LMFDB - Embedded newform 336.2.s.c.155.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(155,336)]

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, 2, 0]))

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

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

chi := DirichletCharacter("336.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.s (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:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			155.9
Character	$\chi$	$=$	336.155
Dual form			336.2.s.c.323.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.230305 - 1.39533i) q^{2} +(-1.57773 - 0.714681i) q^{3} +(-1.89392 + 0.642706i) q^{4} +(-1.31983 + 1.31983i) q^{5} +(-0.633860 + 2.36606i) q^{6} -1.00000 q^{7} +(1.33297 + 2.49463i) q^{8} +(1.97846 + 2.25515i) q^{9} +O(q^{10})$	\(q+(-0.230305 - 1.39533i) q^{2} +(-1.57773 - 0.714681i) q^{3} +(-1.89392 + 0.642706i) q^{4} +(-1.31983 + 1.31983i) q^{5} +(-0.633860 + 2.36606i) q^{6} -1.00000 q^{7} +(1.33297 + 2.49463i) q^{8} +(1.97846 + 2.25515i) q^{9} +(2.14556 + 1.53764i) q^{10} +(1.23544 + 1.23544i) q^{11} +(3.44742 + 0.339531i) q^{12} +(4.57782 - 4.57782i) q^{13} +(0.230305 + 1.39533i) q^{14} +(3.02558 - 1.13907i) q^{15} +(3.17386 - 2.43447i) q^{16} +5.82397i q^{17} +(2.69103 - 3.27999i) q^{18} +(-2.27291 - 2.27291i) q^{19} +(1.65138 - 3.34790i) q^{20} +(1.57773 + 0.714681i) q^{21} +(1.43932 - 2.00838i) q^{22} +2.63707i q^{23} +(-0.320200 - 4.88850i) q^{24} +1.51612i q^{25} +(-7.44189 - 5.33330i) q^{26} +(-1.50977 - 4.97198i) q^{27} +(1.89392 - 0.642706i) q^{28} +(4.30719 + 4.30719i) q^{29} +(-2.28620 - 3.95937i) q^{30} +5.81364i q^{31} +(-4.12785 - 3.86792i) q^{32} +(-1.06624 - 2.83213i) q^{33} +(8.12639 - 1.34129i) q^{34} +(1.31983 - 1.31983i) q^{35} +(-5.19644 - 2.99950i) q^{36} +(6.99022 + 6.99022i) q^{37} +(-2.64800 + 3.69493i) q^{38} +(-10.4943 + 3.95088i) q^{39} +(-5.05177 - 1.53319i) q^{40} -3.57004 q^{41} +(0.633860 - 2.36606i) q^{42} +(2.12307 - 2.12307i) q^{43} +(-3.13384 - 1.54580i) q^{44} +(-5.58763 - 0.365176i) q^{45} +(3.67960 - 0.607331i) q^{46} +11.3696 q^{47} +(-6.74736 + 1.57264i) q^{48} +1.00000 q^{49} +(2.11549 - 0.349170i) q^{50} +(4.16228 - 9.18865i) q^{51} +(-5.72783 + 11.6122i) q^{52} +(0.573389 - 0.573389i) q^{53} +(-6.58987 + 3.25170i) q^{54} -3.26113 q^{55} +(-1.33297 - 2.49463i) q^{56} +(1.96163 + 5.21043i) q^{57} +(5.01800 - 7.00194i) q^{58} +(-8.42236 - 8.42236i) q^{59} +(-4.99812 + 4.10188i) q^{60} +(-6.80408 + 6.80408i) q^{61} +(8.11198 - 1.33891i) q^{62} +(-1.97846 - 2.25515i) q^{63} +(-4.44638 + 6.65054i) q^{64} +12.0839i q^{65} +(-3.70621 + 2.14002i) q^{66} +(1.90390 + 1.90390i) q^{67} +(-3.74310 - 11.0301i) q^{68} +(1.88466 - 4.16058i) q^{69} +(-2.14556 - 1.53764i) q^{70} +13.3926i q^{71} +(-2.98853 + 7.94158i) q^{72} +0.516078i q^{73} +(8.14381 - 11.3636i) q^{74} +(1.08354 - 2.39202i) q^{75} +(5.76551 + 2.84389i) q^{76} +(-1.23544 - 1.23544i) q^{77} +(7.92969 + 13.7331i) q^{78} -3.10873i q^{79} +(-0.975867 + 7.40201i) q^{80} +(-1.17138 + 8.92345i) q^{81} +(0.822200 + 4.98140i) q^{82} +(-2.91252 + 2.91252i) q^{83} +(-3.44742 - 0.339531i) q^{84} +(-7.68663 - 7.68663i) q^{85} +(-3.45135 - 2.47344i) q^{86} +(-3.71731 - 9.87385i) q^{87} +(-1.43516 + 4.72877i) q^{88} -4.34348 q^{89} +(0.777318 + 7.88071i) q^{90} +(-4.57782 + 4.57782i) q^{91} +(-1.69486 - 4.99440i) q^{92} +(4.15490 - 9.17236i) q^{93} +(-2.61847 - 15.8644i) q^{94} +5.99968 q^{95} +(3.74831 + 9.05264i) q^{96} +8.09726 q^{97} +(-0.230305 - 1.39533i) q^{98} +(-0.341828 + 5.23036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	$ 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * 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 $

$2$	−0.230305	−	1.39533i	−0.162850	−	0.986651i
$2$	−0.230305	−	1.39533i	−0.162850	−	0.986651i
$3$	−1.57773	−	0.714681i	−0.910903	−	0.412621i
$3$	−1.57773	−	0.714681i	−0.910903	−	0.412621i
$4$	−1.89392	+	0.642706i	−0.946959	+	0.321353i
$5$	−1.31983	+	1.31983i	−0.590244	+	0.590244i	−0.937697	−	0.347453i	$-0.887047\pi$
$5$	−1.31983	+	1.31983i	−0.590244	+	0.590244i	0.347453	+	0.937697i	$0.387047\pi$
$6$	−0.633860	+	2.36606i	−0.258772	+	0.965938i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	1.33297	+	2.49463i	0.471276	+	0.881986i
$9$	1.97846	+	2.25515i	0.659487	+	0.751716i
$10$	2.14556	+	1.53764i	0.678486	+	0.486243i
$11$	1.23544	+	1.23544i	0.372499	+	0.372499i	0.868387	−	0.495888i	$-0.165157\pi$
$11$	1.23544	+	1.23544i	0.372499	+	0.372499i	−0.495888	+	0.868387i	$0.665157\pi$
$12$	3.44742	+	0.339531i	0.995185	+	0.0980142i
$13$	4.57782	−	4.57782i	1.26966	−	1.26966i	0.323396	−	0.946264i	$-0.395175\pi$
$13$	4.57782	−	4.57782i	1.26966	−	1.26966i	0.946264	−	0.323396i	$-0.104825\pi$
$14$	0.230305	+	1.39533i	0.0615517	+	0.372919i
$15$	3.02558	−	1.13907i	0.781202	−	0.294108i
$16$	3.17386	−	2.43447i	0.793464	−	0.608617i
$17$			5.82397i			1.41252i	0.707952	+	0.706260i	$0.249619\pi$
$17$			5.82397i			1.41252i	−0.707952	+	0.706260i	$0.750381\pi$
$18$	2.69103	−	3.27999i	0.634283	−	0.773101i
$19$	−2.27291	−	2.27291i	−0.521440	−	0.521440i	0.396566	−	0.918006i	$-0.370202\pi$
$19$	−2.27291	−	2.27291i	−0.521440	−	0.521440i	−0.918006	+	0.396566i	$0.870202\pi$
$20$	1.65138	−	3.34790i	0.369261	−	0.748614i
$21$	1.57773	+	0.714681i	0.344289	+	0.155956i
$22$	1.43932	−	2.00838i	0.306865	−	0.428188i
$23$			2.63707i			0.549867i	0.961463	+	0.274934i	$0.0886558\pi$
$23$			2.63707i			0.549867i	−0.961463	+	0.274934i	$0.911344\pi$
$24$	−0.320200	−	4.88850i	−0.0653606	−	0.997862i
$25$			1.51612i			0.303224i
$26$	−7.44189	−	5.33330i	−1.45948	−	1.04595i
$27$	−1.50977	−	4.97198i	−0.290555	−	0.956858i
$28$	1.89392	−	0.642706i	0.357917	−	0.121460i
$29$	4.30719	+	4.30719i	0.799825	+	0.799825i	0.983068	−	0.183243i	$-0.0586594\pi$
$29$	4.30719	+	4.30719i	0.799825	+	0.799825i	−0.183243	+	0.983068i	$0.558659\pi$
$30$	−2.28620	−	3.95937i	−0.417401	−	0.722878i
$31$			5.81364i			1.04416i	0.852896	+	0.522081i	$0.174844\pi$
$31$			5.81364i			1.04416i	−0.852896	+	0.522081i	$0.825156\pi$
$32$	−4.12785	−	3.86792i	−0.729708	−	0.683759i
$33$	−1.06624	−	2.83213i	−0.185609	−	0.493011i
$34$	8.12639	−	1.34129i	1.39366	−	0.230030i
$35$	1.31983	−	1.31983i	0.223091	−	0.223091i
$36$	−5.19644	−	2.99950i	−0.866074	−	0.499916i
$37$	6.99022	+	6.99022i	1.14919	+	1.14919i	0.986713	+	0.162472i	$0.0519467\pi$
$37$	6.99022	+	6.99022i	1.14919	+	1.14919i	0.162472	+	0.986713i	$0.448053\pi$
$38$	−2.64800	+	3.69493i	−0.429563	+	0.599396i
$39$	−10.4943	+	3.95088i	−1.68043	+	0.632648i
$40$	−5.05177	−	1.53319i	−0.798755	−	0.242419i
$41$	−3.57004			−0.557547			−0.278773	−	0.960357i	$-0.589928\pi$
$41$	−3.57004			−0.557547			−0.278773	+	0.960357i	$0.589928\pi$
$42$	0.633860	−	2.36606i	0.0978067	−	0.365090i
$43$	2.12307	−	2.12307i	0.323765	−	0.323765i	−0.526444	−	0.850210i	$-0.676475\pi$
$43$	2.12307	−	2.12307i	0.323765	−	0.323765i	0.850210	+	0.526444i	$0.176475\pi$
$44$	−3.13384	−	1.54580i	−0.472445	−	0.233038i
$45$	−5.58763	−	0.365176i	−0.832954	−	0.0544373i
$46$	3.67960	−	0.607331i	0.542527	−	0.0895461i
$47$	11.3696			1.65842			0.829211	−	0.558935i	$-0.188790\pi$
$47$	11.3696			1.65842			0.829211	+	0.558935i	$0.188790\pi$
$48$	−6.74736	+	1.57264i	−0.973897	+	0.226990i
$49$	1.00000			0.142857
$50$	2.11549	−	0.349170i	0.299176	−	0.0493801i
$51$	4.16228	−	9.18865i	0.582836	−	1.28667i
$52$	−5.72783	+	11.6122i	−0.794307	+	1.61033i
$53$	0.573389	−	0.573389i	0.0787610	−	0.0787610i	−0.666629	−	0.745390i	$-0.732263\pi$
$53$	0.573389	−	0.573389i	0.0787610	−	0.0787610i	0.745390	+	0.666629i	$0.232263\pi$
$54$	−6.58987	+	3.25170i	−0.896768	+	0.442501i
$55$	−3.26113			−0.439730
$56$	−1.33297	−	2.49463i	−0.178126	−	0.333359i
$57$	1.96163	+	5.21043i	0.259824	+	0.690139i
$58$	5.01800	−	7.00194i	0.658896	−	0.919400i
$59$	−8.42236	−	8.42236i	−1.09650	−	1.09650i	−0.994817	−	0.101681i	$-0.967578\pi$
$59$	−8.42236	−	8.42236i	−1.09650	−	1.09650i	−0.101681	−	0.994817i	$-0.532422\pi$
$60$	−4.99812	+	4.10188i	−0.645255	+	0.529550i
$61$	−6.80408	+	6.80408i	−0.871174	+	0.871174i	−0.992600	−	0.121427i	$-0.961253\pi$
$61$	−6.80408	+	6.80408i	−0.871174	+	0.871174i	0.121427	+	0.992600i	$0.461253\pi$
$62$	8.11198	−	1.33891i	1.03022	−	0.170042i
$63$	−1.97846	−	2.25515i	−0.249263	−	0.284122i
$64$	−4.44638	+	6.65054i	−0.555798	+	0.831318i
$65$			12.0839i			1.49882i
$66$	−3.70621	+	2.14002i	−0.456203	+	0.263419i
$67$	1.90390	+	1.90390i	0.232598	+	0.232598i	0.813776	−	0.581178i	$-0.197408\pi$
$67$	1.90390	+	1.90390i	0.232598	+	0.232598i	−0.581178	+	0.813776i	$0.697408\pi$
$68$	−3.74310	−	11.0301i	−0.453918	−	1.33760i
$69$	1.88466	−	4.16058i	0.226887	−	0.500875i
$70$	−2.14556	−	1.53764i	−0.256444	−	0.183783i
$71$			13.3926i			1.58941i	0.606994	+	0.794706i	$0.292375\pi$
$71$			13.3926i			1.58941i	−0.606994	+	0.794706i	$0.707625\pi$
$72$	−2.98853	+	7.94158i	−0.352202	+	0.935924i
$73$			0.516078i			0.0604023i	0.999544	+	0.0302012i	$0.00961479\pi$
$73$			0.516078i			0.0604023i	−0.999544	+	0.0302012i	$0.990385\pi$
