LMFDB - Embedded newform 177.6.d.b.176.9

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			176.9
Character	$\chi$	$=$	177.176
Dual form			177.6.d.b.176.10

$q$-expansion

$f(q)$	$=$	$q-9.63720 q^{2} +(15.3454 - 2.74211i) q^{3} +60.8757 q^{4} -48.0995i q^{5} +(-147.887 + 26.4263i) q^{6} +55.2643 q^{7} -278.281 q^{8} +(227.962 - 84.1575i) q^{9} +O(q^{10})$	\(q-9.63720 q^{2} +(15.3454 - 2.74211i) q^{3} +60.8757 q^{4} -48.0995i q^{5} +(-147.887 + 26.4263i) q^{6} +55.2643 q^{7} -278.281 q^{8} +(227.962 - 84.1575i) q^{9} +463.545i q^{10} -33.0223 q^{11} +(934.161 - 166.928i) q^{12} -847.868i q^{13} -532.594 q^{14} +(-131.894 - 738.106i) q^{15} +733.828 q^{16} -1128.87i q^{17} +(-2196.91 + 811.043i) q^{18} -1381.08 q^{19} -2928.09i q^{20} +(848.052 - 151.541i) q^{21} +318.243 q^{22} +468.321 q^{23} +(-4270.33 + 763.077i) q^{24} +811.434 q^{25} +8171.08i q^{26} +(3267.39 - 1916.53i) q^{27} +3364.25 q^{28} +408.390i q^{29} +(1271.09 + 7113.28i) q^{30} +5084.86i q^{31} +1832.94 q^{32} +(-506.740 + 90.5508i) q^{33} +10879.1i q^{34} -2658.19i q^{35} +(13877.3 - 5123.15i) q^{36} -1578.30i q^{37} +13309.8 q^{38} +(-2324.95 - 13010.9i) q^{39} +13385.2i q^{40} +16986.4i q^{41} +(-8172.85 + 1460.43i) q^{42} -11165.2i q^{43} -2010.26 q^{44} +(-4047.94 - 10964.9i) q^{45} -4513.30 q^{46} -12073.6 q^{47} +(11260.9 - 2012.24i) q^{48} -13752.9 q^{49} -7819.96 q^{50} +(-3095.48 - 17322.9i) q^{51} -51614.6i q^{52} +9984.02i q^{53} +(-31488.5 + 18469.9i) q^{54} +1588.36i q^{55} -15379.0 q^{56} +(-21193.2 + 3787.08i) q^{57} -3935.73i q^{58} +(19800.7 - 17968.2i) q^{59} +(-8029.16 - 44932.7i) q^{60} -50439.9i q^{61} -49003.8i q^{62} +(12598.1 - 4650.91i) q^{63} -41146.9 q^{64} -40782.1 q^{65} +(4883.55 - 872.656i) q^{66} -34064.3i q^{67} -68720.5i q^{68} +(7186.57 - 1284.19i) q^{69} +25617.5i q^{70} -18917.3i q^{71} +(-63437.4 + 23419.4i) q^{72} +23663.0i q^{73} +15210.4i q^{74} +(12451.8 - 2225.04i) q^{75} -84074.3 q^{76} -1824.95 q^{77} +(22406.0 + 125388. i) q^{78} -61929.7 q^{79} -35296.8i q^{80} +(44884.0 - 38369.4i) q^{81} -163701. i q^{82} -31566.8 q^{83} +(51625.8 - 9225.16i) q^{84} -54297.9 q^{85} +107601. i q^{86} +(1119.85 + 6266.90i) q^{87} +9189.48 q^{88} +52358.2 q^{89} +(39010.8 + 105671. i) q^{90} -46856.9i q^{91} +28509.4 q^{92} +(13943.2 + 78029.1i) q^{93} +116356. q^{94} +66429.4i q^{95} +(28127.2 - 5026.12i) q^{96} +25026.4i q^{97} +132539. q^{98} +(-7527.82 + 2779.07i) 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 $

$2$	−9.63720			−1.70363			−0.851817	−	0.523840i	$-0.824499\pi$
$2$	−9.63720			−1.70363			−0.851817	+	0.523840i	$0.824499\pi$
$3$	15.3454	−	2.74211i	0.984407	−	0.175907i
$3$	15.3454	−	2.74211i	0.984407	−	0.175907i
$4$	60.8757			1.90237
$5$		−	48.0995i		−	0.860431i	−0.902726	−	0.430215i	$-0.858438\pi$
$5$		−	48.0995i		−	0.860431i	0.902726	−	0.430215i	$-0.141562\pi$
$6$	−147.887	+	26.4263i	−1.67707	+	0.299680i
$7$	55.2643			0.426285			0.213142	−	0.977021i	$-0.431630\pi$
$7$	55.2643			0.426285			0.213142	+	0.977021i	$0.431630\pi$
$8$	−278.281			−1.53730
$9$	227.962	−	84.1575i	0.938114	−	0.346327i
$10$			463.545i			1.46586i
$11$	−33.0223			−0.0822859			−0.0411430	−	0.999153i	$-0.513100\pi$
$11$	−33.0223			−0.0822859			−0.0411430	+	0.999153i	$0.513100\pi$
$12$	934.161	−	166.928i	1.87270	−	0.334638i
$13$		−	847.868i		−	1.39146i	−0.718305	−	0.695729i	$-0.755082\pi$
$13$		−	847.868i		−	1.39146i	0.718305	−	0.695729i	$-0.244918\pi$
$14$	−532.594			−0.726233
$15$	−131.894	−	738.106i	−0.151355	−	0.847014i
$16$	733.828			0.716629
$17$		−	1128.87i		−	0.947371i	−0.880694	−	0.473686i	$-0.842923\pi$
$17$		−	1128.87i		−	0.947371i	0.880694	−	0.473686i	$-0.157077\pi$
$18$	−2196.91	+	811.043i	−1.59820	+	0.590014i
$19$	−1381.08			−0.877678			−0.438839	−	0.898566i	$-0.644610\pi$
$19$	−1381.08			−0.877678			−0.438839	+	0.898566i	$0.644610\pi$
$20$		−	2928.09i		−	1.63685i
$21$	848.052	−	151.541i	0.419638	−	0.0749863i
$22$	318.243			0.140185
$23$	468.321			0.184597			0.0922984	−	0.995731i	$-0.470579\pi$
$23$	468.321			0.184597			0.0922984	+	0.995731i	$0.470579\pi$
$24$	−4270.33	+	763.077i	−1.51333	+	0.270421i
$25$	811.434			0.259659
$26$			8171.08i			2.37053i
$27$	3267.39	−	1916.53i	0.862564	−	0.505947i
$28$	3364.25			0.810949
$29$			408.390i			0.0901737i	0.998983	+	0.0450868i	$0.0143565\pi$
$29$			408.390i			0.0901737i	−0.998983	+	0.0450868i	$0.985644\pi$
$30$	1271.09	+	7113.28i	0.257854	+	1.44300i
$31$			5084.86i			0.950330i	0.879897	+	0.475165i	$0.157612\pi$
$31$			5084.86i			0.950330i	−0.879897	+	0.475165i	$0.842388\pi$
$32$	1832.94			0.316427
$33$	−506.740	+	90.5508i	−0.0810028	+	0.0144746i
$34$			10879.1i			1.61397i
$35$		−	2658.19i		−	0.366789i
$36$	13877.3	−	5123.15i	1.78464	−	0.658841i
$37$		−	1578.30i		−	0.189533i	−0.995500	−	0.0947666i	$-0.969790\pi$
$37$		−	1578.30i		−	0.189533i	0.995500	−	0.0947666i	$-0.0302105\pi$
$38$	13309.8			1.49524
$39$	−2324.95	−	13010.9i	−0.244766	−	1.36976i
$40$			13385.2i			1.32274i
$41$			16986.4i			1.57813i	0.614312	+	0.789063i	$0.289434\pi$
$41$			16986.4i			1.57813i	−0.614312	+	0.789063i	$0.710566\pi$
$42$	−8172.85	+	1460.43i	−0.714909	+	0.127749i
$43$		−	11165.2i		−	0.920863i	−0.887695	−	0.460431i	$-0.847695\pi$
$43$		−	11165.2i		−	0.920863i	0.887695	−	0.460431i	$-0.152305\pi$
$44$	−2010.26			−0.156538
$45$	−4047.94	−	10964.9i	−0.297991	−	0.807182i
$46$	−4513.30			−0.314485
$47$	−12073.6			−0.797249			−0.398624	−	0.917114i	$-0.630512\pi$
$47$	−12073.6			−0.797249			−0.398624	+	0.917114i	$0.630512\pi$
$48$	11260.9	−	2012.24i	0.705455	−	0.126060i
$49$	−13752.9			−0.818281
$50$	−7819.96			−0.442364
$51$	−3095.48	−	17322.9i	−0.166649	−	0.932599i
$52$		−	51614.6i		−	2.64706i
$53$			9984.02i			0.488220i	0.969748	+	0.244110i	$0.0784958\pi$
$53$			9984.02i			0.488220i	−0.969748	+	0.244110i	$0.921504\pi$
$54$	−31488.5	+	18469.9i	−1.46949	+	0.861948i
$55$			1588.36i			0.0708013i
