LMFDB - Embedded newform 666.2.k.a.175.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.13
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.32

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(0.973034 - 1.43290i) q^{3} -1.00000 q^{4} -0.886006i q^{5} +(-1.43290 - 0.973034i) q^{6} +(1.19538 - 2.07046i) q^{7} +1.00000i q^{8} +(-1.10641 - 2.78852i) q^{9} -0.886006 q^{10} +(-0.472571 - 0.818517i) q^{11} +(-0.973034 + 1.43290i) q^{12} -0.0561596i q^{13} +(-2.07046 - 1.19538i) q^{14} +(-1.26956 - 0.862114i) q^{15} +1.00000 q^{16} +(0.0519814 + 0.0300115i) q^{17} +(-2.78852 + 1.10641i) q^{18} +(-1.66612 + 0.961935i) q^{19} +0.886006i q^{20} +(-1.80362 - 3.72748i) q^{21} +(-0.818517 + 0.472571i) q^{22} +(-0.102782 - 0.0593415i) q^{23} +(1.43290 + 0.973034i) q^{24} +4.21499 q^{25} -0.0561596 q^{26} +(-5.07225 - 1.12795i) q^{27} +(-1.19538 + 2.07046i) q^{28} +(-0.778787 + 0.449633i) q^{29} +(-0.862114 + 1.26956i) q^{30} +(1.53819 + 0.888073i) q^{31} -1.00000i q^{32} +(-1.63268 - 0.119297i) q^{33} +(0.0300115 - 0.0519814i) q^{34} +(-1.83444 - 1.05911i) q^{35} +(1.10641 + 2.78852i) q^{36} +(-5.32577 - 2.93874i) q^{37} +(0.961935 + 1.66612i) q^{38} +(-0.0804712 - 0.0546452i) q^{39} +0.886006 q^{40} -10.7795 q^{41} +(-3.72748 + 1.80362i) q^{42} +(9.54746 - 5.51223i) q^{43} +(0.472571 + 0.818517i) q^{44} +(-2.47065 + 0.980285i) q^{45} +(-0.0593415 + 0.102782i) q^{46} +(1.86939 + 3.23789i) q^{47} +(0.973034 - 1.43290i) q^{48} +(0.642139 + 1.11222i) q^{49} -4.21499i q^{50} +(0.0935831 - 0.0452820i) q^{51} +0.0561596i q^{52} +(1.74232 - 3.01779i) q^{53} +(-1.12795 + 5.07225i) q^{54} +(-0.725211 + 0.418700i) q^{55} +(2.07046 + 1.19538i) q^{56} +(-0.242834 + 3.32338i) q^{57} +(0.449633 + 0.778787i) q^{58} +(-5.87254 + 3.39051i) q^{59} +(1.26956 + 0.862114i) q^{60} +(7.92026 + 4.57276i) q^{61} +(0.888073 - 1.53819i) q^{62} +(-7.09609 - 1.04257i) q^{63} -1.00000 q^{64} -0.0497577 q^{65} +(-0.119297 + 1.63268i) q^{66} +5.47242 q^{67} +(-0.0519814 - 0.0300115i) q^{68} +(-0.185041 + 0.0895358i) q^{69} +(-1.05911 + 1.83444i) q^{70} +(-2.01948 - 3.49783i) q^{71} +(2.78852 - 1.10641i) q^{72} -1.87998 q^{73} +(-2.93874 + 5.32577i) q^{74} +(4.10133 - 6.03967i) q^{75} +(1.66612 - 0.961935i) q^{76} -2.25961 q^{77} +(-0.0546452 + 0.0804712i) q^{78} +(6.19928 + 3.57916i) q^{79} -0.886006i q^{80} +(-6.55172 + 6.17050i) q^{81} +10.7795i q^{82} +8.38591 q^{83} +(1.80362 + 3.72748i) q^{84} +(0.0265903 - 0.0460558i) q^{85} +(-5.51223 - 9.54746i) q^{86} +(-0.113507 + 1.55343i) q^{87} +(0.818517 - 0.472571i) q^{88} +(2.20126 + 1.27090i) q^{89} +(0.980285 + 2.47065i) q^{90} +(-0.116276 - 0.0671320i) q^{91} +(0.102782 + 0.0593415i) q^{92} +(2.76923 - 1.33994i) q^{93} +(3.23789 - 1.86939i) q^{94} +(0.852280 + 1.47619i) q^{95} +(-1.43290 - 0.973034i) q^{96} +(8.14658 - 4.70343i) q^{97} +(1.11222 - 0.642139i) q^{98} +(-1.75960 + 2.22339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.973034	−	1.43290i	0.561781	−	0.827286i
$3$	0.973034	−	1.43290i	0.561781	−	0.827286i
$4$	−1.00000			−0.500000
$5$		−	0.886006i		−	0.396234i	−0.980178	−	0.198117i	$-0.936517\pi$
$5$		−	0.886006i		−	0.396234i	0.980178	−	0.198117i	$-0.0634826\pi$
$6$	−1.43290	−	0.973034i	−0.584979	−	0.397239i
$7$	1.19538	−	2.07046i	0.451811	−	0.782559i	−0.546688	−	0.837336i	$-0.684112\pi$
$7$	1.19538	−	2.07046i	0.451811	−	0.782559i	0.998499	+	0.0547774i	$0.0174449\pi$
$8$			1.00000i			0.353553i
$9$	−1.10641	−	2.78852i	−0.368803	−	0.929507i
$10$	−0.886006			−0.280180
$11$	−0.472571	−	0.818517i	−0.142486	−	0.246792i	0.785947	−	0.618295i	$-0.212176\pi$
$11$	−0.472571	−	0.818517i	−0.142486	−	0.246792i	−0.928432	+	0.371502i	$0.878843\pi$
$12$	−0.973034	+	1.43290i	−0.280891	+	0.413643i
$13$		−	0.0561596i		−	0.0155759i	−0.999970	−	0.00778794i	$-0.997521\pi$
$13$		−	0.0561596i		−	0.0155759i	0.999970	−	0.00778794i	$-0.00247900\pi$
$14$	−2.07046	−	1.19538i	−0.553353	−	0.319478i
$15$	−1.26956	−	0.862114i	−0.327799	−	0.222597i
$16$	1.00000			0.250000
$17$	0.0519814	+	0.0300115i	0.0126073	+	0.00727885i	0.506290	−	0.862363i	$-0.331016\pi$
$17$	0.0519814	+	0.0300115i	0.0126073	+	0.00727885i	−0.493683	+	0.869642i	$0.664350\pi$
$18$	−2.78852	+	1.10641i	−0.657261	+	0.260783i
$19$	−1.66612	+	0.961935i	−0.382234	+	0.220683i	−0.678790	−	0.734332i	$-0.737495\pi$
$19$	−1.66612	+	0.961935i	−0.382234	+	0.220683i	0.296556	+	0.955016i	$0.404162\pi$
$20$			0.886006i			0.198117i
$21$	−1.80362	−	3.72748i	−0.393581	−	0.813404i
$22$	−0.818517	+	0.472571i	−0.174508	+	0.100752i
$23$	−0.102782	−	0.0593415i	−0.0214316	−	0.0123736i	0.489246	−	0.872146i	$-0.337272\pi$
$23$	−0.102782	−	0.0593415i	−0.0214316	−	0.0123736i	−0.510678	+	0.859772i	$0.670605\pi$
$24$	1.43290	+	0.973034i	0.292490	+	0.198620i
$25$	4.21499			0.842999
$26$	−0.0561596			−0.0110138
$27$	−5.07225	−	1.12795i	−0.976155	−	0.217074i
$28$	−1.19538	+	2.07046i	−0.225905	+	0.391280i
$29$	−0.778787	+	0.449633i	−0.144617	+	0.0834947i	−0.570563	−	0.821254i	$-0.693275\pi$
$29$	−0.778787	+	0.449633i	−0.144617	+	0.0834947i	0.425946	+	0.904749i	$0.359941\pi$
$30$	−0.862114	+	1.26956i	−0.157400	+	0.231789i
$31$	1.53819	+	0.888073i	0.276267	+	0.159503i	0.631732	−	0.775187i	$-0.282344\pi$
$31$	1.53819	+	0.888073i	0.276267	+	0.159503i	−0.355465	+	0.934689i	$0.615678\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−1.63268	−	0.119297i	−0.284213	−	0.0207670i
$34$	0.0300115	−	0.0519814i	0.00514693	−	0.00891474i
$35$	−1.83444	−	1.05911i	−0.310076	−	0.179023i
$36$	1.10641	+	2.78852i	0.184402	+	0.464754i
$37$	−5.32577	−	2.93874i	−0.875551	−	0.483126i
$37$	−5.32577	−	2.93874i	−0.875551	−	0.483126i
$38$	0.961935	+	1.66612i	0.156047	+	0.270281i
$39$	−0.0804712	−	0.0546452i	−0.0128857	−	0.00875024i
$40$	0.886006			0.140090
$41$	−10.7795			−1.68348			−0.841738	−	0.539887i	$-0.818467\pi$
$41$	−10.7795			−1.68348			−0.841738	+	0.539887i	$0.818467\pi$
$42$	−3.72748	+	1.80362i	−0.575163	+	0.278304i
$43$	9.54746	−	5.51223i	1.45597	−	0.840607i	0.457164	−	0.889383i	$-0.348865\pi$
$43$	9.54746	−	5.51223i	1.45597	−	0.840607i	0.998810	+	0.0487761i	$0.0155321\pi$
$44$	0.472571	+	0.818517i	0.0712428	+	0.123396i
$45$	−2.47065	+	0.980285i	−0.368302	+	0.146132i
$46$	−0.0593415	+	0.102782i	−0.00874942	+	0.0151544i
$47$	1.86939	+	3.23789i	0.272679	+	0.472294i	0.969547	−	0.244905i	$-0.0787569\pi$
$47$	1.86939	+	3.23789i	0.272679	+	0.472294i	−0.696868	+	0.717200i	$0.745424\pi$
$48$	0.973034	−	1.43290i	0.140445	−	0.206821i
$49$	0.642139	+	1.11222i	0.0917342	+	0.158888i
$50$		−	4.21499i		−	0.596090i
$51$	0.0935831	−	0.0452820i	0.0131043	−	0.00634075i
$52$			0.0561596i			0.00778794i
$53$	1.74232	−	3.01779i	0.239326	−	0.414525i	−0.721195	−	0.692732i	$-0.756407\pi$
$53$	1.74232	−	3.01779i	0.239326	−	0.414525i	0.960521	+	0.278207i	$0.0897401\pi$
$54$	−1.12795	+	5.07225i	−0.153495	+	0.690246i
$55$	−0.725211	+	0.418700i	−0.0977874	+	0.0564576i
$56$	2.07046	+	1.19538i	0.276676	+	0.159739i
$57$	−0.242834	+	3.32338i	−0.0321642	+	0.440193i
$58$	0.449633	+	0.778787i	0.0590397	+	0.102260i
$59$	−5.87254	+	3.39051i	−0.764540	+	0.441407i	−0.830923	−	0.556387i	$-0.812187\pi$
$59$	−5.87254	+	3.39051i	−0.764540	+	0.441407i	0.0663836	+	0.997794i	$0.478854\pi$
$60$	1.26956	+	0.862114i	0.163899	+	0.111298i
$61$	7.92026	+	4.57276i	1.01409	+	0.585482i	0.912385	−	0.409333i	$-0.134239\pi$
$61$	7.92026	+	4.57276i	1.01409	+	0.585482i	0.101700	+	0.994815i	$0.467572\pi$
$62$	0.888073	−	1.53819i	0.112785	−	0.195350i
$63$	−7.09609	−	1.04257i	−0.894024	−	0.131351i
$64$	−1.00000			−0.125000
$65$	−0.0497577			−0.00617169
$66$	−0.119297	+	1.63268i	−0.0146845	+	0.200969i
$67$	5.47242			0.668562			0.334281	−	0.942473i	$-0.391507\pi$
$67$	5.47242			0.668562			0.334281	+	0.942473i	$0.391507\pi$
$68$	−0.0519814	−	0.0300115i	−0.00630367	−	0.00363943i
$69$	−0.185041	+	0.0895358i	−0.0222764	+	0.0107788i
$70$	−1.05911	+	1.83444i	−0.126588	+	0.219257i
$71$	−2.01948	−	3.49783i	−0.239668	−	0.415117i	0.720951	−	0.692986i	$-0.243705\pi$
$71$	−2.01948	−	3.49783i	−0.239668	−	0.415117i	−0.960619	+	0.277869i	$0.910372\pi$
$72$	2.78852	−	1.10641i	0.328631	−	0.130392i
$73$	−1.87998			−0.220035			−0.110017	−	0.993930i	$-0.535091\pi$
$73$	−1.87998			−0.220035			−0.110017	+	0.993930i	$0.535091\pi$
$74$	−2.93874	+	5.32577i	−0.341622	+	0.619108i
$75$	4.10133	−	6.03967i	0.473581	−	0.697401i
$76$	1.66612	−	0.961935i	0.191117	−	0.110342i
$77$	−2.25961			−0.257506
$78$	−0.0546452	+	0.0804712i	−0.00618735	+	0.00911156i
$79$	6.19928	+	3.57916i	0.697474	+	0.402687i	0.806406	−	0.591363i	$-0.201410\pi$
$79$	6.19928	+	3.57916i	0.697474	+	0.402687i	−0.108932	+	0.994049i	$0.534743\pi$
$80$		−	0.886006i		−	0.0990584i
$81$	−6.55172	+	6.17050i	−0.727968	+	0.685611i
$82$			10.7795i			1.19040i
$83$	8.38591			0.920473			0.460237	−	0.887796i	$-0.347765\pi$
