LMFDB - Embedded newform 1050.3.q.e.199.16

Newspace parameters

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1050.q (of order $6$, degree $2$, not minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$28.6104277578$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 210)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.16
Character	$\chi$	$=$	1050.199
Dual form			1050.3.q.e.649.16

$q$-expansion

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-4.61524 + 5.26304i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-4.61524 + 5.26304i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.41099 - 9.37211i) q^{11} +(-1.73205 - 3.00000i) q^{12} +19.2715 q^{13} +(-1.93096 + 9.70935i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-5.13686 + 8.89730i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(18.0756 - 10.4359i) q^{19} +(3.89764 + 11.4808i) q^{21} -15.3046i q^{22} +(18.2511 - 10.5373i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(23.6026 - 13.6270i) q^{26} -5.19615 q^{27} +(4.50061 + 13.2569i) q^{28} -19.0888 q^{29} +(-34.6556 - 20.0084i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-9.37211 - 16.2330i) q^{33} +14.5292i q^{34} -6.00000 q^{36} +(43.6177 - 25.1827i) q^{37} +(14.7586 - 25.5627i) q^{38} +(16.6896 - 28.9072i) q^{39} +22.7706i q^{41} +(12.8918 + 11.3050i) q^{42} -48.4307i q^{43} +(-10.8220 - 18.7442i) q^{44} +(14.9020 - 25.8110i) q^{46} +(-33.2690 - 57.6236i) q^{47} -6.92820 q^{48} +(-6.39913 - 48.5804i) q^{49} +(8.89730 + 15.4106i) q^{51} +(19.2715 - 33.3792i) q^{52} +(-4.28736 - 2.47531i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(14.8861 + 13.0539i) q^{56} -36.1511i q^{57} +(-23.3789 + 13.4978i) q^{58} +(24.4105 + 14.0934i) q^{59} +(-60.6988 + 35.0445i) q^{61} -56.5924 q^{62} +(20.5966 + 4.09619i) q^{63} -8.00000 q^{64} +(-22.9569 - 13.2542i) q^{66} +(16.7193 + 9.65287i) q^{67} +(10.2737 + 17.7946i) q^{68} -36.5023i q^{69} +49.4968 q^{71} +(-7.34847 + 4.24264i) q^{72} +(66.4872 - 115.159i) q^{73} +(35.6137 - 61.6848i) q^{74} -41.7437i q^{76} +(24.3527 + 71.7328i) q^{77} -47.2053i q^{78} +(-45.0404 - 78.0122i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(16.1013 + 27.8882i) q^{82} +101.045 q^{83} +(23.7829 + 4.72987i) q^{84} +(-34.2456 - 59.3152i) q^{86} +(-16.5314 + 28.6332i) q^{87} +(-26.5083 - 15.3046i) q^{88} +(-34.3077 + 19.8075i) q^{89} +(-88.9425 + 101.427i) q^{91} -42.1492i q^{92} +(-60.0253 + 34.6556i) q^{93} +(-81.4920 - 47.0495i) q^{94} +(-8.48528 + 4.89898i) q^{96} +68.6944 q^{97} +(-42.1888 - 54.9737i) q^{98} -32.4659 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) $ 32 * q + 32 * q^4 - 48 * q^9	$ 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) $ 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$2$	1.22474	−	0.707107i	0.612372	−	0.353553i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	1.00000	−	1.73205i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$		−	2.44949i		−	0.408248i
$7$	−4.61524	+	5.26304i	−0.659320	+	0.751863i
$7$	−4.61524	+	5.26304i	−0.659320	+	0.751863i
$8$		−	2.82843i		−	0.353553i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	5.41099	−	9.37211i	0.491908	−	0.852010i	−0.508049	−	0.861328i	$-0.669633\pi$
$11$	5.41099	−	9.37211i	0.491908	−	0.852010i	0.999957	+	0.00931868i	$0.00296627\pi$
$12$	−1.73205	−	3.00000i	−0.144338	−	0.250000i
$13$	19.2715			1.48242			0.741211	−	0.671273i	$-0.234252\pi$
$13$	19.2715			1.48242			0.741211	+	0.671273i	$0.234252\pi$
$14$	−1.93096	+	9.70935i	−0.137926	+	0.693525i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−5.13686	+	8.89730i	−0.302168	+	0.523371i	−0.976627	−	0.214942i	$-0.931044\pi$
$17$	−5.13686	+	8.89730i	−0.302168	+	0.523371i	0.674459	+	0.738313i	$0.264377\pi$
$18$	−3.67423	−	2.12132i	−0.204124	−	0.117851i
$19$	18.0756	−	10.4359i	0.951346	−	0.549260i	0.0578471	−	0.998325i	$-0.481576\pi$
$19$	18.0756	−	10.4359i	0.951346	−	0.549260i	0.893499	+	0.449066i	$0.148243\pi$
$20$		0			0
$21$	3.89764	+	11.4808i	0.185602	+	0.546704i
$22$		−	15.3046i		−	0.695663i
$23$	18.2511	−	10.5373i	0.793527	−	0.458143i	−0.0476755	−	0.998863i	$-0.515181\pi$
$23$	18.2511	−	10.5373i	0.793527	−	0.458143i	0.841203	+	0.540720i	$0.181848\pi$
$24$	−4.24264	−	2.44949i	−0.176777	−	0.102062i
$25$		0			0
$26$	23.6026	−	13.6270i	0.907794	−	0.524115i
$27$	−5.19615			−0.192450
$28$	4.50061	+	13.2569i	0.160736	+	0.473460i
$29$	−19.0888			−0.658235			−0.329118	−	0.944289i	$-0.606751\pi$
$29$	−19.0888			−0.658235			−0.329118	+	0.944289i	$0.606751\pi$
$30$		0			0
$31$	−34.6556	−	20.0084i	−1.11792	−	0.645434i	−0.177054	−	0.984201i	$-0.556657\pi$
$31$	−34.6556	−	20.0084i	−1.11792	−	0.645434i	−0.940870	+	0.338768i	$0.889990\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$	−9.37211	−	16.2330i	−0.284003	−	0.491908i
$34$			14.5292i			0.427330i
$35$		0			0
$36$	−6.00000			−0.166667
$37$	43.6177	−	25.1827i	1.17886	−	0.680614i	0.223107	−	0.974794i	$-0.428380\pi$
$37$	43.6177	−	25.1827i	1.17886	−	0.680614i	0.955750	+	0.294180i	$0.0950466\pi$
$38$	14.7586	−	25.5627i	0.388385	−	0.672703i
$39$	16.6896	−	28.9072i	0.427938	−	0.741211i
$40$		0			0
$41$			22.7706i			0.555382i	0.960671	+	0.277691i	$0.0895691\pi$
$41$			22.7706i			0.555382i	−0.960671	+	0.277691i	$0.910431\pi$
$42$	12.8918	+	11.3050i	0.306947	+	0.269166i
$43$		−	48.4307i		−	1.12629i	−0.826357	−	0.563147i	$-0.809590\pi$
$43$		−	48.4307i		−	1.12629i	0.826357	−	0.563147i	$-0.190410\pi$
$44$	−10.8220	−	18.7442i	−0.245954	−	0.426005i
$45$		0			0
$46$	14.9020	−	25.8110i	0.323956	−	0.561109i
$47$	−33.2690	−	57.6236i	−0.707851	−	1.22603i	−0.965653	−	0.259836i	$-0.916332\pi$
$47$	−33.2690	−	57.6236i	−0.707851	−	1.22603i	0.257802	−	0.966198i	$-0.417002\pi$
$48$	−6.92820			−0.144338
$49$	−6.39913	−	48.5804i	−0.130595	−	0.991436i
$50$		0			0
$51$	8.89730	+	15.4106i	0.174457	+	0.302168i
$52$	19.2715	−	33.3792i	0.370605	−	0.641907i
$53$	−4.28736	−	2.47531i	−0.0808937	−	0.0467040i	0.459008	−	0.888432i	$-0.348205\pi$
$53$	−4.28736	−	2.47531i	−0.0808937	−	0.0467040i	−0.539901	+	0.841728i	$0.681538\pi$
$54$	−6.36396	+	3.67423i	−0.117851	+	0.0680414i
$55$		0			0
$56$	14.8861	+	13.0539i	0.265824	+	0.233105i
$57$		−	36.1511i		−	0.634231i
