LMFDB - Embedded newform 99.3.l.a.26.7

Newspace parameters

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	99.l (of order $10$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.69755461717$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			26.7
Character	$\chi$	$=$	99.26
Dual form			99.3.l.a.80.7

$q$-expansion

$f(q)$	$=$	$q+(1.75181 - 2.41117i) q^{2} +(-1.50880 - 4.64360i) q^{4} +(-4.61811 - 6.35629i) q^{5} +(0.867699 + 2.67050i) q^{7} +(-2.50164 - 0.812833i) q^{8} +O(q^{10})$	\(q+(1.75181 - 2.41117i) q^{2} +(-1.50880 - 4.64360i) q^{4} +(-4.61811 - 6.35629i) q^{5} +(0.867699 + 2.67050i) q^{7} +(-2.50164 - 0.812833i) q^{8} -23.4161 q^{10} +(8.89568 - 6.47047i) q^{11} +(1.22806 + 0.892235i) q^{13} +(7.95907 + 2.58606i) q^{14} +(9.45804 - 6.87167i) q^{16} +(15.5170 + 21.3573i) q^{17} +(-4.49342 + 13.8293i) q^{19} +(-22.5483 + 31.0350i) q^{20} +(-0.0177905 - 32.7840i) q^{22} -25.0726i q^{23} +(-11.3500 + 34.9317i) q^{25} +(4.30265 - 1.39802i) q^{26} +(11.0916 - 8.05850i) q^{28} +(-48.2284 + 15.6704i) q^{29} +(41.7844 + 30.3581i) q^{31} -45.3643i q^{32} +78.6790 q^{34} +(12.9674 - 17.8480i) q^{35} +(-6.04322 - 18.5991i) q^{37} +(25.4731 + 35.0608i) q^{38} +(6.38627 + 19.6549i) q^{40} +(29.4212 + 9.55953i) q^{41} +2.11848 q^{43} +(-43.4680 - 31.5454i) q^{44} +(-60.4543 - 43.9226i) q^{46} +(-38.2998 - 12.4444i) q^{47} +(33.2631 - 24.1671i) q^{49} +(64.3430 + 88.5605i) q^{50} +(2.29029 - 7.04880i) q^{52} +(-24.1836 + 33.2859i) q^{53} +(-82.2094 - 26.6621i) q^{55} -7.38594i q^{56} +(-46.7034 + 143.738i) q^{58} +(-91.3627 + 29.6855i) q^{59} +(2.34234 - 1.70181i) q^{61} +(146.397 - 47.5673i) q^{62} +(-71.5487 - 51.9832i) q^{64} -11.9263i q^{65} -88.2869 q^{67} +(75.7629 - 104.279i) q^{68} +(-20.3182 - 62.5329i) q^{70} +(-6.65733 - 9.16303i) q^{71} +(32.3776 + 99.6480i) q^{73} +(-55.4322 - 18.0110i) q^{74} +70.9975 q^{76} +(24.9982 + 18.1415i) q^{77} +(-13.5822 - 9.86808i) q^{79} +(-87.3566 - 28.3839i) q^{80} +(74.5901 - 54.1929i) q^{82} +(13.3848 + 18.4226i) q^{83} +(64.0940 - 197.261i) q^{85} +(3.71118 - 5.10801i) q^{86} +(-27.5132 + 8.95610i) q^{88} -30.7523i q^{89} +(-1.31713 + 4.05372i) q^{91} +(-116.427 + 37.8295i) q^{92} +(-97.0996 + 70.5470i) q^{94} +(108.654 - 35.3039i) q^{95} +(23.0800 + 16.7686i) q^{97} -122.539i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) $ 32 * q + 16 * q^4 - 16 * q^7	$ 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) $ 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$-1$

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 $

$2$	1.75181	−	2.41117i	0.875907	−	1.20558i	−0.101631	−	0.994822i	$-0.532406\pi$
$2$	1.75181	−	2.41117i	0.875907	−	1.20558i	0.977538	−	0.210760i	$-0.0675940\pi$
$3$		0			0
$3$		0			0
$4$	−1.50880	−	4.64360i	−0.377199	−	1.16090i
$5$	−4.61811	−	6.35629i	−0.923623	−	1.27126i	−0.962296	−	0.272005i	$-0.912313\pi$
$5$	−4.61811	−	6.35629i	−0.923623	−	1.27126i	0.0386732	−	0.999252i	$-0.487687\pi$
$6$		0			0
$7$	0.867699	+	2.67050i	0.123957	+	0.381500i	0.993710	−	0.111988i	$-0.0357217\pi$
$7$	0.867699	+	2.67050i	0.123957	+	0.381500i	−0.869753	+	0.493488i	$0.835722\pi$
$8$	−2.50164	−	0.812833i	−0.312705	−	0.101604i
$9$		0			0
$10$	−23.4161			−2.34161
$11$	8.89568	−	6.47047i	0.808698	−	0.588224i
$11$	8.89568	−	6.47047i	0.808698	−	0.588224i
$12$		0			0
$13$	1.22806	+	0.892235i	0.0944658	+	0.0686334i	0.634016	−	0.773320i	$-0.281406\pi$
$13$	1.22806	+	0.892235i	0.0944658	+	0.0686334i	−0.539550	+	0.841954i	$0.681406\pi$
$14$	7.95907	+	2.58606i	0.568505	+	0.184719i
$15$		0			0
$16$	9.45804	−	6.87167i	0.591128	−	0.429479i
$17$	15.5170	+	21.3573i	0.912765	+	1.25631i	0.966213	+	0.257743i	$0.0829789\pi$
$17$	15.5170	+	21.3573i	0.912765	+	1.25631i	−0.0534480	+	0.998571i	$0.517021\pi$
$18$		0			0
$19$	−4.49342	+	13.8293i	−0.236496	+	0.727859i	0.760424	+	0.649427i	$0.224991\pi$
$19$	−4.49342	+	13.8293i	−0.236496	+	0.727859i	−0.996919	+	0.0784318i	$0.975009\pi$
$20$	−22.5483	+	31.0350i	−1.12741	+	1.55175i
$21$		0			0
$22$	−0.0177905	−	32.7840i	−0.000808661	−	1.49018i
$23$		−	25.0726i		−	1.09011i	−0.838399	−	0.545057i	$-0.816508\pi$
$23$		−	25.0726i		−	1.09011i	0.838399	−	0.545057i	$-0.183492\pi$
$24$		0			0
$25$	−11.3500	+	34.9317i	−0.454000	+	1.39727i
$26$	4.30265	−	1.39802i	0.165487	−	0.0537698i
$27$		0			0
$28$	11.0916	−	8.05850i	0.396127	−	0.287803i
$29$	−48.2284	+	15.6704i	−1.66305	+	0.540358i	−0.981508	−	0.191422i	$-0.938690\pi$
$29$	−48.2284	+	15.6704i	−1.66305	+	0.540358i	−0.681542	+	0.731779i	$0.738690\pi$
$30$		0			0
$31$	41.7844	+	30.3581i	1.34788	+	0.979295i	0.999114	+	0.0420867i	$0.0134006\pi$
$31$	41.7844	+	30.3581i	1.34788	+	0.979295i	0.348770	+	0.937208i	$0.386599\pi$
$32$		−	45.3643i		−	1.41764i
$33$		0			0
$34$	78.6790			2.31409
$35$	12.9674	−	17.8480i	0.370496	−	0.509944i
$36$		0			0
$37$	−6.04322	−	18.5991i	−0.163330	−	0.502679i	0.835579	−	0.549370i	$-0.185132\pi$
$37$	−6.04322	−	18.5991i	−0.163330	−	0.502679i	−0.998909	+	0.0466912i	$0.985132\pi$
$38$	25.4731	+	35.0608i	0.670346	+	0.922652i
$39$		0			0
$40$	6.38627	+	19.6549i	0.159657	+	0.491373i
$41$	29.4212	+	9.55953i	0.717591	+	0.233159i	0.644978	−	0.764201i	$-0.276866\pi$
$41$	29.4212	+	9.55953i	0.717591	+	0.233159i	0.0726124	+	0.997360i	$0.476866\pi$
$42$		0			0
$43$	2.11848			0.0492670			0.0246335	−	0.999697i	$-0.492158\pi$
$43$	2.11848			0.0492670			0.0246335	+	0.999697i	$0.492158\pi$
$44$	−43.4680	−	31.5454i	−0.987910	−	0.716940i
$45$		0			0
$46$	−60.4543	−	43.9226i	−1.31422	−	0.954839i
$47$	−38.2998	−	12.4444i	−0.814890	−	0.264774i	−0.128222	−	0.991745i	$-0.540927\pi$
$47$	−38.2998	−	12.4444i	−0.814890	−	0.264774i	−0.686667	+	0.726972i	$0.740927\pi$
$48$		0			0
$49$	33.2631	−	24.1671i	0.678840	−	0.493206i
$50$	64.3430	+	88.5605i	1.28686	+	1.77121i
$51$		0			0
$52$	2.29029	−	7.04880i	0.0440441	−	0.135554i
$53$	−24.1836	+	33.2859i	−0.456295	+	0.628036i	−0.973735	−	0.227683i	$-0.926885\pi$
$53$	−24.1836	+	33.2859i	−0.456295	+	0.628036i	0.517441	+	0.855719i	$0.326885\pi$
