LMFDB - Embedded newform 770.2.w.b.139.21

Newspace parameters

Level:	$ N $	$=$	$ 770 = 2 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	770.w (of order $10$, degree $4$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$6.14848095564$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			139.21
Character	$\chi$	$=$	770.139
Dual form			770.2.w.b.349.21

$q$-expansion

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(0.732958 - 2.25581i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.464104 - 2.18737i) q^{5} +(1.91891 - 1.39417i) q^{6} +(1.96220 - 1.77476i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.12441 - 1.54347i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(0.732958 - 2.25581i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.464104 - 2.18737i) q^{5} +(1.91891 - 1.39417i) q^{6} +(1.96220 - 1.77476i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.12441 - 1.54347i) q^{9} +(0.910238 - 2.04242i) q^{10} +(-2.63315 - 2.01656i) q^{11} +2.37190 q^{12} +(-0.478040 + 0.657965i) q^{13} +(2.63063 - 0.282464i) q^{14} +(-5.27447 - 0.556321i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.374125 - 0.514939i) q^{17} +(-0.811453 - 2.49739i) q^{18} +(0.231172 - 0.711476i) q^{19} +(1.93690 - 1.11733i) q^{20} +(-2.56533 - 5.72717i) q^{21} +(-0.944954 - 3.17916i) q^{22} +5.84039i q^{23} +(1.91891 + 1.39417i) q^{24} +(-4.56921 + 2.03034i) q^{25} +(-0.773484 + 0.251320i) q^{26} +(0.717833 - 0.521536i) q^{27} +(2.29425 + 1.31773i) q^{28} +(8.07009 - 2.62213i) q^{29} +(-3.94014 - 3.55033i) q^{30} +(-2.72989 + 3.75737i) q^{31} -1.00000 q^{32} +(-6.47898 + 4.46183i) q^{33} -0.636500i q^{34} +(-4.79274 - 3.46838i) q^{35} +(0.811453 - 2.49739i) q^{36} +(-3.85636 + 1.25301i) q^{37} +(0.605217 - 0.439716i) q^{38} +(1.13386 + 1.56063i) q^{39} +(2.22373 + 0.234546i) q^{40} +(0.693842 - 2.13543i) q^{41} +(1.29095 - 6.14124i) q^{42} +1.78702 q^{43} +(1.10418 - 3.12743i) q^{44} +(-2.39021 + 5.36321i) q^{45} +(-3.43289 + 4.72497i) q^{46} +(1.40295 - 4.31784i) q^{47} +(0.732958 + 2.25581i) q^{48} +(0.700426 - 6.96487i) q^{49} +(-4.88998 - 1.04314i) q^{50} +(-1.43582 + 0.466527i) q^{51} +(-0.773484 - 0.251320i) q^{52} +(1.23908 - 1.70545i) q^{53} +0.887291 q^{54} +(-3.18893 + 6.69558i) q^{55} +(1.08155 + 2.41459i) q^{56} +(-1.43552 - 1.04296i) q^{57} +(8.07009 + 2.62213i) q^{58} +(11.4455 - 3.71887i) q^{59} +(-1.10081 - 5.18824i) q^{60} +(9.48273 - 6.88961i) q^{61} +(-4.41705 + 1.43519i) q^{62} +(-6.90781 + 0.741728i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.66108 + 0.740287i) q^{65} +(-7.86420 - 0.198551i) q^{66} +7.11959i q^{67} +(0.374125 - 0.514939i) q^{68} +(13.1748 + 4.28076i) q^{69} +(-1.83874 - 5.62308i) q^{70} +(6.16231 - 4.47718i) q^{71} +(2.12441 - 1.54347i) q^{72} +(-9.50651 + 3.08885i) q^{73} +(-3.85636 - 1.25301i) q^{74} +(1.23103 + 11.7954i) q^{75} +0.748090 q^{76} +(-8.74568 + 0.716320i) q^{77} +1.92904i q^{78} +(-9.15919 + 12.6065i) q^{79} +(1.66117 + 1.49683i) q^{80} +(-3.08470 - 9.49374i) q^{81} +(1.81650 - 1.31977i) q^{82} +(4.36182 + 6.00353i) q^{83} +(4.65414 - 4.20956i) q^{84} +(-0.952731 + 1.05734i) q^{85} +(1.44573 + 1.05039i) q^{86} -20.1265i q^{87} +(2.73155 - 1.88112i) q^{88} -10.1872i q^{89} +(-5.08614 + 2.93400i) q^{90} +(0.229725 + 2.13946i) q^{91} +(-5.55454 + 1.80478i) q^{92} +(6.47503 + 8.91211i) q^{93} +(3.67298 - 2.66857i) q^{94} +(-1.66355 - 0.175462i) q^{95} +(-0.732958 + 2.25581i) q^{96} +(9.78252 + 7.10742i) q^{97} +(4.66050 - 5.22300i) q^{98} +(2.48137 + 8.34821i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	$ 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) $ 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/770\mathbb{Z}\right)^\times$.

$n$	$211$	$617$	$661$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$-1$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i
$3$	0.732958	−	2.25581i	0.423173	−	1.30239i	−0.481559	−	0.876414i	$-0.659929\pi$
$3$	0.732958	−	2.25581i	0.423173	−	1.30239i	0.904733	−	0.425980i	$-0.140071\pi$
$4$	0.309017	+	0.951057i	0.154508	+	0.475528i
$5$	−0.464104	−	2.18737i	−0.207554	−	0.978224i
$5$	−0.464104	−	2.18737i	−0.207554	−	0.978224i
$6$	1.91891	−	1.39417i	0.783391	−	0.569167i
$7$	1.96220	−	1.77476i	0.741640	−	0.670798i
$7$	1.96220	−	1.77476i	0.741640	−	0.670798i
$8$	−0.309017	+	0.951057i	−0.109254	+	0.336249i
$9$	−2.12441	−	1.54347i	−0.708137	−	0.514492i
$10$	0.910238	−	2.04242i	0.287843	−	0.645869i
$11$	−2.63315	−	2.01656i	−0.793924	−	0.608017i
$11$	−2.63315	−	2.01656i	−0.793924	−	0.608017i
$12$	2.37190			0.684709
$13$	−0.478040	+	0.657965i	−0.132584	+	0.182487i	−0.870147	−	0.492792i	$-0.835976\pi$
$13$	−0.478040	+	0.657965i	−0.132584	+	0.182487i	0.737563	+	0.675278i	$0.235976\pi$
$14$	2.63063	−	0.282464i	0.703065	−	0.0754918i
$15$	−5.27447	−	0.556321i	−1.36186	−	0.143641i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−0.374125	−	0.514939i	−0.0907387	−	0.124891i	0.761234	−	0.648477i	$-0.224594\pi$
$17$	−0.374125	−	0.514939i	−0.0907387	−	0.124891i	−0.851973	+	0.523586i	$0.824594\pi$
$18$	−0.811453	−	2.49739i	−0.191261	−	0.588641i
$19$	0.231172	−	0.711476i	0.0530346	−	0.163224i	−0.921031	−	0.389489i	$-0.872652\pi$
$19$	0.231172	−	0.711476i	0.0530346	−	0.163224i	0.974066	+	0.226265i	$0.0726516\pi$
$20$	1.93690	−	1.11733i	0.433104	−	0.249842i
$21$	−2.56533	−	5.72717i	−0.559800	−	1.24977i
$22$	−0.944954	−	3.17916i	−0.201465	−	0.677799i
$23$			5.84039i			1.21781i	0.793245	+	0.608903i	$0.208390\pi$
$23$			5.84039i			1.21781i	−0.793245	+	0.608903i	$0.791610\pi$
$24$	1.91891	+	1.39417i	0.391696	+	0.284583i
$25$	−4.56921	+	2.03034i	−0.913843	+	0.406068i
$26$	−0.773484	+	0.251320i	−0.151693	+	0.0492880i
$27$	0.717833	−	0.521536i	0.138147	−	0.100370i
$28$	2.29425	+	1.31773i	0.433573	+	0.249027i
$29$	8.07009	−	2.62213i	1.49858	−	0.486918i	0.558975	−	0.829184i	$-0.311195\pi$
$29$	8.07009	−	2.62213i	1.49858	−	0.486918i	0.939603	+	0.342267i	$0.111195\pi$
$30$	−3.94014	−	3.55033i	−0.719368	−	0.648199i
$31$	−2.72989	+	3.75737i	−0.490303	+	0.674844i	−0.980444	−	0.196799i	$-0.936945\pi$
$31$	−2.72989	+	3.75737i	−0.490303	+	0.674844i	0.490141	+	0.871643i	$0.336945\pi$
$32$	−1.00000			−0.176777
$33$	−6.47898	+	4.46183i	−1.12785	+	0.776705i
$34$		−	0.636500i		−	0.109159i
$35$	−4.79274	−	3.46838i	−0.810120	−	0.586263i
$36$	0.811453	−	2.49739i	0.135242	−	0.416232i
$37$	−3.85636	+	1.25301i	−0.633982	+	0.205993i	−0.608338	−	0.793678i	$-0.708164\pi$
$37$	−3.85636	+	1.25301i	−0.633982	+	0.205993i	−0.0256440	+	0.999671i	$0.508164\pi$
$38$	0.605217	−	0.439716i	0.0981792	−	0.0713314i
$39$	1.13386	+	1.56063i	0.181563	+	0.249900i
$40$	2.22373	+	0.234546i	0.351603	+	0.0370850i
$41$	0.693842	−	2.13543i	0.108360	−	0.333498i	−0.882144	−	0.470979i	$-0.843901\pi$
$41$	0.693842	−	2.13543i	0.108360	−	0.333498i	0.990504	+	0.137481i	$0.0439007\pi$
$42$	1.29095	−	6.14124i	0.199199	−	0.947614i
$43$	1.78702			0.272519			0.136259	−	0.990673i	$-0.456492\pi$
$43$	1.78702			0.272519			0.136259	+	0.990673i	$0.456492\pi$
$44$	1.10418	−	3.12743i	0.166461	−	0.471477i
$45$	−2.39021	+	5.36321i	−0.356311	+	0.799501i
$46$	−3.43289	+	4.72497i	−0.506153	+	0.696659i
$47$	1.40295	−	4.31784i	0.204642	−	0.629822i	−0.795086	−	0.606496i	$-0.792574\pi$
$47$	1.40295	−	4.31784i	0.204642	−	0.629822i	0.999728	−	0.0233258i	$-0.00742551\pi$
$48$	0.732958	+	2.25581i	0.105793	+	0.325598i
$49$	0.700426	−	6.96487i	0.100061	−	0.994981i
