17.1257	−	19.5042i	−0.604728	−	0.688719i
$803$			11.1485i			0.393422i
$804$	1.09024	−	8.35939i	0.0384499	−	0.294813i
$805$		0			0
$806$	−3.65111	+	3.20585i	−0.128605	+	0.112921i
$807$	4.71912			0.166121
$808$	−25.0288	−	37.3114i	−0.880509	−	1.31261i
$809$	41.6262			1.46350			0.731749	−	0.681574i	$-0.238704\pi$
$809$	41.6262			1.46350			0.731749	+	0.681574i	$0.238704\pi$
$810$	4.19487	−	3.68330i	0.147393	−	0.129418i
$811$		−	18.7227i		−	0.657444i	−0.944427	−	0.328722i	$-0.893382\pi$
$811$		−	18.7227i		−	0.657444i	0.944427	−	0.328722i	$-0.106618\pi$
$812$		0			0
$813$			39.6831i			1.39175i
$814$	−0.591959	−	0.674176i	−0.0207481	−	0.0236299i
$815$	−4.01832			−0.140756
$816$	6.81369	−	25.6775i	0.238527	−	0.898893i
$817$	35.5340			1.24318
$818$	10.9631	+	12.4857i	0.383315	+	0.436554i
$819$		0			0
$820$	6.81369	+	0.888650i	0.237944	+	0.0310330i
$821$			18.7418i			0.654092i	0.945008	+	0.327046i	$0.106053\pi$
$821$			18.7418i			0.654092i	−0.945008	+	0.327046i	$0.893947\pi$
$822$	5.44145	−	4.77785i	0.189792	−	0.166647i
$823$	−20.4423			−0.712572			−0.356286	−	0.934377i	$-0.615957\pi$
$823$	−20.4423			−0.712572			−0.356286	+	0.934377i	$0.615957\pi$
$824$	−44.1101	+	29.5894i	−1.53665	+	1.03080i
$825$	17.6966			0.616116
$826$		0			0
$827$		−	48.6254i		−	1.69087i	−0.534079	−	0.845435i	$-0.679341\pi$
$827$		−	48.6254i		−	1.69087i	0.534079	−	0.845435i	$-0.320659\pi$
$828$	0.314286	−	2.40978i	0.0109222	−	0.0837455i
$829$			6.99948i			0.243102i	0.992585	+	0.121551i	$0.0387868\pi$
$829$			6.99948i			0.243102i	−0.992585	+	0.121551i	$0.961213\pi$
$830$	−0.563987	−	0.642319i	−0.0195763	−	0.0222952i
$831$	−14.8817			−0.516241
$832$	29.3598	+	12.0365i	1.01787	+	0.417290i
$833$		0			0
$834$	−22.5461	−	25.6775i	−0.780707	−	0.889140i
$835$			1.03831i			0.0359321i
$836$	−4.10695	+	31.4899i	−0.142042	+	1.08910i
$837$		−	4.80053i		−	0.165931i
$838$	11.7791	−	10.3426i	0.406902	−	0.357279i
$839$	−40.1867			−1.38740			−0.693700	−	0.720264i	$-0.744021\pi$
$839$	−40.1867			−1.38740			−0.693700	+	0.720264i	$0.744021\pi$
$840$		0			0
$841$	−38.5224			−1.32836
$842$	0.145876	−	0.128086i	0.00502723	−	0.00441415i
$843$			42.2945i			1.45670i
$844$	16.7849	+	2.18911i	0.577760	+	0.0753522i
$845$			1.50210i			0.0516739i
$846$	1.25433	+	1.42855i	0.0431248	+	0.0491144i
$847$		0			0
$848$	−11.0992	+	41.8275i	−0.381148	+	1.43636i
$849$	20.4555			0.702032
$850$	−18.4769	−	21.0431i	−0.633751	−	0.721773i
$851$		−	0.623294i		−	0.0213662i
$852$	−27.3956	−	3.57297i	−0.938557	−	0.122408i
