LMFDB - Embedded newform 336.2.u.a.139.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(139,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.u (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:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.6
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20526 + 0.739825i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.905318 - 1.78337i) q^{4} +(1.32544 - 1.32544i) q^{5} +(-0.329115 + 1.37538i) q^{6} +(2.64192 - 0.142388i) q^{7} +(0.228233 + 2.81920i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.20526 + 0.739825i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.905318 - 1.78337i) q^{4} +(1.32544 - 1.32544i) q^{5} +(-0.329115 + 1.37538i) q^{6} +(2.64192 - 0.142388i) q^{7} +(0.228233 + 2.81920i) q^{8} -1.00000i q^{9} +(-0.616912 + 2.57810i) q^{10} +(-1.18514 + 1.18514i) q^{11} +(-0.620874 - 1.90119i) q^{12} +(-2.02086 - 2.02086i) q^{13} +(-3.07886 + 2.12617i) q^{14} -1.87446i q^{15} +(-2.36080 - 3.22903i) q^{16} -0.276387i q^{17} +(0.739825 + 1.20526i) q^{18} +(4.58131 - 4.58131i) q^{19} +(-1.16380 - 3.56370i) q^{20} +(1.76743 - 1.96880i) q^{21} +(0.551607 - 2.30519i) q^{22} -1.81753 q^{23} +(2.15486 + 1.83209i) q^{24} +1.48640i q^{25} +(3.93076 + 0.940587i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.13785 - 4.84041i) q^{28} +(-2.64137 + 2.64137i) q^{29} +(1.38677 + 2.25922i) q^{30} +7.11326 q^{31} +(5.23430 + 2.14525i) q^{32} +1.67603i q^{33} +(0.204478 + 0.333119i) q^{34} +(3.31298 - 3.69044i) q^{35} +(-1.78337 - 0.905318i) q^{36} +(-0.786692 - 0.786692i) q^{37} +(-2.13232 + 8.91105i) q^{38} -2.85793 q^{39} +(4.03920 + 3.43419i) q^{40} -7.33055 q^{41} +(-0.673655 + 3.68051i) q^{42} +(-1.69851 + 1.69851i) q^{43} +(1.04061 + 3.18646i) q^{44} +(-1.32544 - 1.32544i) q^{45} +(2.19060 - 1.34465i) q^{46} +11.5721 q^{47} +(-3.95261 - 0.613933i) q^{48} +(6.95945 - 0.752353i) q^{49} +(-1.09968 - 1.79150i) q^{50} +(-0.195435 - 0.195435i) q^{51} +(-5.43347 + 1.77442i) q^{52} +(3.85262 + 3.85262i) q^{53} +(1.37538 + 0.329115i) q^{54} +3.14166i q^{55} +(1.00439 + 7.41560i) q^{56} -6.47895i q^{57} +(1.22939 - 5.13770i) q^{58} +(-4.25247 - 4.25247i) q^{59} +(-3.34285 - 1.69698i) q^{60} +(-1.14204 - 1.14204i) q^{61} +(-8.57335 + 5.26257i) q^{62} +(-0.142388 - 2.64192i) q^{63} +(-7.89582 + 1.28687i) q^{64} -5.35708 q^{65} +(-1.23997 - 2.02006i) q^{66} +(-3.05161 - 3.05161i) q^{67} +(-0.492900 - 0.250218i) q^{68} +(-1.28519 + 1.28519i) q^{69} +(-1.26274 + 6.89898i) q^{70} +8.36612 q^{71} +(2.81920 - 0.228233i) q^{72} -16.9603 q^{73} +(1.53018 + 0.366156i) q^{74} +(1.05104 + 1.05104i) q^{75} +(-4.02261 - 12.3177i) q^{76} +(-2.96228 + 3.29978i) q^{77} +(3.44456 - 2.11437i) q^{78} +13.8414i q^{79} +(-7.40900 - 1.15079i) q^{80} -1.00000 q^{81} +(8.83525 - 5.42333i) q^{82} +(-9.90941 + 9.90941i) q^{83} +(-1.91100 - 4.93438i) q^{84} +(-0.366336 - 0.366336i) q^{85} +(0.790551 - 3.30375i) q^{86} +3.73546i q^{87} +(-3.61163 - 3.07065i) q^{88} -7.94992 q^{89} +(2.57810 + 0.616912i) q^{90} +(-5.62670 - 5.05121i) q^{91} +(-1.64544 + 3.24132i) q^{92} +(5.02983 - 5.02983i) q^{93} +(-13.9474 + 8.56132i) q^{94} -12.1445i q^{95} +(5.21813 - 2.18428i) q^{96} +13.1657i q^{97} +(-7.83136 + 6.05556i) q^{98} +(1.18514 + 1.18514i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.20526	+	0.739825i	−0.852250	+	0.523135i
$2$	−1.20526	+	0.739825i	−0.852250	+	0.523135i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$3$	0.707107	−	0.707107i	0.408248	−	0.408248i
$4$	0.905318	−	1.78337i	0.452659	−	0.891684i
$5$	1.32544	−	1.32544i	0.592756	−	0.592756i	−0.345619	−	0.938375i	$-0.612331\pi$
$5$	1.32544	−	1.32544i	0.592756	−	0.592756i	0.938375	+	0.345619i	$0.112331\pi$
$6$	−0.329115	+	1.37538i	−0.134360	+	0.561499i
$7$	2.64192	−	0.142388i	0.998551	−	0.0538175i
$7$	2.64192	−	0.142388i	0.998551	−	0.0538175i
$8$	0.228233	+	2.81920i	0.0806925	+	0.996739i
$9$		−	1.00000i		−	0.333333i
$10$	−0.616912	+	2.57810i	−0.195085	+	0.815268i
$11$	−1.18514	+	1.18514i	−0.357332	+	0.357332i	−0.862829	−	0.505497i	$-0.831309\pi$
$11$	−1.18514	+	1.18514i	−0.357332	+	0.357332i	0.505497	+	0.862829i	$0.331309\pi$
$12$	−0.620874	−	1.90119i	−0.179231	−	0.548826i
$13$	−2.02086	−	2.02086i	−0.560487	−	0.560487i	0.368959	−	0.929446i	$-0.379714\pi$
$13$	−2.02086	−	2.02086i	−0.560487	−	0.560487i	−0.929446	+	0.368959i	$0.879714\pi$
$14$	−3.07886	+	2.12617i	−0.822861	+	0.568243i
$15$		−	1.87446i		−	0.483983i
$16$	−2.36080	−	3.22903i	−0.590199	−	0.807257i
$17$		−	0.276387i		−	0.0670337i	−0.999438	−	0.0335169i	$-0.989329\pi$
$17$		−	0.276387i		−	0.0670337i	0.999438	−	0.0335169i	$-0.0106707\pi$
$18$	0.739825	+	1.20526i	0.174378	+	0.284083i
$19$	4.58131	−	4.58131i	1.05102	−	1.05102i	0.0523978	−	0.998626i	$-0.483314\pi$
$19$	4.58131	−	4.58131i	1.05102	−	1.05102i	0.998626	−	0.0523978i	$-0.0166864\pi$
$20$	−1.16380	−	3.56370i	−0.260235	−	0.796868i
$21$	1.76743	−	1.96880i	0.385686	−	0.429628i
$22$	0.551607	−	2.30519i	0.117603	−	0.491469i
$23$	−1.81753			−0.378981			−0.189491	−	0.981883i	$-0.560684\pi$
$23$	−1.81753			−0.378981			−0.189491	+	0.981883i	$0.560684\pi$
$24$	2.15486	+	1.83209i	0.439860	+	0.373974i
$25$			1.48640i			0.297280i
$26$	3.93076	+	0.940587i	0.770885	+	0.184464i
$27$	−0.707107	−	0.707107i	−0.136083	−	0.136083i
$28$	2.13785	−	4.84041i	0.404015	−	0.914752i
$29$	−2.64137	+	2.64137i	−0.490490	+	0.490490i	−0.908461	−	0.417970i	$-0.862742\pi$
$29$	−2.64137	+	2.64137i	−0.490490	+	0.490490i	0.417970	+	0.908461i	$0.362742\pi$
$30$	1.38677	+	2.25922i	0.253189	+	0.412475i
$31$	7.11326			1.27758			0.638790	−	0.769382i	$-0.279435\pi$
$31$	7.11326			1.27758			0.638790	+	0.769382i	$0.279435\pi$
$32$	5.23430	+	2.14525i	0.925302	+	0.379231i
$33$			1.67603i			0.291760i
$34$	0.204478	+	0.333119i	0.0350677	+	0.0571295i
$35$	3.31298	−	3.69044i	0.559997	−	0.623798i
$36$	−1.78337	−	0.905318i	−0.297228	−	0.150886i
$37$	−0.786692	−	0.786692i	−0.129331	−	0.129331i	0.639478	−	0.768809i	$-0.279150\pi$
$37$	−0.786692	−	0.786692i	−0.129331	−	0.129331i	−0.768809	+	0.639478i	$0.779150\pi$
$38$	−2.13232	+	8.91105i	−0.345907	+	1.44556i
$39$	−2.85793			−0.457636
$40$	4.03920	+	3.43419i	0.638654	+	0.542992i
$41$	−7.33055			−1.14484			−0.572420	−	0.819961i	$-0.693995\pi$
$41$	−7.33055			−1.14484			−0.572420	+	0.819961i	$0.693995\pi$
$42$	−0.673655	+	3.68051i	−0.103947	+	0.567916i
$43$	−1.69851	+	1.69851i	−0.259020	+	0.259020i	−0.824656	−	0.565635i	$-0.808631\pi$
$43$	−1.69851	+	1.69851i	−0.259020	+	0.259020i	0.565635	+	0.824656i	$0.308631\pi$
$44$	1.04061	+	3.18646i	0.156877	+	0.480376i
$45$	−1.32544	−	1.32544i	−0.197585	−	0.197585i
$46$	2.19060	−	1.34465i	0.322987	−	0.198258i
$47$	11.5721			1.68796			0.843982	−	0.536372i	$-0.180205\pi$
$47$	11.5721			1.68796			0.843982	+	0.536372i	$0.180205\pi$
$48$	−3.95261	−	0.613933i	−0.570509	−	0.0886136i
$49$	6.95945	−	0.752353i	0.994207	−	0.107479i
$50$	−1.09968	−	1.79150i	−0.155518	−	0.253357i
$51$	−0.195435	−	0.195435i	−0.0273664	−	0.0273664i
$52$	−5.43347	+	1.77442i	−0.753487	+	0.246067i
$53$	3.85262	+	3.85262i	0.529198	+	0.529198i	0.920333	−	0.391135i	$-0.127917\pi$
$53$	3.85262	+	3.85262i	0.529198	+	0.529198i	−0.391135	+	0.920333i	$0.627917\pi$
$54$	1.37538	+	0.329115i	0.187166	+	0.0447868i
$55$			3.14166i			0.423621i
$56$	1.00439	+	7.41560i	0.134218	+	0.990952i
$57$		−	6.47895i		−	0.858158i
$58$	1.22939	−	5.13770i	0.161427	−	0.674613i
$59$	−4.25247	−	4.25247i	−0.553625	−	0.553625i	0.373860	−	0.927485i	$-0.378034\pi$
$59$	−4.25247	−	4.25247i	−0.553625	−	0.553625i	−0.927485	+	0.373860i	$0.878034\pi$
$60$	−3.34285	−	1.69698i	−0.431560	−	0.219080i
$61$	−1.14204	−	1.14204i	−0.146223	−	0.146223i	0.630206	−	0.776428i	$-0.282971\pi$
$61$	−1.14204	−	1.14204i	−0.146223	−	0.146223i	−0.776428	+	0.630206i	$0.782971\pi$
$62$	−8.57335	+	5.26257i	−1.08882	+	0.668347i
$63$	−0.142388	−	2.64192i	−0.0179392	−	0.332850i
$64$	−7.89582	+	1.28687i	−0.986977	+	0.160859i
$65$	−5.35708			−0.664464
$66$	−1.23997	−	2.02006i	−0.152630	−	0.248653i
$67$	−3.05161	−	3.05161i	−0.372813	−	0.372813i	0.495688	−	0.868501i	$-0.334916\pi$
$67$	−3.05161	−	3.05161i	−0.372813	−	0.372813i	−0.868501	+	0.495688i	$0.834916\pi$
$68$	−0.492900	−	0.250218i	−0.0597729	−	0.0303434i
$69$	−1.28519	+	1.28519i	−0.154718	+	0.154718i
$70$	−1.26274	+	6.89898i	−0.150926	+	0.824586i
$71$	8.36612			0.992876			0.496438	−	0.868072i	$-0.334641\pi$
$71$	8.36612			0.992876			0.496438	+	0.868072i	$0.334641\pi$
$72$	2.81920	−	0.228233i	0.332246	−	0.0268975i
$73$	−16.9603			−1.98505			−0.992527	−	0.122024i	$-0.961061\pi$
$73$	−16.9603			−1.98505			−0.992527	+	0.122024i	$0.961061\pi$
$74$	1.53018	+	0.366156i	0.177880	+	0.0425648i
$75$	1.05104	+	1.05104i	0.121364	+	0.121364i