$56$	−15379.0			−0.655327
$57$	−21193.2	+	3787.08i	−0.863992	+	0.154389i
$58$		−	3935.73i		−	0.153623i
$59$	19800.7	−	17968.2i	0.740543	−	0.672009i
$59$	19800.7	−	17968.2i	0.740543	−	0.672009i
$60$	−8029.16	−	44932.7i	−0.287933	−	1.61133i
$61$		−	50439.9i		−	1.73560i	−0.496914	−	0.867800i	$-0.665534\pi$
$61$		−	50439.9i		−	1.73560i	0.496914	−	0.867800i	$-0.334466\pi$
$62$		−	49003.8i		−	1.61901i
$63$	12598.1	−	4650.91i	0.399904	−	0.147634i
$64$	−41146.9			−1.25570
$65$	−40782.1			−1.19725
$66$	4883.55	−	872.656i	0.137999	−	0.0246595i
$67$		−	34064.3i		−	0.927070i	−0.886079	−	0.463535i	$-0.846581\pi$
$67$		−	34064.3i		−	0.927070i	0.886079	−	0.463535i	$-0.153419\pi$
$68$		−	68720.5i		−	1.80225i
$69$	7186.57	−	1284.19i	0.181718	−	0.0324718i
$70$			25617.5i			0.624873i
$71$		−	18917.3i		−	0.445363i	−0.974891	−	0.222682i	$-0.928519\pi$
$71$		−	18917.3i		−	0.445363i	0.974891	−	0.222682i	$-0.0714810\pi$
$72$	−63437.4	+	23419.4i	−1.44216	+	0.532409i
$73$			23663.0i			0.519711i	0.965647	+	0.259856i	$0.0836750\pi$
$73$			23663.0i			0.519711i	−0.965647	+	0.259856i	$0.916325\pi$
$74$			15210.4i			0.322895i
$75$	12451.8	−	2225.04i	0.255610	−	0.0456757i
$76$	−84074.3			−1.66966
$77$	−1824.95			−0.0350772
$78$	22406.0	+	125388.i	0.416992	+	2.33357i
$79$	−61929.7			−1.11643			−0.558214	−	0.829697i	$-0.688513\pi$
$79$	−61929.7			−1.11643			−0.558214	+	0.829697i	$0.688513\pi$
$80$		−	35296.8i		−	0.616610i
$81$	44884.0	−	38369.4i	0.760115	−	0.649789i
$82$		−	163701.i		−	2.68855i
$83$	−31566.8			−0.502962			−0.251481	−	0.967862i	$-0.580918\pi$
$83$	−31566.8			−0.502962			−0.251481	+	0.967862i	$0.580918\pi$
$84$	51625.8	−	9225.16i	0.798304	−	0.142651i
$85$	−54297.9			−0.815147
$86$			107601.i			1.56881i
$87$	1119.85	+	6266.90i	0.0158621	+	0.0887676i
$88$	9189.48			0.126498
$89$	52358.2			0.700664			0.350332	−	0.936626i	$-0.386069\pi$
$89$	52358.2			0.700664			0.350332	+	0.936626i	$0.386069\pi$
$90$	39010.8	+	105671.i	0.507667	+	1.37514i
$91$		−	46856.9i		−	0.593157i
$92$	28509.4			0.351170
$93$	13943.2	+	78029.1i	0.167169	+	0.935512i
$94$	116356.			1.35822
$95$			66429.4i			0.755181i
$96$	28127.2	−	5026.12i	0.311493	−	0.0556615i
$97$			25026.4i			0.270066i	0.990841	+	0.135033i	$0.0431140\pi$
$97$			25026.4i			0.270066i	−0.990841	+	0.135033i	$0.956886\pi$
$98$	132539.			1.39405
$99$	−7527.82	+	2779.07i	−0.0771936	+	0.0284978i
$100$	49396.6			0.493966
$101$	−43891.2			−0.428128			−0.214064	−	0.976820i	$-0.568670\pi$
$101$	−43891.2			−0.428128			−0.214064	+	0.976820i	$0.568670\pi$
$102$	29831.7	+	166944.i	0.283908	+	1.58881i
$103$			13348.4i			0.123976i	0.998077	+	0.0619880i	$0.0197440\pi$
$103$			13348.4i			0.123976i	−0.998077	+	0.0619880i	$0.980256\pi$
$104$			235946.i			2.13909i
$105$	−7289.05	−	40790.9i	−0.0645205	−	0.361069i
$106$		−	96218.0i		−	0.831748i
$107$		−	202715.i		−	1.71170i	−0.517226	−	0.855849i	$-0.673035\pi$
$107$		−	202715.i		−	1.71170i	0.517226	−	0.855849i	$-0.326965\pi$
$108$	198905.	−	116670.i	1.64091	−	0.962496i
$109$			25308.3i			0.204031i	0.994783	+	0.102016i	$0.0325292\pi$
$109$			25308.3i			0.204031i	−0.994783	+	0.102016i	$0.967471\pi$
$110$		−	15307.3i		−	0.120619i
$111$	−4327.87	−	24219.6i	−0.0333401	−	0.186578i
$112$	40554.5			0.305488
$113$	−158888.			−1.17056			−0.585281	−	0.810831i	$-0.699016\pi$
$113$	−158888.			−1.17056			−0.585281	+	0.810831i	$0.699016\pi$
$114$	204243.	−	36496.8i	1.47193	−	0.263023i
$115$		−	22526.0i		−	0.158833i
$116$			24861.0i			0.171543i
$117$	−71354.5	−	193281.i	−0.481899	−	1.30535i
$118$	−190823.	+	173163.i	−1.26161	+	1.14486i
$119$		−	62386.0i		−	0.403850i
$120$	36703.7	+	205401.i	0.232679	+	1.30211i
$121$	−159961.			−0.993229
$122$			486099.i			2.95682i
$123$	46578.6	+	260663.i	0.277603	+	1.55352i
$124$			309544.i			1.80788i
$125$		−	189341.i		−	1.08385i
$126$	−121411.	+	44821.7i	−0.681289	+	0.251514i
$127$	22410.3			0.123293			0.0616464	−	0.998098i	$-0.480365\pi$
$127$	22410.3			0.123293			0.0616464	+	0.998098i	$0.480365\pi$
$128$	337887.			1.82283
$129$	−30616.2	−	171334.i	−0.161986	−	0.906504i
$130$	393025.			2.03968
$131$	21644.2			0.110195			0.0550976	−	0.998481i	$-0.482453\pi$
$131$	21644.2			0.110195			0.0550976	+	0.998481i	$0.482453\pi$
$132$	−30848.1	+	5512.34i	−0.154097	+	0.0275360i
$133$	−76324.5			−0.374141
$134$			328285.i			1.57939i
$135$	−92184.0	−	157160.i	−0.435333	−	0.742177i
$136$			314142.i			1.45639i
$137$			79532.7i			0.362030i	0.983480	+	0.181015i	$0.0579382\pi$
$137$			79532.7i			0.362030i	−0.983480	+	0.181015i	$0.942062\pi$
$138$	−69258.4	+	12376.0i	−0.309581	+	0.0553200i
$139$	102245.			0.448852			0.224426	−	0.974491i	$-0.427949\pi$
$139$	102245.			0.448852			0.224426	+	0.974491i	$0.427949\pi$
$140$		−	161819.i		−	0.697766i
$141$	−185275.	+	33107.3i	−0.784817	+	0.140241i
$142$			182310.i			0.758735i
$143$			27998.5i			0.114497i
$144$	167285.	−	61757.1i	0.672280	−	0.248188i
$145$	19643.4			0.0775882
$146$		−	228045.i		−	0.885398i
$147$	−211043.	+	37711.9i	−0.805522	+	0.143941i
$148$		−	96080.1i		−	0.360561i
$149$	73849.9			0.272511			0.136256	−	0.990674i	$-0.456493\pi$
$149$	73849.9			0.272511			0.136256	+	0.990674i	$0.456493\pi$
$150$	−120000.	+	21443.2i	−0.435466	+	0.0778146i
$151$		−	396440.i		−	1.41493i	−0.706748	−	0.707465i	$-0.749839\pi$
$151$		−	396440.i		−	1.41493i	0.706748	−	0.707465i	$-0.250161\pi$
$152$	384329.			1.34925
$153$	−95002.5	−	257338.i	−0.328100	−	0.888742i
$154$	17587.5			0.0597587
$155$	244579.			0.817694
$156$	−141533.	−	792045.i	−0.465635	−	2.60578i
$157$			318654.i			1.03174i	0.856667	+	0.515870i	$0.172531\pi$
$157$			318654.i			1.03174i	−0.856667	+	0.515870i	$0.827469\pi$
$158$	596829.			1.90198
$159$	27377.3	+	153209.i	0.0858811	+	0.480607i
$160$		−	88163.5i		−	0.272263i
$161$	25881.4			0.0786908
$162$	−432557.	+	369773.i	−1.29496	+	1.10700i
$163$	−44552.9			−0.131343			−0.0656715	−	0.997841i	$-0.520919\pi$