$853$			30.8071i			1.05482i	0.849612	+	0.527408i	$0.176836\pi$
$853$			30.8071i			1.05482i	−0.849612	+	0.527408i	$0.823164\pi$
$854$		0			0
$855$	1.88873			0.0645933
$856$	−0.534009	−	0.796069i	−0.0182521	−	0.0272091i
$857$	−13.6978			−0.467908			−0.233954	−	0.972248i	$-0.575166\pi$
$857$	−13.6978			−0.467908			−0.233954	+	0.972248i	$0.575166\pi$
$858$	15.8783	−	13.9419i	0.542075	−	0.475968i
$859$			8.69338i			0.296614i	0.988941	+	0.148307i	$0.0473824\pi$
$859$			8.69338i			0.296614i	−0.988941	+	0.148307i	$0.952618\pi$
$860$	0.760758	−	5.83309i	0.0259416	−	0.198907i
$861$		0			0
$862$	−11.6266	−	13.2414i	−0.396002	−	0.451003i
$863$	−0.592349			−0.0201638			−0.0100819	−	0.999949i	$-0.503209\pi$
$863$	−0.592349			−0.0201638			−0.0100819	+	0.999949i	$0.503209\pi$
$864$	−28.0755	+	13.9511i	−0.955147	+	0.474625i
$865$	−9.09961			−0.309396
$866$	−13.2093	−	15.0439i	−0.448869	−	0.511213i
$867$			1.20854i			0.0410440i
$868$		0			0
$869$		−	1.47389i		−	0.0499984i
$870$	7.56399	−	6.64154i	0.256443	−	0.225169i
$871$	−10.6107			−0.359529
$872$	12.2976	+	18.3325i	0.416449	+	0.620816i
$873$	−6.69779			−0.226686
$874$	−16.5784	+	14.5566i	−0.560772	+	0.492385i
$875$		0			0
$876$	14.5717	+	1.90046i	0.492333	+	0.0642108i
$877$			15.2778i			0.515896i	0.966159	+	0.257948i	$0.0830464\pi$
$877$			15.2778i			0.515896i	−0.966159	+	0.257948i	$0.916954\pi$
$878$	−5.09376	−	5.80123i	−0.171906	−	0.195782i
$879$	−15.0680			−0.508232
$880$	5.08129	+	1.34835i	0.171290	+	0.0454529i
$881$	43.1280			1.45302			0.726509	−	0.687157i	$-0.241141\pi$
$881$	43.1280			1.45302			0.726509	+	0.687157i	$0.241141\pi$
$882$		0			0
$883$			20.2255i			0.680642i	0.940309	+	0.340321i	$0.110536\pi$
$883$			20.2255i			0.680642i	−0.940309	+	0.340321i	$0.889464\pi$
$884$	−33.1568	−	4.32435i	−1.11518	−	0.145443i
$885$			3.26956i			0.109905i
$886$	−35.4252	+	31.1050i	−1.19013	+	1.04499i
$887$	−21.5640			−0.724048			−0.362024	−	0.932169i	$-0.617914\pi$
$887$	−21.5640			−0.724048			−0.362024	+	0.932169i	$0.617914\pi$
$888$	−0.982097	+	0.658799i	−0.0329570	+	0.0221078i
$889$		0			0
$890$	−3.73633	+	3.28067i	−0.125242	+	0.109968i
$891$			17.1668i			0.575108i
$892$	−1.50060	+	11.5058i	−0.0502438	+	0.385242i
$893$		−	17.2587i		−	0.577540i
$894$	−10.8549	−	12.3626i	−0.363043	−	0.413466i
$895$	3.04668			0.101839
$896$		0			0
$897$	14.6799			0.490147
$898$	25.1672	+	28.6627i	0.839841	+	0.956486i
$899$		−	7.11772i		−	0.237389i
$900$	−0.628572	+	4.81955i	−0.0209524	+	0.160652i
$901$		−	45.6021i		−	1.51923i
$902$	−15.8783	+	13.9419i	−0.528689	+	0.464214i
