LMFDB - Embedded newform 570.2.u.a.511.1

Newspace parameters

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.u (of order $9$, degree $6$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
Defining polynomial:	$x^{6} - x^{3} + 1$
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			511.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	570.511
Dual form			570.2.u.a.541.1

$q$-expansion

$f(q)$	$=$	$q+(-0.173648 + 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.939693 - 0.342020i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.28699 - 3.96118i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.939693 - 0.342020i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.28699 - 3.96118i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(0.173648 + 0.984808i) q^{10} +(0.173648 - 0.300767i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-4.99273 + 4.18939i) q^{13} +(4.29813 - 1.56439i) q^{14} +(-0.939693 - 0.342020i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.22668 + 6.95686i) q^{17} -1.00000 q^{18} +(-2.82635 + 3.31839i) q^{19} -1.00000 q^{20} +(-0.794263 + 4.50449i) q^{21} +(0.266044 + 0.223238i) q^{22} +(-5.54576 - 2.01849i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(-3.25877 - 5.64436i) q^{26} +(0.500000 - 0.866025i) q^{27} +(0.794263 + 4.50449i) q^{28} +(-0.879385 - 4.98724i) q^{29} +(0.500000 - 0.866025i) q^{30} +(1.18479 + 2.05212i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-0.326352 + 0.118782i) q^{33} +(-6.63816 - 2.41609i) q^{34} +(-3.50387 - 2.94010i) q^{35} +(0.173648 - 0.984808i) q^{36} +7.66044 q^{37} +(-2.77719 - 3.35965i) q^{38} +6.51754 q^{39} +(0.173648 - 0.984808i) q^{40} +(0.364370 + 0.305743i) q^{41} +(-4.29813 - 1.56439i) q^{42} +(-6.71688 + 2.44474i) q^{43} +(-0.266044 + 0.223238i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.95084 - 5.11100i) q^{46} +(-1.01114 - 5.73448i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(-6.96064 + 12.0562i) q^{49} +(0.500000 + 0.866025i) q^{50} +(5.41147 - 4.54077i) q^{51} +(6.12449 - 2.22913i) q^{52} +(-9.70961 - 3.53401i) q^{53} +(0.766044 + 0.642788i) q^{54} +(0.0603074 - 0.342020i) q^{55} -4.57398 q^{56} +(4.29813 - 0.725293i) q^{57} +5.06418 q^{58} +(0.316552 - 1.79525i) q^{59} +(0.766044 + 0.642788i) q^{60} +(-10.8229 - 3.93923i) q^{61} +(-2.22668 + 0.810446i) q^{62} +(3.50387 - 2.94010i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.25877 + 5.64436i) q^{65} +(-0.0603074 - 0.342020i) q^{66} +(0.106067 + 0.601535i) q^{67} +(3.53209 - 6.11776i) q^{68} +(2.95084 + 5.11100i) q^{69} +(3.50387 - 2.94010i) q^{70} +(11.0496 - 4.02174i) q^{71} +(0.939693 + 0.342020i) q^{72} +(-4.94356 - 4.14814i) q^{73} +(-1.33022 + 7.54407i) q^{74} -1.00000 q^{75} +(3.79086 - 2.15160i) q^{76} -1.58853 q^{77} +(-1.13176 + 6.41852i) q^{78} +(6.69459 + 5.61743i) q^{79} +(0.939693 + 0.342020i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.364370 + 0.305743i) q^{82} +(-0.837496 - 1.45059i) q^{83} +(2.28699 - 3.96118i) q^{84} +(1.22668 + 6.95686i) q^{85} +(-1.24123 - 7.03936i) q^{86} +(-2.53209 + 4.38571i) q^{87} +(-0.173648 - 0.300767i) q^{88} +(-8.30200 + 6.96621i) q^{89} +(-0.939693 + 0.342020i) q^{90} +(28.0133 + 10.1960i) q^{91} +(4.52094 + 3.79352i) q^{92} +(0.411474 - 2.33359i) q^{93} +5.82295 q^{94} +(-1.52094 + 4.08494i) q^{95} +1.00000 q^{96} +(0.184793 - 1.04801i) q^{97} +(-10.6643 - 8.94842i) q^{98} +(0.326352 + 0.118782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6q - 6q^{7} + 3q^{8} + O(q^{10}) $	$ 6q - 6q^{7} + 3q^{8} + 3q^{12} - 12q^{13} + 12q^{14} + 6q^{17} - 6q^{18} - 18q^{19} - 6q^{20} - 15q^{21} - 3q^{22} - 3q^{23} + 3q^{26} + 3q^{27} + 15q^{28} + 6q^{29} + 3q^{30} - 3q^{33} - 6q^{34} + 3q^{35} - 6q^{38} - 6q^{39} + 21q^{41} - 12q^{42} - 24q^{43} + 3q^{44} + 3q^{45} + 6q^{46} - 33q^{49} + 3q^{50} + 12q^{51} + 24q^{52} - 24q^{53} + 6q^{55} - 12q^{56} + 12q^{57} + 12q^{58} - 24q^{61} - 3q^{63} - 3q^{64} + 3q^{65} - 6q^{66} - 24q^{67} + 12q^{68} + 6q^{69} - 3q^{70} + 12q^{71} + 15q^{74} - 6q^{75} - 9q^{76} - 30q^{77} - 12q^{78} + 36q^{79} - 21q^{82} + 6q^{84} - 6q^{85} - 30q^{86} - 6q^{87} - 12q^{89} + 24q^{91} + 24q^{92} - 18q^{93} - 6q^{94} - 6q^{95} + 6q^{96} - 6q^{97} + 6q^{98} + 3q^{99} + O(q^{100}) $

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$	$1$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$	0.766044	−	0.642788i	0.312736	−	0.262417i
$7$	−2.28699	−	3.96118i	−0.864401	−	1.49719i	−0.867641	−	0.497191i	$-0.834365\pi$
$7$	−2.28699	−	3.96118i	−0.864401	−	1.49719i	0.00324055	−	0.999995i	$-0.498969\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	0.173648	+	0.984808i	0.0549124	+	0.311424i
$11$	0.173648	−	0.300767i	0.0523569	−	0.0906848i	−0.838659	−	0.544657i	$-0.816660\pi$
$11$	0.173648	−	0.300767i	0.0523569	−	0.0906848i	0.891016	+	0.453972i	$0.149993\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−4.99273	+	4.18939i	−1.38473	+	1.16193i	−0.417310	+	0.908764i	$0.637027\pi$
$13$	−4.99273	+	4.18939i	−1.38473	+	1.16193i	−0.967423	+	0.253165i	$0.918529\pi$
$14$	4.29813	−	1.56439i	1.14872	−	0.418102i
$15$	−0.939693	−	0.342020i	−0.242628	−	0.0883092i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.22668	+	6.95686i	−0.297514	+	1.68729i	0.359291	+	0.933225i	$0.383018\pi$
$17$	−1.22668	+	6.95686i	−0.297514	+	1.68729i	−0.656805	+	0.754060i	$0.728093\pi$
$18$	−1.00000			−0.235702
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$20$	−1.00000			−0.223607
$21$	−0.794263	+	4.50449i	−0.173322	+	0.982960i
$22$	0.266044	+	0.223238i	0.0567209	+	0.0475945i
$23$	−5.54576	−	2.01849i	−1.15637	−	0.420885i	−0.308571	−	0.951201i	$-0.599851\pi$
$23$	−5.54576	−	2.01849i	−1.15637	−	0.420885i	−0.847800	+	0.530317i	$0.822073\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	−3.25877	−	5.64436i	−0.639097	−	1.10695i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	0.794263	+	4.50449i	0.150102	+	0.851268i
$29$	−0.879385	−	4.98724i	−0.163298	−	0.926108i	−0.950802	−	0.309799i	$-0.899738\pi$
$29$	−0.879385	−	4.98724i	−0.163298	−	0.926108i	0.787504	−	0.616309i	$-0.211373\pi$
$30$	0.500000	−	0.866025i	0.0912871	−	0.158114i
$31$	1.18479	+	2.05212i	0.212795	+	0.368572i	0.952588	−	0.304263i	$-0.0984100\pi$
$31$	1.18479	+	2.05212i	0.212795	+	0.368572i	−0.739793	+	0.672834i	$0.765077\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−0.326352	+	0.118782i	−0.0568106	+	0.0206774i
$34$	−6.63816	−	2.41609i	−1.13843	−	0.414356i
$35$	−3.50387	−	2.94010i	−0.592262	−	0.496967i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$	7.66044			1.25937			0.629685	−	0.776851i	$-0.283184\pi$
$37$	7.66044			1.25937			0.629685	+	0.776851i	$0.283184\pi$
$38$	−2.77719	−	3.35965i	−0.450520	−	0.545007i
$39$	6.51754			1.04364
$40$	0.173648	−	0.984808i	0.0274562	−	0.155712i
$41$	0.364370	+	0.305743i	0.0569051	+	0.0477491i	0.670797	−	0.741641i	$-0.265952\pi$
$41$	0.364370	+	0.305743i	0.0569051	+	0.0477491i	−0.613892	+	0.789390i	$0.710397\pi$
$42$	−4.29813	−	1.56439i	−0.663216	−	0.241391i
$43$	−6.71688	+	2.44474i	−1.02431	+	0.372820i	−0.798914	−	0.601446i	$-0.794592\pi$
$43$	−6.71688	+	2.44474i	−1.02431	+	0.372820i	−0.225401	+	0.974266i	$0.572369\pi$
$44$	−0.266044	+	0.223238i	−0.0401077	+	0.0336544i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	2.95084	−	5.11100i	0.435077	−	0.753576i
$47$	−1.01114	−	5.73448i	−0.147491	−	0.836461i	−0.965334	−	0.261019i	$-0.915941\pi$