$83$	8.38591			0.920473			0.460237	+	0.887796i	$0.347765\pi$
$84$	1.80362	+	3.72748i	0.196791	+	0.406702i
$85$	0.0265903	−	0.0460558i	0.00288413	−	0.00499545i
$86$	−5.51223	−	9.54746i	−0.594399	−	1.02953i
$87$	−0.113507	+	1.55343i	−0.0121692	+	0.166545i
$88$	0.818517	−	0.472571i	0.0872542	−	0.0503762i
$89$	2.20126	+	1.27090i	0.233333	+	0.134715i	0.612109	−	0.790774i	$-0.290322\pi$
$89$	2.20126	+	1.27090i	0.233333	+	0.134715i	−0.378776	+	0.925488i	$0.623655\pi$
$90$	0.980285	+	2.47065i	0.103331	+	0.260429i
$91$	−0.116276	−	0.0671320i	−0.0121890	−	0.00703735i
$92$	0.102782	+	0.0593415i	0.0107158	+	0.00618678i
$93$	2.76923	−	1.33994i	0.287156	−	0.138946i
$94$	3.23789	−	1.86939i	0.333962	−	0.192813i
$95$	0.852280	+	1.47619i	0.0874421	+	0.151454i
$96$	−1.43290	−	0.973034i	−0.146245	−	0.0993099i
$97$	8.14658	−	4.70343i	0.827160	−	0.477561i	−0.0257194	−	0.999669i	$-0.508188\pi$
$97$	8.14658	−	4.70343i	0.827160	−	0.477561i	0.852879	+	0.522108i	$0.174854\pi$
$98$	1.11222	−	0.642139i	0.112351	−	0.0648658i
$99$	−1.75960	+	2.22339i	−0.176846	+	0.223459i
$100$	−4.21499			−0.421499
$101$	−5.05680	−	8.75864i	−0.503171	−	0.871517i	−0.999993	−	0.00366527i	$-0.998833\pi$
$101$	−5.05680	−	8.75864i	−0.503171	−	0.871517i	0.496822	−	0.867852i	$-0.334500\pi$
$102$	−0.0452820	−	0.0935831i	−0.00448359	−	0.00926611i
$103$	8.25943	+	4.76858i	0.813826	+	0.469863i	0.848283	−	0.529544i	$-0.177637\pi$
$103$	8.25943	+	4.76858i	0.813826	+	0.469863i	−0.0344568	+	0.999406i	$0.510970\pi$
$104$	0.0561596			0.00550690
$105$	−3.30257	+	1.59801i	−0.322298	+	0.155950i
$106$	−3.01779	−	1.74232i	−0.293114	−	0.169229i
$107$	1.77820	+	3.07993i	0.171905	+	0.297748i	0.939086	−	0.343683i	$-0.111674\pi$
$107$	1.77820	+	3.07993i	0.171905	+	0.297748i	−0.767181	+	0.641431i	$0.778341\pi$
$108$	5.07225	+	1.12795i	0.488078	+	0.108537i
$109$	1.39010	+	0.802574i	0.133147	+	0.0768726i	0.565094	−	0.825026i	$-0.308840\pi$
$109$	1.39010	+	0.802574i	0.133147	+	0.0768726i	−0.431947	+	0.901899i	$0.642173\pi$
$110$	0.418700	+	0.725211i	0.0399215	+	0.0691461i
$111$	−9.39308	+	4.77180i	−0.891552	+	0.452919i
$112$	1.19538	−	2.07046i	0.112953	−	0.195640i
$113$	6.40020	−	3.69516i	0.602080	−	0.347611i	−0.167779	−	0.985825i	$-0.553660\pi$
$113$	6.40020	−	3.69516i	0.602080	−	0.347611i	0.769860	+	0.638213i	$0.220326\pi$
$114$	3.32338	+	0.242834i	0.311263	+	0.0227435i
$115$	−0.0525769	+	0.0910658i	−0.00490282	+	0.00849193i
$116$	0.778787	−	0.449633i	0.0723085	−	0.0417473i
$117$	−0.156602	+	0.0621355i	−0.0144779	+	0.00574443i
$118$	3.39051	+	5.87254i	0.312122	+	0.540611i
$119$	0.124275	−	0.0717502i	0.0113923	−	0.00657733i
$120$	0.862114	−	1.26956i	0.0786998	−	0.115894i
$121$	5.05335	−	8.75266i	0.459396	−	0.795697i
$122$	4.57276	−	7.92026i	0.413998	−	0.717066i
$123$	−10.4888	+	15.4460i	−0.945745	+	1.39272i
$124$	−1.53819	−	0.888073i	−0.138133	−	0.0797513i
$125$		−	8.16454i		−	0.730258i
$126$	−1.04257	+	7.09609i	−0.0928793	+	0.632170i
$127$	−0.619331	+	1.07271i	−0.0549567	+	0.0951878i	−0.892195	−	0.451650i	$-0.850835\pi$
$127$	−0.619331	+	1.07271i	−0.0549567	+	0.0951878i	0.837238	+	0.546838i	$0.184169\pi$
$128$			1.00000i			0.0883883i
$129$	1.39153	−	19.0441i	0.122517	−	1.67674i
$130$			0.0497577i			0.00436404i
$131$	8.27021	−	4.77481i	0.722572	−	0.417177i	−0.0931267	−	0.995654i	$-0.529686\pi$
$131$	8.27021	−	4.77481i	0.722572	−	0.417177i	0.815699	+	0.578477i	$0.196353\pi$
$132$	1.63268	+	0.119297i	0.142107	+	0.0103835i
$133$			4.59951i			0.398828i
$134$		−	5.47242i		−	0.472745i
$135$	−0.999372	+	4.49404i	−0.0860122	+	0.386786i
$136$	−0.0300115	+	0.0519814i	−0.00257346	+	0.00445737i
$137$	−7.21668	−	12.4997i	−0.616563	−	1.06792i	−0.990108	−	0.140306i	$-0.955191\pi$
$137$	−7.21668	−	12.4997i	−0.616563	−	1.06792i	0.373546	−	0.927612i	$-0.378142\pi$
$138$	0.0895358	+	0.185041i	0.00762179	+	0.0157518i
$139$	−2.53522	−	4.39113i	−0.215035	−	0.372451i	0.738249	−	0.674529i	$-0.235653\pi$
$139$	−2.53522	−	4.39113i	−0.215035	−	0.372451i	−0.953283	+	0.302078i	$0.902320\pi$
$140$	1.83444	+	1.05911i	0.155038	+	0.0895113i
$141$	6.45855	+	0.471916i	0.543908	+	0.0397425i
$142$	−3.49783	+	2.01948i	−0.293532	+	0.169471i
$143$	−0.0459676	+	0.0265394i	−0.00384400	+	0.00221934i
$144$	−1.10641	−	2.78852i	−0.0922008	−	0.232377i
$145$	0.398377	+	0.690009i	0.0330834	+	0.0573022i
$146$			1.87998i			0.155588i
$147$	2.21852	+	0.162104i	0.182981	+	0.0133701i
$148$	5.32577	+	2.93874i	0.437775	+	0.241563i
$149$	6.34370	−	10.9876i	0.519696	−	0.900140i	−0.480042	−	0.877245i	$-0.659379\pi$
$149$	6.34370	−	10.9876i	0.519696	−	0.900140i	0.999738	−	0.0228941i	$-0.00728807\pi$
$150$	−6.03967	−	4.10133i	−0.493137	−	0.334872i
$151$	−5.79617	+	10.0393i	−0.471685	+	0.816983i	−0.999475	−	0.0323921i	$-0.989687\pi$
$151$	−5.79617	+	10.0393i	−0.471685	+	0.816983i	0.527790	+	0.849375i	$0.323021\pi$
$152$	−0.961935	−	1.66612i	−0.0780233	−	0.135140i
$153$	0.0261750	−	0.178156i	0.00211612	−	0.0144031i
$154$			2.25961i			0.182084i
$155$	0.786837	−	1.36284i	0.0632003	−	0.109466i
$156$	0.0804712	+	0.0546452i	0.00644285	+	0.00437512i
$157$	1.64261	+	2.84508i	0.131094	+	0.227062i	0.924099	−	0.382154i	$-0.124818\pi$
$157$	1.64261	+	2.84508i	0.131094	+	0.227062i	−0.793004	+	0.609216i	$0.791484\pi$
$158$	3.57916	−	6.19928i	0.284742	−	0.493188i
$159$	−2.62886	−	5.43299i	−0.208482	−	0.430864i
$160$	−0.886006			−0.0700449
$161$	−0.245728	+	0.141871i	−0.0193661	+	0.0111810i
$162$	6.17050	+	6.55172i	0.484800	+	0.514751i
$163$	2.25828	+	1.30382i	0.176882	+	0.102123i	0.585827	−	0.810436i	$-0.300770\pi$
$163$	2.25828	+	1.30382i	0.176882	+	0.102123i	−0.408945	+	0.912559i	$0.634103\pi$
$164$	10.7795			0.841738
$165$	−0.105698	+	1.44656i	−0.00822860	+	0.112615i
$166$		−	8.38591i		−	0.650873i
$167$			10.4610i			0.809497i	0.914428	+	0.404749i	$0.132641\pi$
$167$			10.4610i			0.809497i	−0.914428	+	0.404749i	$0.867359\pi$
$168$	3.72748	−	1.80362i	0.287582	−	0.139152i
$169$	12.9968			0.999757
$170$	−0.0460558	−	0.0265903i	−0.00353232	−	0.00203939i
$171$	4.52579	+	3.58172i	0.346096	+	0.273901i
$172$	−9.54746	+	5.51223i	−0.727987	+	0.420303i
$173$	8.67685			0.659689			0.329844	−	0.944035i	$-0.393004\pi$
$173$	8.67685			0.659689			0.329844	+	0.944035i	$0.393004\pi$
$174$	1.55343	+	0.113507i	0.117765	+	0.00860493i
$175$	5.03851	−	8.72696i	0.380876	−	0.659696i
$176$	−0.472571	−	0.818517i	−0.0356214	−	0.0616980i
$177$	−0.855913	+	11.7139i	−0.0643344	+	0.880467i
$178$	1.27090	−	2.20126i	0.0952577	−	0.164991i
$179$			13.1014i			0.979247i	0.871934	+	0.489624i	$0.162866\pi$
$179$			13.1014i			0.979247i	−0.871934	+	0.489624i	$0.837134\pi$
$180$	2.47065	−	0.980285i	0.184151	−	0.0730661i
$181$	0.0510943	+	0.0884979i	0.00379781	+	0.00657800i	0.867918	−	0.496707i	$-0.165458\pi$
$181$	0.0510943	+	0.0884979i	0.00379781	+	0.00657800i	−0.864120	+	0.503285i	$0.832124\pi$
$182$	−0.0671320	+	0.116276i	−0.00497616	+	0.00861896i
$183$	14.2590	−	6.89949i	1.05406	−	0.510025i
$184$	0.0593415	−	0.102782i	0.00437471	−	0.00757722i
$185$	−2.60374	+	4.71866i	−0.191431	+	0.346923i
$186$	−1.33994	−	2.76923i	−0.0982495	−	0.203050i
$187$		−	0.0567302i		−	0.00414852i
$188$	−1.86939	−	3.23789i	−0.136340	−	0.236147i
$189$	−8.39864	+	9.15355i	−0.610911	+	0.665822i
$190$	1.47619	−	0.852280i	0.107094	−	0.0618309i
$191$	9.78573	−	5.64979i	0.708071	−	0.408805i	−0.102276	−	0.994756i	$-0.532612\pi$
$191$	9.78573	−	5.64979i	0.708071	−	0.408805i	0.810346	+	0.585951i	$0.199279\pi$
$192$	−0.973034	+	1.43290i	−0.0702227	+	0.103411i
$193$	4.36792	+	2.52182i	0.314409	+	0.181524i	0.648898	−	0.760875i	$-0.275230\pi$
$193$	4.36792	+	2.52182i	0.314409	+	0.181524i	−0.334488	+	0.942400i	$0.608564\pi$
$194$	−4.70343	−	8.14658i	−0.337687	−	0.584890i
$195$	−0.0484160	+	0.0712979i	−0.00346714	+	0.00510575i
$196$	−0.642139	−	1.11222i	−0.0458671	−	0.0794441i
$197$	−6.57870	+	11.3946i	−0.468713	+	0.811834i	−0.999360	−	0.0357583i	$-0.988615\pi$
$197$	−6.57870	+	11.3946i	−0.468713	+	0.811834i	0.530648	+	0.847592i	$0.321949\pi$
$198$	2.22339	+	1.75960i	0.158009	+	0.125049i
$199$		−	10.0053i		−	0.709256i	−0.935008	−	0.354628i	$-0.884608\pi$
$199$		−	10.0053i		−	0.709256i	0.935008	−	0.354628i	$-0.115392\pi$
$200$			4.21499i			0.298045i
$201$	5.32485	−	7.84143i	0.375586	−	0.553092i
$202$	−8.75864	+	5.05680i	−0.616256	+	0.355796i
$203$			2.14993i			0.150895i
$204$	−0.0935831	+	0.0452820i	−0.00655213	+	0.00317037i
$205$			9.55070i			0.667050i
$206$	4.76858	−	8.25943i	0.332243	−	0.575462i
$207$	−0.0517555	+	0.352267i	−0.00359726	+	0.0244843i
$208$		−	0.0561596i		−	0.00389397i
$209$	1.57472	+	0.909166i	0.108926	+	0.0628883i
$210$	1.59801	+	3.30257i	0.110273	+	0.227899i
$211$	1.33067	−	2.30479i	0.0916072	−	0.158668i	−0.816580	−	0.577232i	$-0.804133\pi$
$211$	1.33067	−	2.30479i	0.0916072	−	0.158668i	0.908188	+	0.418563i	$0.137466\pi$
