LMFDB - Embedded newform 168.2.ba.c.5.23

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			5.23
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37674 + 0.323405i) q^{2} +(1.70874 + 0.283220i) q^{3} +(1.79082 + 0.890488i) q^{4} +(-2.24840 - 1.29811i) q^{5} +(2.26089 + 0.942534i) q^{6} +(-2.53678 + 0.751482i) q^{7} +(2.17750 + 1.80513i) q^{8} +(2.83957 + 0.967897i) q^{9} +O(q^{10})$	\(q+(1.37674 + 0.323405i) q^{2} +(1.70874 + 0.283220i) q^{3} +(1.79082 + 0.890488i) 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} +(2.83957 + 0.967897i) q^{9} +(-2.67564 - 2.51430i) q^{10} +(-1.63808 - 2.83724i) q^{11} +(2.80784 + 2.02881i) q^{12} -0.912635 q^{13} +(-3.73552 + 0.214186i) q^{14} +(-3.47427 - 2.85492i) q^{15} +(2.41406 + 3.18940i) q^{16} +(-2.39448 - 4.14736i) q^{17} +(3.59633 + 2.25087i) q^{18} +(-2.66693 + 4.61926i) q^{19} +(-2.87052 - 4.32685i) q^{20} +(-4.54754 + 0.565618i) q^{21} +(-1.33763 - 4.43590i) q^{22} +(4.45569 + 2.57249i) q^{23} +(3.20953 + 3.70120i) q^{24} +(0.870190 + 1.50721i) q^{25} +(-1.25646 - 0.295151i) q^{26} +(4.57796 + 2.45811i) q^{27} +(-5.21211 - 0.913209i) q^{28} -1.35950 q^{29} +(-3.85986 - 5.05408i) q^{30} +(8.18469 - 4.72543i) q^{31} +(2.29206 + 5.17170i) q^{32} +(-1.99549 - 5.31204i) 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} +(-5.16556 + 5.49701i) q^{38} +(-1.55945 - 0.258476i) q^{39} +(-2.55263 - 6.88528i) q^{40} -5.91833 q^{41} +(-6.44369 - 0.691987i) q^{42} +8.00125i q^{43} +(-0.406978 - 6.53967i) q^{44} +(-5.12805 - 5.86230i) q^{45} +(5.30236 + 4.98264i) 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} +(-2.91692 - 7.76491i) q^{51} +(-1.63436 - 0.812691i) q^{52} +(-0.841712 - 1.45789i) q^{53} +(5.50769 + 4.86471i) q^{54} +8.50565i q^{55} +(-6.88037 - 2.94287i) q^{56} +(-5.86535 + 7.13777i) q^{57} +(-1.87168 - 0.439670i) q^{58} +(-1.50266 + 0.867561i) q^{59} +(-3.67951 - 8.20645i) q^{60} +(4.72347 - 8.18130i) q^{61} +(12.7964 - 3.85872i) q^{62} +(-7.93074 - 0.321460i) q^{63} +(1.48302 + 7.86134i) q^{64} +(2.05197 + 1.18470i) q^{65} +(-1.02933 - 7.95863i) q^{66} +(10.8634 - 6.27198i) q^{67} +(-0.594903 - 9.55942i) q^{68} +(6.88502 + 5.65766i) q^{69} +(8.67697 + 4.36755i) q^{70} +0.603989i q^{71} +(4.43599 + 7.23339i) q^{72} +(-1.29220 + 0.746053i) q^{73} +(-1.90101 - 1.78638i) q^{74} +(1.06005 + 2.82189i) 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} +(-1.28756 - 10.3048i) q^{80} +(7.12635 + 5.49683i) q^{81} +(-8.14799 - 1.91402i) q^{82} -0.246431i q^{83} +(-8.64749 - 3.03661i) q^{84} +12.4332i q^{85} +(-2.58764 + 11.0156i) q^{86} +(-2.32303 - 0.385038i) q^{87} +(1.55466 - 9.13504i) 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} +(15.3238 - 5.75646i) q^{93} +(-6.37708 + 6.78628i) q^{94} +(11.9926 - 6.92395i) q^{95} +(2.45181 + 9.48623i) q^{96} +5.10324i q^{97} +(9.31526 - 3.35052i) 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 $

$2$	1.37674	+	0.323405i	0.973501	+	0.228682i
$2$	1.37674	+	0.323405i	0.973501	+	0.228682i
$3$	1.70874	+	0.283220i	0.986541	+	0.163517i
$3$	1.70874	+	0.283220i	0.986541	+	0.163517i
$4$	1.79082	+	0.890488i	0.895409	+	0.445244i
$5$	−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
$9$	2.83957	+	0.967897i	0.946524	+	0.322632i
$10$	−2.67564	−	2.51430i	−0.846111	−	0.795093i
$11$	−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	$0.997762\pi$
$12$	2.80784	+	2.02881i	0.810553	+	0.585666i
$13$	−0.912635			−0.253119			−0.126560	−	0.991959i	$-0.540394\pi$
$13$	−0.912635			−0.253119			−0.126560	+	0.991959i	$0.540394\pi$
$14$	−3.73552	+	0.214186i	−0.998360	+	0.0572435i
$15$	−3.47427	−	2.85492i	−0.897052	−	0.737138i
$16$	2.41406	+	3.18940i	0.603516	+	0.797351i
$17$	−2.39448	−	4.14736i	−0.580746	−	1.00588i	−0.995391	−	0.0958985i	$-0.969428\pi$
$17$	−2.39448	−	4.14736i	−0.580746	−	1.00588i	0.414645	−	0.909983i	$-0.363906\pi$
$18$	3.59633	+	2.25087i	0.847662	+	0.530536i
$19$	−2.66693	+	4.61926i	−0.611836	+	1.05973i	0.379095	+	0.925358i	$0.376235\pi$
$19$	−2.66693	+	4.61926i	−0.611836	+	1.05973i	−0.990931	+	0.134373i	$0.957098\pi$
$20$	−2.87052	−	4.32685i	−0.641867	−	0.967514i
$21$	−4.54754	+	0.565618i	−0.992354	+	0.123428i
$22$	−1.33763	−	4.43590i	−0.285184	−	0.945737i
$23$	4.45569	+	2.57249i	0.929075	+	0.536402i	0.886519	−	0.462692i	$-0.153116\pi$
$23$	4.45569	+	2.57249i	0.929075	+	0.536402i	0.0425563	+	0.999094i	$0.486450\pi$
$24$	3.20953	+	3.70120i	0.655143	+	0.755505i
$25$	0.870190	+	1.50721i	0.174038	+	0.301443i
$26$	−1.25646	−	0.295151i	−0.246412	−	0.0578838i
$27$	4.57796	+	2.45811i	0.881029	+	0.473063i
$28$	−5.21211	−	0.913209i	−0.984995	−	0.172580i
$29$	−1.35950			−0.252453			−0.126227	−	0.992001i	$-0.540287\pi$
$29$	−1.35950			−0.252453			−0.126227	+	0.992001i	$0.540287\pi$
$30$	−3.85986	−	5.05408i	−0.704712	−	0.922745i
$31$	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	$0.0107113\pi$
$32$	2.29206	+	5.17170i	0.405183	+	0.914235i
$33$	−1.99549	−	5.31204i	−0.347370	−	0.924707i
$34$	−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	0.362909	−	0.931825i	$-0.381784\pi$
$37$	−1.59746	−	0.922292i	−0.262620	−	0.151624i	−0.625529	+	0.780201i	$0.715117\pi$
$38$	−5.16556	+	5.49701i	−0.837964	+	0.891733i
$39$	−1.55945	−	0.258476i	−0.249713	−	0.0413894i
$40$	−2.55263	−	6.88528i	−0.403605	−	1.08866i
$41$	−5.91833			−0.924288			−0.462144	−	0.886805i	$-0.652920\pi$
$41$	−5.91833			−0.924288			−0.462144	+	0.886805i	$0.652920\pi$
$42$	−6.44369	−	0.691987i	−0.994283	−	0.106776i
$43$			8.00125i			1.22018i	0.792332	+	0.610090i	$0.208867\pi$
$43$			8.00125i			1.22018i	−0.792332	+	0.610090i	$0.791133\pi$
$44$	−0.406978	−	6.53967i	−0.0613542	−	0.985892i
$45$	−5.12805	−	5.86230i	−0.764444	−	0.873900i
$46$	5.30236	+	4.98264i	0.781791	+	0.734650i
$47$	−3.29243	+	5.70266i	−0.480250	+	0.831818i	−0.999743	−	0.0226567i	$-0.992788\pi$
$47$	−3.29243	+	5.70266i	−0.480250	+	0.831818i	0.519493	+	0.854475i	$0.326121\pi$
$48$	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
$51$	−2.91692	−	7.76491i	−0.408451	−	1.08730i
$52$	−1.63436	−	0.812691i	−0.226646	−	0.112700i
$53$	−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	$0.870218\pi$
$54$	5.50769	+	4.86471i	0.749502	+	0.662003i
$55$			8.50565i			1.14690i
$56$	−6.88037	−	2.94287i	−0.919428	−	0.393258i
$57$	−5.86535	+	7.13777i	−0.776885	+	0.945421i
$58$	−1.87168	−	0.439670i	−0.245764	−	0.0577315i
$59$	−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	$0.369362\pi$
$60$	−3.67951	−	8.20645i	−0.475023	−	1.05945i
$61$	4.72347	−	8.18130i	0.604779	−	1.04751i	−0.387308	−	0.921951i	$-0.626595\pi$
$61$	4.72347	−	8.18130i	0.604779	−	1.04751i	0.992086	−	0.125557i	$-0.0400718\pi$
$62$	12.7964	−	3.85872i	1.62515	−	0.490058i
$63$	−7.93074	−	0.321460i	−0.999180	−	0.0405001i
$64$	1.48302	+	7.86134i	0.185378	+	0.982667i
$65$	2.05197	+	1.18470i	0.254515	+	0.146944i
$66$	−1.02933	−	7.95863i	−0.126701	−	0.979640i
$67$	10.8634	−	6.27198i	1.32717	−	0.766245i	0.342313	−	0.939586i	$-0.388790\pi$
$67$	10.8634	−	6.27198i	1.32717	−	0.766245i	0.984862	+	0.173341i	$0.0554564\pi$
$68$	−0.594903	−	9.55942i	−0.0721426	−	1.15925i
$69$	6.88502	+	5.65766i	0.828860	+	0.681102i
$70$	8.67697	+	4.36755i	1.03710	+	0.522022i
$71$			0.603989i			0.0716803i	0.999358	+	0.0358401i	$0.0114107\pi$
$71$			0.603989i			0.0716803i	−0.999358	+	0.0358401i	$0.988589\pi$
$72$	4.43599	+	7.23339i	0.522787	+	0.852463i
$73$	−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	$0.361163\pi$