$163$	−44552.9			−0.131343			−0.0656715	+	0.997841i	$0.520919\pi$
$164$			1.03406e6i			3.00217i
$165$	4355.45	+	24373.9i	0.0124544	+	0.0696973i
$166$	304216.			0.856863
$167$			217795.i			0.604305i	0.953260	+	0.302152i	$0.0977052\pi$
$167$			217795.i			0.604305i	−0.953260	+	0.302152i	$0.902295\pi$
$168$	−235997.	+	42171.0i	−0.645109	+	0.115276i
$169$	−347587.			−0.936153
$170$	523280.			1.38871
$171$	−314834.	+	116228.i	−0.823362	+	0.303964i
$172$		−	679689.i		−	1.75182i
$173$	320693.			0.814657			0.407328	−	0.913282i	$-0.366460\pi$
$173$	320693.			0.814657			0.407328	+	0.913282i	$0.366460\pi$
$174$	−10792.2	−	60395.4i	−0.0270233	−	0.151227i
$175$	44843.4			0.110689
$176$	−24232.7			−0.0589685
$177$	254579.	−	330025.i	0.610785	−	0.791796i
$178$	−504587.			−1.19367
$179$	309289.			0.721492			0.360746	−	0.932664i	$-0.382522\pi$
$179$	309289.			0.721492			0.360746	+	0.932664i	$0.382522\pi$
$180$	−246421.	−	667493.i	−0.566887	−	1.53556i
$181$	−519260.			−1.17812			−0.589058	−	0.808090i	$-0.700501\pi$
$181$	−519260.			−1.17812			−0.589058	+	0.808090i	$0.700501\pi$
$182$			451569.i			1.01052i
$183$	−138312.	−	774019.i	−0.305303	−	1.70854i
$184$	−130325.			−0.283781
$185$	−75915.5			−0.163080
$186$	−134374.	−	751982.i	−0.284795	−	1.59377i
$187$			37277.7i			0.0779553i
$188$	−734992.			−1.51666
$189$	180570.	−	105915.i	0.367698	−	0.215678i
$190$		−	640193.i		−	1.28655i
$191$	−381662.			−0.757000			−0.378500	−	0.925601i	$-0.623560\pi$
$191$	−381662.			−0.757000			−0.378500	+	0.925601i	$0.623560\pi$
$192$	−631415.	+	112829.i	−1.23612	+	0.220887i
$193$	383123.			0.740364			0.370182	−	0.928959i	$-0.379295\pi$
$193$	383123.			0.740364			0.370182	+	0.928959i	$0.379295\pi$
$194$		−	241185.i		−	0.460093i
$195$	−625816.	+	111829.i	−1.17858	+	0.210605i
$196$	−837215.			−1.55667
$197$		−	536432.i		−	0.984802i	−0.870368	−	0.492401i	$-0.836119\pi$
$197$		−	536432.i		−	0.984802i	0.870368	−	0.492401i	$-0.163881\pi$
$198$	72547.1	−	26782.5i	0.131509	−	0.0485499i
$199$	694003.			1.24231			0.621153	−	0.783689i	$-0.286665\pi$
$199$	694003.			1.24231			0.621153	+	0.783689i	$0.286665\pi$
$200$	−225807.			−0.399174
$201$	−93408.1	−	522730.i	−0.163078	−	0.912614i
$202$	422988.			0.729373
$203$			22569.4i			0.0384397i
$204$	−188439.	−	1.05454e6i	−0.317027	−	1.77414i
$205$	817038.			1.35787
$206$		−	128642.i		−	0.211210i
$207$	106759.	−	39412.7i	0.173173	−	0.0639309i
$208$		−	622189.i		−	0.997159i
$209$	45606.5			0.0722205
$210$	70246.1	+	393111.i	0.109919	+	0.615129i
$211$			328315.i			0.507673i	0.967247	+	0.253836i	$0.0816925\pi$
$211$			328315.i			0.507673i	−0.967247	+	0.253836i	$0.918307\pi$
$212$			607784.i			0.928773i
$213$	−51873.5	−	290294.i	−0.0783423	−	0.438419i
$214$			1.95361e6i			2.91611i
$215$	−537040.			−0.792339
$216$	−909252.	+	533333.i	−1.32602	+	0.777792i
$217$			281011.i			0.405111i
$218$		−	243901.i		−	0.347594i
$219$	64886.5	+	363118.i	0.0914206	+	0.511608i
$220$			96692.3i			0.134690i
$221$	−957129.			−1.31823
$222$	41708.6	+	233409.i	0.0567993	+	0.317860i
$223$	1.15178e6			1.55098			0.775492	−	0.631358i	$-0.217502\pi$
$223$	1.15178e6			1.55098			0.775492	+	0.631358i	$0.217502\pi$
$224$	101296.			0.134888
$225$	184976.	−	68288.3i	0.243590	−	0.0899269i
$226$	1.53123e6			1.99421
$227$	1.07066e6			1.37907			0.689535	−	0.724252i	$-0.257815\pi$
$227$	1.07066e6			1.37907			0.689535	+	0.724252i	$0.257815\pi$
$228$	−1.29015e6	+	230541.i	−1.64363	+	0.293705i
$229$			1.32871e6i			1.67433i	0.546950	+	0.837165i	$0.315789\pi$
$229$			1.32871e6i			1.67433i	−0.546950	+	0.837165i	$0.684211\pi$
$230$			217088.i			0.270593i
$231$	−28004.6	+	5004.23i	−0.0345303	+	0.00617031i
$232$		−	113647.i		−	0.138624i
$233$	−1.58830e6			−1.91664			−0.958322	−	0.285690i	$-0.907777\pi$
$233$	−1.58830e6			−1.91664			−0.958322	+	0.285690i	$0.907777\pi$
$234$	687657.	+	1.86269e6i	0.820980	+	2.22383i
$235$			580737.i			0.685977i
$236$	1.20538e6	−	1.09383e6i	1.40878	−	1.27841i
$237$	−950334.	+	169818.i	−1.09902	+	0.196387i
$238$			601227.i			0.688012i
$239$			820213.i			0.928821i	0.885620	+	0.464410i	$0.153734\pi$
$239$			820213.i			0.928821i	−0.885620	+	0.464410i	$0.846266\pi$
$240$	−96787.7	−	541643.i	−0.108466	−	0.606995i
$241$	1.58114e6			1.75359			0.876794	−	0.480867i	$-0.159678\pi$
$241$	1.58114e6			1.75359			0.876794	+	0.480867i	$0.159678\pi$
$242$	1.54157e6			1.69210
$243$	583550.	−	711870.i	0.633960	−	0.773366i
$244$		−	3.07056e6i		−	3.30174i
$245$			661506.i			0.704074i
$246$	−448888.	−	2.51206e6i	−0.472933	−	2.64663i
$247$			1.17097e6i			1.22125i
$248$		−	1.41502e6i		−	1.46094i
$249$	−484405.	+	86559.7i	−0.495120	+	0.0884743i
$250$			1.82471e6i			1.84648i
$251$		−	1.28330e6i		−	1.28572i	−0.765985	−	0.642858i	$-0.777748\pi$
$251$		−	1.28330e6i		−	1.28572i	0.765985	−	0.642858i	$-0.222252\pi$
$252$	766921.	−	283127.i	0.760763	−	0.280854i
$253$	−15465.0			−0.0151897
$254$	−215972.			−0.210046
$255$	−833223.	+	148891.i	−0.802436	+	0.143390i
$256$	−1.93959e6			−1.84973
$257$		−	369551.i		−	0.349013i	−0.984656	−	0.174507i	$-0.944167\pi$
$257$		−	369551.i		−	0.349013i	0.984656	−	0.174507i	$-0.0558330\pi$
$258$	295054.	+	1.65118e6i	0.275964	+	1.54435i
$259$		−	87223.7i		−	0.0807951i
$260$	−2.48264e6			−2.27761
$261$	34369.1	+	93097.2i	0.0312296	+	0.0845932i
$262$	−208589.			−0.187732
$263$			408145.i			0.363852i	0.983312	+	0.181926i	$0.0582332\pi$
$263$			408145.i			0.363852i	−0.983312	+	0.181926i	$0.941767\pi$
$264$	141016.	−	25198.6i	0.124526	−	0.0222518i
$265$	480227.			0.420080
$266$	735555.			0.637399
$267$	803457.	−	143572.i	0.689738	−	0.123251i
$268$		−	2.07369e6i		−	1.76363i
$269$	−1.05990e6			−0.893070			−0.446535	−	0.894766i	$-0.647342\pi$
$269$	−1.05990e6			−0.893070			−0.446535	+	0.894766i	$0.647342\pi$
$270$	888396.	+	1.51458e6i	0.741647	+	1.26440i
$271$	477246.			0.394747			0.197373	−	0.980328i	$-0.436759\pi$
