LMFDB - Embedded newform 170.2.k.b.161.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [170,2,Mod(111,170)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(170, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("170.111");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 170 = 2 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	170.k (of order $8$, degree $4$, 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:	$1.35745683436$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 286x^{12} + 1412x^{10} + 3709x^{8} + 5264x^{6} + 3780x^{4} + 1072x^{2} + 4 $ x^16 + 28x^14 + 286x^12 + 1412x^10 + 3709x^8 + 5264x^6 + 3780x^4 + 1072*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			161.2
Root			$-1.46868i$ of defining polynomial
Character	$\chi$	$=$	170.161
Dual form			170.2.k.b.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-0.179356 + 0.433004i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(-0.179356 - 0.433004i) q^{6} +(1.29538 - 0.536563i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.96600 + 1.96600i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.179356 + 0.433004i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(-0.179356 - 0.433004i) q^{6} +(1.29538 - 0.536563i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.96600 + 1.96600i) q^{9} +(-0.923880 + 0.382683i) q^{10} +(-0.117774 - 0.284332i) q^{11} +(0.433004 + 0.179356i) q^{12} +5.87974i q^{13} +(-0.536563 + 1.29538i) q^{14} +(-0.331407 + 0.331407i) q^{15} -1.00000 q^{16} +(-4.06241 - 0.704847i) q^{17} -2.78034 q^{18} +(5.56677 - 5.56677i) q^{19} +(0.382683 - 0.923880i) q^{20} +0.657139i q^{21} +(0.284332 + 0.117774i) q^{22} +(2.50316 + 6.04316i) q^{23} +(-0.433004 + 0.179356i) q^{24} +(0.707107 + 0.707107i) q^{25} +(-4.15760 - 4.15760i) q^{26} +(-2.50291 + 1.03674i) q^{27} +(-0.536563 - 1.29538i) q^{28} +(-6.96712 - 2.88588i) q^{29} -0.468680i q^{30} +(2.43581 - 5.88055i) q^{31} +(0.707107 - 0.707107i) q^{32} +0.144240 q^{33} +(3.37096 - 2.37416i) q^{34} +1.40211 q^{35} +(1.96600 - 1.96600i) q^{36} +(3.56989 - 8.61849i) q^{37} +7.87260i q^{38} +(-2.54595 - 1.05457i) q^{39} +(0.382683 + 0.923880i) q^{40} +(0.798917 - 0.330922i) q^{41} +(-0.464667 - 0.464667i) q^{42} +(-6.44102 - 6.44102i) q^{43} +(-0.284332 + 0.117774i) q^{44} +(1.06399 + 2.56870i) q^{45} +(-6.04316 - 2.50316i) q^{46} -6.44699i q^{47} +(0.179356 - 0.433004i) q^{48} +(-3.55964 + 3.55964i) q^{49} -1.00000 q^{50} +(1.03382 - 1.63262i) q^{51} +5.87974 q^{52} +(-1.88158 + 1.88158i) q^{53} +(1.03674 - 2.50291i) q^{54} -0.307759i q^{55} +(1.29538 + 0.536563i) q^{56} +(1.41200 + 3.40886i) q^{57} +(6.96712 - 2.88588i) q^{58} +(-0.396017 - 0.396017i) q^{59} +(0.331407 + 0.331407i) q^{60} +(-2.21459 + 0.917313i) q^{61} +(2.43581 + 5.88055i) q^{62} +(3.60159 + 1.49183i) q^{63} +1.00000i q^{64} +(-2.25008 + 5.43217i) q^{65} +(-0.101993 + 0.101993i) q^{66} -7.06507 q^{67} +(-0.704847 + 4.06241i) q^{68} -3.06567 q^{69} +(-0.991439 + 0.991439i) q^{70} +(0.522239 - 1.26080i) q^{71} +2.78034i q^{72} +(3.49827 + 1.44903i) q^{73} +(3.56989 + 8.61849i) q^{74} +(-0.433004 + 0.179356i) q^{75} +(-5.56677 - 5.56677i) q^{76} +(-0.305124 - 0.305124i) q^{77} +(2.54595 - 1.05457i) q^{78} +(-0.547204 - 1.32107i) q^{79} +(-0.923880 - 0.382683i) q^{80} +7.07131i q^{81} +(-0.330922 + 0.798917i) q^{82} +(-4.39134 + 4.39134i) q^{83} +0.657139 q^{84} +(-3.48345 - 2.20581i) q^{85} +9.10898 q^{86} +(2.49919 - 2.49919i) q^{87} +(0.117774 - 0.284332i) q^{88} +12.1292i q^{89} +(-2.56870 - 1.06399i) q^{90} +(3.15485 + 7.61648i) q^{91} +(6.04316 - 2.50316i) q^{92} +(2.10942 + 2.10942i) q^{93} +(4.55871 + 4.55871i) q^{94} +(7.27333 - 3.01271i) q^{95} +(0.179356 + 0.433004i) q^{96} +(-0.700805 - 0.290283i) q^{97} -5.03410i q^{98} +(0.327452 - 0.790540i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * q	$ 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) $ 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/170\mathbb{Z}\right)^\times$.

$n$	$71$	$137$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−0.179356	+	0.433004i	−0.103551	+	0.249995i	−0.967160	−	0.254167i	$-0.918199\pi$
$3$	−0.179356	+	0.433004i	−0.103551	+	0.249995i	0.863609	+	0.504162i	$0.168199\pi$
$4$		−	1.00000i		−	0.500000i
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$5$	0.923880	+	0.382683i	0.413171	+	0.171141i
$6$	−0.179356	−	0.433004i	−0.0732218	−	0.176773i
$7$	1.29538	−	0.536563i	0.489607	−	0.202802i	−0.124201	−	0.992257i	$-0.539637\pi$
$7$	1.29538	−	0.536563i	0.489607	−	0.202802i	0.613808	+	0.789455i	$0.289637\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.96600	+	1.96600i	0.655332	+	0.655332i
$10$	−0.923880	+	0.382683i	−0.292156	+	0.121015i
$11$	−0.117774	−	0.284332i	−0.0355103	−	0.0857294i	0.905129	−	0.425136i	$-0.139774\pi$
$11$	−0.117774	−	0.284332i	−0.0355103	−	0.0857294i	−0.940640	+	0.339407i	$0.889774\pi$
$12$	0.433004	+	0.179356i	0.124997	+	0.0517756i
$13$			5.87974i			1.63075i	0.578936	+	0.815373i	$0.303468\pi$
$13$			5.87974i			1.63075i	−0.578936	+	0.815373i	$0.696532\pi$
$14$	−0.536563	+	1.29538i	−0.143402	+	0.346204i
$15$	−0.331407	+	0.331407i	−0.0855688	+	0.0855688i
$16$	−1.00000			−0.250000
$17$	−4.06241	−	0.704847i	−0.985280	−	0.170951i
$17$	−4.06241	−	0.704847i	−0.985280	−	0.170951i
$18$	−2.78034			−0.655332
$19$	5.56677	−	5.56677i	1.27710	−	1.27710i	0.334823	−	0.942281i	$-0.391323\pi$
$19$	5.56677	−	5.56677i	1.27710	−	1.27710i	0.942281	−	0.334823i	$-0.108677\pi$
$20$	0.382683	−	0.923880i	0.0855706	−	0.206586i
$21$			0.657139i			0.143399i
$22$	0.284332	+	0.117774i	0.0606198	+	0.0251095i
$23$	2.50316	+	6.04316i	0.521945	+	1.26009i	0.936694	+	0.350150i	$0.113869\pi$
$23$	2.50316	+	6.04316i	0.521945	+	1.26009i	−0.414749	+	0.909936i	$0.636131\pi$
$24$	−0.433004	+	0.179356i	−0.0883865	+	0.0366109i
$25$	0.707107	+	0.707107i	0.141421	+	0.141421i
$26$	−4.15760	−	4.15760i	−0.815373	−	0.815373i
$27$	−2.50291	+	1.03674i	−0.481685	+	0.199520i
$28$	−0.536563	−	1.29538i	−0.101401	−	0.244803i
$29$	−6.96712	−	2.88588i	−1.29376	−	0.535894i	−0.373657	−	0.927567i	$-0.621896\pi$
$29$	−6.96712	−	2.88588i	−1.29376	−	0.535894i	−0.920104	+	0.391673i	$0.871896\pi$
$30$		−	0.468680i		−	0.0855688i
$31$	2.43581	−	5.88055i	0.437484	−	1.05618i	−0.539332	−	0.842094i	$-0.681323\pi$
$31$	2.43581	−	5.88055i	0.437484	−	1.05618i	0.976815	−	0.214085i	$-0.0686770\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	0.144240			0.0251090
$34$	3.37096	−	2.37416i	0.578115	−	0.407165i
$35$	1.40211			0.236999
$36$	1.96600	−	1.96600i	0.327666	−	0.327666i
$37$	3.56989	−	8.61849i	0.586887	−	1.41687i	−0.299577	−	0.954072i	$-0.596845\pi$
$37$	3.56989	−	8.61849i	0.586887	−	1.41687i	0.886464	−	0.462798i	$-0.153155\pi$
$38$			7.87260i			1.27710i
$39$	−2.54595	−	1.05457i	−0.407678	−	0.168866i
$40$	0.382683	+	0.923880i	0.0605076	+	0.146078i
$41$	0.798917	−	0.330922i	0.124770	−	0.0516814i	−0.319425	−	0.947612i	$-0.603490\pi$
$41$	0.798917	−	0.330922i	0.124770	−	0.0516814i	0.444195	+	0.895930i	$0.353490\pi$
$42$	−0.464667	−	0.464667i	−0.0716997	−	0.0716997i
$43$	−6.44102	−	6.44102i	−0.982247	−	0.982247i	0.0175982	−	0.999845i	$-0.494398\pi$
$43$	−6.44102	−	6.44102i	−0.982247	−	0.982247i	−0.999845	+	0.0175982i	$0.994398\pi$
$44$	−0.284332	+	0.117774i	−0.0428647	+	0.0177551i
$45$	1.06399	+	2.56870i	0.158610	+	0.382919i
$46$	−6.04316	−	2.50316i	−0.891015	−	0.369071i
$47$		−	6.44699i		−	0.940390i	−0.882562	−	0.470195i	$-0.844184\pi$
$47$		−	6.44699i		−	0.940390i	0.882562	−	0.470195i	$-0.155816\pi$
$48$	0.179356	−	0.433004i	0.0258878	−	0.0624987i
$49$	−3.55964	+	3.55964i	−0.508521	+	0.508521i
$50$	−1.00000			−0.141421
$51$	1.03382	−	1.63262i	0.144764	−	0.228613i
$52$	5.87974			0.815373
$53$	−1.88158	+	1.88158i	−0.258455	+	0.258455i	−0.824426	−	0.565970i	$-0.808502\pi$
$53$	−1.88158	+	1.88158i	−0.258455	+	0.258455i	0.565970	+	0.824426i	$0.308502\pi$
$54$	1.03674	−	2.50291i	0.141082	−	0.340603i
$55$		−	0.307759i		−	0.0414982i
$56$	1.29538	+	0.536563i	0.173102	+	0.0717012i
$57$	1.41200	+	3.40886i	0.187024	+	0.451515i
$58$	6.96712	−	2.88588i	0.914828	−	0.378934i
$59$	−0.396017	−	0.396017i	−0.0515571	−	0.0515571i	0.680858	−	0.732415i	$-0.261607\pi$
$59$	−0.396017	−	0.396017i	−0.0515571	−	0.0515571i	−0.732415	+	0.680858i	$0.761607\pi$
$60$	0.331407	+	0.331407i	0.0427844	+	0.0427844i
$61$	−2.21459	+	0.917313i	−0.283549	+	0.117450i	−0.519925	−	0.854212i	$-0.674040\pi$
$61$	−2.21459	+	0.917313i	−0.283549	+	0.117450i	0.236376	+	0.971662i	$0.424040\pi$
$62$	2.43581	+	5.88055i	0.309348	+	0.746831i
$63$	3.60159	+	1.49183i	0.453758	+	0.187953i
$64$			1.00000i			0.125000i
$65$	−2.25008	+	5.43217i	−0.279088	+	0.673778i
$66$	−0.101993	+	0.101993i	−0.0125545	+	0.0125545i
$67$	−7.06507			−0.863135			−0.431568	−	0.902081i	$-0.642039\pi$
$67$	−7.06507			−0.863135			−0.431568	+	0.902081i	$0.642039\pi$
$68$	−0.704847	+	4.06241i	−0.0854753	+	0.492640i
$69$	−3.06567			−0.369063
$70$	−0.991439	+	0.991439i	−0.118500	+	0.118500i
$71$	0.522239	−	1.26080i	0.0619784	−	0.149629i	−0.889856	−	0.456241i	$-0.849195\pi$
