LMFDB - Embedded newform 252.2.ba.a.155.11

Newspace parameters

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (of order $6$, degree $2$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.11
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.11

$q$-expansion

$f(q)$	$=$	$q+(-0.896785 + 1.09352i) q^{2} +(-1.24317 + 1.20604i) q^{3} +(-0.391553 - 1.96130i) q^{4} +(2.06874 - 1.19439i) q^{5} +(-0.203962 - 2.44098i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +(0.0909512 - 2.99862i) q^{9} +O(q^{10})$	\(q+(-0.896785 + 1.09352i) q^{2} +(-1.24317 + 1.20604i) q^{3} +(-0.391553 - 1.96130i) q^{4} +(2.06874 - 1.19439i) q^{5} +(-0.203962 - 2.44098i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +(0.0909512 - 2.99862i) q^{9} +(-0.549133 + 3.33330i) q^{10} +(3.21792 - 5.57360i) q^{11} +(2.85216 + 1.96600i) q^{12} +(2.15010 + 3.72408i) q^{13} +(1.32340 - 0.498620i) q^{14} +(-1.13132 + 3.97980i) q^{15} +(-3.69337 + 1.53590i) q^{16} -1.89547i q^{17} +(3.19748 + 2.78858i) q^{18} +0.529348i q^{19} +(-3.15256 - 3.58974i) q^{20} +(1.67964 - 0.422873i) q^{21} +(3.20904 + 8.51717i) q^{22} +(2.64942 + 4.58894i) q^{23} +(-4.70763 + 1.35580i) q^{24} +(0.353115 - 0.611613i) q^{25} +(-6.00052 - 0.988535i) q^{26} +(3.50338 + 3.83749i) q^{27} +(-0.641554 + 1.89431i) q^{28} +(-0.301871 - 0.174285i) q^{29} +(-3.33742 - 4.80614i) q^{30} +(5.09757 - 2.94308i) q^{31} +(1.63263 - 5.41614i) q^{32} +(2.72154 + 10.8099i) q^{33} +(2.07272 + 1.69983i) q^{34} -2.38877 q^{35} +(-5.91680 + 0.995736i) q^{36} +0.842466 q^{37} +(-0.578850 - 0.474711i) q^{38} +(-7.16433 - 2.03657i) q^{39} +(6.75261 - 0.228150i) q^{40} +(4.58530 - 2.64733i) q^{41} +(-1.04386 + 2.21593i) q^{42} +(-7.38095 - 4.26140i) q^{43} +(-12.1915 - 4.12894i) q^{44} +(-3.39336 - 6.31199i) q^{45} +(-7.39404 - 1.21810i) q^{46} +(2.04252 - 3.53774i) q^{47} +(2.73914 - 6.36373i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.352140 + 0.934622i) q^{50} +(2.28600 + 2.35639i) q^{51} +(6.46216 - 5.67516i) q^{52} -12.5979i q^{53} +(-7.33813 + 0.389594i) q^{54} -15.3738i q^{55} +(-1.49612 - 2.40034i) q^{56} +(-0.638413 - 0.658070i) q^{57} +(0.461297 - 0.173804i) q^{58} +(2.66171 + 4.61021i) q^{59} +(8.24854 + 0.660558i) q^{60} +(-3.49882 + 6.06013i) q^{61} +(-1.35312 + 8.21358i) q^{62} +(-1.57808 + 2.55141i) q^{63} +(4.45851 + 6.64242i) q^{64} +(8.89599 + 5.13610i) q^{65} +(-14.2614 - 6.71809i) q^{66} +(-9.32818 + 5.38563i) q^{67} +(-3.71758 + 0.742175i) q^{68} +(-8.82811 - 2.50953i) q^{69} +(2.14221 - 2.61216i) q^{70} +6.12137 q^{71} +(4.21725 - 7.36307i) q^{72} +5.07942 q^{73} +(-0.755511 + 0.921250i) q^{74} +(0.298645 + 1.18621i) q^{75} +(1.03821 - 0.207268i) q^{76} +(-5.57360 + 3.21792i) q^{77} +(8.65189 - 6.00793i) q^{78} +(-2.87851 - 1.66191i) q^{79} +(-5.80616 + 7.58869i) q^{80} +(-8.98346 - 0.545456i) q^{81} +(-1.21714 + 7.38818i) q^{82} +(-3.23597 + 5.60486i) q^{83} +(-1.48704 - 3.12869i) q^{84} +(-2.26392 - 3.92122i) q^{85} +(11.2790 - 4.24963i) q^{86} +(0.585472 - 0.147401i) q^{87} +(15.4482 - 9.62880i) q^{88} +14.4170i q^{89} +(9.94537 + 1.94981i) q^{90} -4.30020i q^{91} +(7.96288 - 6.99312i) q^{92} +(-2.78769 + 9.80661i) q^{93} +(2.03688 + 5.40612i) q^{94} +(0.632246 + 1.09508i) q^{95} +(4.50242 + 8.70220i) q^{96} +(-3.86625 + 6.69654i) q^{97} +(-1.39540 - 0.229881i) q^{98} +(-16.4205 - 10.1563i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−0.896785	+	1.09352i	−0.634123	+	0.773232i
$2$	−0.896785	+	1.09352i	−0.634123	+	0.773232i
$3$	−1.24317	+	1.20604i	−0.717745	+	0.696306i
$3$	−1.24317	+	1.20604i	−0.717745	+	0.696306i
$4$	−0.391553	−	1.96130i	−0.195776	−	0.980649i
$5$	2.06874	−	1.19439i	0.925167	−	0.534146i	0.0398874	−	0.999204i	$-0.487300\pi$
$5$	2.06874	−	1.19439i	0.925167	−	0.534146i	0.885280	+	0.465059i	$0.153967\pi$
$6$	−0.203962	−	2.44098i	−0.0832671	−	0.996527i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	2.49585	+	1.33069i	0.882415	+	0.470471i
$9$	0.0909512	−	2.99862i	0.0303171	−	0.999540i
$10$	−0.549133	+	3.33330i	−0.173651	+	1.05408i
$11$	3.21792	−	5.57360i	0.970240	−	1.68050i	0.275416	−	0.961325i	$-0.411184\pi$
$11$	3.21792	−	5.57360i	0.970240	−	1.68050i	0.694824	−	0.719180i	$-0.255482\pi$
$12$	2.85216	+	1.96600i	0.823349	+	0.567536i
$13$	2.15010	+	3.72408i	0.596331	+	1.03288i	0.993358	+	0.115068i	$0.0367086\pi$
$13$	2.15010	+	3.72408i	0.596331	+	1.03288i	−0.397027	+	0.917807i	$0.629958\pi$
$14$	1.32340	−	0.498620i	0.353693	−	0.133262i
$15$	−1.13132	+	3.97980i	−0.292106	+	1.02758i
$16$	−3.69337	+	1.53590i	−0.923343	+	0.383976i
$17$		−	1.89547i		−	0.459718i	−0.973224	−	0.229859i	$-0.926173\pi$
$17$		−	1.89547i		−	0.459718i	0.973224	−	0.229859i	$-0.0738266\pi$
$18$	3.19748	+	2.78858i	0.753652	+	0.657274i
$19$			0.529348i			0.121441i	0.998155	+	0.0607204i	$0.0193398\pi$
$19$			0.529348i			0.121441i	−0.998155	+	0.0607204i	$0.980660\pi$
$20$	−3.15256	−	3.58974i	−0.704935	−	0.802691i
$21$	1.67964	−	0.422873i	0.366527	−	0.0922784i
$22$	3.20904	+	8.51717i	0.684169	+	1.81587i
$23$	2.64942	+	4.58894i	0.552443	+	0.956859i	0.998098	+	0.0616543i	$0.0196376\pi$
$23$	2.64942	+	4.58894i	0.552443	+	0.956859i	−0.445655	+	0.895205i	$0.647029\pi$
$24$	−4.70763	+	1.35580i	−0.960941	+	0.276752i
$25$	0.353115	−	0.611613i	0.0706230	−	0.122323i
$26$	−6.00052	−	0.988535i	−1.17680	−	0.193868i
$27$	3.50338	+	3.83749i	0.674226	+	0.738525i
$28$	−0.641554	+	1.89431i	−0.121242	+	0.357991i
$29$	−0.301871	−	0.174285i	−0.0560561	−	0.0323640i	0.471710	−	0.881754i	$-0.343637\pi$
$29$	−0.301871	−	0.174285i	−0.0560561	−	0.0323640i	−0.527766	+	0.849390i	$0.676970\pi$
$30$	−3.33742	−	4.80614i	−0.609327	−	0.877478i
$31$	5.09757	−	2.94308i	0.915550	−	0.528593i	0.0333376	−	0.999444i	$-0.489386\pi$
$31$	5.09757	−	2.94308i	0.915550	−	0.528593i	0.882213	+	0.470851i	$0.156053\pi$
$32$	1.63263	−	5.41614i	0.288611	−	0.957446i
$33$	2.72154	+	10.8099i	0.473760	+	1.88176i
$34$	2.07272	+	1.69983i	0.355469	+	0.291518i
$35$	−2.38877			−0.403776
$36$	−5.91680	+	0.995736i	−0.986133	+	0.165956i
$37$	0.842466			0.138501			0.0692503	−	0.997599i	$-0.477939\pi$
$37$	0.842466			0.138501			0.0692503	+	0.997599i	$0.477939\pi$
$38$	−0.578850	−	0.474711i	−0.0939019	−	0.0770084i
$39$	−7.16433	−	2.03657i	−1.14721	−	0.326113i
$40$	6.75261	−	0.228150i	1.06768	−	0.0360737i
$41$	4.58530	−	2.64733i	0.716104	−	0.413443i	−0.0972131	−	0.995264i	$-0.530993\pi$
$41$	4.58530	−	2.64733i	0.716104	−	0.413443i	0.813317	+	0.581821i	$0.197660\pi$
$42$	−1.04386	+	2.21593i	−0.161070	+	0.341926i
$43$	−7.38095	−	4.26140i	−1.12559	−	0.649857i	−0.182764	−	0.983157i	$-0.558504\pi$
$43$	−7.38095	−	4.26140i	−1.12559	−	0.649857i	−0.942821	+	0.333300i	$0.891838\pi$
$44$	−12.1915	−	4.12894i	−1.83793	−	0.622461i
$45$	−3.39336	−	6.31199i	−0.505852	−	0.940936i
$46$	−7.39404	−	1.21810i	−1.09019	−	0.179600i
$47$	2.04252	−	3.53774i	0.297932	−	0.516033i	−0.677731	−	0.735310i	$-0.737037\pi$
$47$	2.04252	−	3.53774i	0.297932	−	0.516033i	0.975663	+	0.219277i	$0.0703699\pi$
$48$	2.73914	−	6.36373i	0.395361	−	0.918526i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	0.352140	+	0.934622i	0.0498001	+	0.132176i
$51$	2.28600	+	2.35639i	0.320105	+	0.329961i
$52$	6.46216	−	5.67516i	0.896140	−	0.787003i
