LMFDB - Embedded newform 690.3.b.a.599.14

Newspace parameters

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	690.b (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$18.8011382409$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			599.14
Character	$\chi$	$=$	690.599
Dual form			690.3.b.a.599.13

$q$-expansion

$f(q)$	$=$	$q-1.41421 q^{2} +(-1.52209 + 2.58520i) q^{3} +2.00000 q^{4} +(-4.64244 - 1.85681i) q^{5} +(2.15256 - 3.65602i) q^{6} +10.7642i q^{7} -2.82843 q^{8} +(-4.36648 - 7.86981i) q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +(-1.52209 + 2.58520i) q^{3} +2.00000 q^{4} +(-4.64244 - 1.85681i) q^{5} +(2.15256 - 3.65602i) q^{6} +10.7642i q^{7} -2.82843 q^{8} +(-4.36648 - 7.86981i) q^{9} +(6.56540 + 2.62593i) q^{10} +19.8694i q^{11} +(-3.04418 + 5.17039i) q^{12} +15.8557i q^{13} -15.2228i q^{14} +(11.8664 - 9.17538i) q^{15} +4.00000 q^{16} +9.43625 q^{17} +(6.17514 + 11.1296i) q^{18} +8.14814 q^{19} +(-9.28488 - 3.71363i) q^{20} +(-27.8275 - 16.3841i) q^{21} -28.0995i q^{22} -4.79583 q^{23} +(4.30512 - 7.31204i) q^{24} +(18.1045 + 17.2403i) q^{25} -22.4233i q^{26} +(26.9912 + 0.690351i) q^{27} +21.5284i q^{28} +47.6184i q^{29} +(-16.7817 + 12.9759i) q^{30} -10.4513 q^{31} -5.65685 q^{32} +(-51.3662 - 30.2430i) q^{33} -13.3449 q^{34} +(19.9871 - 49.9720i) q^{35} +(-8.73296 - 15.7396i) q^{36} +0.317500i q^{37} -11.5232 q^{38} +(-40.9901 - 24.1338i) q^{39} +(13.1308 + 5.25186i) q^{40} +30.0257i q^{41} +(39.3540 + 23.1706i) q^{42} +13.3476i q^{43} +39.7387i q^{44} +(5.65836 + 44.6428i) q^{45} +6.78233 q^{46} +16.2940 q^{47} +(-6.08836 + 10.3408i) q^{48} -66.8675 q^{49} +(-25.6036 - 24.3814i) q^{50} +(-14.3628 + 24.3946i) q^{51} +31.7114i q^{52} -77.8949 q^{53} +(-38.1713 - 0.976304i) q^{54} +(36.8937 - 92.2423i) q^{55} -30.4457i q^{56} +(-12.4022 + 21.0645i) q^{57} -67.3426i q^{58} -15.6749i q^{59} +(23.7329 - 18.3508i) q^{60} +12.3081 q^{61} +14.7804 q^{62} +(84.7120 - 47.0016i) q^{63} +8.00000 q^{64} +(29.4410 - 73.6091i) q^{65} +(72.6428 + 42.7700i) q^{66} -42.8194i q^{67} +18.8725 q^{68} +(7.29969 - 12.3982i) q^{69} +(-28.2660 + 70.6711i) q^{70} -97.2496i q^{71} +(12.3503 + 22.2592i) q^{72} -43.7676i q^{73} -0.449013i q^{74} +(-72.1262 + 20.5624i) q^{75} +16.2963 q^{76} -213.877 q^{77} +(57.9687 + 34.1303i) q^{78} +121.730 q^{79} +(-18.5698 - 7.42725i) q^{80} +(-42.8677 + 68.7267i) q^{81} -42.4627i q^{82} -60.3906 q^{83} +(-55.6550 - 32.7681i) q^{84} +(-43.8072 - 17.5213i) q^{85} -18.8763i q^{86} +(-123.103 - 72.4795i) q^{87} -56.1990i q^{88} -5.45726i q^{89} +(-8.00214 - 63.1345i) q^{90} -170.673 q^{91} -9.59166 q^{92} +(15.9078 - 27.0187i) q^{93} -23.0432 q^{94} +(-37.8272 - 15.1296i) q^{95} +(8.61025 - 14.6241i) q^{96} +157.559i q^{97} +94.5650 q^{98} +(156.368 - 86.7592i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88q + 176q^{4} + 8q^{9} + O(q^{10}) $	$ 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	−1.52209	+	2.58520i	−0.507364	+	0.861732i
$3$	−1.52209	+	2.58520i	−0.507364	+	0.861732i
$4$	2.00000			0.500000
$5$	−4.64244	−	1.85681i	−0.928488	−	0.371363i
$5$	−4.64244	−	1.85681i	−0.928488	−	0.371363i
$6$	2.15256	−	3.65602i	0.358760	−	0.609337i
$7$			10.7642i			1.53774i	0.639405	+	0.768870i	$0.279181\pi$
$7$			10.7642i			1.53774i	−0.639405	+	0.768870i	$0.720819\pi$
$8$	−2.82843			−0.353553
$9$	−4.36648	−	7.86981i	−0.485164	−	0.874423i
$10$	6.56540	+	2.62593i	0.656540	+	0.262593i
$11$			19.8694i			1.80631i	0.429319	+	0.903153i	$0.358754\pi$
$11$			19.8694i			1.80631i	−0.429319	+	0.903153i	$0.641246\pi$
$12$	−3.04418	+	5.17039i	−0.253682	+	0.430866i
$13$			15.8557i			1.21967i	0.792529	+	0.609834i	$0.208764\pi$
$13$			15.8557i			1.21967i	−0.792529	+	0.609834i	$0.791236\pi$
$14$		−	15.2228i		−	1.08735i
$15$	11.8664	−	9.17538i	0.791096	−	0.611692i
$16$	4.00000			0.250000
$17$	9.43625			0.555073			0.277537	−	0.960715i	$-0.410482\pi$
$17$	9.43625			0.555073			0.277537	+	0.960715i	$0.410482\pi$
$18$	6.17514	+	11.1296i	0.343063	+	0.618310i
$19$	8.14814			0.428849			0.214425	−	0.976741i	$-0.431212\pi$
$19$	8.14814			0.428849			0.214425	+	0.976741i	$0.431212\pi$
$20$	−9.28488	−	3.71363i	−0.464244	−	0.185681i
$21$	−27.8275	−	16.3841i	−1.32512	−	0.780193i
$22$		−	28.0995i		−	1.27725i
$23$	−4.79583			−0.208514
$23$	−4.79583			−0.208514
$24$	4.30512	−	7.31204i	0.179380	−	0.304668i
$25$	18.1045	+	17.2403i	0.724180	+	0.689611i
$26$		−	22.4233i		−	0.862436i
$27$	26.9912	+	0.690351i	0.999673	+	0.0255686i
$28$			21.5284i			0.768870i
$29$			47.6184i			1.64201i	0.570919	+	0.821007i	$0.306587\pi$
$29$			47.6184i			1.64201i	−0.570919	+	0.821007i	$0.693413\pi$
$30$	−16.7817	+	12.9759i	−0.559389	+	0.432532i
$31$	−10.4513			−0.337139			−0.168569	−	0.985690i	$-0.553915\pi$
$31$	−10.4513			−0.337139			−0.168569	+	0.985690i	$0.553915\pi$
$32$	−5.65685			−0.176777
$33$	−51.3662	−	30.2430i	−1.55655	−	0.916454i
$34$	−13.3449			−0.392496
$35$	19.9871	−	49.9720i	0.571059	−	1.42777i
$36$	−8.73296	−	15.7396i	−0.242582	−	0.437211i
$37$			0.317500i			0.00858109i	0.999991	+	0.00429054i	$0.00136573\pi$
$37$			0.317500i			0.00858109i	−0.999991	+	0.00429054i	$0.998634\pi$
$38$	−11.5232			−0.303242
$39$	−40.9901	−	24.1338i	−1.05103	−	0.618815i
$40$	13.1308	+	5.25186i	0.328270	+	0.131296i
$41$			30.0257i			0.732333i	0.930549	+	0.366167i	$0.119330\pi$
$41$			30.0257i			0.732333i	−0.930549	+	0.366167i	$0.880670\pi$
$42$	39.3540	+	23.1706i	0.937001	+	0.551680i
$43$			13.3476i			0.310408i	0.987882	+	0.155204i	$0.0496036\pi$
$43$			13.3476i			0.310408i	−0.987882	+	0.155204i	$0.950396\pi$
$44$			39.7387i			0.903153i
$45$	5.65836	+	44.6428i	0.125741	+	0.992063i
$46$	6.78233			0.147442
$47$	16.2940			0.346681			0.173341	−	0.984862i	$-0.444544\pi$
$47$	16.2940			0.346681			0.173341	+	0.984862i	$0.444544\pi$
$48$	−6.08836	+	10.3408i	−0.126841	+	0.215433i
$49$	−66.8675			−1.36464
$50$	−25.6036	−	24.3814i	−0.512072	−	0.487629i
$51$	−14.3628	+	24.3946i	−0.281624	+	0.478325i
$52$			31.7114i			0.609834i
$53$	−77.8949			−1.46972			−0.734858	−	0.678221i	$-0.762751\pi$
$53$	−77.8949			−1.46972			−0.734858	+	0.678221i	$0.762751\pi$