$74$	−1.90101	−	1.78638i	−0.220988	−	0.207663i
$75$	1.06005	+	2.82189i	0.122404	+	0.325844i
$76$	−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	$0.168906\pi$
$80$	−1.28756	−	10.3048i	−0.143954	−	1.15211i
$81$	7.12635	+	5.49683i	0.791817	+	0.610759i
$82$	−8.14799	−	1.91402i	−0.899795	−	0.211368i
$83$		−	0.246431i		−	0.0270493i	−0.999909	−	0.0135247i	$-0.995695\pi$
$83$		−	0.246431i		−	0.0270493i	0.999909	−	0.0135247i	$-0.00430516\pi$
$84$	−8.64749	−	3.03661i	−0.943518	−	0.331321i
$85$			12.4332i			1.34857i
$86$	−2.58764	+	11.0156i	−0.279033	+	1.18785i
$87$	−2.32303	−	0.385038i	−0.249055	−	0.0412804i
$88$	1.55466	−	9.13504i	0.165727	−	0.973798i
$89$	−1.80671	+	3.12931i	−0.191511	+	0.331706i	−0.945751	−	0.324892i	$-0.894672\pi$
$89$	−1.80671	+	3.12931i	−0.191511	+	0.331706i	0.754241	+	0.656598i	$0.228005\pi$
$90$	−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
$93$	15.3238	−	5.75646i	1.58901	−	0.596917i
$94$	−6.37708	+	6.78628i	−0.657746	+	0.699951i
$95$	11.9926	−	6.92395i	1.23042	−	0.710382i
$96$	2.45181	+	9.48623i	0.250237	+	0.968185i
$97$			5.10324i			0.518155i	0.965857	+	0.259078i	$0.0834185\pi$
$97$			5.10324i			0.518155i	−0.965857	+	0.259078i	$0.916581\pi$
$98$	9.31526	−	3.35052i	0.940983	−	0.338454i
$99$	−1.90529	−	9.64204i	−0.191489	−	0.969061i
$100$	0.216197	+	3.47404i	0.0216197	+	0.347404i
$101$	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	$0.214842\pi$
$102$	−1.50463	−	11.6336i	−0.148980	−	1.15190i
$103$	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
$105$	10.9589	+	4.63148i	1.06948	+	0.451986i
$106$	−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	$0.918836\pi$
$108$	6.00938	+	8.47864i	0.578253	+	0.815858i
$109$	−12.8015	+	7.39093i	−1.22616	+	0.707923i	−0.966224	−	0.257703i	$-0.917034\pi$
$109$	−12.8015	+	7.39093i	−1.22616	+	0.707923i	−0.259934	+	0.965626i	$0.583701\pi$
$110$	−2.75077	+	11.7101i	−0.262275	+	1.11651i
$111$	−2.46842	−	2.02839i	−0.234292	−	0.192526i
$112$	−8.52073	−	6.27671i	−0.805134	−	0.593093i
$113$		−	16.2708i		−	1.53063i	−0.643657	−	0.765314i	$-0.722584\pi$
$113$		−	16.2708i		−	1.53063i	0.643657	−	0.765314i	$-0.277416\pi$
$114$	−10.3834	+	7.92997i	−0.972499	+	0.742709i
$115$	−6.67877	−	11.5680i	−0.622798	−	1.07872i
$116$	−2.43462	−	1.21062i	−0.226049	−	0.112403i
$117$	−2.59149	−	0.883337i	−0.239584	−	0.0816646i
$118$	−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
$122$	9.14886	−	9.73591i	0.828299	−	0.881448i
$123$	−10.1129	−	1.67619i	−0.911847	−	0.151137i
$124$	18.8652	−	1.17402i	1.69415	−	0.105431i
$125$			8.46270i			0.756927i
$126$	−10.8146	−	3.00741i	−0.963441	−	0.267921i
$127$	−1.59996			−0.141973			−0.0709867	−	0.997477i	$-0.522615\pi$
$127$	−1.59996			−0.141973			−0.0709867	+	0.997477i	$0.522615\pi$
$128$	−0.500664	+	11.3026i	−0.0442529	+	0.999020i
$129$	−2.26611	+	13.6720i	−0.199520	+	1.20376i
$130$	2.44188	+	2.29464i	0.214167	+	0.201253i
$131$	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
$135$	−7.10217	−	11.4695i	−0.611257	−	0.987138i
$136$	2.27254	−	13.3532i	0.194868	−	1.14503i
$137$	−2.43936	+	1.40836i	−0.208408	+	0.120325i	−0.600571	−	0.799571i	$-0.705060\pi$
$137$	−2.43936	+	1.40836i	−0.208408	+	0.120325i	0.392163	+	0.919896i	$0.371727\pi$
$138$	7.64916	+	10.0158i	0.651140	+	0.852599i
$139$	2.80505			0.237921			0.118960	−	0.992899i	$-0.462044\pi$
$139$	2.80505			0.237921			0.118960	+	0.992899i	$0.462044\pi$
$140$	10.5334	+	8.81915i	0.890237	+	0.745354i
$141$	−7.24101	+	8.81187i	−0.609803	+	0.742093i
$142$	−0.195333	+	0.831534i	−0.0163920	+	0.0697808i
$143$	1.49497	+	2.58936i	0.125016	+	0.216533i
$144$	3.76789	+	11.3931i	0.313991	+	0.949426i
$145$	3.05670	+	1.76479i	0.253845	+	0.146558i
$146$	−2.02030	+	0.609216i	−0.167201	+	0.0504190i
$147$	11.1111	−	4.85224i	0.916425	−	0.400206i
$148$	−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	$-0.0847718\pi$
$150$	0.546805	+	4.22783i	0.0446464	+	0.345201i
$151$	−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	$-0.341513\pi$
$152$	−14.1456	+	5.24429i	−1.14736	+	0.425368i
$153$	−2.78508	−	14.0943i	−0.225160	−	1.13946i
$154$	6.72678	+	10.2477i	0.542059	+	0.825784i
$155$	−24.5366			−1.97082
$156$	−2.56253	−	1.85156i	−0.205167	−	0.148243i
$157$	8.55356	+	14.8152i	0.682648	+	1.18238i	0.974170	+	0.225817i	$0.0725052\pi$
$157$	8.55356	+	14.8152i	0.682648	+	1.18238i	−0.291521	+	0.956564i	$0.594161\pi$
$158$	−0.121085	+	0.128855i	−0.00963302	+	0.0102511i
$159$	−1.02536	−	2.72954i	−0.0813165	−	0.216466i
$160$	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	$-0.899385\pi$
$163$	−21.6390	−	12.4933i	−1.69489	−	0.978547i	−0.744436	−	0.667694i	$-0.767282\pi$
$164$	−10.5987	−	5.27020i	−0.827616	−	0.411534i
$165$	−2.40897	+	14.5339i	−0.187538	+	1.13146i
$166$	0.0796970	−	0.339271i	0.00618568	−	0.0263325i
$167$	−9.89286			−0.765532			−0.382766	−	0.923845i	$-0.625028\pi$
$167$	−9.89286			−0.765532			−0.382766	+	0.923845i	$0.625028\pi$
$168$	−10.9233	−	6.97725i	−0.842749	−	0.538307i
$169$	−12.1671			−0.935931
$170$	−4.02096	+	17.1173i	−0.308393	+	1.31283i
$171$	−12.0439	+	10.5354i	−0.921021	+	0.805662i
$172$	−7.12502	+	14.3288i	−0.543278	+	1.09256i
$173$	−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
$177$	−2.81336	+	1.05685i	−0.211465	+	0.0794379i
$178$	−3.49940	+	3.72394i	−0.262291	+	0.279121i
$179$	−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	$0.983350\pi$
$180$	−3.96309	−	15.0648i	−0.295391	−	1.12286i
$181$	−1.41922			−0.105489			−0.0527447	−	0.998608i	$-0.516797\pi$
$181$	−1.41922			−0.105489			−0.0527447	+	0.998608i	$0.516797\pi$
$182$	3.40917	−	0.195473i	0.252704	−	0.0144894i
$183$	10.3883	−	12.6419i	0.767924	−	0.934517i
$184$	5.05858	+	13.6447i	0.372924	+	1.00590i
$185$	2.39448	+	4.14736i	0.176045	+	0.304920i
$186$	22.9586	−	2.96934i	1.68340	−	0.217723i
$187$	−7.84469	+	13.5874i	−0.573661	+	0.993610i
$188$	−10.9743	+	7.28055i	−0.800383	+	0.530989i
$189$	−13.4605	−	2.79543i	−0.979109	−	0.203338i
$190$	18.7500	−	5.65399i	1.36026	−	0.410184i
$191$	−3.62414	−	2.09240i	−0.262234	−	0.151401i	0.363119	−	0.931743i	$-0.381712\pi$
$191$	−3.62414	−	2.09240i	−0.262234	−	0.151401i	−0.625353	+	0.780342i	$0.715045\pi$
$192$	0.307606	+	13.8530i	0.0221995	+	0.999754i
$193$	−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	$-0.565051\pi$
$194$	−1.65041	+	7.02582i	−0.118493	+	0.504425i
$195$	3.17074	+	2.60550i	0.227061	+	0.186584i
$196$	13.9082	−	1.60019i	0.993446	−	0.114299i
$197$	12.6908			0.904184			0.452092	−	0.891971i	$-0.350678\pi$
$197$	12.6908			0.904184			0.452092	+	0.891971i	$0.350678\pi$
$198$	0.495192	−	13.8908i	0.0351918	−	0.987173i
$199$	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	$0.321090\pi$
$200$	−0.825874	+	4.85276i	−0.0583981	+	0.343142i
$201$	20.3390	−	7.64045i	1.43461	−	0.538916i
$202$	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
$206$	0.797987	+	0.749871i	0.0555984	+	0.0522460i
$207$	10.1623	+	11.6174i	0.706332	+	0.807467i
$208$	−2.20316	−	2.91076i	−0.152762	−	0.201825i
$209$	17.4746			1.20874
$210$	13.5897	+	9.92049i	0.937778	+	0.684579i
$211$		−	7.89074i		−	0.543221i	−0.962407	−	0.271610i	$-0.912444\pi$
$211$		−	7.89074i		−	0.543221i	0.962407	−	0.271610i	$-0.0875562\pi$
$212$	−0.209122	−	3.36035i	−0.0143625	−	0.230790i
$213$	−0.171062	+	1.03206i	−0.0117209	+	0.0707155i
$214$	−14.0703	+	14.9731i	−0.961823	+	1.02354i
$215$	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
$219$	−2.41933	+	0.908832i	−0.163483	+	0.0614132i
