LMFDB - Embedded newform 640.2.bm.a.461.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (of order $32$, degree $16$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			461.1
Character	$\chi$	$=$	640.461
Dual form			640.2.bm.a.261.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40522 - 0.159224i) q^{2} +(2.35093 - 0.713148i) q^{3} +(1.94930 + 0.447490i) q^{4} +(-0.995185 + 0.0980171i) q^{5} +(-3.41713 + 0.627806i) q^{6} +(1.13643 - 1.70079i) q^{7} +(-2.66794 - 0.939196i) q^{8} +(2.52390 - 1.68642i) q^{9} +O(q^{10})$	\(q+(-1.40522 - 0.159224i) q^{2} +(2.35093 - 0.713148i) q^{3} +(1.94930 + 0.447490i) q^{4} +(-0.995185 + 0.0980171i) q^{5} +(-3.41713 + 0.627806i) q^{6} +(1.13643 - 1.70079i) q^{7} +(-2.66794 - 0.939196i) q^{8} +(2.52390 - 1.68642i) q^{9} +(1.41406 + 0.0207213i) q^{10} +(-2.93913 - 5.49873i) q^{11} +(4.90179 - 0.338118i) q^{12} +(-0.102591 + 1.04163i) q^{13} +(-1.86774 + 2.20904i) q^{14} +(-2.26971 + 0.940146i) q^{15} +(3.59951 + 1.74458i) q^{16} +(-4.25396 - 1.76205i) q^{17} +(-3.81516 + 1.96793i) q^{18} +(-1.36208 - 1.65970i) q^{19} +(-1.98377 - 0.254270i) q^{20} +(1.45876 - 4.80889i) q^{21} +(3.25460 + 8.19492i) q^{22} +(1.41593 - 7.11835i) q^{23} +(-6.94194 - 0.305352i) q^{24} +(0.980785 - 0.195090i) q^{25} +(0.310016 - 1.44738i) q^{26} +(0.0552877 - 0.0673683i) q^{27} +(2.97633 - 2.80680i) q^{28} +(6.38295 + 3.41176i) q^{29} +(3.33914 - 0.959721i) q^{30} +(1.95608 - 1.95608i) q^{31} +(-4.78033 - 3.02465i) q^{32} +(-10.8311 - 10.8311i) q^{33} +(5.69720 + 3.15340i) q^{34} +(-0.964253 + 1.80399i) q^{35} +(5.67449 - 2.15791i) q^{36} +(5.50196 + 4.51534i) q^{37} +(1.64976 + 2.54912i) q^{38} +(0.501649 + 2.52196i) q^{39} +(2.74715 + 0.673170i) q^{40} +(5.52071 + 1.09814i) q^{41} +(-2.81557 + 6.52529i) q^{42} +(-3.63565 - 1.10286i) q^{43} +(-3.26861 - 12.0339i) q^{44} +(-2.34645 + 1.92568i) q^{45} +(-3.12310 + 9.77741i) q^{46} +(-0.728958 + 1.75986i) q^{47} +(9.70635 + 1.53441i) q^{48} +(1.07757 + 2.60149i) q^{49} +(-1.40928 + 0.117981i) q^{50} +(-11.2574 - 1.10876i) q^{51} +(-0.666099 + 1.98453i) q^{52} +(3.74734 - 2.00300i) q^{53} +(-0.0884181 + 0.0858642i) q^{54} +(3.46395 + 5.18417i) q^{55} +(-4.62931 + 3.47028i) q^{56} +(-4.38577 - 2.93048i) q^{57} +(-8.42623 - 5.81060i) q^{58} +(0.348307 + 3.53642i) q^{59} +(-4.84505 + 0.816950i) q^{60} +(3.20443 + 10.5636i) q^{61} +(-3.06018 + 2.43727i) q^{62} -6.20913i q^{63} +(6.23582 + 5.01144i) q^{64} -1.04667i q^{65} +(13.4956 + 16.9447i) q^{66} +(-0.970541 - 3.19945i) q^{67} +(-7.50373 - 5.33836i) q^{68} +(-1.74768 - 17.7445i) q^{69} +(1.64223 - 2.38147i) q^{70} +(5.35453 + 3.57779i) q^{71} +(-8.31751 + 2.12883i) q^{72} +(-6.07614 - 9.09358i) q^{73} +(-7.01252 - 7.22110i) q^{74} +(2.16663 - 1.15809i) q^{75} +(-1.91240 - 3.84476i) q^{76} +(-12.6923 - 1.25008i) q^{77} +(-0.303372 - 3.62379i) q^{78} +(-4.00245 - 9.66276i) q^{79} +(-3.75317 - 1.38336i) q^{80} +(-3.40294 + 8.21543i) q^{81} +(-7.58298 - 2.42216i) q^{82} +(10.1642 - 8.34153i) q^{83} +(4.99548 - 8.72117i) q^{84} +(4.40619 + 1.33660i) q^{85} +(4.93330 + 2.12865i) q^{86} +(17.4390 + 3.46883i) q^{87} +(2.67705 + 17.4307i) q^{88} +(-0.316830 - 1.59281i) q^{89} +(3.60390 - 2.33240i) q^{90} +(1.65500 + 1.35823i) q^{91} +(5.94545 - 13.2422i) q^{92} +(3.20365 - 5.99360i) q^{93} +(1.30456 - 2.35693i) q^{94} +(1.51820 + 1.51820i) q^{95} +(-13.3953 - 3.70167i) q^{96} +(4.24241 - 4.24241i) q^{97} +(-1.10001 - 3.82725i) q^{98} +(-16.6913 - 8.92166i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{31}{32}\right)$	$1$

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 $

$2$	−1.40522	−	0.159224i	−0.993642	−	0.112588i
$2$	−1.40522	−	0.159224i	−0.993642	−	0.112588i
$3$	2.35093	−	0.713148i	1.35731	−	0.411736i	0.474002	−	0.880524i	$-0.342809\pi$
$3$	2.35093	−	0.713148i	1.35731	−	0.411736i	0.883311	+	0.468788i	$0.155309\pi$
$4$	1.94930	+	0.447490i	0.974648	+	0.223745i
$5$	−0.995185	+	0.0980171i	−0.445060	+	0.0438346i
$5$	−0.995185	+	0.0980171i	−0.445060	+	0.0438346i
$6$	−3.41713	+	0.627806i	−1.39504	+	0.256301i
$7$	1.13643	−	1.70079i	0.429531	−	0.642838i	−0.552067	−	0.833800i	$-0.686161\pi$
$7$	1.13643	−	1.70079i	0.429531	−	0.642838i	0.981597	+	0.190962i	$0.0611606\pi$
$8$	−2.66794	−	0.939196i	−0.943260	−	0.332056i
$9$	2.52390	−	1.68642i	0.841302	−	0.562140i
$10$	1.41406	+	0.0207213i	0.447166	+	0.00655266i
$11$	−2.93913	−	5.49873i	−0.886182	−	1.65793i	−0.744093	−	0.668076i	$-0.767118\pi$
$11$	−2.93913	−	5.49873i	−0.886182	−	1.65793i	−0.142089	−	0.989854i	$-0.545382\pi$
$12$	4.90179	−	0.338118i	1.41503	−	0.0976062i
$13$	−0.102591	+	1.04163i	−0.0284537	+	0.288896i	0.970419	+	0.241427i	$0.0776154\pi$
$13$	−0.102591	+	1.04163i	−0.0284537	+	0.288896i	−0.998873	+	0.0474686i	$0.984885\pi$
$14$	−1.86774	+	2.20904i	−0.499176	+	0.590391i
$15$	−2.26971	+	0.940146i	−0.586038	+	0.242745i
$16$	3.59951	+	1.74458i	0.899877	+	0.436145i
$17$	−4.25396	−	1.76205i	−1.03174	−	0.427360i	−0.198398	−	0.980121i	$-0.563574\pi$
$17$	−4.25396	−	1.76205i	−1.03174	−	0.427360i	−0.833339	+	0.552762i	$0.813574\pi$
$18$	−3.81516	+	1.96793i	−0.899243	+	0.463845i
$19$	−1.36208	−	1.65970i	−0.312482	−	0.380761i	0.592959	−	0.805233i	$-0.297960\pi$
$19$	−1.36208	−	1.65970i	−0.312482	−	0.380761i	−0.905441	+	0.424472i	$0.860460\pi$
$20$	−1.98377	−	0.254270i	−0.443585	−	0.0568566i
$21$	1.45876	−	4.80889i	0.318328	−	1.04939i
$22$	3.25460	+	8.19492i	0.693884	+	1.74716i
$23$	1.41593	−	7.11835i	0.295241	−	1.48428i	−0.493604	−	0.869687i	$-0.664321\pi$
$23$	1.41593	−	7.11835i	0.295241	−	1.48428i	0.788845	−	0.614592i	$-0.210679\pi$
$24$	−6.94194	−	0.305352i	−1.41702	−	0.0623297i
$25$	0.980785	−	0.195090i	0.196157	−	0.0390181i
$26$	0.310016	−	1.44738i	0.0607991	−	0.283855i
$27$	0.0552877	−	0.0673683i	0.0106401	−	0.0129650i
$28$	2.97633	−	2.80680i	0.562473	−	0.530436i
$29$	6.38295	+	3.41176i	1.18528	+	0.633548i	0.941740	−	0.336342i	$-0.109190\pi$
$29$	6.38295	+	3.41176i	1.18528	+	0.633548i	0.243545	+	0.969890i	$0.421690\pi$
$30$	3.33914	−	0.959721i	0.609642	−	0.175220i
$31$	1.95608	−	1.95608i	0.351323	−	0.351323i	−0.509279	−	0.860602i	$-0.670088\pi$
$31$	1.95608	−	1.95608i	0.351323	−	0.351323i	0.860602	+	0.509279i	$0.170088\pi$
$32$	−4.78033	−	3.02465i	−0.845050	−	0.534687i
$33$	−10.8311	−	10.8311i	−1.88546	−	1.88546i
$34$	5.69720	+	3.15340i	0.977062	+	0.540804i
$35$	−0.964253	+	1.80399i	−0.162988	+	0.304930i
$36$	5.67449	−	2.15791i	0.945749	−	0.359651i
$37$	5.50196	+	4.51534i	0.904516	+	0.742317i	0.966744	−	0.255744i	$-0.0823206\pi$
$37$	5.50196	+	4.51534i	0.904516	+	0.742317i	−0.0622279	+	0.998062i	$0.519821\pi$
$38$	1.64976	+	2.54912i	0.267626	+	0.413521i
$39$	0.501649	+	2.52196i	0.0803282	+	0.403837i
$40$	2.74715	+	0.673170i	0.434363	+	0.106438i
$41$	5.52071	+	1.09814i	0.862191	+	0.171500i	0.606330	−	0.795213i	$-0.292641\pi$
$41$	5.52071	+	1.09814i	0.862191	+	0.171500i	0.255861	+	0.966714i	$0.417641\pi$
$42$	−2.81557	+	6.52529i	−0.434452	+	1.00687i
$43$	−3.63565	−	1.10286i	−0.554432	−	0.168185i	0.000621406	−	1.00000i	$-0.499802\pi$
$43$	−3.63565	−	1.10286i	−0.554432	−	0.168185i	−0.555053	+	0.831815i	$0.687302\pi$
$44$	−3.26861	−	12.0339i	−0.492762	−	1.81418i
$45$	−2.34645	+	1.92568i	−0.349789	+	0.287064i
$46$	−3.12310	+	9.77741i	−0.460476	+	1.44160i
$47$	−0.728958	+	1.75986i	−0.106329	+	0.256702i	−0.968085	−	0.250621i	$-0.919365\pi$
$47$	−0.728958	+	1.75986i	−0.106329	+	0.256702i	0.861756	+	0.507323i	$0.169365\pi$
$48$	9.70635	+	1.53441i	1.40099	+	0.221473i
$49$	1.07757	+	2.60149i	0.153939	+	0.371642i
$50$	−1.40928	+	0.117981i	−0.199303	+	0.0166850i
$51$	−11.2574	−	1.10876i	−1.57635	−	0.155257i
$52$	−0.666099	+	1.98453i	−0.0923712	+	0.275205i
$53$	3.74734	−	2.00300i	0.514737	−	0.275133i	−0.193509	−	0.981099i	$-0.561987\pi$
$53$	3.74734	−	2.00300i	0.514737	−	0.275133i	0.708246	+	0.705966i	$0.249487\pi$
$54$	−0.0884181	+	0.0858642i	−0.0120322	+	0.0116846i
$55$	3.46395	+	5.18417i	0.467079	+	0.699033i
$56$	−4.62931	+	3.47028i	−0.618617	+	0.463735i
$57$	−4.38577	−	2.93048i	−0.580909	−	0.388151i
$58$	−8.42623	−	5.81060i	−1.10642	−	0.762969i
$59$	0.348307	+	3.53642i	0.0453457	+	0.460403i	0.990867	+	0.134843i	$0.0430529\pi$
$59$	0.348307	+	3.53642i	0.0453457	+	0.460403i	−0.945521	+	0.325560i	$0.894447\pi$
$60$	−4.84505	+	0.816950i	−0.625493	+	0.105468i
$61$	3.20443	+	10.5636i	0.410286	+	1.35253i	0.882195	+	0.470884i	$0.156065\pi$
$61$	3.20443	+	10.5636i	0.410286	+	1.35253i	−0.471910	+	0.881647i	$0.656435\pi$
$62$	−3.06018	+	2.43727i	−0.388644	+	0.309534i
$63$		−	6.20913i		−	0.782277i
$64$	6.23582	+	5.01144i	0.779478	+	0.626430i
$65$		−	1.04667i		−	0.129823i
$66$	13.4956	+	16.9447i	1.66119	+	2.08575i
$67$	−0.970541	−	3.19945i	−0.118570	−	0.390875i	0.877485	−	0.479604i	$-0.159219\pi$
$67$	−0.970541	−	3.19945i	−0.118570	−	0.390875i	−0.996056	+	0.0887290i	$0.971719\pi$
$68$	−7.50373	−	5.33836i	−0.909962	−	0.647371i
$69$	−1.74768	−	17.7445i	−0.210397	−	2.13619i
$70$	1.64223	−	2.38147i	0.196284	−	0.284641i
$71$	5.35453	+	3.57779i	0.635466	+	0.424605i	0.831139	−	0.556064i	$-0.187689\pi$
$71$	5.35453	+	3.57779i	0.635466	+	0.424605i	−0.195673	+	0.980669i	$0.562689\pi$
$72$	−8.31751	+	2.12883i	−0.980228	+	0.250884i
$73$	−6.07614	−	9.09358i	−0.711158	−	1.06432i	−0.994442	−	0.105287i	$-0.966424\pi$
