LMFDB - Embedded newform 177.6.d.b.176.14

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			176.14
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.13

$q$-expansion

$f(q)$	$=$	$q-8.73168 q^{2} +(1.48415 + 15.5176i) q^{3} +44.2422 q^{4} +95.2512i q^{5} +(-12.9591 - 135.495i) q^{6} +144.410 q^{7} -106.895 q^{8} +(-238.595 + 46.0609i) q^{9} +O(q^{10})$	\(q-8.73168 q^{2} +(1.48415 + 15.5176i) q^{3} +44.2422 q^{4} +95.2512i q^{5} +(-12.9591 - 135.495i) q^{6} +144.410 q^{7} -106.895 q^{8} +(-238.595 + 46.0609i) q^{9} -831.703i q^{10} -217.796 q^{11} +(65.6618 + 686.534i) q^{12} +156.380i q^{13} -1260.94 q^{14} +(-1478.07 + 141.367i) q^{15} -482.379 q^{16} -457.850i q^{17} +(2083.33 - 402.189i) q^{18} +309.656 q^{19} +4214.12i q^{20} +(214.325 + 2240.90i) q^{21} +1901.72 q^{22} -1509.65 q^{23} +(-158.647 - 1658.76i) q^{24} -5947.79 q^{25} -1365.46i q^{26} +(-1068.87 - 3634.07i) q^{27} +6389.00 q^{28} +3620.57i q^{29} +(12906.1 - 1234.37i) q^{30} +6831.48i q^{31} +7632.61 q^{32} +(-323.241 - 3379.68i) q^{33} +3997.80i q^{34} +13755.2i q^{35} +(-10555.9 + 2037.83i) q^{36} +1687.78i q^{37} -2703.81 q^{38} +(-2426.64 + 232.090i) q^{39} -10181.9i q^{40} +7535.31i q^{41} +(-1871.42 - 19566.8i) q^{42} -17278.5i q^{43} -9635.76 q^{44} +(-4387.35 - 22726.4i) q^{45} +13181.8 q^{46} -28422.4 q^{47} +(-715.921 - 7485.39i) q^{48} +4047.18 q^{49} +51934.2 q^{50} +(7104.76 - 679.517i) q^{51} +6918.57i q^{52} -6020.14i q^{53} +(9332.99 + 31731.5i) q^{54} -20745.3i q^{55} -15436.6 q^{56} +(459.574 + 4805.13i) q^{57} -31613.6i q^{58} +(-23993.5 - 11799.8i) q^{59} +(-65393.2 + 6254.37i) q^{60} -40967.9i q^{61} -59650.3i q^{62} +(-34455.4 + 6651.64i) q^{63} -51209.4 q^{64} -14895.3 q^{65} +(2822.43 + 29510.3i) q^{66} +25548.9i q^{67} -20256.3i q^{68} +(-2240.54 - 23426.3i) q^{69} -120106. i q^{70} -28527.7i q^{71} +(25504.5 - 4923.67i) q^{72} +45267.9i q^{73} -14737.2i q^{74} +(-8827.38 - 92295.7i) q^{75} +13699.8 q^{76} -31451.8 q^{77} +(21188.7 - 2026.54i) q^{78} +83601.3 q^{79} -45947.2i q^{80} +(54805.8 - 21979.8i) q^{81} -65795.9i q^{82} -31065.0 q^{83} +(9482.21 + 99142.3i) q^{84} +43610.8 q^{85} +150870. i q^{86} +(-56182.7 + 5373.45i) q^{87} +23281.2 q^{88} -11986.6 q^{89} +(38309.0 + 198440. i) q^{90} +22582.7i q^{91} -66790.3 q^{92} +(-106009. + 10138.9i) q^{93} +248175. q^{94} +29495.1i q^{95} +(11327.9 + 118440. i) q^{96} -85247.4i q^{97} -35338.6 q^{98} +(51964.9 - 10031.9i) 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 $

$2$	−8.73168			−1.54356			−0.771778	−	0.635891i	$-0.780633\pi$
$2$	−8.73168			−1.54356			−0.771778	+	0.635891i	$0.780633\pi$
$3$	1.48415	+	15.5176i	0.0952080	+	0.995457i
$3$	1.48415	+	15.5176i	0.0952080	+	0.995457i
$4$	44.2422			1.38257
$5$			95.2512i			1.70390i	0.523619	+	0.851952i	$0.324582\pi$
$5$			95.2512i			1.70390i	−0.523619	+	0.851952i	$0.675418\pi$
$6$	−12.9591	−	135.495i	−0.146959	−	1.53655i
$7$	144.410			1.11391			0.556957	−	0.830542i	$-0.311969\pi$
$7$	144.410			1.11391			0.556957	+	0.830542i	$0.311969\pi$
$8$	−106.895			−0.590516
$9$	−238.595	+	46.0609i	−0.981871	+	0.189551i
$10$		−	831.703i		−	2.63007i
$11$	−217.796			−0.542710			−0.271355	−	0.962479i	$-0.587472\pi$
$11$	−217.796			−0.542710			−0.271355	+	0.962479i	$0.587472\pi$
$12$	65.6618	+	686.534i	0.131632	+	1.37629i
$13$			156.380i			0.256638i	0.991733	+	0.128319i	$0.0409582\pi$
$13$			156.380i			0.256638i	−0.991733	+	0.128319i	$0.959042\pi$
$14$	−1260.94			−1.71939
$15$	−1478.07	+	141.367i	−1.69616	+	0.162225i
$16$	−482.379			−0.471073
$17$		−	457.850i		−	0.384239i	−0.981372	−	0.192119i	$-0.938464\pi$
$17$		−	457.850i		−	0.384239i	0.981372	−	0.192119i	$-0.0615361\pi$
$18$	2083.33	−	402.189i	1.51557	−	0.292583i
$19$	309.656			0.196786			0.0983932	−	0.995148i	$-0.468630\pi$
$19$	309.656			0.196786			0.0983932	+	0.995148i	$0.468630\pi$
$20$			4214.12i			2.35576i
$21$	214.325	+	2240.90i	0.106053	+	1.10885i
$22$	1901.72			0.837704
$23$	−1509.65			−0.595055			−0.297528	−	0.954713i	$-0.596162\pi$
$23$	−1509.65			−0.595055			−0.297528	+	0.954713i	$0.596162\pi$
$24$	−158.647	−	1658.76i	−0.0562218	−	0.587833i
$25$	−5947.79			−1.90329
$26$		−	1365.46i		−	0.396136i
$27$	−1068.87	−	3634.07i	−0.282172	−	0.959364i
$28$	6389.00			1.54006
$29$			3620.57i			0.799432i	0.916639	+	0.399716i	$0.130891\pi$
$29$			3620.57i			0.799432i	−0.916639	+	0.399716i	$0.869109\pi$
$30$	12906.1	−	1234.37i	2.61813	−	0.250404i
$31$			6831.48i			1.27676i	0.769719	+	0.638382i	$0.220396\pi$
$31$			6831.48i			1.27676i	−0.769719	+	0.638382i	$0.779604\pi$
$32$	7632.61			1.31764
$33$	−323.241	−	3379.68i	−0.0516703	−	0.540245i
$34$			3997.80i			0.593095i
$35$			13755.2i			1.89800i
$36$	−10555.9	+	2037.83i	−1.35750	+	0.262067i
$37$			1687.78i			0.202681i	0.994852	+	0.101340i	$0.0323131\pi$
$37$			1687.78i			0.202681i	−0.994852	+	0.101340i	$0.967687\pi$
$38$	−2703.81			−0.303751
$39$	−2426.64	+	232.090i	−0.255473	+	0.0244340i
$40$		−	10181.9i		−	1.00618i
$41$			7535.31i			0.700070i	0.936737	+	0.350035i	$0.113830\pi$
$41$			7535.31i			0.700070i	−0.936737	+	0.350035i	$0.886170\pi$
$42$	−1871.42	−	19566.8i	−0.163700	−	1.71158i
$43$		−	17278.5i		−	1.42506i	−0.701640	−	0.712532i	$-0.747548\pi$
$43$		−	17278.5i		−	1.42506i	0.701640	−	0.712532i	$-0.252452\pi$
$44$	−9635.76			−0.750334
$45$	−4387.35	−	22726.4i	−0.322977	−	1.67301i
$46$	13181.8			0.918502
$47$	−28422.4			−1.87679			−0.938395	−	0.345565i	$-0.887687\pi$
$47$	−28422.4			−1.87679			−0.938395	+	0.345565i	$0.887687\pi$
$48$	−715.921	−	7485.39i	−0.0448499	−	0.468934i
$49$	4047.18			0.240803
$50$	51934.2			2.93784
$51$	7104.76	−	679.517i	0.382493	−	0.0365826i
$52$			6918.57i			0.354820i
$53$		−	6020.14i		−	0.294386i	−0.989108	−	0.147193i	$-0.952976\pi$
$53$		−	6020.14i		−	0.294386i	0.989108	−	0.147193i	$-0.0470238\pi$
$54$	9332.99	+	31731.5i	0.435548	+	1.48083i
$55$		−	20745.3i		−	0.924726i
$56$	−15436.6			−0.657783
