LMFDB - Embedded newform 525.2.n.d.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.n (of order $5$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			211.2
Character	$\chi$	$=$	525.211
Dual form			525.2.n.d.316.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.24444 + 0.904140i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.113133 - 0.348187i) q^{4} +(-1.50439 - 1.65433i) q^{5} +(0.475335 + 1.46293i) q^{6} -1.00000 q^{7} +(-0.776647 - 2.39027i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-1.24444 + 0.904140i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.113133 - 0.348187i) q^{4} +(-1.50439 - 1.65433i) q^{5} +(0.475335 + 1.46293i) q^{6} -1.00000 q^{7} +(-0.776647 - 2.39027i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(3.36787 + 0.698540i) q^{10} +(-3.07383 + 2.23327i) q^{11} +(-0.296185 - 0.215191i) q^{12} +(2.29557 + 1.66783i) q^{13} +(1.24444 - 0.904140i) q^{14} +(-2.03824 + 0.919544i) q^{15} +(3.72000 + 2.70274i) q^{16} +(1.78651 + 5.49830i) q^{17} +1.53821 q^{18} +(0.919982 + 2.83141i) q^{19} +(-0.746211 + 0.336649i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(1.80601 - 5.55834i) q^{22} +(6.47549 - 4.70472i) q^{23} -2.51328 q^{24} +(-0.473621 + 4.97752i) q^{25} -4.36466 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.113133 + 0.348187i) q^{28} +(-0.447866 + 1.37839i) q^{29} +(1.70508 - 2.98718i) q^{30} +(2.06690 + 6.36127i) q^{31} -2.04642 q^{32} +(1.17410 + 3.61350i) q^{33} +(-7.19443 - 5.22706i) q^{34} +(1.50439 + 1.65433i) q^{35} +(-0.296185 + 0.215191i) q^{36} +(1.66510 + 1.20977i) q^{37} +(-3.70486 - 2.69174i) q^{38} +(2.29557 - 1.66783i) q^{39} +(-2.78592 + 4.88073i) q^{40} +(-2.78358 - 2.02239i) q^{41} +(-0.475335 - 1.46293i) q^{42} +5.43824 q^{43} +(0.429843 + 1.32292i) q^{44} +(0.244686 + 2.22264i) q^{45} +(-3.80465 + 11.7095i) q^{46} +(0.338909 - 1.04305i) q^{47} +(3.72000 - 2.70274i) q^{48} +1.00000 q^{49} +(-3.91098 - 6.62245i) q^{50} +5.78125 q^{51} +(0.840421 - 0.610602i) q^{52} +(-3.18912 + 9.81510i) q^{53} +(0.475335 - 1.46293i) q^{54} +(8.31879 + 1.72542i) q^{55} +(0.776647 + 2.39027i) q^{56} +2.97713 q^{57} +(-0.688914 - 2.12026i) q^{58} +(-6.50669 - 4.72739i) q^{59} +(0.0895807 + 0.813720i) q^{60} +(-2.55590 + 1.85697i) q^{61} +(-8.32362 - 6.04746i) q^{62} +(0.809017 + 0.587785i) q^{63} +(-4.89335 + 3.55523i) q^{64} +(-0.694292 - 6.30671i) q^{65} +(-4.72821 - 3.43524i) q^{66} +(1.05185 + 3.23727i) q^{67} +2.11655 q^{68} +(-2.47342 - 7.61239i) q^{69} +(-3.36787 - 0.698540i) q^{70} +(-4.53370 + 13.9533i) q^{71} +(-0.776647 + 2.39027i) q^{72} +(-4.32172 + 3.13991i) q^{73} -3.16593 q^{74} +(4.58754 + 1.98858i) q^{75} +1.08994 q^{76} +(3.07383 - 2.23327i) q^{77} +(-1.34875 + 4.15104i) q^{78} +(0.406907 - 1.25233i) q^{79} +(-1.12511 - 10.2201i) q^{80} +(0.309017 + 0.951057i) q^{81} +5.29252 q^{82} +(-1.96304 - 6.04162i) q^{83} +(0.296185 + 0.215191i) q^{84} +(6.40840 - 11.2271i) q^{85} +(-6.76758 + 4.91693i) q^{86} +(1.17253 + 0.851891i) q^{87} +(7.72539 + 5.61283i) q^{88} +(-7.80956 + 5.67398i) q^{89} +(-2.31408 - 2.54472i) q^{90} +(-2.29557 - 1.66783i) q^{91} +(-0.905530 - 2.78694i) q^{92} +6.68864 q^{93} +(0.521314 + 1.60444i) q^{94} +(3.30008 - 5.78151i) q^{95} +(-0.632379 + 1.94626i) q^{96} +(0.783499 - 2.41136i) q^{97} +(-1.24444 + 0.904140i) q^{98} +3.79946 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) $ 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{4}{5}\right)$	$1$	$1$

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 $

$2$	−1.24444	+	0.904140i	−0.879953	+	0.639324i	−0.933239	−	0.359256i	$-0.883031\pi$
$2$	−1.24444	+	0.904140i	−0.879953	+	0.639324i	0.0532858	+	0.998579i	$0.483031\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	0.113133	−	0.348187i	0.0565663	−	0.174093i
$5$	−1.50439	−	1.65433i	−0.672784	−	0.739839i
$5$	−1.50439	−	1.65433i	−0.672784	−	0.739839i
$6$	0.475335	+	1.46293i	0.194055	+	0.597238i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−0.776647	−	2.39027i	−0.274586	−	0.845089i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	3.36787	+	0.698540i	1.06501	+	0.220898i
$11$	−3.07383	+	2.23327i	−0.926794	+	0.673355i	−0.945206	−	0.326476i	$-0.894139\pi$
$11$	−3.07383	+	2.23327i	−0.926794	+	0.673355i	0.0184121	+	0.999830i	$0.494139\pi$
$12$	−0.296185	−	0.215191i	−0.0855013	−	0.0621203i
$13$	2.29557	+	1.66783i	0.636678	+	0.462573i	0.858707	−	0.512467i	$-0.171268\pi$
$13$	2.29557	+	1.66783i	0.636678	+	0.462573i	−0.222030	+	0.975040i	$0.571268\pi$
$14$	1.24444	−	0.904140i	0.332591	−	0.241642i
$15$	−2.03824	+	0.919544i	−0.526272	+	0.237425i
$16$	3.72000	+	2.70274i	0.930001	+	0.675685i
$17$	1.78651	+	5.49830i	0.433291	+	1.33353i	0.894828	+	0.446412i	$0.147298\pi$
$17$	1.78651	+	5.49830i	0.433291	+	1.33353i	−0.461536	+	0.887121i	$0.652702\pi$
$18$	1.53821			0.362561
$19$	0.919982	+	2.83141i	0.211058	+	0.649571i	0.999410	+	0.0343460i	$0.0109348\pi$
$19$	0.919982	+	2.83141i	0.211058	+	0.649571i	−0.788352	+	0.615225i	$0.789065\pi$
$20$	−0.746211	+	0.336649i	−0.166858	+	0.0752771i
$21$	−0.309017	+	0.951057i	−0.0674330	+	0.207538i
$22$	1.80601	−	5.55834i	0.385043	−	1.18504i
$23$	6.47549	−	4.70472i	1.35023	−	0.981002i	0.351233	−	0.936288i	$-0.385762\pi$
$23$	6.47549	−	4.70472i	1.35023	−	0.981002i	0.999000	−	0.0447136i	$-0.0142375\pi$
$24$	−2.51328			−0.513021
$25$	−0.473621	+	4.97752i	−0.0947243	+	0.995504i
$26$	−4.36466			−0.855981
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	−0.113133	+	0.348187i	−0.0213801	+	0.0658011i
$29$	−0.447866	+	1.37839i	−0.0831666	+	0.255960i	−0.983990	−	0.178226i	$-0.942964\pi$
$29$	−0.447866	+	1.37839i	−0.0831666	+	0.255960i	0.900823	+	0.434187i	$0.142964\pi$
$30$	1.70508	−	2.98718i	0.311304	−	0.545381i
$31$	2.06690	+	6.36127i	0.371227	+	1.14252i	0.945989	+	0.324198i	$0.105094\pi$
$31$	2.06690	+	6.36127i	0.371227	+	1.14252i	−0.574763	+	0.818320i	$0.694906\pi$
$32$	−2.04642			−0.361760
$33$	1.17410	+	3.61350i	0.204384	+	0.629030i
