LMFDB - Embedded newform 177.6.d.b.176.19

Newspace parameters

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.d (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			176.19
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.20

$q$-expansion

$f(q)$	$=$	$q-7.43533 q^{2} +(-12.1962 - 9.70834i) q^{3} +23.2842 q^{4} +26.1059i q^{5} +(90.6831 + 72.1847i) q^{6} +171.796 q^{7} +64.8050 q^{8} +(54.4964 + 236.810i) q^{9} +O(q^{10})$	\(q-7.43533 q^{2} +(-12.1962 - 9.70834i) q^{3} +23.2842 q^{4} +26.1059i q^{5} +(90.6831 + 72.1847i) q^{6} +171.796 q^{7} +64.8050 q^{8} +(54.4964 + 236.810i) q^{9} -194.106i q^{10} +440.416 q^{11} +(-283.979 - 226.051i) q^{12} -280.019i q^{13} -1277.36 q^{14} +(253.445 - 318.393i) q^{15} -1226.94 q^{16} +1401.23i q^{17} +(-405.199 - 1760.76i) q^{18} +616.070 q^{19} +607.854i q^{20} +(-2095.26 - 1667.85i) q^{21} -3274.64 q^{22} -4168.15 q^{23} +(-790.378 - 629.149i) q^{24} +2443.48 q^{25} +2082.04i q^{26} +(1634.38 - 3417.26i) q^{27} +4000.13 q^{28} +6604.87i q^{29} +(-1884.44 + 2367.36i) q^{30} -5981.69i q^{31} +7048.95 q^{32} +(-5371.42 - 4275.71i) q^{33} -10418.6i q^{34} +4484.88i q^{35} +(1268.90 + 5513.93i) q^{36} -2032.97i q^{37} -4580.68 q^{38} +(-2718.52 + 3415.18i) q^{39} +1691.79i q^{40} +1979.58i q^{41} +(15579.0 + 12401.0i) q^{42} -2469.75i q^{43} +10254.7 q^{44} +(-6182.14 + 1422.68i) q^{45} +30991.6 q^{46} +4981.17 q^{47} +(14964.1 + 11911.6i) q^{48} +12706.9 q^{49} -18168.1 q^{50} +(13603.6 - 17089.7i) q^{51} -6520.02i q^{52} +36193.5i q^{53} +(-12152.2 + 25408.5i) q^{54} +11497.4i q^{55} +11133.2 q^{56} +(-7513.73 - 5981.01i) q^{57} -49109.4i q^{58} +(3990.97 - 26438.5i) q^{59} +(5901.25 - 7413.53i) q^{60} +76.2899i q^{61} +44475.8i q^{62} +(9362.26 + 40683.1i) q^{63} -13149.2 q^{64} +7310.15 q^{65} +(39938.3 + 31791.3i) q^{66} +43781.8i q^{67} +32626.4i q^{68} +(50835.7 + 40465.8i) q^{69} -33346.6i q^{70} -5732.24i q^{71} +(3531.64 + 15346.5i) q^{72} +79764.2i q^{73} +15115.8i q^{74} +(-29801.3 - 23722.2i) q^{75} +14344.7 q^{76} +75661.7 q^{77} +(20213.1 - 25393.0i) q^{78} -52467.3 q^{79} -32030.4i q^{80} +(-53109.3 + 25810.6i) q^{81} -14718.8i q^{82} -12824.6 q^{83} +(-48786.5 - 38834.6i) q^{84} -36580.2 q^{85} +18363.4i q^{86} +(64122.3 - 80554.5i) q^{87} +28541.2 q^{88} +91752.4 q^{89} +(45966.3 - 10578.1i) q^{90} -48106.2i q^{91} -97051.9 q^{92} +(-58072.2 + 72954.1i) q^{93} -37036.7 q^{94} +16083.0i q^{95} +(-85970.7 - 68433.6i) q^{96} -124010. i q^{97} -94479.7 q^{98} +(24001.1 + 104295. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} + O(q^{10}) $	$ 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} - 1244q^{12} + 1116q^{15} + 14724q^{16} + 1784q^{19} + 6388q^{21} - 8140q^{22} - 48208q^{25} - 6458q^{27} - 19092q^{28} - 20832q^{36} - 134984q^{45} + 51180q^{46} + 61720q^{48} + 174556q^{49} + 8332q^{51} + 236784q^{57} + 375208q^{60} - 429890q^{63} + 561472q^{64} - 11596q^{66} + 169948q^{75} + 111488q^{76} + 356264q^{78} + 180260q^{79} + 79554q^{81} + 269308q^{84} + 111028q^{85} - 318764q^{87} - 1242976q^{88} - 513608q^{94} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−7.43533			−1.31439			−0.657197	−	0.753719i	$-0.728258\pi$
$2$	−7.43533			−1.31439			−0.657197	+	0.753719i	$0.728258\pi$
$3$	−12.1962	−	9.70834i	−0.782389	−	0.622790i
$3$	−12.1962	−	9.70834i	−0.782389	−	0.622790i
$4$	23.2842			0.727631
$5$			26.1059i			0.466996i	0.972357	+	0.233498i	$0.0750172\pi$
$5$			26.1059i			0.466996i	−0.972357	+	0.233498i	$0.924983\pi$
$6$	90.6831	+	72.1847i	1.02837	+	0.818591i
$7$	171.796			1.32516			0.662579	−	0.748992i	$-0.269462\pi$
$7$	171.796			1.32516			0.662579	+	0.748992i	$0.269462\pi$
$8$	64.8050			0.358001
$9$	54.4964	+	236.810i	0.224265	+	0.974528i
$10$		−	194.106i		−	0.613816i
$11$	440.416			1.09744			0.548721	−	0.836006i	$-0.315115\pi$
$11$	440.416			1.09744			0.548721	+	0.836006i	$0.315115\pi$
$12$	−283.979	−	226.051i	−0.569290	−	0.453161i
$13$		−	280.019i		−	0.459547i	−0.973244	−	0.229773i	$-0.926201\pi$
$13$		−	280.019i		−	0.459547i	0.973244	−	0.229773i	$-0.0737985\pi$
$14$	−1277.36			−1.74178
$15$	253.445	−	318.393i	0.290840	−	0.365372i
$16$	−1226.94			−1.19818
$17$			1401.23i			1.17594i	0.808882	+	0.587971i	$0.200073\pi$
$17$			1401.23i			1.17594i	−0.808882	+	0.587971i	$0.799927\pi$
$18$	−405.199	−	1760.76i	−0.294772	−	1.28091i
$19$	616.070			0.391513			0.195756	−	0.980653i	$-0.437284\pi$
$19$	616.070			0.391513			0.195756	+	0.980653i	$0.437284\pi$
$20$			607.854i			0.339800i
$21$	−2095.26	−	1667.85i	−1.03679	−	0.825296i
$22$	−3274.64			−1.44247
$23$	−4168.15			−1.64295			−0.821473	−	0.570247i	$-0.806848\pi$
$23$	−4168.15			−1.64295			−0.821473	+	0.570247i	$0.806848\pi$
$24$	−790.378	−	629.149i	−0.280096	−	0.222959i
$25$	2443.48			0.781915
$26$			2082.04i			0.604026i
$27$	1634.38	−	3417.26i	0.431464	−	0.902130i
$28$	4000.13			0.964226
$29$			6604.87i			1.45837i	0.684314	+	0.729187i	$0.260102\pi$
$29$			6604.87i			1.45837i	−0.684314	+	0.729187i	$0.739898\pi$
$30$	−1884.44	+	2367.36i	−0.382279	+	0.480243i
$31$		−	5981.69i		−	1.11794i	−0.829187	−	0.558971i	$-0.811196\pi$
$31$		−	5981.69i		−	1.11794i	0.829187	−	0.558971i	$-0.188804\pi$
$32$	7048.95			1.21689
$33$	−5371.42	−	4275.71i	−0.858626	−	0.683476i
$34$		−	10418.6i		−	1.54565i
$35$			4484.88i			0.618844i
$36$	1268.90	+	5513.93i	0.163182	+	0.709096i
$37$		−	2032.97i		−	0.244133i	−0.992522	−	0.122067i	$-0.961048\pi$
$37$		−	2032.97i		−	0.244133i	0.992522	−	0.122067i	$-0.0389522\pi$
$38$	−4580.68			−0.514602
$39$	−2718.52	+	3415.18i	−0.286201	+	0.359544i
$40$			1691.79i			0.167185i
$41$			1979.58i			0.183913i	0.995763	+	0.0919567i	$0.0293121\pi$
$41$			1979.58i			0.183913i	−0.995763	+	0.0919567i	$0.970688\pi$
$42$	15579.0	+	12401.0i	1.36275	+	1.08476i
$43$		−	2469.75i		−	0.203695i	−0.994800	−	0.101848i	$-0.967525\pi$
$43$		−	2469.75i		−	0.203695i	0.994800	−	0.101848i	$-0.0324755\pi$
$44$	10254.7			0.798532
$45$	−6182.14	+	1422.68i	−0.455101	+	0.104731i
$46$	30991.6			2.15948
$47$	4981.17			0.328917			0.164459	−	0.986384i	$-0.447412\pi$