$76$	−4.02261	−	12.3177i	−0.461425	−	1.41294i
$77$	−2.96228	+	3.29978i	−0.337583	+	0.376045i
$78$	3.44456	−	2.11437i	0.390020	−	0.239405i
$79$			13.8414i			1.55728i	0.627470	+	0.778641i	$0.284091\pi$
$79$			13.8414i			1.55728i	−0.627470	+	0.778641i	$0.715909\pi$
$80$	−7.40900	−	1.15079i	−0.828351	−	0.128663i
$81$	−1.00000			−0.111111
$82$	8.83525	−	5.42333i	0.975690	−	0.598906i
$83$	−9.90941	+	9.90941i	−1.08770	+	1.08770i	−0.0919340	+	0.995765i	$0.529305\pi$
$83$	−9.90941	+	9.90941i	−1.08770	+	1.08770i	−0.995765	+	0.0919340i	$0.970695\pi$
$84$	−1.91100	−	4.93438i	−0.208508	−	0.538385i
$85$	−0.366336	−	0.366336i	−0.0397347	−	0.0397347i
$86$	0.790551	−	3.30375i	0.0852474	−	0.356253i
$87$			3.73546i			0.400484i
$88$	−3.61163	−	3.07065i	−0.385001	−	0.327333i
$89$	−7.94992			−0.842690			−0.421345	−	0.906901i	$-0.638442\pi$
$89$	−7.94992			−0.842690			−0.421345	+	0.906901i	$0.638442\pi$
$90$	2.57810	+	0.616912i	0.271756	+	0.0650282i
$91$	−5.62670	−	5.05121i	−0.589839	−	0.529511i
$92$	−1.64544	+	3.24132i	−0.171549	+	0.337931i
$93$	5.02983	−	5.02983i	0.521569	−	0.521569i
$94$	−13.9474	+	8.56132i	−1.43857	+	0.883033i
$95$		−	12.1445i		−	1.24600i
$96$	5.21813	−	2.18428i	0.532573	−	0.222933i
$97$			13.1657i			1.33678i	0.743812	+	0.668388i	$0.233016\pi$
$97$			13.1657i			1.33678i	−0.743812	+	0.668388i	$0.766984\pi$
$98$	−7.83136	+	6.05556i	−0.791087	+	0.611704i
$99$	1.18514	+	1.18514i	0.119111	+	0.119111i
$100$	2.65080	+	1.34566i	0.265080	+	0.134566i
$101$	1.20635	−	1.20635i	0.120036	−	0.120036i	−0.644537	−	0.764573i	$-0.722950\pi$
$101$	1.20635	−	1.20635i	0.120036	−	0.120036i	0.764573	+	0.644537i	$0.222950\pi$
$102$	0.380139	+	0.0909630i	0.0376393	+	0.00900668i
$103$			11.4220i			1.12544i	0.826647	+	0.562722i	$0.190246\pi$
$103$			11.4220i			1.12544i	−0.826647	+	0.562722i	$0.809754\pi$
$104$	5.23600	−	6.15846i	0.513432	−	0.603886i
$105$	−0.266900	−	4.95217i	−0.0260468	−	0.483282i
$106$	−7.49369	−	1.79316i	−0.727852	−	0.174167i
$107$	9.18783	−	9.18783i	0.888221	−	0.888221i	−0.106131	−	0.994352i	$-0.533846\pi$
$107$	9.18783	−	9.18783i	0.888221	−	0.888221i	0.994352	+	0.106131i	$0.0338464\pi$
$108$	−1.90119	+	0.620874i	−0.182942	+	0.0597437i
$109$	0.541341	−	0.541341i	0.0518511	−	0.0518511i	−0.680706	−	0.732557i	$-0.738327\pi$
$109$	0.541341	−	0.541341i	0.0518511	−	0.0518511i	0.732557	+	0.680706i	$0.238327\pi$
$110$	−2.32428	−	3.78653i	−0.221611	−	0.361031i
$111$	−1.11255			−0.105599
$112$	−6.69681	−	8.19468i	−0.632789	−	0.774325i
$113$	−11.9427			−1.12347			−0.561735	−	0.827317i	$-0.689866\pi$
$113$	−11.9427			−1.12347			−0.561735	+	0.827317i	$0.689866\pi$
$114$	4.79329	+	7.80884i	0.448932	+	0.731365i
$115$	−2.40903	+	2.40903i	−0.224644	+	0.224644i
$116$	2.31925	+	7.10182i	0.215337	+	0.659387i
$117$	−2.02086	+	2.02086i	−0.186829	+	0.186829i
$118$	8.27144	+	1.97926i	0.761447	+	0.182206i
$119$	−0.0393541	−	0.730192i	−0.00360759	−	0.0669366i
$120$	5.28448	−	0.427813i	0.482405	−	0.0390538i
$121$			8.19091i			0.744628i
$122$	2.22136	+	0.531547i	0.201113	+	0.0481240i
$123$	−5.18348	+	5.18348i	−0.467379	+	0.467379i
$124$	6.43976	−	12.6856i	0.578308	−	1.13920i
$125$	8.59736	+	8.59736i	0.768971	+	0.768971i
$126$	2.12617	+	3.07886i	0.189414	+	0.274287i
$127$			18.8618i			1.67371i	0.547422	+	0.836857i	$0.315609\pi$
$127$			18.8618i			1.67371i	−0.547422	+	0.836857i	$0.684391\pi$
$128$	8.56448	−	7.39254i	0.757000	−	0.653414i
$129$			2.40206i			0.211489i
$130$	6.45669	−	3.96330i	0.566289	−	0.347605i
$131$	8.80983	−	8.80983i	0.769718	−	0.769718i	−0.208339	−	0.978057i	$-0.566806\pi$
$131$	8.80983	−	8.80983i	0.769718	−	0.769718i	0.978057	+	0.208339i	$0.0668056\pi$
$132$	2.98899	+	1.51735i	0.260158	+	0.132068i
$133$	11.4511	−	12.7558i	0.992937	−	1.10606i
$134$	5.93565	+	1.42033i	0.512762	+	0.122698i
$135$	−1.87446			−0.161328
$136$	0.779192	−	0.0630806i	0.0668151	−	0.00540912i
$137$			4.34380i			0.371116i	0.982633	+	0.185558i	$0.0594092\pi$
$137$			4.34380i			0.371116i	−0.982633	+	0.185558i	$0.940591\pi$
$138$	0.598176	−	2.49980i	0.0509201	−	0.212797i
$139$	−1.64886	−	1.64886i	−0.139854	−	0.139854i	0.633714	−	0.773568i	$-0.281530\pi$
$139$	−1.64886	−	1.64886i	−0.139854	−	0.139854i	−0.773568	+	0.633714i	$0.781530\pi$
$140$	−3.58210	−	9.24929i	−0.302743	−	0.781708i
$141$	8.18271	−	8.18271i	0.689108	−	0.689108i
$142$	−10.0834	+	6.18946i	−0.846178	+	0.519408i
$143$	4.79000			0.400560
$144$	−3.22903	+	2.36080i	−0.269086	+	0.196733i
$145$			7.00197i			0.581482i
$146$	20.4416	−	12.5477i	1.69176	−	1.03845i
$147$	4.38908	−	5.45307i	0.362005	−	0.449762i
$148$	−2.11517	+	0.690754i	−0.173866	+	0.0567796i
$149$	−10.1553	−	10.1553i	−0.831955	−	0.831955i	0.155829	−	0.987784i	$-0.450195\pi$
$149$	−10.1553	−	10.1553i	−0.831955	−	0.831955i	−0.987784	+	0.155829i	$0.950195\pi$
$150$	−2.04437	−	0.489196i	−0.166922	−	0.0399427i
$151$	−8.92611			−0.726397			−0.363198	−	0.931712i	$-0.618315\pi$
$151$	−8.92611			−0.726397			−0.363198	+	0.931712i	$0.618315\pi$
$152$	13.9612	+	11.8700i	1.13241	+	0.962787i
$153$	−0.276387			−0.0223446
$154$	1.12907	−	6.16867i	0.0909831	−	0.497086i
$155$	9.42822	−	9.42822i	0.757293	−	0.757293i
$156$	−2.58734	+	5.09675i	−0.207153	+	0.408066i
$157$	5.83300	+	5.83300i	0.465524	+	0.465524i	0.900461	−	0.434937i	$-0.143229\pi$
$157$	5.83300	+	5.83300i	0.465524	+	0.465524i	−0.434937	+	0.900461i	$0.643229\pi$
$158$	−10.2402	−	16.6826i	−0.814669	−	1.32719i
$159$	5.44843			0.432089
$160$	9.78118	−	4.09435i	0.773270	−	0.323687i
$161$	−4.80176	+	0.258794i	−0.378432	+	0.0203958i
$162$	1.20526	−	0.739825i	0.0946944	−	0.0581261i
$163$	12.4751	+	12.4751i	0.977129	+	0.977129i	0.999744	−	0.0226151i	$-0.00719923\pi$
$163$	12.4751	+	12.4751i	0.977129	+	0.977129i	−0.0226151	+	0.999744i	$0.507199\pi$
$164$	−6.63648	+	13.0731i	−0.518222	+	1.02084i
$165$	2.22149	+	2.22149i	0.172943	+	0.172943i
$166$	4.61222	−	19.2747i	0.357978	−	1.49600i
$167$			21.3378i			1.65117i	0.564280	+	0.825584i	$0.309154\pi$
$167$			21.3378i			1.65117i	−0.564280	+	0.825584i	$0.690846\pi$
$168$	5.95384	+	4.53341i	0.459348	+	0.349760i
$169$		−	4.83221i		−	0.371709i
$170$	0.712555	+	0.170507i	0.0546505	+	0.0130773i
$171$	−4.58131	−	4.58131i	−0.350341	−	0.350341i
$172$	1.49138	+	4.56676i	0.113716	+	0.348212i
$173$	−10.7377	−	10.7377i	−0.816371	−	0.816371i	0.169209	−	0.985580i	$-0.445879\pi$
$173$	−10.7377	−	10.7377i	−0.816371	−	0.816371i	−0.985580	+	0.169209i	$0.945879\pi$
$174$	−2.76359	−	4.50221i	−0.209507	−	0.341312i
$175$	0.211645	+	3.92695i	0.0159989	+	0.296849i
$176$	6.62470	+	1.02897i	0.499356	+	0.0775618i
$177$	−6.01391			−0.452033
$178$	9.58174	−	5.88155i	0.718182	−	0.440841i
$179$	2.41822	+	2.41822i	0.180746	+	0.180746i	0.791681	−	0.610935i	$-0.209206\pi$
$179$	2.41822	+	2.41822i	0.180746	+	0.180746i	−0.610935	+	0.791681i	$0.709206\pi$
$180$	−3.56370	+	1.16380i	−0.265623	+	0.0867448i
$181$	0.318290	−	0.318290i	0.0236583	−	0.0236583i	−0.695179	−	0.718837i	$-0.744675\pi$
$181$	0.318290	−	0.318290i	0.0236583	−	0.0236583i	0.718837	+	0.695179i	$0.244675\pi$
$182$	10.5187	+	1.92526i	0.779695	+	0.142710i
$183$	−1.61508			−0.119390
$184$	−0.414820	−	5.12399i	−0.0305809	−	0.377745i
$185$	−2.08543			−0.153324
$186$	−2.34108	+	9.78347i	−0.171656	+	0.717359i
$187$	0.327556	+	0.327556i	0.0239533	+	0.0239533i
$188$	10.4764	−	20.6373i	0.764072	−	1.50513i
$189$	−1.96880	−	1.76743i	−0.143209	−	0.128562i
$190$	8.98482	+	14.6374i	0.651828	+	1.06191i
$191$		−	24.4401i		−	1.76842i	−0.467088	−	0.884211i	$-0.654697\pi$
$191$		−	24.4401i		−	1.76842i	0.467088	−	0.884211i	$-0.345303\pi$
$192$	−4.67323	+	6.49314i	−0.337262	+	0.468602i
$193$	22.3910			1.61174			0.805871	−	0.592091i	$-0.201698\pi$
$193$	22.3910			1.61174			0.805871	+	0.592091i	$0.201698\pi$
$194$	−9.74033	−	15.8682i	−0.699315	−	1.13927i
$195$	−3.78803	+	3.78803i	−0.271266	+	0.271266i
$196$	4.95880	−	13.0924i	0.354200	−	0.935170i
$197$	13.4527	+	13.4527i	0.958463	+	0.958463i	0.999171	−	0.0407083i	$-0.0129614\pi$
$197$	13.4527	+	13.4527i	0.958463	+	0.958463i	−0.0407083	+	0.999171i	$0.512961\pi$
$198$	−2.30519	−	0.551607i	−0.163823	−	0.0392010i
$199$		−	5.64437i		−	0.400119i	−0.979784	−	0.200059i	$-0.935886\pi$
$199$		−	5.64437i		−	0.400119i	0.979784	−	0.200059i	$-0.0641135\pi$
$200$	−4.19046	+	0.339245i	−0.296311	+	0.0239883i
$201$	−4.31563			−0.304401
$202$	−0.561482	+	2.34646i	−0.0395057	+	0.165096i
$203$	−6.60218	+	7.35438i	−0.463382	+	0.516176i
$204$	−0.525464	+	0.171602i	−0.0367898	+	0.0120145i
$205$	−9.71623	+	9.71623i	−0.678611	+	0.678611i
$206$	−8.45028	−	13.7665i	−0.588759	−	0.959159i
$207$			1.81753i			0.126327i
$208$	−1.75458	+	11.2963i	−0.121658	+	0.783256i
$209$			10.8589i			0.751129i
$210$	3.98542	+	5.77121i	0.275020	+	0.398251i
