LMFDB - Embedded newform 77.2.i.a.54.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [77,2,Mod(10,77)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			54.4
Root			$0.636099 - 0.367252i$ of defining polynomial
Character	$\chi$	$=$	77.54
Dual form			77.2.i.a.10.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.636099 + 0.367252i) q^{2} +(1.02704 - 0.592963i) q^{3} +(-0.730252 - 1.26483i) q^{4} +(0.136673 + 0.0789082i) q^{5} +0.871067 q^{6} +(-1.12959 + 2.39249i) q^{7} -2.54175i q^{8} +(-0.796790 + 1.38008i) q^{9} +O(q^{10})$	\(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} +(-1.84854 + 2.75370i) 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} +(-0.265689 + 3.92429i) 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} +(4.83288 + 0.327204i) 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} +(-1.61021 + 2.39866i) 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} +(-4.50012 - 7.53319i) 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} +(6.99923 + 4.69854i) 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}+O(q^{10}) $ 12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$45$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	$-0.249714\pi$
$2$	0.636099	+	0.367252i	0.449790	+	0.259686i	−0.257952	+	0.966158i	$0.583048\pi$
$3$	1.02704	−	0.592963i	0.592963	−	0.342347i	−0.173305	−	0.984868i	$-0.555445\pi$
$3$	1.02704	−	0.592963i	0.592963	−	0.342347i	0.766268	+	0.642521i	$0.222111\pi$
$4$	−0.730252	−	1.26483i	−0.365126	−	0.632417i
$5$	0.136673	+	0.0789082i	0.0611221	+	0.0352888i	0.530250	−	0.847842i	$-0.322098\pi$
$5$	0.136673	+	0.0789082i	0.0611221	+	0.0352888i	−0.469128	+	0.883130i	$0.655432\pi$
$6$	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
$11$	−1.84854	+	2.75370i	−0.557357	+	0.830273i
$11$	−1.84854	+	2.75370i	−0.557357	+	0.830273i
$12$	−1.50000	−	0.866025i	−0.433013	−	0.250000i
$13$	2.14326			0.594434			0.297217	−	0.954810i	$-0.403941\pi$
$13$	2.14326			0.594434			0.297217	+	0.954810i	$0.403941\pi$
$14$	−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	−0.999217	−	0.0395673i	$-0.987402\pi$
$17$	−2.20122	−	3.81263i	−0.533875	−	0.924698i	0.465342	−	0.885131i	$-0.345931\pi$
$18$	−1.01367	+	0.585245i	−0.238925	+	0.137943i
$19$	3.07229	−	5.32136i	0.704831	−	1.22080i	−0.261921	−	0.965089i	$-0.584356\pi$
$19$	3.07229	−	5.32136i	0.704831	−	1.22080i	0.966752	−	0.255714i	$-0.0823107\pi$
$20$		−	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	−0.963770	−	0.266734i	$-0.914055\pi$
$23$	−1.20321	+	2.08402i	−0.250887	+	0.434549i	0.712883	+	0.701282i	$0.247389\pi$
$24$	−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	−0.130494	−	0.991449i	$-0.541656\pi$
$31$	3.69076	−	2.13086i	0.662880	−	0.382714i	0.793373	+	0.608735i	$0.208323\pi$
$32$	−5.07295	+	2.92887i	−0.896779	+	0.517755i
$33$	−0.265689	+	3.92429i	−0.0462505	+	0.683131i
$34$		−	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	−0.427771	−	0.903887i	$-0.640701\pi$
$37$	3.46050	−	5.99377i	0.568903	−	0.985370i	0.996675	−	0.0814827i	$-0.0259655\pi$
$38$	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	$-0.332567\pi$
$41$	6.42979			1.00416			0.502082	+	0.864820i	$0.332567\pi$
$42$	−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	$0.821114\pi$
$44$	4.83288	+	0.327204i	0.728585	+	0.0493279i
$45$	−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	0.715974	−	0.698127i	$-0.245983\pi$
$47$	3.21780	+	1.85780i	0.469364	+	0.270988i	−0.246609	+	0.969115i	$0.579316\pi$
$48$			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	0.876813	−	0.480832i	$-0.159665\pi$
$53$	0.160117	+	0.277330i	0.0219937	+	0.0380942i	−0.854819	+	0.518926i	$0.826332\pi$
$54$	−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	−0.522149	+	0.852855i	$0.674869\pi$
$59$	−11.6893	+	6.74882i	−1.52182	+	0.878621i	−0.999668	+	0.0257667i	$0.991797\pi$
$60$	−0.136673	−	0.236725i	−0.0176444	−	0.0305610i
$61$	3.41546	−	5.91575i	0.437305	−	0.757434i	−0.560176	−	0.828374i	$-0.689266\pi$
$61$	3.41546	−	5.91575i	0.437305	−	0.757434i	0.997481	+	0.0709395i	$0.0225997\pi$
$62$	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
$66$	−1.61021	+	2.39866i	−0.198203	+	0.295255i
$67$	1.32743	+	2.29918i	0.162171	+	0.280889i	0.935647	−	0.352937i	$-0.114817\pi$
$67$	1.32743	+	2.29918i	0.162171	+	0.280889i	−0.773476	+	0.633826i	$0.781484\pi$
$68$	−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	$-0.100408\pi$
$73$	1.76569	+	3.05826i	0.206658	+	0.357943i	−0.744002	+	0.668178i	$0.767075\pi$
$74$	4.40244	−	2.54175i	0.511774	−	0.295473i
$75$	−5.10963	−	2.95005i	−0.590009	−	0.340642i