$47$	4981.17			0.328917			0.164459	+	0.986384i	$0.447412\pi$
$48$	14964.1	+	11911.6i	0.937446	+	0.746217i
$49$	12706.9			0.756046
$50$	−18168.1			−1.02774
$51$	13603.6	−	17089.7i	0.732365	−	0.920044i
$52$		−	6520.02i		−	0.334380i
$53$			36193.5i			1.76987i	0.465717	+	0.884934i	$0.345796\pi$
$53$			36193.5i			1.76987i	−0.465717	+	0.884934i	$0.654204\pi$
$54$	−12152.2	+	25408.5i	−0.567114	+	1.18575i
$55$			11497.4i			0.512501i
$56$	11133.2			0.474408
$57$	−7513.73	−	5981.01i	−0.306315	−	0.243830i
$58$		−	49109.4i		−	1.91688i
$59$	3990.97	−	26438.5i	0.149262	−	0.988798i
$59$	3990.97	−	26438.5i	0.149262	−	0.988798i
$60$	5901.25	−	7413.53i	0.211624	−	0.265856i
$61$			76.2899i			0.00262508i	0.999999	+	0.00131254i	$0.000417794\pi$
$61$			76.2899i			0.00262508i	−0.999999	+	0.00131254i	$0.999582\pi$
$62$			44475.8i			1.46942i
$63$	9362.26	+	40683.1i	0.297187	+	1.29140i
$64$	−13149.2			−0.401282
$65$	7310.15			0.214607
$66$	39938.3	+	31791.3i	1.12857	+	0.898356i
$67$			43781.8i			1.19154i	0.803157	+	0.595768i	$0.203152\pi$
$67$			43781.8i			1.19154i	−0.803157	+	0.595768i	$0.796848\pi$
$68$			32626.4i			0.855652i
$69$	50835.7	+	40465.8i	1.28542	+	1.02321i
$70$		−	33346.6i		−	0.813404i
$71$		−	5732.24i		−	0.134952i	−0.997721	−	0.0674759i	$-0.978505\pi$
$71$		−	5732.24i		−	0.134952i	0.997721	−	0.0674759i	$-0.0214946\pi$
$72$	3531.64	+	15346.5i	0.0802870	+	0.348882i
$73$			79764.2i			1.75187i	0.482432	+	0.875933i	$0.339753\pi$
$73$			79764.2i			1.75187i	−0.482432	+	0.875933i	$0.660247\pi$
$74$			15115.8i			0.320887i
$75$	−29801.3	−	23722.2i	−0.611762	−	0.486969i
$76$	14344.7			0.284877
$77$	75661.7			1.45428
$78$	20213.1	−	25393.0i	0.376181	−	0.472583i
$79$	−52467.3			−0.945847			−0.472924	−	0.881103i	$-0.656801\pi$
$79$	−52467.3			−0.945847			−0.472924	+	0.881103i	$0.656801\pi$
$80$		−	32030.4i		−	0.559547i
$81$	−53109.3	+	25810.6i	−0.899410	+	0.437105i
$82$		−	14718.8i		−	0.241735i
$83$	−12824.6			−0.204338			−0.102169	−	0.994767i	$-0.532578\pi$
$83$	−12824.6			−0.204338			−0.102169	+	0.994767i	$0.532578\pi$
$84$	−48786.5	−	38834.6i	−0.754400	−	0.600510i
$85$	−36580.2			−0.549160
$86$			18363.4i			0.267736i
$87$	64122.3	−	80554.5i	0.908261	−	1.14102i
$88$	28541.2			0.392885
$89$	91752.4			1.22784			0.613921	−	0.789367i	$-0.289591\pi$
$89$	91752.4			1.22784			0.613921	+	0.789367i	$0.289591\pi$
$90$	45966.3	−	10578.1i	0.598181	−	0.137658i
$91$		−	48106.2i		−	0.608973i
$92$	−97051.9			−1.19546
$93$	−58072.2	+	72954.1i	−0.696244	+	0.874666i
$94$	−37036.7			−0.432327
$95$			16083.0i			0.182835i
$96$	−85970.7	−	68433.6i	−0.952078	−	0.757864i
$97$		−	124010.i		−	1.33822i	−0.743163	−	0.669111i	$-0.766675\pi$
$97$		−	124010.i		−	1.33822i	0.743163	−	0.669111i	$-0.233325\pi$
$98$	−94479.7			−0.993742
$99$	24001.1	+	104295.i	0.246118	+	1.06949i
$100$	56894.5			0.568945
$101$	25569.9			0.249417			0.124709	−	0.992193i	$-0.460200\pi$
$101$	25569.9			0.249417			0.124709	+	0.992193i	$0.460200\pi$
$102$	−101147.	+	127068.i	−0.962616	+	1.20930i
$103$		−	144114.i		−	1.33848i	−0.743045	−	0.669242i	$-0.766619\pi$
$103$		−	144114.i		−	1.33848i	0.743045	−	0.669242i	$-0.233381\pi$
$104$		−	18146.7i		−	0.164518i
$105$	43540.8	−	54698.7i	0.385410	−	0.484177i
$106$		−	269111.i		−	2.32630i
$107$		−	65308.3i		−	0.551453i	−0.961236	−	0.275727i	$-0.911082\pi$
$107$		−	65308.3i		−	0.551453i	0.961236	−	0.275727i	$-0.0889184\pi$
$108$	38055.3	−	79568.2i	0.313946	−	0.656417i
$109$			113518.i			0.915166i	0.889167	+	0.457583i	$0.151285\pi$
$109$			113518.i			0.915166i	−0.889167	+	0.457583i	$0.848715\pi$
$110$		−	85487.3i		−	0.673628i
$111$	−19736.8	+	24794.6i	−0.152044	+	0.191007i
$112$	−210783.			−1.58778
$113$	−103901.			−0.765464			−0.382732	−	0.923859i	$-0.625017\pi$
$113$	−103901.			−0.765464			−0.382732	+	0.923859i	$0.625017\pi$
$114$	55867.1	+	44470.8i	0.402619	+	0.320489i
$115$		−	108813.i		−	0.767249i
$116$			153789.i			1.06116i
$117$	66311.5	−	15260.1i	0.447841	−	0.103060i
$118$	−29674.2	+	196579.i	−0.196189	+	1.29967i
$119$			240725.i			1.55831i
$120$	16424.5	−	20633.5i	0.104121	−	0.130804i
$121$	32915.4			0.204379
$122$		−	567.241i		−	0.00345039i
$123$	19218.4	−	24143.4i	0.114539	−	0.143892i
$124$		−	139279.i		−	0.813449i
$125$			145370.i			0.832147i
$126$	−69611.5	−	302492.i	−0.390620	−	1.69741i
$127$	239071.			1.31528			0.657639	−	0.753333i	$-0.271555\pi$
$127$	239071.			1.31528			0.657639	+	0.753333i	$0.271555\pi$
$128$	−127798.			−0.689443
$129$	−23977.1	+	30121.6i	−0.126860	+	0.159369i
$130$	−54353.4			−0.282077
$131$	−29466.1			−0.150019			−0.0750093	−	0.997183i	$-0.523899\pi$
$131$	−29466.1			−0.150019			−0.0750093	+	0.997183i	$0.523899\pi$
$132$	−125069.	−	99556.3i	−0.624763	−	0.497318i
$133$	105838.			0.518817
$134$		−	325532.i		−	1.56615i
$135$	89210.6	+	42667.0i	0.421291	+	0.201492i
$136$			90806.6i			0.420988i
$137$			320384.i			1.45837i	0.684314	+	0.729187i	$0.260102\pi$
$137$			320384.i			1.45837i	−0.684314	+	0.729187i	$0.739898\pi$
$138$	−377980.	−	300877.i	−1.68955	−	1.34490i
$139$	46413.4			0.203754			0.101877	−	0.994797i	$-0.467515\pi$
$139$	46413.4			0.203754			0.101877	+	0.994797i	$0.467515\pi$
$140$			104427.i			0.450290i
$141$	−60751.5	−	48358.9i	−0.257341	−	0.204846i
$142$			42621.1i			0.177380i
$143$		−	123325.i		−	0.504326i
$144$	−66863.9	−	290552.i	−0.268711	−	1.16766i
$145$	−172426.			−0.681055
$146$		−	593074.i		−	2.30264i
$147$	−154976.	−	123362.i	−0.591522	−	0.470858i
$148$		−	47336.1i		−	0.177639i
$149$	436747.			1.61163			0.805814	−	0.592169i	$-0.201728\pi$
$149$	436747.			1.61163			0.805814	+	0.592169i	$0.201728\pi$
$150$	221583.	+	176382.i	0.804095	+	0.640069i
$151$			440574.i			1.57245i	0.617942	+	0.786224i	$0.287967\pi$
$151$			440574.i			1.57245i	−0.617942	+	0.786224i	$0.712033\pi$
$152$	39924.4			0.140162
$153$	−331825.	+	76361.8i	−1.14599	+	0.263723i
$154$	−562570.			−1.91150
$155$	156157.			0.522075
$156$	−63298.6	+	79519.7i	−0.208249	+	0.261616i
$157$			254134.i			0.822836i	0.911447	+	0.411418i	$0.134966\pi$