$53$		−	12.5979i		−	1.73046i	−0.501376	−	0.865230i	$-0.667173\pi$
$53$		−	12.5979i		−	1.73046i	0.501376	−	0.865230i	$-0.332827\pi$
$54$	−7.33813	+	0.389594i	−0.998594	+	0.0530171i
$55$		−	15.3738i		−	2.07300i
$56$	−1.49612	−	2.40034i	−0.199928	−	0.320759i
$57$	−0.638413	−	0.658070i	−0.0845599	−	0.0871635i
$58$	0.461297	−	0.173804i	0.0605713	−	0.0228216i
$59$	2.66171	+	4.61021i	0.346524	+	0.600198i	0.985630	−	0.168921i	$-0.0540284\pi$
$59$	2.66171	+	4.61021i	0.346524	+	0.600198i	−0.639105	+	0.769119i	$0.720695\pi$
$60$	8.24854	+	0.660558i	1.06488	+	0.0852776i
$61$	−3.49882	+	6.06013i	−0.447978	+	0.775920i	−0.998254	−	0.0590625i	$-0.981189\pi$
$61$	−3.49882	+	6.06013i	−0.447978	+	0.775920i	0.550277	+	0.834982i	$0.314522\pi$
$62$	−1.35312	+	8.21358i	−0.171846	+	1.04313i
$63$	−1.57808	+	2.55141i	−0.198819	+	0.321447i
$64$	4.45851	+	6.64242i	0.557314	+	0.830302i
$65$	8.89599	+	5.13610i	1.10341	+	0.637055i
$66$	−14.2614	−	6.71809i	−1.75546	−	0.826940i
$67$	−9.32818	+	5.38563i	−1.13962	+	0.657959i	−0.946336	−	0.323184i	$-0.895247\pi$
$67$	−9.32818	+	5.38563i	−1.13962	+	0.657959i	−0.193282	+	0.981143i	$0.561913\pi$
$68$	−3.71758	+	0.742175i	−0.450822	+	0.0900020i
$69$	−8.82811	−	2.50953i	−1.06278	−	0.302112i
$70$	2.14221	−	2.61216i	0.256044	−	0.312213i
$71$	6.12137			0.726473			0.363236	−	0.931697i	$-0.381672\pi$
$71$	6.12137			0.726473			0.363236	+	0.931697i	$0.381672\pi$
$72$	4.21725	−	7.36307i	0.497007	−	0.867746i
$73$	5.07942			0.594501			0.297251	−	0.954799i	$-0.403930\pi$
$73$	5.07942			0.594501			0.297251	+	0.954799i	$0.403930\pi$
$74$	−0.755511	+	0.921250i	−0.0878264	+	0.107093i
$75$	0.298645	+	1.18621i	0.0344846	+	0.136972i
$76$	1.03821	−	0.207268i	0.119091	−	0.0237752i
$77$	−5.57360	+	3.21792i	−0.635171	+	0.366716i
$78$	8.65189	−	6.00793i	0.979633	−	0.680264i
$79$	−2.87851	−	1.66191i	−0.323858	−	0.186979i	0.329253	−	0.944242i	$-0.393203\pi$
$79$	−2.87851	−	1.66191i	−0.323858	−	0.186979i	−0.653111	+	0.757262i	$0.726536\pi$
$80$	−5.80616	+	7.58869i	−0.649148	+	0.848441i
$81$	−8.98346	−	0.545456i	−0.998162	−	0.0606062i
$82$	−1.21714	+	7.38818i	−0.134411	+	0.815888i
$83$	−3.23597	+	5.60486i	−0.355193	+	0.615213i	−0.987151	−	0.159790i	$-0.948918\pi$
$83$	−3.23597	+	5.60486i	−0.355193	+	0.615213i	0.631958	+	0.775003i	$0.282252\pi$
$84$	−1.48704	−	3.12869i	−0.162250	−	0.341368i
$85$	−2.26392	−	3.92122i	−0.245557	−	0.425317i
$86$	11.2790	−	4.24963i	1.21625	−	0.458250i
$87$	0.585472	−	0.147401i	0.0627692	−	0.0158030i
$88$	15.4482	−	9.62880i	1.64678	−	1.02643i
$89$			14.4170i			1.52820i	0.645099	+	0.764099i	$0.276816\pi$
$89$			14.4170i			1.52820i	−0.645099	+	0.764099i	$0.723184\pi$
$90$	9.94537	+	1.94981i	1.04833	+	0.205528i
$91$		−	4.30020i		−	0.450784i
$92$	7.96288	−	6.99312i	0.830187	−	0.729083i
$93$	−2.78769	+	9.80661i	−0.289070	+	1.01690i
$94$	2.03688	+	5.40612i	0.210088	+	0.557599i
$95$	0.632246	+	1.09508i	0.0648670	+	0.112353i
$96$	4.50242	+	8.70220i	0.459526	+	0.888164i
$97$	−3.86625	+	6.69654i	−0.392558	+	0.679931i	−0.992786	−	0.119898i	$-0.961743\pi$
$97$	−3.86625	+	6.69654i	−0.392558	+	0.679931i	0.600228	+	0.799829i	$0.295077\pi$
$98$	−1.39540	−	0.229881i	−0.140957	−	0.0232215i
$99$	−16.4205	−	10.1563i	−1.65032	−	1.02074i
$100$	−1.33782	−	0.453085i	−0.133782	−	0.0453085i
$101$	−14.7999	−	8.54473i	−1.47265	−	0.850233i	−0.473119	−	0.880998i	$-0.656872\pi$
$101$	−14.7999	−	8.54473i	−1.47265	−	0.850233i	−0.999527	+	0.0307657i	$0.990205\pi$
$102$	−4.62681	+	0.386603i	−0.458122	+	0.0382794i
$103$	10.0362	−	5.79440i	0.988896	−	0.570939i	0.0839517	−	0.996470i	$-0.473246\pi$
$103$	10.0362	−	5.79440i	0.988896	−	0.570939i	0.904944	+	0.425531i	$0.139913\pi$
$104$	0.410710	+	12.1559i	0.0402734	+	1.19198i
$105$	2.96965	−	2.88095i	0.289808	−	0.281152i
$106$	13.7760	+	11.2976i	1.33805	+	1.09732i
$107$	−1.66184			−0.160656			−0.0803278	−	0.996768i	$-0.525597\pi$
$107$	−1.66184			−0.160656			−0.0803278	+	0.996768i	$0.525597\pi$
$108$	6.15470	−	8.37375i	0.592237	−	0.805764i
$109$	−8.21513			−0.786867			−0.393434	−	0.919353i	$-0.628713\pi$
$109$	−8.21513			−0.786867			−0.393434	+	0.919353i	$0.628713\pi$
$110$	16.8114	+	13.7870i	1.60291	+	1.31454i
$111$	−1.04733	+	1.01604i	−0.0994082	+	0.0964387i
$112$	3.96651	+	0.516556i	0.374800	+	0.0488100i
$113$	−7.87513	+	4.54671i	−0.740830	+	0.427718i	−0.822371	−	0.568952i	$-0.807349\pi$
$113$	−7.87513	+	4.54671i	−0.740830	+	0.427718i	0.0815410	+	0.996670i	$0.474016\pi$
$114$	1.29213	−	0.107967i	0.121019	−	0.0101120i
$115$	10.9619	+	6.32887i	1.02220	+	0.590170i
$116$	−0.223627	+	0.660301i	−0.0207632	+	0.0613074i
$117$	11.3627	−	6.10863i	1.05048	−	0.564743i
$118$	−7.42831	−	1.22375i	−0.683832	−	0.112655i
$119$	−0.947734	+	1.64152i	−0.0868786	+	0.150478i
$120$	−8.11950	+	8.42753i	−0.741205	+	0.769325i
$121$	−15.2100	−	26.3446i	−1.38273	−	2.39496i
$122$	−3.48916	−	9.26064i	−0.315893	−	0.838419i
$123$	−2.50755	+	8.82112i	−0.226098	+	0.795374i
$124$	−7.76823	−	8.84548i	−0.697607	−	0.794347i
$125$			10.2568i			0.917399i
$126$	−1.37481	−	4.01371i	−0.122478	−	0.357570i
$127$			17.0630i			1.51409i	0.653360	+	0.757047i	$0.273359\pi$
$127$			17.0630i			1.51409i	−0.653360	+	0.757047i	$0.726641\pi$
$128$	−11.2619	−	1.08137i	−0.995422	−	0.0955805i
$129$	14.3152	−	3.60406i	1.26038	−	0.317319i
$130$	−13.5942	+	5.12192i	−1.19229	+	0.449222i
$131$	5.58971	+	9.68166i	0.488375	+	0.845890i	0.999911	−	0.0133718i	$-0.00425652\pi$
$131$	5.58971	+	9.68166i	0.488375	+	0.845890i	−0.511536	+	0.859262i	$0.670923\pi$
$132$	20.1358	−	9.57039i	1.75259	−	0.832995i
$133$	0.264674	−	0.458429i	0.0229501	−	0.0397508i
$134$	2.47611	−	15.0303i	0.213903	−	1.29842i
$135$	11.8310	+	3.75437i	1.01825	+	0.323125i
$136$	2.52229	−	4.73080i	0.216284	−	0.405663i
$137$	4.30543	+	2.48574i	0.367838	+	0.212371i	0.672513	−	0.740085i	$-0.265215\pi$
$137$	4.30543	+	2.48574i	0.367838	+	0.212371i	−0.304676	+	0.952456i	$0.598548\pi$
$138$	10.6611	−	7.40317i	0.907536	−	0.630199i
$139$	−7.46366	+	4.30915i	−0.633060	+	0.365497i	−0.781936	−	0.623359i	$-0.785768\pi$
$139$	−7.46366	+	4.30915i	−0.633060	+	0.365497i	0.148876	+	0.988856i	$0.452434\pi$
$140$	0.935330	+	4.68509i	0.0790498	+	0.395962i
$141$	1.72745	+	6.86137i	0.145477	+	0.577832i
$142$	−5.48955	+	6.69381i	−0.460673	+	0.561732i
$143$	27.6754			2.31434
$144$	4.26967	+	11.2147i	0.355806	+	0.934560i
$145$	−0.832656			−0.0691483
$146$	−4.55515	+	5.55443i	−0.376987	+	0.459688i
$147$	−1.66604	−	0.473600i	−0.137413	−	0.0390619i
$148$	−0.329870	−	1.65233i	−0.0271151	−	0.135820i
$149$	2.18247	−	1.26005i	0.178795	−	0.103227i	−0.407931	−	0.913013i	$-0.633750\pi$
$149$	2.18247	−	1.26005i	0.178795	−	0.103227i	0.586727	+	0.809785i	$0.300416\pi$
$150$	−1.56496	−	0.737202i	−0.127778	−	0.0601923i
$151$	0.331047	+	0.191130i	0.0269402	+	0.0155539i	0.513410	−	0.858144i	$-0.328382\pi$
$151$	0.331047	+	0.191130i	0.0269402	+	0.0155539i	−0.486469	+	0.873698i	$0.661715\pi$
$152$	−0.704400	+	1.32117i	−0.0571344	+	0.107161i
$153$	−5.68379	−	0.172395i	−0.459507	−	0.0139373i
$154$	1.47948	−	8.98061i	0.119220	−	0.723678i
$155$	7.03035	−	12.1769i	0.564691	−	0.978074i
$156$	−1.18912	+	14.8488i	−0.0952056	+	1.18886i
