LMFDB - Embedded newform 336.2.u.a.139.31

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.31
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38724 - 0.274894i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.84887 - 0.762687i) q^{4} +(1.07201 - 1.07201i) q^{5} +(-0.786547 + 1.17531i) q^{6} +(0.929507 + 2.47710i) q^{7} +(2.35516 - 1.56627i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(1.38724 - 0.274894i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.84887 - 0.762687i) q^{4} +(1.07201 - 1.07201i) q^{5} +(-0.786547 + 1.17531i) q^{6} +(0.929507 + 2.47710i) q^{7} +(2.35516 - 1.56627i) q^{8} -1.00000i q^{9} +(1.19245 - 1.78183i) q^{10} +(-1.12178 + 1.12178i) q^{11} +(-0.768045 + 1.84665i) q^{12} +(0.380324 + 0.380324i) q^{13} +(1.97039 + 3.18081i) q^{14} +1.51606i q^{15} +(2.83662 - 2.82021i) q^{16} -4.93076i q^{17} +(-0.274894 - 1.38724i) q^{18} +(-0.00735220 + 0.00735220i) q^{19} +(1.16440 - 2.79962i) q^{20} +(-2.40883 - 1.09431i) q^{21} +(-1.24780 + 1.86454i) q^{22} +1.62475 q^{23} +(-0.557830 + 2.77287i) q^{24} +2.70157i q^{25} +(0.632149 + 0.423052i) q^{26} +(0.707107 + 0.707107i) q^{27} +(3.60779 + 3.87090i) q^{28} +(-3.69584 + 3.69584i) q^{29} +(0.416755 + 2.10314i) q^{30} -1.21242 q^{31} +(3.15981 - 4.69208i) q^{32} -1.58643i q^{33} +(-1.35543 - 6.84014i) q^{34} +(3.65193 + 1.65904i) q^{35} +(-0.762687 - 1.84887i) q^{36} +(-6.70001 - 6.70001i) q^{37} +(-0.00817819 + 0.0122203i) q^{38} -0.537859 q^{39} +(0.845703 - 4.20384i) q^{40} +2.08793 q^{41} +(-3.64245 - 0.855899i) q^{42} +(-7.89391 + 7.89391i) q^{43} +(-1.21845 + 2.92958i) q^{44} +(-1.07201 - 1.07201i) q^{45} +(2.25391 - 0.446633i) q^{46} -2.09637 q^{47} +(-0.0115983 + 3.99998i) q^{48} +(-5.27203 + 4.60496i) q^{49} +(0.742644 + 3.74772i) q^{50} +(3.48657 + 3.48657i) q^{51} +(0.993236 + 0.413100i) q^{52} +(-5.28124 - 5.28124i) q^{53} +(1.17531 + 0.786547i) q^{54} +2.40512i q^{55} +(6.06895 + 4.37811i) q^{56} -0.0103976i q^{57} +(-4.11105 + 6.14298i) q^{58} +(-9.39247 - 9.39247i) q^{59} +(1.15628 + 2.80299i) q^{60} +(-2.45118 - 2.45118i) q^{61} +(-1.68192 + 0.333287i) q^{62} +(2.47710 - 0.929507i) q^{63} +(3.09358 - 7.37765i) q^{64} +0.815426 q^{65} +(-0.436101 - 2.20076i) q^{66} +(4.70113 + 4.70113i) q^{67} +(-3.76062 - 9.11631i) q^{68} +(-1.14887 + 1.14887i) q^{69} +(5.52216 + 1.29759i) q^{70} +5.16953 q^{71} +(-1.56627 - 2.35516i) q^{72} -7.83339 q^{73} +(-11.1363 - 7.45273i) q^{74} +(-1.91030 - 1.91030i) q^{75} +(-0.00798581 + 0.0192007i) q^{76} +(-3.82145 - 1.73605i) q^{77} +(-0.746139 + 0.147854i) q^{78} -4.65497i q^{79} +(0.0175837 - 6.06421i) q^{80} -1.00000 q^{81} +(2.89646 - 0.573959i) q^{82} +(-0.694961 + 0.694961i) q^{83} +(-5.28823 - 0.186051i) q^{84} +(-5.28584 - 5.28584i) q^{85} +(-8.78076 + 13.1207i) q^{86} -5.22671i q^{87} +(-0.884960 + 4.39898i) q^{88} +16.3938 q^{89} +(-1.78183 - 1.19245i) q^{90} +(-0.588586 + 1.29561i) q^{91} +(3.00394 - 1.23917i) q^{92} +(0.857310 - 0.857310i) q^{93} +(-2.90817 + 0.576280i) q^{94} +0.0157633i q^{95} +(1.08348 + 5.55212i) q^{96} +15.8094i q^{97} +(-6.04770 + 7.83743i) q^{98} +(1.12178 + 1.12178i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.38724	−	0.274894i	0.980926	−	0.194379i
$2$	1.38724	−	0.274894i	0.980926	−	0.194379i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.84887	−	0.762687i	0.924433	−	0.381344i
$5$	1.07201	−	1.07201i	0.479420	−	0.479420i	−0.425526	−	0.904946i	$-0.639911\pi$
$5$	1.07201	−	1.07201i	0.479420	−	0.479420i	0.904946	+	0.425526i	$0.139911\pi$
$6$	−0.786547	+	1.17531i	−0.321107	+	0.479817i
$7$	0.929507	+	2.47710i	0.351321	+	0.936255i
$7$	0.929507	+	2.47710i	0.351321	+	0.936255i
$8$	2.35516	−	1.56627i	0.832676	−	0.553761i
$9$		−	1.00000i		−	0.333333i
$10$	1.19245	−	1.78183i	0.377086	−	0.563465i
$11$	−1.12178	+	1.12178i	−0.338229	+	0.338229i	−0.855700	−	0.517472i	$-0.826873\pi$
$11$	−1.12178	+	1.12178i	−0.338229	+	0.338229i	0.517472	+	0.855700i	$0.326873\pi$
$12$	−0.768045	+	1.84665i	−0.221715	+	0.533081i
$13$	0.380324	+	0.380324i	0.105483	+	0.105483i	0.757879	−	0.652396i	$-0.226236\pi$
$13$	0.380324	+	0.380324i	0.105483	+	0.105483i	−0.652396	+	0.757879i	$0.726236\pi$
$14$	1.97039	+	3.18081i	0.526608	+	0.850108i
$15$			1.51606i			0.391444i
$16$	2.83662	−	2.82021i	0.709154	−	0.705054i
$17$		−	4.93076i		−	1.19588i	−0.801539	−	0.597942i	$-0.795985\pi$
$17$		−	4.93076i		−	1.19588i	0.801539	−	0.597942i	$-0.204015\pi$
$18$	−0.274894	−	1.38724i	−0.0647931	−	0.326975i
$19$	−0.00735220	+	0.00735220i	−0.00168671	+	0.00168671i	−0.707950	−	0.706263i	$-0.750380\pi$
$19$	−0.00735220	+	0.00735220i	−0.00168671	+	0.00168671i	0.706263	+	0.707950i	$0.250380\pi$
$20$	1.16440	−	2.79962i	0.260368	−	0.626015i
$21$	−2.40883	−	1.09431i	−0.525651	−	0.238798i
$22$	−1.24780	+	1.86454i	−0.266033	+	0.397522i
$23$	1.62475			0.338783			0.169392	−	0.985549i	$-0.445820\pi$
$23$	1.62475			0.338783			0.169392	+	0.985549i	$0.445820\pi$
$24$	−0.557830	+	2.77287i	−0.113867	+	0.566010i
$25$			2.70157i			0.540314i
$26$	0.632149	+	0.423052i	0.123975	+	0.0829672i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	3.60779	+	3.87090i	0.681808	+	0.731532i
$29$	−3.69584	+	3.69584i	−0.686301	+	0.686301i	−0.961412	−	0.275112i	$-0.911285\pi$
$29$	−3.69584	+	3.69584i	−0.686301	+	0.686301i	0.275112	+	0.961412i	$0.411285\pi$
$30$	0.416755	+	2.10314i	0.0760887	+	0.383978i
$31$	−1.21242			−0.217757			−0.108878	−	0.994055i	$-0.534726\pi$
$31$	−1.21242			−0.217757			−0.108878	+	0.994055i	$0.534726\pi$
$32$	3.15981	−	4.69208i	0.558580	−	0.829451i
$33$		−	1.58643i		−	0.276162i
$34$	−1.35543	−	6.84014i	−0.232455	−	1.17307i
$35$	3.65193	+	1.65904i	0.617289	+	0.280429i
$36$	−0.762687	−	1.84887i	−0.127115	−	0.308144i
$37$	−6.70001	−	6.70001i	−1.10148	−	1.10148i	−0.994233	−	0.107243i	$-0.965798\pi$
$37$	−6.70001	−	6.70001i	−1.10148	−	1.10148i	−0.107243	−	0.994233i	$-0.534202\pi$
$38$	−0.00817819	+	0.0122203i	−0.00132668	+	0.00198240i
$39$	−0.537859			−0.0861264
$40$	0.845703	−	4.20384i	0.133717	−	0.664685i
$41$	2.08793			0.326080			0.163040	−	0.986619i	$-0.447870\pi$
$41$	2.08793			0.326080			0.163040	+	0.986619i	$0.447870\pi$
$42$	−3.64245	−	0.855899i	−0.562042	−	0.132068i
$43$	−7.89391	+	7.89391i	−1.20381	+	1.20381i	−0.230812	+	0.972998i	$0.574138\pi$
$43$	−7.89391	+	7.89391i	−1.20381	+	1.20381i	−0.972998	+	0.230812i	$0.925862\pi$
$44$	−1.21845	+	2.92958i	−0.183688	+	0.441651i
$45$	−1.07201	−	1.07201i	−0.159807	−	0.159807i
$46$	2.25391	−	0.446633i	0.332322	−	0.0658525i
$47$	−2.09637			−0.305787			−0.152894	−	0.988243i	$-0.548859\pi$
$47$	−2.09637			−0.305787			−0.152894	+	0.988243i	$0.548859\pi$
$48$	−0.0115983	+	3.99998i	−0.00167407	+	0.577348i
$49$	−5.27203	+	4.60496i	−0.753148	+	0.657852i
$50$	0.742644	+	3.74772i	0.105026	+	0.530008i
$51$	3.48657	+	3.48657i	0.488218	+	0.488218i
$52$	0.993236	+	0.413100i	0.137737	+	0.0572867i
$53$	−5.28124	−	5.28124i	−0.725434	−	0.725434i	0.244272	−	0.969707i	$-0.421451\pi$
$53$	−5.28124	−	5.28124i	−0.725434	−	0.725434i	−0.969707	+	0.244272i	$0.921451\pi$
$54$	1.17531	+	0.786547i	0.159939	+	0.107036i
$55$			2.40512i			0.324307i
$56$	6.06895	+	4.37811i	0.810998	+	0.585049i
$57$		−	0.0103976i		−	0.00137719i
$58$	−4.11105	+	6.14298i	−0.539808	+	0.806613i
$59$	−9.39247	−	9.39247i	−1.22280	−	1.22280i	−0.966634	−	0.256162i	$-0.917542\pi$
$59$	−9.39247	−	9.39247i	−1.22280	−	1.22280i	−0.256162	−	0.966634i	$-0.582458\pi$
$60$	1.15628	+	2.80299i	0.149275	+	0.361864i
$61$	−2.45118	−	2.45118i	−0.313841	−	0.313841i	0.532555	−	0.846396i	$-0.321232\pi$
$61$	−2.45118	−	2.45118i	−0.313841	−	0.313841i	−0.846396	+	0.532555i	$0.821232\pi$
$62$	−1.68192	+	0.333287i	−0.213604	+	0.0423274i
$63$	2.47710	−	0.929507i	0.312085	−	0.117107i
$64$	3.09358	−	7.37765i	0.386698	−	0.922206i
$65$	0.815426			0.101141
$66$	−0.436101	−	2.20076i	−0.0536803	−	0.270895i
$67$	4.70113	+	4.70113i	0.574334	+	0.574334i	0.933337	−	0.359002i	$-0.116883\pi$
$67$	4.70113	+	4.70113i	0.574334	+	0.574334i	−0.359002	+	0.933337i	$0.616883\pi$
$68$	−3.76062	−	9.11631i	−0.456043	−	1.10551i
$69$	−1.14887	+	1.14887i	−0.138308	+	0.138308i
$70$	5.52216	+	1.29759i	0.660025	+	0.155092i
$71$	5.16953			0.613510			0.306755	−	0.951789i	$-0.400757\pi$
$71$	5.16953			0.613510			0.306755	+	0.951789i	$0.400757\pi$
$72$	−1.56627	−	2.35516i	−0.184587	−	0.277559i
$73$	−7.83339			−0.916828			−0.458414	−	0.888739i	$-0.651582\pi$
$73$	−7.83339			−0.916828			−0.458414	+	0.888739i	$0.651582\pi$
$74$	−11.1363	−	7.45273i	−1.29457	−	0.866362i
$75$	−1.91030	−	1.91030i	−0.220582	−	0.220582i
$76$	−0.00798581	+	0.0192007i	−0.000916035	+	0.00220247i
$77$	−3.82145	−	1.73605i	−0.435495	−	0.197842i
$78$	−0.746139	+	0.147854i	−0.0844837	+	0.0167412i
$79$		−	4.65497i		−	0.523725i	−0.965105	−	0.261863i	$-0.915663\pi$