$74$	8.14381	−	11.3636i	0.946699	−	1.32099i
$75$	1.08354	−	2.39202i	0.125116	−	0.276207i
$76$	5.76551	+	2.84389i	0.661349	+	0.326216i
$77$	−1.23544	−	1.23544i	−0.140791	−	0.140791i
$78$	7.92969	+	13.7331i	0.897860	+	1.55497i
$79$		−	3.10873i		−	0.349759i	−0.984590	−	0.174879i	$-0.944046\pi$
$79$		−	3.10873i		−	0.349759i	0.984590	−	0.174879i	$-0.0559536\pi$
$80$	−0.975867	+	7.40201i	−0.109105	+	0.827570i
$81$	−1.17138	+	8.92345i	−0.130153	+	0.991494i
$82$	0.822200	+	4.98140i	0.0907968	+	0.550104i
$83$	−2.91252	+	2.91252i	−0.319691	+	0.319691i	−0.848648	−	0.528958i	$-0.822583\pi$
$83$	−2.91252	+	2.91252i	−0.319691	+	0.319691i	0.528958	+	0.848648i	$0.322583\pi$
$84$	−3.44742	−	0.339531i	−0.376145	−	0.0370459i
$85$	−7.68663	−	7.68663i	−0.833732	−	0.833732i
$86$	−3.45135	−	2.47344i	−0.372169	−	0.266718i
$87$	−3.71731	−	9.87385i	−0.398538	−	1.05859i
$88$	−1.43516	+	4.72877i	−0.152989	+	0.504088i
$89$	−4.34348			−0.460408			−0.230204	−	0.973142i	$-0.573939\pi$
$89$	−4.34348			−0.460408			−0.230204	+	0.973142i	$0.573939\pi$
$90$	0.777318	+	7.88071i	0.0819365	+	0.830700i
$91$	−4.57782	+	4.57782i	−0.479886	+	0.479886i
$92$	−1.69486	−	4.99440i	−0.176701	−	0.520702i
$93$	4.15490	−	9.17236i	0.430843	−	0.951129i
$94$	−2.61847	−	15.8644i	−0.270075	−	1.63628i
$95$	5.99968			0.615554
$96$	3.74831	+	9.05264i	0.382560	+	0.923931i
$97$	8.09726			0.822152			0.411076	−	0.911601i	$-0.365153\pi$
$97$	8.09726			0.822152			0.411076	+	0.911601i	$0.365153\pi$
$98$	−0.230305	−	1.39533i	−0.0232644	−	0.140950i
$99$	−0.341828	+	5.23036i	−0.0343550	+	0.525671i
$100$	−0.974418	−	2.87140i	−0.0974418	−	0.287140i
$101$	0.961217	−	0.961217i	0.0956447	−	0.0956447i	−0.657665	−	0.753310i	$-0.728456\pi$
$101$	0.961217	−	0.961217i	0.0956447	−	0.0956447i	0.753310	+	0.657665i	$0.228456\pi$
$102$	−13.7798	−	3.69158i	−1.36441	−	0.365521i
$103$	1.57772			0.155457			0.0777286	−	0.996975i	$-0.475233\pi$
$103$	1.57772			0.155457			0.0777286	+	0.996975i	$0.475233\pi$
$104$	17.5221	+	5.31788i	1.71818	+	0.521461i
$105$	−3.02558	+	1.13907i	−0.295267	+	0.111162i
$106$	−0.932123	−	0.668015i	−0.0905358	−	0.0648833i
$107$	−4.53705	−	4.53705i	−0.438613	−	0.438613i	0.452932	−	0.891545i	$-0.350378\pi$
$107$	−4.53705	−	4.53705i	−0.438613	−	0.438613i	−0.891545	+	0.452932i	$0.850378\pi$
$108$	6.05490	+	8.44619i	0.582633	+	0.812735i
$109$	−2.23973	+	2.23973i	−0.214528	+	0.214528i	−0.806188	−	0.591660i	$-0.798473\pi$
$109$	−2.23973	+	2.23973i	−0.214528	+	0.214528i	0.591660	+	0.806188i	$0.298473\pi$
$110$	0.751055	+	4.55037i	0.0716103	+	0.433860i
$111$	−6.03290	−	16.0245i	−0.572617	−	1.52097i
$112$	−3.17386	+	2.43447i	−0.299901	+	0.230036i
$113$		−	16.0755i		−	1.51226i	−0.654424	−	0.756128i	$-0.727089\pi$
$113$		−	16.0755i		−	1.51226i	0.654424	−	0.756128i	$-0.272911\pi$
$114$	6.81853	−	3.93712i	0.638614	−	0.368745i
$115$	−3.48047	−	3.48047i	−0.324556	−	0.324556i
$116$	−10.9257	−	5.38921i	−1.01443	−	0.500376i
$117$	19.3807	+	1.26662i	1.79175	+	0.117099i
$118$	−9.81230	+	13.6917i	−0.903295	+	1.26043i
$119$		−	5.82397i		−	0.533883i
$120$	6.87458	+	6.02937i	0.627561	+	0.550403i
$121$		−	7.94738i		−	0.722489i
$122$	11.0610	+	7.92696i	1.00142	+	0.717673i
$123$	5.63256	+	2.55144i	0.507871	+	0.230056i
$124$	−3.73647	−	11.0106i	−0.335545	−	0.988778i
$125$	−8.60014	−	8.60014i	−0.769220	−	0.769220i
$126$	−2.69103	+	3.27999i	−0.239736	+	0.292205i
$127$			12.1741i			1.08028i	0.841575	+	0.540140i	$0.181629\pi$
$127$			12.1741i			1.08028i	−0.841575	+	0.540140i	$0.818371\pi$
$128$	10.3038	+	4.67254i	0.910732	+	0.412998i
$129$	−4.86695	+	1.83231i	−0.428511	+	0.161326i
$130$	16.8610	−	2.78298i	1.47881	−	0.244083i
$131$	−13.2278	+	13.2278i	−1.15571	+	1.15571i	−0.170327	+	0.985388i	$0.554482\pi$
$131$	−13.2278	+	13.2278i	−1.15571	+	1.15571i	−0.985388	+	0.170327i	$0.945518\pi$
$132$	3.83961	+	4.67855i	0.334195	+	0.407215i
$133$	2.27291	+	2.27291i	0.197086	+	0.197086i
$134$	2.21810	−	3.09505i	0.191614	−	0.267372i
$135$	8.55478	+	4.56952i	0.736278	+	0.393282i
$136$	−14.5287	+	7.76318i	−1.24582	+	0.665687i
$137$	−3.47597			−0.296972			−0.148486	−	0.988915i	$-0.547440\pi$
$137$	−3.47597			−0.296972			−0.148486	+	0.988915i	$0.547440\pi$
$138$	−6.23946	−	1.67153i	−0.531138	−	0.142290i
$139$	7.82479	−	7.82479i	0.663690	−	0.663690i	−0.292558	−	0.956248i	$-0.594506\pi$
$139$	7.82479	−	7.82479i	0.663690	−	0.663690i	0.956248	+	0.292558i	$0.0945064\pi$
$140$	−1.65138	+	3.34790i	−0.139567	+	0.282950i
$141$	−17.9381	−	8.12562i	−1.51066	−	0.684300i
$142$	18.6872	−	3.08439i	1.56819	−	0.258837i
$143$	11.3112			0.945893
$144$	11.7694	+	2.34101i	0.980786	+	0.195085i
$145$	−11.3695			−0.944184
$146$	0.720101	−	0.118855i	0.0595960	−	0.00983655i
$147$	−1.57773	−	0.714681i	−0.130129	−	0.0589459i
$148$	−17.7316	−	8.74625i	−1.45753	−	0.718937i
$149$	3.66058	−	3.66058i	0.299886	−	0.299886i	−0.541083	−	0.840969i	$-0.681986\pi$
$149$	3.66058	−	3.66058i	0.299886	−	0.299886i	0.840969	+	0.541083i	$0.181986\pi$
$150$	−3.58722	−	0.961006i	−0.292895	−	0.0784658i
$151$	0.834525			0.0679127			0.0339563	−	0.999423i	$-0.489189\pi$
$151$	0.834525			0.0679127			0.0339563	+	0.999423i	$0.489189\pi$
$152$	2.64035	−	8.69978i	0.214161	−	0.705645i
$153$	−13.1339	+	11.5225i	−1.06181	+	0.931540i
$154$	−1.43932	+	2.00838i	−0.115984	+	0.161840i
$155$	−7.67300	−	7.67300i	−0.616310	−	0.616310i
$156$	17.3360	−	14.2274i	1.38799	−	1.13910i
$157$	11.1183	−	11.1183i	0.887337	−	0.887337i	−0.106930	−	0.994267i	$-0.534102\pi$
$157$	11.1183	−	11.1183i	0.887337	−	0.887337i	0.994267	+	0.106930i	$0.0341020\pi$
$158$	−4.33771	+	0.715956i	−0.345090	+	0.0569584i
$159$	−1.31444	+	0.494862i	−0.104242	+	0.0392451i
$160$	10.5530	−	0.343063i	0.834291	−	0.0271215i
$161$		−	2.63707i		−	0.207830i
$162$	12.7210	−	0.420655i	0.999454	−	0.0330497i
$163$	−2.39613	−	2.39613i	−0.187680	−	0.187680i	0.607013	−	0.794692i	$-0.292368\pi$
$163$	−2.39613	−	2.39613i	−0.187680	−	0.187680i	−0.794692	+	0.607013i	$0.792368\pi$
$164$	6.76137	−	2.29449i	0.527974	−	0.179169i
$165$	5.14518	+	2.33067i	0.400552	+	0.181442i
$166$	4.73471	+	3.39317i	0.367485	+	0.263361i
$167$		−	4.20664i		−	0.325519i	−0.986666	−	0.162760i	$-0.947961\pi$
$167$		−	4.20664i		−	0.325519i	0.986666	−	0.162760i	$-0.0520395\pi$
$168$	0.320200	+	4.88850i	0.0247040	+	0.377156i
$169$		−	28.9129i		−	2.22407i
$170$	−8.95515	+	12.4957i	−0.686829	+	0.958376i
$171$	0.628879	−	9.62260i	0.0480916	−	0.735858i
$172$	−2.65641	+	5.38544i	−0.202550	+	0.410636i
$173$	6.93594	+	6.93594i	0.527330	+	0.527330i	0.919775	−	0.392445i	$-0.128371\pi$
$173$	6.93594	+	6.93594i	0.527330	+	0.527330i	−0.392445	+	0.919775i	$0.628371\pi$
$174$	−12.9212	+	7.46090i	−0.979554	+	0.565609i
$175$		−	1.51612i		−	0.114608i
$176$	6.92874	+	0.913471i	0.522273	+	0.0688555i
$177$	7.26891	+	19.3075i	0.546364	+	1.45124i
$178$	1.00033	+	6.06060i	0.0749776	+	0.454262i
$179$	−0.640117	+	0.640117i	−0.0478446	+	0.0478446i	−0.730624	−	0.682780i	$-0.760771\pi$
$179$	−0.640117	+	0.640117i	−0.0478446	+	0.0478446i	0.682780	+	0.730624i	$0.260771\pi$
$180$	10.8172	−	2.89959i	0.806268	−	0.216123i
$181$	4.43844	+	4.43844i	0.329906	+	0.329906i	0.852551	−	0.522644i	$-0.175054\pi$
$181$	4.43844	+	4.43844i	0.329906	+	0.329906i	−0.522644	+	0.852551i	$0.675054\pi$
$182$	7.44189	+	5.33330i	0.551630	+	0.395330i
$183$	15.5978	−	5.87225i	1.15302	−	0.434090i
$184$	−6.57852	+	3.51514i	−0.484975	+	0.259139i
$185$	−18.4518			−1.35660
$186$	−13.7554	−	3.68504i	−1.00860	−	0.270200i
$187$	−7.19516	+	7.19516i	−0.526162	+	0.526162i
$188$	−21.5330	+	7.30729i	−1.57046	+	0.532939i
$189$	1.50977	+	4.97198i	0.109819	+	0.361658i
$190$	−1.38176	−	8.37157i	−0.100243	−	0.607337i
$191$	12.2266			0.884684			0.442342	−	0.896847i	$-0.354148\pi$
$191$	12.2266			0.884684			0.442342	+	0.896847i	$0.354148\pi$
$192$	11.7682	−	7.31501i	0.849297	−	0.527915i
$193$	8.96283			0.645159			0.322579	−	0.946542i	$-0.395450\pi$
$193$	8.96283			0.645159			0.322579	+	0.946542i	$0.395450\pi$
$194$	−1.86484	−	11.2984i	−0.133888	−	0.811177i
$195$	8.63611	−	19.0651i	0.618445	−	1.36528i
$196$	−1.89392	+	0.642706i	−0.135280	+	0.0459076i
$197$	7.69332	−	7.69332i	0.548126	−	0.548126i	−0.377772	−	0.925899i	$-0.623310\pi$
$197$	7.69332	−	7.69332i	0.548126	−	0.548126i	0.925899	+	0.377772i	$0.123310\pi$
$198$	7.37683	−	0.727617i	0.524249	−	0.0517095i
$199$	10.4352			0.739734			0.369867	−	0.929085i	$-0.379403\pi$
$199$	10.4352			0.739734			0.369867	+	0.929085i	$0.379403\pi$
$200$	−3.78216	+	2.02094i	−0.267439	+	0.142902i
$201$	−1.64315	−	4.36451i	−0.115899	−	0.307849i
$202$	−1.56259	−	1.11985i	−0.109944	−	0.0787921i
$203$	−4.30719	−	4.30719i	−0.302305	−	0.302305i
$204$	−1.97742	+	20.0777i	−0.138447	+	1.40572i
$205$	4.71183	−	4.71183i	0.329089	−	0.329089i
$206$	−0.363357	−	2.20145i	−0.0253163	−	0.153382i
$207$	−5.94698	+	5.21734i	−0.413344	+	0.362630i
$208$	3.38480	−	25.6739i	0.234694	−	1.78017i
$209$		−	5.61607i		−	0.388472i
$210$	2.28620	+	3.95937i	0.157763	+	0.273222i
$211$	17.9097	+	17.9097i	1.23295	+	1.23295i	0.962825	+	0.270127i	$0.0870658\pi$