$220$	−7.57418	+	15.2321i	−0.510651	+	1.02695i
$221$	2.18528	+	3.78502i	0.146998	+	0.254608i
$222$	−2.74238	−	3.59086i	−0.184057	−	0.241003i
$223$			11.5392i			0.772720i	0.922348	+	0.386360i	$0.126268\pi$
$223$			11.5392i			0.772720i	−0.922348	+	0.386360i	$0.873732\pi$
$224$	−9.70091	−	11.3970i	−0.648169	−	0.761496i
$225$	1.01214	+	5.12210i	0.0674760	+	0.341473i
$226$	5.26206	−	22.4006i	0.350027	−	1.49007i
$227$	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	$0.160513\pi$
$228$	−16.8599	+	7.55943i	−1.11657	+	0.500636i
$229$	1.78238	−	3.08717i	0.117783	−	0.204006i	−0.801106	−	0.598523i	$-0.795755\pi$
$229$	1.78238	−	3.08717i	0.117783	−	0.204006i	0.918889	+	0.394517i	$0.129088\pi$
$230$	−5.45378	−	18.0860i	−0.359612	−	1.19256i
$231$	9.05402	+	11.9759i	0.595711	+	0.787957i
$232$	−2.96032	−	2.45408i	−0.194354	−	0.161118i
$233$	6.60666	+	3.81435i	0.432816	+	0.249887i	0.700546	−	0.713607i	$-0.252940\pi$
$233$	6.60666	+	3.81435i	0.432816	+	0.249887i	−0.267729	+	0.963494i	$0.586273\pi$
$234$	−3.28213	−	2.05423i	−0.214560	−	0.134289i
$235$	14.8054	−	8.54789i	0.965796	−	0.557603i
$236$	−3.46354	+	0.215544i	−0.225458	+	0.0140307i
$237$	−0.137489	+	0.167316i	−0.00893087	+	0.0108683i
$238$	9.83293	+	14.9797i	0.637374	+	0.970988i
$239$			13.2745i			0.858658i	0.903148	+	0.429329i	$0.141250\pi$
$239$			13.2745i			0.858658i	−0.903148	+	0.429329i	$0.858750\pi$
$240$	0.718408	−	17.9728i	0.0463730	−	1.16014i
$241$	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	$0.212957\pi$
$242$	0.258352	−	0.274929i	0.0166075	−	0.0176731i
$243$	10.6203	+	11.4110i	0.681290	+	0.732014i
$244$	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
$248$	26.3522	+	4.48479i	1.67337	+	0.284784i
$249$	0.0697941	−	0.421086i	0.00442302	−	0.0266852i
$250$	−2.73688	+	11.6509i	−0.173095	+	0.736870i
$251$			1.44903i			0.0914619i	0.998954	+	0.0457309i	$0.0145617\pi$
$251$			1.44903i			0.0914619i	−0.998954	+	0.0457309i	$0.985438\pi$
$252$	−13.9163	−	7.63791i	−0.876642	−	0.481143i
$253$		−	16.8558i		−	1.05972i
$254$	−2.20272	−	0.517434i	−0.138211	−	0.0324667i
$255$	−3.52133	+	21.2451i	−0.220514	+	1.33042i
$256$	−4.34461	+	15.3988i	−0.271538	+	0.962428i
$257$	−6.03418	+	10.4515i	−0.376402	+	0.651948i	−0.990536	−	0.137254i	$-0.956172\pi$
$257$	−6.03418	+	10.4515i	−0.376402	+	0.651948i	0.614134	+	0.789202i	$0.289506\pi$
$258$	−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
$261$	−3.86041	−	1.31586i	−0.238953	−	0.0814496i
$262$	9.48070	+	8.90904i	0.585720	+	0.550402i
$263$	−21.7325	+	12.5473i	−1.34008	+	0.773697i	−0.986819	−	0.161827i	$-0.948261\pi$
$263$	−21.7325	+	12.5473i	−1.34008	+	0.773697i	−0.353264	+	0.935524i	$0.614928\pi$
$264$	5.24373	−	15.1691i	0.322729	−	0.933592i
$265$			4.37055i			0.268480i
$266$	8.97300	−	17.8266i	0.550170	−	1.09302i
$267$	−3.97347	+	4.83547i	−0.243172	+	0.295926i
$268$	25.0395	−	1.55826i	1.52953	−	0.0951860i
$269$	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	$0.258488\pi$
$270$	−6.06853	−	18.0874i	−0.369319	−	1.10076i
$271$	−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
$273$	4.15024	−	0.516203i	0.251184	−	0.0312420i
$274$	−3.81383	+	1.15005i	−0.230402	+	0.0694769i
$275$	2.85088	−	4.93787i	0.171915	−	0.297765i
$276$	7.29175	+	16.2629i	0.438912	+	0.978910i
$277$	3.08910	−	1.78349i	0.185606	−	0.107160i	−0.404318	−	0.914618i	$-0.632491\pi$
$277$	3.08910	−	1.78349i	0.185606	−	0.107160i	0.589924	+	0.807459i	$0.299158\pi$
$278$	3.86182	+	0.907166i	0.231616	+	0.0544082i
$279$	27.8148	−	5.49627i	1.66523	−	0.329053i
$280$	11.6496	+	15.5482i	0.696198	+	0.929185i
$281$		−	4.26336i		−	0.254331i	−0.991882	−	0.127165i	$-0.959412\pi$
$281$		−	4.26336i		−	0.254331i	0.991882	−	0.127165i	$-0.0405879\pi$
$282$	−12.8188	+	9.78986i	−0.763347	+	0.582978i
$283$	11.3202	+	19.6072i	0.672918	+	1.16553i	0.977073	+	0.212906i	$0.0682928\pi$
$283$	11.3202	+	19.6072i	0.672918	+	1.16553i	−0.304154	+	0.952623i	$0.598374\pi$
$284$	−0.537845	+	1.08163i	−0.0319152	+	0.0641832i
$285$	22.4533	−	8.43466i	1.33002	−	0.499626i
$286$	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
$290$	3.63754	+	3.41820i	0.213604	+	0.200724i
$291$	−1.44534	+	8.72009i	−0.0847272	+	0.511181i
$292$	−2.97845	+	0.185355i	−0.174301	+	0.0108471i
$293$			5.96057i			0.348220i	0.984726	+	0.174110i	$0.0557049\pi$
$293$			5.96057i			0.348220i	−0.984726	+	0.174110i	$0.944295\pi$
$294$	16.8663	−	3.08689i	0.983661	−	0.180031i
$295$	4.50477			0.262278
$296$	−1.81361	−	4.89191i	−0.105414	−	0.284336i
$297$	−0.524829	−	17.0153i	−0.0304537	−	0.987330i
$298$	16.7933	−	17.8709i	0.972813	−	1.03523i
$299$	−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
$303$	11.8535	−	4.45282i	0.680967	−	0.255808i
$304$	−21.1708	+	2.64526i	−1.21423	+	0.151716i
$305$	−21.2405	+	12.2632i	−1.21623	+	0.702189i
$306$	0.723852	−	20.3049i	0.0413798	−	1.16075i
$307$	5.42113			0.309400			0.154700	−	0.987961i	$-0.450559\pi$
$307$	5.42113			0.309400			0.154700	+	0.987961i	$0.450559\pi$
$308$	5.94686	+	16.2839i	0.338854	+	0.927861i
$309$	1.03617	+	0.851458i	0.0589458	+	0.0484378i
$310$	−33.7804	−	7.93525i	−1.91860	−	0.450692i
$311$	−12.1809	−	21.0979i	−0.690714	−	1.19635i	−0.971604	−	0.236612i	$-0.923963\pi$
$311$	−12.1809	−	21.0979i	−0.690714	−	1.19635i	0.280890	−	0.959740i	$-0.409370\pi$
$312$	−2.92913	−	3.37785i	−0.165829	−	0.191233i
$313$	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
$315$	17.4142	+	11.0178i	0.981177	+	0.620780i
$316$	−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	$0.978086\pi$
$318$	−0.528910	−	4.08947i	−0.0296598	−	0.229326i
$319$	2.22697	+	3.85723i	0.124687	+	0.215964i
$320$	6.87048	−	19.6005i	0.384072	−	1.09570i
$321$	−15.9764	+	19.4423i	−0.891716	+	1.08516i
$322$	−17.1953	−	8.65526i	−0.958257	−	0.482339i
$323$	25.5436			1.42128
$324$	7.86714	+	16.1898i	0.437063	+	0.899431i
$325$	−0.794166	−	1.37554i	−0.0440524	−	0.0763010i
$326$	−25.7508	−	24.1981i	−1.42621	−	1.34021i
$327$	−23.9676	+	9.00354i	−1.32541	+	0.497897i
$328$	−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	0.551387	−	0.834250i	$-0.314099\pi$
$331$	1.90300	+	1.09870i	0.104599	+	0.0603900i	−0.446788	+	0.894640i	$0.647432\pi$
$332$	0.219444	−	0.441313i	0.0120435	−	0.0242202i
$333$	−3.64341	−	4.16509i	−0.199658	−	0.228246i
$334$	−13.6199	−	3.19940i	−0.745247	−	0.175063i
$335$	−32.5669			−1.77932
$336$	−12.7820	−	13.1385i	−0.697316	−	0.716764i
$337$	29.4138			1.60227			0.801135	−	0.598484i	$-0.204230\pi$
$337$	29.4138			1.60227			0.801135	+	0.598484i	$0.204230\pi$
$338$	−16.7509	−	3.93490i	−0.911130	−	0.214030i
$339$	4.60822	−	27.8026i	0.250284	−	1.51003i
$340$	−11.0716	+	22.2656i	−0.600443	+	1.20752i
$341$	−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
$345$	−8.13599	−	21.6582i	−0.438027	−	1.16604i
$346$	−15.9171	−	14.9574i	−0.855710	−	0.804113i
$347$	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	$0.721148\pi$
$348$	−3.81726	−	2.75817i	−0.204627	−	0.147853i
$349$	−30.0571			−1.60892			−0.804460	−	0.594006i	$-0.797545\pi$
$349$	−30.0571			−1.60892			−0.804460	+	0.594006i	$0.797545\pi$
$350$	−3.57344	−	5.44385i	−0.191008	−	0.290986i
$351$	−4.17801	−	2.24335i	−0.223005	−	0.119741i
$352$	10.9188	−	14.9748i	0.581971	−	0.798159i
$353$	12.1069	+	20.9698i	0.644387	+	1.11611i	0.984443	+	0.175705i	$0.0562206\pi$
$353$	12.1069	+	20.9698i	0.644387	+	1.11611i	−0.340056	+	0.940405i	$0.610446\pi$
$354$	−4.21506	+	0.545153i	−0.224028	+	0.0289746i
$355$	0.784045	−	1.35801i	0.0416128	−	0.0720755i