$157$	4.39885	+	7.61904i	0.351067	+	0.608065i	0.986437	−	0.164143i	$-0.0524857\pi$
$157$	4.39885	+	7.61904i	0.351067	+	0.608065i	−0.635370	+	0.772208i	$0.719152\pi$
$158$	4.39873	−	1.65732i	0.349944	−	0.131849i
$159$	15.1936	+	15.6614i	1.20493	+	1.24203i
$160$	−3.09147	−	13.1545i	−0.244402	−	1.03996i
$161$		−	5.29885i		−	0.417608i
$162$	8.65270	−	9.33439i	0.679820	−	0.733379i
$163$		−	10.7694i		−	0.843521i	−0.906707	−	0.421760i	$-0.861412\pi$
$163$		−	10.7694i		−	0.843521i	0.906707	−	0.421760i	$-0.138588\pi$
$164$	−6.98758	−	7.95657i	−0.545638	−	0.621304i
$165$	18.5413	+	19.1122i	1.44344	+	1.48788i
$166$	−3.22703	−	8.56493i	−0.250466	−	0.664768i
$167$	−3.92462	−	6.79765i	−0.303697	−	0.526018i	0.673274	−	0.739393i	$-0.264888\pi$
$167$	−3.92462	−	6.79765i	−0.303697	−	0.526018i	−0.976970	+	0.213375i	$0.931554\pi$
$168$	4.75483	+	1.17966i	0.366843	+	0.0910124i
$169$	−2.74587	+	4.75598i	−0.211221	+	0.365845i
$170$	6.31817	+	1.04086i	0.484582	+	0.0798306i
$171$	1.58731	+	0.0481448i	0.121385	+	0.00368173i
$172$	−5.46783	+	16.1448i	−0.416918	+	1.23103i
$173$	−16.5653	−	9.56396i	−1.25943	−	0.727134i	−0.286469	−	0.958089i	$-0.592482\pi$
$173$	−16.5653	−	9.56396i	−1.25943	−	0.727134i	−0.972964	+	0.230955i	$0.925815\pi$
$174$	−0.363857	+	0.772410i	−0.0275840	+	0.0585562i
$175$	−0.611613	+	0.353115i	−0.0462336	+	0.0266930i
$176$	−3.32448	+	25.5278i	−0.250592	+	1.92423i
$177$	−8.86904	−	2.52117i	−0.666638	−	0.189502i
$178$	−15.7652	−	12.9289i	−1.18165	−	0.969066i
$179$	−26.1468			−1.95431			−0.977153	−	0.212538i	$-0.931827\pi$
$179$	−26.1468			−1.95431			−0.977153	+	0.212538i	$0.931827\pi$
$180$	−11.0510	+	9.12686i	−0.823693	+	0.680276i
$181$	18.9172			1.40610			0.703052	−	0.711139i	$-0.251820\pi$
$181$	18.9172			1.40610			0.703052	+	0.711139i	$0.251820\pi$
$182$	4.70234	+	3.85636i	0.348560	+	0.285852i
$183$	−2.95911	−	11.7535i	−0.218743	−	0.868842i
$184$	0.506090	+	14.9789i	0.0373095	+	1.10426i
$185$	1.74284	−	1.00623i	0.128136	−	0.0739795i
$186$	−8.22373	−	11.8428i	−0.602993	−	0.868356i
$187$	−10.5646	−	6.09947i	−0.772559	−	0.446037i
$188$	−7.73832	−	2.62077i	−0.564375	−	0.191139i
$189$	−1.11527	−	5.07505i	−0.0811239	−	0.369156i
$190$	−1.76448	−	0.290682i	−0.128009	−	0.0210883i
$191$	4.70709	−	8.15291i	0.340593	−	0.589924i	−0.643950	−	0.765068i	$-0.722706\pi$
$191$	4.70709	−	8.15291i	0.340593	−	0.589924i	0.984543	+	0.175143i	$0.0560389\pi$
$192$	−13.5537	−	2.88054i	−0.978153	−	0.207885i
$193$	−0.658744	−	1.14098i	−0.0474174	−	0.0821294i	0.841343	−	0.540502i	$-0.181766\pi$
$193$	−0.658744	−	1.14098i	−0.0474174	−	0.0821294i	−0.888760	+	0.458373i	$0.848432\pi$
$194$	−3.85558	−	10.2332i	−0.276814	−	0.734699i
$195$	−17.2536	+	4.34383i	−1.23555	+	0.311068i
$196$	1.50276	−	1.31974i	0.107340	−	0.0942674i
$197$			3.56413i			0.253933i	0.991907	+	0.126967i	$0.0405241\pi$
$197$			3.56413i			0.253933i	−0.991907	+	0.126967i	$0.959476\pi$
$198$	25.8316	−	8.84804i	1.83577	−	0.628803i
$199$			15.9739i			1.13236i	0.824282	+	0.566179i	$0.191579\pi$
$199$			15.9739i			1.13236i	−0.824282	+	0.566179i	$0.808421\pi$
$200$	1.69519	−	1.05660i	0.119868	−	0.0747132i
$201$	5.10126	−	17.9454i	0.359815	−	1.26577i
$202$	22.6161	−	8.52114i	1.59127	−	0.599546i
$203$	0.174285	+	0.301871i	0.0122324	+	0.0211872i
$204$	3.72649	−	5.40618i	0.260907	−	0.378509i
$205$	6.32386	−	10.9532i	0.441677	−	0.765007i
$206$	−2.66404	+	16.1711i	−0.185613	+	1.12669i
$207$	14.0014	−	7.52725i	0.973168	−	0.523180i
$208$	−13.6610	−	10.4521i	−0.947217	−	0.724722i
$209$	2.95038	+	1.70340i	0.204082	+	0.117827i
$210$	0.487219	+	5.83095i	0.0336213	+	0.402374i
$211$	−3.39401	+	1.95953i	−0.233653	+	0.134900i	−0.612256	−	0.790659i	$-0.709738\pi$
$211$	−3.39401	+	1.95953i	−0.233653	+	0.134900i	0.378603	+	0.925559i	$0.376405\pi$
$212$	−24.7083	+	4.93275i	−1.69697	+	0.338783i
$213$	−7.60991	+	7.38259i	−0.521423	+	0.505847i
$214$	1.49031	−	1.81724i	0.101875	−	0.124224i
$215$	−20.3590			−1.38847
$216$	3.63738	+	14.2397i	0.247492	+	0.968890i
$217$	−5.88617			−0.399579
$218$	7.36721	−	8.98338i	0.498970	−	0.608431i
$219$	−6.31459	+	6.12597i	−0.426701	+	0.413955i
$220$	−30.1525	+	6.01964i	−2.03288	+	0.405844i
$221$	7.05888	−	4.07545i	0.474832	−	0.274144i
$222$	−0.171831	−	2.05645i	−0.0115325	−	0.138020i
$223$	2.25600	+	1.30250i	0.151073	+	0.0872218i	0.573631	−	0.819114i	$-0.305534\pi$
$223$	2.25600	+	1.30250i	0.151073	+	0.0872218i	−0.422558	+	0.906336i	$0.638868\pi$
$224$	−4.12197	+	3.87420i	−0.275410	+	0.258856i
$225$	−1.80188	−	1.11448i	−0.120125	−	0.0742990i
$226$	2.09040	−	12.6890i	0.139052	−	0.844060i
$227$	1.56505	−	2.71075i	0.103876	−	0.179919i	−0.809402	−	0.587254i	$-0.800209\pi$
$227$	1.56505	−	2.71075i	0.103876	−	0.179919i	0.913278	+	0.407336i	$0.133542\pi$
$228$	−1.04070	+	1.50979i	−0.0689220	+	0.0999881i
$229$	−3.33583	−	5.77783i	−0.220438	−	0.381809i	0.734503	−	0.678605i	$-0.237415\pi$
$229$	−3.33583	−	5.77783i	−0.220438	−	0.381809i	−0.954941	+	0.296796i	$0.904082\pi$
$230$	−16.7512	+	6.31140i	−1.10454	+	0.416161i
$231$	3.04801	−	10.7224i	0.200545	−	0.705482i
$232$	−0.521504	−	0.836688i	−0.0342384	−	0.0549312i
$233$			15.0197i			0.983971i	0.870603	+	0.491985i	$0.163729\pi$
$233$			15.0197i			0.983971i	−0.870603	+	0.491985i	$0.836271\pi$
$234$	−3.51000	+	17.9034i	−0.229456	+	1.17038i
$235$		−	9.75821i		−	0.636556i
$236$	7.99979	−	7.02553i	0.520742	−	0.457323i
$237$	5.58281	−	1.40555i	0.362642	−	0.0913004i
$238$	−0.945118	−	2.50846i	−0.0612629	−	0.162599i
$239$	−1.10101	−	1.90701i	−0.0712185	−	0.123354i	0.828217	−	0.560407i	$-0.189355\pi$
$239$	−1.10101	−	1.90701i	−0.0712185	−	0.123354i	−0.899436	+	0.437053i	$0.856022\pi$
$240$	−1.93419	−	16.4365i	−0.124851	−	1.06097i
$241$	−9.28440	+	16.0811i	−0.598061	+	1.03587i	0.395046	+	0.918661i	$0.370729\pi$
$241$	−9.28440	+	16.0811i	−0.598061	+	1.03587i	−0.993107	+	0.117211i	$0.962605\pi$
$242$	42.4483	+	6.99300i	2.72868	+	0.449527i
$243$	11.8258	−	10.1563i	0.758627	−	0.651526i
$244$	13.2557	+	4.48936i	0.848608	+	0.287402i
$245$	2.06874	+	1.19439i	0.132167	+	0.0763065i
$246$	−7.39730	−	10.6527i	−0.471635	−	0.679191i
$247$	−1.97134	+	1.13815i	−0.125433	+	0.0724188i
$248$	16.6391	−	0.562185i	1.05658	−	0.0356988i
$249$	−2.73680	−	10.8705i	−0.173438	−	0.688890i
$250$	−11.2160	−	9.19818i	−0.709363	−	0.581744i
$251$	−6.18166			−0.390183			−0.195092	−	0.980785i	$-0.562500\pi$
$251$	−6.18166			−0.390183			−0.195092	+	0.980785i	$0.562500\pi$
$252$	5.62197	+	2.09607i	0.354151	+	0.132040i
$253$	34.1026			2.14401
$254$	−18.6586	−	15.3018i	−1.17075	−	0.960122i
$255$	7.54358	+	2.14438i	0.472397	+	0.134287i
$256$	11.2820	−	11.3453i	0.705126	−	0.709082i
$257$	6.98685	−	4.03386i	0.435828	−	0.251625i	−0.265998	−	0.963973i	$-0.585702\pi$
$257$	6.98685	−	4.03386i	0.435828	−	0.251625i	0.701826	+	0.712348i	$0.252368\pi$
$258$	−8.89656	+	18.8860i	−0.553876	+	1.17579i
$259$	−0.729597	−	0.421233i	−0.0453350	−	0.0261741i
$260$	6.59017	−	19.4587i	0.408705	−	1.20678i
$261$	−0.550071	+	0.889346i	−0.0340486	+	0.0550491i
$262$	−15.5998	−	2.56993i	−0.963759	−	0.158771i
$263$	0.0757144	−	0.131141i	0.00466875	−	0.00808651i	−0.863682	−	0.504038i	$-0.831847\pi$
$263$	0.0757144	−	0.131141i	0.00466875	−	0.00808651i	0.868350	+	0.495951i	$0.165181\pi$