$212$	−1.74232	+	3.01779i	−0.119663	+	0.207263i
$213$	−6.97707	−	0.509803i	−0.478061	−	0.0349312i
$214$	3.07993	−	1.77820i	0.210540	−	0.121555i
$215$	−4.88386	−	8.45910i	−0.333077	−	0.576906i
$216$	1.12795	−	5.07225i	0.0767474	−	0.345123i
$217$	3.67743	−	2.12317i	0.249640	−	0.144130i
$218$	0.802574	−	1.39010i	0.0543571	−	0.0941493i
$219$	−1.82928	+	2.69382i	−0.123611	+	0.182032i
$220$	0.725211	−	0.418700i	0.0488937	−	0.0282288i
$221$	0.00168543	−	0.00291926i	0.000113374	−	0.000196370i
$222$	4.77180	+	9.39308i	0.320262	+	0.630422i
$223$	11.9150	+	20.6375i	0.797890	+	1.38199i	0.920988	+	0.389591i	$0.127384\pi$
$223$	11.9150	+	20.6375i	0.797890	+	1.38199i	−0.123098	+	0.992395i	$0.539283\pi$
$224$	−2.07046	−	1.19538i	−0.138338	−	0.0798696i
$225$	−4.66351	−	11.7536i	−0.310901	−	0.783574i
$226$	−3.69516	−	6.40020i	−0.245798	−	0.425735i
$227$	3.65778	+	2.11182i	0.242775	+	0.140166i	0.616452	−	0.787393i	$-0.288570\pi$
$227$	3.65778	+	2.11182i	0.242775	+	0.140166i	−0.373676	+	0.927559i	$0.621903\pi$
$228$	0.242834	−	3.32338i	0.0160821	−	0.220096i
$229$	−7.57927			−0.500852			−0.250426	−	0.968136i	$-0.580571\pi$
$229$	−7.57927			−0.500852			−0.250426	+	0.968136i	$0.580571\pi$
$230$	0.0910658	+	0.0525769i	0.00600470	+	0.00346682i
$231$	−2.19867	+	3.23779i	−0.144662	+	0.213031i
$232$	−0.449633	−	0.778787i	−0.0295198	−	0.0511299i
$233$	10.0788			0.660282			0.330141	−	0.943932i	$-0.392904\pi$
$233$	10.0788			0.660282			0.330141	+	0.943932i	$0.392904\pi$
$234$	0.0621355	+	0.156602i	0.00406193	+	0.0102374i
$235$	2.86878	−	1.65629i	0.187139	−	0.108045i
$236$	5.87254	−	3.39051i	0.382270	−	0.220704i
$237$	11.1607	−	5.40031i	0.724965	−	0.350788i
$238$	−0.0717502	−	0.124275i	−0.00465087	−	0.00805555i
$239$	−18.8391	+	10.8768i	−1.21860	+	0.703560i	−0.964619	−	0.263648i	$-0.915074\pi$
$239$	−18.8391	+	10.8768i	−1.21860	+	0.703560i	−0.253983	+	0.967209i	$0.581741\pi$
$240$	−1.26956	−	0.862114i	−0.0819496	−	0.0556492i
$241$	8.36170	+	4.82763i	0.538625	+	0.310975i	0.744521	−	0.667599i	$-0.232678\pi$
$241$	8.36170	+	4.82763i	0.538625	+	0.310975i	−0.205897	+	0.978574i	$0.566011\pi$
$242$	−8.75266	−	5.05335i	−0.562643	−	0.324842i
$243$	2.46667	+	15.3921i	0.158237	+	0.987401i
$244$	−7.92026	−	4.57276i	−0.507043	−	0.292741i
$245$	0.985431	−	0.568939i	0.0629569	−	0.0363482i
$246$	15.4460	+	10.4888i	0.984798	+	0.668743i
$247$	0.0540219	+	0.0935687i	0.00343733	+	0.00595364i
$248$	−0.888073	+	1.53819i	−0.0563927	+	0.0976750i
$249$	8.15978	−	12.0162i	0.517105	−	0.761494i
$250$	−8.16454			−0.516371
$251$			14.3150i			0.903555i	0.892131	+	0.451778i	$0.149210\pi$
$251$			14.3150i			0.903555i	−0.892131	+	0.451778i	$0.850790\pi$
$252$	7.09609	+	1.04257i	0.447012	+	0.0656756i
$253$			0.112172i			0.00705221i
$254$	1.07271	+	0.619331i	0.0673080	+	0.0388603i
$255$	−0.0401201	−	0.0829152i	−0.00251242	−	0.00519235i
$256$	1.00000			0.0625000
$257$	6.43203	−	3.71353i	0.401219	−	0.231644i	−0.285791	−	0.958292i	$-0.592256\pi$
$257$	6.43203	−	3.71353i	0.401219	−	0.231644i	0.687010	+	0.726648i	$0.258923\pi$
$258$	−19.0441	−	1.39153i	−1.18564	−	0.0866326i
$259$	−12.4508	+	7.51386i	−0.773658	+	0.466889i
$260$	0.0497577			0.00308584
$261$	2.11547	+	1.67419i	0.130944	+	0.103630i
$262$	−4.77481	−	8.27021i	−0.294989	−	0.510935i
$263$	−14.3663	+	24.8832i	−0.885864	+	1.53436i	−0.0411442	+	0.999153i	$0.513100\pi$
$263$	−14.3663	+	24.8832i	−0.885864	+	1.53436i	−0.844720	+	0.535209i	$0.820233\pi$
$264$	0.119297	−	1.63268i	0.00734225	−	0.100485i
$265$	−2.67378	−	1.54371i	−0.164249	−	0.0948292i
$266$	4.59951			0.282014
$267$	3.96296	−	1.91756i	0.242530	−	0.117353i
$268$	−5.47242			−0.334281
$269$	−6.26248			−0.381830			−0.190915	−	0.981607i	$-0.561145\pi$
$269$	−6.26248			−0.381830			−0.190915	+	0.981607i	$0.561145\pi$
$270$	4.49404	+	0.999372i	0.273499	+	0.0608198i
$271$	−3.82822	+	6.63066i	−0.232548	+	0.402784i	−0.958557	−	0.284900i	$-0.908039\pi$
$271$	−3.82822	+	6.63066i	−0.232548	+	0.402784i	0.726010	+	0.687685i	$0.241373\pi$
$272$	0.0519814	+	0.0300115i	0.00315184	+	0.00181971i
$273$	−0.209334	+	0.101290i	−0.0126695	+	0.00613037i
$274$	−12.4997	+	7.21668i	−0.755132	+	0.435976i
$275$	−1.99188	−	3.45004i	−0.120115	−	0.208045i
$276$	0.185041	−	0.0895358i	0.0111382	−	0.00538942i
$277$	−26.9020	−	15.5319i	−1.61638	−	0.933220i	−0.987845	−	0.155443i	$-0.950320\pi$
$277$	−26.9020	−	15.5319i	−1.61638	−	0.933220i	−0.628540	−	0.777777i	$-0.716347\pi$
$278$	−4.39113	+	2.53522i	−0.263362	+	0.152052i
$279$	0.774546	−	5.27184i	0.0463708	−	0.315617i
$280$	1.05911	−	1.83444i	0.0632941	−	0.109629i
$281$			12.6036i			0.751867i	0.926647	+	0.375934i	$0.122678\pi$
$281$			12.6036i			0.751867i	−0.926647	+	0.375934i	$0.877322\pi$
$282$	0.471916	−	6.45855i	0.0281022	−	0.384601i
$283$		−	3.40453i		−	0.202378i	−0.994867	−	0.101189i	$-0.967735\pi$
$283$		−	3.40453i		−	0.202378i	0.994867	−	0.101189i	$-0.0322647\pi$
$284$	2.01948	+	3.49783i	0.119834	+	0.207558i
$285$	2.94454	+	0.215153i	0.174419	+	0.0127445i
$286$	0.0265394	+	0.0459676i	0.00156931	+	0.00271812i
$287$	−12.8856	+	22.3185i	−0.760612	+	1.31742i
$288$	−2.78852	+	1.10641i	−0.164315	+	0.0651958i
$289$	−8.49820	−	14.7193i	−0.499894	−	0.865842i
$290$	0.690009	−	0.398377i	0.0405187	−	0.0233935i
$291$	1.18735	−	16.2498i	0.0696037	−	0.952582i
$292$	1.87998			0.110017
$293$	−0.122433			−0.00715259			−0.00357630	−	0.999994i	$-0.501138\pi$
$293$	−0.122433			−0.00715259			−0.00357630	+	0.999994i	$0.501138\pi$
$294$	0.162104	−	2.21852i	0.00945409	−	0.129387i
$295$	3.00401	+	5.20310i	0.174900	+	0.302936i
$296$	2.93874	−	5.32577i	0.170811	−	0.309554i
$297$	1.47375	+	4.68476i	0.0855157	+	0.271837i
$298$	−10.9876	−	6.34370i	−0.636495	−	0.367480i
$299$	−0.00333259	+	0.00577222i	−0.000192729	+	0.000333816i
$300$	−4.10133	+	6.03967i	−0.236791	+	0.348700i
$301$		−	26.3568i		−	1.51918i
$302$	10.0393	+	5.79617i	0.577694	+	0.333532i
$303$	−17.4707	−	1.27656i	−1.00367	−	0.0733363i
$304$	−1.66612	+	0.961935i	−0.0955586	+	0.0551708i
$305$	4.05149	−	7.01739i	0.231988	−	0.401815i
$306$	−0.178156	−	0.0261750i	−0.0101845	−	0.00149632i
$307$	−29.3541			−1.67532			−0.837662	−	0.546189i	$-0.816078\pi$
$307$	−29.3541			−1.67532			−0.837662	+	0.546189i	$0.816078\pi$
$308$	2.25961			0.128753
$309$	14.8696	−	7.19495i	0.845903	−	0.409306i
$310$	−1.36284	−	0.786837i	−0.0774042	−	0.0446894i
$311$	−11.7893	+	6.80655i	−0.668509	+	0.385964i	−0.795511	−	0.605939i	$-0.792798\pi$
$311$	−11.7893	+	6.80655i	−0.668509	+	0.385964i	0.127003	+	0.991902i	$0.459464\pi$
$312$	0.0546452	−	0.0804712i	0.00309368	−	0.00455578i
$313$			17.2691i			0.976105i	0.872814	+	0.488053i	$0.162293\pi$
$313$			17.2691i			0.976105i	−0.872814	+	0.488053i	$0.837707\pi$
$314$	2.84508	−	1.64261i	0.160557	−	0.0926977i
$315$	−0.923720	+	6.28718i	−0.0520458	+	0.354242i
$316$	−6.19928	−	3.57916i	−0.348737	−	0.201343i
$317$	−7.92126			−0.444902			−0.222451	−	0.974944i	$-0.571406\pi$
$317$	−7.92126			−0.444902			−0.222451	+	0.974944i	$0.571406\pi$
$318$	−5.43299	+	2.62886i	−0.304667	+	0.147419i
$319$	0.736064	+	0.424967i	0.0412117	+	0.0237936i
$320$			0.886006i			0.0495292i
$321$	6.14349	+	0.448895i	0.342896	+	0.0250549i
$322$	0.141871	+	0.245728i	0.00790617	+	0.0136939i
$323$	−0.115476			−0.00642528
$324$	6.55172	−	6.17050i	0.363984	−	0.342805i
$325$		−	0.236712i		−	0.0131304i
$326$	1.30382	−	2.25828i	0.0722117	−	0.125074i
$327$	2.50262	−	1.21094i	0.138395	−	0.0669652i
$328$		−	10.7795i		−	0.595198i
$329$	8.93854			0.492797
$330$	1.44656	+	0.105698i	0.0796308	+	0.00581850i
$331$		−	18.2133i		−	1.00109i	−0.865709	−	0.500547i	$-0.833132\pi$
$331$		−	18.2133i		−	1.00109i	0.865709	−	0.500547i	$-0.166868\pi$
$332$	−8.38591			−0.460237
$333$	−2.30227	+	18.1025i	−0.126164	+	0.992009i
$334$	10.4610			0.572401
$335$		−	4.84859i		−	0.264907i
$336$	−1.80362	−	3.72748i	−0.0983953	−	0.203351i
$337$	−26.9317			−1.46707			−0.733533	−	0.679654i	$-0.762130\pi$
$337$	−26.9317			−1.46707			−0.733533	+	0.679654i	$0.762130\pi$
$338$		−	12.9968i		−	0.706935i
$339$	0.932819	−	12.7664i	0.0506638	−	0.693374i
$340$	−0.0265903	+	0.0460558i	−0.00144206	+	0.00249773i
$341$		−	1.67871i		−	0.0909072i
$342$	3.58172	−	4.52579i	0.193677	−	0.244727i
$343$	19.8057			1.06941
$344$	5.51223	+	9.54746i	0.297199	+	0.514764i
$345$	0.0793292	+	0.163948i	0.00427094	+	0.00882664i
$346$		−	8.67685i		−	0.466470i
$347$	−6.99009	−	4.03573i	−0.375247	−	0.216649i	0.300501	−	0.953781i	$-0.402846\pi$
$347$	−6.99009	−	4.03573i	−0.375247	−	0.216649i	−0.675749	+	0.737132i	$0.736179\pi$
$348$	0.113507	−	1.55343i	0.00608461	−	0.0832727i
$349$	1.91930			0.102738			0.0513690	−	0.998680i	$-0.483642\pi$
$349$	1.91930			0.102738			0.0513690	+	0.998680i	$0.483642\pi$
$350$	−8.72696	−	5.03851i	−0.466476	−	0.269320i
$351$	−0.0633453	+	0.284856i	−0.00338112	+	0.0152045i
$352$	−0.818517	+	0.472571i	−0.0436271	+	0.0251881i