$50$	−4.88998	−	1.04314i	−0.691547	−	0.147522i
$51$	−1.43582	+	0.466527i	−0.201056	+	0.0653269i
$52$	−0.773484	−	0.251320i	−0.107263	−	0.0348518i
$53$	1.23908	−	1.70545i	0.170201	−	0.234262i	−0.715392	−	0.698723i	$-0.753752\pi$
$53$	1.23908	−	1.70545i	0.170201	−	0.234262i	0.885594	+	0.464461i	$0.153752\pi$
$54$	0.887291			0.120745
$55$	−3.18893	+	6.69558i	−0.429995	+	0.902831i
$56$	1.08155	+	2.41459i	0.144528	+	0.322663i
$57$	−1.43552	−	1.04296i	−0.190139	−	0.138144i
$58$	8.07009	+	2.62213i	1.05965	+	0.344303i
$59$	11.4455	−	3.71887i	1.49008	−	0.484155i	0.552970	−	0.833201i	$-0.313494\pi$
$59$	11.4455	−	3.71887i	1.49008	−	0.484155i	0.937106	+	0.349046i	$0.113494\pi$
$60$	−1.10081	−	5.18824i	−0.142114	−	0.669798i
$61$	9.48273	−	6.88961i	1.21414	−	0.882124i	0.218540	−	0.975828i	$-0.429871\pi$
$61$	9.48273	−	6.88961i	1.21414	−	0.882124i	0.995600	+	0.0937040i	$0.0298707\pi$
$62$	−4.41705	+	1.43519i	−0.560966	+	0.182269i
$63$	−6.90781	+	0.741728i	−0.870303	+	0.0934489i
$64$	−0.809017	−	0.587785i	−0.101127	−	0.0734732i
$65$	1.66108	+	0.740287i	0.206031	+	0.0918213i
$66$	−7.86420	−	0.198551i	−0.968016	−	0.0244400i
$67$			7.11959i			0.869796i	0.900480	+	0.434898i	$0.143216\pi$
$67$			7.11959i			0.869796i	−0.900480	+	0.434898i	$0.856784\pi$
$68$	0.374125	−	0.514939i	0.0453693	−	0.0624455i
$69$	13.1748	+	4.28076i	1.58606	+	0.515343i
$70$	−1.83874	−	5.62308i	−0.219772	−	0.672087i
$71$	6.16231	−	4.47718i	0.731331	−	0.531343i	−0.158653	−	0.987334i	$-0.550715\pi$
$71$	6.16231	−	4.47718i	0.731331	−	0.531343i	0.889984	+	0.455991i	$0.150715\pi$
$72$	2.12441	−	1.54347i	0.250364	−	0.181900i
$73$	−9.50651	+	3.08885i	−1.11265	+	0.361523i	−0.806959	−	0.590607i	$-0.798888\pi$
$73$	−9.50651	+	3.08885i	−1.11265	+	0.361523i	−0.305693	+	0.952130i	$0.598888\pi$
$74$	−3.85636	−	1.25301i	−0.448293	−	0.145659i
$75$	1.23103	+	11.7954i	0.142147	+	1.36202i
$76$	0.748090			0.0858118
$77$	−8.74568	+	0.716320i	−0.996663	+	0.0816323i
$78$			1.92904i			0.218421i
$79$	−9.15919	+	12.6065i	−1.03049	+	1.41835i	−0.125910	+	0.992042i	$0.540185\pi$
$79$	−9.15919	+	12.6065i	−1.03049	+	1.41835i	−0.904580	+	0.426305i	$0.859815\pi$
$80$	1.66117	+	1.49683i	0.185725	+	0.167351i
$81$	−3.08470	−	9.49374i	−0.342745	−	1.05486i
$82$	1.81650	−	1.31977i	0.200599	−	0.145744i
$83$	4.36182	+	6.00353i	0.478772	+	0.658973i	0.978268	−	0.207343i	$-0.0664815\pi$
$83$	4.36182	+	6.00353i	0.478772	+	0.658973i	−0.499496	+	0.866316i	$0.666482\pi$
$84$	4.65414	−	4.20956i	0.507808	−	0.459301i
$85$	−0.952731	+	1.05734i	−0.103338	+	0.114684i
$86$	1.44573	+	1.05039i	0.155897	+	0.113266i
$87$		−	20.1265i		−	2.15779i
$88$	2.73155	−	1.88112i	0.291185	−	0.200528i
$89$		−	10.1872i		−	1.07984i	−0.841717	−	0.539919i	$-0.818455\pi$
$89$		−	10.1872i		−	1.07984i	0.841717	−	0.539919i	$-0.181545\pi$
$90$	−5.08614	+	2.93400i	−0.536126	+	0.309271i
$91$	0.229725	+	2.13946i	0.0240817	+	0.224277i
$92$	−5.55454	+	1.80478i	−0.579101	+	0.188161i
$93$	6.47503	+	8.91211i	0.671429	+	0.924143i
$94$	3.67298	−	2.66857i	0.378839	−	0.275242i
$95$	−1.66355	−	0.175462i	−0.170677	−	0.0180020i
$96$	−0.732958	+	2.25581i	−0.0748072	+	0.230233i
$97$	9.78252	+	7.10742i	0.993264	+	0.721649i	0.960634	−	0.277819i	$-0.0896115\pi$
$97$	9.78252	+	7.10742i	0.993264	+	0.721649i	0.0326308	+	0.999467i	$0.489611\pi$
$98$	4.66050	−	5.22300i	0.470782	−	0.527602i
$99$	2.48137	+	8.34821i	0.249387	+	0.839026i
$100$	−3.34293	−	3.71817i	−0.334293	−	0.371817i
$101$	−1.69439	−	1.23104i	−0.168598	−	0.122493i	0.500287	−	0.865860i	$-0.333228\pi$
$101$	−1.69439	−	1.23104i	−0.168598	−	0.122493i	−0.668884	+	0.743366i	$0.733228\pi$
$102$	−1.43582	−	0.466527i	−0.142168	−	0.0461931i
$103$	3.03083	+	9.32794i	0.298637	+	0.919110i	0.981976	+	0.189008i	$0.0605272\pi$
$103$	3.03083	+	9.32794i	0.298637	+	0.919110i	−0.683339	+	0.730101i	$0.739473\pi$
$104$	−0.478040	−	0.657965i	−0.0468756	−	0.0645188i
$105$	−11.3369	+	8.26934i	−1.10637	+	0.807005i
$106$	2.00488	−	0.651425i	0.194731	−	0.0632720i
$107$	−0.172623	+	0.531279i	−0.0166881	+	0.0513607i	−0.959054	−	0.283224i	$-0.908596\pi$
$107$	−0.172623	+	0.531279i	−0.0166881	+	0.0513607i	0.942366	+	0.334585i	$0.108596\pi$
$108$	0.717833	+	0.521536i	0.0690735	+	0.0501849i
$109$			2.34499i			0.224609i	0.993674	+	0.112305i	$0.0358232\pi$
$109$			2.34499i			0.224609i	−0.993674	+	0.112305i	$0.964177\pi$
$110$	−6.51546	+	3.54243i	−0.621224	+	0.337758i
$111$			9.61764i			0.912866i
$112$	−0.544270	+	2.58916i	−0.0514287	+	0.244653i
$113$	8.21206	+	2.66826i	0.772526	+	0.251009i	0.668646	−	0.743581i	$-0.266874\pi$
$113$	8.21206	+	2.66826i	0.772526	+	0.251009i	0.103880	+	0.994590i	$0.466874\pi$
$114$	−0.548318	−	1.68755i	−0.0513547	−	0.158054i
$115$	12.7751	−	2.71055i	1.19129	−	0.252760i
$116$	4.98759	+	6.86483i	0.463086	+	0.637383i
$117$	2.03110	−	0.659946i	0.187776	−	0.0610120i
$118$	11.4455	+	3.71887i	1.05364	+	0.342349i
$119$	−1.64800	−	0.346428i	−0.151072	−	0.0317570i
$120$	2.15899	−	4.84441i	0.197088	−	0.442232i
$121$	2.86693	+	10.6198i	0.260630	+	0.965439i
$122$	11.7213			1.06120
$123$	−4.30856	−	3.13036i	−0.388490	−	0.282255i
$124$	−4.41705	−	1.43519i	−0.396663	−	0.128884i
$125$	6.56171	+	9.05229i	0.586897	+	0.809662i
$126$	−6.02451	−	3.46024i	−0.536706	−	0.308263i
$127$	3.94559	−	2.86664i	0.350115	−	0.254373i	−0.398802	−	0.917037i	$-0.630574\pi$
$127$	3.94559	−	2.86664i	0.350115	−	0.254373i	0.748917	+	0.662664i	$0.230574\pi$
$128$	−0.309017	−	0.951057i	−0.0273135	−	0.0840623i
$129$	1.30981	−	4.03119i	0.115323	−	0.354927i
$130$	0.908709	+	1.57526i	0.0796990	+	0.138160i
$131$	−12.5690			−1.09816			−0.549081	−	0.835769i	$-0.685022\pi$
$131$	−12.5690			−1.09816			−0.549081	+	0.835769i	$0.685022\pi$
$132$	−6.24557	−	4.78309i	−0.543607	−	0.416315i
$133$	−0.809096	−	1.80633i	−0.0701575	−	0.156629i
$134$	−4.18479	+	5.75987i	−0.361511	+	0.497577i
$135$	−1.47395	−	1.32812i	−0.126857	−	0.114307i
$136$	0.605347	−	0.196689i	0.0519081	−	0.0168660i
$137$	12.0558	+	16.5933i	1.02999	+	1.41766i	0.904953	+	0.425511i	$0.139906\pi$
$137$	12.0558	+	16.5933i	1.02999	+	1.41766i	0.125039	+	0.992152i	$0.460094\pi$
$138$	8.14249	+	11.2072i	0.693135	+	0.954018i
$139$	−1.58657	−	4.88296i	−0.134571	−	0.414168i	0.860952	−	0.508686i	$-0.169869\pi$
$139$	−1.58657	−	4.88296i	−0.134571	−	0.414168i	−0.995523	+	0.0945189i	$0.969869\pi$
$140$	1.81759	−	5.62995i	0.153614	−	0.475818i
$141$	−8.71194	−	6.32959i	−0.733678	−	0.533048i
$142$	7.61703			0.639207
$143$	2.58558	−	0.768521i	0.216217	−	0.0642670i
$144$	2.62592			0.218826
$145$	−9.48095	−	16.4354i	−0.787350	−	1.36488i
$146$	−9.50651	−	3.08885i	−0.786764	−	0.255635i
$147$	−15.1981	−	6.68498i	−1.25351	−	0.551368i
$148$	−2.38336	−	3.28042i	−0.195911	−	0.269649i
$149$	6.72048	+	9.24994i	0.550563	+	0.757785i	0.990088	−	0.140445i	$-0.0448534\pi$
$149$	6.72048	+	9.24994i	0.550563	+	0.757785i	−0.439526	+	0.898230i	$0.644853\pi$
$150$	−5.93727	+	10.2663i	−0.484776	+	0.838239i
$151$	1.93498	+	0.628714i	0.157467	+	0.0511640i	0.386690	−	0.922210i	$-0.373618\pi$
$151$	1.93498	+	0.628714i	0.157467	+	0.0511640i	−0.229223	+	0.973374i	$0.573618\pi$
$152$	0.605217	+	0.439716i	0.0490896	+	0.0356657i
$153$			1.67139i			0.135124i
$154$	−7.49644	−	4.56107i	−0.604081	−	0.367541i
$155$	9.48573	+	4.22748i	0.761912	+	0.339559i
$156$	−1.13386	+	1.56063i	−0.0907817	+	0.124950i
$157$	1.25232	−	3.85425i	0.0999461	−	0.307602i	−0.888565	−	0.458751i	$-0.848297\pi$