$264$	−7.59208	+	30.6013i	−0.467260	+	1.88338i
$265$	−15.0468	−	26.0618i	−0.924317	−	1.60096i
$266$	0.263943	+	0.700537i	0.0161834	+	0.0429527i
$267$	−17.3874	−	17.9228i	−1.06409	−	1.09686i
$268$	14.2153	+	16.1866i	0.868337	+	0.988752i
$269$		−	2.18065i		−	0.132957i	−0.997788	−	0.0664784i	$-0.978824\pi$
$269$		−	2.18065i		−	0.132957i	0.997788	−	0.0664784i	$-0.0211763\pi$
$270$	−14.7153	+	9.57053i	−0.895547	+	0.582444i
$271$		−	3.08448i		−	0.187369i	−0.995602	−	0.0936844i	$-0.970136\pi$
$271$		−	3.08448i		−	0.187369i	0.995602	−	0.0936844i	$-0.0298645\pi$
$272$	2.91125	+	7.00067i	0.176521	+	0.424478i
$273$	5.18620	+	5.34589i	0.313883	+	0.323548i
$274$	−6.57924	+	2.47888i	−0.397467	+	0.149755i
$275$	−2.27259	−	3.93624i	−0.137042	−	0.237364i
$276$	−1.46527	+	18.2972i	−0.0881989	+	1.10136i
$277$	−8.31095	+	14.3950i	−0.499357	+	0.864911i	−1.00000		0.000742657i	$-0.999764\pi$
$277$	−8.31095	+	14.3950i	−0.499357	+	0.864911i	0.500643	+	0.865654i	$0.333097\pi$
$278$	1.98118	−	12.0260i	0.118823	−	0.721272i
$279$	−8.36156	−	15.5534i	−0.500593	−	0.931155i
$280$	−5.96201	−	3.17872i	−0.356298	−	0.189965i
$281$	8.93878	+	5.16081i	0.533243	+	0.307868i	0.742336	−	0.670028i	$-0.233718\pi$
$281$	8.93878	+	5.16081i	0.533243	+	0.307868i	−0.209093	+	0.977896i	$0.567051\pi$
$282$	−9.05217	−	4.26418i	−0.539049	−	0.253928i
$283$	−12.3659	+	7.13943i	−0.735074	+	0.424395i	−0.820275	−	0.571969i	$-0.806180\pi$
$283$	−12.3659	+	7.13943i	−0.735074	+	0.424395i	0.0852016	+	0.996364i	$0.472847\pi$
$284$	−2.39684	−	12.0058i	−0.142226	−	0.712415i
$285$	−2.10670	−	0.598863i	−0.124790	−	0.0354736i
$286$	−24.8189	+	30.2635i	−1.46757	+	1.78952i
$287$	−5.29465			−0.312533
$288$	−16.0924	−	5.38824i	−0.948257	−	0.317505i
$289$	13.4072			0.788659
$290$	0.746713	−	0.910522i	0.0438485	−	0.0534677i
$291$	−3.26986	−	12.9878i	−0.191683	−	0.761358i
$292$	−1.98886	−	9.96226i	−0.116389	−	0.582997i
$293$	−2.10270	+	1.21399i	−0.122841	+	0.0709223i	−0.560161	−	0.828383i	$-0.689261\pi$
$293$	−2.10270	+	1.21399i	−0.122841	+	0.0709223i	0.437320	+	0.899306i	$0.355928\pi$
$294$	2.01197	−	1.39713i	0.117341	−	0.0814822i
$295$	11.0127	+	6.35821i	0.641186	+	0.370189i
$296$	2.10267	+	1.12106i	0.122215	+	0.0651605i
$297$	32.6623	−	7.17770i	1.89526	−	0.416492i
$298$	−0.579324	+	3.51657i	−0.0335593	+	0.203709i
$299$	−11.3931	+	19.7334i	−0.658877	+	1.14121i
$300$	2.20957	−	1.05020i	0.127570	−	0.0606330i
$301$	4.26140	+	7.38095i	0.245623	+	0.425431i
$302$	−0.505882	+	0.190602i	−0.0291102	+	0.0109679i
$303$	28.7041	−	7.22667i	1.64901	−	0.415161i
$304$	−0.813027	−	1.95508i	−0.0466303	−	0.112131i
$305$			16.7157i			0.957141i
$306$	5.28566	−	6.06071i	0.302161	−	0.346468i
$307$			8.87237i			0.506373i	0.967417	+	0.253187i	$0.0814787\pi$
$307$			8.87237i			0.506373i	−0.967417	+	0.253187i	$0.918521\pi$
$308$	8.49366	+	9.67151i	0.483971	+	0.551085i
$309$	−5.48845	+	19.3075i	−0.312227	+	1.09836i
$310$	7.01094	+	18.6079i	0.398195	+	1.05686i
$311$	−3.03771	−	5.26147i	−0.172253	−	0.298350i	0.766954	−	0.641702i	$-0.221771\pi$
$311$	−3.03771	−	5.26147i	−0.172253	−	0.298350i	−0.939207	+	0.343351i	$0.888438\pi$
$312$	−15.1710	−	14.6165i	−0.858889	−	0.827496i
$313$	−10.3245	+	17.8825i	−0.583575	+	1.01078i	0.411477	+	0.911420i	$0.365013\pi$
$313$	−10.3245	+	17.8825i	−0.583575	+	1.01078i	−0.995051	+	0.0993607i	$0.968320\pi$
$314$	−12.2764	−	2.02242i	−0.692795	−	0.114132i
$315$	−0.217262	+	7.16302i	−0.0122413	+	0.403590i
$316$	−2.13241	+	6.29634i	−0.119957	+	0.354197i
$317$	21.2581	+	12.2734i	1.19397	+	0.689341i	0.959205	−	0.282710i	$-0.0912334\pi$
$317$	21.2581	+	12.2734i	1.19397	+	0.689341i	0.234769	+	0.972051i	$0.424567\pi$
$318$	−30.7513	+	2.56950i	−1.72445	+	0.144090i
$319$	−1.94280	+	1.12167i	−0.108776	+	0.0628017i
$320$	17.1571	+	8.41623i	0.959111	+	0.470482i
$321$	2.06595	−	2.00423i	0.115310	−	0.111865i
$322$	5.79437	+	4.75193i	0.322908	+	0.264815i
$323$	1.00336			0.0558286
$324$	2.44769	+	17.8328i	0.135983	+	0.990711i
$325$	3.03693			0.168459
$326$	11.7765	+	9.65780i	0.652238	+	0.534896i
$327$	10.2128	−	9.90775i	0.564770	−	0.547900i
$328$	14.9670	−	0.505690i	0.826414	−	0.0279220i
$329$	−3.53774	+	2.04252i	−0.195042	+	0.112608i
$330$	−37.5271	+	3.13566i	−2.06580	+	0.172613i
$331$	25.9866	+	15.0034i	1.42835	+	0.824660i	0.996991	−	0.0775195i	$-0.0247000\pi$
$331$	25.9866	+	15.0034i	1.42835	+	0.824660i	0.431362	+	0.902179i	$0.358033\pi$
$332$	12.2598	+	4.15210i	0.672846	+	0.227876i
$333$	0.0766233	−	2.52624i	0.00419893	−	0.138437i
$334$	10.9529	+	1.80439i	0.599315	+	0.0987320i
$335$	−12.8650	+	22.2829i	−0.702892	+	1.21744i
$336$	−5.55403	+	4.14158i	−0.302997	+	0.225942i
$337$	−5.27401	−	9.13486i	−0.287294	−	0.497608i	0.685869	−	0.727725i	$-0.259422\pi$
$337$	−5.27401	−	9.13486i	−0.287294	−	0.497608i	−0.973163	+	0.230117i	$0.926089\pi$
$338$	−2.73829	−	7.26774i	−0.148943	−	0.395313i
$339$	4.30664	−	15.1500i	0.233905	−	0.822837i
$340$	−6.80424	+	5.97559i	−0.369012	+	0.324072i
$341$		−	37.8824i		−	2.05145i
$342$	−1.47613	+	1.69258i	−0.0798198	+	0.0915241i
$343$		−	1.00000i		−	0.0539949i
$344$	−12.7511	−	20.4576i	−0.687495	−	1.10300i
$345$	−21.2604	+	5.35261i	−1.14462	+	0.288175i
$346$	25.3138	−	9.53756i	1.36088	−	0.512742i
$347$	4.55660	+	7.89227i	0.244611	+	0.423679i	0.962022	−	0.272971i	$-0.0880063\pi$
$347$	4.55660	+	7.89227i	0.244611	+	0.423679i	−0.717411	+	0.696650i	$0.754673\pi$
$348$	−0.518340	−	1.09057i	−0.0277860	−	0.0584607i
$349$	11.2978	−	19.5684i	0.604760	−	1.04747i	−0.387330	−	0.921941i	$-0.626602\pi$
$349$	11.2978	−	19.5684i	0.604760	−	1.04747i	0.992089	−	0.125533i	$-0.0400642\pi$
$350$	0.162349	−	0.985476i	0.00867791	−	0.0526759i
$351$	−6.75852	+	21.2979i	−0.360743	+	1.13680i
$352$	−24.9337	−	26.5283i	−1.32897	−	1.41396i
$353$	−5.76564	−	3.32879i	−0.306874	−	0.177174i	0.338653	−	0.940911i	$-0.390029\pi$
$353$	−5.76564	−	3.32879i	−0.306874	−	0.177174i	−0.645527	+	0.763738i	$0.723362\pi$
$354$	10.7106	−	7.43748i	0.569260	−	0.395298i
$355$	12.6635	−	7.31128i	0.672109	−	0.388042i
$356$	28.2760	−	5.64501i	1.49863	−	0.299185i
$357$	−0.801541	−	3.18370i	−0.0424221	−	0.168499i
$358$	23.4481	−	28.5920i	1.23927	−	1.51113i
$359$	−8.03334			−0.423984			−0.211992	−	0.977271i	$-0.567995\pi$
$359$	−8.03334			−0.423984			−0.211992	+	0.977271i	$0.567995\pi$
$360$	−0.0699785	−	20.2693i	−0.00368819	−	1.06828i
$361$	18.7198			0.985252
$362$	−16.9647	+	20.6862i	−0.891643	+	1.08724i
$363$	50.6812	+	14.4069i	2.66007	+	0.756169i
$364$	−8.43397	+	1.68376i	−0.442060	+	0.0882528i
$365$	10.5080	−	6.06679i	0.550013	−	0.317550i
$366$	15.5063	+	7.30452i	0.810527	+	0.381813i
$367$	14.9220	+	8.61523i	0.778923	+	0.449712i	0.836049	−	0.548656i	$-0.184860\pi$
$367$	14.9220	+	8.61523i	0.778923	+	0.449712i	−0.0571254	+	0.998367i	$0.518193\pi$
$368$	−16.8335	−	12.8794i	−0.877505	−	0.671385i
$369$	−7.52129	−	13.9904i	−0.391543	−	0.728309i
$370$	−0.462626	+	2.80820i	−0.0240508	+	0.145991i
$371$	−6.29897	+	10.9101i	−0.327026	+	0.566426i
$372$	20.3252	+	1.62768i	1.05381	+	0.0843912i
$373$	−0.260742	−	0.451618i	−0.0135007	−	0.0233839i	0.859196	−	0.511646i	$-0.170964\pi$
$373$	−0.260742	−	0.451618i	−0.0135007	−	0.0233839i	−0.872697	+	0.488262i	$0.837631\pi$