$34$	−7.19443	−	5.22706i	−1.23384	−	0.896434i
$35$	1.50439	+	1.65433i	0.254288	+	0.279633i
$36$	−0.296185	+	0.215191i	−0.0493642	+	0.0358652i
$37$	1.66510	+	1.20977i	0.273742	+	0.198885i	0.716183	−	0.697912i	$-0.245888\pi$
$37$	1.66510	+	1.20977i	0.273742	+	0.198885i	−0.442441	+	0.896797i	$0.645888\pi$
$38$	−3.70486	−	2.69174i	−0.601008	−	0.436658i
$39$	2.29557	−	1.66783i	0.367586	−	0.267067i
$40$	−2.78592	+	4.88073i	−0.440493	+	0.771712i
$41$	−2.78358	−	2.02239i	−0.434722	−	0.315844i	0.348813	−	0.937193i	$-0.386585\pi$
$41$	−2.78358	−	2.02239i	−0.434722	−	0.315844i	−0.783534	+	0.621349i	$0.786585\pi$
$42$	−0.475335	−	1.46293i	−0.0733457	−	0.225735i
$43$	5.43824			0.829324			0.414662	−	0.909975i	$-0.363900\pi$
$43$	5.43824			0.829324			0.414662	+	0.909975i	$0.363900\pi$
$44$	0.429843	+	1.32292i	0.0648012	+	0.199438i
$45$	0.244686	+	2.22264i	0.0364756	+	0.331332i
$46$	−3.80465	+	11.7095i	−0.560965	+	1.72647i
$47$	0.338909	−	1.04305i	0.0494349	−	0.152145i	−0.923292	−	0.384099i	$-0.874512\pi$
$47$	0.338909	−	1.04305i	0.0494349	−	0.152145i	0.972727	+	0.231954i	$0.0745120\pi$
$48$	3.72000	−	2.70274i	0.536936	−	0.390107i
$49$	1.00000			0.142857
$50$	−3.91098	−	6.62245i	−0.553096	−	0.936556i
$51$	5.78125			0.809537
$52$	0.840421	−	0.610602i	0.116545	−	0.0846752i
$53$	−3.18912	+	9.81510i	−0.438059	+	1.34821i	0.451859	+	0.892089i	$0.350761\pi$
$53$	−3.18912	+	9.81510i	−0.438059	+	1.34821i	−0.889919	+	0.456119i	$0.849239\pi$
$54$	0.475335	−	1.46293i	0.0646848	−	0.199079i
$55$	8.31879	+	1.72542i	1.12171	+	0.232656i
$56$	0.776647	+	2.39027i	0.103784	+	0.319414i
$57$	2.97713			0.394330
$58$	−0.688914	−	2.12026i	−0.0904588	−	0.278403i
$59$	−6.50669	−	4.72739i	−0.847099	−	0.615454i	0.0772453	−	0.997012i	$-0.475388\pi$
$59$	−6.50669	−	4.72739i	−0.847099	−	0.615454i	−0.924345	+	0.381558i	$0.875388\pi$
$60$	0.0895807	+	0.813720i	0.0115648	+	0.105051i
$61$	−2.55590	+	1.85697i	−0.327249	+	0.237760i	−0.739262	−	0.673417i	$-0.764826\pi$
$61$	−2.55590	+	1.85697i	−0.327249	+	0.237760i	0.412013	+	0.911178i	$0.364826\pi$
$62$	−8.32362	−	6.04746i	−1.05710	−	0.768029i
$63$	0.809017	+	0.587785i	0.101927	+	0.0740540i
$64$	−4.89335	+	3.55523i	−0.611669	+	0.444404i
$65$	−0.694292	−	6.30671i	−0.0861163	−	0.782251i
$66$	−4.72821	−	3.43524i	−0.582002	−	0.422849i
$67$	1.05185	+	3.23727i	0.128504	+	0.395496i	0.994523	−	0.104515i	$-0.0333292\pi$
$67$	1.05185	+	3.23727i	0.128504	+	0.395496i	−0.866019	+	0.500011i	$0.833329\pi$
$68$	2.11655			0.256669
$69$	−2.47342	−	7.61239i	−0.297764	−	0.916425i
$70$	−3.36787	−	0.698540i	−0.402538	−	0.0834915i
$71$	−4.53370	+	13.9533i	−0.538052	+	1.65595i	0.198910	+	0.980018i	$0.436260\pi$
$71$	−4.53370	+	13.9533i	−0.538052	+	1.65595i	−0.736962	+	0.675935i	$0.763740\pi$
$72$	−0.776647	+	2.39027i	−0.0915287	+	0.281696i
$73$	−4.32172	+	3.13991i	−0.505819	+	0.367499i	−0.811235	−	0.584720i	$-0.801204\pi$
$73$	−4.32172	+	3.13991i	−0.505819	+	0.367499i	0.305416	+	0.952219i	$0.401204\pi$
$74$	−3.16593			−0.368032
$75$	4.58754	+	1.98858i	0.529724	+	0.229621i
$76$	1.08994			0.125025
$77$	3.07383	−	2.23327i	0.350295	−	0.254504i
$78$	−1.34875	+	4.15104i	−0.152716	+	0.470013i
$79$	0.406907	−	1.25233i	0.0457807	−	0.140898i	−0.925553	−	0.378617i	$-0.876400\pi$
$79$	0.406907	−	1.25233i	0.0457807	−	0.140898i	0.971334	+	0.237719i	$0.0763997\pi$
$80$	−1.12511	−	10.2201i	−0.125791	−	1.14264i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	5.29252			0.584461
$83$	−1.96304	−	6.04162i	−0.215472	−	0.663154i	−0.999120	−	0.0419489i	$-0.986643\pi$
$83$	−1.96304	−	6.04162i	−0.215472	−	0.663154i	0.783648	−	0.621205i	$-0.213357\pi$
$84$	0.296185	+	0.215191i	0.0323165	+	0.0234793i
$85$	6.40840	−	11.2271i	0.695089	−	1.21775i
$86$	−6.76758	+	4.91693i	−0.729767	+	0.530207i
$87$	1.17253	+	0.851891i	0.125708	+	0.0913323i
$88$	7.72539	+	5.61283i	0.823529	+	0.598329i
$89$	−7.80956	+	5.67398i	−0.827812	+	0.601441i	−0.918939	−	0.394399i	$-0.870953\pi$
$89$	−7.80956	+	5.67398i	−0.827812	+	0.601441i	0.0911274	+	0.995839i	$0.470953\pi$
$90$	−2.31408	−	2.54472i	−0.243925	−	0.268237i
$91$	−2.29557	−	1.66783i	−0.240641	−	0.174836i
$92$	−0.905530	−	2.78694i	−0.0944081	−	0.290558i
$93$	6.68864			0.693579
$94$	0.521314	+	1.60444i	0.0537695	+	0.165485i
$95$	3.30008	−	5.78151i	0.338581	−	0.593170i
$96$	−0.632379	+	1.94626i	−0.0645419	+	0.198640i
$97$	0.783499	−	2.41136i	0.0795523	−	0.244837i	−0.903369	−	0.428865i	$-0.858914\pi$
$97$	0.783499	−	2.41136i	0.0795523	−	0.244837i	0.982921	+	0.184028i	$0.0589137\pi$
$98$	−1.24444	+	0.904140i	−0.125708	+	0.0913319i
$99$	3.79946			0.381860
$100$	1.67952	+	0.728029i	0.167952	+	0.0728029i
$101$	6.72468			0.669130			0.334565	−	0.942373i	$-0.391411\pi$
$101$	6.72468			0.669130			0.334565	+	0.942373i	$0.391411\pi$
$102$	−7.19443	+	5.22706i	−0.712355	+	0.517556i
$103$	2.52121	−	7.75948i	0.248422	−	0.764564i	−0.746633	−	0.665236i	$-0.768331\pi$
$103$	2.52121	−	7.75948i	0.248422	−	0.764564i	0.995055	−	0.0993279i	$-0.0316693\pi$
$104$	2.20372	−	6.78236i	0.216093	−	0.665065i
$105$	2.03824	−	0.919544i	0.198912	−	0.0897383i
$106$	−4.90555	−	15.0977i	−0.476469	−	1.46642i
$107$	7.32410			0.708048			0.354024	−	0.935236i	$-0.384813\pi$
$107$	7.32410			0.708048			0.354024	+	0.935236i	$0.384813\pi$
$108$	0.113133	+	0.348187i	0.0108862	+	0.0335043i
$109$	−10.6048	−	7.70485i	−1.01576	−	0.737991i	−0.0503481	−	0.998732i	$-0.516033\pi$
$109$	−10.6048	−	7.70485i	−1.01576	−	0.737991i	−0.965409	+	0.260741i	$0.916033\pi$
$110$	−11.9123	+	5.37416i	−1.13579	+	0.512407i
$111$	1.66510	−	1.20977i	0.158045	−	0.114826i
$112$	−3.72000	−	2.70274i	−0.351507	−	0.255385i
$113$	6.76786	+	4.91714i	0.636667	+	0.462565i	0.858703	−	0.512473i	$-0.171271\pi$
$113$	6.76786	+	4.91714i	0.636667	+	0.462565i	−0.222037	+	0.975038i	$0.571271\pi$
$114$	−3.70486	+	2.69174i	−0.346992	+	0.252104i
$115$	−17.5248	−	3.63487i	−1.63420	−	0.338953i
$116$	0.429268	+	0.311882i	0.0398565	+	0.0289575i
$117$	−0.876831	−	2.69861i	−0.0810631	−	0.249486i
$118$	12.3714			1.13888