$157$	1.25232	−	3.85425i	0.0999461	−	0.307602i	0.988511	+	0.151148i	$0.0482971\pi$
$158$	−14.8199	+	4.81527i	−1.17901	+	0.383082i
$159$	−2.93899	−	4.04517i	−0.233077	−	0.320803i
$160$	0.464104	+	2.18737i	0.0366907	+	0.172927i
$161$	10.3653	+	11.4600i	0.816901	+	0.903174i
$162$	3.08470	−	9.49374i	0.242357	−	0.745899i
$163$	−9.76479	+	13.4401i	−0.764837	+	1.05271i	0.231959	+	0.972726i	$0.425487\pi$
$163$	−9.76479	+	13.4401i	−0.764837	+	1.05271i	−0.996796	+	0.0799827i	$0.974513\pi$
$164$	2.24532			0.175330
$165$	12.7666	+	12.1012i	0.993880	+	0.942077i
$166$			7.42077i			0.575964i
$167$	−1.66365	+	2.28982i	−0.128737	+	0.177192i	−0.868520	−	0.495654i	$-0.834928\pi$
$167$	−1.66365	+	2.28982i	−0.128737	+	0.177192i	0.739783	+	0.672846i	$0.234928\pi$
$168$	6.23959	−	0.669978i	0.481395	−	0.0516899i
$169$	3.81282	+	11.7347i	0.293294	+	0.902667i
$170$	−1.39226	+	0.295402i	−0.106782	+	0.0226563i
$171$	−1.58925	+	1.15466i	−0.121533	+	0.0882989i
$172$	0.552221	+	1.69956i	0.0421065	+	0.129590i
$173$	−19.9440	−	6.48021i	−1.51632	−	0.492681i	−0.571589	−	0.820540i	$-0.693673\pi$
$173$	−19.9440	−	6.48021i	−1.51632	−	0.492681i	−0.944727	+	0.327859i	$0.893673\pi$
$174$	11.8301	−	16.2827i	0.896835	−	1.23439i
$175$	−5.36232	+	12.0932i	−0.405353	+	0.914160i
$176$	3.31557	+	0.0837098i	0.249920	+	0.00630987i
$177$		−	28.5447i		−	2.14555i
$178$	5.98787	−	8.24159i	0.448809	−	0.617733i
$179$	0.393228	−	1.21023i	0.0293912	−	0.0904570i	−0.935285	−	0.353896i	$-0.884857\pi$
$179$	0.393228	−	1.21023i	0.0293912	−	0.0904570i	0.964676	+	0.263439i	$0.0848567\pi$
$180$	−5.83934	−	0.615899i	−0.435238	−	0.0459064i
$181$	−3.21681	−	4.42756i	−0.239103	−	0.329098i	0.672554	−	0.740048i	$-0.265197\pi$
$181$	−3.21681	−	4.42756i	−0.239103	−	0.329098i	−0.911658	+	0.410950i	$0.865197\pi$
$182$	−1.07169	+	1.86589i	−0.0794392	+	0.138309i
$183$	−8.59122	−	26.4411i	−0.635081	−	1.95458i
$184$	−5.55454	−	1.80478i	−0.409486	−	0.133050i
$185$	4.53056	+	7.85379i	0.333093	+	0.577422i
$186$			11.0160i			0.807731i
$187$	−0.0532813	+	2.11036i	−0.00389631	+	0.154325i
$188$	4.54005			0.331117
$189$	0.482926	−	2.29734i	0.0351277	−	0.167107i
$190$	−1.24271	−	1.11976i	−0.0901555	−	0.0812361i
$191$	−2.75958	−	8.49313i	−0.199676	−	0.614541i	−0.999890	−	0.0148259i	$-0.995281\pi$
$191$	−2.75958	−	8.49313i	−0.199676	−	0.614541i	0.800214	−	0.599715i	$-0.204719\pi$
$192$	−1.91891	+	1.39417i	−0.138485	+	0.100615i
$193$	17.0889	−	12.4158i	1.23008	−	0.893709i	0.233188	−	0.972432i	$-0.425084\pi$
$193$	17.0889	−	12.4158i	1.23008	−	0.893709i	0.996897	+	0.0787231i	$0.0250843\pi$
$194$	3.73659	+	11.5000i	0.268272	+	0.825655i
$195$	2.88745	−	3.20448i	0.206774	−	0.229477i
$196$	6.84043	−	1.48612i	0.488602	−	0.106151i
$197$	13.6474			0.972338			0.486169	−	0.873865i	$-0.338394\pi$
$197$	13.6474			0.972338			0.486169	+	0.873865i	$0.338394\pi$
$198$	−2.89948	+	8.21235i	−0.206057	+	0.583627i
$199$		−	5.76658i		−	0.408782i	−0.978889	−	0.204391i	$-0.934479\pi$
$199$		−	5.76658i		−	0.408782i	0.978889	−	0.204391i	$-0.0655214\pi$
$200$	−0.519004	−	4.97299i	−0.0366991	−	0.351644i
$201$	16.0605	+	5.21836i	1.13282	+	0.368075i
$202$	−0.647198	−	1.99187i	−0.0455367	−	0.140147i
$203$	11.1814	−	19.4676i	0.784783	−	1.36636i
$204$	−0.887388	−	1.22138i	−0.0621296	−	0.0855140i
$205$	−4.99299	−	0.526632i	−0.348726	−	0.0367816i
$206$	−3.03083	+	9.32794i	−0.211168	+	0.649909i
$207$	9.01449	−	12.4074i	0.626551	−	0.862373i
$208$		−	0.813289i		−	0.0563915i
$209$	−2.04345	+	1.40725i	−0.141348	+	0.0973413i
$210$	−14.0323	+	0.0263768i	−0.968323	+	0.00182017i
$211$	−12.6807	+	17.4535i	−0.872974	+	1.20155i	0.105343	+	0.994436i	$0.466406\pi$
$211$	−12.6807	+	17.4535i	−0.872974	+	1.20155i	−0.978318	+	0.207110i	$0.933594\pi$
$212$	2.00488	+	0.651425i	0.137696	+	0.0447401i
$213$	−5.58296	−	17.1826i	−0.382538	−	1.17733i
$214$	−0.451933	+	0.328349i	−0.0308935	+	0.0224455i
$215$	−0.829366	−	3.90889i	−0.0565623	−	0.266584i
$216$	0.274188	+	0.843864i	0.0186561	+	0.0574177i
$217$	1.31187	+	12.2176i	0.0890554	+	0.829385i
$218$	−1.37835	+	1.89714i	−0.0933537	+	0.128490i
$219$			23.7089i			1.60210i
$220$	−7.35330	−	0.963803i	−0.495760	−	0.0649796i
$221$	0.517658			0.0348215
$222$	−5.65311	+	7.78083i	−0.379412	+	0.522215i
$223$	−4.89906	+	15.0778i	−0.328065	+	1.00968i	0.641972	+	0.766728i	$0.278116\pi$
$223$	−4.89906	+	15.0778i	−0.328065	+	1.00968i	−0.970038	+	0.242954i	$0.921884\pi$
$224$	−1.96220	+	1.77476i	−0.131105	+	0.118581i
$225$	12.8407	+	2.73919i	0.856044	+	0.182613i
$226$	5.07533	+	6.98560i	0.337606	+	0.464675i
$227$	−14.1957	+	4.61246i	−0.942201	+	0.306140i	−0.739542	−	0.673110i	$-0.764958\pi$
$227$	−14.1957	+	4.61246i	−0.942201	+	0.306140i	−0.202658	+	0.979250i	$0.564958\pi$
$228$	0.548318	−	1.68755i	0.0363133	−	0.111761i
$229$	12.7501	−	17.5490i	0.842548	−	1.15967i	−0.142907	−	0.989736i	$-0.545645\pi$
$229$	12.7501	−	17.5490i	0.842548	−	1.15967i	0.985456	−	0.169932i	$-0.0543549\pi$
$230$	11.9285	+	5.31615i	0.786543	+	0.350536i
$231$	−4.79433	+	20.2536i	−0.315444	+	1.33259i
$232$			8.48540i			0.557094i
$233$	−20.8110	−	15.1201i	−1.36338	−	0.990550i	−0.998222	−	0.0596025i	$-0.981017\pi$
$233$	−20.8110	−	15.1201i	−1.36338	−	0.990550i	−0.365153	−	0.930948i	$-0.618983\pi$
$234$	2.03110	+	0.659946i	0.132777	+	0.0431420i
$235$	−10.0959	−	1.06485i	−0.658581	−	0.0694633i
$236$	7.07370	+	9.73612i	0.460459	+	0.633767i
$237$	21.7247	+	29.9015i	1.41117	+	1.94231i
$238$	−1.12964	−	1.24894i	−0.0732235	−	0.0809566i
$239$	−7.45527	−	2.42237i	−0.482242	−	0.156690i	0.0577999	−	0.998328i	$-0.481591\pi$
$239$	−7.45527	−	2.42237i	−0.482242	−	0.156690i	−0.540041	+	0.841638i	$0.681591\pi$
$240$	4.59414	−	2.65019i	0.296550	−	0.171069i
$241$	−30.5782			−1.96971			−0.984856	−	0.173373i	$-0.944533\pi$
$241$	−30.5782			−1.96971			−0.984856	+	0.173373i	$0.944533\pi$
$242$	−3.92278	+	10.2768i	−0.252166	+	0.660615i
$243$	−21.0152			−1.34813
$244$	9.48273	+	6.88961i	0.607070	+	0.441062i
$245$	−15.5598	+	1.70033i	−0.994082	+	0.108630i
$246$	−1.64573	−	5.06502i	−0.104928	−	0.322934i
$247$	0.357616	+	0.492217i	0.0227546	+	0.0313190i
$248$	−2.72989	−	3.75737i	−0.173348	−	0.238593i
$249$	16.7399	−	5.43911i	1.06085	−	0.344690i
$250$	−0.0122717	+	11.1803i	−0.000776128	+	0.707106i
$251$	−2.29582	+	3.15992i	−0.144911	+	0.199452i	−0.875302	−	0.483576i	$-0.839338\pi$
$251$	−2.29582	+	3.15992i	−0.144911	+	0.199452i	0.730392	+	0.683029i	$0.239338\pi$
$252$	−2.84006	−	6.34051i	−0.178907	−	0.399415i
$253$	11.7775	−	15.3786i	0.740447	−	0.966845i
$254$	4.87702			0.306012
$255$	1.68684	+	2.92417i	0.105634	+	0.183118i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	6.06728	+	18.6732i	0.378466	+	1.16480i	0.941110	+	0.338100i	$0.109784\pi$
$257$	6.06728	+	18.6732i	0.378466	+	1.16480i	−0.562644	+	0.826699i	$0.690216\pi$
$258$	3.42914	−	2.49141i	0.213489	−	0.155109i
$259$	−5.34315	+	9.30279i	−0.332007	+	0.578047i
$260$	−0.190754	+	1.80854i	−0.0118301	+	0.112161i
$261$	−21.1914	−	6.88550i	−1.31171	−	0.426202i
$262$	−10.1686	−	7.38790i	−0.628216	−	0.456426i
$263$	−19.3898			−1.19563			−0.597814	−	0.801634i	$-0.703964\pi$
$263$	−19.3898			−1.19563			−0.597814	+	0.801634i	$0.703964\pi$
$264$	−2.24134	−	7.54065i	−0.137945	−	0.464095i
$265$	−4.30553	−	1.91883i	−0.264487	−	0.117873i
$266$	0.407163	−	1.93693i	0.0249647	−	0.118761i
$267$	−22.9803	−	7.46676i	−1.40637	−	0.456958i
$268$	−6.77113	+	2.20007i	−0.413613	+	0.134391i