$47$	−1.01114	−	5.73448i	−0.147491	−	0.836461i	0.817843	−	0.575441i	$-0.195170\pi$
$48$	−0.173648	−	0.984808i	−0.0250640	−	0.142145i
$49$	−6.96064	+	12.0562i	−0.994377	+	1.72231i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	5.41147	−	4.54077i	0.757758	−	0.635834i
$52$	6.12449	−	2.22913i	0.849313	−	0.309125i
$53$	−9.70961	−	3.53401i	−1.33372	−	0.485433i	−0.425889	−	0.904775i	$-0.640039\pi$
$53$	−9.70961	−	3.53401i	−1.33372	−	0.485433i	−0.907828	+	0.419342i	$0.862261\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	0.0603074	−	0.342020i	0.00813185	−	0.0461180i
$56$	−4.57398			−0.611224
$57$	4.29813	−	0.725293i	0.569302	−	0.0960674i
$58$	5.06418			0.664959
$59$	0.316552	−	1.79525i	0.0412115	−	0.233722i	−0.957244	−	0.289282i	$-0.906583\pi$
$59$	0.316552	−	1.79525i	0.0412115	−	0.233722i	0.998455	+	0.0555602i	$0.0176945\pi$
$60$	0.766044	+	0.642788i	0.0988959	+	0.0829835i
$61$	−10.8229	−	3.93923i	−1.38574	−	0.504367i	−0.461824	−	0.886971i	$-0.652805\pi$
$61$	−10.8229	−	3.93923i	−1.38574	−	0.504367i	−0.923912	+	0.382605i	$0.875027\pi$
$62$	−2.22668	+	0.810446i	−0.282789	+	0.102927i
$63$	3.50387	−	2.94010i	0.441446	−	0.370417i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−3.25877	+	5.64436i	−0.404201	+	0.700096i
$66$	−0.0603074	−	0.342020i	−0.00742333	−	0.0420998i
$67$	0.106067	+	0.601535i	0.0129581	+	0.0734892i	0.990601	−	0.136783i	$-0.0436762\pi$
$67$	0.106067	+	0.601535i	0.0129581	+	0.0734892i	−0.977643	+	0.210272i	$0.932565\pi$
$68$	3.53209	−	6.11776i	0.428329	−	0.741887i
$69$	2.95084	+	5.11100i	0.355239	+	0.615292i
$70$	3.50387	−	2.94010i	0.418793	−	0.351409i
$71$	11.0496	−	4.02174i	1.31135	−	0.477292i	0.410673	−	0.911783i	$-0.365294\pi$
$71$	11.0496	−	4.02174i	1.31135	−	0.477292i	0.900677	+	0.434490i	$0.143071\pi$
$72$	0.939693	+	0.342020i	0.110744	+	0.0403075i
$73$	−4.94356	−	4.14814i	−0.578600	−	0.485503i	0.305887	−	0.952068i	$-0.401047\pi$
$73$	−4.94356	−	4.14814i	−0.578600	−	0.485503i	−0.884487	+	0.466565i	$0.845492\pi$
$74$	−1.33022	+	7.54407i	−0.154635	+	0.876980i
$75$	−1.00000			−0.115470
$76$	3.79086	−	2.15160i	0.434841	−	0.246806i
$77$	−1.58853			−0.181029
$78$	−1.13176	+	6.41852i	−0.128146	+	0.726755i
$79$	6.69459	+	5.61743i	0.753201	+	0.632010i	0.936347	−	0.351075i	$-0.114184\pi$
$79$	6.69459	+	5.61743i	0.753201	+	0.632010i	−0.183147	+	0.983086i	$0.558628\pi$
$80$	0.939693	+	0.342020i	0.105061	+	0.0382390i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−0.364370	+	0.305743i	−0.0402380	+	0.0337637i
$83$	−0.837496	−	1.45059i	−0.0919271	−	0.159222i	0.816395	−	0.577494i	$-0.195969\pi$
$83$	−0.837496	−	1.45059i	−0.0919271	−	0.159222i	−0.908322	+	0.418272i	$0.862636\pi$
$84$	2.28699	−	3.96118i	0.249531	−	0.432200i
$85$	1.22668	+	6.95686i	0.133052	+	0.754577i
$86$	−1.24123	−	7.03936i	−0.133845	−	0.759074i
$87$	−2.53209	+	4.38571i	−0.271468	+	0.470197i
$88$	−0.173648	−	0.300767i	−0.0185110	−	0.0320619i
$89$	−8.30200	+	6.96621i	−0.880011	+	0.738417i	−0.966181	−	0.257864i	$-0.916981\pi$
$89$	−8.30200	+	6.96621i	−0.880011	+	0.738417i	0.0861706	+	0.996280i	$0.472537\pi$
$90$	−0.939693	+	0.342020i	−0.0990523	+	0.0360521i
$91$	28.0133	+	10.1960i	2.93659	+	1.06883i
$92$	4.52094	+	3.79352i	0.471341	+	0.395502i
$93$	0.411474	−	2.33359i	0.0426679	−	0.241982i
$94$	5.82295			0.600591
$95$	−1.52094	+	4.08494i	−0.156046	+	0.419106i
$96$	1.00000			0.102062
$97$	0.184793	−	1.04801i	0.0187628	−	0.106409i	−0.973988	−	0.226599i	$-0.927239\pi$
$97$	0.184793	−	1.04801i	0.0187628	−	0.106409i	0.992751	+	0.120190i	$0.0383503\pi$
$98$	−10.6643	−	8.94842i	−1.07726	−	0.903927i
$99$	0.326352	+	0.118782i	0.0327996	+	0.0119381i
$100$	−0.939693	+	0.342020i	−0.0939693	+	0.0342020i
$101$	9.53983	−	8.00487i	0.949249	−	0.796514i	−0.0299223	−	0.999552i	$-0.509526\pi$
$101$	9.53983	−	8.00487i	0.949249	−	0.796514i	0.979171	+	0.203038i	$0.0650815\pi$
$102$	3.53209	+	6.11776i	0.349729	+	0.605748i
$103$	0.648833	−	1.12381i	0.0639314	−	0.110733i	−0.832288	−	0.554343i	$-0.812969\pi$
$103$	0.648833	−	1.12381i	0.0639314	−	0.110733i	0.896219	+	0.443611i	$0.146303\pi$
$104$	1.13176	+	6.41852i	0.110978	+	0.629388i
$105$	0.794263	+	4.50449i	0.0775121	+	0.439593i
$106$	5.16637	−	8.94842i	0.501803	−	0.869148i
$107$	−8.12836	−	14.0787i	−0.785798	−	1.36104i	−0.928521	−	0.371279i	$-0.878919\pi$
$107$	−8.12836	−	14.0787i	−0.785798	−	1.36104i	0.142724	−	0.989763i	$-0.454414\pi$
$108$	−0.766044	+	0.642788i	−0.0737127	+	0.0618523i
$109$	1.53209	−	0.557635i	0.146748	−	0.0534117i	−0.267602	−	0.963529i	$-0.586231\pi$
$109$	1.53209	−	0.557635i	0.146748	−	0.0534117i	0.414350	+	0.910118i	$0.364009\pi$
$110$	0.326352	+	0.118782i	0.0311164	+	0.0113255i
$111$	−5.86824	−	4.92404i	−0.556989	−	0.467369i
$112$	0.794263	−	4.50449i	0.0750508	−	0.425634i
$113$	4.93582			0.464323			0.232162	−	0.972677i	$-0.425420\pi$
$113$	4.93582			0.464323			0.232162	+	0.972677i	$0.425420\pi$
$114$	−0.0320889	+	4.35878i	−0.00300540	+	0.408237i
$115$	−5.90167			−0.550334
$116$	−0.879385	+	4.98724i	−0.0816489	+	0.463054i
$117$	−4.99273	−	4.18939i	−0.461578	−	0.387310i
$118$	1.71301	+	0.623485i	0.157695	+	0.0573964i
$119$	30.3628	−	11.0511i	2.78335	−	1.01306i
$120$	−0.766044	+	0.642788i	−0.0699300	+	0.0586782i
$121$	5.43969	+	9.42182i	0.494518	+	0.856529i
$122$	5.75877	−	9.97448i	0.521375	−	0.903047i
$123$	−0.0825961	−	0.468426i	−0.00744744	−	0.0422365i
$124$	−0.411474	−	2.33359i	−0.0369515	−	0.209562i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	2.28699	+	3.96118i	0.203741	+	0.352890i
$127$	−1.67159	+	1.40263i	−0.148330	+	0.124463i	−0.713933	−	0.700214i	$-0.753088\pi$
$127$	−1.67159	+	1.40263i	−0.148330	+	0.124463i	0.565603	+	0.824677i	$0.308643\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	6.71688	+	2.44474i	0.591388	+	0.215248i
$130$	−4.99273	−	4.18939i	−0.437891	−	0.367434i
$131$	−0.330222	+	1.87278i	−0.0288516	+	0.163626i	−0.995829	−	0.0912350i	$-0.970919\pi$
$131$	−0.330222	+	1.87278i	−0.0288516	+	0.163626i	0.966978	+	0.254861i	$0.0820297\pi$
$132$	0.347296			0.0302283
$133$	19.6086	+	3.60656i	1.70028	+	0.312729i
$134$	−0.610815			−0.0527663
$135$	0.173648	−	0.984808i	0.0149453	−	0.0847588i
$136$	5.41147	+	4.54077i	0.464030	+	0.389367i
$137$	1.07873	+	0.392624i	0.0921618	+	0.0335441i	0.387690	−	0.921790i	$-0.373273\pi$
$137$	1.07873	+	0.392624i	0.0921618	+	0.0335441i	−0.295528	+	0.955334i	$0.595495\pi$
$138$	−5.54576	+	2.01849i	−0.472086	+	0.171825i
$139$	−17.7934	+	14.9304i	−1.50922	+	1.26638i	−0.643950	+	0.765067i	$0.722706\pi$
$139$	−17.7934	+	14.9304i	−1.50922	+	1.26638i	−0.865265	+	0.501315i	$0.832850\pi$
$140$	2.28699	+	3.96118i	0.193286	+	0.334781i
$141$	−2.91147	+	5.04282i	−0.245190	+	0.424682i
$142$	2.04189	+	11.5801i	0.171352	+	0.971783i
$143$	0.393056	+	2.22913i	0.0328690	+	0.186409i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.53209	−	4.38571i	−0.210279	−	0.364213i
$146$	4.94356	−	4.14814i	0.409132	−	0.343303i
$147$	13.0817	−	4.76136i	1.07896	−	0.392710i
$148$	−7.19846	−	2.62003i	−0.591710	−	0.215365i
$149$	−9.41921	−	7.90366i	−0.771652	−	0.647493i	0.169479	−	0.985534i	$-0.445791\pi$
$149$	−9.41921	−	7.90366i	−0.771652	−	0.647493i	−0.941131	+	0.338041i	$0.890236\pi$
$150$	0.173648	−	0.984808i	0.0141783	−	0.0804092i
$151$	−7.06418			−0.574875			−0.287437	−	0.957799i	$-0.592803\pi$
$151$	−7.06418			−0.574875			−0.287437	+	0.957799i	$0.592803\pi$
$152$	1.46064	+	4.10689i	0.118473	+	0.333113i
$153$	−7.06418			−0.571105