$211$	−13.9095	−	13.9095i	−0.957568	−	0.957568i	0.0415678	−	0.999136i	$-0.486765\pi$
$211$	−13.9095	−	13.9095i	−0.957568	−	0.957568i	−0.999136	+	0.0415678i	$0.986765\pi$
$212$	10.3585	−	3.38279i	0.711424	−	0.232331i
$213$	5.91574	−	5.91574i	0.405340	−	0.405340i
$214$	−4.27637	+	17.8711i	−0.292326	+	1.22165i
$215$			4.50256i			0.307072i
$216$	1.83209	−	2.15486i	0.124658	−	0.146620i
$217$	18.7926	−	1.01284i	1.27573	−	0.0687561i
$218$	−0.251961	+	1.05296i	−0.0170649	+	0.0713152i
$219$	−11.9928	+	11.9928i	−0.810395	+	0.810395i
$220$	5.60273	+	2.84420i	0.377736	+	0.191756i
$221$	−0.558541	+	0.558541i	−0.0375715	+	0.0375715i
$222$	1.34092	−	0.823092i	0.0899963	−	0.0552423i
$223$	−15.4893			−1.03724			−0.518622	−	0.855004i	$-0.673555\pi$
$223$	−15.4893			−1.03724			−0.518622	+	0.855004i	$0.673555\pi$
$224$	14.1340	+	4.92228i	0.944370	+	0.328884i
$225$	1.48640			0.0990933
$226$	14.3940	−	8.83548i	0.957478	−	0.587727i
$227$	−4.24437	+	4.24437i	−0.281709	+	0.281709i	−0.833790	−	0.552081i	$-0.813834\pi$
$227$	−4.24437	+	4.24437i	−0.281709	+	0.281709i	0.552081	+	0.833790i	$0.313834\pi$
$228$	−11.5543	−	5.86551i	−0.765205	−	0.388453i
$229$	−2.39096	+	2.39096i	−0.157999	+	0.157999i	−0.781679	−	0.623680i	$-0.785637\pi$
$229$	−2.39096	+	2.39096i	−0.157999	+	0.157999i	0.623680	+	0.781679i	$0.285637\pi$
$230$	1.12126	−	4.68578i	0.0739334	−	0.308971i
$231$	0.238647	+	4.42795i	0.0157018	+	0.291337i
$232$	−8.04941	−	6.84371i	−0.528470	−	0.449312i
$233$			2.92061i			0.191336i	0.995413	+	0.0956678i	$0.0304987\pi$
$233$			2.92061i			0.191336i	−0.995413	+	0.0956678i	$0.969501\pi$
$234$	0.940587	−	3.93076i	0.0614881	−	0.256962i
$235$	15.3382	−	15.3382i	1.00055	−	1.00055i
$236$	−11.4336	+	3.73388i	−0.744262	+	0.243055i
$237$	9.78736	+	9.78736i	0.635758	+	0.635758i
$238$	0.587646	+	0.850958i	0.0380914	+	0.0551594i
$239$		−	7.83859i		−	0.507036i	−0.967331	−	0.253518i	$-0.918412\pi$
$239$		−	7.83859i		−	0.507036i	0.967331	−	0.253518i	$-0.0815877\pi$
$240$	−6.05269	+	4.42522i	−0.390699	+	0.285647i
$241$		−	18.3656i		−	1.18303i	−0.806293	−	0.591516i	$-0.798530\pi$
$241$		−	18.3656i		−	1.18303i	0.806293	−	0.591516i	$-0.201470\pi$
$242$	−6.05984	−	9.87220i	−0.389541	−	0.634609i
$243$	−0.707107	+	0.707107i	−0.0453609	+	0.0453609i
$244$	−3.07058	+	1.00276i	−0.196574	+	0.0641954i
$245$	8.22716	−	10.2216i	0.525614	−	0.653031i
$246$	2.41259	−	10.0823i	0.153821	−	0.642826i
$247$	−18.5164			−1.17817
$248$	1.62348	+	20.0537i	0.103091	+	1.27341i
$249$			14.0140i			0.888103i
$250$	−16.7226	−	4.00154i	−1.05763	−	0.253079i
$251$	−16.2774	−	16.2774i	−1.02742	−	1.02742i	−0.999613	−	0.0278042i	$-0.991149\pi$
$251$	−16.2774	−	16.2774i	−1.02742	−	1.02742i	−0.0278042	−	0.999613i	$-0.508851\pi$
$252$	−4.84041	−	2.13785i	−0.304917	−	0.134672i
$253$	2.15402	−	2.15402i	0.135422	−	0.135422i
$254$	−13.9544	−	22.7334i	−0.875578	−	1.42642i
$255$	−0.518077			−0.0324432
$256$	−4.85327	+	15.2462i	−0.303329	+	0.952886i
$257$			13.6309i			0.850274i	0.905129	+	0.425137i	$0.139774\pi$
$257$			13.6309i			0.850274i	−0.905129	+	0.425137i	$0.860226\pi$
$258$	−1.77710	−	2.89511i	−0.110637	−	0.180242i
$259$	−2.19039	−	1.96636i	−0.136104	−	0.122184i
$260$	−4.84986	+	9.55365i	−0.300776	+	0.592492i
$261$	2.64137	+	2.64137i	0.163497	+	0.163497i
$262$	−4.10043	+	17.1359i	−0.253325	+	1.05866i
$263$	5.88266			0.362740			0.181370	−	0.983415i	$-0.441947\pi$
$263$	5.88266			0.362740			0.181370	+	0.983415i	$0.441947\pi$
$264$	−4.72508	+	0.382526i	−0.290809	+	0.0235429i
$265$	10.2129			0.627371
$266$	−4.36458	+	23.8459i	−0.267609	+	1.46208i
$267$	−5.62144	+	5.62144i	−0.344027	+	0.344027i
$268$	−8.20481	+	2.67946i	−0.501189	+	0.163674i
$269$	7.28207	+	7.28207i	0.443995	+	0.443995i	0.893352	−	0.449357i	$-0.148347\pi$
$269$	7.28207	+	7.28207i	0.443995	+	0.443995i	−0.449357	+	0.893352i	$0.648347\pi$
$270$	2.25922	−	1.38677i	0.137492	−	0.0843963i
$271$	−7.65390			−0.464941			−0.232471	−	0.972603i	$-0.574681\pi$
$271$	−7.65390			−0.464941			−0.232471	+	0.972603i	$0.574681\pi$
$272$	−0.892462	+	0.652494i	−0.0541135	+	0.0395633i
$273$	−7.55042	+	0.406935i	−0.456972	+	0.0246288i
$274$	−3.21365	−	5.23542i	−0.194144	−	0.316283i
$275$	−1.76159	−	1.76159i	−0.106228	−	0.106228i
$276$	1.12846	+	3.45547i	0.0679252	+	0.207995i
$277$	−20.9351	−	20.9351i	−1.25787	−	1.25787i	−0.952109	−	0.305758i	$-0.901090\pi$
$277$	−20.9351	−	20.9351i	−1.25787	−	1.25787i	−0.305758	−	0.952109i	$-0.598910\pi$
$278$	3.20717	+	0.767440i	0.192353	+	0.0460280i
$279$		−	7.11326i		−	0.425860i
$280$	11.1602	+	8.49770i	0.666951	+	0.507835i
$281$			13.2903i			0.792835i	0.918070	+	0.396417i	$0.129747\pi$
$281$			13.2903i			0.792835i	−0.918070	+	0.396417i	$0.870253\pi$
$282$	−3.80854	+	15.9161i	−0.226796	+	0.947789i
$283$	−7.97242	−	7.97242i	−0.473911	−	0.473911i	0.429267	−	0.903178i	$-0.358772\pi$
$283$	−7.97242	−	7.97242i	−0.473911	−	0.473911i	−0.903178	+	0.429267i	$0.858772\pi$
$284$	7.57400	−	14.9199i	0.449434	−	0.885331i
$285$	−8.58748	−	8.58748i	−0.508678	−	0.508678i
$286$	−5.77321	+	3.54376i	−0.341377	+	0.209547i
$287$	−19.3667	+	1.04378i	−1.14318	+	0.0616124i
$288$	2.14525	−	5.23430i	0.126410	−	0.308434i
$289$	16.9236			0.995506
$290$	−5.18024	−	8.43922i	−0.304194	−	0.495568i
$291$	9.30957	+	9.30957i	0.545737	+	0.545737i
$292$	−15.3545	+	30.2465i	−0.898553	+	1.77004i
$293$	11.7572	−	11.7572i	0.686863	−	0.686863i	−0.274674	−	0.961537i	$-0.588570\pi$
$293$	11.7572	−	11.7572i	0.686863	−	0.686863i	0.961537	+	0.274674i	$0.0885701\pi$
$294$	−1.25568	+	9.81953i	−0.0732328	+	0.572687i
$295$	−11.2728			−0.656329
$296$	2.03829	−	2.39739i	0.118473	−	0.139346i
$297$	1.67603			0.0972534
$298$	19.7530	+	4.72667i	1.14426	+	0.273808i
$299$	3.67298	+	3.67298i	0.212414	+	0.212414i
$300$	2.82593	−	0.922868i	0.163155	−	0.0532818i
$301$	−4.24548	+	4.72917i	−0.244705	+	0.272585i
$302$	10.7583	−	6.60376i	0.619071	−	0.380004i
$303$		−	1.70604i		−	0.0980093i
$304$	−25.6087	−	3.97764i	−1.46876	−	0.228133i
$305$	−3.02741			−0.173349
$306$	0.333119	−	0.204478i	0.0190432	−	0.0116892i
$307$	−20.0939	+	20.0939i	−1.14682	+	1.14682i	−0.159645	+	0.987174i	$0.551035\pi$
$307$	−20.0939	+	20.0939i	−1.14682	+	1.14682i	−0.987174	+	0.159645i	$0.948965\pi$
$308$	3.20291	+	8.27019i	0.182503	+	0.471238i
$309$	8.07657	+	8.07657i	0.459460	+	0.459460i
$310$	−4.38825	+	18.3387i	−0.249236	+	1.04157i
$311$		−	26.0652i		−	1.47802i	−0.673693	−	0.739012i	$-0.735293\pi$
$311$		−	26.0652i		−	1.47802i	0.673693	−	0.739012i	$-0.264707\pi$
$312$	−0.652274	−	8.05710i	−0.0369278	−	0.456143i
$313$	−13.5651			−0.766743			−0.383372	−	0.923594i	$-0.625237\pi$
$313$	−13.5651			−0.766743			−0.383372	+	0.923594i	$0.625237\pi$
$314$	−11.3457	−	2.71490i	−0.640275	−	0.153211i
$315$	−3.69044	−	3.31298i	−0.207933	−	0.186666i
$316$	24.6843	+	12.5309i	1.38860	+	0.704918i
$317$	21.5304	−	21.5304i	1.20927	−	1.20927i	0.238004	−	0.971264i	$-0.423507\pi$
$317$	21.5304	−	21.5304i	1.20927	−	1.20927i	0.971264	−	0.238004i	$-0.0764931\pi$
$318$	−6.56679	+	4.03089i	−0.368247	+	0.226041i
$319$		−	6.26077i		−	0.350536i
$320$	−8.75979	+	12.1711i	−0.489687	+	0.680387i
$321$		−	12.9935i		−	0.725229i
$322$	5.59593	−	3.86438i	0.311849	−	0.215353i
$323$	−1.26621	−	1.26621i	−0.0704541	−	0.0704541i
$324$	−0.905318	+	1.78337i	−0.0502955	+	0.0990760i
$325$	3.00381	−	3.00381i	0.166622	−	0.166622i
$326$	−24.2653	−	5.80641i	−1.34393	−	0.321587i
$327$		−	0.765572i		−	0.0423362i
$328$	−1.67307	−	20.6663i	−0.0923800	−	1.14111i
$329$	30.5725	−	1.64772i	1.68552	−	0.0908420i
$330$	−4.32099	−	1.03397i	−0.237863	−	0.0569180i
$331$	5.85042	−	5.85042i	0.321568	−	0.321568i	−0.527800	−	0.849369i	$-0.676983\pi$
$331$	5.85042	−	5.85042i	0.321568	−	0.321568i	0.849369	+	0.527800i	$0.176983\pi$
$332$	8.70095	+	26.6433i	0.477527	+	1.46224i
$333$	−0.786692	+	0.786692i	−0.0431104	+	0.0431104i
$334$	−15.7862	−	25.7176i	−0.863784	−	1.40721i
$335$	−8.08947			−0.441975
$336$	−10.5299	−	1.05916i	−0.574452	−	0.0577818i
$337$	11.1243			0.605980			0.302990	−	0.952994i	$-0.402015\pi$
$337$	11.1243			0.605980			0.302990	+	0.952994i	$0.402015\pi$
$338$	3.57499	+	5.82409i	0.194454	+	0.316789i
$339$	−8.44474	+	8.44474i	−0.458655	+	0.458655i
$340$	−0.984961	+	0.321661i	−0.0534170	+	0.0174445i
$341$	−8.43018	+	8.43018i	−0.456520	+	0.456520i
$342$	8.91105	+	2.13232i	0.481854	+	0.115302i
$343$	18.2792	−	2.97859i	0.986982	−	0.160829i
$344$	−5.17610	−	4.40079i	−0.279077	−	0.237275i
$345$			3.40689i			0.183421i
$346$	20.8857	+	4.99773i	1.12282	+	0.268680i
$347$	−16.7722	+	16.7722i	−0.900379	+	0.900379i	−0.995469	−	0.0950894i	$-0.969686\pi$
$347$	−16.7722	+	16.7722i	−0.900379	+	0.900379i	0.0950894	+	0.995469i	$0.469686\pi$
$348$	6.66170	+	3.38178i	0.357105	+	0.181283i