$271$	477246.			0.394747			0.197373	+	0.980328i	$0.436759\pi$
$272$		−	828394.i		−	0.678914i
$273$	−128487.	−	719037.i	−0.104340	−	0.583908i
$274$		−	766472.i		−	0.616766i
$275$	−26795.4			−0.0213663
$276$	437487.	−	78175.9i	0.345695	−	0.0617732i
$277$	924308.			0.723798			0.361899	−	0.932217i	$-0.382129\pi$
$277$	924308.			0.723798			0.361899	+	0.932217i	$0.382129\pi$
$278$	−985352.			−0.764679
$279$	427929.	+	1.15915e6i	0.329125	+	0.891518i
$280$			739723.i			0.563864i
$281$		−	621749.i		−	0.469731i	−0.972028	−	0.234865i	$-0.924535\pi$
$281$		−	621749.i		−	0.469731i	0.972028	−	0.234865i	$-0.0754649\pi$
$282$	1.78553e6	−	319062.i	1.33704	−	0.238920i
$283$			325081.i			0.241282i	0.992696	+	0.120641i	$0.0384950\pi$
$283$			325081.i			0.241282i	−0.992696	+	0.120641i	$0.961505\pi$
$284$		−	1.15161e6i		−	0.847244i
$285$	182157.	+	1.01938e6i	0.132841	+	0.743406i
$286$		−	269828.i		−	0.195061i
$287$			938742.i			0.672731i
$288$	417840.	−	154256.i	0.296844	−	0.109587i
$289$	145519.			0.102488
$290$	−189307.			−0.132182
$291$	68625.2	+	384040.i	0.0475063	+	0.265854i
$292$			1.44050e6i			0.988681i
$293$		−	2.07939e6i		−	1.41503i	−0.706697	−	0.707517i	$-0.749815\pi$
$293$		−	2.07939e6i		−	1.41503i	0.706697	−	0.707517i	$-0.250185\pi$
$294$	2.03386e6	−	363437.i	1.37231	−	0.245223i
$295$	−864263.	−	952405.i	−0.578217	−	0.637186i
$296$			439211.i			0.291369i
$297$	−107897.	+	63288.1i	−0.0709769	+	0.0416323i
$298$	−711707.			−0.464259
$299$		−	397074.i		−	0.256858i
$300$	758010.	−	135451.i	0.486264	−	0.0868919i
$301$		−	617037.i		−	0.392550i
$302$			3.82057e6i			2.41052i
$303$	−673527.	+	120354.i	−0.421452	+	0.0753105i
$304$	−1.01348e6			−0.628970
$305$	−2.42614e6			−1.49336
$306$	915559.	+	2.48002e6i	0.558963	+	1.51409i
$307$	−394536.			−0.238913			−0.119457	−	0.992839i	$-0.538115\pi$
$307$	−394536.			−0.238913			−0.119457	+	0.992839i	$0.538115\pi$
$308$	−111095.			−0.0667297
$309$	36602.9	+	204837.i	0.0218082	+	0.122043i
$310$	−2.35706e6			−1.39305
$311$		−	1.25601e6i		−	0.736362i	−0.929754	−	0.368181i	$-0.879981\pi$
$311$		−	1.25601e6i		−	0.736362i	0.929754	−	0.368181i	$-0.120019\pi$
$312$	646989.	+	3.62068e6i	0.376279	+	2.10573i
$313$			2.31075e6i			1.33319i	0.745421	+	0.666594i	$0.232248\pi$
$313$			2.31075e6i			1.33319i	−0.745421	+	0.666594i	$0.767752\pi$
$314$		−	3.07093e6i		−	1.75771i
$315$	−223707.	−	605965.i	−0.127029	−	0.344089i
$316$	−3.77001e6			−2.12386
$317$			1.10004e6i			0.614839i	0.951574	+	0.307419i	$0.0994654\pi$
$317$			1.10004e6i			0.614839i	−0.951574	+	0.307419i	$0.900535\pi$
$318$	−263840.	−	1.47650e6i	−0.146310	−	0.818778i
$319$		−	13486.0i		−	0.00742002i
$320$			1.97915e6i			1.08045i
$321$	−555868.	−	3.11074e6i	−0.301099	−	1.68501i
$322$	−249425.			−0.134060
$323$			1.55906e6i			0.831487i
$324$	2.73235e6	−	2.33576e6i	1.44602	−	1.23614i
$325$		−	687989.i		−	0.361304i
$326$	429365.			0.223760
$327$	69398.2	+	388366.i	0.0358904	+	0.200850i
$328$		−	4.72699e6i		−	2.42605i
$329$	−667242.			−0.339855
$330$	−41974.4	−	234897.i	−0.0212178	−	0.118739i
$331$	1.71679e6			0.861288			0.430644	−	0.902522i	$-0.358287\pi$
$331$	1.71679e6			0.861288			0.430644	+	0.902522i	$0.358287\pi$
$332$	−1.92165e6			−0.956818
$333$	−132826.	−	359792.i	−0.0656405	−	0.177804i
$334$		−	2.09893e6i		−	1.02951i
$335$	−1.63848e6			−0.797680
$336$	622325.	−	111205.i	0.300725	−	0.0537373i
$337$		−	2.23142e6i		−	1.07030i	−0.844757	−	0.535151i	$-0.820255\pi$
$337$		−	2.23142e6i		−	1.07030i	0.844757	−	0.535151i	$-0.179745\pi$
$338$	3.34977e6			1.59486
$339$	−2.43819e6	+	435688.i	−1.15231	+	0.205909i
$340$	−3.30542e6			−1.55071
$341$		−	167914.i		−	0.0781988i
$342$	3.03412e6	−	1.12012e6i	1.40271	−	0.517843i
$343$	−1.68887e6			−0.775106
$344$			3.10706e6i			1.41564i
$345$	−61768.9	−	345671.i	−0.0279397	−	0.156356i
$346$	−3.09059e6			−1.38788
$347$	4.17683e6			1.86219			0.931093	−	0.364781i	$-0.118856\pi$
$347$	4.17683e6			1.86219			0.931093	+	0.364781i	$0.118856\pi$
$348$	68171.6	+	381502.i	0.0301756	+	0.168868i
$349$		−	3.68822e6i		−	1.62089i	−0.585816	−	0.810444i	$-0.699226\pi$
$349$		−	3.68822e6i		−	1.62089i	0.585816	−	0.810444i	$-0.300774\pi$
$350$	−432165.			−0.188573
$351$	−1.62496e6	−	2.77032e6i	−0.704004	−	1.20022i
$352$	−60527.9			−0.0260375
$353$	4.38448e6			1.87276			0.936378	−	0.350993i	$-0.114156\pi$
$353$	4.38448e6			1.87276			0.936378	+	0.350993i	$0.114156\pi$
$354$	−2.45343e6	+	3.18052e6i	−1.04055	+	1.34893i
$355$	−909916.			−0.383204
$356$	3.18734e6			1.33292
$357$	−171069.	−	957338.i	−0.0710398	−	0.397553i
$358$	−2.98068e6			−1.22916
$359$		−	4.69179e6i		−	1.92133i	−0.277704	−	0.960667i	$-0.589573\pi$
$359$		−	4.69179e6i		−	1.92133i	0.277704	−	0.960667i	$-0.410427\pi$
$360$	1.12646e6	+	3.05131e6i	0.458101	+	1.24088i
$361$	−568714.			−0.229681
$362$	5.00421e6			2.00708
$363$	−2.45466e6	+	438630.i	−0.977741	+	0.174715i
$364$		−	2.85244e6i		−	1.12840i
$365$	1.13818e6			0.447176
$366$	1.33294e6	+	7.45938e6i	0.520125	+	2.91072i
$367$			2.42409e6i			0.939471i	0.882807	+	0.469736i	$0.155651\pi$
$367$			2.42409e6i			0.939471i	−0.882807	+	0.469736i	$0.844349\pi$
$368$	343667.			0.132287
$369$	1.42953e6	+	3.87225e6i	0.546548	+	1.48046i
$370$	731613.			0.277829
$371$			551760.i			0.208121i
$372$	848805.	+	4.75008e6i	0.318017	+	1.77969i
$373$	−182981.			−0.0680978			−0.0340489	−	0.999420i	$-0.510840\pi$
$373$	−182981.			−0.0680978			−0.0340489	+	0.999420i	$0.510840\pi$
$374$		−	359253.i		−	0.132807i
$375$	−519193.	−	2.90551e6i	−0.190656	−	1.06695i
$376$	3.35987e6			1.22561
$377$	346261.			0.125473
$378$	−1.74019e6	+	1.02073e6i	−0.626423	+	0.367435i
$379$	2.41234e6			0.862661			0.431330	−	0.902194i	$-0.358044\pi$
$379$	2.41234e6			0.862661			0.431330	+	0.902194i	$0.358044\pi$
$380$			4.04393e6i			1.43663i
$381$	343894.	−	61451.4i	0.121370	−	0.0216880i
$382$	3.67816e6			1.28965
$383$			2.53581e6i			0.883324i	0.897181	+	0.441662i	$0.145611\pi$
