LMFDB - Embedded newform 77.2.i.a.10.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [77,2,Mod(10,77)] 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("77.10"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(77, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 77 = 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	77.i (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:	$0.614848095564$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 8x^{10} + 47x^{8} - 122x^{6} + 233x^{4} - 119x^{2} + 49 $ x^12 - 8x^10 + 47x^8 - 122x^6 + 233x^4 - 119*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			10.3
Root			$-0.636099 - 0.367252i$ of defining polynomial
Character	$\chi$	$=$	77.10
Dual form			77.2.i.a.54.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.636099 + 0.367252i) q^{2} +(1.02704 + 0.592963i) q^{3} +(-0.730252 + 1.26483i) q^{4} +(0.136673 - 0.0789082i) q^{5} -0.871067 q^{6} +(1.12959 + 2.39249i) q^{7} -2.54175i q^{8} +(-0.796790 - 1.38008i) q^{9} +(-0.0579584 + 0.100387i) q^{10} +(3.30905 + 0.224035i) q^{11} +(-1.50000 + 0.866025i) q^{12} -2.14326 q^{13} +(-1.59718 - 1.10702i) q^{14} +0.187159 q^{15} +(-0.527042 - 0.912864i) q^{16} +(2.20122 - 3.81263i) q^{17} +(1.01367 + 0.585245i) q^{18} +(-3.07229 - 5.32136i) q^{19} +0.230492i q^{20} +(-0.258524 + 3.12700i) q^{21} +(-2.18716 + 1.07275i) q^{22} +(-1.20321 - 2.08402i) q^{23} +(1.50717 - 2.61049i) q^{24} +(-2.48755 + 4.30856i) q^{25} +(1.36333 - 0.787117i) q^{26} -5.44765i q^{27} +(-3.85099 - 0.318380i) q^{28} +2.10577i q^{29} +(-0.119051 + 0.0687343i) q^{30} +(3.69076 + 2.13086i) q^{31} +(5.07295 + 2.92887i) q^{32} +(3.26569 + 2.19224i) q^{33} +3.23361i q^{34} +(0.343172 + 0.237856i) q^{35} +2.32743 q^{36} +(3.46050 + 5.99377i) q^{37} +(3.90856 + 2.25661i) q^{38} +(-2.20122 - 1.27088i) q^{39} +(-0.200565 - 0.347389i) q^{40} -6.42979 q^{41} +(-0.983948 - 2.08402i) q^{42} +6.98850i q^{43} +(-2.69981 + 4.02180i) q^{44} +(-0.217799 - 0.125747i) q^{45} +(1.53072 + 0.883762i) q^{46} +(3.21780 - 1.85780i) q^{47} -1.25007i q^{48} +(-4.44805 + 5.40507i) q^{49} -3.65422i q^{50} +(4.52150 - 2.61049i) q^{51} +(1.56512 - 2.71087i) q^{52} +(0.160117 - 0.277330i) q^{53} +(2.00066 + 3.46524i) q^{54} +(0.469936 - 0.230492i) q^{55} +(6.08113 - 2.87114i) q^{56} -7.28701i q^{57} +(-0.773346 - 1.33947i) q^{58} +(-11.6893 - 6.74882i) q^{59} +(-0.136673 + 0.236725i) q^{60} +(-3.41546 - 5.91575i) q^{61} -3.13025 q^{62} +(2.40179 - 3.46524i) q^{63} -2.19436 q^{64} +(-0.292926 + 0.169121i) q^{65} +(-2.88240 - 0.195149i) q^{66} +(1.32743 - 2.29918i) q^{67} +(3.21490 + 5.56836i) q^{68} -2.85384i q^{69} +(-0.305644 - 0.0252690i) q^{70} -3.51459 q^{71} +(-3.50782 + 2.02524i) q^{72} +(-1.76569 + 3.05826i) q^{73} +(-4.40244 - 2.54175i) q^{74} +(-5.10963 + 2.95005i) q^{75} +8.97419 q^{76} +(3.20187 + 8.16995i) q^{77} +1.86693 q^{78} +(1.30660 - 0.754366i) q^{79} +(-0.144065 - 0.0831759i) q^{80} +(0.839883 - 1.45472i) q^{81} +(4.08998 - 2.36135i) q^{82} +9.49123 q^{83} +(-3.76635 - 2.61049i) q^{84} -0.694778i q^{85} +(-2.56654 - 4.44537i) q^{86} +(-1.24864 + 2.16271i) q^{87} +(0.569441 - 8.41078i) q^{88} +(-11.7448 + 6.78089i) q^{89} +0.184723 q^{90} +(-2.42101 - 5.12774i) q^{91} +3.51459 q^{92} +(2.52704 + 4.37697i) q^{93} +(-1.36456 + 2.36348i) q^{94} +(-0.839798 - 0.484858i) q^{95} +(3.47342 + 6.01614i) q^{96} +3.55778i q^{97} +(0.844377 - 5.07171i) q^{98} +(-2.32743 - 4.74526i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{11} - 18 q^{12} + 8 q^{14} - 20 q^{15} + 12 q^{16} - 4 q^{22} - 20 q^{23} + 14 q^{25} + 18 q^{26} + 6 q^{31} + 18 q^{33} - 12 q^{36} + 16 q^{37} - 48 q^{38} + 16 q^{42}+ \cdots + 12 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^11 - 18 * q^12 + 8 * q^14 - 20 * q^15 + 12 * q^16 - 4 * q^22 - 20 * q^23 + 14 * q^25 + 18 * q^26 + 6 * q^31 + 18 * q^33 - 12 * q^36 + 16 * q^37 - 48 * q^38 + 16 * q^42 + 20 * q^44 + 54 * q^45 - 18 * q^47 + 16 * q^49 - 2 * q^53 + 18 * q^56 - 6 * q^58 - 12 * q^59 + 28 * q^64 - 42 * q^66 - 24 * q^67 - 58 * q^70 + 20 * q^71 - 78 * q^75 - 50 * q^77 + 8 * q^78 + 30 * q^80 + 14 * q^81 + 54 * q^82 - 38 * q^86 - 4 * q^88 - 66 * q^89 + 22 * q^91 - 20 * q^92 + 12 * q^93 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/77\mathbb{Z}\right)^\times$.

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.636099	+	0.367252i	−0.449790	+	0.259686i	−0.707741	−	0.706472i	$-0.750286\pi$
$2$	−0.636099	+	0.367252i	−0.449790	+	0.259686i	0.257952	+	0.966158i	$0.416952\pi$
$3$	1.02704	+	0.592963i	0.592963	+	0.342347i	0.766268	−	0.642521i	$-0.222111\pi$
$3$	1.02704	+	0.592963i	0.592963	+	0.342347i	−0.173305	+	0.984868i	$0.555445\pi$
$4$	−0.730252	+	1.26483i	−0.365126	+	0.632417i
$5$	0.136673	−	0.0789082i	0.0611221	−	0.0352888i	−0.469128	−	0.883130i	$-0.655432\pi$
$5$	0.136673	−	0.0789082i	0.0611221	−	0.0352888i	0.530250	+	0.847842i	$0.322098\pi$
$6$	−0.871067			−0.355611
$7$	1.12959	+	2.39249i	0.426945	+	0.904278i
$7$	1.12959	+	2.39249i	0.426945	+	0.904278i
$8$		−	2.54175i		−	0.898645i
$9$	−0.796790	−	1.38008i	−0.265597	−	0.460027i
$10$	−0.0579584	+	0.100387i	−0.0183280	+	0.0317451i
$11$	3.30905	+	0.224035i	0.997716	+	0.0675490i
$11$	3.30905	+	0.224035i	0.997716	+	0.0675490i
$12$	−1.50000	+	0.866025i	−0.433013	+	0.250000i
$13$	−2.14326			−0.594434			−0.297217	−	0.954810i	$-0.596059\pi$
$13$	−2.14326			−0.594434			−0.297217	+	0.954810i	$0.596059\pi$
$14$	−1.59718	−	1.10702i	−0.426864	−	0.295863i
$15$	0.187159			0.0483242
$16$	−0.527042	−	0.912864i	−0.131761	−	0.228216i
$17$	2.20122	−	3.81263i	0.533875	−	0.924698i	−0.465342	−	0.885131i	$-0.654069\pi$
$17$	2.20122	−	3.81263i	0.533875	−	0.924698i	0.999217	−	0.0395673i	$-0.0125980\pi$
$18$	1.01367	+	0.585245i	0.238925	+	0.137943i
$19$	−3.07229	−	5.32136i	−0.704831	−	1.22080i	−0.966752	−	0.255714i	$-0.917689\pi$
$19$	−3.07229	−	5.32136i	−0.704831	−	1.22080i	0.261921	−	0.965089i	$-0.415644\pi$
$20$			0.230492i			0.0515395i
$21$	−0.258524	+	3.12700i	−0.0564145	+	0.682367i
$22$	−2.18716	+	1.07275i	−0.466304	+	0.228710i
$23$	−1.20321	−	2.08402i	−0.250887	−	0.434549i	0.712883	−	0.701282i	$-0.247389\pi$
$23$	−1.20321	−	2.08402i	−0.250887	−	0.434549i	−0.963770	+	0.266734i	$0.914055\pi$
$24$	1.50717	−	2.61049i	0.307649	−	0.532863i
$25$	−2.48755	+	4.30856i	−0.497509	+	0.861712i
$26$	1.36333	−	0.787117i	0.267370	−	0.154366i
$27$		−	5.44765i		−	1.04840i
$28$	−3.85099	−	0.318380i	−0.727769	−	0.0601681i
$29$			2.10577i			0.391031i	0.980701	+	0.195515i	$0.0626380\pi$
$29$			2.10577i			0.391031i	−0.980701	+	0.195515i	$0.937362\pi$
$30$	−0.119051	+	0.0687343i	−0.0217357	+	0.0125491i
$31$	3.69076	+	2.13086i	0.662880	+	0.382714i	0.793373	−	0.608735i	$-0.208323\pi$
$31$	3.69076	+	2.13086i	0.662880	+	0.382714i	−0.130494	+	0.991449i	$0.541656\pi$
$32$	5.07295	+	2.92887i	0.896779	+	0.517755i
$33$	3.26569	+	2.19224i	0.568483	+	0.381620i
$34$			3.23361i			0.554560i
$35$	0.343172	+	0.237856i	0.0580067	+	0.0402049i
$36$	2.32743			0.387905
$37$	3.46050	+	5.99377i	0.568903	+	0.985370i	0.996675	+	0.0814827i	$0.0259655\pi$
$37$	3.46050	+	5.99377i	0.568903	+	0.985370i	−0.427771	+	0.903887i	$0.640701\pi$
$38$	3.90856	+	2.25661i	0.634052	+	0.366070i
$39$	−2.20122	−	1.27088i	−0.352478	−	0.203503i
$40$	−0.200565	−	0.347389i	−0.0317121	−	0.0549270i
$41$	−6.42979			−1.00416			−0.502082	−	0.864820i	$-0.667433\pi$
$41$	−6.42979			−1.00416			−0.502082	+	0.864820i	$0.667433\pi$
$42$	−0.983948	−	2.08402i	−0.151827	−	0.321571i
$43$			6.98850i			1.06574i	0.846198	+	0.532868i	$0.178886\pi$
$43$			6.98850i			1.06574i	−0.846198	+	0.532868i	$0.821114\pi$
$44$	−2.69981	+	4.02180i	−0.407011	+	0.606309i
$45$	−0.217799	−	0.125747i	−0.0324676	−	0.0187452i
$46$	1.53072	+	0.883762i	0.225692	+	0.130304i
$47$	3.21780	−	1.85780i	0.469364	−	0.270988i	−0.246609	−	0.969115i	$-0.579316\pi$
$47$	3.21780	−	1.85780i	0.469364	−	0.270988i	0.715974	+	0.698127i	$0.245983\pi$
$48$		−	1.25007i		−	0.180431i
$49$	−4.44805	+	5.40507i	−0.635436	+	0.772154i
$50$		−	3.65422i		−	0.516785i
$51$	4.52150	−	2.61049i	0.633136	−	0.365541i
$52$	1.56512	−	2.71087i	0.217044	−	0.375931i
$53$	0.160117	−	0.277330i	0.0219937	−	0.0380942i	−0.854819	−	0.518926i	$-0.826332\pi$
$53$	0.160117	−	0.277330i	0.0219937	−	0.0380942i	0.876813	+	0.480832i	$0.159665\pi$
$54$	2.00066	+	3.46524i	0.272255	+	0.471559i
$55$	0.469936	−	0.230492i	0.0633662	−	0.0310795i
$56$	6.08113	−	2.87114i	0.812625	−	0.383672i
$57$		−	7.28701i		−	0.965189i
$58$	−0.773346	−	1.33947i	−0.101545	−	0.175882i
$59$	−11.6893	−	6.74882i	−1.52182	−	0.878621i	−0.999668	−	0.0257667i	$-0.991797\pi$
$59$	−11.6893	−	6.74882i	−1.52182	−	0.878621i	−0.522149	−	0.852855i	$-0.674869\pi$
$60$	−0.136673	+	0.236725i	−0.0176444	+	0.0305610i
$61$	−3.41546	−	5.91575i	−0.437305	−	0.757434i	0.560176	−	0.828374i	$-0.310734\pi$
$61$	−3.41546	−	5.91575i	−0.437305	−	0.757434i	−0.997481	+	0.0709395i	$0.977400\pi$
$62$	−3.13025			−0.397542
$63$	2.40179	−	3.46524i	0.302597	−	0.436579i
$64$	−2.19436			−0.274294
$65$	−0.292926	+	0.169121i	−0.0363331	+	0.0209769i
$66$	−2.88240	−	0.195149i	−0.354799	−	0.0240212i
