LMFDB - Embedded newform 168.2.ba.c.5.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.8
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.968446 - 1.03059i) q^{2} +(0.609093 - 1.62142i) q^{3} +(-0.124224 + 1.99614i) q^{4} +(-2.24840 - 1.29811i) q^{5} +(-2.26089 + 0.942534i) q^{6} +(-2.53678 + 0.751482i) q^{7} +(2.17750 - 1.80513i) q^{8} +(-2.25801 - 1.97519i) q^{9} +O(q^{10})$	\(q+(-0.968446 - 1.03059i) q^{2} +(0.609093 - 1.62142i) q^{3} +(-0.124224 + 1.99614i) q^{4} +(-2.24840 - 1.29811i) q^{5} +(-2.26089 + 0.942534i) q^{6} +(-2.53678 + 0.751482i) q^{7} +(2.17750 - 1.80513i) q^{8} +(-2.25801 - 1.97519i) q^{9} +(0.839632 + 3.57432i) q^{10} +(-1.63808 - 2.83724i) q^{11} +(3.16092 + 1.41725i) q^{12} +0.912635 q^{13} +(3.23121 + 1.88661i) q^{14} +(-3.47427 + 2.85492i) q^{15} +(-3.96914 - 0.495937i) q^{16} +(2.39448 + 4.14736i) q^{17} +(0.151150 + 4.23995i) q^{18} +(2.66693 - 4.61926i) q^{19} +(2.87052 - 4.32685i) q^{20} +(-0.326671 + 4.57092i) q^{21} +(-1.33763 + 4.43590i) q^{22} +(-4.45569 - 2.57249i) q^{23} +(-1.60057 - 4.63014i) q^{24} +(0.870190 + 1.50721i) q^{25} +(-0.883838 - 0.940551i) q^{26} +(-4.57796 + 2.45811i) q^{27} +(-1.18493 - 5.15712i) q^{28} -1.35950 q^{29} +(6.30689 + 0.815700i) q^{30} +(8.18469 - 4.72543i) q^{31} +(3.33279 + 4.57083i) q^{32} +(-5.59810 + 0.927874i) q^{33} +(1.95529 - 6.48421i) q^{34} +(6.67920 + 1.60340i) q^{35} +(4.22326 - 4.26193i) q^{36} +(1.59746 + 0.922292i) q^{37} +(-7.34333 + 1.72500i) q^{38} +(0.555880 - 1.47977i) q^{39} +(-7.23914 + 1.23200i) q^{40} +5.91833 q^{41} +(5.02710 - 4.09002i) q^{42} -8.00125i q^{43} +(5.86701 - 2.91738i) q^{44} +(2.51288 + 7.37217i) q^{45} +(1.66391 + 7.08330i) q^{46} +(3.29243 - 5.70266i) q^{47} +(-3.22170 + 6.13357i) q^{48} +(5.87055 - 3.81269i) q^{49} +(0.710584 - 2.35646i) q^{50} +(8.18307 - 1.35633i) q^{51} +(-0.113371 + 1.82175i) q^{52} +(-0.841712 - 1.45789i) q^{53} +(6.96680 + 2.33745i) q^{54} +8.50565i q^{55} +(-4.16733 + 6.21557i) q^{56} +(-5.86535 - 7.13777i) q^{57} +(1.31661 + 1.40109i) q^{58} +(-1.50266 + 0.867561i) q^{59} +(-5.26724 - 7.28977i) q^{60} +(-4.72347 + 8.18130i) q^{61} +(-12.7964 - 3.85872i) q^{62} +(7.21241 + 3.31379i) q^{63} +(1.48302 - 7.86134i) q^{64} +(-2.05197 - 1.18470i) q^{65} +(6.37772 + 4.87074i) q^{66} +(-10.8634 + 6.27198i) q^{67} +(-8.57615 + 4.26451i) q^{68} +(-6.88502 + 5.65766i) q^{69} +(-4.81600 - 8.43632i) q^{70} -0.603989i q^{71} +(-8.48230 - 0.224987i) q^{72} +(-1.29220 + 0.746053i) q^{73} +(-0.596548 - 2.53951i) q^{74} +(2.97385 - 0.492910i) q^{75} +(8.88938 + 5.89738i) q^{76} +(6.28759 + 5.96647i) q^{77} +(-2.06337 + 0.860190i) q^{78} +(-0.0625152 + 0.108280i) q^{79} +(8.28041 + 6.26745i) q^{80} +(1.19722 + 8.92001i) q^{81} +(-5.73158 - 6.09936i) q^{82} -0.246431i q^{83} +(-9.08360 - 1.21990i) q^{84} -12.4332i q^{85} +(-8.24600 + 7.74878i) q^{86} +(-0.828064 + 2.20433i) q^{87} +(-8.68850 - 3.22114i) q^{88} +(1.80671 - 3.12931i) q^{89} +(5.16408 - 9.72929i) q^{90} +(-2.31516 + 0.685829i) q^{91} +(5.68856 - 8.57461i) q^{92} +(-2.67667 - 16.1491i) q^{93} +(-9.06563 + 2.12958i) q^{94} +(-11.9926 + 6.92395i) q^{95} +(9.44122 - 2.61979i) q^{96} +5.10324i q^{97} +(-9.61463 - 2.35773i) q^{98} +(-1.90529 + 9.64204i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.968446	−	1.03059i	−0.684795	−	0.728736i
$2$	−0.968446	−	1.03059i	−0.684795	−	0.728736i
$3$	0.609093	−	1.62142i	0.351660	−	0.936128i
$3$	0.609093	−	1.62142i	0.351660	−	0.936128i
$4$	−0.124224	+	1.99614i	−0.0621120	+	0.998069i
$5$	−2.24840	−	1.29811i	−1.00551	−	0.580533i	−0.0956384	−	0.995416i	$-0.530489\pi$
$5$	−2.24840	−	1.29811i	−1.00551	−	0.580533i	−0.909875	+	0.414883i	$0.863823\pi$
$6$	−2.26089	+	0.942534i	−0.923005	+	0.384788i
$7$	−2.53678	+	0.751482i	−0.958814	+	0.284033i
$7$	−2.53678	+	0.751482i	−0.958814	+	0.284033i
$8$	2.17750	−	1.80513i	0.769863	−	0.638209i
$9$	−2.25801	−	1.97519i	−0.752670	−	0.658398i
$10$	0.839632	+	3.57432i	0.265515	+	1.13030i
$11$	−1.63808	−	2.83724i	−0.493900	−	0.855460i	0.506075	−	0.862489i	$-0.331096\pi$
$11$	−1.63808	−	2.83724i	−0.493900	−	0.855460i	−0.999975	+	0.00702958i	$0.997762\pi$
$12$	3.16092	+	1.41725i	0.912478	+	0.409126i
$13$	0.912635			0.253119			0.126560	−	0.991959i	$-0.459606\pi$
$13$	0.912635			0.253119			0.126560	+	0.991959i	$0.459606\pi$
$14$	3.23121	+	1.88661i	0.863577	+	0.504218i
$15$	−3.47427	+	2.85492i	−0.897052	+	0.737138i
$16$	−3.96914	−	0.495937i	−0.992284	−	0.123984i
$17$	2.39448	+	4.14736i	0.580746	+	1.00588i	0.995391	+	0.0958985i	$0.0305724\pi$
$17$	2.39448	+	4.14736i	0.580746	+	1.00588i	−0.414645	+	0.909983i	$0.636094\pi$
$18$	0.151150	+	4.23995i	0.0356264	+	0.999365i
$19$	2.66693	−	4.61926i	0.611836	−	1.05973i	−0.379095	−	0.925358i	$-0.623765\pi$
$19$	2.66693	−	4.61926i	0.611836	−	1.05973i	0.990931	−	0.134373i	$-0.0429019\pi$
$20$	2.87052	−	4.32685i	0.641867	−	0.967514i
$21$	−0.326671	+	4.57092i	−0.0712854	+	0.997456i
$22$	−1.33763	+	4.43590i	−0.285184	+	0.945737i
$23$	−4.45569	−	2.57249i	−0.929075	−	0.536402i	−0.0425563	−	0.999094i	$-0.513550\pi$
$23$	−4.45569	−	2.57249i	−0.929075	−	0.536402i	−0.886519	+	0.462692i	$0.846884\pi$
$24$	−1.60057	−	4.63014i	−0.326715	−	0.945123i
$25$	0.870190	+	1.50721i	0.174038	+	0.301443i
$26$	−0.883838	−	0.940551i	−0.173335	−	0.184457i
$27$	−4.57796	+	2.45811i	−0.881029	+	0.473063i
$28$	−1.18493	−	5.15712i	−0.223931	−	0.974605i
$29$	−1.35950			−0.252453			−0.126227	−	0.992001i	$-0.540287\pi$
$29$	−1.35950			−0.252453			−0.126227	+	0.992001i	$0.540287\pi$
$30$	6.30689	+	0.815700i	1.15148	+	0.148926i
$31$	8.18469	−	4.72543i	1.47001	−	0.848713i	0.470580	−	0.882357i	$-0.344045\pi$
$31$	8.18469	−	4.72543i	1.47001	−	0.848713i	0.999434	+	0.0336443i	$0.0107113\pi$
$32$	3.33279	+	4.57083i	0.589159	+	0.808017i
$33$	−5.59810	+	0.927874i	−0.974504	+	0.161522i
$34$	1.95529	−	6.48421i	0.335330	−	1.11203i
$35$	6.67920	+	1.60340i	1.12899	+	0.271024i
$36$	4.22326	−	4.26193i	0.703876	−	0.710322i
$37$	1.59746	+	0.922292i	0.262620	+	0.151624i	0.625529	−	0.780201i	$-0.284883\pi$
$37$	1.59746	+	0.922292i	0.262620	+	0.151624i	−0.362909	+	0.931825i	$0.618216\pi$
$38$	−7.34333	+	1.72500i	−1.19125	+	0.279831i
$39$	0.555880	−	1.47977i	0.0890121	−	0.236952i
$40$	−7.23914	+	1.23200i	−1.14461	+	0.194797i
$41$	5.91833			0.924288			0.462144	−	0.886805i	$-0.347080\pi$
$41$	5.91833			0.924288			0.462144	+	0.886805i	$0.347080\pi$
$42$	5.02710	−	4.09002i	0.775698	−	0.631104i
$43$		−	8.00125i		−	1.22018i	−0.792332	−	0.610090i	$-0.791133\pi$
$43$		−	8.00125i		−	1.22018i	0.792332	−	0.610090i	$-0.208867\pi$
$44$	5.86701	−	2.91738i	0.884485	−	0.439812i
$45$	2.51288	+	7.37217i	0.374598	+	1.09898i
$46$	1.66391	+	7.08330i	0.245331	+	1.04438i
$47$	3.29243	−	5.70266i	0.480250	−	0.831818i	−0.519493	−	0.854475i	$-0.673879\pi$
$47$	3.29243	−	5.70266i	0.480250	−	0.831818i	0.999743	+	0.0226567i	$0.00721246\pi$
$48$	−3.22170	+	6.13357i	−0.465012	+	0.885304i
$49$	5.87055	−	3.81269i	0.838650	−	0.544671i
$50$	0.710584	−	2.35646i	0.100492	−	0.333254i
$51$	8.18307	−	1.35633i	1.14586	−	0.189924i
$52$	−0.113371	+	1.82175i	−0.0157218	+	0.252631i
$53$	−0.841712	−	1.45789i	−0.115618	−	0.200256i	0.802409	−	0.596775i	$-0.203552\pi$
$53$	−0.841712	−	1.45789i	−0.115618	−	0.200256i	−0.918027	+	0.396519i	$0.870218\pi$
$54$	6.96680	+	2.33745i	0.948062	+	0.318086i
$55$			8.50565i			1.14690i
$56$	−4.16733	+	6.21557i	−0.556883	+	0.830591i
$57$	−5.86535	−	7.13777i	−0.776885	−	0.945421i
$58$	1.31661	+	1.40109i	0.172879	+	0.183972i
$59$	−1.50266	+	0.867561i	−0.195630	+	0.112947i	−0.594615	−	0.804010i	$-0.702696\pi$
$59$	−1.50266	+	0.867561i	−0.195630	+	0.112947i	0.398986	+	0.916957i	$0.369362\pi$
$60$	−5.26724	−	7.28977i	−0.679997	−	0.941106i
$61$	−4.72347	+	8.18130i	−0.604779	+	1.04751i	0.387308	+	0.921951i	$0.373405\pi$
$61$	−4.72347	+	8.18130i	−0.604779	+	1.04751i	−0.992086	+	0.125557i	$0.959928\pi$
$62$	−12.7964	−	3.85872i	−1.62515	−	0.490058i
$63$	7.21241	+	3.31379i	0.908678	+	0.417498i
$64$	1.48302	−	7.86134i	0.185378	−	0.982667i
$65$	−2.05197	−	1.18470i	−0.254515	−	0.146944i
$66$	6.37772	+	4.87074i	0.785043	+	0.599547i
$67$	−10.8634	+	6.27198i	−1.32717	+	0.766245i	−0.984862	−	0.173341i	$-0.944544\pi$
$67$	−10.8634	+	6.27198i	−1.32717	+	0.766245i	−0.342313	+	0.939586i	$0.611210\pi$
$68$	−8.57615	+	4.26451i	−1.04001	+	0.517147i
$69$	−6.88502	+	5.65766i	−0.828860	+	0.681102i
$70$	−4.81600	−	8.43632i	−0.575622	−	1.00833i
$71$		−	0.603989i		−	0.0716803i	−0.999358	−	0.0358401i	$-0.988589\pi$
$71$		−	0.603989i		−	0.0716803i	0.999358	−	0.0358401i	$-0.0114107\pi$
$72$	−8.48230	−	0.224987i	−0.999648	−	0.0265149i
$73$	−1.29220	+	0.746053i	−0.151241	+	0.0873189i	−0.573711	−	0.819058i	$-0.694497\pi$
$73$	−1.29220	+	0.746053i	−0.151241	+	0.0873189i	0.422470	+	0.906377i	$0.361163\pi$
$74$	−0.596548	−	2.53951i	−0.0693473	−	0.295212i
$75$	2.97385	−	0.492910i	0.343391	−	0.0569164i
$76$	8.88938	+	5.89738i	1.01968	+	0.676476i
$77$	6.28759	+	5.96647i	0.716537	+	0.679943i
$78$	−2.06337	+	0.860190i	−0.233631	+	0.0973973i
$79$	−0.0625152	+	0.108280i	−0.00703351	+	0.0121824i	−0.869521	−	0.493896i	$-0.835572\pi$