$71$	0.522239	−	1.26080i	0.0619784	−	0.149629i	0.951835	+	0.306612i	$0.0991954\pi$
$72$			2.78034i			0.327666i
$73$	3.49827	+	1.44903i	0.409441	+	0.169596i	0.577891	−	0.816114i	$-0.303876\pi$
$73$	3.49827	+	1.44903i	0.409441	+	0.169596i	−0.168449	+	0.985710i	$0.553876\pi$
$74$	3.56989	+	8.61849i	0.414992	+	1.00188i
$75$	−0.433004	+	0.179356i	−0.0499989	+	0.0207102i
$76$	−5.56677	−	5.56677i	−0.638552	−	0.638552i
$77$	−0.305124	−	0.305124i	−0.0347721	−	0.0347721i
$78$	2.54595	−	1.05457i	0.288272	−	0.119406i
$79$	−0.547204	−	1.32107i	−0.0615653	−	0.148632i	0.890103	−	0.455759i	$-0.150632\pi$
$79$	−0.547204	−	1.32107i	−0.0615653	−	0.148632i	−0.951668	+	0.307128i	$0.900632\pi$
$80$	−0.923880	−	0.382683i	−0.103293	−	0.0427853i
$81$			7.07131i			0.785701i
$82$	−0.330922	+	0.798917i	−0.0365442	+	0.0882256i
$83$	−4.39134	+	4.39134i	−0.482012	+	0.482012i	−0.905774	−	0.423762i	$-0.860709\pi$
$83$	−4.39134	+	4.39134i	−0.482012	+	0.482012i	0.423762	+	0.905774i	$0.360709\pi$
$84$	0.657139			0.0716997
$85$	−3.48345	−	2.20581i	−0.377833	−	0.239254i
$86$	9.10898			0.982247
$87$	2.49919	−	2.49919i	0.267941	−	0.267941i
$88$	0.117774	−	0.284332i	0.0125548	−	0.0303099i
$89$			12.1292i			1.28569i	0.765996	+	0.642845i	$0.222246\pi$
$89$			12.1292i			1.28569i	−0.765996	+	0.642845i	$0.777754\pi$
$90$	−2.56870	−	1.06399i	−0.270765	−	0.112154i
$91$	3.15485	+	7.61648i	0.330718	+	0.798424i
$92$	6.04316	−	2.50316i	0.630043	−	0.260972i
$93$	2.10942	+	2.10942i	0.218737	+	0.218737i
$94$	4.55871	+	4.55871i	0.470195	+	0.470195i
$95$	7.27333	−	3.01271i	0.746228	−	0.309098i
$96$	0.179356	+	0.433004i	0.0183054	+	0.0441932i
$97$	−0.700805	−	0.290283i	−0.0711560	−	0.0294738i	0.346822	−	0.937931i	$-0.387261\pi$
$97$	−0.700805	−	0.290283i	−0.0711560	−	0.0294738i	−0.417978	+	0.908457i	$0.637261\pi$
$98$		−	5.03410i		−	0.508521i
$99$	0.327452	−	0.790540i	0.0329102	−	0.0794522i
$100$	0.707107	−	0.707107i	0.0707107	−	0.0707107i
$101$	6.98477			0.695011			0.347506	−	0.937678i	$-0.387029\pi$
$101$	6.98477			0.695011			0.347506	+	0.937678i	$0.387029\pi$
$102$	0.423416	+	1.88546i	0.0419245	+	0.186688i
$103$	8.13639			0.801703			0.400851	−	0.916143i	$-0.368714\pi$
$103$	8.13639			0.801703			0.400851	+	0.916143i	$0.368714\pi$
$104$	−4.15760	+	4.15760i	−0.407686	+	0.407686i
$105$	−0.251476	+	0.607117i	−0.0245416	+	0.0592485i
$106$		−	2.66096i		−	0.258455i
$107$	−10.6656	−	4.41783i	−1.03108	−	0.427088i	−0.197979	−	0.980206i	$-0.563438\pi$
$107$	−10.6656	−	4.41783i	−1.03108	−	0.427088i	−0.833103	+	0.553118i	$0.813438\pi$
$108$	1.03674	+	2.50291i	0.0997602	+	0.240842i
$109$	4.76906	−	1.97541i	0.456793	−	0.189210i	−0.142409	−	0.989808i	$-0.545485\pi$
$109$	4.76906	−	1.97541i	0.456793	−	0.189210i	0.599202	+	0.800598i	$0.295485\pi$
$110$	0.217618	+	0.217618i	0.0207491	+	0.0207491i
$111$	3.09155	+	3.09155i	0.293437	+	0.293437i
$112$	−1.29538	+	0.536563i	−0.122402	+	0.0507004i
$113$	−6.61563	−	15.9716i	−0.622346	−	1.50248i	−0.848941	−	0.528488i	$-0.822759\pi$
$113$	−6.61563	−	15.9716i	−0.622346	−	1.50248i	0.226594	−	0.973989i	$-0.427241\pi$
$114$	−3.40886	−	1.41200i	−0.319269	−	0.132246i
$115$			6.54107i			0.609958i
$116$	−2.88588	+	6.96712i	−0.267947	+	0.646881i
$117$	−11.5595	+	11.5595i	−1.06868	+	1.06868i
$118$	0.560053			0.0515571
$119$	−5.64055	+	1.26670i	−0.517068	+	0.116118i
$120$	−0.468680			−0.0427844
$121$	7.71120	−	7.71120i	0.701018	−	0.701018i
$122$	0.917313	−	2.21459i	0.0830496	−	0.200499i
$123$			0.405287i			0.0365435i
$124$	−5.88055	−	2.43581i	−0.528089	−	0.218742i
$125$	0.382683	+	0.923880i	0.0342282	+	0.0826343i
$126$	−3.60159	+	1.49183i	−0.320855	+	0.132902i
$127$	5.89171	+	5.89171i	0.522804	+	0.522804i	0.918417	−	0.395613i	$-0.129468\pi$
$127$	5.89171	+	5.89171i	0.522804	+	0.522804i	−0.395613	+	0.918417i	$0.629468\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.94422	−	1.63375i	0.347269	−	0.143844i
$130$	−2.25008	−	5.43217i	−0.197345	−	0.476433i
$131$	−13.8684	−	5.74446i	−1.21168	−	0.501896i	−0.316927	−	0.948450i	$-0.602651\pi$
$131$	−13.8684	−	5.74446i	−1.21168	−	0.501896i	−0.894757	+	0.446554i	$0.852651\pi$
$132$		−	0.144240i		−	0.0125545i
$133$	4.22414	−	10.1980i	0.366280	−	0.884277i
$134$	4.99576	−	4.99576i	0.431568	−	0.431568i
$135$	−2.70913			−0.233165
$136$	−2.37416	−	3.37096i	−0.203582	−	0.289058i
$137$	5.88849			0.503087			0.251544	−	0.967846i	$-0.419062\pi$
$137$	5.88849			0.503087			0.251544	+	0.967846i	$0.419062\pi$
$138$	2.16775	−	2.16775i	0.184531	−	0.184531i
$139$	8.31579	−	20.0761i	0.705336	−	1.70283i	−0.00600312	−	0.999982i	$-0.501911\pi$
$139$	8.31579	−	20.0761i	0.705336	−	1.70283i	0.711339	−	0.702849i	$-0.248089\pi$
$140$		−	1.40211i		−	0.118500i
$141$	2.79157	+	1.15631i	0.235093	+	0.0973786i
$142$	0.522239	+	1.26080i	0.0438253	+	0.105804i
$143$	1.67180	−	0.692481i	0.139803	−	0.0579082i
$144$	−1.96600	−	1.96600i	−0.163833	−	0.163833i
$145$	−5.33240	−	5.33240i	−0.442832	−	0.442832i
$146$	−3.49827	+	1.44903i	−0.289519	+	0.119923i
$147$	−0.902895	−	2.17978i	−0.0744695	−	0.179785i
$148$	−8.61849	−	3.56989i	−0.708435	−	0.293444i
$149$			10.0033i			0.819502i	0.912197	+	0.409751i	$0.134384\pi$
$149$			10.0033i			0.819502i	−0.912197	+	0.409751i	$0.865616\pi$
$150$	0.179356	−	0.433004i	0.0146444	−	0.0353546i
$151$	−11.9180	+	11.9180i	−0.969873	+	0.969873i	−0.999559	−	0.0296865i	$-0.990549\pi$
$151$	−11.9180	+	11.9180i	−0.969873	+	0.969873i	0.0296865	+	0.999559i	$0.490549\pi$
$152$	7.87260			0.638552
$153$	−6.60096	−	9.37242i	−0.533656	−	0.757715i
$154$	0.431511			0.0347721
$155$	4.50078	−	4.50078i	0.361511	−	0.361511i
$156$	−1.05457	+	2.54595i	−0.0844328	+	0.203839i
$157$			9.94318i			0.793552i	0.917915	+	0.396776i	$0.129871\pi$
$157$			9.94318i			0.793552i	−0.917915	+	0.396776i	$0.870129\pi$
$158$	1.32107	+	0.547204i	0.105098	+	0.0435332i
$159$	−0.477259	−	1.15221i	−0.0378491	−	0.0913759i
$160$	0.923880	−	0.382683i	0.0730391	−	0.0302538i
$161$	6.48507	+	6.48507i	0.511095	+	0.511095i
$162$	−5.00017	−	5.00017i	−0.392850	−	0.392850i
$163$	−2.03682	+	0.843679i	−0.159536	+	0.0660820i	−0.461022	−	0.887388i	$-0.652517\pi$
$163$	−2.03682	+	0.843679i	−0.159536	+	0.0660820i	0.301486	+	0.953471i	$0.402517\pi$
$164$	−0.330922	−	0.798917i	−0.0258407	−	0.0623849i
$165$	0.133261	+	0.0551984i	0.0103743	+	0.00429719i
$166$		−	6.21029i		−	0.482012i
$167$	6.43680	−	15.5398i	0.498095	−	1.20251i	−0.452414	−	0.891808i	$-0.649437\pi$
$167$	6.43680	−	15.5398i	0.498095	−	1.20251i	0.950509	−	0.310699i	$-0.100563\pi$
$168$	−0.464667	+	0.464667i	−0.0358499	+	0.0358499i
$169$	−21.5713			−1.65933
$170$	4.02291	−	0.903424i	0.308543	−	0.0692894i
$171$	21.8885			1.67386
$172$	−6.44102	+	6.44102i	−0.491123	+	0.491123i
$173$	5.63748	−	13.6101i	0.428610	−	1.03476i	−0.551119	−	0.834427i	$-0.685799\pi$
$173$	5.63748	−	13.6101i	0.428610	−	1.03476i	0.979729	−	0.200329i	$-0.0642010\pi$
$174$			3.53439i			0.267941i
$175$	1.29538	+	0.536563i	0.0979213	+	0.0405603i
$176$	0.117774	+	0.284332i	0.00887757	+	0.0214323i
$177$	0.242505	−	0.100449i	0.0182278	−	0.00755020i
$178$	−8.57662	−	8.57662i	−0.642845	−	0.642845i
$179$	−2.18976	−	2.18976i	−0.163670	−	0.163670i	0.620520	−	0.784191i	$-0.286922\pi$
$179$	−2.18976	−	2.18976i	−0.163670	−	0.163670i	−0.784191	+	0.620520i	$0.786922\pi$
$180$	2.56870	−	1.06399i	0.191459	−	0.0793051i
$181$	4.64596	+	11.2163i	0.345332	+	0.833705i	0.997158	+	0.0753364i	$0.0240030\pi$
$181$	4.64596	+	11.2163i	0.345332	+	0.833705i	−0.651826	+	0.758368i	$0.725997\pi$
$182$	−7.61648	−	3.15485i	−0.564571	−	0.233853i
$183$		−	1.12345i		−	0.0830478i
$184$	−2.50316	+	6.04316i	−0.184535	+	0.445508i
$185$	6.59630	−	6.59630i	0.484970	−	0.484970i
$186$	−2.98318			−0.218737
$187$	0.278037	+	1.23809i	0.0203321	+	0.0905379i
$188$	−6.44699			−0.470195
$189$	−2.68593	+	2.68593i	−0.195373	+	0.195373i
$190$	−3.01271	+	7.27333i	−0.218565	+	0.527663i
$191$			9.76231i			0.706376i	0.935552	+	0.353188i	$0.114902\pi$
$191$			9.76231i			0.706376i	−0.935552	+	0.353188i	$0.885098\pi$
$192$	−0.433004	−	0.179356i	−0.0312493	−	0.0129439i
$193$	1.06164	+	2.56303i	0.0764188	+	0.184491i	0.957472	−	0.288526i	$-0.0931650\pi$
$193$	1.06164	+	2.56303i	0.0764188	+	0.184491i	−0.881053	+	0.473017i	$0.843165\pi$
$194$	0.700805	−	0.290283i	0.0503149	−	0.0208411i
$195$	−1.94858	−	1.94858i	−0.139541	−	0.139541i
$196$	3.55964	+	3.55964i	0.254260	+	0.254260i
$197$	6.00521	−	2.48744i	0.427854	−	0.177223i	−0.158356	−	0.987382i	$-0.550619\pi$
$197$	6.00521	−	2.48744i	0.427854	−	0.177223i	0.586210	+	0.810159i	$0.300619\pi$
$198$	0.327452	+	0.790540i	0.0232710	+	0.0561812i
$199$	20.5838	+	8.52610i	1.45915	+	0.604399i	0.964355	−	0.264612i	$-0.0852438\pi$
$199$	20.5838	+	8.52610i	1.45915	+	0.604399i	0.494793	+	0.869011i	$0.335244\pi$
$200$			1.00000i			0.0707107i
$201$	1.26716	−	3.05920i	0.0893787	−	0.215779i
$202$	−4.93898	+	4.93898i	−0.347506	+	0.347506i
$203$	−10.5735			−0.742115
$204$	−1.63262	−	1.03382i	−0.114306	−	0.0723818i
$205$	0.864741			0.0603961
$206$	−5.75330	+	5.75330i	−0.400851	+	0.400851i
$207$	−6.95963	+	16.8020i	−0.483728	+	1.16782i
$208$		−	5.87974i		−	0.407686i
$209$	−2.23843	−	0.927189i	−0.154836	−	0.0641350i
