LMFDB - Embedded newform 136.2.s.c.107.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(3,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 8, 1]))

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

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

chi := DirichletCharacter("136.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.s (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			107.11
Character	$\chi$	$=$	136.107
Dual form			136.2.s.c.75.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.06248 - 0.933347i) q^{2} +(-0.241857 - 0.361965i) q^{3} +(0.257725 - 1.98332i) q^{4} +(-1.43785 - 0.286006i) q^{5} +(-0.594807 - 0.158843i) q^{6} +(1.35888 - 0.270298i) q^{7} +(-1.57730 - 2.34779i) q^{8} +(1.07553 - 2.59655i) q^{9} +O(q^{10})$	\(q+(1.06248 - 0.933347i) q^{2} +(-0.241857 - 0.361965i) q^{3} +(0.257725 - 1.98332i) q^{4} +(-1.43785 - 0.286006i) q^{5} +(-0.594807 - 0.158843i) q^{6} +(1.35888 - 0.270298i) q^{7} +(-1.57730 - 2.34779i) q^{8} +(1.07553 - 2.59655i) q^{9} +(-1.79463 + 1.03814i) q^{10} +(4.33828 + 2.89874i) q^{11} +(-0.780227 + 0.386394i) q^{12} +(-4.55546 + 4.55546i) q^{13} +(1.19150 - 1.55549i) q^{14} +(0.244230 + 0.589624i) q^{15} +(-3.86716 - 1.02231i) q^{16} +(0.599136 + 4.07934i) q^{17} +(-1.28076 - 3.76262i) q^{18} +(-0.0890783 - 0.215054i) q^{19} +(-0.937814 + 2.77801i) q^{20} +(-0.426494 - 0.426494i) q^{21} +(7.31487 - 0.969263i) q^{22} +(5.20139 + 3.47546i) q^{23} +(-0.468335 + 1.13876i) q^{24} +(-2.63378 - 1.09095i) q^{25} +(-0.588256 + 9.09191i) q^{26} +(-2.48088 + 0.493478i) q^{27} +(-0.185871 - 2.76476i) q^{28} +(1.29745 - 6.52275i) q^{29} +(0.809813 + 0.398512i) q^{30} +(0.132562 + 0.198393i) q^{31} +(-5.06294 + 2.52322i) q^{32} -2.27139i q^{33} +(4.44401 + 3.77502i) q^{34} -2.03117 q^{35} +(-4.87261 - 2.80232i) q^{36} +(-2.30857 + 1.54254i) q^{37} +(-0.295364 - 0.145350i) q^{38} +(2.75069 + 0.547146i) q^{39} +(1.59644 + 3.82689i) q^{40} +(-0.387768 - 1.94944i) q^{41} +(-0.851207 - 0.0550740i) q^{42} +(-1.82216 + 4.39907i) q^{43} +(6.86724 - 7.85713i) q^{44} +(-2.28908 + 3.42584i) q^{45} +(8.77019 - 1.16210i) q^{46} +(5.81590 - 5.81590i) q^{47} +(0.565260 + 1.64703i) q^{48} +(-4.69366 + 1.94418i) q^{49} +(-3.81658 + 1.29912i) q^{50} +(1.33167 - 1.20348i) q^{51} +(7.86090 + 10.2090i) q^{52} +(3.13050 - 1.29670i) q^{53} +(-2.17530 + 2.83984i) q^{54} +(-5.40873 - 5.40873i) q^{55} +(-2.77797 - 2.76402i) q^{56} +(-0.0562978 + 0.0842556i) q^{57} +(-4.70947 - 8.14126i) q^{58} +(-7.79160 - 3.22739i) q^{59} +(1.23236 - 0.332427i) q^{60} +(-0.796777 - 4.00567i) q^{61} +(0.326014 + 0.0870622i) q^{62} +(0.759669 - 3.81912i) q^{63} +(-3.02423 + 7.40635i) q^{64} +(7.85296 - 5.24718i) q^{65} +(-2.11999 - 2.41330i) q^{66} -8.12540i q^{67} +(8.24507 - 0.136931i) q^{68} -2.72329i q^{69} +(-2.15808 + 1.89579i) q^{70} +(-12.8819 + 8.60743i) q^{71} +(-7.79259 + 1.57044i) q^{72} +(-1.07722 + 5.41554i) q^{73} +(-1.01309 + 3.79362i) q^{74} +(0.242114 + 1.21719i) q^{75} +(-0.449480 + 0.121246i) q^{76} +(6.67873 + 2.76642i) q^{77} +(3.43322 - 1.98601i) q^{78} +(0.800167 - 1.19753i) q^{79} +(5.26800 + 2.57595i) q^{80} +(-5.18330 - 5.18330i) q^{81} +(-2.23150 - 1.70932i) q^{82} +(9.56928 - 3.96373i) q^{83} +(-0.955793 + 0.735957i) q^{84} +(0.305250 - 6.03684i) q^{85} +(2.16986 + 6.37463i) q^{86} +(-2.67480 + 1.10794i) q^{87} +(-0.0371377 - 14.7576i) q^{88} +(-0.0723591 + 0.0723591i) q^{89} +(0.765406 + 5.77639i) q^{90} +(-4.95899 + 7.42166i) q^{91} +(8.23350 - 9.42034i) q^{92} +(0.0397503 - 0.0959657i) q^{93} +(0.751019 - 11.6075i) q^{94} +(0.0665745 + 0.334693i) q^{95} +(2.13783 + 1.22235i) q^{96} +(-8.14867 - 1.62087i) q^{97} +(-3.17232 + 6.44646i) q^{98} +(12.1927 - 8.14688i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) $ 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	1.06248	−	0.933347i	0.751286	−	0.659976i
$2$	1.06248	−	0.933347i	0.751286	−	0.659976i
$3$	−0.241857	−	0.361965i	−0.139636	−	0.208980i	0.755060	−	0.655656i	$-0.227608\pi$
$3$	−0.241857	−	0.361965i	−0.139636	−	0.208980i	−0.894696	+	0.446676i	$0.852608\pi$
$4$	0.257725	−	1.98332i	0.128863	−	0.991662i
$5$	−1.43785	−	0.286006i	−0.643026	−	0.127906i	−0.137203	−	0.990543i	$-0.543811\pi$
$5$	−1.43785	−	0.286006i	−0.643026	−	0.127906i	−0.505823	+	0.862637i	$0.668811\pi$
$6$	−0.594807	−	0.158843i	−0.242829	−	0.0648476i
$7$	1.35888	−	0.270298i	0.513609	−	0.102163i	0.0685202	−	0.997650i	$-0.478172\pi$
$7$	1.35888	−	0.270298i	0.513609	−	0.102163i	0.445088	+	0.895487i	$0.353172\pi$
$8$	−1.57730	−	2.34779i	−0.557661	−	0.830069i
$9$	1.07553	−	2.59655i	0.358509	−	0.865517i
$10$	−1.79463	+	1.03814i	−0.567512	+	0.328288i
$11$	4.33828	+	2.89874i	1.30804	+	0.874004i	0.997076	−	0.0764175i	$-0.0243482\pi$
$11$	4.33828	+	2.89874i	1.30804	+	0.874004i	0.310964	+	0.950422i	$0.399348\pi$
$12$	−0.780227	+	0.386394i	−0.225232	+	0.111542i
$13$	−4.55546	+	4.55546i	−1.26346	+	1.26346i	−0.314051	+	0.949406i	$0.601686\pi$
$13$	−4.55546	+	4.55546i	−1.26346	+	1.26346i	−0.949406	+	0.314051i	$0.898314\pi$
$14$	1.19150	−	1.55549i	0.318442	−	0.415723i
$15$	0.244230	+	0.589624i	0.0630600	+	0.152240i
$16$	−3.86716	−	1.02231i	−0.966789	−	0.255577i
$17$	0.599136	+	4.07934i	0.145312	+	0.989386i
$17$	0.599136	+	4.07934i	0.145312	+	0.989386i
$18$	−1.28076	−	3.76262i	−0.301878	−	0.886859i
$19$	−0.0890783	−	0.215054i	−0.0204360	−	0.0493368i	0.913332	−	0.407215i	$-0.133500\pi$
$19$	−0.0890783	−	0.215054i	−0.0204360	−	0.0493368i	−0.933768	+	0.357879i	$0.883500\pi$
$20$	−0.937814	+	2.77801i	−0.209701	+	0.621183i
$21$	−0.426494	−	0.426494i	−0.0930685	−	0.0930685i
$22$	7.31487	−	0.969263i	1.55953	−	0.206648i
$23$	5.20139	+	3.47546i	1.08457	+	0.724684i	0.963432	−	0.267953i	$-0.0863471\pi$
$23$	5.20139	+	3.47546i	1.08457	+	0.724684i	0.121134	+	0.992636i	$0.461347\pi$
$24$	−0.468335	+	1.13876i	−0.0955985	+	0.232448i
$25$	−2.63378	−	1.09095i	−0.526757	−	0.218190i
$26$	−0.588256	+	9.09191i	−0.115367	+	1.78307i
$27$	−2.48088	+	0.493478i	−0.477446	+	0.0949700i
$28$	−0.185871	−	2.76476i	−0.0351263	−	0.522491i
$29$	1.29745	−	6.52275i	0.240931	−	1.21124i	−0.651002	−	0.759076i	$-0.725651\pi$
$29$	1.29745	−	6.52275i	0.240931	−	1.21124i	0.891933	−	0.452167i	$-0.149349\pi$
$30$	0.809813	+	0.398512i	0.147851	+	0.0727579i
$31$	0.132562	+	0.198393i	0.0238089	+	0.0356325i	0.843183	−	0.537626i	$-0.180679\pi$
$31$	0.132562	+	0.198393i	0.0238089	+	0.0356325i	−0.819374	+	0.573259i	$0.805679\pi$
$32$	−5.06294	+	2.52322i	−0.895010	+	0.446046i
$33$		−	2.27139i		−	0.395398i
$34$	4.44401	+	3.77502i	0.762142	+	0.647410i
$35$	−2.03117			−0.343331
$36$	−4.87261	−	2.80232i	−0.812102	−	0.467053i
$37$	−2.30857	+	1.54254i	−0.379527	+	0.253592i	−0.730671	−	0.682730i	$-0.760793\pi$
$37$	−2.30857	+	1.54254i	−0.379527	+	0.253592i	0.351144	+	0.936321i	$0.385793\pi$
$38$	−0.295364	−	0.145350i	−0.0479144	−	0.0235788i
$39$	2.75069	+	0.547146i	0.440462	+	0.0876134i
$40$	1.59644	+	3.82689i	0.252420	+	0.605084i
$41$	−0.387768	−	1.94944i	−0.0605592	−	0.304452i	0.938620	−	0.344952i	$-0.112105\pi$
$41$	−0.387768	−	1.94944i	−0.0605592	−	0.304452i	−0.999180	+	0.0405004i	$0.987105\pi$
$42$	−0.851207	−	0.0550740i	−0.131344	−	0.00849810i
$43$	−1.82216	+	4.39907i	−0.277876	+	0.670852i	−0.999776	−	0.0211448i	$-0.993269\pi$
$43$	−1.82216	+	4.39907i	−0.277876	+	0.670852i	0.721900	+	0.691997i	$0.243269\pi$
$44$	6.86724	−	7.85713i	1.03527	−	1.18451i
$45$	−2.28908	+	3.42584i	−0.341235	+	0.510695i
$46$	8.77019	−	1.16210i	1.29309	−	0.171343i
$47$	5.81590	−	5.81590i	0.848336	−	0.848336i	−0.141589	−	0.989925i	$-0.545221\pi$
$47$	5.81590	−	5.81590i	0.848336	−	0.848336i	0.989925	+	0.141589i	$0.0452213\pi$
$48$	0.565260	+	1.64703i	0.0815883	+	0.237728i
$49$	−4.69366	+	1.94418i	−0.670523	+	0.277740i
$50$	−3.81658	+	1.29912i	−0.539745	+	0.183724i
$51$	1.33167	−	1.20348i	0.186472	−	0.168522i
$52$	7.86090	+	10.2090i	1.09011	+	1.41574i
$53$	3.13050	−	1.29670i	0.430007	−	0.178115i	−0.157173	−	0.987571i	$-0.550238\pi$
$53$	3.13050	−	1.29670i	0.430007	−	0.178115i	0.587180	+	0.809456i	$0.300238\pi$
$54$	−2.17530	+	2.83984i	−0.296021	+	0.386453i
$55$	−5.40873	−	5.40873i	−0.729313	−	0.729313i
$56$	−2.77797	−	2.76402i	−0.371222	−	0.369358i
$57$	−0.0562978	+	0.0842556i	−0.00745683	+	0.0111599i
$58$	−4.70947	−	8.14126i	−0.618383	−	1.06900i
$59$	−7.79160	−	3.22739i	−1.01438	−	0.420170i	−0.187329	−	0.982297i	$-0.559983\pi$
$59$	−7.79160	−	3.22739i	−1.01438	−	0.420170i	−0.827051	+	0.562127i	$0.809983\pi$
$60$	1.23236	−	0.332427i	0.159097	−	0.0429161i
$61$	−0.796777	−	4.00567i	−0.102017	−	0.512873i	−0.997676	−	0.0681328i	$-0.978296\pi$
$61$	−0.796777	−	4.00567i	−0.102017	−	0.512873i	0.895659	−	0.444741i	$-0.146704\pi$
$62$	0.326014	+	0.0870622i	0.0414039	+	0.0110569i
$63$	0.759669	−	3.81912i	0.0957094	−	0.481163i
$64$	−3.02423	+	7.40635i	−0.378029	+	0.925794i
$65$	7.85296	−	5.24718i	0.974039	−	0.650832i
$66$	−2.11999	−	2.41330i	−0.260953	−	0.297057i
$67$		−	8.12540i		−	0.992675i	−0.868130	−	0.496338i	$-0.834678\pi$
$67$		−	8.12540i		−	0.992675i	0.868130	−	0.496338i	$-0.165322\pi$
$68$	8.24507	−	0.136931i	0.999862	−	0.0166053i
$69$		−	2.72329i		−	0.327845i
$70$	−2.15808	+	1.89579i	−0.257940	+	0.226590i
$71$	−12.8819	+	8.60743i	−1.52880	+	1.02151i	−0.545803	+	0.837914i	$0.683775\pi$
$71$	−12.8819	+	8.60743i	−1.52880	+	1.02151i	−0.983001	+	0.183601i	$0.941225\pi$
$72$	−7.79259	+	1.57044i	−0.918365	+	0.185078i
$73$	−1.07722	+	5.41554i	−0.126079	+	0.633841i	0.865131	+	0.501545i	$0.167235\pi$
$73$	−1.07722	+	5.41554i	−0.126079	+	0.633841i	−0.991210	+	0.132296i	$0.957765\pi$
$74$	−1.01309	+	3.79362i	−0.117769	+	0.440999i