$67$	1.32743	−	2.29918i	0.162171	−	0.280889i	−0.773476	−	0.633826i	$-0.781484\pi$
$67$	1.32743	−	2.29918i	0.162171	−	0.280889i	0.935647	+	0.352937i	$0.114817\pi$
$68$	3.21490	+	5.56836i	0.389863	+	0.675263i
$69$		−	2.85384i		−	0.343562i
$70$	−0.305644	−	0.0252690i	−0.0365315	−	0.00302023i
$71$	−3.51459			−0.417105			−0.208552	−	0.978011i	$-0.566875\pi$
$71$	−3.51459			−0.417105			−0.208552	+	0.978011i	$0.566875\pi$
$72$	−3.50782	+	2.02524i	−0.413401	+	0.238677i
$73$	−1.76569	+	3.05826i	−0.206658	+	0.357943i	−0.950660	−	0.310235i	$-0.899592\pi$
$73$	−1.76569	+	3.05826i	−0.206658	+	0.357943i	0.744002	+	0.668178i	$0.232925\pi$
$74$	−4.40244	−	2.54175i	−0.511774	−	0.295473i
$75$	−5.10963	+	2.95005i	−0.590009	+	0.340642i
$76$	8.97419			1.02941
$77$	3.20187	+	8.16995i	0.364887	+	0.931052i
$78$	1.86693			0.211388
$79$	1.30660	−	0.754366i	0.147004	−	0.0848728i	−0.424694	−	0.905337i	$-0.639618\pi$
$79$	1.30660	−	0.754366i	0.147004	−	0.0848728i	0.571698	+	0.820464i	$0.306285\pi$
$80$	−0.144065	−	0.0831759i	−0.0161070	−	0.00929935i
$81$	0.839883	−	1.45472i	0.0933204	−	0.161636i
$82$	4.08998	−	2.36135i	0.451663	−	0.260768i
$83$	9.49123			1.04180			0.520899	−	0.853618i	$-0.325597\pi$
$83$	9.49123			1.04180			0.520899	+	0.853618i	$0.325597\pi$
$84$	−3.76635	−	2.61049i	−0.410942	−	0.284827i
$85$		−	0.694778i		−	0.0753593i
$86$	−2.56654	−	4.44537i	−0.276757	−	0.479357i
$87$	−1.24864	+	2.16271i	−0.133868	+	0.231867i
$88$	0.569441	−	8.41078i	0.0607026	−	0.896593i
$89$	−11.7448	+	6.78089i	−1.24495	+	0.718773i	−0.970098	−	0.242714i	$-0.921962\pi$
$89$	−11.7448	+	6.78089i	−1.24495	+	0.718773i	−0.274853	+	0.961486i	$0.588629\pi$
$90$	0.184723			0.0194715
$91$	−2.42101	−	5.12774i	−0.253791	−	0.537534i
$92$	3.51459			0.366421
$93$	2.52704	+	4.37697i	0.262042	+	0.453870i
$94$	−1.36456	+	2.36348i	−0.140743	+	0.243775i
$95$	−0.839798	−	0.484858i	−0.0861615	−	0.0497454i
$96$	3.47342	+	6.01614i	0.354504	+	0.614020i
$97$			3.55778i			0.361238i	0.983553	+	0.180619i	$0.0578100\pi$
$97$			3.55778i			0.361238i	−0.983553	+	0.180619i	$0.942190\pi$
$98$	0.844377	−	5.07171i	0.0852949	−	0.512321i
$99$	−2.32743	−	4.74526i	−0.233916	−	0.476917i
$100$	−3.63307	−	6.29267i	−0.363307	−	0.629267i
$101$	−7.06589	+	12.2385i	−0.703082	+	1.21777i	0.264297	+	0.964441i	$0.414860\pi$
$101$	−7.06589	+	12.2385i	−0.703082	+	1.21777i	−0.967379	+	0.253333i	$0.918473\pi$
$102$	−1.91741	+	3.32105i	−0.189852	+	0.328833i
$103$	13.9911	−	8.07779i	1.37859	−	0.795928i	0.386599	−	0.922248i	$-0.373650\pi$
$103$	13.9911	−	8.07779i	1.37859	−	0.795928i	0.991990	+	0.126319i	$0.0403164\pi$
$104$			5.44765i			0.534186i
$105$	0.211413	+	0.447776i	0.0206318	+	0.0436985i
$106$			0.235212i			0.0228458i
$107$	0.496626	−	0.286727i	0.0480107	−	0.0277190i	−0.475803	−	0.879552i	$-0.657842\pi$
$107$	0.496626	−	0.286727i	0.0480107	−	0.0277190i	0.523813	+	0.851833i	$0.324509\pi$
$108$	6.89037	+	3.97816i	0.663026	+	0.382798i
$109$	−11.6766	−	6.74149i	−1.11842	−	0.645718i	−0.177420	−	0.984135i	$-0.556775\pi$
$109$	−11.6766	−	6.74149i	−1.11842	−	0.645718i	−0.940996	+	0.338417i	$0.890109\pi$
$110$	−0.214277	+	0.319200i	−0.0204305	+	0.0304346i
$111$			8.20781i			0.779050i
$112$	1.58868	−	2.29211i	0.150116	−	0.216584i
$113$	5.24844			0.493732			0.246866	−	0.969050i	$-0.420599\pi$
$113$	5.24844			0.493732			0.246866	+	0.969050i	$0.420599\pi$
$114$	2.67617	+	4.63526i	0.250646	+	0.434132i
$115$	−0.328893	−	0.189886i	−0.0306694	−	0.0177070i
$116$	−2.66345	−	1.53774i	−0.247295	−	0.142776i
$117$	1.70773	+	2.95788i	0.157880	+	0.273456i
$118$	9.91406			0.912663
$119$	11.6082	+	0.959702i	1.06412	+	0.0879757i
$120$		−	0.475711i		−	0.0434263i
$121$	10.8996	+	1.48268i	0.990874	+	0.134790i
$122$	4.34514	+	2.50867i	0.393390	+	0.227124i
$123$	−6.60367	−	3.81263i	−0.595433	−	0.343773i
$124$	−5.39037	+	3.11213i	−0.484069	+	0.279478i
$125$			1.57423i			0.140804i
$126$	−0.255158	+	3.08629i	−0.0227313	+	0.274949i
$127$			20.9655i			1.86039i	0.367070	+	0.930193i	$0.380361\pi$
$127$			20.9655i			1.86039i	−0.367070	+	0.930193i	$0.619639\pi$
$128$	−8.75006	+	5.05185i	−0.773404	+	0.446525i
$129$	−4.14392	+	7.17748i	−0.364852	+	0.631942i
$130$	0.124220	−	0.215155i	0.0108948	−	0.0188704i
$131$	−8.25344	−	14.2954i	−0.721106	−	1.24899i	−0.960557	−	0.278084i	$-0.910301\pi$
$131$	−8.25344	−	14.2954i	−0.721106	−	1.24899i	0.239450	−	0.970909i	$-0.423033\pi$
$132$	−5.15759	+	2.52967i	−0.448911	+	0.220179i
$133$	9.26089	−	13.3614i	0.803021	−	1.15858i
$134$			1.95000i			0.168455i
$135$	−0.429864	−	0.744547i	−0.0369968	−	0.0640804i
$136$	−9.69076	−	5.59496i	−0.830976	−	0.479764i
$137$	5.17471	−	8.96285i	0.442105	−	0.765748i	−0.555741	−	0.831356i	$-0.687565\pi$
$137$	5.17471	−	8.96285i	0.442105	−	0.765748i	0.997846	+	0.0656076i	$0.0208985\pi$
$138$	1.04808	+	1.81532i	0.0892182	+	0.154530i
$139$	16.2217			1.37590			0.687952	−	0.725756i	$-0.258510\pi$
$139$	16.2217			1.37590			0.687952	+	0.725756i	$0.258510\pi$
$140$	−0.551450	+	0.260361i	−0.0466060	+	0.0220045i
$141$	4.40642			0.371088
$142$	2.23562	−	1.29074i	0.187609	−	0.108316i
$143$	−7.09217	−	0.480166i	−0.593077	−	0.0401535i
$144$	−0.839883	+	1.45472i	−0.0699903	+	0.121227i
$145$	0.166162	+	0.287802i	0.0137990	+	0.0239006i
$146$		−	2.59381i		−	0.214665i
$147$	−7.77335	+	2.91371i	−0.641135	+	0.240319i
$148$	−10.1082			−0.830886
$149$	14.2554	−	8.23036i	1.16785	−	0.674258i	0.214676	−	0.976685i	$-0.431130\pi$
$149$	14.2554	−	8.23036i	1.16785	−	0.674258i	0.953172	+	0.302428i	$0.0977970\pi$
$150$	2.16682	−	3.75304i	0.176920	−	0.306435i
$151$	8.13439	+	4.69639i	0.661967	+	0.382187i	0.793026	−	0.609188i	$-0.208504\pi$
$151$	8.13439	+	4.69639i	0.661967	+	0.382187i	−0.131059	+	0.991375i	$0.541838\pi$
$152$	−13.5256	+	7.80900i	−1.09707	+	0.633393i
$153$	−7.01564			−0.567181
$154$	−5.03713	−	4.02100i	−0.405904	−	0.324021i
$155$	0.672570			0.0540221
$156$	3.21490	−	1.85612i	0.257398	−	0.148609i
$157$	−1.10078	−	0.635534i	−0.0878515	−	0.0507211i	0.455431	−	0.890271i	$-0.349485\pi$
$157$	−1.10078	−	0.635534i	−0.0878515	−	0.0507211i	−0.543282	+	0.839550i	$0.682819\pi$
$158$	−0.554084	+	0.959702i	−0.0440806	+	0.0763498i
$159$	0.328893	−	0.189886i	0.0260829	−	0.0150590i
$160$	0.924447			0.0730839
$161$	3.62687	−	5.23276i	0.285838	−	0.412400i
$162$			1.23379i			0.0969360i
$163$	−7.55408	−	13.0841i	−0.591682	−	1.02482i	−0.994006	−	0.109325i	$-0.965131\pi$
$163$	−7.55408	−	13.0841i	−0.591682	−	1.02482i	0.402324	−	0.915497i	$-0.368202\pi$
$164$	4.69537	−	8.13262i	0.366647	−	0.635051i
$165$	0.619317	+	0.0419301i	0.0482138	+	0.00326425i
$166$	−6.03736	+	3.48567i	−0.468590	+	0.270541i
$167$	−12.4522			−0.963579			−0.481789	−	0.876287i	$-0.660013\pi$
$167$	−12.4522			−0.963579			−0.481789	+	0.876287i	$0.660013\pi$
$168$	7.94805	+	0.657103i	0.613206	+	0.0506966i
$169$	−8.40642			−0.646648
$170$	0.255158	+	0.441947i	0.0195698	+	0.0338958i
$171$	−4.89594	+	8.48001i	−0.374402	+	0.648483i
$172$	−8.83929	−	5.10337i	−0.673990	−	0.389128i
$173$	10.2305	+	17.7198i	0.777814	+	1.34721i	0.933200	+	0.359359i	$0.117005\pi$
$173$	10.2305	+	17.7198i	0.777814	+	1.34721i	−0.155386	+	0.987854i	$0.549662\pi$
$174$		−	1.83426i		−	0.139055i
$175$	−13.1181	−	1.08454i	−0.991636	−	0.0819832i
$176$	−1.53950	−	3.13879i	−0.116044	−	0.236595i
$177$	−8.00360	−	13.8626i	−0.601587	−	1.04198i
$178$	4.98058	−	8.62663i	0.373311	−	0.646593i
$179$	−1.33988	+	2.32075i	−0.100148	+	0.173461i	−0.911745	−	0.410756i	$-0.865265\pi$
$179$	−1.33988	+	2.32075i	−0.100148	+	0.173461i	0.811598	+	0.584217i	$0.198598\pi$
$180$	0.318097	−	0.183653i	0.0237096	−	0.0136887i
$181$		−	6.69771i		−	0.497837i	−0.968524	−	0.248918i	$-0.919925\pi$
$181$		−	6.69771i		−	0.497837i	0.968524	−	0.248918i	$-0.0800751\pi$
$182$	3.42317	+	2.37263i	0.253743	+	0.175871i
$183$		−	8.10097i		−	0.598841i
$184$	−5.29707	+	3.05826i	−0.390505	+	0.225458i
$185$	0.945916	+	0.546125i	0.0695451	+	0.0401519i
$186$	−3.21490	−	1.85612i	−0.235728	−	0.136097i
$187$	8.13811	−	12.1230i	0.595118	−	0.886523i
$188$			5.42664i			0.395779i
$189$	13.0335	−	6.15361i	0.948045	−	0.447609i
$190$	0.712259			0.0516727
$191$	12.2017	+	21.1340i	0.882887	+	1.52921i	0.848116	+	0.529811i	$0.177737\pi$
$191$	12.2017	+	21.1340i	0.882887	+	1.52921i	0.0347716	+	0.999395i	$0.488930\pi$
$192$	−2.25370	−	1.30117i	−0.162646	−	0.0939040i
$193$	7.68615	+	4.43760i	0.553261	+	0.319425i	0.750436	−	0.660943i	$-0.229843\pi$
$193$	7.68615	+	4.43760i	0.553261	+	0.319425i	−0.197175	+	0.980368i	$0.563177\pi$
$194$	−1.30660	−	2.26310i	−0.0938084	−	0.162481i
$195$	−0.401130			−0.0287255
$196$	−3.58832	−	9.57312i	−0.256309	−	0.683794i
$197$		−	14.5955i		−	1.03988i	−0.854202	−	0.519942i	$-0.825954\pi$
$197$		−	14.5955i		−	1.03988i	0.854202	−	0.519942i	$-0.174046\pi$
$198$	3.22318	+	2.16370i	0.229061	+	0.153768i
$199$	19.6730	+	11.3582i	1.39459	+	0.805164i	0.993819	−	0.111016i	$-0.0354104\pi$
$199$	19.6730	+	11.3582i	1.39459	+	0.805164i	0.400767	+	0.916180i	$0.368744\pi$
$200$	10.9513	+	6.32273i	0.774373	+	0.447084i
$201$	2.72665	−	1.57423i	0.192323	−	0.111038i
$202$		−	10.3798i		−	0.730323i
$203$	−5.03803	+	2.37865i	−0.353601	+	0.166949i
$204$			7.62526i			0.533875i
$205$	−0.878779	+	0.507364i	−0.0613766	+	0.0354358i