$211$	17.9097	+	17.9097i	1.23295	+	1.23295i	0.270127	+	0.962825i	$0.412934\pi$
$212$	−0.717431	+	1.45447i	−0.0492734	+	0.0998935i
$213$	9.57146	−	21.1299i	0.655825	−	1.44780i
$214$	−5.28580	+	7.37561i	−0.361330	+	0.504186i
$215$			5.60417i			0.382201i
$216$	10.3908	−	10.3938i	0.707004	−	0.707210i
$217$		−	5.81364i		−	0.394656i
$218$	3.64100	+	2.60936i	0.246600	+	0.176728i
$219$	0.368831	−	0.814231i	0.0249233	−	0.0550206i
$220$	6.17631	−	2.09595i	0.416407	−	0.141309i
$221$	26.6611	+	26.6611i	1.79342	+	1.79342i
$222$	−20.9701	+	12.1084i	−1.40742	+	0.812665i
$223$			8.27899i			0.554402i	0.960812	+	0.277201i	$0.0894068\pi$
$223$			8.27899i			0.554402i	−0.960812	+	0.277201i	$0.910593\pi$
$224$	4.12785	+	3.86792i	0.275804	+	0.258436i
$225$	−3.41907	+	2.99958i	−0.227938	+	0.199972i
$226$	−22.4307	+	3.70227i	−1.49207	+	0.246272i
$227$	−16.7316	+	16.7316i	−1.11052	+	1.11052i	−0.117437	+	0.993080i	$0.537468\pi$
$227$	−16.7316	+	16.7316i	−1.11052	+	1.11052i	−0.993080	+	0.117437i	$0.962532\pi$
$228$	−7.06394	−	8.60739i	−0.467821	−	0.570038i
$229$	−3.32761	−	3.32761i	−0.219894	−	0.219894i	0.588560	−	0.808454i	$-0.299695\pi$
$229$	−3.32761	−	3.32761i	−0.219894	−	0.219894i	−0.808454	+	0.588560i	$0.799695\pi$
$230$	−4.05485	+	5.65800i	−0.267369	+	0.373077i
$231$	1.06624	+	2.83213i	0.0701537	+	0.186341i
$232$	−5.00350	+	16.4862i	−0.328496	+	1.08237i
$233$	22.4485			1.47065			0.735326	−	0.677713i	$-0.237029\pi$
$233$	22.4485			1.47065			0.735326	+	0.677713i	$0.237029\pi$
$234$	−2.69613	−	27.3343i	−0.176251	−	1.78690i
$235$	−15.0059	+	15.0059i	−0.978874	+	0.978874i
$236$	21.3644	+	10.5382i	1.39070	+	0.685976i
$237$	−2.22175	+	4.90473i	−0.144318	+	0.318596i
$238$	−8.12639	+	1.34129i	−0.526756	+	0.0869431i
$239$	−16.7259			−1.08191			−0.540953	−	0.841053i	$-0.681936\pi$
$239$	−16.7259			−1.08191			−0.540953	+	0.841053i	$0.681936\pi$
$240$	6.82973	−	10.9809i	0.440857	−	0.708817i
$241$	−19.0542			−1.22739			−0.613693	−	0.789545i	$-0.710317\pi$
$241$	−19.0542			−1.22739			−0.613693	+	0.789545i	$0.710317\pi$
$242$	−11.0893	+	1.83033i	−0.712845	+	0.117658i
$243$	8.22553	−	13.2416i	0.527668	−	0.849451i
$244$	8.51335	−	17.2594i	0.545012	−	1.10492i
$245$	−1.31983	+	1.31983i	−0.0843206	+	0.0843206i
$246$	2.26291	−	8.44692i	0.144278	−	0.538556i
$247$	−20.8099			−1.32410
$248$	−14.5029	+	7.74941i	−0.920935	+	0.492088i
$249$	6.67670	−	2.51365i	0.423118	−	0.159296i
$250$	−10.0194	+	13.9807i	−0.633684	+	0.884220i
$251$	2.15390	+	2.15390i	0.135953	+	0.135953i	0.771808	−	0.635855i	$-0.219353\pi$
$251$	2.15390	+	2.15390i	0.135953	+	0.135953i	−0.635855	+	0.771808i	$0.719353\pi$
$252$	5.19644	+	2.99950i	0.327345	+	0.188950i
$253$	−3.25794	+	3.25794i	−0.204825	+	0.204825i
$254$	16.9870	−	2.80377i	1.06586	−	0.175924i
$255$	6.63394	+	17.6209i	0.415433	+	1.10346i
$256$	4.14674	−	15.4533i	0.259171	−	0.965831i
$257$			24.3261i			1.51742i	0.651428	+	0.758711i	$0.274170\pi$
$257$			24.3261i			1.51742i	−0.651428	+	0.758711i	$0.725830\pi$
$258$	3.67758	+	6.36904i	0.228956	+	0.396519i
$259$	−6.99022	−	6.99022i	−0.434351	−	0.434351i
$260$	−7.76637	−	22.8859i	−0.481650	−	1.41932i
$261$	−1.19174	+	18.2350i	−0.0737666	+	1.12872i
$262$	21.5036	+	15.4107i	1.32850	+	0.952078i
$263$		−	8.47386i		−	0.522521i	−0.965268	−	0.261260i	$-0.915862\pi$
$263$		−	8.47386i		−	0.522521i	0.965268	−	0.261260i	$-0.0841381\pi$
$264$	5.64386	−	6.43503i	0.347356	−	0.396049i
$265$			1.51355i			0.0929764i
$266$	2.64800	−	3.69493i	0.162359	−	0.226551i
$267$	6.85283	+	3.10420i	0.419387	+	0.189974i
$268$	−4.82947	−	2.38218i	−0.295007	−	0.145515i
$269$	0.519029	+	0.519029i	0.0316458	+	0.0316458i	0.722753	−	0.691107i	$-0.242877\pi$
$269$	0.519029	+	0.519029i	0.0316458	+	0.0316458i	−0.691107	+	0.722753i	$0.742877\pi$
$270$	4.40580	−	12.9892i	0.268128	−	0.790496i
$271$			0.444161i			0.0269809i	0.999909	+	0.0134904i	$0.00429427\pi$
$271$			0.444161i			0.0269809i	−0.999909	+	0.0134904i	$0.995706\pi$
$272$	14.1783	+	18.4845i	0.859684	+	1.12078i
$273$	10.4943	−	3.95088i	0.635141	−	0.239118i
$274$	0.800534	+	4.85014i	0.0483620	+	0.293008i
$275$	−1.87307	+	1.87307i	−0.112950	+	0.112950i
$276$	−0.895367	+	9.09109i	−0.0538948	+	0.547219i
$277$	−20.3609	−	20.3609i	−1.22337	−	1.22337i	−0.966428	−	0.256939i	$-0.917286\pi$
$277$	−20.3609	−	20.3609i	−1.22337	−	1.22337i	−0.256939	−	0.966428i	$-0.582714\pi$
$278$	−12.7203	−	9.11611i	−0.762912	−	0.546748i
$279$	−13.1106	+	11.5021i	−0.784913	+	0.688611i
$280$	5.05177	+	1.53319i	0.301901	+	0.0916258i
$281$	−13.0109			−0.776163			−0.388082	−	0.921625i	$-0.626862\pi$
$281$	−13.0109			−0.776163			−0.388082	+	0.921625i	$0.626862\pi$
$282$	−7.20671	+	26.9010i	−0.429154	+	1.60193i
$283$	10.7492	−	10.7492i	0.638976	−	0.638976i	−0.311327	−	0.950303i	$-0.600773\pi$
$283$	10.7492	−	10.7492i	0.638976	−	0.638976i	0.950303	+	0.311327i	$0.100773\pi$
$284$	−8.60753	−	25.3645i	−0.510763	−	1.50511i
$285$	−9.46588	−	4.28786i	−0.560710	−	0.253991i
$286$	−2.60504	−	15.7830i	−0.154039	−	0.933266i
$287$	3.57004			0.210733
$288$	0.555935	−	16.9615i	0.0327588	−	0.999463i
$289$	−16.9187			−0.995215
$290$	2.61845	+	15.8642i	0.153761	+	0.931580i
$291$	−12.7753	−	5.78696i	−0.748900	−	0.339237i
$292$	−0.331686	−	0.977409i	−0.0194105	−	0.0571985i
$293$	−6.14398	+	6.14398i	−0.358935	+	0.358935i	−0.863420	−	0.504485i	$-0.831682\pi$
$293$	−6.14398	+	6.14398i	−0.358935	+	0.358935i	0.504485	+	0.863420i	$0.331682\pi$
$294$	−0.633860	+	2.36606i	−0.0369675	+	0.137991i
$295$	22.2321			1.29440
$296$	−8.12027	+	26.7558i	−0.471981	+	1.55515i
$297$	4.27735	−	8.00780i	0.248197	−	0.464660i
$298$	−5.95078	−	4.26468i	−0.344719	−	0.247046i
$299$	12.0720	+	12.0720i	0.698144	+	0.698144i
$300$	−0.514769	+	5.22670i	−0.0297202	+	0.301763i
$301$	−2.12307	+	2.12307i	−0.122372	+	0.122372i
$302$	−0.192196	−	1.16444i	−0.0110596	−	0.0670061i
$303$	−2.20350	+	0.829577i	−0.126588	+	0.0476580i
$304$	−12.7472	−	1.68056i	−0.731102	−	0.0963870i
$305$		−	17.9604i		−	1.02841i
$306$	19.1026	+	15.6725i	1.09202	+	0.895938i
$307$	21.4360	+	21.4360i	1.22342	+	1.22342i	0.966409	+	0.257010i	$0.0827372\pi$
$307$	21.4360	+	21.4360i	1.22342	+	1.22342i	0.257010	+	0.966409i	$0.417263\pi$
$308$	3.13384	+	1.54580i	0.178567	+	0.0880799i
$309$	−2.48921	−	1.12757i	−0.141606	−	0.0641449i
$310$	−8.93927	+	12.4735i	−0.507717	+	0.708449i
$311$		−	27.0587i		−	1.53436i	−0.641432	−	0.767180i	$-0.721659\pi$
$311$		−	27.0587i		−	1.53436i	0.641432	−	0.767180i	$-0.278341\pi$
$312$	−23.8445	−	20.9129i	−1.34993	−	1.18396i
$313$			19.5559i			1.10537i	0.833392	+	0.552683i	$0.186396\pi$
$313$			19.5559i			1.10537i	−0.833392	+	0.552683i	$0.813604\pi$
$314$	−18.0744	−	12.9531i	−1.01999	−	0.730988i
$315$	5.58763	+	0.365176i	0.314827	+	0.0205754i
$316$	1.99800	+	5.88767i	0.112396	+	0.331207i
$317$	−17.8168	−	17.8168i	−1.00069	−	1.00069i	−1.00000		0.000690694i	$-0.999780\pi$
$317$	−17.8168	−	17.8168i	−1.00069	−	1.00069i	−0.000690694	−	1.00000i	$-0.500220\pi$
$318$	0.993222	+	1.72012i	0.0556971	+	0.0964594i
$319$			10.6425i			0.595868i
$320$	−2.90911	−	14.6460i	−0.162624	−	0.818737i
$321$	3.91569	+	10.4008i	0.218553	+	0.580515i
$322$	−3.67960	+	0.607331i	−0.205056	+	0.0338453i
$323$	13.2373	−	13.2373i	0.736545	−	0.736545i
$324$	−3.51666	−	17.6531i	−0.195370	−	0.980730i
$325$	6.94052	+	6.94052i	0.384991	+	0.384991i
$326$	−2.79156	+	3.89525i	−0.154610	+	0.215738i
$327$	5.13439	−	1.93300i	0.283932	−	0.106895i
$328$	−4.75876	−	8.90594i	−0.262758	−	0.491748i
$329$	−11.3696			−0.626825
$330$	2.06710	−	7.71601i	0.113790	−	0.424753i
$331$	−1.41507	+	1.41507i	−0.0777791	+	0.0777791i	−0.744926	−	0.667147i	$-0.767515\pi$
$331$	−1.41507	+	1.41507i	−0.0777791	+	0.0777791i	0.667147	+	0.744926i	$0.267515\pi$
$332$	3.64418	−	7.38798i	0.200001	−	0.405468i
$333$	−1.93409	+	29.5939i	−0.105987	+	1.62173i
$334$	−5.86966	+	0.968811i	−0.321174	+	0.0530110i
$335$	−5.02562			−0.274579
$336$	6.74736	−	1.57264i	0.368098	−	0.0857943i
$337$	−29.1493			−1.58786			−0.793931	−	0.608008i	$-0.791969\pi$
$337$	−29.1493			−1.58786			−0.793931	+	0.608008i	$0.791969\pi$
$338$	−40.3432	+	6.65880i	−2.19438	+	0.362191i
$339$	−11.4889	+	25.3628i	−0.623989	+	1.37752i
$340$	19.4981	+	9.61761i	1.05743	+	0.521588i
$341$	−7.18240	+	7.18240i	−0.388949	+	0.388949i
$342$	−13.5716	+	1.33864i	−0.733867	+	0.0723853i
$343$	−1.00000			−0.0539949
$344$	8.12627	+	2.46629i	0.438139	+	0.132974i
$345$	3.00382	+	7.97868i	0.161720	+	0.429557i
$346$	8.08058	−	11.2753i	0.434415	−	0.606167i
$347$	5.64644	+	5.64644i	0.303117	+	0.303117i	0.842232	−	0.539115i	$-0.181241\pi$
$347$	5.64644	+	5.64644i	0.303117	+	0.303117i	−0.539115	+	0.842232i	$0.681241\pi$
$348$	13.3863	+	16.3111i	0.717580	+	0.874368i
$349$	2.91855	−	2.91855i	0.156226	−	0.156226i	−0.624666	−	0.780892i	$-0.714765\pi$
$349$	2.91855	−	2.91855i	0.156226	−	0.156226i	0.780892	+	0.624666i	$0.214765\pi$
$350$	−2.11549	+	0.349170i	−0.113078	+	0.0186639i
$351$	−29.6723	−	15.8494i	−1.58379	−	0.845979i
$352$	−0.321128	−	9.87829i	−0.0171162	−	0.526515i