$383$			2.53581e6i			0.883324i	−0.897181	+	0.441662i	$0.854389\pi$
$384$	5.18501e6	−	926524.i	1.79441	−	0.320648i
$385$			87779.5i			0.0301815i
$386$	−3.69224e6			−1.26131
$387$	−939634.	−	2.54523e6i	−0.318920	−	0.863874i
$388$			1.52350e6i			0.513764i
$389$			4.74262e6i			1.58908i	0.607214	+	0.794538i	$0.292287\pi$
$389$			4.74262e6i			1.58908i	−0.607214	+	0.794538i	$0.707713\pi$
$390$	6.03112e6	−	1.07772e6i	2.00787	−	0.358793i
$391$		−	528672.i		−	0.174882i
$392$	3.82716e6			1.25794
$393$	332138.	−	59350.7i	0.108477	−	0.0193840i
$394$			5.16970e6i			1.67774i
$395$			2.97879e6i			0.960610i
$396$	−458261.	+	169178.i	−0.146850	+	0.0542133i
$397$			5.12390e6i			1.63164i	0.578306	+	0.815820i	$0.303714\pi$
$397$			5.12390e6i			1.63164i	−0.578306	+	0.815820i	$0.696286\pi$
$398$	−6.68825e6			−2.11643
$399$	−1.17123e6	+	209290.i	−0.368307	+	0.0658138i
$400$	595453.			0.186079
$401$	4.04090e6			1.25492			0.627461	−	0.778648i	$-0.284094\pi$
$401$	4.04090e6			1.25492			0.627461	+	0.778648i	$0.284094\pi$
$402$	900193.	+	5.03765e6i	0.277824	+	1.55476i
$403$	4.31129e6			1.32234
$404$	−2.67190e6			−0.814456
$405$	−1.84555e6	−	2.15890e6i	−0.559098	−	0.654026i
$406$		−	217506.i		−	0.0654871i
$407$			52119.1i			0.0155959i
$408$	861412.	+	4.82063e6i	0.256189	+	1.43368i
$409$		−	3.45461e6i		−	1.02115i	−0.859832	−	0.510577i	$-0.829432\pi$
$409$		−	3.45461e6i		−	1.02115i	0.859832	−	0.510577i	$-0.170568\pi$
$410$	−7.87397e6			−2.31331
$411$	218087.	+	1.22046e6i	0.0636834	+	0.356384i
$412$			812596.i			0.235848i
$413$	1.09427e6	−	993001.i	0.315682	−	0.286467i
$414$	−1.02886e6	+	379828.i	−0.295023	+	0.108915i
$415$			1.51835e6i			0.432764i
$416$		−	1.55409e6i		−	0.440294i
$417$	1.56898e6	−	280366.i	0.441853	−	0.0789560i
$418$	−439519.			−0.123037
$419$	905432.			0.251954			0.125977	−	0.992033i	$-0.459793\pi$
$419$	905432.			0.251954			0.125977	+	0.992033i	$0.459793\pi$
$420$	−443726.	−	2.48318e6i	−0.122742	−	0.686885i
$421$			6.97621e6i			1.91829i	0.282914	+	0.959145i	$0.408699\pi$
$421$			6.97621e6i			1.91829i	−0.282914	+	0.959145i	$0.591301\pi$
$422$		−	3.16403e6i		−	0.864888i
$423$	−2.75233e6	+	1.01609e6i	−0.747910	+	0.276109i
$424$		−	2.77836e6i		−	0.750541i
$425$		−	916000.i		−	0.245993i
$426$	499915.	+	2.79762e6i	0.133467	+	0.746904i
$427$		−	2.78753e6i		−	0.739860i
$428$		−	1.23404e7i		−	3.25628i
$429$	76775.1	+	429648.i	0.0201408	+	0.112712i
$430$	5.17557e6			1.34985
$431$	−5.22450e6			−1.35473			−0.677363	−	0.735649i	$-0.736877\pi$
$431$	−5.22450e6			−1.35473			−0.677363	+	0.735649i	$0.736877\pi$
$432$	2.39770e6	−	1.40640e6i	0.618139	−	0.362576i
$433$	530639.			0.136013			0.0680064	−	0.997685i	$-0.478336\pi$
$433$	530639.			0.136013			0.0680064	+	0.997685i	$0.478336\pi$
$434$		−	2.70816e6i		−	0.690161i
$435$	301435.	−	53864.3i	0.0763784	−	0.0136483i
$436$			1.54066e6i			0.388142i
$437$	−646789.			−0.162017
$438$	−625325.	−	3.49944e6i	−0.155747	−	0.871591i
$439$	−2.98179e6			−0.738441			−0.369221	−	0.929342i	$-0.620375\pi$
$439$	−2.98179e6			−0.738441			−0.369221	+	0.929342i	$0.620375\pi$
$440$		−	442010.i		−	0.108843i
$441$	−3.13512e6	+	1.15741e6i	−0.767641	+	0.283393i
$442$	9.22405e6			2.24577
$443$	6.64975e6			1.60989			0.804944	−	0.593350i	$-0.202195\pi$
$443$	6.64975e6			1.60989			0.804944	+	0.593350i	$0.202195\pi$
$444$	−263462.	−	1.47439e6i	−0.0634251	−	0.354939i
$445$		−	2.51840e6i		−	0.602873i
$446$	−1.10999e7			−2.64231
$447$	1.13326e6	−	202505.i	0.268262	−	0.0479365i
$448$	−2.27396e6			−0.535288
$449$			8.28821e6i			1.94019i	0.242722	+	0.970096i	$0.421960\pi$
$449$			8.28821e6i			1.94019i	−0.242722	+	0.970096i	$0.578040\pi$
$450$	−1.78265e6	+	658108.i	−0.414987	+	0.153203i
$451$		−	560930.i		−	0.129858i
$452$	−9.67240e6			−2.22684
$453$	−1.08708e6	−	6.08352e6i	−0.248895	−	1.39287i
$454$	−1.03182e7			−2.34943
$455$	−2.25379e6			−0.510371
$456$	5.89767e6	−	1.05387e6i	1.32822	−	0.237343i
$457$			3.74700e6i			0.839253i	0.907697	+	0.419626i	$0.137839\pi$
$457$			3.74700e6i			0.839253i	−0.907697	+	0.419626i	$0.862161\pi$
$458$		−	1.28050e7i		−	2.85245i
$459$	−2.16350e6	−	3.68845e6i	−0.479320	−	0.817169i
$460$		−	1.37129e6i		−	0.302158i
$461$		−	3.49127e6i		−	0.765122i	−0.923930	−	0.382561i	$-0.875042\pi$
$461$		−	3.49127e6i		−	0.765122i	0.923930	−	0.382561i	$-0.124958\pi$
$462$	269886.	−	48226.8i	0.0588269	−	0.0105120i
$463$		−	2.88066e6i		−	0.624511i	−0.949998	−	0.312255i	$-0.898916\pi$
$463$		−	2.88066e6i		−	0.624511i	0.949998	−	0.312255i	$-0.101084\pi$
$464$			299688.i			0.0646211i
$465$	3.75316e6	−	670664.i	0.804943	−	0.143838i
$466$	1.53067e7			3.26526
$467$	−1.99736e6			−0.423803			−0.211901	−	0.977291i	$-0.567966\pi$
$467$	−1.99736e6			−0.423803			−0.211901	+	0.977291i	$0.567966\pi$
$468$	−4.34375e6	−	1.17661e7i	−0.916749	−	2.48324i
$469$		−	1.88254e6i		−	0.395196i
$470$		−	5.59668e6i		−	1.16865i
$471$	873785.	+	4.88987e6i	0.181490	+	1.01565i
$472$	−5.51016e6	+	5.00021e6i	−1.13844	+	1.03308i
$473$			368700.i			0.0757740i
$474$	9.15857e6	−	1.63657e6i	1.87233	−	0.334572i
$475$	−1.12066e6			−0.227897
$476$		−	3.79779e6i		−	0.768270i
$477$	840230.	+	2.27597e6i	0.169084	+	0.458006i
$478$		−	7.90456e6i		−	1.58237i
$479$			2.25462e6i			0.448988i	0.974475	+	0.224494i	$0.0720729\pi$
$479$			2.25462e6i			0.448988i	−0.974475	+	0.224494i	$0.927927\pi$
$480$	−241754.	−	1.35290e6i	−0.0478929	−	0.268018i
$481$	−1.33819e6			−0.263727
$482$	−1.52378e7			−2.98747
$483$	397161.	−	70969.8i	0.0774637	−	0.0138422i
$484$	−9.73771e6			−1.88948
$485$	1.20376e6			0.232373
$486$	−5.62379e6	+	6.86043e6i	−1.08004	+	1.31753i
$487$	7.50521e6			1.43397			0.716985	−	0.697088i	$-0.245522\pi$
$487$	7.50521e6			1.43397			0.716985	+	0.697088i	$0.245522\pi$
$488$			1.40365e7i			2.66814i
$489$	−683681.	+	122169.i	−0.129295	+	0.0231041i
$490$		−	6.37507e6i		−	1.19948i
$491$			5.42009e6i			1.01462i	0.861764	+	0.507309i	$0.169360\pi$
