LMFDB - Embedded newform 208.2.n.a.157.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [208,2,Mod(53,208)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(208, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("208.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 208 = 2^{4} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	208.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.66088836204$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.22
Character	$\chi$	$=$	208.157
Dual form			208.2.n.a.53.22

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26448 + 0.633320i) q^{2} +(-1.84134 - 1.84134i) q^{3} +(1.19781 + 1.60164i) q^{4} +(0.917928 - 0.917928i) q^{5} +(-1.16217 - 3.49448i) q^{6} -2.65087i q^{7} +(0.500257 + 2.78384i) q^{8} +3.78103i q^{9} +O(q^{10})$	\(q+(1.26448 + 0.633320i) q^{2} +(-1.84134 - 1.84134i) q^{3} +(1.19781 + 1.60164i) q^{4} +(0.917928 - 0.917928i) q^{5} +(-1.16217 - 3.49448i) q^{6} -2.65087i q^{7} +(0.500257 + 2.78384i) q^{8} +3.78103i q^{9} +(1.74204 - 0.579358i) q^{10} +(4.00913 - 4.00913i) q^{11} +(0.743581 - 5.15473i) q^{12} +(0.707107 + 0.707107i) q^{13} +(1.67885 - 3.35197i) q^{14} -3.38043 q^{15} +(-1.13049 + 3.83692i) q^{16} -4.47964 q^{17} +(-2.39460 + 4.78103i) q^{18} +(0.0709724 + 0.0709724i) q^{19} +(2.56969 + 0.370684i) q^{20} +(-4.88114 + 4.88114i) q^{21} +(7.60852 - 2.53040i) q^{22} +4.88966i q^{23} +(4.20483 - 6.04712i) q^{24} +3.31482i q^{25} +(0.446296 + 1.34195i) q^{26} +(1.43814 - 1.43814i) q^{27} +(4.24574 - 3.17524i) q^{28} +(4.01444 + 4.01444i) q^{29} +(-4.27448 - 2.14089i) q^{30} -3.70615 q^{31} +(-3.85949 + 4.13574i) q^{32} -14.7643 q^{33} +(-5.66441 - 2.83705i) q^{34} +(-2.43331 - 2.43331i) q^{35} +(-6.05584 + 4.52896i) q^{36} +(7.16769 - 7.16769i) q^{37} +(0.0447948 + 0.134691i) q^{38} -2.60404i q^{39} +(3.01456 + 2.09616i) q^{40} +5.68585i q^{41} +(-9.26343 + 3.08078i) q^{42} +(-7.21825 + 7.21825i) q^{43} +(11.2234 + 1.61899i) q^{44} +(3.47071 + 3.47071i) q^{45} +(-3.09672 + 6.18287i) q^{46} -4.79958 q^{47} +(9.14668 - 4.98344i) q^{48} -0.0271196 q^{49} +(-2.09934 + 4.19151i) q^{50} +(8.24852 + 8.24852i) q^{51} +(-0.285549 + 1.97951i) q^{52} +(1.67421 - 1.67421i) q^{53} +(2.72930 - 0.907693i) q^{54} -7.36018i q^{55} +(7.37959 - 1.32612i) q^{56} -0.261368i q^{57} +(2.53375 + 7.61860i) q^{58} +(4.64659 - 4.64659i) q^{59} +(-4.04911 - 5.41422i) q^{60} +(-4.25448 - 4.25448i) q^{61} +(-4.68634 - 2.34718i) q^{62} +10.0230 q^{63} +(-7.49949 + 2.78527i) q^{64} +1.29815 q^{65} +(-18.6691 - 9.35052i) q^{66} +(-4.79556 - 4.79556i) q^{67} +(-5.36577 - 7.17477i) q^{68} +(9.00350 - 9.00350i) q^{69} +(-1.53580 - 4.61793i) q^{70} +1.02247i q^{71} +(-10.5258 + 1.89149i) q^{72} -4.54132i q^{73} +(13.6028 - 4.52395i) q^{74} +(6.10369 - 6.10369i) q^{75} +(-0.0286606 + 0.198684i) q^{76} +(-10.6277 - 10.6277i) q^{77} +(1.64919 - 3.29275i) q^{78} +11.5463 q^{79} +(2.48431 + 4.55973i) q^{80} +6.04690 q^{81} +(-3.60096 + 7.18963i) q^{82} +(9.06663 + 9.06663i) q^{83} +(-13.6645 - 1.97114i) q^{84} +(-4.11199 + 4.11199i) q^{85} +(-13.6988 + 4.55586i) q^{86} -14.7839i q^{87} +(13.1663 + 9.15516i) q^{88} +14.5022i q^{89} +(2.19057 + 6.58671i) q^{90} +(1.87445 - 1.87445i) q^{91} +(-7.83147 + 5.85689i) q^{92} +(6.82426 + 6.82426i) q^{93} +(-6.06896 - 3.03967i) q^{94} +0.130295 q^{95} +(14.7219 - 0.508682i) q^{96} +3.70580 q^{97} +(-0.0342921 - 0.0171754i) q^{98} +(15.1586 + 15.1586i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) $ 48 * q - 4 * q^4 - 12 * q^8	$ 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) $ 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/208\mathbb{Z}\right)^\times$.

$n$	$53$	$79$	$145$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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 $

$2$	1.26448	+	0.633320i	0.894121	+	0.447825i
$2$	1.26448	+	0.633320i	0.894121	+	0.447825i
$3$	−1.84134	−	1.84134i	−1.06310	−	1.06310i	−0.997871	−	0.0652247i	$-0.979224\pi$
$3$	−1.84134	−	1.84134i	−1.06310	−	1.06310i	−0.0652247	−	0.997871i	$-0.520776\pi$
$4$	1.19781	+	1.60164i	0.598906	+	0.800819i
$5$	0.917928	−	0.917928i	0.410510	−	0.410510i	−0.471406	−	0.881916i	$-0.656253\pi$
$5$	0.917928	−	0.917928i	0.410510	−	0.410510i	0.881916	+	0.471406i	$0.156253\pi$
$6$	−1.16217	−	3.49448i	−0.474456	−	1.42662i
$7$		−	2.65087i		−	1.00194i	−0.865466	−	0.500968i	$-0.832978\pi$
$7$		−	2.65087i		−	1.00194i	0.865466	−	0.500968i	$-0.167022\pi$
$8$	0.500257	+	2.78384i	0.176868	+	0.984235i
$9$			3.78103i			1.26034i
$10$	1.74204	−	0.579358i	0.550882	−	0.183209i
$11$	4.00913	−	4.00913i	1.20880	−	1.20880i	0.237381	−	0.971417i	$-0.423711\pi$
$11$	4.00913	−	4.00913i	1.20880	−	1.20880i	0.971417	−	0.237381i	$-0.0762889\pi$
$12$	0.743581	−	5.15473i	0.214653	−	1.48804i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$13$	0.707107	+	0.707107i	0.196116	+	0.196116i
$14$	1.67885	−	3.35197i	0.448691	−	0.895852i
$15$	−3.38043			−0.872822
$16$	−1.13049	+	3.83692i	−0.282624	+	0.959231i
$17$	−4.47964			−1.08647			−0.543236	−	0.839580i	$-0.682801\pi$
$17$	−4.47964			−1.08647			−0.543236	+	0.839580i	$0.682801\pi$
$18$	−2.39460	+	4.78103i	−0.564413	+	1.12690i
$19$	0.0709724	+	0.0709724i	0.0162822	+	0.0162822i	0.715201	−	0.698919i	$-0.246335\pi$
$19$	0.0709724	+	0.0709724i	0.0162822	+	0.0162822i	−0.698919	+	0.715201i	$0.746335\pi$
$20$	2.56969	+	0.370684i	0.574601	+	0.0828875i
$21$	−4.88114	+	4.88114i	−1.06515	+	1.06515i
$22$	7.60852	−	2.53040i	1.62214	−	0.539482i
$23$			4.88966i			1.01956i	0.860303	+	0.509782i	$0.170274\pi$
$23$			4.88966i			1.01956i	−0.860303	+	0.509782i	$0.829726\pi$
$24$	4.20483	−	6.04712i	0.858308	−	1.23436i
$25$			3.31482i			0.662963i
$26$	0.446296	+	1.34195i	0.0875259	+	0.263177i
$27$	1.43814	−	1.43814i	0.276770	−	0.276770i
$28$	4.24574	−	3.17524i	0.802369	−	0.600065i
$29$	4.01444	+	4.01444i	0.745463	+	0.745463i	0.973624	−	0.228161i	$-0.0732711\pi$
$29$	4.01444	+	4.01444i	0.745463	+	0.745463i	−0.228161	+	0.973624i	$0.573271\pi$
$30$	−4.27448	−	2.14089i	−0.780409	−	0.390871i
$31$	−3.70615			−0.665644			−0.332822	−	0.942990i	$-0.608001\pi$
$31$	−3.70615			−0.665644			−0.332822	+	0.942990i	$0.608001\pi$
$32$	−3.85949	+	4.13574i	−0.682267	+	0.731103i
$33$	−14.7643			−2.57013
$34$	−5.66441	−	2.83705i	−0.971438	−	0.486549i
$35$	−2.43331	−	2.43331i	−0.411304	−	0.411304i
$36$	−6.05584	+	4.52896i	−1.00931	+	0.754827i
$37$	7.16769	−	7.16769i	1.17836	−	1.17836i	0.198199	−	0.980162i	$-0.436491\pi$
$37$	7.16769	−	7.16769i	1.17836	−	1.17836i	0.980162	−	0.198199i	$-0.0635091\pi$
$38$	0.0447948	+	0.134691i	0.00726668	+	0.0218498i
$39$		−	2.60404i		−	0.416980i
$40$	3.01456	+	2.09616i	0.476644	+	0.331432i
$41$			5.68585i			0.887980i	0.896032	+	0.443990i	$0.146437\pi$
$41$			5.68585i			0.887980i	−0.896032	+	0.443990i	$0.853563\pi$
$42$	−9.26343	+	3.08078i	−1.42938	+	0.475374i
$43$	−7.21825	+	7.21825i	−1.10077	+	1.10077i	−0.106455	+	0.994318i	$0.533950\pi$
$43$	−7.21825	+	7.21825i	−1.10077	+	1.10077i	−0.994318	+	0.106455i	$0.966050\pi$
$44$	11.2234	+	1.61899i	1.69198	+	0.244073i
$45$	3.47071	+	3.47071i	0.517383	+	0.517383i
$46$	−3.09672	+	6.18287i	−0.456586	+	0.911614i
$47$	−4.79958			−0.700090			−0.350045	−	0.936733i	$-0.613834\pi$
$47$	−4.79958			−0.700090			−0.350045	+	0.936733i	$0.613834\pi$
$48$	9.14668	−	4.98344i	1.32021	−	0.719298i
$49$	−0.0271196			−0.00387422
$50$	−2.09934	+	4.19151i	−0.296891	+	0.592770i
$51$	8.24852	+	8.24852i	1.15502	+	1.15502i
$52$	−0.285549	+	1.97951i	−0.0395985	+	0.274509i
$53$	1.67421	−	1.67421i	0.229970	−	0.229970i	−0.582710	−	0.812680i	$-0.698008\pi$
$53$	1.67421	−	1.67421i	0.229970	−	0.229970i	0.812680	+	0.582710i	$0.198008\pi$
$54$	2.72930	−	0.907693i	0.371410	−	0.123521i
$55$		−	7.36018i		−	0.992447i
$56$	7.37959	−	1.32612i	0.986139	−	0.177210i
$57$		−	0.261368i		−	0.0346190i
$58$	2.53375	+	7.61860i	0.332697	+	1.00037i
$59$	4.64659	−	4.64659i	0.604934	−	0.604934i	−0.336684	−	0.941618i	$-0.609305\pi$
$59$	4.64659	−	4.64659i	0.604934	−	0.604934i	0.941618	+	0.336684i	$0.109305\pi$
$60$	−4.04911	−	5.41422i	−0.522738	−	0.698973i
$61$	−4.25448	−	4.25448i	−0.544731	−	0.544731i	0.380181	−	0.924912i	$-0.375862\pi$
$61$	−4.25448	−	4.25448i	−0.544731	−	0.544731i	−0.924912	+	0.380181i	$0.875862\pi$
$62$	−4.68634	−	2.34718i	−0.595166	−	0.298092i
$63$	10.0230			1.26278
$64$	−7.49949	+	2.78527i	−0.937436	+	0.348159i
$65$	1.29815			0.161015
$66$	−18.6691	−	9.35052i	−2.29801	−	1.15097i
$67$	−4.79556	−	4.79556i	−0.585871	−	0.585871i	0.350640	−	0.936510i	$-0.385964\pi$
$67$	−4.79556	−	4.79556i	−0.585871	−	0.585871i	−0.936510	+	0.350640i	$0.885964\pi$
$68$	−5.36577	−	7.17477i	−0.650695	−	0.870068i
$69$	9.00350	−	9.00350i	1.08389	−	1.08389i
$70$	−1.53580	−	4.61793i	−0.183564	−	0.551948i
$71$			1.02247i			0.121345i	0.998158	+	0.0606727i	$0.0193246\pi$
$71$			1.02247i			0.121345i	−0.998158	+	0.0606727i	$0.980675\pi$
