LMFDB - Embedded newform 147.4.c.b.146.17

Newspace parameters

Level:	$ N $	$=$	$ 147 = 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	147.c (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$8.67328077084$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			146.17
Character	$\chi$	$=$	147.146
Dual form			147.4.c.b.146.7

$q$-expansion

$f(q)$	$=$	$q+2.86969i q^{2} +(-2.76278 - 4.40080i) q^{3} -0.235115 q^{4} -5.57059 q^{5} +(12.6289 - 7.92832i) q^{6} +22.2828i q^{8} +(-11.7341 + 24.3169i) q^{9} +O(q^{10})$	\(q+2.86969i q^{2} +(-2.76278 - 4.40080i) q^{3} -0.235115 q^{4} -5.57059 q^{5} +(12.6289 - 7.92832i) q^{6} +22.2828i q^{8} +(-11.7341 + 24.3169i) q^{9} -15.9859i q^{10} -42.7198i q^{11} +(0.649571 + 1.03469i) q^{12} -69.8357i q^{13} +(15.3903 + 24.5151i) q^{15} -65.8256 q^{16} -67.5034 q^{17} +(-69.7819 - 33.6732i) q^{18} -79.3413i q^{19} +1.30973 q^{20} +122.593 q^{22} -208.831i q^{23} +(98.0622 - 61.5625i) q^{24} -93.9685 q^{25} +200.407 q^{26} +(139.432 - 15.5429i) q^{27} +5.72587i q^{29} +(-70.3506 + 44.1655i) q^{30} +193.293i q^{31} -10.6367i q^{32} +(-188.001 + 118.025i) q^{33} -193.714i q^{34} +(2.75886 - 5.71727i) q^{36} +163.609 q^{37} +227.685 q^{38} +(-307.333 + 192.941i) q^{39} -124.128i q^{40} -58.1164 q^{41} +58.9508 q^{43} +10.0441i q^{44} +(65.3658 - 135.460i) q^{45} +599.280 q^{46} -148.572 q^{47} +(181.862 + 289.685i) q^{48} -269.660i q^{50} +(186.497 + 297.069i) q^{51} +16.4194i q^{52} -100.642i q^{53} +(44.6034 + 400.128i) q^{54} +237.975i q^{55} +(-349.165 + 219.203i) q^{57} -16.4315 q^{58} -738.690 q^{59} +(-3.61850 - 5.76386i) q^{60} -356.946i q^{61} -554.692 q^{62} -496.081 q^{64} +389.026i q^{65} +(-338.696 - 539.505i) q^{66} +721.159 q^{67} +15.8711 q^{68} +(-919.024 + 576.955i) q^{69} +308.915i q^{71} +(-541.849 - 261.468i) q^{72} +827.134i q^{73} +469.506i q^{74} +(259.614 + 413.537i) q^{75} +18.6543i q^{76} +(-553.680 - 881.950i) q^{78} +467.203 q^{79} +366.688 q^{80} +(-453.623 - 570.673i) q^{81} -166.776i q^{82} +274.704 q^{83} +376.034 q^{85} +169.170i q^{86} +(25.1984 - 15.8193i) q^{87} +951.917 q^{88} -541.074 q^{89} +(388.727 + 187.579i) q^{90} +49.0993i q^{92} +(850.645 - 534.027i) q^{93} -426.355i q^{94} +441.978i q^{95} +(-46.8099 + 29.3868i) q^{96} -41.4658i q^{97} +(1038.81 + 501.277i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) $ 24 * q - 96 * q^4 - 64 * q^9	$ 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) $ 24 * q - 96 * q^4 - 64 * q^9 + 256 * q^15 + 864 * q^16 - 32 * q^18 - 384 * q^22 + 744 * q^25 - 1704 * q^30 + 584 * q^36 + 432 * q^37 - 2368 * q^39 - 624 * q^43 + 3744 * q^46 - 2160 * q^51 + 2032 * q^57 + 6384 * q^58 - 5832 * q^60 - 3504 * q^64 + 3792 * q^67 - 7472 * q^72 + 2248 * q^78 + 2784 * q^79 - 1968 * q^81 - 3744 * q^85 - 624 * q^88 - 3232 * q^93 + 1320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/147\mathbb{Z}\right)^\times$.

$n$	$50$	$52$
$\chi(n)$	$-1$	$-1$

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 $

$2$			2.86969i			1.01459i	0.861773	+	0.507294i	$0.169354\pi$
$2$			2.86969i			1.01459i	−0.861773	+	0.507294i	$0.830646\pi$
$3$	−2.76278	−	4.40080i	−0.531698	−	0.846934i
$3$	−2.76278	−	4.40080i	−0.531698	−	0.846934i
$4$	−0.235115			−0.0293894
$5$	−5.57059			−0.498249			−0.249124	−	0.968471i	$-0.580143\pi$
$5$	−5.57059			−0.498249			−0.249124	+	0.968471i	$0.580143\pi$
$6$	12.6289	−	7.92832i	0.859290	−	0.539454i
$7$		0			0
$7$		0			0
$8$			22.2828i			0.984770i
$9$	−11.7341	+	24.3169i	−0.434596	+	0.900626i
$10$		−	15.9859i		−	0.505517i
$11$		−	42.7198i		−	1.17095i	−0.810689	−	0.585477i	$-0.800907\pi$
$11$		−	42.7198i		−	1.17095i	0.810689	−	0.585477i	$-0.199093\pi$
$12$	0.649571	+	1.03469i	0.0156263	+	0.0248909i
$13$		−	69.8357i		−	1.48992i	−0.667110	−	0.744959i	$-0.732469\pi$
$13$		−	69.8357i		−	1.48992i	0.667110	−	0.744959i	$-0.267531\pi$
$14$		0			0
$15$	15.3903	+	24.5151i	0.264918	+	0.421984i
$16$	−65.8256			−1.02853
$17$	−67.5034			−0.963058			−0.481529	−	0.876430i	$-0.659918\pi$
$17$	−67.5034			−0.963058			−0.481529	+	0.876430i	$0.659918\pi$
$18$	−69.7819	−	33.6732i	−0.913764	−	0.440936i
$19$		−	79.3413i		−	0.958008i	−0.877813	−	0.479004i	$-0.840998\pi$
$19$		−	79.3413i		−	0.958008i	0.877813	−	0.479004i	$-0.159002\pi$
$20$	1.30973			0.0146432
$21$		0			0
$22$	122.593			1.18804
$23$		−	208.831i		−	1.89323i	−0.322365	−	0.946615i	$-0.604478\pi$
$23$		−	208.831i		−	1.89323i	0.322365	−	0.946615i	$-0.395522\pi$
$24$	98.0622	−	61.5625i	0.834036	−	0.523600i
$25$	−93.9685			−0.751748
$26$	200.407			1.51165
$27$	139.432	−	15.5429i	0.993844	−	0.110787i
$28$		0			0
$29$			5.72587i			0.0366644i	0.999832	+	0.0183322i	$0.00583564\pi$
$29$			5.72587i			0.0366644i	−0.999832	+	0.0183322i	$0.994164\pi$
$30$	−70.3506	+	44.1655i	−0.428140	+	0.268782i
$31$			193.293i			1.11989i	0.828531	+	0.559944i	$0.189177\pi$
$31$			193.293i			1.11989i	−0.828531	+	0.559944i	$0.810823\pi$
$32$		−	10.6367i		−	0.0587599i
$33$	−188.001	+	118.025i	−0.991722	+	0.622594i
$34$		−	193.714i		−	0.977108i
$35$		0			0
$36$	2.75886	−	5.71727i	0.0127725	−	0.0264688i
$37$	163.609			0.726949			0.363474	−	0.931604i	$-0.381590\pi$
$37$	163.609			0.726949			0.363474	+	0.931604i	$0.381590\pi$
$38$	227.685			0.971983
$39$	−307.333	+	192.941i	−1.26186	+	0.792186i
$40$		−	124.128i		−	0.490661i
$41$	−58.1164			−0.221372			−0.110686	−	0.993855i	$-0.535305\pi$
$41$	−58.1164			−0.221372			−0.110686	+	0.993855i	$0.535305\pi$
$42$		0			0
$43$	58.9508			0.209068			0.104534	−	0.994521i	$-0.466665\pi$
$43$	58.9508			0.209068			0.104534	+	0.994521i	$0.466665\pi$
$44$			10.0441i			0.0344136i