$76$	−8.97419			−1.02941
$77$	−4.50012	−	7.53319i	−0.512836	−	0.858486i
$78$	1.86693			0.211388
$79$	−1.30660	−	0.754366i	−0.147004	−	0.0848728i	0.424694	−	0.905337i	$-0.360382\pi$
$79$	−1.30660	−	0.754366i	−0.147004	−	0.0848728i	−0.571698	+	0.820464i	$0.693715\pi$
$80$	−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	$-0.674403\pi$
$83$	−9.49123			−1.04180			−0.520899	+	0.853618i	$0.674403\pi$
$84$	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
$88$	6.99923	+	4.69854i	0.746121	+	0.500866i
$89$	−11.7448	−	6.78089i	−1.24495	−	0.718773i	−0.274853	−	0.961486i	$-0.588629\pi$
$89$	−11.7448	−	6.78089i	−1.24495	−	0.718773i	−0.970098	+	0.242714i	$0.921962\pi$
$90$	−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	$-0.942190\pi$
$97$		−	3.55778i		−	0.361238i	0.983553	−	0.180619i	$-0.0578100\pi$
$98$	−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	0.967379	+	0.253333i	$0.0815268\pi$
$101$	7.06589	+	12.2385i	0.703082	+	1.21777i	−0.264297	+	0.964441i	$0.585140\pi$
$102$	−1.91741	−	3.32105i	−0.189852	−	0.328833i
$103$	13.9911	+	8.07779i	1.37859	+	0.795928i	0.991990	−	0.126319i	$-0.0403164\pi$
$103$	13.9911	+	8.07779i	1.37859	+	0.795928i	0.386599	+	0.922248i	$0.373650\pi$
$104$		−	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	$-0.342158\pi$
$107$	−0.496626	−	0.286727i	−0.0480107	−	0.0277190i	−0.523813	+	0.851833i	$0.675491\pi$
$108$	6.89037	−	3.97816i	0.663026	−	0.382798i
$109$	11.6766	−	6.74149i	1.11842	−	0.645718i	0.177420	−	0.984135i	$-0.443225\pi$
$109$	11.6766	−	6.74149i	1.11842	−	0.645718i	0.940996	+	0.338417i	$0.109891\pi$
$110$	−0.383574	−	0.0259694i	−0.0365724	−	0.00247608i
$111$		−	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
$121$	−4.16577	−	10.1807i	−0.378706	−	0.925517i
$122$	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	−0.239450	−	0.970909i	$-0.576967\pi$
$131$	8.25344	−	14.2954i	0.721106	−	1.24899i	0.960557	−	0.278084i	$-0.0896994\pi$
$132$	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	0.997846	−	0.0656076i	$-0.0208985\pi$
$137$	5.17471	+	8.96285i	0.442105	+	0.765748i	−0.555741	+	0.831356i	$0.687565\pi$
$138$	−1.04808	+	1.81532i	−0.0892182	+	0.154530i
$139$	−16.2217			−1.37590			−0.687952	−	0.725756i	$-0.741490\pi$
$139$	−16.2217			−1.37590			−0.687952	+	0.725756i	$0.741490\pi$
$140$	0.551450	+	0.260361i	0.0466060	+	0.0220045i
$141$	4.40642			0.371088
$142$	−2.23562	−	1.29074i	−0.187609	−	0.108316i
$143$	−3.96192	+	5.90191i	−0.331312	+	0.493543i
$144$	−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	$-0.568870\pi$
$149$	−14.2554	−	8.23036i	−1.16785	−	0.674258i	−0.953172	+	0.302428i	$0.902203\pi$
$150$	−2.16682	−	3.75304i	−0.176920	−	0.306435i
$151$	−8.13439	+	4.69639i	−0.661967	+	0.382187i	−0.793026	−	0.609188i	$-0.791496\pi$
$151$	−8.13439	+	4.69639i	−0.661967	+	0.382187i	0.131059	+	0.991375i	$0.458162\pi$
$152$	−13.5256	−	7.80900i	−1.09707	−	0.633393i
$153$	7.01564			0.567181
$154$	−0.0959442	−	6.44453i	−0.00773140	−	0.519315i
$155$	0.672570			0.0540221
$156$	−3.21490	−	1.85612i	−0.257398	−	0.148609i
$157$	−1.10078	+	0.635534i	−0.0878515	+	0.0507211i	−0.543282	−	0.839550i	$-0.682819\pi$
$157$	−1.10078	+	0.635534i	−0.0878515	+	0.0507211i	0.455431	+	0.890271i	$0.349485\pi$
$158$	−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	0.402324	+	0.915497i	$0.368202\pi$
$163$	−7.55408	+	13.0841i	−0.591682	+	1.02482i	−0.994006	+	0.109325i	$0.965131\pi$
$164$	−4.69537	−	8.13262i	−0.366647	−	0.635051i
$165$	−0.345971	+	0.515380i	−0.0269338	+	0.0401222i
$166$	−6.03736	−	3.48567i	−0.468590	−	0.270541i
$167$	12.4522			0.963579			0.481789	−	0.876287i	$-0.339987\pi$
$167$	12.4522			0.963579			0.481789	+	0.876287i	$0.339987\pi$
$168$	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	0.155386	+	0.987854i	$0.450338\pi$
$173$	−10.2305	+	17.7198i	−0.777814	+	1.34721i	−0.933200	+	0.359359i	$0.882995\pi$
$174$			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	0.811598	−	0.584217i	$-0.198598\pi$
$179$	−1.33988	−	2.32075i	−0.100148	−	0.173461i	−0.911745	+	0.410756i	$0.865265\pi$
$180$	0.318097	+	0.183653i	0.0237096	+	0.0136887i
$181$			6.69771i			0.497837i	0.968524	+	0.248918i	$0.0800751\pi$
$181$			6.69771i			0.497837i	−0.968524	+	0.248918i	$0.919925\pi$
$182$	−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
$187$	14.5679	+	0.986301i	1.06531	+	0.0721255i
$188$		−	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	0.0347716	−	0.999395i	$-0.488930\pi$
$191$	12.2017	−	21.1340i	0.882887	−	1.52921i	0.848116	−	0.529811i	$-0.177737\pi$
$192$	−2.25370	+	1.30117i	−0.162646	+	0.0939040i