$374$	16.1440	−	6.08263i	0.834788	−	0.314525i
$375$	−12.3701	−	12.7510i	−0.638790	−	0.658459i
$376$	9.80546	−	6.11170i	0.505678	−	0.315187i
$377$		−	1.49892i		−	0.0771985i
$378$	6.54981	+	3.33167i	0.336886	+	0.171363i
$379$			22.8440i			1.17342i	0.809797	+	0.586710i	$0.199577\pi$
$379$			22.8440i			1.17342i	−0.809797	+	0.586710i	$0.800423\pi$
$380$	1.90022	−	1.66880i	0.0974794	−	0.0856078i
$381$	−20.5786	−	21.2122i	−1.05427	−	1.08673i
$382$	4.69409	+	12.4587i	0.240171	+	0.637442i
$383$	−12.4781	−	21.6128i	−0.637603	−	1.10436i	−0.985957	−	0.166998i	$-0.946593\pi$
$383$	−12.4781	−	21.6128i	−0.637603	−	1.10436i	0.348354	−	0.937363i	$-0.386741\pi$
$384$	15.3047	−	12.2379i	0.781013	−	0.624515i
$385$	−7.68688	+	13.3141i	−0.391760	+	0.678548i
$386$	1.83843	+	0.302865i	0.0935736	+	0.0154154i
$387$	−13.4496	+	21.7451i	−0.683683	+	1.10537i
$388$	14.6478	+	4.96082i	0.743627	+	0.251847i
$389$	−22.0002	−	12.7018i	−1.11545	−	0.644007i	−0.175216	−	0.984530i	$-0.556062\pi$
$389$	−22.0002	−	12.7018i	−1.11545	−	0.644007i	−0.940236	+	0.340523i	$0.889396\pi$
$390$	10.7227	−	22.7625i	0.542965	−	1.15263i
$391$	8.69818	−	5.02190i	0.439886	−	0.253968i
$392$	0.0955095	+	2.82681i	0.00482396	+	0.142776i
$393$	−18.6254	−	5.29457i	−0.939527	−	0.267076i
$394$	−3.89743	−	3.19626i	−0.196350	−	0.161025i
$395$	−7.93985			−0.399497
$396$	−13.4900	+	36.1821i	−0.677896	+	1.81822i
$397$	5.32969			0.267489			0.133745	−	0.991016i	$-0.457300\pi$
$397$	5.32969			0.267489			0.133745	+	0.991016i	$0.457300\pi$
$398$	−17.4677	−	14.3251i	−0.875576	−	0.718054i
$399$	0.223847	+	0.889112i	0.0112064	+	0.0445113i
$400$	−0.364807	+	2.80126i	−0.0182404	+	0.140063i
$401$	20.2109	−	11.6688i	1.00928	−	0.582710i	0.0983016	−	0.995157i	$-0.468659\pi$
$401$	20.2109	−	11.6688i	1.00928	−	0.582710i	0.910982	+	0.412447i	$0.135326\pi$
$402$	15.0488	+	21.6715i	0.750567	+	1.08087i
$403$	21.9206	+	12.6558i	1.09194	+	0.630433i
$404$	−10.9638	+	32.3727i	−0.545470	+	1.61060i
$405$	−19.2359	+	9.60131i	−0.955839	+	0.477093i
$406$	−0.486397	−	0.0801298i	−0.0241395	−	0.00397677i
$407$	2.71099	−	4.69557i	0.134379	−	0.232751i
$408$	2.56988	+	8.92317i	0.127228	+	0.441762i
$409$	15.5599	+	26.9506i	0.769389	+	1.33262i	0.937895	+	0.346920i	$0.112772\pi$
$409$	15.5599	+	26.9506i	0.769389	+	1.33262i	−0.168506	+	0.985701i	$0.553894\pi$
$410$	6.30640	+	16.7379i	0.311451	+	0.826628i
$411$	−8.35028	+	2.10230i	−0.411889	+	0.103699i
$412$	−15.2942	−	17.4151i	−0.753493	−	0.857983i
$413$		−	5.32341i		−	0.261948i
$414$	−4.32513	+	22.0611i	−0.212568	+	1.08425i
$415$			15.4600i			0.758900i
$416$	23.6805	−	5.56519i	1.16103	−	0.272856i
$417$	4.08162	−	14.3585i	0.199878	−	0.703137i
$418$	−4.50855	+	1.69870i	−0.220520	+	0.0830860i
$419$	−13.4133	−	23.2325i	−0.655283	−	1.13498i	−0.981823	−	0.189800i	$-0.939216\pi$
$419$	−13.4133	−	23.2325i	−0.655283	−	1.13498i	0.326540	−	0.945183i	$-0.394117\pi$
$420$	−6.81317	−	4.69633i	−0.332448	−	0.229157i
$421$	4.00100	−	6.92994i	0.194997	−	0.337744i	−0.751903	−	0.659274i	$-0.770864\pi$
$421$	4.00100	−	6.92994i	0.194997	−	0.337744i	0.946899	+	0.321530i	$0.104197\pi$
$422$	0.900918	−	5.46868i	0.0438560	−	0.266211i
$423$	−10.4226	−	6.44649i	−0.506763	−	0.313439i
$424$	16.7640	−	31.4425i	0.814131	−	1.52698i
$425$	−1.15929	−	0.669318i	−0.0562339	−	0.0324667i
$426$	−1.24853	−	14.9422i	−0.0604913	−	0.723950i
$427$	6.06013	−	3.49882i	0.293270	−	0.169320i
$428$	0.650696	+	3.25935i	0.0314526	+	0.157547i
$429$	−34.4053	+	33.3776i	−1.66110	+	1.61148i
$430$	18.2577	−	22.2629i	0.880462	−	1.07361i
$431$	23.2635			1.12056			0.560282	−	0.828302i	$-0.310693\pi$
$431$	23.2635			1.12056			0.560282	+	0.828302i	$0.310693\pi$
$432$	−18.8333	−	8.79244i	−0.906117	−	0.423026i
$433$	−40.4077			−1.94187			−0.970936	−	0.239340i	$-0.923069\pi$
$433$	−40.4077			−1.94187			−0.970936	+	0.239340i	$0.923069\pi$
$434$	5.27863	−	6.43661i	0.253382	−	0.308967i
$435$	1.03513	−	1.00421i	0.0496309	−	0.0481484i
$436$	3.21666	+	16.1123i	0.154050	+	0.771640i
$437$	−2.42914	+	1.40247i	−0.116202	+	0.0670891i
$438$	−1.03601	−	12.3988i	−0.0495024	−	0.592437i
$439$	−4.54218	−	2.62243i	−0.216786	−	0.125162i	0.387675	−	0.921796i	$-0.373278\pi$
$439$	−4.54218	−	2.62243i	−0.216786	−	0.125162i	−0.604461	+	0.796634i	$0.706612\pi$
$440$	20.4578	−	38.3706i	0.975286	−	1.82924i
$441$	2.64236	−	1.42054i	0.125827	−	0.0676450i
$442$	−1.87374	+	11.3738i	−0.0891245	+	0.540996i
$443$	−4.84903	+	8.39876i	−0.230384	+	0.399037i	−0.957921	−	0.287031i	$-0.907332\pi$
$443$	−4.84903	+	8.39876i	−0.230384	+	0.399037i	0.727537	+	0.686068i	$0.240665\pi$
$444$	2.40285	+	1.65629i	0.114034	+	0.0786040i
$445$	17.2195	+	29.8250i	0.816280	+	1.41384i
$446$	−3.44745	+	1.29890i	−0.163241	+	0.0615049i
$447$	−1.19352	+	4.19861i	−0.0564516	+	0.198587i
$448$	−0.539975	−	7.98176i	−0.0255114	−	0.377103i
$449$		−	38.7800i		−	1.83014i	−0.403294	−	0.915071i	$-0.632135\pi$
$449$		−	38.7800i		−	1.83014i	0.403294	−	0.915071i	$-0.367865\pi$
$450$	2.83460	−	0.970929i	0.133625	−	0.0457701i
$451$		−	34.0755i		−	1.60455i
$452$	12.0010	+	13.6652i	0.564478	+	0.642757i
$453$	−0.642058	+	0.161647i	−0.0301665	+	0.00759485i
$454$	1.56073	+	4.14237i	0.0732487	+	0.194411i
$455$	−5.13610	−	8.89599i	−0.240784	−	0.417050i
$456$	−0.717692	−	2.49198i	−0.0336090	−	0.116697i
$457$	11.3244	−	19.6145i	0.529735	−	0.917528i	−0.469663	−	0.882846i	$-0.655625\pi$
$457$	11.3244	−	19.6145i	0.529735	−	0.917528i	0.999398	−	0.0346824i	$-0.0110420\pi$
$458$	9.30966	+	1.53369i	0.435012	+	0.0716645i
$459$	7.27384	−	6.64054i	0.339514	−	0.309954i
$460$	8.12062	−	23.9777i	0.378626	−	1.11796i
$461$	32.0052	+	18.4782i	1.49063	+	0.860617i	0.999943	−	0.0107183i	$-0.00341180\pi$
$461$	32.0052	+	18.4782i	1.49063	+	0.860617i	0.490689	+	0.871335i	$0.336745\pi$
$462$	8.99170	+	12.9487i	0.418332	+	0.602430i
$463$	−8.93748	+	5.16006i	−0.415360	+	0.239808i	−0.693090	−	0.720851i	$-0.743751\pi$
$463$	−8.93748	+	5.16006i	−0.415360	+	0.239808i	0.277730	+	0.960659i	$0.410418\pi$
$464$	1.38261	+	0.180056i	0.0641860	+	0.00835891i
$465$	5.94589	+	23.6169i	0.275734	+	1.09521i
$466$	−16.4242	−	13.4694i	−0.760838	−	0.623958i
$467$	0.900019			0.0416479			0.0208239	−	0.999783i	$-0.493371\pi$
$467$	0.900019			0.0416479			0.0208239	+	0.999783i	$0.493371\pi$
$468$	−16.4299	−	19.8937i	−0.759473	−	0.919588i
$469$	10.7713			0.497370
$470$	10.6708	+	8.75102i	0.492205	+	0.403654i
$471$	−14.6574	−	4.16659i	−0.675376	−	0.191986i
$472$	0.508436	+	15.0483i	0.0234027	+	0.692654i
$473$	−47.5027	+	27.4257i	−2.18418	+	1.26103i
$474$	−3.46959	+	7.36537i	−0.159363	+	0.338303i
$475$	0.323756	+	0.186921i	0.0148549	+	0.00857651i
$476$	3.59060	+	1.21605i	0.164575	+	0.0557373i
$477$	−37.7764	−	1.14580i	−1.72966	−	0.0524624i
$478$	3.07271	+	0.506203i	0.140543	+	0.0231532i
$479$	−15.9460	+	27.6192i	−0.728590	+	1.26195i	0.228889	+	0.973452i	$0.426491\pi$
$479$	−15.9460	+	27.6192i	−0.728590	+	1.26195i	−0.957479	+	0.288502i	$0.906843\pi$
$480$	19.7081	+	12.6249i	0.899548	+	0.576247i
$481$	1.81139	+	3.13741i	0.0825921	+	0.143054i
$482$	−9.25877	−	24.5739i	−0.421725	−	1.11931i
$483$	6.39060	+	6.58738i	0.290783	+	0.299736i
$484$	−45.7140	+	40.1467i	−2.07791	+	1.82485i
$485$			18.4712i			0.838733i