$206$	−5.93316	+	10.2765i	−0.413383	+	0.716001i
$207$	−1.91741	+	3.32105i	−0.133269	+	0.230829i
$208$	1.12959	+	1.95651i	0.0783230	+	0.135659i
$209$	−8.97419	−	18.2969i	−0.620757	−	1.26563i
$210$	−0.298926	−	0.207188i	−0.0206278	−	0.0142973i
$211$			3.88944i			0.267760i	0.990998	+	0.133880i	$0.0427436\pi$
$211$			3.88944i			0.267760i	−0.990998	+	0.133880i	$0.957256\pi$
$212$	0.233851	+	0.405042i	0.0160610	+	0.0278184i
$213$	−3.60963	−	2.08402i	−0.247328	−	0.142795i
$214$	−0.210602	+	0.364774i	−0.0143965	+	0.0249354i
$215$	0.551450	+	0.955140i	0.0376086	+	0.0651400i
$216$	−13.8466			−0.942139
$217$	−0.929025	+	11.2371i	−0.0630663	+	0.762825i
$218$	9.90330			0.670736
$219$	−3.62687	+	2.09398i	−0.245081	+	0.141498i
$220$	−0.0516382	+	0.762709i	−0.00348145	+	0.0514218i
$221$	−4.71780	+	8.17147i	−0.317354	+	0.549672i
$222$	−3.01433	−	5.22097i	−0.202309	−	0.350409i
$223$			19.4273i			1.30095i	0.759529	+	0.650473i	$0.225429\pi$
$223$			19.4273i			1.30095i	−0.759529	+	0.650473i	$0.774571\pi$
$224$	−1.27694	+	15.4454i	−0.0853195	+	1.03199i
$225$	7.92821			0.528547
$226$	−3.33853	+	1.92750i	−0.222075	+	0.128215i
$227$	7.27417	−	12.5992i	0.482803	−	0.836240i	−0.517002	−	0.855984i	$-0.672952\pi$
$227$	7.27417	−	12.5992i	0.482803	−	0.836240i	0.999805	+	0.0197443i	$0.00628521\pi$
$228$	9.21687	+	5.32136i	0.610402	+	0.352416i
$229$	−3.11849	+	1.80046i	−0.206075	+	0.118978i	−0.599486	−	0.800385i	$-0.704628\pi$
$229$	−3.11849	+	1.80046i	−0.206075	+	0.118978i	0.393411	+	0.919363i	$0.371295\pi$
$230$	0.278944			0.0183931
$231$	−1.55602	+	10.2895i	−0.102379	+	0.676997i
$232$	5.35234			0.351398
$233$	−13.2213	+	7.63333i	−0.866157	+	0.500076i	−0.866069	−	0.499924i	$-0.833361\pi$
$233$	−13.2213	+	7.63333i	−0.866157	+	0.500076i	−8.78090e−5		1.00000i	$0.500028\pi$
$234$	−2.17257	−	1.25433i	−0.142025	−	0.0819984i
$235$	0.293191	−	0.507822i	0.0191257	−	0.0331266i
$236$	17.0723	−	9.85668i	1.11131	−	0.641615i
$237$	1.78924			0.116224
$238$	−7.73639	+	3.65265i	−0.501476	+	0.236766i
$239$			5.99520i			0.387797i	0.981022	+	0.193899i	$0.0621133\pi$
$239$			5.99520i			0.387797i	−0.981022	+	0.193899i	$0.937887\pi$
$240$	−0.0986405	−	0.170850i	−0.00636722	−	0.0110283i
$241$	2.05090	−	3.55227i	0.132110	−	0.228822i	−0.792380	−	0.610028i	$-0.791158\pi$
$241$	2.05090	−	3.55227i	0.132110	−	0.228822i	0.924490	+	0.381207i	$0.124491\pi$
$242$	−7.47775	+	3.05977i	−0.480688	+	0.196689i
$243$	−12.4282	+	7.17543i	−0.797270	+	0.460304i
$244$	9.97659			0.638686
$245$	−0.181424	+	1.08972i	−0.0115908	+	0.0696194i
$246$	5.60078			0.357092
$247$	6.58472	+	11.4051i	0.418976	+	0.725688i
$248$	5.41612	−	9.38099i	0.343924	−	0.595694i
$249$	9.74790	+	5.62795i	0.617748	+	0.356657i
$250$	−0.578140	−	1.00137i	−0.0365648	−	0.0633321i
$251$			6.99234i			0.441353i	0.975347	+	0.220676i	$0.0708265\pi$
$251$			6.99234i			0.441353i	−0.975347	+	0.220676i	$0.929174\pi$
$252$	2.62904	+	5.56836i	0.165614	+	0.350774i
$253$	−3.51459	−	7.16569i	−0.220960	−	0.450503i
$254$	−7.69961	−	13.3361i	−0.483117	−	0.836783i
$255$	0.411978	−	0.713567i	0.0257991	−	0.0446853i
$256$	5.90496	−	10.2277i	0.369060	−	0.639230i
$257$	17.1981	−	9.92936i	1.07279	−	0.619376i	0.143848	−	0.989600i	$-0.454052\pi$
$257$	17.1981	−	9.92936i	1.07279	−	0.619376i	0.928943	+	0.370224i	$0.120719\pi$
$258$		−	6.08745i		−	0.378988i
$259$	−10.4311	+	15.0497i	−0.648157	+	0.935145i
$260$		−	0.494005i		−	0.0306369i
$261$	2.90613	−	1.67785i	0.179885	−	0.103856i
$262$	10.5000	+	6.06218i	0.648692	+	0.374523i
$263$	5.55559	+	3.20752i	0.342572	+	0.197784i	0.661409	−	0.750025i	$-0.269959\pi$
$263$	5.55559	+	3.20752i	0.342572	+	0.197784i	−0.318837	+	0.947810i	$0.603292\pi$
$264$	5.57212	−	8.30057i	0.342941	−	0.510865i
$265$		−	0.0505381i		−	0.00310453i
$266$	−0.983849	+	11.9002i	−0.0603236	+	0.729650i
$267$	−16.0833			−0.984280
$268$	1.93872	+	3.35796i	0.118426	+	0.205120i
$269$	−16.7989	−	9.69886i	−1.02425	−	0.591350i	−0.108917	−	0.994051i	$-0.534738\pi$
$269$	−16.7989	−	9.69886i	−1.02425	−	0.591350i	−0.915332	+	0.402701i	$0.868072\pi$
$270$	0.546872	+	0.315737i	0.0332816	+	0.0192151i
$271$	−5.73573	−	9.93458i	−0.348421	−	0.603483i	0.637548	−	0.770411i	$-0.279949\pi$
$271$	−5.73573	−	9.93458i	−0.348421	−	0.603483i	−0.985969	+	0.166928i	$0.946615\pi$
$272$	−4.64055			−0.281374
$273$	0.554084	−	6.70198i	0.0335347	−	0.405622i
$274$			7.60168i			0.459234i
$275$	−9.19668	+	13.6999i	−0.554581	+	0.826137i
$276$	3.60963	+	2.08402i	0.217274	+	0.125443i
$277$	4.09367	+	2.36348i	0.245965	+	0.142008i	0.617915	−	0.786245i	$-0.287977\pi$
$277$	4.09367	+	2.36348i	0.245965	+	0.142008i	−0.371950	+	0.928253i	$0.621311\pi$
$278$	−10.3186	+	5.95743i	−0.618867	+	0.357303i
$279$		−	6.79139i		−	0.406590i
$280$	0.604570	−	0.872258i	0.0361300	−	0.0521274i
$281$		−	21.1824i		−	1.26364i	−0.775116	−	0.631818i	$-0.782309\pi$
$281$		−	21.1824i		−	1.26364i	0.775116	−	0.631818i	$-0.217691\pi$
$282$	−2.80292	+	1.61827i	−0.166911	+	0.0963663i
$283$	14.4827	−	25.0847i	0.860905	−	1.49113i	−0.0101515	−	0.999948i	$-0.503231\pi$
$283$	14.4827	−	25.0847i	0.860905	−	1.49113i	0.871057	−	0.491183i	$-0.163435\pi$
$284$	2.56654	−	4.44537i	0.152296	−	0.263784i
$285$	−0.575006	−	0.995939i	−0.0340604	−	0.0589943i
$286$	4.68766	−	2.29918i	0.277187	−	0.135953i
$287$	−7.26303	−	15.3832i	−0.428723	−	0.908044i
$288$		−	9.33476i		−	0.550056i
$289$	−1.19076	−	2.06245i	−0.0700445	−	0.121321i
$290$	−0.211391	−	0.122047i	−0.0124133	−	0.00716683i
$291$	−2.10963	+	3.65399i	−0.123669	+	0.214201i
$292$	−2.57880	−	4.46661i	−0.150913	−	0.261388i
$293$	−9.39074			−0.548613			−0.274306	−	0.961642i	$-0.588448\pi$
$293$	−9.39074			−0.548613			−0.274306	+	0.961642i	$0.588448\pi$
$294$	3.87455	−	4.70818i	0.225968	−	0.274587i
$295$	−2.13015			−0.124022
$296$	15.2347	−	8.79575i	0.885498	−	0.511242i
$297$	1.22046	−	18.0265i	0.0708184	−	1.04601i
$298$	−6.04523	+	10.4706i	−0.350191	+	0.606548i
$299$	2.57880	+	4.46661i	0.149136	+	0.258311i
$300$		−	8.61712i		−	0.497509i
$301$	−16.7199	+	7.89414i	−0.963721	+	0.455011i
$302$	−6.89903			−0.396994
$303$	−14.5139	+	8.37962i	−0.833804	+	0.481397i
$304$	−3.23845	+	5.60916i	−0.185738	+	0.321707i
$305$	−0.933603	−	0.539016i	−0.0534580	−	0.0308640i
$306$	4.46264	−	2.57651i	0.255112	−	0.147289i
$307$	3.76948			0.215136			0.107568	−	0.994198i	$-0.465694\pi$
$307$	3.76948			0.215136			0.107568	+	0.994198i	$0.465694\pi$
$308$	−12.6718	−	1.91629i	−0.722043	−	0.109191i
$309$	19.1593			1.08994
$310$	−0.427821	+	0.247002i	−0.0242986	+	0.0140288i
$311$	7.48181	+	4.31963i	0.424255	+	0.244944i	0.696896	−	0.717172i	$-0.254564\pi$
$311$	7.48181	+	4.31963i	0.424255	+	0.244944i	−0.272641	+	0.962116i	$0.587897\pi$
$312$	−3.23025	+	5.59496i	−0.182877	+	0.316752i
$313$	−9.09192	+	5.24922i	−0.513906	+	0.296704i	−0.734438	−	0.678676i	$-0.762554\pi$
$313$	−9.09192	+	5.24922i	−0.513906	+	0.296704i	0.220532	+	0.975380i	$0.429221\pi$
$314$	0.933603			0.0526863
$315$	0.0548237	−	0.663126i	0.00308897	−	0.0373629i
$316$			2.20351i			0.123957i
$317$	−11.6424	−	20.1652i	−0.653903	−	1.13259i	−0.982168	−	0.188007i	$-0.939797\pi$
$317$	−11.6424	−	20.1652i	−0.653903	−	1.13259i	0.328265	−	0.944586i	$-0.393536\pi$
$318$	−0.139472	+	0.241573i	−0.00782121	+	0.0135467i
$319$	−0.471765	+	6.96808i	−0.0264138	+	0.390138i
$320$	−0.299909	+	0.173153i	−0.0167654	+	0.00967953i
$321$	0.680075			0.0379581
$322$	−0.385308	+	4.66053i	−0.0214724	+	0.259721i
$323$	−27.0512			−1.50517
$324$	1.22665	+	2.12463i	0.0681474	+	0.118035i
$325$	5.33147	−	9.23438i	0.295737	−	0.512231i
$326$	9.61028	+	5.54850i	0.532264	+	0.307303i
$327$	−7.99491	−	13.8476i	−0.442120	−	0.765774i
$328$			16.3429i			0.902388i
$329$	8.07956	+	5.60001i	0.445441	+	0.308739i
$330$	−0.409346	+	0.200774i	−0.0225337	+	0.0110522i
$331$	−8.14766	−	14.1122i	−0.447836	−	0.775675i	0.550409	−	0.834895i	$-0.314472\pi$
$331$	−8.14766	−	14.1122i	−0.447836	−	0.775675i	−0.998245	+	0.0592204i	$0.981139\pi$
$332$	−6.93100	+	12.0048i	−0.380388	+	0.658851i
$333$	5.51459	−	9.55155i	0.302198	−	0.523422i
$334$	7.92082	−	4.57308i	0.433408	−	0.250228i
$335$		−	0.418981i		−	0.0228914i
$336$	2.99077	−	1.41206i	0.163160	−	0.0770343i
$337$			17.1952i			0.936684i	0.883547	+	0.468342i	$0.155148\pi$
$337$			17.1952i			0.936684i	−0.883547	+	0.468342i	$0.844852\pi$
$338$	5.34731	−	3.08727i	0.290855	−	0.167925i
$339$	5.39037	+	3.11213i	0.292765	+	0.169028i
$340$	0.878779	+	0.507364i	0.0476585	+	0.0275157i
$341$	11.7355	+	7.87798i	0.635514	+	0.426616i
$342$		−	7.19216i		−	0.388908i
$343$	−17.9561	−	4.53642i	−0.969537	−	0.244943i
$344$	17.7630			0.957718
$345$	−0.225191	−	0.390043i	−0.0121239	−	0.0209992i
$346$	−13.0153	−	7.51437i	−0.699705	−	0.403975i
$347$	−2.57880	−	1.48887i	−0.138437	−	0.0799267i	0.429182	−	0.903218i	$-0.358802\pi$
$347$	−2.57880	−	1.48887i	−0.138437	−	0.0799267i	−0.567619	+	0.823291i	$0.692135\pi$
$348$	−1.82365	−	3.15865i	−0.0977577	−	0.169321i
$349$	−17.9638			−0.961580			−0.480790	−	0.876836i	$-0.659650\pi$
$349$	−17.9638			−0.961580			−0.480790	+	0.876836i	$0.659650\pi$
$350$	8.74271	−	4.12777i	0.467317	−	0.220639i
$351$			11.6757i			0.623205i