$903$		0			0
$904$	5.91288	−	3.96641i	0.196659	−	0.131921i
$905$	−5.48894			−0.182459
$906$	13.9498	−	12.2486i	0.463451	−	0.406932i
$907$			31.5677i			1.04819i	0.851661	+	0.524094i	$0.175596\pi$
$907$			31.5677i			1.04819i	−0.851661	+	0.524094i	$0.824404\pi$
$908$	22.6542	+	2.95459i	0.751807	+	0.0980516i
$909$		−	8.21720i		−	0.272547i
$910$		0			0
$911$	15.6873			0.519744			0.259872	−	0.965643i	$-0.416320\pi$
$911$	15.6873			0.519744			0.259872	+	0.965643i	$0.416320\pi$
$912$	40.4590	+	10.7360i	1.33973	+	0.355506i
$913$	2.62857			0.0869930
$914$	−17.8160	−	20.2905i	−0.589301	−	0.671149i
$915$		−	6.18184i		−	0.204365i
$916$	−36.6997	−	4.78642i	−1.21259	−	0.158148i
$917$		0			0
$918$	24.8250	−	21.7975i	0.819346	−	0.719425i
$919$	15.5881			0.514205			0.257103	−	0.966384i	$-0.417232\pi$
$919$	15.5881			0.514205			0.257103	+	0.966384i	$0.417232\pi$
$920$	2.03461	+	3.03307i	0.0670790	+	0.0999974i
$921$	19.2571			0.634544
$922$	−20.1038	+	17.6521i	−0.662084	+	0.581342i
$923$			34.7735i			1.14458i
$924$		0			0
$925$			1.24659i			0.0409875i
$926$	−0.802810	−	0.914313i	−0.0263820	−	0.0300462i
$927$	−9.71449			−0.319066
$928$	−41.6274	+	20.6852i	−1.36649	+	0.679025i
$929$	−41.3851			−1.35780			−0.678901	−	0.734230i	$-0.737543\pi$
$929$	−41.3851			−1.35780			−0.678901	+	0.734230i	$0.737543\pi$
$930$	0.700104	+	0.797341i	0.0229573	+	0.0261459i
$931$		0			0
$932$	2.85844	−	21.9170i	0.0936315	−	0.717916i
$933$		−	50.2365i		−	1.64467i
$934$	−19.8596	+	17.4376i	−0.649825	+	0.570577i
$935$	−5.53984			−0.181172
$936$	3.23300	+	4.81955i	0.105674	+	0.157532i
$937$	23.9308			0.781785			0.390892	−	0.920436i	$-0.372166\pi$
$937$	23.9308			0.781785			0.390892	+	0.920436i	$0.372166\pi$
$938$		0			0
$939$		−	33.9137i		−	1.10673i
$940$	−2.83310	−	0.369496i	−0.0924055	−	0.0120516i
$941$		−	38.4844i		−	1.25456i	−0.778795	−	0.627278i	$-0.784169\pi$
$941$		−	38.4844i		−	1.25456i	0.778795	−	0.627278i	$-0.215831\pi$
$942$	10.4928	+	11.9501i	0.341873	+	0.389356i
$943$	−14.6799			−0.478043
$944$	3.87244	−	14.5934i	0.126037	−	0.474974i
$945$		0			0
$946$	11.9354	+	13.5931i	0.388054	+	0.441951i
$947$		−	9.65559i		−	0.313764i	−0.987617	−	0.156882i	$-0.949856\pi$
$947$		−	9.65559i		−	0.313764i	0.987617	−	0.156882i	$-0.0501443\pi$
$948$	−1.92646	−	0.251252i	−0.0625686	−	0.00816028i
$949$		−	18.4961i		−	0.600408i
$950$	33.1568	−	29.1132i	1.07575	−	0.944557i
$951$	−36.4757			−1.18280
$952$		0			0
$953$	−19.3777			−0.627704			−0.313852	−	0.949472i	$-0.601620\pi$
$953$	−19.3777			−0.627704			−0.313852	+	0.949472i	$0.601620\pi$