$157$			254134.i			0.822836i	−0.911447	+	0.411418i	$0.865034\pi$
$158$	390112.			1.24322
$159$	351379.	−	441424.i	1.10226	−	1.38472i
$160$			184019.i			0.568280i
$161$	−716071.			−2.17717
$162$	394885.	−	191911.i	1.18218	−	0.574528i
$163$	−375888.			−1.10813			−0.554063	−	0.832475i	$-0.686923\pi$
$163$	−375888.			−1.10813			−0.554063	+	0.832475i	$0.686923\pi$
$164$			46092.9i			0.133821i
$165$	111621.	−	140226.i	0.319180	−	0.400975i
$166$	95355.3			0.268580
$167$			154944.i			0.429916i	0.976623	+	0.214958i	$0.0689614\pi$
$167$			154944.i			0.429916i	−0.976623	+	0.214958i	$0.931039\pi$
$168$	−135784.	−	108085.i	−0.371171	−	0.295456i
$169$	292882.			0.788817
$170$	271986.			0.721813
$171$	33573.6	+	145892.i	0.0878026	+	0.381540i
$172$		−	57506.0i		−	0.148215i
$173$	−262409.			−0.666597			−0.333298	−	0.942821i	$-0.608162\pi$
$173$	−262409.			−0.666597			−0.333298	+	0.942821i	$0.608162\pi$
$174$	−476771.	+	598950.i	−1.19381	+	1.49974i
$175$	419781.			1.03616
$176$	−540365.			−1.31494
$177$	−305349.	+	283705.i	−0.732594	+	0.680666i
$178$	−682210.			−1.61387
$179$	261369.			0.609708			0.304854	−	0.952399i	$-0.401392\pi$
$179$	261369.			0.609708			0.304854	+	0.952399i	$0.401392\pi$
$180$	−143946.	+	33125.8i	−0.331145	+	0.0762054i
$181$	134751.			0.305729			0.152865	−	0.988247i	$-0.451150\pi$
$181$	134751.			0.305729			0.152865	+	0.988247i	$0.451150\pi$
$182$			357686.i			0.800430i
$183$	740.648	−	930.450i	0.00163487	−	0.00205383i
$184$	−270117.			−0.588176
$185$	53072.5			0.114009
$186$	431786.	−	542438.i	0.915138	−	1.14966i
$187$			617123.i			1.29053i
$188$	115982.			0.239330
$189$	280781.	−	587072.i	0.571758	−	1.19547i
$190$		−	119583.i		−	0.240317i
$191$	848340.			1.68262			0.841311	−	0.540552i	$-0.181785\pi$
$191$	848340.			1.68262			0.841311	+	0.540552i	$0.181785\pi$
$192$	160371.	+	127657.i	0.313958	+	0.249914i
$193$	880120.			1.70078			0.850391	−	0.526152i	$-0.176366\pi$
$193$	880120.			1.70078			0.850391	+	0.526152i	$0.176366\pi$
$194$			922057.i			1.75895i
$195$	−89156.3	−	70969.4i	−0.167906	−	0.133655i
$196$	295869.			0.550122
$197$			100950.i			0.185329i	0.995697	+	0.0926643i	$0.0295383\pi$
$197$			100950.i			0.185329i	−0.995697	+	0.0926643i	$0.970462\pi$
$198$	−178456.	−	775469.i	−0.323496	−	1.40573i
$199$	321301.			0.575148			0.287574	−	0.957758i	$-0.407151\pi$
$199$	321301.			0.575148			0.287574	+	0.957758i	$0.407151\pi$
$200$	158350.			0.279926
$201$	425049.	−	533974.i	0.742076	−	0.932244i
$202$	−190121.			−0.327832
$203$			1.13469e6i			1.93258i
$204$	316748.	−	397919.i	0.532891	−	0.669452i
$205$	−51678.7			−0.0858868
$206$			1.07154e6i			1.75929i
$207$	−227149.	−	987060.i	−0.368455	−	1.60110i
$208$			343567.i			0.550622i
$209$	271327.			0.429663
$210$	−323740.	+	406703.i	−0.506580	+	0.636398i
$211$			1.10823e6i			1.71366i	0.515603	+	0.856828i	$0.327568\pi$
$211$			1.10823e6i			1.71366i	−0.515603	+	0.856828i	$0.672432\pi$
$212$			842735.i			1.28781i
$213$	−55650.6	+	69911.8i	−0.0840467	+	0.105585i
$214$			485589.i			0.724827i
$215$	64474.9			0.0951250
$216$	105916.	−	221456.i	0.154464	−	0.322963i
$217$		−	1.02763e6i		−	1.48145i
$218$		−	844047.i		−	1.20289i
$219$	774378.	−	972823.i	1.09105	−	1.37064i
$220$			267709.i			0.372911i
$221$	392371.			0.540401
$222$	146749.	−	184356.i	0.199845	−	0.251059i
$223$	890367.			1.19897			0.599483	−	0.800387i	$-0.295373\pi$
$223$	890367.			1.19897			0.599483	+	0.800387i	$0.295373\pi$
$224$	1.21098e6			1.61257
$225$	133161.	+	578642.i	0.175356	+	0.761998i
$226$	772540.			1.00612
$227$	−1.50924e6			−1.94398			−0.971991	−	0.235017i	$-0.924485\pi$
$227$	−1.50924e6			−1.94398			−0.971991	+	0.235017i	$0.924485\pi$
$228$	−174951.	−	139263.i	−0.222884	−	0.177418i
$229$			667818.i			0.841530i	0.907170	+	0.420765i	$0.138238\pi$
$229$			667818.i			0.841530i	−0.907170	+	0.420765i	$0.861762\pi$
$230$			809062.i			1.00847i
$231$	−922788.	−	734550.i	−1.13782	−	0.905714i
$232$			428029.i			0.522099i
$233$	−982501.			−1.18561			−0.592807	−	0.805345i	$-0.701980\pi$
$233$	−982501.			−1.18561			−0.592807	+	0.805345i	$0.701980\pi$
$234$	−493048.	+	113464.i	−0.588640	+	0.135462i
$235$			130038.i			0.153603i
$236$	92926.6	−	615600.i	0.108608	−	0.719479i
$237$	639904.	+	509370.i	0.740020	+	0.589064i
$238$		−	1.78987e6i		−	2.04823i
$239$		−	152933.i		−	0.173183i	−0.996244	−	0.0865917i	$-0.972402\pi$
$239$		−	152933.i		−	0.173183i	0.996244	−	0.0865917i	$-0.0275976\pi$
$240$	−310961.	+	390650.i	−0.348480	+	0.437784i
$241$	139801.			0.155048			0.0775241	−	0.996990i	$-0.475299\pi$
$241$	139801.			0.155048			0.0775241	+	0.996990i	$0.475299\pi$
$242$	−244737.			−0.268634
$243$	898312.	+	200810.i	0.975914	+	0.218158i
$244$			1776.35i			0.00191009i
$245$			331724.i			0.353070i
$246$	−142895.	+	179514.i	−0.150550	+	0.189131i
$247$		−	172512.i		−	0.179919i
$248$		−	387644.i		−	0.400224i
$249$	156412.	+	124506.i	0.159872	+	0.127260i
$250$		−	1.08088e6i		−	1.09377i
$251$			787440.i			0.788920i	0.918913	+	0.394460i	$0.129068\pi$
$251$			787440.i			0.788920i	−0.918913	+	0.394460i	$0.870932\pi$
$252$	217993.	+	947272.i	0.216242	+	0.939665i
$253$	−1.83572e6			−1.80304
$254$	−1.77757e6			−1.72879
$255$	446141.	+	355133.i	0.429657	+	0.342012i
$256$	1.37099e6			1.30748
$257$		−	381321.i		−	0.360129i	−0.983655	−	0.180064i	$-0.942369\pi$
$257$		−	381321.i		−	0.360129i	0.983655	−	0.180064i	$-0.0576306\pi$
$258$	178278.	−	223964.i	0.166743	−	0.209474i
$259$		−	349256.i		−	0.323515i
$260$	170211.			0.156154
$261$	−1.56410e6	+	359942.i	−1.42123	+	0.327062i
$262$	219090.			0.197183
$263$			234006.i			0.208611i	0.994545	+	0.104306i	$0.0332620\pi$
$263$			234006.i			0.208611i	−0.994545	+	0.104306i	$0.966738\pi$
$264$	−348095.	−	277087.i	−0.307389	−	0.244685i
$265$	−944862.			−0.826521
$266$	−786943.			−0.681929
$267$	−1.11903e6	−	890763.i	−0.960650	−	0.764688i
$268$			1.01942e6i			0.866997i
$269$	−275892.			−0.232466			−0.116233	−	0.993222i	$-0.537082\pi$
$269$	−275892.			−0.232466			−0.116233	+	0.993222i	$0.537082\pi$
$270$	−663311.	−	317243.i	−0.553742	−	0.264840i