$54$	−38.1713	−	0.976304i	−0.706876	−	0.0180797i
$55$	36.8937	−	92.2423i	0.670794	−	1.67713i
$56$		−	30.4457i		−	0.543673i
$57$	−12.4022	+	21.0645i	−0.217583	+	0.369553i
$58$		−	67.3426i		−	1.16108i
$59$		−	15.6749i		−	0.265676i	−0.991138	−	0.132838i	$-0.957591\pi$
$59$		−	15.6749i		−	0.265676i	0.991138	−	0.132838i	$-0.0424089\pi$
$60$	23.7329	−	18.3508i	0.395548	−	0.305846i
$61$	12.3081			0.201772			0.100886	−	0.994898i	$-0.467832\pi$
$61$	12.3081			0.201772			0.100886	+	0.994898i	$0.467832\pi$
$62$	14.7804			0.238393
$63$	84.7120	−	47.0016i	1.34463	−	0.746057i
$64$	8.00000			0.125000
$65$	29.4410	−	73.6091i	0.452939	−	1.13245i
$66$	72.6428	+	42.7700i	1.10065	+	0.648031i
$67$		−	42.8194i		−	0.639095i	−0.947570	−	0.319548i	$-0.896469\pi$
$67$		−	42.8194i		−	0.639095i	0.947570	−	0.319548i	$-0.103531\pi$
$68$	18.8725			0.277537
$69$	7.29969	−	12.3982i	0.105793	−	0.179684i
$70$	−28.2660	+	70.6711i	−0.403800	+	1.00959i
$71$		−	97.2496i		−	1.36971i	−0.728678	−	0.684856i	$-0.759865\pi$
$71$		−	97.2496i		−	1.36971i	0.728678	−	0.684856i	$-0.240135\pi$
$72$	12.3503	+	22.2592i	0.171532	+	0.309155i
$73$		−	43.7676i		−	0.599556i	−0.954009	−	0.299778i	$-0.903087\pi$
$73$		−	43.7676i		−	0.599556i	0.954009	−	0.299778i	$-0.0969127\pi$
$74$		−	0.449013i		−	0.00606774i
$75$	−72.1262	+	20.5624i	−0.961683	+	0.274165i
$76$	16.2963			0.214425
$77$	−213.877			−2.77763
$78$	57.9687	+	34.1303i	0.743189	+	0.437568i
$79$	121.730			1.54089			0.770443	−	0.637509i	$-0.220035\pi$
$79$	121.730			1.54089			0.770443	+	0.637509i	$0.220035\pi$
$80$	−18.5698	−	7.42725i	−0.232122	−	0.0928406i
$81$	−42.8677	+	68.7267i	−0.529231	+	0.848478i
$82$		−	42.4627i		−	0.517838i
$83$	−60.3906			−0.727597			−0.363799	−	0.931478i	$-0.618520\pi$
$83$	−60.3906			−0.727597			−0.363799	+	0.931478i	$0.618520\pi$
$84$	−55.6550	−	32.7681i	−0.662560	−	0.390097i
$85$	−43.8072	−	17.5213i	−0.515379	−	0.206133i
$86$		−	18.8763i		−	0.219492i
$87$	−123.103	−	72.4795i	−1.41498	−	0.833098i
$88$		−	56.1990i		−	0.638626i
$89$		−	5.45726i		−	0.0613176i	−0.999530	−	0.0306588i	$-0.990239\pi$
$89$		−	5.45726i		−	0.0613176i	0.999530	−	0.0306588i	$-0.00976052\pi$
$90$	−8.00214	−	63.1345i	−0.0889126	−	0.701495i
$91$	−170.673			−1.87553
$92$	−9.59166			−0.104257
$93$	15.9078	−	27.0187i	0.171052	−	0.290523i
$94$	−23.0432			−0.245141
$95$	−37.8272	−	15.1296i	−0.398182	−	0.159259i
$96$	8.61025	−	14.6241i	0.0896901	−	0.152334i
$97$			157.559i			1.62432i	0.583432	+	0.812162i	$0.301710\pi$
$97$			157.559i			1.62432i	−0.583432	+	0.812162i	$0.698290\pi$
$98$	94.5650			0.964949
$99$	156.368	−	86.7592i	1.57948	−	0.876355i
$100$	36.2090	+	34.4806i	0.362090	+	0.344806i
$101$		−	125.568i		−	1.24325i	−0.783315	−	0.621625i	$-0.786473\pi$
$101$		−	125.568i		−	1.24325i	0.783315	−	0.621625i	$-0.213527\pi$
$102$	20.3121	−	34.4991i	0.199138	−	0.338227i
$103$		−	135.773i		−	1.31818i	−0.752062	−	0.659092i	$-0.770941\pi$
$103$		−	135.773i		−	1.31818i	0.752062	−	0.659092i	$-0.229059\pi$
$104$		−	44.8467i		−	0.431218i
$105$	98.7654	+	127.732i	0.940623	+	1.21650i
$106$	110.160			1.03925
$107$	−26.9644			−0.252004			−0.126002	−	0.992030i	$-0.540215\pi$
$107$	−26.9644			−0.252004			−0.126002	+	0.992030i	$0.540215\pi$
$108$	53.9823	+	1.38070i	0.499837	+	0.0127843i
$109$	−107.331			−0.984685			−0.492342	−	0.870402i	$-0.663859\pi$
$109$	−107.331			−0.984685			−0.492342	+	0.870402i	$0.663859\pi$
$110$	−52.1755	+	130.450i	−0.474323	+	1.18591i
$111$	−0.820800	−	0.483264i	−0.00739460	−	0.00435373i
$112$			43.0567i			0.384435i
$113$	204.412			1.80895			0.904477	−	0.426522i	$-0.140261\pi$
$113$	204.412			1.80895			0.904477	+	0.426522i	$0.140261\pi$
$114$	17.5394	−	29.7898i	0.153854	−	0.261314i
$115$	22.2644	+	8.90496i	0.193603	+	0.0774344i
$116$			95.2368i			0.821007i
$117$	124.781	−	69.2335i	1.06651	−	0.591740i
$118$			22.1676i			0.187861i
$119$			101.573i			0.853558i
$120$	−33.5634	+	25.9519i	−0.279695	+	0.216266i
$121$	−273.792			−2.26274
$122$	−17.4063			−0.142674
$123$	−77.6222	−	45.7018i	−0.631075	−	0.371559i
$124$	−20.9026			−0.168569
$125$	−52.0371	−	113.654i	−0.416296	−	0.909229i
$126$	−119.801	+	66.4703i	−0.950800	+	0.527542i
$127$		−	63.8176i		−	0.502500i	−0.967922	−	0.251250i	$-0.919158\pi$
$127$		−	63.8176i		−	0.502500i	0.967922	−	0.251250i	$-0.0808417\pi$
$128$	−11.3137			−0.0883883
$129$	−34.5061	−	20.3162i	−0.267489	−	0.157490i
$130$	−41.6359	+	104.099i	−0.320276	+	0.800761i
$131$			110.013i			0.839795i	0.907571	+	0.419898i	$0.137934\pi$
$131$			110.013i			0.839795i	−0.907571	+	0.419898i	$0.862066\pi$
$132$	−102.732	−	60.4859i	−0.778276	−	0.458227i
$133$			87.7080i			0.659459i
$134$			60.5558i			0.451909i
$135$	−124.023	−	53.3225i	−0.918689	−	0.394981i
$136$	−26.6897			−0.196248
$137$	−50.0168			−0.365086			−0.182543	−	0.983198i	$-0.558433\pi$
$137$	−50.0168			−0.365086			−0.182543	+	0.983198i	$0.558433\pi$
$138$	−10.3233	+	17.5337i	−0.0748067	+	0.127055i
$139$	264.133			1.90024			0.950120	−	0.311883i	$-0.100960\pi$
$139$	264.133			1.90024			0.950120	+	0.311883i	$0.100960\pi$
$140$	39.9741	−	99.9441i	0.285529	−	0.713886i
$141$	−24.8010	+	42.1232i	−0.175893	+	0.298746i
$142$			137.532i			0.968533i
$143$	−315.042			−2.20309
$144$	−17.4659	−	31.4792i	−0.121291	−	0.218606i
$145$	88.4184	−	221.065i	0.609782	−	1.52459i
$146$			61.8968i			0.423950i
$147$	101.778	−	172.866i	0.692370	−	1.17596i
$148$			0.635000i			0.00429054i
$149$			99.4139i			0.667207i	0.942713	+	0.333604i	$0.108265\pi$
$149$			99.4139i			0.667207i	−0.942713	+	0.333604i	$0.891735\pi$
$150$	102.002	−	29.0796i	0.680012	−	0.193864i
$151$	44.2803			0.293247			0.146623	−	0.989192i	$-0.453159\pi$
$151$	44.2803			0.293247			0.146623	+	0.989192i	$0.453159\pi$
$152$	−23.0464			−0.151621
$153$	−41.2032	−	74.2614i	−0.269302	−	0.485369i
$154$	302.468			1.96408
$155$	48.5195	+	19.4061i	0.313029	+	0.125201i
$156$	−81.9801	−	48.2676i	−0.525514	−	0.309408i
$157$			131.707i			0.838899i	0.907779	+	0.419449i	$0.137777\pi$
$157$			131.707i			0.838899i	−0.907779	+	0.419449i	$0.862223\pi$
$158$	−172.152			−1.08957
$159$	118.563	−	201.374i	0.745680	−	1.26650i
$160$	26.2616	+	10.5037i	0.164135	+	0.0656482i