$349$	11.9769	+	11.9769i	0.641110	+	0.641110i	0.950828	−	0.309718i	$-0.100235\pi$
$349$	11.9769	+	11.9769i	0.641110	+	0.641110i	−0.309718	+	0.950828i	$0.600235\pi$
$350$	−3.16034	−	4.57642i	−0.168927	−	0.244620i
$351$			2.85793i			0.152545i
$352$	−8.74577	+	3.66094i	−0.466151	+	0.195129i
$353$		−	34.7417i		−	1.84912i	−0.381041	−	0.924558i	$-0.624434\pi$
$353$		−	34.7417i		−	1.84912i	0.381041	−	0.924558i	$-0.375566\pi$
$354$	7.24834	−	4.44924i	0.385245	−	0.236474i
$355$	11.0888	−	11.0888i	0.588533	−	0.588533i
$356$	−7.19721	+	14.1776i	−0.381451	+	0.751413i
$357$	−0.544151	−	0.488496i	−0.0287995	−	0.0258540i
$358$	−4.70364	−	1.12553i	−0.248595	−	0.0594861i
$359$	22.2884			1.17634			0.588168	−	0.808739i	$-0.299850\pi$
$359$	22.2884			1.17634			0.588168	+	0.808739i	$0.299850\pi$
$360$	3.43419	−	4.03920i	0.180997	−	0.212885i
$361$		−	22.9768i		−	1.20930i
$362$	−0.148144	+	0.619102i	−0.00778629	+	0.0325393i
$363$	5.79185	+	5.79185i	0.303993	+	0.303993i
$364$	−14.1021	+	5.46152i	−0.739152	+	0.286262i
$365$	−22.4799	+	22.4799i	−1.17665	+	1.17665i
$366$	1.94660	−	1.19488i	0.101750	−	0.0624573i
$367$	35.3887			1.84728			0.923639	−	0.383264i	$-0.125200\pi$
$367$	35.3887			1.84728			0.923639	+	0.383264i	$0.125200\pi$
$368$	4.29082	+	5.86886i	0.223675	+	0.305935i
$369$			7.33055i			0.381613i
$370$	2.51349	−	1.54285i	0.130670	−	0.0802091i
$371$	10.7269	+	9.62974i	0.556912	+	0.499951i
$372$	−4.41644	−	13.5236i	−0.228982	−	0.701168i
$373$	6.16397	+	6.16397i	0.319158	+	0.319158i	0.848444	−	0.529285i	$-0.177540\pi$
$373$	6.16397	+	6.16397i	0.319158	+	0.319158i	−0.529285	+	0.848444i	$0.677540\pi$
$374$	−0.637126	−	0.152457i	−0.0329450	−	0.00788337i
$375$	12.1585			0.627862
$376$	2.64113	+	32.6241i	0.136206	+	1.68246i
$377$	10.6757			0.549827
$378$	3.68051	+	0.673655i	0.189305	+	0.0346491i
$379$	7.14409	−	7.14409i	0.366967	−	0.366967i	−0.499403	−	0.866370i	$-0.666447\pi$
$379$	7.14409	−	7.14409i	0.366967	−	0.366967i	0.866370	+	0.499403i	$0.166447\pi$
$380$	−21.6582	−	10.9947i	−1.11104	−	0.564014i
$381$	13.3373	+	13.3373i	0.683291	+	0.683291i
$382$	18.0814	+	29.4567i	0.925123	+	1.50714i
$383$	−15.8856			−0.811718			−0.405859	−	0.913936i	$-0.633028\pi$
$383$	−15.8856			−0.811718			−0.405859	+	0.913936i	$0.633028\pi$
$384$	0.828688	−	11.2833i	0.0422888	−	0.575799i
$385$	0.447334	+	8.30001i	0.0227982	+	0.423007i
$386$	−26.9871	+	16.5654i	−1.37361	+	0.843159i
$387$	1.69851	+	1.69851i	0.0863401	+	0.0863401i
$388$	23.4793	+	11.9192i	1.19198	+	0.605104i
$389$	3.30347	+	3.30347i	0.167493	+	0.167493i	0.785876	−	0.618384i	$-0.212212\pi$
$389$	3.30347	+	3.30347i	0.167493	+	0.167493i	−0.618384	+	0.785876i	$0.712212\pi$
$390$	1.76309	−	7.36805i	0.0892777	−	0.373096i
$391$			0.502342i			0.0254045i
$392$	3.70941	+	19.4484i	0.187354	+	0.982293i
$393$		−	12.4590i		−	0.628472i
$394$	−26.1666	−	6.26139i	−1.31826	−	0.315444i
$395$	18.3460	+	18.3460i	0.923088	+	0.923088i
$396$	3.18646	−	1.04061i	0.160125	−	0.0522925i
$397$	−11.0837	−	11.0837i	−0.556274	−	0.556274i	0.371971	−	0.928244i	$-0.378682\pi$
$397$	−11.0837	−	11.0837i	−0.556274	−	0.556274i	−0.928244	+	0.371971i	$0.878682\pi$
$398$	4.17585	+	6.80295i	0.209316	+	0.341001i
$399$	−0.922522	−	17.1168i	−0.0461839	−	0.856914i
$400$	4.79963	−	3.50909i	0.239981	−	0.175454i
$401$	−12.6471			−0.631566			−0.315783	−	0.948831i	$-0.602267\pi$
$401$	−12.6471			−0.631566			−0.315783	+	0.948831i	$0.602267\pi$
$402$	5.20146	−	3.19281i	0.259425	−	0.159243i
$403$	−14.3749	−	14.3749i	−0.716066	−	0.716066i
$404$	−1.05924	−	3.24350i	−0.0526989	−	0.161370i
$405$	−1.32544	+	1.32544i	−0.0658618	+	0.0658618i
$406$	2.51641	−	13.7484i	0.124888	−	0.682323i
$407$	1.86467			0.0924284
$408$	0.506367	−	0.595576i	0.0250689	−	0.0294854i
$409$	6.39999			0.316459			0.158230	−	0.987402i	$-0.449421\pi$
$409$	6.39999			0.316459			0.158230	+	0.987402i	$0.449421\pi$
$410$	4.52231	−	18.8989i	0.223341	−	0.933352i
$411$	3.07153	+	3.07153i	0.151507	+	0.151507i
$412$	20.3696	+	10.3405i	1.00354	+	0.509442i
$413$	−11.8402	−	10.6292i	−0.582617	−	0.523028i
$414$	−1.34465	−	2.19060i	−0.0660861	−	0.107662i
$415$			26.2687i			1.28948i
$416$	−6.24254	−	14.9131i	−0.306066	−	0.731174i
$417$	−2.33183			−0.114190
$418$	−8.03372	−	13.0879i	−0.392942	−	0.640149i
$419$	3.92319	−	3.92319i	0.191660	−	0.191660i	−0.604753	−	0.796413i	$-0.706728\pi$
$419$	3.92319	−	3.92319i	0.191660	−	0.191660i	0.796413	+	0.604753i	$0.206728\pi$
$420$	−9.07316	−	4.00731i	−0.442725	−	0.195537i
$421$	−19.9120	−	19.9120i	−0.970449	−	0.970449i	0.0291264	−	0.999576i	$-0.490727\pi$
$421$	−19.9120	−	19.9120i	−0.970449	−	0.970449i	−0.999576	+	0.0291264i	$0.990727\pi$
$422$	27.0552	+	6.47400i	1.31702	+	0.315149i
$423$		−	11.5721i		−	0.562655i
$424$	−9.98203	+	11.7406i	−0.484770	+	0.570175i
$425$	0.410822			0.0199278
$426$	−2.75341	+	11.5066i	−0.133403	+	0.557498i
$427$	−3.17978	−	2.85455i	−0.153880	−	0.138142i
$428$	−8.06736	−	24.7032i	−0.389951	−	1.19407i
$429$	3.38704	−	3.38704i	0.163528	−	0.163528i
$430$	−3.33110	−	5.42677i	−0.160640	−	0.261702i
$431$			23.6983i			1.14151i	0.821122	+	0.570753i	$0.193349\pi$
$431$			23.6983i			1.14151i	−0.821122	+	0.570753i	$0.806651\pi$
$432$	−0.613933	+	3.95261i	−0.0295379	+	0.190170i
$433$		−	25.8198i		−	1.24082i	−0.784278	−	0.620410i	$-0.786966\pi$
$433$		−	25.8198i		−	1.24082i	0.784278	−	0.620410i	$-0.213034\pi$
$434$	−21.9008	+	15.1240i	−1.05127	+	0.725975i
$435$	4.95114	+	4.95114i	0.237389	+	0.237389i
$436$	−0.475324	−	1.45550i	−0.0227639	−	0.0697056i
$437$	−8.32666	+	8.32666i	−0.398318	+	0.398318i
$438$	5.58188	−	23.3270i	0.266713	−	1.11461i
$439$		−	13.7981i		−	0.658548i	−0.944234	−	0.329274i	$-0.893196\pi$
$439$		−	13.7981i		−	0.658548i	0.944234	−	0.329274i	$-0.106804\pi$
$440$	−8.85698	+	0.717030i	−0.422240	+	0.0341831i
$441$	−0.752353	−	6.95945i	−0.0358263	−	0.331402i
$442$	0.259966	−	1.08641i	0.0123653	−	0.0516753i
$443$	9.61155	−	9.61155i	0.456658	−	0.456658i	−0.440898	−	0.897557i	$-0.645340\pi$
$443$	9.61155	−	9.61155i	0.456658	−	0.456658i	0.897557	+	0.440898i	$0.145340\pi$
$444$	−1.00721	+	1.98408i	−0.0478001	+	0.0941605i
$445$	−10.5372	+	10.5372i	−0.499510	+	0.499510i
$446$	18.6687	−	11.4594i	0.883990	−	0.542619i
$447$	−14.3618			−0.679288
$448$	−20.6769	+	4.52407i	−0.976890	+	0.213742i
$449$	−27.2681			−1.28686			−0.643430	−	0.765505i	$-0.722489\pi$
$449$	−27.2681			−1.28686			−0.643430	+	0.765505i	$0.722489\pi$
$450$	−1.79150	+	1.09968i	−0.0844523	+	0.0518392i
$451$	8.68770	−	8.68770i	0.409088	−	0.409088i
$452$	−10.8119	+	21.2981i	−0.508549	+	1.00178i
$453$	−6.31171	+	6.31171i	−0.296550	+	0.296550i
$454$	1.97549	−	8.25567i	0.0927144	−	0.387458i
$455$	−14.1530	+	0.762782i	−0.663501	+	0.0357598i
$456$	18.2655	−	1.47871i	0.855359	−	0.0692469i
$457$		−	15.7041i		−	0.734607i	−0.930101	−	0.367303i	$-0.880281\pi$
$457$		−	15.7041i		−	0.734607i	0.930101	−	0.367303i	$-0.119719\pi$
$458$	1.11284	−	4.65062i	0.0519997	−	0.217309i
$459$	−0.195435	+	0.195435i	−0.00912214	+	0.00912214i
$460$	2.11525	+	6.47713i	0.0986240	+	0.301998i
$461$	8.60225	+	8.60225i	0.400647	+	0.400647i	0.878461	−	0.477814i	$-0.158571\pi$
$461$	8.60225	+	8.60225i	0.400647	+	0.400647i	−0.477814	+	0.878461i	$0.658571\pi$
$462$	−3.56354	−	5.16028i	−0.165791	−	0.240078i
$463$			1.85673i			0.0862897i	0.999069	+	0.0431449i	$0.0137377\pi$
$463$			1.85673i			0.0862897i	−0.999069	+	0.0431449i	$0.986262\pi$
$464$	14.7648	+	2.29332i	0.685439	+	0.106465i
$465$		−	13.3335i		−	0.618327i
$466$	−2.16074	−	3.52011i	−0.100094	−	0.163066i
$467$	12.0605	−	12.0605i	0.558093	−	0.558093i	−0.370671	−	0.928764i	$-0.620872\pi$
$467$	12.0605	−	12.0605i	0.558093	−	0.558093i	0.928764	+	0.370671i	$0.120872\pi$
$468$	1.77442	+	5.43347i	0.0820225	+	0.251162i
$469$	−8.49661	−	7.62758i	−0.392337	−	0.352209i
$470$	−7.13896	+	29.8341i	−0.329296	+	1.37614i
$471$	8.24911			0.380099
$472$	11.0180	−	12.9591i	0.507146	−	0.596493i
$473$		−	4.02593i		−	0.185112i
$474$	−19.0373	−	4.55541i	−0.874411	−	0.209237i
$475$	6.80966	+	6.80966i	0.312448	+	0.312448i
$476$	−1.33783	−	0.590873i	−0.0613193	−	0.0270826i
$477$	3.85262	−	3.85262i	0.176399	−	0.176399i
$478$	5.79918	+	9.44756i	0.265248	+	0.432121i
$479$	14.9496			0.683063			0.341531	−	0.939870i	$-0.389054\pi$
$479$	14.9496			0.683063			0.341531	+	0.939870i	$0.389054\pi$
$480$	4.02119	−	9.81148i	0.183541	−	0.447831i
$481$			3.17959i			0.144977i
$482$	13.5873	+	22.1354i	0.618886	+	1.00824i
$483$	−3.21236	+	3.57835i	−0.146168	+	0.162821i
$484$	14.6074	+	7.41538i	0.663973	+	0.337063i
$485$	17.4504	+	17.4504i	0.792383	+	0.792383i
$486$	0.329115	−	1.37538i	0.0149289	−	0.0623887i
$487$	2.67317			0.121133			0.0605664	−	0.998164i	$-0.480709\pi$