$58$	−23.3789	+	13.4978i	−0.403085	+	0.232721i
$59$	24.4105	+	14.0934i	0.413737	+	0.238871i	0.692394	−	0.721520i	$-0.256556\pi$
$59$	24.4105	+	14.0934i	0.413737	+	0.238871i	−0.278657	+	0.960391i	$0.589889\pi$
$60$		0			0
$61$	−60.6988	+	35.0445i	−0.995062	+	0.574499i	−0.906784	−	0.421596i	$-0.861470\pi$
$61$	−60.6988	+	35.0445i	−0.995062	+	0.574499i	−0.0882785	+	0.996096i	$0.528137\pi$
$62$	−56.5924			−0.912781
$63$	20.5966	+	4.09619i	0.326931	+	0.0650188i
$64$	−8.00000			−0.125000
$65$		0			0
$66$	−22.9569	−	13.2542i	−0.347832	−	0.200821i
$67$	16.7193	+	9.65287i	0.249541	+	0.144073i	0.619554	−	0.784954i	$-0.287313\pi$
$67$	16.7193	+	9.65287i	0.249541	+	0.144073i	−0.370013	+	0.929027i	$0.620647\pi$
$68$	10.2737	+	17.7946i	0.151084	+	0.261685i
$69$		−	36.5023i		−	0.529018i
$70$		0			0
$71$	49.4968			0.697138			0.348569	−	0.937283i	$-0.386668\pi$
$71$	49.4968			0.697138			0.348569	+	0.937283i	$0.386668\pi$
$72$	−7.34847	+	4.24264i	−0.102062	+	0.0589256i
$73$	66.4872	−	115.159i	0.910783	−	1.57752i	0.0978221	−	0.995204i	$-0.468812\pi$
$73$	66.4872	−	115.159i	0.910783	−	1.57752i	0.812961	−	0.582318i	$-0.197854\pi$
$74$	35.6137	−	61.6848i	0.481266	−	0.833578i
$75$		0			0
$76$		−	41.7437i		−	0.549260i
$77$	24.3527	+	71.7328i	0.316269	+	0.931594i
$78$		−	47.2053i		−	0.605196i
$79$	−45.0404	−	78.0122i	−0.570132	−	0.987497i	−0.996552	−	0.0829717i	$-0.973559\pi$
$79$	−45.0404	−	78.0122i	−0.570132	−	0.987497i	0.426420	−	0.904525i	$-0.359774\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	16.1013	+	27.8882i	0.196357	+	0.340100i
$83$	101.045			1.21741			0.608706	−	0.793396i	$-0.291689\pi$
$83$	101.045			1.21741			0.608706	+	0.793396i	$0.291689\pi$
$84$	23.7829	+	4.72987i	0.283130	+	0.0563080i
$85$		0			0
$86$	−34.2456	−	59.3152i	−0.398205	−	0.689712i
$87$	−16.5314	+	28.6332i	−0.190016	+	0.329118i
$88$	−26.5083	−	15.3046i	−0.301231	−	0.173916i
$89$	−34.3077	+	19.8075i	−0.385479	+	0.222557i	−0.680200	−	0.733027i	$-0.738107\pi$
$89$	−34.3077	+	19.8075i	−0.385479	+	0.222557i	0.294720	+	0.955584i	$0.404774\pi$
$90$		0			0
$91$	−88.9425	+	101.427i	−0.977390	+	1.11458i
$92$		−	42.1492i		−	0.458143i
$93$	−60.0253	+	34.6556i	−0.645434	+	0.372641i
$94$	−81.4920	−	47.0495i	−0.866937	−	0.500526i
$95$		0			0
$96$	−8.48528	+	4.89898i	−0.0883883	+	0.0510310i
$97$	68.6944			0.708190			0.354095	−	0.935210i	$-0.384789\pi$
$97$	68.6944			0.708190			0.354095	+	0.935210i	$0.384789\pi$
$98$	−42.1888	−	54.9737i	−0.430498	−	0.560956i
$99$	−32.4659			−0.327939
$100$		0			0
$101$	−6.96199	−	4.01951i	−0.0689306	−	0.0397971i	0.465139	−	0.885238i	$-0.346004\pi$
$101$	−6.96199	−	4.01951i	−0.0689306	−	0.0397971i	−0.534069	+	0.845441i	$0.679338\pi$
$102$	21.7939	+	12.5827i	0.213665	+	0.123360i
$103$	102.282	+	177.158i	0.993033	+	1.71998i	0.598568	+	0.801072i	$0.295737\pi$
$103$	102.282	+	177.158i	0.993033	+	1.71998i	0.394465	+	0.918911i	$0.370930\pi$
$104$		−	54.5080i		−	0.524115i
$105$		0			0
$106$	−7.00124			−0.0660494
$107$	−142.508	+	82.2769i	−1.33185	+	0.768943i	−0.985583	−	0.169193i	$-0.945884\pi$
$107$	−142.508	+	82.2769i	−1.33185	+	0.768943i	−0.346266	+	0.938136i	$0.612551\pi$
$108$	−5.19615	+	9.00000i	−0.0481125	+	0.0833333i
$109$	−39.5050	+	68.4247i	−0.362432	+	0.627750i	−0.988360	−	0.152130i	$-0.951387\pi$
$109$	−39.5050	+	68.4247i	−0.362432	+	0.627750i	0.625929	+	0.779880i	$0.284720\pi$
$110$		0			0
$111$		−	87.2354i		−	0.785905i
$112$	27.4622	+	5.46158i	0.245198	+	0.0487641i
$113$			84.5690i			0.748398i	0.927348	+	0.374199i	$0.122082\pi$
$113$			84.5690i			0.748398i	−0.927348	+	0.374199i	$0.877918\pi$
$114$	−25.5627	−	44.2759i	−0.224234	−	0.388385i
$115$		0			0
$116$	−19.0888	+	33.0628i	−0.164559	+	0.285024i
$117$	−28.9072	−	50.0688i	−0.247070	−	0.427938i
$118$	39.8621			0.337815
$119$	−23.1190	−	68.0987i	−0.194277	−	0.572258i
$120$		0			0
$121$	1.94240	+	3.36434i	0.0160529	+	0.0278044i
$122$	−49.5603	+	85.8410i	−0.406232	+	0.703615i
$123$	34.1560	+	19.7200i	0.277691	+	0.160325i
$124$	−69.3113	+	40.0169i	−0.558962	+	0.322717i
$125$		0			0
$126$	28.1221	−	9.54723i	0.223191	−	0.0757717i
$127$			101.777i			0.801393i	0.916211	+	0.400697i	$0.131232\pi$
$127$			101.777i			0.801393i	−0.916211	+	0.400697i	$0.868768\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$	−72.6460	−	41.9422i	−0.563147	−	0.325133i
$130$		0			0
$131$	61.2264	−	35.3491i	0.467377	−	0.269840i	−0.247764	−	0.968820i	$-0.579696\pi$
$131$	61.2264	−	35.3491i	0.467377	−	0.269840i	0.715141	+	0.698980i	$0.246362\pi$
$132$	−37.4884			−0.284003
$133$	−28.4984	+	143.297i	−0.214273	+	1.07742i
$134$	27.3024			0.203750
$135$		0			0
$136$	25.1654	+	14.5292i	0.185039	+	0.106833i
$137$	−102.042	−	58.9138i	−0.744829	−	0.430027i	0.0789932	−	0.996875i	$-0.474829\pi$
$137$	−102.042	−	58.9138i	−0.744829	−	0.430027i	−0.823823	+	0.566848i	$0.808163\pi$
$138$	−25.8110	−	44.7060i	−0.187036	−	0.323956i
$139$			158.507i			1.14034i	0.821528	+	0.570168i	$0.193122\pi$
$139$			158.507i			1.14034i	−0.821528	+	0.570168i	$0.806878\pi$
$140$		0			0
$141$	−115.247			−0.817356
$142$	60.6209	−	34.9995i	0.426908	−	0.246475i
$143$	104.278	−	180.614i	0.729215	−	1.26304i
$144$	−6.00000	+	10.3923i	−0.0416667	+	0.0721688i
$145$		0			0
$146$		−	188.054i		−	1.28804i
$147$	−78.4123	−	32.4731i	−0.533417	−	0.220906i
$148$		−	100.731i		−	0.680614i
$149$	−147.948	−	256.254i	−0.992940	−	1.71982i	−0.599193	−	0.800604i	$-0.704512\pi$
$149$	−147.948	−	256.254i	−0.992940	−	1.71982i	−0.393747	−	0.919219i	$-0.628821\pi$
$150$		0			0
$151$	62.6478	−	108.509i	0.414886	−	0.718604i	−0.580530	−	0.814239i	$-0.697155\pi$
$151$	62.6478	−	108.509i	0.414886	−	0.718604i	0.995417	+	0.0956344i	$0.0304880\pi$
$152$	−29.5173	−	51.1254i	−0.194193	−	0.336352i
$153$	30.8212			0.201445
$154$	80.5486	+	70.6343i	0.523043	+	0.458665i
$155$		0			0
$156$	−33.3792	−	57.8144i	−0.213969	−	0.370605i
$157$	2.66684	−	4.61909i	0.0169862	−	0.0294210i	−0.857407	−	0.514638i	$-0.827926\pi$
$157$	2.66684	−	4.61909i	0.0169862	−	0.0294210i	0.874394	+	0.485217i	$0.161260\pi$
$158$	−110.326	−	63.6967i	−0.698266	−	0.403144i
$159$	−7.42593	+	4.28736i	−0.0467040	+	0.0269646i
$160$		0			0
$161$	−28.7752	+	144.689i	−0.178728	+	0.898686i
$162$			12.7279i			0.0785674i