$353$		−	33.2445i		−	1.76943i	−0.466136	−	0.884713i	$-0.654354\pi$
$353$		−	33.2445i		−	1.76943i	0.466136	−	0.884713i	$-0.345646\pi$
$354$	25.2664	−	14.5892i	1.34289	−	0.775406i
$355$	−17.6759	−	17.6759i	−0.938142	−	0.938142i
$356$	8.22619	−	2.79158i	0.435987	−	0.147953i
$357$	−4.16228	+	9.18865i	−0.220291	+	0.486315i
$358$	1.04060	+	0.745755i	0.0549974	+	0.0394144i
$359$			22.1409i			1.16855i	0.811555	+	0.584276i	$0.198621\pi$
$359$			22.1409i			1.16855i	−0.811555	+	0.584276i	$0.801379\pi$
$360$	−6.53716	−	14.4258i	−0.344539	−	0.760309i
$361$		−	8.66780i		−	0.456200i
$362$	5.17091	−	7.21530i	0.271777	−	0.379228i
$363$	−5.67984	+	12.5388i	−0.298115	+	0.658117i
$364$	5.72783	−	11.6122i	0.300220	−	0.608646i
$365$	−0.681133	−	0.681133i	−0.0356521	−	0.0356521i
$366$	−11.7860	−	20.4117i	−0.616065	−	1.06694i
$367$			13.1466i			0.686245i	0.939291	+	0.343123i	$0.111485\pi$
$367$			13.1466i			0.686245i	−0.939291	+	0.343123i	$0.888515\pi$
$368$	6.41986	+	8.36968i	0.334658	+	0.436300i
$369$	−7.06319	−	8.05097i	−0.367695	−	0.419117i
$370$	4.24954	+	25.7464i	0.220923	+	1.33849i
$371$	−0.573389	+	0.573389i	−0.0297688	+	0.0297688i
$372$	−1.97391	+	20.0421i	−0.102343	+	1.03913i
$373$	−6.88134	−	6.88134i	−0.356302	−	0.356302i	0.506146	−	0.862448i	$-0.331070\pi$
$373$	−6.88134	−	6.88134i	−0.356302	−	0.356302i	−0.862448	+	0.506146i	$0.831070\pi$
$374$	11.6967	+	8.38257i	0.604824	+	0.433453i
$375$	7.42234	+	19.7151i	0.383288	+	1.01808i
$376$	15.1553	+	28.3629i	0.781575	+	1.46270i
$377$	39.4351			2.03101
$378$	6.58987	−	3.25170i	0.338946	−	0.167250i
$379$	−8.62629	+	8.62629i	−0.443103	+	0.443103i	−0.893053	−	0.449951i	$-0.851442\pi$
$379$	−8.62629	+	8.62629i	−0.443103	+	0.443103i	0.449951	+	0.893053i	$0.351442\pi$
$380$	−11.3629	+	3.85603i	−0.582905	+	0.197810i
$381$	8.70062	−	19.2075i	0.445746	−	0.984030i
$382$	−2.81585	−	17.0602i	−0.144071	−	0.872874i
$383$	11.3881			0.581902			0.290951	−	0.956738i	$-0.406028\pi$
$383$	11.3881			0.581902			0.290951	+	0.956738i	$0.406028\pi$
$384$	−12.9172	−	14.7359i	−0.659177	−	0.751988i
$385$	3.26113			0.166203
$386$	−2.06419	−	12.5062i	−0.105064	−	0.636546i
$387$	8.98825	+	0.587422i	0.456899	+	0.0298604i
$388$	−15.3356	+	5.20416i	−0.778545	+	0.264201i
$389$	−2.70246	+	2.70246i	−0.137020	+	0.137020i	−0.772290	−	0.635270i	$-0.780889\pi$
$389$	−2.70246	+	2.70246i	−0.137020	+	0.137020i	0.635270	+	0.772290i	$0.280889\pi$
$390$	−28.5911	−	7.65947i	−1.44777	−	0.387853i
$391$	−15.3582			−0.776699
$392$	1.33297	+	2.49463i	0.0673252	+	0.125998i
$393$	30.3235	−	11.4162i	1.52962	−	0.575871i
$394$	−12.5066	−	8.96294i	−0.630072	−	0.451546i
$395$	4.10298	+	4.10298i	0.206443	+	0.206443i
$396$	−2.71419	−	10.1256i	−0.136393	−	0.508830i
$397$	13.4550	−	13.4550i	0.675285	−	0.675285i	−0.283645	−	0.958929i	$-0.591544\pi$
$397$	13.4550	−	13.4550i	0.675285	−	0.675285i	0.958929	+	0.283645i	$0.0915437\pi$
$398$	−2.40329	−	14.5606i	−0.120466	−	0.729859i
$399$	−1.96163	−	5.21043i	−0.0982042	−	0.260848i
$400$	3.69094	+	4.81194i	0.184547	+	0.240597i
$401$		−	20.8404i		−	1.04072i	−0.853947	−	0.520360i	$-0.825798\pi$
$401$		−	20.8404i		−	1.04072i	0.853947	−	0.520360i	$-0.174202\pi$
$402$	−5.71153	+	3.29792i	−0.284865	+	0.164485i
$403$	26.6138	+	26.6138i	1.32573	+	1.32573i
$404$	−1.20269	+	2.43825i	−0.0598359	+	0.121307i
$405$	−10.2314	−	13.3234i	−0.508402	−	0.662046i
$406$	−5.01800	+	7.00194i	−0.249039	+	0.347500i
$407$			17.2720i			0.856140i
$408$	28.4705	−	1.86484i	1.40950	−	0.0923232i
$409$		−	5.40841i		−	0.267429i	−0.991020	−	0.133714i	$-0.957310\pi$
$409$		−	5.40841i		−	0.267429i	0.991020	−	0.133714i	$-0.0426904\pi$
$410$	−7.65975	−	5.48943i	−0.378288	−	0.271103i
$411$	5.48414	+	2.48421i	0.270513	+	0.122537i
$412$	−2.98807	+	1.01401i	−0.147212	+	0.0499567i
$413$	8.42236	+	8.42236i	0.414437	+	0.414437i
$414$	8.64956	+	7.09645i	0.425103	+	0.348771i
$415$		−	7.68804i		−	0.377391i
$416$	−36.6033	+	1.18991i	−1.79462	+	0.0583404i
$417$	−17.9376	+	6.75317i	−0.878409	+	0.330704i
$418$	−7.83630	+	1.29341i	−0.383286	+	0.0632628i
$419$	7.34358	−	7.34358i	0.358757	−	0.358757i	−0.504598	−	0.863355i	$-0.668359\pi$
$419$	7.34358	−	7.34358i	0.358757	−	0.358757i	0.863355	+	0.504598i	$0.168359\pi$
$420$	4.99812	−	4.10188i	0.243883	−	0.200151i
$421$	−27.6477	−	27.6477i	−1.34746	−	1.34746i	−0.888406	−	0.459059i	$-0.848187\pi$
$421$	−27.6477	−	27.6477i	−1.34746	−	1.34746i	−0.459059	−	0.888406i	$-0.651813\pi$
$422$	20.8653	−	29.1147i	1.01571	−	1.41728i
$423$	22.4943	+	25.6401i	1.09371	+	1.24666i
$424$	2.19470	+	0.666084i	0.106584	+	0.0323479i
$425$	−8.82983			−0.428310
$426$	−31.6877	−	8.48905i	−1.53527	−	0.411296i
$427$	6.80408	−	6.80408i	0.329273	−	0.329273i
$428$	11.5088	+	5.67681i	0.556298	+	0.274399i
$429$	−17.8461	−	8.08393i	−0.861617	−	0.390296i
$430$	7.81969	−	1.29067i	0.377099	−	0.0622417i
$431$	24.7167			1.19056			0.595280	−	0.803518i	$-0.297041\pi$
$431$	24.7167			1.19056			0.595280	+	0.803518i	$0.297041\pi$
$432$	−16.8959	−	12.1049i	−0.812905	−	0.582396i
$433$	8.30731			0.399224			0.199612	−	0.979875i	$-0.436032\pi$
$433$	8.30731			0.399224			0.199612	+	0.979875i	$0.436032\pi$
$434$	−8.11198	+	1.33891i	−0.389388	+	0.0642699i
$435$	17.9380	+	8.12555i	0.860060	+	0.389591i
$436$	2.80238	−	5.68137i	0.134210	−	0.272088i
$437$	5.99381	−	5.99381i	0.286723	−	0.286723i
$438$	−1.22107	−	0.327121i	−0.0583449	−	0.0156304i
$439$	−11.3849			−0.543372			−0.271686	−	0.962386i	$-0.587581\pi$
$439$	−11.3849			−0.543372			−0.271686	+	0.962386i	$0.587581\pi$
$440$	−4.34699	−	8.13532i	−0.207234	−	0.387836i
$441$	1.97846	+	2.25515i	0.0942125	+	0.107388i
$442$	31.0610	−	43.3414i	1.47742	−	2.06154i
$443$	−22.3778	−	22.3778i	−1.06320	−	1.06320i	−0.997863	−	0.0653386i	$-0.979187\pi$
$443$	−22.3778	−	22.3778i	−1.06320	−	1.06320i	−0.0653386	−	0.997863i	$-0.520813\pi$
$444$	21.7248	+	26.4716i	1.03102	+	1.25629i
$445$	5.73263	−	5.73263i	0.271753	−	0.271753i
$446$	11.5520	−	1.90670i	0.547001	−	0.0902846i
$447$	−8.39155	+	3.15926i	−0.396906	+	0.149428i
$448$	4.44638	−	6.65054i	0.210072	−	0.314209i
$449$		−	1.78966i		−	0.0844591i	−0.999108	−	0.0422296i	$-0.986554\pi$
$449$		−	1.78966i		−	0.0844591i	0.999108	−	0.0422296i	$-0.0134461\pi$
$450$	4.97285	+	4.07993i	0.234422	+	0.192330i
$451$	−4.41057	−	4.41057i	−0.207685	−	0.207685i
$452$	10.3318	+	30.4457i	0.485968	+	1.43204i
$453$	−1.31665	−	0.596419i	−0.0618618	−	0.0280222i
$454$	27.1996	+	19.4928i	1.27654	+	0.914845i
$455$		−	12.0839i		−	0.566500i
$456$	−10.3833	+	11.8389i	−0.486244	+	0.554407i
$457$			39.7567i			1.85974i	0.367891	+	0.929869i	$0.380080\pi$
$457$			39.7567i			1.85974i	−0.367891	+	0.929869i	$0.619920\pi$
$458$	−3.87676	+	5.40949i	−0.181149	+	0.252769i
$459$	28.9567	−	8.79284i	1.35158	−	0.410415i
$460$	8.82866	+	4.35481i	0.411638	+	0.203044i
$461$	1.66514	+	1.66514i	0.0775534	+	0.0775534i	0.744819	−	0.667266i	$-0.232536\pi$
$461$	1.66514	+	1.66514i	0.0775534	+	0.0775534i	−0.667266	+	0.744819i	$0.732536\pi$
$462$	3.70621	−	2.14002i	0.172429	−	0.0995628i
$463$		−	6.79248i		−	0.315674i	−0.987465	−	0.157837i	$-0.949548\pi$
$463$		−	6.79248i		−	0.315674i	0.987465	−	0.157837i	$-0.0504520\pi$
$464$	24.1561	+	3.18469i	1.12142	+	0.147846i
$465$	6.62217	+	17.5897i	0.307096	+	0.815701i
$466$	−5.17002	−	31.3232i	−0.239496	−	1.45102i
$467$	−8.95396	+	8.95396i	−0.414340	+	0.414340i	−0.883247	−	0.468907i	$-0.844648\pi$
$467$	−8.95396	+	8.95396i	−0.414340	+	0.414340i	0.468907	+	0.883247i	$0.344648\pi$
$468$	−37.5196	+	10.0572i	−1.73434	+	0.464896i
$469$	−1.90390	−	1.90390i	−0.0879138	−	0.0879138i
$470$	24.3941	+	17.4823i	1.12522	+	0.806397i
$471$	−25.4877	+	9.59563i	−1.17441	+	0.442143i
$472$	9.78394	−	32.2374i	0.450342	−	1.48385i
$473$	5.24585			0.241204
$474$	7.35542	+	1.97050i	0.337846	+	0.0905079i
$475$	3.44599	−	3.44599i	0.158113	−	0.158113i
$476$	3.74310	+	11.0301i	0.171565	+	0.505565i
$477$	2.42750	+	0.158648i	0.111148	+	0.00726400i
$478$	3.85206	+	23.3382i	0.176189	+	1.06746i
$479$	17.2099			0.786340			0.393170	−	0.919466i	$-0.371378\pi$
$479$	17.2099			0.786340			0.393170	+	0.919466i	$0.371378\pi$
$480$	−16.8950	−	7.00079i	−0.771148	−	0.319541i
$481$	64.0000			2.91815
$482$	4.38828	+	26.5869i	0.199880	+	1.21100i
$483$	−1.88466	+	4.16058i	−0.0857552	+	0.189313i
$484$	5.10783	+	15.0517i	0.232174	+	0.684168i
$485$	−10.6870	+	10.6870i	−0.485270	+	0.485270i
$486$	−20.3709	−	8.42776i	−0.924042	−	0.382291i
$487$	27.8022			1.25984			0.629918	−	0.776662i	$-0.283089\pi$
$487$	27.8022			1.25984			0.629918	+	0.776662i	$0.283089\pi$
$488$	−26.0433	−	7.90405i	−1.17893	−	0.357799i
$489$	2.06798	+	5.49292i	0.0935172	+	0.248398i
$490$	2.14556	+	1.53764i	0.0969266	+	0.0694633i
$491$	5.65204	+	5.65204i	0.255073	+	0.255073i	0.823047	−	0.567974i	$-0.192272\pi$
$491$	5.65204	+	5.65204i	0.255073	+	0.255073i	−0.567974	+	0.823047i	$0.692272\pi$
$492$	−12.3074	−	1.21214i	−0.554862	−	0.0546475i
$493$	−25.0850	+	25.0850i	−1.12977	+	1.12977i
$494$	4.79264	+	29.0368i	0.215631	+	1.30643i
$495$	−6.45202	−	7.35432i	−0.289997	−	0.330552i