$487$	2.67317			0.121133			0.0605664	+	0.998164i	$0.480709\pi$
$488$	2.95898	−	3.48028i	0.133947	−	0.157545i
$489$	17.6425			0.797823
$490$	−2.35373	+	18.4063i	−0.106330	+	0.831513i
$491$	−7.71425	+	7.71425i	−0.348139	+	0.348139i	−0.859416	−	0.511277i	$-0.829173\pi$
$491$	−7.71425	+	7.71425i	−0.348139	+	0.348139i	0.511277	+	0.859416i	$0.329173\pi$
$492$	4.55135	+	13.9368i	0.205191	+	0.628318i
$493$	0.730041	+	0.730041i	0.0328794	+	0.0328794i
$494$	22.3171	−	13.6989i	1.00410	−	0.616342i
$495$	3.14166			0.141207
$496$	−16.7930	−	22.9689i	−0.754026	−	1.03134i
$497$	22.1026	−	1.19123i	0.991437	−	0.0534341i
$498$	−10.3679	−	16.8906i	−0.464598	−	0.756885i
$499$	−10.9644	−	10.9644i	−0.490835	−	0.490835i	0.417734	−	0.908569i	$-0.362824\pi$
$499$	−10.9644	−	10.9644i	−0.490835	−	0.490835i	−0.908569	+	0.417734i	$0.862824\pi$
$500$	23.1156	−	7.54890i	1.03376	−	0.337597i
$501$	15.0881	+	15.0881i	0.674086	+	0.674086i
$502$	31.6609	+	7.57610i	1.41309	+	0.338138i
$503$		−	16.3842i		−	0.730533i	−0.930903	−	0.365267i	$-0.880978\pi$
$503$		−	16.3842i		−	0.730533i	0.930903	−	0.365267i	$-0.119022\pi$
$504$	7.41560	−	1.00439i	0.330317	−	0.0447392i
$505$		−	3.19790i		−	0.142305i
$506$	−1.00256	+	4.18976i	−0.0445694	+	0.186257i
$507$	−3.41689	−	3.41689i	−0.151749	−	0.151749i
$508$	33.6375	+	17.0759i	1.49242	+	0.757622i
$509$	−18.7512	−	18.7512i	−0.831133	−	0.831133i	0.156539	−	0.987672i	$-0.449966\pi$
$509$	−18.7512	−	18.7512i	−0.831133	−	0.831133i	−0.987672	+	0.156539i	$0.949966\pi$
$510$	0.624419	−	0.383286i	0.0276497	−	0.0169722i
$511$	−44.8077	+	2.41494i	−1.98218	+	0.106831i
$512$	−5.43003	−	21.9662i	−0.239976	−	0.970779i
$513$	−6.47895			−0.286053
$514$	−10.0845	−	16.4288i	−0.444808	−	0.724645i
$515$	15.1392	+	15.1392i	0.667113	+	0.667113i
$516$	4.28375	+	2.17463i	0.188581	+	0.0957325i
$517$	−13.7145	+	13.7145i	−0.603163	+	0.603163i
$518$	4.09476	+	0.749475i	0.179913	+	0.0329300i
$519$	−15.1854			−0.666564
$520$	−1.22266	−	15.1027i	−0.0536173	−	0.662297i
$521$	4.36154			0.191083			0.0955413	−	0.995425i	$-0.469542\pi$
$521$	4.36154			0.191083			0.0955413	+	0.995425i	$0.469542\pi$
$522$	−5.13770	−	1.22939i	−0.224871	−	0.0538092i
$523$	28.7720	+	28.7720i	1.25811	+	1.25811i	0.951994	+	0.306118i	$0.0990301\pi$
$523$	28.7720	+	28.7720i	1.25811	+	1.25811i	0.306118	+	0.951994i	$0.400970\pi$
$524$	−7.73546	−	23.6869i	−0.337925	−	1.03477i
$525$	2.92643	+	2.62711i	0.127720	+	0.114657i
$526$	−7.09015	+	4.35214i	−0.309145	+	0.189762i
$527$		−	1.96601i		−	0.0856409i
$528$	5.41197	−	3.95678i	0.235526	−	0.172197i
$529$	−19.6966			−0.856373
$530$	−12.3092	+	7.55573i	−0.534677	+	0.328200i
$531$	−4.25247	+	4.25247i	−0.184542	+	0.184542i
$532$	−12.3813	−	31.9696i	−0.536797	−	1.38606i
$533$	14.8141	+	14.8141i	0.641668	+	0.641668i
$534$	2.61643	−	10.9342i	0.113224	−	0.473169i
$535$		−	24.3559i		−	1.05300i
$536$	7.90663	−	9.29958i	0.341514	−	0.401681i
$537$	3.41987			0.147578
$538$	−14.1643	−	3.38935i	−0.610665	−	0.146125i
$539$	−7.35625	+	9.13953i	−0.316856	+	0.393668i
$540$	−1.69698	+	3.34285i	−0.0730265	+	0.143853i
$541$	−11.4795	+	11.4795i	−0.493541	+	0.493541i	−0.909420	−	0.415879i	$-0.863474\pi$
$541$	−11.4795	+	11.4795i	−0.493541	+	0.493541i	0.415879	+	0.909420i	$0.363474\pi$
$542$	9.22496	−	5.66254i	0.396246	−	0.243227i
$543$		−	0.450130i		−	0.0193169i
$544$	0.592921	−	1.44669i	0.0254213	−	0.0620265i
$545$		−	1.43503i		−	0.0614701i
$546$	8.79919	−	6.07645i	0.376570	−	0.260048i
$547$	−27.5701	−	27.5701i	−1.17881	−	1.17881i	−0.980047	−	0.198764i	$-0.936307\pi$
$547$	−27.5701	−	27.5701i	−1.17881	−	1.17881i	−0.198764	−	0.980047i	$-0.563693\pi$
$548$	7.74659	+	3.93252i	0.330918	+	0.167989i
$549$	−1.14204	+	1.14204i	−0.0487409	+	0.0487409i
$550$	3.42644	+	0.819909i	0.146104	+	0.0349610i
$551$			24.2019i			1.03103i
$552$	−3.91653	−	3.32988i	−0.166699	−	0.141729i
$553$	1.97085	+	36.5679i	0.0838090	+	1.55502i
$554$	40.7206	+	9.74399i	1.73005	+	0.413982i
$555$	−1.47462	+	1.47462i	−0.0625942	+	0.0625942i
$556$	−4.43325	+	1.44778i	−0.188012	+	0.0613994i
$557$	7.84102	−	7.84102i	0.332235	−	0.332235i	−0.521200	−	0.853435i	$-0.674515\pi$
$557$	7.84102	−	7.84102i	0.332235	−	0.332235i	0.853435	+	0.521200i	$0.174515\pi$
$558$	5.26257	+	8.57335i	0.222782	+	0.362939i
$559$	6.86492			0.290355
$560$	−19.7378	−	1.98535i	−0.834075	−	0.0838963i
$561$	0.463235			0.0195578
$562$	−9.83252	−	16.0183i	−0.414760	−	0.675693i
$563$	−20.5300	+	20.5300i	−0.865238	+	0.865238i	−0.991941	−	0.126703i	$-0.959561\pi$
$563$	−20.5300	+	20.5300i	−0.865238	+	0.865238i	0.126703	+	0.991941i	$0.459561\pi$
$564$	−7.18482	−	22.0007i	−0.302535	−	0.926398i
$565$	−15.8293	+	15.8293i	−0.665944	+	0.665944i
$566$	15.5071	+	3.71067i	0.651810	+	0.155971i
$567$	−2.64192	+	0.142388i	−0.110950	+	0.00597972i
$568$	1.90942	+	23.5858i	0.0801176	+	0.989638i
$569$		−	8.26625i		−	0.346539i	−0.984874	−	0.173270i	$-0.944567\pi$
$569$		−	8.26625i		−	0.346539i	0.984874	−	0.173270i	$-0.0554332\pi$
$570$	16.7034	+	3.99694i	0.699628	+	0.167413i
$571$	11.1033	−	11.1033i	0.464659	−	0.464659i	−0.435520	−	0.900179i	$-0.643435\pi$
$571$	11.1033	−	11.1033i	0.464659	−	0.464659i	0.900179	+	0.435520i	$0.143435\pi$
$572$	4.33647	−	8.54232i	0.181317	−	0.357172i
$573$	−17.2817	−	17.2817i	−0.721955	−	0.721955i
$574$	22.5698	−	15.5860i	0.942044	−	0.650547i
$575$		−	2.70158i		−	0.112664i
$576$	1.28687	+	7.89582i	0.0536196	+	0.328992i
$577$			1.00276i			0.0417454i	0.999782	+	0.0208727i	$0.00664447\pi$
$577$			1.00276i			0.0417454i	−0.999782	+	0.0208727i	$0.993356\pi$
$578$	−20.3974	+	12.5205i	−0.848420	+	0.520784i
$579$	15.8328	−	15.8328i	0.657991	−	0.657991i
$580$	12.4871	+	6.33902i	0.518498	+	0.263213i
$581$	−24.7689	+	27.5908i	−1.02759	+	1.14466i
$582$	−18.1079	−	4.33303i	−0.750598	−	0.179610i
$583$	−9.13176			−0.378199
$584$	−3.87090	−	47.8146i	−0.160179	−	1.97858i
$585$			5.35708i			0.221488i
$586$	−5.47225	+	22.8688i	−0.226057	+	0.944701i
$587$	2.42198	+	2.42198i	0.0999658	+	0.0999658i	0.755321	−	0.655355i	$-0.227481\pi$
$587$	2.42198	+	2.42198i	0.0999658	+	0.0999658i	−0.655355	+	0.755321i	$0.727481\pi$
$588$	−5.75131	−	12.7641i	−0.237180	−	0.526383i
$589$	32.5880	−	32.5880i	1.34277	−	1.34277i
$590$	13.5867	−	8.33992i	0.559357	−	0.343349i
$591$	19.0249			0.782582
$592$	−0.683031	+	4.39747i	−0.0280724	+	0.180735i
$593$			22.2544i			0.913881i	0.889497	+	0.456940i	$0.151055\pi$
$593$			22.2544i			0.913881i	−0.889497	+	0.456940i	$0.848945\pi$
$594$	−2.02006	+	1.23997i	−0.0828842	+	0.0508767i
$595$	−1.01999	−	0.915666i	−0.0418155	−	0.0375387i
$596$	−27.3044	+	8.91686i	−1.11843	+	0.365249i
$597$	−3.99117	−	3.99117i	−0.163348	−	0.163348i
$598$	−7.14427	−	1.70955i	−0.292151	−	0.0699085i
$599$	−6.97729			−0.285085			−0.142542	−	0.989789i	$-0.545528\pi$
$599$	−6.97729			−0.285085			−0.142542	+	0.989789i	$0.545528\pi$
$600$	−2.72322	+	3.20299i	−0.111175	+	0.130761i
$601$	9.75706			0.397999			0.198999	−	0.980000i	$-0.436231\pi$
$601$	9.75706			0.397999			0.198999	+	0.980000i	$0.436231\pi$
$602$	1.61816	−	8.84080i	0.0659512	−	0.360324i
$603$	−3.05161	+	3.05161i	−0.124271	+	0.124271i
$604$	−8.08097	+	15.9185i	−0.328810	+	0.647716i
$605$	10.8566	+	10.8566i	0.441383	+	0.441383i
$606$	1.26217	+	2.05622i	0.0512721	+	0.0835284i
$607$	0.646351			0.0262346			0.0131173	−	0.999914i	$-0.495825\pi$
$607$	0.646351			0.0262346			0.0131173	+	0.999914i	$0.495825\pi$
$608$	33.8080	−	14.1519i	1.37110	−	0.573934i
$609$	0.531884	+	9.86878i	0.0215530	+	0.399903i
$610$	3.64882	−	2.23975i	0.147737	−	0.0906849i
$611$	−23.3856	−	23.3856i	−0.946082	−	0.946082i
$612$	−0.250218	+	0.492900i	−0.0101145	+	0.0199243i
$613$	−22.8864	−	22.8864i	−0.924372	−	0.924372i	0.0729627	−	0.997335i	$-0.476755\pi$
$613$	−22.8864	−	22.8864i	−0.924372	−	0.924372i	−0.997335	+	0.0729627i	$0.976755\pi$
$614$	9.35247	−	39.0844i	0.377435	−	1.57732i
$615$			13.7408i			0.554084i
$616$	−9.97884	−	7.59816i	−0.402059	−	0.306138i
$617$			28.2900i			1.13891i	0.822022	+	0.569456i	$0.192846\pi$
$617$			28.2900i			1.13891i	−0.822022	+	0.569456i	$0.807154\pi$
$618$	−15.7096	−	3.75915i	−0.631935	−	0.151215i
$619$	27.0007	+	27.0007i	1.08525	+	1.08525i	0.996010	+	0.0892388i	$0.0284434\pi$
$619$	27.0007	+	27.0007i	1.08525	+	1.08525i	0.0892388	+	0.996010i	$0.471557\pi$
$620$	−8.27844	−	25.3495i	−0.332470	−	1.01806i
$621$	1.28519	+	1.28519i	0.0515728	+	0.0515728i
$622$	19.2837	+	31.4155i	0.773206	+	1.25964i
$623$	−21.0030	+	1.13197i	−0.841468	+	0.0453514i
$624$	6.74700	+	9.22835i	0.270096	+	0.369430i
$625$	15.3586			0.614345
$626$	16.3495	−	10.0358i	0.653457	−	0.401110i
$627$	7.67843	+	7.67843i	0.306647	+	0.306647i
$628$	15.6831	−	5.12166i	0.625824	−	0.204376i
$629$	−0.217431	+	0.217431i	−0.00866956	+	0.00866956i