$45$	65.3658	−	135.460i	0.216537	−	0.448736i
$46$	599.280			1.92085
$47$	−148.572			−0.461094			−0.230547	−	0.973061i	$-0.574052\pi$
$47$	−148.572			−0.461094			−0.230547	+	0.973061i	$0.574052\pi$
$48$	181.862	+	289.685i	0.546865	+	0.871094i
$49$		0			0
$50$		−	269.660i		−	0.762715i
$51$	186.497	+	297.069i	0.512056	+	0.815647i
$52$			16.4194i			0.0437878i
$53$		−	100.642i		−	0.260834i	−0.991459	−	0.130417i	$-0.958368\pi$
$53$		−	100.642i		−	0.260834i	0.991459	−	0.130417i	$-0.0416316\pi$
$54$	44.6034	+	400.128i	0.112403	+	1.00834i
$55$			237.975i			0.583427i
$56$		0			0
$57$	−349.165	+	219.203i	−0.811370	+	0.509370i
$58$	−16.4315			−0.0371993
$59$	−738.690			−1.62999			−0.814994	−	0.579469i	$-0.803260\pi$
$59$	−738.690			−1.62999			−0.814994	+	0.579469i	$0.803260\pi$
$60$	−3.61850	−	5.76386i	−0.00778577	−	0.0124019i
$61$		−	356.946i		−	0.749218i	−0.927183	−	0.374609i	$-0.877777\pi$
$61$		−	356.946i		−	0.749218i	0.927183	−	0.374609i	$-0.122223\pi$
$62$	−554.692			−1.13622
$63$		0			0
$64$	−496.081			−0.968909
$65$			389.026i			0.742350i
$66$	−338.696	−	539.505i	−0.631676	−	1.00619i
$67$	721.159			1.31498			0.657489	−	0.753464i	$-0.271619\pi$
$67$	721.159			1.31498			0.657489	+	0.753464i	$0.271619\pi$
$68$	15.8711			0.0283037
$69$	−919.024	+	576.955i	−1.60344	+	1.00663i
$70$		0			0
$71$			308.915i			0.516359i	0.966097	+	0.258180i	$0.0831226\pi$
$71$			308.915i			0.516359i	−0.966097	+	0.258180i	$0.916877\pi$
$72$	−541.849	−	261.468i	−0.886909	−	0.427977i
$73$			827.134i			1.32615i	0.748555	+	0.663073i	$0.230748\pi$
$73$			827.134i			1.32615i	−0.748555	+	0.663073i	$0.769252\pi$
$74$			469.506i			0.737554i
$75$	259.614	+	413.537i	0.399703	+	0.636681i
$76$			18.6543i			0.0281552i
$77$		0			0
$78$	−553.680	−	881.950i	−0.803743	−	1.28027i
$79$	467.203			0.665373			0.332686	−	0.943038i	$-0.392045\pi$
$79$	467.203			0.665373			0.332686	+	0.943038i	$0.392045\pi$
$80$	366.688			0.512462
$81$	−453.623	−	570.673i	−0.622253	−	0.782816i
$82$		−	166.776i		−	0.224602i
$83$	274.704			0.363285			0.181643	−	0.983365i	$-0.441859\pi$
$83$	274.704			0.363285			0.181643	+	0.983365i	$0.441859\pi$
$84$		0			0
$85$	376.034			0.479843
$86$			169.170i			0.212118i
$87$	25.1984	−	15.8193i	0.0310523	−	0.0194944i
$88$	951.917			1.15312
$89$	−541.074			−0.644424			−0.322212	−	0.946668i	$-0.604426\pi$
$89$	−541.074			−0.644424			−0.322212	+	0.946668i	$0.604426\pi$
$90$	388.727	+	187.579i	0.455282	+	0.219696i
$91$		0			0
$92$			49.0993i			0.0556409i
$93$	850.645	−	534.027i	0.948471	−	0.595441i
$94$		−	426.355i		−	0.467821i
$95$			441.978i			0.477326i
$96$	−46.8099	+	29.3868i	−0.0497658	+	0.0312425i
$97$		−	41.4658i		−	0.0434042i	−0.999764	−	0.0217021i	$-0.993091\pi$
$97$		−	41.4658i		−	0.0434042i	0.999764	−	0.0217021i	$-0.00690854\pi$
$98$		0			0
$99$	1038.81	+	501.277i	1.05459	+	0.508892i
$100$	22.0934			0.0220934
$101$	1263.68			1.24496			0.622479	−	0.782637i	$-0.286126\pi$
$101$	1263.68			1.24496			0.622479	+	0.782637i	$0.286126\pi$
$102$	−852.496	+	535.189i	−0.827546	+	0.519526i
$103$		−	309.423i		−	0.296003i	−0.988987	−	0.148001i	$-0.952716\pi$
$103$		−	309.423i		−	0.296003i	0.988987	−	0.148001i	$-0.0472840\pi$
$104$	1556.14			1.46723
$105$		0			0
$106$	288.810			0.264639
$107$			895.715i			0.809272i	0.914478	+	0.404636i	$0.132602\pi$
$107$			895.715i			0.809272i	−0.914478	+	0.404636i	$0.867398\pi$
$108$	−32.7827	+	3.65438i	−0.0292085	+	0.00325595i
$109$	−1590.61			−1.39773			−0.698865	−	0.715254i	$-0.746311\pi$
$109$	−1590.61			−1.39773			−0.698865	+	0.715254i	$0.746311\pi$
$110$	−682.913			−0.591938
$111$	−452.015	−	720.009i	−0.386517	−	0.615678i
$112$		0			0
$113$		−	859.839i		−	0.715812i	−0.933758	−	0.357906i	$-0.883491\pi$
$113$		−	859.839i		−	0.715812i	0.933758	−	0.357906i	$-0.116509\pi$
$114$	−629.044	−	1002.00i	−0.516801	−	0.823206i
$115$			1163.31i			0.943300i
$116$		−	1.34624i		−	0.00107754i
$117$	1698.19	+	819.458i	1.34186	+	0.647512i
$118$		−	2119.81i		−	1.65377i
$119$		0			0
$120$	−546.264	+	342.940i	−0.415557	+	0.260883i
$121$	−493.980			−0.371135
$122$	1024.32			0.760147
$123$	160.563	+	255.759i	0.117703	+	0.187488i
$124$		−	45.4462i		−	0.0329128i
$125$	1219.78			0.872807
$126$		0			0
$127$	1382.66			0.966075			0.483038	−	0.875600i	$-0.339533\pi$
$127$	1382.66			0.966075			0.483038	+	0.875600i	$0.339533\pi$
$128$		−	1508.69i		−	1.04180i
$129$	−162.868	−	259.431i	−0.111161	−	0.177067i
$130$	−1116.38			−0.753180
$131$	879.895			0.586846			0.293423	−	0.955983i	$-0.405206\pi$
$131$	879.895			0.586846			0.293423	+	0.955983i	$0.405206\pi$
$132$	44.2019	−	27.7496i	0.0291461	−	0.0182976i
$133$		0			0
$134$			2069.50i			1.33416i
$135$	−776.721	+	86.5833i	−0.495182	+	0.0551993i
$136$		−	1504.17i		−	0.948391i
$137$		−	3037.41i		−	1.89419i	−0.320958	−	0.947093i	$-0.604005\pi$
$137$		−	3037.41i		−	1.89419i	0.320958	−	0.947093i	$-0.395995\pi$
$138$	−1655.68	−	2637.31i	−1.02131	−	1.62683i
$139$			652.162i			0.397954i	0.980004	+	0.198977i	$0.0637620\pi$
$139$			652.162i			0.397954i	−0.980004	+	0.198977i	$0.936238\pi$
$140$		0			0
$141$	410.472	+	653.835i	0.245163	+	0.390517i
$142$	−886.491			−0.523892
$143$	−2983.37			−1.74463
$144$	772.403	−	1600.68i	0.446993	−	0.926317i
$145$		−	31.8965i		−	0.0182680i
$146$	−2373.62			−1.34549
$147$		0			0
$148$	−38.4669			−0.0213646
$149$			395.474i			0.217440i	0.994072	+	0.108720i	$0.0346752\pi$
$149$			395.474i			0.217440i	−0.994072	+	0.108720i	$0.965325\pi$
$150$	−1186.72	+	745.013i	−0.645969	+	0.405534i
$151$	−705.128			−0.380017			−0.190008	−	0.981782i	$-0.560852\pi$
$151$	−705.128			−0.380017			−0.190008	+	0.981782i	$0.560852\pi$