$352$	16.1305	+	10.8283i	0.859756	+	0.577149i
$353$	27.2798	+	15.7500i	1.45195	+	0.838287i	0.998592	−	0.0530398i	$-0.0168910\pi$
$353$	27.2798	+	15.7500i	1.45195	+	0.838287i	0.453362	+	0.891326i	$0.350224\pi$
$354$	10.1822	+	5.87867i	0.541175	+	0.312448i
$355$	−0.480350	+	0.277330i	−0.0254943	+	0.0147192i
$356$		−	19.8070i		−	1.04977i
$357$	11.3530	+	7.86887i	0.600865	+	0.416465i
$358$		−	1.96830i		−	0.104028i
$359$	14.4293	−	8.33075i	0.761548	−	0.439680i	−0.0683030	−	0.997665i	$-0.521758\pi$
$359$	14.4293	−	8.33075i	0.761548	−	0.439680i	0.829851	+	0.557984i	$0.188425\pi$
$360$	−0.319617	+	0.553592i	−0.0168453	+	0.0291769i
$361$	−9.37792	+	16.2430i	−0.493575	+	0.854896i
$362$	2.45975	+	4.26040i	0.129281	+	0.223922i
$363$	10.3152	+	7.98585i	0.541407	+	0.419148i
$364$	8.25370	+	0.682372i	0.432611	+	0.0357660i
$365$			0.557310i			0.0291709i
$366$	2.97509	+	5.15301i	0.155511	+	0.269352i
$367$	14.2345	+	8.21831i	0.743036	+	0.428992i	0.823172	−	0.567792i	$-0.192202\pi$
$367$	14.2345	+	8.21831i	0.743036	+	0.428992i	−0.0801361	+	0.996784i	$0.525535\pi$
$368$	−1.26829	+	2.19673i	−0.0661139	+	0.114513i
$369$	5.12319	+	8.87363i	0.266703	+	0.461943i
$370$	−0.802261			−0.0417076
$371$	0.844377	+	0.0698086i	0.0438378	+	0.00362428i
$372$	−7.38151			−0.382714
$373$	−18.7583	+	10.8301i	−0.971270	+	0.560763i	−0.899623	−	0.436667i	$-0.856159\pi$
$373$	−18.7583	+	10.8301i	−0.971270	+	0.560763i	−0.0716470	+	0.997430i	$0.522826\pi$
$374$	−0.724441	+	10.7002i	−0.0374600	+	0.553293i
$375$	−0.933463	+	1.61680i	−0.0482038	+	0.0834914i
$376$	−4.72206	−	8.17885i	−0.243522	−	0.421792i
$377$		−	4.51321i		−	0.232442i
$378$	−6.03064	+	8.70086i	−0.310183	+	0.447524i
$379$	25.1842			1.29363			0.646814	−	0.762648i	$-0.276101\pi$
$379$	25.1842			1.29363			0.646814	+	0.762648i	$0.276101\pi$
$380$	1.22653	−	0.708137i	0.0629196	−	0.0363267i
$381$	−12.4318	+	21.5324i	−0.636898	+	1.10314i
$382$	−15.5230	−	8.96222i	−0.794227	−	0.458547i
$383$	−17.9552	+	10.3665i	−0.917470	+	0.529702i	−0.882827	−	0.469698i	$-0.844363\pi$
$383$	−17.9552	+	10.3665i	−0.917470	+	0.529702i	−0.0346432	+	0.999400i	$0.511029\pi$
$384$	−11.9822			−0.611466
$385$	1.08229	+	0.863958i	0.0551584	+	0.0440314i
$386$	−6.51886			−0.331801
$387$	9.64469	−	5.56836i	0.490267	−	0.283056i
$388$	−4.50000	−	2.59808i	−0.228453	−	0.131897i
$389$	12.8851	−	22.3177i	0.653301	−	1.13155i	−0.329016	−	0.944324i	$-0.606717\pi$
$389$	12.8851	−	22.3177i	0.653301	−	1.13155i	0.982317	−	0.187226i	$-0.0599498\pi$
$390$	0.255158	−	0.147316i	0.0129205	−	0.00745963i
$391$	−10.5941			−0.535768
$392$	13.7384	+	11.3058i	0.693892	+	0.571031i
$393$		−	19.5759i		−	0.987475i
$394$	5.36021	+	9.28415i	0.270043	+	0.467729i
$395$	0.119051	−	0.206203i	0.00599012	−	0.0103752i
$396$	7.70158	+	0.521426i	0.387019	+	0.0262026i
$397$	−23.5045	+	13.5703i	−1.17966	+	0.681074i	−0.955935	−	0.293579i	$-0.905154\pi$
$397$	−23.5045	+	13.5703i	−1.17966	+	0.681074i	−0.223721	+	0.974653i	$0.571820\pi$
$398$	−16.6853			−0.836360
$399$	17.4341	−	8.23134i	0.872798	−	0.412082i
$400$	5.24417			0.262208
$401$	10.1498	+	17.5800i	0.506857	+	0.877902i	0.999969	+	0.00793574i	$0.00252605\pi$
$401$	10.1498	+	17.5800i	0.506857	+	0.877902i	−0.493112	+	0.869966i	$0.664141\pi$
$402$	−1.15628	+	2.00274i	−0.0576700	+	0.0998874i
$403$	−7.91027	−	4.56699i	−0.394038	−	0.227498i
$404$	−10.3198	−	17.8744i	−0.513428	−	0.889283i
$405$		−	0.265095i		−	0.0131727i
$406$	2.33112	−	3.36328i	0.115692	−	0.166917i
$407$	10.1082	+	20.6090i	0.501043	+	1.02155i
$408$	−6.63521	−	11.4925i	−0.328492	−	0.568965i
$409$	9.99557	−	17.3128i	0.494249	−	0.856065i	−0.505729	−	0.862692i	$-0.668776\pi$
$409$	9.99557	−	17.3128i	0.494249	−	0.856065i	0.999978	+	0.00662777i	$0.00210970\pi$
$410$	0.372660	−	0.645466i	0.0184044	−	0.0318773i
$411$	10.6293	−	6.13682i	0.524304	−	0.302707i
$412$			23.5953i			1.16246i
$413$	2.94239	−	35.5900i	0.144786	−	1.75127i
$414$		−	2.81669i		−	0.138433i
$415$	1.29720	−	0.748936i	0.0636769	−	0.0367638i
$416$	−10.8727	−	6.27733i	−0.533076	−	0.307772i
$417$	16.6603	+	9.61885i	0.815860	+	0.471037i
$418$	12.4280	+	8.34287i	0.607876	+	0.408063i
$419$			0.494451i			0.0241555i	0.999927	+	0.0120778i	$0.00384456\pi$
$419$			0.494451i			0.0241555i	−0.999927	+	0.0120778i	$0.996155\pi$
$420$	−0.720747	−	0.0595876i	−0.0351689	−	0.00290757i
$421$	−22.9971			−1.12081			−0.560404	−	0.828219i	$-0.689354\pi$
$421$	−22.9971			−1.12081			−0.560404	+	0.828219i	$0.689354\pi$
$422$	−1.42840	−	2.47406i	−0.0695335	−	0.120436i
$423$	−5.12782	−	2.96055i	−0.249323	−	0.143947i
$424$	−0.704904	−	0.406977i	−0.0342332	−	0.0197645i
$425$	10.9513	+	18.9682i	0.531215	+	0.920092i
$426$	3.06144			0.148327
$427$	10.2953	−	14.8538i	0.498226	−	0.718828i
$428$			0.837533i			0.0404837i
$429$	−6.99923	−	4.69854i	−0.337926	−	0.226848i
$430$	−0.701553	−	0.405042i	−0.0338319	−	0.0195329i
$431$	−21.8886	−	12.6374i	−1.05434	−	0.608721i	−0.130476	−	0.991451i	$-0.541651\pi$
$431$	−21.8886	−	12.6374i	−1.05434	−	0.608721i	−0.923860	+	0.382730i	$0.874984\pi$
$432$	−4.97296	+	2.87114i	−0.239262	+	0.138138i
$433$			5.33297i			0.256286i	0.991756	+	0.128143i	$0.0409017\pi$
$433$			5.33297i			0.256286i	−0.991756	+	0.128143i	$0.959098\pi$
$434$	−3.53590	−	7.48910i	−0.169728	−	0.359488i
$435$			0.394112i			0.0188962i
$436$	17.0537	−	9.84599i	0.816726	−	0.471537i
$437$	−7.39322	+	12.8054i	−0.353666	+	0.612567i
$438$	1.53803	−	2.66395i	0.0734900	−	0.127288i
$439$	11.1143	+	19.2506i	0.530457	+	0.918779i	0.999368	+	0.0355336i	$0.0113131\pi$
$439$	11.1143	+	19.2506i	0.530457	+	0.918779i	−0.468911	+	0.883245i	$0.655354\pi$
$440$	−0.585853	−	1.19446i	−0.0279294	−	0.0569437i
$441$	11.0036	+	1.83196i	0.523981	+	0.0872362i
$442$		−	6.93048i		−	0.329649i
$443$	−11.9466	−	20.6921i	−0.567600	−	0.983111i	−0.996803	−	0.0799033i	$-0.974539\pi$
$443$	−11.9466	−	20.6921i	−0.567600	−	0.983111i	0.429203	−	0.903208i	$-0.358794\pi$
$444$	−10.3815	−	5.99377i	−0.492685	−	0.284452i
$445$	−1.07014	+	1.85353i	−0.0507293	+	0.0878657i
$446$	−7.13470	−	12.3577i	−0.337838	−	0.585152i
$447$	19.5212			0.923321
$448$	−2.47872	−	5.24998i	−0.117109	−	0.248038i
$449$	20.6198			0.973110			0.486555	−	0.873650i	$-0.338253\pi$
$449$	20.6198			0.973110			0.486555	+	0.873650i	$0.338253\pi$
$450$	−5.04312	+	2.91165i	−0.237735	+	0.137256i
$451$	−21.2765	−	1.44050i	−1.00187	−	0.0678304i
$452$	−3.83269	+	6.63841i	−0.180274	+	0.312244i
$453$	5.56957	+	9.64678i	0.261681	+	0.453245i
$454$			10.6858i			0.501509i
$455$	−0.735508	−	0.509787i	−0.0344812	−	0.0238992i
$456$	−18.5218			−0.867362
$457$	−0.929025	+	0.536373i	−0.0434580	+	0.0250905i	−0.521572	−	0.853208i	$-0.674654\pi$
$457$	−0.929025	+	0.536373i	−0.0434580	+	0.0250905i	0.478114	+	0.878298i	$0.341321\pi$
$458$	1.32244	−	2.29054i	0.0617937	−	0.107030i
$459$	−20.7698	−	11.9915i	−0.969454	−	0.559714i
$460$	0.480350	−	0.277330i	0.0223964	−	0.0129306i
$461$	10.8005			0.503032			0.251516	−	0.967853i	$-0.419071\pi$
$461$	10.8005			0.503032			0.251516	+	0.967853i	$0.419071\pi$
$462$	−2.78904	−	7.11657i	−0.129758	−	0.331093i
$463$	−3.80564			−0.176863			−0.0884316	−	0.996082i	$-0.528185\pi$
$463$	−3.80564			−0.176863			−0.0884316	+	0.996082i	$0.528185\pi$
$464$	1.92228	−	1.10983i	0.0892395	−	0.0515224i
$465$	0.690757	+	0.398809i	0.0320331	+	0.0184943i
$466$	5.60671	−	9.71110i	0.259726	−	0.449858i
$467$	1.31858	−	0.761280i	0.0610164	−	0.0352278i	−0.469181	−	0.883102i	$-0.655451\pi$
$467$	1.31858	−	0.761280i	0.0610164	−	0.0352278i	0.530198	+	0.847874i	$0.322118\pi$
$468$	−4.98830			−0.230584
$469$	7.00022	+	0.578741i	0.323240	+	0.0267238i
$470$			0.430700i			0.0198667i
$471$	−0.753696	−	1.30544i	−0.0347285	−	0.0601515i
$472$	−17.1538	+	29.7113i	−0.789569	+	1.36757i
$473$	−1.56567	+	23.1253i	−0.0719894	+	1.06330i
$474$	−1.13814	+	0.657103i	−0.0522763	+	0.0301817i
$475$	30.5699			1.40264
$476$	−9.69076	+	13.9816i	−0.444175	+	0.640845i
$477$	−0.510317			−0.0233658
$478$	−2.20175	−	3.81354i	−0.100706	−	0.174427i
$479$	1.82365	−	3.15865i	0.0833246	−	0.144322i	−0.821351	−	0.570422i	$-0.806780\pi$
$479$	1.82365	−	3.15865i	0.0833246	−	0.144322i	0.904676	+	0.426100i	$0.140113\pi$
$480$	0.949446	+	0.548163i	0.0433361	+	0.0250201i
$481$	−7.41677	−	12.8462i	−0.338176	−	0.585738i
$482$			3.01279i			0.137229i
$483$	6.82779	−	3.22367i	0.310675	−	0.146682i
$484$	−9.83482	+	12.7035i	−0.447037	+	0.577431i
$485$	0.280738	+	0.486253i	0.0127477	+	0.0220796i
$486$	5.27038	−	9.12856i	0.239069	−	0.414080i
$487$	13.0957	−	22.6824i	0.593424	−	1.02784i	−0.400344	−	0.916365i	$-0.631109\pi$
$487$	13.0957	−	22.6824i	0.593424	−	1.02784i	0.993767	−	0.111475i	$-0.0355574\pi$
$488$	−15.0364	+	8.68126i	−0.680665	+	0.392982i
$489$		−	17.9172i		−	0.810242i
$490$	−0.284797	−	0.759795i	−0.0128658	−	0.0343240i
$491$		−	9.63328i		−	0.434744i	−0.976089	−	0.217372i	$-0.930252\pi$
$491$		−	9.63328i		−	0.434744i	0.976089	−	0.217372i	$-0.0697484\pi$
$492$	9.64469	−	5.56836i	0.434816	−	0.251041i
$493$	8.02850	+	4.63526i	0.361586	+	0.208762i
$494$	−8.37707	−	4.83650i	−0.376902	−	0.217605i
$495$	−0.692537	−	0.464896i	−0.0311272	−	0.0208955i
$496$		−	4.49221i		−	0.201706i
$497$	−3.97005	−	8.40863i	−0.178081	−	0.377179i