$630$	6.89898	+	1.26274i	0.274862	+	0.0503088i
$631$	31.2622			1.24453			0.622265	−	0.782807i	$-0.286213\pi$
$631$	31.2622			1.24453			0.622265	+	0.782807i	$0.286213\pi$
$632$	−39.0218	+	3.15907i	−1.55220	+	0.125661i
$633$	−19.6710			−0.781851
$634$	−10.0211	+	41.8785i	−0.397988	+	1.66321i
$635$	25.0002	+	25.0002i	0.992104	+	0.992104i
$636$	4.93256	−	9.71655i	0.195589	−	0.385286i
$637$	−15.5845	−	12.5437i	−0.617481	−	0.497000i
$638$	4.63187	+	7.54587i	0.183377	+	0.298744i
$639$		−	8.36612i		−	0.330959i
$640$	1.55334	−	21.1501i	0.0614012	−	0.836032i
$641$	13.0504			0.515458			0.257729	−	0.966217i	$-0.417026\pi$
$641$	13.0504			0.515458			0.257729	+	0.966217i	$0.417026\pi$
$642$	9.61295	+	15.6606i	0.379393	+	0.618076i
$643$	−0.786696	+	0.786696i	−0.0310242	+	0.0310242i	−0.722449	−	0.691424i	$-0.756983\pi$
$643$	−0.786696	+	0.786696i	−0.0310242	+	0.0310242i	0.691424	+	0.722449i	$0.256983\pi$
$644$	−3.88560	+	8.79760i	−0.153114	+	0.346674i
$645$	3.18379	+	3.18379i	0.125362	+	0.125362i
$646$	2.46290	+	0.589345i	0.0969015	+	0.0231875i
$647$		−	22.9721i		−	0.903125i	−0.892239	−	0.451563i	$-0.850867\pi$
$647$		−	22.9721i		−	0.903125i	0.892239	−	0.451563i	$-0.149133\pi$
$648$	−0.228233	−	2.81920i	−0.00896583	−	0.110749i
$649$	10.0795			0.395656
$650$	−1.39809	+	5.84268i	−0.0548376	+	0.229169i
$651$	12.5722	−	14.0046i	0.492744	−	0.548883i
$652$	33.5418	−	10.9538i	1.31360	−	0.428984i
$653$	−11.7129	+	11.7129i	−0.458362	+	0.458362i	−0.898118	−	0.439756i	$-0.855065\pi$
$653$	−11.7129	+	11.7129i	−0.458362	+	0.458362i	0.439756	+	0.898118i	$0.355065\pi$
$654$	0.566389	+	0.922715i	0.0221476	+	0.0360810i
$655$		−	23.3539i		−	0.912511i
$656$	17.3060	+	23.6706i	0.675684	+	0.924181i
$657$			16.9603i			0.661685i
$658$	−35.6289	+	24.6042i	−1.38896	+	0.959174i
$659$	28.8441	+	28.8441i	1.12361	+	1.12361i	0.991195	+	0.132413i	$0.0422725\pi$
$659$	28.8441	+	28.8441i	1.12361	+	1.12361i	0.132413	+	0.991195i	$0.457728\pi$
$660$	5.97289	−	1.95058i	0.232494	−	0.0759261i
$661$	−20.5775	+	20.5775i	−0.800371	+	0.800371i	−0.983153	−	0.182782i	$-0.941490\pi$
$661$	−20.5775	+	20.5775i	−0.800371	+	0.800371i	0.182782	+	0.983153i	$0.441490\pi$
$662$	−2.72301	+	11.3796i	−0.105833	+	0.442280i
$663$			0.789896i			0.0306770i
$664$	−30.1983	−	25.6750i	−1.17192	−	0.996383i
$665$	−1.72923	−	32.0848i	−0.0670567	−	1.24420i
$666$	0.366156	−	1.53018i	0.0141883	−	0.0592934i
$667$	4.80077	−	4.80077i	0.185887	−	0.185887i
$668$	38.0531	+	19.3175i	1.47232	+	0.747416i
$669$	−10.9526	+	10.9526i	−0.423453	+	0.423453i
$670$	9.74994	−	5.98479i	0.376673	−	0.231213i
$671$	2.70694			0.104500
$672$	13.4749	−	6.51370i	0.519804	−	0.251271i
$673$	19.3585			0.746215			0.373108	−	0.927788i	$-0.378292\pi$
$673$	19.3585			0.746215			0.373108	+	0.927788i	$0.378292\pi$
$674$	−13.4077	+	8.23004i	−0.516446	+	0.317009i
$675$	1.05104	−	1.05104i	0.0404547	−	0.0404547i
$676$	−8.61761	−	4.37469i	−0.331447	−	0.168257i
$677$	−26.0458	+	26.0458i	−1.00102	+	1.00102i	−0.00102364	+	0.999999i	$0.500326\pi$
$677$	−26.0458	+	26.0458i	−1.00102	+	1.00102i	−0.999999	+	0.00102364i	$0.999674\pi$
$678$	3.93050	−	16.4258i	0.150950	−	0.630827i
$679$	1.87464	+	34.7828i	0.0719420	+	1.33484i
$680$	0.949165	−	1.11638i	0.0363988	−	0.0428114i
$681$			6.00245i			0.230014i
$682$	3.92373	−	16.3974i	0.150247	−	0.627890i
$683$	−21.8826	+	21.8826i	−0.837315	+	0.837315i	−0.988505	−	0.151189i	$-0.951690\pi$
$683$	−21.8826	+	21.8826i	−0.837315	+	0.837315i	0.151189	+	0.988505i	$0.451690\pi$
$684$	−12.3177	+	4.02261i	−0.470979	+	0.153808i
$685$	5.75746	+	5.75746i	0.219981	+	0.219981i
$686$	−19.8276	+	17.1134i	−0.757020	+	0.653392i
$687$			3.38133i			0.129006i
$688$	9.49438	+	1.47470i	0.361970	+	0.0562225i
$689$		−	15.5713i		−	0.593218i
$690$	−2.52050	−	4.10620i	−0.0959538	−	0.156320i
$691$	12.1294	−	12.1294i	0.461424	−	0.461424i	−0.437698	−	0.899122i	$-0.644206\pi$
$691$	12.1294	−	12.1294i	0.461424	−	0.461424i	0.899122	+	0.437698i	$0.144206\pi$
$692$	−28.8703	+	9.42821i	−1.09748	+	0.358407i
$693$	3.29978	+	2.96228i	0.125348	+	0.112528i
$694$	7.80643	−	32.6234i	0.296328	−	1.23837i
$695$	−4.37093			−0.165799
$696$	−10.5310	+	0.852555i	−0.399178	+	0.0323160i
$697$			2.02607i			0.0767429i
$698$	−23.2962	−	5.57452i	−0.881774	−	0.210999i
$699$	2.06518	+	2.06518i	0.0781125	+	0.0781125i
$700$	7.19479	+	3.17769i	0.271938	+	0.120106i
$701$	−1.76393	+	1.76393i	−0.0666225	+	0.0666225i	−0.739633	−	0.673010i	$-0.765001\pi$
$701$	−1.76393	+	1.76393i	−0.0666225	+	0.0666225i	0.673010	+	0.739633i	$0.265001\pi$
$702$	−2.11437	−	3.44456i	−0.0798018	−	0.130007i
$703$	−7.20815			−0.271861
$704$	7.83250	−	10.8827i	0.295199	−	0.410158i
$705$		−	21.6914i		−	0.816947i
$706$	25.7028	+	41.8729i	0.967338	+	1.57591i
$707$	3.01531	−	3.35885i	0.113402	−	0.126322i
$708$	−5.44450	+	10.7250i	−0.204617	+	0.403070i
$709$	24.0457	+	24.0457i	0.903055	+	0.903055i	0.995699	−	0.0926439i	$-0.0295318\pi$
$709$	24.0457	+	24.0457i	0.903055	+	0.903055i	−0.0926439	+	0.995699i	$0.529532\pi$
$710$	−5.16116	+	21.5687i	−0.193695	+	0.809460i
$711$	13.8414			0.519094
$712$	−1.81443	−	22.4124i	−0.0679987	−	0.839942i
$713$	−12.9286			−0.484178
$714$	1.01725	+	0.186190i	0.0380695	+	0.00696797i
$715$	6.34887	−	6.34887i	0.237434	−	0.237434i
$716$	6.50182	−	2.12331i	0.242984	−	0.0793519i
$717$	−5.54272	−	5.54272i	−0.206997	−	0.206997i
$718$	−26.8633	+	16.4895i	−1.00253	+	0.615382i
$719$	21.8470			0.814754			0.407377	−	0.913260i	$-0.366444\pi$
$719$	21.8470			0.814754			0.407377	+	0.913260i	$0.366444\pi$
$720$	−1.15079	+	7.40900i	−0.0428875	+	0.276117i
$721$	1.62635	+	30.1760i	0.0605685	+	1.12381i
$722$	16.9988	+	27.6930i	0.632629	+	1.03063i
$723$	−12.9864	−	12.9864i	−0.482971	−	0.482971i
$724$	−0.279474	−	0.855781i	−0.0103866	−	0.0318049i
$725$	−3.92613	−	3.92613i	−0.145813	−	0.145813i
$726$	−11.2656	−	2.69575i	−0.418107	−	0.100049i
$727$		−	42.6131i		−	1.58043i	−0.612829	−	0.790216i	$-0.709969\pi$
$727$		−	42.6131i		−	1.58043i	0.612829	−	0.790216i	$-0.290031\pi$
$728$	12.9562	−	17.0157i	0.480188	−	0.630643i
$729$			1.00000i			0.0370370i
$730$	10.4630	−	43.7254i	0.387254	−	1.61835i
$731$	0.469446	+	0.469446i	0.0173631	+	0.0173631i
$732$	−1.46216	+	2.88029i	−0.0540432	+	0.106458i
$733$	−27.0115	−	27.0115i	−0.997693	−	0.997693i	0.00230393	−	0.999997i	$-0.499267\pi$
$733$	−27.0115	−	27.0115i	−0.997693	−	0.997693i	−0.999997	+	0.00230393i	$0.999267\pi$
$734$	−42.6528	+	26.1815i	−1.57434	+	0.966376i
$735$	−1.41026	−	13.0452i	−0.0520180	−	0.481180i
$736$	−9.51350	−	3.89906i	−0.350672	−	0.143721i
$737$	7.23314			0.266436
$738$	−5.42333	−	8.83525i	−0.199635	−	0.325230i
$739$	−1.43265	−	1.43265i	−0.0527008	−	0.0527008i	0.680265	−	0.732966i	$-0.261865\pi$
$739$	−1.43265	−	1.43265i	−0.0527008	−	0.0527008i	−0.732966	+	0.680265i	$0.761865\pi$
$740$	−1.88798	+	3.71909i	−0.0694034	+	0.136716i
$741$	−13.0931	+	13.0931i	−0.480986	+	0.480986i
$742$	−20.0530	−	3.67037i	−0.736170	−	0.134743i
$743$	−21.5309			−0.789892			−0.394946	−	0.918704i	$-0.629237\pi$
$743$	−21.5309			−0.789892			−0.394946	+	0.918704i	$0.629237\pi$
$744$	15.3281	+	13.0322i	0.561955	+	0.477782i
$745$	−26.9206			−0.986293
$746$	−11.9895	−	2.86895i	−0.438966	−	0.105040i
$747$	9.90941	+	9.90941i	0.362566	+	0.362566i
$748$	0.880696	−	0.287610i	0.0322014	−	0.0105161i
$749$	22.9652	−	25.5817i	0.839132	−	0.934735i
$750$	−14.6542	+	8.99516i	−0.535095	+	0.328457i
$751$		−	4.47866i		−	0.163429i	−0.996656	−	0.0817143i	$-0.973960\pi$
$751$		−	4.47866i		−	0.163429i	0.996656	−	0.0817143i	$-0.0260395\pi$
$752$	−27.3194	−	37.3666i	−0.996235	−	1.36262i
$753$	−23.0197			−0.838883
$754$	−12.8670	+	7.89815i	−0.468590	+	0.287634i
$755$	−11.8311	+	11.8311i	−0.430576	+	0.430576i
$756$	−4.93438	+	1.91100i	−0.179462	+	0.0695026i
$757$	−13.9860	−	13.9860i	−0.508329	−	0.508329i	0.405684	−	0.914013i	$-0.367033\pi$
$757$	−13.9860	−	13.9860i	−0.508329	−	0.508329i	−0.914013	+	0.405684i	$0.867033\pi$
$758$	−3.32513	+	13.8959i	−0.120774	+	0.504721i
$759$		−	3.04624i		−	0.110572i
$760$	34.2379	−	2.77178i	1.24194	−	0.100543i
$761$	−26.8043			−0.971653			−0.485827	−	0.874055i	$-0.661481\pi$
$761$	−26.8043			−0.971653			−0.485827	+	0.874055i	$0.661481\pi$
$762$	−25.9422	−	6.20769i	−0.939788	−	0.224881i
$763$	1.35310	−	1.50726i	0.0489854	−	0.0545664i
$764$	−43.5856	−	22.1260i	−1.57687	−	0.800492i
$765$	−0.366336	+	0.366336i	−0.0132449	+	0.0132449i
$766$	19.1464	−	11.7526i	0.691787	−	0.424638i
$767$			17.1873i			0.620599i
$768$	7.34889	+	14.2125i	0.265180	+	0.512848i
$769$		−	31.2390i		−	1.12651i	−0.826285	−	0.563253i	$-0.809550\pi$
$769$		−	31.2390i		−	1.12651i	0.826285	−	0.563253i	$-0.190450\pi$
$770$	−6.67971	−	9.67274i	−0.240720	−	0.348581i
$771$	9.63852	+	9.63852i	0.347123	+	0.347123i