$54$		0			0
$55$	−82.2094	−	26.6621i	−1.49472	−	0.484766i
$56$		−	7.38594i		−	0.131892i
$57$		0			0
$58$	−46.7034	+	143.738i	−0.805231	+	2.47825i
$59$	−91.3627	+	29.6855i	−1.54852	+	0.503145i	−0.953712	−	0.300723i	$-0.902772\pi$
$59$	−91.3627	+	29.6855i	−1.54852	+	0.503145i	−0.594808	+	0.803868i	$0.702772\pi$
$60$		0			0
$61$	2.34234	−	1.70181i	0.0383990	−	0.0278985i	−0.568420	−	0.822738i	$-0.692445\pi$
$61$	2.34234	−	1.70181i	0.0383990	−	0.0278985i	0.606819	+	0.794840i	$0.292445\pi$
$62$	146.397	−	47.5673i	2.36124	−	0.767214i
$63$		0			0
$64$	−71.5487	−	51.9832i	−1.11795	−	0.812237i
$65$		−	11.9263i		−	0.183482i
$66$		0			0
$67$	−88.2869			−1.31772			−0.658858	−	0.752268i	$-0.728960\pi$
$67$	−88.2869			−1.31772			−0.658858	+	0.752268i	$0.728960\pi$
$68$	75.7629	−	104.279i	1.11416	−	1.53351i
$69$		0			0
$70$	−20.3182	−	62.5329i	−0.290259	−	0.893326i
$71$	−6.65733	−	9.16303i	−0.0937652	−	0.129057i	0.759557	−	0.650441i	$-0.225416\pi$
$71$	−6.65733	−	9.16303i	−0.0937652	−	0.129057i	−0.853322	+	0.521384i	$0.825416\pi$
$72$		0			0
$73$	32.3776	+	99.6480i	0.443529	+	1.36504i	0.884089	+	0.467318i	$0.154780\pi$
$73$	32.3776	+	99.6480i	0.443529	+	1.36504i	−0.440560	+	0.897723i	$0.645220\pi$
$74$	−55.4322	−	18.0110i	−0.749083	−	0.243392i
$75$		0			0
$76$	70.9975			0.934178
$77$	24.9982	+	18.1415i	0.324652	+	0.235604i
$78$		0			0
$79$	−13.5822	−	9.86808i	−0.171927	−	0.124912i	0.498494	−	0.866893i	$-0.333887\pi$
$79$	−13.5822	−	9.86808i	−0.171927	−	0.124912i	−0.670421	+	0.741981i	$0.733887\pi$
$80$	−87.3566	−	28.3839i	−1.09196	−	0.354799i
$81$		0			0
$82$	74.5901	−	54.1929i	0.909636	−	0.660889i
$83$	13.3848	+	18.4226i	0.161263	+	0.221959i	0.882000	−	0.471249i	$-0.156197\pi$
$83$	13.3848	+	18.4226i	0.161263	+	0.221959i	−0.720738	+	0.693208i	$0.756197\pi$
$84$		0			0
$85$	64.0940	−	197.261i	0.754048	−	2.32072i
$86$	3.71118	−	5.10801i	0.0431533	−	0.0593954i
$87$		0			0
$88$	−27.5132	+	8.95610i	−0.312650	+	0.101774i
$89$		−	30.7523i		−	0.345531i	−0.984963	−	0.172766i	$-0.944730\pi$
$89$		−	30.7523i		−	0.345531i	0.984963	−	0.172766i	$-0.0552703\pi$
$90$		0			0
$91$	−1.31713	+	4.05372i	−0.0144740	+	0.0445463i
$92$	−116.427	+	37.8295i	−1.26551	+	0.411191i
$93$		0			0
$94$	−97.0996	+	70.5470i	−1.03297	+	0.750500i
$95$	108.654	−	35.3039i	1.14373	−	0.371620i
$96$		0			0
$97$	23.0800	+	16.7686i	0.237939	+	0.172872i	0.700364	−	0.713785i	$-0.253021\pi$
$97$	23.0800	+	16.7686i	0.237939	+	0.172872i	−0.462426	+	0.886658i	$0.653021\pi$
$98$		−	122.539i		−	1.25040i
$99$		0			0
$100$	179.334			1.79334
$101$	1.99764	−	2.74952i	0.0197786	−	0.0272230i	−0.799013	−	0.601314i	$-0.794644\pi$
$101$	1.99764	−	2.74952i	0.0197786	−	0.0272230i	0.818792	+	0.574091i	$0.194644\pi$
$102$		0			0
$103$	6.89465	+	21.2195i	0.0669383	+	0.206015i	0.978931	−	0.204192i	$-0.0654566\pi$
$103$	6.89465	+	21.2195i	0.0669383	+	0.206015i	−0.911993	+	0.410207i	$0.865457\pi$
$104$	−2.34692	−	3.23026i	−0.0225665	−	0.0310602i
$105$		0			0
$106$	37.8926	+	116.621i	0.357477	+	1.10020i
$107$	12.2413	+	3.97744i	0.114405	+	0.0371724i	0.365660	−	0.930749i	$-0.380843\pi$
$107$	12.2413	+	3.97744i	0.114405	+	0.0371724i	−0.251255	+	0.967921i	$0.580843\pi$
$108$		0			0
$109$	109.301			1.00277			0.501383	−	0.865226i	$-0.332825\pi$
$109$	109.301			1.00277			0.501383	+	0.865226i	$0.332825\pi$
$110$	−208.302	+	151.513i	−1.89366	+	1.37739i
$111$		0			0
$112$	26.5575	+	19.2952i	0.237121	+	0.172278i
$113$	87.5285	+	28.4397i	0.774589	+	0.251679i	0.669528	−	0.742787i	$-0.266496\pi$
$113$	87.5285	+	28.4397i	0.774589	+	0.251679i	0.105061	+	0.994466i	$0.466496\pi$
$114$		0			0
$115$	−159.369	+	115.788i	−1.38582	+	1.00685i
$116$	145.534	+	200.310i	1.25460	+	1.72681i
$117$		0			0
$118$	−88.4737	+	272.294i	−0.749777	+	2.30758i
$119$	−43.5707	+	59.9700i	−0.366141	+	0.503949i
$120$		0			0
$121$	37.2661	−	115.118i	0.307985	−	0.951391i
$122$		−	8.62901i		−	0.0707296i
$123$		0			0
$124$	77.9269	−	239.834i	0.628443	−	1.93415i
$125$	87.6447	−	28.4775i	0.701158	−	0.227820i
$126$		0			0
$127$	6.70109	−	4.86862i	0.0527645	−	0.0383356i	−0.561090	−	0.827755i	$-0.689618\pi$
$127$	6.70109	−	4.86862i	0.0527645	−	0.0383356i	0.613855	+	0.789419i	$0.289618\pi$
$128$	−78.1040	+	25.3775i	−0.610187	+	0.198262i
$129$		0			0
$130$	−28.7563	−	20.8927i	−0.221202	−	0.160713i
$131$			1.63767i			0.0125013i	0.999980	+	0.00625065i	$0.00198966\pi$
$131$			1.63767i			0.0125013i	−0.999980	+	0.00625065i	$0.998010\pi$
$132$		0			0
$133$	−40.8302			−0.306994
$134$	−154.662	+	212.874i	−1.15420	+	1.58861i
$135$		0			0
$136$	−21.4581	−	66.0412i	−0.157780	−	0.485597i
$137$	116.451	+	160.281i	0.850008	+	1.16994i	0.983861	+	0.178935i	$0.0572651\pi$
$137$	116.451	+	160.281i	0.850008	+	1.16994i	−0.133853	+	0.991001i	$0.542735\pi$
$138$		0			0
$139$	−57.9241	−	178.272i	−0.416720	−	1.28253i	−0.910703	−	0.413062i	$-0.864459\pi$
$139$	−57.9241	−	178.272i	−0.416720	−	1.28253i	0.493982	−	0.869472i	$-0.335541\pi$
$140$	−102.444	−	33.2861i	−0.731744	−	0.237758i
$141$		0			0
$142$	−33.7560			−0.237718
$143$	16.6976	−	0.00906108i	0.116766	−	6.33642e-5i
$144$		0			0
$145$	322.330	+	234.186i	2.22296	+	1.61508i
$146$	296.987	+	96.4970i	2.03416	+	0.660939i
$147$		0			0
$148$	−77.2489	+	56.1246i	−0.521952	+	0.379220i
$149$	−140.590	−	193.505i	−0.943555	−	1.29869i	−0.954331	−	0.298750i	$-0.903430\pi$
$149$	−140.590	−	193.505i	−0.943555	−	1.29869i	0.0107766	−	0.999942i	$-0.496570\pi$
$150$		0			0
$151$	18.1318	−	55.8039i	0.120078	−	0.369562i	−0.872894	−	0.487909i	$-0.837760\pi$
$151$	18.1318	−	55.8039i	0.120078	−	0.369562i	0.992972	+	0.118347i	$0.0377596\pi$
$152$	22.4819	−	30.9436i	0.147907	−	0.203577i
$153$		0			0
$154$	87.5343	−	28.4942i	0.568405	−	0.185027i
$155$		−	405.791i		−	2.61801i
$156$		0			0
$157$	6.31024	−	19.4209i	0.0401926	−	0.123700i	−0.928947	−	0.370213i	$-0.879285\pi$
$157$	6.31024	−	19.4209i	0.0401926	−	0.123700i	0.969140	+	0.246513i	$0.0792847\pi$
$158$	−47.5871	+	15.4620i	−0.301184	+	0.0978607i
$159$		0			0
$160$	−288.349	+	209.498i	−1.80218	+	1.30936i