$152$	1767.95			0.943417
$153$	792.091	−	1641.47i	0.418541	−	0.867355i
$154$		0			0
$155$		−	1076.76i		−	0.557983i
$156$	72.2586	−	45.3633i	0.0370854	−	0.0232819i
$157$		−	1597.79i		−	0.812214i	−0.913825	−	0.406107i	$-0.866886\pi$
$157$		−	1597.79i		−	0.812214i	0.913825	−	0.406107i	$-0.133114\pi$
$158$			1340.73i			0.675079i
$159$	−442.903	+	278.051i	−0.220909	+	0.138685i
$160$			59.2526i			0.0292771i
$161$		0			0
$162$	1637.65	−	1301.76i	0.794236	−	0.631331i
$163$	−2736.42			−1.31493			−0.657463	−	0.753487i	$-0.728370\pi$
$163$	−2736.42			−1.31493			−0.657463	+	0.753487i	$0.728370\pi$
$164$	13.6640			0.00650599
$165$	1047.28	−	657.472i	0.494124	−	0.310207i
$166$			788.315i			0.368585i
$167$	24.6732			0.0114328			0.00571638	−	0.999984i	$-0.498180\pi$
$167$	24.6732			0.0114328			0.00571638	+	0.999984i	$0.498180\pi$
$168$		0			0
$169$	−2680.03			−1.21986
$170$			1079.10i			0.486843i
$171$	1929.33	+	930.997i	0.862806	+	0.416346i
$172$	−13.8602			−0.00614437
$173$	−1403.61			−0.616847			−0.308424	−	0.951249i	$-0.599801\pi$
$173$	−1403.61			−0.616847			−0.308424	+	0.951249i	$0.599801\pi$
$174$	45.3965	+	72.3116i	0.0197787	+	0.0315053i
$175$		0			0
$176$			2812.06i			1.20436i
$177$	2040.84	+	3250.83i	0.866661	+	1.38049i
$178$		−	1552.71i		−	0.653825i
$179$			1714.52i			0.715919i	0.933737	+	0.357959i	$0.116527\pi$
$179$			1714.52i			0.715919i	−0.933737	+	0.357959i	$0.883473\pi$
$180$	−15.3685	+	31.8486i	−0.00636388	+	0.0131881i
$181$			2046.41i			0.840377i	0.907437	+	0.420189i	$0.138036\pi$
$181$			2046.41i			0.840377i	−0.907437	+	0.420189i	$0.861964\pi$
$182$		0			0
$183$	−1570.85	+	986.164i	−0.634538	+	0.398357i
$184$	4653.34			1.86440
$185$	−911.397			−0.362201
$186$	1532.49	+	2441.09i	0.604128	+	0.962307i
$187$			2883.73i			1.12770i
$188$	34.9315			0.0135513
$189$		0			0
$190$	−1268.34			−0.484290
$191$		−	3373.11i		−	1.27785i	−0.769268	−	0.638926i	$-0.779379\pi$
$191$		−	3373.11i		−	1.27785i	0.769268	−	0.638926i	$-0.220621\pi$
$192$	1370.56	+	2183.15i	0.515166	+	0.820602i
$193$	−424.928			−0.158482			−0.0792409	−	0.996855i	$-0.525250\pi$
$193$	−424.928			−0.158482			−0.0792409	+	0.996855i	$0.525250\pi$
$194$	118.994			0.0440374
$195$	1712.03	−	1074.79i	0.628722	−	0.394706i
$196$		0			0
$197$		−	4420.59i		−	1.59875i	−0.600832	−	0.799375i	$-0.705164\pi$
$197$		−	4420.59i		−	1.59875i	0.600832	−	0.799375i	$-0.294836\pi$
$198$	−1438.51	+	2981.07i	−0.516316	+	1.06998i
$199$			1577.80i			0.562046i	0.959701	+	0.281023i	$0.0906737\pi$
$199$			1577.80i			0.562046i	−0.959701	+	0.281023i	$0.909326\pi$
$200$		−	2093.88i		−	0.740299i
$201$	−1992.40	−	3173.67i	−0.699171	−	1.11370i
$202$			3626.36i			1.26312i
$203$		0			0
$204$	−43.8483	−	69.8454i	−0.0150490	−	0.0239714i
$205$	323.743			0.110298
$206$	887.946			0.300321
$207$	5078.13	+	2450.44i	1.70509	+	0.822790i
$208$			4596.98i			1.53242i
$209$	−3389.44			−1.12178
$210$		0			0
$211$	911.064			0.297252			0.148626	−	0.988893i	$-0.452515\pi$
$211$	911.064			0.297252			0.148626	+	0.988893i	$0.452515\pi$
$212$			23.6623i			0.00766574i
$213$	1359.47	−	853.465i	0.437322	−	0.274547i
$214$	−2570.42			−0.821078
$215$	−328.391			−0.104168
$216$	346.340	+	3106.95i	0.109099	+	0.978708i
$217$		0			0
$218$		−	4564.55i		−	1.41812i
$219$	3640.05	−	2285.19i	1.12316	−	0.705109i
$220$		−	55.9514i		−	0.0171466i
$221$			4714.15i			1.43488i
$222$	2066.20	−	1297.14i	0.624659	−	0.392155i
$223$			3070.23i			0.921964i	0.887410	+	0.460982i	$0.152503\pi$
$223$			3070.23i			0.921964i	−0.887410	+	0.460982i	$0.847497\pi$
$224$		0			0
$225$	1102.63	−	2285.02i	0.326706	−	0.677044i
$226$	2467.47			0.726255
$227$	3352.67			0.980284			0.490142	−	0.871643i	$-0.336945\pi$
$227$	3352.67			0.980284			0.490142	+	0.871643i	$0.336945\pi$
$228$	82.0940	−	51.5378i	0.0238456	−	0.0149701i
$229$		−	4353.50i		−	1.25628i	−0.778102	−	0.628138i	$-0.783817\pi$
$229$		−	4353.50i		−	1.25628i	0.778102	−	0.628138i	$-0.216183\pi$
$230$	−3338.35			−0.957061
$231$		0			0
$232$	−127.588			−0.0361060
$233$		−	3683.52i		−	1.03569i	−0.855475	−	0.517844i	$-0.826735\pi$
$233$		−	3683.52i		−	1.03569i	0.855475	−	0.517844i	$-0.173265\pi$
$234$	−2351.59	+	4873.27i	−0.656958	+	1.36143i
$235$	827.633			0.229740
$236$	173.677			0.0479043
$237$	−1290.78	−	2056.07i	−0.353777	−	0.563527i
$238$		0			0
$239$			4537.46i			1.22805i	0.789287	+	0.614025i	$0.210451\pi$
$239$			4537.46i			1.22805i	−0.789287	+	0.614025i	$0.789549\pi$
$240$	−1013.08	−	1613.72i	−0.272475	−	0.434021i
$241$		−	2221.10i		−	0.593666i	−0.954929	−	0.296833i	$-0.904069\pi$
$241$		−	2221.10i		−	0.593666i	0.954929	−	0.296833i	$-0.0959305\pi$
$242$		−	1417.57i		−	0.376549i
$243$	−1258.16	+	3572.95i	−0.332143	+	0.943229i
$244$			83.9234i			0.0220190i
$245$		0			0
$246$	−733.948	+	460.766i	−0.190223	+	0.119420i
$247$	−5540.86			−1.42735
$248$	−4307.12			−1.10283
$249$	−758.947	−	1208.92i	−0.193158	−	0.307679i
$250$			3500.40i			0.885539i
$251$	652.142			0.163995			0.0819976	−	0.996633i	$-0.473870\pi$
$251$	652.142			0.163995			0.0819976	+	0.996633i	$0.473870\pi$
$252$		0			0
$253$	−8921.22			−2.21689
$254$			3967.82i			0.980169i
$255$	−1038.90	−	1654.85i	−0.255131	−	0.406395i
$256$	360.828			0.0880927
$257$	6873.84			1.66840			0.834199	−	0.551464i	$-0.185931\pi$
$257$	6873.84			1.66840			0.834199	+	0.551464i	$0.185931\pi$
$258$	744.485	−	467.381i	0.179650	−	0.112782i
$259$		0			0
$260$		−	91.4659i		−	0.0218172i
$261$	−139.235	−	67.1878i	−0.0330209	−	0.0159342i
$262$			2525.03i			0.595407i
$263$		−	3285.60i		−	0.770337i	−0.922846	−	0.385169i	$-0.874143\pi$
$263$		−	3285.60i		−	0.770337i	0.922846	−	0.385169i	$-0.125857\pi$