$161$		−	51.6232i		−	0.320641i
$162$	60.6241	−	97.1942i	0.374223	−	0.599964i
$163$		−	154.197i		−	0.945995i	−0.881064	−	0.472998i	$-0.843172\pi$
$163$		−	154.197i		−	0.945995i	0.881064	−	0.472998i	$-0.156828\pi$
$164$			60.0513i			0.366167i
$165$	182.309	+	235.779i	1.10490	+	1.42896i
$166$	85.4052			0.514489
$167$	−27.2956			−0.163446			−0.0817232	−	0.996655i	$-0.526042\pi$
$167$	−27.2956			−0.163446			−0.0817232	+	0.996655i	$0.526042\pi$
$168$	78.7081	+	46.3411i	0.468501	+	0.275840i
$169$	−82.4028			−0.487591
$170$	61.9527	+	24.7789i	0.364428	+	0.145758i
$171$	−35.5787	−	64.1243i	−0.208063	−	0.374996i
$172$			26.6951i			0.155204i
$173$	−229.104			−1.32430			−0.662150	−	0.749371i	$-0.730356\pi$
$173$	−229.104			−1.32430			−0.662150	+	0.749371i	$0.730356\pi$
$174$	174.094	+	102.501i	1.00054	+	0.589089i
$175$	−185.577	+	194.880i	−1.06044	+	1.11360i
$176$			79.4775i			0.451576i
$177$	40.5226	+	23.8586i	0.228941	+	0.134794i
$178$			7.71774i			0.0433581i
$179$			349.348i			1.95167i	0.218518	+	0.975833i	$0.429878\pi$
$179$			349.348i			1.95167i	−0.218518	+	0.975833i	$0.570122\pi$
$180$	11.3167	+	89.2857i	0.0628707	+	0.496032i
$181$	252.087			1.39274			0.696372	−	0.717681i	$-0.254796\pi$
$181$	252.087			1.39274			0.696372	+	0.717681i	$0.254796\pi$
$182$	241.369			1.32620
$183$	−18.7340	+	31.8188i	−0.102372	+	0.173873i
$184$	13.5647			0.0737210
$185$	0.589538	−	1.47398i	0.00318669	−	0.00796744i
$186$	−22.4971	+	38.2102i	−0.120952	+	0.205431i
$187$			187.492i			1.00263i
$188$	32.5880			0.173341
$189$	−7.43106	+	290.538i	−0.0393178	+	1.53724i
$190$	53.4958	+	21.3964i	0.281557	+	0.112613i
$191$			250.898i			1.31360i	0.754065	+	0.656800i	$0.228090\pi$
$191$			250.898i			1.31360i	−0.754065	+	0.656800i	$0.771910\pi$
$192$	−12.1767	+	20.6816i	−0.0634204	+	0.107717i
$193$		−	167.717i		−	0.869002i	−0.900671	−	0.434501i	$-0.856925\pi$
$193$		−	167.717i		−	0.869002i	0.900671	−	0.434501i	$-0.143075\pi$
$194$		−	222.823i		−	1.14857i
$195$	145.482	+	188.151i	0.746061	+	0.964875i
$196$	−133.735			−0.682322
$197$	127.097			0.645164			0.322582	−	0.946541i	$-0.395449\pi$
$197$	127.097			0.645164			0.322582	+	0.946541i	$0.395449\pi$
$198$	−221.138	+	122.696i	−1.11686	+	0.619677i
$199$	−275.113			−1.38248			−0.691238	−	0.722628i	$-0.742934\pi$
$199$	−275.113			−1.38248			−0.691238	+	0.722628i	$0.742934\pi$
$200$	−51.2072	−	48.7629i	−0.256036	−	0.243814i
$201$	110.697	+	65.1750i	0.550729	+	0.324254i
$202$			177.580i			0.879111i
$203$	−512.573			−2.52499
$204$	−28.7256	+	48.7891i	−0.140812	+	0.239162i
$205$	55.7520	−	139.392i	0.271961	−	0.679963i
$206$			192.012i			0.932097i
$207$	20.9409	+	37.7423i	0.101164	+	0.182330i
$208$			63.4228i			0.304917i
$209$			161.898i			0.774633i
$210$	−139.675	−	180.641i	−0.665121	−	0.860195i
$211$	131.348			0.622501			0.311251	−	0.950328i	$-0.399252\pi$
$211$	131.348			0.622501			0.311251	+	0.950328i	$0.399252\pi$
$212$	−155.790			−0.734858
$213$	251.409	+	148.023i	1.18033	+	0.694942i
$214$	38.1334			0.178194
$215$	24.7839	−	61.9653i	0.115274	−	0.288210i
$216$	−76.3426	−	1.95261i	−0.353438	−	0.00903985i
$217$		−	112.500i		−	0.518432i
$218$	151.788			0.696277
$219$	113.148	+	66.6183i	0.516657	+	0.304193i
$220$	73.7874	−	184.485i	0.335397	−	0.838567i
$221$			149.618i			0.677005i
$222$	1.16079	+	0.683439i	0.00522877	+	0.00307855i
$223$		−	113.849i		−	0.510534i	−0.966871	−	0.255267i	$-0.917837\pi$
$223$		−	113.849i		−	0.510534i	0.966871	−	0.255267i	$-0.0821634\pi$
$224$		−	60.8914i		−	0.271837i
$225$	56.6248	−	217.758i	0.251666	−	0.967814i
$226$	−289.082			−1.27912
$227$	421.895			1.85857			0.929284	−	0.369367i	$-0.120425\pi$
$227$	421.895			1.85857			0.929284	+	0.369367i	$0.120425\pi$
$228$	−24.8044	+	42.1291i	−0.108791	+	0.184777i
$229$	390.869			1.70685			0.853426	−	0.521215i	$-0.174521\pi$
$229$	390.869			1.70685			0.853426	+	0.521215i	$0.174521\pi$
$230$	−31.4866	−	12.5935i	−0.136898	−	0.0547544i
$231$	325.541	−	552.915i	1.40927	−	2.39357i
$232$		−	134.685i		−	0.580539i
$233$	196.510			0.843390			0.421695	−	0.906738i	$-0.361435\pi$
$233$	196.510			0.843390			0.421695	+	0.906738i	$0.361435\pi$
$234$	−176.467	+	97.9110i	−0.754134	+	0.418423i
$235$	−75.6440	−	30.2549i	−0.321889	−	0.128744i
$236$		−	31.3497i		−	0.132838i
$237$	−185.284	+	314.696i	−0.781789	+	1.32783i
$238$		−	143.647i		−	0.603557i
$239$		−	216.164i		−	0.904451i	−0.891904	−	0.452225i	$-0.850630\pi$
$239$		−	216.164i		−	0.904451i	0.891904	−	0.452225i	$-0.149370\pi$
$240$	47.4658	−	36.7015i	0.197774	−	0.152923i
$241$	−338.017			−1.40256			−0.701280	−	0.712886i	$-0.747388\pi$
$241$	−338.017			−1.40256			−0.701280	+	0.712886i	$0.747388\pi$
$242$	387.200			1.60000
$243$	−112.423	−	215.430i	−0.462648	−	0.886542i
$244$	24.6162			0.100886
$245$	310.428	+	124.160i	1.26706	+	0.506777i
$246$	109.774	+	64.6321i	0.446237	+	0.262732i
$247$			129.194i			0.523054i
$248$	29.5607			0.119197
$249$	91.9199	−	156.121i	0.369156	−	0.626994i
$250$	73.5915	+	160.730i	0.294366	+	0.642922i
$251$			377.506i			1.50401i	0.659159	+	0.752004i	$0.270913\pi$
$251$			377.506i			1.50401i	−0.659159	+	0.752004i	$0.729087\pi$
$252$	169.424	−	94.0031i	0.672317	−	0.373028i
$253$		−	95.2901i		−	0.376641i
$254$			90.2517i			0.355321i
$255$	111.975	−	86.5812i	0.439116	−	0.339534i
$256$	16.0000			0.0625000
$257$	371.605			1.44594			0.722968	−	0.690882i	$-0.242777\pi$
$257$	371.605			1.44594			0.722968	+	0.690882i	$0.242777\pi$
$258$	48.7989	+	28.7314i	0.189143	+	0.111362i
$259$	−3.41763			−0.0131955
$260$	58.8821	−	147.218i	0.226470	−	0.566224i
$261$	374.747	−	207.925i	1.43581	−	0.796647i
$262$		−	155.582i		−	0.593825i
$263$	81.0593			0.308210			0.154105	−	0.988054i	$-0.450751\pi$
$263$	81.0593			0.308210			0.154105	+	0.988054i	$0.450751\pi$
$264$	145.286	+	85.5400i	0.550324	+	0.324015i
$265$	361.623	+	144.636i	1.36461	+	0.545797i
$266$		−	124.038i		−	0.466308i
$267$	14.1081	+	8.30645i	0.0528393	+	0.0311103i
$268$		−	85.6388i		−	0.319548i
$269$			165.483i			0.615179i	0.951519	+	0.307590i	$0.0995224\pi$
$269$			165.483i			0.615179i	−0.951519	+	0.307590i	$0.900478\pi$
$270$	175.395	+	75.4093i	0.649611	+	0.279294i