$57$	459.574	+	4805.13i	0.0187356	+	0.195892i
$58$		−	31613.6i		−	1.23397i
$59$	−23993.5	−	11799.8i	−0.897354	−	0.441312i
$59$	−23993.5	−	11799.8i	−0.897354	−	0.441312i
$60$	−65393.2	+	6254.37i	−2.34506	+	0.224288i
$61$		−	40967.9i		−	1.40968i	−0.709369	−	0.704838i	$-0.751020\pi$
$61$		−	40967.9i		−	1.40968i	0.709369	−	0.704838i	$-0.248980\pi$
$62$		−	59650.3i		−	1.97076i
$63$	−34455.4	+	6651.64i	−1.09372	+	0.211143i
$64$	−51209.4			−1.56279
$65$	−14895.3			−0.437288
$66$	2822.43	+	29510.3i	0.0797561	+	0.833899i
$67$			25548.9i			0.695322i	0.937620	+	0.347661i	$0.113024\pi$
$67$			25548.9i			0.695322i	−0.937620	+	0.347661i	$0.886976\pi$
$68$		−	20256.3i		−	0.531236i
$69$	−2240.54	−	23426.3i	−0.0566540	−	0.592352i
$70$		−	120106.i		−	2.92968i
$71$		−	28527.7i		−	0.671616i	−0.941930	−	0.335808i	$-0.890991\pi$
$71$		−	28527.7i		−	0.671616i	0.941930	−	0.335808i	$-0.109009\pi$
$72$	25504.5	−	4923.67i	0.579810	−	0.111933i
$73$			45267.9i			0.994221i	0.867687	+	0.497110i	$0.165606\pi$
$73$			45267.9i			0.994221i	−0.867687	+	0.497110i	$0.834394\pi$
$74$		−	14737.2i		−	0.312849i
$75$	−8827.38	−	92295.7i	−0.181209	−	1.89465i
$76$	13699.8			0.272071
$77$	−31451.8			−0.604532
$78$	21188.7	−	2026.54i	0.394337	−	0.0377153i
$79$	83601.3			1.50711			0.753556	−	0.657384i	$-0.228337\pi$
$79$	83601.3			1.50711			0.753556	+	0.657384i	$0.228337\pi$
$80$		−	45947.2i		−	0.802664i
$81$	54805.8	−	21979.8i	0.928141	−	0.372229i
$82$		−	65795.9i		−	1.08060i
$83$	−31065.0			−0.494966			−0.247483	−	0.968892i	$-0.579603\pi$
$83$	−31065.0			−0.494966			−0.247483	+	0.968892i	$0.579603\pi$
$84$	9482.21	+	99142.3i	0.146626	+	1.53307i
$85$	43610.8			0.654707
$86$			150870.i			2.19967i
$87$	−56182.7	+	5373.45i	−0.795800	+	0.0761123i
$88$	23281.2			0.320479
$89$	−11986.6			−0.160406			−0.0802028	−	0.996779i	$-0.525557\pi$
$89$	−11986.6			−0.160406			−0.0802028	+	0.996779i	$0.525557\pi$
$90$	38309.0	+	198440.i	0.498533	+	2.58239i
$91$			22582.7i			0.285873i
$92$	−66790.3			−0.822705
$93$	−106009.	+	10138.9i	−1.27096	+	0.121558i
$94$	248175.			2.89693
$95$			29495.1i			0.335305i
$96$	11327.9	+	118440.i	0.125450	+	1.31166i
$97$		−	85247.4i		−	0.919923i	−0.887939	−	0.459962i	$-0.847863\pi$
$97$		−	85247.4i		−	0.919923i	0.887939	−	0.459962i	$-0.152137\pi$
$98$	−35338.6			−0.371693
$99$	51964.9	−	10031.9i	0.532871	−	0.102871i
$100$	−263143.			−2.63143
$101$	118099.			1.15197			0.575986	−	0.817459i	$-0.304618\pi$
$101$	118099.			1.15197			0.575986	+	0.817459i	$0.304618\pi$
$102$	−62036.5	+	5933.32i	−0.590400	+	0.0564673i
$103$			173141.i			1.60808i	0.594577	+	0.804038i	$0.297319\pi$
$103$			173141.i			1.60808i	−0.594577	+	0.804038i	$0.702681\pi$
$104$		−	16716.2i		−	0.151549i
$105$	−213448.	+	20414.7i	−1.88938	+	0.180705i
$106$			52565.9i			0.454402i
$107$			110167.i			0.930230i	0.885250	+	0.465115i	$0.153987\pi$
$107$			110167.i			0.930230i	−0.885250	+	0.465115i	$0.846013\pi$
$108$	−47288.9	−	160779.i	−0.390122	−	1.32639i
$109$		−	94217.1i		−	0.759562i	−0.925076	−	0.379781i	$-0.875999\pi$
$109$		−	94217.1i		−	0.759562i	0.925076	−	0.379781i	$-0.124001\pi$
$110$			181141.i			1.42737i
$111$	−26190.4	+	2504.92i	−0.201760	+	0.0192968i
$112$	−69660.3			−0.524735
$113$	176217.			1.29823			0.649116	−	0.760690i	$-0.275139\pi$
$113$	176217.			1.29823			0.649116	+	0.760690i	$0.275139\pi$
$114$	−4012.85	−	41956.8i	−0.0289195	−	0.302371i
$115$		−	143796.i		−	1.01392i
$116$			160182.i			1.10527i
$117$	−7202.98	−	37311.3i	−0.0486461	−	0.251986i
$118$	209504.	+	103032.i	1.38512	+	0.681190i
$119$		−	66118.1i		−	0.428009i
$120$	157998.	−	15111.4i	1.00161	−	0.0957966i
$121$	−113616.			−0.705466
$122$			357718.i			2.17591i
$123$	−116930.	+	11183.5i	−0.696890	+	0.0666523i
$124$			302240.i			1.76521i
$125$		−	268874.i		−	1.53912i
$126$	300853.	−	58080.0i	1.68822	−	0.325912i
$127$	353974.			1.94743			0.973714	−	0.227774i	$-0.0731446\pi$
$127$	353974.			1.94743			0.973714	+	0.227774i	$0.0731446\pi$
$128$	202900.			1.09460
$129$	268121.	−	25643.8i	1.41859	−	0.135677i
$130$	130061.			0.674978
$131$	−191902.			−0.977014			−0.488507	−	0.872560i	$-0.662458\pi$
$131$	−191902.			−0.977014			−0.488507	+	0.872560i	$0.662458\pi$
$132$	−14300.9	−	149524.i	−0.0714378	−	0.746925i
$133$	44717.3			0.219203
$134$		−	223085.i		−	1.07327i
$135$	346149.	−	101811.i	1.63466	−	0.480794i
$136$			48941.8i			0.226899i
$137$		−	382198.i		−	1.73975i	−0.493273	−	0.869875i	$-0.664200\pi$
$137$		−	382198.i		−	1.73975i	0.493273	−	0.869875i	$-0.335800\pi$
$138$	19563.7	+	204550.i	0.0874487	+	0.914330i
$139$	−37587.9			−0.165011			−0.0825053	−	0.996591i	$-0.526292\pi$
$139$	−37587.9			−0.165011			−0.0825053	+	0.996591i	$0.526292\pi$
$140$			608560.i			2.62412i
$141$	−42182.9	−	441048.i	−0.178685	−	1.86826i
$142$			249095.i			1.03668i
$143$		−	34058.8i		−	0.139280i
$144$	115093.	−	22218.8i	0.462533	−	0.0892924i
$145$	−344863.			−1.36216
$146$		−	395264.i		−	1.53464i
$147$	6006.60	+	62802.7i	0.0229264	+	0.239709i
$148$			74671.3i			0.280220i
$149$	−43754.1			−0.161455			−0.0807277	−	0.996736i	$-0.525724\pi$
$149$	−43754.1			−0.161455			−0.0807277	+	0.996736i	$0.525724\pi$
$150$	77077.8	+	805896.i	0.279706	+	2.92449i
$151$			478677.i			1.70844i	0.519911	+	0.854221i	$0.325965\pi$
$151$			478677.i			1.70844i	−0.519911	+	0.854221i	$0.674035\pi$
$152$	−33100.6			−0.116205
$153$	21089.0	+	109241.i	0.0728329	+	0.377273i
$154$	274627.			0.933130
$155$	−650707.			−2.17549
$156$	−107360.	+	10268.2i	−0.353208	+	0.0337817i
$157$		−	167723.i		−	0.543053i	−0.962431	−	0.271527i	$-0.912472\pi$
$157$		−	167723.i		−	0.543053i	0.962431	−	0.271527i	$-0.0875285\pi$
$158$	−729980.			−2.32631
$159$	93418.5	−	8934.77i	0.293049	−	0.0280279i
$160$			727015.i			2.24514i
$161$	−218009.			−0.662840
$162$	−478546.	+	191920.i	−1.43264	+	0.574557i
$163$	−381537.			−1.12478			−0.562390	−	0.826872i	$-0.690118\pi$