$496$	14.1531	+	18.4517i	0.635494	+	0.828505i
$497$		−	13.3926i		−	0.600741i
$498$	−5.04506	−	8.73732i	−0.226075	−	0.391529i
$499$	−15.1120	−	15.1120i	−0.676506	−	0.676506i	0.282701	−	0.959208i	$-0.408769\pi$
$499$	−15.1120	−	15.1120i	−0.676506	−	0.676506i	−0.959208	+	0.282701i	$0.908769\pi$
$500$	21.8153	+	10.7606i	0.975612	+	0.481229i
$501$	−3.00640	+	6.63693i	−0.134316	+	0.296516i
$502$	2.50935	−	3.50146i	0.111998	−	0.156278i
$503$		−	16.9039i		−	0.753707i	−0.926273	−	0.376854i	$-0.877006\pi$
$503$		−	16.9039i		−	0.753707i	0.926273	−	0.376854i	$-0.122994\pi$
$504$	2.98853	−	7.94158i	0.133120	−	0.353746i
$505$			2.53728i			0.112907i
$506$	5.29623	+	3.79559i	0.235446	+	0.168735i
$507$	−20.6635	+	45.6168i	−0.917699	+	2.02591i
$508$	−7.82439	−	23.0568i	−0.347151	−	1.02298i
$509$	22.6903	+	22.6903i	1.00573	+	1.00573i	0.999984	+	0.00574435i	$0.00182849\pi$
$509$	22.6903	+	22.6903i	1.00573	+	1.00573i	0.00574435	+	0.999984i	$0.498172\pi$
$510$	23.0593	−	13.3148i	1.02108	−	0.589587i
$511$		−	0.516078i		−	0.0228299i
$512$	−22.5175	−	2.22711i	−0.995144	−	0.0984254i
$513$	−7.86929	+	14.7324i	−0.347438	+	0.650452i
$514$	33.9431	−	5.60244i	1.49717	−	0.247113i
$515$	−2.08231	+	2.08231i	−0.0917577	+	0.0917577i
$516$	8.03997	−	6.59827i	0.353940	−	0.290473i
$517$	14.0464	+	14.0464i	0.617760	+	0.617760i
$518$	−8.14381	+	11.3636i	−0.357819	+	0.499287i
$519$	−5.98606	−	15.9000i	−0.262759	−	0.697934i
$520$	−30.1448	+	16.1074i	−1.32194	+	0.706357i
$521$	7.32638			0.320974			0.160487	−	0.987038i	$-0.448693\pi$
$521$	7.32638			0.320974			0.160487	+	0.987038i	$0.448693\pi$
$522$	25.7183	−	2.53674i	1.12566	−	0.111030i
$523$	14.9784	−	14.9784i	0.654958	−	0.654958i	−0.299225	−	0.954183i	$-0.596728\pi$
$523$	14.9784	−	14.9784i	0.654958	−	0.654958i	0.954183	+	0.299225i	$0.0967280\pi$
$524$	16.5507	−	33.5539i	0.723022	−	1.46581i
$525$	−1.08354	+	2.39202i	−0.0472896	+	0.104396i
$526$	−11.8239	+	1.95158i	−0.515546	+	0.0850928i
$527$	−33.8585			−1.47490
$528$	−10.2788	−	6.39305i	−0.447329	−	0.278222i
$529$	16.0459			0.697646
$530$	2.11190	−	0.348578i	0.0917353	−	0.0151413i
$531$	2.33034	−	35.6570i	0.101128	−	1.54738i
$532$	−5.76551	−	2.84389i	−0.249967	−	0.123298i
$533$	−16.3430	+	16.3430i	−0.707895	+	0.707895i
$534$	2.75316	−	10.2769i	0.119141	−	0.444725i
$535$	11.9762			0.517778
$536$	−2.21168	+	7.28736i	−0.0955302	+	0.314766i
$537$	1.46741	−	0.552452i	0.0633234	−	0.0238401i
$538$	0.604684	−	0.843755i	0.0260698	−	0.0363769i
$539$	1.23544	+	1.23544i	0.0532141	+	0.0532141i
$540$	−19.1389	−	3.15609i	−0.823608	−	0.135817i
$541$	−4.34392	+	4.34392i	−0.186760	+	0.186760i	−0.794294	−	0.607534i	$-0.792159\pi$
$541$	−4.34392	+	4.34392i	−0.186760	+	0.186760i	0.607534	+	0.794294i	$0.292159\pi$
$542$	0.619754	−	0.102293i	0.0266207	−	0.00439385i
$543$	−3.83059	−	10.1747i	−0.164386	−	0.436639i
$544$	22.5267	−	24.0405i	0.965823	−	1.03073i
$545$		−	5.91212i		−	0.253247i
$546$	−7.92969	−	13.7331i	−0.339359	−	0.587722i
$547$	21.3206	+	21.3206i	0.911603	+	0.911603i	0.996398	−	0.0847958i	$-0.0270238\pi$
$547$	21.3206	+	21.3206i	0.911603	+	0.911603i	−0.0847958	+	0.996398i	$0.527024\pi$
$548$	6.58320	−	2.23403i	0.281220	−	0.0954329i
$549$	−28.8058	−	1.88259i	−1.22940	−	0.0803469i
$550$	3.04494	+	2.18218i	0.129837	+	0.0930486i
$551$		−	19.5797i		−	0.834122i
$552$	12.8913	−	0.844390i	0.548691	−	0.0359396i
$553$			3.10873i			0.132196i
$554$	−23.7210	+	33.0995i	−1.00781	+	1.40626i
$555$	29.1119	+	13.1871i	1.23573	+	0.559762i
$556$	−9.79047	+	19.8486i	−0.415209	+	0.841766i
$557$	−19.4928	−	19.4928i	−0.825938	−	0.825938i	0.161014	−	0.986952i	$-0.448523\pi$
$557$	−19.4928	−	19.4928i	−0.825938	−	0.825938i	−0.986952	+	0.161014i	$0.948523\pi$
$558$	19.0687	+	15.6447i	0.807242	+	0.662294i
$559$		−	19.4381i		−	0.822144i
$560$	0.975867	−	7.40201i	0.0412379	−	0.312792i
$561$	16.4943	−	6.20977i	0.696388	−	0.262177i
$562$	2.99647	+	18.1545i	0.126399	+	0.765802i
$563$	−8.52509	+	8.52509i	−0.359290	+	0.359290i	−0.863551	−	0.504261i	$-0.831765\pi$
$563$	−8.52509	+	8.52509i	−0.359290	+	0.359290i	0.504261	+	0.863551i	$0.331765\pi$
$564$	39.1957	+	3.86032i	1.65044	+	0.162549i
$565$	21.2169	+	21.2169i	0.892600	+	0.892600i
$566$	−17.4744	−	12.5232i	−0.734503	−	0.526388i
$567$	1.17138	−	8.92345i	0.0491932	−	0.374749i
$568$	−33.4097	+	17.8520i	−1.40184	+	0.749052i
$569$	8.02648			0.336488			0.168244	−	0.985745i	$-0.446190\pi$
$569$	8.02648			0.336488			0.168244	+	0.985745i	$0.446190\pi$
$570$	−3.80296	+	14.1956i	−0.159288	+	0.594588i
$571$	−14.7516	+	14.7516i	−0.617337	+	0.617337i	−0.944848	−	0.327511i	$-0.893790\pi$
$571$	−14.7516	+	14.7516i	−0.617337	+	0.617337i	0.327511	+	0.944848i	$0.393790\pi$
$572$	−21.4226	+	7.26980i	−0.895723	+	0.303966i
$573$	−19.2902	−	8.73810i	−0.805861	−	0.365039i
$574$	−0.822200	−	4.98140i	−0.0343180	−	0.207920i
$575$	−3.99811			−0.166733
$576$	−23.7949	+	3.13060i	−0.991456	+	0.130442i
$577$	8.97453			0.373614			0.186807	−	0.982397i	$-0.440186\pi$
$577$	8.97453			0.373614			0.186807	+	0.982397i	$0.440186\pi$
$578$	3.89646	+	23.6072i	0.162071	+	0.981930i
$579$	−14.1409	−	6.40557i	−0.587677	−	0.266206i
$580$	21.5329	−	7.30724i	0.894104	−	0.303417i
$581$	2.91252	−	2.91252i	0.120832	−	0.120832i
$582$	−5.13253	+	19.1586i	−0.212750	+	0.794148i
$583$	1.41677			0.0586767
$584$	−1.28742	+	0.687916i	−0.0532740	+	0.0284662i
$585$	−27.2509	+	23.9075i	−1.12669	+	0.988452i
$586$	9.98790	+	7.15792i	0.412596	+	0.295691i
$587$	−10.9929	−	10.9929i	−0.453727	−	0.453727i	0.442863	−	0.896589i	$-0.353963\pi$
$587$	−10.9929	−	10.9929i	−0.453727	−	0.453727i	−0.896589	+	0.442863i	$0.853963\pi$
$588$	3.44742	+	0.339531i	0.142169	+	0.0140020i
$589$	13.2139	−	13.2139i	0.544468	−	0.544468i
$590$	−5.12017	−	31.0212i	−0.210794	−	1.27712i
$591$	−17.6362	+	6.63971i	−0.725458	+	0.273121i
$592$	39.2034	+	5.16850i	1.61125	+	0.212424i
$593$		−	31.8111i		−	1.30632i	−0.757218	−	0.653162i	$-0.773442\pi$
$593$		−	31.8111i		−	1.30632i	0.757218	−	0.653162i	$-0.226558\pi$
$594$	−12.1587	−	4.12410i	−0.498876	−	0.169214i
$595$	7.68663	+	7.68663i	0.315121	+	0.315121i
$596$	−4.58016	+	9.28551i	−0.187611	+	0.380349i
$597$	−16.4640	−	7.45786i	−0.673826	−	0.305230i
$598$	14.0643	−	19.6248i	0.575131	−	0.802517i
$599$		−	30.5728i		−	1.24917i	−0.780957	−	0.624585i	$-0.785268\pi$
$599$		−	30.5728i		−	1.24917i	0.780957	−	0.624585i	$-0.214732\pi$
$600$	7.41155	−	0.485461i	0.302575	−	0.0198189i
$601$			24.7270i			1.00863i	0.863519	+	0.504317i	$0.168256\pi$
$601$			24.7270i			1.00863i	−0.863519	+	0.504317i	$0.831744\pi$
$602$	3.45135	+	2.47344i	0.140667	+	0.100810i
$603$	−0.526780	+	8.06035i	−0.0214521	+	0.328243i
$604$	−1.58052	+	0.536354i	−0.0643105	+	0.0218239i
$605$	10.4892	+	10.4892i	0.426445	+	0.426445i
$606$	1.66502	+	2.88357i	0.0676367	+	0.117137i
$607$		−	23.2149i		−	0.942264i	−0.882063	−	0.471132i	$-0.843846\pi$
$607$		−	23.2149i		−	0.942264i	0.882063	−	0.471132i	$-0.156154\pi$
$608$	0.590797	+	18.1736i	0.0239600	+	0.737039i
$609$	3.71731	+	9.87385i	0.150633	+	0.400109i
$610$	−25.0608	+	4.13638i	−1.01468	+	0.167477i
$611$	52.0479	−	52.0479i	2.10563	−	2.10563i
$612$	17.4690	−	30.2639i	0.706142	−	1.22335i
$613$	4.54522	+	4.54522i	0.183580	+	0.183580i	0.792914	−	0.609334i	$-0.208563\pi$
$613$	4.54522	+	4.54522i	0.183580	+	0.183580i	−0.609334	+	0.792914i	$0.708563\pi$
$614$	24.9736	−	34.8473i	1.00785	−	1.40632i
$615$	−10.8015	+	4.06654i	−0.435557	+	0.163979i
$616$	1.43516	−	4.72877i	0.0578243	−	0.190527i
$617$	15.7116			0.632526			0.316263	−	0.948671i	$-0.397572\pi$
$617$	15.7116			0.632526			0.316263	+	0.948671i	$0.397572\pi$
$618$	−1.00005	+	3.73297i	−0.0402280	+	0.150162i
$619$	25.9169	−	25.9169i	1.04169	−	1.04169i	0.0425971	−	0.999092i	$-0.486437\pi$
$619$	25.9169	−	25.9169i	1.04169	−	1.04169i	0.999092	−	0.0425971i	$-0.0135632\pi$
$620$	19.4635	+	9.60056i	0.781674	+	0.385568i
$621$	13.1115	−	3.98136i	0.526145	−	0.159767i
$622$	−37.7560	+	6.23177i	−1.51388	+	0.249871i
$623$	4.34348			0.174018
$624$	−23.6890	+	38.0875i	−0.948317	+	1.52472i
$625$	15.1208			0.604832
$626$	27.2871	−	4.50383i	1.09061	−	0.180009i
$627$	−4.01370	+	8.86064i	−0.160292	+	0.353860i
$628$	−13.9114	+	28.2030i	−0.555123	+	1.12542i
$629$	−40.7109	+	40.7109i	−1.62325	+	1.62325i
$630$	−0.777318	−	7.88071i	−0.0309691	−	0.313975i
$631$	−30.9855			−1.23351			−0.616756	−	0.787154i	$-0.711554\pi$
$631$	−30.9855			−1.23351			−0.616756	+	0.787154i	$0.711554\pi$
$632$	7.75513	−	4.14384i	0.308482	−	0.164833i
$633$	−15.4569	−	41.0563i	−0.614357	−	1.63184i
$634$	−20.7571	+	28.9637i	−0.824369	+	1.15029i
$635$	−16.0677	−	16.0677i	−0.637629	−	0.637629i
$636$	2.17140	−	1.78203i	0.0861014	−	0.0706620i
$637$	4.57782	−	4.57782i	0.181380	−	0.181380i
$638$	14.8499	−	2.45103i	0.587913	−	0.0970373i
$639$	−30.2023	+	26.4968i	−1.19479	+	1.04820i
$640$	−19.7661	+	7.43223i	−0.781324	+	0.293785i
$641$		−	36.3928i		−	1.43743i	−0.695306	−	0.718714i	$-0.744731\pi$
$641$		−	36.3928i		−	1.43743i	0.695306	−	0.718714i	$-0.255269\pi$
$642$	13.6108	−	7.85906i	0.537174	−	0.310172i