$73$	−6.07614	−	9.09358i	−0.711158	−	1.06432i	0.283284	−	0.959036i	$-0.408576\pi$
$74$	−7.01252	−	7.22110i	−0.815189	−	0.839436i
$75$	2.16663	−	1.15809i	0.250181	−	0.133725i
$76$	−1.91240	−	3.84476i	−0.219367	−	0.441024i
$77$	−12.6923	−	1.25008i	−1.44642	−	0.142460i
$78$	−0.303372	−	3.62379i	−0.0343501	−	0.410313i
$79$	−4.00245	−	9.66276i	−0.450310	−	1.08715i	−0.972204	−	0.234135i	$-0.924774\pi$
$79$	−4.00245	−	9.66276i	−0.450310	−	1.08715i	0.521894	−	0.853010i	$-0.325226\pi$
$80$	−3.75317	−	1.38336i	−0.419617	−	0.154665i
$81$	−3.40294	+	8.21543i	−0.378105	+	0.912826i
$82$	−7.58298	−	2.42216i	−0.837400	−	0.267482i
$83$	10.1642	−	8.34153i	1.11566	−	0.915602i	0.118659	−	0.992935i	$-0.462141\pi$
$83$	10.1642	−	8.34153i	1.11566	−	0.915602i	0.997005	+	0.0773333i	$0.0246405\pi$
$84$	4.99548	−	8.72117i	0.545052	−	0.951558i
$85$	4.40619	+	1.33660i	0.477919	+	0.144975i
$86$	4.93330	+	2.12865i	0.531971	+	0.229538i
$87$	17.4390	+	3.46883i	1.86966	+	0.371898i
$88$	2.67705	+	17.4307i	0.285374	+	1.85812i
$89$	−0.316830	−	1.59281i	−0.0335839	−	0.168838i	0.960354	−	0.278785i	$-0.0899317\pi$
$89$	−0.316830	−	1.59281i	−0.0335839	−	0.168838i	−0.993937	+	0.109948i	$0.964932\pi$
$90$	3.60390	−	2.33240i	0.379885	−	0.245857i
$91$	1.65500	+	1.35823i	0.173491	+	0.142381i
$92$	5.94545	−	13.2422i	0.619856	−	1.38059i
$93$	3.20365	−	5.99360i	0.332203	−	0.621507i
$94$	1.30456	−	2.35693i	0.134555	−	0.243098i
$95$	1.51820	+	1.51820i	0.155764	+	0.155764i
$96$	−13.3953	−	3.70167i	−1.36715	−	0.377800i
$97$	4.24241	−	4.24241i	0.430751	−	0.430751i	−0.458133	−	0.888884i	$-0.651481\pi$
$97$	4.24241	−	4.24241i	0.430751	−	0.430751i	0.888884	+	0.458133i	$0.151481\pi$
$98$	−1.10001	−	3.82725i	−0.111118	−	0.386611i
$99$	−16.6913	−	8.92166i	−1.67753	−	0.896661i
$100$	1.99914	+	0.0586025i	0.199914	+	0.00586025i
$101$	3.08732	−	3.76191i	0.307200	−	0.374324i	−0.596410	−	0.802680i	$-0.703407\pi$
$101$	3.08732	−	3.76191i	0.307200	−	0.374324i	0.903610	+	0.428355i	$0.140907\pi$
$102$	15.6426	+	3.35049i	1.54885	+	0.331748i
$103$	5.10290	−	1.01503i	0.502804	−	0.100014i	0.0628295	−	0.998024i	$-0.479988\pi$
$103$	5.10290	−	1.01503i	0.502804	−	0.100014i	0.439974	+	0.898010i	$0.354988\pi$
$104$	1.25200	−	2.68265i	0.122769	−	0.263055i
$105$	−0.980383	+	4.92872i	−0.0956756	+	0.480994i
$106$	−5.58477	+	2.21799i	−0.542441	+	0.215430i
$107$	−2.28370	+	7.52836i	−0.220774	+	0.727794i	0.774663	+	0.632374i	$0.217919\pi$
$107$	−2.28370	+	7.52836i	−0.220774	+	0.727794i	−0.995437	+	0.0954201i	$0.969581\pi$
$108$	0.137919	−	0.106580i	0.0132712	−	0.0102557i
$109$	−7.99896	−	9.74677i	−0.766162	−	0.933571i	0.233082	−	0.972457i	$-0.425119\pi$
$109$	−7.99896	−	9.74677i	−0.766162	−	0.933571i	−0.999244	+	0.0388863i	$0.987619\pi$
$110$	−4.04217	−	7.83645i	−0.385406	−	0.747176i
$111$	16.1549	+	6.69156i	1.53335	+	0.635135i
$112$	7.05776	−	4.13941i	0.666895	−	0.391137i
$113$	−15.4691	+	6.40751i	−1.45521	+	0.602768i	−0.963432	−	0.267952i	$-0.913653\pi$
$113$	−15.4691	+	6.40751i	−1.45521	+	0.602768i	−0.491779	+	0.870720i	$0.663653\pi$
$114$	5.69637	+	4.81629i	0.533514	+	0.451087i
$115$	−0.711389	+	7.22286i	−0.0663374	+	0.673535i
$116$	10.9155	+	9.50684i	1.01348	+	0.882687i
$117$	1.49769	+	2.80198i	0.138462	+	0.259043i
$118$	0.0736340	−	5.02492i	0.00677856	−	0.462581i
$119$	−7.83122	+	5.23265i	−0.717886	+	0.479676i
$120$	6.93844	−	0.376548i	0.633390	−	0.0343740i
$121$	−15.4863	+	23.1768i	−1.40784	+	2.10699i
$122$	−2.82096	−	15.3544i	−0.255398	−	1.39012i
$123$	13.7620	−	1.35544i	1.24088	−	0.122216i
$124$	4.68831	−	2.93766i	0.421023	−	0.263809i
$125$	−0.956940	+	0.290285i	−0.0855913	+	0.0259639i
$126$	−0.988642	+	8.72521i	−0.0880752	+	0.777303i
$127$	−2.08372			−0.184900			−0.0924500	−	0.995717i	$-0.529470\pi$
$127$	−2.08372			−0.184900			−0.0924500	+	0.995717i	$0.529470\pi$
$128$	−7.96477	−	8.03508i	−0.703993	−	0.710207i
$129$	−9.33369			−0.821786
$130$	−0.166654	+	1.47080i	−0.0146166	+	0.128998i
$131$	2.87649	−	0.872573i	0.251320	−	0.0762371i	−0.162111	−	0.986773i	$-0.551830\pi$
$131$	2.87649	−	0.872573i	0.251320	−	0.0762371i	0.413431	+	0.910535i	$0.364330\pi$
$132$	−16.2662	−	25.9599i	−1.41579	−	2.25952i
$133$	−4.37071	+	0.430477i	−0.378988	+	0.0373271i
$134$	0.854398	+	4.65046i	0.0738087	+	0.401739i
$135$	−0.0484182	+	0.0724630i	−0.00416718	+	0.00623662i
$136$	9.69442	+	8.69635i	0.831289	+	0.745706i
$137$	3.92015	−	2.61936i	0.334921	−	0.223787i	−0.376725	−	0.926325i	$-0.622950\pi$
$137$	3.92015	−	2.61936i	0.334921	−	0.223787i	0.711646	+	0.702538i	$0.247950\pi$
$138$	−0.369470	+	25.2133i	−0.0314513	+	2.14630i
$139$	10.7799	+	20.1678i	0.914341	+	1.71061i	0.672199	+	0.740370i	$0.265350\pi$
$139$	10.7799	+	20.1678i	0.914341	+	1.71061i	0.242142	+	0.970241i	$0.422150\pi$
$140$	−2.68688	+	3.08502i	−0.227083	+	0.260732i
$141$	−0.458691	+	4.65717i	−0.0386288	+	0.392205i
$142$	−6.95464	−	5.88015i	−0.583620	−	0.493451i
$143$	6.02916	−	2.49736i	0.504184	−	0.208840i
$144$	12.0269	−	1.66713i	1.00224	−	0.138927i
$145$	−6.68663	−	2.76969i	−0.555294	−	0.230010i
$146$	7.09040	+	13.7460i	0.586806	+	1.13762i
$147$	4.38856	+	5.34747i	0.361962	+	0.441052i
$148$	8.70438	+	11.2638i	0.715495	+	0.925879i
$149$	−6.96919	+	22.9743i	−0.570938	+	1.88213i	−0.111887	+	0.993721i	$0.535690\pi$
$149$	−6.96919	+	22.9743i	−0.570938	+	1.88213i	−0.459051	+	0.888410i	$0.651810\pi$
$150$	−3.22900	+	1.28239i	−0.263646	+	0.104707i
$151$	0.209701	−	1.05424i	0.0170652	−	0.0857927i	−0.971314	−	0.237800i	$-0.923574\pi$
$151$	0.209701	−	1.05424i	0.0170652	−	0.0857927i	0.988379	+	0.152007i	$0.0485737\pi$
$152$	2.07516	+	5.70723i	0.168318	+	0.462918i
$153$	−13.7082	+	2.72672i	−1.10824	+	0.220442i
$154$	17.6365	+	3.77756i	1.42119	+	0.304405i
$155$	−1.75493	+	2.13839i	−0.140960	+	0.171760i
$156$	−0.150689	+	5.14053i	−0.0120648	+	0.411572i
$157$	5.65527	+	3.02280i	0.451340	+	0.241246i	0.681372	−	0.731937i	$-0.261383\pi$
$157$	5.65527	+	3.02280i	0.451340	+	0.241246i	−0.230033	+	0.973183i	$0.573883\pi$
$158$	4.08578	+	14.2156i	0.325047	+	1.13093i
$159$	7.38132	−	7.38132i	0.585377	−	0.585377i
$160$	5.05377	+	2.54153i	0.399536	+	0.200925i
$161$	−10.4977	−	10.4977i	−0.827336	−	0.827336i
$162$	6.08998	−	11.0027i	0.478474	−	0.864452i
$163$	7.29881	−	13.6551i	0.571687	−	1.06955i	−0.415441	−	0.909620i	$-0.636373\pi$
$163$	7.29881	−	13.6551i	0.571687	−	1.06955i	0.987128	−	0.159931i	$-0.0511271\pi$
$164$	10.2701	+	4.61106i	0.801960	+	0.360063i
$165$	11.8406	+	9.71733i	0.921790	+	0.756493i
$166$	−15.6111	+	10.1033i	−1.21166	+	0.784170i
$167$	1.33147	+	6.69374i	0.103032	+	0.517977i	0.997489	+	0.0708231i	$0.0225626\pi$
$167$	1.33147	+	6.69374i	0.103032	+	0.517977i	−0.894457	+	0.447154i	$0.852437\pi$
$168$	−8.40838	+	11.4598i	−0.648721	+	0.884141i
$169$	11.6757	+	2.32245i	0.898134	+	0.178650i
$170$	−5.97886	−	2.57980i	−0.458557	−	0.197861i
$171$	−6.23670	−	1.89188i	−0.476932	−	0.144676i
$172$	−6.59344	−	3.77672i	−0.502745	−	0.287973i
$173$	−16.5309	+	13.5666i	−1.25682	+	1.03145i	−0.258972	+	0.965885i	$0.583384\pi$
$173$	−16.5309	+	13.5666i	−1.25682	+	1.03145i	−0.997849	+	0.0655610i	$0.979116\pi$
$174$	−23.9533	−	7.65118i	−1.81590	−	0.580035i
$175$	0.782788	−	1.88982i	0.0591732	−	0.142857i
$176$	−0.986457	−	24.9203i	−0.0743570	−	1.87844i
$177$	3.34084	+	8.06550i	0.251113	+	0.606240i
$178$	0.191603	+	2.28870i	0.0143612	+	0.171545i
$179$	13.9163	+	1.37064i	1.04015	+	0.102446i	0.603644	−	0.797254i	$-0.293715\pi$
$179$	13.9163	+	1.37064i	1.04015	+	0.102446i	0.436509	+	0.899700i	$0.356215\pi$
$180$	−5.43565	+	2.70371i	−0.405150	+	0.201523i
$181$	22.5304	−	12.0428i	1.67467	−	0.895131i	0.689350	−	0.724429i	$-0.257896\pi$
$181$	22.5304	−	12.0428i	1.67467	−	0.895131i	0.985323	−	0.170702i	$-0.0546036\pi$
$182$	−2.10938	−	2.17212i	−0.156358	−	0.161008i
$183$	15.0668	+	22.5491i	1.11377	+	1.66688i
$184$	−10.4631	+	17.6615i	−0.771353	+	1.30202i
$185$	−5.91805	−	3.95431i	−0.435103	−	0.290727i
$186$	−5.45616	+	7.91224i	−0.400065	+	0.580154i
$187$	2.81393	+	28.5703i	0.205775	+	2.08927i
$188$	−2.20847	+	3.10429i	−0.161069	+	0.226403i
$189$	−0.0517486	−	0.170592i	−0.00376416	−	0.0124088i
$190$	−1.89167	−	2.37514i	−0.137236	−	0.172311i
$191$			23.7735i			1.72019i	0.510136	+	0.860094i	$0.329595\pi$
$191$			23.7735i			1.72019i	−0.510136	+	0.860094i	$0.670405\pi$
$192$	18.2339	+	7.33451i	1.31592	+	0.529322i
$193$		−	19.2454i		−	1.38532i	−0.721266	−	0.692658i	$-0.756439\pi$
$193$		−	19.2454i		−	1.38532i	0.721266	−	0.692658i	$-0.243561\pi$
$194$	−6.63702	+	5.28603i	−0.476510	+	0.379515i
$195$	−0.746429	−	2.46065i	−0.0534529	−	0.176211i
$196$	0.936369	+	5.55328i	0.0668835	+	0.396663i
$197$	0.831980	+	8.44724i	0.0592761	+	0.601841i	0.978237	+	0.207492i	$0.0665300\pi$
$197$	0.831980	+	8.44724i	0.0592761	+	0.601841i	−0.918961	+	0.394349i	$0.870970\pi$
$198$	22.0344	+	15.1946i	1.56591	+	1.07983i
$199$	7.17245	+	4.79248i	0.508441	+	0.339730i	0.783186	−	0.621788i	$-0.213593\pi$
$199$	7.17245	+	4.79248i	0.508441	+	0.339730i	−0.274744	+	0.961517i	$0.588593\pi$
$200$	−2.79991	−	0.400660i	−0.197983	−	0.0283310i
$201$	−4.56336	−	6.82955i	−0.321874	−	0.481719i
$202$	−4.93736	+	4.79474i	−0.347391	+	0.337357i
$203$	13.0565	−	6.97883i	0.916385	−	0.489818i
$204$	−21.4478	−	7.19886i	−1.50165	−	0.504021i
$205$	−5.60177	−	0.551726i	−0.391244	−	0.0385342i
$206$	−7.33232	+	0.613839i	−0.510867	+	0.0427682i