$193$	−7.68615	+	4.43760i	−0.553261	+	0.319425i	−0.750436	−	0.660943i	$-0.770157\pi$
$193$	−7.68615	+	4.43760i	−0.553261	+	0.319425i	0.197175	+	0.980368i	$0.436823\pi$
$194$	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	$-0.174046\pi$
$198$	0.262230	−	3.87321i	0.0186359	−	0.275257i
$199$	19.6730	−	11.3582i	1.39459	−	0.805164i	0.400767	−	0.916180i	$-0.368744\pi$
$199$	19.6730	−	11.3582i	1.39459	−	0.805164i	0.993819	+	0.111016i	$0.0354104\pi$
$200$	−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
$220$	0.634706	+	0.426074i	0.0427919	+	0.0287259i
$221$	−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	$-0.774571\pi$
$223$		−	19.4273i		−	1.30095i	0.759529	−	0.650473i	$-0.225429\pi$
$224$	−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	$-0.327048\pi$
$227$	−7.27417	−	12.5992i	−0.482803	−	0.836240i	−0.999805	+	0.0197443i	$0.993715\pi$
$228$	−9.21687	+	5.32136i	−0.610402	+	0.352416i
$229$	−3.11849	−	1.80046i	−0.206075	−	0.118978i	0.393411	−	0.919363i	$-0.371295\pi$
$229$	−3.11849	−	1.80046i	−0.206075	−	0.118978i	−0.599486	+	0.800385i	$0.704628\pi$
$230$	−0.278944			−0.0183931
$231$	−9.08871	−	5.06850i	−0.597994	−	0.333483i
$232$	5.35234			0.351398
$233$	13.2213	+	7.63333i	0.866157	+	0.500076i	0.866069	−	0.499924i	$-0.166639\pi$
$233$	13.2213	+	7.63333i	0.866157	+	0.500076i	8.78090e−5		1.00000i	$0.499972\pi$
$234$	−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	$-0.208842\pi$
$241$	−2.05090	−	3.55227i	−0.132110	−	0.228822i	−0.924490	+	0.381207i	$0.875509\pi$
$242$	1.08904	−	8.00580i	0.0700059	−	0.514633i
$243$	−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	$-0.929174\pi$
$251$		−	6.99234i		−	0.441353i	0.975347	−	0.220676i	$-0.0708265\pi$
$252$	−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	0.928943	−	0.370224i	$-0.120719\pi$
$257$	17.1981	+	9.92936i	1.07279	+	0.619376i	0.143848	+	0.989600i	$0.454052\pi$
$258$			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	$-0.730041\pi$
$263$	−5.55559	+	3.20752i	−0.342572	+	0.197784i	0.318837	+	0.947810i	$0.396708\pi$
$264$	9.97457	+	0.675315i	0.613892	+	0.0415628i
$265$			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	−0.915332	−	0.402701i	$-0.868072\pi$
$269$	−16.7989	+	9.69886i	−1.02425	+	0.591350i	−0.108917	+	0.994051i	$0.534738\pi$
$270$	−0.546872	+	0.315737i	−0.0332816	+	0.0192151i
$271$	5.73573	−	9.93458i	0.348421	−	0.603483i	−0.637548	−	0.770411i	$-0.720051\pi$
$271$	5.73573	−	9.93458i	0.348421	−	0.603483i	0.985969	+	0.166928i	$0.0533846\pi$
$272$	4.64055			0.281374
$273$	0.554084	+	6.70198i	0.0335347	+	0.405622i
$274$			7.60168i			0.459234i
$275$	16.4628	+	1.11459i	0.992746	+	0.0672126i
$276$	3.60963	−	2.08402i	0.217274	−	0.125443i
$277$	−4.09367	+	2.36348i	−0.245965	+	0.142008i	−0.617915	−	0.786245i	$-0.712023\pi$
$277$	−4.09367	+	2.36348i	−0.245965	+	0.142008i	0.371950	+	0.928253i	$0.378689\pi$
$278$	−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	−0.871057	−	0.491183i	$-0.836565\pi$
$283$	−14.4827	−	25.0847i	−0.860905	−	1.49113i	0.0101515	−	0.999948i	$-0.496769\pi$
$284$	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	$-0.411552\pi$
$293$	9.39074			0.548613			0.274306	+	0.961642i	$0.411552\pi$
$294$	−3.87455	−	4.70818i	−0.225968	−	0.274587i
$295$	−2.13015			−0.124022
$296$	−15.2347	−	8.79575i	−0.885498	−	0.511242i
$297$	−15.0012	−	10.0702i	−0.870458	−	0.584333i
$298$	−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	$-0.534306\pi$
$307$	−3.76948			−0.215136			−0.107568	+	0.994198i	$0.534306\pi$
$308$	−6.24201	+	11.1930i	−0.355672	+	0.637782i
$309$	19.1593			1.08994
$310$	0.427821	+	0.247002i	0.0242986	+	0.0140288i
$311$	7.48181	−	4.31963i	0.424255	−	0.244944i	−0.272641	−	0.962116i	$-0.587897\pi$
$311$	7.48181	−	4.31963i	0.424255	−	0.244944i	0.696896	+	0.717172i	$0.254564\pi$
$312$	−3.23025	−	5.59496i	−0.182877	−	0.316752i
$313$	−9.09192	−	5.24922i	−0.513906	−	0.296704i	0.220532	−	0.975380i	$-0.429221\pi$
$313$	−9.09192	−	5.24922i	−0.513906	−	0.296704i	−0.734438	+	0.678676i	$0.762554\pi$
$314$	−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	0.328265	+	0.944586i	$0.393536\pi$
$317$	−11.6424	+	20.1652i	−0.653903	+	1.13259i	−0.982168	+	0.188007i	$0.939797\pi$
$318$	0.139472	+	0.241573i	0.00782121	+	0.0135467i
$319$	−5.79866	−	3.89260i	−0.324662	−	0.217944i
$320$	−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	−0.998245	−	0.0592204i	$-0.981139\pi$
$331$	−8.14766	+	14.1122i	−0.447836	+	0.775675i	0.550409	+	0.834895i	$0.314472\pi$
$332$	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
$341$	−0.954774	+	14.1022i	−0.0517039	+	0.763679i