$643$	−33.1871	−	33.1871i	−1.30877	−	1.30877i	−0.922303	−	0.386468i	$-0.873695\pi$
$643$	−33.1871	−	33.1871i	−1.30877	−	1.30877i	−0.386468	−	0.922303i	$-0.626305\pi$
$644$	1.69486	+	4.99440i	0.0667869	+	0.196807i
$645$	4.00519	−	8.84187i	0.157704	−	0.348148i
$646$	−21.5192	−	15.4219i	−0.846660	−	0.606766i
$647$		−	21.9570i		−	0.863217i	−0.902061	−	0.431608i	$-0.857946\pi$
$647$		−	21.9570i		−	0.863217i	0.902061	−	0.431608i	$-0.142054\pi$
$648$	−23.8221	+	8.97253i	−0.935821	+	0.352474i
$649$		−	20.8106i		−	0.816888i
$650$	8.08591	−	11.2828i	0.317155	−	0.442547i
$651$	−4.15490	+	9.17236i	−0.162843	+	0.359493i
$652$	6.07809	+	2.99807i	0.238036	+	0.117413i
$653$	−28.1079	−	28.1079i	−1.09995	−	1.09995i	−0.994416	−	0.105532i	$-0.966345\pi$
$653$	−28.1079	−	28.1079i	−1.09995	−	1.09995i	−0.105532	−	0.994416i	$-0.533655\pi$
$654$	−3.87966	−	6.71901i	−0.151707	−	0.262734i
$655$		−	34.9167i		−	1.36431i
$656$	−11.3308	+	8.69115i	−0.442393	+	0.339332i
$657$	−1.16383	+	1.02104i	−0.0454054	+	0.0398346i
$658$	2.61847	+	15.8644i	0.102079	+	0.618457i
$659$	−27.8370	+	27.8370i	−1.08438	+	1.08438i	−0.0882817	+	0.996096i	$0.528138\pi$
$659$	−27.8370	+	27.8370i	−1.08438	+	1.08438i	−0.996096	+	0.0882817i	$0.971862\pi$
$660$	−11.2425	−	1.10725i	−0.437613	−	0.0430998i
$661$	25.8418	+	25.8418i	1.00513	+	1.00513i	0.999987	+	0.00514248i	$0.00163691\pi$
$661$	25.8418	+	25.8418i	1.00513	+	1.00513i	0.00514248	+	0.999987i	$0.498363\pi$
$662$	2.30039	+	1.64859i	0.0894072	+	0.0640744i
$663$	−23.0098	−	61.1182i	−0.893628	−	2.37364i
$664$	−11.1480	−	3.38337i	−0.432625	−	0.131300i
$665$	−5.99968			−0.232658
$666$	41.7388	−	4.11692i	1.61734	−	0.159527i
$667$	−11.3584	+	11.3584i	−0.439797	+	0.439797i
$668$	2.70363	+	7.96703i	0.104607	+	0.308253i
$669$	5.91684	−	13.0620i	0.228758	−	0.505006i
$670$	1.15743	+	7.01243i	0.0447154	+	0.270914i
$671$	−16.8121			−0.649022
$672$	−3.74831	−	9.05264i	−0.144594	−	0.349213i
$673$	−22.1619			−0.854277			−0.427139	−	0.904186i	$-0.640478\pi$
$673$	−22.1619			−0.854277			−0.427139	+	0.904186i	$0.640478\pi$
$674$	6.71323	+	40.6730i	0.258584	+	1.56667i
$675$	7.53811	−	2.28898i	0.290142	−	0.0881031i
$676$	18.5825	+	54.7587i	0.714712	+	2.10611i
$677$	−22.4728	+	22.4728i	−0.863700	+	0.863700i	−0.991766	−	0.128065i	$-0.959123\pi$
$677$	−22.4728	+	22.4728i	−0.863700	+	0.863700i	0.128065	+	0.991766i	$0.459123\pi$
$678$	38.0355	+	10.1896i	1.46075	+	0.391330i
$679$	−8.09726			−0.310744
$680$	8.92927	−	29.4214i	0.342422	−	1.12826i
$681$	38.3558	−	14.4402i	1.46980	−	0.553350i
$682$	11.6760	+	8.36771i	0.447097	+	0.320416i
$683$	8.67868	+	8.67868i	0.332080	+	0.332080i	0.853376	−	0.521296i	$-0.174551\pi$
$683$	8.67868	+	8.67868i	0.332080	+	0.332080i	−0.521296	+	0.853376i	$0.674551\pi$
$684$	4.99346	+	18.6286i	0.190930	+	0.712282i
$685$	4.58767	−	4.58767i	0.175286	−	0.175286i
$686$	0.230305	+	1.39533i	0.00879310	+	0.0532741i
$687$	2.87189	+	7.62824i	0.109569	+	0.291035i
$688$	1.56978	−	11.9069i	0.0598472	−	0.453945i
$689$		−	5.24974i		−	0.199999i
$690$	10.4411	−	6.02886i	0.397487	−	0.229515i
$691$	−10.6368	−	10.6368i	−0.404644	−	0.404644i	0.475222	−	0.879866i	$-0.342368\pi$
$691$	−10.6368	−	10.6368i	−0.404644	−	0.404644i	−0.879866	+	0.475222i	$0.842368\pi$
$692$	−17.5939	−	8.67834i	−0.668819	−	0.329901i
$693$	0.341828	−	5.23036i	0.0129850	−	0.198685i
$694$	6.57827	−	9.17908i	0.249708	−	0.348433i
$695$			20.6547i			0.783478i
$696$	19.6766	−	22.4349i	0.745838	−	0.850392i
$697$		−	20.7918i		−	0.787546i
$698$	−4.74451	−	3.40020i	−0.179583	−	0.128699i
$699$	−35.4177	−	16.0435i	−1.33962	−	0.606822i
$700$	0.974418	+	2.87140i	0.0368295	+	0.108529i
$701$	27.3460	+	27.3460i	1.03285	+	1.03285i	0.999442	+	0.0334040i	$0.0106348\pi$
$701$	27.3460	+	27.3460i	1.03285	+	1.03285i	0.0334040	+	0.999442i	$0.489365\pi$
$702$	−15.2815	+	45.0530i	−0.576765	+	1.70042i
$703$		−	31.7762i		−	1.19846i
$704$	−13.7096	+	2.72310i	−0.516699	+	0.102631i
$705$	34.3996	−	12.9508i	1.29556	−	0.487755i
$706$	−46.3872	+	7.65639i	−1.74581	+	0.288152i
$707$	−0.961217	+	0.961217i	−0.0361503	+	0.0361503i
$708$	−26.1758	−	31.8951i	−0.983746	−	1.19869i
$709$	−3.83200	−	3.83200i	−0.143914	−	0.143914i	0.631479	−	0.775393i	$-0.282448\pi$
$709$	−3.83200	−	3.83200i	−0.143914	−	0.143914i	−0.775393	+	0.631479i	$0.782448\pi$
$710$	−20.5930	+	28.7347i	−0.772841	+	1.07839i
$711$	7.01063	−	6.15049i	0.262919	−	0.230662i
$712$	−5.78973	−	10.8354i	−0.216979	−	0.406073i
$713$	−15.3310			−0.574150
$714$	13.7798	+	3.69158i	0.515698	+	0.138154i
$715$	−14.9289	+	14.9289i	−0.558308	+	0.558308i
$716$	0.800922	−	1.62374i	0.0299319	−	0.0606819i
$717$	26.3889	+	11.9537i	0.985512	+	0.446418i
$718$	30.8939	−	5.09916i	1.15295	−	0.190299i
$719$	28.2350			1.05299			0.526494	−	0.850179i	$-0.323506\pi$
$719$	28.2350			1.05299			0.526494	+	0.850179i	$0.323506\pi$
$720$	−18.6233	+	12.4439i	−0.694051	+	0.463756i
$721$	−1.57772			−0.0587573
$722$	−12.0945	+	1.99624i	−0.450110	+	0.0742924i
$723$	30.0623	+	13.6176i	1.11803	+	0.506446i
$724$	−11.2586	−	5.55343i	−0.418424	−	0.206392i
$725$	−6.53021	+	6.53021i	−0.242526	+	0.242526i
$726$	18.8040	+	5.03753i	0.697880	+	0.186960i
$727$	8.86990			0.328966			0.164483	−	0.986380i	$-0.447404\pi$
$727$	8.86990			0.328966			0.164483	+	0.986380i	$0.447404\pi$
$728$	−17.5221	−	5.31788i	−0.649412	−	0.197094i
$729$	−22.4412	+	15.0131i	−0.831156	+	0.556040i
$730$	−0.793540	+	1.10728i	−0.0293702	+	0.0409821i
$731$	12.3647	+	12.3647i	0.457325	+	0.457325i
$732$	−25.7667	+	21.1463i	−0.952366	+	0.781591i
$733$	−21.0124	+	21.0124i	−0.776112	+	0.776112i	−0.979167	−	0.203055i	$-0.934913\pi$
$733$	−21.0124	+	21.0124i	−0.776112	+	0.776112i	0.203055	+	0.979167i	$0.434913\pi$
$734$	18.3439	−	3.02773i	0.677084	−	0.111755i
$735$	3.02558	−	1.13907i	0.111600	−	0.0420154i
$736$	10.2000	−	10.8854i	0.375976	−	0.401243i
$737$			4.70429i			0.173285i
$738$	−9.60711	+	11.7097i	−0.353642	+	0.431040i
$739$	−20.4672	−	20.4672i	−0.752898	−	0.752898i	0.222121	−	0.975019i	$-0.428702\pi$
$739$	−20.4672	−	20.4672i	−0.752898	−	0.752898i	−0.975019	+	0.222121i	$0.928702\pi$
$740$	34.9461	−	11.8591i	1.28464	−	0.435948i
$741$	32.8324	+	14.8725i	1.20613	+	0.546353i
$742$	0.932123	+	0.668015i	0.0342193	+	0.0245236i
$743$		−	1.56551i		−	0.0574330i	−0.999588	−	0.0287165i	$-0.990858\pi$
$743$		−	1.56551i		−	0.0574330i	0.999588	−	0.0287165i	$-0.00914200\pi$
$744$	28.4200	−	1.86153i	1.04193	−	0.0682470i
$745$			9.66265i			0.354012i
$746$	−8.01696	+	11.1866i	−0.293522	+	0.409570i
$747$	−12.3305	−	0.805852i	−0.451149	−	0.0294846i
$748$	9.00268	−	18.2514i	0.329170	−	0.667338i
$749$	4.53705	+	4.53705i	0.165780	+	0.165780i
$750$	25.7997	−	14.8971i	0.942072	−	0.543966i
$751$		−	33.8650i		−	1.23575i	−0.786275	−	0.617876i	$-0.787993\pi$
$751$		−	33.8650i		−	1.23575i	0.786275	−	0.617876i	$-0.212007\pi$
$752$	36.0854	−	27.6788i	1.31590	−	1.00934i
$753$	−1.85892	−	4.93762i	−0.0677428	−	0.179937i
$754$	−9.08212	−	55.0252i	−0.330751	−	2.00390i
$755$	−1.10143	+	1.10143i	−0.0400851	+	0.0400851i
$756$	−6.05490	−	8.44619i	−0.220215	−	0.307185i
$757$	12.4442	+	12.4442i	0.452291	+	0.452291i	0.896114	−	0.443823i	$-0.146378\pi$
$757$	12.4442	+	12.4442i	0.452291	+	0.452291i	−0.443823	+	0.896114i	$0.646378\pi$
$758$	14.0232	+	10.0499i	0.509347	+	0.365028i
$759$	7.46853	−	2.81176i	0.271091	−	0.102060i
$760$	7.99740	+	14.9670i	0.290096	+	0.542910i
$761$	−46.8851			−1.69958			−0.849791	−	0.527119i	$-0.823272\pi$
$761$	−46.8851			−1.69958			−0.849791	+	0.527119i	$0.823272\pi$
$762$	−28.8047	−	7.71669i	−1.04348	−	0.279546i
$763$	2.23973	−	2.23973i	0.0810838	−	0.0810838i
$764$	−23.1561	+	7.85809i	−0.837760	+	0.284296i
$765$	2.12678	−	32.5422i	0.0768938	−	1.17657i
$766$	−2.62273	−	15.8901i	−0.0947631	−	0.574134i
$767$	−77.1121			−2.78436
$768$	−17.5866	+	21.4175i	−0.634602	+	0.772839i
$769$	12.9505			0.467005			0.233503	−	0.972356i	$-0.424981\pi$
$769$	12.9505			0.467005			0.233503	+	0.972356i	$0.424981\pi$
$770$	−0.751055	−	4.55037i	−0.0270662	−	0.163984i
$771$	17.3854	−	38.3800i	0.626121	−	1.38222i
$772$	−16.9749	+	5.76047i	−0.610939	+	0.207324i
$773$	17.9424	−	17.9424i	0.645342	−	0.645342i	−0.306522	−	0.951864i	$-0.599165\pi$
$773$	17.9424	−	17.9424i	0.645342	−	0.645342i	0.951864	+	0.306522i	$0.0991653\pi$
$774$	−1.25039	−	12.6769i	−0.0449444	−	0.455662i
$775$	−8.81417			−0.316614
$776$	10.7934	+	20.1997i	0.387461	+	0.725126i
$777$	6.03290	+	16.0245i	0.216429	+	0.574874i
$778$	4.39322	+	3.14844i	0.157505	+	0.112877i
$779$	8.11437	+	8.11437i	0.290727	+	0.290727i
$780$	−4.10285	+	41.6582i	−0.146906	+	1.49160i
$781$	−16.5458	+	16.5458i	−0.592054	+	0.592054i
$782$	3.53708	+	21.4299i	0.126486	+	0.766330i
$783$	14.9124	−	27.9181i	0.532926	−	0.997712i
$784$	3.17386	−	2.43447i	0.113352	−	0.0869453i
$785$			29.3484i			1.04749i
$786$	−22.9131	−	39.6822i	−0.817282	−	1.41542i
$787$	−25.3110	−	25.3110i	−0.902240	−	0.902240i	0.0933900	−	0.995630i	$-0.470230\pi$
$787$	−25.3110	−	25.3110i	−0.902240	−	0.902240i	−0.995630	+	0.0933900i	$0.970230\pi$