$161$	66.9566	−	21.7555i	0.415879	−	0.135127i
$162$		0			0
$163$	−84.5857	−	61.4551i	−0.518931	−	0.377025i	0.297270	−	0.954793i	$-0.403924\pi$
$163$	−84.5857	−	61.4551i	−0.518931	−	0.377025i	−0.816201	+	0.577768i	$0.803924\pi$
$164$		−	151.044i		−	0.920999i
$165$		0			0
$166$	67.8676			0.408841
$167$	23.0472	−	31.7217i	0.138007	−	0.189950i	−0.734419	−	0.678696i	$-0.762545\pi$
$167$	23.0472	−	31.7217i	0.138007	−	0.189950i	0.872426	+	0.488746i	$0.162545\pi$
$168$		0			0
$169$	−51.5118	−	158.537i	−0.304804	−	0.938089i
$170$	−363.348	−	500.106i	−2.13734	−	2.94180i
$171$		0			0
$172$	−3.19636	−	9.83738i	−0.0185835	−	0.0571940i
$173$	86.9529	+	28.2527i	0.502618	+	0.163310i	0.549342	−	0.835597i	$-0.314878\pi$
$173$	86.9529	+	28.2527i	0.502618	+	0.163310i	−0.0467245	+	0.998908i	$0.514878\pi$
$174$		0			0
$175$	−103.134			−0.589334
$176$	39.6728	−	122.326i	0.225414	−	0.695035i
$177$		0			0
$178$	−74.1488	−	53.8723i	−0.416566	−	0.302653i
$179$	207.504	+	67.4220i	1.15924	+	0.376659i	0.824616	−	0.565693i	$-0.191391\pi$
$179$	207.504	+	67.4220i	1.15924	+	0.376659i	0.334623	+	0.942352i	$0.391391\pi$
$180$		0			0
$181$	36.2608	−	26.3450i	0.200336	−	0.145553i	−0.483094	−	0.875568i	$-0.660487\pi$
$181$	36.2608	−	26.3450i	0.200336	−	0.145553i	0.683431	+	0.730016i	$0.260487\pi$
$182$	7.46681	+	10.2772i	0.0410264	+	0.0564680i
$183$		0			0
$184$	−20.3799	+	62.7228i	−0.110760	+	0.340885i
$185$	−90.3131	+	124.305i	−0.488179	+	0.671921i
$186$		0			0
$187$	276.226	+	89.5857i	1.47715	+	0.479068i
$188$			196.625i			1.04588i
$189$		0			0
$190$	105.219	−	323.829i	0.553782	−	1.70436i
$191$	−141.682	+	46.0353i	−0.741790	+	0.241022i	−0.655445	−	0.755243i	$-0.727519\pi$
$191$	−141.682	+	46.0353i	−0.741790	+	0.241022i	−0.0863454	+	0.996265i	$0.527519\pi$
$192$		0			0
$193$	−156.712	+	113.858i	−0.811978	+	0.589936i	−0.914403	−	0.404804i	$-0.867340\pi$
$193$	−156.712	+	113.858i	−0.811978	+	0.589936i	0.102426	+	0.994741i	$0.467340\pi$
$194$	80.8639	−	26.2743i	0.416824	−	0.135434i
$195$		0			0
$196$	−162.410	−	117.998i	−0.828621	−	0.602028i
$197$			331.307i			1.68176i	0.541220	+	0.840881i	$0.317963\pi$
$197$			331.307i			1.68176i	−0.541220	+	0.840881i	$0.682037\pi$
$198$		0			0
$199$	−294.829			−1.48155			−0.740775	−	0.671753i	$-0.765542\pi$
$199$	−294.829			−1.48155			−0.740775	+	0.671753i	$0.765542\pi$
$200$	56.7873	−	78.1610i	0.283936	−	0.390805i
$201$		0			0
$202$	−3.13005	−	9.63329i	−0.0154953	−	0.0476896i
$203$	−83.6955	−	115.197i	−0.412293	−	0.567473i
$204$		0			0
$205$	−75.1074	−	231.157i	−0.366377	−	1.12759i
$206$	63.2420	+	20.5486i	0.307000	+	0.0997503i
$207$		0			0
$208$	17.7461			0.0853180
$209$	49.5102	+	152.096i	0.236891	+	0.727731i
$210$		0			0
$211$	93.6252	+	68.0227i	0.443721	+	0.322382i	0.787112	−	0.616810i	$-0.211575\pi$
$211$	93.6252	+	68.0227i	0.443721	+	0.322382i	−0.343391	+	0.939193i	$0.611575\pi$
$212$	191.055	+	62.0774i	0.901201	+	0.292818i
$213$		0			0
$214$	31.0348	−	22.5481i	0.145022	−	0.105365i
$215$	−9.78338	−	13.4657i	−0.0455041	−	0.0626310i
$216$		0			0
$217$	−44.8152	+	137.927i	−0.206522	+	0.635609i
$218$	191.476	−	263.544i	0.878329	−	1.20892i
$219$		0			0
$220$	0.228989	+	421.975i	0.00104086	+	1.91807i
$221$			40.0728i			0.181325i
$222$		0			0
$223$	−75.4285	+	232.145i	−0.338245	+	1.04101i	0.626857	+	0.779134i	$0.284341\pi$
$223$	−75.4285	+	232.145i	−0.338245	+	1.04101i	−0.965102	+	0.261876i	$0.915659\pi$
$224$	121.146	−	39.3626i	0.540828	−	0.175726i
$225$		0			0
$226$	221.907	−	161.225i	0.981888	−	0.713383i
$227$	−255.097	+	82.8861i	−1.12378	+	0.365137i	−0.811208	−	0.584758i	$-0.801189\pi$
$227$	−255.097	+	82.8861i	−1.12378	+	0.365137i	−0.312569	+	0.949895i	$0.601189\pi$
$228$		0			0
$229$	−150.551	−	109.382i	−0.657430	−	0.477651i	0.208364	−	0.978051i	$-0.433186\pi$
$229$	−150.551	−	109.382i	−0.657430	−	0.477651i	−0.865794	+	0.500401i	$0.833186\pi$
$230$			587.104i			2.55263i
$231$		0			0
$232$	133.388			0.574947
$233$	−95.3276	+	131.207i	−0.409131	+	0.563121i	−0.963006	−	0.269479i	$-0.913149\pi$
$233$	−95.3276	+	131.207i	−0.409131	+	0.563121i	0.553875	+	0.832600i	$0.313149\pi$
$234$		0			0
$235$	97.7729	+	300.914i	0.416055	+	1.28049i
$236$	275.696	+	379.462i	1.16820	+	1.60789i
$237$		0			0
$238$	68.2697	+	210.112i	0.286847	+	0.882826i
$239$	−67.6141	−	21.9692i	−0.282904	−	0.0919212i	0.164128	−	0.986439i	$-0.447519\pi$
$239$	−67.6141	−	21.9692i	−0.282904	−	0.0919212i	−0.447032	+	0.894518i	$0.647519\pi$
$240$		0			0
$241$	212.799			0.882984			0.441492	−	0.897265i	$-0.354449\pi$
$241$	212.799			0.882984			0.441492	+	0.897265i	$0.354449\pi$
$242$	−212.286	−	291.521i	−0.877215	−	1.20463i
$243$		0			0
$244$	−11.4366	−	8.30919i	−0.0468714	−	0.0340541i
$245$	−307.226	−	99.8238i	−1.25398	−	0.407444i
$246$		0			0
$247$	−17.8572	+	12.9740i	−0.0722962	+	0.0525263i
$248$	−79.8536	−	109.909i	−0.321990	−	0.443181i
$249$		0			0
$250$	84.8733	−	261.213i	0.339493	−	1.04485i
$251$	110.272	−	151.777i	0.439332	−	0.604689i	−0.530731	−	0.847540i	$-0.678083\pi$
$251$	110.272	−	151.777i	0.439332	−	0.604689i	0.970064	+	0.242851i	$0.0780827\pi$
$252$		0			0
$253$	−162.232	−	223.038i	−0.641232	−	0.881573i
$254$		−	24.6864i		−	0.0971904i
$255$		0			0
$256$	33.6825	−	103.664i	0.131572	−	0.404937i
$257$	−276.561	+	89.8603i	−1.07611	+	0.349651i	−0.792866	−	0.609396i	$-0.791412\pi$
$257$	−276.561	+	89.8603i	−1.07611	+	0.349651i	−0.283248	+	0.959047i	$0.591412\pi$
$258$		0			0
$259$	44.4253	−	32.2769i	0.171526	−	0.124621i
$260$	−55.3810	+	17.9944i	−0.213004	+	0.0692092i
$261$		0			0
$262$	3.94869	+	2.86889i	0.0150714	+	0.0109500i
$263$		−	458.564i		−	1.74359i	−0.489870	−	0.871795i	$-0.662956\pi$
$263$		−	458.564i		−	1.74359i	0.489870	−	0.871795i	$-0.337044\pi$
$264$		0			0
$265$	323.257			1.21984
$266$	−71.5269	+	98.4483i	−0.268898	+	0.370106i
$267$		0			0
$268$	133.207	+	409.969i	0.497041	+	1.52974i
$269$	122.701	+	168.884i	0.456139	+	0.627822i	0.973703	−	0.227823i	$-0.0731608\pi$
$269$	122.701	+	168.884i	0.456139	+	0.627822i	−0.517563	+	0.855645i	$0.673161\pi$