$271$	2.13938e6			1.76956			0.884779	−	0.466012i	$-0.154310\pi$
$271$	2.13938e6			1.76956			0.884779	+	0.466012i	$0.154310\pi$
$272$		−	1.71922e6i		−	1.40900i
$273$	−467031.	+	586715.i	−0.379262	+	0.476453i
$274$		−	2.38216e6i		−	1.91688i
$275$	1.07615e6			0.858106
$276$	1.18367e6	+	942212.i	0.935313	+	0.744519i
$277$	−1.60167e6			−1.25422			−0.627109	−	0.778931i	$-0.715762\pi$
$277$	−1.60167e6			−1.25422			−0.627109	+	0.778931i	$0.715762\pi$
$278$	−345099.			−0.267813
$279$	1.41653e6	−	325980.i	1.08947	−	0.250715i
$280$			290643.i			0.221546i
$281$		−	255652.i		−	0.193145i	−0.995326	−	0.0965724i	$-0.969212\pi$
$281$		−	255652.i		−	0.193145i	0.995326	−	0.0965724i	$-0.0307879\pi$
$282$	451708.	+	359564.i	0.338248	+	0.269249i
$283$		−	2.43336e6i		−	1.80609i	−0.429541	−	0.903047i	$-0.641325\pi$
$283$		−	2.43336e6i		−	1.80609i	0.429541	−	0.903047i	$-0.358675\pi$
$284$		−	133471.i		−	0.0981951i
$285$	156140.	−	196153.i	0.113868	−	0.143048i
$286$			916963.i			0.662883i
$287$			340084.i			0.243715i
$288$	384142.	+	1.66926e6i	0.272905	+	1.18589i
$289$	−543579.			−0.382841
$290$	1.28204e6			0.895175
$291$	−1.20393e6	+	1.51246e6i	−0.833431	+	1.04701i
$292$			1.85724e6i			1.27471i
$293$		−	858924.i		−	0.584501i	−0.956342	−	0.292251i	$-0.905596\pi$
$293$		−	858924.i		−	0.584501i	0.956342	−	0.292251i	$-0.0944042\pi$
$294$	1.15230e6	+	917241.i	0.777492	+	0.618892i
$295$	690201.	+	104188.i	0.461764	+	0.0697047i
$296$		−	131747.i		−	0.0873999i
$297$	719809.	−	1.50502e6i	0.473507	−	0.990035i
$298$	−3.24736e6			−2.11831
$299$			1.16716e6i			0.755011i
$300$	−693899.	−	552351.i	−0.445136	−	0.354333i
$301$		−	424293.i		−	0.269929i
$302$		−	3.27581e6i		−	2.06682i
$303$	−311857.	−	248242.i	−0.195141	−	0.155335i
$304$	−755881.			−0.469105
$305$	−1991.61			−0.00122590
$306$	2.46723e6	−	567775.i	1.50628	−	0.346635i
$307$	239480.			0.145019			0.0725094	−	0.997368i	$-0.476899\pi$
$307$	239480.			0.145019			0.0725094	+	0.997368i	$0.476899\pi$
$308$	1.76172e6			1.05818
$309$	−1.39911e6	+	1.75765e6i	−0.833594	+	1.04721i
$310$	−1.16108e6			−0.686212
$311$			2.91324e6i			1.70795i	0.520312	+	0.853976i	$0.325816\pi$
$311$			2.91324e6i			1.70795i	−0.520312	+	0.853976i	$0.674184\pi$
$312$	−176174.	+	221321.i	−0.102460	+	0.128717i
$313$			1.30732e6i			0.754261i	0.926160	+	0.377130i	$0.123089\pi$
$313$			1.30732e6i			0.754261i	−0.926160	+	0.377130i	$0.876911\pi$
$314$		−	1.88957e6i		−	1.08153i
$315$	−1.06207e6	+	244410.i	−0.603081	+	0.138785i
$316$	−1.22166e6			−0.688227
$317$		−	2.26014e6i		−	1.26324i	−0.775277	−	0.631622i	$-0.782390\pi$
$317$		−	2.26014e6i		−	1.26324i	0.775277	−	0.631622i	$-0.217610\pi$
$318$	−2.61262e6	+	3.28214e6i	−1.44880	+	1.82007i
$319$			2.90889e6i			1.60048i
$320$		−	343271.i		−	0.187397i
$321$	−634035.	+	796515.i	−0.343440	+	0.431451i
$322$	5.32423e6			2.86165
$323$			863254.i			0.460397i
$324$	−1.23661e6	+	600979.i	−0.654438	+	0.318051i
$325$		−	684223.i		−	0.359327i
$326$	2.79485e6			1.45651
$327$	1.10207e6	−	1.38450e6i	0.569956	−	0.716016i
$328$			128287.i			0.0658411i
$329$	855745.			0.435868
$330$	−829940.	+	1.04262e6i	−0.419529	+	0.527039i
$331$	967839.			0.485549			0.242775	−	0.970083i	$-0.421942\pi$
$331$	967839.			0.485549			0.242775	+	0.970083i	$0.421942\pi$
$332$	−298611.			−0.148683
$333$	481429.	−	110790.i	0.237915	−	0.0547506i
$334$		−	1.15206e6i		−	0.565078i
$335$	−1.14296e6			−0.556442
$336$	2.57077e6	+	2.04636e6i	1.24227	+	0.988856i
$337$		−	3.29932e6i		−	1.58252i	−0.611479	−	0.791261i	$-0.709425\pi$
$337$		−	3.29932e6i		−	1.58252i	0.611479	−	0.791261i	$-0.290575\pi$
$338$	−2.17768e6			−1.03682
$339$	1.26720e6	+	1.00871e6i	0.598891	+	0.476723i
$340$	−851741.			−0.399586
$341$		−	2.63443e6i		−	1.22688i
$342$	−249631.	−	1.08475e6i	−0.115407	−	0.501494i
$343$	−704388.			−0.323278
$344$		−	160052.i		−	0.0729231i
$345$	−1.05639e6	+	1.32711e6i	−0.477835	+	0.600287i
$346$	1.95110e6			0.876171
$347$	−378954.			−0.168952			−0.0844760	−	0.996426i	$-0.526922\pi$
$347$	−378954.			−0.168952			−0.0844760	+	0.996426i	$0.526922\pi$
$348$	1.49303e6	−	1.87565e6i	0.660879	−	0.830238i
$349$			1.47081e6i			0.646388i	0.946333	+	0.323194i	$0.104757\pi$
$349$			1.47081e6i			0.646388i	−0.946333	+	0.323194i	$0.895243\pi$
$350$	−3.12121e6			−1.36192
$351$	−956901.	−	457659.i	−0.414571	−	0.198278i
$352$	3.10447e6			1.33546
$353$	877815.			0.374944			0.187472	−	0.982270i	$-0.439971\pi$
$353$	877815.			0.374944			0.187472	+	0.982270i	$0.439971\pi$
$354$	2.27037e6	−	2.10944e6i	0.962917	−	0.894662i
$355$	149645.			0.0630220
$356$	2.13638e6			0.893415
$357$	2.33704e6	−	2.93594e6i	0.970500	−	1.21920i
$358$	−1.94337e6			−0.801396
$359$		−	3.25620e6i		−	1.33344i	−0.745306	−	0.666722i	$-0.767697\pi$
$359$		−	3.25620e6i		−	1.33344i	0.745306	−	0.666722i	$-0.232303\pi$
$360$	−400634.	+	92196.6i	−0.162926	+	0.0374937i
$361$	−2.09656e6			−0.846718
$362$	−1.00192e6			−0.401849
$363$	−401444.	−	319554.i	−0.159904	−	0.127285i
$364$		−	1.12011e6i		−	0.443107i
$365$	−2.08231e6			−0.818115
$366$	−5506.96	+	6918.20i	−0.00214887	+	0.00269955i
$367$			3.59027e6i			1.39143i	0.718316	+	0.695717i	$0.244913\pi$
$367$			3.59027e6i			1.39143i	−0.718316	+	0.695717i	$0.755087\pi$
$368$	5.11407e6			1.96855
$369$	−468785.	+	107880.i	−0.179229	+	0.0412454i
$370$	−394612.			−0.149853
$371$			6.21790e6i			2.34536i
$372$	−1.35216e6	+	1.69868e6i	−0.506608	+	0.636434i
$373$	−1.15069e6			−0.428238			−0.214119	−	0.976808i	$-0.568688\pi$
$373$	−1.15069e6			−0.428238			−0.214119	+	0.976808i	$0.568688\pi$
$374$		−	4.58851e6i		−	1.69626i
$375$	1.41130e6	−	1.77297e6i	0.518253	−	0.651063i
$376$	322805.			0.117753
$377$	1.84949e6			0.670192
$378$	−2.08770e6	+	4.36508e6i	−0.751515	+	1.57131i
$379$	−238627.			−0.0853338			−0.0426669	−	0.999089i	$-0.513585\pi$
$379$	−238627.			−0.0853338			−0.0426669	+	0.999089i	$0.513585\pi$
$380$			374480.i			0.133036i
$381$	−2.91577e6	−	2.32098e6i	−1.02906	−	0.819142i
$382$	−6.30769e6			−2.21163
$383$			1.38488e6i			0.482410i	0.970474	+	0.241205i	$0.0775427\pi$