$353$		−	22.3379i		−	1.18893i	−0.804123	−	0.594463i	$-0.797365\pi$
$353$		−	22.3379i		−	1.18893i	0.804123	−	0.594463i	$-0.202635\pi$
$354$	11.7139	+	0.855913i	0.622584	+	0.0454913i
$355$	−3.09910	+	1.78927i	−0.164483	+	0.0949644i
$356$	−2.20126	−	1.27090i	−0.116666	−	0.0673573i
$357$	0.0181129	−	0.247889i	0.000958634	−	0.0131197i
$358$	13.1014			0.692432
$359$	5.88845			0.310781			0.155390	−	0.987853i	$-0.450336\pi$
$359$	5.88845			0.310781			0.155390	+	0.987853i	$0.450336\pi$
$360$	−0.980285	−	2.47065i	−0.0516656	−	0.130215i
$361$	−7.64936	+	13.2491i	−0.402598	+	0.697320i
$362$	0.0884979	−	0.0510943i	0.00465135	−	0.00268546i
$363$	−7.62462	−	15.7576i	−0.400189	−	0.827059i
$364$	0.116276	+	0.0671320i	0.00609452	+	0.00351867i
$365$			1.66567i			0.0871852i
$366$	−6.89949	−	14.2590i	−0.360642	−	0.745330i
$367$	−8.14610	+	14.1095i	−0.425223	+	0.736507i	−0.996441	−	0.0842906i	$-0.973138\pi$
$367$	−8.14610	+	14.1095i	−0.425223	+	0.736507i	0.571218	+	0.820798i	$0.306471\pi$
$368$	−0.102782	−	0.0593415i	−0.00535791	−	0.00309339i
$369$	11.9265	+	30.0589i	0.620871	+	1.56480i
$370$	4.71866	+	2.60374i	0.245311	+	0.135362i
$371$	−4.16547	−	7.21481i	−0.216260	−	0.374574i
$372$	−2.76923	+	1.33994i	−0.143578	+	0.0694729i
$373$	−26.8249			−1.38894			−0.694470	−	0.719522i	$-0.744361\pi$
$373$	−26.8249			−1.38894			−0.694470	+	0.719522i	$0.744361\pi$
$374$	−0.0567302			−0.00293345
$375$	−11.6990	−	7.94437i	−0.604132	−	0.410246i
$376$	−3.23789	+	1.86939i	−0.166981	+	0.0964066i
$377$	0.0252512	+	0.0437364i	0.00130050	+	0.00225254i
$378$	9.15355	+	8.39864i	0.470808	+	0.431979i
$379$	−6.83491	+	11.8384i	−0.351086	+	0.608098i	−0.986440	−	0.164123i	$-0.947521\pi$
$379$	−6.83491	+	11.8384i	−0.351086	+	0.608098i	0.635354	+	0.772221i	$0.280854\pi$
$380$	−0.852280	−	1.47619i	−0.0437211	−	0.0757271i
$381$	0.934461	+	1.93123i	0.0478739	+	0.0989397i
$382$	−5.64979	−	9.78573i	−0.289069	−	0.500682i
$383$			34.7986i			1.77812i	0.457787	+	0.889062i	$0.348642\pi$
$383$			34.7986i			1.77812i	−0.457787	+	0.889062i	$0.651358\pi$
$384$	1.43290	+	0.973034i	0.0731224	+	0.0496549i
$385$			2.00202i			0.102033i
$386$	2.52182	−	4.36792i	0.128357	−	0.222321i
$387$	−25.9344	−	20.5245i	−1.31832	−	1.04332i
$388$	−8.14658	+	4.70343i	−0.413580	+	0.238780i
$389$	−7.14182	−	4.12333i	−0.362105	−	0.209061i	0.307899	−	0.951419i	$-0.400374\pi$
$389$	−7.14182	−	4.12333i	−0.362105	−	0.209061i	−0.670004	+	0.742358i	$0.733707\pi$
$390$	0.0712979	+	0.0484160i	0.00361031	+	0.00245164i
$391$	−0.00356185	−	0.00616931i	−0.000180131	−	0.000311995i
$392$	−1.11222	+	0.642139i	−0.0561755	+	0.0324329i
$393$	1.20537	−	16.4964i	0.0608029	−	0.832136i
$394$	11.3946	+	6.57870i	0.574053	+	0.331430i
$395$	3.17115	−	5.49260i	0.159558	−	0.276363i
$396$	1.75960	−	2.22339i	0.0884230	−	0.111730i
$397$	−24.2614			−1.21765			−0.608823	−	0.793306i	$-0.708358\pi$
$397$	−24.2614			−1.21765			−0.608823	+	0.793306i	$0.708358\pi$
$398$	−10.0053			−0.501520
$399$	6.59064	+	4.47548i	0.329945	+	0.224054i
$400$	4.21499			0.210750
$401$	12.1447	+	7.01176i	0.606479	+	0.350151i	0.771586	−	0.636125i	$-0.219464\pi$
$401$	12.1447	+	7.01176i	0.606479	+	0.350151i	−0.165107	+	0.986276i	$0.552797\pi$
$402$	−7.84143	−	5.32485i	−0.391095	−	0.265579i
$403$	0.0498738	−	0.0863840i	0.00248439	−	0.00430309i
$404$	5.05680	+	8.75864i	0.251585	+	0.435759i
$405$	5.46709	+	5.80486i	0.271662	+	0.288446i
$406$	2.14993			0.106699
$407$	0.111392	+	5.74799i	0.00552152	+	0.284918i
$408$	0.0452820	+	0.0935831i	0.00224179	+	0.00463306i
$409$	2.44126	−	1.40946i	0.120713	−	0.0696935i	−0.438428	−	0.898766i	$-0.644465\pi$
$409$	2.44126	−	1.40946i	0.120713	−	0.0696935i	0.559141	+	0.829073i	$0.311131\pi$
$410$	9.55070			0.471675
$411$	−24.9328	−	1.82180i	−1.22985	−	0.0898630i
$412$	−8.25943	−	4.76858i	−0.406913	−	0.234931i
$413$			16.2118i			0.797730i
$414$	0.352267	+	0.0517555i	0.0173130	+	0.00254365i
$415$		−	7.42996i		−	0.364723i
$416$	−0.0561596			−0.00275345
$417$	−8.75891	−	0.640000i	−0.428926	−	0.0313409i
$418$	0.909166	−	1.57472i	0.0444687	−	0.0770221i
$419$	0.264120	+	0.457469i	0.0129031	+	0.0223488i	0.872405	−	0.488784i	$-0.162559\pi$
$419$	0.264120	+	0.457469i	0.0129031	+	0.0223488i	−0.859502	+	0.511133i	$0.829226\pi$
$420$	3.30257	−	1.59801i	0.161149	−	0.0779751i
$421$	3.39154	−	1.95811i	0.165294	−	0.0954323i	−0.415071	−	0.909789i	$-0.636243\pi$
$421$	3.39154	−	1.95811i	0.165294	−	0.0954323i	0.580365	+	0.814357i	$0.302910\pi$
$422$	−2.30479	−	1.33067i	−0.112195	−	0.0647760i
$423$	6.96060	−	8.79528i	0.338436	−	0.427641i
$424$	3.01779	+	1.74232i	0.146557	+	0.0846147i
$425$	0.219101	+	0.126498i	0.0106280	+	0.00613606i
$426$	−0.509803	+	6.97707i	−0.0247001	+	0.338040i
$427$	18.9354	−	10.9324i	0.916349	−	0.529054i
$428$	−1.77820	−	3.07993i	−0.0859525	−	0.148874i
$429$	−0.00669970	+	0.0916907i	−0.000323465	+	0.00442687i
$430$	−8.45910	+	4.88386i	−0.407934	+	0.235521i
$431$	−35.2095	+	20.3282i	−1.69598	+	0.979176i	−0.746485	+	0.665402i	$0.768260\pi$
$431$	−35.2095	+	20.3282i	−1.69598	+	0.979176i	−0.949498	+	0.313774i	$0.898406\pi$
$432$	−5.07225	−	1.12795i	−0.244039	−	0.0542686i
$433$	8.57685			0.412177			0.206088	−	0.978533i	$-0.433927\pi$
$433$	8.57685			0.412177			0.206088	+	0.978533i	$0.433927\pi$
$434$	−2.12317	−	3.67743i	−0.101915	−	0.176522i
$435$	1.37635	+	0.100568i	0.0659909	+	0.00482185i
$436$	−1.39010	−	0.802574i	−0.0665736	−	0.0384363i
$437$	0.228331			0.0109225
$438$	2.69382	+	1.82928i	0.128716	+	0.0874064i
$439$	−1.32136	−	0.762890i	−0.0630653	−	0.0364107i	0.468136	−	0.883657i	$-0.344926\pi$
$439$	−1.32136	−	0.762890i	−0.0630653	−	0.0364107i	−0.531201	+	0.847246i	$0.678259\pi$
$440$	−0.418700	−	0.725211i	−0.0199608	−	0.0345731i
$441$	2.39097	−	3.02119i	0.113856	−	0.143866i
$442$	−0.00291926	−	0.00168543i	−0.000138855	−	8.01679e-5i
$443$	8.14632	+	14.1098i	0.387044	+	0.670379i	0.992050	−	0.125841i	$-0.0401630\pi$
$443$	8.14632	+	14.1098i	0.387044	+	0.670379i	−0.605007	+	0.796220i	$0.706830\pi$
$444$	9.39308	−	4.77180i	0.445776	−	0.226460i
$445$	1.12602	−	1.95033i	0.0533785	−	0.0924543i
$446$	20.6375	−	11.9150i	0.977212	−	0.564193i
$447$	−9.57152	−	19.7812i	−0.452717	−	0.935619i
$448$	−1.19538	+	2.07046i	−0.0564763	+	0.0978199i
$449$	23.5757	−	13.6114i	1.11261	−	0.642364i	0.173103	−	0.984904i	$-0.444621\pi$
$449$	23.5757	−	13.6114i	1.11261	−	0.642364i	0.939503	+	0.342540i	$0.111287\pi$
$450$	−11.7536	+	4.66351i	−0.554070	+	0.219840i
$451$	5.09408	+	8.82320i	0.239871	+	0.415468i
$452$	−6.40020	+	3.69516i	−0.301040	+	0.173806i
$453$	8.74539	+	18.0739i	0.410894	+	0.849184i
$454$	2.11182	−	3.65778i	0.0991126	−	0.171668i
$455$	−0.0594793	+	0.103021i	−0.00278843	+	0.00482971i
$456$	−3.32338	−	0.242834i	−0.155632	−	0.0113718i
$457$	5.23289	+	3.02121i	0.244784	+	0.141326i	0.617374	−	0.786670i	$-0.288197\pi$
$457$	5.23289	+	3.02121i	0.244784	+	0.141326i	−0.372589	+	0.927996i	$0.621530\pi$
$458$			7.57927i			0.354156i
$459$	−0.229811	−	0.210858i	−0.0107267	−	0.00984202i
$460$	0.0525769	−	0.0910658i	0.00245141	−	0.00424597i
$461$		−	33.4341i		−	1.55718i	−0.627532	−	0.778591i	$-0.715935\pi$
$461$		−	33.4341i		−	1.55718i	0.627532	−	0.778591i	$-0.284065\pi$
$462$	3.23779	+	2.19867i	0.150636	+	0.102292i
$463$			17.2487i			0.801617i	0.916162	+	0.400808i	$0.131271\pi$
$463$			17.2487i			0.801617i	−0.916162	+	0.400808i	$0.868729\pi$
$464$	−0.778787	+	0.449633i	−0.0361543	+	0.0208737i
$465$	−1.18720	−	2.45355i	−0.0550550	−	0.113781i
$466$		−	10.0788i		−	0.466890i
$467$			15.9028i			0.735895i	0.929847	+	0.367947i	$0.119939\pi$
$467$			15.9028i			0.735895i	−0.929847	+	0.367947i	$0.880061\pi$
$468$	0.156602	−	0.0621355i	0.00723895	−	0.00287222i
$469$	6.54161	−	11.3304i	0.302064	−	0.523189i
$470$	−1.65629	−	2.86878i	−0.0763991	−	0.132327i
$471$	5.67503	+	0.414666i	0.261492	+	0.0191068i
$472$	−3.39051	−	5.87254i	−0.156061	−	0.270306i
$473$	−9.02370	−	5.20984i	−0.414910	−	0.239548i
$474$	−5.40031	−	11.1607i	−0.248045	−	0.512627i
$475$	−7.02269	+	4.05455i	−0.322223	+	0.186036i
$476$	−0.124275	+	0.0717502i	−0.00569613	+	0.00328866i
$477$	−10.3429	−	1.51959i	−0.473569	−	0.0695773i
$478$	10.8768	+	18.8391i	0.497492	+	0.861682i
$479$			12.1996i			0.557415i	0.960376	+	0.278708i	$0.0899060\pi$
$479$			12.1996i			0.557415i	−0.960376	+	0.278708i	$0.910094\pi$
$480$	−0.862114	+	1.26956i	−0.0393499	+	0.0579471i
$481$	−0.165039	+	0.299093i	−0.00752511	+	0.0136375i
$482$	4.82763	−	8.36170i	0.219893	−	0.380865i
$483$	−0.0358144	+	0.490149i	−0.00162961	+	0.0223026i
$484$	−5.05335	+	8.75266i	−0.229698	+	0.397848i
$485$	−4.16726	−	7.21791i	−0.189226	−	0.327749i
$486$	15.3921	−	2.46667i	0.698198	−	0.111890i
$487$			22.4792i			1.01863i	0.860581	+	0.509314i	$0.170101\pi$
$487$			22.4792i			1.01863i	−0.860581	+	0.509314i	$0.829899\pi$
$488$	−4.57276	+	7.92026i	−0.206999	+	0.358533i