$79$		−	4.65497i		−	0.523725i	0.965105	−	0.261863i	$-0.0843368\pi$
$80$	0.0175837	−	6.06421i	0.00196592	−	0.677999i
$81$	−1.00000			−0.111111
$82$	2.89646	−	0.573959i	0.319861	−	0.0633832i
$83$	−0.694961	+	0.694961i	−0.0762819	+	0.0762819i	−0.744218	−	0.667936i	$-0.767178\pi$
$83$	−0.694961	+	0.694961i	−0.0762819	+	0.0762819i	0.667936	+	0.744218i	$0.267178\pi$
$84$	−5.28823	−	0.186051i	−0.576993	−	0.0202998i
$85$	−5.28584	−	5.28584i	−0.573330	−	0.573330i
$86$	−8.78076	+	13.1207i	−0.946854	+	1.41485i
$87$		−	5.22671i		−	0.560362i
$88$	−0.884960	+	4.39898i	−0.0943371	+	0.468932i
$89$	16.3938			1.73774			0.868869	−	0.495043i	$-0.164848\pi$
$89$	16.3938			1.73774			0.868869	+	0.495043i	$0.164848\pi$
$90$	−1.78183	−	1.19245i	−0.187822	−	0.125695i
$91$	−0.588586	+	1.29561i	−0.0617006	+	0.135817i
$92$	3.00394	−	1.23917i	0.313183	−	0.129193i
$93$	0.857310	−	0.857310i	0.0888989	−	0.0888989i
$94$	−2.90817	+	0.576280i	−0.299955	+	0.0594387i
$95$			0.0157633i			0.00161728i
$96$	1.08348	+	5.55212i	0.110582	+	0.566661i
$97$			15.8094i			1.60520i	0.596516	+	0.802601i	$0.296551\pi$
$97$			15.8094i			1.60520i	−0.596516	+	0.802601i	$0.703449\pi$
$98$	−6.04770	+	7.83743i	−0.610910	+	0.791700i
$99$	1.12178	+	1.12178i	0.112743	+	0.112743i
$100$	2.06045	+	4.99484i	0.206045	+	0.499484i
$101$	11.6943	−	11.6943i	1.16363	−	1.16363i	0.179951	−	0.983676i	$-0.442406\pi$
$101$	11.6943	−	11.6943i	1.16363	−	1.16363i	0.983676	−	0.179951i	$-0.0575940\pi$
$102$	5.79515	+	3.87827i	0.573805	+	0.384006i
$103$			17.2578i			1.70046i	0.526408	+	0.850232i	$0.323539\pi$
$103$			17.2578i			1.70046i	−0.526408	+	0.850232i	$0.676461\pi$
$104$	1.49142	+	0.300034i	0.146245	+	0.0294208i
$105$	−3.75542	+	1.40919i	−0.366492	+	0.137523i
$106$	−8.77813	−	5.87457i	−0.852607	−	0.570588i
$107$	−0.486324	+	0.486324i	−0.0470148	+	0.0470148i	−0.730223	−	0.683209i	$-0.760584\pi$
$107$	−0.486324	+	0.486324i	−0.0470148	+	0.0470148i	0.683209	+	0.730223i	$0.260584\pi$
$108$	1.84665	+	0.768045i	0.177694	+	0.0739052i
$109$	4.59269	−	4.59269i	0.439900	−	0.439900i	−0.452078	−	0.891978i	$-0.649317\pi$
$109$	4.59269	−	4.59269i	0.439900	−	0.439900i	0.891978	+	0.452078i	$0.149317\pi$
$110$	0.661154	+	3.33648i	0.0630385	+	0.318121i
$111$	9.47525			0.899351
$112$	9.62260	+	4.40517i	0.909251	+	0.416249i
$113$	16.4776			1.55009			0.775043	−	0.631908i	$-0.217728\pi$
$113$	16.4776			1.55009			0.775043	+	0.631908i	$0.217728\pi$
$114$	−0.00285823	−	0.0144239i	−0.000267698	−	0.00135093i
$115$	1.74175	−	1.74175i	0.162419	−	0.162419i
$116$	−4.01435	+	9.65189i	−0.372723	+	0.896156i
$117$	0.380324	−	0.380324i	0.0351610	−	0.0351610i
$118$	−15.6115	−	10.4477i	−1.43716	−	0.961787i
$119$	12.2140	−	4.58317i	1.11965	−	0.420139i
$120$	2.37456	+	3.57056i	0.216767	+	0.325946i
$121$			8.48323i			0.771203i
$122$	−4.07418	−	2.72656i	−0.368859	−	0.246851i
$123$	−1.47639	+	1.47639i	−0.133122	+	0.133122i
$124$	−2.24160	+	0.924697i	−0.201302	+	0.0830402i
$125$	8.25620	+	8.25620i	0.738457	+	0.738457i
$126$	3.18081	−	1.97039i	0.283369	−	0.175536i
$127$		−	11.8244i		−	1.04925i	−0.851335	−	0.524623i	$-0.824206\pi$
$127$		−	11.8244i		−	1.04925i	0.851335	−	0.524623i	$-0.175794\pi$
$128$	2.26347	−	11.0850i	0.200065	−	0.979783i
$129$		−	11.1637i		−	0.982907i
$130$	1.13119	−	0.224156i	0.0992120	−	0.0196597i
$131$	−9.68747	+	9.68747i	−0.846398	+	0.846398i	−0.989682	−	0.143283i	$-0.954234\pi$
$131$	−9.68747	+	9.68747i	−0.846398	+	0.846398i	0.143283	+	0.989682i	$0.454234\pi$
$132$	−1.20995	−	2.93310i	−0.105313	−	0.255294i
$133$	−0.0250460	−	0.0113782i	−0.00217177	−	0.000986615i
$134$	7.81390	+	5.22928i	0.675018	+	0.451741i
$135$	1.51606			0.130481
$136$	−7.72290	−	11.6127i	−0.662234	−	0.995784i
$137$			0.638902i			0.0545851i	0.999627	+	0.0272925i	$0.00868856\pi$
$137$			0.638902i			0.0545851i	−0.999627	+	0.0272925i	$0.991311\pi$
$138$	−1.27794	+	1.90958i	−0.108786	+	0.162554i
$139$	8.78705	+	8.78705i	0.745308	+	0.745308i	0.973594	−	0.228286i	$-0.0733121\pi$
$139$	8.78705	+	8.78705i	0.745308	+	0.745308i	−0.228286	+	0.973594i	$0.573312\pi$
$140$	8.01726	+	0.282063i	0.677583	+	0.0238387i
$141$	1.48236	−	1.48236i	0.124837	−	0.124837i
$142$	7.17137	−	1.42107i	0.601808	−	0.119254i
$143$	−0.853277			−0.0713546
$144$	−2.82021	−	2.83662i	−0.235018	−	0.236385i
$145$			7.92400i			0.658052i
$146$	−10.8668	+	2.15335i	−0.899341	+	0.178212i
$147$	0.471690	−	6.98409i	0.0389044	−	0.576038i
$148$	−17.4974	−	7.27742i	−1.43828	−	0.598200i
$149$	−6.68763	−	6.68763i	−0.547872	−	0.547872i	0.377953	−	0.925825i	$-0.376628\pi$
$149$	−6.68763	−	6.68763i	−0.547872	−	0.547872i	−0.925825	+	0.377953i	$0.876628\pi$
$150$	−3.17517	−	2.12491i	−0.259251	−	0.173498i
$151$	11.7089			0.952854			0.476427	−	0.879214i	$-0.341932\pi$
$151$	11.7089			0.952854			0.476427	+	0.879214i	$0.341932\pi$
$152$	−0.00580008	+	0.0288312i	−0.000470449	+	0.00233852i
$153$	−4.93076			−0.398628
$154$	−5.77850	−	1.35783i	−0.465645	−	0.109417i
$155$	−1.29973	+	1.29973i	−0.104397	+	0.104397i
$156$	−0.994430	+	0.410218i	−0.0796181	+	0.0328437i
$157$	−7.87159	−	7.87159i	−0.628221	−	0.628221i	0.319399	−	0.947620i	$-0.396519\pi$
$157$	−7.87159	−	7.87159i	−0.628221	−	0.628221i	−0.947620	+	0.319399i	$0.896519\pi$
$158$	−1.27962	−	6.45756i	−0.101801	−	0.513736i
$159$	7.46881			0.592315
$160$	−1.64262	−	8.41734i	−0.129861	−	0.665449i
$161$	1.51021	+	4.02466i	0.119022	+	0.317188i
$162$	−1.38724	+	0.274894i	−0.108992	+	0.0215977i
$163$	4.16256	+	4.16256i	0.326037	+	0.326037i	0.851077	−	0.525041i	$-0.175950\pi$
$163$	4.16256	+	4.16256i	0.326037	+	0.326037i	−0.525041	+	0.851077i	$0.675950\pi$
$164$	3.86031	−	1.59244i	0.301439	−	0.124349i
$165$	−1.70068	−	1.70068i	−0.132398	−	0.132398i
$166$	−0.773037	+	1.15512i	−0.0599993	+	0.0896546i
$167$		−	5.10931i		−	0.395370i	−0.980266	−	0.197685i	$-0.936658\pi$
$167$		−	5.10931i		−	0.395370i	0.980266	−	0.197685i	$-0.0633423\pi$
$168$	−7.38719	+	1.19561i	−0.569934	+	0.0922430i
$169$		−	12.7107i		−	0.977747i
$170$	−8.78578	−	5.87968i	−0.673838	−	0.450951i
$171$	0.00735220	+	0.00735220i	0.000562237	+	0.000562237i
$172$	−8.57421	+	20.6154i	−0.653777	+	1.57191i
$173$	6.04872	+	6.04872i	0.459876	+	0.459876i	0.898615	−	0.438739i	$-0.144575\pi$
$173$	6.04872	+	6.04872i	0.459876	+	0.459876i	−0.438739	+	0.898615i	$0.644575\pi$
$174$	−1.43679	−	7.25070i	−0.108923	−	0.549674i
$175$	−6.69205	+	2.51113i	−0.505871	+	0.189823i
$176$	−0.0183999	+	6.34570i	−0.00138695	+	0.478325i
$177$	13.2830			0.998409
$178$	22.7421	−	4.50655i	1.70459	−	0.337780i
$179$	−11.3303	−	11.3303i	−0.846868	−	0.846868i	0.142873	−	0.989741i	$-0.454366\pi$
$179$	−11.3303	−	11.3303i	−0.846868	−	0.846868i	−0.989741	+	0.142873i	$0.954366\pi$
$180$	−2.79962	−	1.16440i	−0.208672	−	0.0867893i
$181$	−3.12921	+	3.12921i	−0.232593	+	0.232593i	−0.813774	−	0.581181i	$-0.802591\pi$
$181$	−3.12921	+	3.12921i	−0.232593	+	0.232593i	0.581181	+	0.813774i	$0.302591\pi$
$182$	−0.460353	+	1.95912i	−0.0341237	+	0.145220i
$183$	3.46649			0.256250
$184$	3.82655	−	2.54480i	0.282097	−	0.187605i
$185$	−14.3650			−1.05614
$186$	0.953625	−	1.42496i	0.0699232	−	0.104483i
$187$	5.53121	+	5.53121i	0.404482	+	0.404482i
$188$	−3.87591	+	1.59888i	−0.282680	+	0.116610i
$189$	−1.09431	+	2.40883i	−0.0795995	+	0.175217i
$190$	0.00433324	+	0.0218675i	0.000314367	+	0.00158644i
$191$		−	11.2514i		−	0.814126i	−0.913400	−	0.407063i	$-0.866553\pi$
$191$		−	11.2514i		−	0.814126i	0.913400	−	0.407063i	$-0.133447\pi$
$192$	3.02929	+	7.40428i	0.218620	+	0.534358i
$193$	15.6044			1.12323			0.561613	−	0.827400i	$-0.310181\pi$
$193$	15.6044			1.12323			0.561613	+	0.827400i	$0.310181\pi$
$194$	4.34591	+	21.9314i	0.312018	+	1.57458i
$195$	−0.576593	+	0.576593i	−0.0412907	+	0.0412907i
$196$	−6.23514	+	12.5349i	−0.445367	+	0.895348i
$197$	6.75482	+	6.75482i	0.481261	+	0.481261i	0.905534	−	0.424273i	$-0.139470\pi$
$197$	6.75482	+	6.75482i	0.481261	+	0.481261i	−0.424273	+	0.905534i	$0.639470\pi$
$198$	1.86454	+	1.24780i	0.132507	+	0.0886776i
$199$		−	22.4644i		−	1.59246i	−0.604996	−	0.796229i	$-0.706825\pi$
$199$		−	22.4644i		−	1.59246i	0.604996	−	0.796229i	$-0.293175\pi$
$200$	4.23139	+	6.36263i	0.299204	+	0.449906i
$201$	−6.64840			−0.468942
$202$	13.0081	−	19.4375i	0.915247	−	1.36762i
$203$	−12.5903	−	5.71965i	−0.883664	−	0.401441i
$204$	9.10537	+	3.78704i	0.637503	+	0.265146i
$205$	2.23829	−	2.23829i	0.156329	−	0.156329i
$206$	4.74407	+	23.9407i	0.330535	+	1.66803i
$207$		−	1.62475i		−	0.112928i
$208$	2.15143	+	0.00623825i	0.149175	+	0.000432545i
$209$		−	0.0164951i		−	0.00114099i
$210$	−4.82230	+	2.98722i	−0.332770	+	0.206138i
$211$	3.76337	+	3.76337i	0.259081	+	0.259081i	0.824680	−	0.565599i	$-0.191355\pi$
$211$	3.76337	+	3.76337i	0.259081	+	0.259081i	−0.565599	+	0.824680i	$0.691355\pi$