$163$	−381537.			−1.12478			−0.562390	+	0.826872i	$0.690118\pi$
$164$			333379.i			0.967895i
$165$	321918.	−	30789.1i	0.920526	−	0.0880413i
$166$	271249.			0.764009
$167$		−	130083.i		−	0.360936i	−0.983581	−	0.180468i	$-0.942239\pi$
$167$		−	130083.i		−	0.360936i	0.983581	−	0.180468i	$-0.0577612\pi$
$168$	−22910.2	−	239540.i	−0.0626262	−	0.654795i
$169$	346838.			0.934137
$170$	−380795.			−1.01058
$171$	−73882.2	+	14263.0i	−0.193219	+	0.0373010i
$172$		−	764437.i		−	1.97025i
$173$	555383.			1.41084			0.705419	−	0.708791i	$-0.250759\pi$
$173$	555383.			1.41084			0.705419	+	0.708791i	$0.250759\pi$
$174$	490569.	−	46919.2i	1.22836	−	0.117484i
$175$	−858919.			−2.12010
$176$	105060.			0.255656
$177$	147496.	−	389835.i	0.353872	−	0.935294i
$178$	104663.			0.247595
$179$	−391499.			−0.913269			−0.456634	−	0.889654i	$-0.650945\pi$
$179$	−391499.			−0.913269			−0.456634	+	0.889654i	$0.650945\pi$
$180$	−194106.	−	1.00547e6i	−0.446537	−	2.31306i
$181$	−460900.			−1.04571			−0.522854	−	0.852422i	$-0.675133\pi$
$181$	−460900.			−1.04571			−0.522854	+	0.852422i	$0.675133\pi$
$182$		−	197185.i		−	0.441261i
$183$	635725.	−	60802.3i	1.40327	−	0.134212i
$184$	161374.			0.351390
$185$	−160763.			−0.345349
$186$	925632.	−	88529.7i	1.96181	−	0.187632i
$187$			99717.9i			0.208530i
$188$	−1.25747e6			−2.59479
$189$	−154355.	−	524795.i	−0.314315	−	1.06865i
$190$		−	257541.i		−	0.517563i
$191$	−588891.			−1.16802			−0.584012	−	0.811745i	$-0.698518\pi$
$191$	−588891.			−1.16802			−0.584012	+	0.811745i	$0.698518\pi$
$192$	−76002.1	−	794649.i	−0.148790	−	1.55569i
$193$	−13813.2			−0.0266931			−0.0133466	−	0.999911i	$-0.504248\pi$
$193$	−13813.2			−0.0266931			−0.0133466	+	0.999911i	$0.504248\pi$
$194$			744352.i			1.41995i
$195$	−22106.9	−	231141.i	−0.0416333	−	0.435301i
$196$	179056.			0.332927
$197$			499597.i			0.917179i	0.888648	+	0.458590i	$0.151645\pi$
$197$			499597.i			0.917179i	−0.888648	+	0.458590i	$0.848355\pi$
$198$	−453741.	+	87595.0i	−0.822517	+	0.158788i
$199$	712826.			1.27600			0.638000	−	0.770036i	$-0.279762\pi$
$199$	712826.			1.27600			0.638000	+	0.770036i	$0.279762\pi$
$200$	635787.			1.12392
$201$	−396460.	+	37918.4i	−0.692164	+	0.0662002i
$202$	−1.03120e6			−1.77814
$203$			522845.i			0.890498i
$204$	314330.	−	30063.3i	0.528823	−	0.0505779i
$205$	−717747.			−1.19285
$206$		−	1.51181e6i		−	2.48216i
$207$	360195.	−	69535.9i	0.584268	−	0.112793i
$208$		−	75434.3i		−	0.120896i
$209$	−67441.7			−0.106798
$210$	1.86376e6	−	178255.i	2.91637	−	0.278928i
$211$		−	736655.i		−	1.13909i	−0.821960	−	0.569545i	$-0.807119\pi$
$211$		−	736655.i		−	1.13909i	0.821960	−	0.569545i	$-0.192881\pi$
$212$		−	266344.i		−	0.407009i
$213$	442683.	−	42339.3i	0.668566	−	0.0639432i
$214$		−	961938.i		−	1.43586i
$215$	1.64580e6			2.42817
$216$	114256.	+	388463.i	0.166627	+	0.566520i
$217$			986533.i			1.42221i
$218$			822673.i			1.17243i
$219$	−702451.	+	67184.1i	−0.989704	+	0.0946577i
$220$		−	917818.i		−	1.27850i
$221$	71598.5			0.0986105
$222$	228686.	−	21872.1i	0.311428	−	0.0297858i
$223$	−1.08470e6			−1.46065			−0.730327	−	0.683098i	$-0.760632\pi$
$223$	−1.08470e6			−1.46065			−0.730327	+	0.683098i	$0.760632\pi$
$224$	1.10222e6			1.46774
$225$	1.41911e6	−	273960.i	1.86879	−	0.360771i
$226$	−1.53867e6			−2.00389
$227$	1.18705e6			1.52899			0.764493	−	0.644632i	$-0.222989\pi$
$227$	1.18705e6			1.52899			0.764493	+	0.644632i	$0.222989\pi$
$228$	20332.6	+	212589.i	0.0259033	+	0.270835i
$229$			1.02701e6i			1.29415i	0.762426	+	0.647076i	$0.224008\pi$
$229$			1.02701e6i			1.29415i	−0.762426	+	0.647076i	$0.775992\pi$
$230$			1.25558e6i			1.56504i
$231$	−46679.1	−	488059.i	−0.0575563	−	0.601786i
$232$		−	387020.i		−	0.472077i
$233$	−730905.			−0.882005			−0.441002	−	0.897506i	$-0.645377\pi$
$233$	−730905.			−0.882005			−0.441002	+	0.897506i	$0.645377\pi$
$234$	62894.1	+	325790.i	0.0750880	+	0.388954i
$235$		−	2.70726e6i		−	3.19787i
$236$	−1.06152e6	−	522050.i	−1.24065	−	0.610144i
$237$	124077.	+	1.29730e6i	0.143489	+	1.50027i
$238$			577322.i			0.660656i
$239$		−	138876.i		−	0.157265i	−0.996904	−	0.0786324i	$-0.974945\pi$
$239$		−	138876.i		−	0.157265i	0.996904	−	0.0786324i	$-0.0250553\pi$
$240$	712992.	−	68192.3i	0.799018	−	0.0764200i
$241$	−438905.			−0.486775			−0.243387	−	0.969929i	$-0.578259\pi$
$241$	−438905.			−0.486775			−0.243387	+	0.969929i	$0.578259\pi$
$242$	992058.			1.08893
$243$	422414.	+	817836.i	0.458905	+	0.888486i
$244$		−	1.81251e6i		−	1.94897i
$245$			385498.i			0.410306i
$246$	1.02100e6	−	97650.7i	1.07569	−	0.102882i
$247$			48423.8i			0.0505029i
$248$		−	730250.i		−	0.753950i
$249$	−46104.9	−	482055.i	−0.0471247	−	0.492718i
$250$			2.34772e6i			2.37573i
$251$			303320.i			0.303891i	0.988389	+	0.151945i	$0.0485538\pi$
$251$			303320.i			0.303891i	−0.988389	+	0.151945i	$0.951446\pi$
$252$	−1.52438e6	+	294283.i	−1.51214	+	0.291920i
$253$	328796.			0.322943
$254$	−3.09078e6			−3.00597
$255$	64724.8	+	676737.i	0.0623333	+	0.651733i
$256$	−132958.			−0.126799
$257$			845091.i			0.798125i	0.916924	+	0.399062i	$0.130664\pi$
$257$			845091.i			0.798125i	−0.916924	+	0.399062i	$0.869336\pi$
$258$	−2.34115e6	+	223913.i	−2.18967	+	0.209426i
$259$			243733.i			0.225769i
$260$	−659002.			−0.604580
$261$	−166766.	−	863848.i	−0.151533	−	0.784939i
$262$	1.67562e6			1.50808
$263$		−	1.21321e6i		−	1.08155i	−0.841168	−	0.540774i	$-0.818132\pi$
$263$		−	1.21321e6i		−	1.08155i	0.841168	−	0.540774i	$-0.181868\pi$
$264$	34552.7	+	361270.i	0.0305121	+	0.319023i
$265$	573426.			0.501606
$266$	−390457.			−0.338352
$267$	−17789.8	−	186003.i	−0.0152719	−	0.159677i
$268$			1.13034e6i			0.961330i
$269$	834151.			0.702853			0.351426	−	0.936216i	$-0.385697\pi$
$269$	834151.			0.702853			0.351426	+	0.936216i	$0.385697\pi$
$270$	−3.02246e6	+	888978.i	−2.52320	+	0.742133i
$271$	−1.22568e6			−1.01380			−0.506901	−	0.862004i	$-0.669209\pi$
$271$	−1.22568e6			−1.01380			−0.506901	+	0.862004i	$0.669209\pi$