$356$	−6.02209	+	3.99517i	−0.319170	+	0.211744i
$357$	13.2348	+	17.5059i	0.700459	+	0.926510i
$358$	−4.96044	−	16.4500i	−0.262168	−	0.869409i
$359$	3.16884	+	1.82953i	0.167245	+	0.0965590i	0.581286	−	0.813699i	$-0.302550\pi$
$359$	3.16884	+	1.82953i	0.167245	+	0.0965590i	−0.414041	+	0.910258i	$0.635883\pi$
$360$	−0.584116	−	22.0219i	−0.0307856	−	1.16066i
$361$	−4.72503	−	8.18398i	−0.248686	−	0.430736i
$362$	−1.95389	−	0.458981i	−0.102694	−	0.0241235i
$363$	0.293351	−	0.356991i	0.0153970	−	0.0187372i
$364$	4.75675	+	0.833426i	0.249322	+	0.0436834i
$365$	3.87384			0.202766
$366$	18.3904	−	14.0450i	0.961282	−	0.734143i
$367$	−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	$0.484745\pi$
$368$	2.55159	+	20.4212i	0.133011	+	1.06453i
$369$	−16.8055	−	5.72834i	−0.874861	−	0.298205i
$370$	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	0.413307	−	0.910592i	$-0.364374\pi$
$373$	−3.25687	−	1.88036i	−0.168635	−	0.0973612i	−0.581942	+	0.813230i	$0.697707\pi$
$374$	−15.1943	+	16.1693i	−0.785680	+	0.836094i
$375$	−2.39681	+	14.4605i	−0.123771	+	0.746739i
$376$	−17.4633	+	6.47428i	−0.900601	+	0.333886i
$377$	1.24073			0.0639008
$378$	−17.6276	−	8.20178i	−0.906664	−	0.421854i
$379$		−	12.2799i		−	0.630774i	−0.948963	−	0.315387i	$-0.897866\pi$
$379$		−	12.2799i		−	0.630774i	0.948963	−	0.315387i	$-0.102134\pi$
$380$	27.6423	−	1.72024i	1.41802	−	0.0882465i
$381$	−2.73391	−	0.453140i	−0.140062	−	0.0232151i
$382$	−4.31281	−	4.05275i	−0.220662	−	0.207357i
$383$	−3.77515	+	6.53874i	−0.192901	+	0.334114i	−0.946210	−	0.323552i	$-0.895123\pi$
$383$	−3.77515	+	6.53874i	−0.192901	+	0.334114i	0.753309	+	0.657666i	$0.228456\pi$
$384$	−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
$387$	−7.74439	+	22.7201i	−0.393670	+	1.15493i
$388$	−4.54437	+	9.13897i	−0.230705	+	0.463961i
$389$	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	$0.455211\pi$
$390$	3.52265	+	4.61253i	0.178376	+	0.233565i
$391$		−	24.6391i		−	1.24605i
$392$	19.6655	+	2.29495i	0.993259	+	0.115913i
$393$	12.3105	+	10.1160i	0.620984	+	0.510283i
$394$	17.4720	+	4.10428i	0.880224	+	0.206770i
$395$	0.281118	−	0.162304i	0.0141446	−	0.00816638i
$396$	5.17409	−	18.9638i	0.260008	−	0.952966i
$397$	3.83449	−	6.64152i	0.192447	−	0.333329i	−0.753613	−	0.657318i	$-0.771691\pi$
$397$	3.83449	−	6.64152i	0.192447	−	0.333329i	0.946061	+	0.323989i	$0.105024\pi$
$398$	1.46901	−	0.442975i	0.0736348	−	0.0222043i
$399$	9.51522	−	22.5147i	0.476357	−	1.12714i
$400$	−2.70642	+	6.41389i	−0.135321	+	0.320695i
$401$	20.5062	+	11.8393i	1.02403	+	0.591224i	0.915269	−	0.402844i	$-0.131978\pi$
$401$	20.5062	+	11.8393i	1.02403	+	0.591224i	0.108761	+	0.994068i	$0.465312\pi$
$402$	30.4725	−	3.94115i	1.51983	−	0.196567i
$403$	−7.46964	+	4.31260i	−0.372089	+	0.214826i
$404$	14.5929	−	0.908149i	0.726025	−	0.0451821i
$405$	−8.88735	−	21.6099i	−0.441616	−	1.07380i
$406$	5.07845	−	0.291186i	0.252039	−	0.0144513i
$407$			6.04316i			0.299548i
$408$	7.66507	−	22.1735i	0.379477	−	1.09775i
$409$	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	$0.206747\pi$
$410$	15.8353	+	14.8805i	0.782050	+	0.734894i
$411$	−4.56710	+	1.71565i	−0.225278	+	0.0846267i
$412$	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
$416$	−2.09182	−	4.71987i	−0.102560	−	0.231411i
$417$	4.79309	+	0.794445i	0.234719	+	0.0389041i
$418$	24.0579	+	5.65136i	1.17671	+	0.276417i
$419$		−	35.4540i		−	1.73204i	−0.500009	−	0.866020i	$-0.666670\pi$
$419$		−	35.4540i		−	1.73204i	0.500009	−	0.866020i	$-0.333330\pi$
$420$	15.5011	+	18.0529i	0.756377	+	0.880891i
$421$		−	8.00460i		−	0.390120i	−0.980791	−	0.195060i	$-0.937510\pi$
$421$		−	8.00460i		−	0.390120i	0.980791	−	0.195060i	$-0.0624902\pi$
$422$	2.55190	−	10.8635i	0.124225	−	0.528826i
$423$	−14.8687	+	13.0064i	−0.722940	+	0.632392i
$424$	0.798847	−	4.69395i	0.0387954	−	0.227958i
$425$	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
$429$	1.82115	+	4.84795i	0.0879261	+	0.234061i
$430$	20.1176	−	21.4085i	0.970156	−	1.03241i
$431$	25.8583	−	14.9293i	1.24555	−	0.719118i	0.275331	−	0.961350i	$-0.411213\pi$
$431$	25.8583	−	14.9293i	1.24555	−	0.719118i	0.970219	+	0.242231i	$0.0778793\pi$
$432$	3.21158	+	20.5350i	0.154517	+	0.987990i
$433$			1.70747i			0.0820557i	0.999158	+	0.0410278i	$0.0130632\pi$
$433$			1.70747i			0.0820557i	−0.999158	+	0.0410278i	$0.986937\pi$
$434$	−29.5620	+	19.4050i	−1.41902	+	0.931470i
$435$	4.72328	+	3.88128i	0.226464	+	0.186093i
$436$	−29.5066	+	1.83626i	−1.41311	+	0.0879410i
$437$	−23.7660	+	13.7213i	−1.13688	+	0.656379i
$438$	−3.62471	+	0.468801i	−0.173195	+	0.0224002i
$439$	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
$441$	20.3602	−	5.14433i	0.969531	−	0.244968i
$442$	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	$0.276555\pi$
$444$	−2.61425	−	5.83058i	−0.124067	−	0.276707i
$445$	8.12438	−	4.69062i	0.385133	−	0.222356i
$446$	−3.73182	+	15.8864i	−0.176707	+	0.752244i
$447$	19.0684	−	23.2051i	0.901904	−	1.09756i
$448$	−9.66976	−	18.8281i	−0.456853	−	0.889542i
$449$			2.18010i			0.102885i	0.998676	+	0.0514426i	$0.0163819\pi$
$449$			2.18010i			0.102885i	−0.998676	+	0.0514426i	$0.983618\pi$
$450$	−0.263059	+	7.37912i	−0.0124007	+	0.347855i
$451$	9.69470	+	16.7917i	0.456506	+	0.790691i
$452$	14.4890	−	29.1381i	0.681503	−	1.37054i
$453$	−7.81529	−	20.8045i	−0.367194	−	0.977480i
$454$	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	$0.895540\pi$
$458$	3.45227	−	3.67379i	0.161314	−	0.171665i
$459$	−0.767174	−	24.8723i	−0.0358086	−	1.16094i
$460$	−1.65933	−	26.6635i	−0.0773665	−	1.24319i
$461$		−	13.9258i		−	0.648588i	−0.945956	−	0.324294i	$-0.894873\pi$
$461$		−	13.9258i		−	0.648588i	0.945956	−	0.324294i	$-0.105127\pi$
$462$	8.59195	+	19.4158i	0.399734	+	0.903306i
$463$	15.5838			0.724239			0.362120	−	0.932132i	$-0.382053\pi$
$463$	15.5838			0.724239			0.362120	+	0.932132i	$0.382053\pi$
$464$	−3.28192	−	4.33600i	−0.152359	−	0.201294i
$465$	−41.9266	−	6.94925i	−1.94430	−	0.322264i
$466$	7.86206	+	7.38799i	0.364203	+	0.342242i
$467$	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
$471$	10.4198	+	27.7378i	0.480121	+	1.27809i
$472$	−4.83810	−	0.823380i	−0.222692	−	0.0378991i
$473$	22.7015	−	13.1067i	1.04381	−	0.602647i
$474$	−0.243397	+	0.185886i	−0.0111796	+	0.00853800i
$475$	−9.28294			−0.425931
$476$	8.69287	+	23.8031i	0.398437	+	1.09101i
$477$	−0.979016	−	4.95447i	−0.0448261	−	0.226850i
$478$	−4.29305	+	18.2755i	−0.196359	+	0.835904i
$479$	−3.02090	−	5.23235i	−0.138028	−	0.239072i	0.788722	−	0.614750i	$-0.210743\pi$
$479$	−3.02090	−	5.23235i	−0.138028	−	0.239072i	−0.926750	+	0.375678i	$0.877410\pi$
$480$	6.80156	−	24.5115i	0.310447	−	1.11879i
$481$	1.45790	+	0.841716i	0.0664743	+	0.0383790i
$482$	15.5219	−	4.68058i	0.707003	−	0.213195i
$483$	−21.7174	−	9.17829i	−0.988178	−	0.417626i
$484$	0.444596	−	0.294954i	0.0202089	−	0.0134070i
$485$	6.62457	−	11.4741i	0.300806	−	0.521012i
$486$	10.9309	+	19.1446i	0.495838	+	0.868415i
$487$	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	$0.664923\pi$
$488$	25.0537	−	9.28830i	1.13413	−	0.420462i
$489$	−33.4370	−	27.4763i	−1.51207	−	1.24252i
$490$	−25.2937	−	4.55895i	−1.14265	−	0.205953i
$491$	4.63965			0.209384			0.104692	−	0.994505i	$-0.466614\pi$
$491$	4.63965			0.209384			0.104692	+	0.994505i	$0.466614\pi$
$492$	−16.6177	−	12.0071i	−0.749184	−	0.541324i
$493$	3.25530	+	5.63834i	0.146611	+	0.253938i
$494$	4.71427	−	5.01677i	0.212105	−	0.225715i
$495$	−8.23260	+	24.1524i	−0.370028	+	1.08557i