$491$			5.42009e6i			1.01462i	−0.861764	+	0.507309i	$0.830640\pi$
$492$	2.83551e6	+	1.58680e7i	0.528102	+	2.95536i
$493$	461017.			0.0854279
$494$		−	1.12849e7i		−	2.08056i
$495$	133672.	+	362084.i	0.0245204	+	0.0664197i
$496$			3.73141e6i			0.681034i
$497$		−	1.04545e6i		−	0.189852i
$498$	4.66831e6	−	834193.i	0.843502	−	0.150728i
$499$	−7.03295e6			−1.26441			−0.632203	−	0.774803i	$-0.717849\pi$
$499$	−7.03295e6			−1.26441			−0.632203	+	0.774803i	$0.717849\pi$
$500$		−	1.15262e7i		−	2.06188i
$501$	597217.	+	3.34214e6i	0.106301	+	0.594882i
$502$			1.23675e7i			2.19039i
$503$	−3.22241e6			−0.567885			−0.283942	−	0.958841i	$-0.591642\pi$
$503$	−3.22241e6			−0.567885			−0.283942	+	0.958841i	$0.591642\pi$
$504$	−3.50583e6	+	1.29426e6i	−0.614772	+	0.226958i
$505$			2.11114e6i			0.368374i
$506$	149040.			0.0258777
$507$	−5.33386e6	+	953123.i	−0.921556	+	0.164675i
$508$	1.36424e6			0.234548
$509$	7.78339e6			1.33160			0.665800	−	0.746130i	$-0.268090\pi$
$509$	7.78339e6			1.33160			0.665800	+	0.746130i	$0.268090\pi$
$510$	8.02994e6	−	1.43489e6i	1.36706	−	0.244283i
$511$			1.30772e6i			0.221545i
$512$	7.87980e6			1.32843
$513$	−4.51253e6	+	2.64688e6i	−0.757054	+	0.444059i
$514$			3.56144e6i			0.594590i
$515$	642054.			0.106673
$516$	−1.86378e6	−	1.04301e7i	−0.308156	−	1.72450i
$517$	398699.			0.0656023
$518$			840593.i			0.137645i
$519$	4.92116e6	−	879377.i	0.801954	−	0.143303i
$520$	1.13489e7			1.84054
$521$		−	3.75797e6i		−	0.606539i	−0.952905	−	0.303270i	$-0.901922\pi$
$521$		−	3.75797e6i		−	0.606539i	0.952905	−	0.303270i	$-0.0980783\pi$
$522$	−331222.	−	897197.i	−0.0532038	−	0.144116i
$523$	−1.66971e6			−0.266923			−0.133462	−	0.991054i	$-0.542609\pi$
$523$	−1.66971e6			−0.266923			−0.133462	+	0.991054i	$0.542609\pi$
$524$	1.31760e6			0.209631
$525$	688139.	−	122965.i	0.108963	−	0.0194709i
$526$		−	3.93338e6i		−	0.619871i
$527$	5.74012e6			0.900316
$528$	−371860.	+	66448.7i	−0.0580490	+	0.0103729i
$529$	−6.21702e6			−0.965924
$530$	−4.62804e6			−0.715661
$531$	3.00164e6	−	5.76244e6i	0.461979	−	0.886891i
$532$	−4.64631e6			−0.711753
$533$	1.44022e7			2.19590
$534$	−7.74307e6	+	1.38363e6i	−1.17506	+	0.209975i
$535$	−9.75051e6			−1.47280
$536$			9.47945e6i			1.42518i
$537$	4.74615e6	−	848104.i	0.710241	−	0.126915i
$538$	1.02145e7			1.52146
$539$	454151.			0.0673330
$540$	−5.61176e6	−	9.56722e6i	−0.828162	−	1.41189i
$541$		−	9.67521e6i		−	1.42124i	−0.703576	−	0.710620i	$-0.748415\pi$
$541$		−	9.67521e6i		−	1.42124i	0.703576	−	0.710620i	$-0.251585\pi$
$542$	−4.59931e6			−0.672504
$543$	−7.96824e6	+	1.42387e6i	−1.15975	+	0.207238i
$544$		−	2.06914e6i		−	0.299774i
$545$	1.21732e6			0.175555
$546$	1.23825e6	+	6.92950e6i	0.177757	+	0.994765i
$547$	5.44757e6			0.778456			0.389228	−	0.921141i	$-0.372742\pi$
$547$	5.44757e6			0.778456			0.389228	+	0.921141i	$0.372742\pi$
$548$			4.84161e6i			0.688713i
$549$	−4.24490e6	−	1.14984e7i	−0.601085	−	1.62819i
$550$	258233.			0.0364003
$551$		−	564019.i		−	0.0791435i
$552$	−1.99988e6	+	357365.i	−0.279355	+	0.0499188i
$553$	−3.42250e6			−0.475917
$554$	−8.90775e6			−1.23309
$555$	−1.16495e6	+	208169.i	−0.160537	+	0.0286869i
$556$	6.22421e6			0.853881
$557$		−	1.58568e6i		−	0.216560i	−0.994120	−	0.108280i	$-0.965466\pi$
$557$		−	1.58568e6i		−	0.216560i	0.994120	−	0.108280i	$-0.0345343\pi$
$558$	−4.12404e6	−	1.11710e7i	−0.560709	−	1.51882i
$559$	−9.46661e6			−1.28134
$560$		−	1.95065e6i		−	0.262851i
$561$	102220.	+	572041.i	0.0137128	+	0.0767397i
$562$			5.99192e6i			0.800249i
$563$	−9.24513e6			−1.22925			−0.614627	−	0.788818i	$-0.710694\pi$
$563$	−9.24513e6			−1.22925			−0.614627	+	0.788818i	$0.710694\pi$
$564$	−1.12787e7	+	2.01543e6i	−1.49301	+	0.266790i
$565$			7.64242e6i			1.00719i
$566$		−	3.13287e6i		−	0.411057i
$567$	2.48049e6	−	2.12046e6i	0.324025	−	0.276995i
$568$			5.26434e6i			0.684657i
$569$	5.61709e6			0.727328			0.363664	−	0.931530i	$-0.381526\pi$
$569$	5.61709e6			0.727328			0.363664	+	0.931530i	$0.381526\pi$
$570$	−1.75548e6	−	9.82401e6i	−0.226313	−	1.26649i
$571$			4.82900e6i			0.619822i	0.950766	+	0.309911i	$0.100299\pi$
$571$			4.82900e6i			0.619822i	−0.950766	+	0.309911i	$0.899701\pi$
$572$			1.70443e6i			0.217816i
$573$	−5.85676e6	+	1.04656e6i	−0.745196	+	0.133161i
$574$		−	9.04685e6i		−	1.14609i
$575$	380012.			0.0479322
$576$	−9.37992e6	+	3.46282e6i	−1.17799	+	0.434884i
$577$	3.89350e6			0.486856			0.243428	−	0.969919i	$-0.421728\pi$
$577$	3.89350e6			0.486856			0.243428	+	0.969919i	$0.421728\pi$
$578$	−1.40239e6			−0.174602
$579$	5.87917e6	−	1.05057e6i	0.728819	−	0.130235i
$580$	1.19580e6			0.147601
$581$	−1.74452e6			−0.214405
$582$	−661355.	−	3.70107e6i	−0.0809333	−	0.452918i
$583$		−	329695.i		−	0.0401736i
$584$		−	6.58496e6i		−	0.798952i
$585$	−9.29675e6	+	3.43212e6i	−1.12316	+	0.414641i
$586$			2.00395e7i			2.41070i
$587$	−4.16847e6			−0.499323			−0.249661	−	0.968333i	$-0.580319\pi$
$587$	−4.16847e6			−0.499323			−0.249661	+	0.968333i	$0.580319\pi$
$588$	−1.28474e7	+	2.29574e6i	−1.53240	+	0.273828i
$589$		−	7.02260e6i		−	0.834084i
$590$	8.32907e6	+	9.17852e6i	0.985069	+	1.08553i
$591$	−1.47096e6	−	8.23175e6i	−0.173233	−	0.969446i
$592$		−	1.15820e6i		−	0.135825i
$593$			4.87840e6i			0.569692i	0.958573	+	0.284846i	$0.0919425\pi$
$593$			4.87840e6i			0.569692i	−0.958573	+	0.284846i	$0.908057\pi$
$594$	1.03982e6	−	609920.i	0.120919	−	0.0709262i
$595$	−3.00074e6			−0.347485
$596$	4.49566e6			0.518416
$597$	1.06497e7	−	1.90303e6i	1.22293	−	0.218530i
$598$			3.82669e6i			0.437593i
$599$		−	1.20293e7i		−	1.36985i	−0.728613	−	0.684925i	$-0.759835\pi$
$599$		−	1.20293e7i		−	1.36985i	0.728613	−	0.684925i	$-0.240165\pi$
$600$	−3.46509e6	+	619187.i	−0.392949	+	0.0702172i
$601$			1.12790e6i			0.127375i	0.997970	+	0.0636874i	$0.0202861\pi$
$601$			1.12790e6i			0.127375i	−0.997970	+	0.0636874i	$0.979714\pi$
$602$			5.94651e6i			0.668761i
$603$	−2.86677e6	−	7.76536e6i	−0.321070	−	0.869697i