$210$	−0.251476	−	0.607117i	−0.0173535	−	0.0418951i
$211$	−22.6978	+	9.40174i	−1.56258	+	0.647243i	−0.985536	−	0.169469i	$-0.945795\pi$
$211$	−22.6978	+	9.40174i	−1.56258	+	0.647243i	−0.577046	+	0.816711i	$0.695795\pi$
$212$	1.88158	+	1.88158i	0.129228	+	0.129228i
$213$	0.452263	+	0.452263i	0.0309885	+	0.0309885i
$214$	10.6656	−	4.41783i	0.729085	−	0.301997i
$215$	−3.48586	−	8.41560i	−0.237733	−	0.573939i
$216$	−2.50291	−	1.03674i	−0.170301	−	0.0705411i
$217$		−	8.92450i		−	0.605834i
$218$	−1.97541	+	4.76906i	−0.133791	+	0.323001i
$219$	−1.25487	+	1.25487i	−0.0847962	+	0.0847962i
$220$	−0.307759			−0.0207491
$221$	4.14432	−	23.8859i	0.278777	−	1.60674i
$222$	−4.37212			−0.293437
$223$	−7.62493	+	7.62493i	−0.510603	+	0.510603i	−0.914711	−	0.404108i	$-0.867582\pi$
$223$	−7.62493	+	7.62493i	−0.510603	+	0.510603i	0.404108	+	0.914711i	$0.367582\pi$
$224$	0.536563	−	1.29538i	0.0358506	−	0.0865510i
$225$			2.78034i			0.185356i
$226$	15.9716	+	6.61563i	1.06241	+	0.440065i
$227$	2.44756	+	5.90892i	0.162450	+	0.392189i	0.984054	−	0.177870i	$-0.0569205\pi$
$227$	2.44756	+	5.90892i	0.162450	+	0.392189i	−0.821604	+	0.570059i	$0.806921\pi$
$228$	3.40886	−	1.41200i	0.225757	−	0.0935118i
$229$	6.06531	+	6.06531i	0.400807	+	0.400807i	0.878517	−	0.477711i	$-0.158533\pi$
$229$	6.06531	+	6.06531i	0.400807	+	0.400807i	−0.477711	+	0.878517i	$0.658533\pi$
$230$	−4.62523	−	4.62523i	−0.304979	−	0.304979i
$231$	0.186846	−	0.0773940i	0.0122935	−	0.00509215i
$232$	−2.88588	−	6.96712i	−0.189467	−	0.457414i
$233$	17.0245	+	7.05179i	1.11531	+	0.461978i	0.862764	−	0.505606i	$-0.168731\pi$
$233$	17.0245	+	7.05179i	1.11531	+	0.461978i	0.252549	+	0.967584i	$0.418731\pi$
$234$		−	16.3477i		−	1.06868i
$235$	2.46716	−	5.95624i	0.160940	−	0.388543i
$236$	−0.396017	+	0.396017i	−0.0257785	+	0.0257785i
$237$	0.670171			0.0435323
$238$	3.09278	−	4.88416i	0.200475	−	0.316593i
$239$	16.4014			1.06092			0.530459	−	0.847710i	$-0.322019\pi$
$239$	16.4014			1.06092			0.530459	+	0.847710i	$0.322019\pi$
$240$	0.331407	−	0.331407i	0.0213922	−	0.0213922i
$241$	−10.6273	+	25.6567i	−0.684567	+	1.65269i	0.0708819	+	0.997485i	$0.477419\pi$
$241$	−10.6273	+	25.6567i	−0.684567	+	1.65269i	−0.755449	+	0.655207i	$0.772581\pi$
$242$			10.9053i			0.701018i
$243$	−10.5706	−	4.37849i	−0.678106	−	0.280881i
$244$	0.917313	+	2.21459i	0.0587249	+	0.141775i
$245$	−4.65090	+	1.92647i	−0.297135	+	0.123077i
$246$	−0.286581	−	0.286581i	−0.0182717	−	0.0182717i
$247$	32.7311	+	32.7311i	2.08263	+	2.08263i
$248$	5.88055	−	2.43581i	0.373416	−	0.154674i
$249$	−1.11385	−	2.68908i	−0.0705875	−	0.170413i
$250$	−0.923880	−	0.382683i	−0.0584313	−	0.0242030i
$251$			25.6739i			1.62052i	0.586070	+	0.810260i	$0.300674\pi$
$251$			25.6739i			1.62052i	−0.586070	+	0.810260i	$0.699326\pi$
$252$	1.49183	−	3.60159i	0.0939763	−	0.226879i
$253$	1.42346	−	1.42346i	0.0894919	−	0.0894919i
$254$	−8.33213			−0.522804
$255$	1.57990	−	1.11272i	0.0989372	−	0.0696812i
$256$	1.00000			0.0625000
$257$	10.2731	−	10.2731i	0.640817	−	0.640817i	−0.309939	−	0.950756i	$-0.600309\pi$
$257$	10.2731	−	10.2731i	0.640817	−	0.640817i	0.950756	+	0.309939i	$0.100309\pi$
$258$	−1.63375	+	3.94422i	−0.101713	+	0.245557i
$259$		−	13.0797i		−	0.812731i
$260$	5.43217	+	2.25008i	0.336889	+	0.139544i
$261$	−8.02371	−	19.3710i	−0.496655	−	1.19903i
$262$	13.8684	−	5.74446i	0.856790	−	0.354894i
$263$	−4.97231	−	4.97231i	−0.306606	−	0.306606i	0.536986	−	0.843591i	$-0.319563\pi$
$263$	−4.97231	−	4.97231i	−0.306606	−	0.306606i	−0.843591	+	0.536986i	$0.819563\pi$
$264$	0.101993	+	0.101993i	0.00627725	+	0.00627725i
$265$	−2.45841	+	1.01831i	−0.151019	+	0.0625540i
$266$	4.22414	+	10.1980i	0.258999	+	0.625279i
$267$	−5.25198	−	2.17544i	−0.321416	−	0.133135i
$268$			7.06507i			0.431568i
$269$	2.03987	−	4.92467i	0.124373	−	0.300263i	−0.849413	−	0.527728i	$-0.823044\pi$
$269$	2.03987	−	4.92467i	0.124373	−	0.300263i	0.973786	+	0.227466i	$0.0730439\pi$
$270$	1.91564	−	1.91564i	0.116582	−	0.116582i
$271$	6.44084			0.391253			0.195627	−	0.980678i	$-0.437326\pi$
$271$	6.44084			0.391253			0.195627	+	0.980678i	$0.437326\pi$
$272$	4.06241	+	0.704847i	0.246320	+	0.0427376i
$273$	−3.86380			−0.233848
$274$	−4.16379	+	4.16379i	−0.251544	+	0.251544i
$275$	0.117774	−	0.284332i	0.00710205	−	0.0171459i
$276$			3.06567i			0.184531i
$277$	−9.41675	−	3.90055i	−0.565798	−	0.234361i	0.0814022	−	0.996681i	$-0.474060\pi$
$277$	−9.41675	−	3.90055i	−0.565798	−	0.234361i	−0.647200	+	0.762320i	$0.724060\pi$
$278$	8.31579	+	20.0761i	0.498748	+	1.20408i
$279$	16.3499	−	6.77236i	0.978845	−	0.405451i
$280$	0.991439	+	0.991439i	0.0592498	+	0.0592498i
$281$	−12.8739	−	12.8739i	−0.767995	−	0.767995i	0.209759	−	0.977753i	$-0.432732\pi$
$281$	−12.8739	−	12.8739i	−0.767995	−	0.767995i	−0.977753	+	0.209759i	$0.932732\pi$
$282$	−2.79157	+	1.15631i	−0.166236	+	0.0688570i
$283$	1.13461	+	2.73919i	0.0674457	+	0.162828i	0.954008	−	0.299781i	$-0.0969135\pi$
$283$	1.13461	+	2.73919i	0.0674457	+	0.162828i	−0.886563	+	0.462609i	$0.846913\pi$
$284$	−1.26080	−	0.522239i	−0.0748145	−	0.0309892i
$285$			3.68973i			0.218561i
$286$	−0.692481	+	1.67180i	−0.0409473	+	0.0988555i
$287$	0.857338	−	0.857338i	0.0506071	−	0.0506071i
$288$	2.78034			0.163833
$289$	16.0064	+	5.72676i	0.941552	+	0.336868i
$290$	7.54116			0.442832
$291$	0.251387	−	0.251387i	0.0147366	−	0.0147366i
$292$	1.44903	−	3.49827i	0.0847980	−	0.204721i
$293$		−	7.29230i		−	0.426021i	−0.977050	−	0.213010i	$-0.931673\pi$
$293$		−	7.29230i		−	0.426021i	0.977050	−	0.213010i	$-0.0683268\pi$
$294$	2.17978	+	0.902895i	0.127127	+	0.0526579i
$295$	−0.214323	−	0.517422i	−0.0124784	−	0.0301255i
$296$	8.61849	−	3.56989i	0.500939	−	0.207496i
$297$	0.589556	+	0.589556i	0.0342095	+	0.0342095i
$298$	−7.07340	−	7.07340i	−0.409751	−	0.409751i
$299$	−35.5322	+	14.7179i	−2.05488	+	0.851159i
$300$	0.179356	+	0.433004i	0.0103551	+	0.0249995i
$301$	−11.7996	−	4.88754i	−0.680116	−	0.281713i
$302$		−	16.8546i		−	0.969873i
$303$	−1.25276	+	3.02443i	−0.0719692	+	0.173749i
$304$	−5.56677	+	5.56677i	−0.319276	+	0.319276i
$305$	−2.39705			−0.137255
$306$	11.2949	+	1.95971i	0.645686	+	0.112029i
$307$	−31.3043			−1.78663			−0.893315	−	0.449431i	$-0.851627\pi$
$307$	−31.3043			−1.78663			−0.893315	+	0.449431i	$0.851627\pi$
$308$	−0.305124	+	0.305124i	−0.0173861	+	0.0173861i
$309$	−1.45931	+	3.52309i	−0.0830173	+	0.200421i
$310$			6.36507i			0.361511i
$311$	12.1039	+	5.01360i	0.686350	+	0.284295i	0.698479	−	0.715631i	$-0.253861\pi$
$311$	12.1039	+	5.01360i	0.686350	+	0.284295i	−0.0121286	+	0.999926i	$0.503861\pi$
$312$	−1.05457	−	2.54595i	−0.0597030	−	0.144136i
$313$	14.1757	−	5.87179i	0.801261	−	0.331893i	0.0557993	−	0.998442i	$-0.482229\pi$
$313$	14.1757	−	5.87179i	0.801261	−	0.331893i	0.745461	+	0.666549i	$0.232229\pi$
$314$	−7.03089	−	7.03089i	−0.396776	−	0.396776i
$315$	2.75654	+	2.75654i	0.155313	+	0.155313i
$316$	−1.32107	+	0.547204i	−0.0743158	+	0.0307826i
$317$	−1.98791	−	4.79925i	−0.111652	−	0.269553i	0.858170	−	0.513366i	$-0.171602\pi$
$317$	−1.98791	−	4.79925i	−0.111652	−	0.269553i	−0.969822	+	0.243813i	$0.921602\pi$
$318$	1.15221	+	0.477259i	0.0646125	+	0.0267634i
$319$			2.32086i			0.129943i
$320$	−0.382683	+	0.923880i	−0.0213927	+	0.0516464i
$321$	3.82587	−	3.82587i	0.213539	−	0.213539i
$322$	−9.17127			−0.511095
$323$	−26.5382	+	18.6908i	−1.47663	+	1.03998i
$324$	7.07131			0.392850
$325$	−4.15760	+	4.15760i	−0.230622	+	0.230622i
$326$	0.843679	−	2.03682i	0.0467270	−	0.112809i
$327$			2.41932i			0.133789i
$328$	0.798917	+	0.330922i	0.0441128	+	0.0182721i
$329$	−3.45922	−	8.35129i	−0.190713	−	0.460421i
$330$	−0.133261	+	0.0551984i	−0.00733576	+	0.00303857i
$331$	−14.9156	−	14.9156i	−0.819833	−	0.819833i	0.166250	−	0.986084i	$-0.446834\pi$
$331$	−14.9156	−	14.9156i	−0.819833	−	0.819833i	−0.986084	+	0.166250i	$0.946834\pi$
$332$	4.39134	+	4.39134i	0.241006	+	0.241006i
$333$	23.9623	−	9.92552i	1.31313	−	0.543915i
$334$	6.43680	+	15.5398i	0.352206	+	0.850301i
$335$	−6.52727	−	2.70368i	−0.356623	−	0.147718i
$336$		−	0.657139i		−	0.0358499i
$337$	−9.19341	+	22.1949i	−0.500797	+	1.20903i	0.448253	+	0.893906i	$0.352046\pi$
$337$	−9.19341	+	22.1949i	−0.500797	+	1.20903i	−0.949050	+	0.315124i	$0.897954\pi$
$338$	15.2532	−	15.2532i	0.829666	−	0.829666i
$339$	8.10229			0.440056
$340$	−2.20581	+	3.48345i	−0.119627	+	0.188916i
$341$	−1.95891			−0.106081
$342$	−15.4775	+	15.4775i	−0.836928	+	0.836928i
$343$	−6.45705	+	15.5887i	−0.348648	+	0.841711i
$344$		−	9.10898i		−	0.491123i
$345$	−2.83231	−	1.17318i	−0.152486	−	0.0631618i
$346$	5.63748	+	13.6101i	0.303073	+	0.731682i
$347$	5.64684	−	2.33900i	0.303138	−	0.125564i	−0.225929	−	0.974144i	$-0.572542\pi$
$347$	5.64684	−	2.33900i	0.303138	−	0.125564i	0.529068	+	0.848580i	$0.322542\pi$
$348$	−2.49919	−	2.49919i	−0.133971	−	0.133971i
$349$	−2.33500	−	2.33500i	−0.124990	−	0.124990i	0.641845	−	0.766835i	$-0.278169\pi$
$349$	−2.33500	−	2.33500i	−0.124990	−	0.124990i	−0.766835	+	0.641845i	$0.778169\pi$
$350$	−1.29538	+	0.536563i	−0.0692408	+	0.0286805i
$351$	−6.09575	−	14.7164i	−0.325367	−	0.785505i