$271$	321.114			1.18492			0.592461	−	0.805599i	$-0.298157\pi$
$271$	321.114			1.18492			0.592461	+	0.805599i	$0.298157\pi$
$272$	37.7450			0.138768
$273$	259.780	−	441.224i	0.951577	−	1.61621i
$274$	70.7345			0.258155
$275$	−342.553	+	359.725i	−1.24565	+	1.30809i
$276$	14.5994	−	24.7963i	0.0528963	−	0.0898418i
$277$		−	93.4085i		−	0.337215i	−0.985683	−	0.168607i	$-0.946073\pi$
$277$		−	93.4085i		−	0.337215i	0.985683	−	0.168607i	$-0.0539270\pi$
$278$	−373.541			−1.34367
$279$	45.6354	+	82.2497i	0.163568	+	0.294802i
$280$	−56.5319	+	141.342i	−0.201900	+	0.504794i
$281$		−	343.933i		−	1.22396i	−0.790872	−	0.611981i	$-0.790373\pi$
$281$		−	343.933i		−	1.22396i	0.790872	−	0.611981i	$-0.209627\pi$
$282$	35.0739	−	59.5712i	0.124375	−	0.211245i
$283$		−	232.475i		−	0.821465i	−0.911756	−	0.410733i	$-0.865273\pi$
$283$		−	232.475i		−	0.821465i	0.911756	−	0.410733i	$-0.134727\pi$
$284$		−	194.499i		−	0.684856i
$285$	96.6894	−	74.7623i	0.339261	−	0.262324i
$286$	445.537			1.55782
$287$	−323.202			−1.12614
$288$	24.7005	+	44.5183i	0.0857658	+	0.154578i
$289$	−199.957			−0.691894
$290$	−125.043	+	312.634i	−0.431181	+	1.07805i
$291$	−407.322	−	239.820i	−1.39973	−	0.824123i
$292$		−	87.5352i		−	0.299778i
$293$	19.7017			0.0672413			0.0336207	−	0.999435i	$-0.489296\pi$
$293$	19.7017			0.0672413			0.0336207	+	0.999435i	$0.489296\pi$
$294$	−143.936	+	244.469i	−0.489580	+	0.831527i
$295$	−29.1053	+	72.7696i	−0.0986620	+	0.246677i
$296$		−	0.898026i		−	0.00303387i
$297$	−13.7168	+	536.297i	−0.0461846	+	1.80572i
$298$		−	140.592i		−	0.471787i
$299$		−	76.0412i		−	0.254318i
$300$	−144.252	+	41.1248i	−0.480841	+	0.137083i
$301$	−143.676			−0.477327
$302$	−62.6217			−0.207357
$303$	324.619	+	191.126i	1.07135	+	0.630780i
$304$	32.5926			0.107212
$305$	−57.1396	−	22.8538i	−0.187343	−	0.0749306i
$306$	58.2701	+	105.022i	0.190425	+	0.343208i
$307$		−	49.3669i		−	0.160804i	−0.996763	−	0.0804021i	$-0.974380\pi$
$307$		−	49.3669i		−	0.160804i	0.996763	−	0.0804021i	$-0.0256204\pi$
$308$	−427.755			−1.38881
$309$	351.000	+	206.659i	1.13592	+	0.668799i
$310$	−68.6170	−	27.4444i	−0.221345	−	0.0885303i
$311$			37.9233i			0.121940i	0.998140	+	0.0609699i	$0.0194194\pi$
$311$			37.9233i			0.121940i	−0.998140	+	0.0609699i	$0.980581\pi$
$312$	115.937	+	68.2607i	0.371594	+	0.218784i
$313$			105.976i			0.338582i	0.985566	+	0.169291i	$0.0541478\pi$
$313$			105.976i			0.338582i	−0.985566	+	0.169291i	$0.945852\pi$
$314$		−	186.262i		−	0.593191i
$315$	−480.543	+	60.9076i	−1.52553	+	0.193358i
$316$	243.460			0.770443
$317$	94.9663			0.299578			0.149789	−	0.988718i	$-0.452141\pi$
$317$	94.9663			0.299578			0.149789	+	0.988718i	$0.452141\pi$
$318$	−167.674	+	284.785i	−0.527276	+	0.895552i
$319$	−946.147			−2.96598
$320$	−37.1395	−	14.8545i	−0.116061	−	0.0464203i
$321$	41.0423	−	69.7083i	0.127858	−	0.217160i
$322$			73.0062i			0.226727i
$323$	76.8879			0.238043
$324$	−85.7354	+	137.453i	−0.264615	+	0.424239i
$325$	−273.357	+	287.059i	−0.841097	+	0.883259i
$326$			218.068i			0.668920i
$327$	163.367	−	277.471i	0.499593	−	0.848534i
$328$		−	84.9254i		−	0.258919i
$329$			175.392i			0.533105i
$330$	−257.824	−	333.441i	−0.781284	−	1.01043i
$331$	−47.3795			−0.143141			−0.0715703	−	0.997436i	$-0.522801\pi$
$331$	−47.3795			−0.143141			−0.0715703	+	0.997436i	$0.522801\pi$
$332$	−120.781			−0.363799
$333$	2.49867	−	1.38636i	0.00750350	−	0.00416324i
$334$	38.6017			0.115574
$335$	−79.5076	+	198.786i	−0.237336	+	0.593392i
$336$	−111.310	−	65.5362i	−0.331280	−	0.195048i
$337$			554.880i			1.64653i	0.567659	+	0.823264i	$0.307849\pi$
$337$			554.880i			1.64653i	−0.567659	+	0.823264i	$0.692151\pi$
$338$	116.535			0.344779
$339$	−311.133	+	528.445i	−0.917798	+	1.55883i
$340$	−87.6144	−	35.0427i	−0.257689	−	0.103067i
$341$		−	207.661i		−	0.608976i
$342$	50.3159	+	90.6854i	0.147122	+	0.265162i
$343$		−	192.329i		−	0.560727i
$344$		−	37.7526i		−	0.109746i
$345$	−56.9094	+	44.0036i	−0.164955	+	0.127547i
$346$	324.002			0.936422
$347$	1.81515			0.00523097			0.00261549	−	0.999997i	$-0.499167\pi$
$347$	1.81515			0.00523097			0.00261549	+	0.999997i	$0.499167\pi$
$348$	−246.206	−	144.959i	−0.707488	−	0.416549i
$349$	−602.109			−1.72524			−0.862620	−	0.505853i	$-0.831178\pi$
$349$	−602.109			−1.72524			−0.862620	+	0.505853i	$0.831178\pi$
$350$	262.446	−	275.602i	0.749846	−	0.787434i
$351$	−10.9460	+	427.964i	−0.0311852	+	1.21927i
$352$		−	112.398i		−	0.319313i
$353$	32.9038			0.0932120			0.0466060	−	0.998913i	$-0.485159\pi$
$353$	32.9038			0.0932120			0.0466060	+	0.998913i	$0.485159\pi$
$354$	−57.3076	−	33.7411i	−0.161886	−	0.0953138i
$355$	−180.574	+	451.475i	−0.508660	+	1.27176i
$356$		−	10.9145i		−	0.0306588i
$357$	−262.587	−	154.604i	−0.735539	−	0.433064i
$358$		−	494.053i		−	1.38004i
$359$			14.4746i			0.0403193i	0.999797	+	0.0201597i	$0.00641746\pi$
$359$			14.4746i			0.0403193i	−0.999797	+	0.0201597i	$0.993583\pi$
$360$	−16.0043	−	126.269i	−0.0444563	−	0.350747i
$361$	−294.608			−0.816088
$362$	−356.505			−0.984819
$363$	416.736	−	707.805i	1.14803	−	1.94988i
$364$	−341.347			−0.937766
$365$	−81.2683	+	203.189i	−0.222653	+	0.556681i
$366$	26.4939	−	44.9986i	0.0723878	−	0.122947i
$367$			501.552i			1.36663i	0.730126	+	0.683313i	$0.239462\pi$
$367$			501.552i			1.36663i	−0.730126	+	0.683313i	$0.760538\pi$
$368$	−19.1833			−0.0521286
$369$	236.296	−	131.106i	0.640369	−	0.355302i
$370$	−0.833733	+	2.08452i	−0.00225333	+	0.00563383i
$371$		−	838.475i		−	2.26004i
$372$	31.8157	−	54.0373i	0.0855260	−	0.145262i
$373$		−	290.424i		−	0.778616i	−0.921108	−	0.389308i	$-0.872714\pi$
$373$		−	290.424i		−	0.778616i	0.921108	−	0.389308i	$-0.127286\pi$
$374$		−	265.154i		−	0.708968i
$375$	373.022	+	38.4651i	0.994725	+	0.102574i
$376$	−46.0864			−0.122570
$377$	−755.022			−2.00271
$378$	10.5091	−	410.882i	0.0278019	−	1.08699i
$379$	392.815			1.03645			0.518226	−	0.855244i	$-0.326593\pi$
$379$	392.815			1.03645			0.518226	+	0.855244i	$0.326593\pi$
$380$	−75.6545	−	30.2591i	−0.199091	−	0.0796293i
$381$	164.981	+	97.1361i	0.433021	+	0.254950i
$382$		−	354.823i		−	0.928856i