$604$		−	2.41336e7i		−	2.69171i
$605$			7.69403e6i			0.854605i
$606$	6.49091e6	−	1.15988e6i	0.718000	−	0.128301i
$607$	1.48593e7			1.63691			0.818457	−	0.574568i	$-0.194830\pi$
$607$	1.48593e7			1.63691			0.818457	+	0.574568i	$0.194830\pi$
$608$	−2.53144e6			−0.277721
$609$	61887.8	+	346336.i	0.00676179	+	0.0378403i
$610$	2.33812e7			2.54414
$611$			1.02369e7i			1.10934i
$612$	−5.78335e6	−	1.56656e7i	−0.624167	−	1.69071i
$613$			8.32649e6i			0.894975i	0.894290	+	0.447488i	$0.147681\pi$
$613$			8.32649e6i			0.894975i	−0.894290	+	0.447488i	$0.852319\pi$
$614$	3.80222e6			0.407021
$615$	1.25378e7	−	2.24041e6i	1.33670	−	0.238858i
$616$	507850.			0.0539242
$617$			1.68119e7i			1.77789i	0.458016	+	0.888944i	$0.348560\pi$
$617$			1.68119e7i			1.77789i	−0.458016	+	0.888944i	$0.651440\pi$
$618$	−352750.	−	1.97406e6i	−0.0371531	−	0.207916i
$619$	1.19071e7			1.24905			0.624525	−	0.781005i	$-0.285293\pi$
$619$	1.19071e7			1.24905			0.624525	+	0.781005i	$0.285293\pi$
$620$	1.48889e7			1.55555
$621$	1.53019e6	−	897549.i	0.159227	−	0.0933962i
$622$			1.21044e7i			1.25449i
$623$	2.89354e6			0.298682
$624$	−1.70611e6	−	9.54774e6i	−0.175407	−	0.981610i
$625$	−6.57147e6			−0.672918
$626$		−	2.22691e7i		−	2.27126i
$627$	699849.	−	125058.i	0.0710944	−	0.0127041i
$628$			1.93983e7i			1.96275i
$629$	−1.78169e6			−0.179558
$630$	2.15591e6	+	5.83981e6i	0.216411	+	0.586202i
$631$	−3.12556e6			−0.312503			−0.156251	−	0.987717i	$-0.549941\pi$
$631$	−3.12556e6			−0.312503			−0.156251	+	0.987717i	$0.549941\pi$
$632$	1.72338e7			1.71629
$633$	900275.	+	5.03811e6i	0.0893030	+	0.499757i
$634$		−	1.06013e7i		−	1.04746i
$635$		−	1.07792e6i		−	0.106085i
$636$	1.66661e6	+	9.32668e6i	0.163377	+	0.914291i
$637$			1.16606e7i			1.13860i
$638$			129967.i			0.0126410i
$639$	−1.59204e6	−	4.31243e6i	−0.154241	−	0.417801i
$640$		−	1.62522e7i		−	1.56842i
$641$			9.31161e6i			0.895116i	0.894255	+	0.447558i	$0.147706\pi$
$641$			9.31161e6i			0.895116i	−0.894255	+	0.447558i	$0.852294\pi$
$642$	5.35701e6	+	2.99789e7i	0.512962	+	2.87063i
$643$	1.32930e7			1.26793			0.633965	−	0.773362i	$-0.281426\pi$
$643$	1.32930e7			1.26793			0.633965	+	0.773362i	$0.281426\pi$
$644$	1.57555e6			0.149699
$645$	−8.24109e6	+	1.47262e6i	−0.779984	+	0.139378i
$646$		−	1.50249e7i		−	1.41655i
$647$		−	9.08894e6i		−	0.853597i	−0.904347	−	0.426798i	$-0.859641\pi$
$647$		−	9.08894e6i		−	0.853597i	0.904347	−	0.426798i	$-0.140359\pi$
$648$	−1.24904e7	+	1.06775e7i	−1.16852	+	0.998920i
$649$	−653865.	+	593351.i	−0.0609363	+	0.0552968i
$650$			6.63029e6i			0.615530i
$651$	770564.	+	4.31223e6i	0.0712617	+	0.398794i
$652$	−2.71219e6			−0.249862
$653$			1.83478e7i			1.68384i	0.539605	+	0.841919i	$0.318574\pi$
$653$			1.83478e7i			1.68384i	−0.539605	+	0.841919i	$0.681426\pi$
$654$	−668804.	−	3.74276e6i	−0.0611441	−	0.342174i
$655$		−	1.04107e6i		−	0.0948153i
$656$			1.24651e7i			1.13093i
$657$	1.99142e6	+	5.39425e6i	0.179990	+	0.487548i
$658$	6.43035e6			0.578988
$659$	−5.04508e6			−0.452537			−0.226269	−	0.974065i	$-0.572653\pi$
$659$	−5.04508e6			−0.452537			−0.226269	+	0.974065i	$0.572653\pi$
$660$	265141.	+	1.48378e6i	0.0236929	+	0.132590i
$661$	−1.92331e7			−1.71216			−0.856081	−	0.516842i	$-0.827108\pi$
$661$	−1.92331e7			−1.71216			−0.856081	+	0.516842i	$0.827108\pi$
$662$	−1.65451e7			−1.46732
$663$	−1.46875e7	+	2.62456e6i	−1.29767	+	0.231885i
$664$	8.78444e6			0.773204
$665$			3.67117e6i			0.321922i
$666$	1.28007e6	+	3.46739e6i	0.111827	+	0.302912i
$667$			191257.i			0.0166458i
$668$			1.32584e7i			1.14961i
$669$	1.76745e7	−	3.15831e6i	1.52680	−	0.272828i
$670$	1.57903e7			1.35895
$671$			1.66564e6i			0.142815i
$672$	1.55443e6	−	277765.i	0.132785	−	0.0237277i
$673$			3.51575e6i			0.299213i	0.988746	+	0.149607i	$0.0478007\pi$
$673$			3.51575e6i			0.299213i	−0.988746	+	0.149607i	$0.952199\pi$
$674$			2.15046e7i			1.82340i
$675$	2.65127e6	−	1.55513e6i	0.223973	−	0.131374i
$676$	−2.11596e7			−1.78091
$677$		−	4.86746e6i		−	0.408160i	−0.978954	−	0.204080i	$-0.934580\pi$
$677$		−	4.86746e6i		−	0.408160i	0.978954	−	0.204080i	$-0.0654203\pi$
$678$	2.34974e7	−	4.19881e6i	1.96311	−	0.350794i
$679$			1.38307e6i			0.115125i
$680$	1.51101e7			1.25313
$681$	1.64297e7	−	2.93587e6i	1.35757	−	0.242587i
$682$			1.61822e6i			0.133222i
$683$	1.34481e7			1.10308			0.551541	−	0.834148i	$-0.314040\pi$
$683$	1.34481e7			1.10308			0.551541	+	0.834148i	$0.314040\pi$
$684$	−1.91657e7	+	7.07548e6i	−1.56634	+	0.578250i
$685$	3.82548e6			0.311501
$686$	1.62760e7			1.32050
$687$	3.64347e6	+	2.03896e7i	0.294526	+	1.64822i
$688$		−	8.19333e6i		−	0.659917i
$689$	8.46513e6			0.679337
$690$	595279.	+	3.33130e6i	0.0475990	+	0.266373i
$691$		−	2.19353e7i		−	1.74763i	−0.486262	−	0.873813i	$-0.661640\pi$
$691$		−	2.19353e7i		−	1.74763i	0.486262	−	0.873813i	$-0.338360\pi$
$692$	1.95224e7			1.54978
$693$	−416020.	+	153584.i	−0.0329064	+	0.0121482i
$694$	−4.02530e7			−3.17248
$695$		−	4.91792e6i		−	0.386206i
$696$	−311633.	−	1.74396e6i	−0.0243849	−	0.136462i
$697$	1.91754e7			1.49507
$698$			3.55441e7i			2.76140i
$699$	−2.43730e7	+	4.35528e6i	−1.88676	+	0.337150i
$700$	2.72987e6			0.210570
$701$	2.35117e7			1.80713			0.903565	−	0.428452i	$-0.140941\pi$
$701$	2.35117e7			1.80713			0.903565	+	0.428452i	$0.140941\pi$
$702$	1.56601e7	+	2.66981e7i	1.19936	+	2.04474i
$703$			2.17976e6i			0.166349i
$704$	1.35877e6			0.103327
$705$	1.59245e6	+	8.91163e6i	0.120668	+	0.675281i
$706$	−4.22541e7			−3.19049
$707$	−2.42562e6			−0.182504
$708$	1.54976e7	−	2.00905e7i	1.16194	−	1.50629i
$709$	−1.29200e7			−0.965263			−0.482632	−	0.875823i	$-0.660319\pi$
$709$	−1.29200e7			−0.965263			−0.482632	+	0.875823i	$0.660319\pi$
$710$	8.76904e6			0.652839
$711$	−1.41176e7	+	5.21185e6i	−1.04734	+	0.386650i
$712$	−1.45703e7			−1.07713
$713$			2.38135e6i			0.175428i
$714$	1.64863e6	+	9.22606e6i	0.121026	+	0.677284i
$715$	1.34672e6			0.0985170