$489$	4.06562	−	1.96723i	0.183854	−	0.0889611i
$490$	−0.568939	−	0.985431i	−0.0257020	−	0.0445172i
$491$	−5.13837	+	8.89992i	−0.231891	+	0.401648i	−0.958365	−	0.285547i	$-0.907825\pi$
$491$	−5.13837	+	8.89992i	−0.231891	+	0.401648i	0.726473	+	0.687195i	$0.241158\pi$
$492$	10.4888	−	15.4460i	0.472873	−	0.696358i
$493$	−0.0539766			−0.00243098
$494$	0.0935687	−	0.0540219i	0.00420986	−	0.00243056i
$495$	1.96994	+	1.55901i	0.0885420	+	0.0700724i
$496$	1.53819	+	0.888073i	0.0690666	+	0.0398756i
$497$	−9.65615			−0.433138
$498$	−12.0162	−	8.15978i	−0.538458	−	0.365648i
$499$		−	36.1940i		−	1.62026i	−0.586248	−	0.810132i	$-0.699395\pi$
$499$		−	36.1940i		−	1.62026i	0.586248	−	0.810132i	$-0.300605\pi$
$500$			8.16454i			0.365129i
$501$	14.9896	+	10.1789i	0.669686	+	0.454761i
$502$	14.3150			0.638910
$503$	17.8803	+	10.3232i	0.797245	+	0.460290i	0.842507	−	0.538685i	$-0.181079\pi$
$503$	17.8803	+	10.3232i	0.797245	+	0.460290i	−0.0452617	+	0.998975i	$0.514412\pi$
$504$	1.04257	−	7.09609i	0.0464396	−	0.316085i
$505$	−7.76021	+	4.48036i	−0.345325	+	0.199373i
$506$	0.112172			0.00498666
$507$	12.6464	−	18.6232i	0.561645	−	0.827085i
$508$	0.619331	−	1.07271i	0.0274784	−	0.0475939i
$509$	20.9641	+	36.3110i	0.929219	+	1.60945i	0.784631	+	0.619963i	$0.212852\pi$
$509$	20.9641	+	36.3110i	0.929219	+	1.60945i	0.144588	+	0.989492i	$0.453814\pi$
$510$	−0.0829152	+	0.0401201i	−0.00367155	+	0.00177655i
$511$	−2.24728	+	3.89241i	−0.0994140	+	0.172190i
$512$		−	1.00000i		−	0.0441942i
$513$	9.53600	−	2.99987i	0.421025	−	0.132448i
$514$	−3.71353	−	6.43203i	−0.163797	−	0.283705i
$515$	4.22499	−	7.31790i	0.186175	−	0.322465i
$516$	−1.39153	+	19.0441i	−0.0612585	+	0.838371i
$517$	1.76684	−	3.06026i	0.0777057	−	0.134590i
$518$	7.51386	+	12.4508i	0.330140	+	0.547059i
$519$	8.44287	−	12.4331i	0.370601	−	0.545751i
$520$		−	0.0497577i		−	0.00218202i
$521$	2.24380	+	3.88638i	0.0983028	+	0.170265i	0.910982	−	0.412446i	$-0.135325\pi$
$521$	2.24380	+	3.88638i	0.0983028	+	0.170265i	−0.812679	+	0.582711i	$0.801992\pi$
$522$	1.67419	−	2.11547i	0.0732771	−	0.0925915i
$523$	30.9787	−	17.8856i	1.35460	−	0.782081i	0.365713	−	0.930728i	$-0.380825\pi$
$523$	30.9787	−	17.8856i	1.35460	−	0.782081i	0.988890	+	0.148647i	$0.0474918\pi$
$524$	−8.27021	+	4.77481i	−0.361286	+	0.208589i
$525$	−7.60223	−	15.7113i	−0.331788	−	0.685698i
$526$	24.8832	+	14.3663i	1.08496	+	0.626401i
$527$	0.0533047	+	0.0923265i	0.00232199	+	0.00402181i
$528$	−1.63268	−	0.119297i	−0.0710533	−	0.00519176i
$529$	−11.4930	−	19.9064i	−0.499694	−	0.865495i
$530$	−1.54371	+	2.67378i	−0.0670544	+	0.116142i
$531$	15.9520	+	12.6244i	0.692256	+	0.547853i
$532$		−	4.59951i		−	0.199414i
$533$			0.605373i			0.0262216i
$534$	−1.91756	−	3.96296i	−0.0829808	−	0.171494i
$535$	2.72884	−	1.57549i	0.117978	−	0.0681146i
$536$			5.47242i			0.236372i
$537$	18.7731	+	12.7481i	0.810117	+	0.550123i
$538$			6.26248i			0.269995i
$539$	0.606913	−	1.05120i	0.0261416	−	0.0452785i
$540$	0.999372	−	4.49404i	0.0430061	−	0.193393i
$541$			8.78428i			0.377666i	0.982009	+	0.188833i	$0.0604705\pi$
$541$			8.78428i			0.377666i	−0.982009	+	0.188833i	$0.939530\pi$
$542$	6.63066	+	3.82822i	0.284811	+	0.164436i
$543$	0.176525	+	0.0128984i	0.00757542	+	0.000553524i
$544$	0.0300115	−	0.0519814i	0.00128673	−	0.00222868i
$545$	0.711085	−	1.23163i	0.0304595	−	0.0527574i
$546$	0.101290	+	0.209334i	0.00433483	+	0.00895867i
$547$	17.5743	−	10.1465i	0.751423	−	0.433834i	−0.0747851	−	0.997200i	$-0.523827\pi$
$547$	17.5743	−	10.1465i	0.751423	−	0.433834i	0.826208	+	0.563366i	$0.190494\pi$
$548$	7.21668	+	12.4997i	0.308281	+	0.533959i
$549$	3.98820	−	27.1452i	0.170212	−	1.15853i
$550$	−3.45004	+	1.99188i	−0.147110	+	0.0849342i
$551$	0.865035	−	1.49829i	0.0368517	−	0.0638291i
$552$	−0.0895358	−	0.185041i	−0.00381090	−	0.00787588i
$553$	14.8210	−	8.55690i	0.630252	−	0.363876i
$554$	−15.5319	+	26.9020i	−0.659886	+	1.14296i
$555$	4.22784	+	8.32232i	0.179462	+	0.353263i
$556$	2.53522	+	4.39113i	0.107517	+	0.186225i
$557$	34.9845	+	20.1983i	1.48234	+	0.855830i	0.999799	−	0.0200424i	$-0.00638011\pi$
$557$	34.9845	+	20.1983i	1.48234	+	0.855830i	0.482542	+	0.875873i	$0.339713\pi$
$558$	−5.27184	−	0.774546i	−0.223175	−	0.0327891i
$559$	−0.309564	−	0.536181i	−0.0130932	−	0.0226781i
$560$	−1.83444	−	1.05911i	−0.0775191	−	0.0447557i
$561$	−0.0812888	−	0.0552004i	−0.00343201	−	0.00233056i
$562$	12.6036			0.531651
$563$	−2.74941	−	1.58737i	−0.115874	−	0.0668997i	0.440943	−	0.897535i	$-0.354644\pi$
$563$	−2.74941	−	1.58737i	−0.115874	−	0.0668997i	−0.556817	+	0.830635i	$0.687977\pi$
$564$	−6.45855	−	0.471916i	−0.271954	−	0.0198713i
$565$	−3.27393	−	5.67062i	−0.137735	−	0.238565i
$566$	−3.40453			−0.143103
$567$	4.94396	+	20.9411i	0.207627	+	0.879445i
$568$	3.49783	−	2.01948i	0.146766	−	0.0847353i
$569$	1.90616	−	1.10052i	0.0799104	−	0.0461363i	−0.459512	−	0.888171i	$-0.651976\pi$
$569$	1.90616	−	1.10052i	0.0799104	−	0.0461363i	0.539423	+	0.842035i	$0.318642\pi$
$570$	0.215153	−	2.94454i	0.00901175	−	0.123333i
$571$	−10.7191	−	18.5661i	−0.448582	−	0.776966i	0.549712	−	0.835354i	$-0.314737\pi$
$571$	−10.7191	−	18.5661i	−0.448582	−	0.776966i	−0.998294	+	0.0583879i	$0.981404\pi$
$572$	0.0459676	−	0.0265394i	0.00192200	−	0.00110967i
$573$	1.42625	−	19.5194i	0.0595826	−	0.815436i
$574$	22.3185	+	12.8856i	0.931556	+	0.537834i
$575$	−0.433227	−	0.250124i	−0.0180668	−	0.0104309i
$576$	1.10641	+	2.78852i	0.0461004	+	0.116188i
$577$	−39.0326	−	22.5355i	−1.62495	−	0.938164i	−0.985569	−	0.169272i	$-0.945858\pi$
$577$	−39.0326	−	22.5355i	−1.62495	−	0.938164i	−0.639378	−	0.768892i	$-0.720808\pi$
$578$	−14.7193	+	8.49820i	−0.612243	+	0.353478i
$579$	7.86364	−	3.80498i	0.326802	−	0.158129i
$580$	−0.398377	−	0.690009i	−0.0165417	−	0.0286511i
$581$	10.0243	−	17.3627i	0.415880	−	0.720325i
$582$	−16.2498	−	1.18735i	−0.673577	−	0.0492172i
$583$	−3.29348			−0.136402
$584$		−	1.87998i		−	0.0777940i
$585$	0.0550524	+	0.138751i	0.00227614	+	0.00573663i
$586$			0.122433i			0.00505765i
$587$	−27.2216	−	15.7164i	−1.12356	−	0.648686i	−0.181250	−	0.983437i	$-0.558014\pi$
$587$	−27.2216	−	15.7164i	−1.12356	−	0.648686i	−0.942306	+	0.334752i	$0.891348\pi$
$588$	−2.21852	−	0.162104i	−0.0914903	−	0.00668505i
$589$	−3.41707			−0.140798
$590$	5.20310	−	3.00401i	0.214208	−	0.123673i
$591$	9.92609	+	20.5140i	0.408305	+	0.843833i
$592$	−5.32577	−	2.93874i	−0.218888	−	0.120782i
$593$	27.9062			1.14597			0.572984	−	0.819566i	$-0.305786\pi$
$593$	27.9062			1.14597			0.572984	+	0.819566i	$0.305786\pi$
$594$	4.68476	−	1.47375i	0.192218	−	0.0604687i
$595$	−0.0635710	−	0.110108i	−0.00260616	−	0.00451400i
$596$	−6.34370	+	10.9876i	−0.259848	+	0.450070i
$597$	−14.3366	−	9.73548i	−0.586757	−	0.398447i
$598$	0.00577222	+	0.00333259i	0.000236044	+	0.000136280i
$599$	15.7464			0.643381			0.321691	−	0.946845i	$-0.395749\pi$
$599$	15.7464			0.643381			0.321691	+	0.946845i	$0.395749\pi$
$600$	6.03967	+	4.10133i	0.246568	+	0.167436i
$601$	9.55208			0.389637			0.194819	−	0.980839i	$-0.437588\pi$
$601$	9.55208			0.389637			0.194819	+	0.980839i	$0.437588\pi$
$602$	−26.3568			−1.07422
$603$	−6.05474	−	15.2600i	−0.246568	−	0.621434i
$604$	5.79617	−	10.0393i	0.235843	−	0.408491i
$605$	−7.75491	−	4.47730i	−0.315282	−	0.182028i
$606$	−1.27656	+	17.4707i	−0.0518566	+	0.709699i
$607$	−9.14791	+	5.28155i	−0.371302	+	0.214372i	−0.674027	−	0.738706i	$-0.735437\pi$
$607$	−9.14791	+	5.28155i	−0.371302	+	0.214372i	0.302725	+	0.953078i	$0.402104\pi$
$608$	0.961935	+	1.66612i	0.0390116	+	0.0675701i
$609$	3.08063	+	2.09195i	0.124833	+	0.0847701i
$610$	−7.01739	−	4.05149i	−0.284126	−	0.164040i
$611$	0.181838	−	0.104984i	0.00735639	−	0.00424722i
$612$	−0.0261750	+	0.178156i	−0.00105806	+	0.00720154i
$613$	−10.3008	+	17.8415i	−0.416045	+	0.720611i	−0.995538	−	0.0943666i	$-0.969917\pi$
$613$	−10.3008	+	17.8415i	−0.416045	+	0.720611i	0.579493	+	0.814977i	$0.303251\pi$
$614$			29.3541i			1.18463i
$615$	13.6852	+	9.29315i	0.551841	+	0.374736i
$616$		−	2.25961i		−	0.0910421i
$617$	0.544877	+	0.943755i	0.0219359	+	0.0379941i	0.876785	−	0.480883i	$-0.159684\pi$
$617$	0.544877	+	0.943755i	0.0219359	+	0.0379941i	−0.854849	+	0.518877i	$0.826350\pi$
$618$	−7.19495	−	14.8696i	−0.289423	−	0.598144i
$619$	−4.29133	−	7.43281i	−0.172483	−	0.298750i	0.766804	−	0.641881i	$-0.221846\pi$
$619$	−4.29133	−	7.43281i	−0.172483	−	0.298750i	−0.939287	+	0.343131i	$0.888512\pi$
$620$	−0.786837	+	1.36284i	−0.0316002	+	0.0547331i
$621$	0.454404	+	0.416928i	0.0182346	+	0.0167308i
$622$	6.80655	+	11.7893i	0.272918	+	0.472707i
$623$	5.26267	−	3.03840i	0.210844	−	0.121731i
$624$	−0.0804712	−	0.0546452i	−0.00322142	−	0.00218756i
$625$	13.8411			0.553646
$626$	17.2691			0.690211
$627$	2.83500	−	1.37177i	0.113219	−	0.0547832i
$628$	−1.64261	−	2.84508i	−0.0655472	−	0.113531i