$352$	−0.284332	−	0.117774i	−0.0151550	−	0.00627739i
$353$			5.06691i			0.269684i	0.990867	+	0.134842i	$0.0430527\pi$
$353$			5.06691i			0.269684i	−0.990867	+	0.134842i	$0.956947\pi$
$354$	−0.100449	+	0.242505i	−0.00533880	+	0.0128890i
$355$	0.964972	−	0.964972i	0.0512154	−	0.0512154i
$356$	12.1292			0.642845
$357$	0.463182	−	2.66957i	0.0245142	−	0.141289i
$358$	3.09679			0.163670
$359$	−2.48719	+	2.48719i	−0.131269	+	0.131269i	−0.769689	−	0.638420i	$-0.779588\pi$
$359$	−2.48719	+	2.48719i	−0.131269	+	0.131269i	0.638420	+	0.769689i	$0.279588\pi$
$360$	−1.06399	+	2.56870i	−0.0560772	+	0.135382i
$361$		−	42.9778i		−	2.26199i
$362$	−11.2163	−	4.64596i	−0.589518	−	0.244186i
$363$	1.95593	+	4.72203i	0.102660	+	0.247842i
$364$	7.61648	−	3.15485i	0.399212	−	0.165359i
$365$	2.67746	+	2.67746i	0.140145	+	0.140145i
$366$	0.794399	+	0.794399i	0.0415239	+	0.0415239i
$367$	6.79293	−	2.81372i	0.354588	−	0.146875i	−0.198277	−	0.980146i	$-0.563535\pi$
$367$	6.79293	−	2.81372i	0.354588	−	0.146875i	0.552865	+	0.833271i	$0.313535\pi$
$368$	−2.50316	−	6.04316i	−0.130486	−	0.315021i
$369$	2.22126	+	0.920076i	0.115634	+	0.0478972i
$370$			9.32858i			0.484970i
$371$	−1.42777	+	3.44695i	−0.0741263	+	0.178957i
$372$	2.10942	−	2.10942i	0.109369	−	0.109369i
$373$	−15.3213			−0.793305			−0.396652	−	0.917969i	$-0.629828\pi$
$373$	−15.3213			−0.793305			−0.396652	+	0.917969i	$0.629828\pi$
$374$	−1.07206	−	0.678858i	−0.0554350	−	0.0351029i
$375$	−0.468680			−0.0242025
$376$	4.55871	−	4.55871i	0.235098	−	0.235098i
$377$	16.9682	−	40.9648i	0.873906	−	2.10980i
$378$		−	3.79848i		−	0.195373i
$379$	−11.6620	−	4.83055i	−0.599036	−	0.248129i	0.0624969	−	0.998045i	$-0.480094\pi$
$379$	−11.6620	−	4.83055i	−0.599036	−	0.248129i	−0.661533	+	0.749916i	$0.730094\pi$
$380$	−3.01271	−	7.27333i	−0.154549	−	0.373114i
$381$	−3.60784	+	1.49442i	−0.184835	+	0.0765613i
$382$	−6.90300	−	6.90300i	−0.353188	−	0.353188i
$383$	7.34144	+	7.34144i	0.375130	+	0.375130i	0.869342	−	0.494212i	$-0.164543\pi$
$383$	7.34144	+	7.34144i	0.375130	+	0.375130i	−0.494212	+	0.869342i	$0.664543\pi$
$384$	0.433004	−	0.179356i	0.0220966	−	0.00915272i
$385$	−0.165132	−	0.398664i	−0.00841590	−	0.0203178i
$386$	−2.56303	−	1.06164i	−0.130455	−	0.0540362i
$387$		−	25.3261i		−	1.28740i
$388$	−0.290283	+	0.700805i	−0.0147369	+	0.0355780i
$389$	−23.0678	+	23.0678i	−1.16958	+	1.16958i	−0.187275	+	0.982308i	$0.559965\pi$
$389$	−23.0678	+	23.0678i	−1.16958	+	1.16958i	−0.982308	+	0.187275i	$0.940035\pi$
$390$	2.75571			0.139541
$391$	−5.90936	−	26.3141i	−0.298849	−	1.33076i
$392$	−5.03410			−0.254260
$393$	4.97474	−	4.97474i	0.250943	−	0.250943i
$394$	−2.48744	+	6.00521i	−0.125315	+	0.302538i
$395$		−	1.42991i		−	0.0719467i
$396$	−0.790540	−	0.327452i	−0.0397261	−	0.0164551i
$397$	−4.03153	−	9.73297i	−0.202337	−	0.488484i	0.789842	−	0.613310i	$-0.210163\pi$
$397$	−4.03153	−	9.73297i	−0.202337	−	0.488484i	−0.992179	+	0.124827i	$0.960163\pi$
$398$	−20.5838	+	8.52610i	−1.03177	+	0.427375i
$399$	3.65814	+	3.65814i	0.183136	+	0.183136i
$400$	−0.707107	−	0.707107i	−0.0353553	−	0.0353553i
$401$	−2.06854	+	0.856816i	−0.103298	+	0.0427873i	−0.433734	−	0.901041i	$-0.642804\pi$
$401$	−2.06854	+	0.856816i	−0.103298	+	0.0427873i	0.330436	+	0.943828i	$0.392804\pi$
$402$	1.26716	+	3.05920i	0.0632003	+	0.152579i
$403$	34.5761	+	14.3219i	1.72236	+	0.713424i
$404$		−	6.98477i		−	0.347506i
$405$	−2.70607	+	6.53303i	−0.134466	+	0.324629i
$406$	7.47660	−	7.47660i	0.371057	−	0.371057i
$407$	−2.87095			−0.142308
$408$	1.88546	−	0.423416i	0.0933440	−	0.0209622i
$409$	−13.6810			−0.676483			−0.338241	−	0.941059i	$-0.609832\pi$
$409$	−13.6810			−0.676483			−0.338241	+	0.941059i	$0.609832\pi$
$410$	−0.611464	+	0.611464i	−0.0301981	+	0.0301981i
$411$	−1.05613	+	2.54974i	−0.0520953	+	0.125769i
$412$		−	8.13639i		−	0.400851i
$413$	−0.725480	−	0.300504i	−0.0356986	−	0.0147868i
$414$	−6.95963	−	16.8020i	−0.342047	−	0.825775i
$415$	−5.73756	+	2.37657i	−0.281646	+	0.116661i
$416$	4.15760	+	4.15760i	0.203843	+	0.203843i
$417$	7.20153	+	7.20153i	0.352660	+	0.352660i
$418$	2.23843	−	0.927189i	0.109485	−	0.0453503i
$419$	8.55468	+	20.6528i	0.417923	+	1.00896i	0.982948	+	0.183882i	$0.0588666\pi$
$419$	8.55468	+	20.6528i	0.417923	+	1.00896i	−0.565025	+	0.825074i	$0.691133\pi$
$420$	0.607117	+	0.251476i	0.0296243	+	0.0122708i
$421$			4.55307i			0.221903i	0.993826	+	0.110952i	$0.0353899\pi$
$421$			4.55307i			0.221903i	−0.993826	+	0.110952i	$0.964610\pi$
$422$	9.40174	−	22.6978i	0.457670	−	1.10491i
$423$	12.6748	−	12.6748i	0.616268	−	0.616268i
$424$	−2.66096			−0.129228
$425$	−2.37416	−	3.37096i	−0.115164	−	0.163516i
$426$	−0.639596			−0.0309885
$427$	−2.37653	+	2.37653i	−0.115008	+	0.115008i
$428$	−4.41783	+	10.6656i	−0.213544	+	0.515541i
$429$			0.848095i			0.0409464i
$430$	8.41560	+	3.48586i	0.405836	+	0.168103i
$431$	−12.5150	−	30.2138i	−0.602826	−	1.45535i	−0.870660	−	0.491885i	$-0.836308\pi$
$431$	−12.5150	−	30.2138i	−0.602826	−	1.45535i	0.267834	−	0.963465i	$-0.413692\pi$
$432$	2.50291	−	1.03674i	0.120421	−	0.0498801i
$433$	−0.684375	−	0.684375i	−0.0328889	−	0.0328889i	0.690471	−	0.723360i	$-0.257403\pi$
$433$	−0.684375	−	0.684375i	−0.0328889	−	0.0328889i	−0.723360	+	0.690471i	$0.757403\pi$
$434$	6.31057	+	6.31057i	0.302917	+	0.302917i
$435$	3.26535	−	1.35255i	0.156561	−	0.0648499i
$436$	−1.97541	−	4.76906i	−0.0946049	−	0.228396i
$437$	47.5754	+	19.7064i	2.27584	+	0.942683i
$438$		−	1.77465i		−	0.0847962i
$439$	11.2648	−	27.1957i	0.537642	−	1.29798i	−0.388723	−	0.921354i	$-0.627084\pi$
$439$	11.2648	−	27.1957i	0.537642	−	1.29798i	0.926365	−	0.376627i	$-0.122916\pi$
$440$	0.217618	−	0.217618i	0.0103745	−	0.0103745i
$441$	−13.9965			−0.666500
$442$	13.9594	+	19.8204i	0.663982	+	0.942759i
$443$	−20.1909			−0.959297			−0.479648	−	0.877461i	$-0.659236\pi$
$443$	−20.1909			−0.959297			−0.479648	+	0.877461i	$0.659236\pi$
$444$	3.09155	−	3.09155i	0.146719	−	0.146719i
$445$	−4.64164	+	11.2059i	−0.220035	+	0.531211i
$446$		−	10.7833i		−	0.510603i
$447$	−4.33146	−	1.79415i	−0.204871	−	0.0848604i
$448$	0.536563	+	1.29538i	0.0253502	+	0.0612008i
$449$	−11.4145	+	4.72803i	−0.538682	+	0.223129i	−0.635401	−	0.772182i	$-0.719165\pi$
$449$	−11.4145	+	4.72803i	−0.538682	+	0.223129i	0.0967189	+	0.995312i	$0.469165\pi$
$450$	−1.96600	−	1.96600i	−0.0926780	−	0.0926780i
$451$	−0.188184	−	0.188184i	−0.00886122	−	0.00886122i
$452$	−15.9716	+	6.61563i	−0.751239	+	0.311173i
$453$	−3.02297	−	7.29810i	−0.142032	−	0.342895i
$454$	−5.90892	−	2.44756i	−0.277319	−	0.114869i
$455$			8.24402i			0.386485i
$456$	−1.41200	+	3.40886i	−0.0661228	+	0.159635i
$457$	−20.8508	+	20.8508i	−0.975361	+	0.975361i	−0.999704	−	0.0243427i	$-0.992251\pi$
$457$	−20.8508	+	20.8508i	−0.975361	+	0.975361i	0.0243427	+	0.999704i	$0.492251\pi$
$458$	−8.57764			−0.400807
$459$	10.8986	−	2.44749i	0.508702	−	0.114239i
$460$	6.54107			0.304979
$461$	15.4484	−	15.4484i	0.719502	−	0.719502i	−0.249001	−	0.968503i	$-0.580102\pi$
$461$	15.4484	−	15.4484i	0.719502	−	0.719502i	0.968503	+	0.249001i	$0.0801023\pi$
$462$	−0.0773940	+	0.186846i	−0.00360069	+	0.00869284i
$463$			29.9326i			1.39109i	0.718484	+	0.695544i	$0.244837\pi$
$463$			29.9326i			1.39109i	−0.718484	+	0.695544i	$0.755163\pi$
$464$	6.96712	+	2.88588i	0.323440	+	0.133973i
$465$	1.14161	+	2.75610i	0.0529410	+	0.127811i
$466$	−17.0245	+	7.05179i	−0.788646	+	0.326668i
$467$	11.3554	+	11.3554i	0.525468	+	0.525468i	0.919218	−	0.393750i	$-0.128822\pi$
$467$	11.3554	+	11.3554i	0.525468	+	0.525468i	−0.393750	+	0.919218i	$0.628822\pi$
$468$	11.5595	+	11.5595i	0.534340	+	0.534340i
$469$	−9.15193	+	3.79085i	−0.422597	+	0.175045i
$470$	2.46716	+	5.95624i	0.113801	+	0.274741i
$471$	−4.30543	−	1.78337i	−0.198384	−	0.0821733i
$472$		−	0.560053i		−	0.0257785i
$473$	−1.07280	+	2.58998i	−0.0493276	+	0.119087i
$474$	−0.473882	+	0.473882i	−0.0217661	+	0.0217661i
$475$	7.87260			0.361220
$476$	1.26670	+	5.64055i	0.0580589	+	0.258534i
$477$	−7.39838			−0.338748
$478$	−11.5975	+	11.5975i	−0.530459	+	0.530459i
$479$	−1.98019	+	4.78059i	−0.0904770	+	0.218431i	−0.962640	−	0.270785i	$-0.912717\pi$
$479$	−1.98019	+	4.78059i	−0.0904770	+	0.218431i	0.872163	+	0.489215i	$0.162717\pi$
$480$			0.468680i			0.0213922i
$481$	50.6744	+	20.9900i	2.31056	+	0.957063i
$482$	−10.6273	−	25.6567i	−0.484062	−	1.16863i
$483$	−3.97119	+	1.64492i	−0.180696	+	0.0748465i
$484$	−7.71120	−	7.71120i	−0.350509	−	0.350509i
$485$	−0.536373	−	0.536373i	−0.0243554	−	0.0243554i
$486$	10.5706	−	4.37849i	0.479493	−	0.198613i
$487$	11.0542	+	26.6873i	0.500915	+	1.20932i	0.948986	+	0.315318i	$0.102111\pi$
$487$	11.0542	+	26.6873i	0.500915	+	1.20932i	−0.448071	+	0.893998i	$0.647889\pi$
$488$	−2.21459	−	0.917313i	−0.100250	−	0.0415248i
$489$		−	1.03327i		−	0.0467261i
$490$	1.92647	−	4.65090i	0.0870289	−	0.210106i
$491$	13.9948	−	13.9948i	0.631575	−	0.631575i	−0.316888	−	0.948463i	$-0.602638\pi$
$491$	13.9948	−	13.9948i	0.631575	−	0.631575i	0.948463	+	0.316888i	$0.102638\pi$
$492$	0.405287			0.0182717
$493$	26.2692	+	16.6344i	1.18311	+	0.749174i
$494$	−46.2888			−2.08263