$72$	−10.5258	+	1.89149i	−1.24047	+	0.222914i
$73$		−	4.54132i		−	0.531521i	−0.964039	−	0.265761i	$-0.914377\pi$
$73$		−	4.54132i		−	0.531521i	0.964039	−	0.265761i	$-0.0856231\pi$
$74$	13.6028	−	4.52395i	1.58130	−	0.525898i
$75$	6.10369	−	6.10369i	0.704793	−	0.704793i
$76$	−0.0286606	+	0.198684i	−0.00328759	+	0.0227906i
$77$	−10.6277	−	10.6277i	−1.21114	−	1.21114i
$78$	1.64919	−	3.29275i	0.186734	−	0.372831i
$79$	11.5463			1.29906			0.649531	−	0.760335i	$-0.274965\pi$
$79$	11.5463			1.29906			0.649531	+	0.760335i	$0.274965\pi$
$80$	2.48431	+	4.55973i	0.277754	+	0.509794i
$81$	6.04690			0.671878
$82$	−3.60096	+	7.18963i	−0.397660	+	0.793962i
$83$	9.06663	+	9.06663i	0.995192	+	0.995192i	0.999988	−	0.00479648i	$-0.00152677\pi$
$83$	9.06663	+	9.06663i	0.995192	+	0.995192i	−0.00479648	+	0.999988i	$0.501527\pi$
$84$	−13.6645	−	1.97114i	−1.49092	−	0.215069i
$85$	−4.11199	+	4.11199i	−0.446008	+	0.446008i
$86$	−13.6988	+	4.55586i	−1.47718	+	0.491271i
$87$		−	14.7839i		−	1.58500i
$88$	13.1663	+	9.15516i	1.40354	+	0.975943i
$89$			14.5022i			1.53723i	0.639713	+	0.768614i	$0.279053\pi$
$89$			14.5022i			1.53723i	−0.639713	+	0.768614i	$0.720947\pi$
$90$	2.19057	+	6.58671i	0.230906	+	0.694301i
$91$	1.87445	−	1.87445i	0.196496	−	0.196496i
$92$	−7.83147	+	5.85689i	−0.816487	+	0.610623i
$93$	6.82426	+	6.82426i	0.707643	+	0.707643i
$94$	−6.06896	−	3.03967i	−0.625966	−	0.313518i
$95$	0.130295			0.0133680
$96$	14.7219	−	0.508682i	1.50255	−	0.0519171i
$97$	3.70580			0.376267			0.188133	−	0.982144i	$-0.439756\pi$
$97$	3.70580			0.376267			0.188133	+	0.982144i	$0.439756\pi$
$98$	−0.0342921	−	0.0171754i	−0.00346402	−	0.00173497i
$99$	15.1586	+	15.1586i	1.52350	+	1.52350i
$100$	−5.30914	+	3.97053i	−0.530914	+	0.397053i
$101$	7.30110	−	7.30110i	0.726487	−	0.726487i	−0.243432	−	0.969918i	$-0.578273\pi$
$101$	7.30110	−	7.30110i	0.726487	−	0.726487i	0.969918	+	0.243432i	$0.0782731\pi$
$102$	5.20612	+	15.6540i	0.515483	+	1.54998i
$103$		−	9.23250i		−	0.909706i	−0.890567	−	0.454853i	$-0.849692\pi$
$103$		−	9.23250i		−	0.909706i	0.890567	−	0.454853i	$-0.150308\pi$
$104$	−1.61473	+	2.32220i	−0.158338	+	0.227711i
$105$			8.96108i			0.874511i
$106$	3.17731	−	1.05669i	0.308607	−	0.102635i
$107$	−10.3092	+	10.3092i	−0.996623	+	0.996623i	−0.999994	−	0.00337103i	$-0.998927\pi$
$107$	−10.3092	+	10.3092i	−0.996623	+	0.996623i	0.00337103	+	0.999994i	$0.498927\pi$
$108$	4.02600	+	0.580759i	0.387402	+	0.0558836i
$109$	−9.18172	−	9.18172i	−0.879449	−	0.879449i	0.114028	−	0.993478i	$-0.463625\pi$
$109$	−9.18172	−	9.18172i	−0.879449	−	0.879449i	−0.993478	+	0.114028i	$0.963625\pi$
$110$	4.66135	−	9.30679i	0.444442	−	0.887368i
$111$	−26.3962			−2.50542
$112$	10.1712	+	2.99679i	0.961087	+	0.283170i
$113$	−8.04305			−0.756627			−0.378313	−	0.925678i	$-0.623496\pi$
$113$	−8.04305			−0.756627			−0.378313	+	0.925678i	$0.623496\pi$
$114$	0.165530	−	0.330494i	0.0155033	−	0.0309536i
$115$	4.48836	+	4.48836i	0.418541	+	0.418541i
$116$	−1.62114	+	11.2382i	−0.150519	+	1.04344i
$117$	−2.67359	+	2.67359i	−0.247174	+	0.247174i
$118$	8.81828	−	2.93273i	0.811789	−	0.269980i
$119$			11.8750i			1.08858i
$120$	−1.69108	−	9.41055i	−0.154374	−	0.859062i
$121$		−	21.1462i		−	1.92238i
$122$	−2.68525	−	8.07415i	−0.243111	−	0.730999i
$123$	10.4696	−	10.4696i	0.944008	−	0.944008i
$124$	−4.43927	−	5.93591i	−0.398658	−	0.533061i
$125$	7.63240	+	7.63240i	0.682663	+	0.682663i
$126$	12.6739	+	6.34778i	1.12908	+	0.565505i
$127$	−11.2656			−0.999658			−0.499829	−	0.866124i	$-0.666604\pi$
$127$	−11.2656			−0.999658			−0.499829	+	0.866124i	$0.666604\pi$
$128$	−11.2469	−	1.22766i	−0.994095	−	0.108511i
$129$	26.5824			2.34045
$130$	1.64148	+	0.822142i	0.143967	+	0.0721066i
$131$	1.42059	+	1.42059i	0.124117	+	0.124117i	0.766437	−	0.642320i	$-0.222028\pi$
$131$	1.42059	+	1.42059i	0.124117	+	0.124117i	−0.642320	+	0.766437i	$0.722028\pi$
$132$	−17.6848	−	23.6471i	−1.53927	−	2.05821i
$133$	0.188139	−	0.188139i	0.0163137	−	0.0163137i
$134$	−3.02676	−	9.10100i	−0.261472	−	0.786207i
$135$		−	2.64021i		−	0.227233i
$136$	−2.24097	−	12.4706i	−0.192162	−	1.06934i
$137$			6.40523i			0.547236i	0.961838	+	0.273618i	$0.0882204\pi$
$137$			6.40523i			0.547236i	−0.961838	+	0.273618i	$0.911780\pi$
$138$	17.0868	−	5.68264i	1.45453	−	0.483738i
$139$	−12.3442	+	12.3442i	−1.04702	+	1.04702i	−0.0481825	+	0.998839i	$0.515343\pi$
$139$	−12.3442	+	12.3442i	−1.04702	+	1.04702i	−0.998839	+	0.0481825i	$0.984657\pi$
$140$	0.982636	−	6.81193i	0.0830479	−	0.575713i
$141$	8.83763	+	8.83763i	0.744263	+	0.744263i
$142$	−0.647554	+	1.29290i	−0.0543415	+	0.108498i
$143$	5.66976			0.474129
$144$	−14.5075	−	4.27443i	−1.20896	−	0.356203i
$145$	7.36993			0.612040
$146$	2.87611	−	5.74240i	0.238028	−	0.475245i
$147$	0.0499362	+	0.0499362i	0.00411867	+	0.00411867i
$148$	20.0656	+	2.89451i	1.64938	+	0.237927i
$149$	−9.58811	+	9.58811i	−0.785489	+	0.785489i	−0.980751	−	0.195262i	$-0.937444\pi$
$149$	−9.58811	+	9.58811i	−0.785489	+	0.785489i	0.195262	+	0.980751i	$0.437444\pi$
$150$	11.5836	−	3.85239i	0.945794	−	0.314547i
$151$		−	13.7871i		−	1.12198i	−0.827822	−	0.560991i	$-0.810420\pi$
$151$		−	13.7871i		−	1.12198i	0.827822	−	0.560991i	$-0.189580\pi$
$152$	−0.162071	+	0.233080i	−0.0131457	+	0.0189053i
$153$		−	16.9377i		−	1.36933i
$154$	−6.70775	−	20.1692i	−0.540526	−	1.62528i
$155$	−3.40198	+	3.40198i	−0.273253	+	0.273253i
$156$	4.17073	−	3.11915i	0.333926	−	0.249732i
$157$	−7.41316	−	7.41316i	−0.591635	−	0.591635i	0.346438	−	0.938073i	$-0.387391\pi$
$157$	−7.41316	−	7.41316i	−0.591635	−	0.591635i	−0.938073	+	0.346438i	$0.887391\pi$
$158$	14.6001	+	7.31251i	1.16152	+	0.581752i
$159$	−6.16555			−0.488960
$160$	0.253584	+	7.33904i	0.0200476	+	0.580202i
$161$	12.9619			1.02154
$162$	7.64618	+	3.82962i	0.600740	+	0.300884i
$163$	−13.0609	−	13.0609i	−1.02301	−	1.02301i	−0.999729	−	0.0232787i	$-0.992590\pi$
$163$	−13.0609	−	13.0609i	−1.02301	−	1.02301i	−0.0232787	−	0.999729i	$-0.507410\pi$
$164$	−9.10667	+	6.81057i	−0.711112	+	0.531817i
$165$	−13.5526	+	13.5526i	−1.05507	+	1.05507i
$166$	5.72248	+	17.2066i	0.444151	+	1.33549i
$167$		−	11.9255i		−	0.922823i	−0.887186	−	0.461411i	$-0.847343\pi$
$167$		−	11.9255i		−	0.922823i	0.887186	−	0.461411i	$-0.152657\pi$
$168$	−16.0301	−	11.1465i	−1.23675	−	0.859969i
$169$			1.00000i			0.0769231i
$170$	−7.80372	+	2.59532i	−0.598518	+	0.199052i
$171$	−0.268349	+	0.268349i	−0.0205211	+	0.0205211i
$172$	−20.2071	−	2.91492i	−1.54078	−	0.222261i
$173$	−4.88723	−	4.88723i	−0.371569	−	0.371569i	0.496479	−	0.868049i	$-0.334626\pi$
$173$	−4.88723	−	4.88723i	−0.371569	−	0.371569i	−0.868049	+	0.496479i	$0.834626\pi$
$174$	9.36291	−	18.6939i	0.709801	−	1.41718i
$175$	8.78715			0.664246
$176$	10.8504	+	19.9150i	0.817881	+	1.50115i
$177$	−17.1118			−1.28621
$178$	−9.18452	+	18.3377i	−0.688409	+	1.37447i
$179$	−1.26880	−	1.26880i	−0.0948344	−	0.0948344i	0.658098	−	0.752932i	$-0.271361\pi$
$179$	−1.26880	−	1.26880i	−0.0948344	−	0.0948344i	−0.752932	+	0.658098i	$0.771361\pi$
$180$	−1.40157	+	9.71609i	−0.104467	+	0.724195i
$181$	11.0932	−	11.0932i	0.824552	−	0.824552i	−0.162205	−	0.986757i	$-0.551861\pi$
$181$	11.0932	−	11.0932i	0.824552	−	0.824552i	0.986757	+	0.162205i	$0.0518606\pi$
$182$	3.55733	−	1.18307i	0.263687	−	0.0876953i
$183$			15.6679i			1.15820i
$184$	−13.6120	+	2.44609i	−1.00349	+	0.180328i
$185$		−	13.1588i		−	0.967457i
$186$	4.30719	+	12.9511i	0.315819	+	0.949619i
$187$	−17.9595	+	17.9595i	−1.31333	+	1.31333i
$188$	−5.74899	−	7.68719i	−0.419288	−	0.560646i
$189$	−3.81232	−	3.81232i	−0.277305	−	0.277305i
$190$	0.164755	+	0.0825185i	0.0119526	+	0.00598652i
$191$	1.88207			0.136182			0.0680910	−	0.997679i	$-0.478309\pi$
$191$	1.88207			0.136182			0.0680910	+	0.997679i	$0.478309\pi$
$192$	18.9377	+	8.68045i	1.36671	+	0.626458i
$193$	−12.2519			−0.881908			−0.440954	−	0.897530i	$-0.645360\pi$
$193$	−12.2519			−0.881908			−0.440954	+	0.897530i	$0.645360\pi$
$194$	4.68590	+	2.34695i	0.336428	+	0.168501i
$195$	−2.39032	−	2.39032i	−0.171175	−	0.171175i
$196$	−0.0324841	−	0.0434357i	−0.00232029	−	0.00310255i
$197$	10.7167	−	10.7167i	0.763531	−	0.763531i	−0.213428	−	0.976959i	$-0.568463\pi$
$197$	10.7167	−	10.7167i	0.763531	−	0.763531i	0.976959	+	0.213428i	$0.0684628\pi$
$198$	9.56750	+	28.7680i	0.679933	+	2.04445i
$199$			17.2070i			1.21977i	0.792489	+	0.609886i	$0.208785\pi$
$199$			17.2070i			1.21977i	−0.792489	+	0.609886i	$0.791215\pi$
$200$	−9.22790	+	1.65826i	−0.652511	+	0.117257i
$201$			17.6605i			1.24567i
$202$	13.8560	−	4.60815i	0.974906	−	0.324228i
$203$	10.6418	−	10.6418i	0.746906	−	0.746906i
$204$	−3.33098	+	23.0913i	−0.233215	+	1.61672i
$205$	5.21920	+	5.21920i	0.364525	+	0.364525i
$206$	5.84713	−	11.6743i	0.407389	−	0.813387i
$207$	−18.4879			−1.28500
$208$	−3.51249	+	1.91373i	−0.243548	+	0.132694i
$209$	0.569075			0.0393637
$210$	−5.67523	+	11.3311i	−0.391628	+	0.781919i