$207$	−8.43085	−	20.3539i	−0.585985	−	1.41469i
$208$	−2.18648	+	3.57037i	−0.151605	+	0.247560i
$209$	−5.12290	+	12.3678i	−0.354358	+	0.855497i
$210$	2.16242	−	6.76984i	0.149221	−	0.467163i
$211$	−0.461437	+	0.378692i	−0.0317666	+	0.0260702i	−0.650143	−	0.759812i	$-0.725291\pi$
$211$	−0.461437	+	0.378692i	−0.0317666	+	0.0260702i	0.618376	+	0.785882i	$0.287791\pi$
$212$	8.20100	−	2.22753i	0.563247	−	0.152988i
$213$	15.1397	+	4.59256i	1.03735	+	0.314677i
$214$	4.40780	−	10.2154i	0.301311	−	0.698310i
$215$	3.72625	+	0.741197i	0.254128	+	0.0505492i
$216$	−0.210776	+	0.127809i	−0.0143415	+	0.00869627i
$217$	−1.10393	−	5.54984i	−0.0749398	−	0.376748i
$218$	9.68840	+	14.9700i	0.656181	+	1.01390i
$219$	−20.7697	−	17.0452i	−1.40348	−	1.15181i
$220$	4.43240	+	11.6556i	0.298832	+	0.785818i
$221$	2.27182	−	4.25028i	0.152819	−	0.285905i
$222$	−21.6357	−	11.9754i	−1.45209	−	0.803734i
$223$	3.58493	+	3.58493i	0.240065	+	0.240065i	0.816877	−	0.576812i	$-0.195703\pi$
$223$	3.58493	+	3.58493i	0.240065	+	0.240065i	−0.576812	+	0.816877i	$0.695703\pi$
$224$	−10.5768	+	4.69303i	−0.706692	+	0.313566i
$225$	2.14640	−	2.14640i	0.143094	−	0.143094i
$226$	22.7578	−	6.54093i	1.51382	−	0.435096i
$227$	−21.5689	−	11.5288i	−1.43158	−	0.765194i	−0.440408	−	0.897798i	$-0.645166\pi$
$227$	−21.5689	−	11.5288i	−1.43158	−	0.765194i	−0.991169	+	0.132603i	$0.957666\pi$
$228$	−7.23780	−	7.67495i	−0.479335	−	0.508286i
$229$	−5.31482	+	6.47613i	−0.351213	+	0.427955i	−0.918411	−	0.395627i	$-0.870527\pi$
$229$	−5.31482	+	6.47613i	−0.351213	+	0.427955i	0.567198	+	0.823581i	$0.308027\pi$
$230$	2.14971	−	10.0364i	0.141748	−	0.661784i
$231$	−30.7303	+	6.11264i	−2.02190	+	0.402182i
$232$	−13.8250	−	15.0972i	−0.907658	−	0.991181i
$233$	5.07152	−	25.4963i	0.332246	−	1.67032i	−0.348125	−	0.937448i	$-0.613182\pi$
$233$	5.07152	−	25.4963i	0.332246	−	1.67032i	0.680371	−	0.732867i	$-0.261818\pi$
$234$	−1.65844	−	4.17587i	−0.108416	−	0.272985i
$235$	0.552951	−	1.82284i	0.0360706	−	0.118909i
$236$	−0.903559	+	7.04940i	−0.0588167	+	0.458877i
$237$	−16.3005	−	19.8622i	−1.05883	−	1.29019i
$238$	11.8378	−	6.10612i	0.767328	−	0.395801i
$239$	−21.9115	−	9.07606i	−1.41734	−	0.587081i	−0.463149	−	0.886281i	$-0.653280\pi$
$239$	−21.9115	−	9.07606i	−1.41734	−	0.587081i	−0.954191	+	0.299199i	$0.903280\pi$
$240$	−9.81001	−	0.575633i	−0.633233	−	0.0371569i
$241$	16.4822	−	6.82715i	1.06171	−	0.439775i	0.217653	−	0.976026i	$-0.430160\pi$
$241$	16.4822	−	6.82715i	1.06171	−	0.439775i	0.844059	+	0.536251i	$0.180160\pi$
$242$	25.4519	−	30.1028i	1.63611	−	1.93508i
$243$	−2.16690	+	22.0009i	−0.139007	+	1.41136i
$244$	1.51929	+	22.0255i	0.0972623	+	1.41004i
$245$	−1.32738	−	2.48335i	−0.0848029	−	0.158655i
$246$	−19.5544	−	0.286546i	−1.24675	−	0.0182695i
$247$	1.86852	−	1.24851i	0.118891	−	0.0794407i
$248$	−7.05586	+	3.38157i	−0.448048	+	0.214730i
$249$	17.9466	−	26.8590i	1.13732	−	1.70212i
$250$	1.39093	−	0.255547i	0.0879704	−	0.0161622i
$251$	8.06370	−	0.794205i	0.508976	−	0.0501298i	0.159730	−	0.987161i	$-0.448938\pi$
$251$	8.06370	−	0.794205i	0.508976	−	0.0501298i	0.349246	+	0.937031i	$0.386438\pi$
$252$	2.77852	−	12.1034i	0.175030	−	0.762445i
$253$	−43.3035	+	13.1360i	−2.72247	+	0.825851i
$254$	2.92808	+	0.331777i	0.183724	+	0.0208176i
$255$	11.3119			0.708376
$256$	9.91289	+	12.5592i	0.619556	+	0.784953i
$257$	13.5580			0.845725			0.422863	−	0.906194i	$-0.361025\pi$
$257$	13.5580			0.845725			0.422863	+	0.906194i	$0.361025\pi$
$258$	13.1159	+	1.48615i	0.816560	+	0.0925234i
$259$	13.9322	−	4.22630i	0.865708	−	0.262610i
$260$	0.468373	−	2.04026i	0.0290473	−	0.126532i
$261$	21.8636	−	2.15338i	1.35332	−	0.133291i
$262$	−4.18104	+	0.768153i	−0.258305	+	0.0474567i
$263$	3.90791	−	5.84860i	0.240972	−	0.360640i	−0.691195	−	0.722668i	$-0.742916\pi$
$263$	3.90791	−	5.84860i	0.240972	−	0.360640i	0.932167	+	0.362028i	$0.117916\pi$
$264$	18.7242	+	39.0693i	1.15240	+	2.40455i
$265$	−3.53297	+	2.36065i	−0.217029	+	0.145014i
$266$	6.21035	+	0.0910051i	0.380781	+	0.00557988i
$267$	−1.88076	−	3.51865i	−0.115100	−	0.215338i
$268$	−0.460153	−	6.67097i	−0.0281083	−	0.407495i
$269$	−0.414309	+	4.20655i	−0.0252608	+	0.256478i	0.974257	+	0.225439i	$0.0723816\pi$
$269$	−0.414309	+	4.20655i	−0.0252608	+	0.256478i	−0.999518	+	0.0310389i	$0.990118\pi$
$270$	0.0795762	−	0.0941173i	0.00484285	−	0.00572779i
$271$	23.4465	−	9.71186i	1.42427	−	0.589954i	0.468343	−	0.883547i	$-0.344851\pi$
$271$	23.4465	−	9.71186i	1.42427	−	0.589954i	0.955931	+	0.293593i	$0.0948510\pi$
$272$	−12.2381	−	13.7639i	−0.742046	−	0.834558i
$273$	4.85942	+	2.01284i	0.294105	+	0.121822i
$274$	−5.92575	+	3.05660i	−0.357988	+	0.184656i
$275$	−3.95541	−	4.81968i	−0.238520	−	0.290638i
$276$	4.53374	−	35.3714i	0.272899	−	2.12911i
$277$	−3.54217	+	11.6770i	−0.212829	+	0.701602i	0.783908	+	0.620877i	$0.213223\pi$
$277$	−3.54217	+	11.6770i	−0.212829	+	0.701602i	−0.996736	+	0.0807245i	$0.974277\pi$
$278$	−11.9370	−	30.0567i	−0.715932	−	1.80268i
$279$	1.63819	−	8.23574i	0.0980759	−	0.493061i
$280$	4.26687	−	3.90732i	0.254994	−	0.233507i
$281$	−9.61162	+	1.91187i	−0.573381	+	0.114053i	−0.473260	−	0.880923i	$-0.656923\pi$
$281$	−9.61162	+	1.91187i	−0.573381	+	0.114053i	−0.100121	+	0.994975i	$0.531923\pi$
$282$	1.38610	−	6.47132i	0.0825408	−	0.385362i
$283$	−19.2351	+	23.4380i	−1.14341	+	1.39325i	−0.236650	+	0.971595i	$0.576050\pi$
$283$	−19.2351	+	23.4380i	−1.14341	+	1.39325i	−0.906758	+	0.421652i	$0.861450\pi$
$284$	8.83655	+	9.37026i	0.524353	+	0.556023i
$285$	4.65189	+	2.48648i	0.275554	+	0.147287i
$286$	−8.86995	+	2.54936i	−0.524491	+	0.150747i
$287$	8.14162	−	8.14162i	0.480584	−	0.480584i
$288$	−17.1659	+	0.427711i	−1.01151	+	0.0252031i
$289$	2.97058	+	2.97058i	0.174740	+	0.174740i
$290$	8.95520	+	4.95670i	0.525867	+	0.291068i
$291$	6.94816	−	12.9991i	0.407308	−	0.762020i
$292$	−7.77490	−	20.4451i	−0.454992	−	1.19646i
$293$	5.31073	+	4.35840i	0.310256	+	0.254620i	0.776616	−	0.629975i	$-0.216935\pi$
$293$	5.31073	+	4.35840i	0.310256	+	0.254620i	−0.466360	+	0.884595i	$0.654435\pi$
$294$	−5.31545	−	8.21314i	−0.310003	−	0.479000i
$295$	−0.693260	−	3.48525i	−0.0403632	−	0.202919i
$296$	−10.4381	−	17.2141i	−0.606703	−	1.00055i
$297$	−0.532938	−	0.106008i	−0.0309242	−	0.00615120i
$298$	13.4513	−	31.1744i	0.779214	−	1.80588i
$299$	7.26941	+	2.20515i	0.420401	+	0.127527i
$300$	4.74164	−	1.28791i	0.273759	−	0.0743577i
$301$	−6.00741	+	4.93016i	−0.346261	+	0.284169i
$302$	−0.462536	+	1.44805i	−0.0266160	+	0.0833258i
$303$	4.57529	−	11.0457i	0.262844	−	0.634560i
$304$	−2.00734	−	8.35034i	−0.115129	−	0.478925i
$305$	−4.22442	−	10.1986i	−0.241889	−	0.583973i
$306$	19.6972	−	1.64898i	1.12601	−	0.0942661i
$307$	−7.77006	−	0.765284i	−0.443461	−	0.0436771i	−0.126177	−	0.992008i	$-0.540271\pi$
$307$	−7.77006	−	0.765284i	−0.443461	−	0.0436771i	−0.317284	+	0.948331i	$0.602771\pi$
$308$	−24.1817	−	8.11646i	−1.37788	−	0.462478i
$309$	11.2727	−	6.02539i	0.641283	−	0.342773i
$310$	2.80655	−	2.72549i	0.159402	−	0.154797i
$311$	−7.78141	−	11.6457i	−0.441243	−	0.660367i	0.542478	−	0.840070i	$-0.317486\pi$
$311$	−7.78141	−	11.6457i	−0.441243	−	0.660367i	−0.983721	+	0.179703i	$0.942486\pi$
$312$	1.03025	−	7.19959i	0.0583262	−	0.407597i
$313$	−15.2709	−	10.2037i	−0.863165	−	0.576748i	0.0432847	−	0.999063i	$-0.486218\pi$
$313$	−15.2709	−	10.2037i	−0.863165	−	0.576748i	−0.906449	+	0.422315i	$0.861218\pi$
$314$	−7.46560	−	5.14816i	−0.421308	−	0.290528i
$315$	0.608601	+	6.17923i	0.0342908	+	0.348160i
$316$	−3.47797	−	20.6266i	−0.195651	−	1.16034i
$317$	6.33112	+	20.8709i	0.355591	+	1.17223i	0.934239	+	0.356649i	$0.116081\pi$
$317$	6.33112	+	20.8709i	0.355591	+	1.17223i	−0.578648	+	0.815578i	$0.696419\pi$
$318$	−11.5477	+	9.19711i	−0.647561	+	0.515748i
$319$		−	45.1258i		−	2.52656i
$320$	−6.69700	−	4.37609i	−0.374374	−	0.244631i
$321$			19.3273i			1.07874i
$322$	13.0801	+	16.4231i	0.728927	+	0.915224i
$323$	2.86976	+	9.46034i	0.159678	+	0.526388i
$324$	−10.3097	+	14.4915i	−0.572759	+	0.805085i
$325$	0.102591	+	1.04163i	0.00569075	+	0.0577791i
$326$	−12.4307	+	18.0263i	−0.688471	+	0.998385i
$327$	−25.7559	−	17.2096i	−1.42431	−	0.951691i
$328$	−13.6976	−	8.11480i	−0.756322	−	0.448065i
$329$	2.16474	+	3.23977i	0.119346	+	0.178614i
$330$	−15.0914	−	15.5403i	−0.830756	−	0.855466i
$331$	5.24323	−	2.80256i	0.288194	−	0.154043i	−0.320965	−	0.947091i	$-0.604007\pi$
$331$	5.24323	−	2.80256i	0.288194	−	0.154043i	0.609159	+	0.793048i	$0.291507\pi$
$332$	23.5457	−	11.7117i	1.29224	−	0.642765i
$333$	21.5012	+	2.11768i	1.17826	+	0.116048i
$334$	−0.805205	−	9.61820i	−0.0440588	−	0.526284i
$335$	1.27947	+	3.08891i	0.0699048	+	0.168765i
$336$	13.6403	−	14.7647i	0.744140	−	0.805481i
$337$	3.12669	−	7.54851i	0.170322	−	0.411193i	−0.815552	−	0.578684i	$-0.803566\pi$
$337$	3.12669	−	7.54851i	0.170322	−	0.411193i	0.985874	+	0.167491i	$0.0535664\pi$
$338$	−16.0372	−	5.12261i	−0.872310	−	0.278633i
$339$	−31.7974	+	26.0954i	−1.72700	+	1.41731i
$340$	7.99085	+	4.57716i	0.433365	+	0.248231i
$341$	−16.5052	−	5.00679i	−0.893805	−	0.271133i
$342$	8.46271	+	3.65155i	0.457611	+	0.197453i
$343$	19.6927	+	3.91712i	1.06331	+	0.211505i
$344$	8.66391	+	6.35697i	0.467126	+	0.342745i
$345$	3.47854	+	17.4878i	0.187278	+	0.941511i
$346$	25.3897	−	16.4319i	1.36496	−	0.883384i