$154$	0.275845	−	1.56439i	0.0222282	−	0.126062i
$155$	1.81521	+	1.52314i	0.145801	+	0.122342i
$156$	−6.12449	−	2.22913i	−0.490351	−	0.178473i
$157$	−1.01367	+	0.368946i	−0.0808997	+	0.0294451i	−0.382153	−	0.924099i	$-0.624817\pi$
$157$	−1.01367	+	0.368946i	−0.0808997	+	0.0294451i	0.301253	+	0.953544i	$0.402595\pi$
$158$	−6.69459	+	5.61743i	−0.532593	+	0.446899i
$159$	5.16637	+	8.94842i	0.409720	+	0.709656i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	4.68748	+	26.5840i	0.369425	+	2.09511i
$162$	−0.173648	−	0.984808i	−0.0136431	−	0.0773738i
$163$	−6.36959	+	11.0324i	−0.498904	+	0.864128i	−0.999999	−	0.00126462i	$-0.999597\pi$
$163$	−6.36959	+	11.0324i	−0.498904	+	0.864128i	0.501095	+	0.865392i	$0.332931\pi$
$164$	−0.237826	−	0.411927i	−0.0185711	−	0.0321661i
$165$	−0.266044	+	0.223238i	−0.0207115	+	0.0173790i
$166$	1.57398	−	0.572881i	0.122164	−	0.0444642i
$167$	0.168900	+	0.0614747i	0.0130699	+	0.00475706i	0.348547	−	0.937291i	$-0.386675\pi$
$167$	0.168900	+	0.0614747i	0.0130699	+	0.00475706i	−0.335477	+	0.942048i	$0.608897\pi$
$168$	3.50387	+	2.94010i	0.270329	+	0.226833i
$169$	5.11886	−	29.0305i	0.393758	−	2.23312i
$170$	−7.06418			−0.541798
$171$	−3.75877	−	2.20718i	−0.287440	−	0.168787i
$172$	7.14796			0.545027
$173$	−2.37077	+	13.4453i	−0.180246	+	1.02223i	0.751666	+	0.659543i	$0.229250\pi$
$173$	−2.37077	+	13.4453i	−0.180246	+	1.02223i	−0.931913	+	0.362683i	$0.881861\pi$
$174$	−3.87939	−	3.25519i	−0.294095	−	0.246775i
$175$	−4.29813	−	1.56439i	−0.324908	−	0.118257i
$176$	0.326352	−	0.118782i	0.0245997	−	0.00895356i
$177$	−1.39646	+	1.17177i	−0.104964	+	0.0880755i
$178$	−5.41875	−	9.38555i	−0.406152	−	0.703476i
$179$	10.6951	−	18.5244i	0.799386	−	1.38458i	−0.120630	−	0.992698i	$-0.538491\pi$
$179$	10.6951	−	18.5244i	0.799386	−	1.38458i	0.920016	−	0.391880i	$-0.128175\pi$
$180$	−0.173648	−	0.984808i	−0.0129430	−	0.0734032i
$181$	1.44057	+	8.16988i	0.107077	+	0.607262i	0.990370	+	0.138442i	$0.0442096\pi$
$181$	1.44057	+	8.16988i	0.107077	+	0.607262i	−0.883294	+	0.468820i	$0.844679\pi$
$182$	−14.9055	+	25.8172i	−1.10487	+	1.91370i
$183$	5.75877	+	9.97448i	0.425701	+	0.737335i
$184$	−4.52094	+	3.79352i	−0.333288	+	0.279662i
$185$	7.19846	−	2.62003i	0.529242	−	0.192628i
$186$	2.22668	+	0.810446i	0.163268	+	0.0594248i
$187$	1.87939	+	1.57699i	0.137434	+	0.115321i
$188$	−1.01114	+	5.73448i	−0.0737453	+	0.418230i
$189$	−4.57398			−0.332708
$190$	−3.75877	−	2.20718i	−0.272690	−	0.160126i
$191$	−12.9513			−0.937123			−0.468562	−	0.883431i	$-0.655228\pi$
$191$	−12.9513			−0.937123			−0.468562	+	0.883431i	$0.655228\pi$
$192$	−0.173648	+	0.984808i	−0.0125320	+	0.0710724i
$193$	−9.88713	−	8.29628i	−0.711691	−	0.597180i	0.213382	−	0.976969i	$-0.431552\pi$
$193$	−9.88713	−	8.29628i	−0.711691	−	0.597180i	−0.925073	+	0.379789i	$0.875997\pi$
$194$	1.00000	+	0.363970i	0.0717958	+	0.0261315i
$195$	6.12449	−	2.22913i	0.438583	−	0.159631i
$196$	10.6643	−	8.94842i	0.761737	−	0.639173i
$197$	5.75537	+	9.96859i	0.410053	+	0.710232i	0.994895	−	0.100915i	$-0.0321769\pi$
$197$	5.75537	+	9.96859i	0.410053	+	0.710232i	−0.584842	+	0.811147i	$0.698844\pi$
$198$	−0.173648	+	0.300767i	−0.0123406	+	0.0213746i
$199$	−4.19934	−	23.8156i	−0.297683	−	1.68825i	−0.656092	−	0.754681i	$-0.727792\pi$
$199$	−4.19934	−	23.8156i	−0.297683	−	1.68825i	0.358408	−	0.933565i	$-0.383320\pi$
$200$	−0.173648	−	0.984808i	−0.0122788	−	0.0696364i
$201$	0.305407	−	0.528981i	0.0215418	−	0.0373114i
$202$	6.22668	+	10.7849i	0.438108	+	0.758825i
$203$	−17.7442	+	14.8892i	−1.24540	+	1.04501i
$204$	−6.63816	+	2.41609i	−0.464764	+	0.169160i
$205$	0.446967	+	0.162683i	0.0312175	+	0.0113622i
$206$	0.994070	+	0.834124i	0.0692602	+	0.0581162i
$207$	1.02481	−	5.81201i	0.0712296	−	0.403963i
$208$	−6.51754			−0.451910
$209$	0.507274	+	1.42631i	0.0350889	+	0.0986598i
$210$	−4.57398			−0.315634
$211$	−0.989322	+	5.61073i	−0.0681078	+	0.386258i	0.931631	+	0.363405i	$0.118386\pi$
$211$	−0.989322	+	5.61073i	−0.0681078	+	0.386258i	−0.999739	+	0.0228529i	$0.992725\pi$
$212$	7.91534	+	6.64176i	0.543628	+	0.456158i
$213$	−11.0496	−	4.02174i	−0.757108	−	0.275565i
$214$	15.2763	−	5.56012i	1.04427	−	0.380082i
$215$	−5.47565	+	4.59462i	−0.373436	+	0.313350i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	5.41921	−	9.38636i	0.367880	−	0.637187i
$218$	0.283119	+	1.60565i	0.0191752	+	0.108748i
$219$	1.12061	+	6.35532i	0.0757241	+	0.429453i
$220$	−0.173648	+	0.300767i	−0.0117074	+	0.0202777i
$221$	−23.0205	−	39.8727i	−1.54853	−	2.68213i
$222$	5.86824	−	4.92404i	0.393851	−	0.330480i
$223$	22.1348	−	8.05639i	1.48225	−	0.539496i	0.530855	−	0.847462i	$-0.321871\pi$
$223$	22.1348	−	8.05639i	1.48225	−	0.539496i	0.951397	+	0.307967i	$0.0996485\pi$
$224$	4.29813	+	1.56439i	0.287181	+	0.104525i
$225$	0.766044	+	0.642788i	0.0510696	+	0.0428525i
$226$	−0.857097	+	4.86084i	−0.0570132	+	0.323338i
$227$	24.9513			1.65608			0.828038	−	0.560672i	$-0.189457\pi$
$227$	24.9513			1.65608			0.828038	+	0.560672i	$0.189457\pi$
$228$	−4.28699	−	0.788496i	−0.283913	−	0.0522194i
$229$	4.09926			0.270887			0.135443	−	0.990785i	$-0.456754\pi$
$229$	4.09926			0.270887			0.135443	+	0.990785i	$0.456754\pi$
$230$	1.02481	−	5.81201i	0.0675743	−	0.383233i
$231$	1.21688	+	1.02108i	0.0800649	+	0.0671824i
$232$	−4.75877	−	1.73205i	−0.312429	−	0.113715i
$233$	14.5817	−	5.30731i	0.955280	−	0.347694i	0.183098	−	0.983095i	$-0.441387\pi$
$233$	14.5817	−	5.30731i	0.955280	−	0.347694i	0.772182	+	0.635401i	$0.219165\pi$
$234$	4.99273	−	4.18939i	0.326385	−	0.273869i
$235$	−2.91147	−	5.04282i	−0.189924	−	0.328957i
$236$	−0.911474	+	1.57872i	−0.0593319	+	0.102766i
$237$	−1.51754	−	8.60640i	−0.0985749	−	0.559046i
$238$	5.61081	+	31.8205i	0.363695	+	2.06262i
$239$	−2.17024	+	3.75897i	−0.140381	+	0.243148i	−0.927640	−	0.373475i	$-0.878166\pi$
$239$	−2.17024	+	3.75897i	−0.140381	+	0.243148i	0.787259	+	0.616623i	$0.211500\pi$
$240$	−0.500000	−	0.866025i	−0.0322749	−	0.0559017i
$241$	8.99273	−	7.54579i	0.579272	−	0.486067i	−0.305436	−	0.952213i	$-0.598802\pi$
$241$	8.99273	−	7.54579i	0.579272	−	0.486067i	0.884708	+	0.466145i	$0.154358\pi$
$242$	−10.2233	+	3.72097i	−0.657177	+	0.239193i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	8.82295	+	7.40333i	0.564831	+	0.473950i
$245$	−2.41740	+	13.7098i	−0.154442	+	0.875886i
$246$	0.475652			0.0303265
$247$	0.209141	−	28.4085i	0.0133073	−	1.80759i
$248$	2.36959			0.150469
$249$	−0.290859	+	1.64955i	−0.0184325	+	0.104536i
$250$	0.766044	+	0.642788i	0.0484489	+	0.0406535i
$251$	3.80453	+	1.38474i	0.240140	+	0.0874037i	0.459287	−	0.888288i	$-0.348105\pi$
$251$	3.80453	+	1.38474i	0.240140	+	0.0874037i	−0.219147	+	0.975692i	$0.570327\pi$
$252$	−4.29813	+	1.56439i	−0.270757	+	0.0985475i
$253$	−1.57011	+	1.31748i	−0.0987118	+	0.0828290i
$254$	−1.09105	−	1.88976i	−0.0684587	−	0.118574i
$255$	3.53209	−	6.11776i	0.221188	−	0.383109i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.47565	−	14.0401i	−0.154427	−	0.875799i	−0.959308	−	0.282362i	$-0.908882\pi$
$257$	−2.47565	−	14.0401i	−0.154427	−	0.875799i	0.804881	−	0.593436i	$-0.202229\pi$
$258$	−3.57398	+	6.19031i	−0.222506	+	0.385392i
$259$	−17.5194	−	30.3444i	−1.08860	−	1.88551i
$260$	4.99273	−	4.18939i	0.309636	−	0.259815i
$261$	4.75877	−	1.73205i	0.294560	−	0.107211i
$262$	−1.78699	−	0.650411i	−0.110401	−	0.0401825i
$263$	−11.0890	−	9.30477i	−0.683777	−	0.573757i	0.233331	−	0.972397i	$-0.425038\pi$