$272$			220858.i			0.181005i
$273$	−350431.	+	33516.1i	−0.284574	+	0.0272174i
$274$			3.33723e6i			2.68540i
$275$	1.29540e6			1.03294
$276$	−99126.6	−	1.03643e6i	−0.0783280	−	0.818968i
$277$	−995993.			−0.779932			−0.389966	−	0.920829i	$-0.627513\pi$
$277$	−995993.			−0.779932			−0.389966	+	0.920829i	$0.627513\pi$
$278$	328206.			0.254703
$279$	−314664.	−	1.62996e6i	−0.242012	−	1.25362i
$280$		−	1.47036e6i		−	1.12080i
$281$			1.11245e6i			0.840453i	0.907419	+	0.420226i	$0.138049\pi$
$281$			1.11245e6i			0.840453i	−0.907419	+	0.420226i	$0.861951\pi$
$282$	368328.	+	3.85109e6i	0.275811	+	2.88377i
$283$			82590.3i			0.0613003i	0.999530	+	0.0306502i	$0.00975778\pi$
$283$			82590.3i			0.0613003i	−0.999530	+	0.0306502i	$0.990242\pi$
$284$		−	1.26213e6i		−	0.928556i
$285$	−457694.	+	43775.0i	−0.333782	+	0.0319237i
$286$			297391.i			0.214987i
$287$			1.08817e6i			0.779818i
$288$	−1.82110e6	+	351565.i	−1.29376	+	0.249761i
$289$	1.21023e6			0.852360
$290$	3.01123e6			2.10257
$291$	1.32284e6	−	126519.i	0.915744	−	0.0875840i
$292$			2.00275e6i			1.37458i
$293$			691968.i			0.470887i	0.971888	+	0.235444i	$0.0756543\pi$
$293$			691968.i			0.470887i	−0.971888	+	0.235444i	$0.924346\pi$
$294$	−52447.7	−	548373.i	−0.0353882	−	0.370005i
$295$	1.12395e6	−	2.28541e6i	0.751954	−	1.52901i
$296$		−	180415.i		−	0.119686i
$297$	232794.	+	791484.i	0.153138	+	0.520656i
$298$	382046.			0.249216
$299$		−	236079.i		−	0.152714i
$300$	−390543.	−	4.08336e6i	−0.250533	−	2.61948i
$301$		−	2.49518e6i		−	1.58740i
$302$		−	4.17965e6i		−	2.63708i
$303$	175276.	+	1.83262e6i	0.109677	+	1.14674i
$304$	−149371.			−0.0927008
$305$	3.90224e6			2.40195
$306$	−184142.	−	953854.i	−0.112422	−	0.582342i
$307$	−1.88853e6			−1.14361			−0.571804	−	0.820391i	$-0.693756\pi$
$307$	−1.88853e6			−1.14361			−0.571804	+	0.820391i	$0.693756\pi$
$308$	−1.39150e6			−0.835807
$309$	−2.68674e6	+	256966.i	−1.60077	+	0.153102i
$310$	5.68176e6			3.35799
$311$			1.74107e6i			1.02074i	0.859955	+	0.510369i	$0.170491\pi$
$311$			1.74107e6i			1.02074i	−0.859955	+	0.510369i	$0.829509\pi$
$312$	259395.	−	24809.2i	0.150861	−	0.0144287i
$313$			630418.i			0.363721i	0.983324	+	0.181860i	$0.0582119\pi$
$313$			630418.i			0.363721i	−0.983324	+	0.181860i	$0.941788\pi$
$314$			1.46450e6i			0.838233i
$315$	−633577.	−	3.28192e6i	−0.359768	−	1.86359i
$316$	3.69871e6			2.08368
$317$			1.54644e6i			0.864339i	0.901792	+	0.432169i	$0.142252\pi$
$317$			1.54644e6i			0.864339i	−0.901792	+	0.432169i	$0.857748\pi$
$318$	−815700.	+	78015.5i	−0.452337	+	0.0432627i
$319$		−	788544.i		−	0.433860i
$320$		−	4.87775e6i		−	2.66284i
$321$	−1.70952e6	+	163503.i	−0.926004	+	0.0885653i
$322$	1.90358e6			1.02313
$323$		−	141776.i		−	0.0756130i
$324$	2.42473e6	−	972432.i	1.28322	−	0.514632i
$325$		−	930113.i		−	0.488458i
$326$	3.33146e6			1.73616
$327$	1.46203e6	−	139832.i	0.756112	−	0.0723164i
$328$		−	805485.i		−	0.413402i
$329$	−4.10447e6			−2.09058
$330$	−2.81089e6	+	268840.i	−1.42088	+	0.135897i
$331$	−3.13699e6			−1.57378			−0.786888	−	0.617096i	$-0.788309\pi$
$331$	−3.13699e6			−1.57378			−0.786888	+	0.617096i	$0.788309\pi$
$332$	−1.37438e6			−0.684325
$333$	−77740.8	−	402696.i	−0.0384183	−	0.199006i
$334$			1.13584e6i			0.557125i
$335$	−2.43357e6			−1.18476
$336$	−103386.	−	1.08096e6i	−0.0499590	−	0.522351i
$337$			2.22407e6i			1.06678i	0.845871	+	0.533388i	$0.179081\pi$
$337$			2.22407e6i			1.06678i	−0.845871	+	0.533388i	$0.820919\pi$
$338$	−3.02848e6			−1.44189
$339$	261532.	+	2.73448e6i	0.123602	+	1.29233i
$340$	1.92944e6			0.905176
$341$		−	1.48787e6i		−	0.692913i
$342$	645115.	−	124540.i	0.298244	−	0.0575763i
$343$	−1.84264e6			−0.845680
$344$			1.84698e6i			0.841523i
$345$	2.23138e6	−	213414.i	1.00931	−	0.0965331i
$346$	−4.84942e6			−2.17771
$347$	−1.28027e6			−0.570794			−0.285397	−	0.958409i	$-0.592125\pi$
$347$	−1.28027e6			−0.570794			−0.285397	+	0.958409i	$0.592125\pi$
$348$	−2.48564e6	+	237733.i	−1.10025	+	0.105230i
$349$			2.22537e6i			0.977999i	0.872284	+	0.488999i	$0.162638\pi$
$349$			2.22537e6i			0.977999i	−0.872284	+	0.488999i	$0.837362\pi$
$350$	7.49980e6			3.27250
$351$	568294.	−	167149.i	0.246210	−	0.0724161i
$352$	−1.66235e6			−0.715099
$353$	−3.33127e6			−1.42290			−0.711449	−	0.702738i	$-0.751961\pi$
$353$	−3.33127e6			−1.42290			−0.711449	+	0.702738i	$0.751961\pi$
$354$	−1.28789e6	+	3.40392e6i	−0.546222	+	1.44368i
$355$	2.71730e6			1.14437
$356$	−530312.			−0.221772
$357$	1.02600e6	−	98128.8i	0.426065	−	0.0407499i
$358$	3.41845e6			1.40968
$359$		−	3.86339e6i		−	1.58209i	−0.611756	−	0.791046i	$-0.709537\pi$
$359$		−	3.86339e6i		−	1.58209i	0.611756	−	0.791046i	$-0.290463\pi$
$360$	468985.	+	2.42934e6i	0.190723	+	0.987942i
$361$	−2.38021e6			−0.961275
$362$	4.02443e6			1.61411
$363$	−168623.	−	1.76305e6i	−0.0671660	−	0.702261i
$364$			999110.i			0.395239i
$365$	−4.31182e6			−1.69406
$366$	−5.55095e6	+	530906.i	−2.16603	+	0.207164i
$367$			3.94334e6i			1.52827i	0.645058	+	0.764134i	$0.276833\pi$
$367$			3.94334e6i			1.52827i	−0.645058	+	0.764134i	$0.723167\pi$
$368$	728225.			0.280315
$369$	−347083.	−	1.79788e6i	−0.132699	−	0.687378i
$370$	1.40373e6			0.533066
$371$		−	869367.i		−	0.327921i
$372$	−4.69005e6	+	448568.i	−1.75720	+	0.168062i
$373$	2.27599e6			0.847031			0.423515	−	0.905889i	$-0.360796\pi$
$373$	2.27599e6			0.847031			0.423515	+	0.905889i	$0.360796\pi$
$374$		−	870705.i		−	0.321878i
$375$	4.17229e6	−	399048.i	1.53213	−	0.146537i
$376$	3.03820e6			1.10827
$377$	−566183.			−0.205165
$378$	1.34777e6	+	4.58234e6i	0.485163	+	1.64952i
$379$	386178.			0.138099			0.0690493	−	0.997613i	$-0.478003\pi$
$379$	386178.			0.138099			0.0690493	+	0.997613i	$0.478003\pi$
$380$			1.30493e6i			0.463582i
$381$	525348.	+	5.49284e6i	0.185411	+	1.93858i
$382$	5.14201e6			1.80291
$383$		−	1.51157e6i		−	0.526539i	−0.964722	−	0.263269i	$-0.915199\pi$