$496$	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	0.827959	−	0.560789i	$-0.189502\pi$
$499$	16.8940	+	9.75377i	0.756280	+	0.436639i	−0.0716782	+	0.997428i	$0.522835\pi$
$500$	−7.53594	+	15.1552i	−0.337017	+	0.677760i
$501$	−16.9043	−	2.80185i	−0.755229	−	0.125178i
$502$	−0.468623	+	1.99493i	−0.0209157	+	0.0890383i
$503$	33.9146			1.51218			0.756090	−	0.654468i	$-0.227107\pi$
$503$	33.9146			1.51218			0.756090	+	0.654468i	$0.227107\pi$
$504$	−16.6889	−	15.0160i	−0.743384	−	0.668865i
$505$	−18.9799			−0.844594
$506$	5.45125	−	23.2060i	0.242338	−	1.03163i
$507$	−20.7904	−	3.44596i	−0.923333	−	0.153041i
$508$	−2.86524	−	1.42474i	−0.127124	−	0.0632128i
$509$	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
$513$	−23.5637	+	14.5912i	−1.04036	+	0.644216i
$514$	−11.6876	+	12.4375i	−0.515516	+	0.548595i
$515$	−1.00513	−	1.74094i	−0.0442914	−	0.0767150i
$516$	−16.2330	+	22.4662i	−0.714618	+	0.989020i
$517$	21.5731			0.948782
$518$	6.16488	+	3.10309i	0.270869	+	0.136342i
$519$	−20.6681	−	16.9837i	−0.907230	−	0.745501i
$520$	2.32962	+	6.28375i	0.102160	+	0.275561i
$521$	−2.98225	−	5.16541i	−0.130655	−	0.226301i	0.793274	−	0.608864i	$-0.208375\pi$
$521$	−2.98225	−	5.16541i	−0.130655	−	0.226301i	−0.923929	+	0.382564i	$0.875041\pi$
$522$	−4.88922	−	3.06007i	−0.213995	−	0.133936i
$523$	−6.49701	+	11.2532i	−0.284095	+	0.492066i	−0.972389	−	0.233365i	$-0.925026\pi$
$523$	−6.49701	+	11.2532i	−0.284095	+	0.492066i	0.688295	+	0.725431i	$0.258360\pi$
$524$	10.1712	+	15.3315i	0.444332	+	0.669761i
$525$	−4.80973	−	6.36191i	−0.209914	−	0.277656i
$526$	−33.9778	+	10.2459i	−1.48150	+	0.446743i
$527$	−39.1961	−	22.6299i	−1.70741	−	0.985774i
$528$	12.1250	−	19.1880i	0.527673	−	0.835051i
$529$	1.73544	+	3.00587i	0.0754539	+	0.130690i
$530$	−1.41346	+	6.01710i	−0.0613966	+	0.261366i
$531$	−5.10662	+	1.00908i	−0.221609	+	0.0437905i
$532$	18.1187	−	21.6406i	0.785544	−	0.938239i
$533$	5.40127			0.233955
$534$	−7.03425	+	5.37214i	−0.304402	+	0.232475i
$535$	32.6663	−	18.8599i	1.41229	−	0.815383i
$536$	34.9768	+	5.95258i	1.51077	+	0.257112i
$537$	−7.40002	−	19.6990i	−0.319335	−	0.850076i
$538$	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	0.845578	−	0.533851i	$-0.179256\pi$
$541$	18.7480	+	10.8242i	0.806039	+	0.465367i	−0.0395397	+	0.999218i	$0.512589\pi$
$542$	−11.0416	−	10.3758i	−0.474278	−	0.445680i
$543$	−2.42507	−	0.401950i	−0.104070	−	0.0172493i
$544$	15.9606	−	21.8895i	0.684304	−	0.938505i
$545$	38.3770			1.64389
$546$	5.88074	+	0.631532i	0.251672	+	0.0270271i
$547$		−	15.8930i		−	0.679536i	−0.940509	−	0.339768i	$-0.889651\pi$
$547$		−	15.8930i		−	0.679536i	0.940509	−	0.339768i	$-0.110349\pi$
$548$	−5.62257	+	0.349905i	−0.240184	+	0.0149472i
$549$	21.3313	−	18.6596i	0.910398	−	0.796370i
$550$	5.52185	−	5.87617i	0.235453	−	0.250561i
$551$	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
$555$	2.91692	+	7.76491i	0.123816	+	0.329602i
$556$	5.02333	+	2.49786i	0.213037	+	0.105933i
$557$	−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	$-0.497404\pi$
$558$	40.0712	+	1.42850i	1.69635	+	0.0604733i
$559$		−	7.30223i		−	0.308851i
$560$	11.0101	+	25.1734i	0.465262	+	1.06377i
$561$	−17.2528	+	20.9956i	−0.728412	+	0.886433i
$562$	1.37879	−	5.86953i	0.0581608	−	0.247591i
$563$	−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	$0.938519\pi$
$564$	−20.8142	+	9.33242i	−0.876436	+	0.392966i
$565$	−21.1213	+	36.5832i	−0.888581	+	1.53907i
$566$	9.24394	+	30.6550i	0.388552	+	1.28853i
$567$	−22.2088	−	8.58895i	−0.932681	−	0.360702i
$568$	−1.09028	+	1.31519i	−0.0457470	+	0.0551840i
$569$	−12.8893	−	7.44164i	−0.540347	−	0.311970i	0.204872	−	0.978789i	$-0.434322\pi$
$569$	−12.8893	−	7.44164i	−0.540347	−	0.311970i	−0.745220	+	0.666819i	$0.767655\pi$
$570$	33.6401	−	4.35083i	1.40903	−	0.182236i
$571$	−6.27344	+	3.62197i	−0.262535	+	0.151575i	−0.625490	−	0.780232i	$-0.715101\pi$
$571$	−6.27344	+	3.62197i	−0.262535	+	0.151575i	0.362955	+	0.931807i	$0.381768\pi$
$572$	0.371422	+	5.96833i	0.0155299	+	0.249549i
$573$	−5.60010	−	4.60179i	−0.233948	−	0.192243i
$574$	22.1080	−	1.26762i	0.922772	−	0.0529095i
$575$			8.95423i			0.373417i
$576$	−3.39783	+	23.7583i	−0.141576	+	0.989927i
$577$	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	$0.171695\pi$
$578$	−5.74685	+	6.11560i	−0.239037	+	0.254376i
$579$	−16.0686	−	42.7748i	−0.667786	−	1.77766i
$580$	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
$584$	−4.16049	−	0.708059i	−0.172162	−	0.0292997i
$585$	4.68003	+	5.35014i	0.193496	+	0.221201i
$586$	−1.92768	+	8.20615i	−0.0796316	+	0.338993i
$587$		−	8.33175i		−	0.343888i	−0.985107	−	0.171944i	$-0.944995\pi$
$587$		−	8.33175i		−	0.343888i	0.985107	−	0.171944i	$-0.0550048\pi$
$588$	24.2188	+	1.20479i	0.998765	+	0.0496846i
$589$			50.4096i			2.07709i
$590$	6.20189	+	1.45686i	0.255328	+	0.0599781i
$591$	21.6853	+	3.59430i	0.892014	+	0.147850i
$592$	−0.914797	−	7.32141i	−0.0375979	−	0.300908i
$593$	−19.8845	+	34.4410i	−0.816560	+	1.41432i	0.0916424	+	0.995792i	$0.470788\pi$
$593$	−19.8845	+	34.4410i	−0.816560	+	1.41432i	−0.908202	+	0.418531i	$0.862545\pi$
$594$	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
$597$	1.75915	−	0.660834i	0.0719974	−	0.0270461i
$598$	−4.83912	−	4.54733i	−0.197886	−	0.185954i
$599$	−12.0202	+	6.93989i	−0.491134	+	0.283556i	−0.725045	−	0.688702i	$-0.758181\pi$
$599$	−12.0202	+	6.93989i	−0.491134	+	0.283556i	0.233911	+	0.972258i	$0.424848\pi$
$600$	−2.78560	+	8.05820i	−0.113722	+	0.328975i
$601$			17.2223i			0.702512i	0.936279	+	0.351256i	$0.114245\pi$
$601$			17.2223i			0.702512i	−0.936279	+	0.351256i	$0.885755\pi$
$602$	−1.71375	−	29.8889i	−0.0698474	−	1.21818i
$603$	36.9180	−	7.29510i	1.50342	−	0.297080i
$604$	−1.59392	−	25.6125i	−0.0648557	−	1.04216i
$605$	−0.599803	+	0.346296i	−0.0243855	+	0.0140790i
$606$	17.7593	−	2.29689i	0.721421	−	0.0933047i
$607$	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
$609$	6.18239	−	0.768959i	0.250523	−	0.0311598i
$610$	−33.2086	+	10.0139i	−1.34458	+	0.405453i
$611$	3.00479	−	5.20445i	0.121561	−	0.210549i
$612$	7.56326	−	27.7205i	0.305727	−	1.12053i
$613$	36.3973	−	21.0140i	1.47007	−	0.848747i	0.470637	−	0.882327i	$-0.344024\pi$
$613$	36.3973	−	21.0140i	1.47007	−	0.848747i	0.999436	+	0.0335801i	$0.0106909\pi$
$614$	7.46348	+	1.75322i	0.301202	+	0.0707542i
$615$	20.5619	+	16.8964i	0.829134	+	0.681328i
$616$	2.92098	+	24.3419i	0.117690	+	0.980764i
$617$			16.0083i			0.644471i	0.946660	+	0.322236i	$0.104434\pi$
$617$			16.0083i			0.644471i	−0.946660	+	0.322236i	$0.895566\pi$
$618$	1.15117	+	1.50734i	0.0463070	+	0.0606341i
$619$	−10.1543	−	17.5878i	−0.408136	−	0.706913i	0.586545	−	0.809917i	$-0.300488\pi$
$619$	−10.1543	−	17.5878i	−0.408136	−	0.706913i	−0.994681	+	0.103004i	$0.967155\pi$
$620$	−43.9405	−	21.8495i	−1.76469	−	0.877498i
$621$	14.0745	+	22.7293i	0.564790	+	0.912096i
$622$	−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
$626$	16.8259	+	15.8114i	0.672500	+	0.631950i
$627$	29.8595	+	4.94915i	1.19247	+	0.197650i
$628$	2.12511	+	34.1482i	0.0848013	+	1.36266i
$629$			8.83363i			0.352220i
$630$	20.4115	+	20.8004i	0.813215	+	0.828708i
$631$	−28.0435			−1.11639			−0.558197	−	0.829708i	$-0.688507\pi$
$631$	−28.0435			−1.11639			−0.558197	+	0.829708i	$0.688507\pi$
$632$	−0.331585	+	0.122931i	−0.0131898	+	0.00488992i
$633$	2.23481	−	13.4832i	0.0888259	−	0.535909i
$634$	−19.2563	+	20.4919i	−0.764765	+	0.813837i
$635$	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