$383$	−686.622			−1.79275			−0.896374	−	0.443299i	$-0.853808\pi$
$383$	−686.622			−1.79275			−0.896374	+	0.443299i	$0.853808\pi$
$384$	17.2205	−	29.2482i	0.0448450	−	0.0761671i
$385$	992.913	+	397.130i	2.57899	+	1.03151i
$386$			237.188i			0.614477i
$387$	105.043	−	58.2819i	0.271428	−	0.150599i
$388$			315.119i			0.812162i
$389$			259.878i			0.668067i	0.942561	+	0.334033i	$0.108410\pi$
$389$			259.878i			0.668067i	−0.942561	+	0.334033i	$0.891590\pi$
$390$	−205.743	−	266.085i	−0.527545	−	0.682269i
$391$	−45.2547			−0.115741
$392$	189.130			0.482474
$393$	−284.406	−	167.450i	−0.723678	−	0.426081i
$394$	−179.743			−0.456200
$395$	−565.124	−	226.030i	−1.43069	−	0.572227i
$396$	312.736	−	173.518i	0.789738	−	0.438178i
$397$			458.235i			1.15424i	0.816658	+	0.577122i	$0.195824\pi$
$397$			458.235i			1.15424i	−0.816658	+	0.577122i	$0.804176\pi$
$398$	389.068			0.977558
$399$	−226.742	−	133.500i	−0.568277	−	0.334585i
$400$	72.4180	+	68.9611i	0.181045	+	0.172403i
$401$		−	340.506i		−	0.849143i	−0.905394	−	0.424572i	$-0.860425\pi$
$401$		−	340.506i		−	0.849143i	0.905394	−	0.424572i	$-0.139575\pi$
$402$	−156.549	−	92.1714i	−0.389424	−	0.229282i
$403$		−	165.713i		−	0.411197i
$404$		−	251.137i		−	0.621625i
$405$	326.623	−	239.462i	0.806477	−	0.591265i
$406$	724.887			1.78544
$407$	−6.30853			−0.0155001
$408$	40.6242	−	68.9982i	0.0995691	−	0.169113i
$409$	−339.445			−0.829939			−0.414970	−	0.909835i	$-0.636208\pi$
$409$	−339.445			−0.829939			−0.414970	+	0.909835i	$0.636208\pi$
$410$	−78.8453	+	197.131i	−0.192306	+	0.480806i
$411$	76.1302	−	129.303i	0.185232	−	0.314607i
$412$		−	271.546i		−	0.659092i
$413$	168.727			0.408540
$414$	−29.6149	−	53.3756i	−0.0715336	−	0.128927i
$415$	280.360	+	112.134i	0.675565	+	0.270202i
$416$		−	89.6933i		−	0.215609i
$417$	−402.035	+	682.837i	−0.964113	+	1.63750i
$418$		−	228.959i		−	0.547748i
$419$		−	680.712i		−	1.62461i	−0.583232	−	0.812306i	$-0.698212\pi$
$419$		−	680.712i		−	1.62461i	0.583232	−	0.812306i	$-0.301788\pi$
$420$	197.531	+	255.465i	0.470312	+	0.608250i
$421$	−318.476			−0.756475			−0.378237	−	0.925709i	$-0.623470\pi$
$421$	−318.476			−0.756475			−0.378237	+	0.925709i	$0.623470\pi$
$422$	−185.754			−0.440175
$423$	−71.1475	−	128.231i	−0.168197	−	0.303146i
$424$	220.320			0.519623
$425$	170.838	+	162.684i	0.401973	+	0.382785i
$426$	−355.546	−	209.336i	−0.834616	−	0.491398i
$427$			132.487i			0.310273i
$428$	−53.9288			−0.126002
$429$	479.523	−	814.447i	1.11777	−	1.89848i
$430$	−35.0498	+	87.6321i	−0.0815111	+	0.203796i
$431$		−	442.057i		−	1.02565i	−0.858492	−	0.512827i	$-0.828598\pi$
$431$		−	442.057i		−	1.02565i	0.858492	−	0.512827i	$-0.171402\pi$
$432$	107.965	+	2.76140i	0.249918	+	0.00639214i
$433$			368.341i			0.850672i	0.905036	+	0.425336i	$0.139844\pi$
$433$			368.341i			0.850672i	−0.905036	+	0.425336i	$0.860156\pi$
$434$			159.099i			0.366587i
$435$	436.917	+	565.061i	1.00441	+	1.29899i
$436$	−214.661			−0.492342
$437$	−39.0771			−0.0894213
$438$	−160.015	−	94.2125i	−0.365332	−	0.215097i
$439$	−330.632			−0.753148			−0.376574	−	0.926387i	$-0.622898\pi$
$439$	−330.632			−0.753148			−0.376574	+	0.926387i	$0.622898\pi$
$440$	−104.351	+	260.901i	−0.237162	+	0.592956i
$441$	291.976	+	526.235i	0.662077	+	1.19328i
$442$		−	211.592i		−	0.478715i
$443$	−33.7464			−0.0761770			−0.0380885	−	0.999274i	$-0.512127\pi$
$443$	−33.7464			−0.0761770			−0.0380885	+	0.999274i	$0.512127\pi$
$444$	−1.64160	−	0.966528i	−0.00369730	−	0.00217687i
$445$	−10.1331	+	25.3350i	−0.0227710	+	0.0569326i
$446$			161.007i			0.361002i
$447$	−257.004	−	151.317i	−0.574954	−	0.338517i
$448$			86.1134i			0.192217i
$449$			559.220i			1.24548i	0.782429	+	0.622739i	$0.213980\pi$
$449$			559.220i			1.24548i	−0.782429	+	0.622739i	$0.786020\pi$
$450$	−80.0795	+	307.957i	−0.177954	+	0.684348i
$451$	−596.591			−1.32282
$452$	408.824			0.904477
$453$	−67.3986	+	114.473i	−0.148783	+	0.252700i
$454$	−596.649			−1.31421
$455$	792.341	+	316.909i	1.74141	+	0.696502i
$456$	35.0787	−	59.5795i	0.0769271	−	0.130657i
$457$		−	492.326i		−	1.07730i	−0.842530	−	0.538650i	$-0.818935\pi$
$457$		−	492.326i		−	1.07730i	0.842530	−	0.538650i	$-0.181065\pi$
$458$	−552.772			−1.20693
$459$	254.695	+	6.51432i	0.554892	+	0.0141924i
$460$	44.5287	+	17.8099i	0.0968016	+	0.0387172i
$461$		−	289.785i		−	0.628601i	−0.949324	−	0.314300i	$-0.898230\pi$
$461$		−	289.785i		−	0.628601i	0.949324	−	0.314300i	$-0.101770\pi$
$462$	−460.384	+	781.940i	−0.996502	+	1.69251i
$463$		−	887.597i		−	1.91706i	−0.284999	−	0.958528i	$-0.591993\pi$
$463$		−	887.597i		−	1.91706i	0.284999	−	0.958528i	$-0.408007\pi$
$464$			190.474i			0.410503i
$465$	−124.020	+	95.8947i	−0.266709	+	0.206225i
$466$	−277.907			−0.596367
$467$	383.155			0.820459			0.410230	−	0.911982i	$-0.365449\pi$
$467$	383.155			0.820459			0.410230	+	0.911982i	$0.365449\pi$
$468$	249.562	−	138.467i	0.533253	−	0.295870i
$469$	460.916			0.982762
$470$	106.977	+	42.7869i	0.227610	+	0.0910360i
$471$	−340.489	−	200.470i	−0.722906	−	0.425627i
$472$			44.3352i			0.0939305i
$473$	−265.208			−0.560693
$474$	262.031	−	445.047i	0.552809	−	0.938918i
$475$	147.518	+	140.476i	0.310564	+	0.295739i
$476$			203.147i			0.426779i
$477$	340.127	+	613.018i	0.713054	+	1.28515i
$478$			305.702i			0.639543i
$479$		−	116.267i		−	0.242728i	−0.992608	−	0.121364i	$-0.961273\pi$
$479$		−	116.267i		−	0.242728i	0.992608	−	0.121364i	$-0.0387268\pi$
$480$	−67.1267	+	51.9038i	−0.139847	+	0.108133i
$481$	−5.03418			−0.0104661
$482$	478.028			0.991760
$483$	133.456	+	78.5752i	0.276307	+	0.162682i
$484$	−547.583			−1.13137
$485$	292.558	−	731.460i	0.603213	−	1.50817i
$486$	158.991	+	304.664i	0.327142	+	0.626880i
$487$		−	802.923i		−	1.64871i	−0.566072	−	0.824356i	$-0.691538\pi$
$487$		−	802.923i		−	1.64871i	0.566072	−	0.824356i	$-0.308462\pi$
$488$	−34.8126			−0.0713372
$489$	398.630	+	234.702i	0.815194	+	0.479964i
$490$	−439.012	−	175.589i	−0.895943	−	0.358346i
$491$		−	292.031i		−	0.594768i	−0.954758	−	0.297384i	$-0.903886\pi$
$491$		−	292.031i		−	0.594768i	0.954758	−	0.297384i	$-0.0961142\pi$
$492$	−155.244	−	91.4036i	−0.315537	−	0.185780i
$493$			449.339i			0.911438i