$269$	17.4834	+	24.0639i	1.06598	+	1.46720i	0.874076	+	0.485789i	$0.161468\pi$
$269$	17.4834	+	24.0639i	1.06598	+	1.46720i	0.191909	+	0.981413i	$0.438532\pi$
$270$	−0.411796	−	1.94084i	−0.0250611	−	0.118116i
$271$	0.613137	+	1.88704i	0.0372454	+	0.114630i	0.967951	−	0.251141i	$-0.0808056\pi$
$271$	0.613137	+	1.88704i	0.0372454	+	0.114630i	−0.930705	+	0.365770i	$0.880806\pi$
$272$	0.605347	+	0.196689i	0.0367046	+	0.0119260i
$273$	4.99461	+	1.04992i	0.302287	+	0.0635440i
$274$			20.5105i			1.23908i
$275$	16.1257	+	3.86793i	0.972418	+	0.233245i
$276$			13.8528i			0.833842i
$277$	17.8717	+	12.9845i	1.07380	+	0.780165i	0.976592	−	0.215099i	$-0.0690073\pi$
$277$	17.8717	+	12.9845i	1.07380	+	0.780165i	0.0972125	+	0.995264i	$0.469007\pi$
$278$	1.58657	−	4.88296i	0.0951562	−	0.292861i
$279$	11.5988	−	3.76868i	0.694403	−	0.225625i
$280$	4.77966	−	3.48638i	0.285640	−	0.208351i
$281$	−14.5120	−	19.9741i	−0.865716	−	1.19156i	−0.980176	−	0.198128i	$-0.936514\pi$
$281$	−14.5120	−	19.9741i	−0.865716	−	1.19156i	0.114460	−	0.993428i	$-0.463486\pi$
$282$	−3.32766	−	10.2415i	−0.198160	−	0.609872i
$283$	−19.4605	−	6.32311i	−1.15681	−	0.375870i	−0.333105	−	0.942890i	$-0.608096\pi$
$283$	−19.4605	−	6.32311i	−1.15681	−	0.375870i	−0.823704	+	0.567020i	$0.808096\pi$
$284$	6.16231	+	4.47718i	0.365666	+	0.265672i
$285$	−1.61512	+	3.62405i	−0.0956716	+	0.214670i
$286$	2.54350	+	0.898018i	0.150400	+	0.0531009i
$287$	−2.42842	−	5.42153i	−0.143345	−	0.320023i
$288$	2.12441	+	1.54347i	0.125182	+	0.0909501i
$289$	5.12810	−	15.7827i	0.301653	−	0.928392i
$290$	1.99022	−	18.8693i	0.116870	−	1.10804i
$291$	23.2032	−	16.8581i	1.36019	−	0.988239i
$292$	−5.87534	−	8.08672i	−0.343829	−	0.473239i
$293$	13.3177	−	4.32720i	0.778031	−	0.252798i	0.107032	−	0.994256i	$-0.465865\pi$
$293$	13.3177	−	4.32720i	0.778031	−	0.252798i	0.670999	+	0.741458i	$0.265865\pi$
$294$	−8.36615	−	14.3415i	−0.487924	−	0.836411i
$295$	−13.4465	−	23.3096i	−0.782883	−	1.35714i
$296$		−	4.05482i		−	0.235682i
$297$	−2.94187	−	0.0742750i	−0.170705	−	0.00430987i
$298$			11.4336i			0.662328i
$299$	−3.84277	−	2.79194i	−0.222233	−	0.161462i
$300$	−10.8377	+	4.81577i	−0.625716	+	0.278038i
$301$	3.50649	−	3.17155i	0.202111	−	0.182805i
$302$	1.19589	+	1.64599i	0.0688155	+	0.0947164i
$303$	−4.01892	+	2.91991i	−0.230881	+	0.167745i
$304$	0.231172	+	0.711476i	0.0132586	+	0.0408059i
$305$	−19.4711	−	17.5448i	−1.11491	−	1.00461i
$306$	−0.982421	+	1.35219i	−0.0561613	+	0.0772993i
$307$			19.9751i			1.14004i	0.821630	+	0.570021i	$0.193065\pi$
$307$			19.9751i			1.14004i	−0.821630	+	0.570021i	$0.806935\pi$
$308$	−3.38382	−	8.09628i	−0.192811	−	0.461328i
$309$	23.2636			1.32342
$310$	5.18927	+	8.99567i	0.294731	+	0.510920i
$311$	−29.0709	−	9.44572i	−1.64846	−	0.535618i	−0.670056	−	0.742310i	$-0.733730\pi$
$311$	−29.0709	−	9.44572i	−1.64846	−	0.535618i	−0.978406	+	0.206693i	$0.933730\pi$
$312$	−1.83463	+	0.596107i	−0.103865	+	0.0337479i
$313$	−8.35933	+	6.07341i	−0.472497	+	0.343289i	−0.798414	−	0.602109i	$-0.794327\pi$
$313$	−8.35933	+	6.07341i	−0.472497	+	0.343289i	0.325917	+	0.945399i	$0.394327\pi$
$314$	3.27862	−	2.38206i	0.185023	−	0.134427i
$315$	4.82838	+	14.7657i	0.272049	+	0.831955i
$316$	−14.8199	−	4.81527i	−0.833683	−	0.270880i
$317$	−1.53946	+	2.11889i	−0.0864649	+	0.119009i	−0.850058	−	0.526689i	$-0.823433\pi$
$317$	−1.53946	+	2.11889i	−0.0864649	+	0.119009i	0.763593	+	0.645698i	$0.223433\pi$
$318$		−	5.00010i		−	0.280392i
$319$	−26.5374	−	9.36940i	−1.48581	−	0.524586i
$320$	−0.910238	+	2.04242i	−0.0508839	+	0.114175i
$321$	1.07194	+	0.778811i	0.0598299	+	0.0434690i
$322$	1.64970	+	15.3639i	0.0919343	+	0.856197i
$323$	−0.452854	+	0.147141i	−0.0251975	+	0.00818715i
$324$	8.07586	−	5.86746i	0.448659	−	0.325970i
$325$	0.848372	−	3.97697i	0.0470592	−	0.220602i
$326$	−15.7998	+	5.13365i	−0.875068	+	0.284327i
$327$	5.28986	+	1.71878i	0.292530	+	0.0950487i
$328$	1.81650	+	1.31977i	0.100300	+	0.0728719i
$329$	−4.91028	−	10.9624i	−0.270713	−	0.604375i
$330$	3.21550	+	17.2941i	0.177008	+	0.952009i
$331$	9.65619			0.530752			0.265376	−	0.964145i	$-0.414504\pi$
$331$	9.65619			0.530752			0.265376	+	0.964145i	$0.414504\pi$
$332$	−4.36182	+	6.00353i	−0.239386	+	0.329487i
$333$	10.1265	+	3.29030i	0.554928	+	0.180307i
$334$	−2.69185	+	0.874634i	−0.147291	+	0.0478578i
$335$	15.5732	−	3.30423i	0.850855	−	0.180530i
$336$	5.44174	+	3.12552i	0.296871	+	0.170511i
$337$	6.71481	+	20.6661i	0.365779	+	1.12575i	0.949492	+	0.313792i	$0.101599\pi$
$337$	6.71481	+	20.6661i	0.365779	+	1.12575i	−0.583713	+	0.811960i	$0.698401\pi$
$338$	−3.81282	+	11.7347i	−0.207390	+	0.638282i
$339$	12.0382	−	16.5691i	0.653825	−	0.899913i
$340$	−1.30000	−	0.579366i	−0.0705023	−	0.0314205i
$341$	14.7652	−	4.38871i	0.799580	−	0.237662i
$342$	−1.96442			−0.106224
$343$	−10.9866	−	14.9095i	−0.593222	−	0.805039i
$344$	−0.552221	+	1.69956i	−0.0297738	+	0.0916342i
$345$	3.24913	−	30.8050i	0.174927	−	1.65848i
$346$	−12.3261	−	16.9654i	−0.662654	−	0.912066i
$347$	5.89044	−	4.27966i	0.316216	−	0.229744i	−0.418343	−	0.908289i	$-0.637389\pi$
$347$	5.89044	−	4.27966i	0.316216	−	0.229744i	0.734559	+	0.678545i	$0.237389\pi$
$348$	19.1415	−	6.21944i	1.02609	−	0.333397i
$349$	3.04276	−	9.36466i	0.162875	−	0.501279i	−0.835998	−	0.548732i	$-0.815111\pi$
$349$	3.04276	−	9.36466i	0.162875	−	0.501279i	0.998873	+	0.0474536i	$0.0151106\pi$
$350$	−11.4464	+	6.63171i	−0.611837	+	0.354480i
$351$			0.721624i			0.0385175i
$352$	2.63315	+	2.01656i	0.140347	+	0.107483i
$353$	7.84044			0.417305			0.208652	−	0.977990i	$-0.433092\pi$
$353$	7.84044			0.417305			0.208652	+	0.977990i	$0.433092\pi$
$354$	16.7781	−	23.0931i	0.891747	−	1.22738i
$355$	−12.6532	−	11.4014i	−0.671563	−	0.605123i
$356$	9.68857	−	3.14801i	0.513493	−	0.166844i
$357$	−1.98939	+	3.46367i	−0.105290	+	0.183317i
$358$	1.02948	−	0.747964i	0.0544099	−	0.0395311i
$359$	32.5863	−	10.5879i	1.71984	−	0.558809i	0.727917	−	0.685665i	$-0.240488\pi$
$359$	32.5863	−	10.5879i	1.71984	−	0.558809i	0.991921	+	0.126855i	$0.0404884\pi$
$360$	−4.36211	−	3.93055i	−0.229903	−	0.207158i
$361$	14.9186	+	10.8390i	0.785188	+	0.570472i
$362$		−	5.47276i		−	0.287642i
$363$	26.0577	+	1.31662i	1.36767	+	0.0691047i
$364$	−1.96376	+	0.879612i	−0.102929	+	0.0461042i
$365$	11.1685	+	19.3607i	0.584585	+	1.01339i
$366$	8.59122	−	26.4411i	0.449070	−	1.38210i
$367$	−8.93956	−	27.5131i	−0.466641	−	1.43617i	−0.856907	−	0.515472i	$-0.827617\pi$
$367$	−8.93956	−	27.5131i	−0.466641	−	1.43617i	0.390266	−	0.920702i	$-0.372383\pi$
$368$	−3.43289	−	4.72497i	−0.178952	−	0.246306i
$369$	−4.76998	+	3.46559i	−0.248315	+	0.180412i
$370$	−0.951044	+	9.01684i	−0.0494424	+	0.468763i
$371$	−0.595451	−	5.54552i	−0.0309143	−	0.287909i
$372$	−6.47503	+	8.91211i	−0.335715	+	0.462072i
$373$	−25.7514			−1.33336			−0.666678	−	0.745346i	$-0.732285\pi$
$373$	−25.7514			−1.33336			−0.666678	+	0.745346i	$0.732285\pi$
$374$	−1.28354	+	1.67600i	−0.0663704	+	0.0866638i
$375$	25.2297	−	8.16703i	1.30286	−	0.421744i
$376$	3.67298	+	2.66857i	0.189419	+	0.137621i
$377$	−2.13255	+	6.56332i	−0.109832	+	0.338028i
$378$	1.74104	−	1.57473i	0.0895494	−	0.0809955i
$379$	−9.34352	+	6.78846i	−0.479944	+	0.348700i	−0.801304	−	0.598257i	$-0.795860\pi$
$379$	−9.34352	+	6.78846i	−0.479944	+	0.348700i	0.321360	+	0.946957i	$0.395860\pi$
$380$	−0.347192	−	1.63635i	−0.0178106	−	0.0839431i
$381$	−3.57465	−	11.0016i	−0.183135	−	0.563631i
$382$	2.75958	−	8.49313i	0.141193	−	0.434546i