$772$	20.2710	−	39.9314i	0.729570	−	1.43716i
$773$	−21.9282	+	21.9282i	−0.788703	+	0.788703i	−0.981282	−	0.192578i	$-0.938315\pi$
$773$	−21.9282	+	21.9282i	−0.788703	+	0.788703i	0.192578	+	0.981282i	$0.438315\pi$
$774$	−3.30375	−	0.790551i	−0.118751	−	0.0284158i
$775$			10.5731i			0.379799i
$776$	−37.1169	+	3.00485i	−1.33242	+	0.107868i
$777$	−2.93926	+	0.158413i	−0.105446	+	0.00568305i
$778$	−6.42554	−	1.53756i	−0.230367	−	0.0551242i
$779$	−33.5835	+	33.5835i	−1.20325	+	1.20325i
$780$	3.32608	+	10.1848i	0.119093	+	0.364675i
$781$	−9.91499	+	9.91499i	−0.354786	+	0.354786i
$782$	−0.371645	−	0.605454i	−0.0132900	−	0.0216510i
$783$	3.73546			0.133495
$784$	−18.8592	−	20.6961i	−0.673544	−	0.739147i
$785$	15.4626			0.551885
$786$	9.21746	+	15.0163i	0.328776	+	0.535615i
$787$	−33.9965	+	33.9965i	−1.21184	+	1.21184i	−0.241424	+	0.970420i	$0.577615\pi$
$787$	−33.9965	+	33.9965i	−1.21184	+	1.21184i	−0.970420	+	0.241424i	$0.922385\pi$
$788$	36.1700	−	11.8121i	1.28850	−	0.420789i
$789$	4.15967	−	4.15967i	0.148088	−	0.148088i
$790$	−35.6846	−	8.53894i	−1.26960	−	0.303802i
$791$	−31.5515	+	1.70049i	−1.12184	+	0.0604624i
$792$	−3.07065	+	3.61163i	−0.109111	+	0.128334i
$793$			4.61580i			0.163912i
$794$	21.5587	+	5.15877i	0.765091	+	0.183078i
$795$	7.22159	−	7.22159i	0.256123	−	0.256123i
$796$	−10.0660	−	5.10995i	−0.356780	−	0.181117i
$797$	−4.75244	−	4.75244i	−0.168340	−	0.168340i	0.617909	−	0.786249i	$-0.287980\pi$
$797$	−4.75244	−	4.75244i	−0.168340	−	0.168340i	−0.786249	+	0.617909i	$0.787980\pi$
$798$	13.7753	+	19.9478i	0.487642	+	0.706144i
$799$		−	3.19838i		−	0.113151i
$800$	−3.18870	+	7.78026i	−0.112738	+	0.275074i
$801$			7.94992i			0.280897i
$802$	15.2431	−	9.35664i	0.538252	−	0.330395i
$803$	20.1003	−	20.1003i	0.709323	−	0.709323i
$804$	−3.90701	+	7.69634i	−0.137790	+	0.271429i
$805$	−6.02145	+	6.70748i	−0.212228	+	0.236408i
$806$	27.9605	+	6.69064i	0.984867	+	0.235668i
$807$	10.2984			0.362521
$808$	3.67628	+	3.12562i	0.129331	+	0.109959i
$809$		−	32.4123i		−	1.13956i	−0.821798	−	0.569778i	$-0.807029\pi$
$809$		−	32.4123i		−	1.13956i	0.821798	−	0.569778i	$-0.192971\pi$
$810$	0.616912	−	2.57810i	0.0216761	−	0.0905853i
$811$	0.225151	+	0.225151i	0.00790612	+	0.00790612i	0.711049	−	0.703143i	$-0.248220\pi$
$811$	0.225151	+	0.225151i	0.00790612	+	0.00790612i	−0.703143	+	0.711049i	$0.748220\pi$
$812$	7.13849	+	18.4322i	0.250512	+	0.646843i
$813$	−5.41212	+	5.41212i	−0.189811	+	0.189811i
$814$	−2.24742	+	1.37953i	−0.0787721	+	0.0483525i
$815$	33.0702			1.15840
$816$	−0.169683	+	1.09245i	−0.00594010	+	0.0382434i
$817$			15.5628i			0.544473i
$818$	−7.71367	+	4.73487i	−0.269702	+	0.165551i
$819$	−5.05121	+	5.62670i	−0.176504	+	0.196613i
$820$	8.53133	+	26.1239i	0.297927	+	0.912286i
$821$	−37.0047	−	37.0047i	−1.29147	−	1.29147i	−0.933875	−	0.357599i	$-0.883595\pi$
$821$	−37.0047	−	37.0047i	−1.29147	−	1.29147i	−0.357599	−	0.933875i	$-0.616405\pi$
$822$	−5.97440	−	1.42961i	−0.208381	−	0.0498633i
$823$	−1.21299			−0.0422821			−0.0211411	−	0.999777i	$-0.506730\pi$
$823$	−1.21299			−0.0422821			−0.0211411	+	0.999777i	$0.506730\pi$
$824$	−32.2009	+	2.60688i	−1.12177	+	0.0908148i
$825$	−2.49126			−0.0867345
$826$	22.1343	+	4.05130i	0.770150	+	0.140963i
$827$	22.1226	−	22.1226i	0.769278	−	0.769278i	−0.208701	−	0.977979i	$-0.566924\pi$
$827$	22.1226	−	22.1226i	0.769278	−	0.769278i	0.977979	+	0.208701i	$0.0669236\pi$
$828$	3.24132	+	1.64544i	0.112644	+	0.0571831i
$829$	27.0435	+	27.0435i	0.939258	+	0.939258i	0.998258	−	0.0589998i	$-0.0187911\pi$
$829$	27.0435	+	27.0435i	0.939258	+	0.939258i	−0.0589998	+	0.998258i	$0.518791\pi$
$830$	−19.4343	−	31.6607i	−0.674573	−	1.09896i
$831$	−29.6067			−1.02704
$832$	18.5570	+	13.3558i	0.643347	+	0.463029i
$833$	−0.207941	−	1.92350i	−0.00720472	−	0.0666454i
$834$	2.81047	−	1.72515i	0.0973187	−	0.0597370i
$835$	28.2820	+	28.2820i	0.978740	+	0.978740i
$836$	19.3655	+	9.83080i	0.669769	+	0.340005i
$837$	−5.02983	−	5.02983i	−0.173856	−	0.173856i
$838$	−1.82600	+	7.63095i	−0.0630783	+	0.263607i
$839$		−	18.8066i		−	0.649277i	−0.945838	−	0.324639i	$-0.894757\pi$
$839$		−	18.8066i		−	0.649277i	0.945838	−	0.324639i	$-0.105243\pi$
$840$	13.9003	−	1.88269i	0.479604	−	0.0649591i
$841$			15.0463i			0.518839i
$842$	38.7305	+	9.26778i	1.33474	+	0.319389i
$843$	9.39768	+	9.39768i	0.323673	+	0.323673i
$844$	−37.3982	+	12.2132i	−1.28730	+	0.420396i
$845$	−6.40483	−	6.40483i	−0.220333	−	0.220333i
$846$	8.56132	+	13.9474i	0.294344	+	0.479522i
$847$	1.16628	+	21.6397i	0.0400740	+	0.743549i
$848$	3.34497	−	21.5355i	0.114867	−	0.739532i
$849$	−11.2747			−0.386947
$850$	−0.495148	+	0.303936i	−0.0169835	+	0.0104249i
$851$	1.42984	+	1.42984i	0.0490141	+	0.0490141i
$852$	−5.19431	−	15.9056i	−0.177954	−	0.544916i
$853$	13.4226	−	13.4226i	0.459581	−	0.459581i	−0.438937	−	0.898518i	$-0.644645\pi$
$853$	13.4226	−	13.4226i	0.459581	−	0.459581i	0.898518	+	0.438937i	$0.144645\pi$
$854$	5.94434	+	1.08801i	0.203411	+	0.0372309i
$855$	−12.1445			−0.415334
$856$	27.9993	+	23.8054i	0.956997	+	0.813652i
$857$	−14.2069			−0.485297			−0.242649	−	0.970114i	$-0.578016\pi$
$857$	−14.2069			−0.485297			−0.242649	+	0.970114i	$0.578016\pi$
$858$	−1.57646	+	6.58809i	−0.0538194	+	0.224914i
$859$	−12.7166	−	12.7166i	−0.433886	−	0.433886i	0.456062	−	0.889948i	$-0.349259\pi$
$859$	−12.7166	−	12.7166i	−0.433886	−	0.433886i	−0.889948	+	0.456062i	$0.849259\pi$
$860$	8.02971	+	4.07625i	0.273811	+	0.138999i
$861$	−12.9563	+	14.4324i	−0.441549	+	0.491855i
$862$	−17.5326	−	28.5627i	−0.597162	−	0.972849i
$863$			0.417666i			0.0142175i	0.999975	+	0.00710875i	$0.00226281\pi$
$863$			0.417666i			0.0142175i	−0.999975	+	0.00710875i	$0.997737\pi$
$864$	−2.18428	−	5.21813i	−0.0743109	−	0.177524i
$865$	−28.4644			−0.967818
$866$	19.1021	+	31.1196i	0.649116	+	1.05749i
$867$	11.9668	−	11.9668i	0.406414	−	0.406414i
$868$	15.2071	−	34.4311i	0.516161	−	1.16867i
$869$	−16.4040	−	16.4040i	−0.556466	−	0.556466i
$870$	−9.63041	−	2.30445i	−0.326501	−	0.0781282i
$871$			12.3338i			0.417914i
$872$	1.64970	+	1.40260i	0.0558660	+	0.0474980i
$873$	13.1657			0.445592
$874$	3.87555	−	16.1961i	0.131092	−	0.547841i
$875$	23.9377	+	21.4893i	0.809241	+	0.726472i
$876$	10.5302	+	32.2447i	0.355783	+	1.08945i
$877$	−37.3450	+	37.3450i	−1.26105	+	1.26105i	−0.310468	+	0.950584i	$0.600486\pi$
$877$	−37.3450	+	37.3450i	−1.26105	+	1.26105i	−0.950584	+	0.310468i	$0.899514\pi$
$878$	10.2082	+	16.6303i	0.344509	+	0.561247i
$879$		−	16.6272i		−	0.560821i
$880$	10.1445	−	7.41682i	0.341972	−	0.250021i
$881$		−	40.8076i		−	1.37484i	−0.726259	−	0.687421i	$-0.758743\pi$
$881$		−	40.8076i		−	1.37484i	0.726259	−	0.687421i	$-0.241257\pi$
$882$	6.05556	+	7.83136i	0.203901	+	0.263696i
$883$	38.1593	+	38.1593i	1.28416	+	1.28416i	0.938277	+	0.345886i	$0.112421\pi$
$883$	38.1593	+	38.1593i	1.28416	+	1.28416i	0.345886	+	0.938277i	$0.387579\pi$
$884$	0.490426	+	1.50174i	0.0164948	+	0.0505090i
$885$	−7.97109	+	7.97109i	−0.267945	+	0.267945i
$886$	−4.47358	+	18.6953i	−0.150293	+	0.628081i
$887$		−	34.0533i		−	1.14340i	−0.820464	−	0.571698i	$-0.806285\pi$
$887$		−	34.0533i		−	1.14340i	0.820464	−	0.571698i	$-0.193715\pi$
$888$	−0.253920	−	3.13650i	−0.00852101	−	0.105254i
$889$	2.68569	+	49.8313i	0.0900750	+	1.67129i
$890$	4.90440	−	20.4957i	0.164396	−	0.687018i
$891$	1.18514	−	1.18514i	0.0397035	−	0.0397035i
$892$	−14.0228	+	27.6232i	−0.469518	+	0.924893i
$893$	53.0153	−	53.0153i	1.77409	−	1.77409i
$894$	17.3097	−	10.6252i	0.578923	−	0.355360i
$895$	6.41042			0.214277
$896$	21.5740	−	20.7500i	0.720738	−	0.693207i
$897$	5.19438			0.173435
$898$	32.8652	−	20.1736i	1.09673	−	0.673201i
$899$	−18.7888	+	18.7888i	−0.626640	+	0.626640i
$900$	1.34566	−	2.65080i	0.0448555	−	0.0883599i
$901$	1.06482	−	1.06482i	0.0354741	−	0.0354741i
$902$	−4.04359	+	16.8983i	−0.134637	+	0.562653i
$903$	0.342023	+	6.34603i	0.0113818	+	0.211183i
$904$	−2.72571	−	33.6688i	−0.0906557	−	1.11981i
$905$		−	0.843750i		−	0.0280472i
$906$	2.93771	−	12.2768i	0.0975990	−	0.407871i
$907$	−1.29406	+	1.29406i	−0.0429685	+	0.0429685i	−0.728265	−	0.685296i	$-0.759673\pi$
$907$	−1.29406	+	1.29406i	−0.0429685	+	0.0429685i	0.685296	+	0.728265i	$0.259673\pi$
$908$	3.72677	+	11.4118i	0.123677	+	0.378713i
$909$	−1.20635	−	1.20635i	−0.0400121	−	0.0400121i
$910$	16.4937	−	11.3901i	0.546762	−	0.377577i
$911$		−	21.1193i		−	0.699715i	−0.936803	−	0.349857i	$-0.886230\pi$
$911$		−	21.1193i		−	0.699715i	0.936803	−	0.349857i	$-0.113770\pi$
$912$	−20.9207	+	15.2955i	−0.692754	+	0.506484i
$913$		−	23.4880i		−	0.777339i
$914$	11.6183	+	18.9276i	0.384299	+	0.626068i
$915$	−2.14070	+	2.14070i	−0.0707694	+	0.0707694i
$916$	2.09938	+	6.42853i	0.0693654	+	0.212405i