$75$	0.242114	+	1.21719i	0.0279570	+	0.140549i
$76$	−0.449480	+	0.121246i	−0.0515589	+	0.0139079i
$77$	6.67873	+	2.76642i	0.761112	+	0.315263i
$78$	3.43322	−	1.98601i	0.388736	−	0.224872i
$79$	0.800167	−	1.19753i	0.0900259	−	0.134733i	−0.783723	−	0.621110i	$-0.786682\pi$
$79$	0.800167	−	1.19753i	0.0900259	−	0.134733i	0.873749	+	0.486377i	$0.161682\pi$
$80$	5.26800	+	2.57595i	0.588981	+	0.288000i
$81$	−5.18330	−	5.18330i	−0.575922	−	0.575922i
$82$	−2.23150	−	1.70932i	−0.246428	−	0.188763i
$83$	9.56928	−	3.96373i	1.05037	−	0.435076i	0.210343	−	0.977628i	$-0.432542\pi$
$83$	9.56928	−	3.96373i	1.05037	−	0.435076i	0.840022	+	0.542552i	$0.182542\pi$
$84$	−0.955793	+	0.735957i	−0.104286	+	0.0802995i
$85$	0.305250	−	6.03684i	0.0331090	−	0.654787i
$86$	2.16986	+	6.37463i	0.233982	+	0.687394i
$87$	−2.67480	+	1.10794i	−0.286769	+	0.118784i
$88$	−0.0371377	−	14.7576i	−0.00395890	−	1.57316i
$89$	−0.0723591	+	0.0723591i	−0.00767005	+	0.00767005i	−0.710931	−	0.703261i	$-0.751726\pi$
$89$	−0.0723591	+	0.0723591i	−0.00767005	+	0.00767005i	0.703261	+	0.710931i	$0.251726\pi$
$90$	0.765406	+	5.77639i	0.0806809	+	0.608885i
$91$	−4.95899	+	7.42166i	−0.519844	+	0.778001i
$92$	8.23350	−	9.42034i	0.858402	−	0.982138i
$93$	0.0397503	−	0.0959657i	0.00412191	−	0.00995117i
$94$	0.751019	−	11.6075i	0.0774617	−	1.19722i
$95$	0.0665745	+	0.334693i	0.00683040	+	0.0343387i
$96$	2.13783	+	1.22235i	0.218191	+	0.124755i
$97$	−8.14867	−	1.62087i	−0.827372	−	0.164574i	−0.236799	−	0.971559i	$-0.576098\pi$
$97$	−8.14867	−	1.62087i	−0.827372	−	0.164574i	−0.590573	+	0.806984i	$0.701098\pi$
$98$	−3.17232	+	6.44646i	−0.320453	+	0.651191i
$99$	12.1927	−	8.14688i	1.22541	−	0.818792i
$100$	−2.84250	+	4.94249i	−0.284250	+	0.494249i
$101$	1.85107			0.184189			0.0920944	−	0.995750i	$-0.470644\pi$
$101$	1.85107			0.184189			0.0920944	+	0.995750i	$0.470644\pi$
$102$	0.291607	−	2.52159i	0.0288734	−	0.249675i
$103$		−	8.14168i		−	0.802223i	−0.916029	−	0.401112i	$-0.868624\pi$
$103$		−	8.14168i		−	0.802223i	0.916029	−	0.401112i	$-0.131376\pi$
$104$	17.8806	+	3.50992i	1.75334	+	0.344176i
$105$	0.491254	+	0.735213i	0.0479415	+	0.0717495i
$106$	2.11582	−	4.29956i	0.205507	−	0.417610i
$107$	−1.79069	+	9.00243i	−0.173113	+	0.870298i	0.792412	+	0.609986i	$0.208825\pi$
$107$	−1.79069	+	9.00243i	−0.173113	+	0.870298i	−0.965525	+	0.260311i	$0.916175\pi$
$108$	0.339341	+	5.04758i	0.0326531	+	0.485704i
$109$	6.01331	−	1.19612i	0.575971	−	0.114568i	0.101495	−	0.994836i	$-0.467637\pi$
$109$	6.01331	−	1.19612i	0.575971	−	0.114568i	0.474476	+	0.880268i	$0.342637\pi$
$110$	−10.7949	−	0.698441i	−1.02925	−	0.0665938i
$111$	1.11669	+	0.462548i	0.105991	+	0.0439031i
$112$	−5.53133	−	0.343907i	−0.522662	−	0.0324962i
$113$	10.3062	+	6.88641i	0.969529	+	0.647819i	0.936141	−	0.351624i	$-0.114370\pi$
$113$	10.3062	+	6.88641i	0.969529	+	0.647819i	0.0333877	+	0.999442i	$0.489370\pi$
$114$	0.0188245	+	0.142065i	0.00176308	+	0.0133056i
$115$	−6.48482	−	6.48482i	−0.604713	−	0.604713i
$116$	−12.6023	−	4.25435i	−1.17010	−	0.395007i
$117$	6.92896	+	16.7280i	0.640583	+	1.54650i
$118$	−11.2907	+	3.84324i	−1.03939	+	0.353799i
$119$	1.91679	+	5.38140i	0.175712	+	0.493312i
$120$	0.999087	−	1.50342i	0.0912038	−	0.137243i
$121$	6.20841	+	14.9884i	0.564401	+	1.36259i
$122$	−4.58524	−	3.51227i	−0.415128	−	0.317986i
$123$	−0.611845	+	0.611845i	−0.0551682	+	0.0551682i
$124$	0.427643	−	0.211783i	0.0384035	−	0.0190187i
$125$	9.56972	+	6.39428i	0.855942	+	0.571922i
$126$	−2.75743	−	4.76677i	−0.245651	−	0.424657i
$127$	−4.61852	+	11.1501i	−0.409827	+	0.989411i	0.575355	+	0.817903i	$0.304864\pi$
$127$	−4.61852	+	11.1501i	−0.409827	+	0.989411i	−0.985183	+	0.171507i	$0.945136\pi$
$128$	3.69952	+	10.6918i	0.326994	+	0.945026i
$129$	2.03301	−	0.404391i	0.178997	−	0.0356046i
$130$	3.44617	−	12.9046i	0.302249	−	1.13180i
$131$	−7.44514	−	1.48093i	−0.650485	−	0.129390i	−0.141191	−	0.989982i	$-0.545093\pi$
$131$	−7.44514	−	1.48093i	−0.650485	−	0.129390i	−0.509294	+	0.860593i	$0.670093\pi$
$132$	−4.50490	−	0.585394i	−0.392101	−	0.0509520i
$133$	−0.179176	−	0.268155i	−0.0155365	−	0.0232520i
$134$	−7.58382	−	8.63307i	−0.655142	−	0.745784i
$135$	3.70828			0.319158
$136$	8.63242	−	7.84100i	0.740224	−	0.672361i
$137$	−11.0731			−0.946039			−0.473020	−	0.881052i	$-0.656836\pi$
$137$	−11.0731			−0.946039			−0.473020	+	0.881052i	$0.656836\pi$
$138$	−2.54177	−	2.89344i	−0.216370	−	0.246306i
$139$	6.29836	+	9.42617i	0.534220	+	0.799517i	0.996174	−	0.0873866i	$-0.0278515\pi$
$139$	6.29836	+	9.42617i	0.534220	+	0.799517i	−0.461954	+	0.886904i	$0.652852\pi$
$140$	−0.523485	+	4.02848i	−0.0442426	+	0.340468i
$141$	−3.51177	−	0.698534i	−0.295744	−	0.0588272i
$142$	−5.65306	+	21.1685i	−0.474395	+	1.77642i
$143$	−32.9680	+	6.55773i	−2.75692	+	0.548385i
$144$	−6.81370	+	8.94175i	−0.567808	+	0.745146i
$145$	−3.73109	+	9.00765i	−0.309850	+	0.748045i
$146$	3.91006	+	6.75932i	0.323599	+	0.559406i
$147$	1.83892	+	1.22873i	0.151672	+	0.101344i
$148$	2.46438	+	4.97620i	0.202571	+	0.409041i
$149$	2.47133	−	2.47133i	0.202459	−	0.202459i	−0.598594	−	0.801053i	$-0.704274\pi$
$149$	2.47133	−	2.47133i	0.202459	−	0.202459i	0.801053	+	0.598594i	$0.204274\pi$
$150$	1.39330	+	1.06726i	0.113763	+	0.0871417i
$151$	−5.03288	−	12.1504i	−0.409570	−	0.988789i	−0.985251	−	0.171115i	$-0.945263\pi$
$151$	−5.03288	−	12.1504i	−0.409570	−	0.988789i	0.575681	−	0.817674i	$-0.304737\pi$
$152$	−0.364398	+	0.548343i	−0.0295566	+	0.0444765i
$153$	11.2366	+	2.83175i	0.908426	+	0.228934i
$154$	9.67804	−	3.29431i	0.779879	−	0.265463i
$155$	−0.133863	−	0.323173i	−0.0107521	−	0.0259579i
$156$	1.79409	−	5.31449i	0.143642	−	0.425500i
$157$	−5.32674	−	5.32674i	−0.425120	−	0.425120i	0.461842	−	0.886962i	$-0.347189\pi$
$157$	−5.32674	−	5.32674i	−0.425120	−	0.425120i	−0.886962	+	0.461842i	$0.847189\pi$
$158$	−0.267555	−	2.01919i	−0.0212855	−	0.160638i
$159$	−1.22649	−	0.819516i	−0.0972671	−	0.0649918i
$160$	8.00140	−	2.17998i	0.632567	−	0.172343i
$161$	8.00749	+	3.31681i	0.631078	+	0.261401i
$162$	−10.3450	−	0.669331i	−0.812778	−	0.0525876i
$163$	13.3347	−	2.65243i	1.04445	−	0.207755i	0.357091	−	0.934070i	$-0.383769\pi$
$163$	13.3347	−	2.65243i	1.04445	−	0.207755i	0.687362	+	0.726315i	$0.258769\pi$
$164$	−3.96631	+	0.266649i	−0.309717	+	0.0208218i
$165$	−0.649630	+	3.26591i	−0.0505736	+	0.254251i
$166$	6.46763	−	13.1428i	0.501986	−	1.02008i
$167$	9.88964	+	14.8009i	0.765283	+	1.14533i	0.985467	+	0.169869i	$0.0543344\pi$
$167$	9.88964	+	14.8009i	0.765283	+	1.14533i	−0.220183	+	0.975459i	$0.570666\pi$
$168$	−0.328607	+	1.67403i	−0.0253526	+	0.129154i
$169$		−	28.5044i		−	2.19265i
$170$	−5.31015	−	6.69892i	−0.407270	−	0.513784i
$171$	−0.654205			−0.0500283
$172$	8.25518	+	4.74768i	0.629451	+	0.362007i
$173$	9.86324	−	6.59041i	0.749888	−	0.501059i	−0.120932	−	0.992661i	$-0.538588\pi$
$173$	9.86324	−	6.59041i	0.749888	−	0.501059i	0.870820	+	0.491601i	$0.163588\pi$
$174$	−1.80783	+	3.67368i	−0.137051	+	0.278501i
$175$	−3.87388	−	0.770563i	−0.292838	−	0.0582491i
$176$	−13.8134	−	15.6449i	−1.04122	−	1.17928i
$177$	0.716254	+	3.60085i	0.0538369	+	0.270657i
$178$	−0.00934389	+	0.144416i	−0.000700354	+	0.0108245i
$179$	5.16545	−	12.4705i	0.386084	−	0.932089i	−0.604677	−	0.796471i	$-0.706698\pi$
$179$	5.16545	−	12.4705i	0.386084	−	0.932089i	0.990761	−	0.135618i	$-0.0433021\pi$
$180$	6.20461	+	5.42291i	0.462464	+	0.404200i
$181$	−6.94265	+	10.3904i	−0.516043	+	0.772313i	−0.994381	−	0.105863i	$-0.966240\pi$
$181$	−6.94265	+	10.3904i	−0.516043	+	0.772313i	0.478337	+	0.878176i	$0.341240\pi$
$182$	1.65816	+	12.5138i	0.122911	+	0.927586i
$183$	−1.25721	+	1.25721i	−0.0929353	+	0.0929353i
$184$	−0.0445264	−	17.6936i	−0.00328253	−	1.30439i
$185$	3.76056	−	1.55767i	0.276482	−	0.114522i
$186$	−0.0473354	−	0.139062i	−0.00347080	−	0.0101965i
$187$	−9.22575	+	19.4341i	−0.674654	+	1.42116i
$188$	−10.0359	−	13.0337i	−0.731944	−	0.950582i
$189$	−3.23784	+	1.34116i	−0.235518	+	0.0975548i
$190$	0.383118	+	0.293467i	0.0277943	+	0.0212903i
$191$	16.1916	+	16.1916i	1.17158	+	1.17158i	0.981832	+	0.189751i	$0.0607682\pi$
$191$	16.1916	+	16.1916i	1.17158	+	1.17158i	0.189751	+	0.981832i	$0.439232\pi$
$192$	3.41227	−	0.696614i	0.246259	−	0.0502738i
$193$	1.00950	−	1.51082i	0.0726652	−	0.108751i	−0.793357	−	0.608757i	$-0.791669\pi$
$193$	1.00950	−	1.51082i	0.0726652	−	0.108751i	0.866022	+	0.500005i	$0.166669\pi$
$194$	−10.1706	+	5.88339i	−0.730208	+	0.422403i
$195$	−3.79859	−	1.57343i	−0.272022	−	0.112675i
$196$	2.64626	+	9.81012i	0.189019	+	0.700723i
$197$	−2.76838	−	13.9176i	−0.197239	−	0.991588i	−0.944863	−	0.327466i	$-0.893805\pi$
$197$	−2.76838	−	13.9176i	−0.197239	−	0.991588i	0.747624	−	0.664122i	$-0.231195\pi$
$198$	5.35059	−	20.0359i	0.380250	−	1.42389i
$199$	4.84948	−	24.3800i	0.343771	−	1.72825i	−0.292039	−	0.956406i	$-0.594334\pi$
$199$	4.84948	−	24.3800i	0.343771	−	1.72825i	0.635810	−	0.771846i	$-0.280666\pi$
$200$	1.59296	+	7.90433i	0.112639	+	0.558920i
$201$	−2.94111	+	1.96519i	−0.207450	+	0.138614i
$202$	1.96673	−	1.72770i	0.138379	−	0.121560i
$203$		−	9.21433i		−	0.646719i
$204$	−2.04369	−	2.95131i	−0.143087	−	0.206633i
$205$			2.91391i			0.203516i
$206$	−7.59901	−	8.65037i	−0.529448	−	0.602700i
$207$	14.6184	−	9.76773i	1.01605	−	0.678904i
$208$	22.2737	−	12.9596i	1.54441	−	0.898586i
$209$	0.236940	−	1.19118i	0.0163895	−	0.0823956i
$210$	1.20816	+	0.322639i	0.0833707	+	0.0222642i
$211$	−2.36667	−	11.8980i	−0.162928	−	0.819095i	−0.972649	−	0.232280i	$-0.925382\pi$
$211$	−2.36667	−	11.8980i	−0.162928	−	0.819095i	0.809721	−	0.586815i	$-0.199618\pi$
$212$	−1.76496	−	6.54299i	−0.121218	−	0.449374i