$347$	19.7020	+	16.1690i	1.05766	+	0.868000i	0.991539	−	0.129812i	$-0.0414373\pi$
$347$	19.7020	+	16.1690i	1.05766	+	0.868000i	0.0661221	+	0.997812i	$0.478937\pi$
$348$	32.4415	+	14.5656i	1.73905	+	0.780796i
$349$	−0.837709	+	1.56724i	−0.0448416	+	0.0838926i	−0.903344	−	0.428917i	$-0.858895\pi$
$349$	−0.837709	+	1.56724i	−0.0448416	+	0.0838926i	0.858502	+	0.512810i	$0.171395\pi$
$350$	−1.40089	+	2.53097i	−0.0748809	+	0.135286i
$351$	0.0645006	+	0.0645006i	0.00344279	+	0.00344279i
$352$	−2.58171	+	35.1756i	−0.137606	+	1.87486i
$353$	−12.3912	+	12.3912i	−0.659515	+	0.659515i	−0.955265	−	0.295751i	$-0.904430\pi$
$353$	−12.3912	+	12.3912i	−0.659515	+	0.659515i	0.295751	+	0.955265i	$0.404430\pi$
$354$	−3.41040	−	11.8658i	−0.181261	−	0.630658i
$355$	−5.67943	−	3.03572i	−0.301433	−	0.161119i
$356$	0.0951714	−	3.24664i	0.00504407	−	0.172071i
$357$	−14.6790	+	17.8864i	−0.776896	+	0.946651i
$358$	−19.3373	−	4.14186i	−1.02201	−	0.218904i
$359$	15.8006	−	3.14292i	0.833921	−	0.165877i	0.240378	−	0.970679i	$-0.422729\pi$
$359$	15.8006	−	3.14292i	0.833921	−	0.165877i	0.593543	+	0.804802i	$0.297729\pi$
$360$	8.06880	−	2.93383i	0.425263	−	0.154627i
$361$	2.80738	−	14.1136i	0.147757	−	0.742823i
$362$	−33.5777	+	13.3354i	−1.76481	+	0.700891i
$363$	−19.8787	+	65.5313i	−1.04336	+	3.43950i
$364$	2.61830	+	3.38818i	0.137236	+	0.177589i
$365$	6.93820	+	8.45423i	0.363162	+	0.442514i
$366$	−17.5819	−	34.0855i	−0.919019	−	1.78168i
$367$	−6.72870	−	2.78712i	−0.351235	−	0.145486i	0.200088	−	0.979778i	$-0.435877\pi$
$367$	−6.72870	−	2.78712i	−0.351235	−	0.145486i	−0.551324	+	0.834291i	$0.685877\pi$
$368$	17.5152	−	23.1523i	0.913041	−	1.20690i
$369$	15.7857	−	6.53864i	0.821770	−	0.340388i
$370$	7.68655	+	6.49898i	0.399604	+	0.337866i
$371$	0.851922	−	8.64971i	0.0442296	−	0.449070i
$372$	8.92693	−	10.2497i	0.462840	−	0.531422i
$373$	−4.16920	−	7.80003i	−0.215873	−	0.403870i	0.750555	−	0.660808i	$-0.229786\pi$
$373$	−4.16920	−	7.80003i	−0.215873	−	0.403870i	−0.966428	+	0.256938i	$0.917286\pi$
$374$	0.594879	−	40.5957i	0.0307605	−	2.09915i
$375$	−2.04269	+	1.36488i	−0.105484	+	0.0704821i
$376$	3.59767	−	4.01057i	0.185536	−	0.206829i
$377$	−4.20862	+	6.29865i	−0.216755	+	0.324397i
$378$	0.0455559	+	0.247959i	0.00234314	+	0.0127537i
$379$	−35.0934	+	3.45640i	−1.80263	+	0.177543i	−0.942871	−	0.333159i	$-0.891886\pi$
$379$	−35.0934	+	3.45640i	−1.80263	+	0.177543i	−0.859758	+	0.510702i	$0.829386\pi$
$380$	2.28004	+	3.63879i	0.116964	+	0.186666i
$381$	−4.89868	+	1.48600i	−0.250967	+	0.0761300i
$382$	3.78530	−	33.4070i	0.193673	−	1.70925i
$383$	17.6039			0.899520			0.449760	−	0.893150i	$-0.351510\pi$
$383$	17.6039			0.899520			0.449760	+	0.893150i	$0.351510\pi$
$384$	−24.4549	−	13.2099i	−1.24796	−	0.674114i
$385$	12.7537			0.649990
$386$	−3.06433	+	27.0441i	−0.155970	+	1.37651i
$387$	−11.0359	+	3.34771i	−0.560988	+	0.170174i
$388$	10.1681	−	6.37128i	0.516209	−	0.323452i
$389$	20.5560	−	2.02459i	1.04223	−	0.102651i	0.437612	−	0.899164i	$-0.355824\pi$
$389$	20.5560	−	2.02459i	1.04223	−	0.102651i	0.604621	+	0.796513i	$0.293324\pi$
$390$	0.657105	+	3.57660i	0.0332738	+	0.181108i
$391$	−18.5662	+	27.7863i	−0.938933	+	1.40521i
$392$	−0.431591	−	7.95268i	−0.0217986	−	0.401671i
$393$	6.14016	−	4.10273i	0.309730	−	0.206955i
$394$	0.175885	−	12.0027i	0.00886096	−	0.604688i
$395$	4.93029	+	9.22392i	0.248070	+	0.464106i
$396$	−28.5438	−	24.8601i	−1.43438	−	1.24927i
$397$	−0.848081	+	8.61071i	−0.0425640	+	0.432159i	0.950161	+	0.311758i	$0.100918\pi$
$397$	−0.848081	+	8.61071i	−0.0425640	+	0.432159i	−0.992725	+	0.120401i	$0.961582\pi$
$398$	−9.31580	−	7.87652i	−0.466959	−	0.394814i
$399$	−9.96825	+	4.12898i	−0.499037	+	0.206708i
$400$	3.87069	+	1.00883i	0.193535	+	0.0504414i
$401$	−21.8578	−	9.05379i	−1.09152	−	0.452124i	−0.236987	−	0.971513i	$-0.576160\pi$
$401$	−21.8578	−	9.05379i	−1.09152	−	0.452124i	−0.854538	+	0.519388i	$0.826160\pi$
$402$	5.32510	+	10.3236i	0.265592	+	0.514896i
$403$	1.83683	+	2.23819i	0.0914992	+	0.111492i
$404$	7.70152	−	5.95153i	0.383165	−	0.296100i
$405$	2.58130	−	8.50942i	0.128266	−	0.422836i
$406$	−19.4584	+	7.72791i	−0.965706	+	0.383530i
$407$	8.65766	−	43.5250i	0.429144	−	2.15745i
$408$	28.9927	+	13.5310i	1.43535	+	0.669884i
$409$	33.3513	−	6.63399i	1.64912	−	0.328030i	0.718921	−	0.695092i	$-0.244637\pi$
$409$	33.3513	−	6.63399i	1.64912	−	0.328030i	0.930196	+	0.367063i	$0.119637\pi$
$410$	7.78388	+	1.66723i	0.384418	+	0.0823387i
$411$	7.34803	−	8.95360i	0.362452	−	0.441648i
$412$	10.4013	+	0.304901i	0.512434	+	0.0150214i
$413$	6.41054	+	3.42651i	0.315442	+	0.168607i
$414$	8.60639	+	29.9441i	0.422981	+	1.47167i
$415$	−9.29763	+	9.29763i	−0.456403	+	0.456403i
$416$	3.64098	−	4.66902i	0.178514	−	0.228917i
$417$	39.7255	+	39.7255i	1.94537	+	1.94537i
$418$	9.16805	−	16.5638i	0.448424	−	0.810161i
$419$	5.71047	−	10.6835i	0.278975	−	0.521925i	−0.702940	−	0.711249i	$-0.748130\pi$
$419$	5.71047	−	10.6835i	0.278975	−	0.521925i	0.981915	+	0.189324i	$0.0606297\pi$
$420$	−4.11661	+	9.16882i	−0.200870	+	0.447392i
$421$	−15.4202	−	12.6550i	−0.751535	−	0.616769i	0.178627	−	0.983917i	$-0.442834\pi$
$421$	−15.4202	−	12.6550i	−0.751535	−	0.616769i	−0.930163	+	0.367148i	$0.880334\pi$
$422$	0.708718	−	0.458674i	0.0344998	−	0.0223279i
$423$	1.12804	+	5.67105i	0.0548473	+	0.275736i
$424$	−11.8789	+	1.82439i	−0.576890	+	0.0886000i
$425$	−4.51598	−	0.898285i	−0.219057	−	0.0435732i
$426$	−20.5433	−	8.86416i	−0.995327	−	0.429470i
$427$	21.6081	+	6.55474i	1.04569	+	0.317206i
$428$	−7.82048	+	13.6531i	−0.378017	+	0.659946i
$429$	12.3932	−	10.1708i	0.598348	−	0.491052i
$430$	−5.11819	−	1.63485i	−0.246821	−	0.0788396i
$431$	−8.74158	+	21.1040i	−0.421067	+	1.01655i	0.560966	+	0.827839i	$0.310430\pi$
$431$	−8.74158	+	21.1040i	−0.421067	+	1.01655i	−0.982033	+	0.188707i	$0.939570\pi$
$432$	0.316538	−	0.146039i	0.0152294	−	0.00702629i
$433$	8.46603	+	20.4388i	0.406852	+	0.982226i	0.985961	+	0.166977i	$0.0534004\pi$
$433$	8.46603	+	20.4388i	0.406852	+	0.982226i	−0.579109	+	0.815250i	$0.696600\pi$
$434$	0.667602	+	7.97453i	0.0320459	+	0.382790i
$435$	−17.6950	−	1.74281i	−0.848412	−	0.0835613i
$436$	−11.2308	−	22.5788i	−0.537856	−	1.08133i
$437$	−13.7429	+	7.34574i	−0.657412	+	0.351394i
$438$	26.4720	+	27.2593i	1.26488	+	1.30250i
$439$	−15.1249	−	22.6360i	−0.721872	−	1.08036i	−0.993034	−	0.117825i	$-0.962408\pi$
$439$	−15.1249	−	22.6360i	−0.721872	−	1.08036i	0.271162	−	0.962534i	$-0.412592\pi$
$440$	−4.37266	−	17.0844i	−0.208459	−	0.814466i
$441$	7.10690	+	4.74868i	0.338424	+	0.226128i
$442$	−3.86916	+	5.61085i	−0.184037	+	0.266881i
$443$	−2.10866	−	21.4096i	−0.100185	−	1.01720i	−0.905498	−	0.424350i	$-0.860503\pi$
$443$	−2.10866	−	21.4096i	−0.100185	−	1.01720i	0.805313	−	0.592850i	$-0.201997\pi$
$444$	28.4962	+	20.2730i	1.35237	+	0.962112i
$445$	0.471427	+	1.55409i	0.0223478	+	0.0736708i
$446$	−4.46682	−	5.60843i	−0.211510	−	0.265567i
$447$			58.9812i			2.78972i
$448$	15.6100	−	4.91066i	0.737503	−	0.232007i
$449$		−	7.46129i		−	0.352120i	−0.984379	−	0.176060i	$-0.943665\pi$
$449$		−	7.46129i		−	0.352120i	0.984379	−	0.176060i	$-0.0563353\pi$
$450$	−3.35793	+	2.67442i	−0.158294	+	0.126073i
$451$	−10.1877	−	33.5845i	−0.479722	−	1.58143i
$452$	−33.0212	+	5.56787i	−1.55318	+	0.261891i
$453$	−0.258835	−	2.62799i	−0.0121611	−	0.123474i
$454$	28.4734	+	19.6348i	1.33632	+	0.921508i
$455$	−1.78016	−	1.18947i	−0.0834553	−	0.0557630i
$456$	8.94868	+	11.9374i	0.419060	+	0.559022i
$457$	1.73287	+	2.59342i	0.0810602	+	0.121315i	0.869784	−	0.493432i	$-0.164258\pi$
$457$	1.73287	+	2.59342i	0.0810602	+	0.121315i	−0.788724	+	0.614747i	$0.789258\pi$
$458$	8.49966	−	8.25415i	0.397163	−	0.385691i
$459$	−0.353898	+	0.189163i	−0.0165186	+	0.00882935i
$460$	−4.61886	+	13.7611i	−0.215356	+	0.641617i
$461$	−29.5169	−	2.90716i	−1.37474	−	0.135400i	−0.616489	−	0.787363i	$-0.711446\pi$
$461$	−29.5169	−	2.90716i	−1.37474	−	0.135400i	−0.758251	+	0.651963i	$0.773946\pi$
$462$	44.1561	−	3.69661i	2.05433	−	0.171982i
$463$	−6.49875	−	15.6894i	−0.302023	−	0.729147i	−0.999916	−	0.0129455i	$-0.995879\pi$
$463$	−6.49875	−	15.6894i	−0.302023	−	0.729147i	0.697894	−	0.716201i	$-0.254121\pi$
$464$	17.0234	+	23.4162i	0.790292	+	1.08707i
$465$	−2.60074	+	6.27875i	−0.120607	+	0.291170i
$466$	−11.1862	+	35.0204i	−0.518192	+	1.62229i
$467$	−6.67175	+	5.47536i	−0.308732	+	0.253370i	−0.775981	−	0.630756i	$-0.782745\pi$
$467$	−6.67175	+	5.47536i	−0.308732	+	0.253370i	0.467250	+	0.884125i	$0.345245\pi$
$468$	1.66558	+	6.13209i	0.0769916	+	0.283456i
$469$	−6.54454	−	1.98526i	−0.302199	−	0.0916710i
$470$	−1.06726	+	2.47345i	−0.0492289	+	0.114092i
$471$	15.4509	+	3.07337i	0.711939	+	0.141613i
$472$	2.39213	−	9.76210i	0.110107	−	0.449337i
$473$	4.62132	+	23.2329i	0.212489	+	1.06825i
$474$	19.7432	+	30.5062i	0.906837	+	1.40120i
$475$	−1.65970	−	1.36208i	−0.0761521	−	0.0624964i
$476$	−17.6069	+	6.69560i	−0.807012	+	0.306892i
$477$	6.08004	−	11.3750i	0.278386	−	0.520824i
$478$	29.3454	+	16.2427i	1.34223	+	0.742924i
$479$	−18.0748	−	18.0748i	−0.825860	−	0.825860i	0.161081	−	0.986941i	$-0.448502\pi$
$479$	−18.0748	−	18.0748i	−0.825860	−	0.825860i	−0.986941	+	0.161081i	$0.948502\pi$
$480$	13.6936	+	2.37088i	0.625024	+	0.108215i
$481$	−5.26776	+	5.26776i	−0.240189	+	0.240189i
$482$	−24.2482	+	6.96930i	−1.10447	+	0.317443i