$383$			1.38488e6i			0.482410i	−0.970474	+	0.241205i	$0.922457\pi$
$384$	1.55865e6	+	1.24070e6i	0.539413	+	0.429378i
$385$			1.97521e6i			0.679145i
$386$	−6.54398e6			−2.23550
$387$	584862.	−	134592.i	0.198507	−	0.0456818i
$388$		−	2.88747e6i		−	0.973731i
$389$		−	1.44787e6i		−	0.485126i	−0.970136	−	0.242563i	$-0.922012\pi$
$389$		−	1.44787e6i		−	0.485126i	0.970136	−	0.242563i	$-0.0779880\pi$
$390$	662907.	+	527681.i	0.220694	+	0.175675i
$391$		−	5.84052e6i		−	1.93201i
$392$	823469.			0.270665
$393$	359376.	+	286067.i	0.117373	+	0.0934300i
$394$		−	750599.i		−	0.243595i
$395$		−	1.36970e6i		−	0.441707i
$396$	558846.	+	2.42843e6i	0.179083	+	0.778192i
$397$		−	856129.i		−	0.272623i	−0.990666	−	0.136312i	$-0.956475\pi$
$397$		−	856129.i		−	0.272623i	0.990666	−	0.136312i	$-0.0435248\pi$
$398$	−2.38898e6			−0.755971
$399$	−1.29083e6	−	1.02751e6i	−0.405916	−	0.323114i
$400$	−2.99801e6			−0.936878
$401$	−1.07592e6			−0.334133			−0.167066	−	0.985946i	$-0.553429\pi$
$401$	−1.07592e6			−0.334133			−0.167066	+	0.985946i	$0.553429\pi$
$402$	−3.16038e6	+	3.97027e6i	−0.975380	+	1.22534i
$403$	−1.67499e6			−0.513747
$404$	595375.			0.181484
$405$	−673809.	−	1.38646e6i	−0.204126	−	0.420021i
$406$		−	8.43680e6i		−	2.54017i
$407$		−	895354.i		−	0.267922i
$408$	881581.	−	1.10750e6i	0.262187	−	0.329377i
$409$			473425.i			0.139940i	0.997549	+	0.0699702i	$0.0222904\pi$
$409$			473425.i			0.139940i	−0.997549	+	0.0699702i	$0.977710\pi$
$410$	384248.			0.112889
$411$	3.11039e6	−	3.90748e6i	0.908261	−	1.14102i
$412$		−	3.35557e6i		−	0.973921i
$413$	685633.	−	4.54204e6i	0.197796	−	1.31031i
$414$	1.68893e6	+	7.33912e6i	0.484295	+	2.10447i
$415$		−	334798.i		−	0.0954250i
$416$		−	1.97384e6i		−	0.559216i
$417$	−566069.	−	450597.i	−0.159415	−	0.126896i
$418$	−2.01741e6			−0.564746
$419$	−2.63755e6			−0.733949			−0.366975	−	0.930231i	$-0.619606\pi$
$419$	−2.63755e6			−0.733949			−0.366975	+	0.930231i	$0.619606\pi$
$420$	1.01381e6	−	1.27361e6i	0.280436	−	0.352302i
$421$			224103.i			0.0616231i	0.999525	+	0.0308115i	$0.00980917\pi$
$421$			224103.i			0.0616231i	−0.999525	+	0.0308115i	$0.990191\pi$
$422$		−	8.24006e6i		−	2.25242i
$423$	271456.	+	1.17959e6i	0.0737646	+	0.320539i
$424$			2.34552e6i			0.633614i
$425$			3.42387e6i			0.919487i
$426$	413780.	−	519818.i	0.110470	−	0.138780i
$427$			13106.3i			0.00347865i
$428$		−	1.52065e6i		−	0.401254i
$429$	−1.19728e6	+	1.50410e6i	−0.314089	+	0.394579i
$430$	−479392.			−0.125032
$431$	5.10289e6			1.32319			0.661596	−	0.749860i	$-0.269879\pi$
$431$	5.10289e6			1.32319			0.661596	+	0.749860i	$0.269879\pi$
$432$	−2.00529e6	+	4.19278e6i	−0.516973	+	1.08092i
$433$	5.37069e6			1.37661			0.688304	−	0.725422i	$-0.258355\pi$
$433$	5.37069e6			1.37661			0.688304	+	0.725422i	$0.258355\pi$
$434$			7.64077e6i			1.94721i
$435$	2.10295e6	+	1.67397e6i	0.532850	+	0.424154i
$436$			2.64318e6i			0.665903i
$437$	−2.56787e6			−0.643235
$438$	−5.75776e6	+	7.23327e6i	−1.43406	+	1.80156i
$439$	919173.			0.227634			0.113817	−	0.993502i	$-0.463692\pi$
$439$	919173.			0.227634			0.113817	+	0.993502i	$0.463692\pi$
$440$			745092.i			0.183476i
$441$	692478.	+	3.00912e6i	0.169555	+	0.736788i
$442$	−2.91741e6			−0.710299
$443$	865376.			0.209505			0.104753	−	0.994498i	$-0.466595\pi$
$443$	865376.			0.209505			0.104753	+	0.994498i	$0.466595\pi$
$444$	−459555.	+	577322.i	−0.110632	+	0.138983i
$445$			2.39528e6i			0.573397i
$446$	−6.62018e6			−1.57591
$447$	−5.32667e6	−	4.24009e6i	−1.26092	−	1.00371i
$448$	−2.25898e6			−0.531762
$449$			254593.i			0.0595980i	0.999556	+	0.0297990i	$0.00948671\pi$
$449$			254593.i			0.0595980i	−0.999556	+	0.0297990i	$0.990513\pi$
$450$	−990097.	−	4.30240e6i	−0.230487	−	1.00157i
$451$			871839.i			0.201834i
$452$	−2.41926e6			−0.556975
$453$	4.27724e6	−	5.37334e6i	0.979305	−	1.23027i
$454$	1.12217e7			2.55516
$455$	1.25585e6			0.284388
$456$	−486928.	−	387600.i	−0.109661	−	0.0872914i
$457$			5.19163e6i			1.16282i	0.813610	+	0.581411i	$0.197499\pi$
$457$			5.19163e6i			1.16282i	−0.813610	+	0.581411i	$0.802501\pi$
$458$		−	4.96545e6i		−	1.10610i
$459$	4.78836e6	+	2.29014e6i	1.06085	+	0.507377i
$460$		−	2.53362e6i		−	0.558274i
$461$			6.10693e6i			1.33835i	0.743104	+	0.669176i	$0.233353\pi$
$461$			6.10693e6i			1.33835i	−0.743104	+	0.669176i	$0.766647\pi$
$462$	6.86124e6	+	5.46162e6i	1.49554	+	1.19046i
$463$		−	1.24942e6i		−	0.270866i	−0.990786	−	0.135433i	$-0.956757\pi$
$463$		−	1.24942e6i		−	0.270866i	0.990786	−	0.135433i	$-0.0432426\pi$
$464$		−	8.10378e6i		−	1.74740i
$465$	−1.90453e6	−	1.51603e6i	−0.408465	−	0.325143i
$466$	7.30522e6			1.55836
$467$	851634.			0.180701			0.0903506	−	0.995910i	$-0.471201\pi$
$467$	851634.			0.180701			0.0903506	+	0.995910i	$0.471201\pi$
$468$	1.54401e6	−	355318.i	0.325863	−	0.0749898i
$469$			7.52154e6i			1.57897i
$470$		−	966874.i		−	0.201895i
$471$	2.46722e6	−	3.09948e6i	0.512454	−	0.643778i
$472$	258635.	−	1.71335e6i	0.0534359	−	0.353990i
$473$		−	1.08772e6i		−	0.223544i
$474$	−4.75790e6	−	3.78734e6i	−0.972678	−	0.774262i
$475$	1.50536e6			0.306130
$476$			5.60509e6i			1.13387i
$477$	−8.57099e6	+	1.97241e6i	−1.72479	+	0.396919i
$478$			1.13711e6i			0.227631i
$479$			5.59727e6i			1.11465i	0.830295	+	0.557324i	$0.188172\pi$
$479$			5.59727e6i			1.11465i	−0.830295	+	0.557324i	$0.811828\pi$
$480$	1.78652e6	−	2.24434e6i	0.353919	−	0.444616i
$481$	−569272.			−0.112191
$482$	−1.03947e6			−0.203794
$483$	8.73337e6	+	6.95186e6i	1.70339	+	1.35592i
$484$	766408.			0.148712
$485$	3.23739e6			0.624944
$486$	−6.67925e6	−	1.49309e6i	−1.28273	−	0.286745i
$487$	−2.75944e6			−0.527229			−0.263614	−	0.964628i	$-0.584915\pi$
$487$	−2.75944e6			−0.527229			−0.263614	+	0.964628i	$0.584915\pi$
$488$			4943.97i			0.000939780i
$489$	4.58441e6	+	3.64924e6i	0.866985	+	0.690130i
$490$		−	2.46648e6i		−	0.464073i
$491$		−	8.15857e6i		−	1.52725i	−0.645659	−	0.763626i	$-0.723417\pi$
$491$		−	8.15857e6i		−	1.52725i	0.645659	−	0.763626i	$-0.276583\pi$
$492$	447485.	−	562160.i	0.0833424	−	0.104700i
$493$	−9.25492e6			−1.71496
$494$			1.28268e6i			0.236484i