$495$	0.605053	−	0.605053i	0.0271951	−	0.0271951i
$496$	−2.43581	+	5.88055i	−0.109371	+	0.264045i
$497$		−	1.91342i		−	0.0858287i
$498$	2.68908	+	1.11385i	0.120500	+	0.0499129i
$499$	−3.46665	−	8.36922i	−0.155188	−	0.374658i	0.827094	−	0.562063i	$-0.189992\pi$
$499$	−3.46665	−	8.36922i	−0.155188	−	0.374658i	−0.982283	+	0.187405i	$0.939992\pi$
$500$	0.923880	−	0.382683i	0.0413171	−	0.0171141i
$501$	5.57431	+	5.57431i	0.249042	+	0.249042i
$502$	−18.1542	−	18.1542i	−0.810260	−	0.810260i
$503$	−3.41958	+	1.41644i	−0.152472	+	0.0631558i	−0.457614	−	0.889151i	$-0.651296\pi$
$503$	−3.41958	+	1.41644i	−0.152472	+	0.0631558i	0.305143	+	0.952307i	$0.401296\pi$
$504$	1.49183	+	3.60159i	0.0664512	+	0.160428i
$505$	6.45309	+	2.67296i	0.287159	+	0.118945i
$506$			2.01307i			0.0894919i
$507$	3.86894	−	9.34045i	0.171826	−	0.414824i
$508$	5.89171	−	5.89171i	0.261402	−	0.261402i
$509$	41.9951			1.86140			0.930699	−	0.365785i	$-0.119199\pi$
$509$	41.9951			1.86140			0.930699	+	0.365785i	$0.119199\pi$
$510$	−0.330348	+	1.90397i	−0.0146280	+	0.0843092i
$511$	5.30907			0.234859
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−8.16182	+	19.7044i	−0.360353	+	0.869970i
$514$			14.5283i			0.640817i
$515$	7.51705	+	3.11366i	0.331241	+	0.137204i
$516$	−1.63375	−	3.94422i	−0.0719218	−	0.173635i
$517$	−1.83309	+	0.759289i	−0.0806191	+	0.0333935i
$518$	9.24872	+	9.24872i	0.406365	+	0.406365i
$519$	4.88210	+	4.88210i	0.214300	+	0.214300i
$520$	−5.43217	+	2.25008i	−0.238216	+	0.0986725i
$521$	−0.243542	−	0.587963i	−0.0106698	−	0.0257591i	0.918455	−	0.395526i	$-0.129438\pi$
$521$	−0.243542	−	0.587963i	−0.0106698	−	0.0257591i	−0.929125	+	0.369767i	$0.879438\pi$
$522$	19.3710	+	8.02371i	0.847844	+	0.351188i
$523$			23.6052i			1.03218i	0.856533	+	0.516092i	$0.172614\pi$
$523$			23.6052i			1.03218i	−0.856533	+	0.516092i	$0.827386\pi$
$524$	−5.74446	+	13.8684i	−0.250948	+	0.605842i
$525$	−0.464667	+	0.464667i	−0.0202797	+	0.0202797i
$526$	7.03191			0.306606
$527$	−14.0401	+	22.1724i	−0.611598	+	0.965843i
$528$	−0.144240			−0.00627725
$529$	−13.9905	+	13.9905i	−0.608283	+	0.608283i
$530$	1.01831	−	2.45841i	0.0442324	−	0.106786i
$531$		−	1.55714i		−	0.0675740i
$532$	−10.1980	−	4.22414i	−0.442139	−	0.183140i
$533$	1.94574	+	4.69742i	0.0842791	+	0.203468i
$534$	5.25198	−	2.17544i	0.227275	−	0.0941405i
$535$	−8.16309	−	8.16309i	−0.352921	−	0.352921i
$536$	−4.99576	−	4.99576i	−0.215784	−	0.215784i
$537$	1.34092	−	0.555428i	0.0578650	−	0.0239685i
$538$	2.03987	+	4.92467i	0.0879449	+	0.212318i
$539$	1.43136	+	0.592887i	0.0616529	+	0.0255374i
$540$			2.70913i			0.116582i
$541$	−10.7771	+	26.0183i	−0.463345	+	1.11861i	0.503670	+	0.863896i	$0.331983\pi$
$541$	−10.7771	+	26.0183i	−0.463345	+	1.11861i	−0.967015	+	0.254718i	$0.918017\pi$
$542$	−4.55436	+	4.55436i	−0.195627	+	0.195627i
$543$	−5.69000			−0.244181
$544$	−3.37096	+	2.37416i	−0.144529	+	0.101791i
$545$	5.16199			0.221115
$546$	2.73212	−	2.73212i	0.116924	−	0.116924i
$547$	5.98525	−	14.4497i	0.255911	−	0.617824i	−0.742749	−	0.669570i	$-0.766479\pi$
$547$	5.98525	−	14.4497i	0.255911	−	0.617824i	0.998660	+	0.0517458i	$0.0164786\pi$
$548$		−	5.88849i		−	0.251544i
$549$	−6.15731	−	2.55044i	−0.262788	−	0.108850i
$550$	0.117774	+	0.284332i	0.00502191	+	0.0121240i
$551$	−54.8493	+	22.7193i	−2.33666	+	0.967877i
$552$	−2.16775	−	2.16775i	−0.0922657	−	0.0922657i
$553$	−1.41767	−	1.41767i	−0.0602855	−	0.0602855i
$554$	9.41675	−	3.90055i	0.400080	−	0.165718i
$555$	1.67314	+	4.03931i	0.0710207	+	0.171459i
$556$	−20.0761	−	8.31579i	−0.851416	−	0.352668i
$557$		−	31.1121i		−	1.31826i	−0.752029	−	0.659130i	$-0.770924\pi$
$557$		−	31.1121i		−	1.31826i	0.752029	−	0.659130i	$-0.229076\pi$
$558$	−6.77236	+	16.3499i	−0.286697	+	0.692148i
$559$	37.8715	−	37.8715i	1.60180	−	1.60180i
$560$	−1.40211			−0.0592498
$561$	−0.585964	−	0.101667i	−0.0247394	−	0.00429240i
$562$	18.2065			0.767995
$563$	16.7473	−	16.7473i	0.705814	−	0.705814i	−0.259838	−	0.965652i	$-0.583669\pi$
$563$	16.7473	−	16.7473i	0.705814	−	0.705814i	0.965652	+	0.259838i	$0.0836692\pi$
$564$	1.15631	−	2.79157i	0.0486893	−	0.117546i
$565$		−	17.2875i		−	0.727290i
$566$	−2.73919	−	1.13461i	−0.115137	−	0.0476913i
$567$	3.79420	+	9.16001i	0.159341	+	0.384684i
$568$	1.26080	−	0.522239i	0.0529019	−	0.0219127i
$569$	30.3944	+	30.3944i	1.27420	+	1.27420i	0.943864	+	0.330334i	$0.107161\pi$
$569$	30.3944	+	30.3944i	1.27420	+	1.27420i	0.330334	+	0.943864i	$0.392839\pi$
$570$	−2.60903	−	2.60903i	−0.109280	−	0.109280i
$571$	−0.443423	+	0.183672i	−0.0185567	+	0.00768643i	−0.391942	−	0.919990i	$-0.628197\pi$
$571$	−0.443423	+	0.183672i	−0.0185567	+	0.00768643i	0.373386	+	0.927676i	$0.378197\pi$
$572$	−0.692481	−	1.67180i	−0.0289541	−	0.0699014i
$573$	−4.22712	−	1.75093i	−0.176590	−	0.0731461i
$574$			1.21246i			0.0506071i
$575$	−2.50316	+	6.04316i	−0.104389	+	0.252017i
$576$	−1.96600	+	1.96600i	−0.0819165	+	0.0819165i
$577$	17.3830			0.723664			0.361832	−	0.932243i	$-0.382151\pi$
$577$	17.3830			0.723664			0.361832	+	0.932243i	$0.382151\pi$
$578$	−15.3677	+	7.26879i	−0.639210	+	0.302342i
$579$	−1.30021			−0.0540351
$580$	−5.33240	+	5.33240i	−0.221416	+	0.221416i
$581$	−3.33221	+	8.04467i	−0.138243	+	0.333749i
$582$			0.355515i			0.0147366i
$583$	0.756597	+	0.313393i	0.0313350	+	0.0129794i
$584$	1.44903	+	3.49827i	0.0599613	+	0.144759i
$585$	−15.1033	+	6.25598i	−0.624444	+	0.258653i
$586$	5.15643	+	5.15643i	0.213010	+	0.213010i
$587$	−8.46735	−	8.46735i	−0.349485	−	0.349485i	0.510433	−	0.859918i	$-0.329485\pi$
$587$	−8.46735	−	8.46735i	−0.349485	−	0.349485i	−0.859918	+	0.510433i	$0.829485\pi$
$588$	−2.17978	+	0.902895i	−0.0898927	+	0.0372348i
$589$	−19.1761	−	46.2952i	−0.790138	−	1.90756i
$590$	0.517422	+	0.214323i	0.0213019	+	0.00882354i
$591$			3.04642i			0.125313i
$592$	−3.56989	+	8.61849i	−0.146722	+	0.354218i
$593$	8.94531	−	8.94531i	0.367340	−	0.367340i	−0.499166	−	0.866506i	$-0.666360\pi$
$593$	8.94531	−	8.94531i	0.367340	−	0.367340i	0.866506	+	0.499166i	$0.166360\pi$
$594$	−0.833758			−0.0342095
$595$	−5.69593	−	0.988271i	−0.233511	−	0.0405151i
$596$	10.0033			0.409751
$597$	−7.38366	+	7.38366i	−0.302193	+	0.302193i
$598$	14.7179	−	35.5322i	0.601860	−	1.45302i
$599$			8.77469i			0.358524i	0.983801	+	0.179262i	$0.0573710\pi$
$599$			8.77469i			0.358524i	−0.983801	+	0.179262i	$0.942629\pi$
$600$	−0.433004	−	0.179356i	−0.0176773	−	0.00732218i
$601$	−7.35003	−	17.7445i	−0.299814	−	0.723815i	−0.999952	−	0.00980750i	$-0.996878\pi$
$601$	−7.35003	−	17.7445i	−0.299814	−	0.723815i	0.700138	−	0.714008i	$-0.253122\pi$
$602$	11.7996	−	4.88754i	0.480915	−	0.199201i
$603$	−13.8899	−	13.8899i	−0.565640	−	0.565640i
$604$	11.9180	+	11.9180i	0.484936	+	0.484936i
$605$	10.0752	−	4.17327i	0.409614	−	0.169668i
$606$	−1.25276	−	3.02443i	−0.0508899	−	0.122859i
$607$	6.18789	+	2.56311i	0.251159	+	0.104033i	0.504711	−	0.863288i	$-0.331599\pi$
$607$	6.18789	+	2.56311i	0.251159	+	0.104033i	−0.253552	+	0.967322i	$0.581599\pi$
$608$		−	7.87260i		−	0.319276i
$609$	1.89642	−	4.57836i	0.0768468	−	0.185525i
$610$	1.69497	−	1.69497i	0.0686275	−	0.0686275i
$611$	37.9066			1.53354
$612$	−9.37242	+	6.60096i	−0.378857	+	0.266828i
$613$	−25.0357			−1.01118			−0.505591	−	0.862773i	$-0.668726\pi$
$613$	−25.0357			−1.01118			−0.505591	+	0.862773i	$0.668726\pi$
$614$	22.1355	−	22.1355i	0.893315	−	0.893315i
$615$	−0.155096	+	0.374436i	−0.00625409	+	0.0150987i
$616$		−	0.431511i		−	0.0173861i
$617$	−16.0852	−	6.66269i	−0.647564	−	0.268230i	0.0346310	−	0.999400i	$-0.488974\pi$
$617$	−16.0852	−	6.66269i	−0.647564	−	0.268230i	−0.682195	+	0.731170i	$0.738974\pi$
$618$	−1.45931	−	3.52309i	−0.0587021	−	0.141719i
$619$	6.84685	−	2.83606i	0.275198	−	0.113991i	−0.240816	−	0.970571i	$-0.577415\pi$
$619$	6.84685	−	2.83606i	0.275198	−	0.113991i	0.516014	+	0.856580i	$0.327415\pi$
$620$	−4.50078	−	4.50078i	−0.180756	−	0.180756i
$621$	−12.5303	−	12.5303i	−0.502825	−	0.502825i
$622$	−12.1039	+	5.01360i	−0.485323	+	0.201027i
$623$	6.50807	+	15.7119i	0.260740	+	0.629482i
$624$	2.54595	+	1.05457i	0.101919	+	0.0422164i
$625$			1.00000i			0.0400000i
$626$	−5.87179	+	14.1757i	−0.234684	+	0.566577i
$627$	0.802952	−	0.802952i	0.0320668	−	0.0320668i
$628$	9.94318			0.396776
$629$	−20.5771	+	32.4956i	−0.820463	+	1.29569i
$630$	−3.89833			−0.155313
$631$	5.85376	−	5.85376i	0.233035	−	0.233035i	−0.580923	−	0.813958i	$-0.697308\pi$
$631$	5.85376	−	5.85376i	0.233035	−	0.233035i	0.813958	+	0.580923i	$0.197308\pi$
$632$	0.547204	−	1.32107i	0.0217666	−	0.0525492i
$633$		−	11.5145i		−	0.457660i
$634$	4.79925	+	1.98791i	0.190602	+	0.0789501i
$635$	3.18857	+	7.69789i	0.126534	+	0.305481i
$636$	−1.15221	+	0.477259i	−0.0456879	+	0.0189246i
$637$	−20.9298	−	20.9298i	−0.829268	−	0.829268i
$638$	−1.64109	−	1.64109i	−0.0649715	−	0.0649715i
$639$	3.50544	−	1.45200i	0.138673	−	0.0574403i
$640$	−0.382683	−	0.923880i	−0.0151269	−	0.0365195i
$641$	−31.6832	−	13.1236i	−1.25141	−	0.518351i	−0.344148	−	0.938915i	$-0.611832\pi$
$641$	−31.6832	−	13.1236i	−1.25141	−	0.518351i	−0.907263	+	0.420564i	$0.861832\pi$
$642$			5.41060i			0.213539i