$342$			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	$-0.641198\pi$
$347$	2.57880	−	1.48887i	0.138437	−	0.0799267i	0.567619	+	0.823291i	$0.307865\pi$
$348$	1.82365	−	3.15865i	0.0977577	−	0.169321i
$349$	17.9638			0.961580			0.480790	−	0.876836i	$-0.340350\pi$
$349$	17.9638			0.961580			0.480790	+	0.876836i	$0.340350\pi$
$350$	8.74271	+	4.12777i	0.467317	+	0.220639i
$351$			11.6757i			0.623205i
$352$	1.31234	−	19.3835i	0.0699478	−	1.03315i
$353$	27.2798	−	15.7500i	1.45195	−	0.838287i	0.453362	−	0.891326i	$-0.350224\pi$
$353$	27.2798	−	15.7500i	1.45195	−	0.838287i	0.998592	+	0.0530398i	$0.0168910\pi$
$354$	−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	$-0.478242\pi$
$359$	−14.4293	−	8.33075i	−0.761548	−	0.439680i	−0.829851	+	0.557984i	$0.811575\pi$
$360$	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	−0.0801361	−	0.996784i	$-0.525535\pi$
$367$	14.2345	−	8.21831i	0.743036	−	0.428992i	0.823172	+	0.567792i	$0.192202\pi$
$368$	−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	$-0.143841\pi$
$373$	18.7583	+	10.8301i	0.971270	+	0.560763i	0.0716470	+	0.997430i	$0.477174\pi$
$374$	8.90440	+	5.97747i	0.460436	+	0.309088i
$375$	−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	−0.0346432	−	0.999400i	$-0.511029\pi$
$383$	−17.9552	−	10.3665i	−0.917470	−	0.529702i	−0.882827	+	0.469698i	$0.844363\pi$
$384$	11.9822			0.611466
$385$	−0.0206147	−	1.38468i	−0.00105062	−	0.0705699i
$386$	−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	0.982317	+	0.187226i	$0.0599498\pi$
$389$	12.8851	+	22.3177i	0.653301	+	1.13155i	−0.329016	+	0.944324i	$0.606717\pi$
$390$	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
$396$	−4.30236	+	6.40905i	−0.216202	+	0.322067i
$397$	−23.5045	−	13.5703i	−1.17966	−	0.681074i	−0.223721	−	0.974653i	$-0.571820\pi$
$397$	−23.5045	−	13.5703i	−1.17966	−	0.681074i	−0.955935	+	0.293579i	$0.905154\pi$
$398$	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	−0.493112	−	0.869966i	$-0.664141\pi$
$401$	10.1498	−	17.5800i	0.506857	−	0.877902i	0.999969	−	0.00793574i	$-0.00252605\pi$
$402$	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	$-0.331224\pi$
$409$	−9.99557	−	17.3128i	−0.494249	−	0.856065i	−0.999978	+	0.00662777i	$0.997890\pi$
$410$	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
$418$	−1.01112	+	14.9344i	−0.0494553	+	0.730468i
$419$		−	0.494451i		−	0.0241555i	−0.999927	−	0.0120778i	$-0.996155\pi$
$419$		−	0.494451i		−	0.0241555i	0.999927	−	0.0120778i	$-0.00384456\pi$
$420$	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
$429$	−0.569441	+	8.41078i	−0.0274929	+	0.406076i
$430$	−0.701553	+	0.405042i	−0.0338319	+	0.0195329i
$431$	21.8886	−	12.6374i	1.05434	−	0.608721i	0.130476	−	0.991451i	$-0.458349\pi$
$431$	21.8886	−	12.6374i	1.05434	−	0.608721i	0.923860	+	0.382730i	$0.125016\pi$
$432$	−4.97296	−	2.87114i	−0.239262	−	0.138138i
$433$		−	5.33297i		−	0.256286i	−0.991756	−	0.128143i	$-0.959098\pi$
$433$		−	5.33297i		−	0.256286i	0.991756	−	0.128143i	$-0.0409017\pi$
$434$	−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	0.468911	+	0.883245i	$0.344646\pi$
$439$	−11.1143	+	19.2506i	−0.530457	+	0.918779i	−0.999368	+	0.0355336i	$0.988687\pi$
$440$	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	0.429203	+	0.903208i	$0.358794\pi$
$443$	−11.9466	+	20.6921i	−0.567600	+	0.983111i	−0.996803	+	0.0799033i	$0.974539\pi$
$444$	−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
$451$	−11.8858	+	17.7057i	−0.559678	+	0.833731i
$452$	−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	$-0.325346\pi$
$457$	0.929025	+	0.536373i	0.0434580	+	0.0250905i	−0.478114	+	0.878298i	$0.658679\pi$
$458$	−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	$-0.580929\pi$
$461$	−10.8005			−0.503032			−0.251516	+	0.967853i	$0.580929\pi$
$462$	−3.91990	−	6.56191i	−0.182370	−	0.305288i
$463$	−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	0.530198	−	0.847874i	$-0.322118\pi$
$467$	1.31858	+	0.761280i	0.0610164	+	0.0352278i	−0.469181	+	0.883102i	$0.655451\pi$
$468$	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
$473$	−19.2442	−	12.9185i	−0.884852	−	0.593996i
$474$	−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	$-0.193220\pi$
$479$	−1.82365	−	3.15865i	−0.0833246	−	0.144322i	−0.904676	+	0.426100i	$0.859887\pi$
$480$	−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	0.993767	+	0.111475i	$0.0355574\pi$
$487$	13.0957	+	22.6824i	0.593424	+	1.02784i	−0.400344	+	0.916365i	$0.631109\pi$
$488$	−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
$495$	0.0563432	−	0.832203i	0.00253244	−	0.0374047i
$496$			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	−0.781779	−	0.623556i	$-0.785687\pi$