$788$	−9.62598	+	19.5151i	−0.342911	+	0.695195i
$789$	−6.05611	+	13.3695i	−0.215603	+	0.475966i
$790$	4.78009	−	6.66996i	0.170068	−	0.237307i
$791$			16.0755i			0.571579i
$792$	−13.5035	+	6.11919i	−0.479825	+	0.217436i
$793$			62.2958i			2.21219i
$794$	−21.8729	−	15.6754i	−0.776241	−	0.556300i
$795$	1.08170	−	2.38797i	0.0383641	−	0.0846925i
$796$	−19.7635	+	6.70679i	−0.700498	+	0.237716i
$797$	−6.78134	−	6.78134i	−0.240207	−	0.240207i	0.576729	−	0.816936i	$-0.304329\pi$
$797$	−6.78134	−	6.78134i	−0.240207	−	0.240207i	−0.816936	+	0.576729i	$0.804329\pi$
$798$	−6.81853	+	3.93712i	−0.241373	+	0.139373i
$799$			66.2161i			2.34256i
$800$	5.86423	−	6.25831i	0.207332	−	0.221265i
$801$	−8.59340	−	9.79518i	−0.303633	−	0.346096i
$802$	−29.0793	+	4.79966i	−1.02683	+	0.169482i
$803$	−0.637582	+	0.637582i	−0.0224998	+	0.0224998i
$804$	5.91710	+	7.20997i	0.208680	+	0.254276i
$805$	3.48047	+	3.48047i	0.122671	+	0.122671i
$806$	31.0059	−	43.2645i	1.09214	−	1.52393i
$807$	−0.447948	−	1.18983i	−0.0157685	−	0.0418839i
$808$	3.67916	+	1.11661i	0.129432	+	0.0392822i
$809$	−1.53506			−0.0539699			−0.0269849	−	0.999636i	$-0.508591\pi$
$809$	−1.53506			−0.0539699			−0.0269849	+	0.999636i	$0.508591\pi$
$810$	−16.2343	+	17.3447i	−0.570414	+	0.609429i
$811$	−14.5930	+	14.5930i	−0.512428	+	0.512428i	−0.915270	−	0.402842i	$-0.868022\pi$
$811$	−14.5930	+	14.5930i	−0.512428	+	0.512428i	0.402842	+	0.915270i	$0.368022\pi$
$812$	10.9257	+	5.38921i	0.383418	+	0.189124i
$813$	0.317434	−	0.700766i	0.0111329	−	0.0245769i
$814$	24.1002	−	3.97783i	0.844711	−	0.139423i
$815$	6.32495			0.221553
$816$	−9.15898	−	39.2964i	−0.320629	−	1.37565i
$817$	−9.65108			−0.337649
$818$	−7.54654	+	1.24559i	−0.263859	+	0.0435509i
$819$	−19.3807	−	1.26662i	−0.677217	−	0.0442591i
$820$	−5.89551	+	11.9522i	−0.205880	+	0.417387i
$821$	35.7226	−	35.7226i	1.24673	−	1.24673i	0.289571	−	0.957156i	$-0.406487\pi$
$821$	35.7226	−	35.7226i	1.24673	−	1.24673i	0.957156	−	0.289571i	$-0.0935127\pi$
$822$	2.20328	−	8.22434i	0.0768481	−	0.286857i
$823$	−1.22131			−0.0425722			−0.0212861	−	0.999773i	$-0.506776\pi$
$823$	−1.22131			−0.0425722			−0.0212861	+	0.999773i	$0.506776\pi$
$824$	2.10305	+	3.93583i	0.0732633	+	0.137111i
$825$	4.29385	−	1.61655i	0.149493	−	0.0562811i
$826$	9.81230	−	13.6917i	0.341413	−	0.476396i
$827$	16.3468	+	16.3468i	0.568434	+	0.568434i	0.931689	−	0.363256i	$-0.118335\pi$
$827$	16.3468	+	16.3468i	0.568434	+	0.568434i	−0.363256	+	0.931689i	$0.618335\pi$
$828$	7.90988	−	13.7034i	0.274887	−	0.476226i
$829$	−19.0692	+	19.0692i	−0.662299	+	0.662299i	−0.955921	−	0.293622i	$-0.905139\pi$
$829$	−19.0692	+	19.0692i	−0.662299	+	0.662299i	0.293622	+	0.955921i	$0.405139\pi$
$830$	−10.7274	+	1.77060i	−0.372353	+	0.0614584i
$831$	17.5724	+	46.6755i	0.609581	+	1.61915i
$832$	10.0903	+	50.7997i	0.349817	+	1.76116i
$833$			5.82397i			0.201789i
$834$	13.5541	+	23.4737i	0.469339	+	0.812828i
$835$	5.55203	+	5.55203i	0.192136	+	0.192136i
$836$	3.60948	+	10.6364i	0.124837	+	0.367867i
$837$	28.9053	−	8.77725i	0.999115	−	0.303386i
$838$	−11.9380	−	8.55548i	−0.412392	−	0.295544i
$839$			27.8332i			0.960907i	0.877020	+	0.480454i	$0.159528\pi$
$839$			27.8332i			0.960907i	−0.877020	+	0.480454i	$0.840472\pi$
$840$	−6.87458	−	6.02937i	−0.237196	−	0.208033i
$841$			8.10376i			0.279440i
$842$	−32.2103	+	44.9452i	−1.11004	+	1.54891i
$843$	20.5276	+	9.29862i	0.707009	+	0.320261i
$844$	−45.4301	−	22.4088i	−1.56377	−	0.771342i
$845$	38.1600	+	38.1600i	1.31275	+	1.31275i
$846$	30.5959	−	37.2921i	1.05191	−	1.28213i
$847$			7.94738i			0.273075i
$848$	0.423958	−	3.21575i	0.0145588	−	0.110429i
$849$	−24.6417	+	9.27711i	−0.845700	+	0.318390i
$850$	2.03356	+	12.3206i	0.0697504	+	0.422592i
$851$	−18.4337	+	18.4337i	−0.631899	+	0.631899i
$852$	−4.54722	+	46.1700i	−0.155785	+	1.58176i
$853$	5.17015	+	5.17015i	0.177023	+	0.177023i	0.790057	−	0.613034i	$-0.210051\pi$
$853$	5.17015	+	5.17015i	0.177023	+	0.177023i	−0.613034	+	0.790057i	$0.710051\pi$
$854$	−11.0610	−	7.92696i	−0.378499	−	0.271255i
$855$	11.8701	+	13.5302i	0.405950	+	0.462722i
$856$	5.27052	−	17.3660i	0.180143	−	0.593558i
$857$	16.7170			0.571043			0.285521	−	0.958372i	$-0.407833\pi$
$857$	16.7170			0.571043			0.285521	+	0.958372i	$0.407833\pi$
$858$	−7.16974	+	26.7630i	−0.244771	+	0.913675i
$859$	−23.6679	+	23.6679i	−0.807538	+	0.807538i	−0.984261	−	0.176723i	$-0.943450\pi$
$859$	−23.6679	+	23.6679i	−0.807538	+	0.807538i	0.176723	+	0.984261i	$0.443450\pi$
$860$	−3.60184	−	10.6138i	−0.122822	−	0.361929i
$861$	−5.63256	−	2.55144i	−0.191957	−	0.0869529i
$862$	−5.69238	−	34.4880i	−0.193883	−	1.17467i
$863$	4.35836			0.148360			0.0741802	−	0.997245i	$-0.476366\pi$
$863$	4.35836			0.148360			0.0741802	+	0.997245i	$0.476366\pi$
$864$	−12.9991	+	26.3633i	−0.442240	+	0.896897i
$865$	−18.3085			−0.622507
$866$	−1.91322	−	11.5915i	−0.0650138	−	0.393895i
$867$	26.6931	+	12.0914i	0.906544	+	0.410647i
$868$	3.73647	+	11.0106i	0.126824	+	0.373723i
$869$	3.84064	−	3.84064i	0.130285	−	0.130285i
$870$	7.20666	−	26.9008i	0.244329	−	0.912024i
$871$	17.4314			0.590640
$872$	−8.57281	−	2.60181i	−0.290312	−	0.0881086i
$873$	16.0201	+	18.2605i	0.542199	+	0.618025i
$874$	−9.74378	−	6.98297i	−0.329588	−	0.236202i
$875$	8.60014	+	8.60014i	0.290738	+	0.290738i
$876$	−0.175224	+	1.77914i	−0.00592028	+	0.0601115i
$877$	17.3529	−	17.3529i	0.585967	−	0.585967i	−0.350570	−	0.936537i	$-0.614012\pi$
$877$	17.3529	−	17.3529i	0.585967	−	0.585967i	0.936537	+	0.350570i	$0.114012\pi$
$878$	2.62201	+	15.8858i	0.0884884	+	0.536119i
$879$	14.0845	−	5.30255i	0.475059	−	0.178851i
$880$	−10.3504	+	7.93911i	−0.348910	+	0.267627i
$881$			27.2412i			0.917780i	0.888493	+	0.458890i	$0.151753\pi$
$881$			27.2412i			0.917780i	−0.888493	+	0.458890i	$0.848247\pi$
$882$	2.69103	−	3.27999i	0.0906119	−	0.110443i
$883$	−19.7164	−	19.7164i	−0.663509	−	0.663509i	0.292696	−	0.956205i	$-0.405448\pi$
$883$	−19.7164	−	19.7164i	−0.663509	−	0.663509i	−0.956205	+	0.292696i	$0.905448\pi$
$884$	−67.6293	−	33.3587i	−2.27462	−	1.12198i
$885$	−35.0762	−	15.8889i	−1.17908	−	0.534098i
$886$	−26.0708	+	36.3783i	−0.875866	+	1.22215i
$887$		−	5.06180i		−	0.169959i	−0.996383	−	0.0849793i	$-0.972918\pi$
$887$		−	5.06180i		−	0.169959i	0.996383	−	0.0849793i	$-0.0270824\pi$
$888$	31.9334	−	36.4100i	1.07162	−	1.22184i
$889$		−	12.1741i		−	0.408307i
$890$	−9.31920	−	6.67869i	−0.312380	−	0.223870i
$891$	−12.4715	+	9.57720i	−0.417812	+	0.320848i
$892$	−5.32096	−	15.6797i	−0.178159	−	0.524996i
$893$	−25.8420	−	25.8420i	−0.864768	−	0.864768i
$894$	6.34084	+	10.9814i	0.212069	+	0.367274i
$895$		−	1.68969i		−	0.0564800i
$896$	−10.3038	−	4.67254i	−0.344224	−	0.156098i
$897$	−10.4188	−	27.6741i	−0.347872	−	0.924010i
$898$	−2.49717	+	0.412168i	−0.0833317	+	0.0137542i
$899$	−25.0405	+	25.0405i	−0.835146	+	0.835146i
$900$	4.54759	−	7.87842i	0.151586	−	0.262614i
$901$	3.33940	+	3.33940i	0.111252	+	0.111252i
$902$	−5.13844	+	7.17000i	−0.171091	+	0.238735i
$903$	4.86695	−	1.83231i	0.161962	−	0.0609756i
$904$	40.1025	−	21.4282i	1.33379	−	0.712690i
$905$	−11.7159			−0.389451
$906$	−0.528972	+	1.97453i	−0.0175739	+	0.0655994i
$907$	19.9916	−	19.9916i	0.663812	−	0.663812i	−0.292465	−	0.956276i	$-0.594475\pi$
$907$	19.9916	−	19.9916i	0.663812	−	0.663812i	0.956276	+	0.292465i	$0.0944754\pi$
$908$	20.9348	−	42.4419i	0.694747	−	1.40848i
$909$	4.06942	+	0.265955i	0.134974	+	0.00882115i
$910$	−16.8610	+	2.78298i	−0.558938	+	0.0922548i
$911$	28.5053			0.944423			0.472211	−	0.881485i	$-0.343456\pi$
$911$	28.5053			0.944423			0.472211	+	0.881485i	$0.343456\pi$
$912$	18.9106	+	11.7617i	0.626191	+	0.389467i
$913$	−7.19648			−0.238169
$914$	55.4739	−	9.15617i	1.83491	−	0.302859i
$915$	−12.8360	+	28.3367i	−0.424344	+	0.936782i
$916$	8.44089	+	4.16354i	0.278895	+	0.137567i
$917$	13.2278	−	13.2278i	0.436819	−	0.436819i
$918$	−18.9378	−	38.3792i	−0.625042	−	1.26670i
$919$	−7.25783			−0.239414			−0.119707	−	0.992809i	$-0.538195\pi$
$919$	−7.25783			−0.239414			−0.119707	+	0.992809i	$0.538195\pi$
$920$	4.04313	−	13.3219i	0.133298	−	0.439209i
$921$	−18.5003	−	49.1402i	−0.609607	−	1.61922i
$922$	1.93994	−	2.70692i	0.0638885	−	0.0891477i
$923$	61.3091	+	61.3091i	2.01801	+	2.01801i
$924$	−3.83961	−	4.67855i	−0.126314	−	0.153913i
$925$	−10.5980	+	10.5980i	−0.348460	+	0.348460i
$926$	−9.47779	+	1.56435i	−0.311459	+	0.0514076i
$927$	3.12146	+	3.55799i	0.102522	+	0.116860i
$928$	−1.11957	−	34.4393i	−0.0367516	−	1.13053i
$929$			24.6859i			0.809917i	0.914335	+	0.404958i	$0.132714\pi$
$929$			24.6859i			0.809917i	−0.914335	+	0.404958i	$0.867286\pi$
$930$	23.0184	−	13.2911i	0.754802	−	0.435834i
$931$	−2.27291	−	2.27291i	−0.0744915	−	0.0744915i
$932$	−42.5157	+	14.4278i	−1.39265	+	0.472599i
$933$	−19.3384	+	42.6914i	−0.633110	+	1.39765i
$934$	14.5559	+	10.4316i	0.476284	+	0.341333i
$935$		−	18.9927i		−	0.621128i
$936$	22.6742	+	50.0361i	0.741129	+	1.63548i
$937$		−	47.2256i		−	1.54279i	−0.636354	−	0.771397i	$-0.719558\pi$
$937$		−	47.2256i		−	1.54279i	0.636354	−	0.771397i	$-0.280442\pi$