$119$	−1.78651	−	5.49830i	−0.163769	−	0.504028i
$120$	3.78096	+	4.15780i	0.345152	+	0.379553i
$121$	1.06175	−	3.26772i	0.0965224	−	0.297065i
$122$	1.50171	−	4.62178i	0.135958	−	0.418436i
$123$	−2.78358	+	2.02239i	−0.250987	+	0.182352i
$124$	2.44874			0.219904
$125$	8.94697	−	6.70460i	0.800242	−	0.599678i
$126$	−1.53821			−0.137035
$127$	11.2159	−	8.14883i	0.995250	−	0.723092i	0.0341858	−	0.999415i	$-0.489116\pi$
$127$	11.2159	−	8.14883i	0.995250	−	0.723092i	0.961065	+	0.276324i	$0.0891162\pi$
$128$	4.13983	−	12.7411i	0.365913	−	1.12616i
$129$	1.68051	−	5.17208i	0.147961	−	0.455376i
$130$	6.56615	+	7.22059i	0.575890	+	0.633288i
$131$	2.91422	+	8.96906i	0.254617	+	0.783630i	0.993905	+	0.110241i	$0.0351622\pi$
$131$	2.91422	+	8.96906i	0.254617	+	0.783630i	−0.739288	+	0.673389i	$0.764838\pi$
$132$	1.39100			0.121071
$133$	−0.919982	−	2.83141i	−0.0797726	−	0.245515i
$134$	−4.23592	−	3.07758i	−0.365928	−	0.265862i
$135$	2.18947	+	0.454124i	0.188439	+	0.0390847i
$136$	11.7550	−	8.54047i	1.00798	−	0.732339i
$137$	7.53487	+	5.47440i	0.643748	+	0.467710i	0.861136	−	0.508375i	$-0.169754\pi$
$137$	7.53487	+	5.47440i	0.643748	+	0.467710i	−0.217388	+	0.976085i	$0.569754\pi$
$138$	9.96069	+	7.23687i	0.847911	+	0.616043i
$139$	−7.60518	+	5.52549i	−0.645063	+	0.468666i	−0.861586	−	0.507612i	$-0.830528\pi$
$139$	−7.60518	+	5.52549i	−0.645063	+	0.468666i	0.216523	+	0.976278i	$0.430528\pi$
$140$	0.746211	−	0.336649i	0.0630664	−	0.0284521i
$141$	−0.887274	−	0.644643i	−0.0747220	−	0.0542887i
$142$	−6.97381	−	21.4632i	−0.585229	−	1.80115i
$143$	−10.7809			−0.901545
$144$	−1.42091	−	4.37313i	−0.118410	−	0.364427i
$145$	2.95408	−	1.33272i	0.245323	−	0.110676i
$146$	2.53921	−	7.81487i	0.210146	−	0.646764i
$147$	0.309017	−	0.951057i	0.0254873	−	0.0784418i
$148$	0.609603	−	0.442903i	0.0501091	−	0.0364064i
$149$	24.1131			1.97543			0.987713	−	0.156279i	$-0.0499500\pi$
$149$	24.1131			1.97543			0.987713	+	0.156279i	$0.0499500\pi$
$150$	−7.50689	+	1.67311i	−0.612935	+	0.136609i
$151$	15.3032			1.24535			0.622676	−	0.782479i	$-0.286045\pi$
$151$	15.3032			1.24535			0.622676	+	0.782479i	$0.286045\pi$
$152$	6.05335	−	4.39802i	0.490992	−	0.356726i
$153$	1.78651	−	5.49830i	0.144430	−	0.444511i
$154$	−1.80601	+	5.55834i	−0.145533	+	0.447904i
$155$	7.41422	−	12.9892i	0.595524	−	1.04332i
$156$	−0.321012	−	0.987974i	−0.0257015	−	0.0791012i
$157$	−15.4851			−1.23584			−0.617921	−	0.786240i	$-0.712025\pi$
$157$	−15.4851			−1.23584			−0.617921	+	0.786240i	$0.712025\pi$
$158$	0.625911	+	1.92636i	0.0497948	+	0.153253i
$159$	8.34923	+	6.06607i	0.662137	+	0.481070i
$160$	3.07862	+	3.38546i	0.243386	+	0.267644i
$161$	−6.47549	+	4.70472i	−0.510340	+	0.370784i
$162$	−1.24444	−	0.904140i	−0.0977726	−	0.0710359i
$163$	−9.18318	−	6.67197i	−0.719282	−	0.522589i	0.166873	−	0.985978i	$-0.446633\pi$
$163$	−9.18318	−	6.67197i	−0.719282	−	0.522589i	−0.886155	+	0.463389i	$0.846633\pi$
$164$	−1.01908	+	0.740406i	−0.0795769	+	0.0578160i
$165$	4.21162	−	7.37846i	0.327874	−	0.574412i
$166$	7.90536	+	5.74358i	0.613575	+	0.445789i
$167$	−0.0112468	−	0.0346141i	−0.000870304	−	0.00267852i	0.950620	−	0.310356i	$-0.100448\pi$
$167$	−0.0112468	−	0.0346141i	−0.000870304	−	0.00267852i	−0.951491	+	0.307677i	$0.900448\pi$
$168$	2.51328			0.193904
$169$	−1.52923	−	4.70647i	−0.117633	−	0.362036i
$170$	2.17594	+	19.7655i	0.166887	+	1.51595i
$171$	0.919982	−	2.83141i	0.0703528	−	0.216524i
$172$	0.615243	−	1.89352i	0.0469118	−	0.144380i
$173$	−17.9478	+	13.0398i	−1.36454	+	0.991399i	−0.366402	+	0.930457i	$0.619410\pi$
$173$	−17.9478	+	13.0398i	−1.36454	+	0.991399i	−0.998141	+	0.0609421i	$0.980590\pi$
$174$	−2.22937			−0.169008
$175$	0.473621	−	4.97752i	0.0358024	−	0.376265i
$176$	−17.4706			−1.31689
$177$	−6.50669	+	4.72739i	−0.489073	+	0.355332i
$178$	4.58848	−	14.1219i	0.343921	−	1.05848i
$179$	−6.33535	+	19.4982i	−0.473527	+	1.45736i	0.374408	+	0.927264i	$0.377846\pi$
$179$	−6.33535	+	19.4982i	−0.473527	+	1.45736i	−0.847935	+	0.530101i	$0.822154\pi$
$180$	0.801575	+	0.166257i	0.0597459	+	0.0123921i
$181$	3.14814	+	9.68898i	0.233999	+	0.720176i	0.997253	+	0.0740767i	$0.0236010\pi$
$181$	3.14814	+	9.68898i	0.233999	+	0.720176i	−0.763253	+	0.646100i	$0.776399\pi$
$182$	4.36466			0.323530
$183$	0.976266	+	3.00464i	0.0721677	+	0.222109i
$184$	−16.2747	−	11.8243i	−1.19979	−	0.871698i
$185$	−0.503608	−	4.57460i	−0.0370260	−	0.336331i
$186$	−8.32362	+	6.04746i	−0.610317	+	0.443421i
$187$	−17.7706	−	12.9111i	−1.29951	−	0.944151i
$188$	−0.324836	−	0.236007i	−0.0236911	−	0.0172126i
$189$	0.809017	−	0.587785i	0.0588473	−	0.0427551i
$190$	1.12053	+	10.1785i	0.0812917	+	0.738425i
$191$	−14.7917	−	10.7468i	−1.07029	−	0.777611i	−0.0943252	−	0.995541i	$-0.530069\pi$
$191$	−14.7917	−	10.7468i	−1.07029	−	0.777611i	−0.975964	+	0.217931i	$0.930069\pi$
$192$	1.86910	+	5.75248i	0.134890	+	0.415150i
$193$	−6.61104			−0.475873			−0.237937	−	0.971281i	$-0.576471\pi$
$193$	−6.61104			−0.475873			−0.237937	+	0.971281i	$0.576471\pi$
$194$	1.20519	+	3.70920i	0.0865276	+	0.266305i
$195$	−6.21258	−	1.28857i	−0.444892	−	0.0922763i
$196$	0.113133	−	0.348187i	0.00808090	−	0.0248705i
$197$	6.57683	−	20.2414i	0.468580	−	1.44214i	−0.385844	−	0.922564i	$-0.626090\pi$
$197$	6.57683	−	20.2414i	0.468580	−	1.44214i	0.854424	−	0.519577i	$-0.173910\pi$
$198$	−4.72821	+	3.43524i	−0.336019	+	0.244132i
$199$	24.1144			1.70943			0.854713	−	0.519100i	$-0.173733\pi$
$199$	24.1144			1.70943			0.854713	+	0.519100i	$0.173733\pi$
$200$	12.2655	−	2.73369i	0.867299	−	0.193301i
$201$	3.40387			0.240091
$202$	−8.36847	+	6.08005i	−0.588803	+	0.427791i
$203$	0.447866	−	1.37839i	0.0314340	−	0.0967439i
$204$	0.654049	−	2.01295i	0.0457926	−	0.140935i
$205$	0.841888	+	7.64741i	0.0588000	+	0.534118i
$206$	3.87816	+	11.9357i	0.270204	+	0.831603i
$207$	−8.00415			−0.556327
$208$	4.03182	+	12.4087i	0.279557	+	0.860387i
$209$	−9.15117	−	6.64871i	−0.632999	−	0.459901i
$210$	−1.70508	+	2.98718i	−0.117662	+	0.206135i