$270$		0			0
$271$	−142.441	−	438.388i	−0.525612	−	1.61767i	−0.763102	−	0.646279i	$-0.776324\pi$
$271$	−142.441	−	438.388i	−0.525612	−	1.61767i	0.237489	−	0.971390i	$-0.423676\pi$
$272$	293.521	+	95.3708i	1.07912	+	0.350628i
$273$		0			0
$274$	590.465			2.15498
$275$	125.058	+	384.181i	0.454758	+	1.39702i
$276$		0			0
$277$	85.4746	+	62.1009i	0.308573	+	0.224191i	0.731284	−	0.682073i	$-0.238922\pi$
$277$	85.4746	+	62.1009i	0.308573	+	0.224191i	−0.422711	+	0.906264i	$0.638922\pi$
$278$	−531.316	−	172.635i	−1.91121	−	0.620989i
$279$		0			0
$280$	−46.9472	+	34.1091i	−0.167668	+	0.121818i
$281$	−253.323	−	348.669i	−0.901506	−	1.24082i	−0.969985	−	0.243164i	$-0.921815\pi$
$281$	−253.323	−	348.669i	−0.901506	−	1.24082i	0.0684794	−	0.997653i	$-0.478185\pi$
$282$		0			0
$283$	93.2355	−	286.949i	0.329454	−	1.01396i	−0.639935	−	0.768429i	$-0.721039\pi$
$283$	93.2355	−	286.949i	0.329454	−	1.01396i	0.969390	−	0.245527i	$-0.0789611\pi$
$284$	−32.5049	+	44.7391i	−0.114454	+	0.157532i
$285$		0			0
$286$	29.2292	−	40.2765i	0.102200	−	0.140827i
$287$			86.8643i			0.302663i
$288$		0			0
$289$	−126.052	+	387.949i	−0.436167	+	1.34238i
$290$	1129.32	−	366.939i	3.89422	−	1.26531i
$291$		0			0
$292$	413.874	−	300.697i	1.41738	−	1.02979i
$293$	44.0479	−	14.3120i	0.150334	−	0.0488465i	−0.232883	−	0.972505i	$-0.574816\pi$
$293$	44.0479	−	14.3120i	0.150334	−	0.0488465i	0.383217	+	0.923658i	$0.374816\pi$
$294$		0			0
$295$	610.613	+	443.636i	2.06987	+	1.50385i
$296$			51.4405i			0.173786i
$297$		0			0
$298$	−712.860			−2.39215
$299$	22.3707	−	30.7906i	0.0748183	−	0.102979i
$300$		0			0
$301$	1.83820	+	5.65741i	0.00610699	+	0.0187954i
$302$	−102.789	−	141.477i	−0.340360	−	0.468466i
$303$		0			0
$304$	52.5316	+	161.676i	0.172801	+	0.531828i
$305$	−21.6343	−	7.02943i	−0.0709323	−	0.0230473i
$306$		0			0
$307$	−448.259			−1.46013			−0.730063	−	0.683379i	$-0.760509\pi$
$307$	−448.259			−1.46013			−0.730063	+	0.683379i	$0.760509\pi$
$308$	46.5248	−	143.453i	0.151054	−	0.465758i
$309$		0			0
$310$	−978.429	−	710.870i	−3.15622	−	2.29313i
$311$	−318.294	−	103.420i	−1.02345	−	0.332540i	−0.251255	−	0.967921i	$-0.580843\pi$
$311$	−318.294	−	103.420i	−1.02345	−	0.332540i	−0.772199	+	0.635381i	$0.780843\pi$
$312$		0			0
$313$	−82.7752	+	60.1397i	−0.264458	+	0.192140i	−0.712110	−	0.702068i	$-0.752260\pi$
$313$	−82.7752	+	60.1397i	−0.264458	+	0.192140i	0.447652	+	0.894208i	$0.352260\pi$
$314$	−35.7727	−	49.2369i	−0.113926	−	0.156805i
$315$		0			0
$316$	−25.3306	+	77.9594i	−0.0801600	+	0.246707i
$317$	222.110	−	305.708i	0.700661	−	0.964377i	−0.299287	−	0.954163i	$-0.596749\pi$
$317$	222.110	−	305.708i	0.700661	−	0.964377i	0.999948	−	0.0102140i	$-0.00325128\pi$
$318$		0			0
$319$	−327.630	+	451.459i	−1.02705	+	1.41523i
$320$			694.848i			2.17140i
$321$		0			0
$322$	64.8393	−	199.555i	0.201364	−	0.619736i
$323$	−365.082	+	118.622i	−1.13028	+	0.367252i
$324$		0			0
$325$	−45.1057	+	32.7712i	−0.138787	+	0.100834i
$326$	−296.357	+	96.2922i	−0.909070	+	0.295375i
$327$		0			0
$328$	−65.8311	−	47.8291i	−0.200705	−	0.145820i
$329$		−	113.078i		−	0.343701i
$330$		0			0
$331$	−170.972			−0.516533			−0.258266	−	0.966074i	$-0.583151\pi$
$331$	−170.972			−0.516533			−0.258266	+	0.966074i	$0.583151\pi$
$332$	65.3522	−	89.9496i	0.196844	−	0.270933i
$333$		0			0
$334$	−36.1119	−	111.141i	−0.108120	−	0.332758i
$335$	407.719	+	561.177i	1.21707	+	1.67516i
$336$		0			0
$337$	59.3115	+	182.542i	0.175999	+	0.541668i	0.999678	−	0.0253884i	$-0.00808224\pi$
$337$	59.3115	+	182.542i	0.175999	+	0.541668i	−0.823679	+	0.567056i	$0.808082\pi$
$338$	−472.498	−	153.524i	−1.39792	−	0.454213i
$339$		0			0
$340$	−1012.71			−2.97855
$341$	568.132	−	0.308302i	1.66608	−	0.000904111i
$342$		0			0
$343$	204.712	+	148.732i	0.596829	+	0.433622i
$344$	−5.29968	−	1.72197i	−0.0154061	−	0.00500573i
$345$		0			0
$346$	220.447	−	160.164i	0.637131	−	0.462903i
$347$	109.245	+	150.363i	0.314827	+	0.433322i	0.936879	−	0.349654i	$-0.113701\pi$
$347$	109.245	+	150.363i	0.314827	+	0.433322i	−0.622052	+	0.782976i	$0.713701\pi$
$348$		0			0
$349$	−54.5075	+	167.757i	−0.156182	+	0.480679i	−0.998279	−	0.0586476i	$-0.981321\pi$
$349$	−54.5075	+	167.757i	−0.156182	+	0.480679i	0.842097	+	0.539327i	$0.181321\pi$
$350$	−180.671	+	248.672i	−0.516202	+	0.710491i
$351$		0			0
$352$	−293.528	−	403.546i	−0.833887	−	1.14644i
$353$			232.825i			0.659561i	0.944058	+	0.329780i	$0.106975\pi$
$353$			232.825i			0.659561i	−0.944058	+	0.329780i	$0.893025\pi$
$354$		0			0
$355$	−27.4985	+	84.6318i	−0.0774606	+	0.238399i
$356$	−142.801	+	46.3989i	−0.401127	+	0.130334i
$357$		0			0
$358$	526.074	−	382.215i	1.46948	−	1.06764i
$359$	383.394	−	124.572i	1.06795	−	0.346998i	0.278261	−	0.960506i	$-0.410242\pi$
$359$	383.394	−	124.572i	1.06795	−	0.346998i	0.789689	+	0.613508i	$0.210242\pi$
$360$		0			0
$361$	120.996	+	87.9086i	0.335168	+	0.243514i
$362$		−	133.583i		−	0.369012i
$363$		0			0
$364$	20.8111			0.0571734
$365$	483.868	−	665.987i	1.32567	−	1.82462i
$366$		0			0
$367$	−167.337	−	515.010i	−0.455959	−	1.40330i	−0.870006	−	0.493041i	$-0.835885\pi$
$367$	−167.337	−	515.010i	−0.455959	−	1.40330i	0.414047	−	0.910255i	$-0.364115\pi$
$368$	−172.291	−	237.138i	−0.468182	−	0.644397i
$369$		0			0
$370$	141.509	+	435.520i	0.382456	+	1.17708i
$371$	−109.874	−	35.7003i	−0.296157	−	0.0962272i
$372$		0			0
$373$	−160.025			−0.429021			−0.214510	−	0.976722i	$-0.568816\pi$
$373$	−160.025			−0.429021			−0.214510	+	0.976722i	$0.568816\pi$
$374$	699.903	−	509.090i	1.87140	−	1.36120i
$375$		0			0
$376$	85.6973	+	62.2627i	0.227918	+	0.165592i
$377$	−73.2089	−	23.7870i	−0.194188	−	0.0630955i
$378$		0			0
$379$	306.310	−	222.547i	0.808206	−	0.587196i	−0.105104	−	0.994461i	$-0.533517\pi$
$379$	306.310	−	222.547i	0.808206	−	0.587196i	0.913310	+	0.407265i	$0.133517\pi$
$380$	−327.875	−	451.281i	−0.862828	−	1.18758i
$381$		0			0
$382$	−137.202	+	422.264i	−0.359167	+	1.10540i