$264$	−2629.94	−	4189.20i	−0.613112	−	0.976618i
$265$			560.633i			0.129960i
$266$		0			0
$267$	1494.87	+	2381.16i	0.342638	+	0.545785i
$268$	−169.555			−0.0386464
$269$	−1257.58			−0.285040			−0.142520	−	0.989792i	$-0.545521\pi$
$269$	−1257.58			−0.285040			−0.142520	+	0.989792i	$0.545521\pi$
$270$	−248.467	−	2228.95i	−0.0560046	−	0.502406i
$271$		−	370.755i		−	0.0831061i	−0.999136	−	0.0415530i	$-0.986769\pi$
$271$		−	370.755i		−	0.0831061i	0.999136	−	0.0415530i	$-0.0132306\pi$
$272$	4443.46			0.990530
$273$		0			0
$274$	8716.43			1.92182
$275$			4014.31i			0.880263i
$276$	216.076	−	135.651i	0.0471242	−	0.0295841i
$277$	−1540.16			−0.334078			−0.167039	−	0.985950i	$-0.553421\pi$
$277$	−1540.16			−0.334078			−0.167039	+	0.985950i	$0.553421\pi$
$278$	−1871.50			−0.403760
$279$	−4700.29	−	2268.12i	−1.00860	−	0.486698i
$280$		0			0
$281$			3782.78i			0.803066i	0.915845	+	0.401533i	$0.131522\pi$
$281$			3782.78i			0.803066i	−0.915845	+	0.401533i	$0.868478\pi$
$282$	−1876.30	+	1177.93i	−0.396214	+	0.248739i
$283$		−	9263.07i		−	1.94570i	−0.231441	−	0.972849i	$-0.574344\pi$
$283$		−	9263.07i		−	1.94570i	0.231441	−	0.972849i	$-0.425656\pi$
$284$		−	72.6306i		−	0.0151755i
$285$	1945.06	−	1221.09i	0.404264	−	0.253793i
$286$		−	8561.34i		−	1.77008i
$287$		0			0
$288$	258.651	+	124.812i	0.0529207	+	0.0255368i
$289$	−356.285			−0.0725187
$290$	91.5330			0.0185345
$291$	−182.482	+	114.561i	−0.0367605	+	0.0230779i
$292$		−	194.472i		−	0.0389746i
$293$	7316.39			1.45880			0.729399	−	0.684089i	$-0.239800\pi$
$293$	7316.39			1.45880			0.729399	+	0.684089i	$0.239800\pi$
$294$		0			0
$295$	4114.94			0.812140
$296$			3645.66i			0.715877i
$297$	−663.991	−	5956.53i	−0.129726	−	1.16375i
$298$	−1134.89			−0.220612
$299$	−14583.9			−2.82076
$300$	−61.0393	−	97.2287i	−0.0117470	−	0.0187117i
$301$		0			0
$302$		−	2023.50i		−	0.385561i
$303$	−3491.27	−	5561.20i	−0.661941	−	1.05440i
$304$			5222.69i			0.985335i
$305$			1988.40i			0.373297i
$306$	4710.52	+	2273.05i	0.880008	+	0.424647i
$307$		−	4347.69i		−	0.808260i	−0.914701	−	0.404130i	$-0.867574\pi$
$307$		−	4347.69i		−	0.808260i	0.914701	−	0.404130i	$-0.132426\pi$
$308$		0			0
$309$	−1361.71	+	854.867i	−0.250695	+	0.157384i
$310$	3089.96			0.566123
$311$	4550.35			0.829667			0.414833	−	0.909897i	$-0.363840\pi$
$311$	4550.35			0.829667			0.414833	+	0.909897i	$0.363840\pi$
$312$	−4299.26	−	6848.24i	−0.780121	−	1.24265i
$313$		−	8447.73i		−	1.52554i	−0.646670	−	0.762770i	$-0.723839\pi$
$313$		−	8447.73i		−	1.52554i	0.646670	−	0.762770i	$-0.276161\pi$
$314$	4585.17			0.824063
$315$		0			0
$316$	−109.846			−0.0195549
$317$			3333.54i			0.590632i	0.955400	+	0.295316i	$0.0954249\pi$
$317$			3333.54i			0.590632i	−0.955400	+	0.295316i	$0.904575\pi$
$318$	−797.919	−	1271.00i	−0.140708	−	0.224132i
$319$	244.608			0.0429323
$320$	2763.47			0.482758
$321$	3941.86	−	2474.67i	0.685400	−	0.430288i
$322$		0			0
$323$			5355.81i			0.922617i
$324$	106.654	+	134.174i	0.0182876	+	0.0230065i
$325$			6562.36i			1.12004i
$326$		−	7852.67i		−	1.33411i
$327$	4394.50	+	6999.94i	0.743169	+	1.18379i
$328$		−	1295.00i		−	0.218001i
$329$		0			0
$330$	1886.74	+	3005.36i	0.314732	+	0.501333i
$331$	−7496.89			−1.24491			−0.622457	−	0.782654i	$-0.713865\pi$
$331$	−7496.89			−1.24491			−0.622457	+	0.782654i	$0.713865\pi$
$332$	−64.5870			−0.0106767
$333$	−1919.80	+	3978.46i	−0.315929	+	0.654709i
$334$			70.8045i			0.0115996i
$335$	−4017.28			−0.655186
$336$		0			0
$337$	5107.78			0.825633			0.412817	−	0.910814i	$-0.364545\pi$
$337$	5107.78			0.825633			0.412817	+	0.910814i	$0.364545\pi$
$338$		−	7690.84i		−	1.23765i
$339$	−3783.98	+	2375.55i	−0.606246	+	0.380596i
$340$	−88.4113			−0.0141023
$341$	8257.45			1.31134
$342$	−2671.67	+	5536.59i	−0.422420	+	0.875393i
$343$		0			0
$344$			1313.59i			0.205884i
$345$	5119.51	−	3213.98i	0.798913	−	0.501550i
$346$		−	4027.93i		−	0.625846i
$347$			2966.35i			0.458910i	0.973319	+	0.229455i	$0.0736944\pi$
$347$			2966.35i			0.458910i	−0.973319	+	0.229455i	$0.926306\pi$
$348$	−5.92452	+	3.71936i	−0.000912608	+	0.000572927i
$349$		−	2869.90i		−	0.440178i	−0.975480	−	0.220089i	$-0.929365\pi$
$349$		−	2869.90i		−	0.440178i	0.975480	−	0.220089i	$-0.0706348\pi$
$350$		0			0
$351$	−1085.45	−	9737.37i	−0.165063	−	1.48075i
$352$	−454.397			−0.0688052
$353$	12653.2			1.90783			0.953913	−	0.300083i	$-0.0970143\pi$
$353$	12653.2			1.90783			0.953913	+	0.300083i	$0.0970143\pi$
$354$	−9328.87	+	5856.58i	−1.40063	+	0.879304i
$355$		−	1720.84i		−	0.257275i
$356$	127.215			0.0189392
$357$		0			0
$358$	−4920.15			−0.726363
$359$		−	6591.26i		−	0.969006i	−0.874790	−	0.484503i	$-0.839000\pi$
$359$		−	6591.26i		−	0.969006i	0.874790	−	0.484503i	$-0.161000\pi$
$360$	3018.42	+	1456.53i	0.441902	+	0.213239i
$361$	563.957			0.0822214
$362$	−5872.55			−0.852637
$363$	1364.76	+	2173.91i	0.197331	+	0.314327i
$364$		0			0
$365$		−	4607.62i		−	0.660751i
$366$	−2829.98	−	4507.85i	−0.404168	−	0.643795i
$367$			10286.0i			1.46301i	0.681836	+	0.731505i	$0.261182\pi$
$367$			10286.0i			1.46301i	−0.681836	+	0.731505i	$0.738818\pi$
$368$			13746.4i			1.94724i
$369$	681.943	−	1413.21i	0.0962074	−	0.199373i
$370$		−	2615.43i		−	0.367485i
$371$		0			0
$372$	−199.999	+	125.558i	−0.0278750	+	0.0174996i
$373$	4411.01			0.612314			0.306157	−	0.951981i	$-0.400957\pi$
$373$	4411.01			0.612314			0.306157	+	0.951981i	$0.400957\pi$
$374$	−8275.42			−1.14415
$375$	−3370.00	−	5368.03i	−0.464069	−	0.739210i
$376$		−	3310.60i		−	0.454072i
$377$	399.870			0.0546269
$378$		0			0
$379$	3838.27			0.520207			0.260103	−	0.965581i	$-0.416243\pi$