$263$	−11.0890	−	9.30477i	−0.683777	−	0.573757i	−0.917107	+	0.398641i	$0.869482\pi$
$264$	−0.0603074	+	0.342020i	−0.00371166	+	0.0210499i
$265$	−10.3327			−0.634736
$266$	−6.95677	+	18.6844i	−0.426547	+	1.14562i
$267$	10.8375			0.663244
$268$	0.106067	−	0.601535i	0.00647906	−	0.0367446i
$269$	−2.27126	−	1.90581i	−0.138481	−	0.116199i	0.570916	−	0.821009i	$-0.306588\pi$
$269$	−2.27126	−	1.90581i	−0.138481	−	0.116199i	−0.709397	+	0.704809i	$0.751033\pi$
$270$	0.939693	+	0.342020i	0.0571879	+	0.0208147i
$271$	−26.0847	+	9.49406i	−1.58453	+	0.576723i	−0.976184	−	0.216946i	$-0.930390\pi$
$271$	−26.0847	+	9.49406i	−1.58453	+	0.576723i	−0.608350	+	0.793669i	$0.708168\pi$
$272$	−5.41147	+	4.54077i	−0.328119	+	0.275324i
$273$	−14.9055	−	25.8172i	−0.902125	−	1.56253i
$274$	−0.573978	+	0.994159i	−0.0346753	+	0.0600593i
$275$	−0.0603074	−	0.342020i	−0.00363667	−	0.0206246i
$276$	−1.02481	−	5.81201i	−0.0616866	−	0.349842i
$277$	−1.13041	+	1.95794i	−0.0679201	+	0.117641i	−0.897986	−	0.440025i	$-0.854970\pi$
$277$	−1.13041	+	1.95794i	−0.0679201	+	0.117641i	0.830066	+	0.557666i	$0.188303\pi$
$278$	−11.6138	−	20.1157i	−0.696550	−	1.20646i
$279$	−1.81521	+	1.52314i	−0.108674	+	0.0911880i
$280$	−4.29813	+	1.56439i	−0.256863	+	0.0934903i
$281$	15.3109	+	5.57272i	0.913373	+	0.332441i	0.755599	−	0.655034i	$-0.227346\pi$
$281$	15.3109	+	5.57272i	0.913373	+	0.332441i	0.157774	+	0.987475i	$0.449568\pi$
$282$	−4.46064	−	3.74292i	−0.265627	−	0.222888i
$283$	0.101014	−	0.572881i	0.00600468	−	0.0340542i	−0.981658	−	0.190649i	$-0.938941\pi$
$283$	0.101014	−	0.572881i	0.00600468	−	0.0340542i	0.987663	+	0.156595i	$0.0500518\pi$
$284$	−11.7588			−0.697755
$285$	3.79086	−	2.15160i	0.224551	−	0.127450i
$286$	−2.26352			−0.133845
$287$	0.377793	−	2.14257i	0.0223004	−	0.126472i
$288$	−0.766044	−	0.642788i	−0.0451396	−	0.0378766i
$289$	−30.9183	−	11.2534i	−1.81873	−	0.661962i
$290$	4.75877	−	1.73205i	0.279445	−	0.101710i
$291$	−0.815207	+	0.684040i	−0.0477883	+	0.0400992i
$292$	3.22668	+	5.58878i	0.188827	+	0.327058i
$293$	−11.1295	+	19.2769i	−0.650195	+	1.12617i	0.332881	+	0.942969i	$0.391979\pi$
$293$	−11.1295	+	19.2769i	−0.650195	+	1.12617i	−0.983075	+	0.183201i	$0.941354\pi$
$294$	2.41740	+	13.7098i	0.140986	+	0.799571i
$295$	−0.316552	−	1.79525i	−0.0184303	−	0.104524i
$296$	3.83022	−	6.63414i	0.222627	−	0.385602i
$297$	−0.173648	−	0.300767i	−0.0100761	−	0.0174523i
$298$	9.41921	−	7.90366i	0.545640	−	0.457847i
$299$	36.1447	−	13.1556i	2.09030	−	0.760808i
$300$	0.939693	+	0.342020i	0.0542532	+	0.0197465i
$301$	25.0455	+	21.0157i	1.44360	+	1.21132i
$302$	1.22668	−	6.95686i	0.0705876	−	0.400322i
$303$	−12.4534			−0.715427
$304$	−4.29813	+	0.725293i	−0.246515	+	0.0415984i
$305$	−11.5175			−0.659492
$306$	1.22668	−	6.95686i	0.0701247	−	0.397697i
$307$	−24.5672	−	20.6143i	−1.40212	−	1.17652i	−0.960148	−	0.279493i	$-0.909834\pi$
$307$	−24.5672	−	20.6143i	−1.40212	−	1.17652i	−0.441975	−	0.897027i	$-0.645722\pi$
$308$	1.49273	+	0.543308i	0.0850560	+	0.0309578i
$309$	−1.21941	+	0.443828i	−0.0693697	+	0.0252485i
$310$	−1.81521	+	1.52314i	−0.103097	+	0.0865085i
$311$	9.96316	+	17.2567i	0.564959	+	0.978538i	0.997053	+	0.0767096i	$0.0244414\pi$
$311$	9.96316	+	17.2567i	0.564959	+	0.978538i	−0.432094	+	0.901828i	$0.642225\pi$
$312$	3.25877	−	5.64436i	0.184492	−	0.319549i
$313$	4.88207	+	27.6876i	0.275951	+	1.56500i	0.735924	+	0.677064i	$0.236748\pi$
$313$	4.88207	+	27.6876i	0.275951	+	1.56500i	−0.459973	+	0.887933i	$0.652141\pi$
$314$	−0.187319	−	1.06234i	−0.0105710	−	0.0599512i
$315$	2.28699	−	3.96118i	0.128857	−	0.223187i
$316$	−4.36959	−	7.56834i	−0.245808	−	0.425753i
$317$	−8.52687	+	7.15490i	−0.478917	+	0.401859i	−0.850035	−	0.526727i	$-0.823419\pi$
$317$	−8.52687	+	7.15490i	−0.478917	+	0.401859i	0.371118	+	0.928586i	$0.378975\pi$
$318$	−9.70961	+	3.53401i	−0.544488	+	0.198177i
$319$	−1.65270	−	0.601535i	−0.0925336	−	0.0336795i
$320$	−0.766044	−	0.642788i	−0.0428232	−	0.0359329i
$321$	−2.82295	+	16.0097i	−0.157562	+	0.893576i
$322$	−26.9941			−1.50432
$323$	−19.6186	−	23.7331i	−1.09161	−	1.32055i
$324$	1.00000			0.0555556
$325$	−1.13176	+	6.41852i	−0.0627787	+	0.356036i
$326$	−9.75877	−	8.18858i	−0.540488	−	0.453524i
$327$	−1.53209	−	0.557635i	−0.0847247	−	0.0308373i
$328$	0.446967	−	0.162683i	0.0246796	−	0.00898264i
$329$	−20.4029	+	17.1200i	−1.12485	+	0.943858i
$330$	−0.173648	−	0.300767i	−0.00955902	−	0.0165567i
$331$	−8.04576	+	13.9357i	−0.442235	+	0.765973i	−0.997855	−	0.0654629i	$-0.979148\pi$
$331$	−8.04576	+	13.9357i	−0.442235	+	0.765973i	0.555620	+	0.831436i	$0.312481\pi$
$332$	0.290859	+	1.64955i	0.0159630	+	0.0905306i
$333$	1.33022	+	7.54407i	0.0728957	+	0.413412i
$334$	−0.0898700	+	0.155659i	−0.00491747	+	0.00851731i
$335$	0.305407	+	0.528981i	0.0166862	+	0.0289013i
$336$	−3.50387	+	2.94010i	−0.191152	+	0.160395i
$337$	−25.4739	+	9.27174i	−1.38765	+	0.505064i	−0.924489	−	0.381209i	$-0.875508\pi$
$337$	−25.4739	+	9.27174i	−1.38765	+	0.505064i	−0.463163	+	0.886273i	$0.653285\pi$
$338$	27.7006	+	10.0822i	1.50671	+	0.548399i
$339$	−3.78106	−	3.17269i	−0.205359	−	0.172317i
$340$	1.22668	−	6.95686i	0.0665262	−	0.377289i
$341$	0.822948			0.0445651
$342$	2.82635	−	3.31839i	0.152832	−	0.179438i
$343$	31.6578			1.70936
$344$	−1.24123	+	7.03936i	−0.0669226	+	0.379537i
$345$	4.52094	+	3.79352i	0.243399	+	0.204236i
$346$	−12.8293	−	4.66950i	−0.689710	−	0.251034i
$347$	11.0915	−	4.03698i	0.595424	−	0.216717i	−0.0266894	−	0.999644i	$-0.508497\pi$
$347$	11.0915	−	4.03698i	0.595424	−	0.216717i	0.622113	+	0.782927i	$0.286274\pi$
$348$	3.87939	−	3.25519i	0.207957	−	0.174497i
$349$	13.9094	+	24.0918i	0.744554	+	1.28961i	0.950403	+	0.311021i	$0.100671\pi$
$349$	13.9094	+	24.0918i	0.744554	+	1.28961i	−0.205849	+	0.978584i	$0.565996\pi$
$350$	2.28699	−	3.96118i	0.122245	−	0.211734i
$351$	1.13176	+	6.41852i	0.0604088	+	0.342596i
$352$	0.0603074	+	0.342020i	0.00321439	+	0.0182297i
$353$	8.36959	−	14.4965i	0.445468	−	0.771573i	−0.552617	−	0.833436i	$-0.686371\pi$
$353$	8.36959	−	14.4965i	0.445468	−	0.771573i	0.998085	+	0.0618623i	$0.0197039\pi$
$354$	−0.911474	−	1.57872i	−0.0484443	−	0.0839080i
$355$	9.00774	−	7.55839i	0.478081	−	0.401158i
$356$	10.1839	−	3.70664i	0.539746	−	0.196452i
$357$	−30.3628	−	11.0511i	−1.60697	−	0.584889i
$358$	16.3858	+	13.7493i	0.866015	+	0.726673i
$359$	−0.650015	+	3.68642i	−0.0343065	+	0.194562i	−0.997144	−	0.0755180i	$-0.975939\pi$
$359$	−0.650015	+	3.68642i	−0.0343065	+	0.194562i	0.962838	+	0.270080i	$0.0870501\pi$
$360$	1.00000			0.0527046
$361$	−3.02347	−	18.7579i	−0.159130	−	0.987258i
$362$	−8.29591			−0.436023
$363$	1.88919	−	10.7141i	0.0991565	−	0.562345i
$364$	−22.8366	−	19.1622i	−1.19696	−	1.00437i
$365$	−6.06418	−	2.20718i	−0.317414	−	0.115529i
$366$	−10.8229	+	3.93923i	−0.565725	+	0.205907i
$367$	−3.38460	+	2.84002i	−0.176675	+	0.148248i	−0.726837	−	0.686810i	$-0.759010\pi$
$367$	−3.38460	+	2.84002i	−0.176675	+	0.148248i	0.550162	+	0.835058i	$0.314566\pi$
$368$	−2.95084	−	5.11100i	−0.153823	−	0.266429i
$369$	−0.237826	+	0.411927i	−0.0123807	+	0.0214440i
$370$	1.33022	+	7.54407i	0.0691550	+	0.392197i
$371$	8.20692	+	46.5438i	0.426082	+	2.41643i
$372$	−1.18479	+	2.05212i	−0.0614286	+	0.106398i
$373$	−0.457234	−	0.791952i	−0.0236747	−	0.0410057i	0.853945	−	0.520363i	$-0.174203\pi$
$373$	−0.457234	−	0.791952i	−0.0236747	−	0.0410057i	−0.877620	+	0.479357i	$0.840870\pi$
$374$	−1.87939	+	1.57699i	−0.0971807	+	0.0815443i