$212$	−13.7923	−	5.73638i	−0.947256	−	0.393976i
$213$	−3.65541	+	3.65541i	−0.250464	+	0.250464i
$214$	−0.540961	+	0.808336i	−0.0369793	+	0.0552567i
$215$			16.9248i			1.15426i
$216$	2.77287	+	0.557830i	0.188670	+	0.0379555i
$217$	−1.12695	−	3.00328i	−0.0765025	−	0.203876i
$218$	5.10866	−	7.63367i	0.346002	−	0.517017i
$219$	5.53904	−	5.53904i	0.374294	−	0.374294i
$220$	1.83436	+	4.44675i	0.123672	+	0.299800i
$221$	1.87528	−	1.87528i	0.126145	−	0.126145i
$222$	13.1444	−	2.60469i	0.882197	−	0.174815i
$223$	14.0828			0.943054			0.471527	−	0.881852i	$-0.343703\pi$
$223$	14.0828			0.943054			0.471527	+	0.881852i	$0.343703\pi$
$224$	14.5598	+	3.46583i	0.972818	+	0.231570i
$225$	2.70157			0.180105
$226$	22.8584	−	4.52960i	1.52052	−	0.301305i
$227$	−18.0404	+	18.0404i	−1.19738	+	1.19738i	−0.222436	+	0.974947i	$0.571401\pi$
$227$	−18.0404	+	18.0404i	−1.19738	+	1.19738i	−0.974947	+	0.222436i	$0.928599\pi$
$228$	−0.00793010	−	0.0192237i	−0.000525184	−	0.00127312i
$229$	16.6213	−	16.6213i	1.09837	−	1.09837i	0.103767	−	0.994602i	$-0.466910\pi$
$229$	16.6213	−	16.6213i	1.09837	−	1.09837i	0.994602	−	0.103767i	$-0.0330897\pi$
$230$	1.93743	−	2.89503i	0.127751	−	0.190892i
$231$	3.92975	−	1.47460i	0.258559	−	0.0970216i
$232$	−2.91562	+	14.4930i	−0.191420	+	0.951512i
$233$			9.67000i			0.633503i	0.948509	+	0.316751i	$0.102592\pi$
$233$			9.67000i			0.633503i	−0.948509	+	0.316751i	$0.897408\pi$
$234$	0.423052	−	0.632149i	0.0276557	−	0.0413249i
$235$	−2.24734	+	2.24734i	−0.146600	+	0.146600i
$236$	−24.5290	−	10.2019i	−1.59670	−	0.664088i
$237$	3.29156	+	3.29156i	0.213810	+	0.213810i
$238$	15.6838	−	9.71550i	1.01663	−	0.629763i
$239$		−	22.0336i		−	1.42523i	−0.701553	−	0.712617i	$-0.747510\pi$
$239$		−	22.0336i		−	1.42523i	0.701553	−	0.712617i	$-0.252490\pi$
$240$	4.27561	+	4.30048i	0.275989	+	0.277594i
$241$		−	2.30808i		−	0.148676i	−0.997233	−	0.0743382i	$-0.976316\pi$
$241$		−	2.30808i		−	0.148676i	0.997233	−	0.0743382i	$-0.0236844\pi$
$242$	2.33199	+	11.7683i	0.149906	+	0.756493i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	−6.40138	−	2.66242i	−0.409806	−	0.170444i
$245$	−0.715110	+	10.5883i	−0.0456867	+	0.676461i
$246$	−1.64226	+	2.45396i	−0.104706	+	0.156459i
$247$	−0.00559243			−0.000355838
$248$	−2.85545	+	1.89898i	−0.181321	+	0.120585i
$249$		−	0.982823i		−	0.0622839i
$250$	13.7229	+	9.18374i	0.867912	+	0.580831i
$251$	1.88634	+	1.88634i	0.119065	+	0.119065i	0.764129	−	0.645064i	$-0.223169\pi$
$251$	1.88634	+	1.88634i	0.119065	+	0.119065i	−0.645064	+	0.764129i	$0.723169\pi$
$252$	3.87090	−	3.60779i	0.243844	−	0.227269i
$253$	−1.82261	+	1.82261i	−0.114586	+	0.114586i
$254$	−3.25046	−	16.4033i	−0.203952	−	1.02923i
$255$	7.47531			0.468122
$256$	0.0927859	−	15.9997i	0.00579912	−	0.999983i
$257$		−	3.19078i		−	0.199036i	−0.995036	−	0.0995178i	$-0.968270\pi$
$257$		−	3.19078i		−	0.199036i	0.995036	−	0.0995178i	$-0.0317300\pi$
$258$	−3.06883	−	15.4867i	−0.191057	−	0.964160i
$259$	10.3689	−	22.8243i	0.644291	−	1.41823i
$260$	1.50761	−	0.621915i	0.0934982	−	0.0385695i
$261$	3.69584	+	3.69584i	0.228767	+	0.228767i
$262$	−10.7758	+	16.1019i	−0.665732	+	0.994777i
$263$	−20.1194			−1.24061			−0.620306	−	0.784360i	$-0.712992\pi$
$263$	−20.1194			−1.24061			−0.620306	+	0.784360i	$0.712992\pi$
$264$	−2.48478	−	3.73631i	−0.152928	−	0.229954i
$265$	−11.3231			−0.695575
$266$	−0.0378727	−	0.00889928i	−0.00232212	−	0.000545650i
$267$	−11.5922	+	11.5922i	−0.709428	+	0.709428i
$268$	12.2773	+	5.10627i	0.749952	+	0.311915i
$269$	16.4208	+	16.4208i	1.00119	+	1.00119i	0.999999	+	0.00119219i	$0.000379487\pi$
$269$	16.4208	+	16.4208i	1.00119	+	1.00119i	0.00119219	+	0.999999i	$0.499621\pi$
$270$	2.10314	−	0.416755i	0.127993	−	0.0253629i
$271$	−30.3695			−1.84481			−0.922407	−	0.386218i	$-0.873781\pi$
$271$	−30.3695			−1.84481			−0.922407	+	0.386218i	$0.873781\pi$
$272$	−13.9058	−	13.9867i	−0.843162	−	0.848066i
$273$	−0.499944	−	1.33233i	−0.0302580	−	0.0806363i
$274$	0.175630	+	0.886310i	0.0106102	+	0.0535439i
$275$	−3.03056	−	3.03056i	−0.182750	−	0.182750i
$276$	−1.24788	+	3.00034i	−0.0751135	+	0.180599i
$277$	20.2331	+	20.2331i	1.21569	+	1.21569i	0.969127	+	0.246563i	$0.0793011\pi$
$277$	20.2331	+	20.2331i	1.21569	+	1.21569i	0.246563	+	0.969127i	$0.420699\pi$
$278$	14.6053	+	9.77424i	0.875965	+	0.586220i
$279$			1.21242i			0.0725857i
$280$	11.1994	−	1.81261i	0.669292	−	0.108324i
$281$			28.4713i			1.69846i	0.528026	+	0.849228i	$0.322932\pi$
$281$			28.4713i			1.69846i	−0.528026	+	0.849228i	$0.677068\pi$
$282$	1.64890	−	2.46388i	0.0981903	−	0.146722i
$283$	6.05298	+	6.05298i	0.359813	+	0.359813i	0.863744	−	0.503931i	$-0.168114\pi$
$283$	6.05298	+	6.05298i	0.359813	+	0.359813i	−0.503931	+	0.863744i	$0.668114\pi$
$284$	9.55777	−	3.94273i	0.567149	−	0.233958i
$285$	−0.0111464	−	0.0111464i	−0.000660253	−	0.000660253i
$286$	−1.18370	+	0.234561i	−0.0699936	+	0.0138699i
$287$	1.94075	+	5.17201i	0.114559	+	0.305294i
$288$	−4.69208	−	3.15981i	−0.276484	−	0.186193i
$289$	−7.31235			−0.430138
$290$	2.17826	+	10.9925i	0.127912	+	0.645501i
$291$	−11.1789	−	11.1789i	−0.655321	−	0.655321i
$292$	−14.4829	+	5.97442i	−0.847547	+	0.349627i
$293$	−11.2656	+	11.2656i	−0.658142	+	0.658142i	−0.954940	−	0.296798i	$-0.904081\pi$
$293$	−11.2656	+	11.2656i	−0.658142	+	0.658142i	0.296798	+	0.954940i	$0.404081\pi$
$294$	−1.26554	−	9.81827i	−0.0738076	−	0.572613i
$295$	−20.1377			−1.17246
$296$	−26.2737	−	5.28558i	−1.52713	−	0.307218i
$297$	−1.58643			−0.0920542
$298$	−11.1157	−	7.43896i	−0.643918	−	0.430927i
$299$	0.617930	+	0.617930i	0.0357358	+	0.0357358i
$300$	−4.98884	−	2.07493i	−0.288031	−	0.119796i
$301$	−26.8914	−	12.2165i	−1.55000	−	0.704150i
$302$	16.2430	−	3.21870i	0.934680	−	0.185215i
$303$			16.5382i			0.950097i
$304$	−0.000120594		0.0415901i	−6.91655e−6		0.00238536i
$305$	−5.25540			−0.300923
$306$	−6.84014	+	1.35543i	−0.391025	+	0.0774850i
$307$	19.9262	−	19.9262i	1.13725	−	1.13725i	0.148305	−	0.988942i	$-0.452618\pi$
$307$	19.9262	−	19.9262i	1.13725	−	1.13725i	0.988942	−	0.148305i	$-0.0473818\pi$
$308$	−8.38942	−	0.295157i	−0.478032	−	0.0168181i
$309$	−12.2031	−	12.2031i	−0.694212	−	0.694212i
$310$	−1.44575	+	2.16033i	−0.0821131	+	0.122698i
$311$		−	8.15514i		−	0.462436i	−0.972902	−	0.231218i	$-0.925729\pi$
$311$		−	8.15514i		−	0.462436i	0.972902	−	0.231218i	$-0.0742710\pi$
$312$	−1.26675	+	0.842434i	−0.0717154	+	0.0476934i
$313$	28.5813			1.61551			0.807754	−	0.589520i	$-0.200683\pi$
$313$	28.5813			1.61551			0.807754	+	0.589520i	$0.200683\pi$
$314$	−13.0836	−	8.75593i	−0.738352	−	0.494125i
$315$	1.65904	−	3.65193i	0.0934764	−	0.205763i
$316$	−3.55029	−	8.60642i	−0.199719	−	0.484149i
$317$	−12.7765	+	12.7765i	−0.717599	+	0.717599i	−0.968113	−	0.250514i	$-0.919400\pi$
$317$	−12.7765	+	12.7765i	−0.717599	+	0.717599i	0.250514	+	0.968113i	$0.419400\pi$
$318$	10.3610	−	2.05313i	0.581017	−	0.115134i
$319$		−	8.29182i		−	0.464253i
$320$	−4.59258	−	11.2253i	−0.256733	−	0.627515i
$321$		−	0.687767i		−	0.0383874i
$322$	3.20138	+	5.16802i	0.178406	+	0.288002i
$323$	0.0362519	+	0.0362519i	0.00201711	+	0.00201711i
$324$	−1.84887	+	0.762687i	−0.102715	+	0.0423715i
$325$	−1.02747	+	1.02747i	−0.0569938	+	0.0569938i
$326$	6.91873	+	4.63020i	0.383193	+	0.256443i
$327$			6.49505i			0.359177i
$328$	4.91742	−	3.27027i	0.271519	−	0.180570i
$329$	−1.94859	−	5.19292i	−0.107429	−	0.286295i
$330$	−2.82676	−	1.89174i	−0.155608	−	0.104137i
$331$	−15.1140	+	15.1140i	−0.830739	+	0.830739i	−0.987618	−	0.156879i	$-0.949857\pi$
$331$	−15.1140	+	15.1140i	−0.830739	+	0.830739i	0.156879	+	0.987618i	$0.449857\pi$
$332$	−0.754853	+	1.81493i	−0.0414279	+	0.0996071i
$333$	−6.70001	+	6.70001i	−0.367159	+	0.367159i
$334$	−1.40452	−	7.08783i	−0.0768517	−	0.387829i
$335$	10.0794			0.550694
$336$	−9.91913	+	3.68928i	−0.541133	+	0.201267i
$337$	−7.12166			−0.387942			−0.193971	−	0.981007i	$-0.562137\pi$
$337$	−7.12166			−0.387942			−0.193971	+	0.981007i	$0.562137\pi$
$338$	−3.49410	−	17.6328i	−0.190054	−	0.959098i
$339$	−11.6515	+	11.6515i	−0.632820	+	0.632820i
$340$	−13.8043	−	5.74137i	−0.748641	−	0.311370i
$341$	1.36006	−	1.36006i	0.0736516	−	0.0736516i
$342$	0.0122203	+	0.00817819i	0.000660800	+	0.000442226i
$343$	−16.3073	−	8.77900i	−0.880513	−	0.474021i
$344$	−6.22744	+	30.9555i	−0.335761	+	1.66901i
$345$			2.46321i			0.132615i
$346$	10.0538	+	6.72827i	0.540495	+	0.361714i
$347$	0.263964	−	0.263964i	0.0141704	−	0.0141704i	−0.699986	−	0.714156i	$-0.746810\pi$
$347$	0.263964	−	0.263964i	0.0141704	−	0.0141704i	0.714156	+	0.699986i	$0.246810\pi$
$348$	−3.98635	−	9.66349i	−0.213691	−	0.518017i
$349$	−4.37893	−	4.37893i	−0.234399	−	0.234399i	0.580127	−	0.814526i	$-0.303003\pi$
$349$	−4.37893	−	4.37893i	−0.234399	−	0.234399i	−0.814526	+	0.580127i	$0.803003\pi$