$163$	207.193	−	119.623i	1.27112	−	0.733883i	0.295923	−	0.955212i	$-0.404373\pi$
$163$	207.193	−	119.623i	1.27112	−	0.733883i	0.975199	+	0.221329i	$0.0710394\pi$
$164$	39.4399	+	22.7706i	0.240487	+	0.138845i
$165$		0			0
$166$	123.754	−	71.4497i	0.745509	−	0.430420i
$167$	310.440			1.85892			0.929462	−	0.368918i	$-0.120272\pi$
$167$	310.440			1.85892			0.929462	+	0.368918i	$0.120272\pi$
$168$	32.4726	−	11.0242i	0.193289	−	0.0656202i
$169$	202.390			1.19757
$170$		0			0
$171$	−54.2267	−	31.3078i	−0.317115	−	0.183087i
$172$	−83.8844	−	48.4307i	−0.487700	−	0.281574i
$173$	45.4539	+	78.7285i	0.262739	+	0.455078i	0.966969	−	0.254894i	$-0.0820407\pi$
$173$	45.4539	+	78.7285i	0.262739	+	0.455078i	−0.704230	+	0.709972i	$0.748707\pi$
$174$			46.7579i			0.268723i
$175$		0			0
$176$	−43.2879			−0.245954
$177$	42.2802	−	24.4105i	0.238871	−	0.137912i
$178$	−28.0121	+	48.5184i	−0.157371	+	0.272575i
$179$	−121.577	+	210.577i	−0.679200	+	1.17641i	0.296022	+	0.955181i	$0.404340\pi$
$179$	−121.577	+	210.577i	−0.679200	+	1.17641i	−0.975222	+	0.221228i	$0.928993\pi$
$180$		0			0
$181$		−	245.993i		−	1.35907i	−0.733641	−	0.679537i	$-0.762181\pi$
$181$		−	245.993i		−	1.35907i	0.733641	−	0.679537i	$-0.237819\pi$
$182$	−37.2125	+	187.113i	−0.204464	+	1.02810i
$183$			121.398i			0.663375i
$184$	−29.8040	−	51.6220i	−0.161978	−	0.280554i
$185$		0			0
$186$	−49.0105	+	84.8886i	−0.263497	+	0.456390i
$187$	55.5910	+	96.2864i	0.297278	+	0.514901i
$188$	−133.076			−0.707851
$189$	23.9815	−	27.3475i	0.126886	−	0.144696i
$190$		0			0
$191$	20.6108	+	35.6989i	0.107910	+	0.186905i	0.914923	−	0.403628i	$-0.132251\pi$
$191$	20.6108	+	35.6989i	0.107910	+	0.186905i	−0.807014	+	0.590533i	$0.798918\pi$
$192$	−6.92820	+	12.0000i	−0.0360844	+	0.0625000i
$193$	164.324	+	94.8727i	0.851422	+	0.491568i	0.861130	−	0.508384i	$-0.169757\pi$
$193$	164.324	+	94.8727i	0.851422	+	0.491568i	−0.00970872	+	0.999953i	$0.503090\pi$
$194$	84.1331	−	48.5743i	0.433676	−	0.250383i
$195$		0			0
$196$	−90.5428	−	37.4967i	−0.461953	−	0.191310i
$197$			362.318i			1.83918i	0.392882	+	0.919589i	$0.371478\pi$
$197$			362.318i			1.83918i	−0.392882	+	0.919589i	$0.628522\pi$
$198$	−39.7625	+	22.9569i	−0.200821	+	0.115944i
$199$	33.4433	+	19.3085i	0.168057	+	0.0970278i	0.581669	−	0.813425i	$-0.302400\pi$
$199$	33.4433	+	19.3085i	0.168057	+	0.0970278i	−0.413612	+	0.910453i	$0.635733\pi$
$200$		0			0
$201$	28.9586	−	16.7193i	0.144073	−	0.0831804i
$202$	−11.3689			−0.0562816
$203$	88.0995	−	100.465i	0.433987	−	0.494902i
$204$	35.5892			0.174457
$205$		0			0
$206$	250.540	+	144.649i	1.21621	+	0.702180i
$207$	−54.7534	−	31.6119i	−0.264509	−	0.152714i
$208$	−38.5430	−	66.7584i	−0.185303	−	0.320954i
$209$		−	225.875i		−	1.08074i
$210$		0			0
$211$	−136.551			−0.647163			−0.323581	−	0.946200i	$-0.604887\pi$
$211$	−136.551			−0.647163			−0.323581	+	0.946200i	$0.604887\pi$
$212$	−8.57473	+	4.95062i	−0.0404468	+	0.0233520i
$213$	42.8655	−	74.2452i	0.201246	−	0.348569i
$214$	−116.357	+	201.537i	−0.543725	+	0.941760i
$215$		0			0
$216$			14.6969i			0.0680414i
$217$	265.249	−	90.0502i	1.22235	−	0.414978i
$218$			111.737i			0.512556i
$219$	−115.159	−	199.461i	−0.525841	−	0.910783i
$220$		0			0
$221$	−98.9949	+	171.464i	−0.447941	+	0.775856i
$222$	−61.6848	−	106.841i	−0.277859	−	0.481266i
$223$	−154.949			−0.694839			−0.347419	−	0.937710i	$-0.612942\pi$
$223$	−154.949			−0.694839			−0.347419	+	0.937710i	$0.612942\pi$
$224$	37.4961	−	12.7296i	0.167393	−	0.0568288i
$225$		0			0
$226$	59.7993	+	103.575i	0.264599	+	0.458299i
$227$	11.1769	−	19.3590i	0.0492375	−	0.0852818i	−0.840356	−	0.542034i	$-0.817654\pi$
$227$	11.1769	−	19.3590i	0.0492375	−	0.0852818i	0.889594	+	0.456753i	$0.150988\pi$
$228$	−62.6156	−	36.1511i	−0.274630	−	0.158558i
$229$	−25.9105	+	14.9594i	−0.113146	+	0.0653250i	−0.555505	−	0.831513i	$-0.687475\pi$
$229$	−25.9105	+	14.9594i	−0.113146	+	0.0653250i	0.442359	+	0.896838i	$0.354142\pi$
$230$		0			0
$231$	128.689	+	25.5933i	0.557096	+	0.110793i
$232$			53.9913i			0.232721i
$233$	−219.176	+	126.541i	−0.940669	+	0.543095i	−0.890170	−	0.455629i	$-0.849414\pi$
$233$	−219.176	+	126.541i	−0.940669	+	0.543095i	−0.0504987	+	0.998724i	$0.516081\pi$
$234$	−70.8079	−	40.8810i	−0.302598	−	0.174705i
$235$		0			0
$236$	48.8209	−	28.1868i	0.206868	−	0.119436i
$237$	−156.024			−0.658331
$238$	−76.4679	−	67.0559i	−0.321294	−	0.281747i
$239$	−121.009			−0.506315			−0.253158	−	0.967425i	$-0.581469\pi$
$239$	−121.009			−0.506315			−0.253158	+	0.967425i	$0.581469\pi$
$240$		0			0
$241$	249.755	+	144.196i	1.03633	+	0.598323i	0.918791	−	0.394745i	$-0.129167\pi$
$241$	249.755	+	144.196i	1.03633	+	0.598323i	0.117536	+	0.993069i	$0.462501\pi$
$242$	4.75789	+	2.74697i	0.0196607	+	0.0113511i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			140.178i			0.574499i
$245$		0			0
$246$	55.7765			0.226734
$247$	348.343	−	201.116i	1.41030	−	0.814234i
$248$	−56.5924	+	98.0209i	−0.228195	+	0.395246i
$249$	87.5076	−	151.568i	0.351436	−	0.608706i
$250$		0			0
$251$			422.260i			1.68231i	0.540795	+	0.841155i	$0.318124\pi$
$251$			422.260i			1.68231i	−0.540795	+	0.841155i	$0.681876\pi$
$252$	27.6914	−	31.5782i	0.109887	−	0.125310i
$253$		−	228.069i		−	0.901457i
$254$	71.9672	+	124.651i	0.283335	+	0.490751i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−37.2435	−	64.5077i	−0.144916	−	0.251003i	0.784425	−	0.620223i	$-0.212958\pi$
$257$	−37.2435	−	64.5077i	−0.144916	−	0.251003i	−0.929342	+	0.369221i	$0.879625\pi$
$258$	−118.630			−0.459808
$259$	−68.7687	+	345.786i	−0.265516	+	1.33508i
$260$		0			0
$261$	28.6332	+	49.5942i	0.109706	+	0.190016i
$262$	49.9911	−	86.5872i	0.190806	−	0.330486i
$263$	−271.304	−	156.637i	−1.03157	−	0.595579i	−0.114139	−	0.993465i	$-0.536411\pi$
$263$	−271.304	−	156.637i	−1.03157	−	0.595579i	−0.917435	+	0.397885i	$0.869744\pi$
$264$	−45.9138	+	26.5083i	−0.173916	+	0.100410i
$265$		0			0
$266$	66.4229	+	195.653i	0.249710	+	0.735539i
$267$			68.6153i			0.256986i
$268$	33.4385	−	19.3057i	0.124771	−	0.0720363i
$269$	138.011	+	79.6809i	0.513053	+	0.296211i	0.734088	−	0.679055i	$-0.237610\pi$
$269$	138.011	+	79.6809i	0.513053	+	0.296211i	−0.221035	+	0.975266i	$0.570943\pi$
$270$		0			0
$271$	−163.041	+	94.1320i	−0.601629	+	0.347350i	−0.769682	−	0.638427i	$-0.779585\pi$