$79$	−0.0625152	+	0.108280i	−0.00703351	+	0.0121824i	0.862487	+	0.506079i	$0.168906\pi$
$80$	8.28041	+	6.26745i	0.925778	+	0.700722i
$81$	1.19722	+	8.92001i	0.133025	+	0.991113i
$82$	−5.73158	−	6.09936i	−0.632947	−	0.673562i
$83$		−	0.246431i		−	0.0270493i	−0.999909	−	0.0135247i	$-0.995695\pi$
$83$		−	0.246431i		−	0.0270493i	0.999909	−	0.0135247i	$-0.00430516\pi$
$84$	−9.08360	−	1.21990i	−0.991102	−	0.133102i
$85$		−	12.4332i		−	1.34857i
$86$	−8.24600	+	7.74878i	−0.889189	+	0.835573i
$87$	−0.828064	+	2.20433i	−0.0887778	+	0.236329i
$88$	−8.68850	−	3.22114i	−0.926198	−	0.343375i
$89$	1.80671	−	3.12931i	0.191511	−	0.331706i	−0.754241	−	0.656598i	$-0.771995\pi$
$89$	1.80671	−	3.12931i	0.191511	−	0.331706i	0.945751	+	0.324892i	$0.105328\pi$
$90$	5.16408	−	9.72929i	0.544342	−	1.02556i
$91$	−2.31516	+	0.685829i	−0.242695	+	0.0718944i
$92$	5.68856	−	8.57461i	0.593073	−	0.893964i
$93$	−2.67667	−	16.1491i	−0.277558	−	1.67458i
$94$	−9.06563	+	2.12958i	−0.935049	+	0.219649i
$95$	−11.9926	+	6.92395i	−1.23042	+	0.710382i
$96$	9.44122	−	2.61979i	0.963591	−	0.267381i
$97$			5.10324i			0.518155i	0.965857	+	0.259078i	$0.0834185\pi$
$97$			5.10324i			0.518155i	−0.965857	+	0.259078i	$0.916581\pi$
$98$	−9.61463	−	2.35773i	−0.971224	−	0.238167i
$99$	−1.90529	+	9.64204i	−0.191489	+	0.969061i
$100$	−3.11670	+	1.54979i	−0.311670	+	0.154979i
$101$	6.33114	−	3.65529i	0.629972	−	0.363715i	−0.150769	−	0.988569i	$-0.548175\pi$
$101$	6.33114	−	3.65529i	0.629972	−	0.363715i	0.780741	+	0.624854i	$0.214842\pi$
$102$	−9.32268	−	7.11985i	−0.923083	−	0.704970i
$103$	0.670566	+	0.387151i	0.0660728	+	0.0381472i	0.532672	−	0.846321i	$-0.321188\pi$
$103$	0.670566	+	0.387151i	0.0660728	+	0.0381472i	−0.466600	+	0.884469i	$0.654521\pi$
$104$	1.98726	−	1.64742i	0.194867	−	0.161543i
$105$	6.66805	−	9.85318i	0.650735	−	0.961572i
$106$	−0.687329	+	2.27934i	−0.0667593	+	0.221389i
$107$	−7.26435	+	12.5822i	−0.702271	+	1.21637i	0.265397	+	0.964139i	$0.414497\pi$
$107$	−7.26435	+	12.5822i	−0.702271	+	1.21637i	−0.967667	+	0.252229i	$0.918836\pi$
$108$	−4.33803	−	9.44360i	−0.417427	−	0.908710i
$109$	12.8015	−	7.39093i	1.22616	−	0.707923i	0.259934	−	0.965626i	$-0.416299\pi$
$109$	12.8015	−	7.39093i	1.22616	−	0.707923i	0.966224	+	0.257703i	$0.0829658\pi$
$110$	8.76582	−	8.23726i	0.835788	−	0.785392i
$111$	2.46842	−	2.02839i	0.234292	−	0.192526i
$112$	10.4415	−	1.72465i	0.986632	−	0.162964i
$113$			16.2708i			1.53063i	0.643657	+	0.765314i	$0.277416\pi$
$113$			16.2708i			1.53063i	−0.643657	+	0.765314i	$0.722584\pi$
$114$	−1.67583	+	12.9573i	−0.156956	+	1.21356i
$115$	6.67877	+	11.5680i	0.622798	+	1.07872i
$116$	0.168883	−	2.71376i	0.0156804	−	0.251966i
$117$	−2.06074	−	1.80263i	−0.190515	−	0.166653i
$118$	2.34934	+	0.708437i	0.216275	+	0.0652170i
$119$	−9.19094	−	8.72154i	−0.842532	−	0.799503i
$120$	−2.41172	+	12.4881i	−0.220159	+	1.14000i
$121$	0.133385	−	0.231029i	0.0121259	−	0.0210026i
$122$	13.0060	−	3.05519i	1.17751	−	0.276604i
$123$	3.60482	−	9.59610i	0.325035	−	0.865251i
$124$	8.41588	+	16.9248i	0.755769	+	1.51989i
$125$			8.46270i			0.756927i
$126$	−3.56968	−	10.6422i	−0.318012	−	0.948087i
$127$	−1.59996			−0.141973			−0.0709867	−	0.997477i	$-0.522615\pi$
$127$	−1.59996			−0.141973			−0.0709867	+	0.997477i	$0.522615\pi$
$128$	−9.53803	+	6.08490i	−0.843051	+	0.537834i
$129$	−12.9734	−	4.87351i	−1.14224	−	0.429089i
$130$	0.766277	+	3.26205i	0.0672070	+	0.286101i
$131$	7.96684	+	4.59965i	0.696066	+	0.401874i	0.805880	−	0.592078i	$-0.201692\pi$
$131$	7.96684	+	4.59965i	0.696066	+	0.401874i	−0.109815	+	0.993952i	$0.535026\pi$
$132$	−1.15675	−	11.2898i	−0.100682	−	0.982655i
$133$	−3.29414	+	13.7222i	−0.285638	+	1.18987i
$134$	16.9844	+	5.12161i	1.46723	+	0.442439i
$135$	13.4840	+	0.415906i	1.16051	+	0.0357955i
$136$	12.7005	+	4.70853i	1.08906	+	0.403753i
$137$	2.43936	−	1.40836i	0.208408	−	0.120325i	−0.392163	−	0.919896i	$-0.628273\pi$
$137$	2.43936	−	1.40836i	0.208408	−	0.120325i	0.600571	+	0.799571i	$0.294940\pi$
$138$	12.4985	+	1.61649i	1.06394	+	0.137605i
$139$	−2.80505			−0.237921			−0.118960	−	0.992899i	$-0.537956\pi$
$139$	−2.80505			−0.237921			−0.118960	+	0.992899i	$0.537956\pi$
$140$	−4.03033	+	13.1334i	−0.340625	+	1.10998i
$141$	−7.24101	−	8.81187i	−0.609803	−	0.742093i
$142$	−0.622464	+	0.584930i	−0.0522360	+	0.0490863i
$143$	−1.49497	−	2.58936i	−0.125016	−	0.216533i
$144$	7.98278	+	8.95964i	0.665232	+	0.746637i
$145$	3.05670	+	1.76479i	0.253845	+	0.146558i
$146$	2.02030	+	0.609216i	0.167201	+	0.0504190i
$147$	−2.60627	−	11.8409i	−0.214961	−	0.976623i
$148$	−2.03947	+	3.07417i	−0.167643	+	0.252696i
$149$	8.67025	−	15.0173i	0.710295	−	1.23027i	−0.254451	−	0.967086i	$-0.581895\pi$
$149$	8.67025	−	15.0173i	0.710295	−	1.23027i	0.964746	−	0.263181i	$-0.0847718\pi$
$150$	−3.38800	−	2.58746i	−0.276629	−	0.211265i
$151$	−6.41551	−	11.1120i	−0.522087	−	0.904281i	−0.999670	−	0.0256942i	$-0.991820\pi$
$151$	−6.41551	−	11.1120i	−0.522087	−	0.904281i	0.477583	−	0.878587i	$-0.341513\pi$
$152$	−2.53111	−	14.8726i	−0.205300	−	1.20633i
$153$	2.78508	−	14.0943i	0.225160	−	1.13946i
$154$	0.0597859	−	12.2581i	0.00481769	−	0.987788i
$155$	−24.5366			−1.97082
$156$	2.88476	+	1.29344i	0.230966	+	0.103558i
$157$	−8.55356	−	14.8152i	−0.682648	−	1.18238i	−0.974170	−	0.225817i	$-0.927495\pi$
$157$	−8.55356	−	14.8152i	−0.682648	−	1.18238i	0.291521	−	0.956564i	$-0.405839\pi$
$158$	0.172134	−	0.0404355i	0.0136943	−	0.00321687i
$159$	−2.87653	+	0.476779i	−0.228124	+	0.0378110i
$160$	−1.55998	−	14.6034i	−0.123327	−	1.15450i
$161$	13.2363	+	3.17749i	1.04317	+	0.250421i
$162$	8.03342	−	9.87240i	0.631165	−	0.775649i
$163$	21.6390	+	12.4933i	1.69489	+	0.978547i	0.950458	+	0.310853i	$0.100615\pi$
$163$	21.6390	+	12.4933i	1.69489	+	0.978547i	0.744436	+	0.667694i	$0.232718\pi$
$164$	−0.735199	+	11.8138i	−0.0574094	+	0.922503i
$165$	13.7912	+	5.18073i	1.07365	+	0.403320i
$166$	−0.253969	+	0.238655i	−0.0197118	+	0.0185232i
$167$	9.89286			0.765532			0.382766	−	0.923845i	$-0.374972\pi$
$167$	9.89286			0.765532			0.382766	+	0.923845i	$0.374972\pi$
$168$	7.53977	+	10.5429i	0.581706	+	0.813399i
$169$	−12.1671			−0.935931
$170$	−12.8135	+	12.0409i	−0.982751	+	0.923494i
$171$	−15.1459	+	5.16263i	−1.15823	+	0.394796i
$172$	15.9716	+	0.993948i	1.21782	+	0.0757878i
$173$	−13.3755	−	7.72235i	−1.01692	−	0.587120i	−0.103710	−	0.994608i	$-0.533071\pi$
$173$	−13.3755	−	7.72235i	−1.01692	−	0.587120i	−0.913211	+	0.407488i	$0.866405\pi$
$174$	3.07369	−	1.28138i	0.233016	−	0.0971410i
$175$	−3.34013	−	3.16954i	−0.252490	−	0.239595i
$176$	5.09467	+	12.0738i	0.384026	+	0.910095i
$177$	0.491421	+	2.96487i	0.0369375	+	0.222853i
$178$	−4.97473	+	1.16860i	−0.372871	+	0.0875899i
$179$	−6.07462	−	10.5216i	−0.454038	−	0.786418i	0.544594	−	0.838700i	$-0.316684\pi$
$179$	−6.07462	−	10.5216i	−0.454038	−	0.786418i	−0.998632	+	0.0522822i	$0.983350\pi$
$180$	−15.0280	+	4.10025i	−1.12012	+	0.305615i
$181$	1.41922			0.105489			0.0527447	−	0.998608i	$-0.483203\pi$
$181$	1.41922			0.105489			0.0527447	+	0.998608i	$0.483203\pi$
$182$	2.94891	+	1.72179i	0.218588	+	0.127627i
$183$	10.3883	+	12.6419i	0.767924	+	0.934517i
$184$	−14.3459	+	2.44149i	−1.05760	+	0.179989i
$185$	−2.39448	−	4.14736i	−0.176045	−	0.304920i
$186$	−14.0508	+	18.3980i	−1.03026	+	1.34901i
$187$	7.84469	−	13.5874i	0.573661	−	0.993610i
$188$	10.9743	+	7.28055i	0.800383	+	0.530989i
$189$	9.76607	−	9.67594i	0.710377	−	0.703821i
$190$	18.7500	+	5.65399i	1.36026	+	0.410184i
$191$	3.62414	+	2.09240i	0.262234	+	0.151401i	0.625353	−	0.780342i	$-0.284955\pi$
$191$	3.62414	+	2.09240i	0.262234	+	0.151401i	−0.363119	+	0.931743i	$0.618288\pi$
$192$	−11.8432	−	7.19289i	−0.854712	−	0.519102i
$193$	−13.1905	−	22.8467i	−0.949476	−	1.64454i	−0.746531	−	0.665351i	$-0.768282\pi$
$193$	−13.1905	−	22.8467i	−0.949476	−	1.64454i	−0.202946	−	0.979190i	$-0.565051\pi$
$194$	5.25933	−	4.94221i	0.377598	−	0.354830i
$195$	−3.17074	+	2.60550i	−0.227061	+	0.186584i
$196$	6.88140	+	12.1921i	0.491529	+	0.870861i
$197$	12.6908			0.904184			0.452092	−	0.891971i	$-0.350678\pi$
$197$	12.6908			0.904184			0.452092	+	0.891971i	$0.350678\pi$
$198$	11.7821	−	7.37422i	0.837321	−	0.524063i
$199$	0.939591	−	0.542473i	0.0666058	−	0.0384549i	−0.466327	−	0.884612i	$-0.654423\pi$
$199$	0.939591	−	0.542473i	0.0666058	−	0.0384549i	0.532933	+	0.846157i	$0.321090\pi$
$200$	4.61555	+	1.71115i	0.326369	+	0.120997i
$201$	3.55270	+	21.4344i	0.250588	+	1.51186i
$202$	−9.89847	−	2.98485i	−0.696454	−	0.210014i
$203$	3.44876	−	1.02164i	0.242056	−	0.0717052i
$204$	1.69088	+	16.5030i	0.118386	+	1.15544i
$205$	−13.3067	−	7.68265i	−0.929384	−	0.536580i
$206$	−0.250413	−	1.06601i	−0.0174471	−	0.0742726i
$207$	4.97982	+	14.6096i	0.346121	+	1.01543i
$208$	−3.62237	−	0.452609i	−0.251166	−	0.0313828i
$209$	−17.4746			−1.20874
$210$	−16.6122	+	2.67026i	−1.14635	+	0.184265i
$211$			7.89074i			0.543221i	0.962407	+	0.271610i	$0.0875562\pi$
$211$			7.89074i			0.543221i	−0.962407	+	0.271610i	$0.912444\pi$
$212$	3.01471	−	1.49907i	0.207051	−	0.102956i
$213$	−0.979320	−	0.367886i	−0.0671019	−	0.0252071i
$214$	20.0022	−	4.69865i	1.36732	−	0.321193i