$499$	3.33122	−	5.76985i	0.149126	−	0.258294i	0.930905	+	0.365262i	$0.119021\pi$
$500$	−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	$-0.703136\pi$
$503$	−26.7216			−1.19146			−0.595728	+	0.803186i	$0.703136\pi$
$504$	−8.80778	+	6.10475i	−0.392330	+	0.271927i
$505$			2.23023i			0.0992438i
$506$	0.395987	−	5.84882i	0.0176038	−	0.260012i
$507$	−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	0.512651	−	0.858597i	$-0.328664\pi$
$509$	0.573256	+	0.330969i	0.0254091	+	0.0146700i	−0.487242	+	0.873267i	$0.661997\pi$
$510$		−	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	−0.624384	−	0.781118i	$-0.714650\pi$
$521$	−5.93706	+	3.42776i	−0.260107	+	0.150173i	0.364276	+	0.931291i	$0.381316\pi$
$522$	−1.23239	−	2.13456i	−0.0539402	−	0.0934271i
$523$	−4.86780	+	8.43128i	−0.212854	+	0.368674i	−0.952607	−	0.304205i	$-0.901609\pi$
$523$	−4.86780	+	8.43128i	−0.212854	+	0.368674i	0.739752	+	0.672879i	$0.234943\pi$
$524$	−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
$528$	−3.44231	−	2.31080i	−0.149807	−	0.100565i
$529$	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
$539$	23.1064	−	2.25709i	0.995263	−	0.0972199i
$540$	1.25564			0.0540340
$541$	−12.9628	−	7.48407i	−0.557314	−	0.321765i	0.194753	−	0.980852i	$-0.437610\pi$
$541$	−12.9628	−	7.48407i	−0.557314	−	0.321765i	−0.752067	+	0.659087i	$0.770943\pi$
$542$	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
$550$	10.0626	+	6.75499i	0.429073	+	0.288034i
$551$	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	$-0.485851\pi$
$557$	21.9918	−	12.6970i	0.931822	−	0.537988i	0.887387	+	0.461024i	$0.152518\pi$
$558$	−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	$-0.0650965\pi$
$563$	7.44346	+	12.8925i	0.313705	+	0.543352i	−0.665457	+	0.746436i	$0.731763\pi$
$564$	−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	$-0.0833224\pi$
$569$	29.2157	+	16.8677i	1.22479	+	0.707131i	0.258852	+	0.965917i	$0.416656\pi$
$570$	0.731520	−	0.422343i	0.0306400	−	0.0176900i
$571$	−10.0725	+	5.81536i	−0.421521	+	0.243365i	−0.695728	−	0.718305i	$-0.744918\pi$
$571$	−10.0725	+	5.81536i	−0.421521	+	0.243365i	0.274207	+	0.961671i	$0.411585\pi$
$572$	10.3581	+	0.701284i	0.433096	+	0.0293222i
$573$		−	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	−0.759792	−	0.650166i	$-0.774699\pi$
$577$	−13.8511	+	7.99692i	−0.576628	+	0.332916i	0.183164	+	0.983082i	$0.441366\pi$
$578$	−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
$583$	−1.05967	−	0.0717434i	−0.0438869	−	0.00297131i
$584$	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	$-0.844208\pi$
$587$		−	22.7806i		−	0.940257i	0.882598	−	0.470128i	$-0.155792\pi$
$588$	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	0.454910	+	0.890537i	$0.349671\pi$
$593$	−13.2417	+	22.9354i	−0.543773	+	0.941842i	−0.998683	+	0.0513049i	$0.983662\pi$
$594$	−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	0.752817	−	0.658229i	$-0.228694\pi$
$599$	−4.73911	−	8.20837i	−0.193635	−	0.335385i	−0.946452	+	0.322844i	$0.895361\pi$
$600$	−7.49829	+	12.9874i	−0.306116	+	0.530209i
$601$	43.2756			1.76525			0.882623	−	0.470081i	$-0.155775\pi$
$601$	43.2756			1.76525			0.882623	+	0.470081i	$0.155775\pi$
$602$	−7.73639	−	11.1619i	−0.315312	−	0.454924i
$603$	−4.23073			−0.172289
$604$	11.8803	+	6.85910i	0.483403	+	0.279093i
$605$	0.233992	−	1.72014i	0.00951313	−	0.0699336i
$606$	6.15486	+	10.6605i	0.250024	+	0.433054i
$607$	−1.07163	+	1.85612i	−0.0434962	+	0.0753376i	−0.886954	−	0.461858i	$-0.847183\pi$
$607$	−1.07163	+	1.85612i	−0.0434962	+	0.0753376i	0.843458	+	0.537196i	$0.180516\pi$
$608$			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	$-0.912083\pi$
$613$	−29.8835	+	17.2533i	−1.20698	+	0.696852i	−0.244884	+	0.969552i	$0.578750\pi$
$614$	−2.39776	−	1.38435i	−0.0967658	−	0.0558677i
$615$	1.20339			0.0485254
$616$	−19.1475	+	11.4382i	−0.771475	+	0.460858i
$617$	−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	−0.476822	−	0.879000i	$-0.658211\pi$
$619$	1.14454	−	0.660803i	0.0460031	−	0.0265599i	0.522825	+	0.852440i	$0.324878\pi$
$620$	−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
$627$	20.0663	+	13.4704i	0.801370	+	0.537955i
$628$	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	−0.988917	−	0.148469i	$-0.952566\pi$
$641$	−15.7740	−	27.3214i	−0.623036	−	1.07913i	0.365881	−	0.930662i	$-0.380768\pi$
$642$	−0.432595	−	0.249759i	−0.0170731	−	0.00985719i
$643$			31.8502i			1.25605i	0.778194	+	0.628024i	$0.216136\pi$
$643$			31.8502i			1.25605i	−0.778194	+	0.628024i	$0.783864\pi$