$639$	−0.584599	+	1.71507i	−0.0231264	+	0.0678471i
$640$	15.7978	−	24.7629i	0.624462	−	0.978838i
$641$	9.80778	−	5.66252i	0.387384	−	0.223656i	−0.293642	−	0.955915i	$-0.594867\pi$
$641$	9.80778	−	5.66252i	0.387384	−	0.223656i	0.681026	+	0.732259i	$0.261534\pi$
$642$	−28.2831	+	21.6001i	−1.11624	+	0.852489i
$643$	−32.8892			−1.29702			−0.648512	−	0.761204i	$-0.724608\pi$
$643$	−32.8892			−1.29702			−0.648512	+	0.761204i	$0.724608\pi$
$644$	−20.8743	−	17.4771i	−0.822563	−	0.688693i
$645$	22.8430	−	27.7985i	0.899441	−	1.09457i
$646$	35.1669	+	8.26093i	1.38362	+	0.325022i
$647$	−13.6188	−	23.5884i	−0.535409	−	0.927356i	−0.999143	−	0.0413818i	$-0.986824\pi$
$647$	−13.6188	−	23.5884i	−0.535409	−	0.927356i	0.463734	−	0.885974i	$-0.346509\pi$
$648$	5.59514	+	24.8333i	0.219798	+	0.975545i
$649$	4.92296	+	2.84227i	0.193243	+	0.111569i
$650$	−0.648504	−	2.15059i	−0.0254364	−	0.0843531i
$651$	−34.5474	+	26.1185i	−1.35402	+	1.02366i
$652$	−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	$0.326366\pi$
$654$	−35.9089	+	4.64427i	−1.40415	+	0.181605i
$655$	−11.9417	−	20.6837i	−0.466602	−	0.808179i
$656$	−14.2872	−	18.8759i	−0.557822	−	0.736982i
$657$	−4.39140	+	0.867753i	−0.171325	+	0.0338543i
$658$	11.0775	−	22.0076i	0.431847	−	0.857945i
$659$	−12.1725			−0.474172			−0.237086	−	0.971489i	$-0.576192\pi$
$659$	−12.1725			−0.474172			−0.237086	+	0.971489i	$0.576192\pi$
$660$	−17.2563	+	23.8825i	−0.671701	+	0.929624i
$661$	−4.00322	−	6.93378i	−0.155707	−	0.269693i	0.777609	−	0.628748i	$-0.216432\pi$
$661$	−4.00322	−	6.93378i	−0.155707	−	0.269693i	−0.933316	+	0.359055i	$0.883099\pi$
$662$	2.26461	+	2.12806i	0.0880167	+	0.0827095i
$663$	2.66208	+	7.08653i	0.103387	+	0.275218i
$664$	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
$668$	−17.7163	−	8.80947i	−0.685465	−	0.340849i
$669$	−3.26812	+	19.7174i	−0.126353	+	0.762319i
$670$	−44.8362	−	10.5323i	−1.73217	−	0.406899i
$671$	−30.9497			−1.19480
$672$	−13.3484	−	22.2220i	−0.514927	−	0.857234i
$673$	18.1260			0.698706			0.349353	−	0.936991i	$-0.386401\pi$
$673$	18.1260			0.698706			0.349353	+	0.936991i	$0.386401\pi$
$674$	40.4951	+	9.51255i	1.55981	+	0.366410i
$675$	0.278803	+	9.03898i	0.0107311	+	0.347910i
$676$	−21.7891	−	10.8347i	−0.838041	−	0.416717i
$677$	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
$681$	25.2426	−	9.48249i	0.967298	−	0.363370i
$682$	−31.9097	−	29.9856i	−1.22188	−	1.14821i
$683$	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	$0.754827\pi$
$684$	−30.9501	+	8.14204i	−1.18341	+	0.311319i
$685$	7.31285			0.279410
$686$	−21.1129	+	15.4998i	−0.806096	+	0.591785i
$687$	3.91996	−	4.77036i	0.149556	−	0.182000i
$688$	−25.5192	+	19.3155i	−0.972912	+	0.736397i
$689$	0.768176	+	1.33052i	0.0292652	+	0.0506888i
$690$	−4.19677	−	32.4489i	−0.159768	−	1.23531i
$691$	7.47003	−	12.9385i	0.284173	−	0.492203i	−0.688235	−	0.725488i	$-0.741614\pi$
$691$	7.47003	−	12.9385i	0.284173	−	0.492203i	0.972408	+	0.233285i	$0.0749475\pi$
$692$	−17.0764	−	25.7401i	−0.649149	−	0.978490i
$693$	12.0791	+	23.0280i	0.458848	+	0.874761i
$694$	5.25077	+	17.4128i	0.199316	+	0.660980i
$695$	−6.30686	−	3.64127i	−0.239233	−	0.138121i
$696$	−4.36337	−	5.03180i	−0.165393	−	0.190730i
$697$	14.1713	+	24.5454i	0.536776	+	0.929724i
$698$	−41.3808	−	9.72062i	−1.56629	−	0.367931i
$699$	10.2087	+	8.38887i	0.386130	+	0.317296i
$700$	−3.15912	−	8.65042i	−0.119404	−	0.326955i
$701$	14.3141			0.540636			0.270318	−	0.962771i	$-0.412871\pi$
$701$	14.3141			0.540636			0.270318	+	0.962771i	$0.412871\pi$
$702$	−5.02651	−	4.43970i	−0.189713	−	0.167566i
$703$	8.52061	−	4.91938i	0.321361	−	0.185538i
$704$	19.8752	−	17.0852i	0.749074	−	0.643922i
$705$	27.7194	−	10.4129i	1.04397	−	0.392173i
$706$	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	0.389542	−	0.921009i	$-0.372633\pi$
$709$	−5.67964	−	3.27914i	−0.213303	−	0.123151i	−0.602846	+	0.797858i	$0.705967\pi$
$710$	1.51861	−	1.61605i	0.0569924	−	0.0606495i
$711$	−0.282320	+	0.246959i	−0.0105878	+	0.00926170i
$712$	−9.58291	+	3.55273i	−0.359135	+	0.133144i
$713$	48.6246			1.82100
$714$	12.5594	+	28.3812i	0.470022	+	1.06214i
$715$		−	7.76255i		−	0.290303i
$716$	−1.50923	−	24.2516i	−0.0564025	−	0.906324i
$717$	−3.75961	+	22.6827i	−0.140405	+	0.847100i
$718$	3.77099	+	3.54361i	0.140732	+	0.132246i
$719$	19.5665	−	33.8902i	0.729708	−	1.26389i	−0.227299	−	0.973825i	$-0.572990\pi$
$719$	19.5665	−	33.8902i	0.729708	−	1.26389i	0.957007	−	0.290066i	$-0.0936772\pi$
$720$	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
$723$	18.5876	−	6.98252i	0.691281	−	0.259683i
$724$	−2.54156	−	1.26379i	−0.0944563	−	0.0469686i
$725$	−1.18303	−	2.04906i	−0.0439365	−	0.0761002i
$726$	0.519321	−	0.396612i	0.0192738	−	0.0147196i
$727$			34.4829i			1.27890i	0.768833	+	0.639450i	$0.220838\pi$
$727$			34.4829i			1.27890i	−0.768833	+	0.639450i	$0.779162\pi$
$728$	6.27927	+	2.68577i	0.232725	+	0.0995411i
$729$	14.9154	+	22.5062i	0.552423	+	0.833564i
$730$	5.33327	+	1.25282i	0.197393	+	0.0463689i
$731$	33.1841	−	19.1588i	1.22736	−	0.708615i
$732$	29.8610	−	13.3887i	1.10369	−	0.494862i
$733$	9.89201	−	17.1335i	0.365370	−	0.632839i	−0.623466	−	0.781851i	$-0.714276\pi$
$733$	9.89201	−	17.1335i	0.365370	−	0.632839i	0.988835	+	0.149012i	$0.0476093\pi$
$734$	−23.7567	+	7.16376i	−0.876876	+	0.264419i
$735$	−31.2808	−	3.51365i	−1.15381	−	0.129603i
$736$	−3.09143	+	28.9398i	−0.113952	+	1.06673i
$737$	−35.5902	−	20.5480i	−1.31098	−	0.756896i
$738$	−21.2842	−	13.3214i	−0.783484	−	0.490368i
$739$	−6.03595	+	3.48486i	−0.222036	+	0.128193i	−0.606893	−	0.794784i	$-0.707584\pi$
$739$	−6.03595	+	3.48486i	−0.222036	+	0.128193i	0.384857	+	0.922976i	$0.374251\pi$
$740$	0.594903	+	9.55942i	0.0218691	+	0.351411i
$741$	5.35292	−	6.51418i	0.196645	−	0.239305i
$742$	3.45649	+	5.26569i	0.126892	+	0.193310i
$743$			45.3956i			1.66540i	0.553723	+	0.832701i	$0.313207\pi$
$743$			45.3956i			1.66540i	−0.553723	+	0.832701i	$0.686793\pi$
$744$	43.7588	+	15.1268i	1.60428	+	0.554575i
$745$	−38.9883	+	22.5099i	−1.42842	+	0.824700i
$746$	−3.87575	−	3.64205i	−0.141901	−	0.133345i
$747$	0.238520	−	0.699759i	0.00872698	−	0.0256028i
$748$	−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	$0.290156\pi$
$752$	−26.1362	+	3.26567i	−0.953090	+	0.119087i
$753$	−0.410394	+	2.47601i	−0.0149556	+	0.0902309i
$754$	1.70816	+	0.401258i	0.0622075	+	0.0146130i
$755$			33.3122i			1.21236i
$756$	−21.6160	−	16.9925i	−0.786168	−	0.618013i
$757$		−	30.3555i		−	1.10329i	−0.834079	−	0.551645i	$-0.814000\pi$
$757$		−	30.3555i		−	1.10329i	0.834079	−	0.551645i	$-0.186000\pi$
$758$	3.97137	−	16.9062i	0.144247	−	0.614059i
$759$	4.77390	−	28.8022i	0.173282	−	1.04545i
$760$	38.6126	+	6.57134i	1.40063	+	0.238367i
$761$	−6.12394	+	10.6070i	−0.221993	+	0.384503i	−0.955413	−	0.295273i	$-0.904589\pi$
$761$	−6.12394	+	10.6070i	−0.221993	+	0.384503i	0.733420	+	0.679775i	$0.237923\pi$
$762$	−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
$765$	−12.0341	+	35.3050i	−0.435092	+	1.27645i
$766$	−7.31205	+	7.78124i	−0.264195	+	0.281148i
$767$	1.37138	−	0.791767i	0.0495177	−	0.0285890i
$768$	−11.7851	+	25.0821i	−0.425257	+	0.905073i
$769$		−	19.0816i		−	0.688100i	−0.938951	−	0.344050i	$-0.888201\pi$
$769$		−	19.0816i		−	0.688100i	0.938951	−	0.344050i	$-0.111799\pi$
$770$	−1.82179	−	31.7730i	−0.0656526	−	1.14502i
$771$	−13.2709	+	16.1499i	−0.477940	+	0.581624i
$772$	−3.27717	−	52.6603i	−0.117948	−	1.89529i