$211$	−0.662418	−	0.662418i	−0.0456027	−	0.0456027i	0.683938	−	0.729540i	$-0.260266\pi$
$211$	−0.662418	−	0.662418i	−0.0456027	−	0.0456027i	−0.729540	+	0.683938i	$0.760266\pi$
$212$	4.68686	+	0.676090i	0.321895	+	0.0464341i
$213$	1.88272	−	1.88272i	0.129002	−	0.129002i
$214$	−19.5647	+	6.50671i	−1.33741	+	0.444789i
$215$			13.2517i			0.903756i
$216$	4.72298	+	3.28410i	0.321358	+	0.223455i
$217$			9.82452i			0.666932i
$218$	−5.79512	−	17.4251i	−0.392495	−	1.18017i
$219$	−8.36209	+	8.36209i	−0.565058	+	0.565058i
$220$	11.7884	−	8.81611i	0.794771	−	0.594382i
$221$	−3.16758	−	3.16758i	−0.213075	−	0.213075i
$222$	−33.3775	−	16.7173i	−2.24015	−	1.12199i
$223$	6.72744			0.450502			0.225251	−	0.974301i	$-0.427680\pi$
$223$	6.72744			0.450502			0.225251	+	0.974301i	$0.427680\pi$
$224$	10.9633	+	10.2310i	0.732518	+	0.683588i
$225$	−12.5334			−0.835561
$226$	−10.1703	−	5.09382i	−0.676516	−	0.338836i
$227$	8.33225	+	8.33225i	0.553031	+	0.553031i	0.927314	−	0.374284i	$-0.122111\pi$
$227$	8.33225	+	8.33225i	0.553031	+	0.553031i	−0.374284	+	0.927314i	$0.622111\pi$
$228$	0.418617	−	0.313070i	0.0277236	−	0.0207335i
$229$	7.47698	−	7.47698i	0.494093	−	0.494093i	−0.415500	−	0.909593i	$-0.636393\pi$
$229$	7.47698	−	7.47698i	0.494093	−	0.494093i	0.909593	+	0.415500i	$0.136393\pi$
$230$	2.83286	+	8.51799i	0.186794	+	0.561660i
$231$			39.1382i			2.57511i
$232$	−9.16729	+	13.1838i	−0.601862	+	0.865559i
$233$			8.36515i			0.548019i	0.961727	+	0.274010i	$0.0883500\pi$
$233$			8.36515i			0.548019i	−0.961727	+	0.274010i	$0.911650\pi$
$234$	−5.07394	+	1.68746i	−0.331694	+	0.110313i
$235$	−4.40567	+	4.40567i	−0.287394	+	0.287394i
$236$	13.0079	+	1.87642i	0.846741	+	0.122144i
$237$	−21.2606	−	21.2606i	−1.38103	−	1.38103i
$238$	−7.52064	+	15.0156i	−0.487491	+	0.973318i
$239$	26.2676			1.69911			0.849554	−	0.527502i	$-0.176871\pi$
$239$	26.2676			1.69911			0.849554	+	0.527502i	$0.176871\pi$
$240$	3.82155	−	12.9704i	0.246680	−	0.837238i
$241$	−16.0377			−1.03308			−0.516539	−	0.856264i	$-0.672780\pi$
$241$	−16.0377			−1.03308			−0.516539	+	0.856264i	$0.672780\pi$
$242$	13.3923	−	26.7389i	0.860891	−	1.71884i
$243$	−15.4488	−	15.4488i	−0.991040	−	0.991040i
$244$	1.71808	−	11.9102i	0.109989	−	0.762474i
$245$	−0.0248938	+	0.0248938i	−0.00159041	+	0.00159041i
$246$	19.8691	−	6.60795i	1.26681	−	0.421307i
$247$			0.100370i			0.00638640i
$248$	−1.85403	−	10.3173i	−0.117731	−	0.655150i
$249$		−	33.3894i		−	2.11597i
$250$	4.81726	+	14.4848i	0.304670	+	0.916097i
$251$	−17.9162	+	17.9162i	−1.13086	+	1.13086i	−0.140823	+	0.990035i	$0.544975\pi$
$251$	−17.9162	+	17.9162i	−1.13086	+	1.13086i	−0.990035	+	0.140823i	$0.955025\pi$
$252$	12.0057	+	16.0533i	0.756288	+	1.01126i
$253$	19.6033	+	19.6033i	1.23245	+	1.23245i
$254$	−14.2451	−	7.13471i	−0.893816	−	0.447672i
$255$	15.1431			0.948297
$256$	−13.4440	−	8.67524i	−0.840248	−	0.542202i
$257$	−5.05883			−0.315561			−0.157781	−	0.987474i	$-0.550434\pi$
$257$	−5.05883			−0.315561			−0.157781	+	0.987474i	$0.550434\pi$
$258$	33.6129	+	16.8352i	2.09265	+	1.04811i
$259$	−19.0006	−	19.0006i	−1.18064	−	1.18064i
$260$	1.55493	+	2.07916i	0.0964330	+	0.128944i
$261$	−15.1787	+	15.1787i	−0.939539	+	0.939539i
$262$	0.896615	+	2.69599i	0.0553931	+	0.166559i
$263$			15.7728i			0.972594i	0.873793	+	0.486297i	$0.161653\pi$
$263$			15.7728i			0.972594i	−0.873793	+	0.486297i	$0.838347\pi$
$264$	−7.38595	−	41.1014i	−0.454574	−	2.52961i
$265$		−	3.07360i		−	0.188810i
$266$	0.357049	−	0.118745i	0.0218921	−	0.00728074i
$267$	26.7034	−	26.7034i	1.63422	−	1.63422i
$268$	1.93658	−	13.4249i	0.118295	−	0.820058i
$269$	−18.9245	−	18.9245i	−1.15385	−	1.15385i	−0.985775	−	0.168073i	$-0.946246\pi$
$269$	−18.9245	−	18.9245i	−1.15385	−	1.15385i	−0.168073	−	0.985775i	$-0.553754\pi$
$270$	1.67210	−	3.33849i	0.101761	−	0.203174i
$271$	−15.2188			−0.924474			−0.462237	−	0.886756i	$-0.652953\pi$
$271$	−15.2188			−0.924474			−0.462237	+	0.886756i	$0.652953\pi$
$272$	5.06421	−	17.1880i	0.307063	−	1.04218i
$273$	−6.90298			−0.417787
$274$	−4.05656	+	8.09928i	−0.245066	+	0.489295i
$275$	13.2895	+	13.2895i	0.801388	+	0.801388i
$276$	25.2049	+	3.63586i	1.51715	+	0.218853i
$277$	12.5950	−	12.5950i	0.756762	−	0.756762i	−0.218970	−	0.975732i	$-0.570270\pi$
$277$	12.5950	−	12.5950i	0.756762	−	0.756762i	0.975732	+	0.218970i	$0.0702696\pi$
$278$	−23.4268	+	7.79115i	−1.40505	+	0.467282i
$279$		−	14.0131i		−	0.838940i
$280$	5.55665	−	7.99121i	0.332074	−	0.477566i
$281$		−	17.3966i		−	1.03779i	−0.854837	−	0.518897i	$-0.826343\pi$
$281$		−	17.3966i		−	1.03779i	0.854837	−	0.518897i	$-0.173657\pi$
$282$	5.57795	+	16.7720i	0.332162	+	0.998761i
$283$	21.8585	−	21.8585i	1.29936	−	1.29936i	0.370538	−	0.928817i	$-0.379173\pi$
$283$	21.8585	−	21.8585i	1.29936	−	1.29936i	0.928817	−	0.370538i	$-0.120827\pi$
$284$	−1.63764	+	1.22473i	−0.0971758	+	0.0726745i
$285$	−0.239917	−	0.239917i	−0.0142115	−	0.0142115i
$286$	7.16929	+	3.59077i	0.423929	+	0.212327i
$287$	15.0725			0.889699
$288$	−15.6374	−	14.5928i	−0.921441	−	0.859891i
$289$	3.06718			0.180422
$290$	9.31912	+	4.66753i	0.547238	+	0.274087i
$291$	−6.82361	−	6.82361i	−0.400007	−	0.400007i
$292$	7.27356	−	5.43965i	0.425653	−	0.318331i
$293$	−2.46209	+	2.46209i	−0.143837	+	0.143837i	−0.775358	−	0.631521i	$-0.782431\pi$
$293$	−2.46209	+	2.46209i	−0.143837	+	0.143837i	0.631521	+	0.775358i	$0.282431\pi$
$294$	0.0315177	+	0.0947688i	0.00183815	+	0.00552703i
$295$		−	8.53046i		−	0.496663i
$296$	23.5394	+	16.3680i	1.36820	+	0.951369i
$297$		−	11.5314i		−	0.669117i
$298$	−18.1963	+	6.05162i	−1.05408	+	0.350561i
$299$	−3.45751	+	3.45751i	−0.199953	+	0.199953i
$300$	17.0870	+	2.46483i	0.986517	+	0.142307i
$301$	19.1346	+	19.1346i	1.10290	+	1.10290i
$302$	8.73167	−	17.4335i	0.502451	−	1.00319i
$303$	−26.8875			−1.54465
$304$	−0.352549	+	0.192082i	−0.0202201	+	0.0110166i
$305$	−7.81062			−0.447235
$306$	10.7270	−	21.4173i	0.613219	−	1.22435i
$307$	−10.1354	−	10.1354i	−0.578455	−	0.578455i	0.356022	−	0.934477i	$-0.384133\pi$
$307$	−10.1354	−	10.1354i	−0.578455	−	0.578455i	−0.934477	+	0.356022i	$0.884133\pi$
$308$	4.29175	−	29.7517i	0.244545	−	1.69526i
$309$	−17.0001	+	17.0001i	−0.967104	+	0.967104i
$310$	−6.45627	+	2.14719i	−0.366691	+	0.121952i
$311$			10.6455i			0.603652i	0.953363	+	0.301826i	$0.0975962\pi$
$311$			10.6455i			0.603652i	−0.953363	+	0.301826i	$0.902404\pi$
$312$	7.24922	−	1.30269i	0.410406	−	0.0737503i
$313$			20.8984i			1.18125i	0.806947	+	0.590624i	$0.201118\pi$
$313$			20.8984i			1.18125i	−0.806947	+	0.590624i	$0.798882\pi$
$314$	−4.67888	−	14.0687i	−0.264045	−	0.793942i
$315$	9.20042	−	9.20042i	0.518385	−	0.518385i
$316$	13.8303	+	18.4930i	0.778016	+	1.04031i
$317$	−10.4525	−	10.4525i	−0.587072	−	0.587072i	0.349765	−	0.936837i	$-0.386261\pi$
$317$	−10.4525	−	10.4525i	−0.587072	−	0.587072i	−0.936837	+	0.349765i	$0.886261\pi$
$318$	−7.79621	−	3.90477i	−0.437190	−	0.218968i
$319$	32.1888			1.80223
$320$	−4.32731	+	9.44066i	−0.241904	+	0.527749i
$321$	37.9652			2.11901
$322$	16.3900	+	8.20900i	0.913379	+	0.457470i
$323$	−0.317931	−	0.317931i	−0.0176901	−	0.0176901i
$324$	7.24305	+	9.68495i	0.402392	+	0.538053i
$325$	−2.34393	+	2.34393i	−0.130018	+	0.130018i
$326$	−8.24349	−	24.7869i	−0.456565	−	1.37282i
$327$			33.8133i			1.86988i
$328$	−15.8285	+	2.84439i	−0.873981	+	0.157055i
$329$			12.7231i			0.701445i
$330$	−25.7200	+	8.55381i	−1.41584	+	0.470872i
$331$	1.17911	−	1.17911i	0.0648099	−	0.0648099i	−0.673959	−	0.738769i	$-0.735408\pi$
$331$	1.17911	−	1.17911i	0.0648099	−	0.0648099i	0.738769	+	0.673959i	$0.235408\pi$
$332$	−3.66135	+	25.3816i	−0.200943	+	1.39300i
$333$	27.1012	+	27.1012i	1.48514	+	1.48514i
$334$	7.55266	−	15.0795i	0.413263	−	0.825116i
$335$	−8.80396			−0.481011
$336$	−13.2105	−	24.2467i	−0.720690	−	1.32276i
$337$	10.9651			0.597305			0.298653	−	0.954362i	$-0.403463\pi$
$337$	10.9651			0.597305			0.298653	+	0.954362i	$0.403463\pi$
$338$	−0.633320	+	1.26448i	−0.0344481	+	0.0687786i
$339$	14.8100	+	14.8100i	0.804366	+	0.804366i
$340$	−11.5113	−	1.66053i	−0.624288	−	0.0900550i
$341$	−14.8584	+	14.8584i	−0.804629	+	0.804629i
$342$	−0.509272	+	0.169371i	−0.0275383	+	0.00915851i
$343$		−	18.4842i		−	0.998054i
$344$	−23.7054	−	16.4834i	−1.27811	−	0.888727i
$345$		−	16.5291i		−	0.889899i
$346$	−3.08462	−	9.27498i	−0.165830	−	0.498626i
$347$	22.2351	−	22.2351i	1.19364	−	1.19364i	0.217607	−	0.976037i	$-0.430175\pi$
$347$	22.2351	−	22.2351i	1.19364	−	1.19364i	0.976037	−	0.217607i	$-0.0698250\pi$
$348$	23.6784	−	17.7083i	1.26930	−	0.949264i
$349$	7.97504	+	7.97504i	0.426894	+	0.426894i	0.887569	−	0.460675i	$-0.152393\pi$
$349$	7.97504	+	7.97504i	0.426894	+	0.426894i	−0.460675	+	0.887569i	$0.652393\pi$
$350$	11.1112	+	5.56508i	0.593917	+	0.297466i
$351$	2.03383			0.108558
$352$	1.10755	+	32.0539i	0.0590326	+	1.70848i
$353$	23.6996			1.26140			0.630700	−	0.776027i	$-0.282768\pi$