$215$	−10.3865	+	17.9900i	−0.708355	+	1.22691i
$216$	−5.53131	+	13.6163i	−0.376358	+	0.926474i
$217$	−17.2117	+	18.1381i	−1.16841	+	1.23129i
$218$	−20.0145	−	6.03532i	−1.35556	−	0.408764i
$219$	0.422594	+	2.54962i	0.0285563	+	0.172287i
$220$	−16.9785	−	1.05661i	−1.14469	−	0.0712363i
$221$	2.18528	+	3.78502i	0.146998	+	0.254608i
$222$	−4.48097	−	0.579545i	−0.300743	−	0.0388965i
$223$			11.5392i			0.772720i	0.922348	+	0.386360i	$0.126268\pi$
$223$			11.5392i			0.772720i	−0.922348	+	0.386360i	$0.873732\pi$
$224$	−11.8895	−	9.09069i	−0.794398	−	0.607397i
$225$	1.01214	−	5.12210i	0.0674760	−	0.341473i
$226$	16.7685	−	15.7574i	1.11542	−	1.04817i
$227$	13.4825	−	7.78410i	0.894862	−	0.516649i	0.0193323	−	0.999813i	$-0.493846\pi$
$227$	13.4825	−	7.78410i	0.894862	−	0.516649i	0.875530	+	0.483164i	$0.160513\pi$
$228$	14.9766	−	10.8214i	0.991850	−	0.716663i
$229$	−1.78238	+	3.08717i	−0.117783	+	0.204006i	−0.918889	−	0.394517i	$-0.870912\pi$
$229$	−1.78238	+	3.08717i	−0.117783	+	0.204006i	0.801106	+	0.598523i	$0.204245\pi$
$230$	5.45378	−	18.0860i	0.359612	−	1.19256i
$231$	13.5039	−	6.56069i	0.888491	−	0.431662i
$232$	−2.96032	+	2.45408i	−0.194354	+	0.161118i
$233$	−6.60666	−	3.81435i	−0.432816	−	0.249887i	0.267729	−	0.963494i	$-0.413727\pi$
$233$	−6.60666	−	3.81435i	−0.432816	−	0.249887i	−0.700546	+	0.713607i	$0.747060\pi$
$234$	0.137945	+	3.86953i	0.00901775	+	0.252959i
$235$	−14.8054	+	8.54789i	−0.965796	+	0.557603i
$236$	−1.54511	−	3.10729i	−0.100578	−	0.202267i
$237$	0.137489	+	0.167316i	0.00893087	+	0.0108683i
$238$	−0.0873926	+	17.9184i	−0.00566482	+	1.16148i
$239$		−	13.2745i		−	0.858658i	−0.903148	−	0.429329i	$-0.858750\pi$
$239$		−	13.2745i		−	0.858658i	0.903148	−	0.429329i	$-0.141250\pi$
$240$	15.2057	−	9.60857i	0.981524	−	0.620230i
$241$	9.92793	−	5.73189i	0.639514	−	0.369224i	−0.144913	−	0.989444i	$-0.546290\pi$
$241$	9.92793	−	5.73189i	0.639514	−	0.369224i	0.784427	+	0.620221i	$0.212957\pi$
$242$	−0.367272	+	0.0862745i	−0.0236091	+	0.00554593i
$243$	15.1923	+	3.49192i	0.974588	+	0.224007i
$244$	−15.7442	−	10.4450i	−1.00792	−	0.668674i
$245$	−18.1486	+	0.951816i	−1.15947	+	0.0608093i
$246$	−13.3807	+	5.57823i	−0.853122	+	0.355655i
$247$	2.43393	−	4.21570i	0.154867	−	0.268238i
$248$	9.29216	−	25.0641i	0.590053	−	1.59157i
$249$	−0.399568	−	0.150099i	−0.0253216	−	0.00951217i
$250$	8.72156	−	8.19567i	0.551600	−	0.518340i
$251$			1.44903i			0.0914619i	0.998954	+	0.0457309i	$0.0145617\pi$
$251$			1.44903i			0.0914619i	−0.998954	+	0.0457309i	$0.985438\pi$
$252$	−7.51073	+	13.9853i	−0.473132	+	0.880992i
$253$			16.8558i			1.05972i
$254$	1.54947	+	1.64890i	0.0972226	+	0.103461i
$255$	−20.1594	−	7.57298i	−1.26243	−	0.474238i
$256$	15.5081	+	3.93688i	0.969256	+	0.246055i
$257$	6.03418	−	10.4515i	0.376402	−	0.651948i	−0.614134	−	0.789202i	$-0.710494\pi$
$257$	6.03418	−	10.4515i	0.376402	−	0.651948i	0.990536	+	0.137254i	$0.0438278\pi$
$258$	7.54145	+	18.0900i	0.469510	+	1.12623i
$259$	−4.74549	−	1.13920i	−0.294870	−	0.0707862i
$260$	2.61973	−	3.94884i	0.162469	−	0.244897i
$261$	3.06977	+	2.68528i	0.190014	+	0.166215i
$262$	−2.97510	−	12.6650i	−0.183802	−	0.782449i
$263$	21.7325	−	12.5473i	1.34008	−	0.773697i	0.353264	−	0.935524i	$-0.385072\pi$
$263$	21.7325	−	12.5473i	1.34008	−	0.773697i	0.986819	+	0.161827i	$0.0517385\pi$
$264$	−10.5149	+	12.1257i	−0.647150	+	0.746288i
$265$			4.37055i			0.268480i
$266$	17.3321	−	9.89432i	1.06270	−	0.606660i
$267$	−3.97347	−	4.83547i	−0.243172	−	0.295926i
$268$	−11.1703	−	22.4640i	−0.682332	−	1.37221i
$269$	6.61826	−	3.82105i	0.403522	−	0.232974i	−0.284480	−	0.958682i	$-0.591821\pi$
$269$	6.61826	−	3.82105i	0.403522	−	0.232974i	0.688003	+	0.725708i	$0.258488\pi$
$270$	−12.6299	−	14.2992i	−0.768629	−	0.870221i
$271$	−9.27850	−	5.35694i	−0.563629	−	0.325411i	0.190972	−	0.981595i	$-0.438836\pi$
$271$	−9.27850	−	5.35694i	−0.563629	−	0.325411i	−0.754601	+	0.656184i	$0.772169\pi$
$272$	−7.44718	−	17.6489i	−0.451552	−	1.07012i
$273$	−0.298131	+	4.17158i	−0.0180437	+	0.252476i
$274$	−3.81383	−	1.15005i	−0.230402	−	0.0694769i
$275$	2.85088	−	4.93787i	0.171915	−	0.297765i
$276$	−10.4382	−	14.4463i	−0.628305	−	0.869564i
$277$	−3.08910	+	1.78349i	−0.185606	+	0.107160i	−0.589924	−	0.807459i	$-0.700842\pi$
$277$	−3.08910	+	1.78349i	−0.185606	+	0.107160i	0.404318	+	0.914618i	$0.367509\pi$
$278$	2.71654	+	2.89085i	0.162927	+	0.173382i
$279$	−27.8148	−	5.49627i	−1.66523	−	0.329053i
$280$	17.4383	−	8.56541i	1.04214	−	0.511881i
$281$			4.26336i			0.254331i	0.991882	+	0.127165i	$0.0405879\pi$
$281$			4.26336i			0.254331i	−0.991882	+	0.127165i	$0.959412\pi$
$282$	−2.06888	+	15.9963i	−0.123200	+	0.952567i
$283$	−11.3202	−	19.6072i	−0.672918	−	1.16553i	−0.977073	−	0.212906i	$-0.931707\pi$
$283$	−11.3202	−	19.6072i	−0.672918	−	1.16553i	0.304154	−	0.952623i	$-0.401626\pi$
$284$	1.20564	+	0.0750299i	0.0715419	+	0.00445221i
$285$	3.92200	+	23.6624i	0.232319	+	1.40164i
$286$	−1.22077	+	4.04836i	−0.0721856	+	0.239384i
$287$	−15.0135	+	4.44752i	−0.886220	+	0.262529i
$288$	1.50281	−	16.9039i	0.0885539	−	0.996071i
$289$	−2.96705	+	5.13907i	−0.174532	+	0.302298i
$290$	−1.14148	−	4.85930i	−0.0670301	−	0.285348i
$291$	8.27449	+	3.10835i	0.485059	+	0.182215i
$292$	−1.32870	−	2.67209i	−0.0777564	−	0.156372i
$293$			5.96057i			0.348220i	0.984726	+	0.174110i	$0.0557049\pi$
$293$			5.96057i			0.348220i	−0.984726	+	0.174110i	$0.944295\pi$
$294$	−9.67908	+	14.1533i	−0.564495	+	0.825436i
$295$	4.50477			0.262278
$296$	5.14332	−	0.875323i	0.298949	−	0.0508771i
$297$	14.4733	+	8.96219i	0.839826	+	0.520039i
$298$	−23.8733	+	5.60801i	−1.38295	+	0.324863i
$299$	−4.06642	−	2.34775i	−0.235167	−	0.135774i
$300$	0.614493	+	5.99745i	0.0354778	+	0.346263i
$301$	6.01280	+	20.2975i	0.346572	+	1.16993i
$302$	−5.23881	+	17.3731i	−0.301460	+	0.999710i
$303$	−2.07050	−	12.4919i	−0.118947	−	0.717639i
$304$	−12.8763	+	17.0118i	−0.738505	+	0.975696i
$305$	21.2405	−	12.2632i	1.21623	−	0.702189i
$306$	−17.2226	+	10.7793i	−0.984553	+	0.616213i
$307$	−5.42113			−0.309400			−0.154700	−	0.987961i	$-0.549441\pi$
$307$	−5.42113			−0.309400			−0.154700	+	0.987961i	$0.549441\pi$
$308$	−12.6910	+	11.8097i	−0.723136	+	0.672921i
$309$	1.03617	−	0.851458i	0.0589458	−	0.0484378i
$310$	23.7623	+	25.2871i	1.34961	+	1.43621i
$311$	12.1809	+	21.0979i	0.690714	+	1.19635i	0.971604	+	0.236612i	$0.0760370\pi$
$311$	12.1809	+	21.0979i	0.690714	+	1.19635i	−0.280890	+	0.959740i	$0.590630\pi$
$312$	−1.46074	−	4.22563i	−0.0826980	−	0.239229i
$313$	14.1392	+	8.16327i	0.799195	+	0.461415i	0.843189	−	0.537617i	$-0.180675\pi$
$313$	14.1392	+	8.16327i	0.799195	+	0.461415i	−0.0439948	+	0.999032i	$0.514009\pi$
$314$	−6.98471	+	23.1629i	−0.394170	+	1.30716i
$315$	−11.9147	−	16.8132i	−0.671316	−	0.947317i
$316$	−0.208375	−	0.138240i	−0.0117220	−	0.00777660i
$317$	−9.94185	+	17.2198i	−0.558390	+	0.967160i	0.439241	+	0.898369i	$0.355247\pi$
$317$	−9.94185	+	17.2198i	−0.558390	+	0.967160i	−0.997631	+	0.0687904i	$0.978086\pi$
$318$	3.27713	+	2.50278i	0.183772	+	0.140349i
$319$	2.22697	+	3.85723i	0.124687	+	0.215964i
$320$	−13.5393	+	15.7503i	−0.756871	+	0.880467i
$321$	15.9764	+	19.4423i	0.891716	+	1.08516i
$322$	−9.54396	−	16.7184i	−0.531864	−	0.931680i
$323$	25.5436			1.42128
$324$	−17.9543	+	1.28174i	−0.997462	+	0.0712077i
$325$	0.794166	+	1.37554i	0.0440524	+	0.0763010i
$326$	−8.08076	−	34.3999i	−0.447552	−	1.90523i
$327$	−4.18652	−	25.2583i	−0.231515	−	1.39679i
$328$	12.8872	−	10.6833i	0.711575	−	0.589889i
$329$	−4.06674	+	16.9406i	−0.224207	+	0.933966i
$330$	−8.01686	−	19.2303i	−0.441314	−	1.05860i
$331$	−1.90300	−	1.09870i	−0.104599	−	0.0603900i	0.446788	−	0.894640i	$-0.352568\pi$
$331$	−1.90300	−	1.09870i	−0.104599	−	0.0603900i	−0.551387	+	0.834250i	$0.685901\pi$
$332$	0.491910	+	0.0306126i	0.0269971	+	0.00168009i
$333$	−1.78537	−	5.23783i	−0.0978376	−	0.287031i
$334$	−9.58070	−	10.1955i	−0.524233	−	0.557871i
$335$	32.5669			1.77932
$336$	3.56349	−	17.9806i	0.194404	−	0.980922i
$337$	29.4138			1.60227			0.801135	−	0.598484i	$-0.204230\pi$
$337$	29.4138			1.60227			0.801135	+	0.598484i	$0.204230\pi$
$338$	11.7832	+	12.5393i	0.640920	+	0.682046i
$339$	26.3818	+	9.91044i	1.43286	+	0.538261i
$340$	24.8184	+	1.54450i	1.34597	+	0.0837624i
$341$	−26.8144	−	15.4813i	−1.45208	−	0.838358i
$342$	19.9885	+	10.6094i	1.08086	+	0.573693i
$343$	−12.0271	+	14.0836i	−0.649405	+	0.760443i
$344$	−14.4433	−	17.4227i	−0.778730	−	0.939371i
$345$	22.8245	−	3.78312i	1.22883	−	0.203676i
$346$	4.99489	+	21.2633i	0.268527	+	1.14312i
$347$	6.43016	+	11.1374i	0.345189	+	0.597885i	0.985388	−	0.170324i	$-0.0544815\pi$
$347$	6.43016	+	11.1374i	0.345189	+	0.597885i	−0.640199	+	0.768209i	$0.721148\pi$
$348$	−4.29727	−	1.92676i	−0.230358	−	0.103285i
$349$	30.0571			1.60892			0.804460	−	0.594006i	$-0.202455\pi$
$349$	30.0571			1.60892			0.804460	+	0.594006i	$0.202455\pi$
$350$	−0.0317598	+	6.51183i	−0.00169763	+	0.348072i
$351$	−4.17801	+	2.24335i	−0.223005	+	0.119741i
$352$	7.50917	−	16.9433i	0.400240	−	0.903081i
$353$	−12.1069	−	20.9698i	−0.644387	−	1.11611i	−0.984443	−	0.175705i	$-0.943779\pi$