$629$	−0.188645	−	0.312594i	−0.00752176	−	0.0124639i
$630$	6.28718	+	0.923720i	0.250487	+	0.0368019i
$631$	31.3337	+	18.0905i	1.24737	+	0.720172i	0.970585	−	0.240759i	$-0.0773962\pi$
$631$	31.3337	+	18.0905i	1.24737	+	0.720172i	0.276789	+	0.960931i	$0.410730\pi$
$632$	−3.57916	+	6.19928i	−0.142371	+	0.246594i
$633$	−2.00775	−	4.14936i	−0.0798008	−	0.164922i
$634$			7.92126i			0.314593i
$635$	0.950429	+	0.548731i	0.0377166	+	0.0217757i
$636$	2.62886	+	5.43299i	0.104241	+	0.215432i
$637$	0.0624617	−	0.0360623i	0.00247482	−	0.00142884i
$638$	0.424967	−	0.736064i	0.0168246	−	0.0291410i
$639$	−7.51942	+	9.50139i	−0.297464	+	0.375869i
$640$	0.886006			0.0350224
$641$	−21.8964			−0.864856			−0.432428	−	0.901669i	$-0.642343\pi$
$641$	−21.8964			−0.864856			−0.432428	+	0.901669i	$0.642343\pi$
$642$	0.448895	−	6.14349i	0.0177165	−	0.242464i
$643$	18.8057	+	10.8575i	0.741624	+	0.428177i	0.822660	−	0.568534i	$-0.192489\pi$
$643$	18.8057	+	10.8575i	0.741624	+	0.428177i	−0.0810352	+	0.996711i	$0.525823\pi$
$644$	0.245728	−	0.141871i	0.00968304	−	0.00559050i
$645$	−16.8732	−	1.23290i	−0.664382	−	0.0485454i
$646$			0.115476i			0.00454336i
$647$	8.66390	−	5.00211i	0.340613	−	0.196653i	−0.319930	−	0.947441i	$-0.603659\pi$
$647$	8.66390	−	5.00211i	0.340613	−	0.196653i	0.660543	+	0.750788i	$0.270326\pi$
$648$	−6.17050	−	6.55172i	−0.242400	−	0.257376i
$649$	5.55038	+	3.20452i	0.217872	+	0.125788i
$650$	−0.236712			−0.00928463
$651$	0.535980	−	7.33531i	0.0210067	−	0.287493i
$652$	−2.25828	−	1.30382i	−0.0884409	−	0.0510614i
$653$			11.6059i			0.454176i	0.973874	+	0.227088i	$0.0729204\pi$
$653$			11.6059i			0.454176i	−0.973874	+	0.227088i	$0.927080\pi$
$654$	−1.21094	−	2.50262i	−0.0473516	−	0.0978602i
$655$	−4.23051	−	7.32746i	−0.165300	−	0.286307i
$656$	−10.7795			−0.420869
$657$	2.08002	+	5.24236i	0.0811495	+	0.204524i
$658$		−	8.93854i		−	0.348460i
$659$	5.85639	−	10.1436i	0.228133	−	0.395137i	−0.729122	−	0.684384i	$-0.760071\pi$
$659$	5.85639	−	10.1436i	0.228133	−	0.395137i	0.957255	+	0.289246i	$0.0934047\pi$
$660$	0.105698	−	1.44656i	0.00411430	−	0.0563075i
$661$			4.14062i			0.161051i	0.996753	+	0.0805257i	$0.0256599\pi$
$661$			4.14062i			0.161051i	−0.996753	+	0.0805257i	$0.974340\pi$
$662$	−18.2133			−0.707881
$663$	−0.00254302	−	0.00525559i	−9.87627e−5	−	0.000204110i
$664$			8.38591i			0.325436i
$665$	4.07519			0.158029
$666$	18.1025	+	2.30227i	0.701457	+	0.0892111i
$667$	0.106727			0.00413250
$668$		−	10.4610i		−	0.404749i
$669$	41.1652	+	3.00787i	1.59154	+	0.116291i
$670$	−4.84859			−0.187317
$671$		−	8.64382i		−	0.333691i
$672$	−3.72748	+	1.80362i	−0.143791	+	0.0695760i
$673$	16.9120	−	29.2925i	0.651910	−	1.12914i	−0.330749	−	0.943719i	$-0.607301\pi$
$673$	16.9120	−	29.2925i	0.651910	−	1.12914i	0.982659	−	0.185423i	$-0.0593654\pi$
$674$			26.9317i			1.03737i
$675$	−21.3795	−	4.75431i	−0.822898	−	0.182994i
$676$	−12.9968			−0.499879
$677$	−0.621324	−	1.07616i	−0.0238794	−	0.0413603i	0.853839	−	0.520538i	$-0.174268\pi$
$677$	−0.621324	−	1.07616i	−0.0238794	−	0.0413603i	−0.877718	+	0.479177i	$0.840935\pi$
$678$	−12.7664	−	0.932819i	−0.490290	−	0.0358247i
$679$		−	22.4895i		−	0.863069i
$680$	0.0460558	+	0.0265903i	0.00176616	+	0.00101969i
$681$	6.58517	−	3.18636i	0.252344	−	0.122102i
$682$	−1.67871			−0.0642811
$683$	11.2218	+	6.47890i	0.429390	+	0.247908i	0.699087	−	0.715037i	$-0.253590\pi$
$683$	11.2218	+	6.47890i	0.429390	+	0.247908i	−0.269697	+	0.962945i	$0.586923\pi$
$684$	−4.52579	−	3.58172i	−0.173048	−	0.136951i
$685$	−11.0748	+	6.39402i	−0.423145	+	0.244303i
$686$		−	19.8057i		−	0.756185i
$687$	−7.37489	+	10.8603i	−0.281369	+	0.414348i
$688$	9.54746	−	5.51223i	0.363993	−	0.210152i
$689$	−0.169478	−	0.0978482i	−0.00645660	−	0.00372772i
$690$	0.163948	−	0.0793292i	0.00624138	−	0.00302001i
$691$	7.33550			0.279055			0.139528	−	0.990218i	$-0.455442\pi$
$691$	7.33550			0.279055			0.139528	+	0.990218i	$0.455442\pi$
$692$	−8.67685			−0.329844
$693$	2.50005	+	6.30096i	0.0949690	+	0.239354i
$694$	−4.03573	+	6.99009i	−0.153194	+	0.265340i
$695$	−3.89057	+	2.24622i	−0.147578	+	0.0852039i
$696$	−1.55343	−	0.113507i	−0.0588827	−	0.00430247i
$697$	−0.560334	−	0.323509i	−0.0212241	−	0.0122538i
$698$		−	1.91930i		−	0.0726468i
$699$	9.80698	−	14.4419i	0.370934	−	0.546242i
$700$	−5.03851	+	8.72696i	−0.190438	+	0.329848i
$701$	−7.76759	−	4.48462i	−0.293378	−	0.169382i	0.346086	−	0.938203i	$-0.387510\pi$
$701$	−7.76759	−	4.48462i	−0.293378	−	0.169382i	−0.639464	+	0.768821i	$0.720844\pi$
$702$	0.284856	+	0.0633453i	0.0107512	+	0.00239082i
$703$	11.7003	−	0.226743i	0.441283	−	0.00855179i
$704$	0.472571	+	0.818517i	0.0178107	+	0.0308490i
$705$	0.418121	−	5.72231i	0.0157473	−	0.215515i
$706$	−22.3379			−0.840697
$707$	−24.1792			−0.909352
$708$	0.855913	−	11.7139i	0.0321672	−	0.440234i
$709$	−16.4786	+	9.51391i	−0.618866	+	0.357302i	−0.776427	−	0.630207i	$-0.782970\pi$
$709$	−16.4786	+	9.51391i	−0.618866	+	0.357302i	0.157561	+	0.987509i	$0.449637\pi$
$710$	1.78927	+	3.09910i	0.0671500	+	0.116307i
$711$	3.12161	−	21.2468i	0.117070	−	0.796819i
$712$	−1.27090	+	2.20126i	−0.0476288	+	0.0824956i
$713$	−0.105399	−	0.182557i	−0.00394723	−	0.00683680i
$714$	−0.247889	−	0.0181129i	−0.00927701	−	0.000677857i
$715$	0.0235141	+	0.0407275i	0.000879376	+	0.00152312i
$716$		−	13.1014i		−	0.489624i
$717$	−2.74577	+	37.5781i	−0.102543	+	1.40338i
$718$		−	5.88845i		−	0.219755i
$719$	22.3074	−	38.6375i	0.831924	−	1.44093i	−0.0645867	−	0.997912i	$-0.520573\pi$
$719$	22.3074	−	38.6375i	0.831924	−	1.44093i	0.896511	−	0.443022i	$-0.146094\pi$
$720$	−2.47065	+	0.980285i	−0.0920756	+	0.0365331i
$721$	19.7463	−	11.4005i	0.735391	−	0.424578i
$722$	13.2491	+	7.64936i	0.493080	+	0.284680i
$723$	15.0537	−	7.28404i	0.559855	−	0.270896i
$724$	−0.0510943	−	0.0884979i	−0.00189891	−	0.00328900i
$725$	−3.28258	+	1.89520i	−0.121912	+	0.0703859i
$726$	−15.7576	+	7.62462i	−0.584819	+	0.282976i
$727$	−3.75395	−	2.16734i	−0.139226	−	0.0803823i	0.428769	−	0.903414i	$-0.358947\pi$
$727$	−3.75395	−	2.16734i	−0.139226	−	0.0803823i	−0.567995	+	0.823032i	$0.692281\pi$
$728$	0.0671320	−	0.116276i	0.00248808	−	0.00430948i
$729$	24.4554	+	11.4425i	0.905757	+	0.423797i
$730$	1.66567			0.0616492
$731$	0.661720			0.0244746
$732$	−14.2590	+	6.89949i	−0.527028	+	0.255012i
$733$	−44.3867			−1.63946			−0.819729	−	0.572751i	$-0.805876\pi$
$733$	−44.3867			−1.63946			−0.819729	+	0.572751i	$0.805876\pi$
$734$	14.1095	+	8.14610i	0.520789	+	0.300678i
$735$	0.143625	−	1.96562i	0.00529768	−	0.0725030i
$736$	−0.0593415	+	0.102782i	−0.00218736	+	0.00378861i
$737$	−2.58611	−	4.47927i	−0.0952604	−	0.164996i
$738$	30.0589	−	11.9265i	1.10648	−	0.439022i
$739$	−25.5007			−0.938059			−0.469029	−	0.883183i	$-0.655396\pi$
$739$	−25.5007			−0.938059			−0.469029	+	0.883183i	$0.655396\pi$
$740$	2.60374	−	4.71866i	0.0957155	−	0.173461i
$741$	0.186640	+	0.0136375i	0.00685639	+	0.000500986i
$742$	−7.21481	+	4.16547i	−0.264864	+	0.152919i
$743$	−44.8980			−1.64715			−0.823574	−	0.567209i	$-0.808023\pi$
$743$	−44.8980			−1.64715			−0.823574	+	0.567209i	$0.808023\pi$
$744$	1.33994	+	2.76923i	0.0491248	+	0.101525i
$745$	−9.73508	−	5.62055i	−0.356666	−	0.205921i
$746$			26.8249i			0.982128i
$747$	−9.27825	−	23.3843i	−0.339473	−	0.855587i
$748$			0.0567302i			0.00207426i
$749$	8.50249			0.310674
$750$	−7.94437	+	11.6990i	−0.290087	+	0.427186i
$751$	−18.2503	+	31.6105i	−0.665964	+	1.15348i	0.313059	+	0.949734i	$0.398646\pi$
$751$	−18.2503	+	31.6105i	−0.665964	+	1.15348i	−0.979023	+	0.203750i	$0.934687\pi$
$752$	1.86939	+	3.23789i	0.0681698	+	0.118074i
$753$	20.5120	+	13.9290i	0.747499	+	0.507601i
$754$	0.0437364	−	0.0252512i	0.00159278	−	0.000919594i
$755$	8.89483	+	5.13543i	0.323716	+	0.186898i
$756$	8.39864	−	9.15355i	0.305455	−	0.332911i
$757$	−19.4093	−	11.2059i	−0.705442	−	0.407287i	0.103929	−	0.994585i	$-0.466858\pi$
$757$	−19.4093	−	11.2059i	−0.705442	−	0.407287i	−0.809371	+	0.587298i	$0.800192\pi$
$758$	11.8384	+	6.83491i	0.429990	+	0.248255i
$759$	0.160732	+	0.109147i	0.00583419	+	0.00396180i
$760$	−1.47619	+	0.852280i	−0.0535471	+	0.0309155i
$761$	2.93666	+	5.08644i	0.106454	+	0.184383i	0.914331	−	0.404967i	$-0.132717\pi$
$761$	2.93666	+	5.08644i	0.106454	+	0.184383i	−0.807877	+	0.589351i	$0.799384\pi$
$762$	1.93123	−	0.934461i	0.0699609	−	0.0338519i
$763$	3.32339	−	1.91876i	0.120315	−	0.0694637i
$764$	−9.78573	+	5.64979i	−0.354035	+	0.204402i
$765$	−0.157847	−	0.0231912i	−0.00570699	−	0.000838478i
$766$	34.7986			1.25732
$767$	0.190410	+	0.329800i	0.00687530	+	0.0119084i
$768$	0.973034	−	1.43290i	0.0351113	−	0.0517054i
$769$	35.5421	+	20.5202i	1.28168	+	0.739978i	0.977155	−	0.212526i	$-0.0681691\pi$
$769$	35.5421	+	20.5202i	1.28168	+	0.739978i	0.304524	+	0.952505i	$0.401502\pi$
$770$	2.00202			0.0721479