$271$	−163.041	+	94.1320i	−0.601629	+	0.347350i	0.168053	+	0.985778i	$0.446252\pi$
$272$	41.0949			0.151084
$273$	75.1133	+	221.252i	0.275140	+	0.810446i
$274$	−166.633			−0.608151
$275$		0			0
$276$	−63.2238	−	36.5023i	−0.229072	−	0.132255i
$277$	6.10326	+	3.52372i	0.0220334	+	0.0127210i	0.510976	−	0.859595i	$-0.329284\pi$
$277$	6.10326	+	3.52372i	0.0220334	+	0.0127210i	−0.488943	+	0.872316i	$0.662617\pi$
$278$	112.081	+	194.130i	0.403170	+	0.698311i
$279$			120.051i			0.430289i
$280$		0			0
$281$	198.386			0.705998			0.352999	−	0.935624i	$-0.385162\pi$
$281$	198.386			0.705998			0.352999	+	0.935624i	$0.385162\pi$
$282$	−141.148	+	81.4920i	−0.500526	+	0.288979i
$283$	94.5641	−	163.790i	0.334149	−	0.578763i	−0.649172	−	0.760641i	$-0.724885\pi$
$283$	94.5641	−	163.790i	0.334149	−	0.578763i	0.983321	+	0.181879i	$0.0582179\pi$
$284$	49.4968	−	85.7309i	0.174284	−	0.301869i
$285$		0			0
$286$		−	294.942i		−	1.03127i
$287$	−119.843	−	105.092i	−0.417571	−	0.366174i
$288$			16.9706i			0.0589256i
$289$	91.7253	+	158.873i	0.317389	+	0.549733i
$290$		0			0
$291$	59.4911	−	103.042i	0.204437	−	0.354095i
$292$	−132.974	−	230.318i	−0.455391	−	0.788761i
$293$	−486.090			−1.65901			−0.829505	−	0.558499i	$-0.811378\pi$
$293$	−486.090			−1.65901			−0.829505	+	0.558499i	$0.811378\pi$
$294$	−118.997	+	15.6746i	−0.404752	+	0.0533150i
$295$		0			0
$296$	−71.2274	−	123.370i	−0.240633	−	0.416789i
$297$	−28.1163	+	48.6989i	−0.0946678	+	0.163969i
$298$	−362.397	−	209.230i	−1.21610	−	0.702115i
$299$	351.726	−	203.069i	1.17634	−	0.679161i
$300$		0			0
$301$	254.892	+	223.519i	0.846818	+	0.742588i
$302$		−	177.195i		−	0.586738i
$303$	−12.0585	+	6.96199i	−0.0397971	+	0.0229769i
$304$	−72.3023	−	41.7437i	−0.237836	−	0.137315i
$305$		0			0
$306$	37.7481	−	21.7939i	0.123360	−	0.0712217i
$307$	427.589			1.39280			0.696399	−	0.717655i	$-0.254784\pi$
$307$	427.589			1.39280			0.696399	+	0.717655i	$0.254784\pi$
$308$	148.598	+	29.5526i	0.482460	+	0.0959499i
$309$	354.317			1.14666
$310$		0			0
$311$	−311.852	−	180.048i	−1.00274	−	0.578931i	−0.0936811	−	0.995602i	$-0.529863\pi$
$311$	−311.852	−	180.048i	−1.00274	−	0.578931i	−0.909057	+	0.416671i	$0.863197\pi$
$312$	−81.7620	−	47.2053i	−0.262058	−	0.151299i
$313$	291.964	+	505.696i	0.932792	+	1.61564i	0.778525	+	0.627614i	$0.215968\pi$
$313$	291.964	+	505.696i	0.932792	+	1.61564i	0.154267	+	0.988029i	$0.450698\pi$
$314$		−	7.54295i		−	0.0240221i
$315$		0			0
$316$	−180.162			−0.570132
$317$	−312.982	+	180.700i	−0.987324	+	0.570032i	−0.904473	−	0.426530i	$-0.859736\pi$
$317$	−312.982	+	180.700i	−0.987324	+	0.570032i	−0.0828508	+	0.996562i	$0.526403\pi$
$318$	−6.06325	+	10.5019i	−0.0190668	+	0.0330247i
$319$	−103.289	+	178.902i	−0.323791	+	0.560823i
$320$		0			0
$321$			285.016i			0.887899i
$322$	67.0680	+	197.554i	0.208286	+	0.613521i
$323$			214.432i			0.663875i
$324$	9.00000	+	15.5885i	0.0277778	+	0.0481125i
$325$		0			0
$326$	169.172	−	293.015i	0.518934	−	0.898819i
$327$	68.4247	+	118.515i	0.209250	+	0.362432i
$328$	64.4051			0.196357
$329$	456.819	+	90.8507i	1.38851	+	0.276142i
$330$		0			0
$331$	−147.993	−	256.331i	−0.447108	−	0.774415i	0.551088	−	0.834447i	$-0.314213\pi$
$331$	−147.993	−	256.331i	−0.447108	−	0.774415i	−0.998196	+	0.0600326i	$0.980880\pi$
$332$	101.045	−	175.015i	0.304353	−	0.527154i
$333$	−130.853	−	75.5481i	−0.392952	−	0.226871i
$334$	380.210	−	219.514i	1.13835	−	0.657229i
$335$		0			0
$336$	31.9753	−	36.4634i	0.0951646	−	0.108522i
$337$			22.0162i			0.0653300i	0.999466	+	0.0326650i	$0.0103994\pi$
$337$			22.0162i			0.0653300i	−0.999466	+	0.0326650i	$0.989601\pi$
$338$	247.876	−	143.111i	0.733361	−	0.423406i
$339$	126.854	+	73.2389i	0.374199	+	0.216044i
$340$		0			0
$341$	−375.043	+	216.531i	−1.09983	+	0.634988i
$342$	−88.5519			−0.258924
$343$	285.214	+	190.531i	0.831527	+	0.555484i
$344$	−136.983			−0.398205
$345$		0			0
$346$	111.339	+	64.2815i	0.321789	+	0.185785i
$347$	−245.870	−	141.953i	−0.708559	−	0.409086i	0.101969	−	0.994788i	$-0.467486\pi$
$347$	−245.870	−	141.953i	−0.708559	−	0.409086i	−0.810527	+	0.585701i	$0.800819\pi$
$348$	33.0628	+	57.2665i	0.0950080	+	0.164559i
$349$			317.175i			0.908811i	0.890795	+	0.454406i	$0.150148\pi$
$349$			317.175i			0.908811i	−0.890795	+	0.454406i	$0.849852\pi$
$350$		0			0
$351$	−100.138			−0.285292
$352$	−53.0166	+	30.6092i	−0.150615	+	0.0869579i
$353$	58.4712	−	101.275i	0.165641	−	0.286898i	−0.771242	−	0.636542i	$-0.780364\pi$
$353$	58.4712	−	101.275i	0.165641	−	0.286898i	0.936883	+	0.349644i	$0.113697\pi$
$354$	34.5216	−	59.7932i	0.0975187	−	0.168907i
$355$		0			0
$356$			79.2302i			0.222557i
$357$	−122.170	−	24.2967i	−0.342212	−	0.0680579i
$358$			343.871i			0.960534i
$359$	116.793	+	202.291i	0.325329	+	0.563486i	0.981579	−	0.191058i	$-0.0611918\pi$
$359$	116.793	+	202.291i	0.325329	+	0.563486i	−0.656250	+	0.754543i	$0.727858\pi$
$360$		0			0
$361$	37.3175	−	64.6359i	0.103373	−	0.179047i
$362$	−173.943	−	301.278i	−0.480505	−	0.832260i
$363$	6.72867			0.0185363
$364$	86.7334	+	255.479i	0.238279	+	0.701866i
$365$		0			0
$366$	85.8410	+	148.681i	0.234538	+	0.406232i
$367$	256.037	−	443.469i	0.697648	−	1.20836i	−0.271632	−	0.962401i	$-0.587563\pi$
$367$	256.037	−	443.469i	0.697648	−	1.20836i	0.969280	−	0.245960i	$-0.0791033\pi$
$368$	−73.0045	−	42.1492i	−0.198382	−	0.114536i
$369$	59.1599	−	34.1560i	0.160325	−	0.0925636i
$370$		0			0
$371$	32.8149	−	11.1404i	0.0884498	−	0.0300280i
$372$			138.623i			0.372641i
$373$	−481.863	+	278.204i	−1.29186	+	0.745854i	−0.978983	−	0.203941i	$-0.934625\pi$
$373$	−481.863	+	278.204i	−1.29186	+	0.745854i	−0.312874	+	0.949795i	$0.601292\pi$
$374$	136.170	+	78.6175i	0.364090	+	0.210207i
$375$		0			0
$376$	−162.984	+	94.0989i	−0.433468	+	0.250263i
$377$	−367.870			−0.975782
$378$	10.0336	−	50.4512i	0.0265438	−	0.133469i
$379$	536.301			1.41504			0.707521	−	0.706692i	$-0.249813\pi$
$379$	536.301			1.41504			0.707521	+	0.706692i	$0.249813\pi$
$380$		0			0
$381$	152.665	+	88.1414i	0.400697	+	0.231342i
$382$	50.4859	+	29.1480i	0.132162	+	0.0763038i
$383$	14.6753	+	25.4184i	0.0383168	+	0.0663666i	0.884548	−	0.466450i	$-0.154467\pi$