$495$	−2.72271e6	+	626569.i	−0.499447	+	0.114936i
$496$			7.33918e6i			1.33950i
$497$		−	984777.i		−	0.178833i
$498$	−1.16298e6	−	925741.i	−0.210134	−	0.167269i
$499$	5.01897e6			0.902326			0.451163	−	0.892442i	$-0.351009\pi$
$499$	5.01897e6			0.902326			0.451163	+	0.892442i	$0.351009\pi$
$500$			3.38482e6i			0.605496i
$501$	1.50425e6	−	1.88973e6i	0.267747	−	0.336361i
$502$		−	5.85488e6i		−	1.03695i
$503$	−8.21342e6			−1.44745			−0.723726	−	0.690087i	$-0.757572\pi$
$503$	−8.21342e6			−1.44745			−0.723726	+	0.690087i	$0.757572\pi$
$504$	606722.	+	2.63647e6i	0.106393	+	0.462324i
$505$			667525.i			0.116477i
$506$	1.36492e7			2.36990
$507$	−3.57206e6	−	2.84340e6i	−0.617161	−	0.491267i
$508$	5.56657e6			0.957036
$509$	7.69651e6			1.31674			0.658369	−	0.752695i	$-0.271247\pi$
$509$	7.69651e6			1.31674			0.658369	+	0.752695i	$0.271247\pi$
$510$	−3.31721e6	−	2.64053e6i	−0.564738	−	0.449538i
$511$			1.37032e7i			2.32150i
$512$	−6.10426e6			−1.02910
$513$	1.00689e6	−	2.10527e6i	0.168924	−	0.353196i
$514$			2.83525e6i			0.473351i
$515$	3.76222e6			0.625066
$516$	−558288.	+	701357.i	−0.0923069	+	0.115962i
$517$	2.19379e6			0.360968
$518$			2.59684e6i			0.425227i
$519$	3.20040e6	+	2.54755e6i	0.521538	+	0.415150i
$520$	473735.			0.0768293
$521$		−	131488.i		−	0.0212222i	−0.999944	−	0.0106111i	$-0.996622\pi$
$521$		−	131488.i		−	0.0212222i	0.999944	−	0.0106111i	$-0.00337768\pi$
$522$	1.16296e7	−	2.67629e6i	1.86805	−	0.429889i
$523$	9.59429e6			1.53376			0.766882	−	0.641788i	$-0.221807\pi$
$523$	9.59429e6			1.53376			0.766882	+	0.641788i	$0.221807\pi$
$524$	−686095.			−0.109158
$525$	−5.11974e6	−	4.07537e6i	−0.810681	−	0.645311i
$526$		−	1.73991e6i		−	0.274197i
$527$	8.38170e6			1.31464
$528$	6.59041e6	+	5.24604e6i	1.02879	+	0.818930i
$529$	1.09371e7			1.69927
$530$	7.02537e6			1.08637
$531$	6.47841e6	−	495701.i	0.997085	−	0.0762928i
$532$	2.46436e6			0.377507
$533$	554321.			0.0845169
$534$	8.32039e6	+	6.62312e6i	1.26267	+	1.00510i
$535$	1.70493e6			0.257526
$536$			2.83728e6i			0.426570i
$537$	−3.18772e6	−	2.53746e6i	−0.477029	−	0.379720i
$538$	2.05135e6			0.305552
$539$	5.59631e6			0.829716
$540$	2.07720e6	+	993466.i	0.306544	+	0.146612i
$541$			4.10361e6i			0.602799i	0.953498	+	0.301400i	$0.0974538\pi$
$541$			4.10361e6i			0.602799i	−0.953498	+	0.301400i	$0.902546\pi$
$542$	−1.59070e7			−2.32589
$543$	−1.64346e6	−	1.30821e6i	−0.239199	−	0.190405i
$544$			9.87718e6i			1.43099i
$545$	−2.96350e6			−0.427379
$546$	3.47253e6	−	4.36242e6i	0.498500	−	0.626247i
$547$	−4.10117e6			−0.586057			−0.293028	−	0.956104i	$-0.594663\pi$
$547$	−4.10117e6			−0.586057			−0.293028	+	0.956104i	$0.594663\pi$
$548$			7.45987e6i			1.06116i
$549$	−18066.2	+	4157.52i	−0.00255821	+	0.000588713i
$550$	−8.00153e6			−1.12789
$551$			4.06906e6i			0.570972i
$552$	3.29441e6	+	2.62239e6i	0.460182	+	0.366310i
$553$	−9.01367e6			−1.25340
$554$	1.19089e7			1.64854
$555$	−647285.	−	515246.i	−0.0891996	−	0.0710038i
$556$	1.08070e6			0.148258
$557$		−	8.40721e6i		−	1.14819i	−0.818788	−	0.574095i	$-0.805354\pi$
$557$		−	8.40721e6i		−	1.14819i	0.818788	−	0.574095i	$-0.194646\pi$
$558$	−1.05323e7	+	2.42377e6i	−1.43199	+	0.329539i
$559$	−691577.			−0.0936076
$560$		−	5.50269e6i		−	0.741489i
$561$	5.99124e6	−	7.52658e6i	0.803728	−	1.00970i
$562$			1.90086e6i			0.253868i
$563$	−571838.			−0.0760329			−0.0380165	−	0.999277i	$-0.512104\pi$
$563$	−571838.			−0.0760329			−0.0380165	+	0.999277i	$0.512104\pi$
$564$	−1.41455e6	−	1.12600e6i	−0.187249	−	0.149052i
$565$		−	2.71243e6i		−	0.357469i
$566$			1.80929e7i			2.37392i
$567$	−9.12396e6	+	4.43416e6i	−1.19186	+	0.579234i
$568$		−	371478.i		−	0.0483129i
$569$	−1.04132e7			−1.34836			−0.674178	−	0.738569i	$-0.735502\pi$
$569$	−1.04132e7			−1.34836			−0.674178	+	0.738569i	$0.735502\pi$
$570$	−1.16095e6	+	1.45846e6i	−0.149667	+	0.188021i
$571$		−	1.52434e7i		−	1.95655i	−0.207307	−	0.978276i	$-0.566470\pi$
$571$		−	1.52434e7i		−	1.95655i	0.207307	−	0.978276i	$-0.433530\pi$
$572$		−	2.87152e6i		−	0.366963i
$573$	−1.03466e7	−	8.23597e6i	−1.31646	−	1.04792i
$574$		−	2.52864e6i		−	0.320337i
$575$	−1.01848e7			−1.28464
$576$	−716584.	−	3.11387e6i	−0.0899934	−	0.391060i
$577$	5.95811e6			0.745022			0.372511	−	0.928028i	$-0.378497\pi$
$577$	5.95811e6			0.745022			0.372511	+	0.928028i	$0.378497\pi$
$578$	4.04169e6			0.503203
$579$	−1.07341e7	−	8.54450e6i	−1.33067	−	1.05923i
$580$	−4.01479e6			−0.495557
$581$	−2.20322e6			−0.270780
$582$	8.95164e6	−	1.12456e7i	1.09546	−	1.37618i
$583$			1.59402e7i			1.94233i
$584$			5.16912e6i			0.627169i
$585$	398377.	+	1.73112e6i	0.0481287	+	0.209140i
$586$			6.38638e6i			0.768265i
$587$	−1.27267e7			−1.52448			−0.762240	−	0.647295i	$-0.775900\pi$
$587$	−1.27267e7			−1.52448			−0.762240	+	0.647295i	$0.775900\pi$
$588$	−3.60849e6	−	2.87239e6i	−0.430409	−	0.342610i
$589$		−	3.68514e6i		−	0.437689i
$590$	−5.13187e6	−	774671.i	−0.606940	−	0.0916194i
$591$	980060.	−	1.23121e6i	0.115421	−	0.144999i
$592$			2.49434e6i			0.292517i
$593$		−	1.95292e6i		−	0.228059i	−0.993477	−	0.114030i	$-0.963624\pi$
$593$		−	1.95292e6i		−	0.228059i	0.993477	−	0.114030i	$-0.0363758\pi$
$594$	−5.35202e6	+	1.11903e7i	−0.622374	+	1.30130i
$595$	−6.28434e6			−0.727725
$596$	1.01693e7			1.17267
$597$	−3.91867e6	−	3.11930e6i	−0.449990	−	0.358197i
$598$		−	8.67824e6i		−	0.992382i
$599$			1.05042e7i			1.19618i	0.801429	+	0.598091i	$0.204074\pi$
$599$			1.05042e7i			1.19618i	−0.801429	+	0.598091i	$0.795926\pi$
$600$	−1.93128e6	−	1.53732e6i	−0.219011	−	0.174335i
$601$			1.08997e6i			0.123091i	0.998104	+	0.0615457i	$0.0196030\pi$
$601$			1.08997e6i			0.123091i	−0.998104	+	0.0615457i	$0.980397\pi$
$602$			3.15476e6i			0.354793i
$603$	−1.03680e7	+	2.38595e6i	−1.16118	+	0.267220i
$604$			1.02584e7i			1.14416i
$605$			859285.i			0.0954440i
$606$	2.31876e6	+	1.84576e6i	0.256492	+	0.204171i
$607$	−1.03785e7			−1.14330			−0.571652	−	0.820496i	$-0.693697\pi$
$607$	−1.03785e7			−1.14330			−0.571652	+	0.820496i	$0.693697\pi$
$608$	4.34265e6			0.476426