$383$		−	1.51157e6i		−	0.526539i	0.964722	−	0.263269i	$-0.0848008\pi$
$384$	301133.	+	3.14853e6i	0.104215	+	1.08963i
$385$		−	2.99583e6i		−	1.03007i
$386$	120612.			0.0412024
$387$	795862.	+	4.12255e6i	0.270122	+	1.39923i
$388$		−	3.77153e6i		−	1.27186i
$389$		−	1.73742e6i		−	0.582146i	−0.956701	−	0.291073i	$-0.905988\pi$
$389$		−	1.73742e6i		−	0.582146i	0.956701	−	0.291073i	$-0.0940123\pi$
$390$	193030.	+	2.01825e6i	0.0642633	+	0.671912i
$391$			691195.i			0.228643i
$392$	−432622.			−0.142198
$393$	−284810.	−	2.97786e6i	−0.0930195	−	0.972576i
$394$		−	4.36232e6i		−	1.41572i
$395$			7.96313e6i			2.56798i
$396$	2.29904e6	−	443832.i	0.736731	−	0.142226i
$397$			5.64435e6i			1.79737i	0.438593	+	0.898686i	$0.355477\pi$
$397$			5.64435e6i			1.79737i	−0.438593	+	0.898686i	$0.644523\pi$
$398$	−6.22417e6			−1.96958
$399$	66367.0	+	693907.i	0.0208699	+	0.218207i
$400$	2.86909e6			0.896590
$401$	417749.			0.129734			0.0648671	−	0.997894i	$-0.479338\pi$
$401$	417749.			0.129734			0.0648671	+	0.997894i	$0.479338\pi$
$402$	3.46176e6	−	331091.i	1.06839	−	0.102184i
$403$	−1.06830e6			−0.327667
$404$	5.22495e6			1.59268
$405$	2.09360e6	+	5.22032e6i	0.634243	+	1.58146i
$406$		−	4.56531e6i		−	1.37453i
$407$		−	367592.i		−	0.109997i
$408$	−759462.	+	72636.8i	−0.225868	+	0.0216026i
$409$		−	2.39087e6i		−	0.706720i	−0.935487	−	0.353360i	$-0.885039\pi$
$409$		−	2.39087e6i		−	0.706720i	0.935487	−	0.353360i	$-0.114961\pi$
$410$	6.26714e6			1.84124
$411$	5.93081e6	−	567237.i	1.73185	−	0.165638i
$412$			7.66013e6i			2.22328i
$413$	−3.46490e6	−	1.70401e6i	−0.999574	−	0.491584i
$414$	−3.14511e6	+	607165.i	−0.901850	+	0.174103i
$415$		−	2.95897e6i		−	0.843376i
$416$			1.19358e6i			0.338158i
$417$	−55786.0	−	583276.i	−0.0157103	−	0.164261i
$418$	588879.			0.164849
$419$	5.64700e6			1.57138			0.785692	−	0.618618i	$-0.212307\pi$
$419$	5.64700e6			1.57138			0.785692	+	0.618618i	$0.212307\pi$
$420$	−9.44342e6	+	903192.i	−2.61220	+	0.249837i
$421$			2.96945e6i			0.816528i	0.912864	+	0.408264i	$0.133866\pi$
$421$			2.96945e6i			0.816528i	−0.912864	+	0.408264i	$0.866134\pi$
$422$			6.43223e6i			1.75825i
$423$	6.78142e6	−	1.30916e6i	1.84276	−	0.355747i
$424$			643522.i			0.173840i
$425$			2.72320e6i			0.731319i
$426$	−3.86537e6	+	369693.i	−1.03197	+	0.0987000i
$427$		−	5.91616e6i		−	1.57026i
$428$			4.87401e6i			1.28611i
$429$	528513.	−	50548.3i	0.138648	−	0.0132606i
$430$	−1.43706e7			−3.74802
$431$	998455.			0.258902			0.129451	−	0.991586i	$-0.458679\pi$
$431$	998455.			0.258902			0.129451	+	0.991586i	$0.458679\pi$
$432$	515598.	+	1.75300e6i	0.132924	+	0.451931i
$433$	−930962.			−0.238623			−0.119312	−	0.992857i	$-0.538069\pi$
$433$	−930962.			−0.238623			−0.119312	+	0.992857i	$0.538069\pi$
$434$		−	8.61409e6i		−	2.19526i
$435$	−511827.	−	5.35147e6i	−0.129688	−	1.35597i
$436$		−	4.16837e6i		−	1.05015i
$437$	−467472.			−0.117099
$438$	6.13357e6	−	586630.i	1.52767	−	0.146110i
$439$	2.37455e6			0.588057			0.294028	−	0.955797i	$-0.405004\pi$
$439$	2.37455e6			0.588057			0.294028	+	0.955797i	$0.405004\pi$
$440$			2.21757e6i			0.546066i
$441$	−965635.	+	186417.i	−0.236438	+	0.0456445i
$442$	−625175.			−0.152211
$443$	−1.46413e6			−0.354464			−0.177232	−	0.984169i	$-0.556714\pi$
$443$	−1.46413e6			−0.354464			−0.177232	+	0.984169i	$0.556714\pi$
$444$	−1.15872e6	+	110823.i	−0.278947	+	0.0266792i
$445$		−	1.14173e6i		−	0.273316i
$446$	9.47124e6			2.25460
$447$	−64937.4	−	678960.i	−0.0153718	−	0.160722i
$448$	−7.39513e6			−1.74081
$449$		−	6.38769e6i		−	1.49530i	−0.664094	−	0.747649i	$-0.731182\pi$
$449$		−	6.38769e6i		−	1.49530i	0.664094	−	0.747649i	$-0.268818\pi$
$450$	−1.23912e7	+	2.39213e6i	−2.88458	+	0.556870i
$451$		−	1.64116e6i		−	0.379935i
$452$	7.79623e6			1.79489
$453$	−7.42794e6	+	710426.i	−1.70068	+	0.162657i
$454$	−1.03649e7			−2.36008
$455$	−2.15103e6			−0.487100
$456$	−49126.1	−	513643.i	−0.0110637	−	0.115678i
$457$			3.94017e6i			0.882520i	0.897379	+	0.441260i	$0.145468\pi$
$457$			3.94017e6i			0.882520i	−0.897379	+	0.441260i	$0.854532\pi$
$458$		−	8.96750e6i		−	1.99760i
$459$	−1.66386e6	+	489381.i	−0.368625	+	0.108421i
$460$		−	6.36186e6i		−	1.40181i
$461$			1.83132e6i			0.401340i	0.979659	+	0.200670i	$0.0643118\pi$
$461$			1.83132e6i			0.401340i	−0.979659	+	0.200670i	$0.935688\pi$
$462$	407587.	+	4.26157e6i	0.0888414	+	0.928891i
$463$		−	34543.7i		−	0.00748888i	−0.999993	−	0.00374444i	$-0.998808\pi$
$463$		−	34543.7i		−	0.00748888i	0.999993	−	0.00374444i	$-0.00119189\pi$
$464$		−	1.74649e6i		−	0.376591i
$465$	−965744.	−	1.00974e7i	−0.207124	−	2.16560i
$466$	6.38202e6			1.36142
$467$	−1.09698e6			−0.232759			−0.116379	−	0.993205i	$-0.537129\pi$
$467$	−1.09698e6			−0.232759			−0.116379	+	0.993205i	$0.537129\pi$
$468$	−318676.	−	1.65073e6i	−0.0672565	−	0.348388i
$469$			3.68952e6i			0.774529i
$470$			2.36390e7i			4.93610i
$471$	2.60266e6	−	248925.i	0.540586	−	0.0517030i
$472$	2.56478e6	+	1.26134e6i	0.529901	+	0.260602i
$473$			3.76318e6i			0.773397i
$474$	−1.08340e6	−	1.13276e7i	−0.221484	−	2.31575i
$475$	−1.84177e6			−0.374542
$476$		−	2.92521e6i		−	0.591751i
$477$	277293.	+	1.43637e6i	0.0558012	+	0.289049i
$478$			1.21262e6i			0.242747i
$479$		−	6.36093e6i		−	1.26672i	−0.773856	−	0.633361i	$-0.781675\pi$
$479$		−	6.36093e6i		−	1.26672i	0.773856	−	0.633361i	$-0.218325\pi$
$480$	−1.12816e7	+	1.07900e6i	−2.23494	+	0.213755i
$481$	−263935.			−0.0520157
$482$	3.83238e6			0.751365
$483$	−323556.	−	3.38298e6i	−0.0631077	−	0.659829i
$484$	−5.02662e6			−0.975354
$485$	8.11991e6			1.56746
$486$	−3.68838e6	−	7.14108e6i	−0.708345	−	1.37143i
$487$	728855.			0.139258			0.0696288	−	0.997573i	$-0.477819\pi$
$487$	728855.			0.139258			0.0696288	+	0.997573i	$0.477819\pi$
$488$			4.37925e6i			0.832435i
$489$	−566256.	−	5.92055e6i	−0.107088	−	1.11967i
$490$		−	3.36605e6i		−	0.633330i
$491$		−	8.18233e6i		−	1.53170i	−0.643020	−	0.765849i	$-0.722319\pi$