$954$	−5.94749	+	5.22218i	−0.192557	+	0.169074i
$955$		−	0.0925812i		−	0.00299586i
$956$	5.84830	−	44.8416i	0.189147	−	1.45028i
$957$			30.9542i			1.00061i
$958$	−17.3065	−	19.7101i	−0.559146	−	0.636806i
$959$		0			0
$960$	2.62857	−	6.41169i	0.0848368	−	0.206936i
$961$	−30.2497			−0.975797
$962$	0.982097	+	1.11850i	0.0316641	+	0.0360619i
$963$		−	0.175321i		−	0.00564963i
$964$	3.60292	−	27.6252i	0.116042	−	0.889748i
$965$		−	4.13255i		−	0.133031i
$966$		0			0
$967$	34.8845			1.12181			0.560905	−	0.827880i	$-0.310453\pi$
$967$	34.8845			1.12181			0.560905	+	0.827880i	$0.310453\pi$
$968$	12.4123	−	8.32626i	0.398946	−	0.267616i
$969$	−44.1101			−1.41702
$970$	7.56399	−	6.64154i	0.242865	−	0.213247i
$971$			44.4291i			1.42580i	0.701267	+	0.712899i	$0.252618\pi$
$971$			44.4291i			1.42580i	−0.701267	+	0.712899i	$0.747382\pi$
$972$	−10.5352	−	1.37402i	−0.337917	−	0.0440716i
$973$		0			0
$974$	21.3843	+	24.3544i	0.685197	+	0.780365i
$975$	−29.3598			−0.940265
$976$	−7.32173	+	27.5921i	−0.234363	+	0.883201i
$977$	−27.0871			−0.866594			−0.433297	−	0.901251i	$-0.642650\pi$
$977$	−27.0871			−0.866594			−0.433297	+	0.901251i	$0.642650\pi$
$978$	−10.7468	−	12.2394i	−0.343644	−	0.391373i
$979$		−	15.2902i		−	0.488678i
$980$		0			0
$981$			4.03742i			0.128905i
$982$	26.3535	−	23.1397i	0.840975	−	0.738416i
$983$	−25.0887			−0.800206			−0.400103	−	0.916470i	$-0.631026\pi$
$983$	−25.0887			−0.800206			−0.400103	+	0.916470i	$0.631026\pi$
$984$	15.5161	+	23.1305i	0.494635	+	0.737372i
$985$	0.739840			0.0235733
$986$	36.8079	−	32.3191i	1.17220	−	1.02925i
$987$		0			0
$988$	6.81369	−	52.2437i	0.216772	−	1.66209i
$989$			12.5672i			0.399614i
$990$	0.634401	+	0.722513i	0.0201626	+	0.0229630i
$991$	17.6394			0.560336			0.280168	−	0.959951i	$-0.409610\pi$
$991$	17.6394			0.560336			0.280168	+	0.959951i	$0.409610\pi$
$992$	−2.18048	−	4.38806i	−0.0692304	−	0.139321i
$993$	−46.5068			−1.47585
$994$		0			0
$995$		−	7.01530i		−	0.222400i
$996$	0.448088	−	3.43570i	0.0141982	−	0.108864i
$997$			30.6607i			0.971033i	0.874228	+	0.485516i	$0.161368\pi$
$997$			30.6607i			0.971033i	−0.874228	+	0.485516i	$0.838632\pi$
$998$	41.6853	−	36.6017i	1.31953	−	1.15861i
$999$	−1.47062			−0.0465284

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.2.b.f.197.1		6
4.3	odd	2		1568.2.b.e.785.2		6
7.2	even	3		392.2.p.g.165.3		12
7.3	odd	6		56.2.p.a.37.6	yes	12
7.4	even	3		392.2.p.g.373.6		12
7.5	odd	6		56.2.p.a.53.3	yes	12
7.6	odd	2		392.2.b.e.197.1		6
8.3	odd	2		1568.2.b.e.785.5		6