$383$	−140.814	+	193.814i	−0.367661	+	0.506041i	−0.952263	−	0.305278i	$-0.901250\pi$
$383$	−140.814	+	193.814i	−0.367661	+	0.506041i	0.584603	+	0.811320i	$0.301250\pi$
$384$		0			0
$385$	−0.131690	−	242.675i	−0.000342051	−	0.630325i
$386$			577.315i			1.49564i
$387$		0			0
$388$	43.0437	−	132.475i	0.110937	−	0.341430i
$389$	478.020	−	155.318i	1.22884	−	0.399276i	0.378549	−	0.925581i	$-0.376423\pi$
$389$	478.020	−	155.318i	1.22884	−	0.399276i	0.850295	+	0.526306i	$0.176423\pi$
$390$		0			0
$391$	535.485	−	389.052i	1.36953	−	0.995019i
$392$	−102.856	+	33.4201i	−0.262389	+	0.0852552i
$393$		0			0
$394$	798.836	+	580.389i	2.02750	+	1.47307i
$395$			131.905i			0.333935i
$396$		0			0
$397$	97.1039			0.244594			0.122297	−	0.992494i	$-0.460974\pi$
$397$	97.1039			0.244594			0.122297	+	0.992494i	$0.460974\pi$
$398$	−516.485	+	710.880i	−1.29770	+	1.78613i
$399$		0			0
$400$	132.690	+	408.379i	0.331726	+	1.02095i
$401$	−386.262	−	531.644i	−0.963247	−	1.32580i	−0.945385	−	0.325955i	$-0.894314\pi$
$401$	−386.262	−	531.644i	−0.963247	−	1.32580i	−0.0178620	−	0.999840i	$-0.505686\pi$
$402$		0			0
$403$	24.2270	+	74.5630i	0.0601166	+	0.185020i
$404$	−15.7817	−	5.12779i	−0.0390636	−	0.0126925i
$405$		0			0
$406$	−424.378			−1.04527
$407$	−174.104	−	126.349i	−0.427773	−	0.310441i
$408$		0			0
$409$	−82.1600	−	59.6928i	−0.200880	−	0.145948i	0.482798	−	0.875732i	$-0.339621\pi$
$409$	−82.1600	−	59.6928i	−0.200880	−	0.145948i	−0.683678	+	0.729784i	$0.739621\pi$
$410$	−688.931	−	223.847i	−1.68032	−	0.545969i
$411$		0			0
$412$	88.1325	−	64.0320i	0.213914	−	0.155417i
$413$	−158.551	−	218.226i	−0.383900	−	0.528393i
$414$		0			0
$415$	55.2868	−	170.155i	0.133221	−	0.410013i
$416$	40.4756	−	55.7099i	0.0972972	−	0.133918i
$417$		0			0
$418$	453.460	+	147.066i	1.08483	+	0.351833i
$419$		−	0.439819i		−	0.00104969i	−1.00000		0.000524844i	$-0.999833\pi$
$419$		−	0.439819i		−	0.00104969i	1.00000		0.000524844i	$-0.000167063\pi$
$420$		0			0
$421$	−129.343	+	398.076i	−0.307227	+	0.945548i	0.671610	+	0.740905i	$0.265603\pi$
$421$	−129.343	+	398.076i	−0.307227	+	0.945548i	−0.978837	+	0.204642i	$0.934397\pi$
$422$	328.028	−	106.583i	0.777317	−	0.252566i
$423$		0			0
$424$	87.5547	−	63.6122i	0.206497	−	0.150029i
$425$	−922.166	+	299.630i	−2.16980	+	0.705011i
$426$		0			0
$427$	6.57712	+	4.77856i	0.0154031	+	0.0111910i
$428$		−	62.8449i		−	0.146834i
$429$		0			0
$430$	−49.6066			−0.115364
$431$	148.162	−	203.928i	0.343764	−	0.473150i	−0.601772	−	0.798668i	$-0.705538\pi$
$431$	148.162	−	203.928i	0.343764	−	0.473150i	0.945536	+	0.325517i	$0.105538\pi$
$432$		0			0
$433$	−38.4570	−	118.359i	−0.0888153	−	0.273345i	0.896777	−	0.442482i	$-0.145902\pi$
$433$	−38.4570	−	118.359i	−0.0888153	−	0.273345i	−0.985593	+	0.169137i	$0.945902\pi$
$434$	254.057	+	349.680i	0.585385	+	0.805713i
$435$		0			0
$436$	−164.914	−	507.552i	−0.378243	−	1.16411i
$437$	346.738	+	112.662i	0.793450	+	0.257807i
$438$		0			0
$439$	−73.6933			−0.167866			−0.0839332	−	0.996471i	$-0.526748\pi$
$439$	−73.6933			−0.167866			−0.0839332	+	0.996471i	$0.526748\pi$
$440$	183.987	+	133.522i	0.418152	+	0.303458i
$441$		0			0
$442$	96.6222	+	70.2001i	0.218602	+	0.158824i
$443$	351.831	+	114.317i	0.794200	+	0.258051i	0.677892	−	0.735162i	$-0.262894\pi$
$443$	351.831	+	114.317i	0.794200	+	0.258051i	0.116308	+	0.993213i	$0.462894\pi$
$444$		0			0
$445$	−195.470	+	142.017i	−0.439259	+	0.319140i
$446$	427.604	+	588.546i	0.958753	+	1.31961i
$447$		0			0
$448$	76.7385	−	236.177i	0.171291	−	0.527180i
$449$	−427.055	+	587.791i	−0.951125	+	1.30911i	−9.88759e−5		1.00000i	$0.500031\pi$
$449$	−427.055	+	587.791i	−0.951125	+	1.30911i	−0.951026	+	0.309111i	$0.899969\pi$
$450$		0			0
$451$	323.576	−	105.330i	0.717464	−	0.233549i
$452$		−	449.357i		−	0.994153i
$453$		0			0
$454$	−247.031	+	760.283i	−0.544121	+	1.67463i
$455$	31.8493	−	10.3485i	0.0699984	−	0.0227438i
$456$		0			0
$457$	295.712	−	214.847i	0.647072	−	0.470125i	−0.215201	−	0.976570i	$-0.569041\pi$
$457$	295.712	−	214.847i	0.647072	−	0.470125i	0.862272	+	0.506445i	$0.169041\pi$
$458$	−527.476	+	171.387i	−1.15169	+	0.374208i
$459$		0			0
$460$	778.130	+	565.344i	1.69159	+	1.22901i
$461$		−	153.670i		−	0.333340i	−0.986013	−	0.166670i	$-0.946699\pi$
$461$		−	153.670i		−	0.333340i	0.986013	−	0.166670i	$-0.0533014\pi$
$462$		0			0
$463$	325.357			0.702714			0.351357	−	0.936242i	$-0.385720\pi$
$463$	325.357			0.702714			0.351357	+	0.936242i	$0.385720\pi$
$464$	−348.465	+	479.621i	−0.751002	+	1.03367i
$465$		0			0
$466$	149.366	+	459.701i	0.320528	+	0.986484i
$467$	491.368	+	676.310i	1.05218	+	1.44820i	0.886904	+	0.461954i	$0.152851\pi$
$467$	491.368	+	676.310i	1.05218	+	1.44820i	0.165275	+	0.986247i	$0.447149\pi$
$468$		0			0
$469$	−76.6065	−	235.771i	−0.163340	−	0.502709i
$470$	896.834	+	291.399i	1.90816	+	0.619998i
$471$		0			0
$472$	252.686			0.535352
$473$	18.8453	−	13.7076i	0.0398421	−	0.0289800i
$474$		0			0
$475$	−432.081	−	313.925i	−0.909645	−	0.660896i
$476$	344.216	+	111.843i	0.723143	+	0.234963i
$477$		0			0
$478$	−171.419	+	124.543i	−0.358616	+	0.260550i
$479$	197.344	+	271.621i	0.411992	+	0.567058i	0.963703	−	0.266977i	$-0.0860249\pi$
$479$	197.344	+	271.621i	0.411992	+	0.567058i	−0.551711	+	0.834035i	$0.686025\pi$
$480$		0			0
$481$	9.17337	−	28.2327i	0.0190715	−	0.0586959i
$482$	372.785	−	513.094i	0.773412	−	1.06451i
$483$		0			0
$484$	−590.791	+	0.641196i	−1.22064	+	0.00132479i
$485$		−	224.143i		−	0.462150i
$486$		0			0
$487$	180.912	−	556.789i	0.371482	−	1.14330i	−0.574340	−	0.818617i	$-0.694741\pi$
$487$	180.912	−	556.789i	0.371482	−	1.14330i	0.945822	−	0.324686i	$-0.105259\pi$
$488$	−7.24298	+	2.35339i	−0.0148422	+	0.00482251i
$489$		0			0
$490$	−778.894	+	565.900i	−1.58958	+	1.15490i
$491$	−309.648	+	100.611i	−0.630647	+	0.204910i	−0.606862	−	0.794807i	$-0.707572\pi$
$491$	−309.648	+	100.611i	−0.630647	+	0.204910i	−0.0237854	+	0.999717i	$0.507572\pi$
$492$		0			0
$493$	−1083.04	−	786.874i	−2.19683	−	1.59609i
$494$			65.7846i			0.133167i
$495$		0			0
$496$	603.810			1.21736