$486$	0.500834	+	22.0397i	0.0227183	+	0.999742i
$487$			7.65522i			0.346891i	0.984843	+	0.173446i	$0.0554901\pi$
$487$			7.65522i			0.346891i	−0.984843	+	0.173446i	$0.944510\pi$
$488$	−16.7967	+	10.4693i	−0.760350	+	0.473923i
$489$	12.9882	+	13.3882i	0.587348	+	0.605433i
$490$	−3.16129	+	1.19109i	−0.142813	+	0.0538079i
$491$	−1.59570	−	2.76383i	−0.0720128	−	0.124730i	0.827771	−	0.561067i	$-0.189609\pi$
$491$	−1.59570	−	2.76383i	−0.0720128	−	0.124730i	−0.899783	+	0.436337i	$0.856276\pi$
$492$	18.2827	+	1.46411i	0.824247	+	0.0660071i
$493$	−0.330352	+	0.572187i	−0.0148783	+	0.0257700i
$494$	0.523279	−	3.17636i	0.0235434	−	0.142911i
$495$	−46.1001	−	1.39826i	−2.07204	−	0.0628472i
$496$	−14.3069	+	18.6993i	−0.642400	+	0.839622i
$497$	−5.30126	−	3.06068i	−0.237794	−	0.137290i
$498$	14.3414	+	6.75576i	0.642653	+	0.302733i
$499$	9.07585	−	5.23995i	0.406291	−	0.234572i	−0.282904	−	0.959148i	$-0.591298\pi$
$499$	9.07585	−	5.23995i	0.406291	−	0.234572i	0.689195	+	0.724576i	$0.257964\pi$
$500$	20.1167	−	4.01609i	0.899646	−	0.179605i
$501$	13.0772	+	3.71740i	0.584246	+	0.166081i
$502$	5.54362	−	6.75975i	0.247424	−	0.301702i
$503$	12.6421			0.563685			0.281843	−	0.959461i	$-0.409054\pi$
$503$	12.6421			0.563685			0.281843	+	0.959461i	$0.409054\pi$
$504$	−7.33378	+	4.26799i	−0.326672	+	0.190111i
$505$	−40.8228			−1.81659
$506$	−30.5827	+	37.2917i	−1.35957	+	1.65782i
$507$	−2.32230	−	9.22412i	−0.103137	−	0.409658i
$508$	33.4656	−	6.68106i	1.48479	−	0.296424i
$509$	−23.8125	+	13.7481i	−1.05547	+	0.609376i	−0.924176	−	0.381968i	$-0.875247\pi$
$509$	−23.8125	+	13.7481i	−1.05547	+	0.609376i	−0.131294	+	0.991343i	$0.541913\pi$
$510$	−9.10989	+	6.32597i	−0.403393	+	0.280119i
$511$	−4.39891	−	2.53971i	−0.194596	−	0.112350i
$512$	2.28874	+	22.5114i	0.101149	+	0.994871i
$513$	−2.03137	+	1.85451i	−0.0896871	+	0.0818785i
$514$	−1.85462	+	11.2577i	−0.0818036	+	0.496558i
$515$	13.8415	−	23.9742i	0.609929	−	1.05643i
$516$	−12.6738	−	26.6652i	−0.557932	−	1.17387i
$517$	−13.1453	−	22.7684i	−0.578130	−	1.00135i
$518$	1.11492	−	0.420070i	0.0489866	−	0.0184568i
$519$	32.1280	−	8.08867i	1.41026	−	0.355053i
$520$	15.3685	+	24.6568i	0.673951	+	1.08127i
$521$			16.7533i			0.733975i	0.930226	+	0.366988i	$0.119611\pi$
$521$			16.7533i			0.733975i	−0.930226	+	0.366988i	$0.880389\pi$
$522$	−0.479217	−	1.39906i	−0.0209748	−	0.0612353i
$523$			39.1120i			1.71025i	0.518424	+	0.855124i	$0.326519\pi$
$523$			39.1120i			1.71025i	−0.518424	+	0.855124i	$0.673481\pi$
$524$	16.7999	−	14.7540i	0.733909	−	0.644529i
$525$	0.334470	−	1.17661i	0.0145975	−	0.0513515i
$526$	0.0755054	+	0.200400i	0.00329219	+	0.00873787i
$527$	−5.57852	−	9.66228i	−0.243004	−	0.420895i
$528$	−26.6546	−	35.7449i	−1.15999	−	1.55560i
$529$	−2.53889	+	4.39749i	−0.110387	+	0.191195i
$530$	41.9927	+	6.91794i	1.82405	+	0.300496i
$531$	14.0664	−	7.56214i	0.610428	−	0.328169i
$532$	−1.00275	−	0.339605i	−0.0434747	−	0.0147238i
$533$	19.7177	+	11.3840i	0.854069	+	0.493097i
$534$	35.1916	−	2.94052i	1.52289	−	0.127249i
$535$	−3.43790	+	1.98487i	−0.148633	+	0.0858135i
$536$	−30.4483	+	1.02876i	−1.31517	+	0.0444355i
$537$	32.5050	−	31.5340i	1.40269	−	1.36079i
$538$	2.38458	+	1.95558i	0.102806	+	0.0843109i
$539$	6.43584			0.277211
$540$	2.73098	−	24.6742i	0.117523	−	1.06181i
$541$	−11.1182			−0.478010			−0.239005	−	0.971018i	$-0.576821\pi$
$541$	−11.1182			−0.478010			−0.239005	+	0.971018i	$0.576821\pi$
$542$	3.37293	+	2.76612i	0.144880	+	0.118815i
$543$	−23.5173	+	22.8148i	−1.00922	+	0.979078i
$544$	−10.2661	−	3.09460i	−0.440156	−	0.132680i
$545$	−16.9950	+	9.81204i	−0.727984	+	0.420302i
$546$	−10.4967	+	0.877078i	−0.449218	+	0.0375355i
$547$	−24.1315	−	13.9323i	−1.03179	−	0.595703i	−0.114291	−	0.993447i	$-0.536460\pi$
$547$	−24.1315	−	13.9323i	−1.03179	−	0.595703i	−0.917496	+	0.397745i	$0.869793\pi$
$548$	3.18948	−	9.41753i	0.136248	−	0.402297i
$549$	17.8538	+	11.0428i	0.761982	+	0.471295i
$550$	6.34237	+	1.04485i	0.270440	+	0.0445526i
$551$	0.0922576	−	0.159795i	0.00393031	−	0.00680749i
$552$	−18.6942	−	18.0109i	−0.795678	−	0.766596i
$553$	1.66191	+	2.87851i	0.0706716	+	0.122407i
$554$	−8.28801	−	21.9974i	−0.352124	−	0.934579i
$555$	−0.953100	+	3.35285i	−0.0404569	+	0.142320i
$556$	11.3739	+	12.9512i	0.482362	+	0.549253i
$557$		−	23.5098i		−	0.996142i	−0.867136	−	0.498071i	$-0.834042\pi$
$557$		−	23.5098i		−	0.996142i	0.867136	−	0.498071i	$-0.165958\pi$
$558$	24.5064	+	4.80452i	1.03744	+	0.203392i
$559$		−	36.6497i		−	1.55012i
$560$	8.82262	−	3.66892i	0.372824	−	0.155040i
$561$	20.4898	−	5.15860i	0.865079	−	0.217796i
$562$	−13.6596	+	5.14656i	−0.576195	+	0.217094i
$563$	−16.5569	−	28.6774i	−0.697790	−	1.20861i	−0.969231	−	0.246152i	$-0.920834\pi$
$563$	−16.5569	−	28.6774i	−0.697790	−	1.20861i	0.271442	−	0.962455i	$-0.412500\pi$
$564$	12.7808	−	6.07463i	0.538169	−	0.255788i
$565$	−10.8610	+	18.8119i	−0.456928	+	0.791422i
$566$	3.28244	−	19.9248i	0.137971	−	0.837501i
$567$	7.50717	+	4.96411i	0.315272	+	0.208473i
$568$	15.2780	+	8.14566i	0.641051	+	0.341784i
$569$	16.2900	+	9.40502i	0.682911	+	0.394279i	0.800951	−	0.598730i	$-0.204328\pi$
$569$	16.2900	+	9.40502i	0.682911	+	0.394279i	−0.118040	+	0.993009i	$0.537661\pi$
$570$	2.54412	−	1.76666i	0.106562	−	0.0739971i
$571$	−18.0636	+	10.4290i	−0.755937	+	0.436440i	−0.827835	−	0.560972i	$-0.810428\pi$
$571$	−18.0636	+	10.4290i	−0.755937	+	0.436440i	0.0718982	+	0.997412i	$0.477094\pi$
$572$	−10.8364	−	54.2797i	−0.453092	−	2.26955i
$573$	3.98100	+	15.8124i	0.166309	+	0.660572i
$574$	4.74816	−	5.78978i	0.198185	−	0.241661i
$575$	3.74220			0.156061
$576$	20.3236	−	12.7652i	0.846816	−	0.531885i
$577$	−34.3394			−1.42957			−0.714783	−	0.699346i	$-0.753475\pi$
$577$	−34.3394			−1.42957			−0.714783	+	0.699346i	$0.753475\pi$
$578$	−12.0234	+	14.6610i	−0.500107	+	0.609817i
$579$	2.19499	+	0.623962i	0.0912208	+	0.0259310i
$580$	0.326029	+	1.63309i	0.0135376	+	0.0678102i
$581$	5.60486	−	3.23597i	0.232529	−	0.134251i
$582$	17.1347	+	8.07161i	0.710257	+	0.334579i
$583$	−70.2159	−	40.5392i	−2.90805	−	1.67896i
$584$	12.6775	+	6.75915i	0.524597	+	0.279696i
$585$	16.2103	−	26.2086i	0.670214	−	1.08359i
$586$	0.558148	−	3.38803i	0.0230569	−	0.139958i
$587$	18.1996	−	31.5226i	0.751177	−	1.30108i	−0.196076	−	0.980589i	$-0.562820\pi$
$587$	18.1996	−	31.5226i	0.751177	−	1.30108i	0.947253	−	0.320487i	$-0.103847\pi$
$588$	−0.276526	+	3.45305i	−0.0114037	+	0.142401i
$589$	1.55791	+	2.69839i	0.0641928	+	0.111185i
$590$	−16.8289	+	6.34065i	−0.692833	+	0.261041i
$591$	−4.29847	−	4.43082i	−0.176815	−	0.182260i
$592$	−3.11154	+	1.29395i	−0.127884	+	0.0531808i
$593$			2.74882i			0.112880i	0.998406	+	0.0564402i	$0.0179750\pi$
$593$			2.74882i			0.112880i	−0.998406	+	0.0564402i	$0.982025\pi$
$594$	−21.4421	+	42.1535i	−0.879780	+	1.72958i
$595$			4.52784i			0.185623i
$596$	−3.32589	−	3.78710i	−0.136234	−	0.155126i
$597$	−19.2651	−	19.8583i	−0.788467	−	0.812745i
$598$	−11.3616	−	30.1551i	−0.464611	−	1.23313i
$599$	13.1712	+	22.8132i	0.538162	+	0.932124i	0.999003	+	0.0446413i	$0.0142145\pi$
$599$	13.1712	+	22.8132i	0.538162	+	0.932124i	−0.460841	+	0.887483i	$0.652452\pi$
$600$	−0.833108	+	3.35800i	−0.0340115	+	0.137090i