$771$	0.937457	−	12.8299i	0.0337617	−	0.462056i
$772$	−4.36792	−	2.52182i	−0.157205	−	0.0907622i
$773$	−9.25662	−	16.0329i	−0.332937	−	0.576665i	0.650149	−	0.759807i	$-0.274706\pi$
$773$	−9.25662	−	16.0329i	−0.332937	−	0.576665i	−0.983086	+	0.183142i	$0.941373\pi$
$774$	−20.5245	+	25.9344i	−0.737738	+	0.932191i
$775$	6.48345	+	3.74322i	0.232892	+	0.134460i
$776$	4.70343	+	8.14658i	0.168843	+	0.292445i
$777$	−1.34848	+	25.1521i	−0.0483765	+	0.902326i
$778$	−4.12333	+	7.14182i	−0.147829	+	0.256047i
$779$	17.9600	−	10.3692i	0.643482	−	0.371515i
$780$	0.0484160	−	0.0712979i	0.00173357	−	0.00255287i
$781$	−1.90869	+	3.30595i	−0.0682983	+	0.118296i
$782$	−0.00616931	+	0.00356185i	−0.000220614	+	0.000127372i
$783$	4.45737	−	1.40222i	0.159293	−	0.0501111i
$784$	0.642139	+	1.11222i	0.0229335	+	0.0397221i
$785$	2.52076	−	1.45536i	0.0899697	−	0.0519440i
$786$	−16.4964	−	1.20537i	−0.588409	−	0.0429941i
$787$	4.78663	−	8.29068i	0.170625	−	0.295531i	−0.768014	−	0.640433i	$-0.778755\pi$
$787$	4.78663	−	8.29068i	0.170625	−	0.295531i	0.938638	+	0.344903i	$0.112088\pi$
$788$	6.57870	−	11.3946i	0.234356	−	0.405917i
$789$	21.6762	+	44.7977i	0.771693	+	1.59484i
$790$	−5.49260	−	3.17115i	−0.195418	−	0.112825i
$791$		−	17.6685i		−	0.628218i
$792$	−2.22339	−	1.75960i	−0.0790047	−	0.0625245i
$793$	0.256805	−	0.444799i	0.00911940	−	0.0157953i
$794$			24.2614i			0.861005i
$795$	−4.81366	+	2.32918i	−0.170723	+	0.0826075i
$796$			10.0053i			0.354628i
$797$	19.2852	−	11.1343i	0.683115	−	0.394397i	−0.117912	−	0.993024i	$-0.537620\pi$
$797$	19.2852	−	11.1343i	0.683115	−	0.394397i	0.801028	+	0.598627i	$0.204287\pi$
$798$	4.47548	−	6.59064i	0.158430	−	0.233306i
$799$			0.224413i			0.00793917i
$800$		−	4.21499i		−	0.149023i
$801$	1.10843	−	7.54438i	0.0391645	−	0.266568i
$802$	7.01176	−	12.1447i	0.247594	−	0.428845i
$803$	0.888422	+	1.53879i	0.0313517	+	0.0543028i
$804$	−5.32485	+	7.84143i	−0.187793	+	0.276546i
$805$	0.125699	+	0.217716i	0.00443029	+	0.00767349i
$806$	−0.0863840	−	0.0498738i	−0.00304275	−	0.00175673i
$807$	−6.09360	+	8.97351i	−0.214505	+	0.315882i
$808$	8.75864	−	5.05680i	0.308128	−	0.177898i
$809$	33.7269	−	19.4722i	1.18577	−	0.684607i	0.228430	−	0.973560i	$-0.426641\pi$
$809$	33.7269	−	19.4722i	1.18577	−	0.684607i	0.957343	+	0.288954i	$0.0933073\pi$
$810$	5.80486	−	5.46709i	0.203962	−	0.192094i
$811$	14.7020	+	25.4646i	0.516257	+	0.894183i	0.999822	+	0.0188743i	$0.00600823\pi$
$811$	14.7020	+	25.4646i	0.516257	+	0.894183i	−0.483565	+	0.875308i	$0.660658\pi$
$812$		−	2.14993i		−	0.0754476i
$813$	5.77610	+	11.9373i	0.202577	+	0.418660i
$814$	5.74799	−	0.111392i	0.201467	−	0.00390430i
$815$	1.15519	−	2.00084i	0.0404645	−	0.0700865i
$816$	0.0935831	−	0.0452820i	0.00327607	−	0.00158519i
$817$	−10.6048	+	18.3681i	−0.371015	+	0.642617i
$818$	−1.40946	−	2.44126i	−0.0492807	−	0.0853567i
$819$	−0.0585502	+	0.398514i	−0.00204591	+	0.0139252i
$820$		−	9.55070i		−	0.333525i
$821$	15.5010	−	26.8485i	0.540987	−	0.937018i	−0.457860	−	0.889024i	$-0.651384\pi$
$821$	15.5010	−	26.8485i	0.540987	−	0.937018i	0.998848	−	0.0479935i	$-0.0152827\pi$
$822$	−1.82180	+	24.9328i	−0.0635427	+	0.869633i
$823$	5.52528	+	9.57007i	0.192599	+	0.333592i	0.946111	−	0.323843i	$-0.104975\pi$
$823$	5.52528	+	9.57007i	0.192599	+	0.333592i	−0.753512	+	0.657435i	$0.771642\pi$
$824$	−4.76858	+	8.25943i	−0.166122	+	0.287731i
$825$	−6.88174	−	0.502838i	−0.239591	−	0.0175066i
$826$	16.2118			0.564080
$827$	20.8612	−	12.0442i	0.725414	−	0.418818i	−0.0913278	−	0.995821i	$-0.529111\pi$
$827$	20.8612	−	12.0442i	0.725414	−	0.418818i	0.816742	+	0.577003i	$0.195778\pi$
$828$	0.0517555	−	0.352267i	0.00179863	−	0.0122421i
$829$	−2.38189	−	1.37518i	−0.0827264	−	0.0477621i	0.458066	−	0.888918i	$-0.348542\pi$
$829$	−2.38189	−	1.37518i	−0.0827264	−	0.0477621i	−0.540793	+	0.841156i	$0.681876\pi$
$830$	−7.42996			−0.257898
$831$	−48.4322	+	23.4349i	−1.68009	+	0.812946i
$832$			0.0561596i			0.00194698i
$833$			0.0770862i			0.00267088i
$834$	−0.640000	+	8.75891i	−0.0221614	+	0.303296i
$835$	9.26852			0.320750
$836$	−1.57472	−	0.909166i	−0.0544629	−	0.0314441i
$837$	−6.80037	−	6.23953i	−0.235055	−	0.215670i
$838$	0.457469	−	0.264120i	0.0158030	−	0.00912387i
$839$	37.5651			1.29689			0.648446	−	0.761261i	$-0.275419\pi$
$839$	37.5651			1.29689			0.648446	+	0.761261i	$0.275419\pi$
$840$	−1.59801	−	3.30257i	−0.0551367	−	0.113950i
$841$	−14.0957	+	24.4144i	−0.486057	+	0.841876i
$842$	−1.95811	−	3.39154i	−0.0674808	−	0.116880i
$843$	18.0597	+	12.2637i	0.622009	+	0.422385i
$844$	−1.33067	+	2.30479i	−0.0458036	+	0.0793341i
$845$		−	11.5153i		−	0.396138i
$846$	−8.79528	−	6.96060i	−0.302388	−	0.239310i
$847$	−12.0813	−	20.9255i	−0.415120	−	0.719009i
$848$	1.74232	−	3.01779i	0.0598316	−	0.103631i
$849$	−4.87835	−	3.31272i	−0.167425	−	0.113692i
$850$	0.126498	−	0.219101i	0.00433885	−	0.00751511i
$851$	0.373006	+	0.618090i	0.0127865	+	0.0211879i
$852$	6.97707	+	0.509803i	0.239030	+	0.0174656i
$853$			50.6926i			1.73568i	0.496841	+	0.867841i	$0.334493\pi$
$853$			50.6926i			1.73568i	−0.496841	+	0.867841i	$0.665507\pi$
$854$	−10.9324	−	18.9354i	−0.374098	−	0.647957i
$855$	3.17343	−	4.00988i	0.108529	−	0.137135i
$856$	−3.07993	+	1.77820i	−0.105270	+	0.0607776i
$857$	−45.0648	+	26.0182i	−1.53938	+	0.888763i	−0.540508	+	0.841339i	$0.681768\pi$
$857$	−45.0648	+	26.0182i	−1.53938	+	0.888763i	−0.998875	+	0.0474243i	$0.984899\pi$
$858$	0.0916907	+	0.00669970i	0.00313027	+	0.000228724i
$859$	46.2770	+	26.7180i	1.57895	+	0.911608i	0.995006	+	0.0998150i	$0.0318251\pi$
$859$	46.2770	+	26.7180i	1.57895	+	0.911608i	0.583945	+	0.811793i	$0.301508\pi$
$860$	4.88386	+	8.45910i	0.166538	+	0.288453i
$861$	19.4421	+	40.1804i	0.662584	+	1.36935i
$862$	20.3282	+	35.2095i	0.692382	+	1.19924i
$863$	16.0125	−	27.7344i	0.545071	−	0.944091i	−0.453531	−	0.891240i	$-0.649836\pi$
$863$	16.0125	−	27.7344i	0.545071	−	0.944091i	0.998602	−	0.0528505i	$-0.0168307\pi$
$864$	−1.12795	+	5.07225i	−0.0383737	+	0.172561i
$865$		−	7.68774i		−	0.261391i
$866$		−	8.57685i		−	0.291453i
$867$	−29.3604	−	2.14531i	−0.997130	−	0.0728587i
$868$	−3.67743	+	2.12317i	−0.124820	+	0.0720650i
$869$		−	6.76562i		−	0.229508i
$870$	0.100568	−	1.37635i	0.00340956	−	0.0466626i
$871$		−	0.307329i		−	0.0104134i
$872$	−0.802574	+	1.39010i	−0.0271786	+	0.0470747i
$873$	−22.1291	−	17.5130i	−0.748956	−	0.592725i
$874$		−	0.228331i		−	0.00772340i
$875$	−16.9043	−	9.75971i	−0.571470	−	0.329939i
$876$	1.82928	−	2.69382i	0.0618057	−	0.0910158i
$877$	−26.6687	+	46.1916i	−0.900539	+	1.55978i	−0.0737438	+	0.997277i	$0.523495\pi$
$877$	−26.6687	+	46.1916i	−0.900539	+	1.55978i	−0.826795	+	0.562503i	$0.809839\pi$
$878$	−0.762890	+	1.32136i	−0.0257463	+	0.0445939i
$879$	−0.119131	+	0.175434i	−0.00401819	+	0.00591724i
$880$	−0.725211	+	0.418700i	−0.0244468	+	0.0141144i
$881$	−27.0638	−	46.8758i	−0.911802	−	1.57929i	−0.811517	−	0.584328i	$-0.801358\pi$
$881$	−27.0638	−	46.8758i	−0.911802	−	1.57929i	−0.100284	−	0.994959i	$-0.531975\pi$
$882$	−3.02119	−	2.39097i	−0.101729	−	0.0805083i
$883$	37.9572	−	21.9146i	1.27736	−	0.737485i	0.300999	−	0.953624i	$-0.402680\pi$
$883$	37.9572	−	21.9146i	1.27736	−	0.737485i	0.976363	+	0.216139i	$0.0693466\pi$
$884$	−0.00168543	+	0.00291926i	−5.66872e−5	+	9.81852e-5i
$885$	10.3785	+	0.758344i	0.348871	+	0.0254914i
$886$	14.1098	−	8.14632i	0.474030	−	0.273681i
$887$	−17.8393	+	30.8985i	−0.598984	+	1.03747i	0.393988	+	0.919116i	$0.371095\pi$
$887$	−17.8393	+	30.8985i	−0.598984	+	1.03747i	−0.992971	+	0.118355i	$0.962238\pi$
$888$	−4.77180	−	9.39308i	−0.160131	−	0.315211i
$889$	1.48067	+	2.56460i	0.0496601	+	0.0860138i
$890$	−1.95033	−	1.12602i	−0.0653751	−	0.0377443i
$891$	8.14681	+	2.44669i	0.272928	+	0.0819673i
$892$	−11.9150	−	20.6375i	−0.398945	−	0.690993i
$893$	−6.22927	−	3.59647i	−0.208455	−	0.120351i
$894$	−19.7812	+	9.57152i	−0.661582	+	0.320119i
$895$	11.6079			0.388011
$896$	2.07046	+	1.19538i	0.0691691	+	0.0399348i
$897$	0.00502830	+	0.0103918i	0.000167890	+	0.000346974i
$898$	−13.6114	−	23.5757i	−0.454220	−	0.786732i
$899$	−1.59723			−0.0532705
$900$	4.66351	+	11.7536i	0.155450	+	0.391787i
$901$	0.181137	−	0.104579i	0.00603454	−	0.00348404i
$902$	8.82320	−	5.09408i	0.293781	−	0.169614i
$903$	−37.7667	−	25.6461i	−1.25680	−	0.853447i
$904$	3.69516	+	6.40020i	0.122899	+	0.212868i
$905$	0.0784097	−	0.0452698i	0.00260643	−	0.00150482i
$906$	18.0739	−	8.74539i	0.600464	−	0.290546i
$907$	−37.6515	−	21.7381i	−1.25020	−	0.721801i	−0.279048	−	0.960277i	$-0.590019\pi$
$907$	−37.6515	−	21.7381i	−1.25020	−	0.721801i	−0.971148	+	0.238476i	$0.923352\pi$
$908$	−3.65778	−	2.11182i	−0.121388	−	0.0700832i
$909$	−18.8288	+	23.7917i	−0.624511	+	0.789120i
$910$	0.103021	+	0.0594793i	0.00341512	+	0.00197172i
$911$	−7.65102	+	4.41732i	−0.253489	+	0.146352i	−0.621361	−	0.783524i	$-0.713420\pi$