$375$	−0.939693	+	0.342020i	−0.0485255	+	0.0176618i
$376$	−5.47178	−	1.99157i	−0.282186	−	0.102707i
$377$	25.2841	+	21.2158i	1.30219	+	1.09267i
$378$	0.794263	−	4.50449i	0.0408525	−	0.231686i
$379$	−25.7101			−1.32064			−0.660319	−	0.750985i	$-0.729579\pi$
$379$	−25.7101			−1.32064			−0.660319	+	0.750985i	$0.729579\pi$
$380$	2.82635	−	3.31839i	0.144989	−	0.170230i
$381$	2.18210			0.111793
$382$	2.24897	−	12.7545i	0.115067	−	0.652579i
$383$	11.9244	+	10.0058i	0.609310	+	0.511272i	0.894423	−	0.447222i	$-0.147587\pi$
$383$	11.9244	+	10.0058i	0.609310	+	0.511272i	−0.285113	+	0.958494i	$0.592031\pi$
$384$	−0.939693	−	0.342020i	−0.0479535	−	0.0174536i
$385$	−1.49273	+	0.543308i	−0.0760764	+	0.0276895i
$386$	9.88713	−	8.29628i	0.503241	−	0.422270i
$387$	−3.57398	−	6.19031i	−0.181676	−	0.314671i
$388$	−0.532089	+	0.921605i	−0.0270127	+	0.0467874i
$389$	1.13341	+	6.42788i	0.0574661	+	0.325906i	0.999966	−	0.00830137i	$-0.00264244\pi$
$389$	1.13341	+	6.42788i	0.0574661	+	0.325906i	−0.942499	+	0.334208i	$0.891531\pi$
$390$	1.13176	+	6.41852i	0.0573089	+	0.325015i
$391$	20.8452	−	36.1050i	1.05419	−	1.82591i
$392$	6.96064	+	12.0562i	0.351565	+	0.608929i
$393$	1.45677	−	1.22237i	0.0734842	−	0.0616605i
$394$	−10.8166	+	3.93690i	−0.544930	+	0.198338i
$395$	8.21213	+	2.98897i	0.413197	+	0.150392i
$396$	−0.266044	−	0.223238i	−0.0133692	−	0.0112181i
$397$	−1.54101	+	8.73951i	−0.0773412	+	0.438624i	0.921407	+	0.388599i	$0.127041\pi$
$397$	−1.54101	+	8.73951i	−0.0773412	+	0.438624i	−0.998748	+	0.0500242i	$0.984070\pi$
$398$	24.1830			1.21219
$399$	−12.7028	−	15.3669i	−0.635935	−	0.769310i
$400$	1.00000			0.0500000
$401$	6.64321	−	37.6755i	0.331746	−	1.88142i	−0.125514	−	0.992092i	$-0.540058\pi$
$401$	6.64321	−	37.6755i	0.331746	−	1.88142i	0.457260	−	0.889333i	$-0.348831\pi$
$402$	0.467911	+	0.392624i	0.0233373	+	0.0195823i
$403$	−14.5125	−	5.28211i	−0.722919	−	0.263121i
$404$	−11.7023	+	4.25930i	−0.582213	+	0.211908i
$405$	−0.766044	+	0.642788i	−0.0380651	+	0.0319404i
$406$	−11.5817	−	20.0601i	−0.574791	−	0.995567i
$407$	1.33022	−	2.30401i	0.0659367	−	0.114206i
$408$	−1.22668	−	6.95686i	−0.0607298	−	0.344416i
$409$	0.242574	+	1.37570i	0.0119945	+	0.0680242i	0.990217	−	0.139532i	$-0.0445600\pi$
$409$	0.242574	+	1.37570i	0.0119945	+	0.0680242i	−0.978223	+	0.207557i	$0.933449\pi$
$410$	−0.237826	+	0.411927i	−0.0117454	+	0.0203436i
$411$	−0.573978	−	0.994159i	−0.0283122	−	0.0490382i
$412$	−0.994070	+	0.834124i	−0.0489743	+	0.0410943i
$413$	−7.83527	+	2.85181i	−0.385549	+	0.140328i
$414$	5.54576	+	2.01849i	0.272559	+	0.0992034i
$415$	−1.28312	−	1.07666i	−0.0629858	−	0.0528514i
$416$	1.13176	−	6.41852i	0.0554891	−	0.314694i
$417$	23.2276			1.13746
$418$	−1.49273	+	0.251892i	−0.0730116	+	0.0123204i
$419$	−12.1361			−0.592887			−0.296444	−	0.955050i	$-0.595801\pi$
$419$	−12.1361			−0.592887			−0.296444	+	0.955050i	$0.595801\pi$
$420$	0.794263	−	4.50449i	0.0387561	−	0.219797i
$421$	−0.0523182	−	0.0439002i	−0.00254983	−	0.00213956i	0.641512	−	0.767113i	$-0.278308\pi$
$421$	−0.0523182	−	0.0439002i	−0.00254983	−	0.00213956i	−0.644062	+	0.764974i	$0.722752\pi$
$422$	−5.35369	−	1.94858i	−0.260614	−	0.0948556i
$423$	5.47178	−	1.99157i	0.266047	−	0.0968332i
$424$	−7.91534	+	6.64176i	−0.384403	+	0.322553i
$425$	3.53209	+	6.11776i	0.171331	+	0.296755i
$426$	5.87939	−	10.1834i	0.284857	−	0.493387i
$427$	9.14796	+	51.8806i	0.442701	+	2.51068i
$428$	2.82295	+	16.0097i	0.136452	+	0.773860i
$429$	1.13176	−	1.96026i	0.0546418	−	0.0946425i
$430$	−3.57398	−	6.19031i	−0.172353	−	0.298523i
$431$	−1.55438	+	1.30428i	−0.0748717	+	0.0628248i	−0.679455	−	0.733717i	$-0.737784\pi$
$431$	−1.55438	+	1.30428i	−0.0748717	+	0.0628248i	0.604584	+	0.796542i	$0.293339\pi$
$432$	0.939693	−	0.342020i	0.0452110	−	0.0164555i
$433$	10.5963	+	3.85673i	0.509224	+	0.185342i	0.583838	−	0.811870i	$-0.301550\pi$
$433$	10.5963	+	3.85673i	0.509224	+	0.185342i	−0.0746141	+	0.997212i	$0.523772\pi$
$434$	8.30272	+	6.96681i	0.398543	+	0.334418i
$435$	−0.879385	+	4.98724i	−0.0421633	+	0.239120i
$436$	−1.63041			−0.0780827
$437$	22.3724	−	12.6980i	1.07022	−	0.607430i
$438$	−6.45336			−0.308354
$439$	1.63041	−	9.24654i	0.0778155	−	0.441313i	−0.920861	−	0.389890i	$-0.872513\pi$
$439$	1.63041	−	9.24654i	0.0778155	−	0.441313i	0.998677	−	0.0514235i	$-0.0163758\pi$
$440$	−0.266044	−	0.223238i	−0.0126832	−	0.0106424i
$441$	−13.0817	−	4.76136i	−0.622939	−	0.226731i
$442$	43.2645	−	15.7470i	2.05788	−	0.749007i
$443$	−4.20439	+	3.52790i	−0.199757	+	0.167616i	−0.737179	−	0.675697i	$-0.763843\pi$
$443$	−4.20439	+	3.52790i	−0.199757	+	0.167616i	0.537422	+	0.843313i	$0.319398\pi$
$444$	3.83022	+	6.63414i	0.181774	+	0.314842i
$445$	−5.41875	+	9.38555i	−0.256873	+	0.444918i
$446$	4.09034	+	23.1975i	0.193683	+	1.09843i
$447$	2.13516	+	12.1091i	0.100990	+	0.572741i
$448$	−2.28699	+	3.96118i	−0.108050	+	0.187148i
$449$	9.30200	+	16.1115i	0.438989	+	0.760351i	0.997612	−	0.0690709i	$-0.0220035\pi$
$449$	9.30200	+	16.1115i	0.438989	+	0.760351i	−0.558623	+	0.829422i	$0.688670\pi$
$450$	−0.766044	+	0.642788i	−0.0361117	+	0.0303013i
$451$	0.155230	−	0.0564991i	0.00730949	−	0.00266044i
$452$	−4.63816	−	1.68815i	−0.218160	−	0.0794039i
$453$	5.41147	+	4.54077i	0.254253	+	0.213344i
$454$	−4.33275	+	24.5722i	−0.203346	+	1.15323i
$455$	29.8111			1.39757
$456$	1.52094	−	4.08494i	0.0712248	−	0.191295i
$457$	34.8931			1.63223			0.816115	−	0.577889i	$-0.196123\pi$
$457$	34.8931			1.63223			0.816115	+	0.577889i	$0.196123\pi$
$458$	−0.711829	+	4.03698i	−0.0332616	+	0.188636i
$459$	5.41147	+	4.54077i	0.252586	+	0.211945i
$460$	5.54576	+	2.01849i	0.258572	+	0.0941126i
$461$	−31.4270	+	11.4385i	−1.46370	+	0.532743i	−0.946382	−	0.323051i	$-0.895292\pi$
$461$	−31.4270	+	11.4385i	−1.46370	+	0.532743i	−0.517318	+	0.855794i	$0.673069\pi$
$462$	−1.21688	+	1.02108i	−0.0566144	+	0.0475052i
$463$	3.52094	+	6.09845i	0.163632	+	0.283419i	0.936169	−	0.351551i	$-0.114346\pi$
$463$	3.52094	+	6.09845i	0.163632	+	0.283419i	−0.772537	+	0.634970i	$0.781012\pi$
$464$	2.53209	−	4.38571i	0.117549	−	0.203601i
$465$	−0.411474	−	2.33359i	−0.0190817	−	0.108217i
$466$	2.69459	+	15.2818i	0.124825	+	0.707915i
$467$	−13.4115	+	23.2294i	−0.620609	+	1.07493i	0.368763	+	0.929523i	$0.379781\pi$
$467$	−13.4115	+	23.2294i	−0.620609	+	1.07493i	−0.989373	+	0.145403i	$0.953552\pi$
$468$	3.25877	+	5.64436i	0.150637	+	0.260910i
$469$	2.14022	−	1.79585i	0.0988260	−	0.0829248i
$470$	5.47178	−	1.99157i	0.252394	−	0.0918641i
$471$	1.01367	+	0.368946i	0.0467075	+	0.0170001i
$472$	−1.39646	−	1.17177i	−0.0642773	−	0.0539350i
$473$	−0.431074	+	2.44474i	−0.0198208	+	0.112409i
$474$	8.73917			0.401403
$475$	−0.0320889	+	4.35878i	−0.00147234	+	0.199995i
$476$	−32.3114			−1.48099
$477$	1.79426	−	10.1758i	0.0821537	−	0.465917i
$478$	−3.32501	−	2.79001i	−0.152082	−	0.127612i
$479$	16.9145	+	6.15636i	0.772842	+	0.281291i	0.698185	−	0.715918i	$-0.253992\pi$
$479$	16.9145	+	6.15636i	0.772842	+	0.281291i	0.0746572	+	0.997209i	$0.476214\pi$
$480$	0.939693	−	0.342020i	0.0428909	−	0.0156110i
$481$	−38.2465	+	32.0926i	−1.74389	+	1.46330i
$482$	5.86959	+	10.1664i	0.267352	+	0.463068i
$483$	13.4971	−	23.3776i	0.614138	−	1.06372i
$484$	−1.88919	−	10.7141i	−0.0858721	−	0.487005i
$485$	−0.184793	−	1.04801i	−0.00839100	−	0.0475877i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	6.37851	+	11.0479i	0.289038	+	0.500628i	0.973580	−	0.228345i	$-0.0733313\pi$