$491$		−	8.18233e6i		−	1.53170i	0.643020	−	0.765849i	$-0.277681\pi$
$492$	−5.17325e6	+	494782.i	−0.963498	+	0.0921513i
$493$	1.65768e6			0.307173
$494$		−	422821.i		−	0.0779542i
$495$	955547.	+	4.94972e6i	0.175283	+	0.907962i
$496$		−	3.29537e6i		−	0.601450i
$497$		−	4.11968e6i		−	0.748123i
$498$	402573.	+	4.20915e6i	0.0727397	+	0.760538i
$499$	2.98295e6			0.536284			0.268142	−	0.963379i	$-0.413590\pi$
$499$	2.98295e6			0.536284			0.268142	+	0.963379i	$0.413590\pi$
$500$		−	1.18956e7i		−	2.12794i
$501$	2.01859e6	−	193062.i	0.359296	−	0.0343640i
$502$		−	2.64850e6i		−	0.469072i
$503$	9.05383e6			1.59556			0.797779	−	0.602950i	$-0.206008\pi$
$503$	9.05383e6			1.59556			0.797779	+	0.602950i	$0.206008\pi$
$504$	3.68310e6	−	711026.i	0.645858	−	0.124683i
$505$			1.12491e7i			1.96285i
$506$	−2.87094e6			−0.498480
$507$	514759.	+	5.38212e6i	0.0889373	+	0.929893i
$508$	1.56606e7			2.69245
$509$	−2.07161e6			−0.354416			−0.177208	−	0.984173i	$-0.556707\pi$
$509$	−2.07161e6			−0.354416			−0.177208	+	0.984173i	$0.556707\pi$
$510$	−565156.	−	5.90905e6i	−0.0962150	−	1.00599i
$511$			6.53712e6i			1.10748i
$512$	−5.33186e6			−0.898884
$513$	−330980.	−	1.12531e6i	−0.0555276	−	0.188790i
$514$		−	7.37906e6i		−	1.23195i
$515$	−1.64919e7			−2.74001
$516$	1.18623e7	−	1.13454e6i	1.96130	−	0.187583i
$517$	6.19027e6			1.01855
$518$		−	2.12819e6i		−	0.348487i
$519$	824269.	+	8.61823e6i	0.134323	+	1.40443i
$520$	1.59223e6			0.258225
$521$		−	7.18160e6i		−	1.15912i	−0.814931	−	0.579558i	$-0.803225\pi$
$521$		−	7.18160e6i		−	1.15912i	0.814931	−	0.579558i	$-0.196775\pi$
$522$	1.45615e6	+	7.54284e6i	0.233900	+	1.21160i
$523$	−7.71703e6			−1.23366			−0.616830	−	0.787096i	$-0.711584\pi$
$523$	−7.71703e6			−1.23366			−0.616830	+	0.787096i	$0.711584\pi$
$524$	−8.49015e6			−1.35079
$525$	−1.27476e6	−	1.33284e7i	−0.201851	−	2.11047i
$526$			1.05933e7i			1.66943i
$527$	3.12780e6			0.490583
$528$	155925.	+	1.63029e6i	0.0243405	+	0.254495i
$529$	−4.15729e6			−0.645909
$530$	−5.00697e6			−0.774257
$531$	6.26823e6	+	1.71022e6i	0.964737	+	0.263217i
$532$	1.97839e6			0.303063
$533$	−1.17837e6			−0.179665
$534$	155335.	+	1.62412e6i	0.0235730	+	0.246471i
$535$	−1.04935e7			−1.58502
$536$		−	2.73105e6i		−	0.410599i
$537$	−581042.	−	6.07515e6i	−0.0869505	−	0.909120i
$538$	−7.28354e6			−1.08489
$539$	−881459.			−0.130686
$540$	1.53144e7	−	4.50433e6i	2.26004	−	0.664730i
$541$			502453.i			0.0738078i	0.999319	+	0.0369039i	$0.0117495\pi$
$541$			502453.i			0.0738078i	−0.999319	+	0.0369039i	$0.988250\pi$
$542$	1.07022e7			1.56486
$543$	−684043.	−	7.15208e6i	−0.0995597	−	1.04096i
$544$		−	3.49459e6i		−	0.506290i
$545$	8.97429e6			1.29422
$546$	3.05985e6	−	292651.i	0.439257	−	0.0420116i
$547$	−6.67433e6			−0.953761			−0.476880	−	0.878968i	$-0.658232\pi$
$547$	−6.67433e6			−0.953761			−0.476880	+	0.878968i	$0.658232\pi$
$548$		−	1.69093e7i		−	2.40532i
$549$	1.88702e6	+	9.77472e6i	0.267205	+	1.38412i
$550$	−1.13110e7			−1.59440
$551$			1.12113e6i			0.157317i
$552$	239502.	+	2.50414e6i	0.0334551	+	0.349793i
$553$	1.20728e7			1.67879
$554$	8.69669e6			1.20387
$555$	−238596.	−	2.49467e6i	−0.0328800	−	0.343780i
$556$	−1.66297e6			−0.228138
$557$			7.25630e6i			0.991008i	0.868606	+	0.495504i	$0.165017\pi$
$557$			7.25630e6i			0.991008i	−0.868606	+	0.495504i	$0.834983\pi$
$558$	2.74755e6	+	1.42322e7i	0.373559	+	1.93503i
$559$	2.70200e6			0.365726
$560$		−	6.63522e6i		−	0.894099i
$561$	−1.54739e6	+	147996.i	−0.207583	+	0.0198538i
$562$		−	9.71352e6i		−	1.29729i
$563$	−3.31267e6			−0.440461			−0.220230	−	0.975448i	$-0.570681\pi$
$563$	−3.31267e6			−0.440461			−0.220230	+	0.975448i	$0.570681\pi$
$564$	−1.86626e6	−	1.95129e7i	−0.247045	−	2.58300i
$565$			1.67849e7i			2.21206i
$566$		−	721152.i		−	0.0946206i
$567$	7.91449e6	−	3.17409e6i	1.03387	−	0.414631i
$568$			3.04947e6i			0.396600i
$569$	−1.16764e7			−1.51192			−0.755958	−	0.654620i	$-0.772828\pi$
$569$	−1.16764e7			−1.51192			−0.755958	+	0.654620i	$0.772828\pi$
$570$	3.99644e6	−	382229.i	0.515212	−	0.0492761i
$571$		−	7.84759e6i		−	1.00727i	−0.863916	−	0.503635i	$-0.831996\pi$
$571$		−	7.84759e6i		−	1.00727i	0.863916	−	0.503635i	$-0.168004\pi$
$572$		−	1.50684e6i		−	0.192564i
$573$	−874000.	−	9.13821e6i	−0.111205	−	1.16272i
$574$		−	9.50157e6i		−	1.20369i
$575$	8.97909e6			1.13256
$576$	1.22183e7	−	2.35875e6i	1.53445	−	0.296228i
$577$	−3.59585e6			−0.449638			−0.224819	−	0.974401i	$-0.572179\pi$
$577$	−3.59585e6			−0.449638			−0.224819	+	0.974401i	$0.572179\pi$
$578$	−1.05673e7			−1.31567
$579$	−20500.7	−	214348.i	−0.00254140	−	0.0265719i
$580$	−1.52575e7			−1.88327
$581$	−4.48608e6			−0.551350
$582$	−1.15506e7	+	1.10473e6i	−1.41350	+	0.135191i
$583$			1.31116e6i			0.159766i
$584$		−	4.83890e6i		−	0.587103i
$585$	3.55395e6	−	686093.i	0.429360	−	0.0828883i
$586$		−	6.04204e6i		−	0.726841i
$587$	−3.72961e6			−0.446754			−0.223377	−	0.974732i	$-0.571708\pi$
$587$	−3.72961e6			−0.446754			−0.223377	+	0.974732i	$0.571708\pi$
$588$	265745.	+	2.77853e6i	0.0316973	+	0.331414i
$589$			2.11541e6i			0.251250i
$590$	−9.81395e6	+	1.99555e7i	−1.16068	+	2.36011i
$591$	−7.75257e6	+	741475.i	−0.913013	+	0.0873228i
$592$		−	814152.i		−	0.0954775i
$593$			8.48469e6i			0.990830i	0.868657	+	0.495415i	$0.164984\pi$
$593$			8.48469e6i			0.990830i	−0.868657	+	0.495415i	$0.835016\pi$
$594$	−2.03269e6	−	6.91099e6i	−0.236376	−	0.803663i
$595$	6.29782e6			0.729286
$596$	−1.93577e6			−0.223223
$597$	1.05794e6	+	1.10614e7i	0.121485	+	1.27020i
$598$			2.06136e6i			0.235723i
$599$			6.34558e6i			0.722610i	0.932448	+	0.361305i	$0.117669\pi$
$599$			6.34558e6i			0.722610i	−0.932448	+	0.361305i	$0.882331\pi$
$600$	943601.	+	9.86592e6i	0.107007	+	1.11882i
$601$			419675.i			0.0473944i	0.999719	+	0.0236972i	$0.00754376\pi$
$601$			419675.i			0.0473944i	−0.999719	+	0.0236972i	$0.992456\pi$
$602$			2.17871e7i			2.45024i
$603$	−1.17681e6	−	6.09584e6i	−0.131799	−	0.682717i