$211$	11.3459	−	8.24330i	0.781086	−	0.567492i	−0.124218	−	0.992255i	$-0.539642\pi$
$211$	11.3459	−	8.24330i	0.781086	−	0.567492i	0.905305	+	0.424762i	$0.139642\pi$
$212$	3.05669	+	2.22082i	0.209935	+	0.152526i
$213$	11.8694	+	8.62362i	0.813277	+	0.590880i
$214$	−9.11442	+	6.62201i	−0.623049	+	0.452671i
$215$	−8.18124	−	8.99666i	−0.557956	−	0.613567i
$216$	2.03329	+	1.47727i	0.138348	+	0.100515i
$217$	−2.06690	−	6.36127i	−0.140310	−	0.431831i
$218$	20.1633			1.36563
$219$	1.65075	+	5.08048i	0.111547	+	0.343307i
$220$	1.54190	−	2.70129i	0.103955	−	0.182121i
$221$	−5.06918	+	15.6013i	−0.340990	+	1.04946i
$222$	−0.978325	+	3.01098i	−0.0656609	+	0.202083i
$223$	−8.84194	+	6.42405i	−0.592100	+	0.430186i	−0.843066	−	0.537810i	$-0.819252\pi$
$223$	−8.84194	+	6.42405i	−0.592100	+	0.430186i	0.250966	+	0.967996i	$0.419252\pi$
$224$	2.04642			0.136732
$225$	3.30888	−	3.74851i	0.220592	−	0.249901i
$226$	−12.8680			−0.855966
$227$	1.06238	−	0.771865i	0.0705127	−	0.0512305i	−0.551970	−	0.833864i	$-0.686124\pi$
$227$	1.06238	−	0.771865i	0.0705127	−	0.0512305i	0.622483	+	0.782633i	$0.286124\pi$
$228$	0.336810	−	1.03660i	0.0223058	−	0.0686502i
$229$	−7.55639	+	23.2562i	−0.499341	+	1.53681i	0.310741	+	0.950495i	$0.399423\pi$
$229$	−7.55639	+	23.2562i	−0.499341	+	1.53681i	−0.810081	+	0.586318i	$0.800577\pi$
$230$	25.0951	−	11.3215i	1.65472	−	0.746518i
$231$	−1.17410	−	3.61350i	−0.0772499	−	0.237751i
$232$	3.64256			0.239146
$233$	9.34318	+	28.7554i	0.612092	+	1.88383i	0.437606	+	0.899167i	$0.355827\pi$
$233$	9.34318	+	28.7554i	0.612092	+	1.88383i	0.174487	+	0.984660i	$0.444173\pi$
$234$	3.53109	+	2.56548i	0.230834	+	0.167711i
$235$	−2.23541	+	1.00849i	−0.145822	+	0.0657868i
$236$	−2.38213	+	1.73072i	−0.155064	+	0.112660i
$237$	−1.06530	−	0.773984i	−0.0691985	−	0.0502757i
$238$	7.19443	+	5.22706i	0.466346	+	0.338820i
$239$	−19.4963	+	14.1649i	−1.26111	+	0.916252i	−0.998812	−	0.0487345i	$-0.984481\pi$
$239$	−19.4963	+	14.1649i	−1.26111	+	0.916252i	−0.262301	+	0.964986i	$0.584481\pi$
$240$	−10.0676	−	2.08814i	−0.649858	−	0.134789i
$241$	6.71561	+	4.87918i	0.432590	+	0.314295i	0.782684	−	0.622419i	$-0.213850\pi$
$241$	6.71561	+	4.87918i	0.432590	+	0.314295i	−0.350093	+	0.936715i	$0.613850\pi$
$242$	1.63319	+	5.02645i	0.104986	+	0.323113i
$243$	1.00000			0.0641500
$244$	0.357416	+	1.10001i	0.0228812	+	0.0704211i
$245$	−1.50439	−	1.65433i	−0.0961120	−	0.105691i
$246$	1.63548	−	5.03348i	0.104274	−	0.320923i
$247$	−2.61044	+	8.03410i	−0.166098	+	0.511197i
$248$	13.5999	−	9.88092i	0.863596	−	0.627439i
$249$	−6.35254			−0.402576
$250$	−5.07209	+	16.4328i	−0.320787	+	1.03930i
$251$	−12.1882			−0.769315			−0.384658	−	0.923059i	$-0.625681\pi$
$251$	−12.1882			−0.769315			−0.384658	+	0.923059i	$0.625681\pi$
$252$	0.296185	−	0.215191i	0.0186579	−	0.0135558i
$253$	−9.39764	+	28.9230i	−0.590825	+	1.81837i
$254$	−6.58986	+	20.2815i	−0.413484	+	1.27257i
$255$	−8.69726	−	9.56411i	−0.544644	−	0.598928i
$256$	2.62975	+	8.09355i	0.164360	+	0.505847i
$257$	4.38732			0.273674			0.136837	−	0.990594i	$-0.456306\pi$
$257$	4.38732			0.273674			0.136837	+	0.990594i	$0.456306\pi$
$258$	2.58499	+	7.95577i	0.160934	+	0.495304i
$259$	−1.66510	−	1.20977i	−0.103465	−	0.0751714i
$260$	−2.27446	−	0.471751i	−0.141056	−	0.0292568i
$261$	1.17253	−	0.851891i	0.0725776	−	0.0527307i
$262$	−11.7359	−	8.52661i	−0.725044	−	0.526776i
$263$	8.75952	+	6.36416i	0.540135	+	0.392431i	0.824135	−	0.566393i	$-0.191662\pi$
$263$	8.75952	+	6.36416i	0.540135	+	0.392431i	−0.284000	+	0.958824i	$0.591662\pi$
$264$	7.72539	−	5.61283i	0.475465	−	0.345446i
$265$	21.0351	−	9.48988i	1.29218	−	0.582959i
$266$	3.70486	+	2.69174i	0.227160	+	0.165041i
$267$	2.98299	+	9.18069i	0.182556	+	0.561849i
$268$	1.24617			0.0761222
$269$	6.27871	+	19.3239i	0.382820	+	1.17820i	0.938050	+	0.346501i	$0.112630\pi$
$269$	6.27871	+	19.3239i	0.382820	+	1.17820i	−0.555230	+	0.831697i	$0.687370\pi$
$270$	−3.13526	+	1.41446i	−0.190806	+	0.0860810i
$271$	2.13265	−	6.56362i	0.129549	−	0.398711i	−0.865153	−	0.501508i	$-0.832779\pi$
$271$	2.13265	−	6.56362i	0.129549	−	0.398711i	0.994702	+	0.102796i	$0.0327790\pi$
$272$	−8.21467	+	25.2822i	−0.498087	+	1.53296i
$273$	−2.29557	+	1.66783i	−0.138934	+	0.100942i
$274$	−14.3263			−0.865486
$275$	−9.66029	−	16.3577i	−0.582537	−	0.986409i
$276$	−2.93036			−0.176387
$277$	−1.79317	+	1.30282i	−0.107741	+	0.0782787i	−0.640351	−	0.768082i	$-0.721211\pi$
$277$	−1.79317	+	1.30282i	−0.107741	+	0.0782787i	0.532610	+	0.846361i	$0.321211\pi$
$278$	4.46839	−	13.7523i	0.267996	−	0.824808i
$279$	2.06690	−	6.36127i	0.123742	−	0.380839i
$280$	2.78592	−	4.88073i	0.166491	−	0.291680i
$281$	2.09666	+	6.45286i	0.125076	+	0.384945i	0.993915	−	0.110150i	$-0.0351331\pi$
$281$	2.09666	+	6.45286i	0.125076	+	0.384945i	−0.868839	+	0.495095i	$0.835133\pi$
$282$	1.68701			0.100460
$283$	−7.41121	−	22.8094i	−0.440551	−	1.35588i	−0.887290	−	0.461212i	$-0.847415\pi$
$283$	−7.41121	−	22.8094i	−0.440551	−	1.35588i	0.446739	−	0.894664i	$-0.352585\pi$
$284$	4.34544	+	3.15715i	0.257855	+	0.187342i
$285$	−4.47876	−	4.92515i	−0.265299	−	0.291741i
$286$	13.4162	−	9.74745i	0.793317	−	0.576379i
$287$	2.78358	+	2.02239i	0.164309	+	0.119378i
$288$	1.65559	+	1.20286i	0.0975566	+	0.0708790i
$289$	−13.2864	+	9.65313i	−0.781553	+	0.567831i
$290$	−2.47121	+	4.32939i	−0.145115	+	0.254230i
$291$	−2.05123	−	1.49030i	−0.120245	−	0.0873632i
$292$	0.604347	+	1.85999i	0.0353668	+	0.108848i
$293$	−30.0889			−1.75781			−0.878906	−	0.476995i	$-0.841726\pi$
$293$	−30.0889			−1.75781			−0.878906	+	0.476995i	$0.841726\pi$
$294$	0.475335	+	1.46293i	0.0277221	+	0.0853198i
$295$	1.96794	+	17.8761i	0.114578	+	1.04078i
$296$	1.59848	−	4.91962i	0.0929098	−	0.285947i
$297$	1.17410	−	3.61350i	0.0681280	−	0.209677i
$298$	−30.0074	+	21.8017i	−1.73828	+	1.26294i
$299$	22.7116			1.31345
$300$	1.21140	−	1.37235i	0.0699401	−	0.0792325i
$301$	−5.43824			−0.313455
$302$	−19.0439	+	13.8362i	−1.09585	+	0.796183i
$303$	2.07804	−	6.39555i	0.119380	−	0.367415i