$938$	−2.21810	+	3.09505i	−0.0724234	+	0.101057i
$939$	13.9762	−	30.8540i	0.456097	−	1.00688i
$940$	18.7755	−	38.0642i	0.612390	−	1.24152i
$941$	17.0730	+	17.0730i	0.556564	+	0.556564i	0.928328	−	0.371763i	$-0.121247\pi$
$941$	17.0730	+	17.0730i	0.556564	+	0.556564i	−0.371763	+	0.928328i	$0.621247\pi$
$942$	19.2591	+	33.3540i	0.627495	+	1.08673i
$943$		−	9.41445i		−	0.306577i
$944$	−47.2353	−	6.22741i	−1.53738	−	0.202685i
$945$	−8.55478	−	4.56952i	−0.278287	−	0.148647i
$946$	−1.20815	−	7.31971i	−0.0392802	−	0.237984i
$947$	35.0765	−	35.0765i	1.13983	−	1.13983i	0.151354	−	0.988480i	$-0.451637\pi$
$947$	35.0765	−	35.0765i	1.13983	−	1.13983i	0.988480	−	0.151354i	$-0.0483634\pi$
$948$	1.05551	−	10.7171i	0.0342813	−	0.348075i
$949$	2.36251	+	2.36251i	0.0766904	+	0.0766904i
$950$	−5.60194	−	4.01468i	−0.181751	−	0.130254i
$951$	15.3768	+	40.8434i	0.498625	+	1.32444i
$952$	14.5287	−	7.76318i	0.470877	−	0.251606i
$953$	27.4125			0.887979			0.443990	−	0.896032i	$-0.353563\pi$
$953$	27.4125			0.887979			0.443990	+	0.896032i	$0.353563\pi$
$954$	−0.337700	−	3.42372i	−0.0109334	−	0.110847i
$955$	−16.1369	+	16.1369i	−0.522179	+	0.522179i
$956$	31.6774	−	10.7498i	1.02452	−	0.347674i
$957$	7.60602	−	16.7910i	0.245868	−	0.542777i
$958$	−3.96353	−	24.0136i	−0.128056	−	0.775843i
$959$	3.47597			0.112245
$960$	−5.87744	+	25.1865i	−0.189694	+	0.812892i
$961$	−2.79846			−0.0902730
$962$	−14.7395	−	89.3014i	−0.475222	−	2.87919i
$963$	1.25533	−	19.2081i	0.0404526	−	0.618972i
$964$	36.0870	−	12.2462i	1.16229	−	0.394424i
$965$	−11.8294	+	11.8294i	−0.380801	+	0.380801i
$966$	6.23946	+	1.67153i	0.200751	+	0.0537807i
$967$	9.02426			0.290201			0.145100	−	0.989417i	$-0.453650\pi$
$967$	9.02426			0.290201			0.145100	+	0.989417i	$0.453650\pi$
$968$	19.8258	−	10.5936i	0.637225	−	0.340492i
$969$	−30.3454	+	11.4245i	−0.974836	+	0.367007i
$970$	17.3732	+	12.4506i	0.557819	+	0.399766i
$971$	7.53771	+	7.53771i	0.241897	+	0.241897i	0.817634	−	0.575738i	$-0.195285\pi$
$971$	7.53771	+	7.53771i	0.241897	+	0.241897i	−0.575738	+	0.817634i	$0.695285\pi$
$972$	−7.06802	+	30.3652i	−0.226707	+	0.973963i
$973$	−7.82479	+	7.82479i	−0.250851	+	0.250851i
$974$	−6.40299	−	38.7933i	−0.205165	−	1.24302i
$975$	−5.99000	−	15.9105i	−0.191834	−	0.509544i
$976$	−5.03087	+	38.1595i	−0.161034	+	1.22146i
$977$			0.0758580i			0.00242691i	0.999999	+	0.00121346i	$0.000386255\pi$
$977$			0.0758580i			0.00242691i	−0.999999	+	0.00121346i	$0.999614\pi$
$978$	7.18819	−	4.15057i	0.229853	−	0.132721i
$979$	−5.36610	−	5.36610i	−0.171501	−	0.171501i
$980$	1.65138	−	3.34790i	0.0527515	−	0.106945i
$981$	−9.48216	−	0.619701i	−0.302742	−	0.0197855i
$982$	6.58480	−	9.18819i	0.210129	−	0.293207i
$983$		−	17.1286i		−	0.546318i	−0.961969	−	0.273159i	$-0.911932\pi$
$983$		−	17.1286i		−	0.546318i	0.961969	−	0.273159i	$-0.0880684\pi$
$984$	1.14313	+	17.4522i	0.0364416	+	0.556355i
$985$			20.3077i			0.647057i
$986$	40.7791	+	29.2247i	1.29867	+	0.930704i
$987$	17.9381	+	8.12562i	0.570976	+	0.258641i
$988$	39.4123	−	13.3747i	1.25387	−	0.425505i
$989$	5.59869	+	5.59869i	0.178028	+	0.178028i
$990$	−8.77581	+	10.6965i	−0.278914	+	0.339956i
$991$			52.2548i			1.65993i	0.557816	+	0.829965i	$0.311639\pi$
$991$			52.2548i			1.65993i	−0.557816	+	0.829965i	$0.688361\pi$
$992$	22.4867	−	23.9979i	0.713954	−	0.761933i
$993$	3.24391	−	1.22127i	0.102942	−	0.0387559i
$994$	−18.6872	+	3.08439i	−0.592722	+	0.0978310i
$995$	−13.7727	+	13.7727i	−0.436624	+	0.436624i
$996$	−11.0296	+	9.05180i	−0.349486	+	0.286817i
$997$	−14.7204	−	14.7204i	−0.466200	−	0.466200i	0.434481	−	0.900681i	$-0.356932\pi$
$997$	−14.7204	−	14.7204i	−0.466200	−	0.466200i	−0.900681	+	0.434481i	$0.856932\pi$
$998$	−17.6059	+	24.5667i	−0.557306	+	0.777645i
$999$	24.2016	−	45.3089i	0.765706	−	1.43351i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.s.c.155.9	✓	40
3.2	odd	2	inner	336.2.s.c.155.12	yes	40
4.3	odd	2		1344.2.s.c.911.17		40
12.11	even	2		1344.2.s.c.911.15		40
16.3	odd	4	inner	336.2.s.c.323.12	yes	40
16.13	even	4		1344.2.s.c.239.15		40
48.29	odd	4		1344.2.s.c.239.17		40
48.35	even	4	inner	336.2.s.c.323.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.s.c.155.9	✓	40	1.1	even	1	trivial
336.2.s.c.155.12	yes	40	3.2	odd	2	inner
336.2.s.c.323.9	yes	40	48.35	even	4	inner
336.2.s.c.323.12	yes	40	16.3	odd	4	inner
1344.2.s.c.239.15		40	16.13	even	4
1344.2.s.c.239.17		40	48.29	odd	4
1344.2.s.c.911.15		40	12.11	even	2
1344.2.s.c.911.17		40	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.230305 - 1.39533i) q^{2} +(-1.57773 - 0.714681i) q^{3} +(-1.89392 + 0.642706i) q^{4} +(-1.31983 + 1.31983i) q^{5} +(-0.633860 + 2.36606i) q^{6} -1.00000 q^{7} +(1.33297 + 2.49463i) q^{8} +(1.97846 + 2.25515i) q^{9} +O(q^{10})\)	\(q+(-0.230305 - 1.39533i) q^{2} +(-1.57773 - 0.714681i) q^{3} +(-1.89392 + 0.642706i) q^{4} +(-1.31983 + 1.31983i) q^{5} +(-0.633860 + 2.36606i) q^{6} -1.00000 q^{7} +(1.33297 + 2.49463i) q^{8} +(1.97846 + 2.25515i) q^{9} +(2.14556 + 1.53764i) q^{10} +(1.23544 + 1.23544i) q^{11} +(3.44742 + 0.339531i) q^{12} +(4.57782 - 4.57782i) q^{13} +(0.230305 + 1.39533i) q^{14} +(3.02558 - 1.13907i) q^{15} +(3.17386 - 2.43447i) q^{16} +5.82397i q^{17} +(2.69103 - 3.27999i) q^{18} +(-2.27291 - 2.27291i) q^{19} +(1.65138 - 3.34790i) q^{20} +(1.57773 + 0.714681i) q^{21} +(1.43932 - 2.00838i) q^{22} +2.63707i q^{23} +(-0.320200 - 4.88850i) q^{24} +1.51612i q^{25} +(-7.44189 - 5.33330i) q^{26} +(-1.50977 - 4.97198i) q^{27} +(1.89392 - 0.642706i) q^{28} +(4.30719 + 4.30719i) q^{29} +(-2.28620 - 3.95937i) q^{30} +5.81364i q^{31} +(-4.12785 - 3.86792i) q^{32} +(-1.06624 - 2.83213i) q^{33} +(8.12639 - 1.34129i) q^{34} +(1.31983 - 1.31983i) q^{35} +(-5.19644 - 2.99950i) q^{36} +(6.99022 + 6.99022i) q^{37} +(-2.64800 + 3.69493i) q^{38} +(-10.4943 + 3.95088i) q^{39} +(-5.05177 - 1.53319i) q^{40} -3.57004 q^{41} +(0.633860 - 2.36606i) q^{42} +(2.12307 - 2.12307i) q^{43} +(-3.13384 - 1.54580i) q^{44} +(-5.58763 - 0.365176i) q^{45} +(3.67960 - 0.607331i) q^{46} +11.3696 q^{47} +(-6.74736 + 1.57264i) q^{48} +1.00000 q^{49} +(2.11549 - 0.349170i) q^{50} +(4.16228 - 9.18865i) q^{51} +(-5.72783 + 11.6122i) q^{52} +(0.573389 - 0.573389i) q^{53} +(-6.58987 + 3.25170i) q^{54} -3.26113 q^{55} +(-1.33297 - 2.49463i) q^{56} +(1.96163 + 5.21043i) q^{57} +(5.01800 - 7.00194i) q^{58} +(-8.42236 - 8.42236i) q^{59} +(-4.99812 + 4.10188i) q^{60} +(-6.80408 + 6.80408i) q^{61} +(8.11198 - 1.33891i) q^{62} +(-1.97846 - 2.25515i) q^{63} +(-4.44638 + 6.65054i) q^{64} +12.0839i q^{65} +(-3.70621 + 2.14002i) q^{66} +(1.90390 + 1.90390i) q^{67} +(-3.74310 - 11.0301i) q^{68} +(1.88466 - 4.16058i) q^{69} +(-2.14556 - 1.53764i) q^{70} +13.3926i q^{71} +(-2.98853 + 7.94158i) q^{72} +0.516078i q^{73} +(8.14381 - 11.3636i) q^{74} +(1.08354 - 2.39202i) q^{75} +(5.76551 + 2.84389i) q^{76} +(-1.23544 - 1.23544i) q^{77} +(7.92969 + 13.7331i) q^{78} -3.10873i q^{79} +(-0.975867 + 7.40201i) q^{80} +(-1.17138 + 8.92345i) q^{81} +(0.822200 + 4.98140i) q^{82} +(-2.91252 + 2.91252i) q^{83} +(-3.44742 - 0.339531i) q^{84} +(-7.68663 - 7.68663i) q^{85} +(-3.45135 - 2.47344i) q^{86} +(-3.71731 - 9.87385i) q^{87} +(-1.43516 + 4.72877i) q^{88} -4.34348 q^{89} +(0.777318 + 7.88071i) q^{90} +(-4.57782 + 4.57782i) q^{91} +(-1.69486 - 4.99440i) q^{92} +(4.15490 - 9.17236i) q^{93} +(-2.61847 - 15.8644i) q^{94} +5.99968 q^{95} +(3.74831 + 9.05264i) q^{96} +8.09726 q^{97} +(-0.230305 - 1.39533i) q^{98} +(-0.341828 + 5.23036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7}+O(q^{10}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7	\( 40 q + 4 q^{3} - 2 q^{6} - 40 q^{7} - 8 q^{10} - 2 q^{12} + 24 q^{13} + 36 q^{16} + 12 q^{18} + 16 q^{19} - 4 q^{21} - 8 q^{22} + 6 q^{24} - 32 q^{27} - 32 q^{30} + 24 q^{33} + 12 q^{34} - 4 q^{36} - 8 q^{37} - 64 q^{39} - 60 q^{40} + 2 q^{42} + 24 q^{43} - 28 q^{45} + 20 q^{46} - 26 q^{48} + 40 q^{49} - 32 q^{51} + 84 q^{52} - 14 q^{54} + 16 q^{55} + 12 q^{58} - 24 q^{60} - 48 q^{61} - 12 q^{64} - 36 q^{66} + 40 q^{67} + 4 q^{69} + 8 q^{70} + 8 q^{72} + 40 q^{75} - 44 q^{76} + 24 q^{78} + 56 q^{81} - 84 q^{82} + 2 q^{84} - 48 q^{85} + 32 q^{87} + 52 q^{88} - 76 q^{90} - 24 q^{91} + 56 q^{93} - 62 q^{96} + 16 q^{97} + 24 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 2 * q^6 - 40 * q^7 - 8 * q^10 - 2 * q^12 + 24 * q^13 + 36 * q^16 + 12 * q^18 + 16 * q^19 - 4 * q^21 - 8 * q^22 + 6 * q^24 - 32 * q^27 - 32 * q^30 + 24 * q^33 + 12 * q^34 - 4 * q^36 - 8 * q^37 - 64 * q^39 - 60 * q^40 + 2 * q^42 + 24 * q^43 - 28 * q^45 + 20 * q^46 - 26 * q^48 + 40 * q^49 - 32 * q^51 + 84 * q^52 - 14 * q^54 + 16 * q^55 + 12 * q^58 - 24 * q^60 - 48 * q^61 - 12 * q^64 - 36 * q^66 + 40 * q^67 + 4 * q^69 + 8 * q^70 + 8 * q^72 + 40 * q^75 - 44 * q^76 + 24 * q^78 + 56 * q^81 - 84 * q^82 + 2 * q^84 - 48 * q^85 + 32 * q^87 + 52 * q^88 - 76 * q^90 - 24 * q^91 + 56 * q^93 - 62 * q^96 + 16 * q^97 + 24 * q^99

Introduction

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