$609$	1.10160e7	−	1.38389e7i	1.20359	−	1.51203i
$610$	14808.3			0.00161132
$611$		−	1.39482e6i		−	0.151153i
$612$	−7.72627e6	+	1.77802e6i	−0.833857	+	0.191893i
$613$		−	4.22332e6i		−	0.453945i	−0.973901	−	0.226972i	$-0.927117\pi$
$613$		−	4.22332e6i		−	0.453945i	0.973901	−	0.226972i	$-0.0728827\pi$
$614$	−1.78062e6			−0.190612
$615$	630285.	+	501714.i	0.0671969	+	0.0534895i
$616$	4.90326e6			0.520635
$617$			183600.i			0.0194160i	0.999953	+	0.00970802i	$0.00309021\pi$
$617$			183600.i			0.0194160i	−0.999953	+	0.00970802i	$0.996910\pi$
$618$	1.04028e7	−	1.30687e7i	1.09567	−	1.37645i
$619$	−1.53577e7			−1.61102			−0.805510	−	0.592583i	$-0.798108\pi$
$619$	−1.53577e7			−1.61102			−0.805510	+	0.592583i	$0.798108\pi$
$620$	3.63599e6			0.379877
$621$	−6.81235e6	+	1.42437e7i	−0.708872	+	1.48215i
$622$		−	2.16609e7i		−	2.24492i
$623$	1.57627e7			1.62709
$624$	3.33547e6	−	4.19023e6i	0.342922	−	0.430801i
$625$	3.84087e6			0.393306
$626$		−	9.72037e6i		−	0.991395i
$627$	−3.30917e6	−	2.63414e6i	−0.336163	−	0.267590i
$628$			5.91730e6i			0.598721i
$629$	2.84865e6			0.287087
$630$	7.89682e6	−	1.81727e6i	0.792685	−	0.182418i
$631$	−8.11179e6			−0.811042			−0.405521	−	0.914086i	$-0.632910\pi$
$631$	−8.11179e6			−0.811042			−0.405521	+	0.914086i	$0.632910\pi$
$632$	−3.40015e6			−0.338614
$633$	1.07591e7	−	1.35162e7i	1.06725	−	1.34075i
$634$			1.68049e7i			1.66040i
$635$			6.24115e6i			0.614229i
$636$	8.18156e6	−	1.02782e7i	0.802035	−	1.00757i
$637$		−	3.55817e6i		−	0.347438i
$638$		−	2.16286e7i		−	2.10366i
$639$	1.35745e6	−	312387.i	0.131514	−	0.0302650i
$640$		−	3.33627e6i		−	0.321967i
$641$		−	1.44500e7i		−	1.38907i	−0.719461	−	0.694533i	$-0.755611\pi$
$641$		−	1.44500e7i		−	1.38907i	0.719461	−	0.694533i	$-0.244389\pi$
$642$	4.71426e6	−	5.92235e6i	0.451415	−	0.567096i
$643$	−1.17789e7			−1.12352			−0.561758	−	0.827302i	$-0.689875\pi$
$643$	−1.17789e7			−1.12352			−0.561758	+	0.827302i	$0.689875\pi$
$644$	−1.66731e7			−1.58417
$645$	−786351.	−	625944.i	−0.0744247	−	0.0592429i
$646$		−	6.41858e6i		−	0.605142i
$647$			8.19790e6i			0.769914i	0.922935	+	0.384957i	$0.125784\pi$
$647$			8.19790e6i			0.769914i	−0.922935	+	0.384957i	$0.874216\pi$
$648$	−3.44175e6	+	1.67266e6i	−0.321990	+	0.156484i
$649$	1.75769e6	−	1.16440e7i	0.163806	−	1.08515i
$650$			5.08743e6i			0.472296i
$651$	−9.97658e6	+	1.25332e7i	−0.922633	+	1.15907i
$652$	−8.75223e6			−0.806306
$653$		−	1.14233e7i		−	1.04836i	−0.851608	−	0.524180i	$-0.824372\pi$
$653$		−	1.14233e7i		−	1.04836i	0.851608	−	0.524180i	$-0.175628\pi$
$654$	−8.19429e6	+	1.02942e7i	−0.749147	+	0.941127i
$655$		−	769239.i		−	0.0700580i
$656$		−	2.42883e6i		−	0.220362i
$657$	−1.88890e7	+	4.34686e6i	−1.70724	+	0.392882i
$658$	−6.36275e6			−0.572902
$659$	232316.			0.0208385			0.0104192	−	0.999946i	$-0.496683\pi$
$659$	232316.			0.0208385			0.0104192	+	0.999946i	$0.496683\pi$
$660$	2.59900e6	−	3.26504e6i	0.232245	−	0.291762i
$661$	5.99123e6			0.533350			0.266675	−	0.963787i	$-0.414075\pi$
$661$	5.99123e6			0.533350			0.266675	+	0.963787i	$0.414075\pi$
$662$	−7.19620e6			−0.638203
$663$	−4.78545e6	−	3.80927e6i	−0.422804	−	0.336556i
$664$	−831100.			−0.0731531
$665$			2.76300e6i			0.242285i
$666$	−3.57958e6	+	823758.i	−0.312714	+	0.0719638i
$667$		−	2.75301e7i		−	2.39603i
$668$			3.60774e6i			0.312820i
$669$	−1.08591e7	−	8.64399e6i	−0.938058	−	0.746705i
$670$	8.49831e6			0.731384
$671$			33599.3i			0.00288087i
$672$	−1.47694e7	−	1.17566e7i	−1.26165	−	1.00429i
$673$			7.42847e6i			0.632211i	0.948724	+	0.316105i	$0.102375\pi$
$673$			7.42847e6i			0.632211i	−0.948724	+	0.316105i	$0.897625\pi$
$674$			2.45315e7i			2.08006i
$675$	3.99359e6	−	8.35003e6i	0.337368	−	0.705389i
$676$	6.81952e6			0.573967
$677$		−	1.71931e6i		−	0.144173i	−0.997398	−	0.0720863i	$-0.977034\pi$
$677$		−	1.71931e6i		−	0.144173i	0.997398	−	0.0720863i	$-0.0229657\pi$
$678$	−9.42209e6	−	7.50008e6i	−0.787178	−	0.626602i
$679$		−	2.13045e7i		−	1.77336i
$680$	−2.37058e6			−0.196600
$681$	1.84070e7	+	1.46522e7i	1.52095	+	1.21069i
$682$			1.95879e7i			1.61260i
$683$	5.36526e6			0.440087			0.220044	−	0.975490i	$-0.429380\pi$
$683$	5.36526e6			0.440087			0.220044	+	0.975490i	$0.429380\pi$
$684$	781733.	+	3.39697e6i	0.0638879	+	0.277620i
$685$	−8.36389e6			−0.681055
$686$	5.23736e6			0.424915
$687$	6.48340e6	−	8.14487e6i	0.524097	−	0.658404i
$688$			3.03023e6i			0.244065i
$689$	1.01349e7			0.813337
$690$	7.85464e6	−	9.86751e6i	0.628064	−	0.789014i
$691$			4.91758e6i			0.391793i	0.980625	+	0.195896i	$0.0627616\pi$
$691$			4.91758e6i			0.391793i	−0.980625	+	0.195896i	$0.937238\pi$
$692$	−6.10998e6			−0.485036
$693$	4.12329e6	+	1.79175e7i	0.326145	+	1.41724i
$694$	2.81765e6			0.222069
$695$			1.21166e6i			0.0951524i
$696$	4.15545e6	−	5.22034e6i	0.325158	−	0.408485i
$697$	−2.77384e6			−0.216272
$698$		−	1.09360e7i		−	0.849608i
$699$	1.19828e7	+	9.53845e6i	0.927611	+	0.738388i
$700$	9.77425e6			0.753943
$701$	−1.87262e7			−1.43931			−0.719656	−	0.694331i	$-0.755700\pi$
$701$	−1.87262e7			−1.43931			−0.719656	+	0.694331i	$0.755700\pi$
$702$	7.11487e6	+	3.40285e6i	0.544910	+	0.260615i
$703$		−	1.25245e6i		−	0.0955813i
$704$	−5.79112e6			−0.440383
$705$	1.26245e6	−	1.58597e6i	0.0956624	−	0.120177i
$706$	−6.52685e6			−0.492824
$707$	4.39281e6			0.330517
$708$	−7.10980e6	+	6.60584e6i	−0.533058	+	0.495273i
$709$	3.13769e6			0.234420			0.117210	−	0.993107i	$-0.462605\pi$
$709$	3.13769e6			0.234420			0.117210	+	0.993107i	$0.462605\pi$
$710$	−1.11266e6			−0.0828357
$711$	−2.85928e6	−	1.24248e7i	−0.212120	−	0.921755i
$712$	5.94602e6			0.439568
$713$			2.49326e7i			1.83672i
$714$	−1.73767e7	+	2.18297e7i	−1.27562	+	1.60252i
$715$	3.21951e6			0.235518
$716$	6.08576e6			0.443642
$717$	−1.48473e6	+	1.86521e6i	−0.107857	+	0.135497i
$718$			2.42109e7i			1.75267i
$719$	−1.22765e7			−0.885633			−0.442816	−	0.896612i	$-0.646021\pi$
$719$	−1.22765e7			−0.885633			−0.442816	+	0.896612i	$0.646021\pi$
$720$	7.58512e6	−	1.74554e6i	0.545295	−	0.125487i
$721$		−	2.47582e7i		−	1.77370i
$722$	1.55886e7			1.11292