$379$	3838.27			0.520207			0.260103	+	0.965581i	$0.416243\pi$
$380$		−	103.916i		−	0.0140283i
$381$	−3820.00	−	6084.83i	−0.513660	−	0.818202i
$382$	9679.78			1.29649
$383$	2126.75			0.283739			0.141869	−	0.989885i	$-0.454689\pi$
$383$	2126.75			0.283739			0.141869	+	0.989885i	$0.454689\pi$
$384$	−6639.45	+	4168.19i	−0.882339	+	0.553924i
$385$		0			0
$386$		−	1219.41i		−	0.160794i
$387$	−691.733	+	1433.50i	−0.0908598	+	0.188292i
$388$			9.74922i			0.00127562i
$389$		−	7218.57i		−	0.940864i	−0.882436	−	0.470432i	$-0.844098\pi$
$389$		−	7218.57i		−	0.940864i	0.882436	−	0.470432i	$-0.155902\pi$
$390$	3084.33	+	4912.98i	0.400464	+	0.637894i
$391$			14096.8i			1.82329i
$392$		0			0
$393$	−2430.96	−	3872.24i	−0.312025	−	0.497020i
$394$	12685.7			1.62207
$395$	−2602.60			−0.331521
$396$	−244.240	−	117.858i	−0.0309938	−	0.0149560i
$397$			115.449i			0.0145950i	0.999973	+	0.00729750i	$0.00232289\pi$
$397$			115.449i			0.0145950i	−0.999973	+	0.00729750i	$0.997677\pi$
$398$	−4527.79			−0.570245
$399$		0			0
$400$	6185.54			0.773192
$401$			8905.68i			1.10905i	0.832168	+	0.554524i	$0.187100\pi$
$401$			8905.68i			1.10905i	−0.832168	+	0.554524i	$0.812900\pi$
$402$	9107.46	−	5717.58i	1.12995	−	0.709370i
$403$	13498.8			1.66854
$404$	−297.110			−0.0365885
$405$	2526.95	+	3178.99i	0.310037	+	0.390037i
$406$		0			0
$407$		−	6989.33i		−	0.851224i
$408$	−6619.53	+	4155.68i	−0.803225	+	0.504257i
$409$			6752.61i			0.816370i	0.912899	+	0.408185i	$0.133838\pi$
$409$			6752.61i			0.816370i	−0.912899	+	0.408185i	$0.866162\pi$
$410$			929.041i			0.111908i
$411$	−13367.0	+	8391.70i	−1.60425	+	1.00713i
$412$			72.7499i			0.00869934i
$413$		0			0
$414$	−7032.00	+	14572.6i	−0.834793	+	1.72997i
$415$	−1530.26			−0.181007
$416$	−742.820			−0.0875475
$417$	2870.04	−	1801.78i	0.337041	−	0.211591i
$418$		−	9726.65i		−	1.13815i
$419$	−888.062			−0.103543			−0.0517717	−	0.998659i	$-0.516487\pi$
$419$	−888.062			−0.103543			−0.0517717	+	0.998659i	$0.516487\pi$
$420$		0			0
$421$	−14976.0			−1.73369			−0.866847	−	0.498574i	$-0.833857\pi$
$421$	−14976.0			−1.73369			−0.866847	+	0.498574i	$0.833857\pi$
$422$			2614.47i			0.301589i
$423$	1743.35	−	3612.81i	0.200390	−	0.415273i
$424$	2242.58			0.256861
$425$	6343.20			0.723977
$426$	2449.18	+	3901.27i	0.278552	+	0.443702i
$427$		0			0
$428$		−	210.596i		−	0.0237840i
$429$	8242.39	+	13129.2i	0.927614	+	1.47758i
$430$		−	942.379i		−	0.105687i
$431$			1095.38i			0.122419i	0.998125	+	0.0612095i	$0.0194958\pi$
$431$			1095.38i			0.122419i	−0.998125	+	0.0612095i	$0.980504\pi$
$432$	−9178.23	+	1023.12i	−1.02219	+	0.113947i
$433$		−	12688.2i		−	1.40822i	−0.710093	−	0.704108i	$-0.751347\pi$
$433$		−	12688.2i		−	1.40822i	0.710093	−	0.704108i	$-0.248653\pi$
$434$		0			0
$435$	−140.370	+	88.1230i	−0.0154718	+	0.00971304i
$436$	373.976			0.0410784
$437$	−16568.9			−1.81373
$438$	6557.78	+	10445.8i	0.715395	+	1.13954i
$439$			13445.2i			1.46175i	0.682513	+	0.730873i	$0.260887\pi$
$439$			13445.2i			1.46175i	−0.682513	+	0.730873i	$0.739113\pi$
$440$	−5302.74			−0.574541
$441$		0			0
$442$	−13528.1			−1.45581
$443$			2276.97i			0.244204i	0.992518	+	0.122102i	$0.0389634\pi$
$443$			2276.97i			0.244204i	−0.992518	+	0.122102i	$0.961037\pi$
$444$	106.276	+	169.285i	0.0113595	+	0.0180944i
$445$	3014.10			0.321083
$446$	−8810.61			−0.935414
$447$	1740.40	−	1092.61i	0.184157	−	0.115612i
$448$		0			0
$449$			1685.89i			0.177198i	0.996067	+	0.0885991i	$0.0282390\pi$
$449$			1685.89i			0.177198i	−0.996067	+	0.0885991i	$0.971761\pi$
$450$	6557.30	+	3164.22i	0.686921	+	0.331472i
$451$			2482.72i			0.259217i
$452$			202.161i			0.0210373i
$453$	1948.12	+	3103.13i	0.202054	+	0.321849i
$454$			9621.12i			0.994585i
$455$		0			0
$456$	−4884.45	−	7780.38i	−0.501613	−	0.799013i
$457$	−2083.59			−0.213275			−0.106637	−	0.994298i	$-0.534008\pi$
$457$	−2083.59			−0.213275			−0.106637	+	0.994298i	$0.534008\pi$
$458$	12493.2			1.27460
$459$	−9412.17	+	1049.20i	−0.957130	+	0.106694i
$460$		−	273.512i		−	0.0277230i
$461$	−14128.1			−1.42736			−0.713679	−	0.700473i	$-0.752972\pi$
$461$	−14128.1			−1.42736			−0.713679	+	0.700473i	$0.752972\pi$
$462$		0			0
$463$	16141.5			1.62021			0.810106	−	0.586283i	$-0.199409\pi$
$463$	16141.5			1.62021			0.810106	+	0.586283i	$0.199409\pi$
$464$		−	376.909i		−	0.0377103i
$465$	−4738.60	+	2974.85i	−0.472575	+	0.296678i
$466$	10570.6			1.05080
$467$	6249.38			0.619244			0.309622	−	0.950860i	$-0.399797\pi$
$467$	6249.38			0.619244			0.309622	+	0.950860i	$0.399797\pi$
$468$	−399.269	−	192.667i	−0.0394364	−	0.0190300i
$469$		0			0
$470$			2375.05i			0.233091i
$471$	−7031.56	+	4414.35i	−0.687892	+	0.431852i
$472$		−	16460.1i		−	1.60516i
$473$		−	2518.36i		−	0.244809i
$474$	5900.27	−	3704.14i	0.571748	−	0.358938i
$475$			7455.58i			0.720180i
$476$		0			0
$477$	2447.29	+	1180.94i	0.234914	+	0.113357i
$478$	−13021.1			−1.24597
$479$	−10624.2			−1.01343			−0.506713	−	0.862115i	$-0.669140\pi$
$479$	−10624.2			−1.01343			−0.506713	+	0.862115i	$0.669140\pi$
$480$	260.759	−	163.702i	0.0247957	−	0.0155665i
$481$		−	11425.7i		−	1.08309i
$482$	6373.86			0.602327
$483$		0			0
$484$	116.142			0.0109074
$485$			230.989i			0.0216261i
$486$	−10253.2	−	3610.52i	−0.956989	−	0.336988i
$487$	−3970.15			−0.369414			−0.184707	−	0.982794i	$-0.559134\pi$
$487$	−3970.15			−0.369414			−0.184707	+	0.982794i	$0.559134\pi$
$488$	7953.76			0.737807
$489$	7560.13	+	12042.4i	0.699143	+	1.11366i
$490$		0			0
$491$			4184.69i			0.384628i	0.981333	+	0.192314i	$0.0615993\pi$
$491$			4184.69i			0.384628i	−0.981333	+	0.192314i	$0.938401\pi$
$492$	−37.7508	−	60.1327i	−0.00345922	−	0.00551015i
$493$		−	386.516i		−	0.0353099i