$353$	−12.1069	−	20.9698i	−0.644387	−	1.11611i	0.340056	−	0.940405i	$-0.389554\pi$
$354$	2.57965	−	3.37777i	0.137107	−	0.179526i
$355$	−0.784045	+	1.35801i	−0.0416128	+	0.0720755i
$356$	6.02209	+	3.99517i	0.319170	+	0.211744i
$357$	−19.7394	+	9.59014i	−1.04472	+	0.507564i
$358$	−4.96044	+	16.4500i	−0.262168	+	0.869409i
$359$	−3.16884	−	1.82953i	−0.167245	−	0.0965590i	0.414041	−	0.910258i	$-0.364117\pi$
$359$	−3.16884	−	1.82953i	−0.167245	−	0.0965590i	−0.581286	+	0.813699i	$0.697450\pi$
$360$	18.7795	+	11.5168i	0.989767	+	0.606990i
$361$	−4.72503	−	8.18398i	−0.248686	−	0.430736i
$362$	−1.37443	−	1.46263i	−0.0722387	−	0.0768740i
$363$	−0.293351	−	0.356991i	−0.0153970	−	0.0187372i
$364$	−1.08141	−	4.70657i	−0.0566813	−	0.246691i
$365$	3.87384			0.202766
$366$	2.96811	−	22.9491i	0.155146	−	1.19957i
$367$	−15.1950	+	8.77283i	−0.793172	+	0.457938i	−0.841078	−	0.540914i	$-0.818078\pi$
$367$	−15.1950	+	8.77283i	−0.793172	+	0.457938i	0.0479063	+	0.998852i	$0.484745\pi$
$368$	16.4094	+	12.4203i	0.855401	+	0.647454i
$369$	−13.3636	−	11.6898i	−0.695684	−	0.608549i
$370$	−1.95529	+	6.48421i	−0.101651	+	0.337098i
$371$	3.23082	+	3.06582i	0.167736	+	0.159169i
$372$	32.5683	−	3.33691i	1.68859	−	0.173011i
$373$	3.25687	+	1.88036i	0.168635	+	0.0973612i	0.581942	−	0.813230i	$-0.302293\pi$
$373$	3.25687	+	1.88036i	0.168635	+	0.0973612i	−0.413307	+	0.910592i	$0.635626\pi$
$374$	−21.6002	+	5.07402i	−1.11692	+	0.262372i
$375$	13.7216	+	5.15458i	0.708581	+	0.266181i
$376$	−3.12476	−	18.3608i	−0.161147	−	0.946886i
$377$	−1.24073			−0.0639008
$378$	−19.4298	−	0.694171i	−0.999362	−	0.0357043i
$379$			12.2799i			0.630774i	0.948963	+	0.315387i	$0.102134\pi$
$379$			12.2799i			0.630774i	−0.948963	+	0.315387i	$0.897866\pi$
$380$	−12.3314	−	24.7991i	−0.632587	−	1.27217i
$381$	−0.974524	+	2.59421i	−0.0499264	+	0.132905i
$382$	−1.35338	−	5.76138i	−0.0692452	−	0.294778i
$383$	3.77515	−	6.53874i	0.192901	−	0.334114i	−0.753309	−	0.657666i	$-0.771544\pi$
$383$	3.77515	−	6.53874i	0.192901	−	0.334114i	0.946210	+	0.323552i	$0.104877\pi$
$384$	4.05663	+	19.1714i	0.207014	+	0.978338i
$385$	−6.39184	−	21.5770i	−0.325758	−	1.09967i
$386$	−10.7712	+	35.7198i	−0.548240	+	1.81809i
$387$	−15.8040	+	18.0669i	−0.803364	+	0.918393i
$388$	−10.1868	−	0.633944i	−0.517155	−	0.0321837i
$389$	18.2949	+	31.6877i	0.927588	+	1.60663i	0.787345	+	0.616513i	$0.211455\pi$
$389$	18.2949	+	31.6877i	0.927588	+	1.60663i	0.140244	+	0.990117i	$0.455211\pi$
$390$	5.75589	+	0.744437i	0.291461	+	0.0376960i
$391$		−	24.6391i		−	1.24605i
$392$	5.90072	−	18.8992i	0.298032	−	0.954556i
$393$	12.3105	−	10.1160i	0.620984	−	0.510283i
$394$	−12.2904	−	13.0790i	−0.619181	−	0.658911i
$395$	0.281118	−	0.162304i	0.0141446	−	0.00816638i
$396$	−19.0102	−	5.00100i	−0.955297	−	0.251310i
$397$	−3.83449	+	6.64152i	−0.192447	+	0.333329i	−0.946061	−	0.323989i	$-0.894976\pi$
$397$	−3.83449	+	6.64152i	−0.192447	+	0.333329i	0.753613	+	0.657318i	$0.228309\pi$
$398$	−1.46901	−	0.442975i	−0.0736348	−	0.0222043i
$399$	20.2430	+	13.6993i	1.01342	+	0.685822i
$400$	−2.70642	−	6.41389i	−0.135321	−	0.320695i
$401$	−20.5062	−	11.8393i	−1.02403	−	0.591224i	−0.108761	−	0.994068i	$-0.534688\pi$
$401$	−20.5062	−	11.8393i	−1.02403	−	0.591224i	−0.915269	+	0.402844i	$0.868022\pi$
$402$	18.6494	−	24.4194i	0.930147	−	1.21793i
$403$	7.46964	−	4.31260i	0.372089	−	0.214826i
$404$	6.50998	+	13.0919i	0.323884	+	0.651347i
$405$	8.88735	−	21.6099i	0.441616	−	1.07380i
$406$	−4.39283	−	2.56485i	−0.218013	−	0.127291i
$407$		−	6.04316i		−	0.299548i
$408$	15.3703	−	17.7249i	0.760943	−	0.877513i
$409$	13.5659	−	7.83230i	0.670793	−	0.387283i	−0.125584	−	0.992083i	$-0.540080\pi$
$409$	13.5659	−	7.83230i	0.670793	−	0.387283i	0.796377	+	0.604800i	$0.206747\pi$
$410$	4.96922	+	21.1540i	0.245412	+	1.04472i
$411$	−0.797753	−	4.81305i	−0.0393502	−	0.237410i
$412$	−0.856108	+	1.29045i	−0.0421774	+	0.0635759i
$413$	3.15997	−	3.33004i	0.155492	−	0.163860i
$414$	10.2338	−	19.2807i	0.502962	−	0.947596i
$415$	−0.319895	+	0.554074i	−0.0157030	+	0.0271984i
$416$	3.04162	+	4.17150i	0.149128	+	0.204525i
$417$	−1.70854	+	4.54816i	−0.0836674	+	0.222724i
$418$	16.9232	+	18.0091i	0.827740	+	0.880854i
$419$		−	35.4540i		−	1.73204i	−0.500009	−	0.866020i	$-0.666670\pi$
$419$		−	35.4540i		−	1.73204i	0.500009	−	0.866020i	$-0.333330\pi$
$420$	18.8400	+	14.5343i	0.919297	+	0.709204i
$421$			8.00460i			0.390120i	0.980791	+	0.195060i	$0.0624902\pi$
$421$			8.00460i			0.390120i	−0.980791	+	0.195060i	$0.937510\pi$
$422$	8.13210	−	7.64175i	0.395864	−	0.371995i
$423$	−18.6982	+	6.37347i	−0.909137	+	0.309889i
$424$	−4.46450	−	1.65515i	−0.216815	−	0.0803814i
$425$	−4.16730	+	7.21798i	−0.202144	+	0.350123i
$426$	0.569280	+	1.36555i	0.0275817	+	0.0661612i
$427$	5.83434	−	24.3038i	0.282343	−	1.17614i
$428$	−24.2134	−	16.0637i	−1.17040	−	0.776466i
$429$	−5.10902	+	0.846811i	−0.246666	+	0.0408844i
$430$	28.5991	−	6.71811i	1.37917	−	0.323976i
$431$	−25.8583	+	14.9293i	−1.24555	+	0.719118i	−0.970219	−	0.242231i	$-0.922121\pi$
$431$	−25.8583	+	14.9293i	−1.24555	+	0.719118i	−0.275331	+	0.961350i	$0.588787\pi$
$432$	19.3896	−	7.48619i	0.932883	−	0.360179i
$433$			1.70747i			0.0820557i	0.999158	+	0.0410278i	$0.0130632\pi$
$433$			1.70747i			0.0820557i	−0.999158	+	0.0410278i	$0.986937\pi$
$434$	35.3615	+	0.172467i	1.69741	+	0.00827867i
$435$	4.72328	−	3.88128i	0.226464	−	0.186093i
$436$	13.1631	+	26.4716i	0.630397	+	1.26776i
$437$	−23.7660	+	13.7213i	−1.13688	+	0.656379i
$438$	2.21835	−	2.90469i	0.105997	−	0.138791i
$439$	14.3026	+	8.25762i	0.682627	+	0.394115i	0.800844	−	0.598873i	$-0.204385\pi$
$439$	14.3026	+	8.25762i	0.682627	+	0.394115i	−0.118217	+	0.992988i	$0.537718\pi$
$440$	15.3538	+	18.5211i	0.731963	+	0.882957i
$441$	−20.7866	−	2.98637i	−0.989837	−	0.142208i
$442$	1.78447	−	5.91772i	0.0848786	−	0.281477i
$443$	−7.12265	+	12.3368i	−0.338407	+	0.586138i	−0.984133	−	0.177431i	$-0.943221\pi$
$443$	−7.12265	+	12.3368i	−0.338407	+	0.586138i	0.645726	+	0.763569i	$0.276555\pi$
$444$	3.74231	+	5.17929i	0.177602	+	0.245798i
$445$	−8.12438	+	4.69062i	−0.385133	+	0.222356i
$446$	11.8921	−	11.1751i	0.563109	−	0.529155i
$447$	−19.0684	−	23.2051i	−0.901904	−	1.09756i
$448$	2.14555	+	21.0570i	0.101368	+	0.994849i
$449$		−	2.18010i		−	0.102885i	−0.998676	−	0.0514426i	$-0.983618\pi$
$449$		−	2.18010i		−	0.102885i	0.998676	−	0.0514426i	$-0.0163819\pi$
$450$	−6.25897	+	3.91737i	−0.295051	+	0.184667i
$451$	−9.69470	−	16.7917i	−0.456506	−	0.790691i
$452$	−32.4788	−	2.02123i	−1.52767	−	0.0950704i
$453$	−21.9249	+	3.63400i	−1.03012	+	0.170740i
$454$	−21.0792	−	6.35638i	−0.989297	−	0.298320i
$455$	6.09568	+	1.46332i	0.285770	+	0.0686015i
$456$	−25.6564	−	4.95480i	−1.20147	−	0.232030i
$457$	−16.0855	+	27.8609i	−0.752447	+	1.30328i	0.194186	+	0.980965i	$0.437793\pi$
$457$	−16.0855	+	27.8609i	−0.752447	+	1.30328i	−0.946633	+	0.322312i	$0.895540\pi$
$458$	4.90773	−	1.15286i	0.229323	−	0.0538696i
$459$	−21.1565	−	13.1005i	−0.987499	−	0.611481i
$460$	−23.9209	+	11.8947i	−1.11532	+	0.554594i
$461$		−	13.9258i		−	0.648588i	−0.945956	−	0.324294i	$-0.894873\pi$
$461$		−	13.9258i		−	0.648588i	0.945956	−	0.324294i	$-0.105127\pi$
$462$	−19.8392	−	7.56328i	−0.923001	−	0.351876i
$463$	15.5838			0.724239			0.362120	−	0.932132i	$-0.382053\pi$
$463$	15.5838			0.724239			0.362120	+	0.932132i	$0.382053\pi$
$464$	5.39605	+	0.674227i	0.250505	+	0.0313002i
$465$	−14.9451	+	39.7841i	−0.693061	+	1.84494i
$466$	2.46716	+	10.5027i	0.114289	+	0.486530i
$467$	16.6230	+	9.59729i	0.769220	+	0.444110i	0.832596	−	0.553880i	$-0.186853\pi$
$467$	16.6230	+	9.59729i	0.769220	+	0.444110i	−0.0633760	+	0.997990i	$0.520187\pi$
$468$	3.85429	−	3.88959i	0.178165	−	0.179796i
$469$	22.8448	−	24.0743i	1.05488	−	1.11165i
$470$	23.1476	+	6.98008i	1.06772	+	0.321967i
$471$	−29.2316	+	4.84508i	−1.34692	+	0.223249i
$472$	−1.70598	+	4.60161i	−0.0785243	+	0.211806i
$473$	−22.7015	+	13.1067i	−1.04381	+	0.602647i
$474$	0.0392830	−	0.303731i	0.00180433	−	0.0139508i
$475$	9.28294			0.425931
$476$	18.5511	−	17.2630i	0.850290	−	0.791246i
$477$	−0.979016	+	4.95447i	−0.0448261	+	0.226850i
$478$	−13.6806	+	12.8557i	−0.625735	+	0.588004i
$479$	3.02090	+	5.23235i	0.138028	+	0.239072i	0.926750	−	0.375678i	$-0.122590\pi$
$479$	3.02090	+	5.23235i	0.138028	+	0.239072i	−0.788722	+	0.614750i	$0.789257\pi$
$480$	−24.6284	−	6.36545i	−1.12413	−	0.290542i
$481$	1.45790	+	0.841716i	0.0664743	+	0.0383790i
$482$	−15.5219	−	4.68058i	−0.707003	−	0.213195i
$483$	13.2142	−	19.5262i	0.601267	−	0.888474i
$484$	0.444596	+	0.294954i	0.0202089	+	0.0134070i
$485$	6.62457	−	11.4741i	0.300806	−	0.521012i
$486$	−11.1142	−	19.0388i	−0.504151	−	0.863616i
$487$	11.1385	+	19.2925i	0.504735	+	0.874227i	0.999985	+	0.00547672i	$0.00174330\pi$
$487$	11.1385	+	19.2925i	0.504735	+	0.874227i	−0.495250	+	0.868751i	$0.664923\pi$
$488$	4.48293	+	26.3413i	0.202933	+	1.19241i
$489$	33.4370	−	27.4763i	1.51207	−	1.24252i
$490$	18.5569	+	17.7820i	0.838315	+	0.803308i
$491$	4.63965			0.209384			0.104692	−	0.994505i	$-0.466614\pi$
$491$	4.63965			0.209384			0.104692	+	0.994505i	$0.466614\pi$
$492$	18.7073	+	8.38778i	0.843392	+	0.378150i