$643$	11.6146	−	28.0400i	0.458033	−	1.10579i	−0.511159	−	0.859486i	$-0.670784\pi$
$643$	11.6146	−	28.0400i	0.458033	−	1.10579i	0.969193	−	0.246304i	$-0.0792163\pi$
$644$	6.48507	−	6.48507i	0.255548	−	0.255548i
$645$	4.26920			0.168099
$646$	5.54898	−	31.9817i	0.218322	−	1.25830i
$647$	−9.82033			−0.386077			−0.193039	−	0.981191i	$-0.561834\pi$
$647$	−9.82033			−0.386077			−0.193039	+	0.981191i	$0.561834\pi$
$648$	−5.00017	+	5.00017i	−0.196425	+	0.196425i
$649$	−0.0659598	+	0.159241i	−0.00258915	+	0.00625076i
$650$		−	5.87974i		−	0.230622i
$651$	3.86434	+	1.60066i	0.151455	+	0.0627349i
$652$	0.843679	+	2.03682i	0.0330410	+	0.0797681i
$653$	−3.23871	+	1.34152i	−0.126740	+	0.0524976i	−0.445152	−	0.895455i	$-0.646850\pi$
$653$	−3.23871	+	1.34152i	−0.126740	+	0.0524976i	0.318412	+	0.947952i	$0.396850\pi$
$654$	−1.71072	−	1.71072i	−0.0668943	−	0.0668943i
$655$	−10.6144	−	10.6144i	−0.414738	−	0.414738i
$656$	−0.798917	+	0.330922i	−0.0311925	+	0.0129203i
$657$	4.02879	+	9.72637i	0.157178	+	0.379462i
$658$	8.35129	+	3.45922i	0.325567	+	0.134854i
$659$		−	38.2518i		−	1.49008i	−0.667021	−	0.745039i	$-0.732431\pi$
$659$		−	38.2518i		−	1.49008i	0.667021	−	0.745039i	$-0.267569\pi$
$660$	0.0551984	−	0.133261i	0.00214859	−	0.00518716i
$661$	12.8059	−	12.8059i	0.498092	−	0.498092i	−0.412752	−	0.910844i	$-0.635432\pi$
$661$	12.8059	−	12.8059i	0.498092	−	0.498092i	0.910844	+	0.412752i	$0.135432\pi$
$662$	21.0938			0.819833
$663$	9.59938	+	6.07858i	0.372809	+	0.236073i
$664$	−6.21029			−0.241006
$665$	7.80520	−	7.80520i	0.302673	−	0.302673i
$666$	−9.92552	+	23.9623i	−0.384606	+	0.928521i
$667$		−	49.3272i		−	1.90996i
$668$	−15.5398	−	6.43680i	−0.601253	−	0.249047i
$669$	−1.93404	−	4.66920i	−0.0747745	−	0.180522i
$670$	6.52727	−	2.70368i	0.252170	−	0.104452i
$671$	0.521643	+	0.521643i	0.0201378	+	0.0201378i
$672$	0.464667	+	0.464667i	0.0179249	+	0.0179249i
$673$	−34.0990	+	14.1243i	−1.31442	+	0.544451i	−0.926171	−	0.377104i	$-0.876920\pi$
$673$	−34.0990	+	14.1243i	−1.31442	+	0.544451i	−0.388249	+	0.921554i	$0.626920\pi$
$674$	−9.19341	−	22.1949i	−0.354117	−	0.854914i
$675$	−2.50291	−	1.03674i	−0.0963369	−	0.0399041i
$676$			21.5713i			0.829666i
$677$	−19.1087	+	46.1324i	−0.734406	+	1.77301i	−0.107087	+	0.994250i	$0.534152\pi$
$677$	−19.1087	+	46.1324i	−0.734406	+	1.77301i	−0.627319	+	0.778763i	$0.715848\pi$
$678$	−5.72919	+	5.72919i	−0.220028	+	0.220028i
$679$	−1.06356			−0.0408158
$680$	−0.903424	−	4.02291i	−0.0346447	−	0.154272i
$681$	−2.99757			−0.114867
$682$	1.38516	−	1.38516i	0.0530403	−	0.0530403i
$683$	−0.972099	+	2.34685i	−0.0371963	+	0.0897999i	−0.941386	−	0.337331i	$-0.890476\pi$
$683$	−0.972099	+	2.34685i	−0.0371963	+	0.0897999i	0.904190	+	0.427131i	$0.140476\pi$
$684$		−	21.8885i		−	0.836928i
$685$	5.44025	+	2.25343i	0.207861	+	0.0860990i
$686$	−6.45705	−	15.5887i	−0.246531	−	0.595179i
$687$	−3.71415	+	1.53845i	−0.141704	+	0.0586955i
$688$	6.44102	+	6.44102i	0.245562	+	0.245562i
$689$	−11.0632	−	11.0632i	−0.421475	−	0.421475i
$690$	2.83231	−	1.17318i	0.107824	−	0.0446622i
$691$	15.5210	+	37.4710i	0.590447	+	1.42546i	0.883072	+	0.469237i	$0.155471\pi$
$691$	15.5210	+	37.4710i	0.590447	+	1.42546i	−0.292625	+	0.956227i	$0.594529\pi$
$692$	−13.6101	−	5.63748i	−0.517378	−	0.214305i
$693$		−	1.19975i		−	0.0455746i
$694$	−2.33900	+	5.64684i	−0.0887872	+	0.214351i
$695$	15.3656	−	15.3656i	0.582849	−	0.582849i
$696$	3.53439			0.133971
$697$	−3.47878	+	0.781228i	−0.131768	+	0.0295911i
$698$	3.30219			0.124990
$699$	−6.10690	+	6.10690i	−0.230984	+	0.230984i
$700$	0.536563	−	1.29538i	0.0202802	−	0.0489607i
$701$			27.5987i			1.04239i	0.853438	+	0.521194i	$0.174513\pi$
$701$			27.5987i			1.04239i	−0.853438	+	0.521194i	$0.825487\pi$
$702$	14.7164	+	6.09575i	0.555436	+	0.230069i
$703$	−28.1043	−	67.8499i	−1.05998	−	2.55901i
$704$	0.284332	−	0.117774i	0.0107162	−	0.00443878i
$705$	2.13658	+	2.13658i	0.0804681	+	0.0804681i
$706$	−3.58284	−	3.58284i	−0.134842	−	0.134842i
$707$	9.04792	−	3.74777i	0.340282	−	0.140949i
$708$	−0.100449	−	0.242505i	−0.00377510	−	0.00911390i
$709$	23.3948	+	9.69045i	0.878611	+	0.363933i	0.775958	−	0.630785i	$-0.217267\pi$
$709$	23.3948	+	9.69045i	0.878611	+	0.363933i	0.102653	+	0.994717i	$0.467267\pi$
$710$			1.36468i			0.0512154i
$711$	1.52141	−	3.67302i	0.0570574	−	0.137749i
$712$	−8.57662	+	8.57662i	−0.321423	+	0.321423i
$713$	41.6343			1.55922
$714$	1.56015	+	2.21519i	0.0583872	+	0.0829014i
$715$	1.80954			0.0676730
$716$	−2.18976	+	2.18976i	−0.0818352	+	0.0818352i
$717$	−2.94169	+	7.10187i	−0.109859	+	0.265224i
$718$		−	3.51742i		−	0.131269i
$719$	−13.1305	−	5.43884i	−0.489686	−	0.202834i	0.124157	−	0.992263i	$-0.460377\pi$
$719$	−13.1305	−	5.43884i	−0.489686	−	0.202834i	−0.613843	+	0.789428i	$0.710377\pi$
$720$	−1.06399	−	2.56870i	−0.0396526	−	0.0957297i
$721$	10.5397	−	4.36569i	0.392519	−	0.162587i
$722$	30.3899	+	30.3899i	1.13099	+	1.13099i
$723$	−9.20335	−	9.20335i	−0.342276	−	0.342276i
$724$	11.2163	−	4.64596i	0.416852	−	0.172666i
$725$	−2.88588	−	6.96712i	−0.107179	−	0.258752i
$726$	−4.72203	−	1.95593i	−0.175251	−	0.0725913i
$727$		−	16.6095i		−	0.616011i	−0.951385	−	0.308005i	$-0.900339\pi$
$727$		−	16.6095i		−	0.616011i	0.951385	−	0.308005i	$-0.0996615\pi$
$728$	−3.15485	+	7.61648i	−0.116926	+	0.282285i
$729$	−11.2087	+	11.2087i	−0.415137	+	0.415137i
$730$	−3.78650			−0.140145
$731$	21.6262	+	30.7060i	0.799872	+	1.13570i
$732$	−1.12345			−0.0415239
$733$	−16.4456	+	16.4456i	−0.607432	+	0.607432i	−0.942274	−	0.334842i	$-0.891317\pi$
$733$	−16.4456	+	16.4456i	−0.607432	+	0.607432i	0.334842	+	0.942274i	$0.391317\pi$
$734$	−2.81372	+	6.79293i	−0.103856	+	0.250731i
$735$		−	2.35938i		−	0.0870270i
$736$	6.04316	+	2.50316i	0.222754	+	0.0922676i
$737$	0.832083	+	2.00882i	0.0306502	+	0.0739960i
$738$	−2.22126	+	0.920076i	−0.0817657	+	0.0338685i
$739$	−25.5833	−	25.5833i	−0.941096	−	0.941096i	0.0572629	−	0.998359i	$-0.481763\pi$
$739$	−25.5833	−	25.5833i	−0.941096	−	0.941096i	−0.998359	+	0.0572629i	$0.981763\pi$
$740$	−6.59630	−	6.59630i	−0.242485	−	0.242485i
$741$	−20.0432	+	8.30217i	−0.736306	+	0.304988i
$742$	−1.42777	−	3.44695i	−0.0524152	−	0.126541i
$743$	−50.1024	−	20.7531i	−1.83808	−	0.761357i	−0.958161	−	0.286229i	$-0.907598\pi$
$743$	−50.1024	−	20.7531i	−1.83808	−	0.761357i	−0.879917	−	0.475128i	$-0.842402\pi$
$744$			2.98318i			0.109369i
$745$	−3.82810	+	9.24184i	−0.140251	+	0.338595i
$746$	10.8338	−	10.8338i	0.396652	−	0.396652i
$747$	−17.2667			−0.631756
$748$	1.23809	−	0.278037i	0.0452689	−	0.0101660i
$749$	−16.1864			−0.591438
$750$	0.331407	−	0.331407i	0.0121013	−	0.0121013i
$751$	−10.6610	+	25.7379i	−0.389025	+	0.939190i	0.601122	+	0.799158i	$0.294721\pi$
$751$	−10.6610	+	25.7379i	−0.389025	+	0.939190i	−0.990147	+	0.140033i	$0.955279\pi$
$752$			6.44699i			0.235098i
$753$	−11.1169	−	4.60476i	−0.405121	−	0.167807i
$754$	16.9682	+	40.9648i	0.617945	+	1.49185i
$755$	−15.5716	+	6.44997i	−0.566709	+	0.234739i
$756$	2.68593	+	2.68593i	0.0976865	+	0.0976865i
$757$	36.9843	+	36.9843i	1.34422	+	1.34422i	0.891815	+	0.452401i	$0.149432\pi$
$757$	36.9843	+	36.9843i	1.34422	+	1.34422i	0.452401	+	0.891815i	$0.350568\pi$
$758$	11.6620	−	4.83055i	0.423582	−	0.175453i
$759$	0.361056	+	0.871667i	0.0131055	+	0.0316395i
$760$	7.27333	+	3.01271i	0.263831	+	0.109283i
$761$			18.2289i			0.660798i	0.943841	+	0.330399i	$0.107183\pi$
$761$			18.2289i			0.660798i	−0.943841	+	0.330399i	$0.892817\pi$
$762$	1.49442	−	3.60784i	0.0541370	−	0.130698i
$763$	5.11780	−	5.11780i	0.185277	−	0.185277i
$764$	9.76231			0.353188
$765$	−2.51182	−	11.1851i	−0.0908152	−	0.404397i
$766$	−10.3824			−0.375130
$767$	2.32848	−	2.32848i	0.0840765	−	0.0840765i
$768$	−0.179356	+	0.433004i	−0.00647195	+	0.0156247i
$769$		−	0.418391i		−	0.0150876i	−0.999972	−	0.00754379i	$-0.997599\pi$
$769$		−	0.418391i		−	0.0150876i	0.999972	−	0.00754379i	$-0.00240129\pi$
$770$	0.398664	+	0.165132i	0.0143668	+	0.00595094i
$771$	2.60574	+	6.29082i	0.0938435	+	0.226558i
$772$	2.56303	−	1.06164i	0.0922456	−	0.0382094i
$773$	33.7226	+	33.7226i	1.21292	+	1.21292i	0.970063	+	0.242855i	$0.0780838\pi$
$773$	33.7226	+	33.7226i	1.21292	+	1.21292i	0.242855	+	0.970063i	$0.421916\pi$
$774$	17.9082	+	17.9082i	0.643698	+	0.643698i
$775$	5.88055	−	2.43581i	0.211236	−	0.0874967i
$776$	−0.290283	−	0.700805i	−0.0104206	−	0.0251574i
$777$	5.66354	+	2.34592i	0.203178	+	0.0841593i
$778$		−	32.6228i		−	1.16958i
$779$	2.60522	−	6.28955i	0.0933416	−	0.225347i
$780$	−1.94858	+	1.94858i	−0.0697705	+	0.0697705i
$781$	−0.419991			−0.0150285
$782$	22.7855	+	14.4284i	0.814806	+	0.515957i
$783$	20.4300			0.730107
$784$	3.55964	−	3.55964i	0.127130	−	0.127130i
$785$	−3.80509	+	9.18630i	−0.135809	+	0.327873i
$786$			7.03535i			0.250943i
$787$	−30.4146	−	12.5981i	−1.08416	−	0.449075i	−0.232196	−	0.972669i	$-0.574591\pi$
$787$	−30.4146	−	12.5981i	−1.08416	−	0.449075i	−0.851968	+	0.523594i	$0.824591\pi$
$788$	−2.48744	−	6.00521i	−0.0886114	−	0.213927i
$789$	3.04484	−	1.26121i	0.108399	−	0.0449004i
$790$	1.01110	+	1.01110i	0.0359734	+	0.0359734i
$791$	−17.1395	−	17.1395i	−0.609410	−	0.609410i