$383$	7.03306	+	5.10982i	0.359373	+	0.261100i	0.752790	−	0.658260i	$-0.228707\pi$
$383$	7.03306	+	5.10982i	0.359373	+	0.261100i	−0.393418	+	0.919360i	$0.628707\pi$
$384$	−2.37190			−0.121041
$385$	5.62577	+	18.7976i	0.286716	+	0.958016i
$386$	21.1230			1.07513
$387$	−3.79637	−	2.75823i	−0.192981	−	0.140209i
$388$	−3.73659	+	11.5000i	−0.189697	+	0.583826i
$389$	−8.02071	−	24.6852i	−0.406666	−	1.25159i	−0.919496	−	0.393100i	$-0.871403\pi$
$389$	−8.02071	−	24.6852i	−0.406666	−	1.25159i	0.512830	−	0.858490i	$-0.328597\pi$
$390$	4.21954	−	0.895277i	0.213665	−	0.0453341i
$391$	3.00744	−	2.18504i	0.152093	−	0.110502i
$392$	6.40754	+	2.81841i	0.323630	+	0.142351i
$393$	−9.21258	+	28.3534i	−0.464713	+	1.43024i
$394$	11.0410	+	8.02175i	0.556237	+	0.404130i
$395$	31.8260	+	14.1838i	1.60134	+	0.713666i
$396$	−7.17283	+	4.93966i	−0.360448	+	0.248227i
$397$	16.6671			0.836496			0.418248	−	0.908333i	$-0.362644\pi$
$397$	16.6671			0.836496			0.418248	+	0.908333i	$0.362644\pi$
$398$	3.38951	−	4.66526i	0.169901	−	0.233848i
$399$	−4.66778	+	0.501203i	−0.233681	+	0.0250916i
$400$	2.50317	−	4.32830i	0.125158	−	0.216415i
$401$	17.5610	−	12.7588i	0.876956	−	0.637146i	−0.0554885	−	0.998459i	$-0.517672\pi$
$401$	17.5610	−	12.7588i	0.876956	−	0.637146i	0.932444	+	0.361314i	$0.117672\pi$
$402$	9.92591	+	13.6618i	0.495059	+	0.681391i
$403$	−1.16722	−	3.59234i	−0.0581435	−	0.178947i
$404$	0.647198	−	1.99187i	0.0321993	−	0.0990992i
$405$	−19.3347	+	11.1535i	−0.960751	+	0.554222i
$406$	20.4888	−	9.17737i	1.01684	−	0.455465i
$407$	12.6812	+	4.47725i	0.628581	+	0.221929i
$408$		−	1.50971i		−	0.0747420i
$409$	−0.708496	−	0.514752i	−0.0350329	−	0.0254529i	0.570131	−	0.821554i	$-0.306892\pi$
$409$	−0.708496	−	0.514752i	−0.0350329	−	0.0254529i	−0.605164	+	0.796101i	$0.706892\pi$
$410$	−3.72987	−	3.36086i	−0.184205	−	0.165981i
$411$	46.2678	−	15.0333i	2.28222	−	0.741539i
$412$	−7.93482	+	5.76499i	−0.390921	+	0.284020i
$413$	15.8582	−	27.6102i	0.780330	−	1.35861i
$414$	14.5858	−	4.73920i	0.716851	−	0.232919i
$415$	11.1076	−	12.3272i	0.545252	−	0.605119i
$416$	0.478040	−	0.657965i	0.0234378	−	0.0322594i
$417$	−12.1779			−0.596356
$418$	−2.48034	−	0.0626225i	−0.121318	−	0.00306297i
$419$		−	13.9264i		−	0.680349i	−0.940362	−	0.340174i	$-0.889514\pi$
$419$		−	13.9264i		−	0.680349i	0.940362	−	0.340174i	$-0.110486\pi$
$420$	−11.3679	−	8.22666i	−0.554697	−	0.401420i
$421$	−5.40865	+	16.6461i	−0.263601	+	0.811282i	0.728411	+	0.685140i	$0.240259\pi$
$421$	−5.40865	+	16.6461i	−0.263601	+	0.811282i	−0.992012	+	0.126141i	$0.959741\pi$
$422$	−20.5178	+	6.66663i	−0.998790	+	0.324526i
$423$	−9.64493	+	7.00745i	−0.468952	+	0.340714i
$424$	1.23908	+	1.70545i	0.0601753	+	0.0828242i
$425$	2.75496	+	1.59327i	0.133635	+	0.0772847i
$426$	5.58296	−	17.1826i	0.270495	−	0.832499i
$427$	6.37955	−	30.3484i	0.308728	−	1.46866i
$428$	−0.558620			−0.0270019
$429$	0.161480	−	6.39587i	0.00779632	−	0.308796i
$430$	1.62662	−	3.64985i	0.0784425	−	0.176011i
$431$	2.46504	−	3.39284i	0.118737	−	0.163427i	−0.745511	−	0.666493i	$-0.767795\pi$
$431$	2.46504	−	3.39284i	0.118737	−	0.163427i	0.864248	+	0.503066i	$0.167795\pi$
$432$	−0.274188	+	0.843864i	−0.0131919	+	0.0406004i
$433$	−3.34165	−	10.2845i	−0.160589	−	0.494243i	0.838095	−	0.545525i	$-0.183670\pi$
$433$	−3.34165	−	10.2845i	−0.160589	−	0.494243i	−0.998684	+	0.0512812i	$0.983670\pi$
$434$	−6.12001	+	10.6553i	−0.293770	+	0.511473i
$435$	−44.0242	+	9.34081i	−2.11080	+	0.447857i
$436$	−2.23022	+	0.724642i	−0.106808	+	0.0347040i
$437$	4.15530	+	1.35014i	0.198775	+	0.0645858i
$438$	−13.9357	+	19.1809i	−0.665875	+	0.916499i
$439$	−6.91580			−0.330073			−0.165037	−	0.986287i	$-0.552774\pi$
$439$	−6.91580			−0.330073			−0.165037	+	0.986287i	$0.552774\pi$
$440$	−5.38244	−	5.10190i	−0.256598	−	0.243223i
$441$	−12.2381	+	13.7152i	−0.582766	+	0.653102i
$442$	0.418794	+	0.304272i	0.0199200	+	0.0144727i
$443$	20.7098	+	6.72901i	0.983950	+	0.319705i	0.756434	−	0.654069i	$-0.226940\pi$
$443$	20.7098	+	6.72901i	0.983950	+	0.319705i	0.227516	+	0.973774i	$0.426940\pi$
$444$	−9.14692	+	2.97201i	−0.434093	+	0.141046i
$445$	−22.2831	+	4.72791i	−1.05632	+	0.224124i
$446$	−12.8259	+	9.31857i	−0.607324	+	0.441247i
$447$	25.7920	−	8.38032i	1.21992	−	0.396375i
$448$	−2.63063	+	0.282464i	−0.124286	+	0.0133452i
$449$	−17.2079	−	12.5023i	−0.812091	−	0.590018i	0.102345	−	0.994749i	$-0.467365\pi$
$449$	−17.2079	−	12.5023i	−0.812091	−	0.590018i	−0.914436	+	0.404730i	$0.867365\pi$
$450$	8.77826	+	9.76360i	0.413811	+	0.460261i
$451$	−6.13321	+	4.22372i	−0.288802	+	0.198887i
$452$			8.63467i			0.406141i
$453$	2.83652	−	3.90414i	0.133271	−	0.183432i
$454$	−14.1957	−	4.61246i	−0.666236	−	0.216473i
$455$	4.57319	−	1.49543i	0.214395	−	0.0701068i
$456$	1.43552	−	1.04296i	0.0672242	−	0.0488412i
$457$	−6.90983	+	5.02029i	−0.323228	+	0.234839i	−0.737552	−	0.675291i	$-0.764018\pi$
$457$	−6.90983	+	5.02029i	−0.323228	+	0.234839i	0.414323	+	0.910130i	$0.364018\pi$
$458$	20.6300	−	6.70311i	0.963979	−	0.313216i
$459$	−0.537119	−	0.174521i	−0.0250706	−	0.00814592i
$460$	6.52562	+	11.3123i	0.304258	+	0.527437i
$461$	13.2900			0.618978			0.309489	−	0.950903i	$-0.399842\pi$
$461$	13.2900			0.618978			0.309489	+	0.950903i	$0.399842\pi$
$462$	−15.7835	+	13.5675i	−0.734314	+	0.631217i
$463$		−	22.8521i		−	1.06203i	−0.847363	−	0.531015i	$-0.821811\pi$
$463$		−	22.8521i		−	1.06203i	0.847363	−	0.531015i	$-0.178189\pi$
$464$	−4.98759	+	6.86483i	−0.231543	+	0.318692i
$465$	16.4890	−	18.2995i	0.764661	−	0.848617i
$466$	−7.94910	−	24.4648i	−0.368235	−	1.13331i
$467$	−21.1191	+	15.3439i	−0.977275	+	0.710032i	−0.957098	−	0.289765i	$-0.906423\pi$
$467$	−21.1191	+	15.3439i	−0.977275	+	0.710032i	−0.0201767	+	0.999796i	$0.506423\pi$
$468$	1.25529	+	1.72776i	0.0580259	+	0.0798658i
$469$	12.6356	+	13.9700i	0.583457	+	0.645076i
$470$	−7.54181	−	6.79568i	−0.347878	−	0.313461i
$471$	−7.77656	−	5.65000i	−0.358325	−	0.260338i
$472$			12.0345i			0.553933i
$473$	−4.70550	−	3.60365i	−0.216359	−	0.165696i
$474$			36.9603i			1.69764i
$475$	0.388261	+	3.72024i	0.0178146	+	0.170696i
$476$	−0.179788	−	1.67439i	−0.00824059	−	0.0767458i
$477$	−5.26465	+	1.71059i	−0.241052	+	0.0783225i
$478$	−4.60761	−	6.34184i	−0.210747	−	0.290069i
$479$	−10.9775	+	7.97561i	−0.501574	+	0.364415i	−0.809618	−	0.586957i	$-0.800326\pi$
$479$	−10.9775	+	7.97561i	−0.501574	+	0.364415i	0.308044	+	0.951372i	$0.400326\pi$
$480$	5.27447	+	0.556321i	0.240746	+	0.0253925i
$481$	1.01906	−	3.13634i	0.0464651	−	0.143005i
$482$	−24.7383	−	17.9734i	−1.12680	−	0.818666i
$483$	33.4489	−	14.9825i	1.52198	−	0.681728i
$484$	−9.21412	+	6.00832i	−0.418824	+	0.273106i
$485$	11.0065	−	24.6966i	0.499778	−	1.12142i
$486$	−17.0016	−	12.3524i	−0.771210	−	0.560317i
$487$	−25.0477	−	8.13850i	−1.13502	−	0.368791i	−0.319539	−	0.947573i	$-0.603528\pi$
$487$	−25.0477	−	8.13850i	−1.13502	−	0.368791i	−0.815482	+	0.578782i	$0.803528\pi$
$488$	3.62208	+	11.1476i	0.163964	+	0.504629i
$489$	23.1611	+	31.8785i	1.04738	+	1.44160i
$490$	−13.5876	−	7.77025i	−0.613826	−	0.351024i
$491$	28.3233	−	9.20280i	1.27821	−	0.415317i	0.410262	−	0.911967i	$-0.365437\pi$
$491$	28.3233	−	9.20280i	1.27821	−	0.415317i	0.867950	+	0.496651i	$0.165437\pi$
$492$	1.64573	−	5.06502i	0.0741950	−	0.228349i
$493$	−4.36946	−	3.17460i	−0.196791	−	0.142977i
$494$			0.608413i			0.0273738i
$495$	17.1090	−	9.30213i	0.768994	−	0.418099i