$494$		−	182.708i		−	0.369855i
$495$	−887.025	+	112.428i	−1.79197	+	0.227127i
$496$	−41.8052			−0.0842847
$497$	1046.81			2.10626
$498$	−129.994	+	220.789i	−0.261033	+	0.443352i
$499$	0.617532			0.00123754			0.000618770	−	1.00000i	$-0.499803\pi$
$499$	0.617532			0.00123754			0.000618770		1.00000i	$0.499803\pi$
$500$	−104.074	−	227.307i	−0.208148	−	0.454614i
$501$	41.5463	−	70.5644i	0.0829268	−	0.140847i
$502$		−	533.874i		−	1.06349i
$503$	669.828			1.33167			0.665833	−	0.746101i	$-0.268076\pi$
$503$	669.828			1.33167			0.665833	+	0.746101i	$0.268076\pi$
$504$	−239.602	+	132.941i	−0.475400	+	0.263771i
$505$	−233.157	+	582.943i	−0.461697	+	1.15434i
$506$			134.761i			0.266325i
$507$	125.425	−	213.028i	0.247386	−	0.420173i
$508$		−	127.635i		−	0.251250i
$509$			405.903i			0.797451i	0.917070	+	0.398726i	$0.130547\pi$
$509$			405.903i			0.797451i	−0.917070	+	0.398726i	$0.869453\pi$
$510$	−158.356	+	122.444i	−0.310502	+	0.240087i
$511$	471.122			0.921962
$512$	−22.6274			−0.0441942
$513$	219.928	+	5.62508i	0.428709	+	0.0109651i
$514$	−525.530			−1.02243
$515$	−252.105	+	630.318i	−0.489524	+	1.22392i
$516$	−69.0121	−	40.6324i	−0.133744	−	0.0787450i
$517$			323.752i			0.626212i
$518$	4.83326			0.00933061
$519$	348.717	−	592.279i	0.671902	−	1.14119i
$520$	−83.2718	+	208.198i	−0.160138	+	0.400381i
$521$		−	821.449i		−	1.57668i	−0.615242	−	0.788338i	$-0.710942\pi$
$521$		−	821.449i		−	1.57668i	0.615242	−	0.788338i	$-0.289058\pi$
$522$	−529.973	+	294.050i	−1.01527	+	0.563314i
$523$			839.667i			1.60548i	0.596328	+	0.802741i	$0.296626\pi$
$523$			839.667i			1.60548i	−0.596328	+	0.802741i	$0.703374\pi$
$524$			220.026i			0.419898i
$525$	−221.337	−	776.379i	−0.421595	−	1.47882i
$526$	−114.635			−0.217938
$527$	−98.6211			−0.187137
$528$	−205.465	−	120.972i	−0.389138	−	0.229113i
$529$	23.0000			0.0434783
$530$	−511.411	−	204.547i	−0.964927	−	0.385937i
$531$	−123.358	+	68.4440i	−0.232313	+	0.128896i
$532$			175.416i			0.329729i
$533$	−476.077			−0.893204
$534$	−19.9519	−	11.7471i	−0.0373630	−	0.0219983i
$535$	125.181	+	50.0679i	0.233983	+	0.0935848i
$536$			121.112i			0.225954i
$537$	−903.134	−	531.740i	−1.68181	−	0.990204i
$538$		−	234.029i		−	0.434998i
$539$		−	1328.62i		−	2.46496i
$540$	−248.046	−	106.645i	−0.459345	−	0.197491i
$541$	−698.329			−1.29081			−0.645406	−	0.763840i	$-0.723312\pi$
$541$	−698.329			−1.29081			−0.645406	+	0.763840i	$0.723312\pi$
$542$	−454.123			−0.837866
$543$	−383.699	+	651.694i	−0.706628	+	1.20017i
$544$	−53.3795			−0.0981240
$545$	498.276	+	199.293i	0.914268	+	0.365675i
$546$	−367.385	+	623.985i	−0.672866	+	1.14283i
$547$			294.450i			0.538299i	0.963098	+	0.269150i	$0.0867426\pi$
$547$			294.450i			0.538299i	−0.963098	+	0.269150i	$0.913257\pi$
$548$	−100.034			−0.182543
$549$	−53.7431	−	96.8623i	−0.0978926	−	0.176434i
$550$	484.444	−	508.728i	0.880807	−	0.924959i
$551$			388.001i			0.704177i
$552$	−20.6466	+	35.0673i	−0.0374033	+	0.0635277i
$553$			1310.32i			2.36948i
$554$			132.100i			0.238447i
$555$	2.91319	+	3.76760i	0.00524898	+	0.00678846i
$556$	528.267			0.950120
$557$	981.172			1.76153			0.880765	−	0.473554i	$-0.157029\pi$
$557$	981.172			1.76153			0.880765	+	0.473554i	$0.157029\pi$
$558$	−64.5382	−	116.319i	−0.115660	−	0.208456i
$559$	−211.635			−0.378595
$560$	79.9482	−	199.888i	0.142765	−	0.356943i
$561$	−484.704	−	285.380i	−0.864000	−	0.508699i
$562$			486.395i			0.865472i
$563$	104.996			0.186494			0.0932472	−	0.995643i	$-0.470275\pi$
$563$	104.996			0.186494			0.0932472	+	0.995643i	$0.470275\pi$
$564$	−49.6019	+	84.2464i	−0.0879467	+	0.149373i
$565$	−948.970	−	379.555i	−1.67959	−	0.671778i
$566$			328.769i			0.580864i
$567$	−739.786	−	461.436i	−1.30474	−	0.813819i
$568$			275.063i			0.484267i
$569$		−	756.210i		−	1.32902i	−0.747282	−	0.664508i	$-0.768641\pi$
$569$		−	756.210i		−	1.32902i	0.747282	−	0.664508i	$-0.231359\pi$
$570$	−136.739	+	105.730i	−0.239894	+	0.185491i
$571$	526.804			0.922599			0.461300	−	0.887244i	$-0.347383\pi$
$571$	526.804			0.922599			0.461300	+	0.887244i	$0.347383\pi$
$572$	−630.085			−1.10155
$573$	−648.620	−	381.889i	−1.13197	−	0.666473i
$574$	457.076			0.796300
$575$	−86.8261	−	82.6815i	−0.151002	−	0.143794i
$576$	−34.9318	−	62.9585i	−0.0606456	−	0.109303i
$577$		−	752.642i		−	1.30440i	−0.758045	−	0.652202i	$-0.773845\pi$
$577$		−	752.642i		−	1.30440i	0.758045	−	0.652202i	$-0.226155\pi$
$578$	282.782			0.489243
$579$	433.582	+	255.281i	0.748847	+	0.440900i
$580$	176.837	−	442.131i	0.304891	−	0.762295i
$581$		−	650.055i		−	1.11886i
$582$	576.041	+	339.156i	0.989760	+	0.582743i
$583$		−	1547.72i		−	2.65476i
$584$			123.794i			0.211975i
$585$	−707.843	+	89.7173i	−1.20999	+	0.153363i
$586$	−27.8624			−0.0475468
$587$	317.436			0.540777			0.270388	−	0.962751i	$-0.412848\pi$
$587$	317.436			0.540777			0.270388	+	0.962751i	$0.412848\pi$
$588$	203.557	−	345.731i	0.346185	−	0.587979i
$589$	−85.1587			−0.144582
$590$	41.1611	−	102.912i	0.0697645	−	0.174427i
$591$	−193.454	+	328.572i	−0.327333	+	0.555959i
$592$			1.27000i			0.00214527i
$593$	−248.326			−0.418762			−0.209381	−	0.977834i	$-0.567145\pi$
$593$	−248.326			−0.418762			−0.209381	+	0.977834i	$0.567145\pi$
$594$	19.3985	−	758.439i	0.0326575	−	1.27683i
$595$	188.603	−	471.549i	0.316980	−	0.792519i
$596$			198.828i			0.333604i
$597$	418.746	−	711.220i	0.701418	−	1.19132i
$598$			107.539i			0.179830i
$599$			649.710i			1.08466i	0.840166	+	0.542329i	$0.182457\pi$
$599$			649.710i			1.08466i	−0.840166	+	0.542329i	$0.817543\pi$
$600$	204.004	−	58.1592i	0.340006	−	0.0969321i
$601$	354.948			0.590596			0.295298	−	0.955405i	$-0.404581\pi$
$601$	354.948			0.590596			0.295298	+	0.955405i	$0.404581\pi$
$602$	203.188			0.337521
$603$	−336.980	+	186.970i	−0.558840	+	0.310066i
$604$	88.5605			0.146623
$605$	1271.06	+	508.380i	2.10093	+	0.840297i
$606$	−459.080	−	270.293i	−0.757558	−	0.446029i
$607$			692.227i			1.14041i	0.821503	+	0.570204i	$0.193136\pi$
$607$			692.227i			1.14041i	−0.821503	+	0.570204i	$0.806864\pi$
$608$	−46.0928			−0.0758106
$609$	780.182	−	1325.10i	1.28109	−	2.17586i
$610$	80.8076	+	32.3202i	0.132471	+	0.0529839i