$483$	−32.1659	−	17.1930i	−1.46360	−	0.782309i
$484$	−40.5587	+	38.2486i	−1.84358	+	1.73857i
$485$	−3.80615	+	4.63781i	−0.172828	+	0.210592i
$486$	6.54805	−	30.5712i	0.297026	−	1.38674i
$487$	−31.0793	+	6.18205i	−1.40834	+	0.280135i	−0.839967	−	0.542638i	$-0.817426\pi$
$487$	−31.0793	+	6.18205i	−1.40834	+	0.280135i	−0.568369	+	0.822773i	$0.692426\pi$
$488$	1.37206	−	31.1927i	0.0621100	−	1.41203i
$489$	7.42090	−	37.3074i	0.335585	−	1.68710i
$490$	1.46985	+	3.70100i	0.0664010	+	0.167194i
$491$	−6.56720	+	21.6492i	−0.296373	+	0.977012i	0.674672	+	0.738118i	$0.264285\pi$
$491$	−6.56720	+	21.6492i	−0.296373	+	0.977012i	−0.971045	+	0.238895i	$0.923215\pi$
$492$	27.4327	+	3.51619i	1.23676	+	0.158522i
$493$	−21.1412	−	25.7606i	−0.952150	−	1.16020i
$494$	−2.82448	+	1.45692i	−0.127079	+	0.0655498i
$495$	17.4854	+	7.24267i	0.785909	+	0.325534i
$496$	10.4535	−	3.62839i	0.469375	−	0.162920i
$497$	12.1701	−	5.04103i	0.545905	−	0.226121i
$498$	−29.4955	+	34.8853i	−1.32173	+	1.56325i
$499$	−3.92719	+	39.8734i	−0.175805	+	1.78498i	0.352389	+	0.935854i	$0.385370\pi$
$499$	−3.92719	+	39.8734i	−0.175805	+	1.78498i	−0.528194	+	0.849124i	$0.677130\pi$
$500$	−1.99526	+	0.137630i	−0.0892307	+	0.00615499i
$501$	7.90383	+	14.7870i	0.353117	+	0.660635i
$502$	−11.4577	−	0.167899i	−0.511384	−	0.00749371i
$503$	9.69842	−	6.48028i	0.432431	−	0.288941i	−0.320242	−	0.947336i	$-0.603764\pi$
$503$	9.69842	−	6.48028i	0.432431	−	0.288941i	0.752673	+	0.658395i	$0.228764\pi$
$504$	−5.83159	+	16.5656i	−0.259760	+	0.737890i
$505$	−2.70372	+	4.04641i	−0.120314	+	0.180063i
$506$	62.9426	−	11.5640i	2.79814	−	0.514083i
$507$	29.1052	−	2.86661i	1.29261	−	0.127311i
$508$	−4.06178	−	0.932442i	−0.180212	−	0.0413704i
$509$	20.1710	−	6.11880i	0.894063	−	0.271211i	0.190368	−	0.981713i	$-0.439032\pi$
$509$	20.1710	−	6.11880i	0.894063	−	0.271211i	0.703695	+	0.710502i	$0.251532\pi$
$510$	−15.8957	−	1.80112i	−0.703872	−	0.0797549i
$511$	−22.3714			−0.989652
$512$	−11.9301	−	19.2269i	−0.527240	−	0.849717i
$513$	−0.187117			−0.00826142
$514$	−19.0520	−	2.15876i	−0.840348	−	0.0952188i
$515$	−4.97884	+	1.51031i	−0.219394	+	0.0665524i
$516$	−18.1941	−	4.17673i	−0.800952	−	0.183870i
$517$	11.8195	−	1.16412i	0.519821	−	0.0511979i
$518$	−20.2508	+	3.72054i	−0.889770	+	0.163471i
$519$	−29.1881	+	43.6831i	−1.28121	+	1.91747i
$520$	−0.983027	+	2.79245i	−0.0431086	+	0.122457i
$521$	18.4122	−	12.3027i	0.806655	−	0.538990i	−0.0825024	−	0.996591i	$-0.526291\pi$
$521$	18.4122	−	12.3027i	0.806655	−	0.538990i	0.889158	+	0.457601i	$0.151291\pi$
$522$	−31.0661	−	0.455236i	−1.35973	−	0.0199251i
$523$	−8.22781	−	15.3932i	−0.359777	−	0.673096i	0.635293	−	0.772271i	$-0.280879\pi$
$523$	−8.22781	−	15.3932i	−0.359777	−	0.673096i	−0.995070	+	0.0991757i	$0.968379\pi$
$524$	5.99760	−	0.413705i	0.262006	−	0.0180728i
$525$	0.492563	−	5.00108i	0.0214972	−	0.218265i
$526$	−6.42271	+	7.59634i	−0.280044	+	0.331216i
$527$	−11.7678	+	4.87439i	−0.512614	+	0.212332i
$528$	−20.0909	−	57.8824i	−0.874346	−	2.51901i
$529$	−27.4168	−	11.3564i	−1.19204	−	0.493757i
$530$	5.34048	−	2.75471i	0.231975	−	0.119657i
$531$	6.84299	+	8.33820i	0.296960	+	0.361847i
$532$	−8.71243	−	1.11672i	−0.377732	−	0.0484159i
$533$	−1.71023	+	5.63787i	−0.0740782	+	0.244203i
$534$	2.08263	+	5.24394i	0.0901241	+	0.226928i
$535$	1.53480	−	7.71595i	0.0663551	−	0.333590i
$536$	−0.415561	+	9.44746i	−0.0179495	+	0.408068i
$537$	33.6938	−	6.70211i	1.45399	−	0.289217i
$538$	1.25198	−	5.84516i	0.0539766	−	0.252003i
$539$	11.1378	−	13.5714i	0.479738	−	0.584563i
$540$	−0.126808	+	0.119585i	−0.00545694	+	0.00514613i
$541$	34.8002	+	18.6011i	1.49618	+	0.799724i	0.997740	−	0.0672002i	$-0.0214066\pi$
$541$	34.8002	+	18.6011i	1.49618	+	0.799724i	0.498439	+	0.866924i	$0.333907\pi$
$542$	−34.4939	+	9.91407i	−1.48164	+	0.425846i
$543$	44.3793	−	44.3793i	1.90450	−	1.90450i
$544$	15.0058	+	21.2899i	0.643366	+	0.912797i
$545$	8.91580	+	8.91580i	0.381911	+	0.381911i
$546$	−6.50807	−	3.60222i	−0.278520	−	0.154161i
$547$	−16.5126	+	30.8929i	−0.706028	+	1.32089i	0.231452	+	0.972846i	$0.425652\pi$
$547$	−16.5126	+	30.8929i	−0.706028	+	1.32089i	−0.937480	+	0.348039i	$0.886848\pi$
$548$	8.81367	−	3.35168i	0.376501	−	0.143177i
$549$	25.9023	+	21.2575i	1.10549	+	0.907248i
$550$	4.79082	+	7.40251i	0.204281	+	0.315644i
$551$	−3.03159	−	15.2409i	−0.129150	−	0.649282i
$552$	−12.0029	+	48.9828i	−0.510877	+	2.08485i
$553$	−20.9828	−	4.17374i	−0.892281	−	0.177486i
$554$	6.83679	−	15.8447i	0.290467	−	0.673179i
$555$	−16.7330	−	5.07589i	−0.710274	−	0.215459i
$556$	11.9884	+	44.1369i	0.508420	+	1.87182i
$557$	3.55783	−	2.91983i	0.150750	−	0.123717i	−0.555995	−	0.831185i	$-0.687663\pi$
$557$	3.55783	−	2.91983i	0.150750	−	0.123717i	0.706745	+	0.707468i	$0.250163\pi$
$558$	−3.61335	+	11.3122i	−0.152965	+	0.478884i
$559$	1.52176	−	3.67385i	0.0643636	−	0.155387i
$560$	−6.61804	+	4.81126i	−0.279663	+	0.203313i
$561$	26.9902	+	65.1602i	1.13953	+	2.75106i
$562$	13.8109	−	1.15620i	0.582577	−	0.0487715i
$563$	10.1349	+	0.998204i	0.427136	+	0.0420693i	0.309302	−	0.950964i	$-0.399905\pi$
$563$	10.1349	+	0.998204i	0.427136	+	0.0420693i	0.117835	+	0.993033i	$0.462405\pi$
$564$	−2.97816	+	8.87294i	−0.125403	+	0.373618i
$565$	14.7666	−	7.89290i	0.621234	−	0.332057i
$566$	30.7615	−	29.8730i	1.29300	−	1.25565i
$567$	10.1055	+	15.1240i	0.424392	+	0.635147i
$568$	−10.9253	−	14.5743i	−0.458417	−	0.611523i
$569$	−19.2905	−	12.8895i	−0.808702	−	0.540357i	0.0810992	−	0.996706i	$-0.474157\pi$
$569$	−19.2905	−	12.8895i	−0.808702	−	0.540357i	−0.889801	+	0.456349i	$0.849157\pi$
$570$	−6.14102	−	4.23475i	−0.257219	−	0.177374i
$571$	−2.57527	−	26.1471i	−0.107772	−	1.09422i	−0.885187	−	0.465236i	$-0.845969\pi$
$571$	−2.57527	−	26.1471i	−0.107772	−	1.09422i	0.777415	−	0.628988i	$-0.216531\pi$
$572$	12.8702	−	2.17011i	0.538128	−	0.0907367i
$573$	16.9540	+	55.8899i	0.708264	+	2.33483i
$574$	−12.7371	+	10.1444i	−0.531637	+	0.423421i
$575$		−	7.25781i		−	0.302671i
$576$	24.1900	+	2.13219i	1.00792	+	0.0888414i
$577$		−	4.31668i		−	0.179706i	−0.995955	−	0.0898528i	$-0.971360\pi$
$577$		−	4.31668i		−	0.179706i	0.995955	−	0.0898528i	$-0.0286397\pi$
$578$	−3.70133	−	4.64731i	−0.153955	−	0.193303i
$579$	−13.7248	−	45.2448i	−0.570385	−	1.88031i
$580$	−11.7948	−	8.39115i	−0.489753	−	0.348423i
$581$	−2.63629	−	26.7667i	−0.109372	−	1.11047i
$582$	−11.8335	+	17.1603i	−0.490513	+	0.711317i
$583$	−22.0279	−	14.7186i	−0.912301	−	0.609580i
$584$	7.67012	+	29.9678i	0.317392	+	1.24008i
$585$	−1.76512	−	2.64169i	−0.0729788	−	0.109220i
$586$	−6.76879	−	6.97011i	−0.279616	−	0.287933i
$587$	30.8390	−	16.4838i	1.27286	−	0.680359i	0.310098	−	0.950704i	$-0.399638\pi$
$587$	30.8390	−	16.4838i	1.27286	−	0.680359i	0.962763	+	0.270346i	$0.0871380\pi$
$588$	6.16166	+	12.3876i	0.254102	+	0.510857i
$589$	−5.91084	−	0.582167i	−0.243552	−	0.0239878i
$590$	0.419249	+	5.00794i	0.0172602	+	0.206174i
$591$	7.98006	+	19.2656i	0.328256	+	0.792480i
$592$	11.9270	+	25.8516i	0.490195	+	1.06249i
$593$	−1.05396	+	2.54448i	−0.0432809	+	0.104489i	−0.944042	−	0.329826i	$-0.893010\pi$
$593$	−1.05396	+	2.54448i	−0.0432809	+	0.104489i	0.900761	+	0.434316i	$0.143010\pi$
$594$	0.732017	+	0.233821i	0.0300350	+	0.00959380i
$595$	7.28062	−	5.97505i	0.298476	−	0.244953i
$596$	−23.8658	+	41.6651i	−0.977581	+	1.70667i
$597$	20.2797	+	6.15178i	0.829993	+	0.251776i
$598$	−9.86402	−	4.25619i	−0.403370	−	0.174049i
$599$	11.7332	+	2.33388i	0.479406	+	0.0953598i	0.428877	−	0.903363i	$-0.358909\pi$
$599$	11.7332	+	2.33388i	0.479406	+	0.0953598i	0.0505288	+	0.998723i	$0.483909\pi$
$600$	−6.86813	+	1.05482i	−0.280390	+	0.0430629i
$601$	−7.47892	−	37.5991i	−0.305072	−	1.53370i	−0.763995	−	0.645222i	$-0.776765\pi$
$601$	−7.47892	−	37.5991i	−0.305072	−	1.53370i	0.458923	−	0.888476i	$-0.348235\pi$
$602$	9.22674	−	5.97144i	0.376054	−	0.243378i
$603$	−7.84516	−	6.43836i	−0.319480	−	0.262190i
$604$	0.880530	−	1.96118i	0.0358283	−	0.0797994i
$605$	13.1400	−	24.5832i	0.534216	−	0.999448i
$606$	−8.18804	+	14.7932i	−0.332616	+	0.600933i
$607$	−21.8618	−	21.8618i	−0.887343	−	0.887343i	0.106924	−	0.994267i	$-0.465900\pi$
$607$	−21.8618	−	21.8618i	−0.887343	−	0.887343i	−0.994267	+	0.106924i	$0.965900\pi$
$608$	1.49118	+	12.0537i	0.0604753	+	0.488842i
$609$	25.7180	−	25.7180i	1.04215	−	1.04215i
$610$	4.31237	+	15.0040i	0.174603	+	0.607494i
$611$	−1.75833	−	0.939849i	−0.0711346	−	0.0380222i
$612$	−27.9414	−	0.819070i	−1.12947	−	0.0331090i
$613$	15.8914	−	19.3638i	0.641850	−	0.782096i	−0.345879	−	0.938279i	$-0.612419\pi$
$613$	15.8914	−	19.3638i	0.641850	−	0.782096i	0.987728	+	0.156183i	$0.0499191\pi$
$614$	10.7968	+	2.31257i	0.435724	+	0.0933278i
$615$	−13.5628	+	2.69782i	−0.546907	+	0.108787i
$616$	32.6883	+	15.2557i	1.31705	+	0.614671i
$617$	−5.36540	+	26.9737i	−0.216003	+	1.08592i	0.708781	+	0.705428i	$0.249245\pi$
$617$	−5.36540	+	26.9737i	−0.216003	+	1.08592i	−0.924784	+	0.380492i	$0.875755\pi$
$618$	−16.8001	+	6.67213i	−0.675797	+	0.268392i
$619$	−8.80823	+	29.0368i	−0.354033	+	1.16709i	0.581410	+	0.813611i	$0.302501\pi$
$619$	−8.80823	+	29.0368i	−0.354033	+	1.16709i	−0.935443	+	0.353478i	$0.884999\pi$
$620$	−4.37779	+	3.38305i	−0.175816	+	0.135866i
$621$	−0.401267	−	0.488946i	−0.0161023	−	0.0196207i
$622$	9.08033	+	17.6038i	0.364088	+	0.705847i
$623$	−3.06909	−	1.27126i	−0.122961	−	0.0509319i