$493$	−3.25530	−	5.63834i	−0.146611	−	0.253938i
$494$	−6.70178	+	1.57429i	−0.301527	+	0.0708308i
$495$	16.8003	−	19.2058i	0.755117	−	0.863238i
$496$	−34.8297	+	14.6968i	−1.56390	+	0.659906i
$497$	0.453886	+	1.53219i	0.0203596	+	0.0687281i
$498$	0.232270	+	0.557153i	0.0104082	+	0.0249666i
$499$	−16.8940	−	9.75377i	−0.756280	−	0.436639i	0.0716782	−	0.997428i	$-0.477165\pi$
$499$	−16.8940	−	9.75377i	−0.756280	−	0.436639i	−0.827959	+	0.560789i	$0.810498\pi$
$500$	−16.8927	−	1.05127i	−0.755466	−	0.0470143i
$501$	6.02567	−	16.0405i	0.269207	−	0.716636i
$502$	1.49335	−	1.40331i	0.0666516	−	0.0626326i
$503$	−33.9146			−1.51218			−0.756090	−	0.654468i	$-0.772893\pi$
$503$	−33.9146			−1.51218			−0.756090	+	0.654468i	$0.772893\pi$
$504$	21.6868	−	5.80355i	0.966008	−	0.258511i
$505$	−18.9799			−0.844594
$506$	17.3714	−	16.3239i	0.772252	−	0.725688i
$507$	−7.41090	+	19.7280i	−0.329130	+	0.876150i
$508$	0.198753	−	3.19374i	0.00881825	−	0.141699i
$509$	20.9128	+	12.0740i	0.926946	+	0.535172i	0.885844	−	0.463983i	$-0.153580\pi$
$509$	20.9128	+	12.0740i	0.926946	+	0.535172i	0.0411013	+	0.999155i	$0.486913\pi$
$510$	11.7187	+	28.1101i	0.518913	+	1.24474i
$511$	2.71739	−	2.86364i	0.120210	−	0.126680i
$512$	−10.9615	−	19.7951i	−0.484432	−	0.874829i
$513$	−0.854465	+	27.7024i	−0.0377256	+	1.22309i
$514$	−16.6150	+	3.90297i	−0.732856	+	0.172153i
$515$	−1.00513	−	1.74094i	−0.0442914	−	0.0767150i
$516$	11.3398	−	25.2913i	0.499207	−	1.11339i
$517$	−21.5731			−0.948782
$518$	3.42171	+	5.99390i	0.150341	+	0.263357i
$519$	−20.6681	+	16.9837i	−0.907230	+	0.745501i
$520$	−6.60670	+	1.12437i	−0.289723	+	0.0493069i
$521$	2.98225	+	5.16541i	0.130655	+	0.226301i	0.923929	−	0.382564i	$-0.124959\pi$
$521$	2.98225	+	5.16541i	0.130655	+	0.226301i	−0.793274	+	0.608864i	$0.791625\pi$
$522$	−0.205489	−	5.76422i	−0.00899401	−	0.252293i
$523$	6.49701	−	11.2532i	0.284095	−	0.492066i	−0.688295	−	0.725431i	$-0.741640\pi$
$523$	6.49701	−	11.2532i	0.284095	−	0.492066i	0.972389	+	0.233365i	$0.0749737\pi$
$524$	−10.1712	+	15.3315i	−0.444332	+	0.669761i
$525$	−7.17361	+	3.48520i	−0.313082	+	0.152107i
$526$	−33.9778	−	10.2459i	−1.48150	−	0.446743i
$527$	39.1961	+	22.6299i	1.70741	+	0.985774i
$528$	22.6798	−	0.906555i	0.987012	−	0.0394528i
$529$	1.73544	+	3.00587i	0.0754539	+	0.130690i
$530$	4.50423	−	4.23264i	0.195651	−	0.183854i
$531$	5.10662	+	1.00908i	0.221609	+	0.0437905i
$532$	−26.9822	−	8.28018i	−1.16983	−	0.358991i
$533$	5.40127			0.233955
$534$	−1.13529	+	8.77791i	−0.0491287	+	0.379857i
$535$	32.6663	−	18.8599i	1.41229	−	0.815383i
$536$	−12.3333	+	33.2671i	−0.532718	+	1.43692i
$537$	−20.7599	+	3.44091i	−0.895855	+	0.148486i
$538$	−10.3474	−	3.12022i	−0.446106	−	0.134522i
$539$	−20.4340	−	10.4107i	−0.880153	−	0.448418i
$540$	−2.50524	+	26.8642i	−0.107808	+	1.15605i
$541$	−18.7480	−	10.8242i	−0.806039	−	0.465367i	0.0395397	−	0.999218i	$-0.487411\pi$
$541$	−18.7480	−	10.8242i	−0.806039	−	0.465367i	−0.845578	+	0.533851i	$0.820744\pi$
$542$	3.46492	+	14.7502i	0.148831	+	0.633576i
$543$	0.864435	−	2.30115i	0.0370965	−	0.0987516i
$544$	−10.9766	+	24.7670i	−0.470617	+	1.06188i
$545$	−38.3770			−1.64389
$546$	4.58791	−	3.73270i	0.196344	−	0.159745i
$547$			15.8930i			0.679536i	0.940509	+	0.339768i	$0.110349\pi$
$547$			15.8930i			0.679536i	−0.940509	+	0.339768i	$0.889651\pi$
$548$	2.50826	+	5.04424i	0.107148	+	0.215479i
$549$	26.8253	−	9.14368i	1.14488	−	0.390243i
$550$	−7.84984	+	1.84398i	−0.334718	+	0.0786275i
$551$	−3.62570	+	6.27989i	−0.154460	+	0.267532i
$552$	−4.77935	+	24.7479i	−0.203423	+	1.05334i
$553$	0.0772175	−	0.321661i	0.00328362	−	0.0136784i
$554$	4.82967	+	1.45637i	0.205193	+	0.0618753i
$555$	−8.18307	+	1.35633i	−0.347352	+	0.0575729i
$556$	0.348454	−	5.59926i	0.0147778	−	0.237462i
$557$	−20.3420	−	35.2334i	−0.861919	−	1.49289i	−0.870074	−	0.492921i	$-0.835929\pi$
$557$	−20.3420	−	35.2334i	−0.861919	−	1.49289i	0.00815471	−	0.999967i	$-0.497404\pi$
$558$	21.2727	+	33.9884i	0.900546	+	1.43884i
$559$		−	7.30223i		−	0.308851i
$560$	−25.7155	−	9.67658i	−1.08668	−	0.408910i
$561$	−17.2528	−	20.9956i	−0.728412	−	0.886433i
$562$	4.39377	−	4.12883i	0.185340	−	0.174164i
$563$	−38.8739	+	22.4439i	−1.63834	+	0.945896i	−0.656936	+	0.753947i	$0.728148\pi$
$563$	−38.8739	+	22.4439i	−1.63834	+	0.945896i	−0.981405	+	0.191950i	$0.938519\pi$
$564$	18.4892	−	13.3594i	0.778536	−	0.562533i
$565$	21.1213	−	36.5832i	0.888581	−	1.53907i
$566$	−9.24394	+	30.6550i	−0.388552	+	1.28853i
$567$	−9.74032	−	21.7285i	−0.409055	−	0.912510i
$568$	−1.09028	−	1.31519i	−0.0457470	−	0.0551840i
$569$	12.8893	+	7.44164i	0.540347	+	0.311970i	0.745220	−	0.666819i	$-0.232345\pi$
$569$	12.8893	+	7.44164i	0.540347	+	0.311970i	−0.204872	+	0.978789i	$0.565678\pi$
$570$	20.5880	−	26.9578i	0.862335	−	1.12914i
$571$	6.27344	−	3.62197i	0.262535	−	0.151575i	−0.362955	−	0.931807i	$-0.618232\pi$
$571$	6.27344	−	3.62197i	0.262535	−	0.151575i	0.625490	+	0.780232i	$0.284899\pi$
$572$	5.35444	−	2.66251i	0.223880	−	0.111325i
$573$	5.60010	−	4.60179i	0.233948	−	0.192243i
$574$	19.1233	+	11.1656i	0.798193	+	0.466042i
$575$		−	8.95423i		−	0.373417i
$576$	−18.8763	+	14.8217i	−0.786514	+	0.617572i
$577$	20.2309	−	11.6803i	0.842223	−	0.486258i	−0.0157961	−	0.999875i	$-0.505028\pi$
$577$	20.2309	−	11.6803i	0.842223	−	0.486258i	0.858019	+	0.513617i	$0.171695\pi$
$578$	8.16969	−	1.91911i	0.339814	−	0.0798246i
$579$	−45.0784	+	7.47165i	−1.87339	+	0.310511i
$580$	−3.90247	+	5.88237i	−0.162041	+	0.244252i
$581$	0.185188	+	0.625142i	0.00768291	+	0.0259353i
$582$	−4.80997	−	11.5379i	−0.199380	−	0.478260i
$583$	−2.75758	+	4.77627i	−0.114207	+	0.197813i
$584$	−1.46705	+	3.95712i	−0.0607069	+	0.163747i
$585$	2.29334	+	6.72810i	0.0948180	+	0.278173i
$586$	6.14289	−	5.77249i	0.253761	−	0.238459i
$587$		−	8.33175i		−	0.343888i	−0.985107	−	0.171944i	$-0.944995\pi$
$587$		−	8.33175i		−	0.343888i	0.985107	−	0.171944i	$-0.0550048\pi$
$588$	23.9599	−	3.73155i	0.988089	−	0.153886i
$589$		−	50.4096i		−	2.07709i
$590$	−4.36262	−	4.64256i	−0.179606	−	0.191131i
$591$	7.72990	−	20.5772i	0.317966	−	0.846432i
$592$	−5.88313	−	4.45294i	−0.241795	−	0.183015i
$593$	19.8845	−	34.4410i	0.816560	−	1.41432i	−0.0916424	−	0.995792i	$-0.529212\pi$
$593$	19.8845	−	34.4410i	0.816560	−	1.41432i	0.908202	−	0.418531i	$-0.137455\pi$
$594$	−4.78029	−	23.5954i	−0.196138	−	0.968131i
$595$	9.34332	+	31.5403i	0.383039	+	1.29303i
$596$	28.8996	+	19.1725i	1.18377	+	0.785338i
$597$	−0.307278	−	1.85389i	−0.0125761	−	0.0758746i
$598$	1.51855	+	6.46447i	0.0620980	+	0.264352i
$599$	12.0202	−	6.93989i	0.491134	−	0.283556i	−0.233911	−	0.972258i	$-0.575152\pi$
$599$	12.0202	−	6.93989i	0.491134	−	0.283556i	0.725045	+	0.688702i	$0.241819\pi$
$600$	5.58580	−	6.44150i	0.228039	−	0.262973i
$601$			17.2223i			0.702512i	0.936279	+	0.351256i	$0.114245\pi$
$601$			17.2223i			0.702512i	−0.936279	+	0.351256i	$0.885755\pi$
$602$	15.0952	−	25.8537i	0.615236	−	1.05372i
$603$	36.9180	+	7.29510i	1.50342	+	0.297080i
$604$	22.9780	−	11.4259i	0.934963	−	0.464912i
$605$	−0.599803	+	0.346296i	−0.0243855	+	0.0140790i
$606$	−10.8688	+	14.2315i	−0.441515	+	0.578116i
$607$	7.37230	+	4.25640i	0.299233	+	0.172762i	0.642098	−	0.766622i	$-0.278064\pi$
$607$	7.37230	+	4.25640i	0.299233	+	0.172762i	−0.342865	+	0.939385i	$0.611398\pi$
$608$	30.0022	−	3.20492i	1.21675	−	0.129977i
$609$	0.444110	−	6.21417i	0.0179962	−	0.251811i
$610$	−33.2086	−	10.0139i	−1.34458	−	0.405453i
$611$	3.00479	−	5.20445i	0.121561	−	0.210549i
$612$	27.7883	+	7.31025i	1.12327	+	0.295500i
$613$	−36.3973	+	21.0140i	−1.47007	+	0.848747i	−0.999436	−	0.0335801i	$-0.989309\pi$
$613$	−36.3973	+	21.0140i	−1.47007	+	0.848747i	−0.470637	+	0.882327i	$0.655976\pi$
$614$	5.25007	+	5.58695i	0.211876	+	0.225471i
$615$	−20.5619	+	16.8964i	−0.829134	+	0.681328i
$616$	24.4615	+	1.64209i	0.985581	+	0.0661619i
$617$		−	16.0083i		−	0.644471i	−0.946660	−	0.322236i	$-0.895566\pi$
$617$		−	16.0083i		−	0.644471i	0.946660	−	0.322236i	$-0.104434\pi$
$618$	−1.88098	−	0.243276i	−0.0756641	−	0.00978600i
$619$	10.1543	+	17.5878i	0.408136	+	0.706913i	0.994681	−	0.103004i	$-0.0328455\pi$
$619$	10.1543	+	17.5878i	0.408136	+	0.706913i	−0.586545	+	0.809917i	$0.699512\pi$
$620$	3.04803	−	48.9784i	0.122412	−	1.96702i
$621$	26.7214	+	0.824208i	1.07229	+	0.0330743i
$622$	9.94672	−	32.9856i	0.398827	−	1.32260i
$623$	−2.23161	+	9.29609i	−0.0894075	+	0.372440i
$624$	−2.94023	+	5.59771i	−0.117704	+	0.224088i
$625$	15.3365	−	26.5636i	0.613460	−	1.06254i
$626$	−5.28008	−	22.4774i	−0.211035	−	0.898377i
$627$	−10.6437	+	28.3336i	−0.425067	+	1.13154i
$628$	30.6357	−	15.2337i	1.22250	−	0.607890i
$629$			8.83363i			0.352220i
$630$	−5.78878	+	28.5618i	−0.230630	+	1.13793i
$631$	−28.0435			−1.11639			−0.558197	−	0.829708i	$-0.688507\pi$
$631$	−28.0435			−1.11639			−0.558197	+	0.829708i	$0.688507\pi$
$632$	0.0593316	+	0.348627i	0.00236008	+	0.0138676i
$633$	12.7942	+	4.80620i	0.508524	+	0.191029i
$634$	27.3747	−	6.43048i	1.08719	−	0.255387i
$635$	3.59734	+	2.07693i	0.142756	+	0.0824203i
$636$	−0.594383	−	5.80118i	−0.0235688	−	0.230032i
$637$	5.35767	−	3.47960i	0.212279	−	0.137867i