$213$	6.23117	+	2.58104i	0.426953	+	0.176850i
$214$	6.49982	+	11.2362i	0.444318	+	0.768093i
$215$	3.87815	−	5.80406i	0.264488	−	0.395834i
$216$	5.07169	+	5.04623i	0.345085	+	0.343352i
$217$	0.233761	+	0.233761i	0.0158688	+	0.0158688i
$218$	5.27263	−	6.88337i	0.357107	−	0.466200i
$219$	2.22077	−	0.919873i	0.150066	−	0.0621592i
$220$	−12.1212	+	9.33331i	−0.817214	+	0.629251i
$221$	−21.3126	−	15.8539i	−1.43364	−	1.06645i
$222$	1.61818	−	0.550811i	0.108605	−	0.0369680i
$223$	−8.31618	+	3.44468i	−0.556893	+	0.230673i	−0.643336	−	0.765584i	$-0.722450\pi$
$223$	−8.31618	+	3.44468i	−0.556893	+	0.230673i	0.0864429	+	0.996257i	$0.472450\pi$
$224$	−6.19791	+	4.79726i	−0.414115	+	0.320530i
$225$	−5.66541	+	5.66541i	−0.377694	+	0.377694i
$226$	17.3776	−	2.30263i	1.15594	−	0.153169i
$227$	4.59065	−	6.87039i	0.304692	−	0.456004i	−0.647252	−	0.762276i	$-0.724082\pi$
$227$	4.59065	−	6.87039i	0.304692	−	0.456004i	0.951944	+	0.306272i	$0.0990818\pi$
$228$	0.152597	+	0.133372i	0.0101060	+	0.00883275i
$229$	0.143443	−	0.346302i	0.00947897	−	0.0228843i	−0.919069	−	0.394096i	$-0.871058\pi$
$229$	0.143443	−	0.346302i	0.00947897	−	0.0228843i	0.928548	+	0.371212i	$0.121058\pi$
$230$	−12.9426	−	0.837399i	−0.853408	−	0.0552164i
$231$	−0.613952	−	3.08654i	−0.0403950	−	0.203080i
$232$	−17.3605	+	7.24220i	−1.13977	+	0.475473i
$233$	−6.87556	−	1.36763i	−0.450433	−	0.0895966i	−0.0353391	−	0.999375i	$-0.511251\pi$
$233$	−6.87556	−	1.36763i	−0.450433	−	0.0895966i	−0.415093	+	0.909779i	$0.636251\pi$
$234$	22.9749	+	11.3060i	1.50192	+	0.739098i
$235$	−10.0258	+	6.69901i	−0.654009	+	0.436995i
$236$	−8.40905	+	14.6215i	−0.547382	+	0.951778i
$237$	−0.626992			−0.0407275
$238$	7.05926	+	3.92859i	0.457584	+	0.254653i
$239$		−	6.88573i		−	0.445401i	−0.974887	−	0.222700i	$-0.928513\pi$
$239$		−	6.88573i		−	0.445401i	0.974887	−	0.222700i	$-0.0714872\pi$
$240$	−0.341700	−	2.52984i	−0.0220566	−	0.163301i
$241$	−3.32066	−	4.96972i	−0.213903	−	0.320128i	0.708966	−	0.705243i	$-0.249162\pi$
$241$	−3.32066	−	4.96972i	−0.213903	−	0.320128i	−0.922869	+	0.385115i	$0.874162\pi$
$242$	20.5857	+	10.1303i	1.32330	+	0.651200i
$243$	−2.10299	+	10.5724i	−0.134907	+	0.678223i
$244$	−8.14989	+	0.547905i	−0.521743	+	0.0350760i
$245$	7.30483	−	1.45302i	0.466688	−	0.0928301i
$246$	−0.0790088	+	1.22114i	−0.00503742	+	0.0778568i
$247$	1.38546	+	0.573878i	0.0881549	+	0.0365150i
$248$	0.256695	−	0.624154i	0.0163001	−	0.0396338i
$249$	−3.74913	−	2.50509i	−0.237591	−	0.158754i
$250$	16.1357	−	2.13808i	1.02051	−	0.135224i
$251$	6.67757	+	6.67757i	0.421484	+	0.421484i	0.885715	−	0.464230i	$-0.153669\pi$
$251$	6.67757	+	6.67757i	0.421484	+	0.421484i	−0.464230	+	0.885715i	$0.653669\pi$
$252$	−7.37876	−	2.49095i	−0.464818	−	0.156915i
$253$	12.4906	+	30.1550i	0.785278	+	1.89583i
$254$	5.49983	+	16.1574i	0.345090	+	1.01381i
$255$	−2.25895	+	1.34956i	−0.141461	+	0.0845129i
$256$	13.9098	+	7.90683i	0.869361	+	0.494177i
$257$	−7.10179	−	17.1452i	−0.442998	−	1.06949i	−0.974892	−	0.222680i	$-0.928520\pi$
$257$	−7.10179	−	17.1452i	−0.442998	−	1.06949i	0.531894	−	0.846811i	$-0.321480\pi$
$258$	1.78260	−	2.32716i	0.110980	−	0.144883i
$259$	−2.72013	+	2.72013i	−0.169021	+	0.169021i
$260$	−8.38295	−	16.9273i	−0.519889	−	1.04979i
$261$	−15.5412	−	10.3843i	−0.961976	−	0.642772i
$262$	−9.29254	+	5.37545i	−0.574095	+	0.332096i
$263$	−2.28969	+	5.52779i	−0.141188	+	0.340858i	−0.978618	−	0.205687i	$-0.934057\pi$
$263$	−2.28969	+	5.52779i	−0.141188	+	0.340858i	0.837430	+	0.546545i	$0.184057\pi$
$264$	−5.33274	+	3.58266i	−0.328207	+	0.220498i
$265$	−4.87205	+	0.969111i	−0.299288	+	0.0595320i
$266$	−0.440652	−	0.117676i	−0.0270181	−	0.00721520i
$267$	0.0436920	+	0.00869089i	0.00267391	+	0.000531874i
$268$	−16.1153	−	2.09412i	−0.984399	−	0.127919i
$269$	−12.3478	−	18.4798i	−0.752859	−	1.12673i	−0.987952	−	0.154760i	$-0.950540\pi$
$269$	−12.3478	−	18.4798i	−0.752859	−	1.12673i	0.235093	−	0.971973i	$-0.424460\pi$
$270$	3.93997	−	3.46111i	0.239779	−	0.210636i
$271$	29.6298			1.79988			0.899940	−	0.436013i	$-0.143610\pi$
$271$	29.6298			1.79988			0.899940	+	0.436013i	$0.143610\pi$
$272$	1.85339	−	16.3880i	0.112378	−	0.993666i
$273$	3.88575			0.235176
$274$	−11.7649	+	10.3351i	−0.710746	+	0.624363i
$275$	−8.26370	−	12.3675i	−0.498320	−	0.745789i
$276$	−5.40116	−	0.701860i	−0.325112	−	0.0422470i
$277$	−22.9655	−	4.56813i	−1.37986	−	0.274472i	−0.551273	−	0.834325i	$-0.685858\pi$
$277$	−22.9655	−	4.56813i	−1.37986	−	0.274472i	−0.828592	+	0.559853i	$0.810858\pi$
$278$	15.4898	+	4.13655i	0.929015	+	0.248094i
$279$	0.657712	−	0.130827i	0.0393762	−	0.00783241i
$280$	3.20378	+	4.76877i	0.191462	+	0.284988i
$281$	2.05832	−	4.96922i	0.122789	−	0.296439i	−0.850518	−	0.525946i	$-0.823711\pi$
$281$	2.05832	−	4.96922i	0.122789	−	0.296439i	0.973307	+	0.229507i	$0.0737114\pi$
$282$	−4.38316	+	2.53552i	−0.261013	+	0.150988i
$283$	15.2795	+	10.2095i	0.908273	+	0.606889i	0.919518	−	0.393048i	$-0.128579\pi$
$283$	15.2795	+	10.2095i	0.908273	+	0.606889i	−0.0112446	+	0.999937i	$0.503579\pi$
$284$	13.7513	+	27.7674i	0.815991	+	1.64769i
$285$	0.105045	−	0.105045i	0.00622235	−	0.00622235i
$286$	−28.9071	+	37.7380i	−1.70931	+	2.23150i
$287$	−1.05386	−	2.54424i	−0.0622074	−	0.150182i
$288$	1.10634	+	15.8600i	0.0651918	+	0.934558i
$289$	−16.2821	+	4.88816i	−0.957769	+	0.287539i
$290$	4.44306	+	13.0528i	0.260905	+	0.766490i
$291$	1.38412	+	3.34155i	0.0811383	+	0.195885i
$292$	10.4632	+	3.53220i	0.612310	+	0.206706i
$293$	−2.41443	−	2.41443i	−0.141052	−	0.141052i	0.633055	−	0.774107i	$-0.281801\pi$
$293$	−2.41443	−	2.41443i	−0.141052	−	0.141052i	−0.774107	+	0.633055i	$0.781801\pi$
$294$	3.10064	−	0.410854i	0.180833	−	0.0239615i
$295$	10.2801	+	6.86894i	0.598531	+	0.399925i
$296$	7.26287	+	2.98699i	0.422146	+	0.173615i
$297$	−12.1932	−	5.05060i	−0.707523	−	0.293066i
$298$	0.319128	−	4.93234i	0.0184866	−	0.285723i
$299$	−39.5271	+	7.86242i	−2.28591	+	0.454695i
$300$	2.47648	−	0.166490i	0.142980	−	0.00961233i
$301$	−1.28703	+	6.47034i	−0.0741832	+	0.372944i
$302$	−16.6879	−	8.21217i	−0.960281	−	0.472557i
$303$	−0.447696	−	0.670024i	−0.0257194	−	0.0384919i
$304$	0.124629	+	0.922713i	0.00714794	+	0.0529212i
$305$			5.98743i			0.342839i
$306$	14.5817	−	7.47898i	0.833579	−	0.427545i
$307$	−14.9080			−0.850843			−0.425421	−	0.904995i	$-0.639874\pi$
$307$	−14.9080			−0.850843			−0.425421	+	0.904995i	$0.639874\pi$
$308$	7.20799	−	12.5331i	0.410713	−	0.714140i
$309$	−2.94700	+	1.96912i	−0.167649	+	0.112020i
$310$	−0.443859	−	0.218425i	−0.0252095	−	0.0124057i
$311$	18.7435	+	3.72831i	1.06285	+	0.211413i	0.695393	−	0.718629i	$-0.255230\pi$
$311$	18.7435	+	3.72831i	1.06285	+	0.211413i	0.367452	+	0.930043i	$0.380230\pi$
$312$	−3.05408	−	7.32105i	−0.172903	−	0.414473i
$313$	5.74545	+	28.8843i	0.324752	+	1.63264i	0.706033	+	0.708178i	$0.250483\pi$
$313$	5.74545	+	28.8843i	0.324752	+	1.63264i	−0.381282	+	0.924459i	$0.624517\pi$
$314$	−10.6312	−	0.687853i	−0.599956	−	0.0388178i
$315$	−2.18458	+	5.27405i	−0.123087	+	0.297159i
$316$	−2.16888	−	1.89563i	−0.122009	−	0.106637i
$317$	−10.7186	+	16.0416i	−0.602018	+	0.900984i	−0.999864	−	0.0164684i	$-0.994758\pi$
$317$	−10.7186	+	16.0416i	−0.602018	+	0.900984i	0.397846	+	0.917452i	$0.369758\pi$
$318$	−2.06801	+	0.274024i	−0.115969	+	0.0153665i
$319$	24.5365	−	24.5365i	1.37378	−	1.37378i
$320$	6.46665	−	9.78427i	0.361497	−	0.546958i
$321$	3.69165	−	1.52913i	0.206048	−	0.0853479i
$322$	11.6035	−	3.94972i	0.646639	−	0.220110i
$323$	0.823910	−	0.492228i	0.0458436	−	0.0273883i
$324$	−11.6160	+	8.94430i	−0.645335	+	0.496906i
$325$	16.9679	−	7.02832i	0.941208	−	0.389861i
$326$	11.6922	−	15.2641i	0.647570	−	0.845398i
$327$	−1.88732	−	1.88732i	−0.104369	−	0.104369i
$328$	−3.96525	+	3.98526i	−0.218944	+	0.220049i
$329$	6.33109	−	9.47514i	0.349044	−	0.522381i
$330$	2.35801	+	4.07630i	0.129804	+	0.224393i
$331$	19.6595	+	8.14322i	1.08058	+	0.447592i	0.850713	−	0.525630i	$-0.176170\pi$
$331$	19.6595	+	8.14322i	1.08058	+	0.447592i	0.229869	+	0.973222i	$0.426170\pi$
$332$	−5.39511	−	20.0006i	−0.296095	−	1.09767i
$333$	1.52235	+	7.65337i	0.0834242	+	0.419402i
$334$	24.3219	+	6.49517i	1.33084	+	0.355400i
$335$	−2.32391	+	11.6831i	−0.126969	+	0.638316i
$336$	1.21331	+	2.08532i	0.0661915	+	0.113764i
$337$	24.7025	−	16.5057i	1.34563	−	0.899123i	0.346392	−	0.938090i	$-0.387407\pi$
$337$	24.7025	−	16.5057i	1.34563	−	0.899123i	0.999240	+	0.0389670i	$0.0124067\pi$
$338$	−26.6045	−	30.2854i	−1.44710	−	1.64731i
$339$		−	5.39602i		−	0.293072i
$340$	−11.8943	−	2.16126i	−0.645061	−	0.117211i
$341$			1.24495i			0.0674177i
$342$	−0.695080	+	0.610601i	−0.0375856	+	0.0330175i
$343$	−13.9166	+	9.29880i	−0.751428	+	0.502088i
$344$	13.2022	−	2.66063i	0.711814	−	0.143452i
$345$	−0.778877	+	3.91568i	−0.0419333	+	0.210813i
$346$	4.32835	−	16.2080i	0.232694	−	0.871348i
$347$	1.96663	+	9.88694i	0.105574	+	0.530759i	0.996987	+	0.0775664i	$0.0247150\pi$
$347$	1.96663	+	9.88694i	0.105574	+	0.530759i	−0.891413	+	0.453192i	$0.850285\pi$
$348$	1.50804	+	5.59055i	0.0808394	+	0.299685i
$349$	3.06183	+	1.26825i	0.163896	+	0.0678880i	0.463123	−	0.886294i	$-0.346729\pi$
$349$	3.06183	+	1.26825i	0.163896	+	0.0678880i	−0.299227	+	0.954182i	$0.596729\pi$
$350$	−4.83512	+	2.79697i	−0.258448	+	0.149504i
$351$	9.05354	−	13.5496i	0.483242	−	0.723223i
$352$	−29.2786	−	3.72974i	−1.56055	−	0.198796i
$353$	−12.0787	−	12.0787i	−0.642886	−	0.642886i	0.308378	−	0.951264i	$-0.400214\pi$
$353$	−12.0787	−	12.0787i	−0.642886	−	0.642886i	−0.951264	+	0.308378i	$0.900214\pi$
$354$	4.12185	+	3.15732i	0.219074	+	0.167810i
$355$	20.9841	−	8.69188i	1.11372	−	0.461317i