$601$	10.6251	−	18.4032i	0.433406	−	0.750682i	−0.563758	−	0.825940i	$-0.690645\pi$
$601$	10.6251	−	18.4032i	0.433406	−	0.750682i	0.997164	+	0.0752583i	$0.0239781\pi$
$602$	−11.8927	−	1.95923i	−0.484712	−	0.0798522i
$603$	15.3010	+	28.4615i	0.623107	+	1.15904i
$604$	0.245240	−	0.724119i	0.00997869	−	0.0294640i
$605$	−62.9312	−	36.3333i	−2.55852	−	1.47716i
$606$	−17.8389	+	37.8691i	−0.724657	+	1.53833i
$607$	12.9081	−	7.45251i	0.523924	−	0.302488i	−0.214614	−	0.976699i	$-0.568849\pi$
$607$	12.9081	−	7.45251i	0.523924	−	0.302488i	0.738539	+	0.674211i	$0.235516\pi$
$608$	2.86702	+	0.864229i	0.116273	+	0.0350491i
$609$	−0.580734	−	0.165083i	−0.0235325	−	0.00668950i
$610$	−18.2789	−	14.9904i	−0.740092	−	0.606945i
$611$	17.5665			0.710663
$612$	1.88738	+	11.2151i	0.0762930	+	0.453344i
$613$	0.497742			0.0201036			0.0100518	−	0.999949i	$-0.496800\pi$
$613$	0.497742			0.0201036			0.0100518	+	0.999949i	$0.496800\pi$
$614$	−9.70208	−	7.95661i	−0.391544	−	0.321103i
$615$	5.34837	+	21.2436i	0.215667	+	0.856623i
$616$	−18.1929	+	0.614684i	−0.733014	+	0.0247663i
$617$	−13.3288	+	7.69541i	−0.536599	+	0.309806i	−0.743700	−	0.668514i	$-0.766931\pi$
$617$	−13.3288	+	7.69541i	−0.536599	+	0.309806i	0.207100	+	0.978320i	$0.433597\pi$
$618$	−16.1910	−	23.3163i	−0.651299	−	0.937921i
$619$	6.09500	+	3.51895i	0.244979	+	0.141439i	0.617463	−	0.786600i	$-0.288161\pi$
$619$	6.09500	+	3.51895i	0.244979	+	0.141439i	−0.372484	+	0.928039i	$0.621494\pi$
$620$	−26.6353	−	9.02070i	−1.06970	−	0.362280i
$621$	−8.32807	+	26.2439i	−0.334194	+	1.05313i
$622$	8.47767	+	1.39662i	0.339924	+	0.0559995i
$623$	7.20850	−	12.4855i	0.288802	−	0.500220i
$624$	29.5885	−	3.48187i	1.18449	−	0.139386i
$625$	14.0162	+	24.2768i	0.560648	+	0.971070i
$626$	−10.2960	−	27.3268i	−0.411510	−	1.09220i
$627$	−5.72219	+	1.44064i	−0.228522	+	0.0575337i
$628$	13.2208	−	11.6107i	0.527568	−	0.463318i
$629$		−	1.59687i		−	0.0636713i
$630$	−7.63804	−	6.66127i	−0.304307	−	0.265391i
$631$		−	0.297508i		−	0.0118436i	−0.999982	−	0.00592180i	$-0.998115\pi$
$631$		−	0.297508i		−	0.0118436i	0.999982	−	0.00592180i	$-0.00188498\pi$
$632$	−4.97284	−	7.97829i	−0.197809	−	0.317359i
$633$	1.85607	−	6.52933i	0.0737720	−	0.259518i
$634$	−32.4851	+	12.2395i	−1.29015	+	0.486092i
$635$	20.3798	+	35.2988i	0.808747	+	1.40079i
$636$	24.7676	−	35.9314i	0.982098	−	1.42477i
$637$	−2.15010	+	3.72408i	−0.0851901	+	0.147554i
$638$	0.515703	−	3.13038i	0.0204169	−	0.123933i
$639$	0.556746	−	18.3557i	0.0220245	−	0.726139i
$640$	−24.5895	+	11.2140i	−0.971985	+	0.443272i
$641$	8.18111	+	4.72337i	0.323134	+	0.186562i	0.652789	−	0.757540i	$-0.273599\pi$
$641$	8.18111	+	4.72337i	0.323134	+	0.186562i	−0.329654	+	0.944102i	$0.606932\pi$
$642$	0.338951	+	4.05651i	0.0133773	+	0.160098i
$643$	−29.2594	+	16.8929i	−1.15388	+	0.666193i	−0.949830	−	0.312768i	$-0.898744\pi$
$643$	−29.2594	+	16.8929i	−1.15388	+	0.666193i	−0.204050	+	0.978960i	$0.565410\pi$
$644$	−10.3926	+	2.07478i	−0.409526	+	0.0817577i
$645$	25.3097	−	24.5537i	0.996570	−	0.966801i
$646$	−0.899800	+	1.09719i	−0.0354022	+	0.0431684i
$647$	−8.81904			−0.346712			−0.173356	−	0.984859i	$-0.555461\pi$
$647$	−8.81904			−0.346712			−0.173356	+	0.984859i	$0.555461\pi$
$648$	−21.6955	−	13.3156i	−0.852280	−	0.523086i
$649$	34.2606			1.34485
$650$	−2.72347	+	3.32093i	−0.106823	+	0.130258i
$651$	7.31751	−	7.09893i	0.286796	−	0.278229i
$652$	−21.1219	+	4.21677i	−0.827198	+	0.165141i
$653$	26.1332	−	15.0880i	1.02267	−	0.590440i	0.107795	−	0.994173i	$-0.465621\pi$
$653$	26.1332	−	15.0880i	1.02267	−	0.590440i	0.914877	+	0.403733i	$0.132288\pi$
$654$	1.67558	+	20.0530i	0.0655202	+	0.784135i
$655$	23.1273	+	13.3525i	0.903657	+	0.521727i
$656$	−12.8692	+	16.8201i	−0.502458	+	0.656716i
$657$	0.461979	−	15.2313i	0.0180235	−	0.594228i
$658$	0.939071	−	5.70028i	0.0366088	−	0.222220i
$659$	−4.08576	+	7.07674i	−0.159158	+	0.275671i	−0.934565	−	0.355791i	$-0.884211\pi$
$659$	−4.08576	+	7.07674i	−0.159158	+	0.275671i	0.775407	+	0.631462i	$0.217545\pi$
$660$	30.2248	−	43.8485i	1.17650	−	1.70680i
$661$	−22.1468	−	38.3593i	−0.861409	−	1.49200i	−0.870569	−	0.492046i	$-0.836249\pi$
$661$	−22.1468	−	38.3593i	−0.861409	−	1.49200i	0.00916009	−	0.999958i	$-0.497084\pi$
$662$	−39.7108	+	14.9619i	−1.54340	+	0.581513i
$663$	−3.86026	+	13.5798i	−0.149920	+	0.527394i
$664$	−15.5348	+	9.68279i	−0.602868	+	0.375765i
$665$		−	1.26449i		−	0.0490349i
$666$	2.69376	+	2.34928i	0.104381	+	0.0910328i
$667$		−	1.84702i		−	0.0715170i
$668$	−11.7955	+	10.3590i	−0.456382	+	0.400801i
$669$	−4.37545	+	1.10158i	−0.169165	+	0.0425897i
$670$	−12.8295	−	34.0511i	−0.495647	−	1.31551i
$671$	22.5178	+	39.0020i	0.869291	+	1.50566i
$672$	0.451889	−	9.78753i	0.0174320	−	0.377562i
$673$	6.17994	−	10.7040i	0.238219	−	0.412608i	−0.721984	−	0.691910i	$-0.756770\pi$
$673$	6.17994	−	10.7040i	0.238219	−	0.412608i	0.960203	+	0.279302i	$0.0901030\pi$
$674$	14.7188	+	2.42479i	0.566946	+	0.0933995i
$675$	3.58415	−	0.787637i	0.137954	−	0.0303161i
$676$	10.4030	+	3.52325i	0.400117	+	0.135509i
$677$	−2.57177	−	1.48481i	−0.0988412	−	0.0570660i	0.449765	−	0.893147i	$-0.351508\pi$
$677$	−2.57177	−	1.48481i	−0.0988412	−	0.0570660i	−0.548606	+	0.836081i	$0.684841\pi$
$678$	12.7047	+	18.2957i	0.487920	+	0.702642i
$679$	6.69654	−	3.86625i	0.256990	−	0.148373i
$680$	−0.432452	−	12.7994i	−0.0165838	−	0.490833i
$681$	1.32363	+	5.25744i	0.0507218	+	0.201465i
$682$	41.4250	+	33.9724i	1.58625	+	1.30087i
$683$	13.3131			0.509413			0.254707	−	0.967018i	$-0.418021\pi$
$683$	13.3131			0.509413			0.254707	+	0.967018i	$0.418021\pi$
$684$	−0.527091	−	3.13205i	−0.0201538	−	0.119757i
$685$	11.8757			0.453749
$686$	1.09352	+	0.896785i	0.0417506	+	0.0342394i
$687$	11.1153	+	3.15970i	0.424074	+	0.120550i
$688$	33.8057	+	4.40250i	1.28883	+	0.167844i
$689$	46.9158	−	27.0868i	1.78735	−	1.03193i
$690$	13.2128	−	28.0487i	0.503004	−	1.06780i
$691$	−35.4607	−	20.4733i	−1.34899	−	0.778840i	−0.360884	−	0.932611i	$-0.617525\pi$
$691$	−35.4607	−	20.4733i	−1.34899	−	0.778840i	−0.988107	+	0.153771i	$0.950858\pi$
$692$	−12.2716	+	36.2342i	−0.466496	+	1.37742i
$693$	9.14240	+	17.0058i	0.347291	+	0.645997i
$694$	−12.7166	−	2.09495i	−0.482716	−	0.0795233i
$695$	−10.2936	+	17.8290i	−0.390457	+	0.676292i
$696$	1.65739	+	0.411193i	0.0628234	+	0.0155862i
$697$	−5.01792	−	8.69129i	−0.190067	−	0.329206i
$698$	11.2667	+	29.9031i	0.426449	+	1.13185i
$699$	−18.1143	−	18.6720i	−0.685144	−	0.706241i
$700$	0.932042	+	1.06129i	0.0352279	+	0.0401130i
$701$		−	18.8087i		−	0.710396i	−0.934791	−	0.355198i	$-0.884413\pi$
$701$		−	18.8087i		−	0.710396i	0.934791	−	0.355198i	$-0.115587\pi$
$702$	−17.2286	−	26.4902i	−0.650252	−	0.999807i
$703$			0.445958i			0.0168196i
$704$	51.3693	−	3.47520i	1.93605	−	0.130976i
$705$	11.7688	+	12.1311i	0.443237	+	0.456885i
$706$	8.81063	−	3.31960i	0.331592	−	0.124935i
$707$	8.54473	+	14.7999i	0.321358	+	0.556608i
$708$	−1.47206	+	18.3820i	−0.0553235	+	0.690837i
$709$	19.3884	−	33.5818i	0.728148	−	1.26119i	−0.229517	−	0.973305i	$-0.573715\pi$
$709$	19.3884	−	33.5818i	0.728148	−	1.26119i	0.957665	−	0.287885i	$-0.0929520\pi$
$710$	−3.36145	+	20.4044i	−0.126153	+	0.765763i
$711$	−5.24524	+	8.48042i	−0.196712	+	0.318040i