$624$	−2.59407	+	9.95298i	−0.103846	+	0.398438i
$625$	0.923880	−	0.382683i	0.0369552	−	0.0153073i
$626$	19.8344	+	16.7700i	0.792741	+	0.670263i
$627$	−3.22355	+	32.7292i	−0.128736	+	1.30708i
$628$	9.67112	+	8.42301i	0.385920	+	0.336115i
$629$	−15.4489	−	28.9028i	−0.615987	−	1.15243i
$630$	0.128662	−	8.78010i	0.00512600	−	0.349807i
$631$	−4.10658	+	2.74393i	−0.163480	+	0.109234i	−0.634619	−	0.772825i	$-0.718843\pi$
$631$	−4.10658	+	2.74393i	−0.163480	+	0.109234i	0.471139	+	0.882059i	$0.343843\pi$
$632$	1.60306	+	29.5388i	0.0637664	+	1.17499i
$633$	−0.814745	+	1.21935i	−0.0323832	+	0.0484649i
$634$	−5.57348	−	30.3363i	−0.221351	−	1.20481i
$635$	2.07368	−	0.204240i	0.0822916	−	0.00810502i
$636$	17.6914	−	11.0853i	0.701511	−	0.439561i
$637$	−2.82034	+	0.855540i	−0.111746	+	0.0338977i
$638$	−7.18510	+	63.4117i	−0.284461	+	2.51049i
$639$	19.5480			0.773306
$640$	8.71399	+	7.21570i	0.344451	+	0.285226i
$641$	1.41883			0.0560405			0.0280203	−	0.999607i	$-0.491080\pi$
$641$	1.41883			0.0560405			0.0280203	+	0.999607i	$0.491080\pi$
$642$	3.07737	−	27.1591i	0.121454	−	1.07189i
$643$	−16.7347	+	5.07642i	−0.659952	+	0.200194i	−0.602457	−	0.798151i	$-0.705811\pi$
$643$	−16.7347	+	5.07642i	−0.659952	+	0.200194i	−0.0574955	+	0.998346i	$0.518311\pi$
$644$	−15.7655	−	25.1608i	−0.621249	−	0.991473i
$645$	9.28875	−	0.914862i	0.365744	−	0.0360226i
$646$	−2.52634	−	13.7508i	−0.0993976	−	0.541018i
$647$	−9.91037	+	14.8319i	−0.389617	+	0.583103i	−0.973486	−	0.228745i	$-0.926538\pi$
$647$	−9.91037	+	14.8319i	−0.389617	+	0.583103i	0.583870	+	0.811847i	$0.301538\pi$
$648$	16.7948	−	18.7223i	0.659760	−	0.735480i
$649$	18.4221	−	12.3093i	0.723131	−	0.483181i
$650$	0.0216884	−	1.48005i	0.000850687	−	0.0580525i
$651$	−6.55313	−	12.2600i	−0.256837	−	0.480509i
$652$	20.3381	−	23.3517i	0.796500	−	0.914523i
$653$	−2.15392	+	21.8691i	−0.0842895	+	0.855805i	0.856350	+	0.516397i	$0.172727\pi$
$653$	−2.15392	+	21.8691i	−0.0842895	+	0.855805i	−0.940639	+	0.339409i	$0.889773\pi$
$654$	33.4526	+	28.2842i	1.30810	+	1.10600i
$655$	−2.77711	+	1.15032i	−0.108511	+	0.0449466i
$656$	17.9561	+	13.5841i	0.701066	+	0.530369i
$657$	−30.6712	−	12.7044i	−1.19660	−	0.495647i
$658$	−2.52609	−	4.89727i	−0.0984774	−	0.190915i
$659$	−14.1106	−	17.1938i	−0.549670	−	0.669775i	0.421868	−	0.906657i	$-0.361375\pi$
$659$	−14.1106	−	17.1938i	−0.549670	−	0.669775i	−0.971538	+	0.236882i	$0.923875\pi$
$660$	18.7324	+	24.2405i	0.729159	+	0.943560i
$661$	2.52912	−	8.33740i	0.0983715	−	0.324287i	−0.893918	−	0.448231i	$-0.852054\pi$
$661$	2.52912	−	8.33740i	0.0983715	−	0.324287i	0.992289	+	0.123944i	$0.0395542\pi$
$662$	−7.81413	+	3.10338i	−0.303705	+	0.120616i
$663$	2.30982	−	11.6123i	0.0897061	−	0.450983i
$664$	−34.9518	+	12.7085i	−1.35639	+	0.493187i
$665$	4.30746	−	0.856808i	0.167036	−	0.0332256i
$666$	−29.8767	−	6.39931i	−1.15770	−	0.247968i
$667$	33.3239	−	40.6053i	1.29031	−	1.57224i
$668$	−0.399955	+	13.6439i	−0.0154747	+	0.527899i
$669$	10.9845	+	5.87135i	0.424687	+	0.227000i
$670$	−1.30611	−	4.54432i	−0.0504594	−	0.175563i
$671$	48.6681	−	48.6681i	1.87881	−	1.87881i
$672$	−21.5186	+	18.5758i	−0.830096	+	0.716578i
$673$	0.958762	+	0.958762i	0.0369576	+	0.0369576i	0.725344	−	0.688387i	$-0.241681\pi$
$673$	0.958762	+	0.958762i	0.0369576	+	0.0369576i	−0.688387	+	0.725344i	$0.741681\pi$
$674$	−5.59560	+	10.1095i	−0.215534	+	0.389403i
$675$	0.0410825	−	0.0768599i	0.00158127	−	0.00295834i
$676$	21.7202	+	9.75192i	0.835393	+	0.375074i
$677$	8.41714	+	6.90777i	0.323497	+	0.265487i	0.782098	−	0.623155i	$-0.214149\pi$
$677$	8.41714	+	6.90777i	0.323497	+	0.265487i	−0.458601	+	0.888642i	$0.651649\pi$
$678$	48.8373	−	31.6069i	1.87559	−	1.21386i
$679$	−2.39424	−	12.0367i	−0.0918825	−	0.461924i
$680$	−10.5001	−	7.70426i	−0.402661	−	0.295445i
$681$	−58.9288	−	11.7217i	−2.25816	−	0.449175i
$682$	22.3962	+	9.66366i	0.857595	+	0.370041i
$683$	19.3505	+	5.86990i	0.740426	+	0.224606i	0.637894	−	0.770124i	$-0.279806\pi$
$683$	19.3505	+	5.86990i	0.740426	+	0.224606i	0.102532	+	0.994730i	$0.467306\pi$
$684$	−11.3106	−	6.47870i	−0.432471	−	0.247719i
$685$	−3.64453	+	2.99099i	−0.139250	+	0.114280i
$686$	−27.0489	−	8.63998i	−1.03273	−	0.329876i
$687$	−7.87636	+	19.0152i	−0.300502	+	0.725476i
$688$	−11.1625	−	10.3124i	−0.425567	−	0.393158i
$689$	1.70193	+	4.10883i	0.0648384	+	0.156534i
$690$	−2.10364	−	25.1281i	−0.0800843	−	0.956610i
$691$	1.67906	+	0.165373i	0.0638746	+	0.00629109i	0.129904	−	0.991527i	$-0.458533\pi$
$691$	1.67906	+	0.165373i	0.0638746	+	0.00629109i	−0.0660294	+	0.997818i	$0.521033\pi$
$692$	−38.2945	+	19.0478i	−1.45574	+	0.724089i
$693$	−34.1424	+	18.2495i	−1.29696	+	0.693240i
$694$	−25.1112	−	25.8581i	−0.953209	−	0.981561i
$695$	−12.7048	−	19.0141i	−0.481921	−	0.721245i
$696$	−43.2683	−	25.6333i	−1.64008	−	0.971627i
$697$	−21.5499	−	14.3992i	−0.816262	−	0.545409i
$698$	1.42671	−	2.06894i	0.0540018	−	0.0783106i
$699$	−6.25980	−	63.5568i	−0.236767	−	2.40394i
$700$	2.37156	−	3.33352i	0.0896365	−	0.125995i
$701$	−1.84168	−	6.07122i	−0.0695595	−	0.229307i	0.915267	−	0.402847i	$-0.131979\pi$
$701$	−1.84168	−	6.07122i	−0.0695595	−	0.229307i	−0.984827	+	0.173540i	$0.944479\pi$
$702$	−0.0803676	−	0.100908i	−0.00303328	−	0.00380852i
$703$		−	15.2818i		−	0.576365i
$704$	9.22866	−	49.0184i	0.347818	−	1.84745i
$705$		−	4.67971i		−	0.176248i
$706$	19.3853	−	15.4394i	0.729575	−	0.581068i
$707$	−2.88969	−	9.52604i	−0.108678	−	0.358264i
$708$	2.90306	+	17.2170i	0.109104	+	0.647056i
$709$	−5.06853	−	51.4617i	−0.190353	−	1.93268i	−0.333032	−	0.942916i	$-0.608072\pi$
$709$	−5.06853	−	51.4617i	−0.190353	−	1.93268i	0.142679	−	0.989769i	$-0.454428\pi$
$710$	7.49751	+	5.17016i	0.281376	+	0.194033i
$711$	−26.3973	−	17.6381i	−0.989974	−	0.661480i
$712$	−0.650679	+	4.54709i	−0.0243852	+	0.170409i
$713$	−11.1544	−	16.6938i	−0.417736	−	0.625186i
$714$	23.4752	−	22.7972i	0.878538	−	0.853162i
$715$	−5.75535	+	3.07630i	−0.215238	+	0.115047i
$716$	26.5136	+	8.89918i	0.990861	+	0.332578i
$717$	−57.9852	−	5.71104i	−2.16550	−	0.213283i
$718$	−22.7037	+	1.90068i	−0.847295	+	0.0709328i
$719$	10.8803	+	26.2675i	0.405768	+	0.979611i	0.986238	+	0.165330i	$0.0528688\pi$
$719$	10.8803	+	26.2675i	0.405768	+	0.979611i	−0.580470	+	0.814281i	$0.697131\pi$
$720$	−11.8056	+	2.83794i	−0.439968	+	0.105764i
$721$	4.07274	−	9.83248i	0.151677	−	0.366181i
$722$	−6.19222	+	19.3858i	−0.230450	+	0.721465i
$723$	33.8798	−	27.8044i	1.26000	−	1.03406i
$724$	49.3074	−	13.3928i	1.83250	−	0.497738i
$725$	6.92591	+	2.10095i	0.257222	+	0.0780274i
$726$	38.3681	−	88.9208i	1.42397	−	3.30016i
$727$	17.3006	+	3.44130i	0.641644	+	0.127631i	0.505180	−	0.863014i	$-0.331426\pi$
$727$	17.3006	+	3.44130i	0.641644	+	0.127631i	0.136464	+	0.990645i	$0.456426\pi$
$728$	−3.13981	−	5.17804i	−0.116369	−	0.191911i
$729$	5.39127	+	27.1037i	0.199677	+	1.00384i
$730$	−8.40360	−	12.9848i	−0.311031	−	0.480589i
$731$	13.5226	+	11.0977i	0.500153	+	0.410465i
$732$	19.2792	+	50.6971i	0.712580	+	1.87382i
$733$	5.04172	−	9.43239i	0.186220	−	0.348393i	−0.771436	−	0.636306i	$-0.780461\pi$
$733$	5.04172	−	9.43239i	0.186220	−	0.348393i	0.957657	+	0.287913i	$0.0929614\pi$
$734$	9.01154	+	4.98789i	0.332622	+	0.184106i
$735$	−4.89157	−	4.89157i	−0.180428	−	0.180428i
$736$	−28.2991	+	29.7453i	−1.04312	+	1.09643i
$737$	−14.7403	+	14.7403i	−0.542968	+	0.542968i
$738$	−23.2235	+	6.67478i	−0.854868	+	0.245702i
$739$	32.3314	+	17.2815i	1.18933	+	0.635711i	0.942779	−	0.333419i	$-0.108202\pi$
$739$	32.3314	+	17.2815i	1.18933	+	0.635711i	0.246552	+	0.969129i	$0.420702\pi$
$740$	−9.76651	−	10.3564i	−0.359024	−	0.380708i
$741$	3.50241	−	4.26770i	0.128664	−	0.156778i
$742$	−2.57438	+	12.0191i	−0.0945084	+	0.441235i
$743$	−3.65942	+	0.727903i	−0.134251	+	0.0267042i	−0.261758	−	0.965133i	$-0.584302\pi$
$743$	−3.65942	+	0.727903i	−0.134251	+	0.0267042i	0.127507	+	0.991838i	$0.459302\pi$
$744$	−14.1763	+	12.9817i	−0.519729	+	0.475933i
$745$	4.68375	−	23.5468i	0.171599	−	0.862688i
$746$	4.61670	+	11.6246i	0.169030	+	0.425607i
$747$	11.5861	−	38.1943i	0.423914	−	1.39746i
$748$	−7.29973	+	56.9512i	−0.266905	+	2.08234i
$749$	10.2089	+	12.4396i	0.373025	+	0.454532i
$750$	3.08775	−	1.59272i	0.112749	−	0.0581577i
$751$	−24.8016	−	10.2732i	−0.905023	−	0.374873i	−0.118874	−	0.992909i	$-0.537928\pi$
$751$	−24.8016	−	10.2732i	−0.905023	−	0.374873i	−0.786149	+	0.618037i	$0.787928\pi$
$752$	−5.69410	+	5.06290i	−0.207643	+	0.184625i
$753$	18.3908	−	7.61774i	0.670200	−	0.277606i
$754$	6.91694	−	8.18088i	0.251900	−	0.297930i
$755$	−0.105358	+	1.06972i	−0.00383436	+	0.0389310i
$756$	−0.0245350	−	0.355692i	−0.000892331	−	0.0129364i
$757$	14.7510	+	27.5972i	0.536135	+	1.00304i	0.993508	+	0.113763i	$0.0362904\pi$
$757$	14.7510	+	27.5972i	0.536135	+	1.00304i	−0.457373	+	0.889275i	$0.651210\pi$
$758$	49.8644	+	0.730701i	1.81116	+	0.0265403i
$759$	−92.4358	+	61.7636i	−3.35521	+	2.24188i
$760$	−2.62458	−	5.47635i	−0.0952034	−	0.198648i
$761$	−11.4527	+	17.1401i	−0.415158	+	0.621329i	−0.978831	−	0.204670i	$-0.934388\pi$
$761$	−11.4527	+	17.1401i	−0.415158	+	0.621329i	0.563673	+	0.825998i	$0.309388\pi$
$762$	7.12034	−	1.30817i	0.257943	−	0.0473900i
$763$	−25.6675	+	2.52803i	−0.929225	+	0.0915207i
$764$	−10.6384	+	46.3415i	−0.384883	+	1.67658i
$765$	13.3749	−	4.05723i	0.483570	−	0.146689i