$611$			258.353i			0.422836i
$612$	−82.4064	−	148.523i	−0.134651	−	0.242684i
$613$			803.483i			1.31074i	0.755308	+	0.655370i	$0.227487\pi$
$613$			803.483i			1.31074i	−0.755308	+	0.655370i	$0.772513\pi$
$614$			69.8153i			0.113706i
$615$	275.497	+	356.298i	0.447962	+	0.579346i
$616$	604.937			0.982040
$617$	−232.233			−0.376390			−0.188195	−	0.982132i	$-0.560264\pi$
$617$	−232.233			−0.376390			−0.188195	+	0.982132i	$0.560264\pi$
$618$	−496.389	−	292.260i	−0.803218	−	0.472912i
$619$	1034.13			1.67065			0.835327	−	0.549754i	$-0.185278\pi$
$619$	1034.13			1.67065			0.835327	+	0.549754i	$0.185278\pi$
$620$	97.0391	+	38.8122i	0.156515	+	0.0626003i
$621$	−129.445	−	3.31081i	−0.208446	−	0.00533141i
$622$		−	53.6316i		−	0.0862245i
$623$	58.7429			0.0942904
$624$	−163.960	−	96.5352i	−0.262757	−	0.154704i
$625$	30.5454	+	624.253i	0.0488726	+	0.998805i
$626$		−	149.873i		−	0.239414i
$627$	−418.539	−	246.424i	−0.667526	−	0.393021i
$628$			263.414i			0.419449i
$629$			2.99601i			0.00476313i
$630$	679.591	−	86.1364i	1.07872	−	0.136724i
$631$	−612.871			−0.971270			−0.485635	−	0.874162i	$-0.661412\pi$
$631$	−612.871			−0.971270			−0.485635	+	0.874162i	$0.661412\pi$
$632$	−344.304			−0.544785
$633$	−199.923	+	339.560i	−0.315835	+	0.536430i
$634$	−134.303			−0.211834
$635$	−118.497	+	296.269i	−0.186610	+	0.466566i
$636$	237.126	−	402.747i	0.372840	−	0.633251i
$637$		−	1060.23i		−	1.66441i
$638$	1338.05			2.09726
$639$	−765.335	+	424.638i	−1.19771	+	0.664536i
$640$	52.5232	+	21.0074i	0.0820675	+	0.0328241i
$641$		−	475.721i		−	0.742154i	−0.928602	−	0.371077i	$-0.878989\pi$
$641$		−	475.721i		−	0.742154i	0.928602	−	0.371077i	$-0.121011\pi$
$642$	−58.0426	+	98.5825i	−0.0904090	+	0.153555i
$643$			542.268i			0.843341i	0.906749	+	0.421670i	$0.138556\pi$
$643$			542.268i			0.843341i	−0.906749	+	0.421670i	$0.861444\pi$
$644$		−	103.246i		−	0.160320i
$645$	122.469	+	158.388i	0.189874	+	0.245563i
$646$	−108.736			−0.168322
$647$	312.859			0.483554			0.241777	−	0.970332i	$-0.422270\pi$
$647$	312.859			0.483554			0.241777	+	0.970332i	$0.422270\pi$
$648$	121.248	−	194.388i	0.187111	−	0.299982i
$649$	311.449			0.479891
$650$	386.584	−	405.963i	0.594745	−	0.624559i
$651$	290.834	+	171.235i	0.446749	+	0.263033i
$652$		−	308.394i		−	0.472998i
$653$	206.385			0.316057			0.158029	−	0.987435i	$-0.449486\pi$
$653$	206.385			0.316057			0.158029	+	0.987435i	$0.449486\pi$
$654$	−231.036	+	392.403i	−0.353266	+	0.600004i
$655$	204.274	−	510.729i	0.311868	−	0.779740i
$656$			120.103i			0.183083i
$657$	−344.443	+	191.110i	−0.524266	+	0.290883i
$658$		−	248.041i		−	0.376962i
$659$		−	230.138i		−	0.349222i	−0.984637	−	0.174611i	$-0.944133\pi$
$659$		−	230.138i		−	0.349222i	0.984637	−	0.174611i	$-0.0558669\pi$
$660$	364.618	+	471.557i	0.552451	+	0.714481i
$661$	529.204			0.800611			0.400305	−	0.916382i	$-0.368904\pi$
$661$	529.204			0.800611			0.400305	+	0.916382i	$0.368904\pi$
$662$	67.0048			0.101216
$663$	−386.792	−	227.732i	−0.583397	−	0.343488i
$664$	170.810			0.257244
$665$	162.857	−	407.179i	0.244898	−	0.612300i
$666$	−3.53365	+	1.96061i	−0.00530578	+	0.00294385i
$667$		−	228.370i		−	0.342383i
$668$	−54.5911			−0.0817232
$669$	294.322	+	173.289i	0.439944	+	0.259026i
$670$	112.441	−	281.126i	0.167822	−	0.419592i
$671$			244.554i			0.364462i
$672$	157.416	+	92.6822i	0.234250	+	0.137920i
$673$			194.311i			0.288724i	0.989525	+	0.144362i	$0.0461129\pi$
$673$			194.311i			0.288724i	−0.989525	+	0.144362i	$0.953887\pi$
$674$		−	784.719i		−	1.16427i
$675$	476.760	+	477.834i	0.706311	+	0.707902i
$676$	−164.806			−0.243795
$677$	592.227			0.874782			0.437391	−	0.899271i	$-0.355903\pi$
$677$	592.227			0.874782			0.437391	+	0.899271i	$0.355903\pi$
$678$	440.009	−	747.334i	0.648981	−	1.10226i
$679$	−1696.00			−2.49779
$680$	123.905	+	49.5578i	0.182214	+	0.0728792i
$681$	−642.162	+	1090.68i	−0.942969	+	1.60159i
$682$			293.677i			0.430611i
$683$	−658.091			−0.963531			−0.481765	−	0.876300i	$-0.660004\pi$
$683$	−658.091			−0.963531			−0.481765	+	0.876300i	$0.660004\pi$
$684$	−71.1574	−	128.249i	−0.104031	−	0.187498i
$685$	232.200	+	92.8719i	0.338978	+	0.135579i
$686$			271.995i			0.396494i
$687$	−594.938	+	1010.47i	−0.865994	+	1.47085i
$688$			53.3902i			0.0776021i
$689$		−	1235.08i		−	1.79257i
$690$	80.4821	−	62.2305i	0.116641	−	0.0901891i
$691$	−169.500			−0.245296			−0.122648	−	0.992450i	$-0.539139\pi$
$691$	−169.500			−0.245296			−0.122648	+	0.992450i	$0.539139\pi$
$692$	−458.208			−0.662150
$693$	933.891	+	1683.17i	1.34761	+	2.42882i
$694$	−2.56701			−0.00369886
$695$	−1226.22	−	490.446i	−1.76435	−	0.705678i
$696$	348.188	+	205.003i	0.500269	+	0.294545i
$697$			283.330i			0.406499i
$698$	851.510			1.21993
$699$	−299.106	+	508.017i	−0.427905	+	0.726776i
$700$	−371.155	+	389.760i	−0.530221	+	0.556800i
$701$			248.155i			0.354001i	0.984211	+	0.177001i	$0.0566395\pi$
$701$			248.155i			0.354001i	−0.984211	+	0.177001i	$0.943361\pi$
$702$	15.4800	−	605.232i	0.0220512	−	0.862154i
$703$			2.58704i			0.00367999i
$704$			158.955i			0.225788i
$705$	193.352	−	149.504i	0.274258	−	0.212062i
$706$	−46.5330			−0.0659108
$707$	1351.64			1.91180
$708$	81.0452	+	47.7171i	0.114471	+	0.0673971i
$709$	−1199.85			−1.69231			−0.846157	−	0.532934i	$-0.821089\pi$
$709$	−1199.85			−1.69231			−0.846157	+	0.532934i	$0.821089\pi$
$710$	255.371	−	638.483i	0.359677	−	0.899271i
$711$	−531.532	−	957.992i	−0.747583	−	1.34739i
$712$			15.4355i			0.0216790i
$713$	50.1227			0.0702983
$714$	371.355	+	218.643i	0.520104	+	0.306223i
$715$	1462.57	+	584.975i	2.04555	+	0.818147i
$716$			698.696i			0.975833i
$717$	558.826	+	329.021i	0.779394	+	0.458885i
$718$		−	20.4702i		−	0.0285101i
$719$			1289.31i			1.79319i	0.442849	+	0.896596i	$0.353968\pi$
$719$			1289.31i			1.79319i	−0.442849	+	0.896596i	$0.646032\pi$
$720$	22.6335	+	178.571i	0.0314354	+	0.248016i
$721$	1461.49			2.02703
$722$	416.638			0.577061
$723$	514.493	−	873.841i	0.711608	−	1.20863i
$724$	504.174			0.696372
$725$	−820.954	+	862.107i	−1.13235	+	1.18911i
$726$	−589.353	+	1000.99i	−0.811781	+	1.37877i
$727$		−	427.911i		−	0.588598i	−0.955713	−	0.294299i	$-0.904914\pi$