$353$	23.6996			1.26140			0.630700	+	0.776027i	$0.282768\pi$
$354$	−21.6376	−	10.8373i	−1.15002	−	0.575995i
$355$	0.938558	+	0.938558i	0.0498135	+	0.0498135i
$356$	−23.2272	+	17.3709i	−1.23104	+	0.920655i
$357$	21.8658	−	21.8658i	1.15726	−	1.15726i
$358$	−0.800812	−	2.40792i	−0.0423243	−	0.127263i
$359$			23.5578i			1.24333i	0.783282	+	0.621667i	$0.213544\pi$
$359$			23.5578i			1.24333i	−0.783282	+	0.621667i	$0.786456\pi$
$360$	−7.92565	+	11.3981i	−0.417718	+	0.600735i
$361$		−	18.9899i		−	0.999470i
$362$	21.0527	−	7.00158i	1.10650	−	0.367995i
$363$	−38.9373	+	38.9373i	−2.04368	+	2.04368i
$364$	5.24743	+	0.756954i	0.275040	+	0.0396751i
$365$	−4.16861	−	4.16861i	−0.218195	−	0.218195i
$366$	−9.92277	+	19.8117i	−0.518671	+	1.03557i
$367$	5.73335			0.299279			0.149639	−	0.988741i	$-0.452189\pi$
$367$	5.73335			0.299279			0.149639	+	0.988741i	$0.452189\pi$
$368$	−18.7612	−	5.52773i	−0.977998	−	0.288153i
$369$	−21.4984			−1.11916
$370$	8.33376	−	16.6391i	0.433251	−	0.865024i
$371$	−4.43811	−	4.43811i	−0.230415	−	0.230415i
$372$	−2.75582	+	19.1042i	−0.142883	+	0.990506i
$373$	1.15194	−	1.15194i	0.0596453	−	0.0596453i	−0.676655	−	0.736300i	$-0.736571\pi$
$373$	1.15194	−	1.15194i	0.0596453	−	0.0596453i	0.736300	+	0.676655i	$0.236571\pi$
$374$	−34.0834	+	11.3353i	−1.76241	+	0.586132i
$375$		−	28.1076i		−	1.45147i
$376$	−2.40102	−	13.3612i	−0.123823	−	0.689053i
$377$			5.67728i			0.292395i
$378$	−2.40618	−	7.23501i	−0.123760	−	0.372129i
$379$	2.77349	−	2.77349i	0.142465	−	0.142465i	−0.632277	−	0.774742i	$-0.717880\pi$
$379$	2.77349	−	2.77349i	0.142465	−	0.142465i	0.774742	+	0.632277i	$0.217880\pi$
$380$	0.156069	+	0.208686i	0.00800617	+	0.0107053i
$381$	20.7437	+	20.7437i	1.06273	+	1.06273i
$382$	2.37984	+	1.19195i	0.121763	+	0.0609857i
$383$	13.8947			0.709986			0.354993	−	0.934869i	$-0.384483\pi$
$383$	13.8947			0.709986			0.354993	+	0.934869i	$0.384483\pi$
$384$	18.4488	+	22.9699i	0.941461	+	1.17218i
$385$	−19.5109			−0.994367
$386$	−15.4922	−	7.75935i	−0.788533	−	0.394940i
$387$	−27.2924	−	27.2924i	−1.38735	−	1.38735i
$388$	4.43885	+	5.93535i	0.225348	+	0.301322i
$389$	−19.4629	+	19.4629i	−0.986810	+	0.986810i	−0.999914	−	0.0131042i	$-0.995829\pi$
$389$	−19.4629	+	19.4629i	−0.986810	+	0.986810i	0.0131042	+	0.999914i	$0.495829\pi$
$390$	−1.50867	−	4.53635i	−0.0763946	−	0.229707i
$391$		−	21.9039i		−	1.10773i
$392$	−0.0135668	−	0.0754964i	−0.000685225	−	0.00381314i
$393$		−	5.23155i		−	0.263897i
$394$	20.3381	−	6.76392i	1.02462	−	0.340761i
$395$	10.5987	−	10.5987i	0.533278	−	0.533278i
$396$	−6.12147	+	42.4358i	−0.307615	+	2.13248i
$397$	23.3238	+	23.3238i	1.17059	+	1.17059i	0.982069	+	0.188521i	$0.0603693\pi$
$397$	23.3238	+	23.3238i	1.17059	+	1.17059i	0.188521	+	0.982069i	$0.439631\pi$
$398$	−10.8975	+	21.7579i	−0.546244	+	1.09062i
$399$	−0.692853			−0.0346860
$400$	−12.7187	−	3.74738i	−0.635935	−	0.187369i
$401$	−3.87470			−0.193493			−0.0967465	−	0.995309i	$-0.530844\pi$
$401$	−3.87470			−0.193493			−0.0967465	+	0.995309i	$0.530844\pi$
$402$	−11.1847	+	22.3313i	−0.557843	+	1.11378i
$403$	−2.62064	−	2.62064i	−0.130543	−	0.130543i
$404$	20.4391	+	2.94838i	1.01688	+	0.146688i
$405$	5.55062	−	5.55062i	0.275813	−	0.275813i
$406$	20.1959	−	6.71664i	1.00231	−	0.333341i
$407$		−	57.4723i		−	2.84880i
$408$	−18.8361	+	27.0889i	−0.932528	+	1.34110i
$409$			15.3816i			0.760573i	0.924869	+	0.380286i	$0.124175\pi$
$409$			15.3816i			0.760573i	−0.924869	+	0.380286i	$0.875825\pi$
$410$	3.29414	+	9.90499i	0.162686	+	0.489172i
$411$	11.7942	−	11.7942i	0.581764	−	0.581764i
$412$	14.7871	−	11.0588i	0.728510	−	0.544828i
$413$	−12.3175	−	12.3175i	−0.606105	−	0.606105i
$414$	−23.3776	−	11.7088i	−1.14895	−	0.575455i
$415$	16.6450			0.817072
$416$	−5.65348	+	0.195343i	−0.277185	+	0.00957749i
$417$	45.4596			2.22617
$418$	0.719583	+	0.360406i	0.0351959	+	0.0176281i
$419$	−10.3620	−	10.3620i	−0.506217	−	0.506217i	0.407146	−	0.913363i	$-0.366524\pi$
$419$	−10.3620	−	10.3620i	−0.506217	−	0.506217i	−0.913363	+	0.407146i	$0.866524\pi$
$420$	−14.3524	+	10.7337i	−0.700326	+	0.523750i
$421$	−8.91568	+	8.91568i	−0.434523	+	0.434523i	−0.890164	−	0.455640i	$-0.849410\pi$
$421$	−8.91568	+	8.91568i	−0.434523	+	0.434523i	0.455640	+	0.890164i	$0.349410\pi$
$422$	−0.418091	−	1.25714i	−0.0203523	−	0.0611964i
$423$		−	18.1473i		−	0.882354i
$424$	5.49825	+	3.82318i	0.267019	+	0.185670i
$425$		−	14.8492i		−	0.720291i
$426$	3.57302	−	1.18829i	0.173113	−	0.0575730i
$427$	−11.2781	+	11.2781i	−0.545785	+	0.545785i
$428$	−28.8600	−	4.16312i	−1.39500	−	0.201232i
$429$	−10.4399	−	10.4399i	−0.504045	−	0.504045i
$430$	−8.39254	+	16.7564i	−0.404724	+	0.808067i
$431$	−24.6916			−1.18935			−0.594676	−	0.803965i	$-0.702720\pi$
$431$	−24.6916			−1.18935			−0.594676	+	0.803965i	$0.702720\pi$
$432$	3.89222	+	7.14383i	0.187264	+	0.343708i
$433$	9.02297			0.433616			0.216808	−	0.976214i	$-0.430435\pi$
$433$	9.02297			0.433616			0.216808	+	0.976214i	$0.430435\pi$
$434$	−6.22207	+	12.4229i	−0.298669	+	0.596318i
$435$	−13.5705	−	13.5705i	−0.650657	−	0.650657i
$436$	3.70783	−	25.7038i	0.177573	−	1.23099i
$437$	−0.347031	+	0.347031i	−0.0166007	+	0.0166007i
$438$	−15.8696	+	5.27781i	−0.758277	+	0.252183i
$439$			5.23470i			0.249839i	0.992167	+	0.124919i	$0.0398672\pi$
$439$			5.23470i			0.249839i	−0.992167	+	0.124919i	$0.960133\pi$
$440$	20.4895	−	3.68198i	0.976800	−	0.175532i
$441$		−	0.102540i		−	0.00488285i
$442$	−1.99925	−	6.01144i	−0.0950945	−	0.285935i
$443$	15.2753	−	15.2753i	0.725752	−	0.725752i	−0.244018	−	0.969771i	$-0.578466\pi$
$443$	15.2753	−	15.2753i	0.725752	−	0.725752i	0.969771	+	0.244018i	$0.0784657\pi$
$444$	−31.6177	−	42.2772i	−1.50051	−	2.00639i
$445$	13.3120	+	13.3120i	0.631047	+	0.631047i
$446$	8.50670	+	4.26062i	0.402804	+	0.201746i
$447$	35.3099			1.67010
$448$	7.38339	+	19.8802i	0.348832	+	0.939250i
$449$	−6.25427			−0.295157			−0.147579	−	0.989050i	$-0.547148\pi$
$449$	−6.25427			−0.295157			−0.147579	+	0.989050i	$0.547148\pi$
$450$	−15.8482	−	7.93766i	−0.747093	−	0.374185i
$451$	22.7953	+	22.7953i	1.07339	+	1.07339i
$452$	−9.63406	−	12.8821i	−0.453148	−	0.605921i
$453$	−25.3867	+	25.3867i	−1.19277	+	1.19277i
$454$	5.25897	+	15.8129i	0.246816	+	0.742138i
$455$		−	3.44122i		−	0.161327i
$456$	0.727605	−	0.130751i	0.0340732	−	0.00612299i
$457$			1.30129i			0.0608719i	0.999537	+	0.0304359i	$0.00968956\pi$
$457$			1.30129i			0.0608719i	−0.999537	+	0.0304359i	$0.990310\pi$
$458$	14.1898	−	4.71916i	0.663046	−	0.220512i
$459$	−6.44234	+	6.44234i	−0.300703	+	0.300703i
$460$	−1.81252	+	12.5649i	−0.0845092	+	0.585843i
$461$	−17.0431	−	17.0431i	−0.793774	−	0.793774i	0.188331	−	0.982106i	$-0.439692\pi$
$461$	−17.0431	−	17.0431i	−0.793774	−	0.793774i	−0.982106	+	0.188331i	$0.939692\pi$
$462$	−24.7870	+	49.4895i	−1.15320	+	2.30246i
$463$	−1.92850			−0.0896251			−0.0448125	−	0.998995i	$-0.514269\pi$
$463$	−1.92850			−0.0896251			−0.0448125	+	0.998995i	$0.514269\pi$
$464$	−19.9414	+	10.8648i	−0.925756	+	0.504386i
$465$	12.5284			0.580989
$466$	−5.29782	+	10.5776i	−0.245417	+	0.489996i
$467$	−8.83169	−	8.83169i	−0.408682	−	0.408682i	0.472597	−	0.881279i	$-0.343317\pi$
$467$	−8.83169	−	8.83169i	−0.408682	−	0.408682i	−0.881279	+	0.472597i	$0.843317\pi$
$468$	−7.48459	−	1.07967i	−0.345975	−	0.0499077i
$469$	−12.7124	+	12.7124i	−0.587005	+	0.587005i
$470$	−8.36107	+	2.78067i	−0.385667	+	0.128263i
$471$			27.3002i			1.25793i
$472$	15.2598	+	10.6108i	0.702390	+	0.488404i
$473$			57.8777i			2.66122i
$474$	−13.4188	−	40.3484i	−0.616347	−	1.85326i
$475$	−0.235260	+	0.235260i	−0.0107945	+	0.0107945i
$476$	−19.0194	+	14.2240i	−0.871752	+	0.651954i
$477$	6.33023	+	6.33023i	0.289841	+	0.289841i
$478$	33.2148	+	16.6358i	1.51921	+	0.760903i
$479$	13.1434			0.600536			0.300268	−	0.953855i	$-0.402924\pi$
$479$	13.1434			0.600536			0.300268	+	0.953855i	$0.402924\pi$
$480$	13.0467	−	13.9806i	0.595498	−	0.638123i
$481$	10.1366			0.462191
$482$	−20.2793	−	10.1570i	−0.923697	−	0.462638i
$483$	−23.8671	−	23.8671i	−1.08599	−	1.08599i
$484$	33.8686	−	25.3292i	1.53948	−	1.15133i
$485$	3.40165	−	3.40165i	0.154461	−	0.154461i
$486$	−9.75063	−	29.3187i	−0.442298	−	1.32992i
$487$			18.9055i			0.856688i	0.903616	+	0.428344i	$0.140903\pi$
$487$			18.9055i			0.856688i	−0.903616	+	0.428344i	$0.859097\pi$
$488$	9.71545	−	13.9721i	0.439798	−	0.632488i
$489$			48.0989i			2.17511i
$490$	−0.0472434	+	0.0157119i	−0.00213424	+	0.000709793i
$491$	10.9449	−	10.9449i	0.493938	−	0.493938i	−0.415607	−	0.909544i	$-0.636431\pi$
$491$	10.9449	−	10.9449i	0.493938	−	0.493938i	0.909544	+	0.415607i	$0.136431\pi$
$492$	29.3090	+	4.22789i	1.32135	+	0.190608i
$493$	−17.9833	−	17.9833i	−0.809925	−	0.809925i
$494$	−0.0635664	+	0.126916i	−0.00285999	+	0.00571021i
$495$	27.8291			1.25082
$496$	4.18978	−	14.2202i	0.188127	−	0.638506i
$497$	2.71045			0.121580