$383$	14.6753	+	25.4184i	0.0383168	+	0.0663666i	−0.846231	+	0.532816i	$0.821134\pi$
$384$			19.5959i			0.0510310i
$385$		0			0
$386$	268.341			0.695183
$387$	−125.827	+	72.6460i	−0.325133	+	0.187716i
$388$	68.6944	−	118.982i	0.177047	−	0.306655i
$389$	−349.242	+	604.905i	−0.897795	+	1.55503i	−0.0674875	+	0.997720i	$0.521498\pi$
$389$	−349.242	+	604.905i	−0.897795	+	1.55503i	−0.830307	+	0.557306i	$0.811835\pi$
$390$		0			0
$391$			216.514i			0.553745i
$392$	−137.406	+	18.0995i	−0.350526	+	0.0461721i
$393$		−	122.453i		−	0.311585i
$394$	256.198	+	443.747i	0.650248	+	1.12626i
$395$		0			0
$396$	−32.4659	+	56.2326i	−0.0819847	+	0.142002i
$397$	102.347	+	177.270i	0.257801	+	0.446525i	0.965653	−	0.259837i	$-0.0836687\pi$
$397$	102.347	+	177.270i	0.257801	+	0.446525i	−0.707851	+	0.706361i	$0.750335\pi$
$398$	54.6127			0.137218
$399$	190.265	+	166.846i	0.476854	+	0.418161i
$400$		0			0
$401$	−214.984	−	372.363i	−0.536119	−	0.928585i	−0.999108	−	0.0422215i	$-0.986556\pi$
$401$	−214.984	−	372.363i	−0.536119	−	0.928585i	0.462989	−	0.886364i	$-0.346777\pi$
$402$	23.6446	−	40.9537i	0.0588174	−	0.101875i
$403$	−667.865	−	385.592i	−1.65723	−	0.956805i
$404$	−13.9240	+	8.03902i	−0.0344653	+	0.0198986i
$405$		0			0
$406$	36.8598	−	185.340i	0.0907876	−	0.456502i
$407$		−	545.053i		−	1.33920i
$408$	43.5877	−	25.1654i	0.106833	−	0.0616798i
$409$	−15.3567	−	8.86618i	−0.0375469	−	0.0216777i	0.481109	−	0.876661i	$-0.340234\pi$
$409$	−15.3567	−	8.86618i	−0.0375469	−	0.0216777i	−0.518656	+	0.854983i	$0.673567\pi$
$410$		0			0
$411$	−176.741	+	102.042i	−0.430027	+	0.248276i
$412$	409.129			0.993033
$413$	−186.834	+	63.4289i	−0.452383	+	0.153581i
$414$	−89.4119			−0.215971
$415$		0			0
$416$	−94.4106	−	54.5080i	−0.226948	−	0.131029i
$417$	237.760	+	137.271i	0.570168	+	0.329187i
$418$	−159.718	−	276.639i	−0.382100	−	0.661816i
$419$			440.768i			1.05195i	0.850499	+	0.525977i	$0.176300\pi$
$419$			440.768i			1.05195i	−0.850499	+	0.525977i	$0.823700\pi$
$420$		0			0
$421$	−143.012			−0.339696			−0.169848	−	0.985470i	$-0.554328\pi$
$421$	−143.012			−0.339696			−0.169848	+	0.985470i	$0.554328\pi$
$422$	−167.241	+	96.5564i	−0.396305	+	0.228807i
$423$	−99.8070	+	172.871i	−0.235950	+	0.408678i
$424$	−7.00124	+	12.1265i	−0.0165123	+	0.0286002i
$425$		0			0
$426$		−	121.242i		−	0.284605i
$427$	95.6991	−	481.199i	0.224120	−	1.12693i
$428$			329.108i			0.768943i
$429$	−180.614	−	312.833i	−0.421012	−	0.729215i
$430$		0			0
$431$	391.608	−	678.285i	0.908604	−	1.57375i	0.0925988	−	0.995704i	$-0.470483\pi$
$431$	391.608	−	678.285i	0.908604	−	1.57375i	0.816005	−	0.578045i	$-0.196184\pi$
$432$	10.3923	+	18.0000i	0.0240563	+	0.0416667i
$433$	286.669			0.662053			0.331026	−	0.943622i	$-0.392605\pi$
$433$	286.669			0.662053			0.331026	+	0.943622i	$0.392605\pi$
$434$	261.188	−	297.848i	0.601815	−	0.686286i
$435$		0			0
$436$	79.0101	+	136.849i	0.181216	+	0.313875i
$437$	219.933	−	380.935i	0.503279	−	0.871705i
$438$	−282.081	−	162.860i	−0.644021	−	0.371826i
$439$	295.016	−	170.328i	0.672018	−	0.387990i	−0.124823	−	0.992179i	$-0.539836\pi$
$439$	295.016	−	170.328i	0.672018	−	0.387990i	0.796841	+	0.604189i	$0.206503\pi$
$440$		0			0
$441$	−116.617	+	89.4960i	−0.264437	+	0.202939i
$442$			280.000i			0.633484i
$443$	342.304	−	197.629i	0.772696	−	0.446116i	−0.0611396	−	0.998129i	$-0.519473\pi$
$443$	342.304	−	197.629i	0.772696	−	0.446116i	0.833835	+	0.552013i	$0.186140\pi$
$444$	−151.096	−	87.2354i	−0.340307	−	0.196476i
$445$		0			0
$446$	−189.773	+	109.566i	−0.425500	+	0.245663i
$447$	−512.507			−1.14655
$448$	36.9219	−	42.1043i	0.0824150	−	0.0939828i
$449$	−665.078			−1.48124			−0.740621	−	0.671923i	$-0.765469\pi$
$449$	−665.078			−1.48124			−0.740621	+	0.671923i	$0.765469\pi$
$450$		0			0
$451$	213.409	+	123.212i	0.473190	+	0.273197i
$452$	146.478	+	84.5690i	0.324066	+	0.187100i
$453$	−108.509	−	187.944i	−0.239535	−	0.414886i
$454$		−	31.6131i		−	0.0696323i
$455$		0			0
$456$	−102.251			−0.224234
$457$	−442.484	+	255.468i	−0.968236	+	0.559012i	−0.898698	−	0.438568i	$-0.855486\pi$
$457$	−442.484	+	255.468i	−0.968236	+	0.559012i	−0.0695382	+	0.997579i	$0.522153\pi$
$458$	−21.1558	+	36.6429i	−0.0461917	+	0.0800064i
$459$	26.6919	−	46.2317i	0.0581523	−	0.100723i
$460$		0			0
$461$			174.303i			0.378097i	0.981968	+	0.189049i	$0.0605404\pi$
$461$			174.303i			0.378097i	−0.981968	+	0.189049i	$0.939460\pi$
$462$	175.709	−	59.6518i	0.380322	−	0.129116i
$463$			755.187i			1.63107i	0.578705	+	0.815537i	$0.303558\pi$
$463$			755.187i			1.63107i	−0.578705	+	0.815537i	$0.696442\pi$
$464$	38.1776	+	66.1256i	0.0822794	+	0.142512i
$465$		0			0
$466$	−178.956	+	309.961i	−0.384026	+	0.665153i
$467$	283.286	+	490.666i	0.606609	+	1.05068i	0.991795	+	0.127839i	$0.0408039\pi$
$467$	283.286	+	490.666i	0.606609	+	1.05068i	−0.385186	+	0.922839i	$0.625863\pi$
$468$	−115.629			−0.247070
$469$	−127.967	+	43.4438i	−0.272850	+	0.0926307i
$470$		0			0
$471$	−4.61909	−	8.00051i	−0.00980699	−	0.0169862i
$472$	39.8621	−	69.0432i	0.0844537	−	0.146278i
$473$	−453.897	−	262.058i	−0.959614	−	0.554033i
$474$	−191.090	+	110.326i	−0.403144	+	0.232755i
$475$		0			0
$476$	−141.069	−	28.0554i	−0.296364	−	0.0589399i
$477$			14.8519i			0.0311360i
$478$	−148.206	+	85.5665i	−0.310053	+	0.179009i
$479$	−445.286	−	257.086i	−0.929615	−	0.536714i	−0.0429255	−	0.999078i	$-0.513668\pi$
$479$	−445.286	−	257.086i	−0.929615	−	0.536714i	−0.886690	+	0.462365i	$0.847001\pi$
$480$		0			0
$481$	840.578	−	485.308i	1.74756	−	1.00896i
$482$	407.848			0.846157
$483$	192.113	+	168.467i	0.397749	+	0.348792i
$484$	7.76960			0.0160529
$485$		0			0
$486$	19.0919	+	11.0227i	0.0392837	+	0.0226805i
$487$	283.473	+	163.663i	0.582081	+	0.336064i	0.761960	−	0.647624i	$-0.224237\pi$
$487$	283.473	+	163.663i	0.582081	+	0.336064i	−0.179879	+	0.983689i	$0.557571\pi$
$488$	99.1207	+	171.682i	0.203116	+	0.351808i
$489$		−	414.386i		−	0.847415i
$490$		0			0
$491$	−41.8889			−0.0853134			−0.0426567	−	0.999090i	$-0.513582\pi$
$491$	−41.8889			−0.0853134			−0.0426567	+	0.999090i	$0.513582\pi$
$492$	68.3119	−	39.4399i	0.138845	−	0.0801624i
$493$	98.0566	−	169.839i	0.198898	−	0.344501i
$494$	284.421	−	492.631i	0.575751	−	0.997229i
$495$		0			0
$496$			160.068i			0.322717i