$497$	18.6933	−	25.7292i	0.0376123	−	0.0517689i
$498$		0			0
$499$	124.634	+	383.583i	0.249767	+	0.768703i	0.994816	+	0.101693i	$0.0324261\pi$
$499$	124.634	+	383.583i	0.249767	+	0.768703i	−0.745049	+	0.667010i	$0.767574\pi$
$500$	−264.476	−	364.020i	−0.528953	−	0.728041i
$501$		0			0
$502$	−172.783	−	531.770i	−0.344188	−	1.05930i
$503$	−643.433	−	209.064i	−1.27919	−	0.415634i	−0.410895	−	0.911683i	$-0.634784\pi$
$503$	−643.433	−	209.064i	−1.27919	−	0.415634i	−0.868295	+	0.496048i	$0.834784\pi$
$504$		0			0
$505$	−26.7021			−0.0528754
$506$	−821.981	+	0.446056i	−1.62447	+	0.000881533i
$507$		0			0
$508$	−32.7185	−	23.7714i	−0.0644066	−	0.0467941i
$509$	639.693	+	207.849i	1.25677	+	0.408348i	0.860341	−	0.509720i	$-0.170251\pi$
$509$	639.693	+	207.849i	1.25677	+	0.408348i	0.396425	+	0.918067i	$0.370251\pi$
$510$		0			0
$511$	−238.016	+	172.929i	−0.465785	+	0.338413i
$512$	−384.029	−	528.571i	−0.750057	−	1.03236i
$513$		0			0
$514$	−267.816	+	824.254i	−0.521043	+	1.60361i
$515$	103.037	−	141.819i	0.200072	−	0.275376i
$516$		0			0
$517$	−421.224	+	137.117i	−0.814746	+	0.265216i
$518$		−	163.660i		−	0.315946i
$519$		0			0
$520$	−9.69410	+	29.8354i	−0.0186425	+	0.0573757i
$521$	−70.0098	+	22.7476i	−0.134376	+	0.0436613i	−0.375433	−	0.926850i	$-0.622506\pi$
$521$	−70.0098	+	22.7476i	−0.134376	+	0.0436613i	0.241057	+	0.970511i	$0.422506\pi$
$522$		0			0
$523$	432.771	−	314.426i	0.827478	−	0.601198i	−0.0913670	−	0.995817i	$-0.529124\pi$
$523$	432.771	−	314.426i	0.827478	−	0.601198i	0.918845	+	0.394620i	$0.129124\pi$
$524$	7.60469	−	2.47091i	0.0145128	−	0.00471548i
$525$		0			0
$526$	−1105.67	−	803.320i	−2.10204	−	1.52722i
$527$			1363.47i			2.58723i
$528$		0			0
$529$	−99.6371			−0.188350
$530$	566.287	−	779.427i	1.06847	−	1.47062i
$531$		0			0
$532$	61.6045	+	189.599i	0.115798	+	0.356389i
$533$	27.6016	+	37.9903i	0.0517853	+	0.0712763i
$534$		0			0
$535$	−31.2500	−	96.1775i	−0.0584112	−	0.179771i
$536$	220.862	+	71.7626i	0.412057	+	0.133885i
$537$		0			0
$538$	622.158			1.15643
$539$	139.526	−	430.211i	0.258861	−	0.798165i
$540$		0			0
$541$	−12.4454	−	9.04213i	−0.0230045	−	0.0167137i	0.576224	−	0.817292i	$-0.304526\pi$
$541$	−12.4454	−	9.04213i	−0.0230045	−	0.0167137i	−0.599228	+	0.800578i	$0.704526\pi$
$542$	−1306.56	−	424.526i	−2.41062	−	0.783258i
$543$		0			0
$544$	968.861	−	703.919i	1.78099	−	1.29397i
$545$	−504.766	−	694.751i	−0.926177	−	1.27477i
$546$		0			0
$547$	−56.2850	+	173.227i	−0.102898	+	0.316686i	−0.989231	−	0.146361i	$-0.953244\pi$
$547$	−56.2850	+	173.227i	−0.102898	+	0.316686i	0.886334	+	0.463047i	$0.153244\pi$
$548$	568.581	−	782.584i	1.03756	−	1.42807i
$549$		0			0
$550$	1145.40	+	371.477i	2.08255	+	0.675412i
$551$		−	737.380i		−	1.33826i
$552$		0			0
$553$	14.5674	−	44.8339i	0.0263425	−	0.0810740i
$554$	299.471	−	97.3041i	0.540562	−	0.175639i
$555$		0			0
$556$	−740.429	+	537.953i	−1.33171	+	0.967542i
$557$	255.810	−	83.1179i	0.459265	−	0.149224i	−0.0702419	−	0.997530i	$-0.522377\pi$
$557$	255.810	−	83.1179i	0.459265	−	0.149224i	0.529507	+	0.848306i	$0.322377\pi$
$558$		0			0
$559$	2.60161	+	1.89018i	0.00465405	+	0.00338136i
$560$		−	257.915i		−	0.460562i
$561$		0			0
$562$	−1284.47			−2.28554
$563$	235.669	−	324.370i	0.418594	−	0.576146i	−0.546694	−	0.837332i	$-0.684114\pi$
$563$	235.669	−	324.370i	0.418594	−	0.576146i	0.965288	+	0.261187i	$0.0841139\pi$
$564$		0			0
$565$	−223.445	−	687.694i	−0.395479	−	1.21716i
$566$	−528.551	−	727.489i	−0.933836	−	1.28532i
$567$		0			0
$568$	9.20625	+	28.3339i	0.0162082	+	0.0498837i
$569$	−174.429	−	56.6756i	−0.306554	−	0.0996056i	0.151700	−	0.988427i	$-0.451525\pi$
$569$	−174.429	−	56.6756i	−0.306554	−	0.0996056i	−0.458255	+	0.888821i	$0.651525\pi$
$570$		0			0
$571$	693.995			1.21540			0.607701	−	0.794166i	$-0.292092\pi$
$571$	693.995			1.21540			0.607701	+	0.794166i	$0.292092\pi$
$572$	−25.2353	−	77.5231i	−0.0441177	−	0.135530i
$573$		0			0
$574$	209.444	+	152.170i	0.364885	+	0.265105i
$575$	875.829	+	284.574i	1.52318	+	0.494912i
$576$		0			0
$577$	−429.878	+	312.325i	−0.745023	+	0.541291i	−0.894280	−	0.447507i	$-0.852312\pi$
$577$	−429.878	+	312.325i	−0.745023	+	0.541291i	0.149257	+	0.988798i	$0.452312\pi$
$578$	714.589	+	983.547i	1.23631	+	1.70164i
$579$		0			0
$580$	601.137	−	1850.11i	1.03644	−	3.18985i
$581$	−37.5836	+	51.7294i	−0.0646878	+	0.0890351i
$582$		0			0
$583$	0.245596	+	452.580i	0.000421263	+	0.776295i
$584$		−	275.601i		−	0.471920i
$585$		0			0
$586$	42.6551	−	131.279i	0.0727902	−	0.224025i
$587$	−510.666	+	165.925i	−0.869958	+	0.282667i	−0.709782	−	0.704422i	$-0.751206\pi$
$587$	−510.666	+	165.925i	−0.869958	+	0.282667i	−0.160177	+	0.987088i	$0.551206\pi$
$588$		0			0
$589$	−607.587	+	441.438i	−1.03156	+	0.749470i
$590$	2139.36	−	695.120i	3.62603	−	1.17817i
$591$		0			0
$592$	−184.964	−	134.384i	−0.312439	−	0.227001i
$593$			228.398i			0.385156i	0.981282	+	0.192578i	$0.0616849\pi$
$593$			228.398i			0.385156i	−0.981282	+	0.192578i	$0.938315\pi$
$594$		0			0
$595$	582.401			0.978825
$596$	−686.439	+	944.802i	−1.15174	+	1.58524i
$597$		0			0
$598$	−35.0519	−	107.879i	−0.0586153	−	0.180399i
$599$	−350.082	−	481.846i	−0.584444	−	0.804418i	0.409730	−	0.912207i	$-0.365623\pi$
$599$	−350.082	−	481.846i	−0.584444	−	0.804418i	−0.994174	+	0.107789i	$0.965623\pi$
$600$		0			0
$601$	245.022	+	754.101i	0.407691	+	1.25474i	0.918627	+	0.395125i	$0.129299\pi$
$601$	245.022	+	754.101i	0.407691	+	1.25474i	−0.510936	+	0.859619i	$0.670701\pi$
$602$	16.8611	+	5.47851i	0.0280085	+	0.00910052i
$603$		0			0
$604$	−286.488			−0.474318
$605$	−903.824	+	294.755i	−1.49392	+	0.487199i
$606$		0			0
$607$	706.476	+	513.285i	1.16388	+	0.845610i	0.990264	−	0.139203i	$-0.0444542\pi$
$607$	706.476	+	513.285i	1.16388	+	0.845610i	0.173618	+	0.984813i	$0.444454\pi$
$608$	627.358	+	203.841i	1.03184	+	0.335265i
$609$		0			0
$610$	−54.8485	+	39.8497i	−0.0899155	+	0.0653274i
$611$	−35.9310	−	49.4548i	−0.0588069	−	0.0809408i
$612$		0			0