$304$	−4.23024	+	13.0193i	−0.242621	+	0.746711i
$305$	6.91711	+	1.43470i	0.396072	+	0.0821505i
$306$	2.74803	+	8.45757i	0.157094	+	0.483487i
$307$	23.0343			1.31464			0.657318	−	0.753613i	$-0.271691\pi$
$307$	23.0343			1.31464			0.657318	+	0.753613i	$0.271691\pi$
$308$	−0.429843	−	1.32292i	−0.0244926	−	0.0753804i
$309$	−6.60061	−	4.79562i	−0.375496	−	0.272813i
$310$	2.51746	+	22.8678i	0.142982	+	1.29880i
$311$	14.7041	−	10.6831i	0.833792	−	0.605786i	−0.0868374	−	0.996222i	$-0.527676\pi$
$311$	14.7041	−	10.6831i	0.833792	−	0.605786i	0.920630	+	0.390437i	$0.127676\pi$
$312$	−5.76942	−	4.19173i	−0.326629	−	0.237310i
$313$	−24.4998	−	17.8001i	−1.38481	−	1.00612i	−0.996412	−	0.0846316i	$-0.973029\pi$
$313$	−24.4998	−	17.8001i	−1.38481	−	1.00612i	−0.388398	−	0.921492i	$-0.626971\pi$
$314$	19.2702	−	14.0007i	1.08748	−	0.790103i
$315$	−0.244686	−	2.22264i	−0.0137865	−	0.125232i
$316$	−0.390011	−	0.283359i	−0.0219398	−	0.0159402i
$317$	7.28699	+	22.4270i	0.409278	+	1.25963i	0.917270	+	0.398266i	$0.130388\pi$
$317$	7.28699	+	22.4270i	0.409278	+	1.25963i	−0.507992	+	0.861362i	$0.669612\pi$
$318$	−15.8747			−0.890209
$319$	−1.70165	−	5.23713i	−0.0952739	−	0.293223i
$320$	13.2430	+	2.74677i	0.740308	+	0.153549i
$321$	2.26327	−	6.96563i	0.126323	−	0.388784i
$322$	3.80465	−	11.7095i	0.212025	−	0.652545i
$323$	−13.9244	+	10.1167i	−0.774775	+	0.562907i
$324$	0.366105			0.0203392
$325$	−9.38889	+	10.6363i	−0.520802	+	0.589998i
$326$	17.4603			0.967038
$327$	−10.6048	+	7.70485i	−0.586448	+	0.426079i
$328$	−2.67220	+	8.22419i	−0.147548	+	0.454105i
$329$	−0.338909	+	1.04305i	−0.0186846	+	0.0575054i
$330$	1.43004	+	12.9900i	0.0787210	+	0.715074i
$331$	−9.77916	−	30.0972i	−0.537512	−	1.65429i	−0.738159	−	0.674627i	$-0.764305\pi$
$331$	−9.77916	−	30.0972i	−0.537512	−	1.65429i	0.200647	−	0.979664i	$-0.435695\pi$
$332$	−2.32570			−0.127639
$333$	−0.636013	−	1.95745i	−0.0348533	−	0.107268i
$334$	0.0452920	+	0.0329066i	0.00247827	+	0.00180057i
$335$	3.77312	−	6.61024i	0.206148	−	0.361156i
$336$	−3.72000	+	2.70274i	−0.202943	+	0.147447i
$337$	−18.7548	−	13.6262i	−1.02164	−	0.742265i	−0.0550214	−	0.998485i	$-0.517523\pi$
$337$	−18.7548	−	13.6262i	−1.02164	−	0.742265i	−0.966618	+	0.256220i	$0.917523\pi$
$338$	6.15835	+	4.47430i	0.334970	+	0.243370i
$339$	6.76786	−	4.91714i	0.367580	−	0.267062i
$340$	−3.18411	−	3.50147i	−0.172683	−	0.189894i
$341$	−20.5597	−	14.9375i	−1.11337	−	0.808911i
$342$	1.41513	+	4.35532i	0.0765215	+	0.235509i
$343$	−1.00000			−0.0539949
$344$	−4.22359	−	12.9989i	−0.227721	−	0.700853i
$345$	−8.87244	+	15.5439i	−0.477676	+	0.836853i
$346$	10.5451	−	32.4546i	0.566910	−	1.74477i
$347$	10.7950	−	33.2236i	0.579505	−	1.78353i	−0.0407929	−	0.999168i	$-0.512988\pi$
$347$	10.7950	−	33.2236i	0.579505	−	1.78353i	0.620298	−	0.784366i	$-0.287012\pi$
$348$	0.429268	−	0.311882i	0.0230112	−	0.0167186i
$349$	−15.2551			−0.816584			−0.408292	−	0.912851i	$-0.633875\pi$
$349$	−15.2551			−0.816584			−0.408292	+	0.912851i	$0.633875\pi$
$350$	3.91098	+	6.62245i	0.209051	+	0.353985i
$351$	−2.83748			−0.151454
$352$	6.29034	−	4.57020i	0.335276	−	0.243593i
$353$	−3.24022	+	9.97237i	−0.172460	+	0.530776i	−0.999508	−	0.0313542i	$-0.990018\pi$
$353$	−3.24022	+	9.97237i	−0.172460	+	0.530776i	0.827049	+	0.562130i	$0.190018\pi$
$354$	3.82298	−	11.7659i	0.203189	−	0.625352i
$355$	29.9038	−	13.4910i	1.58713	−	0.716026i
$356$	1.09209	+	3.36110i	0.0578805	+	0.178138i
$357$	−5.78125			−0.305976
$358$	−9.74513	−	29.9924i	−0.515046	−	1.58515i
$359$	26.3745	+	19.1622i	1.39199	+	1.01134i	0.995643	+	0.0932423i	$0.0297231\pi$
$359$	26.3745	+	19.1622i	1.39199	+	1.01134i	0.396349	+	0.918100i	$0.370277\pi$
$360$	5.12268	−	2.31107i	0.269989	−	0.121804i
$361$	8.20078	−	5.95822i	0.431620	−	0.313590i
$362$	−12.6779	−	9.21101i	−0.666334	−	0.484120i
$363$	−2.77969	−	2.01956i	−0.145896	−	0.105999i
$364$	−0.840421	+	0.610602i	−0.0440500	+	0.0320042i
$365$	11.6960	+	2.42590i	0.612197	+	0.126977i
$366$	−3.93152	−	2.85642i	−0.205504	−	0.149307i
$367$	9.38334	+	28.8789i	0.489806	+	1.50747i	0.824897	+	0.565283i	$0.191233\pi$
$367$	9.38334	+	28.8789i	0.489806	+	1.50747i	−0.335091	+	0.942186i	$0.608767\pi$
$368$	36.8045			1.91857
$369$	1.06323	+	3.27229i	0.0553496	+	0.170349i
$370$	4.76279	+	5.23749i	0.247606	+	0.272284i
$371$	3.18912	−	9.81510i	0.165571	−	0.509575i
$372$	0.756703	−	2.32889i	0.0392332	−	0.120747i
$373$	1.40937	−	1.02396i	0.0729742	−	0.0530189i	−0.550700	−	0.834703i	$-0.685639\pi$
$373$	1.40937	−	1.02396i	0.0729742	−	0.0530189i	0.623674	+	0.781684i	$0.285639\pi$
$374$	33.7879			1.74713
$375$	−3.61169	−	10.5809i	−0.186507	−	0.546396i
$376$	−2.75640			−0.142150
$377$	−3.32703	+	2.41723i	−0.171351	+	0.124494i
$378$	−0.475335	+	1.46293i	−0.0244486	+	0.0752450i
$379$	0.812665	−	2.50113i	0.0417438	−	0.128474i	−0.928013	−	0.372548i	$-0.878484\pi$
$379$	0.812665	−	2.50113i	0.0417438	−	0.128474i	0.969757	+	0.244074i	$0.0784840\pi$
$380$	−1.63970	−	1.80312i	−0.0841146	−	0.0924982i
$381$	−4.28409	−	13.1851i	−0.219481	−	0.675492i
$382$	28.1240			1.43895
$383$	−7.95323	−	24.4775i	−0.406391	−	1.25074i	−0.919728	−	0.392556i	$-0.871591\pi$
$383$	−7.95323	−	24.4775i	−0.406391	−	1.25074i	0.513337	−	0.858187i	$-0.328409\pi$
$384$	−10.8382	−	7.87442i	−0.553085	−	0.401840i
$385$	−8.31879	−	1.72542i	−0.423965	−	0.0879357i
$386$	8.22706	−	5.97731i	0.418746	−	0.304237i
$387$	−4.39963	−	3.19652i	−0.223646	−	0.162488i
$388$	−0.750965	−	0.545608i	−0.0381245	−	0.0276990i
$389$	4.88235	−	3.54724i	0.247545	−	0.179852i	−0.457093	−	0.889419i	$-0.651109\pi$
$389$	4.88235	−	3.54724i	0.247545	−	0.179852i	0.704638	+	0.709567i	$0.251109\pi$
$390$	8.89625	−	4.01350i	0.450479	−	0.203231i
$391$	37.4364	+	27.1992i	1.89324	+	1.37552i
$392$	−0.776647	−	2.39027i	−0.0392266	−	0.120727i
$393$	9.43063			0.475712
$394$	10.1166	+	31.1356i	0.509666	+	1.56859i
$395$	−2.68392	+	1.21084i	−0.135043	+	0.0609238i
$396$	0.429843	−	1.32292i	0.0216004	−	0.0664792i