$497$	−228.439	+	260.503i	−0.459637	+	0.524152i
$498$		−	247.509i		−	0.497006i
$499$	207.685	+	359.721i	0.416203	+	0.720885i	0.995554	−	0.0941936i	$-0.0300273\pi$
$499$	207.685	+	359.721i	0.416203	+	0.720885i	−0.579351	+	0.815078i	$0.696694\pi$
$500$		0			0
$501$	268.849	−	465.660i	0.536625	−	0.929462i
$502$	298.583	+	517.160i	0.594786	+	1.03020i
$503$	−51.7604			−0.102903			−0.0514517	−	0.998675i	$-0.516385\pi$
$503$	−51.7604			−0.102903			−0.0514517	+	0.998675i	$0.516385\pi$
$504$	11.5858	−	58.2561i	0.0229876	−	0.115587i
$505$		0			0
$506$	−161.269	−	279.326i	−0.318713	−	0.552028i
$507$	175.275	−	303.585i	0.345709	−	0.598786i
$508$	176.283	+	101.777i	0.347014	+	0.200348i
$509$	−136.916	+	79.0486i	−0.268991	+	0.155302i	−0.628429	−	0.777867i	$-0.716302\pi$
$509$	−136.916	+	79.0486i	−0.268991	+	0.155302i	0.359438	+	0.933169i	$0.382968\pi$
$510$		0			0
$511$	299.233	+	881.411i	0.585583	+	1.72488i
$512$			22.6274i			0.0441942i
$513$	−93.9234	+	54.2267i	−0.183087	+	0.105705i
$514$	−91.2276	−	52.6703i	−0.177486	−	0.102471i
$515$		0			0
$516$	−145.292	+	83.8844i	−0.281574	+	0.162567i
$517$	−720.073			−1.39279
$518$	160.283	+	472.126i	0.309428	+	0.911441i
$519$	157.457			0.303385
$520$		0			0
$521$	306.214	+	176.793i	0.587744	+	0.339334i	0.764205	−	0.644974i	$-0.223132\pi$
$521$	306.214	+	176.793i	0.587744	+	0.339334i	−0.176461	+	0.984308i	$0.556465\pi$
$522$	70.1368	+	40.4935i	0.134362	+	0.0775737i
$523$	−59.7756	−	103.534i	−0.114294	−	0.197962i	0.803204	−	0.595705i	$-0.203127\pi$
$523$	−59.7756	−	103.534i	−0.114294	−	0.197962i	−0.917497	+	0.397742i	$0.869794\pi$
$524$		−	141.396i		−	0.269840i
$525$		0			0
$526$	−443.037			−0.842277
$527$	356.042	−	205.561i	0.675602	−	0.390059i
$528$	−37.4884	+	64.9319i	−0.0710008	+	0.122977i
$529$	−42.4308	+	73.4924i	−0.0802095	+	0.138927i
$530$		0			0
$531$		−	84.5604i		−	0.159247i
$532$	219.699	+	192.657i	0.412968	+	0.362138i
$533$			438.824i			0.823309i
$534$	48.5184	+	84.0363i	0.0908584	+	0.157371i
$535$		0			0
$536$	27.3024	−	47.2892i	0.0509374	−	0.0882261i
$537$	210.577	+	364.731i	0.392136	+	0.679200i
$538$	225.372			0.418906
$539$	−489.926	−	202.894i	−0.908954	−	0.376427i
$540$		0			0
$541$	−272.691	−	472.315i	−0.504051	−	0.873041i	−0.999989	−	0.00468349i	$-0.998509\pi$
$541$	−272.691	−	472.315i	−0.504051	−	0.873041i	0.495938	−	0.868358i	$-0.334824\pi$
$542$	−133.123	+	230.575i	−0.245614	+	0.425416i
$543$	−368.989	−	213.036i	−0.679537	−	0.392331i
$544$	50.3307	−	29.0585i	0.0925197	−	0.0534163i
$545$		0			0
$546$	248.443	+	217.864i	0.455024	+	0.399018i
$547$			117.783i			0.215325i	0.994188	+	0.107663i	$0.0343366\pi$
$547$			117.783i			0.215325i	−0.994188	+	0.107663i	$0.965663\pi$
$548$	−204.083	+	117.828i	−0.372415	+	0.215014i
$549$	182.096	+	105.133i	0.331687	+	0.191500i
$550$		0			0
$551$	−345.041	+	199.210i	−0.626209	+	0.361542i
$552$	−103.244			−0.187036
$553$	618.454	+	122.996i	1.11836	+	0.222416i
$554$	9.96659			0.0179902
$555$		0			0
$556$	274.542	+	158.507i	0.493780	+	0.285084i
$557$	−533.028	−	307.744i	−0.956963	−	0.552503i	−0.0617258	−	0.998093i	$-0.519660\pi$
$557$	−533.028	−	307.744i	−0.956963	−	0.552503i	−0.895237	+	0.445590i	$0.852994\pi$
$558$	84.8886	+	147.031i	0.152130	+	0.263497i
$559$		−	933.330i		−	1.66964i
$560$		0			0
$561$	192.573			0.343267
$562$	242.972	−	140.280i	0.432334	−	0.249608i
$563$	239.628	−	415.047i	0.425626	−	0.737207i	−0.570852	−	0.821053i	$-0.693387\pi$
$563$	239.628	−	415.047i	0.425626	−	0.737207i	0.996479	+	0.0838462i	$0.0267205\pi$
$564$	−115.247	+	199.614i	−0.204339	+	0.353925i
$565$		0			0
$566$		−	267.468i		−	0.472558i
$567$	−20.2527	−	59.6559i	−0.0357191	−	0.105213i
$568$		−	139.998i		−	0.246475i
$569$	−228.674	−	396.074i	−0.401887	−	0.696088i	0.592067	−	0.805889i	$-0.298312\pi$
$569$	−228.674	−	396.074i	−0.401887	−	0.696088i	−0.993954	+	0.109800i	$0.964979\pi$
$570$		0			0
$571$	−186.601	+	323.203i	−0.326797	+	0.566029i	−0.981874	−	0.189532i	$-0.939303\pi$
$571$	−186.601	+	323.203i	−0.326797	+	0.566029i	0.655077	+	0.755562i	$0.272636\pi$
$572$	−208.555	−	361.229i	−0.364607	−	0.631519i
$573$	71.3978			0.124604
$574$	−221.088	−	43.9692i	−0.385171	−	0.0766014i
$575$		0			0
$576$	12.0000	+	20.7846i	0.0208333	+	0.0360844i
$577$	−445.777	+	772.108i	−0.772577	+	1.33814i	0.163569	+	0.986532i	$0.447699\pi$
$577$	−445.777	+	772.108i	−0.772577	+	1.33814i	−0.936146	+	0.351611i	$0.885634\pi$
$578$	224.680	+	129.719i	0.388720	+	0.224428i
$579$	284.618	−	164.324i	0.491568	−	0.283807i
$580$		0			0
$581$	−466.347	+	531.804i	−0.802663	+	0.915326i
$582$		−	168.266i		−	0.289117i
$583$	−46.3978	+	26.7878i	−0.0795845	+	0.0459481i
$584$	−325.719	−	188.054i	−0.557738	−	0.322010i
$585$		0			0
$586$	−595.336	+	343.718i	−1.01593	+	0.586549i
$587$	786.758			1.34030			0.670151	−	0.742224i	$-0.266229\pi$
$587$	786.758			1.34030			0.670151	+	0.742224i	$0.266229\pi$
$588$	−134.657	+	103.341i	−0.229009	+	0.175750i
$589$	−835.227			−1.41804
$590$		0			0
$591$	543.477	+	313.777i	0.919589	+	0.530925i
$592$	−174.471	−	100.731i	−0.294714	−	0.170153i
$593$	−312.676	−	541.571i	−0.527278	−	0.913273i	−0.999495	−	0.0317903i	$-0.989879\pi$
$593$	−312.676	−	541.571i	−0.527278	−	0.913273i	0.472216	−	0.881483i	$-0.343454\pi$
$594$			79.5250i			0.133880i
$595$		0			0
$596$	−591.792			−0.992940
$597$	57.9256	−	33.4433i	0.0970278	−	0.0560190i
$598$	287.183	−	497.416i	0.480240	−	0.831799i
$599$	75.2476	−	130.333i	0.125622	−	0.217584i	−0.796354	−	0.604831i	$-0.793241\pi$
$599$	75.2476	−	130.333i	0.125622	−	0.217584i	0.921976	+	0.387247i	$0.126574\pi$
$600$		0			0
$601$		−	521.601i		−	0.867888i	−0.900940	−	0.433944i	$-0.857122\pi$
$601$		−	521.601i		−	0.867888i	0.900940	−	0.433944i	$-0.142878\pi$
$602$	470.230	+	93.5177i	0.781113	+	0.155345i
$603$		−	57.9172i		−	0.0960485i
$604$	−125.296	−	217.019i	−0.207443	−	0.359302i
$605$		0			0
$606$	−9.84575	+	17.0533i	−0.0162471	+	0.0281408i
$607$	348.375	+	603.404i	0.573930	+	0.994075i	0.996157	+	0.0875852i	$0.0279150\pi$
$607$	348.375	+	603.404i	0.573930	+	0.994075i	−0.422228	+	0.906490i	$0.638752\pi$
$608$	−118.069			−0.194193
$609$	−74.4014	−	219.155i	−0.122170	−	0.359860i
$610$		0			0
$611$	−641.143	−	1110.49i	−1.04933	−	1.81750i
$612$	30.8212	−	53.3838i	0.0503614	−	0.0872285i