$723$	−1.70504e6	−	1.35723e6i	−0.121308	−	0.0965625i
$724$	3.13758e6			0.222458
$725$			1.61389e7i			1.14032i
$726$	2.98487e6	+	2.37599e6i	0.210176	+	0.167303i
$727$	2.24682e7			1.57664			0.788318	−	0.615268i	$-0.210952\pi$
$727$	2.24682e7			1.57664			0.788318	+	0.615268i	$0.210952\pi$
$728$		−	3.11753e6i		−	0.218013i
$729$	−9.00649e6	−	1.11702e7i	−0.627678	−	0.778473i
$730$	1.54827e7			1.07532
$731$	3.46068e6			0.239534
$732$	17245.4	−	21664.8i	0.00118958	−	0.00149443i
$733$	−1.67016e7			−1.14815			−0.574076	−	0.818802i	$-0.694638\pi$
$733$	−1.67016e7			−1.14815			−0.574076	+	0.818802i	$0.694638\pi$
$734$		−	2.66949e7i		−	1.82889i
$735$	3.22048e6	−	4.04578e6i	0.219889	−	0.276238i
$736$	−2.93811e7			−1.99928
$737$			1.92822e7i			1.30764i
$738$	3.48557e6	−	802124.i	0.235577	−	0.0542126i
$739$			9.90722e6i			0.667330i	0.942692	+	0.333665i	$0.108285\pi$
$739$			9.90722e6i			0.667330i	−0.942692	+	0.333665i	$0.891715\pi$
$740$	1.23575e6			0.0829566
$741$	−1.67480e6	+	2.10399e6i	−0.112051	+	0.140766i
$742$		−	4.62321e7i		−	3.08272i
$743$			9.99364e6i			0.664128i	0.943257	+	0.332064i	$0.107745\pi$
$743$			9.99364e6i			0.664128i	−0.943257	+	0.332064i	$0.892255\pi$
$744$	−3.76337e6	+	4.72779e6i	−0.249256	+	0.313131i
$745$			1.14017e7i			0.752623i
$746$	8.55573e6			0.562873
$747$	−698895.	−	3.03700e6i	−0.0458258	−	0.199133i
$748$			1.43692e7i			0.939028i
$749$		−	1.12197e7i		−	0.730763i
$750$	−1.04935e7	+	1.31826e7i	−0.681188	+	0.855753i
$751$		−	8.95464e6i		−	0.579360i	−0.957124	−	0.289680i	$-0.906451\pi$
$751$		−	8.95464e6i		−	0.579360i	0.957124	−	0.289680i	$-0.0935489\pi$
$752$	−6.11160e6			−0.394103
$753$	7.64473e6	−	9.60380e6i	0.491332	−	0.617242i
$754$	−1.37516e7			−0.880896
$755$	−1.15016e7			−0.734327
$756$	6.53774e6	−	1.36695e7i	0.416029	−	0.869857i
$757$	−3.54920e6			−0.225108			−0.112554	−	0.993646i	$-0.535903\pi$
$757$	−3.54920e6			−0.225108			−0.112554	+	0.993646i	$0.535903\pi$
$758$	1.77427e6			0.112162
$759$	2.23889e7	+	1.78218e7i	1.41068	+	1.12291i
$760$			1.04226e6i			0.0654550i
$761$		−	1.57471e7i		−	0.985687i	−0.870118	−	0.492843i	$-0.835958\pi$
$761$		−	1.57471e7i		−	0.985687i	0.870118	−	0.492843i	$-0.164042\pi$
$762$	2.16797e7	+	1.72573e7i	1.35259	+	1.07667i
$763$			1.95020e7i			1.21274i
$764$	1.97529e7			1.22433
$765$	−1.99349e6	−	8.66258e6i	−0.123157	−	0.535172i
$766$		−	1.02971e7i		−	0.634077i
$767$	−7.40331e6	−	1.11755e6i	−0.454399	−	0.0685928i
$768$	−1.67210e7	−	1.33101e7i	−1.02296	−	0.814286i
$769$			3.46575e6i			0.211340i	0.994401	+	0.105670i	$0.0336987\pi$
$769$			3.46575e6i			0.211340i	−0.994401	+	0.105670i	$0.966301\pi$
$770$		−	1.46864e7i		−	0.892664i
$771$	−3.70199e6	+	4.65068e6i	−0.224285	+	0.281761i
$772$	2.04929e7			1.23754
$773$	1.93604e7			1.16537			0.582687	−	0.812697i	$-0.302001\pi$
$773$	1.93604e7			1.16537			0.582687	+	0.812697i	$0.302001\pi$
$774$	−4.34864e6	+	1.00074e6i	−0.260916	+	0.0600438i
$775$		−	1.46162e7i		−	0.874136i
$776$		−	8.03649e6i		−	0.479084i
$777$	−3.39070e6	+	4.25961e6i	−0.201482	+	0.253115i
$778$			1.07654e7i			0.637646i
$779$			1.21956e6i			0.0720045i

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-7.43533 q^{2} +(-12.1962 - 9.70834i) q^{3} +23.2842 q^{4} +26.1059i q^{5} +(90.6831 + 72.1847i) q^{6} +171.796 q^{7} +64.8050 q^{8} +(54.4964 + 236.810i) q^{9} +O(q^{10})\)	\(q-7.43533 q^{2} +(-12.1962 - 9.70834i) q^{3} +23.2842 q^{4} +26.1059i q^{5} +(90.6831 + 72.1847i) q^{6} +171.796 q^{7} +64.8050 q^{8} +(54.4964 + 236.810i) q^{9} -194.106i q^{10} +440.416 q^{11} +(-283.979 - 226.051i) q^{12} -280.019i q^{13} -1277.36 q^{14} +(253.445 - 318.393i) q^{15} -1226.94 q^{16} +1401.23i q^{17} +(-405.199 - 1760.76i) q^{18} +616.070 q^{19} +607.854i q^{20} +(-2095.26 - 1667.85i) q^{21} -3274.64 q^{22} -4168.15 q^{23} +(-790.378 - 629.149i) q^{24} +2443.48 q^{25} +2082.04i q^{26} +(1634.38 - 3417.26i) q^{27} +4000.13 q^{28} +6604.87i q^{29} +(-1884.44 + 2367.36i) q^{30} -5981.69i q^{31} +7048.95 q^{32} +(-5371.42 - 4275.71i) q^{33} -10418.6i q^{34} +4484.88i q^{35} +(1268.90 + 5513.93i) q^{36} -2032.97i q^{37} -4580.68 q^{38} +(-2718.52 + 3415.18i) q^{39} +1691.79i q^{40} +1979.58i q^{41} +(15579.0 + 12401.0i) q^{42} -2469.75i q^{43} +10254.7 q^{44} +(-6182.14 + 1422.68i) q^{45} +30991.6 q^{46} +4981.17 q^{47} +(14964.1 + 11911.6i) q^{48} +12706.9 q^{49} -18168.1 q^{50} +(13603.6 - 17089.7i) q^{51} -6520.02i q^{52} +36193.5i q^{53} +(-12152.2 + 25408.5i) q^{54} +11497.4i q^{55} +11133.2 q^{56} +(-7513.73 - 5981.01i) q^{57} -49109.4i q^{58} +(3990.97 - 26438.5i) q^{59} +(5901.25 - 7413.53i) q^{60} +76.2899i q^{61} +44475.8i q^{62} +(9362.26 + 40683.1i) q^{63} -13149.2 q^{64} +7310.15 q^{65} +(39938.3 + 31791.3i) q^{66} +43781.8i q^{67} +32626.4i q^{68} +(50835.7 + 40465.8i) q^{69} -33346.6i q^{70} -5732.24i q^{71} +(3531.64 + 15346.5i) q^{72} +79764.2i q^{73} +15115.8i q^{74} +(-29801.3 - 23722.2i) q^{75} +14344.7 q^{76} +75661.7 q^{77} +(20213.1 - 25393.0i) q^{78} -52467.3 q^{79} -32030.4i q^{80} +(-53109.3 + 25810.6i) q^{81} -14718.8i q^{82} -12824.6 q^{83} +(-48786.5 - 38834.6i) q^{84} -36580.2 q^{85} +18363.4i q^{86} +(64122.3 - 80554.5i) q^{87} +28541.2 q^{88} +91752.4 q^{89} +(45966.3 - 10578.1i) q^{90} -48106.2i q^{91} -97051.9 q^{92} +(-58072.2 + 72954.1i) q^{93} -37036.7 q^{94} +16083.0i q^{95} +(-85970.7 - 68433.6i) q^{96} -124010. i q^{97} -94479.7 q^{98} +(24001.1 + 104295. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} + O(q^{10}) \)	\( 92q + 22q^{3} + 1724q^{4} - 80q^{7} + 2q^{9} - 1244q^{12} + 1116q^{15} + 14724q^{16} + 1784q^{19} + 6388q^{21} - 8140q^{22} - 48208q^{25} - 6458q^{27} - 19092q^{28} - 20832q^{36} - 134984q^{45} + 51180q^{46} + 61720q^{48} + 174556q^{49} + 8332q^{51} + 236784q^{57} + 375208q^{60} - 429890q^{63} + 561472q^{64} - 11596q^{66} + 169948q^{75} + 111488q^{76} + 356264q^{78} + 180260q^{79} + 79554q^{81} + 269308q^{84} + 111028q^{85} - 318764q^{87} - 1242976q^{88} - 513608q^{94} + O(q^{100}) \)

Introduction

L-functions

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