$613$	97.3458	−	299.600i	0.158802	−	0.488743i	−0.839724	−	0.543014i	$-0.817283\pi$
$613$	97.3458	−	299.600i	0.158802	−	0.488743i	0.998526	+	0.0542702i	$0.0172832\pi$
$614$	−785.266	+	1080.83i	−1.27894	+	1.76030i
$615$		0			0
$616$	−47.7905	−	65.7029i	−0.0775819	−	0.106661i
$617$			738.239i			1.19650i	0.801311	+	0.598249i	$0.204136\pi$
$617$			738.239i			1.19650i	−0.801311	+	0.598249i	$0.795864\pi$
$618$		0			0
$619$	285.874	−	879.831i	0.461832	−	1.42137i	−0.401090	−	0.916038i	$-0.631369\pi$
$619$	285.874	−	879.831i	0.461832	−	1.42137i	0.862923	−	0.505336i	$-0.168631\pi$
$620$	−1884.33	+	612.256i	−3.03924	+	0.987510i
$621$		0			0
$622$	−806.955	+	586.287i	−1.29736	+	0.942584i
$623$	82.1240	−	26.6837i	0.131820	−	0.0428310i
$624$		0			0
$625$	157.102	+	114.141i	0.251363	+	0.182626i
$626$			304.938i			0.487122i
$627$		0			0
$628$	−99.7039			−0.158764
$629$	303.455	−	417.670i	0.482440	−	0.664022i
$630$		0			0
$631$	−108.898	−	335.154i	−0.172580	−	0.531147i	0.826935	−	0.562298i	$-0.190083\pi$
$631$	−108.898	−	335.154i	−0.172580	−	0.531147i	−0.999515	+	0.0311513i	$0.990083\pi$
$632$	25.9568	+	35.7265i	0.0410709	+	0.0565293i
$633$		0			0
$634$	−348.017	−	1071.09i	−0.548922	−	1.68941i
$635$	−61.8927	−	20.1102i	−0.0974689	−	0.0316696i
$636$		0			0
$637$	62.4117			0.0979776
$638$	514.595	+	1580.84i	0.806576	+	2.47781i
$639$		0			0
$640$	522.000	+	379.255i	0.815625	+	0.592586i
$641$	234.944	+	76.3379i	0.366527	+	0.119092i	0.486489	−	0.873687i	$-0.338277\pi$
$641$	234.944	+	76.3379i	0.366527	+	0.119092i	−0.119962	+	0.992778i	$0.538277\pi$
$642$		0			0
$643$	−531.828	+	386.395i	−0.827104	+	0.600926i	−0.918738	−	0.394867i	$-0.870791\pi$
$643$	−531.828	+	386.395i	−0.827104	+	0.600926i	0.0916349	+	0.995793i	$0.470791\pi$
$644$	−202.048	−	278.095i	−0.313739	−	0.431824i
$645$		0			0
$646$	−353.538	+	1088.08i	−0.547272	+	1.68433i
$647$	379.466	−	522.290i	0.586500	−	0.807249i	−0.407889	−	0.913032i	$-0.633735\pi$
$647$	379.466	−	522.290i	0.586500	−	0.807249i	0.994389	+	0.105783i	$0.0337349\pi$
$648$		0			0
$649$	−620.654	+	855.232i	−0.956323	+	1.31777i
$650$			166.166i			0.255640i
$651$		0			0
$652$	−157.750	+	485.506i	−0.241948	+	0.744640i
$653$	33.8048	−	10.9839i	0.0517685	−	0.0168206i	−0.283018	−	0.959115i	$-0.591336\pi$
$653$	33.8048	−	10.9839i	0.0517685	−	0.0168206i	0.334787	+	0.942294i	$0.391336\pi$
$654$		0			0
$655$	10.4095	−	7.56295i	0.0158924	−	0.0115465i
$656$	343.957	−	111.758i	0.524325	−	0.170363i
$657$		0			0
$658$	−272.649	−	198.091i	−0.414360	−	0.301050i
$659$		−	721.237i		−	1.09444i	−0.836988	−	0.547221i	$-0.815686\pi$
$659$		−	721.237i		−	1.09444i	0.836988	−	0.547221i	$-0.184314\pi$
$660$		0			0
$661$	−617.542			−0.934253			−0.467127	−	0.884190i	$-0.654711\pi$
$661$	−617.542			−0.934253			−0.467127	+	0.884190i	$0.654711\pi$
$662$	−299.512	+	412.242i	−0.452435	+	0.622723i
$663$		0			0
$664$	−18.5095	−	56.9664i	−0.0278757	−	0.0857927i
$665$	188.558	+	259.528i	0.283546	+	0.390268i
$666$		0			0
$667$	392.897	+	1209.21i	0.589052	+	1.81291i
$668$	−182.077	−	59.1603i	−0.272570	−	0.0885633i
$669$		0			0
$670$	2067.34			3.08558
$671$	9.82518	−	30.2947i	0.0146426	−	0.0451486i
$672$		0			0
$673$	679.954	+	494.016i	1.01033	+	0.734050i	0.964279	−	0.264889i	$-0.0853353\pi$
$673$	679.954	+	494.016i	1.01033	+	0.734050i	0.0460541	+	0.998939i	$0.485335\pi$
$674$	544.042	+	176.770i	0.807184	+	0.262270i
$675$		0			0
$676$	−658.462	+	478.401i	−0.974057	+	0.707694i
$677$	227.212	+	312.730i	0.335615	+	0.461935i	0.943154	−	0.332355i	$-0.107843\pi$
$677$	227.212	+	312.730i	0.335615	+	0.461935i	−0.607539	+	0.794290i	$0.707843\pi$
$678$		0			0
$679$	−24.7541	+	76.1854i	−0.0364568	+	0.112202i
$680$	−320.681	+	441.379i	−0.471589	+	0.649087i
$681$		0			0
$682$	994.518	−	1370.40i	1.45824	−	2.00938i
$683$			122.406i			0.179219i	0.995977	+	0.0896094i	$0.0285619\pi$
$683$			122.406i			0.179219i	−0.995977	+	0.0896094i	$0.971438\pi$
$684$		0			0
$685$	481.009	−	1480.39i	0.702203	−	2.16116i
$686$	717.236	−	233.044i	1.04553	−	0.339714i
$687$		0			0
$688$	20.0367	−	14.5575i	0.0291231	−	0.0211592i
$689$	−59.3977	+	19.2995i	−0.0862085	+	0.0280108i
$690$		0			0
$691$	−198.194	−	143.996i	−0.286822	−	0.208388i	0.435065	−	0.900399i	$-0.356725\pi$
$691$	−198.194	−	143.996i	−0.286822	−	0.208388i	−0.721888	+	0.692010i	$0.756725\pi$
$692$		−	446.402i		−	0.645090i
$693$		0			0
$694$	553.926			0.798165
$695$	−865.649	+	1191.46i	−1.24554	+	1.71434i
$696$		0			0
$697$	252.363	+	776.694i	0.362071	+	1.11434i
$698$	309.003	+	425.306i	0.442697	+	0.609320i
$699$		0			0
$700$	155.608	+	478.911i	0.222297	+	0.684159i
$701$	−187.720	−	60.9938i	−0.267788	−	0.0870097i	0.172045	−	0.985089i	$-0.444963\pi$
$701$	−187.720	−	60.9938i	−0.267788	−	0.0870097i	−0.439833	+	0.898079i	$0.644963\pi$
$702$		0			0
$703$	284.368			0.404506
$704$	−972.830	+	0.527915i	−1.38186	+	0.000749879i
$705$		0			0
$706$	561.379	+	407.866i	0.795155	+	0.577714i
$707$	9.07595	+	2.94896i	0.0128373	+	0.00417108i
$708$		0			0
$709$	425.433	−	309.095i	0.600046	−	0.435959i	−0.245849	−	0.969308i	$-0.579067\pi$
$709$	425.433	−	309.095i	0.600046	−	0.435959i	0.845895	+	0.533349i	$0.179067\pi$
$710$	155.889	+	214.563i	0.219562	+	0.302201i
$711$		0			0
$712$	−24.9965	+	76.9312i	−0.0351074	+	0.108049i
$713$	761.159	−	1047.65i	1.06754	−	1.46935i
$714$		0			0
$715$	−77.1688	−	106.093i	−0.107928	−	0.148381i
$716$		−	1065.29i		−	1.48784i
$717$		0			0
$718$	371.271	−	1142.65i	0.517090	−	1.59144i
$719$	51.7903	−	16.8277i	0.0720311	−	0.0234043i	−0.272780	−	0.962076i	$-0.587943\pi$
$719$	51.7903	−	16.8277i	0.0720311	−	0.0234043i	0.344811	+	0.938672i	$0.387943\pi$
$720$		0			0
$721$	−50.6844	+	36.8244i	−0.0702973	+	0.0510740i
$722$	423.924	−	137.741i	0.587153	−	0.190777i
$723$		0			0
$724$	−177.046	−	128.632i	−0.244539	−	0.177668i
$725$		−	1862.56i		−	2.56905i
$726$		0			0
$727$	1312.96			1.80600			0.902999	−	0.429642i	$-0.141360\pi$
$727$	1312.96			1.80600			0.902999	+	0.429642i	$0.141360\pi$
$728$	6.58999	−	9.07035i	0.00905219	−	0.0124593i
$729$		0			0