$716$	1.88282e7			1.37254
$717$	2.24912e6	+	1.25865e7i	0.163386	+	0.914338i
$718$			4.52158e7i			3.27325i
$719$	3.00043e6			0.216452			0.108226	−	0.994126i	$-0.465483\pi$
$719$	3.00043e6			0.216452			0.108226	+	0.994126i	$0.465483\pi$
$720$	−2.97049e6	−	8.04632e6i	−0.213549	−	0.578450i
$721$			737693.i			0.0528491i
$722$	5.48081e6			0.391293
$723$	2.42632e7	−	4.33566e6i	1.72624	−	0.308467i
$724$	−3.16103e7			−2.24121
$725$			331381.i			0.0234144i
$726$	2.36560e7	−	4.22716e6i	1.66571	−	0.297651i
$727$	1.45696e7			1.02238			0.511191	−	0.859467i	$-0.329205\pi$
$727$	1.45696e7			1.02238			0.511191	+	0.859467i	$0.329205\pi$
$728$			1.30394e7i			0.911860i
$729$	7.00277e6	−	1.25241e7i	0.488035	−	0.872824i
$730$	−1.09689e7			−0.761823
$731$	−1.26040e7			−0.872399
$732$	−8.41983e6	−	4.71190e7i	−0.580798	−	3.25026i
$733$	3.65619e6			0.251344			0.125672	−	0.992072i	$-0.459891\pi$
$733$	3.65619e6			0.251344			0.125672	+	0.992072i	$0.459891\pi$
$734$		−	2.33614e7i		−	1.60051i
$735$	1.81392e6	+	1.01511e7i	0.123851	+	0.693096i
$736$	858404.			0.0584113
$737$			1.12488e6i			0.0762848i
$738$	−1.37767e7	−	3.73177e7i	−0.931118	−	2.52216i
$739$		−	1.91970e7i		−	1.29307i	−0.762885	−	0.646535i	$-0.776218\pi$
$739$		−	1.91970e7i		−	1.29307i	0.762885	−	0.646535i	$-0.223782\pi$
$740$	−4.62141e6			−0.310238
$741$	3.21094e6	+	1.79691e7i	0.214826	+	1.20221i
$742$		−	5.31742e6i		−	0.354561i
$743$		−	2.03356e7i		−	1.35140i	−0.737175	−	0.675702i	$-0.763841\pi$
$743$		−	2.03356e7i		−	1.35140i	0.737175	−	0.675702i	$-0.236159\pi$
$744$	−3.88014e6	−	2.17140e7i	−0.256989	−	1.43816i
$745$		−	3.55215e6i		−	0.234477i
$746$	1.76342e6			0.116014
$747$	−7.19602e6	+	2.65658e6i	−0.471836	+	0.174190i
$748$			2.26931e6i			0.148299i
$749$		−	1.12029e7i		−	0.729671i
$750$	5.00357e6	+	2.80009e7i	0.324808	+	1.81769i
$751$		−	1.95164e7i		−	1.26270i	−0.775500	−	0.631348i	$-0.782502\pi$
$751$		−	1.95164e7i		−	1.26270i	0.775500	−	0.631348i	$-0.217498\pi$
$752$	−8.85998e6			−0.571332
$753$	−3.51896e6	−	1.96928e7i	−0.226166	−	1.26567i
$754$	−3.33698e6			−0.213760
$755$	−1.90686e7			−1.21745
$756$	1.09923e7	−	6.44768e6i	0.699496	−	0.410298i
$757$	1.06126e7			0.673103			0.336551	−	0.941665i	$-0.390739\pi$
$757$	1.06126e7			0.673103			0.336551	+	0.941665i	$0.390739\pi$
$758$	−2.32482e7			−1.46966
$759$	−237317.	+	42406.8i	−0.0149529	+	0.00267197i
$760$		−	1.84860e7i		−	1.16094i
$761$			2.01406e7i			1.26070i	0.776313	+	0.630348i	$0.217088\pi$
$761$			2.01406e7i			1.26070i	−0.776313	+	0.630348i	$0.782912\pi$
$762$	−3.31418e6	+	592220.i	−0.206770	+	0.0369484i
$763$			1.39865e6i			0.0869754i
$764$	−2.32340e7			−1.44009
$765$	−1.23778e7	+	4.56958e6i	−0.764701	+	0.282308i
$766$		−	2.44381e7i		−	1.50486i
$767$	−1.52347e7	−	1.67884e7i	−0.935071	−	1.03043i
$768$	−2.97637e7	+	5.31856e6i	−1.82089	+	0.325380i
$769$			1.52355e7i			0.929053i	0.885559	+	0.464526i	$0.153775\pi$
$769$			1.52355e7i			0.929053i	−0.885559	+	0.464526i	$0.846225\pi$
$770$		−	845949.i		−	0.0514182i
$771$	−1.01335e6	−	5.67090e6i	−0.0613937	−	0.343571i
$772$	2.33229e7			1.40844
$773$	8.57975e6			0.516447			0.258224	−	0.966085i	$-0.416863\pi$
$773$	8.57975e6			0.516447			0.258224	+	0.966085i	$0.416863\pi$
$774$	9.05545e6	+	2.45289e7i	0.543322	+	1.47172i
$775$			4.12603e6i			0.246762i
$776$		−	6.96438e6i		−	0.415172i
$777$	−239177.	−	1.33848e6i	−0.0142124	−	0.0795353i
$778$		−	4.57056e7i		−	2.70720i
$779$		−	2.34596e7i		−	1.38509i
$780$	−3.80970e7	+	6.80767e6i

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)

\(f(q)\)	\(=\)	\(q-9.63720 q^{2} +(15.3454 - 2.74211i) q^{3} +60.8757 q^{4} -48.0995i q^{5} +(-147.887 + 26.4263i) q^{6} +55.2643 q^{7} -278.281 q^{8} +(227.962 - 84.1575i) q^{9} +O(q^{10})\)	\(q-9.63720 q^{2} +(15.3454 - 2.74211i) q^{3} +60.8757 q^{4} -48.0995i q^{5} +(-147.887 + 26.4263i) q^{6} +55.2643 q^{7} -278.281 q^{8} +(227.962 - 84.1575i) q^{9} +463.545i q^{10} -33.0223 q^{11} +(934.161 - 166.928i) q^{12} -847.868i q^{13} -532.594 q^{14} +(-131.894 - 738.106i) q^{15} +733.828 q^{16} -1128.87i q^{17} +(-2196.91 + 811.043i) q^{18} -1381.08 q^{19} -2928.09i q^{20} +(848.052 - 151.541i) q^{21} +318.243 q^{22} +468.321 q^{23} +(-4270.33 + 763.077i) q^{24} +811.434 q^{25} +8171.08i q^{26} +(3267.39 - 1916.53i) q^{27} +3364.25 q^{28} +408.390i q^{29} +(1271.09 + 7113.28i) q^{30} +5084.86i q^{31} +1832.94 q^{32} +(-506.740 + 90.5508i) q^{33} +10879.1i q^{34} -2658.19i q^{35} +(13877.3 - 5123.15i) q^{36} -1578.30i q^{37} +13309.8 q^{38} +(-2324.95 - 13010.9i) q^{39} +13385.2i q^{40} +16986.4i q^{41} +(-8172.85 + 1460.43i) q^{42} -11165.2i q^{43} -2010.26 q^{44} +(-4047.94 - 10964.9i) q^{45} -4513.30 q^{46} -12073.6 q^{47} +(11260.9 - 2012.24i) q^{48} -13752.9 q^{49} -7819.96 q^{50} +(-3095.48 - 17322.9i) q^{51} -51614.6i q^{52} +9984.02i q^{53} +(-31488.5 + 18469.9i) q^{54} +1588.36i q^{55} -15379.0 q^{56} +(-21193.2 + 3787.08i) q^{57} -3935.73i q^{58} +(19800.7 - 17968.2i) q^{59} +(-8029.16 - 44932.7i) q^{60} -50439.9i q^{61} -49003.8i q^{62} +(12598.1 - 4650.91i) q^{63} -41146.9 q^{64} -40782.1 q^{65} +(4883.55 - 872.656i) q^{66} -34064.3i q^{67} -68720.5i q^{68} +(7186.57 - 1284.19i) q^{69} +25617.5i q^{70} -18917.3i q^{71} +(-63437.4 + 23419.4i) q^{72} +23663.0i q^{73} +15210.4i q^{74} +(12451.8 - 2225.04i) q^{75} -84074.3 q^{76} -1824.95 q^{77} +(22406.0 + 125388. i) q^{78} -61929.7 q^{79} -35296.8i q^{80} +(44884.0 - 38369.4i) q^{81} -163701. i q^{82} -31566.8 q^{83} +(51625.8 - 9225.16i) q^{84} -54297.9 q^{85} +107601. i q^{86} +(1119.85 + 6266.90i) q^{87} +9189.48 q^{88} +52358.2 q^{89} +(39010.8 + 105671. i) q^{90} -46856.9i q^{91} +28509.4 q^{92} +(13943.2 + 78029.1i) q^{93} +116356. q^{94} +66429.4i q^{95} +(28127.2 - 5026.12i) q^{96} +25026.4i q^{97} +132539. q^{98} +(-7527.82 + 2779.07i) 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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