$911$	−7.65102	+	4.41732i	−0.253489	+	0.146352i	0.367872	+	0.929877i	$0.380087\pi$
$912$	−0.242834	+	3.32338i	−0.00804105	+	0.110048i
$913$	−3.96294	−	6.86401i	−0.131154	−	0.227166i
$914$	3.02121	−	5.23289i	0.0999328	−	0.173089i
$915$	−6.11299	−	12.6335i	−0.202089	−	0.417652i
$916$	7.57927			0.250426
$917$		−	22.8308i		−	0.753940i
$918$	−0.210858	+	0.229811i	−0.00695936	+	0.00758490i
$919$		−	4.43160i		−	0.146185i	−0.997325	−	0.0730924i	$-0.976713\pi$
$919$		−	4.43160i		−	0.146185i	0.997325	−	0.0730924i	$-0.0232868\pi$
$920$	−0.0910658	−	0.0525769i	−0.00300235	−	0.00173341i
$921$	−28.5625	+	42.0614i	−0.941166	+	1.38597i
$922$	−33.4341			−1.10109
$923$	−0.196437	+	0.113413i	−0.00646580	+	0.00373303i
$924$	2.19867	−	3.23779i	0.0723310	−	0.106515i
$925$	−22.4481	−	12.3868i	−0.738088	−	0.407275i
$926$	17.2487			0.566828
$927$	4.15899	−	28.3076i	0.136599	−	0.929744i
$928$	0.449633	+	0.778787i	0.0147599	+	0.0255649i
$929$	−12.9189	+	22.3761i	−0.423854	+	0.734137i	−0.996313	−	0.0857970i	$-0.972656\pi$
$929$	−12.9189	+	22.3761i	−0.423854	+	0.734137i	0.572459	+	0.819934i	$0.305990\pi$
$930$	−2.45355	+	1.18720i	−0.0804551	+	0.0389298i
$931$	−2.13976	−	1.23539i	−0.0701279	−	0.0404884i
$932$	−10.0788			−0.330141
$933$	−1.71827	+	23.5159i	−0.0562536	+	0.769875i
$934$	15.9028			0.520356
$935$	−0.0502633			−0.00164379
$936$	−0.0621355	−	0.156602i	−0.00203096	−	0.00511871i
$937$	−22.0145	+	38.1302i	−0.719182	+	1.24566i	0.242143	+	0.970241i	$0.422150\pi$
$937$	−22.0145	+	38.1302i	−0.719182	+	1.24566i	−0.961324	+	0.275418i	$0.911184\pi$
$938$	−11.3304	−	6.54161i	−0.369951	−	0.213591i
$939$	24.7449	+	16.8034i	0.807518	+	0.548358i
$940$	−2.86878	+	1.65629i	−0.0935694	+	0.0540223i
$941$	−14.5666	−	25.2302i	−0.474859	−	0.822480i	0.524726	−	0.851271i	$-0.324168\pi$
$941$	−14.5666	−	25.2302i	−0.474859	−	0.822480i	−0.999585	+	0.0287908i	$0.990834\pi$
$942$	0.414666	−	5.67503i	0.0135105	−	0.184903i
$943$	1.10794	+	0.639672i	0.0360796	+	0.0208306i
$944$	−5.87254	+	3.39051i	−0.191135	+	0.110352i
$945$	8.11009	+	7.44124i	0.263821	+	0.242064i
$946$	−5.20984	+	9.02370i	−0.169386	+	0.293386i
$947$		−	35.3521i		−	1.14879i	−0.818579	−	0.574394i	$-0.805238\pi$
$947$		−	35.3521i		−	1.14879i	0.818579	−	0.574394i	$-0.194762\pi$
$948$	−11.1607	+	5.40031i	−0.362482	+	0.175394i
$949$			0.105579i			0.00342723i
$950$	4.05455	+	7.02269i	0.131547	+	0.227846i
$951$	−7.70765	+	11.3504i	−0.249938	+	0.368061i
$952$	0.0717502	+	0.124275i	0.00232544	+	0.00402777i
$953$	−5.55775	+	9.62630i	−0.180033	+	0.311827i	−0.941892	−	0.335917i	$-0.890954\pi$
$953$	−5.55775	+	9.62630i	−0.180033	+	0.311827i	0.761858	+	0.647744i	$0.224287\pi$
$954$	−1.51959	+	10.3429i	−0.0491986	+	0.334864i
$955$	−5.00575	−	8.67021i	−0.161982	−	0.280561i
$956$	18.8391	−	10.8768i	0.609301	−	0.351780i
$957$	1.32515	−	0.641200i	0.0428360	−	0.0207270i
$958$	12.1996			0.394152
$959$	−34.5067			−1.11428
$960$	1.26956	+	0.862114i	0.0409748	+	0.0278246i
$961$	−13.9227	−	24.1147i	−0.449118	−	0.777895i
$962$	0.299093	+	0.165039i	0.00964315	+	0.00532106i
$963$	6.62104	−	8.36622i	0.213360	−	0.269598i
$964$	−8.36170	−	4.82763i	−0.269312	−	0.155488i
$965$	2.23434	−	3.87000i	0.0719261	−	0.124580i
$966$	0.490149	+	0.0358144i	0.0157703	+	0.00115231i
$967$		−	31.5150i		−	1.01345i	−0.862107	−	0.506726i	$-0.830855\pi$
$967$		−	31.5150i		−	1.01345i	0.862107	−	0.506726i	$-0.169145\pi$
$968$	8.75266	+	5.05335i	0.281321	+	0.162421i
$969$	−0.112362	+	0.165466i	−0.00360960	+	0.00531554i
$970$	−7.21791	+	4.16726i	−0.231753	+	0.133803i
$971$	16.1869	−	28.0366i	0.519464	−	0.899737i	−0.480280	−	0.877115i	$-0.659465\pi$
$971$	16.1869	−	28.0366i	0.519464	−	0.899737i	0.999744	−	0.0226224i	$-0.00720156\pi$
$972$	−2.46667	−	15.3921i	−0.0791184	−	0.493701i
$973$	−12.1222			−0.388620
$974$	22.4792			0.720278
$975$	−0.339185	−	0.230329i	−0.0108626	−	0.00737644i
$976$	7.92026	+	4.57276i	0.253521	+	0.146371i
$977$	35.5863	−	20.5458i	1.13851	−	0.657317i	0.192446	−	0.981308i	$-0.438358\pi$
$977$	35.5863	−	20.5458i	1.13851	−	0.657317i	0.946060	+	0.323991i	$0.105025\pi$
$978$	−1.96723	−	4.06562i	−0.0629050	−	0.130004i
$979$		−	2.40235i		−	0.0767796i
$980$	−0.985431	+	0.568939i	−0.0314784	+	0.0181741i
$981$	0.699977	−	4.76430i	0.0223485	−	0.152112i
$982$	8.89992	+	5.13837i	0.284008	+	0.163972i
$983$	26.8909			0.857687			0.428843	−	0.903379i	$-0.358921\pi$
$983$	26.8909			0.857687			0.428843	+	0.903379i	$0.358921\pi$
$984$	−15.4460	−	10.4888i	−0.492399	−	0.334371i
$985$	10.0957	+	5.82876i	0.321676	+	0.185720i
$986$			0.0539766i			0.00171896i
$987$	8.69750	−	12.8080i	0.276844	−	0.407684i
$988$	−0.0540219	−	0.0935687i	−0.00171867	−	0.00297682i
$989$	−1.30841			−0.0416052
$990$	1.55901	−	1.96994i	0.0495486	−	0.0626087i
$991$			10.2573i			0.325834i	0.986640	+	0.162917i	$0.0520903\pi$
$991$			10.2573i			0.325834i	−0.986640	+	0.162917i	$0.947910\pi$
$992$	0.888073	−	1.53819i	0.0281963	−	0.0488375i
$993$	−26.0979	−	17.7222i	−0.828192	−	0.562397i
$994$			9.65615i			0.306275i
$995$	−8.86474			−0.281031
$996$	−8.15978	+	12.0162i	−0.258552	+	0.380747i
$997$		−	43.2086i		−	1.36843i	−0.729280	−	0.684216i	$-0.760145\pi$
$997$		−	43.2086i		−	1.36843i	0.729280	−	0.684216i	$-0.239855\pi$
$998$	−36.1940			−1.14570
$999$	23.6989	+	20.9132i	0.749799	+	0.661666i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.13	✓	76
3.2	odd	2		1998.2.k.a.1063.30		76
9.2	odd	6		1998.2.t.a.397.31		76
9.7	even	3		666.2.t.a.619.1	yes	76
37.11	even	6		666.2.t.a.85.1	yes	76
111.11	odd	6		1998.2.t.a.307.31		76
333.11	odd	6		1998.2.k.a.1639.9		76
333.196	even	6	inner	666.2.k.a.529.32	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.13	✓	76	1.1	even	1	trivial
666.2.k.a.529.32	yes	76	333.196	even	6	inner
666.2.t.a.85.1	yes	76	37.11	even	6
666.2.t.a.619.1	yes	76	9.7	even	3
1998.2.k.a.1063.30		76	3.2	odd	2
1998.2.k.a.1639.9		76	333.11	odd	6
1998.2.t.a.307.31		76	111.11	odd	6
1998.2.t.a.397.31		76	9.2	odd	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.973034 - 1.43290i) q^{3} -1.00000 q^{4} -0.886006i q^{5} +(-1.43290 - 0.973034i) q^{6} +(1.19538 - 2.07046i) q^{7} +1.00000i q^{8} +(-1.10641 - 2.78852i) q^{9} -0.886006 q^{10} +(-0.472571 - 0.818517i) q^{11} +(-0.973034 + 1.43290i) q^{12} -0.0561596i q^{13} +(-2.07046 - 1.19538i) q^{14} +(-1.26956 - 0.862114i) q^{15} +1.00000 q^{16} +(0.0519814 + 0.0300115i) q^{17} +(-2.78852 + 1.10641i) q^{18} +(-1.66612 + 0.961935i) q^{19} +0.886006i q^{20} +(-1.80362 - 3.72748i) q^{21} +(-0.818517 + 0.472571i) q^{22} +(-0.102782 - 0.0593415i) q^{23} +(1.43290 + 0.973034i) q^{24} +4.21499 q^{25} -0.0561596 q^{26} +(-5.07225 - 1.12795i) q^{27} +(-1.19538 + 2.07046i) q^{28} +(-0.778787 + 0.449633i) q^{29} +(-0.862114 + 1.26956i) q^{30} +(1.53819 + 0.888073i) q^{31} -1.00000i q^{32} +(-1.63268 - 0.119297i) q^{33} +(0.0300115 - 0.0519814i) q^{34} +(-1.83444 - 1.05911i) q^{35} +(1.10641 + 2.78852i) q^{36} +(-5.32577 - 2.93874i) q^{37} +(0.961935 + 1.66612i) q^{38} +(-0.0804712 - 0.0546452i) q^{39} +0.886006 q^{40} -10.7795 q^{41} +(-3.72748 + 1.80362i) q^{42} +(9.54746 - 5.51223i) q^{43} +(0.472571 + 0.818517i) q^{44} +(-2.47065 + 0.980285i) q^{45} +(-0.0593415 + 0.102782i) q^{46} +(1.86939 + 3.23789i) q^{47} +(0.973034 - 1.43290i) q^{48} +(0.642139 + 1.11222i) q^{49} -4.21499i q^{50} +(0.0935831 - 0.0452820i) q^{51} +0.0561596i q^{52} +(1.74232 - 3.01779i) q^{53} +(-1.12795 + 5.07225i) q^{54} +(-0.725211 + 0.418700i) q^{55} +(2.07046 + 1.19538i) q^{56} +(-0.242834 + 3.32338i) q^{57} +(0.449633 + 0.778787i) q^{58} +(-5.87254 + 3.39051i) q^{59} +(1.26956 + 0.862114i) q^{60} +(7.92026 + 4.57276i) q^{61} +(0.888073 - 1.53819i) q^{62} +(-7.09609 - 1.04257i) q^{63} -1.00000 q^{64} -0.0497577 q^{65} +(-0.119297 + 1.63268i) q^{66} +5.47242 q^{67} +(-0.0519814 - 0.0300115i) q^{68} +(-0.185041 + 0.0895358i) q^{69} +(-1.05911 + 1.83444i) q^{70} +(-2.01948 - 3.49783i) q^{71} +(2.78852 - 1.10641i) q^{72} -1.87998 q^{73} +(-2.93874 + 5.32577i) q^{74} +(4.10133 - 6.03967i) q^{75} +(1.66612 - 0.961935i) q^{76} -2.25961 q^{77} +(-0.0546452 + 0.0804712i) q^{78} +(6.19928 + 3.57916i) q^{79} -0.886006i q^{80} +(-6.55172 + 6.17050i) q^{81} +10.7795i q^{82} +8.38591 q^{83} +(1.80362 + 3.72748i) q^{84} +(0.0265903 - 0.0460558i) q^{85} +(-5.51223 - 9.54746i) q^{86} +(-0.113507 + 1.55343i) q^{87} +(0.818517 - 0.472571i) q^{88} +(2.20126 + 1.27090i) q^{89} +(0.980285 + 2.47065i) q^{90} +(-0.116276 - 0.0671320i) q^{91} +(0.102782 + 0.0593415i) q^{92} +(2.76923 - 1.33994i) q^{93} +(3.23789 - 1.86939i) q^{94} +(0.852280 + 1.47619i) q^{95} +(-1.43290 - 0.973034i) q^{96} +(8.14658 - 4.70343i) q^{97} +(1.11222 - 0.642139i) q^{98} +(-1.75960 + 2.22339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

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