$356$	0.124863	+	0.162160i	0.00661772	+	0.00859449i
$357$	1.48429	−	1.99534i	0.0785567	−	0.105605i
$358$	−6.15112	−	18.0708i	−0.325097	−	0.955072i
$359$	−12.9199	+	5.35161i	−0.681888	+	0.282447i	−0.696616	−	0.717444i	$-0.745312\pi$
$359$	−12.9199	+	5.35161i	−0.681888	+	0.282447i	0.0147281	+	0.999892i	$0.495312\pi$
$360$	11.6537	−	0.0293269i	0.614205	−	0.00154566i
$361$	13.3967	−	13.3967i	0.705090	−	0.705090i
$362$	2.32144	+	17.5195i	0.122012	+	0.920805i
$363$	3.92374	−	5.87229i	0.205943	−	0.308215i
$364$	13.4415	+	11.7480i	0.704526	+	0.615765i
$365$	3.09776	−	7.47865i	0.162144	−	0.391450i
$366$	−0.162346	+	2.50916i	−0.00848594	+	0.131156i
$367$	4.29508	+	21.5928i	0.224201	+	1.12714i	0.914803	+	0.403901i	$0.132346\pi$
$367$	4.29508	+	21.5928i	0.224201	+	1.12714i	−0.690601	+	0.723236i	$0.742654\pi$
$368$	−16.5616	−	18.7576i	−0.863334	−	0.977806i
$369$	−5.47888	−	1.08982i	−0.285219	−	0.0567336i
$370$	2.54166	−	5.16490i	0.132135	−	0.268510i
$371$	3.90348	−	2.60822i	0.202659	−	0.135412i
$372$	−0.180086	−	0.103570i	−0.00933705	−	0.00536988i
$373$	10.1057			0.523252			0.261626	−	0.965169i	$-0.415741\pi$
$373$	10.1057			0.523252			0.261626	+	0.965169i	$0.415741\pi$
$374$	8.33656	+	29.2591i	0.431073	+	1.51295i
$375$		−	5.01041i		−	0.258736i
$376$	−22.8279	−	4.48107i	−1.17726	−	0.231094i
$377$	23.8036	+	35.6246i	1.22595	+	1.83476i
$378$	−2.18837	+	4.44698i	−0.112558	+	0.228728i
$379$	3.21425	−	16.1591i	0.165105	−	0.830038i	−0.806098	−	0.591782i	$-0.798424\pi$
$379$	3.21425	−	16.1591i	0.165105	−	0.830038i	0.971203	−	0.238255i	$-0.0765756\pi$
$380$	0.680962	−	0.0457801i	0.0349326	−	0.00234847i
$381$	5.15296	−	1.02499i	0.263994	−	0.0525117i
$382$	32.3156	+	2.09086i	1.65341	+	0.106978i
$383$	−30.9754	−	12.8304i	−1.58277	−	0.655605i	−0.593921	−	0.804523i	$-0.702421\pi$
$383$	−30.9754	−	12.8304i	−1.58277	−	0.655605i	−0.988849	+	0.148918i	$0.952421\pi$
$384$	2.97528	−	3.92497i	0.151832	−	0.200295i
$385$	−8.81179	−	5.88785i	−0.449091	−	0.300073i
$386$	−0.337549	−	2.54743i	−0.0171808	−	0.129661i
$387$	9.46264	+	9.46264i	0.481013	+	0.481013i
$388$	−5.31483	+	15.7437i	−0.269820	+	0.799266i
$389$	2.91362	+	7.03411i	0.147727	+	0.356644i	0.980370	−	0.197166i	$-0.0631737\pi$
$389$	2.91362	+	7.03411i	0.147727	+	0.356644i	−0.832644	+	0.553809i	$0.813174\pi$
$390$	−5.50447	+	1.87367i	−0.278730	+	0.0948769i
$391$	−11.0613	+	23.3005i	−0.559392	+	1.17836i
$392$	11.9678	+	7.95317i	0.604467	+	0.401696i
$393$	1.26462	+	3.05305i	0.0637915	+	0.154006i
$394$	−15.9313	−	12.2033i	−0.802608	−	0.614794i
$395$	−1.49302	+	1.49302i	−0.0751221	+	0.0751221i
$396$	−13.0156	−	26.2817i	−0.654056	−	1.32070i
$397$	−26.6204	−	17.7872i	−1.33604	−	0.892713i	−0.337227	−	0.941423i	$-0.609489\pi$
$397$	−26.6204	−	17.7872i	−1.33604	−	0.892713i	−0.998813	+	0.0487099i	$0.984489\pi$
$398$	−17.6025	−	30.4295i	−0.882335	−	1.52529i
$399$	−0.0537279	+	0.129711i	−0.00268976	+	0.00649365i
$400$	9.06997	+	6.91140i	0.453498	+	0.345570i
$401$	7.55197	−	1.50218i	0.377128	−	0.0750153i	−0.00288699	−	0.999996i	$-0.500919\pi$
$401$	7.55197	−	1.50218i	0.377128	−	0.0750153i	0.380015	+	0.924980i	$0.375919\pi$
$402$	−1.29067	+	4.83305i	−0.0643726	+	0.241050i
$403$	−1.50765	−	0.299891i	−0.0751016	−	0.0149386i
$404$	0.477069	−	3.67128i	0.0237351	−	0.182653i
$405$	5.97035	+	8.93527i	0.296669	+	0.443997i
$406$	−8.60017	−	9.79004i	−0.426819	−	0.485872i
$407$	−14.4866			−0.718077
$408$	−4.92598	−	1.22823i	−0.243872	−	0.0608064i
$409$	−6.33731			−0.313360			−0.156680	−	0.987649i	$-0.550079\pi$
$409$	−6.33731			−0.313360			−0.156680	+	0.987649i	$0.550079\pi$
$410$	2.71969	+	3.09597i	0.134316	+	0.152899i
$411$	2.67811	+	4.00807i	0.132101	+	0.197704i
$412$	−16.1476	−	2.09832i	−0.795535	−	0.103377i
$413$	−11.4602	−	2.27958i	−0.563920	−	0.112171i
$414$	6.41511	−	24.0221i	0.315286	−	1.18062i
$415$	−14.8928	+	2.96237i	−0.731061	+	0.145417i
$416$	11.5696	−	34.5584i	0.567246	−	1.69437i
$417$	1.88864	−	4.55957i	0.0924869	−	0.223283i
$418$	−0.860040	−	1.48675i	−0.0420659	−	0.0727194i
$419$	−1.72909	−	1.15534i	−0.0844718	−	0.0564423i	0.512617	−	0.858617i	$-0.328676\pi$
$419$	−1.72909	−	1.15534i	−0.0844718	−	0.0564423i	−0.597089	+	0.802175i	$0.703676\pi$
$420$	1.58478	−	0.784833i	0.0773291	−	0.0382959i
$421$	−18.5257	+	18.5257i	−0.902887	+	0.902887i	−0.995685	−	0.0927978i	$-0.970419\pi$
$421$	−18.5257	+	18.5257i	−0.902887	+	0.902887i	0.0927978	+	0.995685i	$0.470419\pi$
$422$	−13.6195	−	10.4325i	−0.662989	−	0.507846i
$423$	−8.84612	−	21.3564i	−0.430113	−	1.03839i
$424$	−7.98211	−	5.30447i	−0.387646	−	0.257608i
$425$	2.87236	−	11.3977i	0.139330	−	0.552871i
$426$	9.02950	−	3.07355i	0.437481	−	0.148914i
$427$	−2.16545	−	5.22786i	−0.104793	−	0.252994i
$428$	17.3932	+	5.87168i	0.840734	+	0.283818i
$429$	10.3472	+	10.3472i	0.499568	+	0.499568i
$430$	−1.29675	−	9.78635i	−0.0625348	−	0.471940i
$431$	13.8995	+	9.28736i	0.669516	+	0.447356i	0.843311	−	0.537425i	$-0.180603\pi$
$431$	13.8995	+	9.28736i	0.669516	+	0.447356i	−0.173795	+	0.984782i	$0.555603\pi$
$432$	10.0984	+	0.627865i	0.485862	+	0.0302082i
$433$	10.1794	+	4.21645i	0.489192	+	0.202630i	0.613624	−	0.789598i	$-0.289711\pi$
$433$	10.1794	+	4.21645i	0.489192	+	0.202630i	−0.124432	+	0.992228i	$0.539711\pi$
$434$	0.466547	+	0.0301861i	0.0223950	+	0.00144898i
$435$	4.16284	−	0.828041i	0.199593	−	0.0397015i
$436$	−0.822516	−	12.2346i	−0.0393914	−	0.585932i
$437$	0.284081	−	1.42817i	0.0135894	−	0.0683186i
$438$	1.50096	−	3.05009i	0.0717187	−	0.145739i
$439$	16.1579	+	24.1821i	0.771176	+	1.15415i	0.984193	+	0.177099i	$0.0566711\pi$
$439$	16.1579	+	24.1821i	0.771176	+	1.15415i	−0.213017	+	0.977049i	$0.568329\pi$
$440$	−4.16735	+	21.2298i	−0.198671	+	1.01209i
$441$			14.2783i			0.679921i
$442$	−37.4415	+	3.04759i	−1.78091	+	0.144959i
$443$	11.7925			0.560278			0.280139	−	0.959959i	$-0.409619\pi$
$443$	11.7925			0.560278			0.280139	+	0.959959i	$0.409619\pi$
$444$	1.20518	−	2.09555i	0.0571954	−	0.0994503i
$445$	0.124737	−	0.0833464i	0.00591309	−	0.00395100i
$446$	−5.62069	+	11.4218i	−0.266148	+	0.540837i
$447$	−1.49224	−	0.296825i	−0.0705806	−	0.0140394i
$448$	−2.10764	+	10.8818i	−0.0995768	+	0.514116i
$449$	3.98112	+	20.0144i	0.187881	+	0.944540i	0.953534	+	0.301286i	$0.0974159\pi$
$449$	3.98112	+	20.0144i	0.187881	+	0.944540i	−0.765653	+	0.643254i	$0.777584\pi$
$450$	−0.731587	+	11.3072i	−0.0344873	+	0.533026i
$451$	3.96869	−	9.58125i	0.186878	−	0.451164i
$452$	16.3142	−	18.6658i	0.767353	−	0.877966i
$453$	−3.18080	+	4.76040i	−0.149447	+	0.223663i
$454$	−1.53499	−	11.5843i	−0.0720407	−	0.543679i
$455$	9.25293	−	9.25293i	0.433784	−	0.433784i
$456$	0.286613		0.000721269i	0.0134219		3.37765e-5i
$457$	11.7355	−	4.86100i	0.548963	−	0.227388i	−0.0909229	−	0.995858i	$-0.528982\pi$
$457$	11.7355	−	4.86100i	0.548963	−	0.227388i	0.639886	+	0.768470i	$0.278982\pi$
$458$	−0.170815	−	0.501821i	−0.00798165	−	0.0234485i
$459$	−3.49945	−	9.82471i	−0.163341	−	0.458578i
$460$	−14.5328	+	11.1902i	−0.677596	+	0.521746i
$461$	25.4488	−	10.5412i	1.18527	−	0.490954i	0.299057	−	0.954235i	$-0.403328\pi$
$461$	25.4488	−	10.5412i	1.18527	−	0.490954i	0.886211	+	0.463281i	$0.153328\pi$
$462$	−3.53313	−	2.70636i	−0.164376	−	0.125911i
$463$	−16.2590	−	16.2590i	−0.755618	−	0.755618i	0.219904	−	0.975522i	$-0.429426\pi$
$463$	−16.2590	−	16.2590i	−0.755618	−	0.755618i	−0.975522	+	0.219904i	$0.929426\pi$
$464$	−11.6857	+	23.8981i	−0.542495	+	1.10944i
$465$	−0.0846017	+	0.126615i	−0.00392331	+	0.00587165i
$466$	−8.58161	+	4.96420i	−0.397536	+	0.229962i
$467$	21.8993	+	9.07097i	1.01338	+	0.419754i	0.826686	−	0.562664i	$-0.190224\pi$
$467$	21.8993	+	9.07097i	1.01338	+	0.419754i	0.186691	+	0.982419i	$0.440224\pi$
$468$	34.9628	−	9.43116i	1.61616	−	0.435955i
$469$	−2.19628	−	11.0414i	−0.101415	−	0.509847i
$470$	−4.39968	+	16.4751i	−0.202942	+	0.759939i
$471$	−0.639782	+	3.21640i	−0.0294796	+	0.148204i
$472$	4.71249	+	23.3836i	0.216910	+	1.07632i
$473$	−20.6568	+	13.8024i	−0.949801	+	0.634637i
$474$	−0.666166	+	0.585201i	−0.0305980	+	0.0268792i
$475$			0.663586i			0.0304474i
$476$	11.1671	−	2.41470i	0.511841	−	0.110678i
$477$		−	9.52313i		−	0.436034i
$478$	−6.42678	−	7.31595i	−0.293954	−	0.334624i
$479$	−12.5030	+	8.35421i	−0.571275	+	0.381714i	−0.807396	−	0.590010i	$-0.799124\pi$
$479$	−12.5030	+	8.35421i	−0.571275	+	0.381714i	0.236121	+	0.971724i	$0.424124\pi$
$480$	−2.72427	−	2.36898i	−0.124345	−	0.108129i
$481$	3.48963	−	17.5436i	0.159114	−	0.799918i
$482$	−8.16661	−	2.18090i	−0.371979	−	0.0993371i
$483$	−0.736099	−	3.70062i	−0.0334937	−	0.168384i
$484$	31.3270	−	8.45040i	1.42395	−	0.384109i
$485$	11.2530	+	4.66114i	0.510972	+	0.211651i
$486$	7.63338	+	13.1958i	0.346257	+	0.598575i
$487$	−0.520471	+	0.778940i	−0.0235848	+	0.0352971i	−0.843075	−	0.537796i	$-0.819257\pi$
$487$	−0.520471	+	0.778940i	−0.0235848	+	0.0352971i	0.819490	+	0.573094i	$0.194257\pi$
$488$	−8.14771	+	8.18882i	−0.368829	+	0.370690i
$489$	−4.18518	−	4.18518i	−0.189260	−	0.189260i
$490$	6.40506	−	8.36175i	0.289351	−	0.377745i
$491$	−11.8810	+	4.92128i	−0.536183	+	0.222094i	−0.634309	−	0.773080i	$-0.718715\pi$
$491$	−11.8810	+	4.92128i	−0.536183	+	0.222094i	0.0981257	+	0.995174i	$0.468715\pi$
$492$	1.05580	+	1.37117i	0.0475991	+	0.0618173i
$493$	27.3859	+	1.38475i	1.23340	+	0.0623661i
$494$	2.00765	−	0.683385i	0.0903286	−	0.0307470i
$495$	−19.8613	+	8.22681i	−0.892699	+	0.369768i
$496$	−0.309820	−	0.902737i	−0.0139113	−	0.0405341i
$497$	−15.1784	+	15.1784i	−0.680846	+	0.680846i
$498$	−6.32149	+	0.837635i	−0.283273	+	0.0375353i
$499$	−0.0146425	+	0.0219141i	−0.000655489	+	0.000981009i	−0.831797	−	0.555080i	$-0.812688\pi$