$397$	−2.50019	+	7.69480i	−0.125481	+	0.386191i	−0.993988	−	0.109485i	$-0.965080\pi$
$397$	−2.50019	+	7.69480i	−0.125481	+	0.386191i	0.868507	+	0.495676i	$0.165080\pi$
$398$	−30.0090	+	21.8028i	−1.50422	+	1.09288i
$399$	−2.97713			−0.149043
$400$	−15.2148	+	17.2363i	−0.760741	+	0.861815i
$401$	12.1229			0.605390			0.302695	−	0.953088i	$-0.402114\pi$
$401$	12.1229			0.605390			0.302695	+	0.953088i	$0.402114\pi$
$402$	−4.23592	+	3.07758i	−0.211269	+	0.153496i
$403$	−5.86480	+	18.0500i	−0.292147	+	0.899135i
$404$	0.760780	−	2.34144i	0.0378502	−	0.116491i
$405$	1.10848	−	1.94198i	0.0550808	−	0.0964976i
$406$	0.688914	+	2.12026i	0.0341902	+	0.105227i
$407$	−7.81998			−0.387622
$408$	−4.48999	−	13.8188i	−0.222288	−	0.684131i
$409$	−2.81561	−	2.04566i	−0.139223	−	0.101151i	0.515994	−	0.856592i	$-0.327423\pi$
$409$	−2.81561	−	2.04566i	−0.139223	−	0.101151i	−0.655217	+	0.755441i	$0.727423\pi$
$410$	−7.96201	−	8.75558i	−0.393216	−	0.432407i
$411$	7.53487	−	5.47440i	0.371668	−	0.270032i
$412$	−2.41652	−	1.75570i	−0.119053	−	0.0864972i
$413$	6.50669	+	4.72739i	0.320174	+	0.232620i
$414$	9.96069	−	7.23687i	0.489541	−	0.355673i
$415$	−7.04166	+	12.3365i	−0.345662	+	0.605574i
$416$	−4.69771	−	3.41309i	−0.230324	−	0.167340i
$417$	2.90492	+	8.94042i	0.142255	+	0.437814i
$418$	17.3995			0.851035
$419$	−11.8337	−	36.4204i	−0.578115	−	1.77925i	−0.625319	−	0.780369i	$-0.715031\pi$
$419$	−11.8337	−	36.4204i	−0.578115	−	1.77925i	0.0472042	−	0.998885i	$-0.484969\pi$
$420$	−0.0895807	−	0.813720i	−0.00437109	−	0.0397055i
$421$	−5.57300	+	17.1519i	−0.271611	+	0.835934i	0.718485	+	0.695543i	$0.244836\pi$
$421$	−5.57300	+	17.1519i	−0.271611	+	0.835934i	−0.990096	+	0.140391i	$0.955164\pi$
$422$	−6.66626	+	20.5166i	−0.324508	+	0.998734i
$423$	−0.887274	+	0.644643i	−0.0431408	+	0.0313436i
$424$	25.9376			1.25964
$425$	−28.2140	+	6.28825i	−1.36858	+	0.305025i
$426$	−22.5677			−1.09341
$427$	2.55590	−	1.85697i	0.123689	−	0.0898650i
$428$	0.828595	−	2.55015i	0.0400517	−	0.123266i
$429$	−3.33148	+	10.2533i	−0.160846	+	0.495032i
$430$	18.3153	+	3.79883i	0.883243	+	0.183196i
$431$	2.61336	+	8.04309i	0.125881	+	0.387422i	0.994061	−	0.108828i	$-0.0347098\pi$
$431$	2.61336	+	8.04309i	0.125881	+	0.387422i	−0.868179	+	0.496250i	$0.834710\pi$
$432$	−4.59818			−0.221230
$433$	−5.92032	−	18.2209i	−0.284513	−	0.875640i	−0.986544	−	0.163494i	$-0.947724\pi$
$433$	−5.92032	−	18.2209i	−0.284513	−	0.875640i	0.702032	−	0.712146i	$-0.252276\pi$
$434$	8.32362	+	6.04746i	0.399546	+	0.290288i
$435$	−0.354629	−	3.22132i	−0.0170032	−	0.154451i
$436$	−3.88248	+	2.82078i	−0.185937	+	0.135091i
$437$	19.2783	+	14.0065i	0.922208	+	0.670024i
$438$	−6.64773	−	4.82986i	−0.317641	−	0.230780i
$439$	28.4720	−	20.6862i	1.35890	−	0.987296i	0.360382	−	0.932805i	$-0.382646\pi$
$439$	28.4720	−	20.6862i	1.35890	−	0.987296i	0.998514	−	0.0544914i	$-0.0173537\pi$
$440$	−2.33653	−	21.2242i	−0.111390	−	1.01183i
$441$	−0.809017	−	0.587785i	−0.0385246	−	0.0279898i
$442$	−7.79749	−	23.9982i	−0.370889	−	1.14148i
$443$	23.1563			1.10019			0.550095	−	0.835102i	$-0.314592\pi$
$443$	23.1563			1.10019			0.550095	+	0.835102i	$0.314592\pi$
$444$	−0.232848	−	0.716632i	−0.0110505	−	0.0340098i
$445$	21.1353	+	4.38372i	1.00191	+	0.207808i
$446$	5.19505	−	15.9887i	0.245993	−	0.757087i
$447$	7.45137	−	22.9330i	0.352438	−	1.08469i
$448$	4.89335	−	3.55523i	0.231189	−	0.167969i
$449$	32.8320			1.54944			0.774718	−	0.632307i	$-0.217892\pi$
$449$	32.8320			1.54944			0.774718	+	0.632307i	$0.217892\pi$
$450$	−0.728532	+	7.65649i	−0.0343433	+	0.360930i
$451$	13.0728			0.615572
$452$	2.47775	−	1.80019i	0.116543	−	0.0846737i
$453$	4.72893	−	14.5542i	0.222185	−	0.683814i
$454$	−0.624197	+	1.92108i	−0.0292950	+	0.0901608i
$455$	0.694292	+	6.30671i	0.0325489	+	0.295663i
$456$	−2.31217	−	7.11614i	−0.108277	−	0.333244i
$457$	6.90107			0.322818			0.161409	−	0.986888i	$-0.448396\pi$
$457$	6.90107			0.322818			0.161409	+	0.986888i	$0.448396\pi$
$458$	−11.6234	−	35.7730i	−0.543124	−	1.67156i
$459$	−4.67713	−	3.39814i	−0.218310	−	0.158611i
$460$	−3.24824	+	5.69069i	−0.151450	+	0.265330i
$461$	−23.4971	+	17.0716i	−1.09437	+	0.795104i	−0.980131	−	0.198350i	$-0.936442\pi$
$461$	−23.4971	+	17.0716i	−1.09437	+	0.795104i	−0.114236	+	0.993454i	$0.536442\pi$
$462$	4.72821	+	3.43524i	0.219976	+	0.159822i
$463$	8.11043	+	5.89257i	0.376923	+	0.273851i	0.760076	−	0.649834i	$-0.225162\pi$
$463$	8.11043	+	5.89257i	0.376923	+	0.273851i	−0.383153	+	0.923685i	$0.625162\pi$
$464$	−5.39149	+	3.91715i	−0.250294	+	0.181849i
$465$	−10.0623	−	11.0652i	−0.466629	−	0.513137i
$466$	−37.6259	−	27.3368i	−1.74299	−	1.26635i
$467$	0.738396	+	2.27255i	0.0341689	+	0.105161i	0.966686	−	0.255964i	$-0.0823928\pi$
$467$	0.738396	+	2.27255i	0.0341689	+	0.105161i	−0.932517	+	0.361125i	$0.882393\pi$
$468$	−1.03882			−0.0480194
$469$	−1.05185	−	3.23727i	−0.0485701	−	0.149483i
$470$	1.87002	−	3.27613i	0.0862574	−	0.151117i
$471$	−4.78514	+	14.7272i	−0.220488	+	0.678592i
$472$	−6.24635	+	19.2243i	−0.287512	+	0.884870i
$473$	−16.7162	+	12.1450i	−0.768613	+	0.558430i
$474$	2.02549			0.0930339
$475$	−14.5291	+	3.23821i	−0.666643	+	0.148579i
$476$	−2.11655			−0.0970117
$477$	8.34923	−	6.06607i	0.382285	−	0.277746i
$478$	11.4550	−	35.2548i	0.523939	−	1.61252i
$479$	11.4712	−	35.3046i	0.524131	−	1.61311i	−0.241896	−	0.970302i	$-0.577769\pi$
$479$	11.4712	−	35.3046i	0.524131	−	1.61311i	0.766027	−	0.642808i	$-0.222231\pi$
$480$	4.17111	−	1.88177i	0.190384	−	0.0858908i
$481$	1.80468	+	5.55423i	0.0822863	+	0.253251i
$482$	−12.7686			−0.581596
$483$	2.47342	+	7.61239i	0.112544	+	0.346376i
$484$	−1.01766	−	0.739372i	−0.0462572	−	0.0336078i
$485$	−5.16788	+	2.33146i	−0.234661	+	0.105866i
$486$	−1.24444	+	0.904140i	−0.0564490	+	0.0410126i
$487$	−17.2473	−	12.5309i	−0.781549	−	0.567828i	0.123895	−	0.992295i	$-0.460461\pi$
$487$	−17.2473	−	12.5309i	−0.781549	−	0.567828i	−0.905443	+	0.424467i	$0.860461\pi$
$488$	6.42369	+	4.66708i	0.290787	+	0.211269i