8.5	even	2	inner	392.2.b.f.197.2		6
21.5	even	6		504.2.cj.c.109.4		12
21.17	even	6		504.2.cj.c.37.1		12
28.3	even	6		224.2.t.a.177.5		12
28.11	odd	6		1568.2.t.g.177.2		12
28.19	even	6		224.2.t.a.81.2		12
28.23	odd	6		1568.2.t.g.753.5		12
28.27	even	2		1568.2.b.f.785.5		6
56.3	even	6		224.2.t.a.177.2		12
56.5	odd	6		56.2.p.a.53.6	yes	12
56.11	odd	6		1568.2.t.g.177.5		12
56.13	odd	2		392.2.b.e.197.2		6
56.19	even	6		224.2.t.a.81.5		12
56.27	even	2		1568.2.b.f.785.2		6
56.37	even	6		392.2.p.g.165.6		12
56.45	odd	6		56.2.p.a.37.3	✓	12
56.51	odd	6		1568.2.t.g.753.2		12
56.53	even	6		392.2.p.g.373.3		12
84.47	odd	6		2016.2.cr.c.1873.3		12
84.59	odd	6		2016.2.cr.c.1297.4		12
168.5	even	6		504.2.cj.c.109.1		12
168.59	odd	6		2016.2.cr.c.1297.3		12
168.101	even	6		504.2.cj.c.37.4		12
168.131	odd	6		2016.2.cr.c.1873.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.2.p.a.37.3	✓	12	56.45	odd	6
56.2.p.a.37.6	yes	12	7.3	odd	6
56.2.p.a.53.3	yes	12	7.5	odd	6
56.2.p.a.53.6	yes	12	56.5	odd	6
224.2.t.a.81.2		12	28.19	even	6
224.2.t.a.81.5		12	56.19	even	6
224.2.t.a.177.2		12	56.3	even	6
224.2.t.a.177.5		12	28.3	even	6
392.2.b.e.197.1		6	7.6	odd	2
392.2.b.e.197.2		6	56.13	odd	2
392.2.b.f.197.1		6	1.1	even	1	trivial
392.2.b.f.197.2		6	8.5	even	2	inner
392.2.p.g.165.3		12	7.2	even	3
392.2.p.g.165.6		12	56.37	even	6
392.2.p.g.373.3		12	56.53	even	6
392.2.p.g.373.6		12	7.4	even	3
504.2.cj.c.37.1		12	21.17	even	6
504.2.cj.c.37.4		12	168.101	even	6
504.2.cj.c.109.1		12	168.5	even	6
504.2.cj.c.109.4		12	21.5	even	6
1568.2.b.e.785.2		6	4.3	odd	2
1568.2.b.e.785.5		6	8.3	odd	2
1568.2.b.f.785.2		6	56.27	even	2
1568.2.b.f.785.5		6	28.27	even	2
1568.2.t.g.177.2		12	28.11	odd	6
1568.2.t.g.177.5		12	56.11	odd	6
1568.2.t.g.753.2		12	56.51	odd	6
1568.2.t.g.753.5		12	28.23	odd	6
2016.2.cr.c.1297.3		12	168.59	odd	6
2016.2.cr.c.1297.4		12	84.59	odd	6
2016.2.cr.c.1873.3		12	84.47	odd	6
2016.2.cr.c.1873.4		12	168.131	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	392.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.933099 - 1.06270i) q^{2} +1.57566i q^{3} +(-0.258652 + 1.98320i) q^{4} -0.549738i q^{5} +(1.67445 - 1.47024i) q^{6} +(2.34889 - 1.57566i) q^{8} +0.517304 q^{9} +(-0.584205 + 0.512960i) q^{10} -2.39075i q^{11} +(-3.12485 - 0.407547i) q^{12} +3.96641i q^{13} +0.866198 q^{15} +(-3.86620 - 1.02592i) q^{16} +4.21509 q^{17} +(-0.482696 - 0.549738i) q^{18} +6.64154i q^{19} +(1.09024 + 0.142191i) q^{20} +(-2.54065 + 2.23081i) q^{22} -2.34889 q^{23} +(2.48270 + 3.70105i) q^{24} +4.69779 q^{25} +(4.21509 - 3.70105i) q^{26} +5.54207i q^{27} +8.21720i q^{29} +(-0.808249 - 0.920507i) q^{30} -0.866198 q^{31} +(2.51730 + 5.06588i) q^{32} +3.76700 q^{33} +(-3.93310 - 4.47937i) q^{34} +(-0.133802 + 1.02592i) q^{36} +0.265356i q^{37} +(7.05795 - 6.19722i) q^{38} -6.24970 q^{39} +(-0.866198 - 1.29128i) q^{40} +6.24970 q^{41} -5.35027i q^{43} +(4.74135 + 0.618373i) q^{44} -0.284382i q^{45} +(2.19175 + 2.49616i) q^{46} -2.59859 q^{47} +(1.61650 - 6.09180i) q^{48} +(-4.38350 - 4.99233i) q^{50} +6.64154i q^{51} +(-7.86620 - 1.02592i) q^{52} -10.8188i q^{53} +(5.88954 - 5.17130i) q^{54} -1.31429 q^{55} -10.4648 q^{57} +(8.73240 - 7.66746i) q^{58} +3.77461i q^{59} +(-0.224044 + 1.71785i) q^{60} -7.13675i q^{61} +(0.808249 + 0.920507i) q^{62} +(3.03461 - 7.40210i) q^{64} +2.18048 q^{65} +(-3.51499 - 4.00319i) q^{66} +2.67513i q^{67} +(-1.09024 + 8.35939i) q^{68} -3.70105i q^{69} +8.76700 q^{71} +(1.21509 - 0.815094i) q^{72} -4.66318 q^{73} +(0.281993 - 0.247604i) q^{74} +7.40210i q^{75} +(-13.1715 - 1.71785i) q^{76} +(5.83159 + 6.64154i) q^{78} +0.616498 q^{79} +(-0.563987 + 2.12540i) q^{80} -7.18048 q^{81} +(-5.83159 - 6.64154i) q^{82} +1.09948i q^{83} -2.31720i q^{85} +(-5.68571 + 4.99233i) q^{86} -12.9475 q^{87} +(-3.76700 - 5.61562i) q^{88} +6.39558 q^{89} +(-0.302212 + 0.265356i) q^{90} +(0.607546 - 4.65834i) q^{92} -1.36483i q^{93} +(2.42475 + 2.76152i) q^{94} +3.65111 q^{95} +(-7.98210 + 3.96641i) q^{96} -12.9475 q^{97} -1.23675i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 4 q^{6} + 2 q^{8} - 8 q^{10} - 2 q^{12} - 10 q^{15} - 8 q^{16} - 2 q^{17} - 6 q^{18} - 4 q^{20} + 6 q^{22} - 2 q^{23} + 18 q^{24} + 4 q^{25} - 2 q^{26} - 14 q^{30} + 10 q^{31} + 12 q^{32}+ \cdots - 20 q^{97}+O(q^{100}) \) 6 * q + 2 * q^2 + 4 * q^6 + 2 * q^8 - 8 * q^10 - 2 * q^12 - 10 * q^15 - 8 * q^16 - 2 * q^17 - 6 * q^18 - 4 * q^20 + 6 * q^22 - 2 * q^23 + 18 * q^24 + 4 * q^25 - 2 * q^26 - 14 * q^30 + 10 * q^31 + 12 * q^32 - 14 * q^33 - 16 * q^34 - 16 * q^36 + 18 * q^38 - 4 * q^39 + 10 * q^40 + 4 * q^41 + 30 * q^44 + 4 * q^46 + 30 * q^47 + 28 * q^48 - 8 * q^50 - 32 * q^52 + 2 * q^54 - 2 * q^55 - 2 * q^57 + 22 * q^58 - 6 * q^60 + 14 * q^62 + 12 * q^64 - 8 * q^65 - 38 * q^66 + 4 * q^68 + 16 * q^71 - 20 * q^72 - 10 * q^73 - 18 * q^74 - 26 * q^76 + 26 * q^78 + 22 * q^79 + 36 * q^80 - 22 * q^81 - 26 * q^82 - 40 * q^86 - 20 * q^87 + 14 * q^88 - 10 * q^89 - 26 * q^90 - 10 * q^92 + 42 * q^94 + 34 * q^95 + 16 * q^96 - 20 * q^97

Introduction

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