$350$	−8.59318	+	5.32314i	−0.459325	+	0.284534i
$351$			0.537859i			0.0287088i
$352$	1.71887	+	8.80807i	0.0916161	+	0.469472i
$353$		−	16.9515i		−	0.902238i	−0.892464	−	0.451119i	$-0.851025\pi$
$353$		−	16.9515i		−	0.902238i	0.892464	−	0.451119i	$-0.148975\pi$
$354$	18.4267	−	3.65141i	0.979366	−	0.194070i
$355$	5.54181	−	5.54181i	0.294129	−	0.294129i
$356$	30.3099	−	12.5033i	1.60642	−	0.662675i
$357$	−5.39579	+	11.8774i	−0.285575	+	0.628617i
$358$	−18.8325	−	12.6032i	−0.995329	−	0.666102i
$359$	−29.7322			−1.56921			−0.784603	−	0.619998i	$-0.787133\pi$
$359$	−29.7322			−1.56921			−0.784603	+	0.619998i	$0.787133\pi$
$360$	−4.20384	−	0.845703i	−0.221562	−	0.0445725i
$361$			18.9999i			0.999994i
$362$	−3.48077	+	5.20117i	−0.182945	+	0.273367i
$363$	−5.99855	−	5.99855i	−0.314842	−	0.314842i
$364$	−0.100069	+	2.84432i	−0.00524504	+	0.149083i
$365$	−8.39751	+	8.39751i	−0.439546	+	0.439546i
$366$	4.80885	−	0.952916i	0.251363	−	0.0498097i
$367$	−6.27534			−0.327570			−0.163785	−	0.986496i	$-0.552370\pi$
$367$	−6.27534			−0.327570			−0.163785	+	0.986496i	$0.552370\pi$
$368$	4.60879	−	4.58214i	0.240250	−	0.238860i
$369$		−	2.08793i		−	0.108693i
$370$	−19.9277	+	3.94886i	−1.03599	+	0.205291i
$371$	8.17320	−	17.9911i	0.424332	−	0.934052i
$372$	0.931193	−	2.23891i	0.0482801	−	0.116082i
$373$	0.151895	+	0.151895i	0.00786483	+	0.00786483i	0.711028	−	0.703163i	$-0.248230\pi$
$373$	0.151895	+	0.151895i	0.00786483	+	0.00786483i	−0.703163	+	0.711028i	$0.748230\pi$
$374$	9.19361	+	6.15262i	0.475390	+	0.318144i
$375$	−11.6760			−0.602947
$376$	−4.93730	+	3.28349i	−0.254622	+	0.169333i
$377$	−2.81123			−0.144786
$378$	−0.855899	+	3.64245i	−0.0440227	+	0.187347i
$379$	12.6234	−	12.6234i	0.648420	−	0.648420i	−0.304191	−	0.952611i	$-0.598386\pi$
$379$	12.6234	−	12.6234i	0.648420	−	0.648420i	0.952611	+	0.304191i	$0.0983861\pi$
$380$	0.0120225	+	0.0291443i	0.000616741	+	0.00149507i
$381$	8.36112	+	8.36112i	0.428353	+	0.428353i
$382$	−3.09295	−	15.6084i	−0.158249	−	0.798598i
$383$	−21.5769			−1.10253			−0.551263	−	0.834331i	$-0.685854\pi$
$383$	−21.5769			−1.10253			−0.551263	+	0.834331i	$0.685854\pi$
$384$	6.23775	+	9.43878i	0.318319	+	0.481671i
$385$	−5.95773	+	2.23558i	−0.303634	+	0.113936i
$386$	21.6470	−	4.28954i	1.10180	−	0.218332i
$387$	7.89391	+	7.89391i	0.401270	+	0.401270i
$388$	12.0576	+	29.2295i	0.612133	+	1.48390i
$389$	−4.93088	−	4.93088i	−0.250006	−	0.250006i	0.570967	−	0.820973i	$-0.306568\pi$
$389$	−4.93088	−	4.93088i	−0.250006	−	0.250006i	−0.820973	+	0.570967i	$0.806568\pi$
$390$	−0.641371	+	0.958374i	−0.0324771	+	0.0485292i
$391$		−	8.01123i		−	0.405146i
$392$	−5.20387	+	19.1029i	−0.262835	+	0.964841i
$393$		−	13.7002i		−	0.691081i
$394$	11.2274	+	7.51369i	0.565629	+	0.378534i
$395$	−4.99020	−	4.99020i	−0.251084	−	0.251084i
$396$	2.92958	+	1.21845i	0.147217	+	0.0612295i
$397$	−21.5942	−	21.5942i	−1.08378	−	1.08378i	−0.996153	−	0.0876282i	$-0.972071\pi$
$397$	−21.5942	−	21.5942i	−1.08378	−	1.08378i	−0.0876282	−	0.996153i	$-0.527929\pi$
$398$	−6.17532	−	31.1635i	−0.309541	−	1.56208i
$399$	0.0257558	−	0.00966463i	0.00128940	−	0.000483837i
$400$	7.61900	+	7.66331i	0.380950	+	0.383166i
$401$	−8.58725			−0.428827			−0.214414	−	0.976743i	$-0.568784\pi$
$401$	−8.58725			−0.428827			−0.214414	+	0.976743i	$0.568784\pi$
$402$	−9.22292	+	1.82760i	−0.459998	+	0.0911526i
$403$	−0.461112	−	0.461112i	−0.0229696	−	0.0229696i
$404$	12.7021	−	30.5403i	0.631954	−	1.51944i
$405$	−1.07201	+	1.07201i	−0.0532688	+	0.0532688i
$406$	−19.0380	−	4.47354i	−0.944841	−	0.222018i
$407$	15.0318			0.745101
$408$	13.6724	+	2.75052i	0.676883	+	0.136171i
$409$	−6.59158			−0.325933			−0.162966	−	0.986632i	$-0.552106\pi$
$409$	−6.59158			−0.325933			−0.162966	+	0.986632i	$0.552106\pi$
$410$	2.48976	−	3.72034i	0.122960	−	0.183735i
$411$	−0.451772	−	0.451772i	−0.0222843	−	0.0222843i
$412$	13.1623	+	31.9074i	0.648461	+	1.57197i
$413$	14.5357	−	31.9965i	0.715256	−	1.57444i
$414$	−0.446633	−	2.25391i	−0.0219508	−	0.110774i
$415$			1.49002i			0.0731421i
$416$	2.98626	−	0.582760i	0.146413	−	0.0285722i
$417$	−12.4268			−0.608542
$418$	−0.00453439	−	0.0228826i	−0.000221784	−	0.00111922i
$419$	−3.50670	+	3.50670i	−0.171313	+	0.171313i	−0.787556	−	0.616243i	$-0.788654\pi$
$419$	−3.50670	+	3.50670i	−0.171313	+	0.171313i	0.616243	+	0.787556i	$0.288654\pi$
$420$	−5.86851	+	5.46961i	−0.286354	+	0.266890i
$421$	12.7198	+	12.7198i	0.619924	+	0.619924i	0.945512	−	0.325588i	$-0.105562\pi$
$421$	12.7198	+	12.7198i	0.619924	+	0.619924i	−0.325588	+	0.945512i	$0.605562\pi$
$422$	6.25522	+	4.18617i	0.304499	+	0.203779i
$423$			2.09637i			0.101929i
$424$	−20.7100	−	4.16633i	−1.00577	−	0.202335i
$425$	13.3208			0.646152
$426$	−4.06608	+	6.07578i	−0.197002	+	0.294372i
$427$	3.79342	−	8.35019i	0.183576	−	0.404094i
$428$	−0.528236	+	1.27006i	−0.0255332	+	0.0613908i
$429$	0.603358	−	0.603358i	0.0291304	−	0.0291304i
$430$	4.65252	+	23.4787i	0.224364	+	1.13224i
$431$			35.1089i			1.69114i	0.533867	+	0.845568i	$0.320738\pi$
$431$			35.1089i			1.69114i	−0.533867	+	0.845568i	$0.679262\pi$
$432$	3.99998	+	0.0115983i	0.192449	+	0.000558023i
$433$			27.6070i			1.32671i	0.748306	+	0.663353i	$0.230867\pi$
$433$			27.6070i			1.32671i	−0.748306	+	0.663353i	$0.769133\pi$
$434$	−2.38894	−	3.85648i	−0.114673	−	0.185117i
$435$	−5.60311	−	5.60311i	−0.268649	−	0.268649i
$436$	4.98849	−	11.9941i	0.238905	−	0.574412i
$437$	−0.0119455	+	0.0119455i	−0.000571429	+	0.000571429i
$438$	6.16133	−	9.20662i	0.294400	−	0.439909i
$439$			18.3491i			0.875753i	0.899035	+	0.437877i	$0.144269\pi$
$439$			18.3491i			0.875753i	−0.899035	+	0.437877i	$0.855731\pi$
$440$	3.76708	+	5.66446i	0.179588	+	0.270042i
$441$	4.60496	+	5.27203i	0.219284	+	0.251049i
$442$	2.08596	−	3.11697i	0.0992192	−	0.148259i
$443$	14.7001	−	14.7001i	0.698421	−	0.698421i	−0.265649	−	0.964070i	$-0.585586\pi$
$443$	14.7001	−	14.7001i	0.698421	−	0.698421i	0.964070	+	0.265649i	$0.0855862\pi$
$444$	17.5185	−	7.22665i	0.831390	−	0.342962i
$445$	17.5744	−	17.5744i	0.833105	−	0.833105i
$446$	19.5362	−	3.87127i	0.925066	−	0.183310i
$447$	9.45774			0.447336
$448$	21.1507	+	0.805534i	0.999276	+	0.0380579i
$449$	−5.70106			−0.269050			−0.134525	−	0.990910i	$-0.542951\pi$
$449$	−5.70106			−0.269050			−0.134525	+	0.990910i	$0.542951\pi$
$450$	3.74772	−	0.742644i	0.176669	−	0.0350086i
$451$	−2.34219	+	2.34219i	−0.110290	+	0.110290i
$452$	30.4650	−	12.5673i	1.43295	−	0.591115i
$453$	−8.27942	+	8.27942i	−0.389001	+	0.389001i
$454$	−20.0672	+	29.9855i	−0.941798	+	1.40729i
$455$	0.757944	+	2.01989i	0.0355330	+	0.0946939i
$456$	−0.0162854	−	0.0244880i	−0.000762636	−	0.00114676i
$457$			8.58548i			0.401612i	0.979631	+	0.200806i	$0.0643561\pi$
$457$			8.58548i			0.401612i	−0.979631	+	0.200806i	$0.935644\pi$
$458$	18.4887	−	27.6269i	0.863919	−	1.29092i
$459$	3.48657	−	3.48657i	0.162739	−	0.162739i
$460$	1.89186	−	4.54868i	0.0882083	−	0.212084i
$461$	21.5957	+	21.5957i	1.00581	+	1.00581i	0.999983	+	0.00582709i	$0.00185483\pi$
$461$	21.5957	+	21.5957i	1.00581	+	1.00581i	0.00582709	+	0.999983i	$0.498145\pi$
$462$	5.04615	−	3.12589i	0.234768	−	0.145429i
$463$			22.5950i			1.05008i	0.851078	+	0.525039i	$0.175949\pi$
$463$			22.5950i			1.05008i	−0.851078	+	0.525039i	$0.824051\pi$
$464$	−0.0606209	+	20.9068i	−0.00281425	+	0.970572i
$465$		−	1.83810i		−	0.0852398i
$466$	2.65822	+	13.4146i	0.123140	+	0.621419i
$467$	7.33529	−	7.33529i	0.339437	−	0.339437i	−0.516719	−	0.856155i	$-0.672847\pi$
$467$	7.33529	−	7.33529i	0.339437	−	0.339437i	0.856155	+	0.516719i	$0.172847\pi$
$468$	0.413100	−	0.993236i	0.0190956	−	0.0459124i
$469$	−7.27542	+	16.0149i	−0.335948	+	0.739499i
$470$	−2.49982	+	3.73538i	−0.115308	+	0.172300i
$471$	11.1321			0.512940
$472$	−36.8320	−	7.40964i	−1.69533	−	0.341056i
$473$		−	17.7104i		−	0.814326i
$474$	5.47102	+	3.66136i	0.251292	+	0.168172i
$475$	−0.0198625	−	0.0198625i	−0.000911353	−	0.000911353i
$476$	19.0865	−	17.7891i	0.874827	−	0.815363i
$477$	−5.28124	+	5.28124i	−0.241811	+	0.241811i
$478$	−6.05690	−	30.5658i	−0.277036	−	1.39805i
$479$	30.2356			1.38150			0.690749	−	0.723095i	$-0.257281\pi$
$479$	30.2356			1.38150			0.690749	+	0.723095i	$0.257281\pi$
$480$	7.11347	+	4.79045i	0.324684	+	0.218653i
$481$		−	5.09635i		−	0.232374i
$482$	−0.634477	−	3.20186i	−0.0288996	−	0.145841i
$483$	−3.91375	−	1.77798i	−0.178082	−	0.0809010i
$484$	6.47005	+	15.6844i	0.294093	+	0.712926i
$485$	16.9479	+	16.9479i	0.769565	+	0.769565i
$486$	0.786547	−	1.17531i	0.0356785	−	0.0533130i
$487$	16.2232			0.735144			0.367572	−	0.929995i	$-0.380189\pi$
$487$	16.2232			0.735144			0.367572	+	0.929995i	$0.380189\pi$
$488$	−9.61213	−	1.93371i	−0.435121	−	0.0875350i
$489$	−5.88675			−0.266208
$490$	1.91863	+	14.8851i	0.0866747	+	0.672439i