$499$	−0.0146425	+	0.0219141i	−0.000655489	+	0.000981009i	0.831142	+	0.556061i	$0.187688\pi$
$500$	15.1483	−	17.3319i	0.677453	−	0.775106i
$501$	2.96552	−	7.15940i	0.132490	−	0.319859i
$502$	13.3273	+	0.862288i	0.594825	+	0.0384858i
$503$	−0.627294	−	3.15362i	−0.0279697	−	0.140613i	0.964277	−	0.264895i	$-0.0853373\pi$
$503$	−0.627294	−	3.15362i	−0.0279697	−	0.140613i	−0.992247	+	0.124282i	$0.960337\pi$
$504$	−10.1647	+	4.24036i	−0.452772	+	0.188881i
$505$	−2.66157	−	0.529419i	−0.118438	−	0.0235588i
$506$	41.4161	+	20.3810i	1.84117	+	0.906046i
$507$	−10.3176	+	6.89400i	−0.458220	+	0.306173i
$508$	20.9239	+	12.0337i	0.928350	+	0.533909i
$509$	21.1149			0.935900			0.467950	−	0.883755i	$-0.344993\pi$
$509$	21.1149			0.935900			0.467950	+	0.883755i	$0.344993\pi$
$510$	−1.14048	+	3.54227i	−0.0505012	+	0.156854i
$511$			7.65025i			0.338427i
$512$	22.1587	−	4.58181i	0.979284	−	0.202489i
$513$	0.327118	+	0.489566i	0.0144426	+	0.0216149i
$514$	−23.5480	−	11.5880i	−1.03866	−	0.511126i
$515$	−2.32857	+	11.7065i	−0.102609	+	0.515851i
$516$	−0.278080	−	4.13634i	−0.0122418	−	0.182092i
$517$	42.0898	−	8.37218i	1.85111	−	0.368208i
$518$	−0.351256	+	5.42891i	−0.0154333	+	0.238532i
$519$	−4.77099	−	1.97621i	−0.209423	−	0.0867460i
$520$	−24.7058	−	10.1607i	−1.08342	−	0.445576i
$521$	−22.4645	−	15.0103i	−0.984189	−	0.657614i	−0.0442728	−	0.999019i	$-0.514097\pi$
$521$	−22.4645	−	15.0103i	−0.984189	−	0.657614i	−0.939916	+	0.341405i	$0.889097\pi$
$522$	−26.2044	+	3.47223i	−1.14693	+	0.151976i
$523$	−6.07408	−	6.07408i	−0.265601	−	0.265601i	0.561724	−	0.827325i	$-0.310138\pi$
$523$	−6.07408	−	6.07408i	−0.265601	−	0.265601i	−0.827325	+	0.561724i	$0.810138\pi$
$524$	−4.85597	+	14.3845i	−0.212134	+	0.628388i
$525$	0.658009	+	1.58857i	0.0287179	+	0.0693311i
$526$	2.72661	+	8.01024i	0.118886	+	0.349263i
$527$	−0.729891	+	0.659631i	−0.0317946	+	0.0287340i
$528$	−2.32205	+	8.78380i	−0.101054	+	0.382266i
$529$	6.17396	+	14.9052i	0.268433	+	0.648054i
$530$	−4.27194	+	5.57698i	−0.185561	+	0.242248i
$531$	−16.7601	+	16.7601i	−0.727328	+	0.727328i
$532$	−0.578017	+	0.286253i	−0.0250602	+	0.0124106i
$533$	10.6471	+	7.11414i	0.461175	+	0.308147i
$534$	0.0545335	−	0.0315460i	0.00235990	−	0.00136513i
$535$	5.14950	−	12.4320i	0.222632	−	0.537482i
$536$	−19.0767	+	12.8162i	−0.823989	+	0.553576i
$537$	−5.76318	+	1.14637i	−0.248700	+	0.0494694i
$538$	−30.3674	−	8.10961i	−1.30923	−	0.349630i
$539$	−25.9981	−	5.17134i	−1.11982	−	0.222745i
$540$	0.955717	−	7.35472i	0.0411275	−	0.316497i
$541$	14.9848	+	22.4264i	0.644248	+	0.964186i	0.999567	+	0.0294403i	$0.00937251\pi$
$541$	14.9848	+	22.4264i	0.644248	+	0.964186i	−0.355318	+	0.934745i	$0.615627\pi$
$542$	31.4810	−	27.6549i	1.35223	−	1.18788i
$543$	5.44009			0.233457
$544$	−13.3265	−	19.1417i	−0.571368	−	0.820694i
$545$	−8.98834			−0.385018
$546$	4.12853	−	3.62675i	0.176685	−	0.155211i
$547$	−15.4605	−	23.1382i	−0.661042	−	0.989320i	−0.998842	−	0.0481018i	$-0.984683\pi$
$547$	−15.4605	−	23.1382i	−0.661042	−	0.989320i	0.337800	−	0.941218i	$-0.390317\pi$
$548$	−2.85382	+	21.9616i	−0.121909	+	0.938151i
$549$	−11.2579	−	2.23933i	−0.480475	−	0.0955723i
$550$	−20.3232	−	5.42732i	−0.866584	−	0.231422i
$551$	−1.51832	+	0.302012i	−0.0646825	+	0.0128662i
$552$	−6.39370	+	4.29545i	−0.272134	+	0.182826i
$553$	0.763640	−	1.84359i	0.0324733	−	0.0783975i
$554$	−28.6640	+	16.5813i	−1.21782	+	0.704471i
$555$	−1.47334	−	0.984454i	−0.0625398	−	0.0417878i
$556$	20.3184	−	10.0623i	0.861692	−	0.426738i
$557$	−29.2573	+	29.2573i	−1.23967	+	1.23967i	−0.279538	+	0.960135i	$0.590181\pi$
$557$	−29.2573	+	29.2573i	−1.23967	+	1.23967i	−0.960135	+	0.279538i	$0.909819\pi$
$558$	0.576699	−	0.752875i	0.0244136	−	0.0318717i
$559$	−11.7390	−	28.3406i	−0.496509	−	1.19868i
$560$	7.85486	+	2.07648i	0.331929	+	0.0877474i
$561$	9.26576	−	1.36087i	0.391201	−	0.0574559i
$562$	−2.45109	−	7.20082i	−0.103393	−	0.303748i
$563$	−3.49558	−	8.43906i	−0.147321	−	0.355664i	0.832943	−	0.553359i	$-0.186654\pi$
$563$	−3.49558	−	8.43906i	−0.147321	−	0.355664i	−0.980264	+	0.197695i	$0.936654\pi$
$564$	−2.29049	+	6.78495i	−0.0964471	+	0.285698i
$565$	−12.8493	−	12.8493i	−0.540573	−	0.540573i
$566$	25.7631	−	3.41377i	1.08291	−	0.143491i
$567$	−8.44453	−	5.64245i	−0.354637	−	0.236961i
$568$	40.5271	+	16.6675i	1.70048	+	0.699354i
$569$	25.2721	+	10.4680i	1.05946	+	0.438843i	0.843260	−	0.537505i	$-0.180633\pi$
$569$	25.2721	+	10.4680i	1.05946	+	0.438843i	0.216201	+	0.976349i	$0.430633\pi$
$570$	0.0135647	−	0.209652i	0.000568164	−	0.00878138i
$571$	13.5924	−	2.70370i	0.568825	−	0.113146i	0.0977049	−	0.995215i	$-0.468850\pi$
$571$	13.5924	−	2.70370i	0.568825	−	0.113146i	0.471120	+	0.882069i	$0.343850\pi$
$572$	4.50944	+	67.0763i	0.188549	+	2.80460i
$573$	1.94474	−	9.77685i	0.0812425	−	0.408434i
$574$	−3.49437	−	1.71959i	−0.145852	−	0.0717743i
$575$	−9.90780	−	14.8281i	−0.413184	−	0.618373i
$576$	15.9783	+	15.8183i	0.665764	+	0.659096i
$577$			23.9299i			0.996214i	0.867115	+	0.498107i	$0.165971\pi$
$577$			23.9299i			0.996214i	−0.867115	+	0.498107i	$0.834029\pi$
$578$	−12.7370	+	20.3904i	−0.529790	+	0.848129i
$579$	−0.791017			−0.0328736
$580$	16.9035	+	9.72146i	0.701880	+	0.403662i
$581$	11.9321	−	7.97279i	0.495028	−	0.330767i
$582$	4.58942	+	2.25847i	0.190238	+	0.0936165i
$583$	17.3398	+	3.44909i	0.718140	+	0.142847i
$584$	14.4137	−	6.01287i	0.596441	−	0.248814i
$585$	−5.17850	−	26.0341i	−0.214105	−	1.07638i
$586$	−4.81878	−	0.311780i	−0.199062	−	0.0128795i
$587$	12.7413	−	30.7602i	0.525889	−	1.26961i	−0.408305	−	0.912845i	$-0.633880\pi$
$587$	12.7413	−	30.7602i	0.525889	−	1.26961i	0.934195	−	0.356764i	$-0.116120\pi$
$588$	2.91090	−	3.33050i	0.120044	−	0.137348i
$589$	0.0308569	−	0.0461806i	0.00127144	−	0.00190284i
$590$	17.3335	−	2.29679i	0.713609	−	0.0945575i
$591$	−4.36813	+	4.36813i	−0.179681	+	0.179681i
$592$	10.5046	−	3.60517i	0.431734	−	0.148172i
$593$	−11.7914	+	4.88416i	−0.484215	+	0.200569i	−0.611417	−	0.791308i	$-0.709400\pi$
$593$	−11.7914	+	4.88416i	−0.484215	+	0.200569i	0.127202	+	0.991877i	$0.459400\pi$
$594$	−17.6690	+	6.01436i	−0.724969	+	0.246772i
$595$	−1.21695	−	8.28585i	−0.0498900	−	0.339687i
$596$	−4.26452	−	5.53837i	−0.174682	−	0.226860i
$597$	−9.99758	+	4.14113i	−0.409174	+	0.169485i
$598$	−34.6583	+	45.2461i	−1.41728	+	1.85025i
$599$	4.83896	+	4.83896i	0.197714	+	0.197714i	0.799019	−	0.601305i	$-0.205352\pi$
$599$	4.83896	+	4.83896i	0.197714	+	0.197714i	−0.601305	+	0.799019i	$0.705352\pi$
$600$	2.47582	−	2.48831i	0.101075	−	0.101585i
$601$	−2.50016	+	3.74175i	−0.101984	+	0.152629i	−0.878952	−	0.476911i	$-0.841757\pi$
$601$	−2.50016	+	3.74175i	−0.101984	+	0.152629i	0.776968	+	0.629540i	$0.216757\pi$
$602$	4.67163	+	8.07585i	0.190402	+	0.329147i
$603$	−21.0980	−	8.73908i	−0.859177	−	0.355883i
$604$	−25.3954	+	6.85035i	−1.03332	+	0.278737i
$605$	−4.63998	−	23.3268i	−0.188642	−	0.948368i
$606$	−1.10103	−	0.294031i	−0.0447264	−	0.0119442i
$607$	3.79839	−	19.0958i	0.154172	−	0.775074i	−0.823889	−	0.566752i	$-0.808200\pi$
$607$	3.79839	−	19.0958i	0.154172	−	0.775074i	0.978060	−	0.208322i	$-0.0668002\pi$
$608$	0.993627	+	0.864042i	0.0402969	+	0.0350415i
$609$	−3.33526	+	2.22855i	−0.135152	+	0.0903055i
$610$	5.58836	+	6.36153i	0.226266	+	0.257571i
$611$			52.9882i			2.14367i
$612$	8.51225	−	21.5560i	0.344087	−	0.871351i
$613$			32.1150i			1.29711i	0.761166	+	0.648557i	$0.224627\pi$
$613$			32.1150i			1.29711i	−0.761166	+	0.648557i	$0.775373\pi$
$614$	−15.8394	+	13.9143i	−0.639227	+	0.561536i
$615$	1.05473	−	0.704749i	0.0425309	−	0.0284182i
$616$	−4.03941	−	20.0437i	−0.162752	−	0.807585i
$617$	4.61638	−	23.2081i	0.185848	−	0.934323i	−0.769456	−	0.638700i	$-0.779473\pi$
$617$	4.61638	−	23.2081i	0.185848	−	0.934323i	0.955305	−	0.295623i	$-0.0955273\pi$
$618$	−1.29325	+	4.84273i	−0.0520222	+	0.194803i
$619$	−1.42938	−	7.18596i	−0.0574515	−	0.288828i	0.941369	−	0.337378i	$-0.109540\pi$
$619$	−1.42938	−	7.18596i	−0.0574515	−	0.288828i	−0.998821	+	0.0485498i	$0.984540\pi$
$620$	−0.675457	+	0.182203i	−0.0271270	+	0.00731746i
$621$	−14.6191	−	6.05544i	−0.586645	−	0.242996i
$622$	23.3944	−	13.5329i	0.938029	−	0.542621i
$623$	−0.0787689	+	0.117886i	−0.00315581	+	0.00472300i
$624$	−10.0780	−	4.92794i	−0.403442	−	0.197276i
$625$	−1.85196	−	1.85196i	−0.0740784	−	0.0740784i
$626$	33.0635	+	25.3265i	1.32148	+	1.01225i
$627$	−0.488471	+	0.202331i	−0.0195077	+	0.00808033i
$628$	−11.9375	+	9.19181i	−0.476358	+	0.366793i
$629$	−7.67569	−	8.49327i	−0.306050	−	0.338649i
$630$	2.60144	+	7.64254i	0.103644	+	0.304486i
$631$	−16.3034	+	6.75311i	−0.649030	+	0.268837i	−0.682814	−	0.730592i	$-0.739244\pi$
$631$	−16.3034	+	6.75311i	−0.649030	+	0.268837i	0.0337841	+	0.999429i	$0.489244\pi$
$632$	−4.07367	+	0.0102515i	−0.162042	+	0.000407782i
$633$	−3.73428	+	3.73428i	−0.148424	+	0.148424i
$634$	3.58402	+	27.0480i	0.142340	+	1.07421i
$635$	9.82973	−	14.7112i	0.390081	−	0.583798i
$636$	−1.94146	+	2.22132i	−0.0769840	+	0.0880811i
$637$	12.5252	−	30.2384i	0.496265	−	1.19809i
$638$	3.16845	−	48.9706i	0.125440	−	1.93876i
$639$	8.49477	+	42.7061i	0.336048	+	1.68943i
$640$	−2.26144	−	16.4312i	−0.0893914	−	0.649501i
$641$	−0.478968	−	0.0952727i	−0.0189181	−	0.00376305i	0.185622	−	0.982621i	$-0.440570\pi$
$641$	−0.478968	−	0.0952727i	−0.0189181	−	0.00376305i	−0.204540	+	0.978858i	$0.565570\pi$
$642$	2.49509	−	5.07027i	0.0984735	−	0.200108i
$643$	−18.7046	+	12.4980i	−0.737637	+	0.492873i	−0.866741	−	0.498758i	$-0.833790\pi$
$643$	−18.7046	+	12.4980i	−0.737637	+	0.492873i	0.129105	+	0.991631i	$0.458790\pi$
$644$	8.64204	−	15.0266i	0.340544	−	0.592132i