$496$		−	4.64437i		−	0.208538i
$497$	4.14572	−	19.7217i	0.185961	−	0.884641i
$498$	16.7399	+	5.43911i	0.750132	+	0.243733i
$499$	−4.08584	−	12.5749i	−0.182907	−	0.562931i	0.816999	−	0.576639i	$-0.195636\pi$
$499$	−4.08584	−	12.5749i	−0.182907	−	0.562931i	−0.999906	+	0.0137088i	$0.995636\pi$
$500$	−6.58156	+	9.03787i	−0.294336	+	0.404186i
$501$	3.94602	+	5.43123i	0.176295	+	0.242649i
$502$	−3.71471	+	1.20698i	−0.165796	+	0.0538703i
$503$	−15.6041	−	5.07007i	−0.695752	−	0.226063i	−0.0602731	−	0.998182i	$-0.519197\pi$
$503$	−15.6041	−	5.07007i	−0.695752	−	0.226063i	−0.635479	+	0.772119i	$0.719197\pi$
$504$	1.42921	−	6.79893i	0.0636619	−	0.302848i
$505$	−1.90638	+	4.27759i	−0.0848328	+	0.190350i
$506$	18.5675	−	5.51890i	0.825428	−	0.245345i
$507$	29.2658			1.29974
$508$	3.94559	+	2.86664i	0.175057	+	0.127187i
$509$	39.3139	+	12.7738i	1.74256	+	0.566191i	0.995167	−	0.0981955i	$-0.0313071\pi$
$509$	39.3139	+	12.7738i	1.74256	+	0.566191i	0.747389	+	0.664386i	$0.231307\pi$
$510$	−0.354098	+	3.35720i	−0.0156797	+	0.148659i
$511$	−13.1716	+	22.9327i	−0.582679	+	1.01448i
$512$	0.809017	−	0.587785i	0.0357538	−	0.0259767i
$513$	−0.205117	−	0.631286i	−0.00905615	−	0.0278720i
$514$	−6.06728	+	18.6732i	−0.267616	+	0.823638i
$515$	18.9971	−	10.9587i	0.837111	−	0.482898i
$516$	4.23865			0.186596
$517$	−12.4014	+	8.54037i	−0.545413	+	0.375605i
$518$	−9.79074	+	4.38549i	−0.430180	+	0.192687i
$519$	−29.2363	+	40.2403i	−1.28333	+	1.76635i
$520$	−1.21736	+	1.35102i	−0.0533846	+	0.0592460i
$521$	−40.5006	+	13.1594i	−1.77436	+	0.576526i	−0.998519	−	0.0543984i	$-0.982676\pi$
$521$	−40.5006	+	13.1594i	−1.77436	+	0.576526i	−0.775845	+	0.630924i	$0.782676\pi$
$522$	−13.0970	−	18.0265i	−0.573240	−	0.788997i
$523$	−20.4047	−	28.0847i	−0.892236	−	1.22806i	−0.972879	−	0.231315i	$-0.925697\pi$
$523$	−20.4047	−	28.0847i	−0.892236	−	1.22806i	0.0806429	−	0.996743i	$-0.474303\pi$
$524$	−3.88405	−	11.9539i	−0.169675	−	0.522207i
$525$	23.3496	+	20.9602i	1.01906	+	0.914778i
$526$	−15.6867	−	11.3971i	−0.683973	−	0.496936i
$527$	2.95614			0.128771
$528$	2.61901	−	7.41794i	0.113978	−	0.322825i
$529$	−11.1101			−0.483050
$530$	−2.35539	−	4.08310i	−0.102311	−	0.177358i
$531$	−30.0549	−	9.76543i	−1.30427	−	0.423783i
$532$	1.46790	−	1.32768i	0.0636415	−	0.0575623i
$533$	1.07335	+	1.47734i	0.0464920	+	0.0639908i
$534$	−14.2026	−	19.5482i	−0.614608	−	0.845935i
$535$	1.24222	+	0.131022i	0.0537060	+	0.00566459i
$536$	−6.77113	−	2.20007i	−0.292468	−	0.0950287i
$537$	−2.44184	−	1.77410i	−0.105373	−	0.0765580i
$538$			29.7446i			1.28238i
$539$	−15.8894	+	16.9271i	−0.684406	+	0.729101i
$540$	0.807646	−	1.81222i	0.0347555	−	0.0779854i
$541$	2.63962	−	3.63313i	0.113486	−	0.156200i	−0.748495	−	0.663140i	$-0.769223\pi$
$541$	2.63962	−	3.63313i	0.113486	−	0.156200i	0.861981	+	0.506940i	$0.169223\pi$
$542$	−0.613137	+	1.88704i	−0.0263365	+	0.0810553i
$543$	−12.3455	+	4.01130i	−0.529797	+	0.172141i
$544$	0.374125	+	0.514939i	0.0160405	+	0.0220778i
$545$	5.12937	−	1.08832i	0.219718	−	0.0466185i
$546$	3.42359	+	3.78516i	0.146516	+	0.161990i
$547$	−11.0877	+	34.1243i	−0.474074	+	1.45905i	0.373128	+	0.927780i	$0.378285\pi$
$547$	−11.0877	+	34.1243i	−0.474074	+	1.45905i	−0.847202	+	0.531270i	$0.821715\pi$
$548$	−12.0558	+	16.5933i	−0.514996	+	0.708832i
$549$	−30.7792			−1.31362
$550$	10.7725	+	12.6077i	0.459340	+	0.537594i
$551$		−	6.34784i		−	0.270427i
$552$	−8.14249	+	11.2072i	−0.346567	+	0.477009i
$553$	4.40151	+	40.9919i	0.187171	+	1.74315i
$554$	6.82637	+	21.0094i	0.290025	+	0.892604i
$555$	21.0374	−	4.46359i	0.892987	−	0.189469i
$556$	4.15370	−	3.01784i	0.176156	−	0.127985i
$557$	−14.1950	−	43.6878i	−0.601463	−	1.85111i	−0.519487	−	0.854479i	$-0.673877\pi$
$557$	−14.1950	−	43.6878i	−0.601463	−	1.85111i	−0.0819763	−	0.996634i	$-0.526123\pi$
$558$	11.5988	+	3.76868i	0.491017	+	0.159541i
$559$	−0.854269	+	1.17580i	−0.0361317	+	0.0497310i
$560$	5.91607	−	0.0111205i	0.250000	−	0.000469928i
$561$	4.72152	+	1.66700i	0.199343	+	0.0703806i
$562$		−	24.6894i		−	1.04146i
$563$	−1.67074	+	2.29958i	−0.0704135	+	0.0969158i	−0.842771	−	0.538272i	$-0.819077\pi$
$563$	−1.67074	+	2.29958i	−0.0704135	+	0.0969158i	0.772358	+	0.635188i	$0.219077\pi$
$564$	3.32766	−	10.2415i	0.140120	−	0.431245i
$565$	2.02523	−	19.2012i	0.0852021	−	0.807801i
$566$	−12.0273	−	16.5541i	−0.505544	−	0.695822i
$567$	−22.9020	−	13.1540i	−0.961791	−	0.552415i
$568$	2.35379	+	7.24423i	0.0987629	+	0.303961i
$569$	−16.9563	−	5.50944i	−0.710846	−	0.230968i	−0.0687963	−	0.997631i	$-0.521916\pi$
$569$	−16.9563	−	5.50944i	−0.710846	−	0.230968i	−0.642050	+	0.766663i	$0.721916\pi$
$570$	−3.43683	+	1.98258i	−0.143953	+	0.0830410i
$571$			21.8949i			0.916274i	0.888882	+	0.458137i	$0.151483\pi$
$571$			21.8949i			0.916274i	−0.888882	+	0.458137i	$0.848517\pi$
$572$	1.52989	+	2.22154i	0.0639681	+	0.0928874i
$573$	−21.1816			−0.884872
$574$	1.22206	−	5.81350i	0.0510078	−	0.242651i
$575$	−11.8580	−	26.6860i	−0.494512	−	1.11288i
$576$	0.811453	+	2.49739i	0.0338105	+	0.104058i
$577$	−31.6951	+	23.0279i	−1.31949	+	0.958663i	−0.319547	+	0.947570i	$0.603531\pi$
$577$	−31.6951	+	23.0279i	−1.31949	+	0.958663i	−0.999938	+	0.0110923i	$0.996469\pi$
$578$	13.4255	−	9.75422i	0.558428	−	0.405722i
$579$	−15.4823	−	47.6496i	−0.643422	−	1.98025i
$580$	12.7012	−	14.0957i	0.527388	−	0.585293i
$581$	19.2136	+	4.03890i	0.797114	+	0.167562i
$582$	28.6807			1.18885
$583$	−6.70185	+	1.99202i	−0.277562	+	0.0825009i
$584$		−	9.99573i		−	0.413626i
$585$	−2.38619	−	4.13650i	−0.0986569	−	0.171023i
$586$	13.3177	+	4.32720i	0.550151	+	0.178755i
$587$	4.57871	+	14.0918i	0.188983	+	0.581631i	0.999994	−	0.00340007i	$-0.00108228\pi$
$587$	4.57871	+	14.0918i	0.188983	+	0.581631i	−0.811011	+	0.585031i	$0.801082\pi$
$588$	1.66134	−	16.5200i	0.0685126	−	0.681273i
$589$	2.04220	+	2.81085i	0.0841475	+	0.115819i
$590$	2.82265	−	26.7615i	0.116207	−	1.10175i
$591$	10.0030	−	30.7860i	0.411468	−	1.26637i
$592$	2.38336	−	3.28042i	0.0979557	−	0.134824i
$593$			18.0520i			0.741306i	0.928771	+	0.370653i	$0.120866\pi$
$593$			18.0520i			0.741306i	−0.928771	+	0.370653i	$0.879134\pi$
$594$	−2.33637	−	1.78928i	−0.0958623	−	0.0734150i
$595$	0.00707822	+	3.76558i	0.000290179	+	0.154374i
$596$	−6.72048	+	9.24994i	−0.275281	+	0.378892i
$597$	−13.0083	−	4.22666i	−0.532395	−	0.172986i
$598$	−1.46781	−	4.51745i	−0.0600231	−	0.184732i
$599$	−31.0302	+	22.5447i	−1.26786	+	0.921153i	−0.999115	−	0.0420585i	$-0.986608\pi$
$599$	−31.0302	+	22.5447i	−1.26786	+	0.921153i	−0.268744	+	0.963212i	$0.586608\pi$
$600$	−11.5985	−	2.47422i	−0.473508	−	0.101010i
$601$	13.0875	+	40.2791i	0.533849	+	1.64302i	0.746122	+	0.665809i	$0.231913\pi$
$601$	13.0875	+	40.2791i	0.533849	+	1.64302i	−0.212273	+	0.977210i	$0.568087\pi$
$602$	4.70100	−	0.504771i	0.191599	−	0.0205729i
$603$	10.9889	−	15.1249i	0.447503	−	0.615935i
$604$			2.03456i			0.0827851i
$605$	21.8990	−	11.1998i	0.890320	−	0.455335i
$606$	−4.96765			−0.201797
$607$	14.1598	−	19.4893i	0.574728	−	0.791046i	−0.418377	−	0.908274i	$-0.637401\pi$
$607$	14.1598	−	19.4893i	0.574728	−	0.791046i	0.993105	+	0.117228i	$0.0374008\pi$
$608$	−0.231172	+	0.711476i	−0.00937528	+	0.0288541i
$609$	−35.7198	−	39.4922i	−1.44744	−	1.60030i
$610$	−5.43991	−	25.6389i	−0.220255	−	1.03809i
$611$	2.17032	+	2.98719i	0.0878019	+	0.120849i
$612$	−1.58959	+	0.516489i	−0.0642554	+	0.0208778i
$613$	−7.73309	+	23.8000i	−0.312337	+	0.961273i	0.664500	+	0.747288i	$0.268644\pi$