$638$	1.81851	−	6.03062i	0.0719957	−	0.238754i
$639$	−1.19299	+	1.36381i	−0.0471941	+	0.0539516i
$640$	29.3441	−	1.29984i	1.15993	−	0.0513805i
$641$	−9.80778	+	5.66252i	−0.387384	+	0.223656i	−0.681026	−	0.732259i	$-0.738466\pi$
$641$	−9.80778	+	5.66252i	−0.387384	+	0.223656i	0.293642	+	0.955915i	$0.405133\pi$
$642$	4.56473	−	35.2939i	0.180155	−	1.39294i
$643$	32.8892			1.29702			0.648512	−	0.761204i	$-0.275392\pi$
$643$	32.8892			1.29702			0.648512	+	0.761204i	$0.275392\pi$
$644$	−7.98698	+	26.0268i	−0.314731	+	1.02560i
$645$	22.8430	+	27.7985i	0.899441	+	1.09457i
$646$	−24.7376	−	26.3249i	−0.973288	−	1.03574i
$647$	13.6188	+	23.5884i	0.535409	+	0.927356i	0.999143	+	0.0413818i	$0.0131760\pi$
$647$	13.6188	+	23.5884i	0.535409	+	0.927356i	−0.463734	+	0.885974i	$0.653491\pi$
$648$	18.7087	+	17.2622i	0.734948	+	0.678123i
$649$	4.92296	+	2.84227i	0.193243	+	0.111569i
$650$	0.648504	−	2.15059i	0.0254364	−	0.0843531i
$651$	18.9259	+	38.9552i	0.741763	+	1.52678i
$652$	−27.6263	+	41.6424i	−1.08193	+	1.63084i
$653$	−12.2895	+	21.2860i	−0.480926	+	0.832987i	−0.999760	−	0.0218870i	$-0.993033\pi$
$653$	−12.2895	+	21.2860i	−0.480926	+	0.832987i	0.518835	+	0.854874i	$0.326366\pi$
$654$	−21.9765	+	28.7759i	−0.859350	+	1.12523i
$655$	−11.9417	−	20.6837i	−0.466602	−	0.808179i
$656$	−23.4907	−	2.93512i	−0.917156	−	0.114597i
$657$	4.39140	+	0.867753i	0.171325	+	0.0338543i
$658$	21.3972	−	12.2149i	0.834150	−	0.476188i
$659$	−12.1725			−0.474172			−0.237086	−	0.971489i	$-0.576192\pi$
$659$	−12.1725			−0.474172			−0.237086	+	0.971489i	$0.576192\pi$
$660$	−12.0547	+	26.8856i	−0.469227	+	1.04652i
$661$	4.00322	+	6.93378i	0.155707	+	0.269693i	0.933316	−	0.359055i	$-0.116901\pi$
$661$	4.00322	+	6.93378i	0.155707	+	0.269693i	−0.777609	+	0.628748i	$0.783568\pi$
$662$	0.710650	+	3.02524i	0.0276202	+	0.117579i
$663$	7.46816	−	1.23783i	0.290039	−	0.0480734i
$664$	−0.444840	−	0.536604i	−0.0172631	−	0.0208243i
$665$	25.2195	−	26.5768i	0.977970	−	1.03060i
$666$	−3.66901	+	6.91254i	−0.142171	+	0.267855i
$667$	6.05752	+	3.49731i	0.234548	+	0.135416i
$668$	−1.22893	+	19.7475i	−0.0475487	+	0.764054i
$669$	18.7098	+	7.02843i	0.723364	+	0.271735i
$670$	−31.5393	−	33.5631i	−1.21847	−	1.29666i
$671$	30.9497			1.19480
$672$	−21.9816	+	13.7407i	−0.847960	+	0.530061i
$673$	18.1260			0.698706			0.349353	−	0.936991i	$-0.386401\pi$
$673$	18.1260			0.698706			0.349353	+	0.936991i	$0.386401\pi$
$674$	−28.4856	−	30.3135i	−1.09723	−	1.16763i
$675$	−7.68858	−	4.76094i	−0.295934	−	0.183249i
$676$	1.51145	−	24.2872i	0.0581325	−	0.934123i
$677$	39.1458	+	22.6008i	1.50449	+	0.868620i	0.999986	+	0.00521277i	$0.00165928\pi$
$677$	39.1458	+	22.6008i	1.50449	+	0.868620i	0.504508	+	0.863407i	$0.331674\pi$
$678$	−15.3358	−	36.7865i	−0.588967	−	1.41278i
$679$	−3.83499	−	12.9458i	−0.147173	−	0.496815i
$680$	−22.4435	−	27.0733i	−0.860670	−	1.03821i
$681$	−4.40922	−	26.6020i	−0.168962	−	1.01939i
$682$	10.0134	+	42.6274i	0.383435	+	1.63229i
$683$	6.38047	+	11.0513i	0.244142	+	0.422866i	0.961890	−	0.273437i	$-0.0881604\pi$
$683$	6.38047	+	11.0513i	0.244142	+	0.422866i	−0.717748	+	0.696303i	$0.754827\pi$
$684$	−8.42384	−	30.8746i	−0.322094	−	1.18052i
$685$	−7.31285			−0.279410
$686$	26.1620	−	1.24417i	0.998871	−	0.0475025i
$687$	3.91996	+	4.77036i	0.149556	+	0.182000i
$688$	−3.96811	+	31.7581i	−0.151283	+	1.21077i
$689$	−0.768176	−	1.33052i	−0.0292652	−	0.0506888i
$690$	−26.0032	−	19.8589i	−0.989924	−	0.756017i
$691$	−7.47003	+	12.9385i	−0.284173	+	0.492203i	−0.972408	−	0.233285i	$-0.925052\pi$
$691$	−7.47003	+	12.9385i	−0.284173	+	0.492203i	0.688235	+	0.725488i	$0.258386\pi$
$692$	17.0764	−	25.7401i	0.649149	−	0.978490i
$693$	−2.41250	−	25.8916i	−0.0916433	−	0.983539i
$694$	5.25077	−	17.4128i	0.199316	−	0.660980i
$695$	6.30686	+	3.64127i	0.239233	+	0.138121i
$696$	2.17598	+	6.29468i	0.0824803	+	0.238599i
$697$	14.1713	+	24.5454i	0.536776	+	0.929724i
$698$	−29.1087	−	30.9765i	−1.10178	−	1.17248i
$699$	−10.2087	+	8.38887i	−0.386130	+	0.317296i
$700$	6.74177	−	6.27362i	0.254815	−	0.237121i
$701$	14.3141			0.540636			0.270318	−	0.962771i	$-0.412871\pi$
$701$	14.3141			0.540636			0.270318	+	0.962771i	$0.412871\pi$
$702$	6.35815	+	2.13324i	0.239973	+	0.0805138i
$703$	8.52061	−	4.91938i	0.321361	−	0.185538i
$704$	−24.7338	+	8.66982i	−0.932190	+	0.326756i
$705$	4.84186	+	29.2122i	0.182355	+	1.10020i
$706$	−9.88634	+	32.7854i	−0.372077	+	1.23389i
$707$	−13.3139	+	14.0304i	−0.500719	+	0.527668i
$708$	−5.97934	+	0.612637i	−0.224717	+	0.0230243i
$709$	5.67964	+	3.27914i	0.213303	+	0.123151i	0.602846	−	0.797858i	$-0.294033\pi$
$709$	5.67964	+	3.27914i	0.213303	+	0.123151i	−0.389542	+	0.921009i	$0.627367\pi$
$710$	2.15885	−	0.507128i	0.0810202	−	0.0190322i
$711$	0.355033	−	0.121017i	0.0133148	−	0.00453848i
$712$	−1.71470	−	10.0754i	−0.0642610	−	0.377592i
$713$	−48.6246			−1.82100
$714$	29.0001	+	11.0557i	1.08530	+	0.413749i
$715$			7.76255i			0.290303i
$716$	21.7571	−	10.8188i	0.813101	−	0.404316i
$717$	−21.5236	−	8.08543i	−0.803813	−	0.301956i
$718$	1.18336	+	5.03757i	0.0441626	+	0.188001i
$719$	−19.5665	+	33.8902i	−0.729708	+	1.26389i	0.227299	+	0.973825i	$0.427010\pi$
$719$	−19.5665	+	33.8902i	−0.729708	+	1.26389i	−0.957007	+	0.290066i	$0.906323\pi$
$720$	−6.31783	−	30.5074i	−0.235452	−	1.13694i
$721$	−1.99202	−	0.478202i	−0.0741866	−	0.0178092i
$722$	−3.85838	+	12.7953i	−0.143594	+	0.476192i
$723$	−3.24677	−	19.5886i	−0.120749	−	0.728508i
$724$	−0.176301	+	2.83295i	−0.00655216	+	0.105286i
$725$	−1.18303	−	2.04906i	−0.0439365	−	0.0761002i
$726$	−0.0838155	+	0.648051i	−0.00311068	+	0.0240514i
$727$			34.4829i			1.27890i	0.768833	+	0.639450i	$0.220838\pi$
$727$			34.4829i			1.27890i	−0.768833	+	0.639450i	$0.779162\pi$
$728$	−3.80325	+	5.67255i	−0.140958	+	0.210239i
$729$	14.9154	−	22.5062i	0.552423	−	0.833564i
$730$	−3.75161	−	3.99234i	−0.138853	−	0.147763i
$731$	33.1841	−	19.1588i	1.22736	−	0.708615i
$732$	−26.5255	+	19.1660i	−0.980410	+	0.708397i
$733$	−9.89201	+	17.1335i	−0.365370	+	0.632839i	−0.988835	−	0.149012i	$-0.952391\pi$
$733$	−9.89201	+	17.1335i	−0.365370	+	0.632839i	0.623466	+	0.781851i	$0.285724\pi$
$734$	23.7567	+	7.16376i	0.876876	+	0.264419i
$735$	−9.51092	+	30.0063i	−0.350815	+	1.10680i
$736$	−3.09143	−	28.9398i	−0.113952	−	1.06673i
$737$	35.5902	+	20.5480i	1.31098	+	0.756896i
$738$	0.894557	+	25.0934i	0.0329291	+	0.923701i
$739$	6.03595	−	3.48486i	0.222036	−	0.128193i	−0.384857	−	0.922976i	$-0.625749\pi$
$739$	6.03595	−	3.48486i	0.222036	−	0.128193i	0.606893	+	0.794784i	$0.292416\pi$
$740$	8.57615	−	4.26451i	0.315266	−	0.156766i
$741$	−5.35292	−	6.51418i	−0.196645	−	0.239305i
$742$	0.0307204	−	6.29872i	0.00112778	−	0.231233i
$743$		−	45.3956i		−	1.66540i	−0.553723	−	0.832701i	$-0.686793\pi$
$743$		−	45.3956i		−	1.66540i	0.553723	−	0.832701i	$-0.313207\pi$
$744$	−34.9796	−	30.3329i	−1.28241	−	1.11206i
$745$	−38.9883	+	22.5099i	−1.42842	+	0.824700i
$746$	−1.21623	−	5.17752i	−0.0445295	−	0.189562i
$747$	−0.486749	+	0.556443i	−0.0178092	+	0.0203592i
$748$	26.1478	+	17.3470i	0.956060	+	0.634268i
$749$	8.97277	−	37.3774i	0.327858	−	1.36574i
$750$	−7.97639	−	19.1333i	−0.291257	−	0.698648i
$751$	−10.3669	+	17.9560i	−0.378293	+	0.655223i	−0.990814	−	0.135231i	$-0.956822\pi$
$751$	−10.3669	+	17.9560i	−0.378293	+	0.655223i	0.612521	+	0.790455i	$0.290156\pi$
$752$	−15.8963	+	21.0018i	−0.579677	+	0.765857i
$753$	2.34949	+	0.882594i	0.0856200	+	0.0321635i
$754$	1.20158	+	1.27868i	0.0437590	+	0.0465668i
$755$			33.3122i			1.21236i
$756$	18.1013	+	20.6964i	0.658339	+	0.752721i
$757$			30.3555i			1.10329i	0.834079	+	0.551645i	$0.186000\pi$
$757$			30.3555i			1.10329i	−0.834079	+	0.551645i	$0.814000\pi$
$758$	12.6555	−	11.8924i	0.459668	−	0.431951i
$759$	27.3303	+	10.2668i	0.992029	+	0.372660i
$760$	−13.6153	+	36.7251i	−0.493880	+	1.33216i
$761$	6.12394	−	10.6070i	0.221993	−	0.384503i	−0.733420	−	0.679775i	$-0.762077\pi$
$761$	6.12394	−	10.6070i	0.221993	−	0.384503i	0.955413	+	0.295273i	$0.0954106\pi$
$762$	3.61733	−	1.50802i	0.131042	−	0.0546296i
$763$	−26.9204	+	28.3693i	−0.974585	+	1.02704i
$764$	−4.62693	+	6.97436i	−0.167396	+	0.252324i
$765$	−24.5580	+	28.0743i	−0.887896	+	1.01503i
$766$	−10.3948	+	2.44180i	−0.375579	+	0.0882259i
$767$	−1.37138	+	0.791767i	−0.0495177	+	0.0285890i
$768$	15.8292	−	22.7472i	0.571188	−	0.820819i
$769$		−	19.0816i		−	0.688100i	−0.938951	−	0.344050i	$-0.888201\pi$
$769$		−	19.0816i		−	0.688100i	0.938951	−	0.344050i	$-0.111799\pi$
$770$	−16.0468	+	27.4835i	−0.578288	+	0.990437i
$771$	−13.2709	−	16.1499i	−0.477940	−	0.581624i
$772$	47.2437	−	23.4920i	1.70034	−	0.845497i
$773$	−9.07434	+	5.23907i	−0.326381	+	0.188436i	−0.654233	−	0.756293i	$-0.727009\pi$
$773$	−9.07434	+	5.23907i	−0.326381	+	0.188436i	0.327852	+	0.944729i	$0.393675\pi$
$774$	33.9249	−	1.20939i	1.21941	−	0.0434707i
$775$	14.2445	+	8.22405i	0.511677	+	0.295417i
$776$	9.21200	+	11.1123i	0.330691	+	0.398908i
$777$	−4.73756	+	7.00056i	−0.169959	+	0.251144i
$778$	14.9393	−	49.5423i	0.535601	−	1.77618i
$779$	15.7838	−	27.3383i	0.565512	−	0.979496i
$780$	−4.80707	−	6.65290i	−0.172121	−	0.238212i