$645$	−3.03882			−0.119654
$646$	0.415968	−	1.29198i	0.0163660	−	0.0508321i
$647$		−	11.0668i		−	0.435080i	−0.976051	−	0.217540i	$-0.930197\pi$
$647$		−	11.0668i		−	0.435080i	0.976051	−	0.217540i	$-0.0698032\pi$
$648$	−3.99366	+	20.3449i	−0.156886	+	0.799225i
$649$	−24.4468	−	36.5872i	−0.959619	−	1.43617i
$650$	11.4681	−	23.3044i	0.449818	−	0.914073i
$651$	0.0280765	−	0.141150i	0.00110041	−	0.00553212i
$652$	−1.82395	−	27.1306i	−0.0714314	−	1.06252i
$653$	20.3429	−	4.04646i	0.796081	−	0.158350i	0.219739	−	0.975559i	$-0.429480\pi$
$653$	20.3429	−	4.04646i	0.796081	−	0.158350i	0.576342	+	0.817208i	$0.304480\pi$
$654$	−3.76676	−	0.243713i	−0.147292	−	0.00952994i
$655$	10.2814	+	4.25871i	0.401729	+	0.166402i
$656$	−0.493367	+	7.93521i	−0.0192627	+	0.309818i
$657$	12.9032	+	8.62161i	0.503400	+	0.336361i
$658$	−2.11695	−	15.9762i	−0.0825272	−	0.622819i
$659$	15.1421	+	15.1421i	0.589852	+	0.589852i	0.937591	−	0.347739i	$-0.113051\pi$
$659$	15.1421	+	15.1421i	0.589852	+	0.589852i	−0.347739	+	0.937591i	$0.613051\pi$
$660$	6.30994	+	2.13014i	0.245614	+	0.0829154i
$661$	−8.38399	−	20.2407i	−0.326099	−	0.787273i	−0.998875	−	0.0474266i	$-0.984898\pi$
$661$	−8.38399	−	20.2407i	−0.326099	−	0.787273i	0.672775	−	0.739847i	$-0.265102\pi$
$662$	28.4882	−	9.69711i	1.10723	−	0.376889i
$663$	−0.583959	+	11.5488i	−0.0226791	+	0.448518i
$664$	−24.3997	−	16.2147i	−0.946890	−	0.629251i
$665$	0.180934	+	0.436812i	0.00701630	+	0.0169389i
$666$	8.76071	+	6.71066i	0.339471	+	0.260033i
$667$	29.4181	−	29.4181i	1.13907	−	1.13907i
$668$	31.9038	−	15.7998i	1.23439	−	0.611313i
$669$	3.25818	+	2.17705i	0.125968	+	0.0841695i
$670$	8.43528	+	14.5821i	0.325883	+	0.563355i
$671$	8.15477	−	19.6874i	0.314811	−	0.760022i
$672$	3.23545	+	1.08317i	0.124810	+	0.0417844i
$673$	−7.97726	+	1.58678i	−0.307501	+	0.0611657i	−0.346429	−	0.938076i	$-0.612606\pi$
$673$	−7.97726	+	1.58678i	−0.307501	+	0.0611657i	0.0389278	+	0.999242i	$0.487606\pi$
$674$	10.8404	−	40.5930i	0.417556	−	1.56358i
$675$	7.07247	+	1.40680i	0.272220	+	0.0541479i
$676$	−56.5335	−	7.34631i	−2.17437	−	0.282550i
$677$	−14.1028	−	21.1063i	−0.542013	−	0.811180i	0.454830	−	0.890578i	$-0.349700\pi$
$677$	−14.1028	−	21.1063i	−0.542013	−	0.811180i	−0.996843	+	0.0793984i	$0.974700\pi$
$678$	−5.03636	−	5.73316i	−0.193420	−	0.220181i
$679$	−11.5112			−0.441759
$680$	−14.6547	+	8.80526i	−0.561982	+	0.337666i
$681$	−3.59712			−0.137842
$682$	1.16197	+	1.32273i	0.0444941	+	0.0506500i
$683$	16.6165	+	24.8683i	0.635812	+	0.951560i	0.999797	+	0.0201553i	$0.00641607\pi$
$683$	16.6165	+	24.8683i	0.635812	+	0.951560i	−0.363985	+	0.931405i	$0.618584\pi$
$684$	−0.168605	+	1.29750i	−0.00644678	+	0.0496112i
$685$	15.9215	+	3.16698i	0.608328	+	0.121004i
$686$	−6.10713	+	22.8689i	−0.233171	+	0.873137i
$687$	−0.160042	+	0.0318343i	−0.00610597	+	0.00121455i
$688$	11.5438	−	15.1491i	0.440102	−	0.577554i
$689$	−8.35382	+	20.1679i	−0.318255	+	0.768336i
$690$	2.82715	+	4.88729i	0.107628	+	0.186056i
$691$	−26.5230	−	17.7221i	−1.00898	−	0.674180i	−0.0628699	−	0.998022i	$-0.520025\pi$
$691$	−26.5230	−	17.7221i	−1.00898	−	0.674180i	−0.946111	+	0.323842i	$0.895025\pi$
$692$	−10.5289	−	21.2605i	−0.400249	−	0.808204i
$693$	14.3663	−	14.3663i	0.545731	−	0.545731i
$694$	11.3175	+	8.66912i	0.429605	+	0.329075i
$695$	−6.36016	−	15.3548i	−0.241255	−	0.582440i
$696$	6.82018	+	4.53232i	0.258518	+	0.171797i
$697$	7.72011	−	2.74982i	0.292420	−	0.104157i
$698$	4.43685	−	1.51026i	0.167937	−	0.0571642i
$699$	1.16787	+	2.81948i	0.0441728	+	0.106643i
$700$	−2.52667	+	7.48457i	−0.0954993	+	0.282890i
$701$	−12.6422	−	12.6422i	−0.477491	−	0.477491i	0.426837	−	0.904328i	$-0.359628\pi$
$701$	−12.6422	−	12.6422i	−0.477491	−	0.477491i	−0.904328	+	0.426837i	$0.859628\pi$
$702$	−3.02727	−	22.8463i	−0.114257	−	0.862276i
$703$	0.537373	+	0.359061i	0.0202674	+	0.0135423i
$704$	−34.5891	+	23.3643i	−1.30362	+	0.880577i
$705$	4.84961	+	2.00877i	0.182647	+	0.0756548i
$706$	−24.1071	−	1.55975i	−0.907281	−	0.0587021i
$707$	2.51539	−	0.500342i	0.0946010	−	0.0188173i
$708$	7.32626	−	0.492533i	0.275338	−	0.0185105i
$709$	−7.47608	+	37.5848i	−0.280770	+	1.41153i	0.540671	+	0.841234i	$0.318170\pi$
$709$	−7.47608	+	37.5848i	−0.280770	+	1.41153i	−0.821441	+	0.570293i	$0.806830\pi$
$710$	14.1826	−	28.8204i	0.532263	−	1.08161i
$711$	−2.24886	−	3.36566i	−0.0843388	−	0.126222i
$712$	0.284016	+	0.0557517i	0.0106440	+	0.00208938i
$713$			1.49264i			0.0558996i
$714$	−0.285323	−	3.50536i	−0.0106779	−	0.131185i
$715$	49.2785			1.84291
$716$	−23.4018	−	13.4587i	−0.874566	−	0.502976i
$717$	−2.49239	+	1.66536i	−0.0930801	+	0.0621941i
$718$	−8.73225	+	17.7448i	−0.325885	+	0.662228i
$719$	35.5848	+	7.07826i	1.32709	+	0.263975i	0.807210	−	0.590264i	$-0.200976\pi$
$719$	35.5848	+	7.07826i	1.32709	+	0.263975i	0.519880	+	0.854239i	$0.325976\pi$
$720$	12.3545	−	10.9081i	0.460424	−	0.406522i
$721$	−2.20068	−	11.0636i	−0.0819576	−	0.412029i
$722$	1.72995	−	26.7375i	0.0643819	−	0.995068i
$723$	−0.995739	+	2.40393i	−0.0370319	+	0.0894030i
$724$	18.8183	+	16.4474i	0.699375	+	0.611263i
$725$	−10.5332	+	15.7640i	−0.391193	+	0.585462i
$726$	−1.31199	−	9.90140i	−0.0486927	−	0.367475i
$727$	−5.90074	+	5.90074i	−0.218846	+	0.218846i	−0.808012	−	0.589166i	$-0.799456\pi$
$727$	−5.90074	+	5.90074i	−0.218846	+	0.218846i	0.589166	+	0.808012i	$0.299456\pi$
$728$	25.2463	−	0.0635330i	0.935691	−	0.00235469i
$729$	−15.9815	+	6.61973i	−0.591906	+	0.245175i
$730$	−3.68887	−	10.8372i	−0.136531	−	0.401103i
$731$	−19.0370	−	4.79755i	−0.704111	−	0.177444i
$732$	2.16943	+	2.81746i	0.0801845	+	0.104136i
$733$	−12.4059	+	5.13868i	−0.458221	+	0.189801i	−0.599840	−	0.800120i	$-0.704769\pi$
$733$	−12.4059	+	5.13868i	−0.458221	+	0.189801i	0.141619	+	0.989921i	$0.454769\pi$
$734$	24.7170	+	18.9331i	0.912323	+	0.698835i
$735$	−2.29267	−	2.29267i	−0.0845663	−	0.0845663i
$736$	−35.1037	−	4.47179i	−1.29394	−	0.164832i
$737$	23.5535	−	35.2502i	0.867603	−	1.29846i
$738$	−6.83837	+	3.95579i	−0.251724	+	0.145615i
$739$	−25.3724	−	10.5096i	−0.933338	−	0.386601i	−0.136394	−	0.990655i	$-0.543551\pi$
$739$	−25.3724	−	10.5096i	−0.933338	−	0.386601i	−0.796944	+	0.604053i	$0.793551\pi$
$740$	−2.12018	−	7.85986i	−0.0779394	−	0.288934i
$741$	−0.127361	−	0.640285i	−0.00467871	−	0.0235215i
$742$	1.71299	−	6.41449i	0.0628859	−	0.235483i
$743$	−1.01654	+	5.11049i	−0.0372932	+	0.187486i	−0.994942	−	0.100454i	$-0.967970\pi$
$743$	−1.01654	+	5.11049i	−0.0372932	+	0.187486i	0.957648	+	0.287940i	$0.0929704\pi$
$744$	−0.288005	+	0.0580417i	−0.0105588	+	0.00212791i
$745$	−4.26021	+	2.84658i	−0.156082	+	0.104291i
$746$	10.7371	−	9.43210i	0.393112	−	0.345334i
$747$		−	29.1102i		−	1.06509i
$748$	36.1663	+	23.3063i	1.32237	+	0.852163i
$749$			12.7172i			0.464678i
$750$	−4.67645	−	5.32345i	−0.170760	−	0.194385i
$751$	−9.56355	+	6.39016i	−0.348979	+	0.233180i	−0.717688	−	0.696364i	$-0.754800\pi$
$751$	−9.56355	+	6.39016i	−0.348979	+	0.233180i	0.368709	+	0.929545i	$0.379800\pi$
$752$	−28.4366	+	16.5454i	−1.03698	+	0.603347i
$753$	0.802027	−	4.03206i	0.0292275	−	0.146937i
$754$	58.5410	+	15.6334i	2.13194	+	0.569334i
$755$	3.76142	+	18.9099i	0.136892	+	0.688203i
$756$	1.82548	+	6.76734i	0.0663919	+	0.246126i
$757$	10.5708	+	4.37858i	0.384203	+	0.159142i	0.566421	−	0.824116i	$-0.308328\pi$
$757$	10.5708	+	4.37858i	0.384203	+	0.159142i	−0.182218	+	0.983258i	$0.558328\pi$
$758$	−11.6670	−	20.1687i	−0.423764	−	0.732562i
$759$	7.89411	−	11.8144i	0.286538	−	0.428835i
$760$	0.680779	−	0.684215i	0.0246945	−	0.0248191i
$761$	33.7647	+	33.7647i	1.22397	+	1.22397i	0.966208	+	0.257762i	$0.0829850\pi$
$761$	33.7647	+	33.7647i	1.22397	+	1.22397i	0.257762	+	0.966208i	$0.417015\pi$
$762$	4.51825	−	5.89853i	0.163679	−	0.213681i
$763$	7.84807	−	3.25078i	0.284119	−	0.117686i
$764$	36.2862	−	27.9402i	1.31279	−	1.01084i
$765$	−15.3467	−	7.28538i	−0.554860	−	0.263403i
$766$	−44.8860	+	15.2788i	−1.62180	+	0.552044i
$767$	50.1965	−	20.7921i	1.81249	−	0.750759i
$768$	−0.502184	−	6.94718i	−0.0181210	−	0.250685i
$769$	22.9173	−	22.9173i	0.826419	−	0.826419i	−0.160601	−	0.987019i	$-0.551343\pi$
$769$	22.9173	−	22.9173i	0.826419	−	0.826419i	0.987019	+	0.160601i	$0.0513432\pi$
$770$	−14.8578	+	1.96874i	−0.535437	+	0.0709486i
$771$	−4.48835	+	6.71730i	−0.161644	+	0.241918i
$772$	−2.73627	−	2.39154i	−0.0984806	−	0.0860733i
$773$	−12.7753	+	30.8424i	−0.459497	+	1.10932i	0.509104	+	0.860705i	$0.329977\pi$
$773$	−12.7753	+	30.8424i	−0.459497	+	1.10932i	−0.968601	+	0.248619i	$0.920023\pi$
$774$	18.8858	+	1.22193i	0.678836	+	0.0439214i
$775$	−0.132703	−	0.667144i	−0.00476684	−	0.0239645i
$776$	9.04746	+	21.6880i	0.324785	+	0.778552i
$777$	1.64247	+	0.326708i	0.0589234	+	0.0117206i
$778$	9.66093	+	4.75418i	0.346361	+	0.170445i
$779$	−0.384694	+	0.257044i	−0.0137831	+	0.00920956i
$780$	−4.09961	+	7.12832i	−0.146790	+	0.255235i
$781$	−80.8361			−2.89254
$782$	9.99515	+	35.0803i	0.357426	+	1.25447i
$783$			16.8224i			0.601185i
$784$	20.1387	−	2.72008i	0.719238	−	0.0971457i
$785$	6.13557	+	9.18253i	0.218988	+	0.327738i
$786$	4.19319	+	2.06348i	0.149566	+	0.0736019i
$787$	−10.0277	+	50.4125i	−0.357448	+	1.79701i	0.214504	+	0.976723i	$0.431187\pi$
$787$	−10.0277	+	50.4125i	−0.357448	+	1.79701i	−0.571951	+	0.820288i	$0.693813\pi$
$788$	−28.3166	+	1.90368i	−1.00874	+	0.0678160i
$789$	2.55464	−	0.508150i	0.0909477	−	0.0180906i
$790$	−0.192797	+	2.97982i	−0.00685942	+	0.106017i
$791$	15.8663	+	6.57205i	0.564142	+	0.233675i
$792$	−38.3587	−	15.7757i	−1.36302	−	0.560566i
$793$	21.8773	+	14.6180i	0.776887	+	0.519100i
$794$	−44.8853	+	5.94757i	−1.59292	+	0.211071i