$498$	21.1462	−	42.2202i	0.947583	−	1.89193i
$499$	6.33115	+	6.33115i	0.283421	+	0.283421i	0.834472	−	0.551051i	$-0.185773\pi$
$499$	6.33115	+	6.33115i	0.283421	+	0.283421i	−0.551051	+	0.834472i	$0.685773\pi$
$500$	−3.08217	+	21.3665i	−0.137839	+	0.955540i
$501$	−21.9588	+	21.9588i	−0.981049	+	0.981049i
$502$	−34.0013	+	11.3079i	−1.51755	+	0.504698i
$503$		−	11.8322i		−	0.527571i	−0.964581	−	0.263786i	$-0.915029\pi$
$503$		−	11.8322i		−	0.527571i	0.964581	−	0.263786i	$-0.0849711\pi$
$504$	5.01409	+	27.9025i	0.223345	+	1.24287i
$505$		−	13.4038i		−	0.596460i
$506$	12.3728	+	37.2031i	0.550037	+	1.65388i
$507$	1.84134	−	1.84134i	0.0817766	−	0.0817766i
$508$	−13.4940	−	18.0434i	−0.598701	−	0.800546i
$509$	−13.2572	−	13.2572i	−0.587617	−	0.587617i	0.349369	−	0.936985i	$-0.386396\pi$
$509$	−13.2572	−	13.2572i	−0.587617	−	0.587617i	−0.936985	+	0.349369i	$0.886396\pi$
$510$	19.1481	+	9.59042i	0.847893	+	0.424671i
$511$	−12.0385			−0.532550
$512$	−11.5054	−	19.4840i	−0.508472	−	0.861079i
$513$	0.204136			0.00901283
$514$	−6.39678	−	3.20386i	−0.282150	−	0.141316i
$515$	−8.47477	−	8.47477i	−0.373443	−	0.373443i
$516$	31.8407	+	42.5754i	1.40171	+	1.87428i
$517$	−19.2421	+	19.2421i	−0.846268	+	0.846268i
$518$	−11.9924	−	36.0593i	−0.526916	−	1.58436i
$519$			17.9981i			0.790027i
$520$	0.649407	+	3.61383i	0.0284784	+	0.158477i
$521$		−	30.1752i		−	1.32200i	−0.750386	−	0.660999i	$-0.770133\pi$
$521$		−	30.1752i		−	1.32200i	0.750386	−	0.660999i	$-0.229867\pi$
$522$	−28.8062	+	9.58018i	−1.26081	+	0.419313i
$523$	−12.3183	+	12.3183i	−0.538640	+	0.538640i	−0.923129	−	0.384489i	$-0.874378\pi$
$523$	−12.3183	+	12.3183i	−0.538640	+	0.538640i	0.384489	+	0.923129i	$0.374378\pi$
$524$	−0.573671	+	3.97686i	−0.0250610	+	0.173730i
$525$	−16.1801	−	16.1801i	−0.706157	−	0.706157i
$526$	−9.98925	+	19.9444i	−0.435552	+	0.869617i
$527$	16.6022			0.723204
$528$	16.6910	−	56.6495i	0.726380	−	2.46535i
$529$	−0.908770			−0.0395117
$530$	1.94657	−	3.88650i	0.0845538	−	0.168819i
$531$	17.5689	+	17.5689i	0.762425	+	0.762425i
$532$	0.526685	+	0.0759755i	0.0228347	+	0.00329396i
$533$	−4.02050	+	4.02050i	−0.174147	+	0.174147i
$534$	50.6776	−	16.8541i	2.19303	−	0.729346i
$535$			18.9261i			0.818247i
$536$	10.9510	−	15.7491i	0.473013	−	0.680256i
$537$			4.67256i			0.201636i
$538$	−11.9444	−	35.9149i	−0.514958	−	1.54840i
$539$	−0.108726	+	0.108726i	−0.00468315	+	0.00468315i
$540$	4.22867	−	3.16248i	0.181973	−	0.136091i
$541$	0.427575	+	0.427575i	0.0183829	+	0.0183829i	0.716238	−	0.697856i	$-0.245862\pi$
$541$	0.427575	+	0.427575i	0.0183829	+	0.0183829i	−0.697856	+	0.716238i	$0.745862\pi$
$542$	−19.2438	−	9.63835i	−0.826592	−	0.414002i
$543$	−40.8526			−1.75315
$544$	17.2891	−	18.5266i	0.741264	−	0.794323i
$545$	−16.8563			−0.722045
$546$	−8.72867	−	4.37179i	−0.373552	−	0.187096i
$547$	−6.25850	−	6.25850i	−0.267594	−	0.267594i	0.560536	−	0.828130i	$-0.310595\pi$
$547$	−6.25850	−	6.25850i	−0.267594	−	0.267594i	−0.828130	+	0.560536i	$0.810595\pi$
$548$	−10.2589	+	7.67226i	−0.438237	+	0.327743i
$549$	16.0863	−	16.0863i	0.686548	−	0.686548i
$550$	8.38780	+	25.2208i	0.357657	+	1.07542i
$551$			0.569829i			0.0242755i
$552$	29.5683	+	20.5602i	1.25851	+	0.875100i
$553$		−	30.6078i		−	1.30158i
$554$	23.9028	−	7.94946i	1.01553	−	0.337740i
$555$	−24.2298	+	24.2298i	−1.02850	+	1.02850i
$556$	−34.5570	−	4.98492i	−1.46554	−	0.211408i
$557$	−3.56231	−	3.56231i	−0.150940	−	0.150940i	0.627598	−	0.778538i	$-0.284038\pi$
$557$	−3.56231	−	3.56231i	−0.150940	−	0.150940i	−0.778538	+	0.627598i	$0.784038\pi$
$558$	8.87475	−	17.7192i	0.375698	−	0.750114i
$559$	−10.2081			−0.431758
$560$	12.0873	−	6.58558i	0.510780	−	0.278292i
$561$	66.1387			2.79238
$562$	11.0176	−	21.9976i	0.464750	−	0.927913i
$563$	18.5347	+	18.5347i	0.781142	+	0.781142i	0.980024	−	0.198881i	$-0.0637308\pi$
$563$	18.5347	+	18.5347i	0.781142	+	0.781142i	−0.198881	+	0.980024i	$0.563731\pi$
$564$	−3.56888	+	24.7405i	−0.150277	+	1.04176i
$565$	−7.38294	+	7.38294i	−0.310603	+	0.310603i
$566$	41.4831	−	13.7962i	1.74367	−	0.579898i
$567$		−	16.0296i		−	0.673178i
$568$	−2.84640	+	0.511500i	−0.119432	+	0.0214621i
$569$		−	10.8740i		−	0.455862i	−0.973677	−	0.227931i	$-0.926804\pi$
$569$		−	10.8740i		−	0.455862i	0.973677	−	0.227931i	$-0.0731961\pi$
$570$	−0.151426	−	0.455314i	−0.00634252	−	0.0190710i
$571$	−5.18170	+	5.18170i	−0.216847	+	0.216847i	−0.807168	−	0.590321i	$-0.799001\pi$
$571$	−5.18170	+	5.18170i	−0.216847	+	0.216847i	0.590321	+	0.807168i	$0.299001\pi$
$572$	6.79131	+	9.08091i	0.283959	+	0.379692i
$573$	−3.46553	−	3.46553i	−0.144774	−	0.144774i
$574$	19.0588	+	9.54568i	0.795499	+	0.398429i
$575$	−16.2083			−0.675934
$576$	−10.5312	−	28.3558i	−0.438799	−	1.18149i
$577$	−8.69155			−0.361834			−0.180917	−	0.983498i	$-0.557907\pi$
$577$	−8.69155			−0.361834			−0.180917	+	0.983498i	$0.557907\pi$
$578$	3.87838	+	1.94251i	0.161319	+	0.0807976i
$579$	22.5598	+	22.5598i	0.937552	+	0.937552i
$580$	8.82779	+	11.8040i	0.366554	+	0.490133i
$581$	24.0345	−	24.0345i	0.997118	−	0.997118i
$582$	−4.30678	−	12.9498i	−0.178522	−	0.536788i
$583$		−	13.4242i		−	0.555974i
$584$	12.6423	−	2.27183i	0.523142	−	0.0940090i
$585$			4.90833i			0.202934i
$586$	−4.67255	+	1.55397i	−0.193021	+	0.0641939i
$587$	−0.911083	+	0.911083i	−0.0376044	+	0.0376044i	−0.725659	−	0.688055i	$-0.758465\pi$
$587$	−0.911083	+	0.911083i	−0.0376044	+	0.0376044i	0.688055	+	0.725659i	$0.258465\pi$
$588$	−0.0201656	+	0.139794i	−0.000831615	+	0.00576500i
$589$	−0.263034	−	0.263034i	−0.0108381	−	0.0108381i
$590$	5.40251	−	10.7866i	0.222418	−	0.444077i
$591$	−39.4660			−1.62341
$592$	19.3988	+	35.6049i	0.797287	+	1.46335i
$593$	−42.4674			−1.74393			−0.871964	−	0.489571i	$-0.837153\pi$
$593$	−42.4674			−1.74393			−0.871964	+	0.489571i	$0.837153\pi$
$594$	7.30304	−	14.5812i	0.299647	−	0.598272i
$595$	10.9004	+	10.9004i	0.446871	+	0.446871i
$596$	−26.8414	−	3.87194i	−1.09947	−	0.158601i
$597$	31.6838	−	31.6838i	1.29673	−	1.29673i
$598$	−6.56166	+	2.18224i	−0.268326	+	0.0892383i
$599$		−	24.7338i		−	1.01060i	−0.862945	−	0.505298i	$-0.831383\pi$
$599$		−	24.7338i		−	1.01060i	0.862945	−	0.505298i	$-0.168617\pi$
$600$	20.0451	+	13.9383i	0.818337	+	0.569027i
$601$			28.3758i			1.15747i	0.815514	+	0.578737i	$0.196454\pi$
$601$			28.3758i			1.15747i	−0.815514	+	0.578737i	$0.803546\pi$
$602$	12.0770	+	36.3137i	0.492222	+	1.48004i
$603$	18.1322	−	18.1322i	0.738398	−	0.738398i
$604$	22.0820	−	16.5144i	0.898504	−	0.671961i
$605$	−19.4107	−	19.4107i	−0.789157	−	0.789157i
$606$	−33.9987	−	17.0284i	−1.38110	−	0.691732i
$607$	−2.50927			−0.101848			−0.0509240	−	0.998703i	$-0.516217\pi$
$607$	−2.50927			−0.101848			−0.0509240	+	0.998703i	$0.516217\pi$
$608$	−0.567440	+	0.0196066i	−0.0230127	+	0.000795153i
$609$	−39.1901			−1.58806
$610$	−9.87636	−	4.94662i	−0.399882	−	0.200283i
$611$	−3.39381	−	3.39381i	−0.137299	−	0.137299i
$612$	27.1280	−	20.2881i	1.09658	−	0.820099i
$613$	−26.5676	+	26.5676i	−1.07306	+	1.07306i	−0.0759442	+	0.997112i	$0.524197\pi$
$613$	−26.5676	+	26.5676i	−1.07306	+	1.07306i	−0.997112	+	0.0759442i	$0.975803\pi$
$614$	−6.39702	−	19.2349i	−0.258163	−	0.776256i
$615$		−	19.2206i		−	0.775049i
$616$	24.2691	−	34.9023i	0.977832	−	1.40625i
$617$		−	19.5448i		−	0.786843i	−0.919358	−	0.393421i	$-0.871291\pi$
$617$		−	19.5448i		−	0.786843i	0.919358	−	0.393421i	$-0.128709\pi$
$618$	−32.2628	+	10.7298i	−1.29780	+	0.431615i
$619$	−6.78722	+	6.78722i	−0.272801	+	0.272801i	−0.830227	−	0.557426i	$-0.811789\pi$
$619$	−6.78722	+	6.78722i	−0.272801	+	0.272801i	0.557426	+	0.830227i	$0.311789\pi$
$620$	−9.52367	−	1.37381i	−0.382480	−	0.0551736i
$621$	7.03201	+	7.03201i	0.282185	+	0.282185i
$622$	−6.74202	+	13.4610i	−0.270330	+	0.539738i
$623$	38.4434			1.54020
$624$	9.99151	+	2.94385i	0.399980	+	0.117848i
$625$	−2.56209			−0.102484
$626$	−13.2354	+	26.4256i	−0.528992	+	1.05618i
$627$	−1.04786	−	1.04786i	−0.0418474	−	0.0418474i
$628$	2.99364	−	20.7528i	0.119459	−	0.828126i
$629$	−32.1087	+	32.1087i	−1.28026	+	1.28026i
$630$	17.4605	−	5.80692i	0.695644	−	0.231353i
$631$			12.0264i			0.478763i	0.970926	+	0.239381i	$0.0769446\pi$
$631$			12.0264i			0.478763i	−0.970926	+	0.239381i	$0.923055\pi$
$632$	5.77613	+	32.1430i	0.229762	+	1.27858i
$633$			2.43947i			0.0969601i
$634$	−6.59720	−	19.8368i	−0.262008	−	0.787819i
$635$	−10.3410	+	10.3410i	−0.410370	+	0.410370i
$636$	−7.38517	−	9.87499i	−0.292841	−	0.391569i
$637$	−0.0191764	−	0.0191764i	−0.000759798	−	0.000759798i
$638$	40.7021	+	20.3858i	1.61141	+	0.807082i
$639$	−3.86601			−0.152937
$640$	−11.4508	+	9.19694i	−0.452631	+	0.363541i
$641$	23.6294			0.933305			0.466653	−	0.884441i	$-0.345460\pi$
$641$	23.6294			0.933305			0.466653	+	0.884441i	$0.345460\pi$
$642$	48.0062	+	24.0441i	1.89465	+	0.948946i
$643$	34.4726	+	34.4726i	1.35947	+	1.35947i	0.874571	+	0.484897i	$0.161143\pi$