$644$	−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	−0.902489	−	0.430713i	$-0.858262\pi$
$647$	−24.9459	+	14.4025i	−0.980725	+	0.566222i	−0.0782362	+	0.996935i	$0.524929\pi$
$648$	3.69754	−	2.13478i	0.145253	−	0.0838619i
$649$	3.02394	−	44.6643i	0.118700	−	1.75323i
$650$		−	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	−0.825875	−	0.563853i	$-0.809319\pi$
$653$	1.92607	−	3.33605i	0.0753730	−	0.130550i	0.901248	+	0.433303i	$0.142652\pi$
$654$	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	$-0.130011\pi$
$660$	0.904516	+	0.0612391i	0.0352082	+	0.00238373i
$661$	−23.7738	+	13.7258i	−0.924695	+	0.533873i	−0.885130	−	0.465344i	$-0.845931\pi$
$661$	−23.7738	+	13.7258i	−0.924695	+	0.533873i	−0.0395649	+	0.999217i	$0.512597\pi$
$662$	−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	$-0.830364\pi$
$677$	0.242681	−	0.420336i	0.00932698	−	0.0161548i	0.870651	+	0.491901i	$0.163698\pi$
$678$	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
$682$	−5.78640	+	8.61977i	−0.221573	+	0.330068i
$683$	0.275482	+	0.477149i	0.0105410	+	0.0182576i	0.871248	−	0.490843i	$-0.163311\pi$
$683$	0.275482	+	0.477149i	0.0105410	+	0.0182576i	−0.860707	+	0.509101i	$0.829978\pi$
$684$	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	0.737508	−	0.675338i	$-0.236002\pi$
$691$	13.7060	+	7.91317i	0.521402	+	0.301031i	−0.216106	+	0.976370i	$0.569336\pi$
$692$	29.8835			1.13600
$693$	13.9821	−	0.208161i	0.531134	−	0.00790737i
$694$	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
$704$	4.05636	−	6.04261i	0.152880	−	0.227739i
$705$	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	−0.977694	−	0.210034i	$-0.932643\pi$
$709$	−8.17324	+	14.1565i	−0.306953	+	0.531657i	0.670742	+	0.741691i	$0.265976\pi$
$710$	−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	0.550176	−	0.835049i	$-0.314561\pi$
$719$	2.73745	+	1.58047i	0.102090	+	0.0589415i	−0.448086	+	0.893991i	$0.647894\pi$
$720$		−	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
$726$	−3.62866	−	8.86806i	−0.134672	−	0.329124i
$727$			11.6758i			0.433033i	0.976279	+	0.216516i	$0.0694695\pi$
$727$			11.6758i			0.433033i	−0.976279	+	0.216516i	$0.930531\pi$
$728$	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	$-0.821854\pi$
$733$	0.976136	−	1.69072i	0.0360544	−	0.0624481i	0.883490	+	0.468451i	$0.155188\pi$
$734$	12.0727			0.445613
$735$	−0.832492	−	1.01161i	−0.0307069	−	0.0373137i
$736$		−	14.0962i		−	0.519592i
$737$	−8.78507	−	0.594781i	−0.323602	−	0.0219091i
$738$	−6.51771	+	3.76300i	−0.239920	+	0.138518i
$739$	−42.1645	+	24.3437i	−1.55105	+	0.895498i	−0.552991	+	0.833188i	$0.686513\pi$
$739$	−42.1645	+	24.3437i	−1.55105	+	0.895498i	−0.998057	+	0.0623100i	$0.980153\pi$
$740$	−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	−0.941377	−	0.337356i	$-0.890468\pi$
$751$	−4.89251	+	8.47407i	−0.178530	+	0.309223i	0.762847	+	0.646579i	$0.223801\pi$
$752$	−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
$759$	−7.85862	−	5.27544i	−0.285250	−	0.191487i
$760$	−1.23239	−	2.13456i	−0.0447034	−	0.0774286i
$761$	19.7562	−	34.2187i	0.716161	−	1.24043i	−0.246349	−	0.969181i	$-0.579231\pi$
$761$	19.7562	−	34.2187i	0.716161	−	1.24043i	0.962510	−	0.271246i	$-0.0874356\pi$
$762$			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	$-0.263182\pi$
$769$	37.5601			1.35445			0.677226	+	0.735775i	$0.263182\pi$
$770$	0.495413	−	0.888364i	0.0178535	−	0.0320144i
$771$	23.5510			0.848167
$772$	11.2257	+	6.48113i	0.404020	+	0.233261i
$773$	28.7468	−	16.5970i	1.03395	−	0.596951i	0.115836	−	0.993268i	$-0.463045\pi$
$773$	28.7468	−	16.5970i	1.03395	−	0.596951i	0.918114	+	0.396317i	$0.129712\pi$
$774$	−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
$781$	6.49687	−	9.67814i	0.232476	−	0.346311i
$782$	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	$-0.0242661\pi$
$787$	12.1357	+	21.0197i	0.432591	+	0.749270i	−0.564505	+	0.825430i	$0.690933\pi$
$788$	−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	$-0.908386\pi$
$797$		−	16.0273i		−	0.567716i	0.958866	−	0.283858i	$-0.0916145\pi$
$798$	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
$803$	−11.6855	−	0.791152i	−0.412372	−	0.0279191i
$804$		−	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	$-0.877904\pi$
$809$	−30.3457	+	17.5201i	−1.06690	+	0.615974i	−0.139566	+	0.990213i	$0.544571\pi$
$810$	−0.0973565	+	0.168626i	−0.00342076	+	0.00592493i
$811$	−1.92059			−0.0674409			−0.0337205	−	0.999431i	$-0.510736\pi$
$811$	−1.92059			−0.0674409			−0.0337205	+	0.999431i	$0.510736\pi$
$812$	0.670434	+	8.10929i	0.0235276	+	0.284580i
$813$		−	13.6043i		−	0.477124i