$498$	−8.26750			−0.370475
$499$	3.33122	+	5.76985i	0.149126	+	0.258294i	0.930905	−	0.365262i	$-0.119021\pi$
$499$	3.33122	+	5.76985i	0.149126	+	0.258294i	−0.781779	+	0.623556i	$0.785687\pi$
$500$	−1.99115	−	1.14959i	−0.0890467	−	0.0514112i
$501$	−12.7889	−	7.38368i	−0.571367	−	0.329879i
$502$	−2.56795	−	4.44782i	−0.114613	−	0.198516i
$503$	26.7216			1.19146			0.595728	−	0.803186i	$-0.296864\pi$
$503$	26.7216			1.19146			0.595728	+	0.803186i	$0.296864\pi$
$504$	−8.80778	−	6.10475i	−0.392330	−	0.271927i
$505$			2.23023i			0.0992438i
$506$	4.86724	+	3.26735i	0.216375	+	0.145251i
$507$	−8.63375	−	4.98470i	−0.383438	−	0.221378i
$508$	−26.5179	−	15.3101i	−1.17654	−	0.679276i
$509$	0.573256	−	0.330969i	0.0254091	−	0.0146700i	−0.487242	−	0.873267i	$-0.661997\pi$
$509$	0.573256	−	0.330969i	0.0254091	−	0.0146700i	0.512651	+	0.858597i	$0.328664\pi$
$510$			0.605198i			0.0267986i
$511$	−9.31138	−	0.769816i	−0.411911	−	0.0340546i
$512$		−	11.5330i		−	0.509691i
$513$	−28.9889	+	16.7367i	−1.27989	+	0.738945i
$514$	−7.29315	+	12.6321i	−0.321687	+	0.557178i
$515$	1.27481	−	2.20803i	0.0561748	−	0.0972976i
$516$	−6.05222	−	10.4827i	−0.266434	−	0.461477i
$517$	11.0641	−	5.42664i	0.486597	−	0.238664i
$518$	1.10817	−	13.4040i	0.0486901	−	0.588936i
$519$			24.2653i			1.06513i
$520$	0.429864	+	0.744547i	0.0188508	+	0.0326505i
$521$	−5.93706	−	3.42776i	−0.260107	−	0.150173i	0.364276	−	0.931291i	$-0.381316\pi$
$521$	−5.93706	−	3.42776i	−0.260107	−	0.150173i	−0.624384	+	0.781118i	$0.714650\pi$
$522$	−1.23239	+	2.13456i	−0.0539402	+	0.0934271i
$523$	4.86780	+	8.43128i	0.212854	+	0.368674i	0.952607	−	0.304205i	$-0.0983908\pi$
$523$	4.86780	+	8.43128i	0.212854	+	0.368674i	−0.739752	+	0.672879i	$0.765057\pi$
$524$	24.1084			1.05318
$525$	−12.8298	−	8.89242i	−0.559937	−	0.388097i
$526$	−4.71187			−0.205447
$527$	16.2484	−	9.38099i	0.707789	−	0.408642i
$528$	0.280058	−	4.13653i	0.0121880	−	0.180019i
$529$	8.60457	−	14.9036i	0.374112	−	0.647981i
$530$	0.0185602	+	0.0321472i	0.000806203	+	0.00139638i
$531$			21.5096i			0.933435i
$532$	10.1372	+	21.4707i	0.439501	+	0.930872i
$533$	13.7807			0.596910
$534$	10.2305	−	5.90660i	0.442719	−	0.255604i
$535$	0.0452503	−	0.0783758i	0.00195634	−	0.00338848i
$536$	−5.84394	−	3.37400i	−0.252420	−	0.145735i
$537$	−2.75223	+	1.58900i	−0.118768	+	0.0685705i
$538$	14.2477			0.614262
$539$	−15.9297	+	16.8891i	−0.686143	+	0.727467i
$540$	1.25564			0.0540340
$541$	12.9628	−	7.48407i	0.557314	−	0.321765i	−0.194753	−	0.980852i	$-0.562390\pi$
$541$	12.9628	−	7.48407i	0.557314	−	0.321765i	0.752067	+	0.659087i	$0.229057\pi$
$542$	7.29698	+	4.21292i	0.313432	+	0.180960i
$543$	3.97150	−	6.87883i	0.170433	−	0.295199i
$544$	22.3334	−	12.8942i	0.957535	−	0.552833i
$545$	−2.12784			−0.0911466
$546$	2.10886	+	4.46661i	0.0902509	+	0.191153i
$547$		−	5.42175i		−	0.231817i	−0.993260	−	0.115909i	$-0.963022\pi$
$547$		−	5.42175i		−	0.231817i	0.993260	−	0.115909i	$-0.0369780\pi$
$548$	7.55768	+	13.0903i	0.322848	+	0.559190i
$549$	−5.44281	+	9.42722i	−0.232293	+	0.402344i
$550$	0.818673	−	12.0920i	0.0349083	−	0.515605i
$551$	11.2055	−	6.46952i	0.477372	−	0.275611i
$552$	−7.25375			−0.308740
$553$	3.28074	+	2.27391i	0.139511	+	0.0966964i
$554$	−3.47197			−0.147510
$555$	0.647664	+	1.12179i	0.0274918	+	0.0476172i
$556$	−11.8459	+	20.5177i	−0.502378	+	0.870145i
$557$	−21.9918	−	12.6970i	−0.931822	−	0.537988i	−0.0444350	−	0.999012i	$-0.514149\pi$
$557$	−21.9918	−	12.6970i	−0.931822	−	0.537988i	−0.887387	+	0.461024i	$0.847482\pi$
$558$	2.49415	+	4.31999i	0.105586	+	0.182880i
$559$		−	14.9782i		−	0.633510i
$560$	0.0362635	−	0.438629i	0.00153241	−	0.0185355i
$561$	15.5467	−	7.62526i	0.656382	−	0.321939i
$562$	7.77928	+	13.4741i	0.328149	+	0.568371i
$563$	−7.44346	+	12.8925i	−0.313705	+	0.543352i	−0.979161	−	0.203084i	$-0.934904\pi$
$563$	−7.44346	+	12.8925i	−0.313705	+	0.543352i	0.665457	+	0.746436i	$0.268237\pi$
$564$	−3.21780	+	5.57339i	−0.135494	+	0.234682i
$565$	0.717321	−	0.414145i	0.0301779	−	0.0174232i
$566$			21.2751i			0.894260i
$567$	4.42913	+	0.366177i	0.186006	+	0.0153780i
$568$			8.93321i			0.374829i
$569$	−29.2157	+	16.8677i	−1.22479	+	0.707131i	−0.965935	−	0.258786i	$-0.916678\pi$
$569$	−29.2157	+	16.8677i	−1.22479	+	0.707131i	−0.258852	+	0.965917i	$0.583344\pi$
$570$	0.731520	+	0.422343i	0.0306400	+	0.0176900i
$571$	10.0725	+	5.81536i	0.421521	+	0.243365i	0.695728	−	0.718305i	$-0.255082\pi$
$571$	10.0725	+	5.81536i	0.421521	+	0.243365i	−0.274207	+	0.961671i	$0.588415\pi$
$572$	5.78640	−	8.61977i	0.241942	−	0.360411i
$573$			28.9407i			1.20902i
$574$	10.2695	+	7.11789i	0.428642	+	0.297095i
$575$	11.9722			0.499274
$576$	1.74844	+	3.02839i	0.0728517	+	0.126183i
$577$	−13.8511	−	7.99692i	−0.576628	−	0.332916i	0.183164	−	0.983082i	$-0.441366\pi$
$577$	−13.8511	−	7.99692i	−0.576628	−	0.332916i	−0.759792	+	0.650166i	$0.774699\pi$
$578$	1.51488	+	0.874615i	0.0630106	+	0.0363792i
$579$	5.26266	+	9.11520i	0.218709	+	0.378815i
$580$	−0.485362			−0.0201536
$581$	10.7212	+	22.7077i	0.444790	+	0.942075i
$582$		−	3.09906i		−	0.128460i
$583$	0.591965	−	0.881827i	0.0245167	−	0.0365216i
$584$	7.77335	+	4.48794i	0.321663	+	0.185712i
$585$	0.466802	+	0.269508i	0.0192999	+	0.0111428i
$586$	5.97344	−	3.44877i	0.246760	−	0.142467i
$587$			22.7806i			0.940257i	0.882598	+	0.470128i	$0.155792\pi$
$587$			22.7806i			0.940257i	−0.882598	+	0.470128i	$0.844208\pi$
$588$	1.99115	−	11.9597i	0.0821135	−	0.493211i
$589$		−	26.1865i		−	1.07899i
$590$	1.35498	−	0.782301i	0.0557838	−	0.0322068i
$591$	8.65457	−	14.9902i	0.356001	−	0.616612i
$592$	3.64766	−	6.31794i	0.149918	−	0.259666i
$593$	13.2417	+	22.9354i	0.543773	+	0.941842i	0.998683	+	0.0513049i	$0.0163380\pi$
$593$	13.2417	+	22.9354i	0.543773	+	0.941842i	−0.454910	+	0.890537i	$0.650329\pi$
$594$	5.84394	+	11.9149i	0.239780	+	0.488873i
$595$	1.66225	−	0.784815i	0.0681457	−	0.0321743i
$596$			24.0410i			0.984757i
$597$	13.4700	+	23.3308i	0.551292	+	0.954865i
$598$	−3.28074	−	1.89413i	−0.134159	−	0.0774569i
$599$	−4.73911	+	8.20837i	−0.193635	+	0.335385i	−0.946452	−	0.322844i	$-0.895361\pi$
$599$	−4.73911	+	8.20837i	−0.193635	+	0.335385i	0.752817	+	0.658229i	$0.228694\pi$
$600$	7.49829	+	12.9874i	0.306116	+	0.530209i
$601$	−43.2756			−1.76525			−0.882623	−	0.470081i	$-0.844225\pi$
$601$	−43.2756			−1.76525			−0.882623	+	0.470081i	$0.844225\pi$
$602$	7.73639	−	11.1619i	0.315312	−	0.454924i
$603$	−4.23073			−0.172289
$604$	−11.8803	+	6.85910i	−0.483403	+	0.279093i
$605$	1.60668	−	0.657427i	0.0653208	−	0.0267282i
$606$	6.15486	−	10.6605i	0.250024	−	0.433054i
$607$	1.07163	+	1.85612i	0.0434962	+	0.0753376i	0.886954	−	0.461858i	$-0.152817\pi$
$607$	1.07163	+	1.85612i	0.0434962	+	0.0753376i	−0.843458	+	0.537196i	$0.819484\pi$
$608$		−	35.9933i		−	1.45972i
$609$	−6.58472	−	0.544390i	−0.266827	−	0.0220598i
$610$	0.791818			0.0320598
$611$	−6.89659	+	3.98175i	−0.279006	+	0.161084i
$612$	5.12319	−	8.87363i	0.207093	−	0.358695i
$613$	29.8835	+	17.2533i	1.20698	+	0.696852i	0.962099	−	0.272700i	$-0.0879167\pi$
$613$	29.8835	+	17.2533i	1.20698	+	0.696852i	0.244884	+	0.969552i	$0.421250\pi$
$614$	−2.39776	+	1.38435i	−0.0967658	+	0.0558677i
$615$	−1.20339			−0.0485254
$616$	20.7660	−	8.13836i	0.836685	−	0.327904i
$617$	−19.3537			−0.779150			−0.389575	−	0.920995i	$-0.627378\pi$
$617$	−19.3537			−0.779150			−0.389575	+	0.920995i	$0.627378\pi$
$618$	−12.1872	+	7.03629i	−0.490242	+	0.283041i
$619$	1.14454	+	0.660803i	0.0460031	+	0.0265599i	0.522825	−	0.852440i	$-0.324878\pi$
$619$	1.14454	+	0.660803i	0.0460031	+	0.0265599i	−0.476822	+	0.879000i	$0.658211\pi$
$620$	−0.491146	+	0.850689i	−0.0197249	+	0.0341645i
$621$	−11.3530	+	6.55466i	−0.455581	+	0.263030i
$622$	−6.34556			−0.254434
$623$	−29.4901	−	20.4398i	−1.18150	−	0.818905i
$624$			2.67922i			0.107255i
$625$	−12.3135	−	21.3276i	−0.492541	−	0.853105i
$626$	3.85557	−	6.67805i	0.154100	−	0.266908i
$627$	1.63255	−	24.1131i	0.0651976	−	0.962984i
$628$	1.60769	−	0.928200i	0.0641538	−	0.0370392i
$629$	30.4694			1.21489
$630$	0.208661	+	0.441947i	0.00831324	+	0.0176076i
$631$	−22.5362			−0.897151			−0.448576	−	0.893745i	$-0.648069\pi$
$631$	−22.5362			−0.897151			−0.448576	+	0.893745i	$0.648069\pi$
$632$	−1.91741	−	3.32105i	−0.0762705	−	0.132104i
$633$	−2.30629	+	3.99461i	−0.0916669	+	0.158772i
$634$	14.8114	+	8.55139i	0.588237	+	0.339619i
$635$	1.65435	+	2.86542i	0.0656509	+	0.113711i
$636$			0.554660i			0.0219937i
$637$	9.53335	−	11.5845i	0.377725	−	0.458995i
$638$	−2.25895	−	4.60565i	−0.0894328	−	0.182339i
$639$	2.80039	+	4.85041i	0.110782	+	0.191879i
$640$	−0.797266	+	1.38090i	−0.0315147	+	0.0545850i
$641$	−15.7740	+	27.3214i	−0.623036	+	1.07913i	0.365881	+	0.930662i	$0.380768\pi$
$641$	−15.7740	+	27.3214i	−0.623036	+	1.07913i	−0.988917	+	0.148469i	$0.952566\pi$
$642$	−0.432595	+	0.249759i	−0.0170731	+	0.00985719i
$643$		−	31.8502i		−	1.25605i	−0.778194	−	0.628024i	$-0.783864\pi$
$643$		−	31.8502i		−	1.25605i	0.778194	−	0.628024i	$-0.216136\pi$
$644$	3.97005	+	8.40863i	0.156442	+	0.331347i
$645$			1.30796i			0.0515008i
$646$	17.2072	−	9.93458i	0.677008	−	0.390871i