$643$	34.4726	+	34.4726i	1.35947	+	1.35947i	0.484897	+	0.874571i	$0.338857\pi$
$644$	15.5259	+	20.7602i	0.611805	+	0.818067i
$645$	24.4007	−	24.4007i	0.960779	−	0.960779i
$646$	−0.200665	−	0.603369i	−0.00789505	−	0.0237392i
$647$			11.9917i			0.471442i	0.971821	+	0.235721i	$0.0757451\pi$
$647$			11.9917i			0.471442i	−0.971821	+	0.235721i	$0.924255\pi$
$648$	3.02501	+	16.8336i	0.118833	+	0.661286i
$649$		−	37.2575i		−	1.46249i
$650$	−4.44830	+	1.47939i	−0.174477	+	0.0580265i
$651$	18.0902	−	18.0902i	0.709012	−	0.709012i
$652$	5.27434	−	36.5633i	0.206559	−	1.43193i
$653$	14.9034	+	14.9034i	0.583213	+	0.583213i	0.935785	−	0.352572i	$-0.114693\pi$
$653$	14.9034	+	14.9034i	0.583213	+	0.583213i	−0.352572	+	0.935785i	$0.614693\pi$
$654$	−21.4146	+	42.7561i	−0.837377	+	1.67190i
$655$	2.60799			0.101903
$656$	−21.8162	−	6.42782i	−0.851778	−	0.250964i
$657$	17.1709			0.669899
$658$	−8.05777	+	16.0880i	−0.314125	+	0.627177i
$659$	2.45872	+	2.45872i	0.0957783	+	0.0957783i	0.753372	−	0.657594i	$-0.228426\pi$
$659$	2.45872	+	2.45872i	0.0957783	+	0.0957783i	−0.657594	+	0.753372i	$0.728426\pi$
$660$	−37.9397	−	5.47289i	−1.47680	−	0.213032i
$661$	25.0002	−	25.0002i	0.972394	−	0.972394i	−0.0272352	−	0.999629i	$-0.508670\pi$
$661$	25.0002	−	25.0002i	0.972394	−	0.972394i	0.999629	+	0.0272352i	$0.00867029\pi$
$662$	2.23772	−	0.744207i	0.0869714	−	0.0289244i
$663$			11.6652i			0.453038i
$664$	−20.7044	+	29.7757i	−0.803485	+	1.15552i
$665$		−	0.345396i		−	0.0133939i
$666$	17.1052	+	51.4327i	0.662812	+	1.99298i
$667$	−19.6292	+	19.6292i	−0.760047	+	0.760047i
$668$	19.1003	−	14.2845i	0.739014	−	0.552684i
$669$	−12.3875	−	12.3875i	−0.478927	−	0.478927i
$670$	−11.1324	−	5.57572i	−0.430083	−	0.215409i
$671$	−34.1135			−1.31694
$672$	−1.34845	−	39.0259i	−0.0520176	−	1.50545i
$673$	−44.2126			−1.70427			−0.852135	−	0.523322i	$-0.824693\pi$
$673$	−44.2126			−1.70427			−0.852135	+	0.523322i	$0.824693\pi$
$674$	13.8651	+	6.94439i	0.534063	+	0.267488i
$675$	4.76716	+	4.76716i	0.183488	+	0.183488i
$676$	−1.60164	+	1.19781i	−0.0616015	+	0.0460697i
$677$	−22.0279	+	22.0279i	−0.846603	+	0.846603i	−0.989708	−	0.143105i	$-0.954291\pi$
$677$	−22.0279	+	22.0279i	−0.846603	+	0.846603i	0.143105	+	0.989708i	$0.454291\pi$
$678$	9.34743	+	28.1063i	0.358986	+	1.07942i
$679$		−	9.82359i		−	0.376995i
$680$	−13.5042	−	9.39005i	−0.517861	−	0.360092i
$681$		−	30.6849i		−	1.17585i
$682$	−28.1983	+	9.37802i	−1.07977	+	0.359103i
$683$	−27.1737	+	27.1737i	−1.03977	+	1.03977i	−0.0405954	+	0.999176i	$0.512925\pi$
$683$	−27.1737	+	27.1737i	−1.03977	+	1.03977i	−0.999176	+	0.0405954i	$0.987075\pi$
$684$	−0.751229	−	0.108367i	−0.0287240	−	0.00414350i
$685$	5.87954	+	5.87954i	0.224646	+	0.224646i
$686$	11.7064	−	23.3729i	0.446953	−	0.892381i
$687$	−27.5353			−1.05054
$688$	−19.5357	−	35.8560i	−0.744791	−	1.36700i
$689$	2.36769			0.0902017
$690$	10.4682	−	20.9007i	0.398519	−	0.795677i
$691$	−26.1248	−	26.1248i	−0.993836	−	0.993836i	0.00614507	−	0.999981i	$-0.498044\pi$
$691$	−26.1248	−	26.1248i	−0.993836	−	0.993836i	−0.999981	+	0.00614507i	$0.998044\pi$
$692$	1.97360	−	13.6816i	0.0750249	−	0.520095i
$693$	40.1836	−	40.1836i	1.52645	−	1.52645i
$694$	42.1978	−	14.0339i	1.60180	−	0.532719i
$695$			22.6622i			0.859625i
$696$	41.1558	−	7.39573i	1.56001	−	0.280335i
$697$		−	25.4706i		−	0.964766i
$698$	5.03351	+	15.1350i	0.190521	+	0.572869i
$699$	15.4030	−	15.4030i	0.582597	−	0.582597i
$700$	10.5254	+	14.0738i	0.397821	+	0.531941i
$701$	22.6916	+	22.6916i	0.857049	+	0.857049i	0.990989	−	0.133940i	$-0.0427630\pi$
$701$	22.6916	+	22.6916i	0.857049	+	0.857049i	−0.133940	+	0.990989i	$0.542763\pi$
$702$	2.57174	+	1.28807i	0.0970641	+	0.0486150i
$703$	1.01742			0.0383726
$704$	−18.8999	+	41.2329i	−0.712317	+	1.55402i
$705$	16.2246			0.611055
$706$	29.9676	+	15.0094i	1.12784	+	0.564886i
$707$	−19.3543	−	19.3543i	−0.727892	−	0.727892i
$708$	−20.4968	−	27.4070i	−0.770316	−	1.03002i
$709$	20.6490	−	20.6490i	0.775490	−	0.775490i	−0.203571	−	0.979060i	$-0.565255\pi$
$709$	20.6490	−	20.6490i	0.775490	−	0.775490i	0.979060	+	0.203571i	$0.0652547\pi$
$710$	0.592379	+	1.78119i	0.0222316	+	0.0668470i
$711$			43.6570i			1.63726i
$712$	−40.3717	+	7.25482i	−1.51299	+	0.271886i
$713$		−	18.1218i		−	0.678667i
$714$	41.4968	−	13.8008i	1.55298	−	0.516481i
$715$	5.20443	−	5.20443i	0.194635	−	0.194635i
$716$	0.512375	−	3.55194i	0.0191483	−	0.132742i
$717$	−48.3674	−	48.3674i	−1.80631	−	1.80631i
$718$	−14.9196	+	29.7884i	−0.556796	+	1.11169i
$719$	2.36502			0.0882004			0.0441002	−	0.999027i	$-0.485958\pi$
$719$	2.36502			0.0882004			0.0441002	+	0.999027i	$0.485958\pi$
$720$	−17.2405	+	9.39324i	−0.642515	+	0.350065i
$721$	−24.4742			−0.911466
$722$	12.0267	−	24.0124i	0.447587	−	0.893647i
$723$	29.5307	+	29.5307i	1.09826	+	1.09826i
$724$	31.0549	+	4.47974i	1.15415	+	0.166488i
$725$	−13.3071	+	13.3071i	−0.494215	+	0.494215i
$726$	−73.8951	+	24.5756i	−2.74250	+	0.912085i
$727$		−	20.7902i		−	0.771067i	−0.922694	−	0.385533i	$-0.874017\pi$
$727$		−	20.7902i		−	0.771067i	0.922694	−	0.385533i	$-0.125983\pi$
$728$	6.15587	+	4.28045i	0.228152	+	0.158644i
$729$			38.7521i			1.43526i
$730$	−2.63105	−	7.91117i	−0.0973796	−	0.292806i
$731$	32.3351	−	32.3351i	1.19596	−	1.19596i
$732$	−25.0943	+	18.7671i	−0.927510	+	0.693654i
$733$	21.1462	+	21.1462i	0.781053	+	0.781053i	0.980009	−	0.198955i	$-0.0637548\pi$
$733$	21.1462	+	21.1462i	0.781053	+	0.781053i	−0.198955	+	0.980009i	$0.563755\pi$
$734$	7.24970	+	3.63105i	0.267591	+	0.134024i
$735$	0.0916757			0.00338151
$736$	−20.2224	−	18.8716i	−0.745407	−	0.695615i
$737$	−38.4520			−1.41640
$738$	−27.1842	−	13.6153i	−1.00066	−	0.501188i
$739$	11.1918	+	11.1918i	0.411698	+	0.411698i	0.882330	−	0.470631i	$-0.155974\pi$
$739$	11.1918	+	11.1918i	0.411698	+	0.411698i	−0.470631	+	0.882330i	$0.655974\pi$
$740$	21.0757	−	15.7618i	0.774759	−	0.579416i
$741$	0.184815	−	0.184815i	0.00678935	−	0.00678935i
$742$	−2.80115	−	8.42263i	−0.102833	−	0.309205i
$743$		−	4.68273i		−	0.171793i	−0.996304	−	0.0858964i	$-0.972625\pi$
$743$		−	4.68273i		−	0.171793i	0.996304	−	0.0858964i	$-0.0273754\pi$
$744$	−15.5837	+	22.4115i	−0.571327	+	0.821646i
$745$			17.6024i			0.644902i
$746$	2.18615	−	0.727058i	0.0800408	−	0.0266195i
$747$	−34.2812	+	34.2812i	−1.25428	+	1.25428i
$748$	−50.2766	−	7.25251i	−1.83829	−	0.265178i
$749$	27.3282	+	27.3282i	0.998552	+	0.998552i
$750$	17.8011	−	35.5415i	0.650005	−	1.29779i
$751$	37.0925			1.35353			0.676763	−	0.736201i	$-0.263382\pi$
$751$	37.0925			1.35353			0.676763	+	0.736201i	$0.263382\pi$
$752$	5.42590	−	18.4156i	0.197862	−	0.671548i
$753$	65.9793			2.40442
$754$	−3.59553	+	7.17879i	−0.130942	+	0.261436i
$755$	−12.6556	−	12.6556i	−0.460584	−	0.460584i
$756$	1.53952	−	10.6724i	0.0559917	−	0.388151i
$757$	20.6539	−	20.6539i	0.750679	−	0.750679i	−0.223927	−	0.974606i	$-0.571888\pi$
$757$	20.6539	−	20.6539i	0.750679	−	0.750679i	0.974606	+	0.223927i	$0.0718876\pi$
$758$	5.26353	−	1.75051i	0.191180	−	0.0635815i
$759$		−	72.1924i		−	2.62042i
$760$	0.0651811	+	0.362720i	0.00236437	+	0.0131572i
$761$			24.7607i			0.897573i	0.893639	+	0.448786i	$0.148144\pi$
$761$			24.7607i			0.897573i	−0.893639	+	0.448786i	$0.851856\pi$
$762$	13.0926	+	39.3674i	0.474294	+	1.42613i
$763$	−24.3396	+	24.3396i	−0.881151	+	0.881151i
$764$	2.25437	+	3.01440i	0.0815602	+	0.109057i
$765$	−15.5475	−	15.5475i	−0.562123	−	0.562123i
$766$	17.5695	+	8.79979i	0.634813	+	0.317949i
$767$	6.57127			0.237275
$768$	8.78082	+	40.7289i	0.316851	+	1.46968i
$769$	−27.3269			−0.985432			−0.492716	−	0.870190i	$-0.663996\pi$
$769$	−27.3269			−0.985432			−0.492716	+	0.870190i	$0.663996\pi$
$770$	−24.6711	−	12.3566i	−0.889085	−	0.445302i
$771$	9.31500	+	9.31500i	0.335471	+	0.335471i
$772$	−14.6754	−	19.6231i	−0.528180	−	0.706249i
$773$	5.67585	−	5.67585i	0.204146	−	0.204146i	−0.597628	−	0.801774i	$-0.703890\pi$
$773$	5.67585	−	5.67585i	0.204146	−	0.204146i	0.801774	+	0.597628i	$0.203890\pi$
$774$	−17.2258	−	51.7955i	−0.619170	−	1.86175i
$775$		−	12.2852i		−	0.441297i
$776$	1.85385	+	10.3163i	0.0665494	+	0.370335i
$777$			69.9730i			2.51027i
$778$	−36.9367	+	12.2842i	−1.32425	+	0.440410i
$779$	−0.403538	+	0.403538i	−0.0144583	+	0.0144583i
$780$	0.965277	−	6.69159i	0.0345625	−	0.239597i
$781$	4.09923	+	4.09923i	0.146682	+	0.146682i
$782$	13.8722	−	27.6970i	0.496068	−	0.990444i
$783$	11.5466			0.412643
$784$	0.0306585	−	0.104056i	0.00109495	−	0.00371627i
$785$	−13.6095			−0.485744
$786$	3.31325	−	6.61519i	0.118180	−	0.235956i
$787$	9.96705	+	9.96705i	0.355287	+	0.355287i	0.862072	−	0.506785i	$-0.169166\pi$
$787$	9.96705	+	9.96705i	0.355287	+	0.355287i	−0.506785	+	0.862072i	$0.669166\pi$
$788$	30.0008	+	4.32768i	1.06873	+	0.154167i
$789$	29.0431	−	29.0431i	1.03396	−	1.03396i
$790$	20.1142	−	6.68945i	0.715630	−	0.238000i
$791$			21.3211i			0.758091i
$792$	−34.6159	+	49.7824i	−1.23002	+	1.76894i