$494$		−	15900.5i		−	1.44818i
$495$	−5786.80	−	2792.41i	−0.525449	−	0.253555i
$496$		−	12723.7i		−	1.15183i
$497$		0			0
$498$	3469.22	−	2177.94i	0.312167	−	0.195976i
$499$	18462.3			1.65628			0.828141	−	0.560520i	$-0.189399\pi$
$499$	18462.3			1.65628			0.828141	+	0.560520i	$0.189399\pi$
$500$	−286.790			−0.0256512
$501$	−68.1668	−	108.582i	−0.00607877	−	0.00968280i
$502$			1871.44i			0.166388i
$503$	−11828.5			−1.04853			−0.524263	−	0.851557i	$-0.675659\pi$
$503$	−11828.5			−1.04853			−0.524263	+	0.851557i	$0.675659\pi$
$504$		0			0
$505$	−7039.44			−0.620299
$506$		−	25601.1i		−	2.24923i
$507$	7404.33	+	11794.3i	0.648595	+	1.03314i
$508$	−325.085			−0.0283924
$509$	797.139			0.0694157			0.0347078	−	0.999398i	$-0.488950\pi$
$509$	797.139			0.0694157			0.0347078	+	0.999398i	$0.488950\pi$
$510$	4748.91	−	2981.32i	0.412324	−	0.258853i
$511$		0			0
$512$		−	11034.1i		−	0.952425i
$513$	−1233.20	−	11062.8i	−0.106134	−	0.952110i
$514$			19725.8i			1.69274i
$515$			1723.67i			0.147483i
$516$	38.2927	+	60.9960i	0.00326694	+	0.00520388i
$517$			6346.96i			0.539921i
$518$		0			0
$519$	3877.87	+	6177.01i	0.327976	+	0.522429i
$520$	−8668.60			−0.731044
$521$	8365.75			0.703475			0.351737	−	0.936099i	$-0.385591\pi$
$521$	8365.75			0.703475			0.351737	+	0.936099i	$0.385591\pi$
$522$	192.808	−	399.562i	0.0161666	−	0.0335026i
$523$			3623.04i			0.302915i	0.988464	+	0.151457i	$0.0483966\pi$
$523$			3623.04i			0.302915i	−0.988464	+	0.151457i	$0.951603\pi$
$524$	−206.877			−0.0172470
$525$		0			0
$526$	9428.65			0.781575
$527$		−	13048.0i		−	1.07852i
$528$	12375.3	−	7769.10i	1.02001	−	0.640354i
$529$	−31443.4			−2.58432
$530$	−1608.84			−0.131856
$531$	8667.85	−	17962.7i	0.708386	−	1.46801i
$532$		0			0
$533$			4058.60i			0.329827i
$534$	−6833.18	+	4289.81i	−0.553747	+	0.347637i
$535$		−	4989.66i		−	0.403219i
$536$			16069.4i			1.29495i
$537$	7545.27	−	4736.85i	0.606336	−	0.380652i
$538$		−	3608.86i		−	0.289199i
$539$		0			0
$540$	182.619	−	20.3570i	0.0145531	−	0.00162227i
$541$	2220.96			0.176500			0.0882501	−	0.996098i	$-0.471873\pi$
$541$	2220.96			0.176500			0.0882501	+	0.996098i	$0.471873\pi$
$542$	1063.95			0.0843185
$543$	9005.83	−	5653.78i	0.711744	−	0.446826i
$544$			718.012i			0.0565892i
$545$	8860.62			0.696417
$546$		0			0
$547$	10592.4			0.827969			0.413985	−	0.910284i	$-0.364137\pi$
$547$	10592.4			0.827969			0.413985	+	0.910284i	$0.364137\pi$
$548$			714.141i			0.0556690i
$549$	8679.82	+	4188.43i	0.674765	+	0.325607i
$550$	−11519.8			−0.893104
$551$	454.298			0.0351248
$552$	−12856.2	−	20478.4i	−0.991295	−	1.57902i
$553$		0			0
$554$		−	4419.79i		−	0.338951i
$555$	2517.99	+	4010.88i	0.192582	+	0.306761i
$556$		−	153.333i		−	0.0116956i
$557$			989.584i			0.0752783i	0.999291	+	0.0376392i	$0.0119837\pi$
$557$			989.584i			0.0752783i	−0.999291	+	0.0376392i	$0.988016\pi$
$558$	6508.80	−	13488.4i	0.493798	−	1.02331i
$559$		−	4116.87i		−	0.311494i
$560$		0			0
$561$	12690.7	−	7967.12i	0.955086	−	0.599594i
$562$	−10855.4			−0.814781
$563$	16789.7			1.25684			0.628422	−	0.777872i	$-0.283701\pi$
$563$	16789.7			1.25684			0.628422	+	0.777872i	$0.283701\pi$
$564$	−96.5080	−	153.726i	−0.00720518	−	0.0114770i
$565$			4789.81i			0.356653i
$566$	26582.1			1.97408
$567$		0			0
$568$	−6883.50			−0.508495
$569$			11077.7i			0.816174i	0.912943	+	0.408087i	$0.133804\pi$
$569$			11077.7i			0.816174i	−0.912943	+	0.408087i	$0.866196\pi$
$570$	3504.14	+	5581.71i	0.257496	+	0.410161i
$571$	−4213.19			−0.308785			−0.154393	−	0.988010i	$-0.549342\pi$
$571$	−4213.19			−0.308785			−0.154393	+	0.988010i	$0.549342\pi$
$572$	701.434			0.0512735
$573$	−14844.4	+	9319.17i	−1.08226	+	0.679431i
$574$		0			0
$575$			19623.6i			1.42323i
$576$	5821.06	−	12063.2i	0.421083	−	0.872624i
$577$			1676.34i			0.120948i	0.998170	+	0.0604738i	$0.0192612\pi$
$577$			1676.34i			0.120948i	−0.998170	+	0.0604738i	$0.980739\pi$
$578$		−	1022.43i		−	0.0735767i
$579$	1173.98	+	1870.02i	0.0842644	+	0.134224i
$580$			7.49934i			0.000536885i
$581$		0			0
$582$	−328.754	−	523.668i	−0.0234146	−	0.0372968i
$583$	−4299.39			−0.305424
$584$	−18430.9			−1.30595
$585$	−9459.91	−	4564.86i	−0.668580	−	0.322622i
$586$			20995.8i			1.48008i
$587$	22687.3			1.59524			0.797620	−	0.603161i	$-0.206092\pi$
$587$	22687.3			1.59524			0.797620	+	0.603161i	$0.206092\pi$
$588$		0			0
$589$	15336.1			1.07286
$590$			11808.6i			0.823988i
$591$	−19454.1	+	12213.1i	−1.35404	+	0.850052i
$592$	−10769.6			−0.747685
$593$	−17961.5			−1.24383			−0.621916	−	0.783084i	$-0.713645\pi$
$593$	−17961.5			−1.24383			−0.621916	+	0.783084i	$0.713645\pi$
$594$	17093.4	−	1905.45i	1.18072	−	0.131619i
$595$		0			0
$596$		−	92.9820i		−	0.00639042i
$597$	6943.57	−	4359.11i	0.476016	−	0.298838i
$598$		−	41851.2i		−	2.86191i
$599$		−	6899.45i		−	0.470624i	−0.971920	−	0.235312i	$-0.924389\pi$
$599$		−	6899.45i		−	0.470624i	0.971920	−	0.235312i	$-0.0756112\pi$
$600$	−9214.76	+	5784.94i	−0.626985	+	0.393615i
$601$		−	19792.8i		−	1.34337i	−0.740838	−	0.671684i	$-0.765571\pi$
$601$		−	19792.8i		−	1.34337i	0.740838	−	0.671684i	$-0.234429\pi$
$602$		0			0
$603$	−8462.13	+	17536.3i	−0.571484	+	1.18430i
$604$	165.786			0.0111685
$605$	2751.76			0.184918
$606$	15958.9	−	10018.9i	1.06978	−	0.671597i
$607$		−	17838.2i		−	1.19280i	−0.802688	−	0.596399i	$-0.796598\pi$
$607$		−	17838.2i		−	1.19280i	0.802688	−	0.596399i	$-0.203402\pi$
$608$	−843.928			−0.0562924
$609$		0			0
$610$	−5706.09			−0.378743
$611$			10375.6i			0.686993i
$612$	−186.232	+	385.935i	−0.0123007	+	0.0254910i
$613$	6785.09			0.447059			0.223530	−	0.974697i	$-0.428242\pi$