$647$	−24.9459	−	14.4025i	−0.980725	−	0.566222i	−0.0782362	−	0.996935i	$-0.524929\pi$
$647$	−24.9459	−	14.4025i	−0.980725	−	0.566222i	−0.902489	+	0.430713i	$0.858262\pi$
$648$	−3.69754	−	2.13478i	−0.145253	−	0.0838619i
$649$	−37.1685	−	24.9510i	−1.45899	−	0.979412i
$650$			7.83196i			0.307195i
$651$	−7.61734	+	10.9901i	−0.298547	+	0.430736i
$652$	22.0656			0.864154
$653$	1.92607	+	3.33605i	0.0753730	+	0.130550i	0.901248	−	0.433303i	$-0.142652\pi$
$653$	1.92607	+	3.33605i	0.0753730	+	0.130550i	−0.825875	+	0.563853i	$0.809319\pi$
$654$	10.1711	+	5.87229i	0.397722	+	0.229625i
$655$	−2.25605	−	1.30253i	−0.0881510	−	0.0508940i
$656$	3.38877	+	5.86952i	0.132309	+	0.229166i
$657$	5.62753			0.219551
$658$	−7.19601	−	0.594928i	−0.280530	−	0.0231927i
$659$		−	20.3920i		−	0.794361i	−0.917741	−	0.397180i	$-0.869989\pi$
$659$		−	20.3920i		−	0.794361i	0.917741	−	0.397180i	$-0.130011\pi$
$660$	−0.505293	+	0.752714i	−0.0196685	+	0.0292994i
$661$	−23.7738	−	13.7258i	−0.924695	−	0.533873i	−0.0395649	−	0.999217i	$-0.512597\pi$
$661$	−23.7738	−	13.7258i	−0.924695	−	0.533873i	−0.885130	+	0.465344i	$0.845931\pi$
$662$	10.3654	+	5.98449i	0.402864	+	0.232594i
$663$	−9.69076	+	5.59496i	−0.376358	+	0.217290i
$664$		−	24.1244i		−	0.936207i
$665$	0.211391	−	2.55690i	0.00819740	−	0.0991524i
$666$			8.10097i			0.313906i
$667$	4.38846	−	2.53368i	0.169922	−	0.0981045i
$668$	9.09324	−	15.7499i	0.351828	−	0.609384i
$669$	−11.5197	+	19.9526i	−0.445375	+	0.771413i
$670$	0.153871	+	0.266513i	0.00594457	+	0.0102963i
$671$	−9.97659	−	20.3407i	−0.385142	−	0.785244i
$672$	−10.4700	+	15.1059i	−0.403890	+	0.582723i
$673$		−	18.6224i		−	0.717839i	−0.933368	−	0.358920i	$-0.883145\pi$
$673$		−	18.6224i		−	0.717839i	0.933368	−	0.358920i	$-0.116855\pi$
$674$	−6.31498	−	10.9379i	−0.243244	−	0.421311i
$675$	23.4715	+	13.5513i	0.903418	+	0.521589i
$676$	6.13881	−	10.6327i	0.236108	−	0.408951i
$677$	−0.242681	−	0.420336i	−0.00932698	−	0.0161548i	0.861324	−	0.508056i	$-0.169636\pi$
$677$	−0.242681	−	0.420336i	−0.00932698	−	0.0161548i	−0.870651	+	0.491901i	$0.836302\pi$
$678$	−4.57174			−0.175577
$679$	−8.51196	+	4.01883i	−0.326659	+	0.154229i
$680$	−1.76595			−0.0677213
$681$	14.9418	−	8.62663i	0.572569	−	0.330573i
$682$	−10.3581	−	0.701284i	−0.396634	−	0.0268536i
$683$	0.275482	−	0.477149i	0.0105410	−	0.0182576i	−0.860707	−	0.509101i	$-0.829978\pi$
$683$	0.275482	−	0.477149i	0.0105410	−	0.0182576i	0.871248	+	0.490843i	$0.163311\pi$
$684$	−7.15054	−	12.3851i	−0.273408	−	0.473556i
$685$		−	1.63331i		−	0.0624055i
$686$	13.0878	−	3.70879i	0.499696	−	0.141602i
$687$	−4.27042			−0.162927
$688$	6.37955	−	3.68323i	0.243218	−	0.140422i
$689$	−0.343172	+	0.594391i	−0.0130738	+	0.0226445i
$690$	0.286488	+	0.165404i	0.0109064	+	0.00629681i
$691$	13.7060	−	7.91317i	0.521402	−	0.301031i	−0.216106	−	0.976370i	$-0.569336\pi$
$691$	13.7060	−	7.91317i	0.521402	−	0.301031i	0.737508	+	0.675338i	$0.236002\pi$
$692$	−29.8835			−1.13600
$693$	8.72397	−	10.9286i	0.331396	−	0.415142i
$694$	2.18716			0.0830234
$695$	2.21706	−	1.28002i	0.0840981	−	0.0485540i
$696$	5.49707	+	3.17374i	0.208366	+	0.120300i
$697$	−14.1534	+	24.5144i	−0.536098	+	0.928549i
$698$	11.4267	−	6.59723i	0.432509	−	0.249709i
$699$	−18.1051			−0.684799
$700$	10.9513	−	15.8002i	0.413920	−	0.597193i
$701$			41.7408i			1.57653i	0.615337	+	0.788264i	$0.289020\pi$
$701$			41.7408i			1.57653i	−0.615337	+	0.788264i	$0.710980\pi$
$702$	−4.28794	−	7.42692i	−0.161838	−	0.280311i
$703$	21.2633	−	36.8292i	0.801962	−	1.38904i
$704$	−7.26123	−	0.491612i	−0.273668	−	0.0185283i
$705$	0.602239	−	0.347703i	0.0226816	−	0.0130952i
$706$	−23.1368			−0.870766
$707$	−37.2620	−	3.08063i	−1.40138	−	0.115859i
$708$	23.3786			0.878621
$709$	−8.17324	−	14.1565i	−0.306953	−	0.531657i	0.670742	−	0.741691i	$-0.265976\pi$
$709$	−8.17324	−	14.1565i	−0.306953	−	0.531657i	−0.977694	+	0.210034i	$0.932643\pi$
$710$	0.203700	−	0.352818i	0.00764472	−	0.0132410i
$711$	−2.08217	−	1.20214i	−0.0780875	−	0.0450838i
$712$	17.2353	+	29.8525i	0.645922	+	1.11877i
$713$		−	10.2555i		−	0.384071i
$714$	−10.1115	−	0.835964i	−0.378413	−	0.0312852i
$715$	−1.00720	+	0.494005i	−0.0376670	+	0.0184747i
$716$	−1.95691	−	3.38946i	−0.0731330	−	0.126670i
$717$	−3.55493	+	6.15732i	−0.132761	+	0.229949i
$718$	−6.11896	+	10.5984i	−0.228358	+	0.395527i
$719$	2.73745	−	1.58047i	0.102090	−	0.0589415i	−0.448086	−	0.893991i	$-0.647894\pi$
$719$	2.73745	−	1.58047i	0.102090	−	0.0589415i	0.550176	+	0.835049i	$0.314561\pi$
$720$			0.265095i			0.00987950i
$721$	35.1303	+	24.3491i	1.30832	+	0.906809i
$722$		−	13.7762i		−	0.512698i
$723$	4.21273	−	2.43222i	0.156673	−	0.0904552i
$724$	8.47150	+	4.89102i	0.314841	+	0.181773i
$725$	−9.07282	−	5.23819i	−0.336956	−	0.194542i
$726$	−9.49429	−	1.29152i	−0.352366	−	0.0479327i
$727$		−	11.6758i		−	0.433033i	−0.976279	−	0.216516i	$-0.930531\pi$
$727$		−	11.6758i		−	0.433033i	0.976279	−	0.216516i	$-0.0694695\pi$
$728$	−13.0335	+	6.15361i	−0.483052	+	0.228068i
$729$	−22.0584			−0.816976
$730$	−0.204673	−	0.354504i	−0.00757528	−	0.0131208i
$731$	26.6445	+	15.3832i	0.985484	+	0.568969i
$732$	10.2464	+	5.91575i	0.378717	+	0.218652i
$733$	−0.976136	−	1.69072i	−0.0360544	−	0.0624481i	0.847435	−	0.530899i	$-0.178146\pi$
$733$	−0.976136	−	1.69072i	−0.0360544	−	0.0624481i	−0.883490	+	0.468451i	$0.844812\pi$
$734$	−12.0727			−0.445613
$735$	−0.832492	+	1.01161i	−0.0307069	+	0.0373137i
$736$		−	14.0962i		−	0.519592i
$737$	4.90763	−	7.31070i	0.180775	−	0.269293i
$738$	−6.51771	−	3.76300i	−0.239920	−	0.138518i
$739$	42.1645	+	24.3437i	1.55105	+	0.895498i	0.998057	+	0.0623100i	$0.0198468\pi$
$739$	42.1645	+	24.3437i	1.55105	+	0.895498i	0.552991	+	0.833188i	$0.313487\pi$
$740$	−1.38151	+	0.797618i	−0.0507855	+	0.0293210i
$741$			15.6180i			0.573741i
$742$	−0.562744	+	0.265694i	−0.0206590	+	0.00975392i
$743$			12.4317i			0.456074i	0.973652	+	0.228037i	$0.0732307\pi$
$743$			12.4317i			0.456074i	−0.973652	+	0.228037i	$0.926769\pi$
$744$	11.1252	−	6.42312i	0.407868	−	0.235483i
$745$	1.29889	−	2.24974i	0.0475875	−	0.0824240i
$746$	7.95477	−	13.7781i	0.291245	−	0.504451i
$747$	−7.56252	−	13.0987i	−0.276698	−	0.479255i
$748$	9.39074	+	19.1462i	0.343360	+	0.700056i
$749$	1.24698	+	0.864291i	0.0455636	+	0.0315805i
$750$		−	1.37126i		−	0.0500714i
$751$	−4.89251	−	8.47407i	−0.178530	−	0.309223i	0.762847	−	0.646579i	$-0.223801\pi$
$751$	−4.89251	−	8.47407i	−0.178530	−	0.309223i	−0.941377	+	0.337356i	$0.890468\pi$
$752$	−3.39183	−	1.95827i	−0.123687	−	0.0714109i
$753$	−4.14620	+	7.18143i	−0.151096	+	0.261706i
$754$	1.65748	+	2.87085i	0.0603620	+	0.104550i
$755$	1.48234			0.0539477
$756$	−1.73442	+	20.9789i	−0.0630803	+	0.762993i
$757$	24.2235			0.880419			0.440210	−	0.897895i	$-0.354904\pi$
$757$	24.2235			0.880419			0.440210	+	0.897895i	$0.354904\pi$
$758$	−16.0197	+	9.24895i	−0.581860	+	0.335937i
$759$	0.639359	−	9.44349i	0.0232073	−	0.342777i
$760$	−1.23239	+	2.13456i	−0.0447034	+	0.0774286i
$761$	−19.7562	−	34.2187i	−0.716161	−	1.24043i	−0.962510	−	0.271246i	$-0.912564\pi$
$761$	−19.7562	−	34.2187i	−0.716161	−	1.24043i	0.246349	−	0.969181i	$-0.420769\pi$
$762$		−	18.2623i		−	0.661575i
$763$	2.93920	−	35.5513i	0.106406	−	1.28705i
$764$	−35.6414			−1.28946
$765$	−0.958850	+	0.553592i	−0.0346673	+	0.0200152i
$766$	7.61421	−	13.1882i	0.275112	−	0.476509i
$767$	25.0532	+	14.4645i	0.904620	+	0.522283i
$768$	12.1293	−	7.00284i	0.437678	−	0.252693i
$769$	−37.5601			−1.35445			−0.677226	−	0.735775i	$-0.736818\pi$
$769$	−37.5601			−1.35445			−0.677226	+	0.735775i	$0.736818\pi$
$770$	−1.00573	−	0.152091i	−0.0362440	−	0.00548099i
$771$	23.5510			0.848167
$772$	−11.2257	+	6.48113i	−0.404020	+	0.233261i
$773$	28.7468	+	16.5970i	1.03395	+	0.596951i	0.918114	−	0.396317i	$-0.129712\pi$
$773$	28.7468	+	16.5970i	1.03395	+	0.596951i	0.115836	+	0.993268i	$0.463045\pi$
$774$	−4.08998	+	7.08405i	−0.147011	+	0.254631i
$775$	−18.3619	+	10.6012i	−0.659578	+	0.380807i
$776$	9.04299			0.324624
$777$	−19.6371	+	9.27146i	−0.704478	+	0.332612i
$778$			18.9283i			0.678613i
$779$	19.7542	+	34.2152i	0.707767	+	1.22589i
$780$	0.292926	−	0.507364i	0.0104885	−	0.0181665i
$781$	−11.6299	−	0.787390i	−0.416152	−	0.0281750i
$782$	6.73891	−	3.89071i	0.240983	−	0.139132i
$783$	11.4715			0.409957
$784$	7.27841	+	1.21176i	0.259943	+	0.0432773i
$785$	−0.200595			−0.00715956
$786$	7.18929	+	12.4522i	0.256434	+	0.444156i
$787$	−12.1357	+	21.0197i	−0.432591	+	0.749270i	−0.997096	−	0.0761603i	$-0.975734\pi$
$787$	−12.1357	+	21.0197i	−0.432591	+	0.749270i	0.564505	+	0.825430i	$0.309067\pi$
$788$	18.4608	+	10.6584i	0.657640	+	0.379689i
$789$	3.80388	+	6.58852i	0.135422	+	0.234557i
$790$			0.174887i			0.00622221i
$791$	5.92859	+	12.5569i	0.210796	+	0.446471i
$792$	−12.0613	+	5.91575i	−0.428579	+	0.210207i
$793$	7.32023	+	12.6790i	0.259949	+	0.450245i
$794$	9.96744	−	17.2641i	0.353731	−	0.612680i
$795$	0.0299672	−	0.0519047i	0.00106283	−	0.00184087i
$796$	−28.7326	+	16.5888i	−1.01840	+	0.587973i
$797$			16.0273i			0.567716i	0.958866	+	0.283858i	$0.0916145\pi$
$797$			16.0273i			0.567716i	−0.958866	+	0.283858i	$0.908386\pi$
$798$	−8.06686	+	11.6387i	−0.285564	+	0.412004i