$491$	14.8388	−	14.8388i	0.669668	−	0.669668i	−0.287971	−	0.957639i	$-0.592981\pi$
$491$	14.8388	−	14.8388i	0.669668	−	0.669668i	0.957639	+	0.287971i	$0.0929807\pi$
$492$	−1.60362	+	3.85567i	−0.0722970	+	0.173827i
$493$	18.2233	+	18.2233i	0.820736	+	0.820736i
$494$	−0.00775805	+	0.00153733i	−0.000349051	+	6.91676e-5i
$495$	2.40512			0.108102
$496$	−3.43917	+	3.41928i	−0.154423	+	0.153530i
$497$	4.80511	+	12.8054i	0.215539	+	0.574402i
$498$	−0.270172	−	1.36341i	−0.0121067	−	0.0610959i
$499$	−16.1057	−	16.1057i	−0.720990	−	0.720990i	0.247817	−	0.968807i	$-0.420287\pi$
$499$	−16.1057	−	16.1057i	−0.720990	−	0.720990i	−0.968807	+	0.247817i	$0.920287\pi$
$500$	21.5615	+	8.96771i	0.964260	+	0.401048i
$501$	3.61283	+	3.61283i	0.161409	+	0.161409i
$502$	3.13535	+	2.09826i	0.139937	+	0.0936500i
$503$		−	6.58635i		−	0.293671i	−0.989161	−	0.146835i	$-0.953091\pi$
$503$		−	6.58635i		−	0.293671i	0.989161	−	0.146835i	$-0.0469088\pi$
$504$	4.37811	−	6.06895i	0.195016	−	0.270333i
$505$		−	25.0729i		−	1.11573i
$506$	−2.02737	+	3.02941i	−0.0901275	+	0.134674i
$507$	8.98783	+	8.98783i	0.399163	+	0.399163i
$508$	−9.01832	−	21.8617i	−0.400123	−	0.969958i
$509$	−22.6237	−	22.6237i	−1.00278	−	1.00278i	−0.999996	−	0.00278262i	$-0.999114\pi$
$509$	−22.6237	−	22.6237i	−1.00278	−	1.00278i	−0.00278262	−	0.999996i	$-0.500886\pi$
$510$	10.3700	−	2.05492i	0.459193	−	0.0909933i
$511$	−7.28119	−	19.4041i	−0.322101	−	0.858385i
$512$	−4.26951	−	22.2210i	−0.188688	−	0.982037i
$513$	−0.0103976			−0.000459064
$514$	−0.877126	−	4.42638i	−0.0386884	−	0.195239i
$515$	18.5006	+	18.5006i	0.815236	+	0.815236i
$516$	−8.51439	−	20.6402i	−0.374825	−	0.908632i
$517$	2.35166	−	2.35166i	0.103426	−	0.103426i
$518$	8.10986	−	34.5131i	0.356327	−	1.51642i
$519$	−8.55419			−0.375487
$520$	1.92046	−	1.27718i	0.0842178	−	0.0560080i
$521$	4.23960			0.185740			0.0928701	−	0.995678i	$-0.470396\pi$
$521$	4.23960			0.185740			0.0928701	+	0.995678i	$0.470396\pi$
$522$	6.14298	+	4.11105i	0.268871	+	0.179936i
$523$	−10.3026	−	10.3026i	−0.450501	−	0.450501i	0.445020	−	0.895521i	$-0.353197\pi$
$523$	−10.3026	−	10.3026i	−0.450501	−	0.450501i	−0.895521	+	0.445020i	$0.853197\pi$
$524$	−10.5223	+	25.2994i	−0.459670	+	1.10521i
$525$	2.95636	−	6.50763i	0.129026	−	0.284016i
$526$	−27.9104	+	5.53069i	−1.21695	+	0.241149i
$527$			5.97814i			0.260412i
$528$	−4.47408	−	4.50010i	−0.194709	−	0.195842i
$529$	−20.3602			−0.885226
$530$	−15.7079	+	3.11266i	−0.682308	+	0.135205i
$531$	−9.39247	+	9.39247i	−0.407599	+	0.407599i
$532$	−0.0549848	−	0.00193448i	−0.00238389	−	8.38702e-5i
$533$	0.794090	+	0.794090i	0.0343959	+	0.0343959i
$534$	−12.8945	+	19.2677i	−0.557999	+	0.833795i
$535$			1.04269i			0.0450796i
$536$	18.4352	+	3.70868i	0.796278	+	0.160190i
$537$	16.0235			0.691465
$538$	27.2935	+	18.2656i	1.17671	+	0.787484i
$539$	0.748305	−	11.0798i	0.0322318	−	0.477240i
$540$	2.80299	−	1.15628i	0.120621	−	0.0497583i
$541$	12.0207	−	12.0207i	0.516810	−	0.516810i	−0.399795	−	0.916605i	$-0.630919\pi$
$541$	12.0207	−	12.0207i	0.516810	−	0.516810i	0.916605	+	0.399795i	$0.130919\pi$
$542$	−42.1297	+	8.34838i	−1.80963	+	0.358594i
$543$		−	4.42537i		−	0.189911i
$544$	−23.1355	−	15.5802i	−0.991926	−	0.667997i
$545$		−	9.84687i		−	0.421794i
$546$	−1.05979	−	1.71083i	−0.0453549	−	0.0732167i
$547$	23.7257	+	23.7257i	1.01444	+	1.01444i	0.999894	+	0.0145455i	$0.00463013\pi$
$547$	23.7257	+	23.7257i	1.01444	+	1.01444i	0.0145455	+	0.999894i	$0.495370\pi$
$548$	0.487282	+	1.18124i	0.0208157	+	0.0504602i
$549$	−2.45118	+	2.45118i	−0.104614	+	0.104614i
$550$	−5.03719	−	3.37103i	−0.214787	−	0.143741i
$551$		−	0.0543451i		−	0.00231518i
$552$	−0.906333	+	4.50522i	−0.0385761	+	0.191755i
$553$	11.5308	−	4.32683i	0.490341	−	0.183996i
$554$	33.6301	+	22.5062i	1.42881	+	0.956197i
$555$	10.1576	−	10.1576i	0.431167	−	0.431167i
$556$	22.9479	+	9.54432i	0.973206	+	0.404769i
$557$	−0.791262	+	0.791262i	−0.0335269	+	0.0335269i	−0.723671	−	0.690145i	$-0.757547\pi$
$557$	−0.791262	+	0.791262i	−0.0335269	+	0.0335269i	0.690145	+	0.723671i	$0.257547\pi$
$558$	0.333287	+	1.68192i	0.0141091	+	0.0712012i
$559$	−6.00449			−0.253963
$560$	15.0380	−	5.59317i	0.635471	−	0.236354i
$561$	−7.82231			−0.330258
$562$	7.82659	+	39.4965i	0.330145	+	1.66606i
$563$	−27.1409	+	27.1409i	−1.14385	+	1.14385i	−0.156114	+	0.987739i	$0.549897\pi$
$563$	−27.1409	+	27.1409i	−1.14385	+	1.14385i	−0.987739	+	0.156114i	$0.950103\pi$
$564$	1.61011	−	3.87126i	0.0677978	−	0.163009i
$565$	17.6643	−	17.6643i	0.743142	−	0.743142i
$566$	10.0609	+	6.73301i	0.422890	+	0.283010i
$567$	−0.929507	−	2.47710i	−0.0390356	−	0.104028i
$568$	12.1751	−	8.09689i	0.510855	−	0.339738i
$569$		−	46.0744i		−	1.93154i	−0.259403	−	0.965769i	$-0.583526\pi$
$569$		−	46.0744i		−	1.93154i	0.259403	−	0.965769i	$-0.416474\pi$
$570$	−0.0185267	−	0.0123986i	−0.000776000	−	0.000519320i
$571$	27.3445	−	27.3445i	1.14433	−	1.14433i	0.156684	−	0.987649i	$-0.449920\pi$
$571$	27.3445	−	27.3445i	1.14433	−	1.14433i	0.987649	−	0.156684i	$-0.0500804\pi$
$572$	−1.57760	+	0.650784i	−0.0659626	+	0.0272106i
$573$	7.95597	+	7.95597i	0.332365	+	0.332365i
$574$	4.11404	+	6.64132i	0.171717	+	0.277203i
$575$			4.38937i			0.183049i
$576$	−7.37765	−	3.09358i	−0.307402	−	0.128899i
$577$		−	6.45943i		−	0.268910i	−0.990920	−	0.134455i	$-0.957072\pi$
$577$		−	6.45943i		−	0.268910i	0.990920	−	0.134455i	$-0.0429283\pi$
$578$	−10.1440	+	2.01012i	−0.421934	+	0.0836100i
$579$	−11.0339	+	11.0339i	−0.458555	+	0.458555i
$580$	6.04353	+	14.6504i	0.250944	+	0.608325i
$581$	−2.36746	−	1.07552i	−0.0982187	−	0.0446199i
$582$	−18.5809	−	12.4348i	−0.770202	−	0.515441i
$583$	11.8488			0.490725
$584$	−18.4489	+	12.2692i	−0.763421	+	0.507704i
$585$		−	0.815426i		−	0.0337137i
$586$	−12.5312	+	18.7249i	−0.517660	+	0.773518i
$587$	21.6920	+	21.6920i	0.895325	+	0.895325i	0.995018	−	0.0996934i	$-0.0317862\pi$
$587$	21.6920	+	21.6920i	0.895325	+	0.895325i	−0.0996934	+	0.995018i	$0.531786\pi$
$588$	−4.45458	−	13.2724i	−0.183704	−	0.547345i
$589$	0.00891395	−	0.00891395i	0.000367293	−	0.000367293i
$590$	−27.9359	+	5.53574i	−1.15010	+	0.227903i
$591$	−9.55275			−0.392948
$592$	−37.9008	−	0.109897i	−1.55772	−	0.00451673i
$593$		−	33.5016i		−	1.37575i	−0.725831	−	0.687873i	$-0.758544\pi$
$593$		−	33.5016i		−	1.37575i	0.725831	−	0.687873i	$-0.241456\pi$
$594$	−2.20076	+	0.436101i	−0.0902984	+	0.0178934i
$595$	8.18032	−	18.0068i	0.335361	−	0.738206i
$596$	−17.4651	−	7.26397i	−0.715399	−	0.297544i
$597$	15.8847	+	15.8847i	0.650118	+	0.650118i
$598$	1.02708	+	0.687352i	0.0420005	+	0.0281079i
$599$	2.91644			0.119162			0.0595812	−	0.998223i	$-0.481023\pi$
$599$	2.91644			0.119162			0.0595812	+	0.998223i	$0.481023\pi$
$600$	−7.49111	−	1.50702i	−0.305823	−	0.0615237i
$601$	−4.37362			−0.178404			−0.0892018	−	0.996014i	$-0.528432\pi$
$601$	−4.37362			−0.178404			−0.0892018	+	0.996014i	$0.528432\pi$
$602$	−40.6631	−	9.55499i	−1.65731	−	0.389432i
$603$	4.70113	−	4.70113i	0.191445	−	0.191445i
$604$	21.6481	−	8.93020i	0.880850	−	0.363365i
$605$	9.09415	+	9.09415i	0.369730	+	0.369730i
$606$	4.54626	+	22.9425i	0.184679	+	0.931975i
$607$	−29.8679			−1.21230			−0.606150	−	0.795350i	$-0.707287\pi$
$607$	−29.8679			−1.21230			−0.606150	+	0.795350i	$0.707287\pi$
$608$	0.0112656	+	0.0577286i	0.000456880	+	0.00234121i
$609$	12.9471	−	4.85827i	0.524642	−	0.196867i
$610$	−7.29049	+	1.44468i	−0.295183	+	0.0584932i
$611$	−0.797300	−	0.797300i	−0.0322553	−	0.0322553i
$612$	−9.11631	+	3.76062i	−0.368505	+	0.152014i
$613$	4.86096	+	4.86096i	0.196333	+	0.196333i	0.798426	−	0.602093i	$-0.205666\pi$
$613$	4.86096	+	4.86096i	0.196333	+	0.196333i	−0.602093	+	0.798426i	$0.705666\pi$
$614$	22.1648	−	33.1200i	0.894498	−	1.33661i
$615$			3.16542i			0.127642i
$616$	−11.7193	+	1.89675i	−0.472183	+	0.0764221i
$617$		−	3.74665i		−	0.150835i	−0.997152	−	0.0754173i	$-0.975971\pi$
$617$		−	3.74665i		−	0.150835i	0.997152	−	0.0754173i	$-0.0240289\pi$
$618$	−20.2832	−	13.5741i	−0.815911	−	0.546030i
$619$	19.0497	+	19.0497i	0.765671	+	0.765671i	0.977341	−	0.211670i	$-0.0678903\pi$
$619$	19.0497	+	19.0497i	0.765671	+	0.765671i	−0.211670	+	0.977341i	$0.567890\pi$
$620$	−1.41174	+	3.39432i	−0.0566969	+	0.136319i
$621$	1.14887	+	1.14887i	0.0461026	+	0.0461026i
$622$	−2.24180	−	11.3131i	−0.0898879	−	0.453615i
$623$	15.2381	+	40.6090i	0.610503	+	1.62697i
$624$	−1.52570	+	1.51688i	−0.0610769	+	0.0607237i
$625$	4.19369			0.167748
$626$	39.6490	−	7.85681i	1.58469	−	0.314021i
$627$	0.0116638	+	0.0116638i	0.000465806	+	0.000465806i
$628$	−20.5571	−	8.54996i	−0.820317	−	0.341180i
$629$	−33.0361	+	33.0361i	−1.31724	+	1.31724i
$630$	1.29759	−	5.52216i	0.0516973	−	0.220008i
$631$	28.4844			1.13395			0.566974	−	0.823736i	$-0.308114\pi$