$604$			2.11777e7i			2.36204i
$605$		−	1.08221e7i		−	1.20205i
$606$	−1.53045e6	−	1.60018e7i	−0.169293	−	1.77006i
$607$	1.49015e7			1.64157			0.820784	−	0.571239i	$-0.193537\pi$
$607$	1.49015e7			1.64157			0.820784	+	0.571239i	$0.193537\pi$
$608$	2.36348e6			0.259294
$609$	−8.11332e6	+	775978.i	−0.886453	+	0.0847825i
$610$	−3.40731e7			−3.70755
$611$		−	4.44468e6i		−	0.481656i
$612$	933023.	+	4.83304e6i	0.100696	+	0.521606i
$613$			1.24526e7i			1.33847i	0.743050	+	0.669236i	$0.233379\pi$
$613$			1.24526e7i			1.33847i	−0.743050	+	0.669236i	$0.766621\pi$
$614$	1.64900e7			1.76522
$615$	−1.06524e6	−	1.11377e7i	−0.113569	−	1.18743i
$616$	3.36204e6			0.356986
$617$			1.53268e7i			1.62084i	0.585851	+	0.810419i	$0.300760\pi$
$617$			1.53268e7i			1.62084i	−0.585851	+	0.810419i	$0.699240\pi$
$618$	2.34597e7	−	2.24375e6i	2.47088	−	0.236321i
$619$	1.81170e6			0.190047			0.0950233	−	0.995475i	$-0.469707\pi$
$619$	1.81170e6			0.190047			0.0950233	+	0.995475i	$0.469707\pi$
$620$	−2.87887e7			−3.00776
$621$	1.61362e6	+	5.48618e6i	0.167908	+	0.570875i
$622$		−	1.52024e7i		−	1.57557i
$623$	−1.73098e6			−0.178678
$624$	1.17056e6	−	111955.i	0.120346	−	0.0115102i
$625$	7.02372e6			0.719229
$626$		−	5.50461e6i		−	0.561424i
$627$	−100093.	−	1.04654e6i	−0.0101680	−	0.106313i
$628$		−	7.42041e6i		−	0.750808i
$629$	772753.			0.0778778
$630$	5.53219e6	+	2.86566e7i	0.555323	+	2.87656i
$631$	1.30180e6			0.130158			0.0650790	−	0.997880i	$-0.479270\pi$
$631$	1.30180e6			0.130158			0.0650790	+	0.997880i	$0.479270\pi$
$632$	−8.93655e6			−0.889973
$633$	1.14312e7	−	1.09330e6i	1.13392	−	0.108450i
$634$		−	1.35030e7i		−	1.33416i
$635$			3.37164e7i			3.31823i
$636$	4.13304e6	−	395294.i	0.405160	−	0.0387505i
$637$			632896.i			0.0617993i
$638$			6.88531e6i			0.669687i
$639$	1.31401e6	+	6.80656e6i	0.127306	+	0.659441i
$640$			1.93265e7i			1.86510i
$641$			6.75437e6i			0.649292i	0.945836	+	0.324646i	$0.105245\pi$
$641$			6.75437e6i			0.649292i	−0.945836	+	0.324646i	$0.894755\pi$
$642$	1.49270e7	−	1.42766e6i	1.42934	−	0.136706i
$643$	−1.60869e7			−1.53442			−0.767211	−	0.641395i	$-0.778356\pi$
$643$	−1.60869e7			−1.53442			−0.767211	+	0.641395i	$0.778356\pi$
$644$	−9.64517e6			−0.916422
$645$	2.44260e6	+	2.55389e7i	0.231181	+	2.41714i
$646$			1.23794e6i			0.116713i
$647$			1.76697e6i			0.165947i	0.996552	+	0.0829733i	$0.0264416\pi$
$647$			1.76697e6i			0.165947i	−0.996552	+	0.0829733i	$0.973558\pi$
$648$	−5.85845e6	+	2.34952e6i	−0.548082	+	0.219807i
$649$	5.22569e6	+	2.56996e6i	0.487003	+	0.239505i
$650$			8.12144e6i			0.753963i
$651$	−1.53087e7	+	1.46416e6i	−1.41574	+	0.135405i
$652$	−1.68800e7			−1.55508
$653$			1.06273e7i			0.975305i	0.873038	+	0.487652i	$0.162147\pi$
$653$			1.06273e7i			0.975305i	−0.873038	+	0.487652i	$0.837853\pi$
$654$	−1.27660e7	+	1.22097e6i	−1.16710	+	0.111624i
$655$		−	1.82789e7i		−	1.66474i
$656$		−	3.63488e6i		−	0.329784i
$657$	−2.08508e6	−	1.08007e7i	−0.188455	−	0.976196i
$658$	3.58389e7			3.22693
$659$	−1.82151e7			−1.63387			−0.816937	−	0.576727i	$-0.804330\pi$
$659$	−1.82151e7			−1.63387			−0.816937	+	0.576727i	$0.804330\pi$
$660$	1.42424e7	−	1.36218e6i	1.27269	−	0.121723i
$661$	9.70544e6			0.863996			0.431998	−	0.901875i	$-0.357809\pi$
$661$	9.70544e6			0.863996			0.431998	+	0.901875i	$0.357809\pi$
$662$	2.73912e7			2.42921
$663$	106263.	+	1.11104e6i	0.00938850	+	0.0981625i
$664$	3.32068e6			0.292285
$665$			4.25937e6i			0.373501i
$666$	678808.	+	3.51621e6i	0.0593009	+	0.307178i
$667$		−	5.46580e6i		−	0.475706i
$668$		−	5.75517e6i		−	0.499019i
$669$	−1.60985e6	−	1.68320e7i	−0.139066	−	1.45402i
$670$	2.12491e7			1.82875
$671$			8.92264e6i			0.765045i
$672$	1.63586e6	+	1.71039e7i	0.139741	+	1.46107i
$673$		−	1.50186e7i		−	1.27818i	−0.769131	−	0.639092i	$-0.779310\pi$
$673$		−	1.50186e7i		−	1.27818i	0.769131	−	0.639092i	$-0.220690\pi$
$674$		−	1.94198e7i		−	1.64663i
$675$	6.35739e6	+	2.16147e7i	0.537055	+	1.82595i
$676$	1.53449e7			1.29151
$677$		−	1.77507e6i		−	0.148848i	−0.997227	−	0.0744242i	$-0.976288\pi$
$677$		−	1.77507e6i		−	0.148848i	0.997227	−	0.0744242i	$-0.0237119\pi$
$678$	−2.28361e6	−	2.38766e7i	−0.190787	−	1.99479i
$679$		−	1.23105e7i		−	1.02471i
$680$	−4.66177e6			−0.386615
$681$	1.76175e6	+	1.84202e7i	0.145572	+	1.52204i
$682$			1.29916e7i			1.06955i
$683$	−1.56418e7			−1.28302			−0.641512	−	0.767113i	$-0.721693\pi$
$683$	−1.56418e7			−1.28302			−0.641512	+	0.767113i	$0.721693\pi$
$684$	−3.26871e6	+	631027.i	−0.267138	+	0.0515712i
$685$	3.64048e7			2.96437
$686$	1.60894e7			1.30535
$687$	−1.59367e7	+	1.52423e6i	−1.28827	+	0.123214i
$688$			8.33478e6i			0.671310i
$689$	941428.			0.0755508
$690$	−1.94837e7	+	1.86347e6i	−1.55793	+	0.149004i
$691$			1.77867e7i			1.41710i	0.705663	+	0.708548i	$0.250649\pi$
$691$			1.77867e7i			1.41710i	−0.705663	+	0.708548i	$0.749351\pi$
$692$	2.45713e7			1.95058
$693$	7.50424e6	−	1.44870e6i	0.593572	−	0.114590i
$694$	1.11789e7			0.881053
$695$		−	3.58030e6i		−	0.281162i
$696$	6.00563e6	−	574393.i	0.469933	−	0.0449455i
$697$	3.45005e6			0.268994
$698$		−	1.94312e7i		−	1.50960i
$699$	−1.08477e6	−	1.13419e7i	−0.0839739	−	0.877998i
$700$	−3.80004e7			−2.93119
$701$	1.29116e7			0.992396			0.496198	−	0.868209i	$-0.334729\pi$
$701$	1.29116e7			0.992396			0.496198	+	0.868209i	$0.334729\pi$
$702$	−4.96216e6	+	1.45949e6i	−0.380039	+	0.111778i
$703$			522632.i			0.0398848i
$704$	1.11532e7			0.848140
$705$	4.20104e7	−	4.01797e6i	3.18334	−	0.304463i
$706$	2.90876e7			2.19632
$707$	1.70546e7			1.28320
$708$	6.52554e6	−	1.72472e7i	0.489253	−	1.29311i
$709$	−2.17279e7			−1.62331			−0.811657	−	0.584134i	$-0.801434\pi$
$709$	−2.17279e7			−1.62331			−0.811657	+	0.584134i	$0.801434\pi$
$710$	−2.37266e7			−1.76640
$711$	−1.99468e7	+	3.85075e6i	−1.47979	+	0.285674i
$712$	1.28130e6			0.0947221
$713$		−	1.03132e7i		−	0.759746i
$714$	−8.95867e6	+	856829.i	−0.657655	+	0.0628997i
$715$	3.24414e6			0.237320