$793$		−	6.01675i		−	0.213661i
$794$	14.7210	+	44.2639i	0.522430	+	1.57087i
$795$	−5.65953	+	5.65953i	−0.200723	+	0.200723i
$796$	−27.5594	+	20.6107i	−0.976817	+	0.730528i
$797$	8.85675	+	8.85675i	0.313722	+	0.313722i	0.846350	−	0.532628i	$-0.178795\pi$
$797$	8.85675	+	8.85675i	0.313722	+	0.313722i	−0.532628	+	0.846350i	$0.678795\pi$
$798$	−0.876097	−	0.438797i	−0.0310135	−	0.0155333i
$799$	21.5004			0.760629
$800$	−13.7092	−	12.7935i	−0.484694	−	0.452318i
$801$	−54.8332			−1.93743
$802$	−4.89947	−	2.45392i	−0.173006	−	0.0866510i
$803$	−18.2067	−	18.2067i	−0.642502	−	0.642502i
$804$	−28.2857	+	21.1539i	−0.997559	+	0.746041i
$805$	11.8981	−	11.8981i	0.419351	−	0.419351i
$806$	−1.65404	−	4.97345i	−0.0582611	−	0.175182i
$807$			69.6927i			2.45330i
$808$	23.9775	+	16.6726i	0.843525	+	0.586541i
$809$			12.7610i			0.448652i	0.974514	+	0.224326i	$0.0720181\pi$
$809$			12.7610i			0.448652i	−0.974514	+	0.224326i	$0.927982\pi$
$810$	10.5340	−	3.50332i	0.370126	−	0.123094i
$811$	13.0983	−	13.0983i	0.459944	−	0.459944i	−0.438693	−	0.898637i	$-0.644558\pi$
$811$	13.0983	−	13.0983i	0.459944	−	0.459944i	0.898637	+	0.438693i	$0.144558\pi$
$812$	29.7911	+	4.29743i	1.04546	+	0.150810i
$813$	28.0228	+	28.0228i	0.982804	+	0.982804i
$814$	36.3984	−	72.6725i	1.27576	−	2.54717i
$815$	−23.9779			−0.839910
$816$	−40.9738	+	22.3240i	−1.43437	+	0.781498i
$817$	−1.02459			−0.0358459
$818$	−9.74149	+	19.4497i	−0.340603	+	0.680044i
$819$	7.08735	+	7.08735i	0.247652	+	0.247652i
$820$	−2.10765	+	14.6109i	−0.0736025	+	0.510234i
$821$	29.1527	−	29.1527i	1.01744	−	1.01744i	0.0175917	−	0.999845i	$-0.494400\pi$
$821$	29.1527	−	29.1527i	1.01744	−	1.01744i	0.999845	−	0.0175917i	$-0.00559991\pi$
$822$	22.3830	−	7.44400i	0.780696	−	0.259639i
$823$		−	26.8824i		−	0.937063i	−0.883447	−	0.468531i	$-0.844783\pi$
$823$		−	26.8824i		−	0.937063i	0.883447	−	0.468531i	$-0.155217\pi$
$824$	25.7018	−	4.61863i	0.895364	−	0.160898i
$825$		−	48.9409i		−	1.70390i
$826$	−7.77430	−	23.3761i	−0.270502	−	0.813360i
$827$	11.5128	−	11.5128i	0.400340	−	0.400340i	−0.478013	−	0.878353i	$-0.658643\pi$
$827$	11.5128	−	11.5128i	0.400340	−	0.400340i	0.878353	+	0.478013i	$0.158643\pi$
$828$	−22.1451	−	29.6110i	−0.769595	−	1.02905i
$829$	−2.69015	−	2.69015i	−0.0934328	−	0.0934328i	0.658846	−	0.752278i	$-0.271045\pi$
$829$	−2.69015	−	2.69015i	−0.0934328	−	0.0934328i	−0.752278	+	0.658846i	$0.771045\pi$
$830$	21.0473	+	10.5416i	0.730562	+	0.365905i
$831$	−46.3833			−1.60902
$832$	−7.27242	−	3.33345i	−0.252126	−	0.115567i
$833$	0.121486			0.00420924
$834$	57.4827	+	28.7905i	1.99046	+	0.996933i
$835$	−10.9467	−	10.9467i	−0.378828	−	0.378828i
$836$	0.681644	+	0.911452i	0.0235752	+	0.0315232i
$837$	−5.32995	+	5.32995i	−0.184230	+	0.184230i
$838$	−6.54007	−	19.6650i	−0.225923	−	0.679316i
$839$			12.5560i			0.433481i	0.976229	+	0.216741i	$0.0695426\pi$
$839$			12.5560i			0.433481i	−0.976229	+	0.216741i	$0.930457\pi$
$840$	−24.9462	+	4.48284i	−0.860724	+	0.154673i
$841$			3.23147i			0.111430i
$842$	−16.9202	+	5.62720i	−0.583107	+	0.193926i
$843$	−32.0329	+	32.0329i	−1.10327	+	1.10327i
$844$	0.267502	−	1.85441i	0.00920781	−	0.0638313i
$845$	0.917928	+	0.917928i	0.0315777	+	0.0315777i
$846$	11.4931	−	22.9469i	0.395140	−	0.788932i
$847$	−56.0559			−1.92610
$848$	4.53112	+	8.31649i	0.155599	+	0.285589i
$849$	−80.4978			−2.76268
$850$	9.40429	−	18.7765i	0.322564	−	0.644028i
$851$	35.0476	+	35.0476i	1.20141	+	1.20141i
$852$	5.27058	+	0.760293i	0.180567	+	0.0260472i
$853$	−16.8348	+	16.8348i	−0.576411	+	0.576411i	−0.933913	−	0.357501i	$-0.883629\pi$
$853$	−16.8348	+	16.8348i	−0.576411	+	0.576411i	0.357501	+	0.933913i	$0.383629\pi$
$854$	−21.4035	+	7.11826i	−0.732414	+	0.243582i
$855$			0.492650i			0.0168483i
$856$	−33.8562	−	23.5418i	−1.15718	−	0.804641i
$857$			7.78787i			0.266029i	0.991114	+	0.133014i	$0.0424656\pi$
$857$			7.78787i			0.266029i	−0.991114	+	0.133014i	$0.957534\pi$
$858$	−6.58925	−	19.8129i	−0.224953	−	0.676401i
$859$	20.7467	−	20.7467i	0.707868	−	0.707868i	−0.258219	−	0.966087i	$-0.583135\pi$
$859$	20.7467	−	20.7467i	0.707868	−	0.707868i	0.966087	+	0.258219i	$0.0831355\pi$
$860$	−21.2244	+	15.8730i	−0.723745	+	0.541265i
$861$	−27.7534	−	27.7534i	−0.945834	−	0.945834i
$862$	−31.2220	−	15.6377i	−1.06343	−	0.532622i
$863$	−19.5302			−0.664815			−0.332408	−	0.943136i	$-0.607861\pi$
$863$	−19.5302			−0.664815			−0.332408	+	0.943136i	$0.607861\pi$
$864$	0.397296	+	11.4982i	0.0135163	+	0.391178i
$865$	−8.97225			−0.305066
$866$	11.4094	+	5.71443i	0.387706	+	0.194184i
$867$	−5.64771	−	5.64771i	−0.191806	−	0.191806i
$868$	−15.7353	+	11.7679i	−0.534092	+	0.399429i
$869$	46.2907	−	46.2907i	1.57030	−	1.57030i
$870$	−8.56515	−	25.7541i	−0.290386	−	0.873146i
$871$		−	6.78194i		−	0.229797i
$872$	20.9672	−	30.1536i	0.710038	−	1.02113i
$873$			14.0117i			0.474225i
$874$	−0.658595	+	0.219031i	−0.0222773	+	0.00740885i
$875$	20.2325	−	20.2325i	0.683984	−	0.683984i
$876$	−23.4093	−	3.37684i	−0.790926	−	0.114093i
$877$	−3.02491	−	3.02491i	−0.102144	−	0.102144i	0.654188	−	0.756332i	$-0.273011\pi$
$877$	−3.02491	−	3.02491i	−0.102144	−	0.102144i	−0.756332	+	0.654188i	$0.773011\pi$
$878$	−3.31524	+	6.61917i	−0.111884	+	0.223386i
$879$	9.06707			0.305825
$880$	28.2405	+	8.32064i	0.951985	+	0.280489i
$881$	38.9801			1.31327			0.656637	−	0.754207i	$-0.271978\pi$
$881$	38.9801			1.31327			0.656637	+	0.754207i	$0.271978\pi$
$882$	0.0649405	−	0.129659i	0.00218666	−	0.00436586i
$883$	−7.44889	−	7.44889i	−0.250675	−	0.250675i	0.570572	−	0.821247i	$-0.306721\pi$
$883$	−7.44889	−	7.44889i	−0.250675	−	0.250675i	−0.821247	+	0.570572i	$0.806721\pi$
$884$	1.27916	−	8.86750i	0.0430227	−	0.298246i
$885$	−15.7074	+	15.7074i	−0.528000	+	0.528000i
$886$	28.9895	−	9.64115i	0.973920	−	0.323901i
$887$			27.2789i			0.915935i	0.888969	+	0.457968i	$0.151422\pi$
$887$			27.2789i			0.915935i	−0.888969	+	0.457968i	$0.848578\pi$
$888$	−13.2049	−	73.4828i	−0.443128	−	2.46592i
$889$			29.8636i			1.00159i
$890$	8.40195	+	25.2634i	0.281634	+	0.846831i
$891$	24.2428	−	24.2428i	0.812164	−	0.812164i
$892$	8.05820	+	10.7749i	0.269809	+	0.360771i
$893$	−0.340638	−	0.340638i	−0.0113990	−	0.0113990i
$894$	44.6486	+	22.3624i	1.49327	+	0.747912i
$895$	−2.32933			−0.0778609
$896$	−3.25437	+	29.8141i	−0.108721	+	0.996019i
$897$	12.7329			0.425138
$898$	−7.90839	−	3.96095i	−0.263906	−	0.132179i
$899$	−14.8781	−	14.8781i	−0.496213	−	0.496213i
$900$	−15.0127	−	20.0740i	−0.500423	−	0.669134i
$901$	−7.49985	+	7.49985i	−0.249856	+	0.249856i
$902$	14.3874	+	43.2609i	0.479049	+	1.44043i
$903$		−	70.4666i		−	2.34498i
$904$	−4.02360	−	22.3905i	−0.133823	−	0.744698i
$905$		−	20.3655i		−	0.676973i
$906$	−48.1789	+	16.0231i	−1.60064	+	0.532330i
$907$	−15.5105	+	15.5105i	−0.515017	+	0.515017i	−0.916060	−	0.401042i	$-0.868648\pi$
$907$	−15.5105	+	15.5105i	−0.515017	+	0.515017i	0.401042	+	0.916060i	$0.368648\pi$
$908$	−3.36479	+	23.3257i	−0.111664	+	0.774091i
$909$	27.6057	+	27.6057i	0.915623	+	0.915623i
$910$	2.17939	−	4.35135i	0.0722462	−	0.144246i
$911$	−31.0837			−1.02985			−0.514925	−	0.857235i	$-0.672180\pi$
$911$	−31.0837			−1.02985			−0.514925	+	0.857235i	$0.672180\pi$
$912$	1.00285	+	0.295475i	0.0332076	+	0.00978415i
$913$	72.6986			2.40597
$914$	−0.824134	+	1.64546i	−0.0272599	+	0.0544268i
$915$	14.3820	+	14.3820i	0.475453	+	0.475453i
$916$	20.9314	+	3.01941i	0.691594	+	0.0997641i
$917$	3.76579	−	3.76579i	0.124357	−	0.124357i
$918$	−12.2263	+	4.06614i	−0.403527	+	0.134203i
$919$			54.0308i			1.78231i	0.453698	+	0.891156i	$0.350105\pi$
$919$			54.0308i			1.78231i	−0.453698	+	0.891156i	$0.649895\pi$
$920$	−10.2495	+	14.7402i	−0.337916	+	0.485969i
$921$			37.3252i			1.22991i
$922$	−10.7569	−	32.3443i	−0.354259	−	1.06520i
$923$	−0.722999	+	0.722999i	−0.0237978	+	0.0237978i
$924$	−62.6853	+	46.8803i	−2.06220	+	1.54225i
$925$	23.7596	+	23.7596i	0.781210	+	0.781210i
$926$	−2.43855	−	1.22136i	−0.0801357	−	0.0401363i
$927$	34.9084			1.14654
$928$	−32.0964	+	1.10902i	−1.05361	+	0.0364053i
$929$	−4.69890			−0.154166			−0.0770829	−	0.997025i	$-0.524561\pi$
$929$	−4.69890			−0.154166			−0.0770829	+	0.997025i	$0.524561\pi$
$930$	15.8418	+	7.93446i	0.519474	+	0.260181i
$931$	−0.00192474	−	0.00192474i	−6.30808e−5	−	6.30808e-5i
$932$	−13.3980	+	10.0199i	−0.438864	+	0.328212i
$933$	19.6020	−	19.6020i	0.641740	−	0.641740i
$934$	−5.57419	−	16.7608i	−0.182393	−	0.548429i
$935$			32.9710i			1.07827i
$936$	−8.78033	−	6.10536i	−0.286994	−	0.199560i
$937$			20.1569i			0.658496i	0.944244	+	0.329248i	$0.106795\pi$
$937$			20.1569i			0.658496i	−0.944244	+	0.329248i	$0.893205\pi$
$938$	−24.1256	+	8.02355i	−0.787728	+	0.261978i
$939$	38.4810	−	38.4810i	1.25578	−	1.25578i
$940$	−12.3334	−	1.77913i	−0.402273	−	0.0580288i
$941$	33.7417	+	33.7417i	1.09995	+	1.09995i	0.994416	+	0.105530i	$0.0336540\pi$
$941$	33.7417	+	33.7417i	1.09995	+	1.09995i	0.105530	+	0.994416i	$0.466346\pi$