$795$	1.52912	+	1.52912i	0.0542325	+	0.0542325i
$796$	−47.1036	−	15.9014i	−1.66954	−	0.563612i
$797$	14.8630	+	35.8824i	0.526474	+	1.27102i	0.933819	+	0.357746i	$0.116454\pi$
$797$	14.8630	+	35.8824i	0.526474	+	1.27102i	−0.407345	+	0.913274i	$0.633546\pi$
$798$	0.0639802	+	0.187962i	0.00226488	+	0.00665377i
$799$	27.2096	+	20.2405i	0.962605	+	0.716058i
$800$	16.0874	−	1.12221i	0.568775	−	0.0396760i
$801$	0.110060	+	0.265708i	0.00388878	+	0.00938834i
$802$	6.62176	−	8.64465i	0.233823	−	0.305253i
$803$	−20.3715	+	20.3715i	−0.718896	+	0.718896i
$804$	3.13960	+	6.33965i	0.110725	+	0.223582i
$805$	−10.5649	−	7.05926i	−0.372365	−	0.248806i
$806$	−1.88175	+	1.08854i	−0.0662819	+	0.0383421i
$807$	−3.70263	+	8.93894i	−0.130339	+	0.314666i
$808$	−2.91971	−	4.34593i	−0.102715	−	0.152889i
$809$	11.2171	−	2.23122i	0.394372	−	0.0784454i	0.00607901	−	0.999982i	$-0.498065\pi$
$809$	11.2171	−	2.23122i	0.394372	−	0.0784454i	0.388293	+	0.921536i	$0.373065\pi$
$810$	14.6831	+	3.92112i	0.515911	+	0.137774i
$811$	48.6500	+	9.67709i	1.70833	+	0.339809i	0.950046	−	0.312111i	$-0.101036\pi$
$811$	48.6500	+	9.67709i	1.70833	+	0.339809i	0.758288	+	0.651920i	$0.226036\pi$
$812$	−18.2750	−	2.37477i	−0.641327	−	0.0833380i
$813$	−7.16617	−	10.7249i	−0.251329	−	0.376140i
$814$	−15.3918	+	13.5211i	−0.539481	+	0.473913i
$815$	−19.9319			−0.698184
$816$	−6.38012	+	3.29268i	−0.223349	+	0.115267i
$817$	1.10835			0.0387764
$818$	−6.73327	+	5.91491i	−0.235423	+	0.206810i
$819$	13.9372	+	20.8585i	0.487005	+	0.728854i
$820$	5.77923	+	0.750988i	0.201819	+	0.0262256i
$821$	−23.7984	−	4.73379i	−0.830569	−	0.165211i	−0.238546	−	0.971131i	$-0.576671\pi$
$821$	−23.7984	−	4.73379i	−0.830569	−	0.165211i	−0.592023	+	0.805921i	$0.701671\pi$
$822$	6.58636	+	1.75889i	0.229726	+	0.0613483i
$823$	−4.59543	+	0.914089i	−0.160187	+	0.0318631i	−0.274532	−	0.961578i	$-0.588523\pi$
$823$	−4.59543	+	0.914089i	−0.160187	+	0.0318631i	0.114345	+	0.993441i	$0.463523\pi$
$824$	−19.1149	+	12.8419i	−0.665901	+	0.447369i
$825$	−2.47797	+	5.98234i	−0.0862717	+	0.208278i
$826$	−14.3039	+	8.27436i	−0.497696	+	0.287902i
$827$	−1.19192	−	0.796414i	−0.0414470	−	0.0276940i	0.534674	−	0.845058i	$-0.320434\pi$
$827$	−1.19192	−	0.796414i	−0.0414470	−	0.0276940i	−0.576121	+	0.817364i	$0.695434\pi$
$828$	−15.6050	−	31.5105i	−0.542313	−	1.09507i
$829$	18.8145	−	18.8145i	0.653455	−	0.653455i	−0.300368	−	0.953823i	$-0.597110\pi$
$829$	18.8145	−	18.8145i	0.653455	−	0.653455i	0.953823	+	0.300368i	$0.0971096\pi$
$830$	−13.0584	+	17.0477i	−0.453264	+	0.591733i
$831$	3.90087	+	9.41754i	0.135320	+	0.326691i
$832$	−19.9626	−	47.5161i	−0.692078	−	1.64732i
$833$	−10.7431	−	17.9822i	−0.372227	−	0.623047i
$834$	−2.24903	−	6.60721i	−0.0778774	−	0.228789i
$835$	−9.98667	−	24.1100i	−0.345603	−	0.834360i
$836$	−2.30143	−	0.776927i	−0.0795967	−	0.0268706i
$837$	−0.426774	−	0.426774i	−0.0147515	−	0.0147515i
$838$	−2.91547	+	0.386317i	−0.100713	+	0.0133451i
$839$	−13.8513	−	9.25515i	−0.478200	−	0.319523i	0.293004	−	0.956111i	$-0.405345\pi$
$839$	−13.8513	−	9.25515i	−0.478200	−	0.319523i	−0.771204	+	0.636588i	$0.780345\pi$
$840$	0.951270	−	2.31302i	0.0328219	−	0.0798066i
$841$	−14.0703	−	5.82811i	−0.485183	−	0.200969i
$842$	−2.39226	+	36.9741i	−0.0824428	+	1.27421i
$843$	−2.29650	+	0.456803i	−0.0790958	+	0.0157331i
$844$	−24.2076	+	1.62744i	−0.833261	+	0.0560189i
$845$	−8.15244	+	40.9851i	−0.280452	+	1.40993i
$846$	−29.3318	−	14.4343i	−1.00845	−	0.496260i
$847$	12.4878	+	18.6894i	0.429087	+	0.642175i
$848$	−13.4317	+	1.81419i	−0.461248	+	0.0622996i
$849$		−	7.99988i		−	0.274555i
$850$	−7.58622	−	14.7908i	−0.260205	−	0.507319i
$851$	−17.3688			−0.595396
$852$	6.72497	−	11.6932i	0.230394	−	0.400604i
$853$	11.0802	−	7.40352i	0.379377	−	0.253492i	−0.351231	−	0.936289i	$-0.614237\pi$
$853$	11.0802	−	7.40352i	0.379377	−	0.253492i	0.730608	+	0.682797i	$0.239237\pi$
$854$	−7.18016	−	3.53338i	−0.245700	−	0.120910i
$855$	0.940649	+	0.187107i	0.0321695	+	0.00639891i
$856$	23.9603	−	9.99539i	0.818945	−	0.341635i
$857$	−1.53070	−	7.69537i	−0.0522878	−	0.262869i	0.945795	−	0.324765i	$-0.105285\pi$
$857$	−1.53070	−	7.69537i	−0.0522878	−	0.262869i	−0.998083	+	0.0618962i	$0.980285\pi$
$858$	20.6512	+	1.33616i	0.705021	+	0.0456156i
$859$	−18.0882	+	43.6689i	−0.617163	+	1.48996i	0.237822	+	0.971309i	$0.423567\pi$
$859$	−18.0882	+	43.6689i	−0.617163	+	1.48996i	−0.854984	+	0.518654i	$0.826433\pi$
$860$	−10.5118	−	9.18748i	−0.358451	−	0.313291i
$861$	−0.666043	+	0.996804i	−0.0226987	+	0.0339710i
$862$	23.4363	−	3.10545i	0.798243	−	0.105772i
$863$	−13.6650	+	13.6650i	−0.465164	+	0.465164i	−0.900344	−	0.435180i	$-0.856685\pi$
$863$	−13.6650	+	13.6650i	−0.465164	+	0.465164i	0.435180	+	0.900344i	$0.356685\pi$
$864$	11.3154	−	8.75827i	0.384958	−	0.297962i
$865$	−16.0668	+	6.65507i	−0.546286	+	0.226279i
$866$	14.7508	−	5.02104i	0.501254	−	0.170622i
$867$	5.70728	+	4.71130i	0.193829	+	0.160004i
$868$	0.523871	−	0.403379i	0.0177813	−	0.0136916i
$869$	6.94270	−	2.87576i	0.235515	−	0.0975534i
$870$	3.65009	−	4.76516i	0.123749	−	0.161554i
$871$	37.0149	+	37.0149i	1.25420	+	1.25420i
$872$	−12.2931	−	12.2313i	−0.416296	−	0.414206i
$873$	−12.9728	+	19.4151i	−0.439062	+	0.657103i
$874$	−1.03115	−	1.78255i	−0.0348791	−	0.0602955i
$875$	14.7325	+	6.10239i	0.498049	+	0.206298i
$876$	−1.25206	−	4.64158i	−0.0423031	−	0.156824i
$877$	1.98169	+	9.96262i	0.0669168	+	0.336414i	0.999712	−	0.0239930i	$-0.00763794\pi$
$877$	1.98169	+	9.96262i	0.0669168	+	0.336414i	−0.932795	+	0.360407i	$0.882638\pi$
$878$	39.7378	+	10.6120i	1.34108	+	0.358137i
$879$	−0.289991	+	1.45788i	−0.00978116	+	0.0491732i
$880$	15.3870	+	26.4458i	0.518697	+	0.891487i
$881$	−24.2499	+	16.2033i	−0.817000	+	0.545902i	−0.892397	−	0.451252i	$-0.850978\pi$
$881$	−24.2499	+	16.2033i	−0.817000	+	0.545902i	0.0753971	+	0.997154i	$0.475978\pi$
$882$	13.3267	+	15.1704i	0.448732	+	0.510816i
$883$			26.6746i			0.897672i	0.893614	+	0.448836i	$0.148161\pi$
$883$			26.6746i			0.897672i	−0.893614	+	0.448836i	$0.851839\pi$
$884$	−36.9363	+	38.1839i	−1.24230	+	1.28426i
$885$		−	5.38234i		−	0.180925i
$886$	12.5293	−	11.0065i	0.420929	−	0.369770i
$887$	39.9954	−	26.7241i	1.34292	−	0.897307i	0.343787	−	0.939048i	$-0.388290\pi$
$887$	39.9954	−	26.7241i	1.34292	−	0.897307i	0.999128	+	0.0417406i	$0.0132903\pi$
$888$	−0.675393	−	3.35133i	−0.0226647	−	0.112463i
$889$	−3.26217	+	16.4000i	−0.109410	+	0.550039i
$890$	0.0547391	−	0.204977i	0.00183486	−	0.00687083i
$891$	−7.46153	−	37.5117i	−0.249971	−	1.25669i
$892$	4.68862	+	17.3815i	0.156987	+	0.581975i
$893$	−1.76880	−	0.732662i	−0.0591908	−	0.0245176i
$894$	−1.86252	+	1.07741i	−0.0622919	+	0.0360339i
$895$	−10.9938	+	16.4534i	−0.367482	+	0.549975i
$896$	7.91716	+	13.5288i	0.264494	+	0.451967i
$897$	12.4058	+	12.4058i	0.414218	+	0.414218i
$898$	22.9103	+	17.5492i	0.764526	+	0.585623i
$899$	1.46606	−	0.607263i	0.0488959	−	0.0202533i
$900$	9.77623	+	12.6965i	0.325874	+	0.423216i
$901$	7.16526	+	11.9935i	0.238709	+	0.399561i
$902$	−4.72599	−	13.8840i	−0.157358	−	0.462288i
$903$	2.65331	−	1.09904i	0.0882967	−	0.0365737i
$904$	−0.0882263	−	35.0588i	−0.00293436	−	1.16604i
$905$	12.9542	−	12.9542i	0.430613	−	0.430613i
$906$	1.06357	+	8.02661i	0.0353349	+	0.266666i
$907$	−26.4752	+	39.6229i	−0.879095	+	1.31566i	0.0689827	+	0.997618i	$0.478025\pi$
$907$	−26.4752	+	39.6229i	−0.879095	+	1.31566i	−0.948077	+	0.318040i	$0.896975\pi$
$908$	−12.4431	−	10.8754i	−0.412939	−	0.360914i
$909$	1.99088	−	4.80641i	0.0660333	−	0.159419i
$910$	1.19485	−	18.4672i	0.0396089	−	0.612183i
$911$	−5.18696	−	26.0766i	−0.171852	−	0.863956i	−0.966457	−	0.256830i	$-0.917322\pi$
$911$	−5.18696	−	26.0766i	−0.171852	−	0.863956i	0.794605	−	0.607127i	$-0.207678\pi$
$912$	0.303847	−	0.268276i	0.0100614	−	0.00888350i
$913$	53.0040	+	10.5432i	1.75418	+	0.348928i
$914$	7.93171	−	16.1180i	0.262358	−	0.533136i
$915$	2.16724	−	1.44810i	0.0716468	−	0.0478728i
$916$	−0.649860	−	0.373745i	−0.0214720	−	0.0123489i
$917$	−10.5174			−0.347314
$918$	−12.8880	−	7.17235i	−0.425366	−	0.236723i
$919$		−	18.7989i		−	0.620118i	−0.950717	−	0.310059i	$-0.899651\pi$
$919$		−	18.7989i		−	0.620118i	0.950717	−	0.310059i	$-0.100349\pi$
$920$	−4.99647	+	25.4535i	−0.164729	+	0.839178i
$921$	3.60560	+	5.39616i	0.118809	+	0.177810i
$922$	17.2002	−	34.9524i	0.566458	−	1.15110i
$923$	19.4723	−	97.8939i	0.640939	−	3.22222i
$924$	−6.27985	+	0.422185i	−0.206592	+	0.0138889i
$925$	7.76311	−	1.54418i	0.255250	−	0.0507723i
$926$	−32.4501	−	2.09955i	−1.06638	−	0.0689956i
$927$	−21.1403	−	8.75659i	−0.694338	−	0.287604i
$928$	9.88938	+	36.2980i	0.324635	+	1.19154i
$929$	−41.9868	−	28.0547i	−1.37754	−	0.920444i	−0.377557	−	0.925986i	$-0.623236\pi$
$929$	−41.9868	−	28.0547i	−1.37754	−	0.920444i	−0.999985	+	0.00554253i	$0.998236\pi$
$930$	0.0282886	+	0.213489i	0.000927619	+	0.00700058i
$931$	0.836207	+	0.836207i	0.0274056	+	0.0274056i
$932$	−4.48447	+	13.2840i	−0.146894	+	0.435131i
$933$	−3.18373	−	7.68620i	−0.104231	−	0.251635i
$934$	31.7339	−	10.8019i	1.03836	−	0.353449i
$935$	18.8235	−	25.3046i	0.615595	−	0.827550i
$936$	28.3447	−	42.6529i	0.926477	−	1.39415i
$937$	−11.0148	−	26.5922i	−0.359839	−	0.868728i	−0.995322	−	0.0966132i	$-0.969199\pi$
$937$	−11.0148	−	26.5922i	−0.359839	−	0.868728i	0.635483	−	0.772115i	$-0.280801\pi$
$938$	−12.6390	−	9.68142i	−0.412678	−	0.316110i
$939$	9.06552	−	9.06552i	0.295842	−	0.295842i
$940$	10.7024	+	21.6109i	0.349074	+	0.704869i
$941$	2.23235	+	1.49161i	0.0727725	+	0.0486250i	0.591424	−	0.806361i	$-0.298566\pi$
$941$	2.23235	+	1.49161i	0.0727725	+	0.0486250i	−0.518652	+	0.854986i	$0.673566\pi$