$489$	−9.18318	+	6.67197i	−0.415278	+	0.301717i
$490$	3.36787	+	0.698540i	0.152145	+	0.0315568i
$491$	−21.8714	−	15.8905i	−0.987043	−	0.717129i	−0.0277715	−	0.999614i	$-0.508841\pi$
$491$	−21.8714	−	15.8905i	−0.987043	−	0.717129i	−0.959272	+	0.282486i	$0.908841\pi$
$492$	0.389254	+	1.19800i	0.0175489	+	0.0540101i
$493$	−8.37891			−0.377367
$494$	−4.01541	−	12.3582i	−0.180662	−	0.556020i
$495$	−5.71587	−	6.28556i	−0.256909	−	0.282515i
$496$	−9.50398	+	29.2502i	−0.426741	+	1.31337i
$497$	4.53370	−	13.9533i	0.203364	−	0.625891i
$498$	7.90536	−	5.74358i	0.354248	−	0.257376i
$499$	−10.8449			−0.485485			−0.242742	−	0.970091i	$-0.578047\pi$
$499$	−10.8449			−0.485485			−0.242742	+	0.970091i	$0.578047\pi$
$500$	−1.32226	−	3.87373i	−0.0591331	−	0.173238i
$501$	−0.0363954			−0.00162603
$502$	15.1676	−	11.0199i	0.676962	−	0.491841i
$503$	−1.26699	+	3.89939i	−0.0564923	+	0.173865i	−0.975321	−	0.220791i	$-0.929136\pi$
$503$	−1.26699	+	3.89939i	−0.0564923	+	0.173865i	0.918829	+	0.394656i	$0.129136\pi$
$504$	0.776647	−	2.39027i	0.0345946	−	0.106471i
$505$	−10.1165	−	11.1248i	−0.450180	−	0.495049i
$506$	−14.4556	−	44.4898i	−0.642630	−	1.97781i
$507$	−4.94868			−0.219779
$508$	−1.56843	−	4.82713i	−0.0695877	−	0.214169i
$509$	−17.1027	−	12.4258i	−0.758064	−	0.550766i	0.140252	−	0.990116i	$-0.455209\pi$
$509$	−17.1027	−	12.4258i	−0.758064	−	0.550766i	−0.898316	+	0.439350i	$0.855209\pi$
$510$	19.4705	+	4.03843i	0.862169	+	0.178825i
$511$	4.32172	−	3.13991i	0.191181	−	0.138901i
$512$	11.0861	+	8.05455i	0.489943	+	0.355964i
$513$	−2.40854	−	1.74991i	−0.106340	−	0.0772604i
$514$	−5.45977	+	3.96675i	−0.240820	+	0.174966i
$515$	−16.6296	+	7.50237i	−0.732789	+	0.330594i
$516$	−1.61073	−	1.17026i	−0.0709083	−	0.0515179i
$517$	1.28767	+	3.96304i	0.0566316	+	0.174294i
$518$	3.16593			0.139103
$519$	6.85544	+	21.0989i	0.300920	+	0.926137i
$520$	−14.5355	+	6.55763i	−0.637425	+	0.287571i
$521$	−0.673242	+	2.07203i	−0.0294953	+	0.0907771i	−0.964720	−	0.263276i	$-0.915197\pi$
$521$	−0.673242	+	2.07203i	−0.0294953	+	0.0907771i	0.935225	+	0.354053i	$0.115197\pi$
$522$	−0.688914	+	2.12026i	−0.0301529	+	0.0928012i
$523$	−11.9809	+	8.70466i	−0.523890	+	0.380628i	−0.818067	−	0.575123i	$-0.804954\pi$
$523$	−11.9809	+	8.70466i	−0.523890	+	0.380628i	0.294178	+	0.955751i	$0.404954\pi$
$524$	3.45260			0.150828
$525$	−4.58754	−	1.98858i	−0.200217	−	0.0867887i
$526$	−16.6548			−0.726184
$527$	−31.2836	+	22.7289i	−1.36274	+	0.990086i
$528$	−5.39871	+	16.6155i	−0.234949	+	0.723097i
$529$	12.6902	−	39.0564i	0.551748	−	1.69811i
$530$	−17.5968	+	30.8283i	−0.764356	+	1.33910i
$531$	2.48534	+	7.64908i	0.107854	+	0.331942i
$532$	−1.08994			−0.0472549
$533$	−3.01690	−	9.28507i	−0.130677	−	0.402181i
$534$	−12.0128	−	8.72780i	−0.519844	−	0.377689i
$535$	−11.0183	−	12.1165i	−0.476363	−	0.523841i
$536$	6.92105	−	5.02844i	0.298944	−	0.217195i
$537$	16.5862	+	12.0506i	0.715746	+	0.520020i
$538$	−25.2850	−	18.3706i	−1.09011	−	0.792014i
$539$	−3.07383	+	2.23327i	−0.132399	+	0.0961936i
$540$	0.405820	−	0.710967i	0.0174637	−	0.0305952i
$541$	19.8392	+	14.4140i	0.852953	+	0.619707i	0.925959	−	0.377625i	$-0.123259\pi$
$541$	19.8392	+	14.4140i	0.852953	+	0.619707i	−0.0730057	+	0.997332i	$0.523259\pi$
$542$	3.28047	+	10.0963i	0.140908	+	0.433671i
$543$	10.1876			0.437192
$544$	−3.65594	−	11.2518i	−0.156747	−	0.482418i
$545$	3.20741	+	29.1350i	0.137390	+	1.24800i
$546$	1.34875	−	4.15104i	0.0577214	−	0.177648i
$547$	2.31358	−	7.12046i	0.0989214	−	0.304449i	−0.889334	−	0.457257i	$-0.848832\pi$
$547$	2.31358	−	7.12046i	0.0989214	−	0.304449i	0.988256	+	0.152809i	$0.0488318\pi$
$548$	2.75855	−	2.00421i	0.117840	−	0.0856155i
$549$	3.15926			0.134834
$550$	26.8114	+	11.6220i	1.14324	+	0.495564i
$551$	−4.31482			−0.183817
$552$	−16.2747	+	11.8243i	−0.692698	+	0.503275i
$553$	−0.406907	+	1.25233i	−0.0173035	+	0.0532546i
$554$	1.05357	−	3.24256i	0.0447620	−	0.137763i
$555$	−4.50633	−	0.934669i	−0.191283	−	0.0396745i
$556$	1.06351	+	3.27313i	0.0451027	+	0.138812i
$557$	−16.2935			−0.690377			−0.345189	−	0.938533i	$-0.612185\pi$
$557$	−16.2935			−0.690377			−0.345189	+	0.938533i	$0.612185\pi$
$558$	3.17934	+	9.78500i	0.134592	+	0.414232i
$559$	12.4839	+	9.07008i	0.528012	+	0.383623i
$560$	1.12511	+	10.2201i	0.0475445	+	0.431878i
$561$	−17.7706	+	12.9111i	−0.750274	+	0.545106i
$562$	−8.44346	−	6.13453i	−0.356166	−	0.258770i
$563$	−19.7832	−	14.3733i	−0.833763	−	0.605764i	0.0868583	−	0.996221i	$-0.472317\pi$
$563$	−19.7832	−	14.3733i	−0.833763	−	0.605764i	−0.920621	+	0.390456i	$0.872317\pi$
$564$	−0.324836	+	0.236007i	−0.0136780	+	0.00993768i
$565$	−2.04693	−	18.5936i	−0.0861149	−	0.782237i
$566$	29.8457	+	21.6842i	1.25451	+	0.911453i
$567$	−0.309017	−	0.951057i	−0.0129775	−	0.0399406i
$568$	36.8733			1.54717
$569$	−5.15457	−	15.8641i	−0.216091	−	0.665059i	−0.999074	−	0.0430164i	$-0.986303\pi$
$569$	−5.15457	−	15.8641i	−0.216091	−	0.665059i	0.782984	−	0.622042i	$-0.213697\pi$
$570$	10.0266	+	2.07964i	0.419967	+	0.0871065i
$571$	−8.34314	+	25.6775i	−0.349150	+	1.07457i	0.610175	+	0.792267i	$0.291099\pi$
$571$	−8.34314	+	25.6775i	−0.349150	+	1.07457i	−0.959325	+	0.282305i	$0.908901\pi$
$572$	−1.21967	+	3.75377i	−0.0509971	+	0.156953i
$573$	−14.7917	+	10.7468i	−0.617932	+	0.448954i
$574$	−5.29252			−0.220905
$575$	20.3509	+	34.4601i	0.848691	+	1.43709i
$576$	6.04852			0.252022
$577$	−5.27455	+	3.83218i	−0.219582	+	0.159536i	−0.692139	−	0.721765i	$-0.743331\pi$
$577$	−5.27455	+	3.83218i	−0.219582	+	0.159536i	0.472556	+	0.881300i	$0.343331\pi$
$578$	7.80637	−	24.0255i	0.324702	−	0.999330i
$579$	−2.04292	+	6.28747i	−0.0849010	+	0.261299i
$580$	−0.129831	−	1.17934i	−0.00539095	−	0.0489696i
$581$	1.96304	+	6.04162i	0.0814407	+	0.250649i
$582$	3.90008			0.161663
$583$	−12.1169	−	37.2921i	−0.501832	−	1.54448i
$584$	10.8617	+	7.89148i	0.449460	+	0.326552i
$585$	−3.14530	+	5.51033i	−0.130042	+	0.227824i
$586$	37.4439	−	27.2046i	1.54679	−	1.12381i
$587$	37.6868	+	27.3810i	1.55550	+	1.13014i	0.939581	+	0.342327i	$0.111215\pi$