$730$	−758.158	−	2333.37i	−1.03857	−	3.19640i
$731$	32.8725	+	45.2451i	0.0449692	+	0.0618948i
$732$		0			0
$733$	122.245	+	376.231i	0.166774	+	0.513276i	0.999163	−	0.0409155i	$-0.0130275\pi$
$733$	122.245	+	376.231i	0.166774	+	0.513276i	−0.832389	+	0.554192i	$0.813027\pi$
$734$	−1534.92	−	498.725i	−2.09117	−	0.679461i
$735$		0			0
$736$	−1137.40			−1.54538
$737$	−785.372	+	571.258i	−1.06563	+	0.775112i
$738$		0			0
$739$	−1153.17	−	837.830i	−1.56045	−	1.13374i	−0.935637	−	0.352963i	$-0.885174\pi$
$739$	−1153.17	−	837.830i	−1.56045	−	1.13374i	−0.624816	−	0.780772i	$-0.714826\pi$
$740$	713.488	+	231.826i	0.964174	+	0.313279i
$741$		0			0
$742$	−278.558	+	202.385i	−0.375416	+	0.272755i
$743$	381.078	+	524.508i	0.512890	+	0.705933i	0.984403	−	0.175926i	$-0.0562920\pi$
$743$	381.078	+	524.508i	0.512890	+	0.705933i	−0.471513	+	0.881859i	$0.656292\pi$
$744$		0			0
$745$	−580.715	+	1787.26i	−0.779483	+	2.39900i
$746$	−280.334	+	385.846i	−0.375783	+	0.517220i
$747$		0			0
$748$	−0.769410	−	1417.85i	−0.00102862	−	1.89552i
$749$			36.1417i			0.0482532i
$750$		0			0
$751$	−160.859	+	495.074i	−0.214193	+	0.659220i	0.785016	+	0.619475i	$0.212654\pi$
$751$	−160.859	+	495.074i	−0.214193	+	0.659220i	−0.999210	+	0.0397446i	$0.987346\pi$
$752$	−447.755	+	145.484i	−0.595419	+	0.193463i
$753$		0			0
$754$	−185.603	+	134.848i	−0.246157	+	0.178844i
$755$	−438.440	+	142.458i	−0.580715	+	0.188686i
$756$		0			0
$757$	442.250	+	321.314i	0.584214	+	0.424456i	0.840241	−	0.542213i	$-0.182414\pi$
$757$	442.250	+	321.314i	0.584214	+	0.424456i	−0.256027	+	0.966670i	$0.582414\pi$
$758$		−	1128.43i		−	1.48869i
$759$		0			0
$760$	−300.510			−0.395408
$761$	485.510	−	668.247i	0.637990	−	0.878118i	−0.360517	−	0.932753i	$-0.617400\pi$
$761$	485.510	−	668.247i	0.637990	−	0.878118i	0.998506	+	0.0546352i	$0.0173996\pi$
$762$		0			0
$763$	94.8408	+	291.890i	0.124300	+	0.382555i
$764$	427.539	+	588.457i	0.559606	+	0.770231i
$765$		0			0
$766$	220.637	+	679.052i	0.288038	+	0.886491i
$767$	−138.685	−	45.0615i	−0.180815	−	0.0587503i
$768$		0			0
$769$	712.096			0.926003			0.463001	−	0.886358i	$-0.346772\pi$
$769$	712.096			0.926003			0.463001	+	0.886358i	$0.346772\pi$
$770$	−585.360	−	424.804i	−0.760208	−	0.551694i
$771$		0			0
$772$	765.156	+	555.918i	0.991135	+	0.720102i
$773$	−262.790	−	85.3856i	−0.339961	−	0.110460i	0.134061	−	0.990973i	$-0.457198\pi$
$773$	−262.790	−	85.3856i	−0.339961	−	0.110460i	−0.474022	+	0.880513i	$0.657198\pi$
$774$		0			0
$775$	−1534.71	+	1115.03i	−1.98028	+	1.43875i
$776$	−44.1079	−	60.7094i	−0.0568401	−	0.0782337i
$777$		0			0
$778$	462.905	−	1424.67i	0.594993	−	1.83120i
$779$	−264.404	+	363.921i	−0.339414	+	0.467164i
$780$		0			0
$781$	−118.510	−	38.4353i	−0.151742	−	0.0492129i
$782$		−	1972.69i		−	2.52262i
$783$		0			0
$784$	148.536	−	457.147i	0.189459	−	0.583095i
$785$	−152.586	+	49.5783i	−0.194377	+	0.0631571i
$786$		0			0
$787$	−773.348	+	561.870i	&mi

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	99.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.75181 - 2.41117i) q^{2} +(-1.50880 - 4.64360i) q^{4} +(-4.61811 - 6.35629i) q^{5} +(0.867699 + 2.67050i) q^{7} +(-2.50164 - 0.812833i) q^{8} +O(q^{10})\)	\(q+(1.75181 - 2.41117i) q^{2} +(-1.50880 - 4.64360i) q^{4} +(-4.61811 - 6.35629i) q^{5} +(0.867699 + 2.67050i) q^{7} +(-2.50164 - 0.812833i) q^{8} -23.4161 q^{10} +(8.89568 - 6.47047i) q^{11} +(1.22806 + 0.892235i) q^{13} +(7.95907 + 2.58606i) q^{14} +(9.45804 - 6.87167i) q^{16} +(15.5170 + 21.3573i) q^{17} +(-4.49342 + 13.8293i) q^{19} +(-22.5483 + 31.0350i) q^{20} +(-0.0177905 - 32.7840i) q^{22} -25.0726i q^{23} +(-11.3500 + 34.9317i) q^{25} +(4.30265 - 1.39802i) q^{26} +(11.0916 - 8.05850i) q^{28} +(-48.2284 + 15.6704i) q^{29} +(41.7844 + 30.3581i) q^{31} -45.3643i q^{32} +78.6790 q^{34} +(12.9674 - 17.8480i) q^{35} +(-6.04322 - 18.5991i) q^{37} +(25.4731 + 35.0608i) q^{38} +(6.38627 + 19.6549i) q^{40} +(29.4212 + 9.55953i) q^{41} +2.11848 q^{43} +(-43.4680 - 31.5454i) q^{44} +(-60.4543 - 43.9226i) q^{46} +(-38.2998 - 12.4444i) q^{47} +(33.2631 - 24.1671i) q^{49} +(64.3430 + 88.5605i) q^{50} +(2.29029 - 7.04880i) q^{52} +(-24.1836 + 33.2859i) q^{53} +(-82.2094 - 26.6621i) q^{55} -7.38594i q^{56} +(-46.7034 + 143.738i) q^{58} +(-91.3627 + 29.6855i) q^{59} +(2.34234 - 1.70181i) q^{61} +(146.397 - 47.5673i) q^{62} +(-71.5487 - 51.9832i) q^{64} -11.9263i q^{65} -88.2869 q^{67} +(75.7629 - 104.279i) q^{68} +(-20.3182 - 62.5329i) q^{70} +(-6.65733 - 9.16303i) q^{71} +(32.3776 + 99.6480i) q^{73} +(-55.4322 - 18.0110i) q^{74} +70.9975 q^{76} +(24.9982 + 18.1415i) q^{77} +(-13.5822 - 9.86808i) q^{79} +(-87.3566 - 28.3839i) q^{80} +(74.5901 - 54.1929i) q^{82} +(13.3848 + 18.4226i) q^{83} +(64.0940 - 197.261i) q^{85} +(3.71118 - 5.10801i) q^{86} +(-27.5132 + 8.95610i) q^{88} -30.7523i q^{89} +(-1.31713 + 4.05372i) q^{91} +(-116.427 + 37.8295i) q^{92} +(-97.0996 + 70.5470i) q^{94} +(108.654 - 35.3039i) q^{95} +(23.0800 + 16.7686i) q^{97} -122.539i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 16 q^{7}+O(q^{10}) \) 32 * q + 16 * q^4 - 16 * q^7	\( 32 q + 16 q^{4} - 16 q^{7} + 48 q^{10} + 8 q^{13} + 96 q^{16} - 40 q^{19} - 60 q^{22} - 188 q^{25} - 348 q^{28} - 164 q^{31} + 296 q^{34} - 36 q^{37} + 48 q^{40} + 544 q^{43} + 296 q^{46} + 196 q^{49} - 640 q^{52} - 440 q^{55} - 208 q^{58} - 432 q^{61} - 328 q^{64} + 48 q^{67} + 112 q^{70} + 712 q^{73} + 2104 q^{76} + 432 q^{79} + 676 q^{82} - 68 q^{85} - 176 q^{88} + 64 q^{91} - 1360 q^{94} + 132 q^{97}+O(q^{100}) \) 32 * q + 16 * q^4 - 16 * q^7 + 48 * q^10 + 8 * q^13 + 96 * q^16 - 40 * q^19 - 60 * q^22 - 188 * q^25 - 348 * q^28 - 164 * q^31 + 296 * q^34 - 36 * q^37 + 48 * q^40 + 544 * q^43 + 296 * q^46 + 196 * q^49 - 640 * q^52 - 440 * q^55 - 208 * q^58 - 432 * q^61 - 328 * q^64 + 48 * q^67 + 112 * q^70 + 712 * q^73 + 2104 * q^76 + 432 * q^79 + 676 * q^82 - 68 * q^85 - 176 * q^88 + 64 * q^91 - 1360 * q^94 + 132 * q^97

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