$799$		−	16.3577i		−	0.578694i
$800$	−25.2384	+	14.5714i	−0.892312	+	0.515176i
$801$	18.7163	+	10.8059i	0.661309	+	0.381807i
$802$	−12.9125	−	7.45506i	−0.455958	−	0.263247i
$803$	−6.52791	+	9.72437i	−0.230365	+	0.343165i
$804$			4.59835i			0.162171i
$805$	0.0827878	−	1.00137i	0.00291789	−	0.0352936i
$806$	6.70895			0.236313
$807$	−11.5021	−	19.9223i	−0.404894	−	0.701298i
$808$	31.1072	+	17.9597i	1.09435	+	0.631822i
$809$	30.3457	+	17.5201i	1.06690	+	0.615974i	0.927333	−	0.374238i	$-0.122096\pi$
$809$	30.3457	+	17.5201i	1.06690	+	0.615974i	0.139566	+	0.990213i	$0.455429\pi$
$810$	0.0973565	+	0.168626i	0.00342076	+	0.00592493i
$811$	1.92059			0.0674409			0.0337205	−	0.999431i	$-0.489264\pi$
$811$	1.92059			0.0674409			0.0337205	+	0.999431i	$0.489264\pi$
$812$	0.670434	−	8.10929i	0.0235276	−	0.284580i
$813$		−	13.6043i		−	0.477124i
$814$	−13.9985	−	9.39709i	−0.490646	−	0.329368i
$815$	−2.06488	−	1.19216i	−0.0723296	−	0.0417595i
$816$	−4.76604	−	2.75167i	−0.166845	−	0.0963278i
$817$	37.1883	−	21.4707i	1.30105	−	0.751164i
$818$			14.6836i			0.513399i
$819$	−5.14766	+	7.42692i	−0.179874	+	0.259518i
$820$		−	1.48201i		−	0.0517542i
$821$	−24.3669	+	14.0682i	−0.850411	+	0.490985i	−0.860789	−	0.508961i	$-0.830030\pi$
$821$	−24.3669	+	14.0682i	−0.850411	+	0.490985i	0.0103788	+	0.999946i	$0.496696\pi$
$822$	−4.50751	+	7.80724i	−0.157218	+	0.272309i
$823$	0.636673	−	1.10275i	0.0221930	−	0.0384395i	−0.854716	−	0.519097i	$-0.826268\pi$
$823$	0.636673	−	1.10275i	0.0221930	−	0.0384395i	0.876909	+	0.480657i	$0.159602\pi$
$824$	−20.5317	−	35.5620i	−0.715257	−	1.23886i
$825$	−17.5689	+	8.61712i	−0.611672	+	0.300009i
$826$	11.1988	+	23.7193i	0.389657	+	0.825301i
$827$			15.2216i			0.529309i	0.964343	+	0.264654i	$0.0852578\pi$
$827$			15.2216i			0.529309i	−0.964343	+	0.264654i	$0.914742\pi$
$828$	−2.80039	−	4.85041i	−0.0973202	−	0.168564i
$829$	1.49359	+	0.862326i	0.0518746	+	0.0299498i	0.525713	−	0.850662i	$-0.323799\pi$
$829$	1.49359	+	0.862326i	0.0518746	+	0.0299498i	−0.473838	+	0.880612i	$0.657132\pi$
$830$	−0.550096	+	0.952795i	−0.0190941	+	0.0330720i
$831$	2.80292	+	4.85480i	0.0972321	+	0.168411i
$832$	4.70308			0.163050
$833$	10.8164	+	28.8565i	0.374766	+	0.999820i
$834$	−14.1301			−0.489287
$835$	−1.70188	+	0.982580i	−0.0588959	+	0.0340036i
$836$	29.6960	+	2.01053i	1.02706	+	0.0695356i
$837$	11.6082	−	20.1059i	0.401237	−	0.694963i
$838$	−0.181588	−	0.314519i	−0.00627285	−	0.0108649i
$839$			15.7719i			0.544506i	0.962226	+	0.272253i	$0.0877687\pi$
$839$			15.7719i			0.544506i	−0.962226	+	0.272253i	$0.912231\pi$
$840$	1.13814	−	0.537359i	0.0392694	−	0.0185406i
$841$	24.5657			0.847095
$842$	14.6284	−	8.44571i	0.504128	−	0.291059i
$843$	12.5604	−	21.7552i	0.432603	−	0.749290i
$844$	−4.91949	−	2.84027i	−0.169336	−	0.0977661i
$845$	−1.14893	+	0.663336i	−0.0395244	+	0.0228194i
$846$	4.34906			0.149524
$847$	8.76479	+	27.7521i	0.301162	+	0.953573i
$848$	−0.337553			−0.0115916
$849$	29.7486	−	17.1754i	1.02097	−	0.589457i
$850$	−13.9322	−	8.04376i	−0.477870	−	0.275899i
$851$	8.32743	−	14.4235i	0.285461	−	0.494432i
$852$	5.27188	−	3.04372i	0.180612	−	0.104276i
$853$	−12.7654			−0.437078			−0.218539	−	0.975828i	$-0.570129\pi$
$853$	−12.7654			−0.437078			−0.218539	+	0.975828i	$0.570129\pi$
$854$	−1.09374	+	13.2295i	−0.0374271	+	0.452704i
$855$			1.54532i			0.0528488i
$856$	−0.728790	−	1.26230i	−0.0249095	−	0.0431446i
$857$	1.62935	−	2.82212i	0.0556576	−	0.0964017i	−0.836854	−	0.547426i	$-0.815608\pi$
$857$	1.62935	−	2.82212i	0.0556576	−	0.0964017i	0.892512	+	0.451024i	$0.148941\pi$
$858$	6.17775	+	0.418256i	0.210905	+	0.0142790i
$859$	7.53736	−	4.35170i	0.257171	−	0.148478i	−0.365872	−	0.930665i	$-0.619229\pi$
$859$	7.53736	−	4.35170i	0.257171	−	0.148478i	0.623044	+	0.782187i	$0.285896\pi$
$860$	−1.61079			−0.0549275
$861$	1.66225	−	20.1059i	0.0566494	−	0.685209i
$862$	18.5644			0.632306
$863$	−20.8528	−	36.1181i	−0.709838	−	1.22948i	−0.964917	−	0.262555i	$-0.915435\pi$
$863$	−20.8528	−	36.1181i	−0.709838	−	1.22948i	0.255079	−	0.966920i	$-0.417899\pi$
$864$	15.9554	−	27.6356i	0.542815	−	0.940183i
$865$	2.79648	+	1.61455i	0.0950831	+	0.0548963i
$866$	−1.95854	−	3.39229i	−0.0665539	−	0.115275i
$867$		−	2.82430i		−	0.0959183i
$868$	−13.5347	−	9.38099i	−0.459396	−	0.318412i
$869$	4.49261	−	2.20351i	0.152401	−	0.0747490i
$870$	−0.144738	−	0.250694i	−0.00490709	−	0.00849933i
$871$	−2.84503	+	4.92774i	−0.0964003	+	0.166970i
$872$	−17.1352	+	29.6791i	−0.580271	+	1.00506i
$873$	4.91002	−	2.83480i	0.166179	−	0.0959435i
$874$		−	10.8607i		−	0.367368i
$875$	−3.76635	+	1.77824i	−0.127326	+	0.0601155i
$876$		−	6.11653i		−	0.206658i
$877$	−3.03162	+	1.75030i	−0.102370	+	0.0591036i	−0.550311	−	0.834960i	$-0.685491\pi$
$877$	−3.03162	+	1.75030i	−0.102370	+	0.0591036i	0.447941	+	0.894063i	$0.352158\pi$
$878$	−14.1396	−	8.16350i	−0.477188	−	0.275505i
$879$	−9.64469	−	5.56836i	−0.325307	−	0.187816i
$880$	−0.458084	−	0.307509i	−0.0154420	−	0.0103661i
$881$		−	24.6580i		−	0.830750i	−0.909650	−	0.415375i	$-0.863650\pi$
$881$		−	24.6580i		−	0.830750i	0.909650	−	0.415375i	$-0.136350\pi$
$882$	−7.67216	+	2.87578i	−0.258335	+	0.0968326i
$883$	29.0918			0.979017			0.489509	−	0.871998i	$-0.337176\pi$
$883$	29.0918			0.979017			0.489509	+	0.871998i	$0.337176\pi$
$884$	−6.89037	−	11.9345i	−0.231748	−	0.401400i
$885$	−2.18775	−	1.26310i	−0.0735405	−	0.0424586i
$886$	15.1984	+	8.77481i	0.510601	+	0.294795i
$887$	−21.3901	−	37.0487i	−0.718209	−	1.24398i	−0.961709	−	0.274074i	$-0.911629\pi$
$887$	−21.3901	−	37.0487i	−0.718209	−	1.24398i	0.243499	−	0.969901i	$-0.421705\pi$
$888$	20.8622			0.700090
$889$	−50.1598	+	23.6824i	−1.68231	+	0.794283i
$890$		−	1.57204i		−	0.0526948i
$891$	3.10512	−	4.62558i	0.104026	−	0.154963i
$892$	−24.5723	−	14.1868i	−0.822741	−	0.475009i
$893$	−19.7720	−	11.4154i	−0.661645	−	0.382001i
$894$	−12.4174	+	7.16920i	−0.415300	+	0.239774i
$895$			0.422911i			0.0141364i
$896$	−21.9705	−	15.2280i	−0.733983	−	0.508730i
$897$			6.11653i			0.204225i
$898$	−13.1162	+	7.57267i	−0.437695	+	0.252703i
$899$	−4.48709	+	7.77187i	−0.149653	+	0.259206i
$900$	−5.78959	+	10.0279i	−0.192986	+	0.334262i
$901$	−0.704904	−	1.22093i	−0.0234838	−	0.0406751i
$902$	14.0630	−	6.89753i	0.468246	−	0.229663i
$903$	−21.8530	−	1.80669i	−0.727223	−	0.0601229i
$904$		−	13.3402i		−	0.443690i
$905$	−0.528505	−	0.915397i	−0.0175681	−	0.0304288i
$906$	−7.08559	−	4.09087i	−0.235403	−	0.135910i
$907$	−10.7484	+	18.6168i	−0.356896	+	0.618162i	−0.987441	−	0.157991i	$-0.949498\pi$
$907$	−10.7484	+	18.6168i	−0.356896	+	0.618162i	0.630544	+	0.776153i	$0.282832\pi$
$908$	10.6240	+	18.4012i	0.352568	+	0.610666i
$909$	22.5201			0.746945
$910$	0.655076	+	0.0541582i	0.0217156	+	0.00179533i
$911$	−28.7998			−0.954180			−0.477090	−	0.878855i	$-0.658308\pi$
$911$	−28.7998			−0.954180			−0.477090	+	0.878855i	$0.658308\pi$
$912$	−6.65205	+	3.84056i	−0.220271	+	0.127174i
$913$	31.4070	+	2.12637i	1.03942	+	0.0703725i
$914$	0.393968	−	0.682372i	0.0130313	−	0.0225709i
$915$	−0.639233	−	1.10718i	−0.0211324	−	0.0366024i
$916$		−	5.25916i		−	0.173767i
$917$	24.8786	−	35.8942i	0.821563	−	1.18533i
$918$	17.6156			0.581400
$919$	−12.2281	+	7.05987i	−0.403367	+	0.232884i	−0.687936	−	0.725772i	$-0.741483\pi$
$919$	−12.2281	+	7.05987i	−0.403367	+	0.232884i	0.284569	+	0.958656i	$0.408150\pi$
$920$	−0.482644	+	0.835964i	−0.0159123	+	0.0275609i
$921$	3.87141	+	2.23516i	0.127567	+	0.0736511i
$922$	−6.87021	+	3.96652i	−0.226258	+	0.130630i
$923$	7.53269			0.247942
$924$	−11.8782	−	9.48202i	−0.390764	−	0.311936i
$925$	−34.4327			−1.13214
$926$	2.42076	−	1.39763i	0.0795513	−	0.0459289i
$927$	−22.2960	−	12.8726i	−0.732297	−	0.422792i
$928$	−6.16751	+	10.6824i	−0.202458	+	0.350668i
$929$	−18.9203	+	10.9237i	−0.620756	+	0.358394i	−0.777163	−	0.629299i	$-0.783342\pi$
$929$	−18.9203	+	10.9237i	−0.620756	+	0.358394i	0.156407	+	0.987693i	$0.450009\pi$
$930$	−0.585853			−0.0192109
$931$	42.4280	+	7.06374i	1.39052	+	0.231505i
$932$		−	22.2970i		−	0.730363i
$933$	5.12276	+	8.87288i	0.167712	+	0.290485i
$934$	−0.559163	+	0.968498i	−0.0182964	+	0.0316902i
$935$	0.155655	−	2.29906i	0.00509045	−	0.0751872i
$936$	7.51819	−	4.34063i	0.245740	−	0.141878i
$937$	−12.3580			−0.403717			−0.201858	−	0.979415i	$-0.564698\pi$
$937$	−12.3580			−0.403717			−0.201858	+	0.979415i	$0.564698\pi$
$938$	−4.66537	+	2.20271i	−0.152330	+	0.0719209i
$939$	−12.4504			−0.406303
$940$	0.428207	+	0.741676i	0.0139666	+	0.0241908i
$941$	−5.18742	+	8.98487i	−0.169105	+	0.292898i	−0.938105	−	0.346350i	$-0.887421\pi$
$941$	−5.18742	+	8.98487i	−0.169105	+	0.292898i	0.769000	+	0.639248i	$0.220754\pi$
$942$	0.958850	+	0.553592i	0.0312410	+	0.0180370i
$943$	7.73639	+	13.3998i	0.251932	+	0.436358i
$944$			14.2276i			0.463070i
$945$	1.29575	−	1.86948i	0.0421508	−	0.0608142i
$946$	−7.49688	−	15.2850i	−0.243745	−	0.496957i
$947$	22.3602	+	38.7290i	0.726609	+	1.25852i	0.958308	+	0.285736i	$0.0922382\pi$
$947$	22.3602	+	38.7290i	0.726609	+	1.25852i	−0.231699	+	0.972787i	$0.574428\pi$
$948$	−1.30660	+	2.26310i	−0.0424364	+	0.0735020i
$949$	3.78434	−	6.55466i	0.122845	−	0.212773i