$613$	−46.9809	−	27.1244i	−0.0766410	−	0.0442487i	0.461190	−	0.887302i	$-0.347423\pi$
$613$	−46.9809	−	27.1244i	−0.0766410	−	0.0442487i	−0.537831	+	0.843053i	$0.680756\pi$
$614$	523.687	−	302.351i	0.852911	−	0.492428i
$615$		0			0
$616$	202.891	−	68.8800i	0.329368	−	0.111818i
$617$			969.852i			1.57188i	0.618301	+	0.785941i	$0.287821\pi$
$617$			969.852i			1.57188i	−0.618301	+	0.785941i	$0.712179\pi$
$618$	433.947	−	250.540i	0.702180	−	0.405404i
$619$	111.240	+	64.2247i	0.179710	+	0.103756i	0.587156	−	0.809474i	$-0.300247\pi$
$619$	111.240	+	64.2247i	0.179710	+	0.103756i	−0.407446	+	0.913229i	$0.633581\pi$
$620$		0			0
$621$	−94.8357	+	54.7534i	−0.152714	+	0.0881697i
$622$	−509.252			−0.818733
$623$	54.0903	−	271.979i	0.0868223	−	0.436564i
$624$	−133.517			−0.213969
$625$		0			0
$626$	715.163	+	412.899i	1.14243	+	0.659584i
$627$	−338.812	−	195.613i	−0.540371	−	0.311983i
$628$	−5.33367	−	9.23819i	−0.00849311	−	0.0147105i
$629$			517.440i			0.822639i
$630$		0			0
$631$	115.457			0.182975			0.0914877	−	0.995806i	$-0.470838\pi$
$631$	115.457			0.182975			0.0914877	+	0.995806i	$0.470838\pi$
$632$	−220.652	+	127.393i	−0.349133	+	0.201572i
$633$	−118.257	+	204.827i	−0.186820	+	0.323581i
$634$	−255.549	+	442.623i	−0.403073	+	0.698144i
$635$		0			0
$636$			17.1495i			0.0269646i
$637$	−123.321	−	936.215i	−0.193596	−	1.46973i
$638$			292.146i			0.457910i
$639$	−74.2452	−	128.596i	−0.116190	−	0.201246i
$640$		0			0
$641$	476.249	−	824.887i	0.742978	−	1.28688i	−0.208156	−	0.978096i	$-0.566746\pi$
$641$	476.249	−	824.887i	0.742978	−	1.28688i	0.951134	−	0.308780i	$-0.0999206\pi$
$642$	201.537	+	349.072i	0.313920	+	0.543725i
$643$	−253.254			−0.393863			−0.196931	−	0.980417i	$-0.563098\pi$
$643$	−253.254			−0.393863			−0.196931	+	0.980417i	$0.563098\pi$
$644$	221.833	+	194.529i	0.344461	+	0.302063i
$645$		0			0
$646$	151.626	+	262.624i	0.234715	+	0.406539i
$647$	502.388	−	870.161i	0.776488	−	1.34492i	−0.157466	−	0.987524i	$-0.550332\pi$
$647$	502.388	−	870.161i	0.776488	−	1.34492i	0.933954	−	0.357393i	$-0.116334\pi$
$648$	22.0454	+	12.7279i	0.0340207	+	0.0196419i
$649$	264.170	−	152.518i	0.407041	−	0.235005i
$650$		0			0
$651$	94.6373	−	475.860i	0.145372	−	0.730967i
$652$		−	478.492i		−	0.733883i
$653$	922.831	−	532.797i	1.41322	−	0.815922i	0.417528	−	0.908664i	$-0.362897\pi$
$653$	922.831	−	532.797i	1.41322	−	0.815922i	0.995690	+	0.0927422i	$0.0295632\pi$
$654$	167.606	+	96.7672i	0.256278	+	0.147962i
$655$		0			0
$656$	78.8798	−	45.5413i	0.120244	−	0.0694227i
$657$	−398.923			−0.607189
$658$	623.728	−	211.751i	0.947915	−	0.321810i
$659$	−432.265			−0.655941			−0.327970	−	0.944688i	$-0.606365\pi$
$659$	−432.265			−0.655941			−0.327970	+	0.944688i	$0.606365\pi$
$660$		0			0
$661$	327.626	+	189.155i	0.495652	+	0.286165i	0.726916	−	0.686726i	$-0.240953\pi$
$661$	327.626	+	189.155i	0.495652	+	0.286165i	−0.231264	+	0.972891i	$0.574286\pi$
$662$	−362.507	−	209.294i	−0.547594	−	0.316153i
$663$	171.464	+	296.985i	0.258619	+	0.447941i
$664$		−	285.799i		−	0.430420i
$665$		0			0
$666$	−213.682			−0.320844
$667$	−348.392	+	201.144i	−0.522328	+	0.301566i
$668$	310.440	−	537.698i	0.464731	−	0.804937i
$669$	−134.190	+	232.424i	−0.200583	+	0.347419i
$670$		0			0
$671$			758.501i			1.13040i
$672$	13.3781	−	67.2683i	0.0199079	−	0.100102i
$673$		−	689.666i		−	1.02476i	−0.858758	−	0.512382i	$-0.828763\pi$
$673$		−	689.666i		−	1.02476i	0.858758	−	0.512382i	$-0.171237\pi$
$674$	15.5678	+	26.9642i	0.0230976	+	0.0400063i
$675$		0			0
$676$	202.390	−	350.549i	0.299393	−	0.518564i
$677$	−189.754	−	328.663i	−0.280286	−	0.485470i	0.691169	−	0.722693i	$-0.257096\pi$
$677$	−189.754	−	328.663i	−0.280286	−	0.485470i	−0.971455	+	0.237223i	$0.923763\pi$
$678$	207.151			0.305532
$679$	−317.041	+	361.541i	−0.466924	+	0.532461i
$680$		0			0
$681$	−19.3590	−	33.5307i	−0.0284273	−	0.0492375i
$682$	−306.221	+	530.390i	−0.449004	+	0.777698i
$683$	−647.360	−	373.753i	−0.947818	−	0.547223i	−0.0554159	−	0.998463i	$-0.517648\pi$
$683$	−647.360	−	373.753i	−0.947818	−	0.547223i	−0.892403	+	0.451240i	$0.850982\pi$
$684$	−108.453	+	62.6156i	−0.158558	+	0.0915433i
$685$		0			0
$686$	484.040	+	31.6754i	0.705598	+	0.0461740i
$687$			51.8209i			0.0754308i
$688$	−167.769	+	96.8613i	−0.243850	+	0.140787i
$689$	−82.6238	−	47.7029i	−0.119918	−	0.0692350i
$690$		0			0
$691$	771.026	−	445.152i	1.11581	−	0.644214i	0.175483	−	0.984482i	$-0.443851\pi$
$691$	771.026	−	445.152i	1.11581	−	0.644214i	0.940328	+	0.340268i	$0.110518\pi$
$692$	181.816			0.262739
$693$	149.838	−	170.869i	0.216217	−	0.246565i
$694$	−401.504			−0.578536
$695$		0			0
$696$	80.9870	+	46.7579i	0.116361	+	0.0671808i
$697$	−202.597	−	116.970i	−0.290670	−	0.167819i
$698$	224.277	+	388.459i	0.321313	+	0.556531i
$699$			438.352i			0.627112i
$700$		0			0
$701$	−650.703			−0.928250			−0.464125	−	0.885770i	$-0.653631\pi$
$701$	−650.703			−0.928250			−0.464125	+	0.885770i	$0.653631\pi$
$702$	−122.643	+	70.8079i	−0.174705	+	0.100866i
$703$	525.610	−	910.384i	0.747667	−	1.29500i
$704$	−43.2879	+	74.9769i	−0.0614885	+	0.106501i
$705$		0			0
$706$		−	165.382i		−	0.234251i
$707$	53.2861	−	18.0902i	0.0753693	−	0.0255873i
$708$		−	97.6419i		−	0.137912i
$709$	−196.427	−	340.222i	−0.277048	−	0.479862i	0.693602	−	0.720359i	$-0.256023\pi$
$709$	−196.427	−	340.222i	−0.277048	−	0.479862i	−0.970650	+	0.240497i	$0.922690\pi$
$710$		0			0
$711$	−135.121	+	234.037i	−0.190044	+	0.329166i
$712$	56.0242	+	97.0368i	0.0786857	+	0.136288i
$713$	−843.339			−1.18280
$714$	−166.807	+	56.6298i	−0.233623	+	0.0793134i
$715$		0			0
$716$	243.154	+	421.155i	0.339600	+	0.588205i
$717$	−104.797	+	181.514i	−0.146161	+	0.253158i
$718$	286.083	+	165.170i	0.398444	+	0.230042i
$719$	−899.919	+	519.569i	−1.25163	+	0.722627i	−0.971432	−	0.237317i	$-0.923732\pi$
$719$	−899.919	+	519.569i	−1.25163	+	0.722627i	−0.280194	+	0.959943i	$0.590399\pi$
$720$		0			0
$721$	−1404.45	−	279.312i	−1.94792	−	0.387395i
$722$		−	105.550i		−	0.146191i
$723$	432.588	−	249.755i	0.598323	−	0.345442i
$724$	−426.072	−	245.993i	−0.588497	−	0.339769i
$725$		0			0
$726$	8.24091	−	4.75789i	0.0113511	−	0.00655357i
$727$	−610.568			−0.839846			−0.419923	−	0.907560i	$-0.637943\pi$