$792$	0.790540	−	0.327452i	0.0280906	−	0.0116355i
$793$	−5.39356	−	13.0212i	−0.191531	−	0.462396i
$794$	9.73297	+	4.03153i	0.345410	+	0.143074i
$795$		−	1.24714i		−	0.0442314i
$796$	8.52610	−	20.5838i	0.302200	−	0.729574i
$797$	19.0261	−	19.0261i	0.673938	−	0.673938i	−0.284684	−	0.958622i	$-0.591889\pi$
$797$	19.0261	−	19.0261i	0.673938	−	0.673938i	0.958622	+	0.284684i	$0.0918885\pi$
$798$	−5.17339			−0.183136
$799$	−4.54414	+	26.1903i	−0.160760	+	0.926548i
$800$	1.00000			0.0353553
$801$	−23.8459	+	23.8459i	−0.842554	+	0.842554i
$802$	0.856816	−	2.06854i	0.0302552	−	0.0730425i
$803$		−	1.16533i		−	0.0411235i
$804$	−3.05920	−	1.26716i	−0.107890	−	0.0446893i
$805$	3.50969	+	8.47315i	0.123700	+	0.298639i
$806$	−34.5761	+	14.3219i	−1.21789	+	0.504467i
$807$	1.76654	+	1.76654i	0.0621851	+	0.0621851i
$808$	4.93898	+	4.93898i	0.173753	+	0.173753i
$809$	5.96396	−	2.47035i	0.209682	−	0.0868529i	−0.275371	−	0.961338i	$-0.588801\pi$
$809$	5.96396	−	2.47035i	0.209682	−	0.0868529i	0.485052	+	0.874485i	$0.338801\pi$
$810$	−2.70607	−	6.53303i	−0.0950817	−	0.229547i
$811$	30.8076	+	12.7609i	1.08180	+	0.448096i	0.851140	−	0.524938i	$-0.175912\pi$
$811$	30.8076	+	12.7609i	1.08180	+	0.448096i	0.230660	+	0.973034i	$0.425912\pi$
$812$			10.5735i			0.371057i
$813$	−1.15520	+	2.78891i	−0.0405147	+	0.0978112i
$814$	2.03007	−	2.03007i	0.0711540	−	0.0711540i
$815$	−2.20464			−0.0772251
$816$	−1.03382	+	1.63262i	−0.0361909	+	0.0571531i
$817$	−71.7114			−2.50886
$818$	9.67394	−	9.67394i	0.338241	−	0.338241i
$819$	−8.77155	+	21.1764i	−0.306503	+	0.739963i
$820$		−	0.864741i		−	0.0301981i
$821$	23.8028	+	9.85946i	0.830725	+	0.344097i	0.757190	−	0.653195i	$-0.226572\pi$
$821$	23.8028	+	9.85946i	0.830725	+	0.344097i	0.0735351	+	0.997293i	$0.476572\pi$
$822$	−1.05613	−	2.54974i	−0.0368369	−	0.0889322i
$823$	4.45167	−	1.84394i	0.155175	−	0.0642757i	−0.303744	−	0.952754i	$-0.598237\pi$
$823$	4.45167	−	1.84394i	0.155175	−	0.0642757i	0.458919	+	0.888478i	$0.348237\pi$
$824$	5.75330	+	5.75330i	0.200426	+	0.200426i
$825$	0.101993	+	0.101993i	0.00355095	+	0.00355095i
$826$	0.725480	−	0.300504i	0.0252427	−	0.0104559i
$827$	13.5131	+	32.6235i	0.469896	+	1.13443i	0.964209	+	0.265145i	$0.0854199\pi$
$827$	13.5131	+	32.6235i	0.469896	+	1.13443i	−0.494312	+	0.869284i	$0.664580\pi$
$828$	16.8020	+	6.95963i	0.583911	+	0.241864i
$829$		−	25.7997i		−	0.896060i	−0.894019	−	0.448030i	$-0.852126\pi$
$829$		−	25.7997i		−	0.896060i	0.894019	−	0.448030i	$-0.147874\pi$
$830$	2.37657	−	5.73756i	0.0824921	−	0.199154i
$831$	3.37790	−	3.37790i	0.117178	−	0.117178i
$832$	−5.87974			−0.203843
$833$	16.9697	−	11.9517i	0.587967	−	0.414103i
$834$	−10.1845			−0.352660
$835$	11.8937	−	11.8937i	0.411597	−	0.411597i
$836$	−0.927189	+	2.23843i	−0.0320675	+	0.0774178i
$837$			17.2438i			0.596032i
$838$	−20.6528	−	8.55468i	−0.713440	−	0.295516i
$839$	12.9903	+	31.3614i	0.448476	+	1.08272i	0.972893	+	0.231256i	$0.0742834\pi$
$839$	12.9903	+	31.3614i	0.448476	+	1.08272i	−0.524417	+	0.851462i	$0.675717\pi$
$840$	−0.607117	+	0.251476i	−0.0209475	+	0.00867675i
$841$	19.7064	+	19.7064i	0.679531	+	0.679531i
$842$	−3.21951	−	3.21951i	−0.110952	−	0.110952i
$843$	7.88348	−	3.26544i	0.271521	−	0.112468i
$844$	9.40174	+	22.6978i	0.323621	+	0.781291i
$845$	−19.9293	−	8.25498i	−0.685589	−	0.283980i
$846$			17.9248i			0.616268i
$847$	5.85137	−	14.1265i	0.201055	−	0.485391i
$848$	1.88158	−	1.88158i	0.0646139	−	0.0646139i
$849$	−1.38958			−0.0476903
$850$	4.06241	+	0.704847i	0.139340	+	0.0241761i
$851$	61.0189			2.09170
$852$	0.452263	−	0.452263i	0.0154943	−	0.0154943i
$853$	9.95319	−	24.0291i	0.340791	−	0.822741i	−0.656846	−	0.754025i	$-0.728110\pi$
$853$	9.95319	−	24.0291i	0.340791	−	0.822741i	0.997636	−	0.0687163i	$-0.0218903\pi$
$854$		−	3.36092i		−	0.115008i
$855$	20.2223	+	8.37636i	0.691589	+	0.286466i
$856$	−4.41783	−	10.6656i	−0.150998	−	0.364542i
$857$	10.3288	−	4.27831i	0.352824	−	0.146144i	−0.199230	−	0.979953i	$-0.563844\pi$
$857$	10.3288	−	4.27831i	0.352824	−	0.146144i	0.552054	+	0.833808i	$0.313844\pi$
$858$	−0.599694	−	0.599694i	−0.0204732	−	0.0204732i
$859$	−13.3428	−	13.3428i	−0.455251	−	0.455251i	0.441842	−	0.897093i	$-0.354325\pi$
$859$	−13.3428	−	13.3428i	−0.455251	−	0.455251i	−0.897093	+	0.441842i	$0.854325\pi$
$860$	−8.41560	+	3.48586i	−0.286970	+	0.118867i
$861$	0.217462	+	0.524999i	0.00741108	+	0.0178919i
$862$	30.2138	+	12.5150i	1.02909	+	0.426262i
$863$		−	13.6451i		−	0.464484i	−0.972658	−	0.232242i	$-0.925394\pi$
$863$		−	13.6451i		−	0.464484i	0.972658	−	0.232242i	$-0.0746062\pi$
$864$	−1.03674	+	2.50291i	−0.0352705	+	0.0851506i
$865$	10.4167	−	10.4167i	0.354179	−	0.354179i
$866$	0.967852			0.0328889
$867$	−5.35055	+	5.90369i	−0.181714	+	0.200500i
$868$	−8.92450			−0.302917
$869$	−0.311175	+	0.311175i	−0.0105559	+	0.0105559i
$870$	−1.35255	+	3.26535i	−0.0458558	+	0.110706i
$871$		−	41.5407i		−	1.40755i
$872$	4.76906	+	1.97541i	0.161501	+	0.0668957i
$873$	−0.807085	−	1.94848i	−0.0273157	−	0.0659459i
$874$	−47.5754	+	19.7064i	−1.60926	+	0.666578i
$875$	0.991439	+	0.991439i	0.0335168	+	0.0335168i
$876$	1.25487	+	1.25487i	0.0423981	+	0.0423981i
$877$	−8.85437	+	3.66760i	−0.298991	+	0.123846i	−0.527136	−	0.849781i	$-0.676734\pi$
$877$	−8.85437	+	3.66760i	−0.298991	+	0.123846i	0.228145	+	0.973627i	$0.426734\pi$
$878$	11.2648	+	27.1957i	0.380170	+	0.917812i
$879$	3.15759	+	1.30792i	0.106503	+	0.0441149i
$880$			0.307759i			0.0103745i
$881$	−9.49133	+	22.9141i	−0.319771	+	0.771996i	0.679495	+	0.733680i	$0.262199\pi$
$881$	−9.49133	+	22.9141i	−0.319771	+	0.771996i	−0.999266	+	0.0383152i	$0.987801\pi$
$882$	9.89702	−	9.89702i	0.333250	−	0.333250i
$883$	13.8918			0.467496			0.233748	−	0.972297i	$-0.424901\pi$
$883$	13.8918			0.467496			0.233748	+	0.972297i	$0.424901\pi$
$884$	−23.8859	−	4.14432i	−0.803370	−	0.139388i
$885$	0.262486			0.00882336
$886$	14.2771	−	14.2771i	0.479648	−	0.479648i
$887$	18.6708	−	45.0753i	0.626904	−	1.51348i	−0.216546	−	0.976272i	$-0.569479\pi$
$887$	18.6708	−	45.0753i	0.626904	−	1.51348i	0.843450	−	0.537207i	$-0.180521\pi$
$888$			4.37212i			0.146719i
$889$	10.7933	+	4.47071i	0.361994	+	0.149943i
$890$	−4.64164	−	11.2059i	−0.155588	−	0.375623i
$891$	2.01060	−	0.832817i	0.0673576	−	0.0279004i
$892$	7.62493	+	7.62493i	0.255301	+	0.255301i
$893$	−35.8889	−	35.8889i	−1.20098	−	1.20098i
$894$	4.33146	−	1.79415i	0.144866	−	0.0600054i
$895$	−1.18509	−	2.86106i	−0.0396132	−	0.0956347i
$896$	−1.29538	−	0.536563i	−0.0432755	−	0.0179253i
$897$		−	18.0253i		−	0.601847i
$898$	4.72803	−	11.4145i	0.157776	−	0.380906i
$899$	−33.9411	+	33.9411i	−1.13200	+	1.13200i
$900$	2.78034			0.0926780
$901$	8.97000	−	6.31754i	0.298834	−	0.210468i
$902$	0.266132			0.00886122
$903$	4.23265	−	4.23265i	0.140854	−	0.140854i
$904$	6.61563	−	15.9716i	0.220033	−	0.531206i
$905$			12.1405i			0.403563i
$906$	7.29810	+	3.02297i	0.242463	+	0.100431i
$907$	13.7123	+	33.1045i	0.455311	+	1.09922i	0.970275	+	0.242006i	$0.0778054\pi$
$907$	13.7123	+	33.1045i	0.455311	+	1.09922i	−0.514964	+	0.857212i	$0.672195\pi$
$908$	5.90892	−	2.44756i	0.196094	−	0.0812250i
$909$	13.7320	+	13.7320i	0.455463	+	0.455463i
$910$	−5.82940	−	5.82940i	−0.193243	−	0.193243i
$911$	−17.0313	+	7.05458i	−0.564271	+	0.233729i	−0.646538	−	0.762882i	$-0.723784\pi$
$911$	−17.0313	+	7.05458i	−0.564271	+	0.233729i	0.0822674	+	0.996610i	$0.473784\pi$
$912$	−1.41200	−	3.40886i	−0.0467559	−	0.112879i
$913$	1.76578	+	0.731412i	0.0584389	+	0.0242062i
$914$		−	29.4875i		−	0.975361i
$915$	0.429926	−	1.03793i	0.0142129	−	0.0343130i
$916$	6.06531	−	6.06531i	0.200403	−	0.200403i
$917$	−21.0470			−0.695034
$918$	−5.97582	+	9.43710i	−0.197232	+	0.311471i
$919$	−28.2940			−0.933332			−0.466666	−	0.884434i	$-0.654545\pi$
$919$	−28.2940			−0.933332			−0.466666	+	0.884434i	$0.654545\pi$
$920$	−4.62523	+	4.62523i	−0.152489	+	0.152489i
$921$	5.61461	−	13.5549i	0.185008	−	0.446648i
$922$			21.8473i			0.719502i
$923$	7.41316	+	3.07063i	0.244007	+	0.101071i
$924$	−0.0773940	−	0.186846i	−0.00254608	−	0.00614677i
$925$	8.61849	−	3.56989i	0.283374	−	0.117377i
$926$	−21.1656	−	21.1656i	−0.695544	−	0.695544i
$927$	15.9961	+	15.9961i	0.525382	+	0.525382i
$928$	−6.96712	+	2.88588i	−0.228707	+	0.0947335i
$929$	16.9707	+	40.9709i	0.556790	+	1.34421i	0.912294	+	0.409536i	$0.134309\pi$
$929$	16.9707	+	40.9709i	0.556790	+	1.34421i	−0.355504	+	0.934675i	$0.615691\pi$
$930$	−2.75610	−	1.14161i	−0.0903759	−	0.0374349i
$931$			39.6314i			1.29887i
$932$	7.05179	−	17.0245i	0.230989	−	0.557657i
$933$	−4.34182	+	4.34182i	−0.142145	+	0.142145i
$934$	−16.0590			−0.525468
$935$	−0.216923	+	1.25024i	−0.00709414	+	0.0408873i
$936$	−16.3477			−0.534340
$937$	−0.812419	+	0.812419i	−0.0265406	+	0.0265406i	−0.720253	−	0.693712i	$-0.755974\pi$
$937$	−0.812419	+	0.812419i	−0.0265406	+	0.0265406i	0.693712	+	0.720253i	$0.255974\pi$
$938$	3.79085	−	9.15193i	0.123776	−	0.298821i
$939$			7.19129i			0.234679i
$940$	−5.95624	−	2.46716i	−0.194271	−	0.0804698i
$941$	15.6853	+	37.8676i	0.511325	+	1.23445i	0.943113	+	0.332473i	$0.107883\pi$