$613$	−7.73309	+	23.8000i	−0.312337	+	0.961273i	−0.976837	+	0.213985i	$0.931356\pi$
$614$	−11.7411	+	16.1602i	−0.473832	+	0.652174i
$615$	−4.84764	+	10.8773i	−0.195476	+	0.438613i
$616$	2.02130	−	8.53899i	0.0814406	−	0.344046i
$617$			9.96719i			0.401264i	0.979667	+	0.200632i	$0.0642995\pi$
$617$			9.96719i			0.401264i	−0.979667	+	0.200632i	$0.935700\pi$
$618$	18.8206	+	13.6740i	0.757076	+	0.550048i
$619$	17.5478	+	5.70164i	0.705307	+	0.229168i	0.639641	−	0.768674i	$-0.279083\pi$
$619$	17.5478	+	5.70164i	0.705307	+	0.229168i	0.0656656	+	0.997842i	$0.479083\pi$
$620$	−1.08932	+	10.3278i	−0.0437481	+	0.414776i
$621$	3.04598	+	4.19243i	0.122231	+	0.168236i
$622$	−17.9668	−	24.7292i	−0.720404	−	0.991552i
$623$	−18.0798	−	19.9892i	−0.724352	−	0.800851i
$624$	−1.83463	−	0.596107i	−0.0734439	−	0.0238634i
$625$	16.7554	−	18.5541i	0.670217	−	0.742165i
$626$	−10.3327			−0.412978
$627$	1.67672	+	5.64109i	0.0669618	+	0.225283i
$628$	4.05259			0.161716
$629$	2.08799	+	1.51701i	0.0832534	+	0.0604872i
$630$	−4.77284	+	14.7838i	−0.190154	+	0.589000i
$631$	7.41037	+	22.8068i	0.295002	+	0.907924i	0.983221	+	0.182420i	$0.0583931\pi$
$631$	7.41037	+	22.8068i	0.295002	+	0.907924i	−0.688218	+	0.725504i	$0.741607\pi$
$632$	−9.15919	−	12.6065i	−0.364333	−	0.501461i
$633$	30.0773	+	41.3979i	1.19547	+	1.64542i
$634$	−2.49090	+	0.809344i	−0.0989264	+	0.0321431i
$635$	−8.10159	−	7.30007i	−0.321502	−	0.289694i
$636$	2.93899	−	4.04517i	0.116538	−	0.160401i
$637$	4.24781	+	3.79034i	0.168304	+	0.150179i
$638$	−15.9620	−	23.1783i	−0.631943	−	0.917638i
$639$	−20.0017			−0.791254
$640$	−1.93690	+	1.11733i	−0.0765627	+	0.0441662i
$641$	−13.5051	+	41.5643i	−0.533417	+	1.64169i	0.213627	+	0.976915i	$0.431472\pi$
$641$	−13.5051	+	41.5643i	−0.533417	+	1.64169i	−0.747044	+	0.664775i	$0.768528\pi$
$642$	0.409445	+	1.26014i	0.0161595	+	0.0497339i
$643$	−31.0256	+	22.5414i	−1.22353	+	0.888947i	−0.996388	−	0.0849146i	$-0.972938\pi$
$643$	−31.0256	+	22.5414i	−1.22353	+	0.888947i	−0.227142	+	0.973862i	$0.572938\pi$
$644$	−7.69604	+	13.3993i	−0.303266	+	0.528008i
$645$	−9.42562	−	0.994159i	−0.371133	−	0.0391450i
$646$	−0.452854	−	0.147141i	−0.0178173	−	0.00578919i
$647$	−10.9257	−	7.93796i	−0.429532	−	0.312073i	0.351930	−	0.936026i	$-0.385526\pi$
$647$	−10.9257	−	7.93796i	−0.429532	−	0.312073i	−0.781462	+	0.623953i	$0.785526\pi$
$648$	9.98231			0.392142
$649$	−37.6370	−	13.2883i	−1.47738	−	0.521610i
$650$	3.02395	−	2.71877i	0.118609	−	0.106639i
$651$	28.5222	+	5.99566i	1.11787	+	0.234989i
$652$	−15.7998	−	5.13365i	−0.618766	−	0.201049i
$653$	31.7819	−	10.3266i	1.24372	−	0.404109i	0.388054	−	0.921637i	$-0.373147\pi$
$653$	31.7819	−	10.3266i	1.24372	−	0.404109i	0.855667	+	0.517527i	$0.173147\pi$
$654$	3.26931	+	4.49982i	0.127840	+	0.175957i
$655$	5.83335	+	27.4932i	0.227928	+	1.07425i
$656$	0.693842	+	2.13543i	0.0270900	+	0.0833744i
$657$	24.9633	+	8.11106i	0.973911	+	0.316443i
$658$	2.47101	−	11.7549i	0.0963301	−	0.458255i
$659$		−	5.15933i		−	0.200979i	−0.994938	−	0.100489i	$-0.967959\pi$
$659$		−	5.15933i		−	0.200979i	0.994938	−	0.100489i	$-0.0320409\pi$
$660$	−7.56382	+	15.8812i	−0.294421	+	0.618177i
$661$		−	33.9879i		−	1.32198i	−0.750396	−	0.660989i	$-0.770137\pi$
$661$		−	33.9879i		−	1.32198i	0.750396	−	0.660989i	$-0.229863\pi$
$662$	7.81203	+	5.67577i	0.303623	+	0.220595i
$663$	0.379422	−	1.16774i	0.0147355	−	0.0453513i
$664$	−7.05758	+	2.29315i	−0.273887	+	0.0889913i
$665$	−3.57562	+	2.60812i	−0.138657	+	0.101139i
$666$	6.25851	+	8.61411i	0.242512	+	0.333790i
$667$	15.3143	+	47.1325i	0.592971	+	1.82498i
$668$	−2.69185	−	0.874634i	−0.104151	−	0.0338406i
$669$	30.4218	+	22.1027i	1.17617	+	0.854541i
$670$	14.5412	+	6.48052i	0.561774	+	0.250364i
$671$	−38.8628	−	0.981188i	−1.50028	−	0.0378784i
$672$	2.56533	+	5.72717i	0.0989596	+	0.220930i
$673$	13.2169	+	9.60262i	0.509473	+	0.370154i	0.812624	−	0.582789i	$-0.198039\pi$
$673$	13.2169	+	9.60262i	0.509473	+	0.370154i	−0.303151	+	0.952943i	$0.598039\pi$
$674$	−6.71481	+	20.6661i	−0.258645	+	0.796027i
$675$	−2.22104	+	3.84046i	−0.0854878	+	0.147819i
$676$	−9.98211	+	7.25242i	−0.383927	+	0.278939i
$677$	−11.3366	−	15.6036i	−0.435703	−	0.599693i	0.533548	−	0.845770i	$-0.320858\pi$
$677$	−11.3366	−	15.6036i	−0.435703	−	0.599693i	−0.969250	+	0.246077i	$0.920858\pi$
$678$	19.4782	−	6.32885i	0.748056	−	0.243058i
$679$	31.8092	−	3.41552i	1.22073	−	0.131076i
$680$	−0.711177	−	1.23284i	−0.0272724	−	0.0472771i
$681$			35.4035i			1.35667i
$682$	14.5249	+	5.12821i	0.556187	+	0.196369i
$683$			42.7262i			1.63487i	0.576020	+	0.817435i	$0.304605\pi$
$683$			42.7262i			1.63487i	−0.576020	+	0.817435i	$0.695395\pi$
$684$	−1.58925	−	1.15466i	−0.0607665	−	0.0441494i
$685$	30.7007	−	34.0715i	1.17301	−	1.30180i
$686$	−0.124766	−	18.5198i	−0.00476357	−	0.707091i
$687$	−30.2419	−	41.6244i	−1.15380	−	1.58807i
$688$	−1.44573	+	1.05039i	−0.0551181	+	0.0400456i
$689$	0.529797	+	1.63055i	0.0201837	+	0.0621190i
$690$	20.7353	−	23.0120i	0.789380	−	0.876051i
$691$	−22.0867	+	30.3997i	−0.840216	+	1.15646i	0.145718	+	0.989326i	$0.453451\pi$
$691$	−22.0867	+	30.3997i	−0.840216	+	1.15646i	−0.985934	+	0.167132i	$0.946549\pi$
$692$		−	20.9704i		−	0.797175i
$693$	19.6850	+	11.9770i	0.747773	+	0.454968i
$694$	7.28099			0.276382
$695$	−9.94453	+	5.73663i	−0.377218	+	0.217603i
$696$	19.1415	+	6.21944i	0.725555	+	0.235747i
$697$	−1.35920	+	0.441630i	−0.0514833	+	0.0167279i
$698$	7.96605	−	5.78768i	0.301520	−	0.219067i
$699$	−49.3617	+	35.8634i	−1.86703	+	1.35648i
$700$	−13.1584	−	1.36286i	−0.497339	−	0.0515114i
$701$	−9.48040	−	3.08037i	−0.358070	−	0.116344i	0.124457	−	0.992225i	$-0.460281\pi$
$701$	−9.48040	−	3.08037i	−0.358070	−	0.116344i	−0.482527	+	0.875881i	$0.660281\pi$
$702$	−0.424160	+	0.583806i	−0.0160089	+	0.0220343i
$703$			3.03337i			0.114406i
$704$	0.944954	+	3.17916i	0.0356143	+	0.119819i
$705$	−9.80194	+	21.9939i	−0.369163	+	0.828337i
$706$	6.34305	+	4.60850i	0.238724	+	0.173443i
$707$	−5.50953	+	0.591587i	−0.207207	+	0.0222489i
$708$	27.1476	−	8.82078i	1.02027	−	0.331505i
$709$	14.2703	−	10.3680i	0.535932	−	0.389377i	−0.286640	−	0.958038i	$-0.592538\pi$
$709$	14.2703	−	10.3680i	0.535932	−	0.389377i	0.822572	+	0.568661i	$0.192538\pi$
$710$	−3.53510	−	16.6613i	−0.132670	−	0.625288i
$711$	38.9158	−	12.6445i	1.45945	−	0.474206i
$712$	9.68857	+	3.14801i	0.363094	+	0.117977i
$713$	−21.9445	−	15.9436i	−0.821828	−	0.597093i
$714$	−3.64534	+	1.63283i	−0.136424	+	0.0611071i
$715$	−2.88102	−	5.29895i	−0.107744	−	0.198170i
$716$	1.27251			0.0475560
$717$	−10.9288	+	15.0422i	−0.408144	+	0.561762i
$718$	32.5863	+	10.5879i	1.21611	+	0.395138i
$719$	6.31619	−	2.05225i	0.235554	−	0.0765361i	−0.188861	−	0.982004i	$-0.560480\pi$
$719$	6.31619	−	2.05225i	0.235554	−	0.0765361i	0.424415	+	0.905468i	$0.360480\pi$
$720$	−1.21870	−	5.74386i	−0.0454182	−	0.214061i
$721$	22.5020	+	12.9242i	0.838018	+	0.481324i
$722$	5.69839	+	17.5378i	0.212072	+	0.652690i
$723$	−22.4125	+	68.9786i	−0.833530	+	2.56534i
$724$	3.21681	−	4.42756i	0.119552	−	0.164549i
$725$	−31.5502	+	28.3661i	−1.17174	+	1.05349i
$726$	20.3072	+	16.3815i	0.753671	+	0.607974i
$727$	40.8132			1.51368			0.756839	−	0.653601i	$-0.226742\pi$
$727$	40.8132			1.51368			0.756839	+	0.653601i	$0.226742\pi$
$728$	−2.10574	−	0.442649i	−0.0780439	−	0.0164057i
$729$	−6.14913	+	18.9251i	−0.227746	+	0.700929i
$730$	−2.34446	+	22.2278i	−0.0867725	+	0.822689i