$773$	−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	$0.393675\pi$
$774$	−18.0098	+	28.7751i	−0.647349	+	1.03430i
$775$	14.2445	+	8.22405i	0.511677	+	0.295417i
$776$	−9.21200	+	11.1123i	−0.330691	+	0.398908i
$777$	7.78616	+	3.29061i	0.279327	+	0.118050i
$778$	14.9393	+	49.5423i	0.535601	+	1.77618i
$779$	15.7838	−	27.3383i	0.565512	−	0.979496i
$780$	3.35805	+	7.48949i	0.120237	+	0.268167i
$781$	1.71366	−	0.989382i	0.0613196	−	0.0354029i
$782$	7.96841	−	33.9216i	0.284950	−	1.21303i
$783$	−6.22375	−	3.34180i	−0.222419	−	0.119426i
$784$	26.3321	+	9.51948i	0.940432	+	0.339981i
$785$		−	44.4139i		−	1.58520i
$786$	13.6768	+	17.9083i	0.487836	+	0.638769i
$787$	6.93206	+	12.0067i	0.247101	+	0.427992i	0.962720	−	0.270499i	$-0.0871887\pi$
$787$	6.93206	+	12.0067i	0.247101	+	0.427992i	−0.715619	+	0.698491i	$0.753855\pi$
$788$	22.7270	+	11.3010i	0.809615	+	0.402583i
$789$	−40.6888	+	15.2849i	−1.44856	+	0.544157i
$790$	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
$794$	7.42699	−	7.90355i	0.263574	−	0.280487i
$795$	−1.23783	+	7.46812i	−0.0439011	+	0.264867i
$796$	2.16570	−	0.134776i	0.0767613	−	0.00477702i
$797$		−	29.4639i		−	1.04366i	−0.853048	−	0.521832i	$-0.825249\pi$
$797$		−	29.4639i		−	1.04366i	0.853048	−	0.521832i	$-0.174751\pi$
$798$	20.3813	−	27.9196i	0.721491	−	0.988343i
$799$	31.5346			1.11561
$800$	−5.80032	+	7.95499i	−0.205072	+	0.281251i
$801$	−8.15912	+	7.13719i	−0.288288	+	0.252180i
$802$	24.4028	+	22.9314i	0.861692	+	0.809734i
$803$	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
$807$	12.3911	−	4.65476i	0.436186	−	0.163855i
$808$	20.3843	+	3.46914i	0.717118	+	0.122044i
$809$	−42.7554	+	24.6848i	−1.50320	+	0.867873i	−0.503207	+	0.864166i	$0.667847\pi$
$809$	−42.7554	+	24.6848i	−1.50320	+	0.867873i	−0.999993	+	0.00370713i	$0.998820\pi$
$810$	−5.24683	−	32.6253i	−0.184355	−	1.14634i
$811$	−0.180195			−0.00632751			−0.00316376	−	0.999995i	$-0.501007\pi$
$811$	−0.180195			−0.00632751			−0.00316376	+	0.999995i	$0.501007\pi$
$812$	7.08587	+	1.24151i	0.248665	+	0.0435684i
$813$	−14.3373	−	11.7815i	−0.502832	−	0.413194i
$814$	−1.95439	+	8.31985i	−0.0685012	+	0.291610i
$815$	32.4353	+	56.1796i	1.13616	+	1.96788i
$816$	17.7238	−	28.0482i	0.620458	−	0.981884i
$817$	−36.9598	−	21.3388i	−1.29306	−	0.746549i
$818$	21.2098	−	6.39574i	0.741582	−	0.223622i
$819$	7.23787	+	0.293375i	0.252912	+	0.0102514i
$820$	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	$0.0353792\pi$
$822$	−6.84255	+	0.884979i	−0.238661	+	0.0308672i
$823$	−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	$-0.445960\pi$
$824$	0.761300	+	2.05348i	0.0265211	+	0.0715364i
$825$	6.26992	−	7.63011i	0.218290	−	0.265646i
$826$	5.42740	−	3.56264i	0.188843	−	0.123960i
$827$	−19.7749			−0.687641			−0.343821	−	0.939035i	$-0.611721\pi$
$827$	−19.7749			−0.687641			−0.343821	+	0.939035i	$0.611721\pi$
$828$	7.85373	+	29.8542i	0.272936	+	1.03750i
$829$	−13.8197	−	23.9365i	−0.479979	−	0.831349i	0.519757	−	0.854314i	$-0.326023\pi$
$829$	−13.8197	−	23.9365i	−0.479979	−	0.831349i	−0.999736	+	0.0229656i	$0.992689\pi$
$830$	−0.619602	+	0.659360i	−0.0215067	+	0.0228867i
$831$	5.78358	−	2.17263i	0.200630	−	0.0753676i
$832$	−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
$836$	31.2938	+	15.5609i	1.08232	+	0.538185i
$837$	49.0848	−	1.51400i	1.69662	−	0.0523313i
$838$	11.4660	−	48.8109i	0.396086	−	1.68614i
$839$	−28.3920			−0.980200			−0.490100	−	0.871666i	$-0.663040\pi$
$839$	−28.3920			−0.980200			−0.490100	+	0.871666i	$0.663040\pi$
$840$	15.5026	+	29.8673i	0.534890	+	1.03052i
$841$	−27.1518			−0.936267
$842$	2.58873	−	11.0202i	0.0892134	−	0.379783i
$843$	1.20747	−	7.28496i	0.0415874	−	0.250907i
$844$	7.02661	−	14.1309i	0.241866	−	0.486405i
$845$	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
$849$	13.7902	+	36.7097i	0.473277	+	1.25987i
$850$	8.07161	−	8.58954i	0.276854	−	0.294619i
$851$	−4.74518	−	8.21889i	−0.162663	−	0.281740i
$852$	−1.22538	+	1.69590i	−0.0419807	+	0.0581006i
$853$	−30.7041			−1.05129			−0.525645	−	0.850704i	$-0.676176\pi$
$853$	−30.7041			−1.05129			−0.525645	+	0.850704i	$0.676176\pi$
$854$	−15.8923	+	31.5731i	−0.543824	+	1.08041i
$855$	40.7556	−	8.05342i	1.39381	−	0.275421i
$856$	−38.5306	+	14.2847i	−1.31695	+	0.488241i
$857$	11.5192	+	19.9518i	0.393487	+	0.681539i	0.992907	−	0.118895i	$-0.0379353\pi$
$857$	11.5192	+	19.9518i	0.393487	+	0.681539i	−0.599420	+	0.800435i	$0.704602\pi$
$858$	0.939401	+	7.26333i	0.0320706	+	0.247966i
$859$	26.3268	−	45.5994i	0.898260	−	1.55583i	0.0685424	−	0.997648i	$-0.478165\pi$
$859$	26.3268	−	45.5994i	0.898260	−	1.55583i	0.829717	−	0.558184i	$-0.188502\pi$
$860$	34.6202	−	22.9677i	1.18054	−	0.783193i
$861$	26.9138	−	3.34751i	0.917220	−	0.114083i
$862$	40.4283	−	12.1910i	1.37699	−	0.415228i
$863$	22.4451	+	12.9587i	0.764040	+	0.441119i	0.830744	−	0.556654i	$-0.187915\pi$
$863$	22.4451	+	12.9587i	0.764040	+	0.441119i	−0.0667045	+	0.997773i	$0.521248\pi$
$864$	−2.21961	+	29.3100i	−0.0755127	+	0.997145i
$865$	20.0490	+	34.7258i	0.681685	+	1.18071i
$866$	−0.552203	+	2.35074i	−0.0187646	+	0.0798813i
$867$	−6.52539	+	7.94100i	−0.221614	+	0.269691i
$868$	−46.9748	+	17.1551i	−1.59443	+	0.582283i
$869$	0.409620			0.0138954
$870$	5.24750	+	6.87103i	0.177907	+	0.232950i
$871$	−9.91432	+	5.72403i	−0.335934	+	0.193951i
$872$	−41.2168	−	7.01454i	−1.39578	−	0.237542i
$873$	−4.93941	+	14.4910i	−0.167174	+	0.490446i
$874$	−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	−0.358472	−	0.933540i	$-0.616702\pi$
$877$	−39.8660	−	23.0166i	−1.34618	−	0.777216i	−0.987706	+	0.156324i	$0.950036\pi$
$878$	17.0204	+	15.9941i	0.574411	+	0.539775i
$879$	−1.68815	+	10.1851i	−0.0569400	+	0.343533i
$880$	−27.1280	+	20.5332i	−0.914483	+	0.692173i
$881$	−25.6170			−0.863060			−0.431530	−	0.902099i	$-0.642026\pi$
$881$	−25.6170			−0.863060			−0.431530	+	0.902099i	$0.642026\pi$
$882$	29.6943	−	0.497831i	0.999859	−	0.0167628i
$883$			54.2412i			1.82536i	0.408674	+	0.912680i	$0.365991\pi$
$883$			54.2412i			1.82536i	−0.408674	+	0.912680i	$0.634009\pi$
$884$	0.542930	+	8.72426i	0.0182607	+	0.293429i
$885$	7.69747	+	1.27584i	0.258748	+	0.0428869i
$886$	−13.7958	+	14.6810i	−0.463479	+	0.493219i
$887$	17.2509	−	29.8794i	0.579228	−	1.00325i	−0.416340	−	0.909209i	$-0.636687\pi$
$887$	17.2509	−	29.8794i	0.579228	−	1.00325i	0.995568	−	0.0940438i	$-0.0299794\pi$
$888$	−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
$891$	3.92229	−	29.2234i	0.131402	−	0.979021i
$892$	−10.2755	+	20.6646i	−0.344049	+	0.691900i
$893$	−17.5614	−	30.4172i	−0.587669	−	1.01787i
$894$	33.7568	−	25.7805i	1.12900	−	0.862230i
$895$			31.5422i			1.05434i
$896$	−7.22364	−	29.0486i	−0.241325	−	0.970444i
$897$	−6.28352	−	5.16338i	−0.209800	−	0.172400i
$898$	−0.705055	+	3.00143i	−0.0235280	+	0.100159i
$899$	−11.1271	+	6.42424i	−0.371110	+	0.214260i
$900$	−2.74861	+	10.0740i	−0.0916202	+	0.335801i
$901$	−4.03092	+	6.98176i	−0.134289	+	0.232596i
$902$	7.91654	+	26.2531i	0.263592	+	0.874133i
$903$	−4.52565	−	36.3860i	−0.150604	−	1.21085i
$904$	29.3709	−	35.4297i	0.976862	−	1.17837i
$905$	3.19096	+	1.84230i	0.106071	+	0.0612402i
$906$	−4.03134	−	31.1698i	−0.133932	−	1.03555i
$907$	−11.9718	+	6.91190i	−0.397516	+	0.229506i	−0.685412	−	0.728156i	$-0.740378\pi$
$907$	−11.9718	+	6.91190i	−0.397516	+	0.229506i	0.287896	+	0.957662i	$0.407044\pi$
$908$	31.0763	−	1.93394i	1.03130	−	0.0641802i
$909$	21.5157	−	4.25156i	0.713630	−	0.141015i
$910$	−7.91891	−	3.98598i	−0.262509	−	0.132134i