$631$	28.4844			1.13395			0.566974	+	0.823736i	$0.308114\pi$
$632$	−7.29095	−	10.9632i	−0.290019	−	0.436093i
$633$	−5.32221			−0.211539
$634$	−14.2119	+	21.2362i	−0.564426	+	0.843399i
$635$	−12.6759	−	12.6759i	−0.503029	−	0.503029i
$636$	13.8088	−	5.69636i	0.547556	−	0.225875i
$637$	−3.75646	−	0.253703i	−0.148836	−	0.0100521i
$638$	−2.27937	−	11.5027i	−0.0902412	−	0.455398i
$639$		−	5.16953i		−	0.204503i
$640$	−9.45678	−	14.3097i	−0.373812	−	0.565642i
$641$	−23.3813			−0.923506			−0.461753	−	0.887009i	$-0.652779\pi$
$641$	−23.3813			−0.923506			−0.461753	+	0.887009i	$0.652779\pi$
$642$	−0.189063	−	0.954097i	−0.00746171	−	0.0376552i
$643$	−4.17454	+	4.17454i	−0.164628	+	0.164628i	−0.784613	−	0.619985i	$-0.787138\pi$
$643$	−4.17454	+	4.17454i	−0.164628	+	0.164628i	0.619985	+	0.784613i	$0.287138\pi$
$644$	5.86174	+	6.28924i	0.230985	+	0.247831i
$645$	−11.9676	−	11.9676i	−0.471225	−	0.471225i
$646$	0.0602555	+	0.0403246i	0.00237072	+	0.00158655i
$647$		−	17.1525i		−	0.674335i	−0.941445	−	0.337168i	$-0.890531\pi$
$647$		−	17.1525i		−	0.674335i	0.941445	−	0.337168i	$-0.109469\pi$
$648$	−2.35516	+	1.56627i	−0.0925195	+	0.0615290i
$649$	21.0725			0.827169
$650$	−1.14290	+	1.70779i	−0.0448283	+	0.0669852i
$651$	2.92052	+	1.32677i	0.114464	+	0.0520000i
$652$	10.8707	+	4.52129i	0.425731	+	0.177067i
$653$	6.83742	−	6.83742i	0.267569	−	0.267569i	−0.560551	−	0.828120i	$-0.689411\pi$
$653$	6.83742	−	6.83742i	0.267569	−	0.267569i	0.828120	+	0.560551i	$0.189411\pi$
$654$	1.78545	+	9.01019i	0.0698166	+	0.352326i
$655$			20.7702i			0.811560i
$656$	5.92266	−	5.88841i	0.231241	−	0.229904i
$657$			7.83339i			0.305609i
$658$	−4.13067	−	6.66817i	−0.161030	−	0.259952i
$659$	−18.8182	−	18.8182i	−0.733054	−	0.733054i	0.238170	−	0.971224i	$-0.423453\pi$
$659$	−18.8182	−	18.8182i	−0.733054	−	0.733054i	−0.971224	+	0.238170i	$0.923453\pi$
$660$	−4.44142	−	1.84724i	−0.172882	−	0.0719038i
$661$	23.9718	−	23.9718i	0.932396	−	0.932396i	−0.0654588	−	0.997855i	$-0.520851\pi$
$661$	23.9718	−	23.9718i	0.932396	−	0.932396i	0.997855	+	0.0654588i	$0.0208511\pi$
$662$	−16.8120	+	25.1214i	−0.653415	+	0.976372i
$663$			2.65205i			0.102997i
$664$	−0.548249	+	2.72524i	−0.0212762	+	0.105760i
$665$	−0.0390473	+	0.0146521i	−0.00151419	+	0.000568185i
$666$	−7.45273	+	11.1363i	−0.288787	+	0.431524i
$667$	−6.00481	+	6.00481i	−0.232507	+	0.232507i
$668$	−3.89680	−	9.44643i	−0.150772	−	0.365493i
$669$	−9.95804	+	9.95804i	−0.385000	+	0.385000i
$670$	13.9825	−	2.77075i	0.540191	−	0.107044i
$671$	5.49935			0.212300
$672$	−12.7461	+	7.84463i	−0.491690	+	0.302613i
$673$	3.36157			0.129579			0.0647896	−	0.997899i	$-0.479362\pi$
$673$	3.36157			0.129579			0.0647896	+	0.997899i	$0.479362\pi$
$674$	−9.87945	+	1.95770i	−0.380542	+	0.0754078i
$675$	−1.91030	+	1.91030i	−0.0735274	+	0.0735274i
$676$	−9.69429	−	23.5004i	−0.372857	−	0.903862i
$677$	16.3331	−	16.3331i	0.627731	−	0.627731i	−0.319766	−	0.947497i	$-0.603604\pi$
$677$	16.3331	−	16.3331i	0.627731	−	0.627731i	0.947497	+	0.319766i	$0.103604\pi$
$678$	−12.9604	+	19.3663i	−0.497743	+	0.743757i
$679$	−39.1615	+	14.6950i	−1.50288	+	0.563941i
$680$	−20.7281	−	4.16995i	−0.794886	−	0.159910i
$681$		−	25.5130i		−	0.977659i
$682$	1.51286	−	2.26061i	0.0579305	−	0.0865632i
$683$	−6.36376	+	6.36376i	−0.243503	+	0.243503i	−0.818298	−	0.574795i	$-0.805082\pi$
$683$	−6.36376	+	6.36376i	−0.243503	+	0.243503i	0.574795	+	0.818298i	$0.305082\pi$
$684$	0.0192007	+	0.00798581i	0.000734156	+	0.000305345i
$685$	0.684912	+	0.684912i	0.0261691	+	0.0261691i
$686$	−25.0355	−	7.69579i	−0.955859	−	0.293826i
$687$			23.5061i			0.896814i
$688$	−0.129480	+	44.6545i	−0.00493636	+	1.70244i
$689$		−	4.01717i		−	0.153042i
$690$	0.677122	+	3.41707i	0.0257776	+	0.130085i
$691$	5.76023	−	5.76023i	0.219129	−	0.219129i	−0.589002	−	0.808131i	$-0.700479\pi$
$691$	5.76023	−	5.76023i	0.219129	−	0.219129i	0.808131	+	0.589002i	$0.200479\pi$
$692$	15.7966	+	6.57000i	0.600495	+	0.249754i
$693$	−1.73605	+	3.82145i	−0.0659472	+	0.145165i
$694$	0.293620	−	0.438744i	0.0111457	−	0.0166545i
$695$	18.8397			0.714631
$696$	−8.18645	−	12.3098i	−0.310307	−	0.466600i
$697$		−	10.2951i		−	0.389954i
$698$	−7.27837	−	4.87089i	−0.275490	−	0.184366i
$699$	−6.83772	−	6.83772i	−0.258626	−	0.258626i
$700$	−10.4575	+	9.74668i	−0.395256	+	0.368390i
$701$	−2.52774	+	2.52774i	−0.0954714	+	0.0954714i	−0.753229	−	0.657758i	$-0.771505\pi$
$701$	−2.52774	+	2.52774i	−0.0954714	+	0.0954714i	0.657758	+	0.753229i	$0.271505\pi$
$702$	0.147854	+	0.746139i	0.00558040	+	0.0281612i
$703$	0.0985197			0.00371574
$704$	4.80577	+	11.7464i	0.181124	+	0.442709i
$705$		−	3.17822i		−	0.119699i
$706$	−4.65986	−	23.5158i	−0.175376	−	0.885029i
$707$	39.8379	+	18.0980i	1.49826	+	0.680645i
$708$	24.5584	−	10.1307i	0.922962	−	0.380737i
$709$	−25.4224	−	25.4224i	−0.954759	−	0.954759i	0.0442613	−	0.999020i	$-0.485907\pi$
$709$	−25.4224	−	25.4224i	−0.954759	−	0.954759i	−0.999020	+	0.0442613i	$0.985907\pi$
$710$	6.16441	−	9.21123i	0.231346	−	0.345691i
$711$	−4.65497			−0.174575
$712$	38.6100	−	25.6771i	1.44697	−	0.962291i
$713$	−1.96988			−0.0737724
$714$	−4.22023	+	17.9600i	−0.157938	+	0.672137i
$715$	−0.914726	+	0.914726i	−0.0342088	+	0.0342088i
$716$	−29.5897	−	12.3068i	−1.10582	−	0.459925i
$717$	15.5801	+	15.5801i	0.581849	+	0.581849i
$718$	−41.2457	+	8.17321i	−1.53928	+	0.305021i
$719$	−8.26294			−0.308156			−0.154078	−	0.988059i	$-0.549241\pi$
$719$	−8.26294			−0.308156			−0.154078	+	0.988059i	$0.549241\pi$
$720$	−6.06421	−	0.0175837i	−0.226000	−	0.000655305i
$721$	−42.7493	+	16.0413i	−1.59207	+	0.597408i
$722$	5.22295	+	26.3574i	0.194378	+	0.980921i
$723$	1.63206	+	1.63206i	0.0606969	+	0.0606969i
$724$	−3.39889	+	8.17211i	−0.126319	+	0.303714i
$725$	−9.98457	−	9.98457i	−0.370818	−	0.370818i
$726$	−9.97039	−	6.67246i	−0.370036	−	0.247638i
$727$		−	3.21095i		−	0.119087i	−0.998226	−	0.0595437i	$-0.981035\pi$
$727$		−	3.21095i		−	0.119087i	0.998226	−	0.0595437i	$-0.0189646\pi$
$728$	0.643067	+	3.97327i	0.0238337	+	0.147259i
$729$			1.00000i			0.0370370i
$730$	−9.34093	+	13.9578i	−0.345723	+	0.516600i
$731$	38.9230	+	38.9230i	1.43962	+	1.43962i
$732$	6.40907	−	2.64385i	0.236886	−	0.0977194i
$733$	−9.97638	−	9.97638i	−0.368486	−	0.368486i	0.498439	−	0.866925i	$-0.333907\pi$
$733$	−9.97638	−	9.97638i	−0.368486	−	0.368486i	−0.866925	+	0.498439i	$0.833907\pi$
$734$	−8.70540	+	1.72505i	−0.321322	+	0.0636728i
$735$	−6.98139	−	7.99271i	−0.257512	−	0.294815i
$736$	5.13389	−	7.62345i	0.189238	−	0.281004i
$737$	−10.5472			−0.388513
$738$	−0.573959	−	2.89646i	−0.0211277	−	0.106620i
$739$	14.7848	+	14.7848i	0.543868	+	0.543868i	0.924660	−	0.380793i	$-0.124349\pi$
$739$	14.7848	+	14.7848i	0.543868	+	0.543868i	−0.380793	+	0.924660i	$0.624349\pi$
$740$	−26.5590	+	10.9560i	−0.976329	+	0.402751i
$741$	0.00395445	−	0.00395445i	0.000145270	−	0.000145270i
$742$	6.39255	−	27.2047i	0.234678	−	0.998718i
$743$	−24.4950			−0.898634			−0.449317	−	0.893372i	$-0.648333\pi$
$743$	−24.4950			−0.898634			−0.449317	+	0.893372i	$0.648333\pi$
$744$	0.676324	−	3.36189i	0.0247952	−	0.123253i
$745$	−14.3385			−0.525322
$746$	0.252470	+	0.168960i	0.00924358	+	0.00618606i
$747$	0.694961	+	0.694961i	0.0254273	+	0.0254273i
$748$	14.4451	+	6.00789i	0.528163	+	0.219670i
$749$	−1.65672	−	0.752631i	−0.0605351	−	0.0275006i
$750$	−16.1974	+	3.20967i	−0.591447	+	0.117200i
$751$			9.30768i			0.339642i	0.985475	+	0.169821i	$0.0543190\pi$
$751$			9.30768i			0.339642i	−0.985475	+	0.169821i	$0.945681\pi$
$752$	−5.94660	+	5.91222i	−0.216850	+	0.215596i
$753$	−2.66769			−0.0972159
$754$	−3.89985	+	0.772791i	−0.142024	+	0.0281434i
$755$	12.5521	−	12.5521i	0.456817	−	0.456817i
$756$	−0.186051	+	5.28823i	−0.00676659	+	0.192331i
$757$	4.71911	+	4.71911i	0.171519	+	0.171519i	0.787647	−	0.616127i	$-0.211299\pi$
$757$	4.71911	+	4.71911i	0.171519	+	0.171519i	−0.616127	+	0.787647i	$0.711299\pi$
$758$	14.0416	−	20.9818i	0.510013	−	0.762092i
$759$		−	2.57755i		−	0.0935593i
$760$	0.0246897	+	0.0371252i	0.000895588	+	0.00134667i
$761$	−6.21468			−0.225282			−0.112641	−	0.993636i	$-0.535931\pi$
$761$	−6.21468			−0.225282			−0.112641	+	0.993636i	$0.535931\pi$
$762$	13.8973	+	9.30045i	0.503446	+	0.336920i
$763$	15.6455	+	7.10761i	0.566405	+	0.257313i
$764$	−8.58133	−	20.8024i	−0.310462	−	0.752605i
$765$	−5.28584	+	5.28584i	−0.191110	+	0.191110i
$766$	−29.9323	+	5.93135i	−1.08150	+	0.214308i
$767$		−	7.14436i		−	0.257968i
$768$	11.2479	+	11.3791i	0.405874	+	0.410609i
$769$		−	36.6035i		−	1.31995i	−0.751286	−	0.659977i	$-0.770566\pi$
$769$		−	36.6035i		−	1.31995i	0.751286	−	0.659977i	$-0.229434\pi$
$770$	−7.65025	+	4.73903i	−0.275696	+	0.170783i
$771$	2.25622	+	2.25622i	0.0812559	+	0.0812559i
$772$	28.8504	−	11.9012i	1.03835	−	0.428335i