$487$	6.37851	+	11.0479i	0.289038	+	0.500628i	−0.684543	+	0.728973i	$0.739998\pi$
$488$	−8.82295	+	7.40333i	−0.399396	+	0.335133i
$489$	11.9709	−	4.35705i	0.541343	−	0.197033i
$490$	−13.0817	−	4.76136i	−0.590972	−	0.215096i
$491$	−16.9283	−	14.2045i	−0.763963	−	0.641041i	0.175192	−	0.984534i	$-0.443945\pi$
$491$	−16.9283	−	14.2045i	−0.763963	−	0.641041i	−0.939155	+	0.343493i	$0.888390\pi$
$492$	−0.0825961	+	0.468426i	−0.00372372	+	0.0211183i
$493$	35.7743			1.61119
$494$	27.9406	+	5.13905i	1.25711	+	0.231217i
$495$	0.347296			0.0156098
$496$	−0.411474	+	2.33359i	−0.0184757	+	0.104781i
$497$	−41.2012	−	34.5719i	−1.84813	−	1.55076i
$498$	−1.57398	−	0.572881i	−0.0705316	−	0.0256714i
$499$	−36.3282	+	13.2224i	−1.62627	+	0.591915i	−0.984563	−	0.175033i	$-0.943997\pi$
$499$	−36.3282	+	13.2224i	−1.62627	+	0.591915i	−0.641709	+	0.766948i	$0.721774\pi$
$500$	−0.766044	+	0.642788i	−0.0342585	+	0.0287463i
$501$	−0.0898700	−	0.155659i	−0.00401510	−	0.00695435i
$502$	−2.02435	+	3.50627i	−0.0903511	+	0.156493i
$503$	−4.58734	−	26.0161i	−0.204540	−	1.16000i	−0.898163	−	0.439663i	$-0.855098\pi$
$503$	−4.58734	−	26.0161i	−0.204540	−	1.16000i	0.693623	−	0.720338i	$-0.256013\pi$
$504$	−0.794263	−	4.50449i	−0.0353793	−	0.200646i
$505$	6.22668	−	10.7849i	0.277084	−	0.479923i
$506$	−1.02481	−	1.77503i	−0.0455586	−	0.0789098i
$507$	−22.5817	+	18.9483i	−1.00289	+	0.841524i
$508$	2.05051	−	0.746324i	0.0909765	−	0.0331128i
$509$	17.5303	+	6.38052i	0.777018	+	0.282812i	0.699929	−	0.714213i	$-0.253215\pi$
$509$	17.5303	+	6.38052i	0.777018	+	0.282812i	0.0770896	+	0.997024i	$0.475437\pi$
$510$	5.41147	+	4.54077i	0.239624	+	0.201068i
$511$	−5.12567	+	29.0691i	−0.226746	+	1.28594i
$512$	−1.00000			−0.0441942
$513$	1.46064	+	4.10689i	0.0644887	+	0.181324i
$514$	14.2567			0.628837
$515$	0.225337	−	1.27795i	0.00992955	−	0.0563133i
$516$	−5.47565	−	4.59462i	−0.241052	−	0.202267i
$517$	−1.90033	−	0.691663i	−0.0835764	−	0.0304193i
$518$	32.9256	−	11.9839i	1.44667	−	0.526544i
$519$	10.4586	−	8.77579i	0.459081	−	0.385214i
$520$	3.25877	+	5.64436i	0.142907	+	0.247521i
$521$	15.5817	−	26.9883i	0.682647	−	1.18238i	−0.291522	−	0.956564i	$-0.594162\pi$
$521$	15.5817	−	26.9883i	0.682647	−	1.18238i	0.974170	−	0.225816i	$-0.0725049\pi$
$522$	0.879385	+	4.98724i	0.0384896	+	0.218286i
$523$	2.83481	+	16.0770i	0.123957	+	0.702998i	0.981922	+	0.189288i	$0.0606180\pi$
$523$	2.83481	+	16.0770i	0.123957	+	0.702998i	−0.857964	+	0.513710i	$0.828271\pi$
$524$	0.950837	−	1.64690i	0.0415375	−	0.0719451i
$525$	2.28699	+	3.96118i	0.0998124	+	0.172880i
$526$	11.0890	−	9.30477i	0.483503	−	0.405707i
$527$	−15.7297	+	5.72513i	−0.685195	+	0.249391i
$528$	−0.326352	−	0.118782i	−0.0142026	−	0.00516934i
$529$	9.06212	+	7.60402i	0.394005	+	0.330610i
$530$	1.79426	−	10.1758i	0.0779378	−	0.442007i
$531$	1.82295			0.0791092
$532$	−17.1925	−	10.0956i	−0.745391	−	0.437699i
$533$	−3.10008			−0.134279
$534$	−1.88191	+	10.6729i	−0.0814383	+	0.461859i
$535$	−12.4534	−	10.4496i	−0.538406	−	0.451776i
$536$	0.573978	+	0.208911i	0.0247921	+	0.00902358i
$537$	−20.1001	+	7.31585i	−0.867385	+	0.315702i
$538$	2.27126	−	1.90581i	0.0979209	−	0.0821654i
$539$	2.41740	+	4.18707i	0.104125	+	0.180350i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	−4.79055	−	27.1686i	−0.205962	−	1.16807i	−0.895919	−	0.444218i	$-0.853482\pi$
$541$	−4.79055	−	27.1686i	−0.205962	−	1.16807i	0.689957	−	0.723851i	$-0.257630\pi$
$542$	−4.82026	−	27.3371i	−0.207048	−	1.17423i
$543$	4.14796	−	7.18447i	0.178006	−	0.308315i
$544$	−3.53209	−	6.11776i	−0.151437	−	0.262297i
$545$	1.24897	−	1.04801i	0.0535000	−	0.0448918i
$546$	28.0133	−	10.1960i	1.19886	−	0.436348i
$547$	15.7151	+	5.71984i	0.671930	+	0.244563i	0.655379	−	0.755300i	$-0.272509\pi$
$547$	15.7151	+	5.71984i	0.671930	+	0.244563i	0.0165515	+	0.999863i	$0.494731\pi$
$548$	−0.879385	−	0.737892i	−0.0375655	−	0.0315212i
$549$	2.00000	−	11.3426i	0.0853579	−	0.484089i
$550$	0.347296			0.0148088
$551$	19.0351	+	11.1776i	0.810922	+	0.476180i
$552$	5.90167			0.251192
$553$	6.94120	−	39.3655i	0.295170	−	1.67399i
$554$	−1.73190	−	1.45323i	−0.0735812	−	0.0617420i
$555$	−7.19846	−	2.62003i	−0.305558	−	0.111214i
$556$	21.8268	−	7.94431i	0.925663	−	0.336914i
$557$	7.92720	−	6.65171i	0.335886	−	0.281842i	−0.459207	−	0.888329i	$-0.651866\pi$
$557$	7.92720	−	6.65171i	0.335886	−	0.281842i	0.795093	+	0.606487i	$0.207422\pi$
$558$	−1.18479	−	2.05212i	−0.0501563	−	0.0868732i
$559$	23.2935	−	40.3456i	0.985212	−	1.70644i
$560$	−0.794263	−	4.50449i	−0.0335637	−	0.190349i
$561$	−0.426022	−	2.41609i	−0.0179867	−	0.102007i
$562$	−8.14677	+	14.1106i	−0.343651	+	0.595221i
$563$	21.9094	+	37.9482i	0.923372	+	1.59933i	0.794159	+	0.607710i	$0.207912\pi$
$563$	21.9094	+	37.9482i	0.923372	+	1.59933i	0.129213	+	0.991617i	$0.458755\pi$
$564$	4.46064	−	3.74292i	0.187827	−	0.157605i
$565$	4.63816	−	1.68815i	0.195129	−	0.0710210i
$566$	0.546637	+	0.198960i	0.0229769	+	0.00836289i
$567$	3.50387	+	2.94010i	0.147149	+	0.123472i
$568$	2.04189	−	11.5801i	0.0856758	−	0.485891i
$569$	−26.1070			−1.09446			−0.547231	−	0.836981i	$-0.684318\pi$
$569$	−26.1070			−1.09446			−0.547231	+	0.836981i	$0.684318\pi$
$570$	1.46064	+	4.10689i	0.0611794	+	0.172019i
$571$	−39.3560			−1.64700			−0.823498	−	0.567319i	$-0.807981\pi$
$571$	−39.3560			−1.64700			−0.823498	+	0.567319i	$0.807981\pi$
$572$	0.393056	−	2.22913i	0.0164345	−	0.0932046i
$573$	9.92127	+	8.32494i	0.414467	+	0.347779i
$574$	2.04442	+	0.744106i	0.0853322	+	0.0310584i
$575$	−5.54576	+	2.01849i	−0.231274	+	0.0841769i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	8.64590	+	14.9751i	0.359933	+	0.623423i	0.987949	−	0.154778i	$-0.0494661\pi$
$577$	8.64590	+	14.9751i	0.359933	+	0.623423i	−0.628016	+	0.778200i	$0.716133\pi$
$578$	16.4513	−	28.4945i	0.684284	−	1.18521i
$579$	2.24123	+	12.7106i	0.0931423	+	0.528236i
$580$	0.879385	+	4.98724i	0.0365145	+	0.207084i
$581$	−3.83069	+	6.63495i	−0.158924	+	0.275264i
$582$	−0.532089	−	0.921605i	−0.0220558	−	0.0382018i
$583$	−2.74897	+	2.30666i	−0.113851	+	0.0955321i
$584$	−6.06418	+	2.20718i	−0.250937	+	0.0913338i
$585$	−6.12449	−	2.22913i	−0.253216	−	0.0921632i
$586$	−17.0514	−	14.3079i	−0.704389	−	0.591052i
$587$	0.681799	−	3.86668i	0.0281409	−	0.159595i	−0.967499	−	0.252875i	$-0.918624\pi$
$587$	0.681799	−	3.86668i	0.0281409	−	0.159595i	0.995640	+	0.0932798i	$0.0297351\pi$
$588$	−13.9213			−0.574104
$589$	−10.1584	−	1.86841i	−0.418569	−	0.0769864i
$590$	1.82295			0.0750496
$591$	1.99882	−	11.3359i	0.0822204	−	0.466295i
$592$	5.86824	+	4.92404i	0.241183	+	0.202377i
$593$	−31.8307	−	11.5854i	−1.30713	−	0.475756i	−0.407818	−	0.913063i	$-0.633710\pi$
$593$	−31.8307	−	11.5854i	−1.30713	−	0.475756i	−0.899312	+	0.437307i	$0.855932\pi$
$594$	0.326352	−	0.118782i	0.0133904	−	0.00487370i
$595$	24.7520	−	20.7694i	1.01473	−	0.851461i
$596$	6.14796	+	10.6486i	0.251830	+	0.436183i
$597$	−12.0915	+	20.9431i	−0.494873	+	0.857145i
$598$	6.67927	+	37.8800i	0.273136	+	1.54903i
$599$	−4.21894	−	23.9268i	−0.172381	−	0.977623i	−0.941123	−	0.338064i	$-0.890228\pi$
$599$	−4.21894	−	23.9268i	−0.172381	−	0.977623i	0.768742	−	0.639559i	$-0.220883\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	18.6270	+	32.2629i	0.759812	+	1.31603i	0.942946	+	0.332945i	$0.108042\pi$
$601$	18.6270	+	32.2629i	0.759812	+	1.31603i	−0.183135	+	0.983088i	$0.558624\pi$
$602$	−25.0455	+	21.0157i	−1.02078	+	0.856535i
$603$	−0.573978	+	0.208911i	−0.0233742	+	0.00850751i