$781$	−1.71366	+	0.989382i	−0.0613196	+	0.0354029i
$782$	−25.3928	+	23.8616i	−0.908044	+	0.853291i
$783$	6.22375	−	3.34180i	0.222419	−	0.119426i
$784$	−25.1919	+	12.2217i	−0.899710	+	0.436489i
$785$			44.4139i			1.58520i
$786$	−22.3475	−	2.89030i	−0.797108	−	0.103094i
$787$	−6.93206	−	12.0067i	−0.247101	−	0.427992i	0.715619	−	0.698491i	$-0.246145\pi$
$787$	−6.93206	−	12.0067i	−0.247101	−	0.427992i	−0.962720	+	0.270499i	$0.912811\pi$
$788$	−1.57651	+	25.3327i	−0.0561607	+	0.902438i
$789$	−7.10727	−	42.8800i	−0.253025	−	1.52657i
$790$	−0.439516	−	0.132535i	−0.0156373	−	0.00471537i
$791$	−12.2272	−	41.2755i	−0.434750	−	1.46759i
$792$	13.2563	+	24.4348i	0.471044	+	0.868255i
$793$	−4.31081	+	7.46654i	−0.153081	+	0.265145i
$794$	10.5582	−	2.48018i	0.374695	−	0.0880184i
$795$	7.08649	+	2.66207i	0.251332	+	0.0944139i
$796$	0.966132	+	1.94294i	0.0342436	+	0.0688657i
$797$		−	29.4639i		−	1.04366i	−0.853048	−	0.521832i	$-0.825249\pi$
$797$		−	29.4639i		−	1.04366i	0.853048	−	0.521832i	$-0.174751\pi$
$798$	−5.48596	−	34.1293i	−0.194201	−	1.20816i
$799$	31.5346			1.11561
$800$	−3.98906	+	9.00072i	−0.141035	+	0.318223i
$801$	−10.2606	+	3.49741i	−0.362539	+	0.123575i
$802$	7.65775	+	32.5991i	0.270404	+	1.15111i
$803$	4.23346	+	2.44419i	0.149396	+	0.0862536i
$804$	−43.2273	+	4.42902i	−1.52451	+	0.156200i
$805$	−25.6357	−	24.3265i	−0.903540	−	0.857395i
$806$	−11.6785	−	3.52160i	−0.411356	−	0.124043i
$807$	−2.16440	−	13.0584i	−0.0761904	−	0.459676i
$808$	7.18781	−	19.3879i	0.252866	−	0.682065i
$809$	42.7554	−	24.6848i	1.50320	−	0.867873i	0.503207	−	0.864166i	$-0.332153\pi$
$809$	42.7554	−	24.6848i	1.50320	−	0.867873i	0.999993	−	0.00370713i	$-0.00118002\pi$
$810$	−30.8778	+	11.7688i	−1.08493	+	0.413513i
$811$	0.180195			0.00632751			0.00316376	−	0.999995i	$-0.498993\pi$
$811$	0.180195			0.00632751			0.00316376	+	0.999995i	$0.498993\pi$
$812$	1.61092	+	7.01112i	0.0565321	+	0.246042i
$813$	−14.3373	+	11.7815i	−0.502832	+	0.413194i
$814$	−6.22801	+	5.85247i	−0.218291	+	0.205129i
$815$	−32.4353	−	56.1796i	−1.13616	−	1.96788i
$816$	−33.1524	+	1.32516i	−1.16057	+	0.0463900i
$817$	−36.9598	−	21.3388i	−1.29306	−	0.746549i
$818$	−21.2098	−	6.39574i	−0.741582	−	0.223622i
$819$	6.58230	+	3.02428i	0.230004	+	0.105677i
$820$	16.9887	−	25.6077i	0.593270	−	0.894261i
$821$	11.4858	−	19.8940i	0.400857	−	0.694304i	−0.592973	−	0.805223i	$-0.702046\pi$
$821$	11.4858	−	19.8940i	0.400857	−	0.694304i	0.993830	+	0.110918i	$0.0353792\pi$
$822$	−4.18769	+	5.48333i	−0.146062	+	0.191253i
$823$	−22.0638	−	38.2157i	−0.769097	−	1.33212i	−0.938053	−	0.346492i	$-0.887373\pi$
$823$	−22.0638	−	38.2157i	−0.769097	−	1.33212i	0.168956	−	0.985624i	$-0.445960\pi$
$824$	2.15902	−	0.367435i	0.0752129	−	0.0128002i
$825$	−6.26992	−	7.63011i	−0.218290	−	0.265646i
$826$	−6.49216	−	0.0316639i	−0.225891	−	0.00110173i
$827$	−19.7749			−0.687641			−0.343821	−	0.939035i	$-0.611721\pi$
$827$	−19.7749			−0.687641			−0.343821	+	0.939035i	$0.611721\pi$
$828$	−29.7813	+	8.12555i	−1.03497	+	0.282382i
$829$	13.8197	+	23.9365i	0.479979	+	0.831349i	0.999736	−	0.0229656i	$-0.00731081\pi$
$829$	13.8197	+	23.9365i	0.479979	+	0.831349i	−0.519757	+	0.854314i	$0.673977\pi$
$830$	0.880823	−	0.206911i	0.0305738	−	0.00718199i
$831$	1.01024	+	6.09504i	0.0350449	+	0.211435i
$832$	1.35346	−	7.17453i	0.0469227	−	0.248732i
$833$	29.8695	+	15.2179i	1.03492	+	0.527267i
$834$	6.34191	−	2.64385i	0.219602	−	0.0915491i
$835$	−22.2431	−	12.8420i	−0.769753	−	0.444417i
$836$	2.17076	−	34.8817i	0.0750774	−	1.20641i
$837$	−25.8536	+	41.7517i	−0.893630	+	1.44315i
$838$	−36.5385	+	34.3353i	−1.26220	+	1.18609i
$839$	28.3920			0.980200			0.490100	−	0.871666i	$-0.336960\pi$
$839$	28.3920			0.980200			0.490100	+	0.871666i	$0.336960\pi$
$840$	−3.26657	−	33.4920i	−0.112707	−	1.15558i
$841$	−27.1518			−0.936267
$842$	8.24945	−	7.75203i	0.284295	−	0.267152i
$843$	6.91270	+	2.59678i	0.238086	+	0.0894380i
$844$	−15.7510	−	0.980219i	−0.542172	−	0.0337405i
$845$	27.3565	+	15.7943i	0.941091	+	0.543339i
$846$	24.6766	+	13.0978i	0.848400	+	0.450311i
$847$	−0.164754	+	0.686307i	−0.00566101	+	0.0235818i
$848$	2.61785	+	6.20399i	0.0898973	+	0.213046i
$849$	−38.6866	+	6.41223i	−1.32772	+	0.220067i
$850$	11.4746	−	2.69545i	0.393574	−	0.0924532i
$851$	−4.74518	−	8.21889i	−0.162663	−	0.281740i
$852$	0.856005	−	1.90916i	0.0293263	−	0.0654067i
$853$	30.7041			1.05129			0.525645	−	0.850704i	$-0.323824\pi$
$853$	30.7041			1.05129			0.525645	+	0.850704i	$0.323824\pi$
$854$	−30.6974	+	17.5241i	−1.05044	+	0.599663i
$855$	40.7556	+	8.05342i	1.39381	+	0.275421i
$856$	6.89440	+	40.5109i	0.235646	+	1.38463i
$857$	−11.5192	−	19.9518i	−0.393487	−	0.681539i	0.599420	−	0.800435i	$-0.295398\pi$
$857$	−11.5192	−	19.9518i	−0.393487	−	0.681539i	−0.992907	+	0.118895i	$0.962065\pi$
$858$	5.82053	+	4.44521i	0.198710	+	0.151757i
$859$	−26.3268	+	45.5994i	−0.898260	+	1.55583i	−0.0685424	+	0.997648i	$0.521835\pi$
$859$	−26.3268	+	45.5994i	−0.898260	+	1.55583i	−0.829717	+	0.558184i	$0.811498\pi$
$860$	−34.6202	−	22.9677i	−1.18054	−	0.783193i
$861$	−1.93334	+	27.0522i	−0.0658882	+	0.921936i
$862$	40.4283	+	12.1910i	1.37699	+	0.415228i
$863$	−22.4451	−	12.9587i	−0.764040	−	0.441119i	0.0667045	−	0.997773i	$-0.478752\pi$
$863$	−22.4451	−	12.9587i	−0.764040	−	0.441119i	−0.830744	+	0.556654i	$0.812085\pi$
$864$	−26.4930	−	12.7327i	−0.901309	−	0.433177i
$865$	20.0490	+	34.7258i	0.681685	+	1.18071i
$866$	1.75970	−	1.65359i	0.0597969	−	0.0561913i
$867$	6.52539	+	7.94100i	0.221614	+	0.269691i
$868$	−34.0680	−	36.6102i	−1.15634	−	1.24263i
$869$	0.409620			0.0138954
$870$	−8.57424	−	1.10895i	−0.290694	−	0.0375968i
$871$	−9.91432	+	5.72403i	−0.335934	+	0.193951i
$872$	14.5336	−	39.2021i	0.492171	−	1.32755i
$873$	10.0799	−	11.5232i	0.341152	−	0.390000i
$874$	37.1571	+	11.2046i	1.25686	+	0.379002i
$875$	−6.35957	−	21.4681i	−0.214993	−	0.725753i
$876$	−5.14189	+	0.526833i	−0.173728	+	0.0178000i
$877$	39.8660	+	23.0166i	1.34618	+	0.777216i	0.987706	−	0.156324i	$-0.0499644\pi$
$877$	39.8660	+	23.0166i	1.34618	+	0.777216i	0.358472	+	0.933540i	$0.383298\pi$
$878$	−5.34111	−	22.7372i	−0.180254	−	0.767342i
$879$	9.66459	+	3.63054i	0.325979	+	0.122455i
$880$	4.21826	−	33.7601i	0.142198	−	1.13805i
$881$	25.6170			0.863060			0.431530	−	0.902099i	$-0.357974\pi$
$881$	25.6170			0.863060			0.431530	+	0.902099i	$0.357974\pi$
$882$	17.0530	+	24.3145i	0.574203	+	0.818713i
$883$		−	54.2412i		−	1.82536i	−0.408674	−	0.912680i	$-0.634009\pi$
$883$		−	54.2412i		−	1.82536i	0.408674	−	0.912680i	$-0.365991\pi$
$884$	−7.82690	+	3.89194i	−0.263247	+	0.130900i
$885$	2.74382	−	7.30412i	0.0922326	−	0.245525i
$886$	19.6120	−	4.60700i	0.658880	−	0.154775i
$887$	−17.2509	+	29.8794i	−0.579228	+	1.00325i	0.416340	+	0.909209i	$0.363313\pi$
$887$	−17.2509	+	29.8794i	−0.579228	+	1.00325i	−0.995568	+	0.0940438i	$0.970021\pi$
$888$	1.71350	−	8.87264i	0.0575011	−	0.297746i
$889$	4.05875	−	1.20234i	0.136126	−	0.0403252i
$890$	12.7021	+	3.83029i	0.425776	+	0.128391i
$891$	23.3471	−	18.0085i	0.782156	−	0.603308i
$892$	−23.0338	−	1.43344i	−0.771228	−	0.0479952i
$893$	−17.5614	−	30.4172i	−0.587669	−	1.01787i
$894$	−5.44816	+	42.1245i	−0.182214	+	1.40886i
$895$			31.5422i			1.05434i
$896$	19.6232	−	22.6037i	0.655566	−	0.755138i
$897$	−6.28352	+	5.16338i	−0.209800	+	0.172400i
$898$	−2.24678	+	2.11131i	−0.0749762	+	0.0704553i
$899$	−11.1271	+	6.42424i	−0.371110	+	0.214260i
$900$	10.0987	+	2.65666i	0.336623	+	0.0885553i
$901$	4.03092	−	6.98176i	0.134289	−	0.232596i
$902$	−7.91654	+	26.2531i	−0.263592	+	0.874133i
$903$	36.5731	+	2.61377i	1.21708	+	0.0869810i
$904$	29.3709	+	35.4297i	0.976862	+	1.17837i
$905$	−3.19096	−	1.84230i	−0.106071	−	0.0612402i
$906$	24.9782	+	19.0762i	0.829845	+	0.633763i
$907$	11.9718	−	6.91190i	0.397516	−	0.229506i	−0.287896	−	0.957662i	$-0.592956\pi$
$907$	11.9718	−	6.91190i	0.397516	−	0.229506i	0.685412	+	0.728156i	$0.259622\pi$
$908$	13.8633	+	27.8798i	0.460070	+	0.925224i
$909$	−21.5157	−	4.25156i	−0.713630	−	0.141015i
$910$	−4.39525	−	7.69928i	−0.145701	−	0.255229i
$911$		−	22.6663i		−	0.750969i	−0.926829	−	0.375484i	$-0.877476\pi$
$911$		−	22.6663i		−	0.750969i	0.926829	−	0.375484i	$-0.122524\pi$
$912$	19.7405	+	31.2396i	0.653673	+	1.03445i
$913$	−0.699183	+	0.403674i	−0.0231396	+	0.0133596i
$914$	44.2910	−	10.4042i	1.46502	−	0.344142i
$915$	−6.94636	−	41.9092i	−0.229640	−	1.38548i
$916$	−5.94100	−	3.94137i	−0.196296	−	0.130227i
$917$	−23.6667	−	5.68140i	−0.781543	−	0.187616i
$918$	6.98763	+	34.4908i	0.230626	+	1.13837i
$919$	−6.58509	+	11.4057i	−0.217222	+	0.376240i	−0.953958	−	0.299941i	$-0.903033\pi$
$919$	−6.58509	+	11.4057i	−0.217222	+	0.376240i	0.736736	+	0.676181i	$0.236366\pi$
$920$	35.4247	+	13.1332i	1.16792	+	0.432989i
$921$	−3.30198	+	8.78993i	−0.108804	+	0.289638i
$922$	−14.3517	+	13.4864i	−0.472649	+	0.444150i
$923$		−	0.551221i		−	0.0181437i
$924$	11.4185	+	27.7706i	0.375642	+	0.913587i
$925$			3.21028i			0.105553i
$926$	−15.0920	−	16.0605i	−0.495955	−	0.527779i
$927$	−0.749446	−	2.19869i	−0.0246150	−	0.0722144i
$928$	−4.53093	−	6.21406i	−0.148735	−	0.203987i