$941$	15.6853	+	37.8676i	0.511325	+	1.23445i	−0.431788	+	0.901975i	$0.642117\pi$
$942$	4.30543	−	1.78337i	0.140279	−	0.0581053i
$943$	3.99963	+	3.99963i	0.130246	+	0.130246i
$944$	0.396017	+	0.396017i	0.0128893	+	0.0128893i
$945$	−3.50934	+	1.45362i	−0.114159	+	0.0472862i
$946$	−1.07280	−	2.58998i	−0.0348798	−	0.0842074i
$947$	−33.8661	−	14.0278i	−1.10050	−	0.455842i	−0.242843	−	0.970066i	$-0.578080\pi$
$947$	−33.8661	−	14.0278i	−1.10050	−	0.455842i	−0.857656	+	0.514224i	$0.828080\pi$
$948$		−	0.670171i		−	0.0217661i
$949$	−8.51991	+	20.5689i	−0.276568	+	0.667694i
$950$	−5.56677	+	5.56677i	−0.180610	+	0.180610i
$951$	2.43463			0.0789484
$952$	−4.88416	−	3.09278i	−0.158297	−	0.100238i
$953$	10.4161			0.337410			0.168705	−	0.985667i	$-0.446041\pi$
$953$	10.4161			0.337410			0.168705	+	0.985667i	$0.446041\pi$
$954$	5.23144	−	5.23144i	0.169374	−	0.169374i
$955$	−3.73588	+	9.01920i	−0.120890	+	0.291855i
$956$		−	16.4014i		−	0.530459i
$957$	−1.00494	−	0.416260i	−0.0324851	−	0.0134558i
$958$	−1.98019	−	4.78059i	−0.0639769	−	0.154454i
$959$	7.62781	−	3.15954i	0.246315	−	0.102027i
$960$	−0.331407	−	0.331407i	−0.0106961	−	0.0106961i
$961$	−6.72746	−	6.72746i	−0.217015	−	0.217015i
$962$	−50.6744	+	20.9900i	−1.63381	+	0.676746i
$963$	−12.2831	−	29.6540i	−0.395816	−	0.955586i
$964$	25.6567	+	10.6273i	0.826346	+	0.342284i
$965$			2.77421i			0.0893049i
$966$	1.64492	−	3.97119i	0.0529245	−	0.127771i
$967$	11.7811	−	11.7811i	0.378856	−	0.378856i	−0.491833	−	0.870689i	$-0.663673\pi$
$967$	11.7811	−	11.7811i	0.378856	−	0.378856i	0.870689	+	0.491833i	$0.163673\pi$
$968$	10.9053			0.350509
$969$	−3.33339	−	14.8434i	−0.107084	−	0.476840i
$970$	0.758546			0.0243554
$971$	11.2284	−	11.2284i	0.360337	−	0.360337i	−0.503600	−	0.863937i	$-0.667991\pi$
$971$	11.2284	−	11.2284i	0.360337	−	0.360337i	0.863937	+	0.503600i	$0.167991\pi$
$972$	−4.37849	+	10.5706i	−0.140440	+	0.339053i
$973$		−	30.4680i		−	0.976761i
$974$	−26.6873	−	11.0542i	−0.855115	−	0.354200i
$975$	−1.05457	−	2.54595i	−0.0337731	−	0.0815356i
$976$	2.21459	−	0.917313i	0.0708873	−	0.0293625i
$977$	15.7158	+	15.7158i	0.502793	+	0.502793i	0.912305	−	0.409512i	$-0.134301\pi$
$977$	15.7158	+	15.7158i	0.502793	+	0.502793i	−0.409512	+	0.912305i	$0.634301\pi$
$978$	0.730632	+	0.730632i	0.0233630	+	0.0233630i
$979$	3.44871	−	1.42850i	0.110221	−	0.0456552i
$980$	1.92647	+	4.65090i	0.0615387	+	0.148568i
$981$	13.2596	+	5.49230i	0.423346	+	0.175356i
$982$			19.7916i			0.631575i
$983$	−4.41378	+	10.6558i	−0.140778	+	0.339868i	−0.978506	−	0.206220i	$-0.933884\pi$
$983$	−4.41378	+	10.6558i	−0.140778	+	0.339868i	0.837728	+	0.546088i	$0.183884\pi$
$984$	−0.286581	+	0.286581i	−0.00913586	+	0.00913586i
$985$	6.50000			0.207107
$986$	−30.3374	+	6.81286i	−0.966140	+	0.216966i
$987$	4.23657			0.134851
$988$	32.7311	−	32.7311i	1.04132	−	1.04132i
$989$	22.8012	−	55.0470i	0.725037	−	1.75039i
$990$			0.855674i			0.0271951i
$991$	−23.8040	−	9.85995i	−0.756160	−	0.313212i	−0.0289077	−	0.999582i	$-0.509203\pi$
$991$	−23.8040	−	9.85995i	−0.756160	−	0.313212i	−0.727252	+	0.686370i	$0.759203\pi$
$992$	−2.43581	−	5.88055i	−0.0773369	−	0.186708i
$993$	9.13368	−	3.78330i	0.289849	−	0.120059i
$994$	1.35299	+	1.35299i	0.0429144	+	0.0429144i
$995$	15.7542	+	15.7542i	0.499441	+	0.499441i
$996$	−2.68908	+	1.11385i	−0.0852067	+	0.0352938i
$997$	−12.4988	−	30.1748i	−0.395841	−	0.955646i	−0.988641	−	0.150296i	$-0.951977\pi$
$997$	−12.4988	−	30.1748i	−0.395841	−	0.955646i	0.592800	−	0.805350i	$-0.298023\pi$
$998$	8.36922	+	3.46665i	0.264923	+	0.109735i
$999$			25.2723i			0.799581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	170.2.k.b.161.2	yes	16
5.2	odd	4		850.2.o.j.399.3		16
5.3	odd	4		850.2.o.g.399.2		16
5.4	even	2		850.2.l.e.501.3		16
17.6	odd	16		2890.2.b.r.2311.10		16
17.7	odd	16		2890.2.a.bi.1.6		8
17.10	odd	16		2890.2.a.bj.1.3		8
17.11	odd	16		2890.2.b.r.2311.7		16
17.15	even	8	inner	170.2.k.b.151.2	✓	16
85.32	odd	8		850.2.o.g.49.2		16
85.49	even	8		850.2.l.e.151.3		16
85.83	odd	8		850.2.o.j.49.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
170.2.k.b.151.2	✓	16	17.15	even	8	inner
170.2.k.b.161.2	yes	16	1.1	even	1	trivial
850.2.l.e.151.3		16	85.49	even	8
850.2.l.e.501.3		16	5.4	even	2
850.2.o.g.49.2		16	85.32	odd	8
850.2.o.g.399.2		16	5.3	odd	4
850.2.o.j.49.3		16	85.83	odd	8
850.2.o.j.399.3		16	5.2	odd	4
2890.2.a.bi.1.6		8	17.7	odd	16
2890.2.a.bj.1.3		8	17.10	odd	16
2890.2.b.r.2311.7		16	17.11	odd	16
2890.2.b.r.2311.10		16	17.6	odd	16

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:	\( N \)	\(=\)	\( 170 = 2 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	170.k (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.179356 + 0.433004i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(-0.179356 - 0.433004i) q^{6} +(1.29538 - 0.536563i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.96600 + 1.96600i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-0.179356 + 0.433004i) q^{3} -1.00000i q^{4} +(0.923880 + 0.382683i) q^{5} +(-0.179356 - 0.433004i) q^{6} +(1.29538 - 0.536563i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.96600 + 1.96600i) q^{9} +(-0.923880 + 0.382683i) q^{10} +(-0.117774 - 0.284332i) q^{11} +(0.433004 + 0.179356i) q^{12} +5.87974i q^{13} +(-0.536563 + 1.29538i) q^{14} +(-0.331407 + 0.331407i) q^{15} -1.00000 q^{16} +(-4.06241 - 0.704847i) q^{17} -2.78034 q^{18} +(5.56677 - 5.56677i) q^{19} +(0.382683 - 0.923880i) q^{20} +0.657139i q^{21} +(0.284332 + 0.117774i) q^{22} +(2.50316 + 6.04316i) q^{23} +(-0.433004 + 0.179356i) q^{24} +(0.707107 + 0.707107i) q^{25} +(-4.15760 - 4.15760i) q^{26} +(-2.50291 + 1.03674i) q^{27} +(-0.536563 - 1.29538i) q^{28} +(-6.96712 - 2.88588i) q^{29} -0.468680i q^{30} +(2.43581 - 5.88055i) q^{31} +(0.707107 - 0.707107i) q^{32} +0.144240 q^{33} +(3.37096 - 2.37416i) q^{34} +1.40211 q^{35} +(1.96600 - 1.96600i) q^{36} +(3.56989 - 8.61849i) q^{37} +7.87260i q^{38} +(-2.54595 - 1.05457i) q^{39} +(0.382683 + 0.923880i) q^{40} +(0.798917 - 0.330922i) q^{41} +(-0.464667 - 0.464667i) q^{42} +(-6.44102 - 6.44102i) q^{43} +(-0.284332 + 0.117774i) q^{44} +(1.06399 + 2.56870i) q^{45} +(-6.04316 - 2.50316i) q^{46} -6.44699i q^{47} +(0.179356 - 0.433004i) q^{48} +(-3.55964 + 3.55964i) q^{49} -1.00000 q^{50} +(1.03382 - 1.63262i) q^{51} +5.87974 q^{52} +(-1.88158 + 1.88158i) q^{53} +(1.03674 - 2.50291i) q^{54} -0.307759i q^{55} +(1.29538 + 0.536563i) q^{56} +(1.41200 + 3.40886i) q^{57} +(6.96712 - 2.88588i) q^{58} +(-0.396017 - 0.396017i) q^{59} +(0.331407 + 0.331407i) q^{60} +(-2.21459 + 0.917313i) q^{61} +(2.43581 + 5.88055i) q^{62} +(3.60159 + 1.49183i) q^{63} +1.00000i q^{64} +(-2.25008 + 5.43217i) q^{65} +(-0.101993 + 0.101993i) q^{66} -7.06507 q^{67} +(-0.704847 + 4.06241i) q^{68} -3.06567 q^{69} +(-0.991439 + 0.991439i) q^{70} +(0.522239 - 1.26080i) q^{71} +2.78034i q^{72} +(3.49827 + 1.44903i) q^{73} +(3.56989 + 8.61849i) q^{74} +(-0.433004 + 0.179356i) q^{75} +(-5.56677 - 5.56677i) q^{76} +(-0.305124 - 0.305124i) q^{77} +(2.54595 - 1.05457i) q^{78} +(-0.547204 - 1.32107i) q^{79} +(-0.923880 - 0.382683i) q^{80} +7.07131i q^{81} +(-0.330922 + 0.798917i) q^{82} +(-4.39134 + 4.39134i) q^{83} +0.657139 q^{84} +(-3.48345 - 2.20581i) q^{85} +9.10898 q^{86} +(2.49919 - 2.49919i) q^{87} +(0.117774 - 0.284332i) q^{88} +12.1292i q^{89} +(-2.56870 - 1.06399i) q^{90} +(3.15485 + 7.61648i) q^{91} +(6.04316 - 2.50316i) q^{92} +(2.10942 + 2.10942i) q^{93} +(4.55871 + 4.55871i) q^{94} +(7.27333 - 3.01271i) q^{95} +(0.179356 + 0.433004i) q^{96} +(-0.700805 - 0.290283i) q^{97} -5.03410i q^{98} +(0.327452 - 0.790540i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * q	\( 16 q - 8 q^{11} - 8 q^{14} + 8 q^{15} - 16 q^{16} + 8 q^{18} - 8 q^{22} + 8 q^{23} - 24 q^{27} - 8 q^{28} + 8 q^{29} + 32 q^{31} + 16 q^{33} + 16 q^{34} + 16 q^{35} - 8 q^{37} - 32 q^{39} - 32 q^{41} + 32 q^{42} - 16 q^{43} + 8 q^{44} - 16 q^{45} - 24 q^{46} - 8 q^{49} - 16 q^{50} - 8 q^{51} - 8 q^{52} - 40 q^{53} - 16 q^{57} - 8 q^{58} + 16 q^{59} - 8 q^{60} - 24 q^{61} + 32 q^{62} + 56 q^{63} - 8 q^{65} - 8 q^{66} + 16 q^{67} - 16 q^{69} + 8 q^{70} + 8 q^{71} + 16 q^{73} - 8 q^{74} + 24 q^{77} + 32 q^{78} + 40 q^{79} + 16 q^{82} + 32 q^{83} + 16 q^{84} + 16 q^{85} - 32 q^{87} + 8 q^{88} + 24 q^{91} + 24 q^{92} - 32 q^{93} + 40 q^{94} + 16 q^{95} + 24 q^{97} - 56 q^{99}+O(q^{100}) \) 16 * q - 8 * q^11 - 8 * q^14 + 8 * q^15 - 16 * q^16 + 8 * q^18 - 8 * q^22 + 8 * q^23 - 24 * q^27 - 8 * q^28 + 8 * q^29 + 32 * q^31 + 16 * q^33 + 16 * q^34 + 16 * q^35 - 8 * q^37 - 32 * q^39 - 32 * q^41 + 32 * q^42 - 16 * q^43 + 8 * q^44 - 16 * q^45 - 24 * q^46 - 8 * q^49 - 16 * q^50 - 8 * q^51 - 8 * q^52 - 40 * q^53 - 16 * q^57 - 8 * q^58 + 16 * q^59 - 8 * q^60 - 24 * q^61 + 32 * q^62 + 56 * q^63 - 8 * q^65 - 8 * q^66 + 16 * q^67 - 16 * q^69 + 8 * q^70 + 8 * q^71 + 16 * q^73 - 8 * q^74 + 24 * q^77 + 32 * q^78 + 40 * q^79 + 16 * q^82 + 32 * q^83 + 16 * q^84 + 16 * q^85 - 32 * q^87 + 8 * q^88 + 24 * q^91 + 24 * q^92 - 32 * q^93 + 40 * q^94 + 16 * q^95 + 24 * q^97 - 56 * q^99

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