$942$	−17.2898	+	34.5206i	−0.563332	+	1.12474i
$943$	−27.8019			−0.905353
$944$	12.5757	+	23.0815i	0.409303	+	0.751240i
$945$	−6.99887			−0.227673
$946$	−36.6551	+	73.1852i	−1.19176	+	2.37945i
$947$	0.0852297	+	0.0852297i	0.00276959	+	0.00276959i	0.708490	−	0.705721i	$-0.249377\pi$
$947$	0.0852297	+	0.0852297i	0.00276959	+	0.00276959i	−0.705721	+	0.708490i	$0.749377\pi$
$948$	8.58562	−	59.5181i	0.278848	−	1.93306i
$949$	3.21120	−	3.21120i	0.104240	−	0.104240i
$950$	−0.446477	+	0.148487i	−0.0144856	+	0.00481754i
$951$			38.4932i			1.24823i
$952$	−33.0579	+	5.94053i	−1.07141	+	0.192534i
$953$			12.7074i			0.411634i	0.978591	+	0.205817i	$0.0659852\pi$
$953$			12.7074i			0.411634i	−0.978591	+	0.205817i	$0.934015\pi$
$954$	3.99538	+	12.0135i	0.129355	+	0.388951i
$955$	1.72761	−	1.72761i	0.0559041	−	0.0559041i
$956$	31.4636	+	42.0712i	1.01761	+	1.36068i
$957$	−59.2704	−	59.2704i	−1.91594	−	1.91594i
$958$	16.6195	+	8.32396i	0.536952	+	0.268935i
$959$	16.9794			0.548295
$960$	25.3515	−	9.41539i	0.818215	−	0.303881i
$961$	−17.2645			−0.556918
$962$	12.8176	+	6.41974i	0.413255	+	0.206981i
$963$	−38.9792	−	38.9792i	−1.25609	−	1.25609i
$964$	−19.2101	−	25.6866i	−0.618716	−	0.827309i
$965$	−11.2463	+	11.2463i	−0.362032	+	0.362032i
$966$	−15.0639	−	45.2950i	−0.484674	−	1.45734i
$967$			26.5134i			0.852612i	0.904579	+	0.426306i	$0.140185\pi$
$967$			26.5134i			0.852612i	−0.904579	+	0.426306i	$0.859815\pi$
$968$	58.8676	−	10.5785i	1.89208	−	0.340007i
$969$			1.17083i			0.0376126i
$970$	6.45565	−	2.14698i	0.207279	−	0.0689355i
$971$	29.3794	−	29.3794i	0.942831	−	0.942831i	−0.0556208	−	0.998452i	$-0.517714\pi$
$971$	29.3794	−	29.3794i	0.942831	−	0.942831i	0.998452	+	0.0556208i	$0.0177138\pi$
$972$	6.23864	−	43.2481i	0.200104	−	1.38718i
$973$	32.7229	+	32.7229i	1.04905	+	1.04905i
$974$	−11.9732	+	23.9055i	−0.383646	+	0.765983i
$975$	8.63192			0.276443
$976$	21.1338	−	11.5145i	0.676476	−	0.368569i
$977$	38.5415			1.23305			0.616526	−	0.787334i	$-0.288539\pi$
$977$	38.5415			1.23305			0.616526	+	0.787334i	$0.288539\pi$
$978$	−30.4620	+	60.8201i	−0.974068	+	1.94481i
$979$	58.1411	+	58.1411i	1.85820	+	1.85820i
$980$	−0.0696890	−	0.0100528i	−0.00222613	−	0.000321125i
$981$	34.7164	−	34.7164i	1.10841	−	1.10841i
$982$	20.7713	−	6.90799i	0.662838	−	0.220443i
$983$			8.36234i			0.266717i	0.991068	+	0.133359i	$0.0425762\pi$
$983$			8.36234i			0.266717i	−0.991068	+	0.133359i	$0.957424\pi$
$984$	34.3830	+	23.9080i	1.09609	+	0.762161i
$985$		−	19.6743i		−	0.626874i
$986$	−11.3503	−	34.1286i	−0.361467	−	1.08688i
$987$	23.4274	−	23.4274i	0.745703	−	0.745703i
$988$	−0.160757	+	0.120224i	−0.00511435	+	0.00382485i
$989$	−35.2948	−	35.2948i	−1.12231	−	1.12231i
$990$	35.1893	+	17.6247i	1.11839	+	0.560150i
$991$	30.1736			0.958498			0.479249	−	0.877679i	$-0.340909\pi$
$991$	30.1736			0.958498			0.479249	+	0.877679i	$0.340909\pi$
$992$	14.3038	−	15.3277i	0.454147	−	0.486654i
$993$	−4.34229			−0.137798
$994$	3.42730	+	1.71658i	0.108708	+	0.0544467i
$995$	15.7948	+	15.7948i	0.500728	+	0.500728i
$996$	53.4778	−	39.9942i	1.69451	−	1.26727i
$997$	−27.5024	+	27.5024i	−0.871011	+	0.871011i	−0.992583	−	0.121572i	$-0.961207\pi$
$997$	−27.5024	+	27.5024i	−0.871011	+	0.871011i	0.121572	+	0.992583i	$0.461207\pi$
$998$	3.99596	+	12.0152i	0.126490	+	0.380336i
$999$		−	20.6162i		−	0.652269i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	208.2.n.a.157.22	yes	48
4.3	odd	2		832.2.n.a.209.21		48
8.3	odd	2		1664.2.n.a.417.4		48
8.5	even	2		1664.2.n.b.417.21		48
16.3	odd	4		1664.2.n.a.1249.4		48
16.5	even	4	inner	208.2.n.a.53.22	✓	48
16.11	odd	4		832.2.n.a.625.21		48
16.13	even	4		1664.2.n.b.1249.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
208.2.n.a.53.22	✓	48	16.5	even	4	inner
208.2.n.a.157.22	yes	48	1.1	even	1	trivial
832.2.n.a.209.21		48	4.3	odd	2
832.2.n.a.625.21		48	16.11	odd	4
1664.2.n.a.417.4		48	8.3	odd	2
1664.2.n.a.1249.4		48	16.3	odd	4
1664.2.n.b.417.21		48	8.5	even	2
1664.2.n.b.1249.21		48	16.13	even	4

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:	\( N \)	\(=\)	\( 208 = 2^{4} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	208.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26448 + 0.633320i) q^{2} +(-1.84134 - 1.84134i) q^{3} +(1.19781 + 1.60164i) q^{4} +(0.917928 - 0.917928i) q^{5} +(-1.16217 - 3.49448i) q^{6} -2.65087i q^{7} +(0.500257 + 2.78384i) q^{8} +3.78103i q^{9} +O(q^{10})\)	\(q+(1.26448 + 0.633320i) q^{2} +(-1.84134 - 1.84134i) q^{3} +(1.19781 + 1.60164i) q^{4} +(0.917928 - 0.917928i) q^{5} +(-1.16217 - 3.49448i) q^{6} -2.65087i q^{7} +(0.500257 + 2.78384i) q^{8} +3.78103i q^{9} +(1.74204 - 0.579358i) q^{10} +(4.00913 - 4.00913i) q^{11} +(0.743581 - 5.15473i) q^{12} +(0.707107 + 0.707107i) q^{13} +(1.67885 - 3.35197i) q^{14} -3.38043 q^{15} +(-1.13049 + 3.83692i) q^{16} -4.47964 q^{17} +(-2.39460 + 4.78103i) q^{18} +(0.0709724 + 0.0709724i) q^{19} +(2.56969 + 0.370684i) q^{20} +(-4.88114 + 4.88114i) q^{21} +(7.60852 - 2.53040i) q^{22} +4.88966i q^{23} +(4.20483 - 6.04712i) q^{24} +3.31482i q^{25} +(0.446296 + 1.34195i) q^{26} +(1.43814 - 1.43814i) q^{27} +(4.24574 - 3.17524i) q^{28} +(4.01444 + 4.01444i) q^{29} +(-4.27448 - 2.14089i) q^{30} -3.70615 q^{31} +(-3.85949 + 4.13574i) q^{32} -14.7643 q^{33} +(-5.66441 - 2.83705i) q^{34} +(-2.43331 - 2.43331i) q^{35} +(-6.05584 + 4.52896i) q^{36} +(7.16769 - 7.16769i) q^{37} +(0.0447948 + 0.134691i) q^{38} -2.60404i q^{39} +(3.01456 + 2.09616i) q^{40} +5.68585i q^{41} +(-9.26343 + 3.08078i) q^{42} +(-7.21825 + 7.21825i) q^{43} +(11.2234 + 1.61899i) q^{44} +(3.47071 + 3.47071i) q^{45} +(-3.09672 + 6.18287i) q^{46} -4.79958 q^{47} +(9.14668 - 4.98344i) q^{48} -0.0271196 q^{49} +(-2.09934 + 4.19151i) q^{50} +(8.24852 + 8.24852i) q^{51} +(-0.285549 + 1.97951i) q^{52} +(1.67421 - 1.67421i) q^{53} +(2.72930 - 0.907693i) q^{54} -7.36018i q^{55} +(7.37959 - 1.32612i) q^{56} -0.261368i q^{57} +(2.53375 + 7.61860i) q^{58} +(4.64659 - 4.64659i) q^{59} +(-4.04911 - 5.41422i) q^{60} +(-4.25448 - 4.25448i) q^{61} +(-4.68634 - 2.34718i) q^{62} +10.0230 q^{63} +(-7.49949 + 2.78527i) q^{64} +1.29815 q^{65} +(-18.6691 - 9.35052i) q^{66} +(-4.79556 - 4.79556i) q^{67} +(-5.36577 - 7.17477i) q^{68} +(9.00350 - 9.00350i) q^{69} +(-1.53580 - 4.61793i) q^{70} +1.02247i q^{71} +(-10.5258 + 1.89149i) q^{72} -4.54132i q^{73} +(13.6028 - 4.52395i) q^{74} +(6.10369 - 6.10369i) q^{75} +(-0.0286606 + 0.198684i) q^{76} +(-10.6277 - 10.6277i) q^{77} +(1.64919 - 3.29275i) q^{78} +11.5463 q^{79} +(2.48431 + 4.55973i) q^{80} +6.04690 q^{81} +(-3.60096 + 7.18963i) q^{82} +(9.06663 + 9.06663i) q^{83} +(-13.6645 - 1.97114i) q^{84} +(-4.11199 + 4.11199i) q^{85} +(-13.6988 + 4.55586i) q^{86} -14.7839i q^{87} +(13.1663 + 9.15516i) q^{88} +14.5022i q^{89} +(2.19057 + 6.58671i) q^{90} +(1.87445 - 1.87445i) q^{91} +(-7.83147 + 5.85689i) q^{92} +(6.82426 + 6.82426i) q^{93} +(-6.06896 - 3.03967i) q^{94} +0.130295 q^{95} +(14.7219 - 0.508682i) q^{96} +3.70580 q^{97} +(-0.0342921 - 0.0171754i) q^{98} +(15.1586 + 15.1586i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{4} - 12 q^{8}+O(q^{10}) \) 48 * q - 4 * q^4 - 12 * q^8	\( 48 q - 4 q^{4} - 12 q^{8} - 4 q^{10} - 8 q^{11} + 8 q^{12} - 4 q^{14} - 16 q^{15} + 12 q^{16} - 16 q^{19} - 28 q^{20} + 12 q^{22} + 28 q^{24} - 16 q^{29} + 4 q^{30} + 24 q^{31} - 20 q^{32} - 40 q^{34} + 24 q^{35} + 8 q^{36} - 16 q^{37} + 32 q^{40} + 40 q^{42} - 8 q^{43} + 20 q^{44} - 32 q^{46} - 40 q^{47} - 52 q^{48} - 48 q^{49} - 16 q^{50} - 24 q^{51} - 8 q^{52} + 16 q^{53} + 20 q^{54} + 20 q^{56} - 16 q^{58} - 68 q^{60} + 32 q^{61} - 32 q^{62} + 40 q^{63} + 32 q^{64} - 32 q^{66} + 16 q^{67} + 40 q^{68} + 32 q^{69} - 60 q^{70} + 40 q^{72} + 72 q^{74} - 40 q^{75} - 28 q^{76} + 16 q^{77} + 32 q^{79} - 52 q^{80} - 48 q^{81} + 40 q^{82} + 40 q^{83} - 36 q^{84} - 32 q^{85} - 72 q^{86} - 8 q^{88} + 28 q^{90} + 36 q^{92} + 28 q^{94} - 48 q^{95} + 68 q^{96} + 64 q^{98} - 40 q^{99}+O(q^{100}) \) 48 * q - 4 * q^4 - 12 * q^8 - 4 * q^10 - 8 * q^11 + 8 * q^12 - 4 * q^14 - 16 * q^15 + 12 * q^16 - 16 * q^19 - 28 * q^20 + 12 * q^22 + 28 * q^24 - 16 * q^29 + 4 * q^30 + 24 * q^31 - 20 * q^32 - 40 * q^34 + 24 * q^35 + 8 * q^36 - 16 * q^37 + 32 * q^40 + 40 * q^42 - 8 * q^43 + 20 * q^44 - 32 * q^46 - 40 * q^47 - 52 * q^48 - 48 * q^49 - 16 * q^50 - 24 * q^51 - 8 * q^52 + 16 * q^53 + 20 * q^54 + 20 * q^56 - 16 * q^58 - 68 * q^60 + 32 * q^61 - 32 * q^62 + 40 * q^63 + 32 * q^64 - 32 * q^66 + 16 * q^67 + 40 * q^68 + 32 * q^69 - 60 * q^70 + 40 * q^72 + 72 * q^74 - 40 * q^75 - 28 * q^76 + 16 * q^77 + 32 * q^79 - 52 * q^80 - 48 * q^81 + 40 * q^82 + 40 * q^83 - 36 * q^84 - 32 * q^85 - 72 * q^86 - 8 * q^88 + 28 * q^90 + 36 * q^92 + 28 * q^94 - 48 * q^95 + 68 * q^96 + 64 * q^98 - 40 * q^99

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