$942$	2.32226	+	4.01450i	0.0756635	+	0.130799i
$943$	4.75827	−	11.4875i	0.154951	−	0.374084i
$944$	26.8320	+	20.4462i	0.873306	+	0.665467i
$945$	5.03911	−	1.00234i	0.163922	−	0.0326061i
$946$	−9.06496	+	33.9448i	−0.294727	+	1.10364i
$947$	47.8644	+	9.52082i	1.55538	+	0.309385i	0.896563	−	0.442915i	$-0.146056\pi$
$947$	47.8644	+	9.52082i	1.55538	+	0.309385i	0.658820	+	0.752300i	$0.271056\pi$
$948$	−0.161592	+	1.24353i	−0.00524825	+	0.0403879i
$949$	−19.7631	−	29.5775i	−0.641536	−	0.960127i
$950$	0.619357	+	0.705047i	0.0200946	+	0.0228747i
$951$	8.39886			0.272352
$952$	9.61102	−	12.9883i	0.311495	−	0.420954i
$953$	20.6569			0.669144			0.334572	−	0.942370i	$-0.391408\pi$
$953$	20.6569			0.669144			0.334572	+	0.942370i	$0.391408\pi$
$954$	−8.88839	−	10.1181i	−0.287772	−	0.327587i
$955$	−18.6502	−	27.9120i	−0.603506	−	0.903211i
$956$	−13.6566	−	1.77463i	−0.441687	−	0.0573955i
$957$	−14.8157	−	2.94702i	−0.478923	−	0.0952636i
$958$	−5.48676	+	20.5458i	−0.177269	+	0.663804i
$959$	−15.0470	+	2.99304i	−0.485894	+	0.0966503i
$960$	−5.10557	+	0.0256967i	−0.164782	+	0.000829358i
$961$	11.8414	−	28.5877i	0.381981	−	0.922183i
$962$	−12.6666	−	21.8967i	−0.408387	−	0.705979i
$963$	21.4493	+	14.3320i	0.691195	+	0.461842i
$964$	−10.7124	+	5.30513i	−0.345023	+	0.170867i
$965$	−1.88361	+	1.88361i	−0.0606355	+	0.0606355i
$966$	−4.23606	−	3.24480i	−0.136293	−	0.104400i
$967$	9.50144	+	22.9385i	0.305546	+	0.737652i	0.999839	+	0.0179600i	$0.00571716\pi$
$967$	9.50144	+	22.9385i	0.305546	+	0.737652i	−0.694293	+	0.719692i	$0.744283\pi$
$968$	25.3971	−	38.2174i	0.816295	−	1.22835i
$969$	−0.377438	−	0.179177i	−0.0121250	−	0.00575601i
$970$	16.3065	−	5.55058i	0.523571	−	0.178218i
$971$	−2.15902	−	5.21234i	−0.0692863	−	0.167272i	0.885443	−	0.464748i	$-0.153855\pi$
$971$	−2.15902	−	5.21234i	−0.0692863	−	0.167272i	−0.954729	+	0.297476i	$0.903855\pi$
$972$	20.4266	+	6.89570i	0.655183	+	0.221180i
$973$	11.1066	+	11.1066i	0.356061	+	0.356061i
$974$	0.174032	+	1.31339i	0.00557634	+	0.0420837i
$975$	−6.64781	−	4.44192i	−0.212900	−	0.142255i
$976$	−1.01376	+	16.3051i	−0.0324497	+	0.521913i
$977$	−35.5322	−	14.7179i	−1.13678	−	0.470868i	−0.266697	−	0.963781i	$-0.585932\pi$
$977$	−35.5322	−	14.7179i	−1.13678	−	0.470868i	−0.870079	+	0.492913i	$0.835932\pi$
$978$	−8.35289	−	0.540441i	−0.267096	−	0.0172814i
$979$	−0.523665	+	0.104163i	−0.0167364	+	0.00332908i
$980$	−0.999172	−	14.8623i	−0.0319174	−	0.474760i
$981$	3.36169	−	16.9003i	0.107330	−	0.539586i
$982$	−8.03008	+	16.3179i	−0.256250	+	0.520725i
$983$	−19.3105	−	28.9003i	−0.615910	−	0.921775i	0.384088	−	0.923296i	$-0.374516\pi$
$983$	−19.3105	−	28.9003i	−0.615910	−	0.921775i	−0.999999	+	0.00152129i	$0.999516\pi$
$984$	2.40155	+	0.471418i	0.0765585	+	0.0150283i
$985$			20.8032i			0.662845i
$986$	30.3894	−	24.0893i	0.967795	−	0.767158i
$987$	−4.96089			−0.157907
$988$	1.49525	−	2.59992i	0.0475704	−	0.0827145i
$989$	−24.7666	+	16.5485i	−0.787531	+	0.526211i
$990$	−13.4237	+	27.2783i	−0.426634	+	0.866961i
$991$	−15.9019	−	3.16309i	−0.505141	−	0.100479i	−0.0640599	−	0.997946i	$-0.520405\pi$
$991$	−15.9019	−	3.16309i	−0.505141	−	0.100479i	−0.441081	+	0.897467i	$0.645405\pi$
$992$	−1.17174	−	0.669970i	−0.0372029	−	0.0212716i
$993$	−1.80722	−	9.08553i	−0.0573505	−	0.288321i
$994$	−1.96002	+	30.2935i	−0.0621682	+	0.960852i
$995$	−13.9457	+	33.6678i	−0.442107	+	1.06734i
$996$	−5.93465	+	6.79012i	−0.188047	+	0.215153i
$997$	26.1663	−	39.1606i	0.828694	−	1.24023i	−0.139548	−	0.990215i	$-0.544565\pi$
$997$	26.1663	−	39.1606i	0.828694	−	1.24023i	0.968242	−	0.250014i	$-0.0804351\pi$
$998$	0.00489607	+	0.0369498i	0.000154982	+	0.00116963i
$999$	4.96609	−	4.96609i	0.157120	−	0.157120i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.s.c.107.11	yes	112
4.3	odd	2		544.2.cc.c.175.5		112
8.3	odd	2	inner	136.2.s.c.107.1	yes	112
8.5	even	2		544.2.cc.c.175.6		112
17.7	odd	16	inner	136.2.s.c.75.1	✓	112
68.7	even	16		544.2.cc.c.143.6		112
136.75	even	16	inner	136.2.s.c.75.11	yes	112
136.109	odd	16		544.2.cc.c.143.5		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.s.c.75.1	✓	112	17.7	odd	16	inner
136.2.s.c.75.11	yes	112	136.75	even	16	inner
136.2.s.c.107.1	yes	112	8.3	odd	2	inner
136.2.s.c.107.11	yes	112	1.1	even	1	trivial
544.2.cc.c.143.5		112	136.109	odd	16
544.2.cc.c.143.6		112	68.7	even	16
544.2.cc.c.175.5		112	4.3	odd	2
544.2.cc.c.175.6		112	8.5	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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.s (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.06248 - 0.933347i) q^{2} +(-0.241857 - 0.361965i) q^{3} +(0.257725 - 1.98332i) q^{4} +(-1.43785 - 0.286006i) q^{5} +(-0.594807 - 0.158843i) q^{6} +(1.35888 - 0.270298i) q^{7} +(-1.57730 - 2.34779i) q^{8} +(1.07553 - 2.59655i) q^{9} +O(q^{10})\)	\(q+(1.06248 - 0.933347i) q^{2} +(-0.241857 - 0.361965i) q^{3} +(0.257725 - 1.98332i) q^{4} +(-1.43785 - 0.286006i) q^{5} +(-0.594807 - 0.158843i) q^{6} +(1.35888 - 0.270298i) q^{7} +(-1.57730 - 2.34779i) q^{8} +(1.07553 - 2.59655i) q^{9} +(-1.79463 + 1.03814i) q^{10} +(4.33828 + 2.89874i) q^{11} +(-0.780227 + 0.386394i) q^{12} +(-4.55546 + 4.55546i) q^{13} +(1.19150 - 1.55549i) q^{14} +(0.244230 + 0.589624i) q^{15} +(-3.86716 - 1.02231i) q^{16} +(0.599136 + 4.07934i) q^{17} +(-1.28076 - 3.76262i) q^{18} +(-0.0890783 - 0.215054i) q^{19} +(-0.937814 + 2.77801i) q^{20} +(-0.426494 - 0.426494i) q^{21} +(7.31487 - 0.969263i) q^{22} +(5.20139 + 3.47546i) q^{23} +(-0.468335 + 1.13876i) q^{24} +(-2.63378 - 1.09095i) q^{25} +(-0.588256 + 9.09191i) q^{26} +(-2.48088 + 0.493478i) q^{27} +(-0.185871 - 2.76476i) q^{28} +(1.29745 - 6.52275i) q^{29} +(0.809813 + 0.398512i) q^{30} +(0.132562 + 0.198393i) q^{31} +(-5.06294 + 2.52322i) q^{32} -2.27139i q^{33} +(4.44401 + 3.77502i) q^{34} -2.03117 q^{35} +(-4.87261 - 2.80232i) q^{36} +(-2.30857 + 1.54254i) q^{37} +(-0.295364 - 0.145350i) q^{38} +(2.75069 + 0.547146i) q^{39} +(1.59644 + 3.82689i) q^{40} +(-0.387768 - 1.94944i) q^{41} +(-0.851207 - 0.0550740i) q^{42} +(-1.82216 + 4.39907i) q^{43} +(6.86724 - 7.85713i) q^{44} +(-2.28908 + 3.42584i) q^{45} +(8.77019 - 1.16210i) q^{46} +(5.81590 - 5.81590i) q^{47} +(0.565260 + 1.64703i) q^{48} +(-4.69366 + 1.94418i) q^{49} +(-3.81658 + 1.29912i) q^{50} +(1.33167 - 1.20348i) q^{51} +(7.86090 + 10.2090i) q^{52} +(3.13050 - 1.29670i) q^{53} +(-2.17530 + 2.83984i) q^{54} +(-5.40873 - 5.40873i) q^{55} +(-2.77797 - 2.76402i) q^{56} +(-0.0562978 + 0.0842556i) q^{57} +(-4.70947 - 8.14126i) q^{58} +(-7.79160 - 3.22739i) q^{59} +(1.23236 - 0.332427i) q^{60} +(-0.796777 - 4.00567i) q^{61} +(0.326014 + 0.0870622i) q^{62} +(0.759669 - 3.81912i) q^{63} +(-3.02423 + 7.40635i) q^{64} +(7.85296 - 5.24718i) q^{65} +(-2.11999 - 2.41330i) q^{66} -8.12540i q^{67} +(8.24507 - 0.136931i) q^{68} -2.72329i q^{69} +(-2.15808 + 1.89579i) q^{70} +(-12.8819 + 8.60743i) q^{71} +(-7.79259 + 1.57044i) q^{72} +(-1.07722 + 5.41554i) q^{73} +(-1.01309 + 3.79362i) q^{74} +(0.242114 + 1.21719i) q^{75} +(-0.449480 + 0.121246i) q^{76} +(6.67873 + 2.76642i) q^{77} +(3.43322 - 1.98601i) q^{78} +(0.800167 - 1.19753i) q^{79} +(5.26800 + 2.57595i) q^{80} +(-5.18330 - 5.18330i) q^{81} +(-2.23150 - 1.70932i) q^{82} +(9.56928 - 3.96373i) q^{83} +(-0.955793 + 0.735957i) q^{84} +(0.305250 - 6.03684i) q^{85} +(2.16986 + 6.37463i) q^{86} +(-2.67480 + 1.10794i) q^{87} +(-0.0371377 - 14.7576i) q^{88} +(-0.0723591 + 0.0723591i) q^{89} +(0.765406 + 5.77639i) q^{90} +(-4.95899 + 7.42166i) q^{91} +(8.23350 - 9.42034i) q^{92} +(0.0397503 - 0.0959657i) q^{93} +(0.751019 - 11.6075i) q^{94} +(0.0665745 + 0.334693i) q^{95} +(2.13783 + 1.22235i) q^{96} +(-8.14867 - 1.62087i) q^{97} +(-3.17232 + 6.44646i) q^{98} +(12.1927 - 8.14688i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 112 q - 8 q^{2} - 16 q^{3} - 8 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} - 8 q^{10} - 16 q^{11} + 24 q^{12} - 8 q^{14} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 8 q^{20} - 8 q^{22} - 56 q^{24} - 16 q^{25} - 40 q^{26} + 32 q^{27} + 40 q^{28} - 72 q^{30} + 32 q^{32} - 72 q^{34} - 32 q^{35} + 56 q^{36} + 48 q^{38} + 56 q^{40} - 16 q^{41} - 56 q^{42} - 96 q^{43} + 24 q^{44} - 24 q^{46} + 16 q^{48} - 16 q^{49} - 16 q^{51} - 16 q^{52} - 24 q^{54} + 32 q^{56} + 32 q^{57} + 48 q^{58} - 16 q^{59} + 96 q^{60} + 48 q^{62} + 40 q^{64} + 64 q^{65} - 16 q^{66} + 80 q^{68} + 64 q^{70} + 96 q^{72} - 96 q^{73} + 40 q^{74} - 16 q^{75} + 48 q^{76} + 96 q^{78} + 8 q^{80} - 96 q^{81} + 32 q^{82} + 128 q^{83} + 64 q^{86} - 72 q^{88} - 16 q^{89} + 152 q^{90} - 16 q^{91} - 120 q^{92} + 88 q^{94} - 160 q^{96} - 16 q^{97} + 128 q^{98} + 48 q^{99}+O(q^{100}) \) 112 * q - 8 * q^2 - 16 * q^3 - 8 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 - 8 * q^10 - 16 * q^11 + 24 * q^12 - 8 * q^14 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 8 * q^20 - 8 * q^22 - 56 * q^24 - 16 * q^25 - 40 * q^26 + 32 * q^27 + 40 * q^28 - 72 * q^30 + 32 * q^32 - 72 * q^34 - 32 * q^35 + 56 * q^36 + 48 * q^38 + 56 * q^40 - 16 * q^41 - 56 * q^42 - 96 * q^43 + 24 * q^44 - 24 * q^46 + 16 * q^48 - 16 * q^49 - 16 * q^51 - 16 * q^52 - 24 * q^54 + 32 * q^56 + 32 * q^57 + 48 * q^58 - 16 * q^59 + 96 * q^60 + 48 * q^62 + 40 * q^64 + 64 * q^65 - 16 * q^66 + 80 * q^68 + 64 * q^70 + 96 * q^72 - 96 * q^73 + 40 * q^74 - 16 * q^75 + 48 * q^76 + 96 * q^78 + 8 * q^80 - 96 * q^81 + 32 * q^82 + 128 * q^83 + 64 * q^86 - 72 * q^88 - 16 * q^89 + 152 * q^90 - 16 * q^91 - 120 * q^92 + 88 * q^94 - 160 * q^96 - 16 * q^97 + 128 * q^98 + 48 * q^99

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