$613$	6785.09			0.447059			0.223530	+	0.974697i	$0.428242\pi$
$614$	12476.5			0.820052
$615$	−894.431	−	1424.73i	−0.0586454	−	0.0934155i
$616$		0			0
$617$			3472.07i			0.226549i	0.993564	+	0.113274i	$0.0361339\pi$
$617$			3472.07i			0.226549i	−0.993564	+	0.113274i	$0.963866\pi$
$618$	−2453.20	−	3907.67i	−0.159680	−	0.254352i
$619$		−	7359.94i		−	0.477901i	−0.971032	−	0.238951i	$-0.923197\pi$
$619$		−	7359.94i		−	0.477901i	0.971032	−	0.238951i	$-0.0768034\pi$
$620$			253.162i			0.0163988i
$621$	−3245.85	−	29117.8i	−0.209745	−	1.88158i
$622$			13058.1i			0.841770i
$623$		0			0
$624$	20230.4	−	12700.5i	1.29786	−	0.814784i
$625$	4951.14			0.316873
$626$	24242.4			1.54780
$627$	9364.29	+	14916.3i	0.596449	+	0.950077i
$628$			375.665i			0.0238705i
$629$	−11044.2			−0.700094
$630$		0			0
$631$	−14566.0			−0.918957			−0.459479	−	0.888189i	$-0.651964\pi$
$631$	−14566.0			−0.918957			−0.459479	+	0.888189i	$0.651964\pi$
$632$			10410.6i			0.655239i
$633$	−2517.07	−	4009.41i	−0.158048	−	0.251753i
$634$	−9566.23			−0.599248
$635$	−7702.26			−0.481346
$636$	104.133	−	65.3739i	0.00649238	−	0.00407585i
$637$		0			0
$638$			701.949i			0.0435586i
$639$	−7511.86	−	3624.84i	−0.465046	−	0.224407i
$640$			8404.31i			0.519077i
$641$			2089.00i			0.128722i	0.997927	+	0.0643609i	$0.0205009\pi$
$641$			2089.00i			0.128722i	−0.997927	+	0.0643609i	$0.979499\pi$
$642$	7101.52	+	11311.9i	0.436565	+	0.695399i
$643$			9732.76i			0.596925i	0.954421	+	0.298462i	$0.0964737\pi$
$643$			9732.76i			0.596925i	−0.954421	+	0.298462i	$0.903526\pi$
$644$		0			0
$645$	907.272	+	1445.18i	0.0553857	+	0.0882232i
$646$	−15369.5			−0.936077
$647$	−18491.0			−1.12358			−0.561790	−	0.827280i	$-0.689887\pi$
$647$	−18491.0			−1.12358			−0.561790	+	0.827280i	$0.689887\pi$
$648$	12716.2	−	10108.0i	0.770894	−	0.612777i
$649$			31556.7i			1.90864i
$650$	−18831.9			−1.13638
$651$		0			0
$652$	643.373			0.0386449
$653$			5592.68i			0.335158i	0.985859	+	0.167579i	$0.0535950\pi$
$653$			5592.68i			0.335158i	−0.985859	+	0.167579i	$0.946405\pi$
$654$	−20087.7	+	12610.8i	−1.20105	+	0.754011i
$655$	−4901.54			−0.292395
$656$	3825.55			0.227687
$657$	−20113.3	−	9705.65i	−1.19436	−	0.576337i
$658$		0			0
$659$		−	9543.49i		−	0.564130i	−0.959395	−	0.282065i	$-0.908981\pi$
$659$		−	9543.49i		−	0.564130i	0.959395	−	0.282065i	$-0.0910193\pi$
$660$	−246.231	+	154.581i	−0.0145220	+	0.00911678i
$661$		−	6778.91i		−	0.398894i	−0.979909	−	0.199447i	$-0.936085\pi$
$661$		−	6778.91i		−	0.398894i	0.979909	−	0.199447i	$-0.0639146\pi$
$662$		−	21513.7i		−	1.26307i
$663$	20746.0	−	13024.2i	1.21525	−	0.762921i
$664$			6121.18i			0.357753i
$665$		0			0
$666$	−11416.9	−	5509.22i	−0.664260	−	0.320538i
$667$	1195.74			0.0694141
$668$	−5.80105			−0.000336002
$669$	13511.5	−	8482.38i	0.780843	−	0.490206i
$670$		−	11528.3i		−	0.664744i
$671$	−15248.7			−0.877300
$672$		0			0
$673$	−25094.5			−1.43733			−0.718663	−	0.695359i	$-0.755246\pi$
$673$	−25094.5			−1.43733			−0.718663	+	0.695359i	$0.755246\pi$
$674$			14657.7i			0.837678i
$675$	−13102.3	+	1460.55i	−0.747120	+	0.0832836i
$676$	630.114			0.0358508
$677$	−26332.2			−1.49487			−0.747435	−	0.664335i	$-0.768715\pi$
$677$	−26332.2			−1.49487			−0.747435	+	0.664335i	$0.768715\pi$
$678$	−6817.08	−	10858.8i	−0.386148	−	0.615090i
$679$		0			0
$680$			8379.10i			0.472535i
$681$	−9262.69	−	14754.4i	−0.521214	−	0.830236i
$682$			23696.3i			1.33047i
$683$			2346.73i			0.131472i	0.997837	+	0.0657359i	$0.0209395\pi$
$683$			2346.73i			0.131472i	−0.997837	+	0.0657359i	$0.979061\pi$
$684$	−453.615	−	218.891i	−0.0253573	−	0.0122361i
$685$			16920.2i			0.943777i
$686$		0			0
$687$	−19158.9	+	12027.8i	−1.06398	+	0.667959i
$688$	−3880.47			−0.215031
$689$	−7028.38			−0.388621
$690$	9223.12	+	14691.4i	0.508867	+	0.810568i
$691$			11233.2i			0.618421i	0.950994	+	0.309211i	$0.100065\pi$
$691$			11233.2i			0.618421i	−0.950994	+	0.309211i	$0.899935\pi$
$692$	330.010			0.0181288
$693$		0			0
$694$	−8512.50			−0.465605
$695$		−	3632.93i		−	0.198280i
$696$	352.499	+	561.491i	0.0191975	+	0.0305794i
$697$	3923.06			0.213194
$698$	8235.72			0.446600
$699$	−16210.4	+	10176.8i	−0.877160	+	0.550673i
$700$		0			0
$701$		−	17277.2i		−	0.930887i	−0.885078	−	0.465443i	$-0.845895\pi$
$701$		−	17277.2i		−	0.930887i	0.885078	−	0.465443i	$-0.154105\pi$
$702$	27943.2	−	3114.91i	1.50235	−	0.167471i
$703$		−	12980.9i		−	0.696422i
$704$			21192.5i			1.13455i
$705$	−2286.57	−	3642.25i	−0.122152	−	0.194574i
$706$			36310.8i			1.93566i
$707$		0			0
$708$	−479.832	−	764.319i	−0.0254706	−	0.0405718i
$709$	18839.1			0.997910			0.498955	−	0.866628i	$-0.333717\pi$
$709$	18839.1			0.997910			0.498955	+	0.866628i	$0.333717\pi$
$710$	4938.28			0.261029
$711$	−5482.20	+	11360.9i	−0.289168	+	0.599252i
$712$		−	12056.6i		−	0.634609i
$713$	40365.7			2.12020
$714$		0			0
$715$	16619.1			0.869259
$716$		−	403.110i		−	0.0210404i
$717$	19968.5	−	12536.0i	1.04008	−	0.652951i
$718$	18914.9			0.983142
$719$	10519.4			0.545630			0.272815	−	0.962067i	$-0.412045\pi$
$719$	10519.4			0.545630			0.272815	+	0.962067i	$0.412045\pi$
$720$	−4302.74	+	8916.71i	−0.222714	+	0.461536i
$721$		0			0
$722$			1618.38i			0.0834209i
$723$	−9774.61	+	6136.41i	−0.502796	+	0.315651i
$724$		−	481.141i		−	0.0246982i
$725$		−	538.051i		−	0.0275624i
$726$	−6238.44	+	3916.44i	−0.318912	+	0.200210i
$727$		−	1692.44i		−	0.0863401i	−0.999068	−	0.0431700i	$-0.986254\pi$
$727$		−	1692.44i		−	0.0863401i	0.999068	−	0.0431700i	$-0.0137457\pi$
$728$		0			0
$729$	19199.8	−	4334.38i	0.975453	−	0.220209i
$730$	13222.5			0.670390
$731$	−3979.38			−0.201344
$732$	369.330	−	231.862i	0.0186487	−	0.0117075i