$773$	−14.9532	+	14.9532i	−0.537831	+	0.537831i	−0.922891	−	0.385061i	$-0.874181\pi$
$773$	−14.9532	+	14.9532i	−0.537831	+	0.537831i	0.385061	+	0.922891i	$0.374181\pi$
$774$	13.1207	+	8.78076i	0.471615	+	0.315618i
$775$		−	3.27543i		−	0.117657i
$776$	24.7618	+	37.2337i	0.888898	+	1.33661i
$777$	8.80731	+	23.4711i	0.315961	+	0.842022i
$778$	−8.19578	−	5.48484i	−0.293833	−	0.196641i
$779$	−0.0153509	+	0.0153509i	−0.000550003	+	0.000550003i
$780$	−0.626284	+	1.50580i	−0.0224245	+	0.0539164i
$781$	−5.79906	+	5.79906i	−0.207507	+	0.207507i
$782$	−2.20224	−	11.1135i	−0.0787519	−	0.397418i
$783$	−5.22671			−0.186787
$784$	−1.96776	+	27.9308i	−0.0702770	+	0.997528i
$785$	−16.8769			−0.602363
$786$	−3.76609	−	19.0054i	−0.134332	−	0.677900i
$787$	−28.5199	+	28.5199i	−1.01662	+	1.01662i	−0.0167646	+	0.999859i	$0.505337\pi$
$787$	−28.5199	+	28.5199i	−1.01662	+	1.01662i	−0.999859	+	0.0167646i	$0.994663\pi$
$788$	17.6406	+	7.33694i	0.628419	+	0.261368i
$789$	14.2265	−	14.2265i	0.506478	−	0.506478i
$790$	−8.29438	−	5.55083i	−0.295101	−	0.197490i
$791$	15.3161	+	40.8167i	0.544577	+	1.45128i
$792$	4.39898	+	0.884960i	0.156311	+	0.0314457i
$793$		−	1.86448i		−	0.0662097i
$794$	−35.8924	−	24.0202i	−1.27377	−	0.852445i
$795$	8.00667	−	8.00667i	0.283967	−	0.283967i
$796$	−17.1333	−	41.5336i	−0.607273	−	1.47212i
$797$	−30.0556	−	30.0556i	−1.06462	−	1.06462i	−0.997762	−	0.0668612i	$-0.978702\pi$
$797$	−30.0556	−	30.0556i	−1.06462	−	1.06462i	−0.0668612	−	0.997762i	$-0.521298\pi$
$798$	0.0330728	−	0.0204873i	0.00117076	−	0.000725242i
$799$			10.3367i			0.365686i
$800$	12.6760	+	8.53643i	0.448163	+	0.301808i
$801$		−	16.3938i		−	0.579246i
$802$	−11.9126	+	2.36058i	−0.420648	+	0.0833551i
$803$	8.78731	−	8.78731i	0.310098	−	0.310098i
$804$	−12.2920	+	5.07065i	−0.433506	+	0.178828i
$805$	5.93347	+	2.69552i	0.209127	+	0.0950047i
$806$	−0.766430	−	0.512916i	−0.0269963	−	0.0180667i
$807$	−23.2225			−0.817469
$808$	9.22553	−	45.8584i	0.324553	−	1.61329i
$809$		−	42.1631i		−	1.48238i	−0.671297	−	0.741188i	$-0.734263\pi$
$809$		−	42.1631i		−	1.48238i	0.671297	−	0.741188i	$-0.265737\pi$
$810$	−1.19245	+	1.78183i	−0.0418985	+	0.0626072i
$811$	−25.2514	−	25.2514i	−0.886696	−	0.886696i	0.107508	−	0.994204i	$-0.465713\pi$
$811$	−25.2514	−	25.2514i	−0.886696	−	0.886696i	−0.994204	+	0.107508i	$0.965713\pi$
$812$	−27.6401	−	0.972432i	−0.969976	−	0.0341257i
$813$	21.4745	−	21.4745i	0.753142	−	0.753142i
$814$	20.8528	−	4.13216i	0.730889	−	0.144832i
$815$	8.92465			0.312617
$816$	19.7229	+	0.0571883i	0.690441	+	0.00200199i
$817$		−	0.116075i		−	0.00406096i
$818$	−9.14410	+	1.81199i	−0.319716	+	0.0633546i
$819$	1.29561	+	0.588586i	0.0452724	+	0.0205669i
$820$	2.43119	−	5.84542i	0.0849008	−	0.204131i
$821$	20.8479	+	20.8479i	0.727597	+	0.727597i	0.970140	−	0.242544i	$-0.0779818\pi$
$821$	20.8479	+	20.8479i	0.727597	+	0.727597i	−0.242544	+	0.970140i	$0.577982\pi$
$822$	−0.750905	−	0.502526i	−0.0261908	−	0.0175276i
$823$	22.9417			0.799696			0.399848	−	0.916582i	$-0.369063\pi$
$823$	22.9417			0.799696			0.399848	+	0.916582i	$0.369063\pi$
$824$	27.0305	+	40.6450i	0.941650	+	1.41594i
$825$	4.28586			0.149214
$826$	11.3689	−	48.3825i	0.395574	−	1.68344i
$827$	16.6173	−	16.6173i	0.577841	−	0.577841i	−0.356467	−	0.934308i	$-0.616019\pi$
$827$	16.6173	−	16.6173i	0.577841	−	0.577841i	0.934308	+	0.356467i	$0.116019\pi$
$828$	−1.23917	−	3.00394i	−0.0430643	−	0.104394i
$829$	37.4650	+	37.4650i	1.30121	+	1.30121i	0.927573	+	0.373641i	$0.121891\pi$
$829$	37.4650	+	37.4650i	1.30121	+	1.30121i	0.373641	+	0.927573i	$0.378109\pi$
$830$	0.409597	+	2.06701i	0.0142173	+	0.0717470i
$831$	−28.6139			−0.992606
$832$	3.98246	−	1.62933i	0.138067	−	0.0564869i
$833$	22.7059	+	25.9951i	0.786714	+	0.900677i
$834$	−17.2389	+	3.41604i	−0.596935	+	0.118288i
$835$	−5.47725	−	5.47725i	−0.189548	−	0.189548i
$836$	−0.0125806	−	0.0304972i	−0.000435108	−	0.00105477i
$837$	−0.857310	−	0.857310i	−0.0296330	−	0.0296330i
$838$	−3.90066	+	5.82860i	−0.134746	+	0.201346i
$839$		−	46.1798i		−	1.59431i	−0.603778	−	0.797153i	$-0.706339\pi$
$839$		−	46.1798i		−	1.59431i	0.603778	−	0.797153i	$-0.293661\pi$
$840$	−6.63747	+	9.20088i	−0.229014	+	0.317461i
$841$			1.68150i			0.0579827i
$842$	21.1420	+	14.1488i	0.728600	+	0.487599i
$843$	−20.1323	−	20.1323i	−0.693392	−	0.693392i
$844$	9.82824	+	4.08769i	0.338302	+	0.140704i
$845$	−13.6261	−	13.6261i	−0.468751	−	0.468751i
$846$	0.576280	+	2.90817i	0.0198129	+	0.0999849i
$847$	−21.0138	+	7.88523i	−0.722043	+	0.270940i
$848$	−29.8751	−	0.0866254i	−1.02591	−	0.00297473i
$849$	−8.56021			−0.293786
$850$	18.4791	−	3.66180i	0.633828	−	0.125599i
$851$	−10.8858	−	10.8858i	−0.373162	−	0.373162i
$852$	−3.97043	+	9.54629i	−0.136025	+	0.327051i
$853$	12.7966	−	12.7966i	0.438147	−	0.438147i	−0.453241	−	0.891388i	$-0.649732\pi$
$853$	12.7966	−	12.7966i	0.438147	−	0.438147i	0.891388	+	0.453241i	$0.149732\pi$
$854$	2.96696	−	12.6265i	0.101527	−	0.432070i
$855$	0.0157633			0.000539095
$856$	−0.383657	+	1.90709i	−0.0131131	+	0.0651830i
$857$	−50.6120			−1.72887			−0.864437	−	0.502741i	$-0.832325\pi$
$857$	−50.6120			−1.72887			−0.864437	+	0.502741i	$0.832325\pi$
$858$	0.671143	−	1.00286i	0.0229124	−	0.0342371i
$859$	18.5878	+	18.5878i	0.634209	+	0.634209i	0.949121	−	0.314912i	$-0.101975\pi$
$859$	18.5878	+	18.5878i	0.634209	+	0.634209i	−0.314912	+	0.949121i	$0.601975\pi$
$860$	12.9083	+	31.2917i	0.440170	+	1.06704i
$861$	−5.02948	−	2.28485i	−0.171404	−	0.0778674i
$862$	9.65122	+	48.7045i	0.328722	+	1.65888i
$863$			11.9291i			0.406072i	0.979171	+	0.203036i	$0.0650809\pi$
$863$			11.9291i			0.406072i	−0.979171	+	0.203036i	$0.934919\pi$
$864$	5.55212	−	1.08348i	0.188887	−	0.0368608i
$865$	12.9686			0.440947
$866$	7.58899	+	38.2975i	0.257884	+	1.30140i
$867$	5.17061	−	5.17061i	0.175603	−	0.175603i
$868$	−4.37415	−	4.69316i	−0.148468	−	0.159296i
$869$	5.22184	+	5.22184i	0.177139	+	0.177139i
$870$	−9.31312	−	6.23260i	−0.315744	−	0.211305i
$871$			3.57590i			0.121165i
$872$	3.62314	−	18.0100i	0.122695	−	0.609894i
$873$	15.8094			0.535067
$874$	−0.0132875	+	0.0198550i	−0.000449456	+	0.000671604i
$875$	−12.7772	+	28.1256i	−0.431949	+	0.950819i
$876$	6.01639	−	14.4655i	0.203275	−	0.488744i
$877$	0.656007	−	0.656007i	0.0221518	−	0.0221518i	−0.695944	−	0.718096i	$-0.745014\pi$
$877$	0.656007	−	0.656007i	0.0221518	−	0.0221518i	0.718096	+	0.695944i	$0.245014\pi$
$878$	5.04405	+	25.4546i	0.170228	+	0.859050i
$879$		−	15.9319i		−	0.537371i
$880$	6.78296	+	6.82241i	0.228654	+	0.229984i
$881$		−	25.1066i		−	0.845862i	−0.906162	−	0.422931i	$-0.861001\pi$
$881$		−	25.1066i		−	0.845862i	0.906162	−	0.422931i	$-0.138999\pi$
$882$	7.83743	+	6.04770i	0.263900	+	0.203637i
$883$	23.0181	+	23.0181i	0.774622	+	0.774622i	0.978911	−	0.204289i	$-0.0654883\pi$
$883$	23.0181	+	23.0181i	0.774622	+	0.774622i	−0.204289	+	0.978911i	$0.565488\pi$
$884$	2.03690	−	4.89741i	0.0685082	−	0.164718i
$885$	14.2395	−	14.2395i	0.478657	−	0.478657i
$886$	16.3515	−	24.4335i	0.549341	−	0.820858i
$887$			35.2156i			1.18243i	0.806516	+	0.591213i	$0.201351\pi$
$887$			35.2156i			1.18243i	−0.806516	+	0.591213i	$0.798649\pi$
$888$	22.3158	−	14.8408i	0.748868	−	0.498025i
$889$	29.2902	−	10.9909i	0.982362	−	0.368622i
$890$	19.5488	−	29.2110i	0.655277	−	0.979154i
$891$	1.12178	−	1.12178i	0.0375810	−	0.0375810i
$892$	26.0372	−	10.7408i	0.871790	−	0.359628i
$893$	0.0154129	−	0.0154129i	0.000515774	−	0.000515774i
$894$	13.1202	−	2.59988i	0.438804	−	0.0869528i
$895$	−24.2925			−0.812010
$896$	29.5625	−	4.69672i	0.987613	−	0.156906i
$897$	−0.873886			−0.0291782
$898$	−7.90873	+	1.56719i	−0.263918	+	0.0522977i
$899$	4.48091	−	4.48091i	0.149447	−	0.149447i
$900$	4.99484	−	2.06045i	0.166495	−	0.0686817i
$901$	−26.0405	+	26.0405i	−0.867535	+	0.867535i
$902$	−2.60533	+	3.89304i	−0.0867480	+	0.129624i
$903$	27.6535	−	10.3767i	0.920252	−	0.345316i
$904$	38.8075	−	25.8085i	1.29072	−	0.858377i
$905$			6.70912i			0.223019i
$906$	−9.20957	+	13.7615i	−0.305968	+	0.457195i
$907$	1.59277	−	1.59277i	0.0528870	−	0.0528870i	−0.680169	−	0.733056i	$-0.738093\pi$
$907$	1.59277	−	1.59277i	0.0528870	−	0.0528870i	0.733056	+	0.680169i	$0.238093\pi$
$908$	−19.5951	+	47.1135i	−0.650287	+	1.56352i
$909$	−11.6943	−	11.6943i	−0.387876	−	0.387876i
$910$	1.60671	+	2.59372i	0.0532618	+	0.0859809i
$911$		−	19.7779i		−	0.655273i	−0.944804	−	0.327636i	$-0.893748\pi$
$911$		−	19.7779i		−	0.655273i	0.944804	−	0.327636i	$-0.106252\pi$
$912$	−0.0293234	−	0.0294939i	−0.000970995	−	0.000976642i
$913$		−	1.55918i		−	0.0516014i
$914$	2.36010	+	11.9101i	0.0780651	+	0.393952i
$915$	3.71613	−	3.71613i	0.122851	−	0.122851i
$916$	18.0538	−	43.4075i	0.596513	−	1.43422i
$917$	−33.0014	−	14.9922i	−1.08980	−	0.495088i
$918$	3.87827	−	5.79515i	0.128002	−	0.191268i