$950$	−19.4454	+	11.2268i	−0.630893	+	0.364246i
$951$		−	27.6141i		−	0.895448i
$952$	2.43932	−	29.5051i	0.0790590	−	0.956265i
$953$		−	2.52561i		−	0.0818124i	−0.999163	−	0.0409062i	$-0.986976\pi$
$953$		−	2.52561i		−	0.0818124i	0.999163	−	0.0409062i	$-0.0130245\pi$
$954$	0.324612	−	0.187415i	0.0105097	−	0.00606778i
$955$	3.33530	+	1.92564i	0.107928	+	0.0623122i
$956$	−7.58294	−	4.37801i	−0.245250	−	0.141595i
$957$	−4.61634	+	6.87678i	−0.149225	+	0.222295i
$958$			2.67895i			0.0865529i
$959$	27.2889	+	2.25610i	0.881203	+	0.0728532i
$960$	−0.410693			−0.0132551
$961$	−6.41887	−	11.1178i	−0.207060	−	0.358639i
$962$	9.43560	+	5.44765i	0.304216	+	0.175639i
$963$	−0.791413	−	0.456923i	−0.0255029	−	0.0147241i
$964$	2.99535	+	5.18810i	0.0964738	+	0.167098i
$965$	1.40065			0.0450886
$966$	−3.15925	+	4.55809i	−0.101647	+	0.146654i
$967$		−	31.8090i		−	1.02291i	−0.859311	−	0.511454i	$-0.829107\pi$
$967$		−	31.8090i		−	1.02291i	0.859311	−	0.511454i	$-0.170893\pi$
$968$	3.76862	−	27.7041i	0.121128	−	0.890444i
$969$	−27.7827	−	16.0403i	−0.892508	−	0.515290i
$970$	−0.357154	−	0.206203i	−0.0114675	−	0.00662078i
$971$	35.4415	−	20.4622i	1.13737	−	0.656662i	0.191594	−	0.981474i	$-0.438634\pi$
$971$	35.4415	−	20.4622i	1.13737	−	0.656662i	0.945779	+	0.324812i	$0.105301\pi$
$972$		−	20.9595i		−	0.672276i
$973$	18.3238	+	38.8102i	0.587435	+	1.24420i
$974$			19.2377i			0.616415i
$975$	10.9513	−	6.32273i	0.350722	−	0.202489i
$976$	−3.60018	+	6.23570i	−0.115239	+	0.199600i
$977$	19.9269	−	34.5145i	0.637519	−	1.10422i	−0.348456	−	0.937325i	$-0.613294\pi$
$977$	19.9269	−	34.5145i	0.637519	−	1.10422i	0.985975	−	0.166891i	$-0.0533727\pi$
$978$	6.58011	+	11.3971i	0.210409	+	0.364439i
$979$	−40.3834	+	19.8070i	−1.29066	+	0.633036i
$980$	−1.24583	−	1.02524i	−0.0397964	−	0.0327501i
$981$			21.4862i			0.686002i
$982$	3.53784	+	6.12772i	0.112897	+	0.195543i
$983$	−14.8515	−	8.57454i	−0.473691	−	0.273486i	0.244093	−	0.969752i	$-0.421510\pi$
$983$	−14.8515	−	8.57454i	−0.473691	−	0.273486i	−0.717783	+	0.696266i	$0.754843\pi$
$984$	−9.69076	+	16.7849i	−0.308930	+	0.535083i
$985$	−1.15170	−	1.99481i	−0.0366963	−	0.0635598i
$986$	−6.80923			−0.216850
$987$	4.97745	+	10.5423i	0.158434	+	0.335566i
$988$	−19.2340			−0.611917
$989$	14.5642	−	8.40863i	0.463114	−	0.267379i
$990$	0.611256	+	0.0413843i	0.0194270	+	0.00131528i
$991$	−12.5921	+	21.8102i	−0.400002	+	0.692823i	−0.993726	−	0.111845i	$-0.964324\pi$
$991$	−12.5921	+	21.8102i	−0.400002	+	0.692823i	0.593724	+	0.804669i	$0.297657\pi$
$992$	12.4820	+	21.6195i	0.396304	+	0.686419i
$993$		−	19.3251i		−	0.613262i
$994$	5.61342	+	3.89071i	0.178047	+	0.123406i
$995$	3.58504			0.113653
$996$	−14.2368	+	8.21965i	−0.451112	+	0.260450i
$997$	−21.3480	+	36.9758i	−0.676098	+	1.17104i	0.300049	+	0.953924i	$0.402997\pi$
$997$	−21.3480	+	36.9758i	−0.676098	+	1.17104i	−0.976147	+	0.217112i	$0.930336\pi$
$998$	−4.23797	−	2.44679i	−0.134151	−	0.0774519i
$999$	32.6519	−	18.8516i	1.03306	−	0.596438i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	77.2.i.a.10.3	✓	12
3.2	odd	2		693.2.bg.a.10.4		12
4.3	odd	2		1232.2.bn.a.241.1		12
7.2	even	3		539.2.i.c.362.4		12
7.3	odd	6		539.2.b.b.538.6		12
7.4	even	3		539.2.b.b.538.5		12
7.5	odd	6	inner	77.2.i.a.54.4	yes	12
7.6	odd	2		539.2.i.c.472.3		12
11.2	odd	10		847.2.r.b.766.3		48
11.3	even	5		847.2.r.b.717.4		48
11.4	even	5		847.2.r.b.94.3		48
11.5	even	5		847.2.r.b.360.4		48
11.6	odd	10		847.2.r.b.360.3		48
11.7	odd	10		847.2.r.b.94.4		48
11.8	odd	10		847.2.r.b.717.3		48
11.9	even	5		847.2.r.b.766.4		48
11.10	odd	2	inner	77.2.i.a.10.4	yes	12
21.5	even	6		693.2.bg.a.208.3		12
28.19	even	6		1232.2.bn.a.593.2		12
33.32	even	2		693.2.bg.a.10.3		12
44.43	even	2		1232.2.bn.a.241.2		12
77.5	odd	30		847.2.r.b.481.3		48
77.10	even	6		539.2.b.b.538.8		12
77.19	even	30		847.2.r.b.838.3		48
77.26	odd	30		847.2.r.b.215.3		48
77.32	odd	6		539.2.b.b.538.7		12
77.40	even	30		847.2.r.b.215.4		48
77.47	odd	30		847.2.r.b.838.4		48
77.54	even	6	inner	77.2.i.a.54.3	yes	12
77.61	even	30		847.2.r.b.481.4		48
77.65	odd	6		539.2.i.c.362.3		12
77.68	even	30		847.2.r.b.40.4		48
77.75	odd	30		847.2.r.b.40.3		48
77.76	even	2		539.2.i.c.472.4		12
231.131	odd	6		693.2.bg.a.208.4		12
308.131	odd	6		1232.2.bn.a.593.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.i.a.10.3	✓	12	1.1	even	1	trivial
77.2.i.a.10.4	yes	12	11.10	odd	2	inner
77.2.i.a.54.3	yes	12	77.54	even	6	inner
77.2.i.a.54.4	yes	12	7.5	odd	6	inner
539.2.b.b.538.5		12	7.4	even	3
539.2.b.b.538.6		12	7.3	odd	6
539.2.b.b.538.7		12	77.32	odd	6
539.2.b.b.538.8		12	77.10	even	6
539.2.i.c.362.3		12	77.65	odd	6
539.2.i.c.362.4		12	7.2	even	3
539.2.i.c.472.3		12	7.6	odd	2
539.2.i.c.472.4		12	77.76	even	2
693.2.bg.a.10.3		12	33.32	even	2
693.2.bg.a.10.4		12	3.2	odd	2
693.2.bg.a.208.3		12	21.5	even	6
693.2.bg.a.208.4		12	231.131	odd	6
847.2.r.b.40.3		48	77.75	odd	30
847.2.r.b.40.4		48	77.68	even	30
847.2.r.b.94.3		48	11.4	even	5
847.2.r.b.94.4		48	11.7	odd	10
847.2.r.b.215.3		48	77.26	odd	30
847.2.r.b.215.4		48	77.40	even	30
847.2.r.b.360.3		48	11.6	odd	10
847.2.r.b.360.4		48	11.5	even	5
847.2.r.b.481.3		48	77.5	odd	30
847.2.r.b.481.4		48	77.61	even	30
847.2.r.b.717.3		48	11.8	odd	10
847.2.r.b.717.4		48	11.3	even	5
847.2.r.b.766.3		48	11.2	odd	10
847.2.r.b.766.4		48	11.9	even	5
847.2.r.b.838.3		48	77.19	even	30
847.2.r.b.838.4		48	77.47	odd	30
1232.2.bn.a.241.1		12	4.3	odd	2
1232.2.bn.a.241.2		12	44.43	even	2
1232.2.bn.a.593.1		12	308.131	odd	6
1232.2.bn.a.593.2		12	28.19	even	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:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.636099 + 0.367252i) q^{2} +(1.02704 + 0.592963i) q^{3} +(-0.730252 + 1.26483i) q^{4} +(0.136673 - 0.0789082i) q^{5} -0.871067 q^{6} +(1.12959 + 2.39249i) q^{7} -2.54175i q^{8} +(-0.796790 - 1.38008i) q^{9} +(-0.0579584 + 0.100387i) q^{10} +(3.30905 + 0.224035i) q^{11} +(-1.50000 + 0.866025i) q^{12} -2.14326 q^{13} +(-1.59718 - 1.10702i) q^{14} +0.187159 q^{15} +(-0.527042 - 0.912864i) q^{16} +(2.20122 - 3.81263i) q^{17} +(1.01367 + 0.585245i) q^{18} +(-3.07229 - 5.32136i) q^{19} +0.230492i q^{20} +(-0.258524 + 3.12700i) q^{21} +(-2.18716 + 1.07275i) q^{22} +(-1.20321 - 2.08402i) q^{23} +(1.50717 - 2.61049i) q^{24} +(-2.48755 + 4.30856i) q^{25} +(1.36333 - 0.787117i) q^{26} -5.44765i q^{27} +(-3.85099 - 0.318380i) q^{28} +2.10577i q^{29} +(-0.119051 + 0.0687343i) q^{30} +(3.69076 + 2.13086i) q^{31} +(5.07295 + 2.92887i) q^{32} +(3.26569 + 2.19224i) q^{33} +3.23361i q^{34} +(0.343172 + 0.237856i) q^{35} +2.32743 q^{36} +(3.46050 + 5.99377i) q^{37} +(3.90856 + 2.25661i) q^{38} +(-2.20122 - 1.27088i) q^{39} +(-0.200565 - 0.347389i) q^{40} -6.42979 q^{41} +(-0.983948 - 2.08402i) q^{42} +6.98850i q^{43} +(-2.69981 + 4.02180i) q^{44} +(-0.217799 - 0.125747i) q^{45} +(1.53072 + 0.883762i) q^{46} +(3.21780 - 1.85780i) q^{47} -1.25007i q^{48} +(-4.44805 + 5.40507i) q^{49} -3.65422i q^{50} +(4.52150 - 2.61049i) q^{51} +(1.56512 - 2.71087i) q^{52} +(0.160117 - 0.277330i) q^{53} +(2.00066 + 3.46524i) q^{54} +(0.469936 - 0.230492i) q^{55} +(6.08113 - 2.87114i) q^{56} -7.28701i q^{57} +(-0.773346 - 1.33947i) q^{58} +(-11.6893 - 6.74882i) q^{59} +(-0.136673 + 0.236725i) q^{60} +(-3.41546 - 5.91575i) q^{61} -3.13025 q^{62} +(2.40179 - 3.46524i) q^{63} -2.19436 q^{64} +(-0.292926 + 0.169121i) q^{65} +(-2.88240 - 0.195149i) q^{66} +(1.32743 - 2.29918i) q^{67} +(3.21490 + 5.56836i) q^{68} -2.85384i q^{69} +(-0.305644 - 0.0252690i) q^{70} -3.51459 q^{71} +(-3.50782 + 2.02524i) q^{72} +(-1.76569 + 3.05826i) q^{73} +(-4.40244 - 2.54175i) q^{74} +(-5.10963 + 2.95005i) q^{75} +8.97419 q^{76} +(3.20187 + 8.16995i) q^{77} +1.86693 q^{78} +(1.30660 - 0.754366i) q^{79} +(-0.144065 - 0.0831759i) q^{80} +(0.839883 - 1.45472i) q^{81} +(4.08998 - 2.36135i) q^{82} +9.49123 q^{83} +(-3.76635 - 2.61049i) q^{84} -0.694778i q^{85} +(-2.56654 - 4.44537i) q^{86} +(-1.24864 + 2.16271i) q^{87} +(0.569441 - 8.41078i) q^{88} +(-11.7448 + 6.78089i) q^{89} +0.184723 q^{90} +(-2.42101 - 5.12774i) q^{91} +3.51459 q^{92} +(2.52704 + 4.37697i) q^{93} +(-1.36456 + 2.36348i) q^{94} +(-0.839798 - 0.484858i) q^{95} +(3.47342 + 6.01614i) q^{96} +3.55778i q^{97} +(0.844377 - 5.07171i) q^{98} +(-2.32743 - 4.74526i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{11} - 18 q^{12} + 8 q^{14} - 20 q^{15} + 12 q^{16} - 4 q^{22} - 20 q^{23} + 14 q^{25} + 18 q^{26} + 6 q^{31} + 18 q^{33} - 12 q^{36} + 16 q^{37} - 48 q^{38} + 16 q^{42}+ \cdots + 12 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9 - 4 * q^11 - 18 * q^12 + 8 * q^14 - 20 * q^15 + 12 * q^16 - 4 * q^22 - 20 * q^23 + 14 * q^25 + 18 * q^26 + 6 * q^31 + 18 * q^33 - 12 * q^36 + 16 * q^37 - 48 * q^38 + 16 * q^42 + 20 * q^44 + 54 * q^45 - 18 * q^47 + 16 * q^49 - 2 * q^53 + 18 * q^56 - 6 * q^58 - 12 * q^59 + 28 * q^64 - 42 * q^66 - 24 * q^67 - 58 * q^70 + 20 * q^71 - 78 * q^75 - 50 * q^77 + 8 * q^78 + 30 * q^80 + 14 * q^81 + 54 * q^82 - 38 * q^86 - 4 * q^88 - 66 * q^89 + 22 * q^91 - 20 * q^92 + 12 * q^93 + 12 * q^99

Introduction

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