$814$	−1.13888	+	16.8216i	−0.0399178	+	0.589596i
$815$	−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	$-0.169970\pi$
$821$	24.3669	+	14.0682i	0.850411	+	0.490985i	−0.0103788	+	0.999946i	$0.503304\pi$
$822$	4.50751	+	7.80724i	0.157218	+	0.272309i
$823$	0.636673	+	1.10275i	0.0221930	+	0.0384395i	0.876909	−	0.480657i	$-0.159602\pi$
$823$	0.636673	+	1.10275i	0.0221930	+	0.0384395i	−0.854716	+	0.519097i	$0.826268\pi$
$824$	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	−0.473838	−	0.880612i	$-0.657132\pi$
$829$	1.49359	−	0.862326i	0.0518746	−	0.0299498i	0.525713	+	0.850662i	$0.323799\pi$
$830$	−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
$836$	16.5892	−	24.7122i	0.573749	−	0.854691i
$837$	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	$-0.912231\pi$
$839$		−	15.7719i		−	0.544506i	0.962226	−	0.272253i	$-0.0877687\pi$
$840$	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
$847$	29.0628	+	1.53344i	0.998611	+	0.0526895i
$848$	−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	$-0.429871\pi$
$853$	12.7654			0.437078			0.218539	+	0.975828i	$0.429871\pi$
$854$	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	$-0.184392\pi$
$857$	−1.62935	−	2.82212i	−0.0556576	−	0.0964017i	−0.892512	+	0.451024i	$0.851059\pi$
$858$	−3.45110	+	5.14096i	−0.117818	+	0.175509i
$859$	7.53736	+	4.35170i	0.257171	+	0.148478i	0.623044	−	0.782187i	$-0.285896\pi$
$859$	7.53736	+	4.35170i	0.257171	+	0.148478i	−0.365872	+	0.930665i	$0.619229\pi$
$860$	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	0.255079	+	0.966920i	$0.417899\pi$
$863$	−20.8528	+	36.1181i	−0.709838	+	1.22948i	−0.964917	+	0.262555i	$0.915435\pi$
$864$	−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	$-0.314509\pi$
$877$	3.03162	+	1.75030i	0.102370	+	0.0591036i	−0.447941	+	0.894063i	$0.647842\pi$
$878$	−14.1396	+	8.16350i	−0.477188	+	0.275505i
$879$	9.64469	−	5.56836i	0.325307	−	0.187816i
$880$	0.0372686	−	0.550467i	0.00125632	−	0.0185562i
$881$			24.6580i			0.830750i	0.909650	+	0.415375i	$0.136350\pi$
$881$			24.6580i			0.830750i	−0.909650	+	0.415375i	$0.863650\pi$
$882$	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	−0.243499	−	0.969901i	$-0.578295\pi$
$887$	21.3901	−	37.0487i	0.718209	−	1.24398i	0.961709	−	0.274074i	$-0.0883714\pi$
$888$	−20.8622			−0.700090
$889$	−50.1598	−	23.6824i	−1.68231	−	0.794283i
$890$		−	1.57204i		−	0.0526948i
$891$	−5.55843	−	0.376326i	−0.186214	−	0.0126074i
$892$	−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	0.630544	−	0.776153i	$-0.282832\pi$
$907$	−10.7484	−	18.6168i	−0.356896	−	0.618162i	−0.987441	+	0.157991i	$0.949498\pi$
$908$	−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
$913$	17.5450	−	26.1360i	0.580654	−	0.864977i
$914$	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	$-0.258517\pi$
$919$	12.2281	+	7.05987i	0.403367	+	0.232884i	−0.284569	+	0.958656i	$0.591850\pi$
$920$	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
$924$	0.226248	+	15.1970i	0.00744302	+	0.499945i
$925$	−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	0.156407	−	0.987693i	$-0.450009\pi$
$929$	−18.9203	−	10.9237i	−0.620756	−	0.358394i	−0.777163	+	0.629299i	$0.783342\pi$
$930$	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
$935$	1.91321	+	1.28433i	0.0625688	+	0.0420020i
$936$	7.51819	+	4.34063i	0.245740	+	0.141878i
$937$	12.3580			0.403717			0.201858	−	0.979415i	$-0.435302\pi$
$937$	12.3580			0.403717			0.201858	+	0.979415i	$0.435302\pi$
$938$	−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	$-0.112579\pi$
$941$	5.18742	+	8.98487i	0.169105	+	0.292898i	−0.769000	+	0.639248i	$0.779246\pi$
$942$	−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	−0.231699	−	0.972787i	$-0.574428\pi$
$947$	22.3602	−	38.7290i	0.726609	−	1.25852i	0.958308	−	0.285736i	$-0.0922382\pi$
$948$	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
$957$	−8.26363	−	0.559478i	−0.267125	−	0.0180854i
$958$		−	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	$-0.170893\pi$
$968$	−25.8768	+	10.5883i	−0.831711	+	0.340322i
$969$	−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	0.945779	−	0.324812i	$-0.105301\pi$
$971$	35.4415	+	20.4622i	1.13737	+	0.656662i	0.191594	+	0.981474i	$0.438634\pi$
$972$			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	0.985975	+	0.166891i	$0.0533727\pi$
$977$	19.9269	+	34.5145i	0.637519	+	1.10422i	−0.348456	+	0.937325i	$0.613294\pi$
$978$	−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	−0.717783	−	0.696266i	$-0.754843\pi$
$983$	−14.8515	+	8.57454i	−0.473691	+	0.273486i	0.244093	+	0.969752i	$0.421510\pi$