$911$			22.6663i			0.750969i	0.926829	+	0.375484i	$0.122524\pi$
$911$			22.6663i			0.750969i	−0.926829	+	0.375484i	$0.877476\pi$
$912$	−36.9246	−	1.47595i	−1.22269	−	0.0488735i
$913$	−0.699183	+	0.403674i	−0.0231396	+	0.0133596i
$914$	−31.1559	+	33.1550i	−1.03054	+	1.09667i
$915$	−39.7676	+	14.9389i	−1.31468	+	0.493864i
$916$	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	$0.236366\pi$
$920$	6.33864	−	37.2453i	0.208979	−	1.22794i
$921$	9.26329	+	1.53537i	0.305236	+	0.0505922i
$922$	4.50366	−	19.1722i	0.148320	−	0.631401i
$923$		−	0.551221i		−	0.0181437i
$924$	5.54970	+	29.5092i	0.182572	+	0.970781i
$925$		−	3.21028i		−	0.105553i
$926$	21.4548	+	5.03987i	0.705048	+	0.165620i
$927$	1.52940	+	1.74838i	0.0502320	+	0.0574245i
$928$	−3.11607	−	7.03093i	−0.102290	−	0.230802i
$929$	27.9226	−	48.3634i	0.916111	−	1.58675i	0.110844	−	0.993838i	$-0.464645\pi$
$929$	27.9226	−	48.3634i	0.916111	−	1.58675i	0.805267	−	0.592912i	$-0.202022\pi$
$930$	−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
$933$	−14.8386	−	39.5006i	−0.485793	−	1.29319i
$934$	19.7817	+	18.5889i	0.647277	+	0.608248i
$935$	35.2760	−	20.3666i	1.15365	−	0.666058i
$936$	−4.04844	−	6.60145i	−0.132328	−	0.215775i
$937$		−	32.0973i		−	1.04857i	−0.851541	−	0.524287i	$-0.824332\pi$
$937$		−	32.0973i		−	1.04857i	0.851541	−	0.524287i	$-0.175668\pi$
$938$	−39.2371	+	25.7559i	−1.28114	+	0.840960i
$939$	21.8482	+	17.9534i	0.712989	+	0.585887i
$940$	34.1255	−	2.12371i	1.11305	−	0.0692677i
$941$	−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	$0.484900\pi$
$942$	5.37484	+	41.5576i	0.175122	+	1.35402i
$943$	−26.3702	−	15.2249i	−0.858733	−	0.495790i
$944$	−6.39452	−	2.69825i	−0.208124	−	0.0878204i
$945$	26.6358	+	23.7585i	0.866462	+	0.772864i
$946$	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	$0.0503420\pi$
$948$	−0.395211	+	0.177200i	−0.0128358	+	0.00575519i
$949$	1.17931	−	0.680874i	0.0382820	−	0.0221021i
$950$	−12.7802	−	3.00215i	−0.414644	−	0.0974026i
$951$	−21.8650	+	26.6084i	−0.709021	+	0.862836i
$952$	4.26976	+	35.5820i	0.138384	+	1.15322i
$953$		−	48.0977i		−	1.55804i	−0.627001	−	0.779018i	$-0.715718\pi$
$953$		−	48.0977i		−	1.55804i	0.627001	−	0.779018i	$-0.284282\pi$
$954$	0.254450	−	7.13763i	0.00823812	−	0.231089i
$955$	5.43234	+	9.40909i	0.175786	+	0.304471i
$956$	−11.8208	+	23.7723i	−0.382312	+	0.768850i
$957$	2.71287	+	7.22173i	0.0876947	+	0.233445i
$958$	−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
$962$	1.73493	+	1.63031i	0.0559363	+	0.0525634i
$963$	−32.8059	+	28.6970i	−1.05716	+	0.924747i
$964$	22.8833	−	1.42408i	0.737022	−	0.0458665i
$965$			68.4912i			2.20481i
$966$	−26.9309	−	19.6596i	−0.866489	−	0.632538i
$967$	11.0279			0.354635			0.177317	−	0.984154i	$-0.443258\pi$
$967$	11.0279			0.354635			0.177317	+	0.984154i	$0.443258\pi$
$968$	0.707482	−	0.262289i	0.0227393	−	0.00843030i
$969$	43.6473	+	7.23446i	1.40215	+	0.232404i
$970$	12.8311	−	13.6544i	0.411981	−	0.438417i
$971$	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
$975$	−0.967443	−	2.57535i	−0.0309830	−	0.0824773i
$976$	37.4962	−	4.68509i	1.20023	−	0.149966i
$977$	21.7078	−	12.5330i	0.694494	−	0.400967i	−0.110799	−	0.993843i	$-0.535341\pi$
$977$	21.7078	−	12.5330i	0.694494	−	0.400967i	0.805294	+	0.592876i	$0.202008\pi$
$978$	−37.1480	−	48.6413i	−1.18786	−	1.55538i
$979$	11.8381			0.378348
$980$	−33.3485	−	14.4566i	−1.06528	−	0.461799i
$981$	−43.5044	+	8.59658i	−1.38899	+	0.274468i
$982$	6.38758	+	1.50048i	0.203836	+	0.0478824i
$983$	−12.9850	−	22.4907i	−0.414157	−	0.717342i	0.581182	−	0.813773i	$-0.302590\pi$
$983$	−12.9850	−	22.4907i	−0.414157	−	0.717342i	−0.995340	+	0.0964318i	$0.969257\pi$
$984$	−18.9951	−	21.9049i	−0.605540	−	0.698304i
$985$	−28.5340	−	16.4741i	−0.909169	−	0.524909i
$986$	2.65823	+	8.81530i	0.0846552	+	0.280736i
$987$	11.7469	−	27.7953i	0.373909	−	0.884734i
$988$	8.11276	−	5.38216i	0.258101	−	0.171229i
$989$	−20.5832	+	35.6511i	−0.654507	+	1.13364i
$990$	−19.1451	+	30.5891i	−0.608472	+	0.972185i
$991$	−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	$0.929000\pi$
$992$	43.1983	+	31.4977i	1.37155	+	1.00005i
$993$	2.94056	+	2.41636i	0.0933159	+	0.0766808i
$994$	−0.129366	−	2.25621i	−0.00410323	−	0.0715627i
$995$	−2.81676			−0.0892974
$996$	0.499961	−	0.691938i	0.0158419	−	0.0219249i
$997$	−12.6672	−	21.9402i	−0.401173	−	0.694853i	0.592694	−	0.805427i	$-0.298064\pi$
$997$	−12.6672	−	21.9402i	−0.401173	−	0.694853i	−0.993868	+	0.110575i	$0.964731\pi$
$998$	20.1042	+	18.8920i	0.636389	+	0.598016i
$999$	−5.04600	−	8.14894i	−0.159648	−	0.257821i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.37674 + 0.323405i) q^{2} +(1.70874 + 0.283220i) q^{3} +(1.79082 + 0.890488i) q^{4} +(-2.24840 - 1.29811i) q^{5} +(2.26089 + 0.942534i) q^{6} +(-2.53678 + 0.751482i) q^{7} +(2.17750 + 1.80513i) q^{8} +(2.83957 + 0.967897i) q^{9} +O(q^{10})\)	\(q+(1.37674 + 0.323405i) q^{2} +(1.70874 + 0.283220i) q^{3} +(1.79082 + 0.890488i) 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} +(2.83957 + 0.967897i) q^{9} +(-2.67564 - 2.51430i) q^{10} +(-1.63808 - 2.83724i) q^{11} +(2.80784 + 2.02881i) q^{12} -0.912635 q^{13} +(-3.73552 + 0.214186i) q^{14} +(-3.47427 - 2.85492i) q^{15} +(2.41406 + 3.18940i) q^{16} +(-2.39448 - 4.14736i) q^{17} +(3.59633 + 2.25087i) q^{18} +(-2.66693 + 4.61926i) q^{19} +(-2.87052 - 4.32685i) q^{20} +(-4.54754 + 0.565618i) q^{21} +(-1.33763 - 4.43590i) q^{22} +(4.45569 + 2.57249i) q^{23} +(3.20953 + 3.70120i) q^{24} +(0.870190 + 1.50721i) q^{25} +(-1.25646 - 0.295151i) q^{26} +(4.57796 + 2.45811i) q^{27} +(-5.21211 - 0.913209i) q^{28} -1.35950 q^{29} +(-3.85986 - 5.05408i) q^{30} +(8.18469 - 4.72543i) q^{31} +(2.29206 + 5.17170i) q^{32} +(-1.99549 - 5.31204i) 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} +(-5.16556 + 5.49701i) q^{38} +(-1.55945 - 0.258476i) q^{39} +(-2.55263 - 6.88528i) q^{40} -5.91833 q^{41} +(-6.44369 - 0.691987i) q^{42} +8.00125i q^{43} +(-0.406978 - 6.53967i) q^{44} +(-5.12805 - 5.86230i) q^{45} +(5.30236 + 4.98264i) 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} +(-2.91692 - 7.76491i) q^{51} +(-1.63436 - 0.812691i) q^{52} +(-0.841712 - 1.45789i) q^{53} +(5.50769 + 4.86471i) q^{54} +8.50565i q^{55} +(-6.88037 - 2.94287i) q^{56} +(-5.86535 + 7.13777i) q^{57} +(-1.87168 - 0.439670i) q^{58} +(-1.50266 + 0.867561i) q^{59} +(-3.67951 - 8.20645i) q^{60} +(4.72347 - 8.18130i) q^{61} +(12.7964 - 3.85872i) q^{62} +(-7.93074 - 0.321460i) q^{63} +(1.48302 + 7.86134i) q^{64} +(2.05197 + 1.18470i) q^{65} +(-1.02933 - 7.95863i) q^{66} +(10.8634 - 6.27198i) q^{67} +(-0.594903 - 9.55942i) q^{68} +(6.88502 + 5.65766i) q^{69} +(8.67697 + 4.36755i) q^{70} +0.603989i q^{71} +(4.43599 + 7.23339i) q^{72} +(-1.29220 + 0.746053i) q^{73} +(-1.90101 - 1.78638i) q^{74} +(1.06005 + 2.82189i) 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} +(-1.28756 - 10.3048i) q^{80} +(7.12635 + 5.49683i) q^{81} +(-8.14799 - 1.91402i) q^{82} -0.246431i q^{83} +(-8.64749 - 3.03661i) q^{84} +12.4332i q^{85} +(-2.58764 + 11.0156i) q^{86} +(-2.32303 - 0.385038i) q^{87} +(1.55466 - 9.13504i) 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} +(15.3238 - 5.75646i) q^{93} +(-6.37708 + 6.78628i) q^{94} +(11.9926 - 6.92395i) q^{95} +(2.45181 + 9.48623i) q^{96} +5.10324i q^{97} +(9.31526 - 3.35052i) 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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