$766$	−24.7374	−	2.80297i	−0.893800	−	0.101275i
$767$	−3.71937			−0.134299
$768$	32.2612	+	22.4566i	1.16412	+	0.810333i
$769$	20.6272			0.743838			0.371919	−	0.928265i	$-0.378700\pi$
$769$	20.6272			0.743838			0.371919	+	0.928265i	$0.378700\pi$
$770$	−17.9218	−	2.03070i	−0.645857	−	0.0731812i
$771$	31.8740	−	9.66887i	1.14791	−	0.348216i
$772$	8.61213	−	37.5150i	0.309957	−	1.35020i
$773$	5.87489	−	0.578626i	0.211305	−	0.0208117i	0.00818925	−	0.999966i	$-0.497393\pi$
$773$	5.87489	−	0.578626i	0.211305	−	0.0208117i	0.203116	+	0.979155i	$0.434893\pi$
$774$	16.0410	−	2.94710i	0.576581	−	0.105931i
$775$	1.53688	−	2.30011i	0.0552065	−	0.0826224i
$776$	−15.3030	+	7.33404i	−0.549344	+	0.263277i
$777$	29.7398	−	19.8715i	1.06691	−	0.712887i
$778$	−29.2082	−	0.428010i	−1.04716	−	0.0153449i
$779$	−5.69707	−	10.6585i	−0.204119	−	0.381879i
$780$	−0.353897	−	5.13055i	−0.0126716	−	0.183703i
$781$	3.93559	−	39.9587i	0.140827	−	1.42984i
$782$	30.5138	−	36.0897i	1.09117	−	1.29056i
$783$	0.582743	−	0.241380i	0.0208255	−	0.00862622i
$784$	−0.659777	+	11.2440i	−0.0235635	+	0.401572i
$785$	−5.92432	−	2.45393i	−0.211448	−	0.0875847i
$786$	−9.28154	+	4.78758i	−0.331062	+	0.170767i
$787$	15.9208	+	19.3995i	0.567515	+	0.691519i	0.975130	−	0.221635i	$-0.0711394\pi$
$787$	15.9208	+	19.3995i	0.567515	+	0.691519i	−0.407615	+	0.913154i	$0.633639\pi$
$788$	−2.15828	+	16.8385i	−0.0768854	+	0.599846i
$789$	5.01632	−	16.5366i	0.178586	−	0.588718i
$790$	−5.45948	−	13.7467i	−0.194240	−	0.489085i
$791$	−6.68175	+	33.5914i	−0.237576	+	1.19437i
$792$	36.1521	+	39.4788i	1.28461	+	1.40282i
$793$	−11.3321	+	2.25409i	−0.402414	+	0.0800452i
$794$	2.56277	−	11.9649i	0.0909494	−	0.424619i
$795$	−6.62228	+	8.06927i	−0.234868	+	0.286188i
$796$	11.8366	+	12.5516i	0.419539	+	0.444878i
$797$	−44.7584	−	23.9239i	−1.58542	−	0.847426i	−0.999308	−	0.0371986i	$-0.988157\pi$
$797$	−44.7584	−	23.9239i	−1.58542	−	0.847426i	−0.586115	−	0.810228i	$-0.699343\pi$
$798$	14.6650	−	4.21495i	0.519136	−	0.149208i
$799$	6.20192	−	6.20192i	0.219408	−	0.219408i
$800$	−5.27855	−	2.03393i	−0.186625	−	0.0719104i
$801$	−3.48579	−	3.48579i	−0.123165	−	0.123165i
$802$	29.2734	+	16.2029i	1.03368	+	0.572143i
$803$	−32.1446	+	60.1383i	−1.13436	+	2.12223i
$804$	−5.83918	−	15.3549i	−0.205932	−	0.541524i
$805$	11.4761	+	9.41821i	0.404480	+	0.331948i
$806$	−2.22478	−	3.43762i	−0.0783647	−	0.121085i
$807$	2.02588	+	10.1848i	0.0713143	+	0.358521i
$808$	−11.7700	+	7.13696i	−0.414066	+	0.251077i
$809$	−4.62388	−	0.919747i	−0.162567	−	0.0323366i	0.113136	−	0.993580i	$-0.463911\pi$
$809$	−4.62388	−	0.919747i	−0.162567	−	0.0323366i	−0.275703	+	0.961243i	$0.588911\pi$
$810$	−4.98221	+	11.5466i	−0.175057	+	0.405707i
$811$	−21.0275	−	6.37862i	−0.738376	−	0.223984i	−0.101376	−	0.994848i	$-0.532325\pi$
$811$	−21.0275	−	6.37862i	−0.738376	−	0.223984i	−0.636999	+	0.770864i	$0.719825\pi$
$812$	28.5739	−	7.76117i	1.00275	−	0.272364i
$813$	48.1952	−	39.5528i	1.69028	−	1.38718i
$814$	−19.0961	+	59.7837i	−0.669319	+	2.09542i
$815$	−5.92523	+	14.3048i	−0.207552	+	0.501074i
$816$	−38.5868	−	23.6304i	−1.35081	−	0.827229i
$817$	3.12163	+	7.53627i	0.109212	+	0.263661i
$818$	−47.9223	+	4.01190i	−1.67556	+	0.140273i
$819$	6.46761	+	0.637004i	0.225996	+	0.0222587i
$820$	−10.6726	−	3.58221i	−0.372704	−	0.125096i
$821$	−41.4270	+	22.1432i	−1.44581	+	0.772803i	−0.992923	−	0.118763i	$-0.962107\pi$
$821$	−41.4270	+	22.1432i	−1.44581	+	0.772803i	−0.452890	+	0.891566i	$0.649607\pi$
$822$	−11.7512	+	11.4118i	−0.409871	+	0.398033i
$823$	11.4692	+	17.1648i	0.399790	+	0.598328i	0.975680	−	0.219199i	$-0.0703445\pi$
$823$	11.4692	+	17.1648i	0.399790	+	0.598328i	−0.575890	+	0.817527i	$0.695344\pi$
$824$	−14.5676	−	2.08459i	−0.507485	−	0.0726200i
$825$	−12.7361	−	8.50996i	−0.443412	−	0.296279i
$826$	−8.46265	−	5.83571i	−0.294453	−	0.203050i
$827$	2.29720	+	23.3238i	0.0798813	+	0.811049i	0.948754	+	0.316014i	$0.102345\pi$
$827$	2.29720	+	23.3238i	0.0798813	+	0.811049i	−0.868873	+	0.495035i	$0.835155\pi$
$828$	−7.32608	−	43.4485i	−0.254599	−	1.50994i
$829$	12.0586	+	39.7519i	0.418813	+	1.38064i	0.872122	+	0.489288i	$0.162743\pi$
$829$	12.0586	+	39.7519i	0.418813	+	1.38064i	−0.453309	+	0.891353i	$0.649757\pi$
$830$	14.5456	−	11.5848i	0.504886	−	0.402115i
$831$			29.9779i			1.03992i
$832$	−5.85980	+	5.98127i	−0.203152	+	0.207363i
$833$		−	12.9654i		−	0.449224i
$834$	−49.4979	−	62.1484i	−1.71397	−	2.15202i
$835$	−1.98116	−	6.53101i	−0.0685608	−	0.226015i
$836$	−15.5205	+	21.8160i	−0.536788	+	0.754522i
$837$	−0.0236306	−	0.239925i	−0.000816792	−	0.00829303i
$838$	−9.72556	+	14.1035i	−0.335964	+	0.487197i
$839$	27.5486	+	18.4074i	0.951082	+	0.635493i	0.931277	−	0.364311i	$-0.118695\pi$
$839$	27.5486	+	18.4074i	0.951082	+	0.635493i	0.0198050	+	0.999804i	$0.493695\pi$
$840$	7.24464	−	12.2288i	0.249964	−	0.421932i
$841$	12.9905	+	19.4416i	0.447947	+	0.670400i
$842$	19.6538	+	20.2384i	0.677316	+	0.697462i
$843$	−21.2329	+	11.3492i	−0.731298	+	0.390887i
$844$	−1.06894	+	0.531693i	−0.0367943	+	0.0183016i
$845$	−11.8472	−	1.16684i	−0.407555	−	0.0401406i
$846$	−0.682182	−	8.14869i	−0.0234539	−	0.280158i
$847$	21.8199	+	52.6778i	0.749739	+	1.81003i
$848$	16.9830	−	0.672263i	0.583197	−	0.0230856i
$849$	−28.5057	+	68.8188i	−0.978312	+	2.36185i
$850$	6.20293	+	1.98134i	0.212759	+	0.0679595i
$851$	39.9321	−	32.7715i	1.36886	−	1.12339i
$852$	27.4565	+	15.7271i	0.940645	+	0.538802i
$853$	15.4645	+	4.69112i	0.529496	+	0.160621i	0.543702	−	0.839278i	$-0.317022\pi$
$853$	15.4645	+	4.69112i	0.529496	+	0.160621i	−0.0142062	+	0.999899i	$0.504522\pi$
$854$	−29.3205	−	12.6514i	−1.00333	−	0.432922i
$855$	6.39211	+	1.27147i	0.218605	+	0.0434833i
$856$	13.1634	−	17.9404i	0.449916	−	0.613190i
$857$	3.57666	+	17.9811i	0.122176	+	0.614222i	0.992551	+	0.121832i	$0.0388769\pi$
$857$	3.57666	+	17.9811i	0.122176	+	0.614222i	−0.870374	+	0.492391i	$0.836123\pi$
$858$	−19.0346	+	12.3190i	−0.649830	+	0.420562i
$859$	15.2162	+	12.4876i	0.519169	+	0.426071i	0.857138	−	0.515086i	$-0.172240\pi$
$859$	15.2162	+	12.4876i	0.519169	+	0.426071i	−0.337970	+	0.941157i	$0.609740\pi$
$860$	6.93188	+	3.11227i	0.236375	+	0.106127i
$861$	13.3342	−	24.9466i	0.454429	−	0.850177i
$862$	15.6441	−	28.2640i	0.532841	−	0.962675i
$863$	36.2923	+	36.2923i	1.23540	+	1.23540i	0.961860	+	0.273543i	$0.0881957\pi$
$863$	36.2923	+	36.2923i	1.23540	+	1.23540i	0.273543	+	0.961860i	$0.411804\pi$
$864$	−0.468058	+	0.154816i	−0.0159237	+	0.00526696i
$865$	15.1215	−	15.1215i	0.514148	−	0.514148i
$866$	−8.64230	−	30.0690i	−0.293677	−	1.02179i
$867$	9.10210	+	4.86517i	0.309124	+	0.165230i
$868$	0.331606	−	11.3123i	0.0112554	−	0.383964i
$869$	−41.3692	+	50.4085i	−1.40335	+	1.70999i
$870$	24.5879	+	5.26650i	0.833609	+	0.178551i
$871$	3.43220	−	0.682707i	0.116296	−	0.0231327i
$872$	12.1866	+	33.5164i	0.412692	+	1.13501i
$873$	3.55296	−	17.8619i	0.120249	−	0.604534i
$874$	20.4814	−	8.13419i	0.692795	−	0.275143i
$875$	−0.593784	+	1.95744i	−0.0200736	+	0.0661737i
$876$	−32.8587	−	42.5204i	−1.11019	−	1.43663i
$877$	−7.29341	−	8.88705i	−0.246281	−	0.300094i	0.635167	−	0.772374i	$-0.280931\pi$
$877$	−7.29341	−	8.88705i	−0.246281	−	0.300094i	−0.881449	+	0.472280i	$0.843431\pi$
$878$	17.6496	+	34.2169i	0.595647	+	1.15476i
$879$	15.5934	+	6.45898i	0.525951	+	0.217856i
$880$	3.42432	+	24.7036i	0.115434	+	0.832758i
$881$	−2.16506	+	0.896797i	−0.0729427	+	0.0302139i	−0.418856	−	0.908052i	$-0.637569\pi$
$881$	−2.16506	+	0.896797i	−0.0729427	+	0.0302139i	0.345914	+	0.938266i	$0.387569\pi$
$882$	−9.23067	−	7.80454i	−0.310813	−	0.262792i
$883$	3.03791	−	30.8444i	0.102234	−	1.03800i	−0.798020	−	0.602631i	$-0.794119\pi$
$883$	3.03791	−	30.8444i	0.102234	−	1.03800i	0.900254	−	0.435366i	$-0.143381\pi$
$884$	6.33040	−	7.26843i	0.212915	−	0.244464i
$885$	−4.11531	−	7.69921i	−0.138335	−	0.258806i
$886$	−0.445781	+	30.4209i	−0.0149763	+	1.02201i
$887$	−3.42310	+	2.28724i	−0.114936	+	0.0767980i	−0.611710	−	0.791082i	$-0.709518\pi$
$887$	−3.42310	+	2.28724i	−0.114936	+	0.0767980i	0.496773	+	0.867880i	$0.334518\pi$
$888$	−36.8155	−	33.0253i	−1.23545	−	1.10826i
$889$	−2.36800	+	3.54397i	−0.0794202	+	0.118861i
$890$	−0.415012	−	2.25890i	−0.0139112	−	0.0757184i
$891$	55.1762	−	5.43438i	1.84847	−	0.182058i
$892$	5.38387	+	8.59231i	0.180265	+	0.287692i
$893$	3.91373	−	1.18722i	0.130968	−	0.0397287i
$894$	9.39122	−	82.8817i	0.314089	−	2.77198i
$895$	−13.9836			−0.467422
$896$	−22.7174	+	4.41508i	−0.758935	+	0.147498i
$897$	18.6625			0.623123
$898$	−1.18802	+	10.4848i	−0.0396446	+	0.349881i
$899$	19.1593	−	5.81190i	0.638998	−	0.193838i
$900$	5.14447	−	3.22348i	0.171482	−	0.107449i
$901$	−19.4704	+	1.91767i	−0.648654	+	0.0638869i
$902$	8.96859	+	48.8158i	0.298621	+	1.62539i
$903$	−10.6071	+	15.8746i	−0.352982	+	0.528275i
$904$	47.2886	−	2.56634i	1.57279	−	0.0853553i
$905$	−21.2415	+	14.1931i	−0.706092	+	0.471796i
$906$	−0.0547190	+	3.73413i	−0.00181792	+	0.124058i
$907$	−9.87824	−	18.4809i	−0.328002	−	0.613648i	0.662827	−	0.748773i	$-0.269356\pi$
$907$	−9.87824	−	18.4809i	−0.328002	−	0.613648i	−0.990829	+	0.135125i	$0.956856\pi$
$908$	−36.8851	−	32.1249i	−1.22408	−	1.06610i
$909$	1.44794	−	14.7012i	0.0480253	−	0.487609i
$910$	2.31213	+	1.95491i	0.0766464	+	0.0648046i
$911$	20.6272	−	8.54405i	0.683408	−	0.283077i	−0.0138425	−	0.999904i	$-0.504406\pi$