$984$	−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
$990$	0.341468	−	0.508671i	0.0108526	−	0.0161666i
$991$	−12.5921	−	21.8102i	−0.400002	−	0.692823i	0.593724	−	0.804669i	$-0.297657\pi$
$991$	−12.5921	−	21.8102i	−0.400002	−	0.692823i	−0.993726	+	0.111845i	$0.964324\pi$
$992$	−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	0.976147	+	0.217112i	$0.0696636\pi$
$997$	21.3480	+	36.9758i	0.676098	+	1.17104i	−0.300049	+	0.953924i	$0.597003\pi$
$998$	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.54.4	yes	12
3.2	odd	2		693.2.bg.a.208.3		12
4.3	odd	2		1232.2.bn.a.593.2		12
7.2	even	3		539.2.b.b.538.6		12
7.3	odd	6	inner	77.2.i.a.10.3	✓	12
7.4	even	3		539.2.i.c.472.3		12
7.5	odd	6		539.2.b.b.538.5		12
7.6	odd	2		539.2.i.c.362.4		12
11.2	odd	10		847.2.r.b.40.4		48
11.3	even	5		847.2.r.b.838.4		48
11.4	even	5		847.2.r.b.215.3		48
11.5	even	5		847.2.r.b.481.3		48
11.6	odd	10		847.2.r.b.481.4		48
11.7	odd	10		847.2.r.b.215.4		48
11.8	odd	10		847.2.r.b.838.3		48
11.9	even	5		847.2.r.b.40.3		48
11.10	odd	2	inner	77.2.i.a.54.3	yes	12
21.17	even	6		693.2.bg.a.10.4		12
28.3	even	6		1232.2.bn.a.241.1		12
33.32	even	2		693.2.bg.a.208.4		12
44.43	even	2		1232.2.bn.a.593.1		12
77.3	odd	30		847.2.r.b.717.4		48
77.10	even	6	inner	77.2.i.a.10.4	yes	12
77.17	even	30		847.2.r.b.360.3		48
77.24	even	30		847.2.r.b.766.3		48
77.31	odd	30		847.2.r.b.766.4		48
77.32	odd	6		539.2.i.c.472.4		12
77.38	odd	30		847.2.r.b.360.4		48
77.52	even	30		847.2.r.b.717.3		48
77.54	even	6		539.2.b.b.538.7		12
77.59	odd	30		847.2.r.b.94.3		48
77.65	odd	6		539.2.b.b.538.8		12
77.73	even	30		847.2.r.b.94.4		48
77.76	even	2		539.2.i.c.362.3		12
231.164	odd	6		693.2.bg.a.10.3		12
308.87	odd	6		1232.2.bn.a.241.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.i.a.10.3	✓	12	7.3	odd	6	inner
77.2.i.a.10.4	yes	12	77.10	even	6	inner
77.2.i.a.54.3	yes	12	11.10	odd	2	inner
77.2.i.a.54.4	yes	12	1.1	even	1	trivial
539.2.b.b.538.5		12	7.5	odd	6
539.2.b.b.538.6		12	7.2	even	3
539.2.b.b.538.7		12	77.54	even	6
539.2.b.b.538.8		12	77.65	odd	6
539.2.i.c.362.3		12	77.76	even	2
539.2.i.c.362.4		12	7.6	odd	2
539.2.i.c.472.3		12	7.4	even	3
539.2.i.c.472.4		12	77.32	odd	6
693.2.bg.a.10.3		12	231.164	odd	6
693.2.bg.a.10.4		12	21.17	even	6
693.2.bg.a.208.3		12	3.2	odd	2
693.2.bg.a.208.4		12	33.32	even	2
847.2.r.b.40.3		48	11.9	even	5
847.2.r.b.40.4		48	11.2	odd	10
847.2.r.b.94.3		48	77.59	odd	30
847.2.r.b.94.4		48	77.73	even	30
847.2.r.b.215.3		48	11.4	even	5
847.2.r.b.215.4		48	11.7	odd	10
847.2.r.b.360.3		48	77.17	even	30
847.2.r.b.360.4		48	77.38	odd	30
847.2.r.b.481.3		48	11.5	even	5
847.2.r.b.481.4		48	11.6	odd	10
847.2.r.b.717.3		48	77.52	even	30
847.2.r.b.717.4		48	77.3	odd	30
847.2.r.b.766.3		48	77.24	even	30
847.2.r.b.766.4		48	77.31	odd	30
847.2.r.b.838.3		48	11.8	odd	10
847.2.r.b.838.4		48	11.3	even	5
1232.2.bn.a.241.1		12	28.3	even	6
1232.2.bn.a.241.2		12	308.87	odd	6
1232.2.bn.a.593.1		12	44.43	even	2
1232.2.bn.a.593.2		12	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 77 = 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	77.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.636099 + 0.367252i) q^{2} +(1.02704 - 0.592963i) q^{3} +(-0.730252 - 1.26483i) q^{4} +(0.136673 + 0.0789082i) q^{5} +0.871067 q^{6} +(-1.12959 + 2.39249i) q^{7} -2.54175i q^{8} +(-0.796790 + 1.38008i) q^{9} +O(q^{10})\)	\(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} +(-1.84854 + 2.75370i) 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} +(-0.265689 + 3.92429i) 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} +(4.83288 + 0.327204i) 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} +(-1.61021 + 2.39866i) 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} +(-4.50012 - 7.53319i) 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} +(6.99923 + 4.69854i) 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 4 q^{4} - 4 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 4 * q^4 - 4 * q^9	\( 12 q - 6 q^{3} + 4 q^{4} - 4 q^{9} - 4 q^{11} - 18 q^{12} + 8 q^{14} - 20 q^{15} + 12 q^{16} - 4 q^{22} - 20 q^{23} + 14 q^{25} + 18 q^{26} + 6 q^{31} + 18 q^{33} - 12 q^{36} + 16 q^{37} - 48 q^{38} + 16 q^{42} + 20 q^{44} + 54 q^{45} - 18 q^{47} + 16 q^{49} - 2 q^{53} + 18 q^{56} - 6 q^{58} - 12 q^{59} + 28 q^{64} - 42 q^{66} - 24 q^{67} - 58 q^{70} + 20 q^{71} - 78 q^{75} - 50 q^{77} + 8 q^{78} + 30 q^{80} + 14 q^{81} + 54 q^{82} - 38 q^{86} - 4 q^{88} - 66 q^{89} + 22 q^{91} - 20 q^{92} + 12 q^{93} + 12 q^{99}+O(q^{100}) \) 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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