$919$	13.7184			0.452528			0.226264	−	0.974066i	$-0.427349\pi$
$919$	13.7184			0.452528			0.226264	+	0.974066i	$0.427349\pi$
$920$	1.37405	−	6.83017i	0.0453012	−	0.225184i
$921$			28.1799i			0.928558i
$922$	35.8949	+	24.0218i	1.18213	+	0.791117i
$923$	1.96609	+	1.96609i	0.0647148	+	0.0647148i
$924$	6.14092	−	5.72351i	0.202022	−	0.188290i
$925$	18.1005	−	18.1005i	0.595142	−	0.595142i
$926$	6.21123	+	31.3447i	0.204114	+	1.03005i
$927$	17.2578			0.566821
$928$	5.66304	+	29.0193i	0.185898	+	0.952606i
$929$			37.2406i			1.22182i	0.791698	+	0.610912i	$0.209197\pi$
$929$			37.2406i			1.22182i	−0.791698	+	0.610912i	$0.790803\pi$
$930$	−0.505282	−	2.54988i	−0.0165688	−	0.0836139i
$931$	0.00490444	−	0.0726176i	0.000160736	−	0.00237995i
$932$	7.37518	+	17.8785i	0.241582	+	0.585631i
$933$	5.76655	+	5.76655i	0.188789	+	0.188789i
$934$	8.15938	−	12.1922i	0.266983	−	0.398942i
$935$	11.8591			0.387833
$936$	0.300034	−	1.49142i	0.00980692	−	0.0487484i
$937$	−13.5853			−0.443813			−0.221906	−	0.975068i	$-0.571228\pi$
$937$	−13.5853			−0.443813			−0.221906	+	0.975068i	$0.571228\pi$
$938$	−5.69036	+	24.2165i	−0.185797	+	0.790695i
$939$	−20.2100	+	20.2100i	−0.659528	+	0.659528i
$940$	−2.44102	+	5.86905i	−0.0796172	+	0.191427i
$941$	18.5023	+	18.5023i	0.603158	+	0.603158i	0.941149	−	0.337991i	$-0.109747\pi$
$941$	18.5023	+	18.5023i	0.603158	+	0.603158i	−0.337991	+	0.941149i	$0.609747\pi$
$942$	15.4429	−	3.06015i	0.503157	−	0.0997050i
$943$	3.39236			0.110471
$944$	−53.1316	−	0.154060i	−1.72929	−	0.00501422i
$945$	1.40919	+	3.75542i	0.0458409	+	0.122164i
$946$	−4.86849	−	24.5686i	−0.158288	−	0.798794i
$947$	1.34969	+	1.34969i	0.0438590	+	0.0438590i	0.728696	−	0.684837i	$-0.240127\pi$
$947$	1.34969	+	1.34969i	0.0438590	+	0.0438590i	−0.684837	+	0.728696i	$0.740127\pi$
$948$	8.59609	+	3.57523i	0.279188	+	0.116118i
$949$	−2.97922	−	2.97922i	−0.0967097	−	0.0967097i
$950$	−0.0330141	−	0.0220939i	−0.00107112	−	0.000716822i
$951$		−	18.0687i		−	0.585917i
$952$	21.5874	−	29.9245i	0.699651	−	0.969859i
$953$			42.8779i			1.38895i	0.719516	+	0.694476i	$0.244364\pi$
$953$			42.8779i			1.38895i	−0.719516	+	0.694476i	$0.755636\pi$
$954$	−5.87457	+	8.77813i	−0.190196	+	0.284202i
$955$	−12.0617	−	12.0617i	−0.390308	−	0.390308i
$956$	−16.8047	−	40.7372i	−0.543504	−	1.31753i
$957$	5.86320	+	5.86320i	0.189530	+	0.189530i
$958$	41.9440	−	8.31157i	1.35515	−	0.268535i
$959$	−1.58262	+	0.593864i	−0.0511055	+	0.0191769i
$960$	11.1849	+	4.69005i	0.360993	+	0.151371i
$961$	−29.5300			−0.952582
$962$	−1.40096	−	7.06986i	−0.0451686	−	0.227941i
$963$	0.486324	+	0.486324i	0.0156716	+	0.0156716i
$964$	−1.76034	−	4.26733i	−0.0566968	−	0.137441i
$965$	16.7281	−	16.7281i	0.538496	−	0.538496i
$966$	−5.91806	−	1.39062i	−0.190411	−	0.0447425i
$967$	−51.9878			−1.67181			−0.835907	−	0.548871i	$-0.815058\pi$
$967$	−51.9878			−1.67181			−0.835907	+	0.548871i	$0.815058\pi$
$968$	13.2870	+	19.9794i	0.427062	+	0.642162i
$969$	−0.0512679			−0.00164696
$970$	28.1697	+	18.8519i	0.904475	+	0.605299i
$971$	−0.444804	−	0.444804i	−0.0142744	−	0.0142744i	0.699934	−	0.714208i	$-0.253213\pi$
$971$	−0.444804	−	0.444804i	−0.0142744	−	0.0142744i	−0.714208	+	0.699934i	$0.753213\pi$
$972$	0.768045	−	1.84665i	0.0246351	−	0.0592312i
$973$	−13.5988	+	29.9340i	−0.435956	+	0.959641i
$974$	22.5055	−	4.45966i	0.721122	−	0.142897i
$975$		−	1.45306i		−	0.0465353i
$976$	−13.8659	−	0.0402053i	−0.443836	−	0.00128694i
$977$	−8.31426			−0.265997			−0.132998	−	0.991116i	$-0.542461\pi$
$977$	−8.31426			−0.265997			−0.132998	+	0.991116i	$0.542461\pi$
$978$	−8.16633	+	1.61823i	−0.261130	+	0.0517453i
$979$	−18.3902	+	18.3902i	−0.587752	+	0.587752i
$980$	6.75341	+	20.1217i	0.215730	+	0.642765i
$981$	−4.59269	−	4.59269i	−0.146633	−	0.146633i
$982$	16.5059	−	24.6641i	0.526725	−	0.787065i
$983$		−	20.8780i		−	0.665903i	−0.942944	−	0.332952i	$-0.891955\pi$
$983$		−	20.8780i		−	0.665903i	0.942944	−	0.332952i	$-0.108045\pi$
$984$	−1.16471	+	5.78957i	−0.0371296	+	0.184565i
$985$	14.4825			0.461452
$986$	30.2895	+	20.2706i	0.964616	+	0.645547i
$987$	5.04981	+	2.29409i	0.160737	+	0.0730215i
$988$	−0.0103397	+	0.00426528i	−0.000328949	+	0.000135697i
$989$	−12.8256	+	12.8256i	−0.407831	+	0.407831i
$990$	3.33648	−	0.661154i	0.106040	−	0.0210128i
$991$		−	36.7988i		−	1.16895i	−0.811411	−	0.584476i	$-0.801300\pi$
$991$		−	36.7988i		−	1.16895i	0.811411	−	0.584476i	$-0.198700\pi$
$992$	−3.83101	+	5.68877i	−0.121635	+	0.180619i
$993$		−	21.3744i		−	0.678296i
$994$	10.1860	+	16.4433i	0.323080	+	0.521550i
$995$	−24.0821	−	24.0821i	−0.763455	−	0.763455i
$996$	−0.749587	−	1.81711i	−0.0237516	−	0.0575773i
$997$	−14.9272	+	14.9272i	−0.472748	+	0.472748i	−0.902803	−	0.430055i	$-0.858494\pi$
$997$	−14.9272	+	14.9272i	−0.472748	+	0.472748i	0.430055	+	0.902803i	$0.358494\pi$
$998$	−26.7698	−	17.9151i	−0.847383	−	0.567092i
$999$		−	9.47525i		−	0.299784i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.31	✓	64
4.3	odd	2		1344.2.u.a.1231.26		64
7.6	odd	2	inner	336.2.u.a.139.32	yes	64
16.3	odd	4	inner	336.2.u.a.307.32	yes	64
16.13	even	4		1344.2.u.a.559.7		64
28.27	even	2		1344.2.u.a.1231.7		64
112.13	odd	4		1344.2.u.a.559.26		64
112.83	even	4	inner	336.2.u.a.307.31	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.31	✓	64	1.1	even	1	trivial
336.2.u.a.139.32	yes	64	7.6	odd	2	inner
336.2.u.a.307.31	yes	64	112.83	even	4	inner
336.2.u.a.307.32	yes	64	16.3	odd	4	inner
1344.2.u.a.559.7		64	16.13	even	4
1344.2.u.a.559.26		64	112.13	odd	4
1344.2.u.a.1231.7		64	28.27	even	2
1344.2.u.a.1231.26		64	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.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.38724 - 0.274894i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.84887 - 0.762687i) q^{4} +(1.07201 - 1.07201i) q^{5} +(-0.786547 + 1.17531i) q^{6} +(0.929507 + 2.47710i) q^{7} +(2.35516 - 1.56627i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(1.38724 - 0.274894i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.84887 - 0.762687i) q^{4} +(1.07201 - 1.07201i) q^{5} +(-0.786547 + 1.17531i) q^{6} +(0.929507 + 2.47710i) q^{7} +(2.35516 - 1.56627i) q^{8} -1.00000i q^{9} +(1.19245 - 1.78183i) q^{10} +(-1.12178 + 1.12178i) q^{11} +(-0.768045 + 1.84665i) q^{12} +(0.380324 + 0.380324i) q^{13} +(1.97039 + 3.18081i) q^{14} +1.51606i q^{15} +(2.83662 - 2.82021i) q^{16} -4.93076i q^{17} +(-0.274894 - 1.38724i) q^{18} +(-0.00735220 + 0.00735220i) q^{19} +(1.16440 - 2.79962i) q^{20} +(-2.40883 - 1.09431i) q^{21} +(-1.24780 + 1.86454i) q^{22} +1.62475 q^{23} +(-0.557830 + 2.77287i) q^{24} +2.70157i q^{25} +(0.632149 + 0.423052i) q^{26} +(0.707107 + 0.707107i) q^{27} +(3.60779 + 3.87090i) q^{28} +(-3.69584 + 3.69584i) q^{29} +(0.416755 + 2.10314i) q^{30} -1.21242 q^{31} +(3.15981 - 4.69208i) q^{32} -1.58643i q^{33} +(-1.35543 - 6.84014i) q^{34} +(3.65193 + 1.65904i) q^{35} +(-0.762687 - 1.84887i) q^{36} +(-6.70001 - 6.70001i) q^{37} +(-0.00817819 + 0.0122203i) q^{38} -0.537859 q^{39} +(0.845703 - 4.20384i) q^{40} +2.08793 q^{41} +(-3.64245 - 0.855899i) q^{42} +(-7.89391 + 7.89391i) q^{43} +(-1.21845 + 2.92958i) q^{44} +(-1.07201 - 1.07201i) q^{45} +(2.25391 - 0.446633i) q^{46} -2.09637 q^{47} +(-0.0115983 + 3.99998i) q^{48} +(-5.27203 + 4.60496i) q^{49} +(0.742644 + 3.74772i) q^{50} +(3.48657 + 3.48657i) q^{51} +(0.993236 + 0.413100i) q^{52} +(-5.28124 - 5.28124i) q^{53} +(1.17531 + 0.786547i) q^{54} +2.40512i q^{55} +(6.06895 + 4.37811i) q^{56} -0.0103976i q^{57} +(-4.11105 + 6.14298i) q^{58} +(-9.39247 - 9.39247i) q^{59} +(1.15628 + 2.80299i) q^{60} +(-2.45118 - 2.45118i) q^{61} +(-1.68192 + 0.333287i) q^{62} +(2.47710 - 0.929507i) q^{63} +(3.09358 - 7.37765i) q^{64} +0.815426 q^{65} +(-0.436101 - 2.20076i) q^{66} +(4.70113 + 4.70113i) q^{67} +(-3.76062 - 9.11631i) q^{68} +(-1.14887 + 1.14887i) q^{69} +(5.52216 + 1.29759i) q^{70} +5.16953 q^{71} +(-1.56627 - 2.35516i) q^{72} -7.83339 q^{73} +(-11.1363 - 7.45273i) q^{74} +(-1.91030 - 1.91030i) q^{75} +(-0.00798581 + 0.0192007i) q^{76} +(-3.82145 - 1.73605i) q^{77} +(-0.746139 + 0.147854i) q^{78} -4.65497i q^{79} +(0.0175837 - 6.06421i) q^{80} -1.00000 q^{81} +(2.89646 - 0.573959i) q^{82} +(-0.694961 + 0.694961i) q^{83} +(-5.28823 - 0.186051i) q^{84} +(-5.28584 - 5.28584i) q^{85} +(-8.78076 + 13.1207i) q^{86} -5.22671i q^{87} +(-0.884960 + 4.39898i) q^{88} +16.3938 q^{89} +(-1.78183 - 1.19245i) q^{90} +(-0.588586 + 1.29561i) q^{91} +(3.00394 - 1.23917i) q^{92} +(0.857310 - 0.857310i) q^{93} +(-2.90817 + 0.576280i) q^{94} +0.0157633i q^{95} +(1.08348 + 5.55212i) q^{96} +15.8094i q^{97} +(-6.04770 + 7.83743i) q^{98} +(1.12178 + 1.12178i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

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