$911$	20.6272	−	8.54405i	0.683408	−	0.283077i	0.697251	+	0.716827i	$0.254406\pi$
$912$	−10.6741	−	18.1996i	−0.353456	−	0.602648i
$913$	−75.7417	−	31.3732i	−2.50669	−	1.03830i
$914$	−2.02213	−	3.92025i	−0.0668861	−	0.129670i
$915$	−17.2045	−	20.9637i	−0.568762	−	0.693039i
$916$	−13.2582	+	10.2456i	−0.438062	+	0.338523i
$917$	1.78487	−	5.88392i	0.0589416	−	0.194304i
$918$	0.527425	−	0.209466i	0.0174076	−	0.00691342i
$919$	−7.25906	+	36.4938i	−0.239454	+	1.20382i	0.654640	+	0.755940i	$0.272820\pi$
$919$	−7.25906	+	36.4938i	−0.239454	+	1.20382i	−0.894095	+	0.447878i	$0.852180\pi$
$920$	8.68163	−	18.6020i	0.286225	−	0.613291i
$921$	−18.8127	+	3.74207i	−0.619898	+	0.123305i
$922$	41.0149	+	8.78500i	1.35075	+	0.289319i
$923$	−4.27605	+	5.21038i	−0.140748	+	0.171502i
$924$	−62.6378	−	1.83615i	−2.06063	−	0.0604050i
$925$	6.27714	+	3.35520i	0.206391	+	0.110318i
$926$	6.63406	+	23.0818i	0.218009	+	0.758515i
$927$	11.1675	−	11.1675i	0.366788	−	0.366788i
$928$	−20.1932	−	35.6155i	−0.662875	−	1.16914i
$929$	22.7814	+	22.7814i	0.747434	+	0.747434i	0.973997	−	0.226563i	$-0.0727488\pi$
$929$	22.7814	+	22.7814i	0.747434	+	0.747434i	−0.226563	+	0.973997i	$0.572749\pi$
$930$	4.65435	−	8.40894i	0.152622	−	0.275740i
$931$	2.84995	−	5.33188i	0.0934034	−	0.174745i
$932$	21.2952	−	47.4303i	0.697548	−	1.55363i
$933$	−26.5987	−	21.8290i	−0.870802	−	0.714649i
$934$	10.2471	−	6.63180i	0.335295	−	0.216999i
$935$	−5.60076	−	28.1569i	−0.183164	−	0.920830i
$936$	−1.36414	−	8.88215i	−0.0445883	−	0.290322i
$937$	−48.4091	−	9.62918i	−1.58146	−	0.314571i	−0.675310	−	0.737534i	$-0.735990\pi$
$937$	−48.4091	−	9.62918i	−1.58146	−	0.314571i	−0.906147	+	0.422962i	$0.860990\pi$
$938$	8.88043	+	3.83178i	0.289956	+	0.125112i
$939$	−43.1777	−	13.0978i	−1.40905	−	0.427431i
$940$	1.89357	−	3.30581i	0.0617613	−	0.107824i
$941$	10.1870	−	8.36022i	0.332085	−	0.272535i	−0.453543	−	0.891235i	$-0.649840\pi$
$941$	10.1870	−	8.36022i	0.332085	−	0.272535i	0.785628	+	0.618699i	$0.212340\pi$
$942$	−21.2225	−	6.77891i	−0.691468	−	0.220869i
$943$	15.6339	−	37.7435i	0.509109	−	1.22910i
$944$	−4.91583	+	13.3370i	−0.159997	+	0.434083i
$945$	0.0682204	+	0.164699i	0.00221921	+	0.00535764i
$946$	−2.79474	−	33.3833i	−0.0908648	−	1.08538i
$947$	−21.7450	−	2.14170i	−0.706618	−	0.0695958i	−0.261677	−	0.965156i	$-0.584275\pi$
$947$	−21.7450	−	2.14170i	−0.706618	−	0.0695958i	−0.444941	+	0.895560i	$0.646775\pi$
$948$	−22.8863	−	46.0115i	−0.743313	−	1.49439i
$949$	10.0955	−	5.39615i	0.327713	−	0.175166i
$950$	2.11537	+	2.17829i	0.0686316	+	0.0706729i
$951$	29.7681	+	44.5511i	0.965296	+	1.44467i
$952$	25.8077	−	6.60536i	0.836433	−	0.214081i
$953$	25.8227	+	17.2542i	0.836481	+	0.558919i	0.898408	−	0.439162i	$-0.144725\pi$
$953$	25.8227	+	17.2542i	0.836481	+	0.558919i	−0.0619271	+	0.998081i	$0.519725\pi$
$954$	−10.3550	+	15.0162i	−0.335255	+	0.486169i
$955$	−2.33021	−	23.6590i	−0.0754038	−	0.765587i
$956$	−38.6506	−	27.4971i	−1.25005	−	0.889320i
$957$	−32.1814	−	106.088i	−1.04028	−	3.42933i
$958$	22.5212	+	28.2771i	0.727627	+	0.913591i
$959$		−	9.64408i		−	0.311424i
$960$	−18.8650	−	5.51195i	−0.608866	−	0.177898i
$961$			23.3475i			0.753145i
$962$	8.24112	−	6.56362i	0.265704	−	0.211619i
$963$	6.93212	+	22.8521i	0.223385	+	0.736400i
$964$	35.1837	−	5.93252i	1.13319	−	0.191074i
$965$	1.88638	+	19.1528i	0.0607248	+	0.616549i
$966$	42.4626	+	29.2816i	1.36621	+	0.942119i
$967$	−3.05666	−	2.04239i	−0.0982955	−	0.0656789i	0.505451	−	0.862855i	$-0.331326\pi$
$967$	−3.05666	−	2.04239i	−0.0982955	−	0.0656789i	−0.603747	+	0.797176i	$0.706326\pi$
$968$	63.0841	−	47.2898i	2.02760	−	1.51995i
$969$	13.4933	+	20.1941i	0.433466	+	0.648727i
$970$	6.08694	−	5.91112i	0.195440	−	0.189795i
$971$	3.82829	−	2.04626i	0.122856	−	0.0656677i	−0.408824	−	0.912613i	$-0.634061\pi$
$971$	3.82829	−	2.04626i	0.122856	−	0.0656677i	0.531680	+	0.846946i	$0.321561\pi$
$972$	−14.0691	+	41.9167i	−0.451267	+	1.34448i
$973$	46.5519	+	4.58496i	1.49238	+	0.146987i
$974$	44.6576	−	3.73859i	1.43092	−	0.119792i
$975$	0.984021	+	2.37564i	0.0315139	+	0.0760812i
$976$	−6.89466	+	43.6141i	−0.220693	+	1.39605i
$977$	5.36236	−	12.9459i	0.171557	−	0.414175i	−0.814593	−	0.580034i	$-0.803039\pi$
$977$	5.36236	−	12.9459i	0.171557	−	0.414175i	0.986150	+	0.165858i	$0.0530394\pi$
$978$	−16.3682	+	51.2436i	−0.523399	+	1.63859i
$979$	−7.82723	+	6.42365i	−0.250159	+	0.205301i
$980$	−1.47618	−	5.43476i	−0.0471547	−	0.173607i
$981$	−36.6258	−	11.1103i	−1.16937	−	0.354725i
$982$	12.6754	−	29.3762i	0.404489	−	0.937432i
$983$	−14.8707	−	2.95796i	−0.474301	−	0.0943443i	−0.0478489	−	0.998855i	$-0.515237\pi$
$983$	−14.8707	−	2.95796i	−0.474301	−	0.0943443i	−0.426452	+	0.904510i	$0.640237\pi$
$984$	−37.9892	−	9.30897i	−1.21105	−	0.296759i
$985$	−1.65595	−	8.32501i	−0.0527629	−	0.265257i
$986$	25.6063	+	39.5655i	0.815472	+	1.26002i
$987$	7.39960	+	6.07269i	0.235532	+	0.193296i
$988$	4.20100	−	1.59757i	0.133652	−	0.0508253i
$989$	−12.9984	+	24.3183i	−0.413325	+	0.773276i
$990$	−23.4176	−	12.9616i	−0.744260	−	0.411948i
$991$	26.9793	+	26.9793i	0.857025	+	0.857025i	0.990987	−	0.133962i	$-0.0427699\pi$
$991$	26.9793	+	26.9793i	0.857025	+	0.857025i	−0.133962	+	0.990987i	$0.542770\pi$
$992$	−15.2672	+	3.43425i	−0.484733	+	0.109038i
$993$	10.3278	−	10.3278i	0.327744	−	0.327744i
$994$	−17.9044	+	5.14599i	−0.567892	+	0.163221i
$995$	−7.60766	−	4.06638i	−0.241179	−	0.128913i
$996$	47.0023	−	44.3251i	1.48932	−	1.40450i
$997$	−3.75462	+	4.57502i	−0.118910	+	0.144892i	−0.829063	−	0.559155i	$-0.811126\pi$
$997$	−3.75462	+	4.57502i	−0.118910	+	0.144892i	0.710153	+	0.704047i	$0.248626\pi$
$998$	11.8674	−	55.4056i	0.375655	−	1.75383i
$999$	0.608381	−	0.121015i	0.0192483	−	0.00382873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.461.1	yes	1024
128.5	even	32	inner	640.2.bm.a.261.1	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.261.1	✓	1024	128.5	even	32	inner
640.2.bm.a.461.1	yes	1024	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40522 - 0.159224i) q^{2} +(2.35093 - 0.713148i) q^{3} +(1.94930 + 0.447490i) q^{4} +(-0.995185 + 0.0980171i) q^{5} +(-3.41713 + 0.627806i) q^{6} +(1.13643 - 1.70079i) q^{7} +(-2.66794 - 0.939196i) q^{8} +(2.52390 - 1.68642i) q^{9} +O(q^{10})\)	\(q+(-1.40522 - 0.159224i) q^{2} +(2.35093 - 0.713148i) q^{3} +(1.94930 + 0.447490i) q^{4} +(-0.995185 + 0.0980171i) q^{5} +(-3.41713 + 0.627806i) q^{6} +(1.13643 - 1.70079i) q^{7} +(-2.66794 - 0.939196i) q^{8} +(2.52390 - 1.68642i) q^{9} +(1.41406 + 0.0207213i) q^{10} +(-2.93913 - 5.49873i) q^{11} +(4.90179 - 0.338118i) q^{12} +(-0.102591 + 1.04163i) q^{13} +(-1.86774 + 2.20904i) q^{14} +(-2.26971 + 0.940146i) q^{15} +(3.59951 + 1.74458i) q^{16} +(-4.25396 - 1.76205i) q^{17} +(-3.81516 + 1.96793i) q^{18} +(-1.36208 - 1.65970i) q^{19} +(-1.98377 - 0.254270i) q^{20} +(1.45876 - 4.80889i) q^{21} +(3.25460 + 8.19492i) q^{22} +(1.41593 - 7.11835i) q^{23} +(-6.94194 - 0.305352i) q^{24} +(0.980785 - 0.195090i) q^{25} +(0.310016 - 1.44738i) q^{26} +(0.0552877 - 0.0673683i) q^{27} +(2.97633 - 2.80680i) q^{28} +(6.38295 + 3.41176i) q^{29} +(3.33914 - 0.959721i) q^{30} +(1.95608 - 1.95608i) q^{31} +(-4.78033 - 3.02465i) q^{32} +(-10.8311 - 10.8311i) q^{33} +(5.69720 + 3.15340i) q^{34} +(-0.964253 + 1.80399i) q^{35} +(5.67449 - 2.15791i) q^{36} +(5.50196 + 4.51534i) q^{37} +(1.64976 + 2.54912i) q^{38} +(0.501649 + 2.52196i) q^{39} +(2.74715 + 0.673170i) q^{40} +(5.52071 + 1.09814i) q^{41} +(-2.81557 + 6.52529i) q^{42} +(-3.63565 - 1.10286i) q^{43} +(-3.26861 - 12.0339i) q^{44} +(-2.34645 + 1.92568i) q^{45} +(-3.12310 + 9.77741i) q^{46} +(-0.728958 + 1.75986i) q^{47} +(9.70635 + 1.53441i) q^{48} +(1.07757 + 2.60149i) q^{49} +(-1.40928 + 0.117981i) q^{50} +(-11.2574 - 1.10876i) q^{51} +(-0.666099 + 1.98453i) q^{52} +(3.74734 - 2.00300i) q^{53} +(-0.0884181 + 0.0858642i) q^{54} +(3.46395 + 5.18417i) q^{55} +(-4.62931 + 3.47028i) q^{56} +(-4.38577 - 2.93048i) q^{57} +(-8.42623 - 5.81060i) q^{58} +(0.348307 + 3.53642i) q^{59} +(-4.84505 + 0.816950i) q^{60} +(3.20443 + 10.5636i) q^{61} +(-3.06018 + 2.43727i) q^{62} -6.20913i q^{63} +(6.23582 + 5.01144i) q^{64} -1.04667i q^{65} +(13.4956 + 16.9447i) q^{66} +(-0.970541 - 3.19945i) q^{67} +(-7.50373 - 5.33836i) q^{68} +(-1.74768 - 17.7445i) q^{69} +(1.64223 - 2.38147i) q^{70} +(5.35453 + 3.57779i) q^{71} +(-8.31751 + 2.12883i) q^{72} +(-6.07614 - 9.09358i) q^{73} +(-7.01252 - 7.22110i) q^{74} +(2.16663 - 1.15809i) q^{75} +(-1.91240 - 3.84476i) q^{76} +(-12.6923 - 1.25008i) q^{77} +(-0.303372 - 3.62379i) q^{78} +(-4.00245 - 9.66276i) q^{79} +(-3.75317 - 1.38336i) q^{80} +(-3.40294 + 8.21543i) q^{81} +(-7.58298 - 2.42216i) q^{82} +(10.1642 - 8.34153i) q^{83} +(4.99548 - 8.72117i) q^{84} +(4.40619 + 1.33660i) q^{85} +(4.93330 + 2.12865i) q^{86} +(17.4390 + 3.46883i) q^{87} +(2.67705 + 17.4307i) q^{88} +(-0.316830 - 1.59281i) q^{89} +(3.60390 - 2.33240i) q^{90} +(1.65500 + 1.35823i) q^{91} +(5.94545 - 13.2422i) q^{92} +(3.20365 - 5.99360i) q^{93} +(1.30456 - 2.35693i) q^{94} +(1.51820 + 1.51820i) q^{95} +(-13.3953 - 3.70167i) q^{96} +(4.24241 - 4.24241i) q^{97} +(-1.10001 - 3.82725i) q^{98} +(-16.6913 - 8.92166i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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