$712$	−19.1846	+	35.9826i	−0.718973	+	1.34851i
$713$	27.0112	+	15.5949i	1.01158	+	0.584035i
$714$	4.20023	+	1.97859i	0.157190	+	0.0740470i
$715$	57.2532	−	33.0551i	2.14115	−	1.23619i
$716$	10.2379	+	51.2817i	0.382607	+	1.91649i
$717$	3.66867	+	1.04288i	0.137009	+	0.0389470i
$718$	7.20418	−	8.78459i	0.268858	−	0.327838i
$719$	27.9873			1.04375			0.521875	−	0.853022i	$-0.325233\pi$
$719$	27.9873			1.04375			0.521875	+	0.853022i	$0.325233\pi$
$720$	22.2275	+	18.1007i	0.828371	+	0.674572i
$721$	−11.5888			−0.431589
$722$	−16.7876	+	20.4704i	−0.624771	+	0.761829i
$723$	−7.85224	−	31.1888i	−0.292028	−	1.15993i
$724$	−7.40708	−	37.1022i	−0.275282	−	1.37889i
$725$	−0.213190	+	0.123085i	−0.00791769	+	0.00457128i
$726$	−61.2044	+	42.5007i	−2.27151	+	1.57735i
$727$	11.9395	+	6.89330i	0.442813	+	0.255658i	0.704790	−	0.709416i	$-0.251041\pi$
$727$	11.9395	+	6.89330i	0.442813	+	0.255658i	−0.261977	+	0.965074i	$0.584374\pi$
$728$	5.72225	−	10.7326i	0.212081	−	0.397778i
$729$	−2.45267	+	26.8884i	−0.0908397	+	0.995866i
$730$	−2.78928	+	16.9313i	−0.103236	+	0.626654i
$731$	−8.07734	+	13.9904i	−0.298751	+	0.517452i
$732$	−21.8934	+	10.4058i	−0.809204	+	0.384609i
$733$	20.9012	+	36.2020i	0.772005	+	1.33715i	0.936463	+	0.350767i	$0.114079\pi$
$733$	20.9012	+	36.2020i	0.772005	+	1.33715i	−0.164458	+	0.986384i	$0.552588\pi$
$734$	−22.8027	+	8.59145i	−0.841664	+	0.317116i
$735$	−4.01227	+	1.01015i	−0.147995	+	0.0372598i
$736$	29.1798	−	6.85760i	1.07558	−	0.252775i
$737$			69.3221i			2.55351i
$738$	22.0437	+	4.32170i	0.811438	+	0.159084i
$739$		−	47.3413i		−	1.74148i	−0.491746	−	0.870739i	$-0.663641\pi$
$739$		−	47.3413i		−	1.74148i	0.491746	−	0.870739i	$-0.336359\pi$
$740$	−2.65593	−	3.02424i	−0.0976339	−	0.111173i
$741$	1.07806	−	3.79242i	0.0396034	−	0.139318i
$742$	−6.28158	−	16.6721i	−0.230604	−	0.612051i
$743$	1.10160	+	1.90802i	0.0404136	+	0.0699984i	0.885525	−	0.464592i	$-0.153799\pi$
$743$	1.10160	+	1.90802i	0.0404136	+	0.0699984i	−0.845111	+	0.534591i	$0.820466\pi$
$744$	−20.0072	+	20.7663i	−0.733501	+	0.761328i
$745$	3.00998	−	5.21343i	0.110277	−	0.191005i
$746$	0.727681	+	0.119879i	0.0266423	+	0.00438909i
$747$	16.5125	+	10.2132i	0.604162	+	0.373682i
$748$	−7.82628	+	23.1086i	−0.286157	+	0.844933i
$749$	1.43919	+	0.830918i	0.0525869	+	0.0303611i
$750$	25.0368	−	2.09200i	0.914213	−	0.0763892i
$751$	9.02644	−	5.21142i	0.329379	−	0.190167i	−0.326186	−	0.945306i	$-0.605764\pi$
$751$	9.02644	−	5.21142i	0.329379	−	0.190167i	0.655566	+	0.755138i	$0.272430\pi$
$752$	−2.11015	+	16.2033i	−0.0769492	+	0.590874i
$753$	7.68487	−	7.45531i	0.280052	−	0.271687i
$754$	1.63910	+	1.34421i	0.0596924	+	0.0489534i
$755$	0.913132			0.0332323
$756$	−9.51700	+	4.17453i	−0.346130	+	0.151826i
$757$	14.0656			0.511224			0.255612	−	0.966779i	$-0.417723\pi$
$757$	14.0656			0.511224			0.255612	+	0.966779i	$0.417723\pi$
$758$	−24.9803	−	20.4862i	−0.907326	−	0.744092i
$759$	−42.3953	+	41.1289i	−1.53885	+	1.49289i
$760$	0.120771	+	3.57448i	0.00438082	+	0.129660i
$761$	−23.2533	+	13.4253i	−0.842931	+	0.486667i	−0.858260	−	0.513216i	$-0.828454\pi$
$761$	−23.2533	+	13.4253i	−0.842931	+	0.486667i	0.0153283	+	0.999883i	$0.495121\pi$
$762$	41.6505	−	3.48020i	1.50884	−	0.126074i
$763$	7.11451	+	4.10757i	0.257563	+	0.148704i
$764$	−17.8334	−	6.03970i	−0.645188	−	0.218509i
$765$	−11.9642	+	6.43200i	−0.432566	+	0.232549i
$766$	34.8241	+	5.73697i	1.25825	+	0.207285i
$767$	−11.4459	+	19.8248i	−0.413286	+	0.715833i
$768$	−0.342604	+	27.7107i	−0.0123626	+	0.999924i
$769$	18.9397	+	32.8045i	0.682983	+	1.18296i	0.974066	+	0.226263i	$0.0726510\pi$
$769$	18.9397	+	32.8045i	0.682983	+	1.18296i	−0.291083	+	0.956698i	$0.594016\pi$
$770$	−7.66566	−	20.3456i	−0.276251	−	0.733204i
$771$	−3.82087	+	13.4412i	−0.137605	+	0.484072i
$772$	−1.97986	+	1.73875i	−0.0712569	+	0.0625788i
$773$			26.0697i			0.937662i	0.883288	+	0.468831i	$0.155325\pi$
$773$			26.0697i			0.937662i

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.896785 + 1.09352i) q^{2} +(-1.24317 + 1.20604i) q^{3} +(-0.391553 - 1.96130i) q^{4} +(2.06874 - 1.19439i) q^{5} +(-0.203962 - 2.44098i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +(0.0909512 - 2.99862i) q^{9} +O(q^{10})\)	\(q+(-0.896785 + 1.09352i) q^{2} +(-1.24317 + 1.20604i) q^{3} +(-0.391553 - 1.96130i) q^{4} +(2.06874 - 1.19439i) q^{5} +(-0.203962 - 2.44098i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(2.49585 + 1.33069i) q^{8} +(0.0909512 - 2.99862i) q^{9} +(-0.549133 + 3.33330i) q^{10} +(3.21792 - 5.57360i) q^{11} +(2.85216 + 1.96600i) q^{12} +(2.15010 + 3.72408i) q^{13} +(1.32340 - 0.498620i) q^{14} +(-1.13132 + 3.97980i) q^{15} +(-3.69337 + 1.53590i) q^{16} -1.89547i q^{17} +(3.19748 + 2.78858i) q^{18} +0.529348i q^{19} +(-3.15256 - 3.58974i) q^{20} +(1.67964 - 0.422873i) q^{21} +(3.20904 + 8.51717i) q^{22} +(2.64942 + 4.58894i) q^{23} +(-4.70763 + 1.35580i) q^{24} +(0.353115 - 0.611613i) q^{25} +(-6.00052 - 0.988535i) q^{26} +(3.50338 + 3.83749i) q^{27} +(-0.641554 + 1.89431i) q^{28} +(-0.301871 - 0.174285i) q^{29} +(-3.33742 - 4.80614i) q^{30} +(5.09757 - 2.94308i) q^{31} +(1.63263 - 5.41614i) q^{32} +(2.72154 + 10.8099i) q^{33} +(2.07272 + 1.69983i) q^{34} -2.38877 q^{35} +(-5.91680 + 0.995736i) q^{36} +0.842466 q^{37} +(-0.578850 - 0.474711i) q^{38} +(-7.16433 - 2.03657i) q^{39} +(6.75261 - 0.228150i) q^{40} +(4.58530 - 2.64733i) q^{41} +(-1.04386 + 2.21593i) q^{42} +(-7.38095 - 4.26140i) q^{43} +(-12.1915 - 4.12894i) q^{44} +(-3.39336 - 6.31199i) q^{45} +(-7.39404 - 1.21810i) q^{46} +(2.04252 - 3.53774i) q^{47} +(2.73914 - 6.36373i) q^{48} +(0.500000 + 0.866025i) q^{49} +(0.352140 + 0.934622i) q^{50} +(2.28600 + 2.35639i) q^{51} +(6.46216 - 5.67516i) q^{52} -12.5979i q^{53} +(-7.33813 + 0.389594i) q^{54} -15.3738i q^{55} +(-1.49612 - 2.40034i) q^{56} +(-0.638413 - 0.658070i) q^{57} +(0.461297 - 0.173804i) q^{58} +(2.66171 + 4.61021i) q^{59} +(8.24854 + 0.660558i) q^{60} +(-3.49882 + 6.06013i) q^{61} +(-1.35312 + 8.21358i) q^{62} +(-1.57808 + 2.55141i) q^{63} +(4.45851 + 6.64242i) q^{64} +(8.89599 + 5.13610i) q^{65} +(-14.2614 - 6.71809i) q^{66} +(-9.32818 + 5.38563i) q^{67} +(-3.71758 + 0.742175i) q^{68} +(-8.82811 - 2.50953i) q^{69} +(2.14221 - 2.61216i) q^{70} +6.12137 q^{71} +(4.21725 - 7.36307i) q^{72} +5.07942 q^{73} +(-0.755511 + 0.921250i) q^{74} +(0.298645 + 1.18621i) q^{75} +(1.03821 - 0.207268i) q^{76} +(-5.57360 + 3.21792i) q^{77} +(8.65189 - 6.00793i) q^{78} +(-2.87851 - 1.66191i) q^{79} +(-5.80616 + 7.58869i) q^{80} +(-8.98346 - 0.545456i) q^{81} +(-1.21714 + 7.38818i) q^{82} +(-3.23597 + 5.60486i) q^{83} +(-1.48704 - 3.12869i) q^{84} +(-2.26392 - 3.92122i) q^{85} +(11.2790 - 4.24963i) q^{86} +(0.585472 - 0.147401i) q^{87} +(15.4482 - 9.62880i) q^{88} +14.4170i q^{89} +(9.94537 + 1.94981i) q^{90} -4.30020i q^{91} +(7.96288 - 6.99312i) q^{92} +(-2.78769 + 9.80661i) q^{93} +(2.03688 + 5.40612i) q^{94} +(0.632246 + 1.09508i) q^{95} +(4.50242 + 8.70220i) q^{96} +(-3.86625 + 6.69654i) q^{97} +(-1.39540 - 0.229881i) q^{98} +(-16.4205 - 10.1563i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Introduction

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