$604$	6.63816	+	2.41609i	0.270103	+	0.0983094i
$605$	8.33409	+	6.99313i	0.338829	+	0.284311i
$606$	2.16250	−	12.2642i	0.0878457	−	0.498198i
$607$	17.4023			0.706338			0.353169	−	0.935560i	$-0.385104\pi$
$607$	17.4023			0.706338			0.353169	+	0.935560i	$0.385104\pi$
$608$	0.0320889	−	4.35878i	0.00130138	−	0.176772i
$609$	23.1634			0.938630
$610$	2.00000	−	11.3426i	0.0809776	−	0.459247i
$611$	29.0724	+	24.3946i	1.17614	+	0.986901i
$612$	6.63816	+	2.41609i	0.268332	+	0.0976647i
$613$	28.8371	−	10.4958i	1.16472	−	0.423923i	0.313938	−	0.949443i	$-0.398352\pi$
$613$	28.8371	−	10.4958i	1.16472	−	0.423923i	0.850781	+	0.525520i	$0.176129\pi$
$614$	24.5672	−	20.6143i	0.991450	−	0.831926i
$615$	−0.237826	−	0.411927i	−0.00959007	−	0.0166105i
$616$	−0.794263	+	1.37570i	−0.0320018	+	0.0554287i
$617$	2.71419	+	15.3930i	0.109269	+	0.619697i	0.989429	+	0.145019i	$0.0463243\pi$
$617$	2.71419	+	15.3930i	0.109269	+	0.619697i	−0.880160	+	0.474678i	$0.842565\pi$
$618$	−0.225337	−	1.27795i	−0.00906440	−	0.0514068i
$619$	12.8319	−	22.2255i	0.515756	−	0.893316i	−0.484076	−	0.875026i	$-0.660844\pi$
$619$	12.8319	−	22.2255i	0.515756	−	0.893316i	0.999833	−	0.0182906i	$-0.00582239\pi$
$620$	−1.18479	−	2.05212i	−0.0475824	−	0.0824152i
$621$	−4.52094	+	3.79352i	−0.181419	+	0.152229i
$622$	−18.7246	+	6.81521i	−0.750789	+	0.273265i
$623$	46.5810	+	16.9541i	1.86623	+	0.679252i
$624$	4.99273	+	4.18939i	0.199869	+	0.167710i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	−28.1147			−1.12369
$627$	0.528218	−	1.41868i	0.0210950	−	0.0566568i
$628$	1.07873			0.0430458
$629$	−9.39693	+	53.2926i	−0.374680	+	2.12492i
$630$	3.50387	+	2.94010i	0.139598	+	0.117136i
$631$	5.92902	+	2.15799i	0.236030	+	0.0859080i	0.457327	−	0.889298i	$-0.348807\pi$
$631$	5.92902	+	2.15799i	0.236030	+	0.0859080i	−0.221297	+	0.975206i	$0.571029\pi$
$632$	8.21213	−	2.98897i	0.326661	−	0.118895i
$633$	4.36437	−	3.66214i	0.173468	−	0.145557i
$634$	−5.56552	−	9.63977i	−0.221035	−	0.382844i
$635$	−1.09105	+	1.88976i	−0.0432971	+	0.0749927i
$636$	−1.79426	−	10.1758i	−0.0711472	−	0.403496i
$637$	−15.7555	−	89.3540i	−0.624257	−	3.54034i
$638$	0.879385	−	1.52314i	0.0348152	−	0.0603017i
$639$	5.87939	+	10.1834i	0.232585	+	0.402849i
$640$	0.766044	−	0.642788i	0.0302806	−	0.0254084i
$641$	6.88831	−	2.50714i	0.272072	−	0.0990260i	−0.202381	−	0.979307i	$-0.564868\pi$
$641$	6.88831	−	2.50714i	0.272072	−	0.0990260i	0.474453	+	0.880281i	$0.342646\pi$
$642$	−15.2763	−	5.56012i	−0.602908	−	0.219441i
$643$	−2.45748	−	2.06207i	−0.0969136	−	0.0813202i	0.593044	−	0.805170i	$-0.297926\pi$
$643$	−2.45748	−	2.06207i	−0.0969136	−	0.0813202i	−0.689957	+	0.723850i	$0.742371\pi$
$644$	4.68748	−	26.5840i	0.184713	−	1.04756i
$645$	7.14796			0.281450
$646$	26.7793	−	15.1993i	1.05362	−	0.598008i
$647$	−20.8767			−0.820748			−0.410374	−	0.911917i	$-0.634602\pi$
$647$	−20.8767			−0.820748			−0.410374	+	0.911917i	$0.634602\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	−0.484985	−	0.406951i	−0.0190373	−	0.0159742i
$650$	−6.12449	−	2.22913i	−0.240222	−	0.0874337i
$651$	−10.1848	+	3.70696i	−0.399173	+	0.145287i
$652$	9.75877	−	8.18858i	0.382183	−	0.320690i
$653$	18.8414	+	32.6342i	0.737320	+	1.27708i	0.953698	+	0.300766i	$0.0972422\pi$
$653$	18.8414	+	32.6342i	0.737320	+	1.27708i	−0.216378	+	0.976310i	$0.569425\pi$
$654$	0.815207	−	1.41198i	0.0318771	−	0.0552128i
$655$	0.330222	+	1.87278i	0.0129028	+	0.0731757i
$656$	0.0825961	+	0.468426i	0.00322484	+	0.0182890i
$657$	3.22668	−	5.58878i	0.125885	−	0.218039i
$658$	−13.3170	−	23.0658i	−0.519151	−	0.899197i
$659$	−4.39440	+	3.68734i	−0.171182	+	0.143638i	−0.724354	−	0.689429i	$-0.757862\pi$
$659$	−4.39440	+	3.68734i	−0.171182	+	0.143638i	0.553172	+	0.833067i	$0.313417\pi$
$660$	0.326352	−	0.118782i	0.0127032	−	0.00462360i
$661$	10.6604	+	3.88008i	0.414643	+	0.150918i	0.540914	−	0.841078i	$-0.318079\pi$
$661$	10.6604	+	3.88008i	0.414643	+	0.150918i	−0.126271	+	0.991996i	$0.540301\pi$
$662$	−12.3268	−	10.3434i	−0.479095	−	0.402009i
$663$	−7.99495	+	45.3416i	−0.310498	+	1.76092i
$664$	−1.67499			−0.0650023
$665$	19.6596	−	3.31747i	0.762365	−	0.128646i
$666$	−7.66044			−0.296836
$667$	−5.18984	+	29.4331i	−0.200952	+	1.13965i
$668$	−0.137689	−	0.115535i	−0.00532734	−	0.00447017i
$669$	−22.1348	−	8.05639i	−0.855779	−	0.311478i
$670$	−0.573978	+	0.208911i	−0.0221747	+	0.00807093i
$671$	−3.06418	+	2.57115i	−0.118291	+	0.0992582i
$672$	−2.28699	−	3.96118i	−0.0882225	−	0.152806i
$673$	11.7861	−	20.4141i	0.454321	−	0.786907i	−0.544328	−	0.838873i	$-0.683215\pi$
$673$	11.7861	−	20.4141i	0.454321	−	0.786907i	0.998649	+	0.0519653i	$0.0165485\pi$
$674$	−4.70739	−	26.6969i	−0.181322	−	1.02833i
$675$	−0.173648	−	0.984808i	−0.00668372	−	0.0379053i
$676$	−14.7392	+	25.5290i	−0.566891	+	0.981884i
$677$	2.35457	+	4.07824i	0.0904935	+	0.156739i	0.907719	−	0.419579i	$-0.137822\pi$
$677$	2.35457	+	4.07824i	0.0904935	+	0.156739i	−0.817225	+	0.576318i	$0.804489\pi$
$678$	3.78106	−	3.17269i	0.145211	−	0.121846i
$679$	−4.57398	+	1.66479i	−0.175533	+	0.0638888i
$680$	6.63816	+	2.41609i	0.254562	+	0.0926529i
$681$	−19.1138	−	16.0384i	−0.732443	−	0.614592i
$682$	−0.142903	+	0.810446i	−0.00547206	+	0.0310336i
$683$	−6.18655			−0.236722			−0.118361	−	0.992971i	$-0.537764\pi$
$683$	−6.18655			−0.236722			−0.118361	+	0.992971i	$0.537764\pi$
$684$	2.77719	+	3.35965i	0.106188	+	0.128459i
$685$	1.14796			0.0438611
$686$	−5.49731	+	31.1768i	−0.209888	+	1.19034i
$687$	−3.14022	−	2.63495i	−0.119807	−	0.100530i
$688$	−6.71688	−	2.44474i	−0.256079	−	0.0932050i
$689$	63.2828	−	23.0330i	2.41088	−	0.877489i
$690$	−4.52094	+	3.79352i	−0.172109	+	0.144417i
$691$	−11.8748	−	20.5678i	−0.451739	−	0.782434i	0.546755	−	0.837292i	$-0.315863\pi$
$691$	−11.8748	−	20.5678i	−0.451739	−	0.782434i	−0.998494	+	0.0548580i	$0.982529\pi$
$692$	6.82635	−	11.8236i	0.259499	−	0.449465i
$693$	−0.275845	−	1.56439i	−0.0104785	−	0.0594264i
$694$	2.04963	+	11.6240i	0.0778029	+	0.441242i
$695$	−11.6138	+	20.1157i	−0.440537	+	0.763032i
$696$	2.53209	+	4.38571i	0.0959786	+	0.166240i
$697$	−2.57398	+	2.15982i	−0.0974964	+	0.0818092i
$698$	−26.1411	+	9.51460i	−0.989457	+	0.360133i
$699$	−14.5817	−	5.30731i	−0.551531	−	0.200741i
$700$	3.50387	+	2.94010i	0.132434	+	0.111125i
$701$	5.60307	−	31.7766i	0.211625	−	1.20019i	−0.675043	−	0.737779i	$-0.735875\pi$
$701$	5.60307	−	31.7766i	0.211625	−	1.20019i	0.886668	−	0.462407i	$-0.153014\pi$
$702$	−6.51754			−0.245989
$703$	−21.6511	+	25.4204i	−0.816587	+	0.958747i
$704$	−0.347296			−0.0130892
$705$	−1.01114	+	5.73448i	−0.0380819	+	0.215973i
$706$	12.8229	+	10.7597i	0.482598	+	0.404948i
$707$	−53.5262	−	19.4819i	−2.01306	−	0.732694i
$708$	1.71301	−	0.623485i	0.0643789	−	0.0234320i
$709$	−37.0428	+	31.0826i	−1.39117	+	1.16733i	−0.426310	+	0.904577i	$0.640187\pi$
$709$	−37.0428	+	31.0826i	−1.39117	+	1.16733i	−0.964863	+	0.262755i	$0.915369\pi$
$710$	5.87939	+	10.1834i	0.220649	+	0.382176i
$711$	−4.36959	+	7.56834i	−0.163872	+	0.283835i
$712$	1.88191	+	10.6729i	0.0705276	+	0.399982i
$713$	−2.42839	−	13.7721i	−0.0909438	−	0.515768i
$714$	16.1557	−	27.9825i	0.604612	−	1.04722i
$715$	1.13176	+	1.96026i	0.0423254	+	0.0733097i
$716$	−16.3858	+	13.7493i	−0.612365	+	0.513836i
$717$	4.07873	−	1.48453i	0.152323	−	0.0554410i
$718$	−3.51754	−	1.28028i	−0.131273	−	0.0477796i
$719$	−3.04189	−	2.55245i	−0.113443	−	0.0951902i	0.584301	−	0.811537i	$-0.301369\pi$