$733$			30431.1i			1.53342i	0.641991	+	0.766712i	$0.278108\pi$
$733$			30431.1i			1.53342i	−0.641991	+	0.766712i	$0.721892\pi$
$734$	−29517.6			−1.48435
$735$		0			0
$736$	−2221.27			−0.111246
$737$		−	30807.7i		−	1.53978i
$738$	4055.48	+	1956.96i	0.202282	+	0.0976109i
$739$	4913.38			0.244576			0.122288	−	0.992495i	$-0.460977\pi$
$739$	4913.38			0.244576			0.122288	+	0.992495i	$0.460977\pi$
$740$	214.283			0.0106449
$741$	15308.2	+	24384.2i	0.758920	+	1.20887i
$742$		0			0
$743$		−	27101.5i		−	1.33816i	−0.743188	−	0.669082i	$-0.766687\pi$
$743$		−	27101.5i		−	1.33816i	0.743188	−	0.669082i	$-0.233313\pi$
$744$	11899.6	+	18954.8i	0.586373	+	0.934026i
$745$		−	2203.03i		−	0.108339i
$746$			12658.2i			0.621247i
$747$	−3223.40	+	6679.95i	−0.157882	+	0.327184i
$748$		−	678.009i		−	0.0331423i
$749$		0			0
$750$	15404.6	−	9670.84i	0.749994	−	0.470839i
$751$	16616.9			0.807403			0.403701	−	0.914891i	$-0.367723\pi$
$751$	16616.9			0.807403			0.403701	+	0.914891i	$0.367723\pi$
$752$	9779.84			0.474247
$753$	−1801.72	−	2869.94i	−0.0871959	−	0.138893i
$754$			1147.50i			0.0554239i
$755$	3927.98			0.189343
$756$		0			0
$757$	−29748.9			−1.42833			−0.714163	−	0.699980i	$-0.753192\pi$
$757$	−29748.9			−1.42833			−0.714163	+	0.699980i	$0.753192\pi$
$758$			11014.6i			0.527796i
$759$	24647.4	+	39260.5i	1.17871	+	1.87756i
$760$	−9848.51			−0.470057
$761$	4756.16			0.226558			0.113279	−	0.993563i	$-0.463865\pi$
$761$	4756.16			0.226558			0.113279	+	0.993563i	$0.463865\pi$
$762$	17461.6	−	10962.2i	0.830139	−	0.521153i
$763$		0			0
$764$			793.069i			0.0375553i
$765$	−4412.41	+	9143.98i	−0.208538	+	0.432159i
$766$			6103.12i			0.287878i
$767$			51587.0i			2.42855i
$768$	−996.888	−	1587.93i	−0.0468387	−	0.0746088i
$769$		−	9226.71i		−	0.432671i	−0.976319	−	0.216335i	$-0.930590\pi$
$769$		−	9226.71i		−	0.432671i	0.976319	−	0.216335i	$-0.0694104\pi$
$770$		0			0
$771$	−18990.9	−	30250.4i	−0.887083	−	1.41302i
$772$	99.9070			0.00465768
$773$	4745.02			0.220785			0.110392	−	0.993888i	$-0.464789\pi$
$773$	4745.02			0.220785			0.110392	+	0.993888i	$0.464789\pi$
$774$	−4113.70	−	1985.06i	−0.191039	−	0.0921853i
$775$		−	18163.5i		−	0.841873i
$776$	923.973			0.0427432
$777$		0			0
$778$	20715.1			0.954590
$779$			4611.03i			0.212076i
$780$	−402.523	+	252.700i	−0.0184777	+	0.0116002i
$781$	13196.8			0.604633
$782$	−40453.5			−1.84989
$783$	88.9968	+	798.372i	0.00406192	+	0.0364387i
$784$		0			0
$785$			8900.65i			0.404685i
$786$	11112.1	−	6976.09i	0.504271	−

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:	\( N \)	\(=\)	\( 147 = 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	147.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.86969i q^{2} +(-2.76278 - 4.40080i) q^{3} -0.235115 q^{4} -5.57059 q^{5} +(12.6289 - 7.92832i) q^{6} +22.2828i q^{8} +(-11.7341 + 24.3169i) q^{9} +O(q^{10})\)	\(q+2.86969i q^{2} +(-2.76278 - 4.40080i) q^{3} -0.235115 q^{4} -5.57059 q^{5} +(12.6289 - 7.92832i) q^{6} +22.2828i q^{8} +(-11.7341 + 24.3169i) q^{9} -15.9859i q^{10} -42.7198i q^{11} +(0.649571 + 1.03469i) q^{12} -69.8357i q^{13} +(15.3903 + 24.5151i) q^{15} -65.8256 q^{16} -67.5034 q^{17} +(-69.7819 - 33.6732i) q^{18} -79.3413i q^{19} +1.30973 q^{20} +122.593 q^{22} -208.831i q^{23} +(98.0622 - 61.5625i) q^{24} -93.9685 q^{25} +200.407 q^{26} +(139.432 - 15.5429i) q^{27} +5.72587i q^{29} +(-70.3506 + 44.1655i) q^{30} +193.293i q^{31} -10.6367i q^{32} +(-188.001 + 118.025i) q^{33} -193.714i q^{34} +(2.75886 - 5.71727i) q^{36} +163.609 q^{37} +227.685 q^{38} +(-307.333 + 192.941i) q^{39} -124.128i q^{40} -58.1164 q^{41} +58.9508 q^{43} +10.0441i q^{44} +(65.3658 - 135.460i) q^{45} +599.280 q^{46} -148.572 q^{47} +(181.862 + 289.685i) q^{48} -269.660i q^{50} +(186.497 + 297.069i) q^{51} +16.4194i q^{52} -100.642i q^{53} +(44.6034 + 400.128i) q^{54} +237.975i q^{55} +(-349.165 + 219.203i) q^{57} -16.4315 q^{58} -738.690 q^{59} +(-3.61850 - 5.76386i) q^{60} -356.946i q^{61} -554.692 q^{62} -496.081 q^{64} +389.026i q^{65} +(-338.696 - 539.505i) q^{66} +721.159 q^{67} +15.8711 q^{68} +(-919.024 + 576.955i) q^{69} +308.915i q^{71} +(-541.849 - 261.468i) q^{72} +827.134i q^{73} +469.506i q^{74} +(259.614 + 413.537i) q^{75} +18.6543i q^{76} +(-553.680 - 881.950i) q^{78} +467.203 q^{79} +366.688 q^{80} +(-453.623 - 570.673i) q^{81} -166.776i q^{82} +274.704 q^{83} +376.034 q^{85} +169.170i q^{86} +(25.1984 - 15.8193i) q^{87} +951.917 q^{88} -541.074 q^{89} +(388.727 + 187.579i) q^{90} +49.0993i q^{92} +(850.645 - 534.027i) q^{93} -426.355i q^{94} +441.978i q^{95} +(-46.8099 + 29.3868i) q^{96} -41.4658i q^{97} +(1038.81 + 501.277i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 96 q^{4} - 64 q^{9}+O(q^{10}) \) 24 * q - 96 * q^4 - 64 * q^9	\( 24 q - 96 q^{4} - 64 q^{9} + 256 q^{15} + 864 q^{16} - 32 q^{18} - 384 q^{22} + 744 q^{25} - 1704 q^{30} + 584 q^{36} + 432 q^{37} - 2368 q^{39} - 624 q^{43} + 3744 q^{46} - 2160 q^{51} + 2032 q^{57} + 6384 q^{58} - 5832 q^{60} - 3504 q^{64} + 3792 q^{67} - 7472 q^{72} + 2248 q^{78} + 2784 q^{79} - 1968 q^{81} - 3744 q^{85} - 624 q^{88} - 3232 q^{93} + 1320 q^{99}+O(q^{100}) \) 24 * q - 96 * q^4 - 64 * q^9 + 256 * q^15 + 864 * q^16 - 32 * q^18 - 384 * q^22 + 744 * q^25 - 1704 * q^30 + 584 * q^36 + 432 * q^37 - 2368 * q^39 - 624 * q^43 + 3744 * q^46 - 2160 * q^51 + 2032 * q^57 + 6384 * q^58 - 5832 * q^60 - 3504 * q^64 + 3792 * q^67 - 7472 * q^72 + 2248 * q^78 + 2784 * q^79 - 1968 * q^81 - 3744 * q^85 - 624 * q^88 - 3232 * q^93 + 1320 * q^99

Introduction

L-functions

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