$917$	22.0204	−	24.5292i	0.727178	−	0.810027i
$918$	0.0909630	−	0.380139i	0.00300223	−	0.0125464i
$919$	0.462843			0.0152678			0.00763389	−	0.999971i	$-0.497570\pi$
$919$	0.462843			0.0152678			0.00763389	+	0.999971i	$0.497570\pi$
$920$	−7.34138	−	6.24173i	−0.242038	−	0.205784i
$921$			28.4171i			0.936374i
$922$	−16.7321	−	4.00382i	−0.551044	−	0.131859i
$923$	−16.9068	−	16.9068i	−0.556494	−	0.556494i
$924$	8.11270	+	3.58311i	0.266888	+	0.117876i
$925$	1.16934	−	1.16934i	0.0384476	−	0.0384476i
$926$	−1.37366	−	2.23785i	−0.0451412	−	0.0735404i
$927$	11.4220			0.375148
$928$	−19.4921	+	8.15931i	−0.639861	+	0.267843i
$929$		−	7.13095i		−	0.233959i	−0.993134	−	0.116980i	$-0.962679\pi$
$929$		−	7.13095i		−	0.233959i	0.993134	−	0.116980i	$-0.0373212\pi$
$930$	9.86447	+	16.0704i	0.323469	+	0.526969i
$931$	28.4366	−	35.3301i	0.931973	−	1.15790i
$932$	5.20852	+	2.64408i	0.170611	+	0.0866098i
$933$	−18.4309	−	18.4309i	−0.603400	−	0.603400i
$934$	−5.61342	+	23.4587i	−0.183677	+	0.767593i
$935$	0.868315			0.0283969
$936$	−6.15846	−	5.23600i	−0.201295	−	0.171144i
$937$	5.02900			0.164290			0.0821452	−	0.996620i	$-0.473823\pi$
$937$	5.02900			0.164290			0.0821452	+	0.996620i	$0.473823\pi$
$938$	15.8837	+	2.90724i	0.518622	+	0.0949249i
$939$	−9.59195	+	9.59195i	−0.313022	+	0.313022i
$940$	−13.4677	−	41.2395i	−0.439266	−	1.34508i
$941$	38.2671	+	38.2671i	1.24747	+	1.24747i	0.956833	+	0.290639i	$0.0938679\pi$
$941$	38.2671	+	38.2671i	1.24747	+	1.24747i	0.290639	+	0.956833i	$0.406132\pi$
$942$	−9.94235	+	6.10290i	−0.323939	+	0.198843i
$943$	13.3235			0.433873
$944$	−3.69214	+	23.7706i	−0.120169	+	0.773667i
$945$	−4.95217	+	0.266900i	−0.161094	+	0.00868226i
$946$	2.97848	+	4.85230i	0.0968388	+	0.157762i
$947$	−4.42949	−	4.42949i	−0.143939	−	0.143939i	0.631465	−	0.775404i	$-0.282454\pi$
$947$	−4.42949	−	4.42949i	−0.143939	−	0.143939i	−0.775404	+	0.631465i	$0.782454\pi$
$948$	26.3151	−	8.59378i	0.854676	−	0.279113i
$949$	34.2745	+	34.2745i	1.11260	+	1.11260i
$950$	−13.2454	−	3.16947i	−0.429737	−	0.102831i
$951$		−	30.4486i		−	0.987363i
$952$	2.04958	−	0.277601i	0.0664272	−	0.00899710i
$953$		−	40.8007i		−	1.32166i	−0.750534	−	0.660832i	$-0.770204\pi$
$953$		−	40.8007i		−	1.32166i	0.750534	−	0.660832i	$-0.229796\pi$
$954$	−1.79316	+	7.49369i	−0.0580556	+	0.242617i
$955$	−32.3939	−	32.3939i	−1.04824	−	1.04824i
$956$	−13.9791	−	7.09642i	−0.452116	−	0.229514i
$957$	−4.42703	−	4.42703i	−0.143106	−	0.143106i
$958$	−18.0181	+	11.0601i	−0.582140	+	0.357334i
$959$	0.618504	+	11.4760i	0.0199725	+	0.370578i
$960$	2.41219	+	14.8004i	0.0778530	+	0.477681i
$961$	19.5985			0.632208
$962$	−2.35234	−	3.83225i	−0.0758426	−	0.123557i
$963$	−9.18783	−	9.18783i	−0.296074	−	0.296074i
$964$	−32.7526	−	16.6267i	−1.05489	−	0.535510i
$965$	29.6780	−	29.6780i	0.955370	−	0.955370i
$966$	1.22439	−	6.68945i	0.0393941	−	0.215229i
$967$	−2.09367			−0.0673278			−0.0336639	−	0.999433i	$-0.510718\pi$
$967$	−2.09367			−0.0673278			−0.0336639	+	0.999433i	$0.510718\pi$
$968$	−23.0918	+	1.86943i	−0.742200	+	0.0600859i
$969$	−1.79070			−0.0575255
$970$	−33.9426	−	8.12209i	−1.08983	−	0.260785i
$971$	−12.1592	−	12.1592i	−0.390208	−	0.390208i	0.484554	−	0.874762i	$-0.338982\pi$
$971$	−12.1592	−	12.1592i	−0.390208	−	0.390208i	−0.874762	+	0.484554i	$0.838982\pi$
$972$	0.620874	+	1.90119i	0.0199146	+	0.0609806i
$973$	−4.59092	−	4.12136i	−0.147178	−	0.132125i
$974$	−3.22187	+	1.97768i	−0.103235	+	0.0633689i
$975$		−	4.24803i		−	0.136046i
$976$	−0.991553	+	6.38379i	−0.0317388	+	0.204340i
$977$	45.8415			1.46660			0.733300	−	0.679906i	$-0.237979\pi$
$977$	45.8415			1.46660			0.733300	+	0.679906i	$0.237979\pi$
$978$	−21.2639	+	13.0524i	−0.679944	+	0.417369i
$979$	9.42173	−	9.42173i	0.301120	−	0.301120i
$980$	−10.7806	−	23.9258i	−0.344374	−	0.764282i
$981$	−0.541341	−	0.541341i	−0.0172837	−	0.0172837i
$982$	3.59051	−	15.0049i	0.114578	−	0.478825i
$983$			7.70439i			0.245732i	0.992423	+	0.122866i	$0.0392085\pi$
$983$			7.70439i			0.245732i	−0.992423	+	0.122866i	$0.960791\pi$
$984$	−15.7963	−	13.4303i	−0.503569	−	0.428141i
$985$	35.6615			1.13627
$986$	−1.41999	−	0.339789i	−0.0452218	−	0.0108211i
$987$	20.4529	−	22.7832i	0.651024	−	0.725196i
$988$	−16.7632	+	33.0215i	−0.533310	+	1.05056i
$989$	3.08709	−	3.08709i	0.0981639	−	0.0981639i
$990$	−3.78653	+	2.32428i	−0.120344	+	0.0738704i
$991$		−	6.61965i		−	0.210280i	−0.994457	−	0.105140i	$-0.966471\pi$
$991$		−	6.61965i		−	0.210280i	0.994457	−	0.105140i	$-0.0335291\pi$
$992$	37.2329	+	15.2597i	1.18215	+	0.484497i
$993$		−	8.27375i		−	0.262559i
$994$	−25.7581	+	17.7878i	−0.816999	+	0.564195i
$995$	−7.48130	−	7.48130i	−0.237173	−	0.237173i
$996$	24.9922	+	12.6872i	0.791907	+	0.402008i
$997$	20.8831	−	20.8831i	0.661376	−	0.661376i	−0.294329	−	0.955704i	$-0.595096\pi$
$997$	20.8831	−	20.8831i	0.661376	−	0.661376i	0.955704	+	0.294329i	$0.0950960\pi$
$998$	21.3268	+	5.10326i	0.675087	+	0.161541i
$999$			1.11255i			0.0351995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.6	yes	64
4.3	odd	2		1344.2.u.a.1231.12		64
7.6	odd	2	inner	336.2.u.a.139.5	✓	64
16.3	odd	4	inner	336.2.u.a.307.5	yes	64
16.13	even	4		1344.2.u.a.559.21		64
28.27	even	2		1344.2.u.a.1231.21		64
112.13	odd	4		1344.2.u.a.559.12		64
112.83	even	4	inner	336.2.u.a.307.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.5	✓	64	7.6	odd	2	inner
336.2.u.a.139.6	yes	64	1.1	even	1	trivial
336.2.u.a.307.5	yes	64	16.3	odd	4	inner
336.2.u.a.307.6	yes	64	112.83	even	4	inner
1344.2.u.a.559.12		64	112.13	odd	4
1344.2.u.a.559.21		64	16.13	even	4
1344.2.u.a.1231.12		64	4.3	odd	2
1344.2.u.a.1231.21		64	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20526 + 0.739825i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.905318 - 1.78337i) q^{4} +(1.32544 - 1.32544i) q^{5} +(-0.329115 + 1.37538i) q^{6} +(2.64192 - 0.142388i) q^{7} +(0.228233 + 2.81920i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.20526 + 0.739825i) q^{2} +(0.707107 - 0.707107i) q^{3} +(0.905318 - 1.78337i) q^{4} +(1.32544 - 1.32544i) q^{5} +(-0.329115 + 1.37538i) q^{6} +(2.64192 - 0.142388i) q^{7} +(0.228233 + 2.81920i) q^{8} -1.00000i q^{9} +(-0.616912 + 2.57810i) q^{10} +(-1.18514 + 1.18514i) q^{11} +(-0.620874 - 1.90119i) q^{12} +(-2.02086 - 2.02086i) q^{13} +(-3.07886 + 2.12617i) q^{14} -1.87446i q^{15} +(-2.36080 - 3.22903i) q^{16} -0.276387i q^{17} +(0.739825 + 1.20526i) q^{18} +(4.58131 - 4.58131i) q^{19} +(-1.16380 - 3.56370i) q^{20} +(1.76743 - 1.96880i) q^{21} +(0.551607 - 2.30519i) q^{22} -1.81753 q^{23} +(2.15486 + 1.83209i) q^{24} +1.48640i q^{25} +(3.93076 + 0.940587i) q^{26} +(-0.707107 - 0.707107i) q^{27} +(2.13785 - 4.84041i) q^{28} +(-2.64137 + 2.64137i) q^{29} +(1.38677 + 2.25922i) q^{30} +7.11326 q^{31} +(5.23430 + 2.14525i) q^{32} +1.67603i q^{33} +(0.204478 + 0.333119i) q^{34} +(3.31298 - 3.69044i) q^{35} +(-1.78337 - 0.905318i) q^{36} +(-0.786692 - 0.786692i) q^{37} +(-2.13232 + 8.91105i) q^{38} -2.85793 q^{39} +(4.03920 + 3.43419i) q^{40} -7.33055 q^{41} +(-0.673655 + 3.68051i) q^{42} +(-1.69851 + 1.69851i) q^{43} +(1.04061 + 3.18646i) q^{44} +(-1.32544 - 1.32544i) q^{45} +(2.19060 - 1.34465i) q^{46} +11.5721 q^{47} +(-3.95261 - 0.613933i) q^{48} +(6.95945 - 0.752353i) q^{49} +(-1.09968 - 1.79150i) q^{50} +(-0.195435 - 0.195435i) q^{51} +(-5.43347 + 1.77442i) q^{52} +(3.85262 + 3.85262i) q^{53} +(1.37538 + 0.329115i) q^{54} +3.14166i q^{55} +(1.00439 + 7.41560i) q^{56} -6.47895i q^{57} +(1.22939 - 5.13770i) q^{58} +(-4.25247 - 4.25247i) q^{59} +(-3.34285 - 1.69698i) q^{60} +(-1.14204 - 1.14204i) q^{61} +(-8.57335 + 5.26257i) q^{62} +(-0.142388 - 2.64192i) q^{63} +(-7.89582 + 1.28687i) q^{64} -5.35708 q^{65} +(-1.23997 - 2.02006i) q^{66} +(-3.05161 - 3.05161i) q^{67} +(-0.492900 - 0.250218i) q^{68} +(-1.28519 + 1.28519i) q^{69} +(-1.26274 + 6.89898i) q^{70} +8.36612 q^{71} +(2.81920 - 0.228233i) q^{72} -16.9603 q^{73} +(1.53018 + 0.366156i) q^{74} +(1.05104 + 1.05104i) q^{75} +(-4.02261 - 12.3177i) q^{76} +(-2.96228 + 3.29978i) q^{77} +(3.44456 - 2.11437i) q^{78} +13.8414i q^{79} +(-7.40900 - 1.15079i) q^{80} -1.00000 q^{81} +(8.83525 - 5.42333i) q^{82} +(-9.90941 + 9.90941i) q^{83} +(-1.91100 - 4.93438i) q^{84} +(-0.366336 - 0.366336i) q^{85} +(0.790551 - 3.30375i) q^{86} +3.73546i q^{87} +(-3.61163 - 3.07065i) q^{88} -7.94992 q^{89} +(2.57810 + 0.616912i) q^{90} +(-5.62670 - 5.05121i) q^{91} +(-1.64544 + 3.24132i) q^{92} +(5.02983 - 5.02983i) q^{93} +(-13.9474 + 8.56132i) q^{94} -12.1445i q^{95} +(5.21813 - 2.18428i) q^{96} +13.1657i q^{97} +(-7.83136 + 6.05556i) q^{98} +(1.18514 + 1.18514i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

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