$731$	−0.668571	−	0.920209i	−0.0247280	−	0.0340352i
$732$	22.4921	−	16.3415i	0.831332	−	0.603998i
$733$	20.9481	−	6.80646i	0.773737	−	0.251402i	0.104573	−	0.994517i	$-0.466652\pi$
$733$	20.9481	−	6.80646i	0.773737	−	0.251402i	0.669164	+	0.743115i	$0.266652\pi$
$734$	8.93956	−	27.5131i	0.329965	−	1.01553i
$735$	−7.56908	+	36.3464i	−0.279190	+	1.34066i
$736$		−	5.84039i		−	0.215280i
$737$	14.3571	−	18.7469i	0.528851	−	0.690552i
$738$	−5.89602			−0.217036
$739$	15.4581	−	21.2762i	0.568635	−	0.782659i	−0.423757	−	0.905776i	$-0.639289\pi$
$739$	15.4581	−	21.2762i	0.568635	−	0.782659i	0.992392	+	0.123117i	$0.0392891\pi$
$740$	−6.06938	+	6.73577i	−0.223115	+	0.247612i
$741$	1.37247	−	0.445941i	0.0504188	−	0.0163821i
$742$	2.77784	−	4.83642i	0.101978	−	0.177550i
$743$	42.4776	−	30.8618i	1.55835	−	1.13221i	0.621005	−	0.783806i	$-0.286725\pi$
$743$	42.4776	−	30.8618i	1.55835	−	1.13221i	0.937345	−	0.348402i	$-0.113275\pi$
$744$	−10.4768	+	3.40412i	−0.384099	+	0.124801i
$745$	17.1141	−	18.9931i	0.627012	−	0.695855i
$746$	−20.8333	−	15.1363i	−0.762762	−	0.554179i
$747$		−	19.4863i		−	0.712967i
$748$	−2.02353	+	0.601463i	−0.0739877	+	0.0219917i
$749$	0.604175	+	1.34884i	0.0220761	+	0.0492855i
$750$	25.2117	+	8.22240i	0.920602	+	0.300239i
$751$	−0.953302	+	2.93396i	−0.0347865	+	0.107062i	−0.966942	−	0.254996i	$-0.917926\pi$
$751$	−0.953302	+	2.93396i	−0.0347865	+	0.107062i	0.932156	+	0.362058i	$0.117926\pi$
$752$	1.40295	+	4.31784i	0.0511604	+	0.157456i
$753$	5.44545	+	7.49502i	0.198443	+	0.273134i
$754$	−5.58309	+	4.05635i	−0.203324	+	0.147724i
$755$	0.477199	−	4.52432i	0.0173670	−	0.164657i
$756$	2.33413	−	0.250628i	0.0848916	−	0.00911525i
$757$	−18.8592	+	25.9575i	−0.685450	+	0.943440i	−0.999983	−	0.00580602i	$-0.998152\pi$
$757$	−18.8592	+	25.9575i	−0.685450	+	0.943440i	0.314534	+	0.949246i	$0.398152\pi$
$758$	−11.5492			−0.419487
$759$	−26.0588	−	37.8398i	−0.945875	−	1.37350i
$760$	0.680940	−	1.52791i	0.0247003	−	0.0554232i
$761$	−20.1886	−	14.6679i	−0.731836	−	0.531710i	0.158308	−	0.987390i	$-0.449396\pi$
$761$	−20.1886	−	14.6679i	−0.731836	−	0.531710i	−0.890144	+	0.455680i	$0.849396\pi$
$762$	3.57465	−	11.0016i	0.129496	−	0.398548i
$763$	4.16180	+	4.60133i	0.150667	+	0.166579i
$764$	7.22468	−	5.24904i	0.261380	−	0.189904i
$765$	3.65597	−	0.775701i	0.132182	−	0.0280455i
$766$	2.68639	+	8.26786i	0.0970633	+	0.298730i
$767$	−3.02451	+	9.30850i	−0.109209	+	0.336110i
$768$	−1.91891	−	1.39417i	−0.0692426	−	0.0503077i
$769$	−4.84628			−0.174761			−0.0873807	−	0.996175i	$-0.527850\pi$
$769$	−4.84628			−0.174761			−0.0873807	+	0.996175i	$0.527850\pi$
$770$	−6.49763	+	18.5143i	−0.234158	+	0.667211i
$771$	46.5702			1.67718
$772$	17.0889	+	12.4158i	0.615042	+	0.446854i
$773$	4.04957	−	12.4633i	0.145653	−	0.448274i	−0.851441	−	0.524450i	$-0.824271\pi$
$773$	4.04957	−	12.4633i	0.145653	−	0.448274i

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:	\( N \)	\(=\)	\( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	770.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.732958 - 2.25581i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.464104 - 2.18737i) q^{5} +(1.91891 - 1.39417i) q^{6} +(1.96220 - 1.77476i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.12441 - 1.54347i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(0.732958 - 2.25581i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.464104 - 2.18737i) q^{5} +(1.91891 - 1.39417i) q^{6} +(1.96220 - 1.77476i) q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.12441 - 1.54347i) q^{9} +(0.910238 - 2.04242i) q^{10} +(-2.63315 - 2.01656i) q^{11} +2.37190 q^{12} +(-0.478040 + 0.657965i) q^{13} +(2.63063 - 0.282464i) q^{14} +(-5.27447 - 0.556321i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-0.374125 - 0.514939i) q^{17} +(-0.811453 - 2.49739i) q^{18} +(0.231172 - 0.711476i) q^{19} +(1.93690 - 1.11733i) q^{20} +(-2.56533 - 5.72717i) q^{21} +(-0.944954 - 3.17916i) q^{22} +5.84039i q^{23} +(1.91891 + 1.39417i) q^{24} +(-4.56921 + 2.03034i) q^{25} +(-0.773484 + 0.251320i) q^{26} +(0.717833 - 0.521536i) q^{27} +(2.29425 + 1.31773i) q^{28} +(8.07009 - 2.62213i) q^{29} +(-3.94014 - 3.55033i) q^{30} +(-2.72989 + 3.75737i) q^{31} -1.00000 q^{32} +(-6.47898 + 4.46183i) q^{33} -0.636500i q^{34} +(-4.79274 - 3.46838i) q^{35} +(0.811453 - 2.49739i) q^{36} +(-3.85636 + 1.25301i) q^{37} +(0.605217 - 0.439716i) q^{38} +(1.13386 + 1.56063i) q^{39} +(2.22373 + 0.234546i) q^{40} +(0.693842 - 2.13543i) q^{41} +(1.29095 - 6.14124i) q^{42} +1.78702 q^{43} +(1.10418 - 3.12743i) q^{44} +(-2.39021 + 5.36321i) q^{45} +(-3.43289 + 4.72497i) q^{46} +(1.40295 - 4.31784i) q^{47} +(0.732958 + 2.25581i) q^{48} +(0.700426 - 6.96487i) q^{49} +(-4.88998 - 1.04314i) q^{50} +(-1.43582 + 0.466527i) q^{51} +(-0.773484 - 0.251320i) q^{52} +(1.23908 - 1.70545i) q^{53} +0.887291 q^{54} +(-3.18893 + 6.69558i) q^{55} +(1.08155 + 2.41459i) q^{56} +(-1.43552 - 1.04296i) q^{57} +(8.07009 + 2.62213i) q^{58} +(11.4455 - 3.71887i) q^{59} +(-1.10081 - 5.18824i) q^{60} +(9.48273 - 6.88961i) q^{61} +(-4.41705 + 1.43519i) q^{62} +(-6.90781 + 0.741728i) q^{63} +(-0.809017 - 0.587785i) q^{64} +(1.66108 + 0.740287i) q^{65} +(-7.86420 - 0.198551i) q^{66} +7.11959i q^{67} +(0.374125 - 0.514939i) q^{68} +(13.1748 + 4.28076i) q^{69} +(-1.83874 - 5.62308i) q^{70} +(6.16231 - 4.47718i) q^{71} +(2.12441 - 1.54347i) q^{72} +(-9.50651 + 3.08885i) q^{73} +(-3.85636 - 1.25301i) q^{74} +(1.23103 + 11.7954i) q^{75} +0.748090 q^{76} +(-8.74568 + 0.716320i) q^{77} +1.92904i q^{78} +(-9.15919 + 12.6065i) q^{79} +(1.66117 + 1.49683i) q^{80} +(-3.08470 - 9.49374i) q^{81} +(1.81650 - 1.31977i) q^{82} +(4.36182 + 6.00353i) q^{83} +(4.65414 - 4.20956i) q^{84} +(-0.952731 + 1.05734i) q^{85} +(1.44573 + 1.05039i) q^{86} -20.1265i q^{87} +(2.73155 - 1.88112i) q^{88} -10.1872i q^{89} +(-5.08614 + 2.93400i) q^{90} +(0.229725 + 2.13946i) q^{91} +(-5.55454 + 1.80478i) q^{92} +(6.47503 + 8.91211i) q^{93} +(3.67298 - 2.66857i) q^{94} +(-1.66355 - 0.175462i) q^{95} +(-0.732958 + 2.25581i) q^{96} +(9.78252 + 7.10742i) q^{97} +(4.66050 - 5.22300i) q^{98} +(2.48137 + 8.34821i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9}+O(q^{10}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9	\( 96 q + 24 q^{2} - 24 q^{4} + 3 q^{7} + 24 q^{8} - 18 q^{9} + 4 q^{11} - 3 q^{14} - 6 q^{15} - 24 q^{16} + 28 q^{18} - 4 q^{22} + 38 q^{25} - 2 q^{28} + 6 q^{30} - 96 q^{32} + 46 q^{35} - 28 q^{36} + 10 q^{39} - 24 q^{43} - 16 q^{44} + 37 q^{49} - 8 q^{50} - 30 q^{51} + 40 q^{53} + 2 q^{56} - 20 q^{57} + 14 q^{60} + 63 q^{63} - 24 q^{64} - 40 q^{65} + 39 q^{70} - 20 q^{71} + 18 q^{72} - 16 q^{77} - 126 q^{81} + 60 q^{85} - 36 q^{86} - 14 q^{88} - 31 q^{91} - 10 q^{92} + 20 q^{93} - 44 q^{95} + 18 q^{98} + 100 q^{99}+O(q^{100}) \) 96 * q + 24 * q^2 - 24 * q^4 + 3 * q^7 + 24 * q^8 - 18 * q^9 + 4 * q^11 - 3 * q^14 - 6 * q^15 - 24 * q^16 + 28 * q^18 - 4 * q^22 + 38 * q^25 - 2 * q^28 + 6 * q^30 - 96 * q^32 + 46 * q^35 - 28 * q^36 + 10 * q^39 - 24 * q^43 - 16 * q^44 + 37 * q^49 - 8 * q^50 - 30 * q^51 + 40 * q^53 + 2 * q^56 - 20 * q^57 + 14 * q^60 + 63 * q^63 - 24 * q^64 - 40 * q^65 + 39 * q^70 - 20 * q^71 + 18 * q^72 - 16 * q^77 - 126 * q^81 + 60 * q^85 - 36 * q^86 - 14 * q^88 - 31 * q^91 - 10 * q^92 + 20 * q^93 - 44 * q^95 + 18 * q^98 + 100 * q^99

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