$716$	−1.73208e7			−1.26266
$717$	2.15502e6	−	206112.i	0.156550	−	0.0149729i
$718$			3.37338e7i			2.44205i
$719$	−7.86562e6			−0.567428			−0.283714	−	0.958909i	$-0.591567\pi$
$719$	−7.86562e6			−0.567428			−0.283714	+	0.958909i	$0.591567\pi$
$720$	2.11637e6	+	1.09628e7i	0.152146	+	0.788113i
$721$			2.50032e7i			1.79126i
$722$	2.07832e7			1.48378
$723$	−651399.	−	6.81078e6i	−0.0463449	−	0.484564i
$724$	−2.03912e7			−1.44576
$725$		−	2.15344e7i		−	1.52155i
$726$	1.47236e6	+	1.53944e7i	0.103674	+	1.08398i
$727$	−2.35104e7			−1.64977			−0.824886	−	0.565300i	$-0.808761\pi$
$727$	−2.35104e7			−1.64977			−0.824886	+	0.565300i	$0.808761\pi$
$728$		−	2.41398e6i		−	0.168813i
$729$	−1.20640e7	+	7.76866e6i	−0.840758	+	0.541411i
$730$	3.76494e7			2.61487
$731$	−7.91096e6			−0.547565
$732$	2.81259e7	−	2.69003e6i	1.94012	−	0.185558i
$733$	−1.03370e7			−0.710615			−0.355308	−	0.934749i	$-0.615624\pi$
$733$	−1.03370e7			−0.710615			−0.355308	+	0.934749i	$0.615624\pi$
$734$		−	3.44320e7i		−	2.35897i
$735$	−5.98203e6	+	572136.i	−0.408442	+	0.0390644i
$736$	−1.15226e7			−0.784072
$737$		−	5.56446e6i		−	0.377358i
$738$	3.03062e6	+	1.56985e7i	0.204828	+	1.06101i
$739$		−	1.98195e7i		−	1.33500i	−0.744611	−	0.667499i	$-0.767365\pi$
$739$		−	1.98195e7i		−	1.33500i	0.744611	−	0.667499i	$-0.232635\pi$
$740$	−7.11253e6			−0.477468
$741$	−751424.	+	71868.0i	−0.0502735	+	0.00480828i
$742$			7.59104e6i			0.506164i
$743$			1.67323e7i			1.11195i	0.831200	+	0.555973i	$0.187654\pi$
$743$			1.67323e7i			1.11195i	−0.831200	+	0.555973i	$0.812346\pi$
$744$	1.13318e7	−	1.08380e6i	0.750525	−	0.0717820i
$745$		−	4.16763e6i		−	0.275105i
$746$	−1.98732e7			−1.30744
$747$	7.41193e6	−	1.43088e6i	0.485993	−	0.0938213i
$748$			4.41174e6i			0.288307i
$749$			1.59091e7i			1.03620i
$750$	−3.64311e7	+	3.48436e6i	−2.36493	+	0.226188i
$751$			6.30270e6i			0.407781i	0.978994	+	0.203890i	$0.0653586\pi$
$751$			6.30270e6i			0.407781i	−0.978994	+	0.203890i	$0.934641\pi$
$752$	1.37104e7			0.884106
$753$	−4.70682e6	+	450172.i	−0.302510	+	0.0289328i
$754$	4.94372e6			0.316684
$755$	−4.55945e7			−2.91102
$756$	−6.82898e6	−	2.32181e7i	−0.434562	−	1.47748i
$757$	1.17960e7			0.748161			0.374081	−	0.927396i	$-0.377958\pi$
$757$	1.17960e7			0.748161			0.374081	+	0.927396i	$0.377958\pi$
$758$	−3.37198e6			−0.213163
$759$	487981.	+	5.10214e6i	0.0307467	+	0.321476i
$760$		−	3.15287e6i		−	0.198003i
$761$		−	1.13477e7i		−	0.710306i	−0.934808	−	0.355153i	$-0.884429\pi$
$761$		−	1.13477e7i		−	0.710306i	0.934808	−	0.355153i	$-0.115571\pi$
$762$	−4.58717e6	−	4.79617e7i	−0.286192	−	2.99231i
$763$		−	1.36059e7i		−	0.846087i
$764$	−2.60538e7			−1.61487
$765$	−1.04053e7	+	2.00875e6i	−0.642837	+	0.124100i
$766$			1.31985e7i			0.812743i
$767$	1.84525e6	−	3.75209e6i	0.113258	−	0.230295i
$768$	−197329.	−	2.06320e6i	−0.0120722	−	0.126223i
$769$			3.63980e6i			0.221954i	0.993823	+	0.110977i	$0.0353979\pi$
$769$			3.63980e6i			0.221954i	−0.993823	+	0.110977i	$0.964602\pi$
$770$			2.61586e7i			1.58996i
$771$	−1.31138e7	+	1.25424e6i	−0.794499	+	0.0759878i
$772$	−611124.			−0.0369051
$773$	−2.88048e7			−1.73387			−0.866934	−	0.498423i	$-0.833913\pi$
$773$	−2.88048e7			−1.73387			−0.866934	+	0.498423i	$0.833913\pi$
$774$	−6.94921e6	−	3.59968e7i	−0.416949	−	2.15979i
$775$		−	4.06322e7i		−	2.43006i
$776$			9.11250e6i			0.543229i
$777$	−3.78215e6	+	361734.i	−0.224743	+	0.0214950i
$778$			1.51706e7i			0.898576i
$779$			2.33335e6i

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)

\(f(q)\)	\(=\)	\(q-8.73168 q^{2} +(1.48415 + 15.5176i) q^{3} +44.2422 q^{4} +95.2512i q^{5} +(-12.9591 - 135.495i) q^{6} +144.410 q^{7} -106.895 q^{8} +(-238.595 + 46.0609i) q^{9} +O(q^{10})\)	\(q-8.73168 q^{2} +(1.48415 + 15.5176i) q^{3} +44.2422 q^{4} +95.2512i q^{5} +(-12.9591 - 135.495i) q^{6} +144.410 q^{7} -106.895 q^{8} +(-238.595 + 46.0609i) q^{9} -831.703i q^{10} -217.796 q^{11} +(65.6618 + 686.534i) q^{12} +156.380i q^{13} -1260.94 q^{14} +(-1478.07 + 141.367i) q^{15} -482.379 q^{16} -457.850i q^{17} +(2083.33 - 402.189i) q^{18} +309.656 q^{19} +4214.12i q^{20} +(214.325 + 2240.90i) q^{21} +1901.72 q^{22} -1509.65 q^{23} +(-158.647 - 1658.76i) q^{24} -5947.79 q^{25} -1365.46i q^{26} +(-1068.87 - 3634.07i) q^{27} +6389.00 q^{28} +3620.57i q^{29} +(12906.1 - 1234.37i) q^{30} +6831.48i q^{31} +7632.61 q^{32} +(-323.241 - 3379.68i) q^{33} +3997.80i q^{34} +13755.2i q^{35} +(-10555.9 + 2037.83i) q^{36} +1687.78i q^{37} -2703.81 q^{38} +(-2426.64 + 232.090i) q^{39} -10181.9i q^{40} +7535.31i q^{41} +(-1871.42 - 19566.8i) q^{42} -17278.5i q^{43} -9635.76 q^{44} +(-4387.35 - 22726.4i) q^{45} +13181.8 q^{46} -28422.4 q^{47} +(-715.921 - 7485.39i) q^{48} +4047.18 q^{49} +51934.2 q^{50} +(7104.76 - 679.517i) q^{51} +6918.57i q^{52} -6020.14i q^{53} +(9332.99 + 31731.5i) q^{54} -20745.3i q^{55} -15436.6 q^{56} +(459.574 + 4805.13i) q^{57} -31613.6i q^{58} +(-23993.5 - 11799.8i) q^{59} +(-65393.2 + 6254.37i) q^{60} -40967.9i q^{61} -59650.3i q^{62} +(-34455.4 + 6651.64i) q^{63} -51209.4 q^{64} -14895.3 q^{65} +(2822.43 + 29510.3i) q^{66} +25548.9i q^{67} -20256.3i q^{68} +(-2240.54 - 23426.3i) q^{69} -120106. i q^{70} -28527.7i q^{71} +(25504.5 - 4923.67i) q^{72} +45267.9i q^{73} -14737.2i q^{74} +(-8827.38 - 92295.7i) q^{75} +13699.8 q^{76} -31451.8 q^{77} +(21188.7 - 2026.54i) q^{78} +83601.3 q^{79} -45947.2i q^{80} +(54805.8 - 21979.8i) q^{81} -65795.9i q^{82} -31065.0 q^{83} +(9482.21 + 99142.3i) q^{84} +43610.8 q^{85} +150870. i q^{86} +(-56182.7 + 5373.45i) q^{87} +23281.2 q^{88} -11986.6 q^{89} +(38309.0 + 198440. i) q^{90} +22582.7i q^{91} -66790.3 q^{92} +(-106009. + 10138.9i) q^{93} +248175. q^{94} +29495.1i q^{95} +(11327.9 + 118440. i) q^{96} -85247.4i q^{97} -35338.6 q^{98} +(51964.9 - 10031.9i) 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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