$727$		−	427.911i		−	0.588598i	0.955713	−	0.294299i	$-0.0950862\pi$
$728$	482.737			0.663101
$729$	728.047	+	37.2668i	0.998692	+	0.0511204i
$730$	114.931	−	287.352i	0.157439	−	0.393633i
$731$			125.951i			0.172299i
$732$	−37.4681	+	63.6377i	−0.0511859	+	0.0869367i
$733$			339.385i			0.463008i	0.972834	+	0.231504i	$0.0743647\pi$
$733$			339.385i			0.463008i	−0.972834	+	0.231504i	$0.925635\pi$
$734$		−	709.301i		−	0.966351i
$735$	−793.480	+	613.535i	−1.07956	+	0.834742i
$736$	27.1293			0.0368605
$737$	850.794			1.15440
$738$	−334.173	+	185.413i	−0.452809	+	0.251236i
$739$	−609.402			−0.824631			−0.412315	−	0.911041i	$-0.635280\pi$
$739$	−609.402			−0.824631			−0.412315	+	0.911041i	$0.635280\pi$
$740$	1.17908	−	2.94795i	0.00159335	−	0.00398372i
$741$	−333.993	−	196.646i	−0.450733	−	0.265379i
$742$			1185.78i			1.59809i
$743$	−441.745			−0.594543			−0.297271	−	0.954793i	$-0.596077\pi$
$743$	−441.745			−0.594543			−0.297271	+	0.954793i	$0.596077\pi$
$744$	−44.9941	+	76.4203i	−0.0604760	+	0.102715i
$745$	184.593	−	461.523i	0.247776	−	0.619494i
$746$			410.721i			0.550565i
$747$	263.694	+	475.262i	0.353004	+	0.636228i
$748$			374.984i			0.501316i
$749$		−	290.250i		−	0.387516i
$750$	−527.533	−	54.3979i	−0.703377	−	0.0725305i
$751$	−221.822			−0.295369			−0.147684	−	0.989035i	$-0.547182\pi$
$751$	−221.822			−0.295369			−0.147684	+	0.989035i	$0.547182\pi$
$752$	65.1760			0.0866703
$753$	−975.927	−	574.598i	−1.29605	−	0.763079i
$754$	1067.76			1.41613
$755$	−205.568	−	82.2201i	−0.272276	−	0.108901i
$756$	−14.8621	+	581.076i	−0.0196589	+	0.768619i
$757$		−	422.828i		−	0.558557i	−0.960210	−	0.279279i	$-0.909905\pi$
$757$		−	422.828i		−	0.558557i	0.960210	−	0.279279i	$-0.0900953\pi$
$758$	−555.525			−0.732882
$759$	246.344	+	145.040i	0.324563	+	0.191094i
$760$	106.992	+	42.7929i	0.140778	+	0.0563064i
$761$			205.533i			0.270083i	0.990840	+	0.135041i	$0.0431167\pi$
$761$			205.533i			0.270083i	−0.990840	+	0.135041i	$0.956883\pi$
$762$	−233.318	−	137.371i	−0.306192	−	0.180277i
$763$		−	1155.33i		−	1.51419i
$764$			501.795i			0.656800i
$765$	53.3937	+	421.261i	0.0697957	+	0.550668i
$766$	971.031			1.26766
$767$	248.536			0.324036
$768$	−24.3535	+	41.3631i	−0.0317102	+	0.0538583i
$769$	1032.56			1.34274			0.671368	−	0.741124i	$-0.265707\pi$
$769$	1032.56			1.34274			0.671368	+	0.741124i	$0.265707\pi$
$770$	−1404.19	−	561.627i	−1.82362	−	0.729386i
$771$	−565.617	+	960.673i	−0.733615	+	1.24601i
$772$		−	335.435i		−	0.434501i
$773$	−503.805			−0.651752			−0.325876	−	0.945412i	$-0.605659\pi$
$773$	−503.805			−0.651752			−0.325876	+	0.945412i	$0.605659\pi$
$774$	−148.553	+	82.4230i	−0.191929	+	0.106490i
$775$	−189.216	−	180.183i	−0.244149	−	0.232495i
$776$		−	445.645i		−	0.574285i
$777$	5.20194	−	8.83524i	0.00669490	−	0.0113710i
$778$		−	367.523i		−	0.472395i
$779$			244.653i			0.314061i
$780$	290.964	+	376.301i	0.373031	+	0.482437i
$781$	1932.29			2.47412
$782$	63.9997			0.0818411
$783$	−32.8734	+	1285.28i	−0.0419839

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	690.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +(-1.52209 + 2.58520i) q^{3} +2.00000 q^{4} +(-4.64244 - 1.85681i) q^{5} +(2.15256 - 3.65602i) q^{6} +10.7642i q^{7} -2.82843 q^{8} +(-4.36648 - 7.86981i) q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +(-1.52209 + 2.58520i) q^{3} +2.00000 q^{4} +(-4.64244 - 1.85681i) q^{5} +(2.15256 - 3.65602i) q^{6} +10.7642i q^{7} -2.82843 q^{8} +(-4.36648 - 7.86981i) q^{9} +(6.56540 + 2.62593i) q^{10} +19.8694i q^{11} +(-3.04418 + 5.17039i) q^{12} +15.8557i q^{13} -15.2228i q^{14} +(11.8664 - 9.17538i) q^{15} +4.00000 q^{16} +9.43625 q^{17} +(6.17514 + 11.1296i) q^{18} +8.14814 q^{19} +(-9.28488 - 3.71363i) q^{20} +(-27.8275 - 16.3841i) q^{21} -28.0995i q^{22} -4.79583 q^{23} +(4.30512 - 7.31204i) q^{24} +(18.1045 + 17.2403i) q^{25} -22.4233i q^{26} +(26.9912 + 0.690351i) q^{27} +21.5284i q^{28} +47.6184i q^{29} +(-16.7817 + 12.9759i) q^{30} -10.4513 q^{31} -5.65685 q^{32} +(-51.3662 - 30.2430i) q^{33} -13.3449 q^{34} +(19.9871 - 49.9720i) q^{35} +(-8.73296 - 15.7396i) q^{36} +0.317500i q^{37} -11.5232 q^{38} +(-40.9901 - 24.1338i) q^{39} +(13.1308 + 5.25186i) q^{40} +30.0257i q^{41} +(39.3540 + 23.1706i) q^{42} +13.3476i q^{43} +39.7387i q^{44} +(5.65836 + 44.6428i) q^{45} +6.78233 q^{46} +16.2940 q^{47} +(-6.08836 + 10.3408i) q^{48} -66.8675 q^{49} +(-25.6036 - 24.3814i) q^{50} +(-14.3628 + 24.3946i) q^{51} +31.7114i q^{52} -77.8949 q^{53} +(-38.1713 - 0.976304i) q^{54} +(36.8937 - 92.2423i) q^{55} -30.4457i q^{56} +(-12.4022 + 21.0645i) q^{57} -67.3426i q^{58} -15.6749i q^{59} +(23.7329 - 18.3508i) q^{60} +12.3081 q^{61} +14.7804 q^{62} +(84.7120 - 47.0016i) q^{63} +8.00000 q^{64} +(29.4410 - 73.6091i) q^{65} +(72.6428 + 42.7700i) q^{66} -42.8194i q^{67} +18.8725 q^{68} +(7.29969 - 12.3982i) q^{69} +(-28.2660 + 70.6711i) q^{70} -97.2496i q^{71} +(12.3503 + 22.2592i) q^{72} -43.7676i q^{73} -0.449013i q^{74} +(-72.1262 + 20.5624i) q^{75} +16.2963 q^{76} -213.877 q^{77} +(57.9687 + 34.1303i) q^{78} +121.730 q^{79} +(-18.5698 - 7.42725i) q^{80} +(-42.8677 + 68.7267i) q^{81} -42.4627i q^{82} -60.3906 q^{83} +(-55.6550 - 32.7681i) q^{84} +(-43.8072 - 17.5213i) q^{85} -18.8763i q^{86} +(-123.103 - 72.4795i) q^{87} -56.1990i q^{88} -5.45726i q^{89} +(-8.00214 - 63.1345i) q^{90} -170.673 q^{91} -9.59166 q^{92} +(15.9078 - 27.0187i) q^{93} -23.0432 q^{94} +(-37.8272 - 15.1296i) q^{95} +(8.61025 - 14.6241i) q^{96} +157.559i q^{97} +94.5650 q^{98} +(156.368 - 86.7592i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88q + 176q^{4} + 8q^{9} + O(q^{10}) \)	\( 88q + 176q^{4} + 8q^{9} + 32q^{10} - 12q^{15} + 352q^{16} - 16q^{19} - 176q^{21} + 72q^{25} - 72q^{30} + 32q^{31} + 160q^{34} + 16q^{36} + 144q^{39} + 64q^{40} + 92q^{45} - 360q^{49} + 48q^{51} - 144q^{54} + 16q^{55} - 24q^{60} + 208q^{61} + 704q^{64} + 512q^{66} + 304q^{70} + 536q^{75} - 32q^{76} + 448q^{79} - 24q^{81} - 352q^{84} - 96q^{85} + 32q^{90} - 64q^{91} + 160q^{94} + 296q^{99} + O(q^{100}) \)

Introduction

L-functions

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