$727$	−610.568			−0.839846			−0.419923	+	0.907560i	$0.637943\pi$
$728$	286.877	+	251.567i	0.394062	+	0.345559i
$729$	27.0000			0.0370370
$730$		0			0
$731$	430.902	+	248.781i	0.589469	+	0.340330i
$732$	210.267	+	121.398i	0.287250	+	0.165844i
$733$	539.576	+	934.574i	0.736121	+	1.27500i	0.954230	+	0.299074i	$0.0966777\pi$
$733$	539.576	+	934.574i	0.736121	+	1.27500i	−0.218109	+	0.975924i	$0.569989\pi$
$734$		−	724.181i		−	0.986623i
$735$		0			0
$736$	−119.216			−0.161978
$737$	180.935	−	104.463i	0.245503	−	0.141741i
$738$	48.3038	−	83.6647i	0.0654523	−	0.113367i
$739$	378.082	−	654.857i	0.511613	−	0.886139i	−0.488297	−	0.872678i	$-0.662382\pi$
$739$	378.082	−	654.857i	0.511613	−	0.886139i	0.999909	−	0.0134615i	$-0.00428507\pi$
$740$		0			0
$741$		−	696.686i		−	0.940197i
$742$	32.3124	−	36.8478i	0.0435477	−	0.0496601i
$743$			963.993i			1.29743i	0.761030	+	0.648717i	$0.224694\pi$
$743$			963.993i			1.29743i	−0.761030	+	0.648717i	$0.775306\pi$
$744$	98.0209	+	169.777i	0.131749	+	0.228195i
$745$		0			0
$746$	−393.439	+	681.457i	−0.527398	+	0.913481i
$747$	−151.568	−	262.523i	−0.202902	−	0.351436i
$748$	222.364			0.297278
$749$	224.681	−	1129.75i	0.299975	−	1.50835i
$750$		0			0
$751$	−416.806	−	721.929i	−0.555001	−	0.961290i	−0.997903	−	0.0647203i	$-0.979384\pi$
$751$	−416.806	−	721.929i	−0.555001	−	0.961290i	0.442902	−	0.896570i	$-0.353949\pi$
$752$	−133.076	+	230.494i	−0.176963	+	0.306508i
$753$	633.389	+	365.688i	0.841155	+	0.485641i
$754$	−450.547	+	260.123i	−0.597542	+	0.344991i
$755$		0			0
$756$	−23.3859	−	68.8847i	−0.0309337	−	0.0911173i
$757$			744.966i			0.984103i	0.870566	+	0.492051i	$0.163753\pi$
$757$			744.966i			0.984103i	−0.870566	+	0.492051i	$0.836247\pi$
$758$	656.832	−	379.222i	0.866533	−	0.500293i
$759$	−342.103	−	197.513i	−0.450729	−	0.260228i
$760$		0			0
$761$	−64.1518	+	37.0381i	−0.0842993	+	0.0486702i	−0.541557	−	0.840664i	$-0.682165\pi$
$761$	−64.1518	+	37.0381i	−0.0842993	+	0.0486702i	0.457258	+	0.889334i	$0.348832\pi$
$762$	249.302			0.327167
$763$	−177.797	−	523.713i	−0.233023	−	0.686387i
$764$	82.4431			0.107910
$765$		0			0
$766$	35.9471	+	20.7540i	0.0469283	+	0.0270941i
$767$	470.426	+	271.601i	0.613332	+	0.354108i
$768$	13.8564	+	24.0000i	0.0180422	+	0.0312500i
$769$		−	961.553i		−	1.25039i	−0.780467	−	0.625197i	$-0.785019\pi$
$769$		−	961.553i		−	1.25039i	0.780467	−	0.625197i	$-0.214981\pi$
$770$		0			0
$771$	−129.015			−0.167335
$772$	328.649	−	189.745i	0.425711	−	0.245784i
$773$	687.723	−	1191.17i	0.889680	−	1.54097i	0.0494271	−	0.998778i	$-0.484260\pi$
$773$	687.723	−	1191.17i	0.889680	−	1.54097i	0.840253	−	0.542194i	$-0.182406\pi$
$774$	−102.737	+	177.946i	−0.132735	+	0.229904i
$775$		0			0
$776$		−	194.297i		−	0.250383i
$777$	459.123	+	402.612i	0.590892	+	0.518163i
$778$			987.806i			1.26967i
$779$	237.633	+	411.592i	0.305049	+	0.528360i
$780$		0			0
$781$	267.826	−	463.889i	0.342928	−	0.593968i
$782$	153.099	+	265.175i	0.195779	+	0.339098i
$783$	99.1884			0.126677

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:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1050.q (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-4.61524 + 5.26304i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(0.866025 - 1.50000i) q^{3} +(1.00000 - 1.73205i) q^{4} -2.44949i q^{6} +(-4.61524 + 5.26304i) q^{7} -2.82843i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.41099 - 9.37211i) q^{11} +(-1.73205 - 3.00000i) q^{12} +19.2715 q^{13} +(-1.93096 + 9.70935i) q^{14} +(-2.00000 - 3.46410i) q^{16} +(-5.13686 + 8.89730i) q^{17} +(-3.67423 - 2.12132i) q^{18} +(18.0756 - 10.4359i) q^{19} +(3.89764 + 11.4808i) q^{21} -15.3046i q^{22} +(18.2511 - 10.5373i) q^{23} +(-4.24264 - 2.44949i) q^{24} +(23.6026 - 13.6270i) q^{26} -5.19615 q^{27} +(4.50061 + 13.2569i) q^{28} -19.0888 q^{29} +(-34.6556 - 20.0084i) q^{31} +(-4.89898 - 2.82843i) q^{32} +(-9.37211 - 16.2330i) q^{33} +14.5292i q^{34} -6.00000 q^{36} +(43.6177 - 25.1827i) q^{37} +(14.7586 - 25.5627i) q^{38} +(16.6896 - 28.9072i) q^{39} +22.7706i q^{41} +(12.8918 + 11.3050i) q^{42} -48.4307i q^{43} +(-10.8220 - 18.7442i) q^{44} +(14.9020 - 25.8110i) q^{46} +(-33.2690 - 57.6236i) q^{47} -6.92820 q^{48} +(-6.39913 - 48.5804i) q^{49} +(8.89730 + 15.4106i) q^{51} +(19.2715 - 33.3792i) q^{52} +(-4.28736 - 2.47531i) q^{53} +(-6.36396 + 3.67423i) q^{54} +(14.8861 + 13.0539i) q^{56} -36.1511i q^{57} +(-23.3789 + 13.4978i) q^{58} +(24.4105 + 14.0934i) q^{59} +(-60.6988 + 35.0445i) q^{61} -56.5924 q^{62} +(20.5966 + 4.09619i) q^{63} -8.00000 q^{64} +(-22.9569 - 13.2542i) q^{66} +(16.7193 + 9.65287i) q^{67} +(10.2737 + 17.7946i) q^{68} -36.5023i q^{69} +49.4968 q^{71} +(-7.34847 + 4.24264i) q^{72} +(66.4872 - 115.159i) q^{73} +(35.6137 - 61.6848i) q^{74} -41.7437i q^{76} +(24.3527 + 71.7328i) q^{77} -47.2053i q^{78} +(-45.0404 - 78.0122i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(16.1013 + 27.8882i) q^{82} +101.045 q^{83} +(23.7829 + 4.72987i) q^{84} +(-34.2456 - 59.3152i) q^{86} +(-16.5314 + 28.6332i) q^{87} +(-26.5083 - 15.3046i) q^{88} +(-34.3077 + 19.8075i) q^{89} +(-88.9425 + 101.427i) q^{91} -42.1492i q^{92} +(-60.0253 + 34.6556i) q^{93} +(-81.4920 - 47.0495i) q^{94} +(-8.48528 + 4.89898i) q^{96} +68.6944 q^{97} +(-42.1888 - 54.9737i) q^{98} -32.4659 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{4} - 48 q^{9}+O(q^{10}) \) 32 * q + 32 * q^4 - 48 * q^9	\( 32 q + 32 q^{4} - 48 q^{9} - 8 q^{11} - 16 q^{14} - 64 q^{16} + 144 q^{19} - 48 q^{21} - 144 q^{29} + 240 q^{31} - 192 q^{36} - 72 q^{39} + 16 q^{44} + 16 q^{46} + 80 q^{49} - 24 q^{51} + 32 q^{56} - 264 q^{59} + 192 q^{61} - 256 q^{64} + 144 q^{66} - 272 q^{71} + 224 q^{74} - 560 q^{79} - 144 q^{81} + 48 q^{84} - 176 q^{86} + 600 q^{89} - 544 q^{91} + 48 q^{99}+O(q^{100}) \) 32 * q + 32 * q^4 - 48 * q^9 - 8 * q^11 - 16 * q^14 - 64 * q^16 + 144 * q^19 - 48 * q^21 - 144 * q^29 + 240 * q^31 - 192 * q^36 - 72 * q^39 + 16 * q^44 + 16 * q^46 + 80 * q^49 - 24 * q^51 + 32 * q^56 - 264 * q^59 + 192 * q^61 - 256 * q^64 + 144 * q^66 - 272 * q^71 + 224 * q^74 - 560 * q^79 - 144 * q^81 + 48 * q^84 - 176 * q^86 + 600 * q^89 - 544 * q^91 + 48 * q^99

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