$719$	−3.04189	−	2.55245i	−0.113443	−	0.0951902i	−0.697745	+	0.716346i	$0.745813\pi$
$720$	−0.173648	+	0.984808i	−0.00647149	+	0.0367016i
$721$	−5.93550			−0.221049
$722$	18.9979	+	0.279737i	0.707030	+	0.0104107i
$723$	−11.7392			−0.436584
$724$	1.44057	−	8.16988i	0.0535384	−	0.303631i
$725$	−3.87939	−	3.25519i	−0.144077	−	0.120895i
$726$	10.2233	+	3.72097i	0.379421	+	0.138098i
$727$	22.5817	−	8.21907i	0.837510	−	0.304829i	0.112572	−	0.993644i	$-0.464091\pi$
$727$	22.5817	−	8.21907i	0.837510	−	0.304829i	0.724937	+	0.688815i	$0.241869\pi$
$728$	22.8366	−	19.1622i	0.846381	−	0.710198i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	3.22668	−	5.58878i	0.119425	−	0.206850i
$731$	−8.76827	−	49.7273i	−0.324306	−	1.83923i
$732$	−2.00000	−	11.3426i	−0.0739221	−	0.419233i
$733$	−7.91235	+	13.7046i	−0.292249	+	0.506191i	−0.974341	−	0.225076i	$-0.927737\pi$
$733$	−7.91235	+	13.7046i	−0.292249	+	0.506191i	0.682092	+	0.731266i	$0.261070\pi$
$734$	−2.20914	−	3.82634i	−0.0815409	−	0.141233i
$735$	10.6643	−	8.94842i	0.393359	−	0.330068i
$736$	5.54576	−	2.01849i	0.204419	−	0.0744026i
$737$	0.199340	+	0.0725540i	0.00734280	+	0.00267256i
$738$	−0.364370	−	0.305743i	−0.0134127	−	0.0112546i
$739$	−6.64068	+	37.6612i	−0.244281	+	1.38539i	0.577874	+	0.816126i	$0.303882\pi$
$739$	−6.64068	+	37.6612i	−0.244281	+	1.38539i	−0.822156	+	0.569263i	$0.807229\pi$
$740$	−7.66044			−0.281604
$741$	−18.4209	+	21.6278i	−0.676707	+	0.794516i
$742$	−47.2618			−1.73503
$743$	8.71823	−	49.4435i	0.319841	−	1.81391i	−0.223853	−	0.974623i	$-0.571864\pi$
$743$	8.71823	−	49.4435i	0.319841	−	1.81391i	0.543694	−	0.839284i	$-0.317025\pi$
$744$	−1.81521	−	1.52314i	−0.0665487	−	0.0558410i
$745$	−11.5544	−	4.20545i	−0.423320	−	0.154076i
$746$	0.859318	−	0.312766i	0.0314619	−	0.0114512i
$747$	1.28312	−	1.07666i	0.0469469	−	0.0393931i
$748$	−1.22668	−	2.12467i	−0.0448519	−	0.0776858i
$749$	−37.1789	+	64.3958i	−1.35849	+	2.35297i
$750$	−0.173648	−	0.984808i	−0.00634073	−	0.0359601i
$751$	8.22163	+	46.6272i	0.300012	+	1.70145i	0.646104	+	0.763249i	$0.276397\pi$
$751$	8.22163	+	46.6272i	0.300012	+	1.70145i	−0.346092	+	0.938200i	$0.612492\pi$
$752$	2.91147	−	5.04282i	0.106171	−	0.183893i
$753$	−2.02435	−	3.50627i	−0.0737713	−	0.127776i
$754$	−25.2841	+	21.2158i	−0.920791	+	0.772635i
$755$	−6.63816	+	2.41609i	−0.241587	+	0.0879306i
$756$	4.29813	+	1.56439i	0.156322	+	0.0568964i
$757$	−7.16772	−	6.01443i	−0.260515	−	0.218598i	0.503169	−	0.864188i	$-0.332167\pi$
$757$	−7.16772	−	6.01443i	−0.260515	−	0.218598i	−0.763684	+	0.645590i	$0.776612\pi$
$758$	4.46451	−	25.3195i	0.162158	−	0.919645i
$759$	2.04963			0.0743969
$760$	2.77719	+	3.35965i	0.100739	+	0.121867i
$761$	−24.4757			−0.887242			−0.443621	−	0.896215i	$-0.646306\pi$
$761$	−24.4757			−0.887242			−0.443621	+	0.896215i	$0.646306\pi$
$762$	−0.378918	+	2.14895i	−0.0137268	+	0.0778484i
$763$	−5.71276	−	4.79358i	−0.206816	−	0.173539i
$764$	12.1702	+	4.42961i	0.440304	+	0.160258i
$765$	−6.63816	+	2.41609i	−0.240003	+	0.0873540i
$766$	−11.9244	+	10.0058i	−0.430847	+	0.361524i
$767$	5.94057	+	10.2894i	0.214502	+	0.371528i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−1.88784	−	10.7065i	−0.0680773	−	0.386086i	−0.999741	−	0.0227634i	$-0.992754\pi$
$769$	−1.88784	−	10.7065i	−0.0680773	−	0.386086i	0.931664	−	0.363322i	$-0.118358\pi$
$770$	−0.275845	−	1.56439i	−0.00994075	−	0.0563768i
$771$	−7.12836	+	12.3467i	−0.256721	+	0.444655i
$772$	6.45336	+	11.1776i	0.232262	+

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.939693 - 0.342020i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.28699 - 3.96118i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +O(q^{10})\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(0.939693 - 0.342020i) q^{5} +(0.766044 - 0.642788i) q^{6} +(-2.28699 - 3.96118i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(0.173648 + 0.984808i) q^{10} +(0.173648 - 0.300767i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-4.99273 + 4.18939i) q^{13} +(4.29813 - 1.56439i) q^{14} +(-0.939693 - 0.342020i) q^{15} +(0.766044 + 0.642788i) q^{16} +(-1.22668 + 6.95686i) q^{17} -1.00000 q^{18} +(-2.82635 + 3.31839i) q^{19} -1.00000 q^{20} +(-0.794263 + 4.50449i) q^{21} +(0.266044 + 0.223238i) q^{22} +(-5.54576 - 2.01849i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(0.766044 - 0.642788i) q^{25} +(-3.25877 - 5.64436i) q^{26} +(0.500000 - 0.866025i) q^{27} +(0.794263 + 4.50449i) q^{28} +(-0.879385 - 4.98724i) q^{29} +(0.500000 - 0.866025i) q^{30} +(1.18479 + 2.05212i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-0.326352 + 0.118782i) q^{33} +(-6.63816 - 2.41609i) q^{34} +(-3.50387 - 2.94010i) q^{35} +(0.173648 - 0.984808i) q^{36} +7.66044 q^{37} +(-2.77719 - 3.35965i) q^{38} +6.51754 q^{39} +(0.173648 - 0.984808i) q^{40} +(0.364370 + 0.305743i) q^{41} +(-4.29813 - 1.56439i) q^{42} +(-6.71688 + 2.44474i) q^{43} +(-0.266044 + 0.223238i) q^{44} +(0.500000 + 0.866025i) q^{45} +(2.95084 - 5.11100i) q^{46} +(-1.01114 - 5.73448i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(-6.96064 + 12.0562i) q^{49} +(0.500000 + 0.866025i) q^{50} +(5.41147 - 4.54077i) q^{51} +(6.12449 - 2.22913i) q^{52} +(-9.70961 - 3.53401i) q^{53} +(0.766044 + 0.642788i) q^{54} +(0.0603074 - 0.342020i) q^{55} -4.57398 q^{56} +(4.29813 - 0.725293i) q^{57} +5.06418 q^{58} +(0.316552 - 1.79525i) q^{59} +(0.766044 + 0.642788i) q^{60} +(-10.8229 - 3.93923i) q^{61} +(-2.22668 + 0.810446i) q^{62} +(3.50387 - 2.94010i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-3.25877 + 5.64436i) q^{65} +(-0.0603074 - 0.342020i) q^{66} +(0.106067 + 0.601535i) q^{67} +(3.53209 - 6.11776i) q^{68} +(2.95084 + 5.11100i) q^{69} +(3.50387 - 2.94010i) q^{70} +(11.0496 - 4.02174i) q^{71} +(0.939693 + 0.342020i) q^{72} +(-4.94356 - 4.14814i) q^{73} +(-1.33022 + 7.54407i) q^{74} -1.00000 q^{75} +(3.79086 - 2.15160i) q^{76} -1.58853 q^{77} +(-1.13176 + 6.41852i) q^{78} +(6.69459 + 5.61743i) q^{79} +(0.939693 + 0.342020i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(-0.364370 + 0.305743i) q^{82} +(-0.837496 - 1.45059i) q^{83} +(2.28699 - 3.96118i) q^{84} +(1.22668 + 6.95686i) q^{85} +(-1.24123 - 7.03936i) q^{86} +(-2.53209 + 4.38571i) q^{87} +(-0.173648 - 0.300767i) q^{88} +(-8.30200 + 6.96621i) q^{89} +(-0.939693 + 0.342020i) q^{90} +(28.0133 + 10.1960i) q^{91} +(4.52094 + 3.79352i) q^{92} +(0.411474 - 2.33359i) q^{93} +5.82295 q^{94} +(-1.52094 + 4.08494i) q^{95} +1.00000 q^{96} +(0.184793 - 1.04801i) q^{97} +(-10.6643 - 8.94842i) q^{98} +(0.326352 + 0.118782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6q - 6q^{7} + 3q^{8} + O(q^{10}) \)	\( 6q - 6q^{7} + 3q^{8} + 3q^{12} - 12q^{13} + 12q^{14} + 6q^{17} - 6q^{18} - 18q^{19} - 6q^{20} - 15q^{21} - 3q^{22} - 3q^{23} + 3q^{26} + 3q^{27} + 15q^{28} + 6q^{29} + 3q^{30} - 3q^{33} - 6q^{34} + 3q^{35} - 6q^{38} - 6q^{39} + 21q^{41} - 12q^{42} - 24q^{43} + 3q^{44} + 3q^{45} + 6q^{46} - 33q^{49} + 3q^{50} + 12q^{51} + 24q^{52} - 24q^{53} + 6q^{55} - 12q^{56} + 12q^{57} + 12q^{58} - 24q^{61} - 3q^{63} - 3q^{64} + 3q^{65} - 6q^{66} - 24q^{67} + 12q^{68} + 6q^{69} - 3q^{70} + 12q^{71} + 15q^{74} - 6q^{75} - 9q^{76} - 30q^{77} - 12q^{78} + 36q^{79} - 21q^{82} + 6q^{84} - 6q^{85} - 30q^{86} - 6q^{87} - 12q^{89} + 24q^{91} + 24q^{92} - 18q^{93} - 6q^{94} - 6q^{95} + 6q^{96} - 6q^{97} + 6q^{98} + 3q^{99} + O(q^{100}) \)

Introduction

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