$929$	−27.9226	+	48.3634i	−0.916111	+	1.58675i	−0.110844	+	0.993838i	$0.535355\pi$
$929$	−27.9226	+	48.3634i	−0.916111	+	1.58675i	−0.805267	+	0.592912i	$0.797978\pi$
$930$	55.4745	−	23.1266i	1.81908	−	0.758350i
$931$	−1.95547	−	37.2858i	−0.0640881	−	1.22199i
$932$	8.43468	−	12.7140i	0.276287	−	0.416460i
$933$	41.6279	−	6.89973i	1.36283	−	0.225887i
$934$	−6.20762	−	26.4259i	−0.203120	−	0.864682i
$935$	−35.2760	+	20.3666i	−1.15365	+	0.666058i
$936$	−7.74124	−	0.205331i	−0.253030	−	0.00671144i
$937$		−	32.0973i		−	1.04857i	−0.851541	−	0.524287i	$-0.824332\pi$
$937$		−	32.0973i		−	1.04857i	0.851541	−	0.524287i	$-0.175668\pi$
$938$	−46.9347	−	0.228912i	−1.53247	−	0.00747424i
$939$	21.8482	−	17.9534i	0.712989	−	0.585887i
$940$	−15.2236	−	30.6154i	−0.496539	−	0.998565i
$941$	−24.3540	+	14.0608i	−0.793919	+	0.458370i	−0.841341	−	0.540505i	$-0.818233\pi$
$941$	−24.3540	+	14.0608i	−0.793919	+	0.458370i	0.0474212	+	0.998875i	$0.484900\pi$
$942$	33.3025	+	25.4335i	1.08505	+	0.828669i
$943$	−26.3702	−	15.2249i	−0.858733	−	0.495790i
$944$	6.39452	−	2.69825i	0.208124	−	0.0878204i
$945$	−34.5185	+	9.07789i	−1.12289	+	0.295304i
$946$	35.4928	+	10.7027i	1.15397	+	0.347976i
$947$	10.9973	−	19.0479i	0.357365	−	0.618974i	−0.630155	−	0.776469i	$-0.717009\pi$
$947$	10.9973	−	19.0479i	0.357365	−	0.618974i	0.987520	+	0.157495i	$0.0503420\pi$
$948$	−0.351065	+	0.253663i	−0.0114021	+	0.00823858i
$949$	−1.17931	+	0.680874i	−0.0382820	+	0.0221021i
$950$	−8.99003	−	9.56689i	−0.291675	−	0.310391i
$951$	21.8650	+	26.6084i	0.709021	+	0.862836i
$952$	−35.7568	−	2.40035i	−1.15888	−	0.0777956i
$953$			48.0977i			1.55804i	0.627001	+	0.779018i	$0.284282\pi$
$953$			48.0977i			1.55804i	−0.627001	+	0.779018i	$0.715718\pi$
$954$	6.05414	−	3.78917i	0.196010	−	0.122679i
$955$	−5.43234	−	9.40909i	−0.175786	−	0.304471i
$956$	26.4978	+	1.64901i	0.857000	+	0.0533329i
$957$	7.61063	−	1.26145i	0.246017	−	0.0407768i
$958$	2.46682	−	8.18055i	0.0796993	−	0.264301i
$959$	−5.12976	+	5.40584i	−0.165649	+	0.174564i
$960$	17.2911	+	31.5463i	0.558068	+	1.01815i
$961$	29.1595	−	50.5057i	0.940628	−	1.62921i
$962$	−0.544430	−	2.31765i	−0.0175531	−	0.0747239i
$963$	41.2553	−	14.0623i	1.32943	−	0.453151i
$964$	10.2084	+	20.5296i	0.328789	+	0.661213i
$965$			68.4912i			2.20481i
$966$	−32.9207	+	5.29171i	−1.05921	+	0.170258i
$967$	11.0279			0.354635			0.177317	−	0.984154i	$-0.443258\pi$
$967$	11.0279			0.354635			0.177317	+	0.984154i	$0.443258\pi$
$968$	−0.126592	−	0.743842i	−0.00406882	−	0.0239080i
$969$	15.5584	−	41.4169i	0.499809	−	1.33050i
$970$	−18.2406	+	4.28484i	−0.585671	+	0.137578i
$971$	2.36459	+	1.36519i	0.0758832	+	0.0438112i	0.537461	−	0.843288i	$-0.319383\pi$
$971$	2.36459	+	1.36519i	0.0758832	+	0.0438112i	−0.461578	+	0.887099i	$0.652717\pi$
$972$	−8.85762	+	29.8922i	−0.284108	+	0.958792i
$973$	7.11580	−	2.10794i	0.228122	−	0.0675775i
$974$	9.09556	−	30.1630i	0.291441	−	0.966485i
$975$	2.71404	−	0.449847i	0.0869189	−	0.0144066i
$976$	22.8055	−	30.1301i	0.729987	−	0.964442i
$977$	−21.7078	+	12.5330i	−0.694494	+	0.400967i	−0.805294	−	0.592876i	$-0.797992\pi$
$977$	−21.7078	+	12.5330i	−0.694494	+	0.400967i	0.110799	+	0.993843i	$0.464659\pi$
$978$	−60.6986	−	7.85044i	−1.94093	−	0.251029i
$979$	−11.8381			−0.378348
$980$	0.354540	−	36.3454i	0.0113254	−	1.16101i
$981$	−43.5044	−	8.59658i	−1.38899	−	0.274468i
$982$	−4.49325	−	4.78157i	−0.143385	−	0.152586i
$983$	12.9850	+	22.4907i	0.414157	+	0.717342i	0.995340	−	0.0964318i	$-0.0307430\pi$
$983$	12.9850	+	22.4907i	0.414157	+	0.717342i	−0.581182	+	0.813773i	$0.697410\pi$
$984$	−9.47271	−	27.4027i	−0.301979	−	0.873565i
$985$	−28.5340	−	16.4741i	−0.909169	−	0.524909i
$986$	−2.65823	+	8.81530i	−0.0846552	+	0.280736i
$987$	24.9908	+	16.9123i	0.795467	+	0.538325i
$988$	8.11276	+	5.38216i	0.258101	+	0.171229i
$989$	−20.5832	+	35.6511i	−0.654507	+	1.13364i
$990$	−36.0635	+	1.28563i	−1.14617	+	0.0408600i
$991$	−9.31944	−	16.1417i	−0.296042	−	0.512759i	0.679185	−	0.733967i	$-0.262333\pi$
$991$	−9.31944	−	16.1417i	−0.296042	−	0.512759i	−0.975227	+	0.221208i	$0.929000\pi$
$992$	48.8770	+	21.6620i	1.55185	+	0.687769i
$993$	−2.94056	+	2.41636i	−0.0933159	+	0.0766808i
$994$	1.13949	−	1.95161i	0.0361425	−	0.0619014i
$995$	−2.81676			−0.0892974
$996$	0.349255	−	0.778947i	0.0110666	−	0.0246819i
$997$	12.6672	+	21.9402i	0.401173	+	0.694853i	0.993868	−	0.110575i	$-0.0352691\pi$
$997$	12.6672	+	21.9402i	0.401173	+	0.694853i	−0.592694	+	0.805427i	$0.701936\pi$
$998$	6.30883	+	26.8568i	0.199703	+	0.850137i
$999$	−9.58019	−	0.295496i	−0.303104	−	0.00934908i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.5.8	yes	48
3.2	odd	2	inner	168.2.ba.c.5.17	yes	48
4.3	odd	2		672.2.bi.c.593.9		48
7.3	odd	6	inner	168.2.ba.c.101.23	yes	48
8.3	odd	2		672.2.bi.c.593.16		48
8.5	even	2	inner	168.2.ba.c.5.2	✓	48
12.11	even	2		672.2.bi.c.593.24		48
21.17	even	6	inner	168.2.ba.c.101.2	yes	48
24.5	odd	2	inner	168.2.ba.c.5.23	yes	48
24.11	even	2		672.2.bi.c.593.1		48
28.3	even	6		672.2.bi.c.17.1		48
56.3	even	6		672.2.bi.c.17.24		48
56.45	odd	6	inner	168.2.ba.c.101.17	yes	48
84.59	odd	6		672.2.bi.c.17.16		48
168.59	odd	6		672.2.bi.c.17.9		48
168.101	even	6	inner	168.2.ba.c.101.8	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.2	✓	48	8.5	even	2	inner
168.2.ba.c.5.8	yes	48	1.1	even	1	trivial
168.2.ba.c.5.17	yes	48	3.2	odd	2	inner
168.2.ba.c.5.23	yes	48	24.5	odd	2	inner
168.2.ba.c.101.2	yes	48	21.17	even	6	inner
168.2.ba.c.101.8	yes	48	168.101	even	6	inner
168.2.ba.c.101.17	yes	48	56.45	odd	6	inner
168.2.ba.c.101.23	yes	48	7.3	odd	6	inner
672.2.bi.c.17.1		48	28.3	even	6
672.2.bi.c.17.9		48	168.59	odd	6
672.2.bi.c.17.16		48	84.59	odd	6
672.2.bi.c.17.24		48	56.3	even	6
672.2.bi.c.593.1		48	24.11	even	2
672.2.bi.c.593.9		48	4.3	odd	2
672.2.bi.c.593.16		48	8.3	odd	2
672.2.bi.c.593.24		48	12.11	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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.968446 - 1.03059i) q^{2} +(0.609093 - 1.62142i) q^{3} +(-0.124224 + 1.99614i) q^{4} +(-2.24840 - 1.29811i) q^{5} +(-2.26089 + 0.942534i) q^{6} +(-2.53678 + 0.751482i) q^{7} +(2.17750 - 1.80513i) q^{8} +(-2.25801 - 1.97519i) q^{9} +O(q^{10})\)	\(q+(-0.968446 - 1.03059i) q^{2} +(0.609093 - 1.62142i) q^{3} +(-0.124224 + 1.99614i) q^{4} +(-2.24840 - 1.29811i) q^{5} +(-2.26089 + 0.942534i) q^{6} +(-2.53678 + 0.751482i) q^{7} +(2.17750 - 1.80513i) q^{8} +(-2.25801 - 1.97519i) q^{9} +(0.839632 + 3.57432i) q^{10} +(-1.63808 - 2.83724i) q^{11} +(3.16092 + 1.41725i) q^{12} +0.912635 q^{13} +(3.23121 + 1.88661i) q^{14} +(-3.47427 + 2.85492i) q^{15} +(-3.96914 - 0.495937i) q^{16} +(2.39448 + 4.14736i) q^{17} +(0.151150 + 4.23995i) q^{18} +(2.66693 - 4.61926i) q^{19} +(2.87052 - 4.32685i) q^{20} +(-0.326671 + 4.57092i) q^{21} +(-1.33763 + 4.43590i) q^{22} +(-4.45569 - 2.57249i) q^{23} +(-1.60057 - 4.63014i) q^{24} +(0.870190 + 1.50721i) q^{25} +(-0.883838 - 0.940551i) q^{26} +(-4.57796 + 2.45811i) q^{27} +(-1.18493 - 5.15712i) q^{28} -1.35950 q^{29} +(6.30689 + 0.815700i) q^{30} +(8.18469 - 4.72543i) q^{31} +(3.33279 + 4.57083i) q^{32} +(-5.59810 + 0.927874i) q^{33} +(1.95529 - 6.48421i) q^{34} +(6.67920 + 1.60340i) q^{35} +(4.22326 - 4.26193i) q^{36} +(1.59746 + 0.922292i) q^{37} +(-7.34333 + 1.72500i) q^{38} +(0.555880 - 1.47977i) q^{39} +(-7.23914 + 1.23200i) q^{40} +5.91833 q^{41} +(5.02710 - 4.09002i) q^{42} -8.00125i q^{43} +(5.86701 - 2.91738i) q^{44} +(2.51288 + 7.37217i) q^{45} +(1.66391 + 7.08330i) q^{46} +(3.29243 - 5.70266i) q^{47} +(-3.22170 + 6.13357i) q^{48} +(5.87055 - 3.81269i) q^{49} +(0.710584 - 2.35646i) q^{50} +(8.18307 - 1.35633i) q^{51} +(-0.113371 + 1.82175i) q^{52} +(-0.841712 - 1.45789i) q^{53} +(6.96680 + 2.33745i) q^{54} +8.50565i q^{55} +(-4.16733 + 6.21557i) q^{56} +(-5.86535 - 7.13777i) q^{57} +(1.31661 + 1.40109i) q^{58} +(-1.50266 + 0.867561i) q^{59} +(-5.26724 - 7.28977i) q^{60} +(-4.72347 + 8.18130i) q^{61} +(-12.7964 - 3.85872i) q^{62} +(7.21241 + 3.31379i) q^{63} +(1.48302 - 7.86134i) q^{64} +(-2.05197 - 1.18470i) q^{65} +(6.37772 + 4.87074i) q^{66} +(-10.8634 + 6.27198i) q^{67} +(-8.57615 + 4.26451i) q^{68} +(-6.88502 + 5.65766i) q^{69} +(-4.81600 - 8.43632i) q^{70} -0.603989i q^{71} +(-8.48230 - 0.224987i) q^{72} +(-1.29220 + 0.746053i) q^{73} +(-0.596548 - 2.53951i) q^{74} +(2.97385 - 0.492910i) q^{75} +(8.88938 + 5.89738i) q^{76} +(6.28759 + 5.96647i) q^{77} +(-2.06337 + 0.860190i) q^{78} +(-0.0625152 + 0.108280i) q^{79} +(8.28041 + 6.26745i) q^{80} +(1.19722 + 8.92001i) q^{81} +(-5.73158 - 6.09936i) q^{82} -0.246431i q^{83} +(-9.08360 - 1.21990i) q^{84} -12.4332i q^{85} +(-8.24600 + 7.74878i) q^{86} +(-0.828064 + 2.20433i) q^{87} +(-8.68850 - 3.22114i) q^{88} +(1.80671 - 3.12931i) q^{89} +(5.16408 - 9.72929i) q^{90} +(-2.31516 + 0.685829i) q^{91} +(5.68856 - 8.57461i) q^{92} +(-2.67667 - 16.1491i) q^{93} +(-9.06563 + 2.12958i) q^{94} +(-11.9926 + 6.92395i) q^{95} +(9.44122 - 2.61979i) q^{96} +5.10324i q^{97} +(-9.61463 - 2.35773i) q^{98} +(-1.90529 + 9.64204i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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