$587$	37.6868	+	27.3810i	1.55550	+	1.13014i	0.615919	+	0.787810i	$0.288785\pi$
$588$	−0.296185	−	0.215191i	−0.0122145	−	0.00887433i
$589$	−16.1099	+	11.7045i	−0.663796	+	0.482276i
$590$	−18.6115	−	20.4664i	−0.766221	−	0.842590i
$591$	−17.2184	−	12.5099i	−0.708269	−	0.514588i
$592$	2.92450	+	9.00069i	0.120196	+	0.369926i
$593$	−13.6025			−0.558589			−0.279294	−	0.960205i	$-0.590101\pi$
$593$	−13.6025			−0.558589			−0.279294	+	0.960205i	$0.590101\pi$
$594$	1.80601	+	5.55834i	0.0741016	+	0.228061i
$595$	−6.40840	+	11.2271i	−0.262719	+	0.460264i
$596$	2.72798	−	8.39587i	0.111743	−	0.343908i
$597$	7.45177	−	22.9342i	0.304981	−	0.938634i
$598$	−28.2633	+	20.5345i	−1.15577	+	0.839718i
$599$	−4.97691			−0.203351			−0.101676	−	0.994818i	$-0.532420\pi$
$599$	−4.97691			−0.203351			−0.101676	+	0.994818i	$0.532420\pi$
$600$	1.19034	−	12.5099i	0.0485956	−	0.510715i
$601$	34.8341			1.42091			0.710456	−	0.703741i	$-0.248489\pi$
$601$	34.8341			1.42091			0.710456	+	0.703741i	$0.248489\pi$
$602$	6.76758	−	4.91693i	0.275826	−	0.200399i
$603$	1.05185	−	3.23727i	0.0428348	−	0.131832i
$604$	1.73129	−	5.32835i	0.0704450	−	0.216808i
$605$	−7.00317	+	3.15944i	−0.284719	+	0.128450i
$606$	3.19647	+	9.83772i	0.129848	+	0.399630i
$607$	32.3697			1.31385			0.656924	−	0.753957i	$-0.271857\pi$
$607$	32.3697			1.31385			0.656924	+	0.753957i	$0.271857\pi$
$608$	−1.88267	−	5.79427i	−0.0763524	−	0.234989i
$609$	−1.17253	−	0.851891i	−0.0475132	−	0.0345204i
$610$	−9.90510	+	4.46864i	−0.401046	+	0.180930i
$611$	2.51763	−	1.82916i	0.101852	−	0.0740000i
$612$	−1.71232	−	1.24407i	−0.0692165	−	0.0502887i
$613$	−20.4305	−	14.8436i	−0.825180	−	0.599529i	0.0930114	−	0.995665i	$-0.470351\pi$
$613$	−20.4305	−	14.8436i	−0.825180	−	0.599529i	−0.918192	+	0.396137i	$0.870351\pi$
$614$	−28.6648	+	20.8262i	−1.15682	+	0.840478i
$615$	7.53328	+	1.56250i	0.303771	+	0.0630060i
$616$	−7.72539	−	5.61283i	−0.311265	−	0.226147i
$617$	−7.57127	−	23.3020i	−0.304808	−	0.938103i	−0.979749	−	0.200231i	$-0.935831\pi$
$617$	−7.57127	−	23.3020i	−0.304808	−	0.938103i	0.674941	−	0.737872i	$-0.264169\pi$
$618$	12.5500			0.504835
$619$	3.22721	+	9.93232i	0.129712	+	0.399214i	0.994730	−	0.102528i	$-0.0326930\pi$
$619$	3.22721	+	9.93232i	0.129712	+	0.399214i	−0.865018	+	0.501741i	$0.832693\pi$
$620$	−3.68386	−	4.05103i	−0.147948	−	0.162693i
$621$	−2.47342	+	7.61239i	−0.0992548	+	0.305475i
$622$	−8.63932	+	26.5891i	−0.346405	+	1.06613i
$623$	7.80956	−	5.67398i	0.312884	−	0.227323i
$624$	13.0473			0.522308
$625$	−24.5514	−	4.71492i	−0.982055	−	0.188597i
$626$	46.5824			1.86181
$627$	−9.15117	+	6.64871i	−0.365462	+	0.265524i
$628$	−1.75187	+	5.39169i	−0.0699070	+	0.215152i
$629$	−3.67696	+	11.3165i	−0.146610	+	0.451219i
$630$	2.31408	+	2.54472i	0.0921950	+	0.101384i
$631$	8.78123	+	27.0258i	0.349575	+	1.07588i	0.959089	+	0.283106i	$0.0913648\pi$
$631$	8.78123	+	27.0258i	0.349575	+	1.07588i	−0.609513	+	0.792776i	$0.708635\pi$
$632$	−3.30944			−0.131642
$633$	−4.33376	−	13.3379i	−0.172252	−	0.530136i
$634$	−29.3454	−	21.3207i	−1.16546	−	0.846753i
$635$	−30.3540	−	6.29580i	−1.20456	−	0.249841i
$636$	3.05669	−	2.22082i	0.121206	−	0.0880612i
$637$	2.29557	+	1.66783i	0.0909539	+	0.0660819i
$638$	6.85270	+	4.97878i	0.271301	+	0.197112i
$639$	11.8694	−	8.62362i	0.469546	−	0.341145i
$640$	−27.3059	+	12.3189i	−1.07936	+	0.486948i
$641$	15.6681	+	11.3835i	0.618852	+	0.449622i	0.852520	−	0.522694i	$-0.175073\pi$
$641$	15.6681	+	11.3835i	0.618852	+	0.449622i	−0.233669	+	0.972316i	$0.575073\pi$
$642$	3.48140	+	10.7146i	0.137400	+	0.422873i
$643$	−24.0098			−0.946855			−0.473428	−	0.880833i	$-0.656983\pi$
$643$	−24.0098			−0.946855			−0.473428	+	0.880833i	$0.656983\pi$
$644$	0.905530	+	2.78694i	0.0356829	+	0.109821i
$645$	−11.0845	+	5.00070i	−0.436451	+	0.196902i
$646$	8.18123	−	25.1792i	0.321886	−	0.990664i
$647$	−9.14533	+	28.1464i	−0.359540	+	1.10655i	0.593790	+	0.804620i	$0.297631\pi$
$647$	−9.14533	+	28.1464i	−0.359540	+	1.10655i	−0.953330	+	0.301930i	$0.902369\pi$
$648$	2.03329	−	1.47727i	0.0798751	−	0.0580326i
$649$	30.5580			1.19951
$650$	2.06720	−	21.7252i	0.0810822	−	0.852132i
$651$	−6.68864			−0.262148
$652$	−3.36201	+	2.44264i	−0.131666	+	0.0956612i
$653$	−7.25904	+	22.3410i	−0.284068	+	0.874272i	0.702608	+	0.711577i	$0.252019\pi$
$653$	−7.25904	+	22.3410i	−0.284068	+	0.874272i	−0.986676	+	0.162695i	$0.947981\pi$
$654$	6.23081	−	19.1765i	0.243644	−	0.749859i
$655$	10.4537	−	18.3141i	0.408458	−	0.715589i
$656$	−4.88893	−	15.0466i	−0.190880	−	0.587470i
$657$	5.34194			0.208409
$658$	−0.521314	−	1.60444i	−0.0203230	−	0.0625476i
$659$	−2.74820	−	1.99668i	−0.107055	−	0.0777797i	0.532970	−	0.846134i	$-0.321076\pi$
$659$	−2.74820	−	1.99668i	−0.107055	−	0.0777797i	−0.640025	+	0.768354i	$0.721076\pi$
$660$	−2.09261	−	2.30118i	−0.0814546	−	0.0895731i
$661$	−21.6710	+	15.7449i	−0.842904	+	0.612406i	−0.923180	−	0.384367i	$-0.874420\pi$
$661$	−21.6710	+	15.7449i	−0.842904	+	0.612406i	0.0802761	+	0.996773i	$0.474420\pi$
$662$	39.3817	+	28.6125i	1.53061	+	1.11205i
$663$	13.2713	+	9.64216i	0.515414	+	0.374470i
$664$	−12.9165	+	9.38441i	−0.501259	+	0.364186i
$665$	−3.30008	+	5.78151i	−0.127972	+	0.224197i
$666$	2.56129	+	1.86089i	0.0992479	+	0.0721078i
$667$	3.58478	+	11.0328i	0.138803	+	0.427193i
$668$	−0.0133245			−0.000515542
$669$	3.37732	+	10.3943i	0.130575	+	0.401868i
$670$	1.28115	+	11.6375i	0.0494950	+	0.449595i
$671$	3.70928	−	11.4160i	0.143195	−	0.440710i
$672$	0.632379	−	1.94626i	0.0243945	−	0.0750787i
$673$	24.9023	−	18.0925i	0.959911	−	0.697416i	0.00678118	−	0.999977i	$-0.497841\pi$
$673$	24.9023	−	18.0925i	0.959911	−	0.697416i	0.953130	+	0.302561i	$0.0978415\pi$
$674$	35.6592			1.37354
$675$	−2.54254	−	4.30528i	−0.0978626	−	0.165710i
$676$	−1.81174			−0.0696822
$677$	30.9408	−	22.4798i	1.18915	−	0.863970i	0.195979	−	0.980608i	$-0.437212\pi$
$677$	30.9408	−	22.4798i	1.18915	−	0.863970i	0.993175	+	0.116638i	$0.0372116\pi$
$678$	−3.97643	+	12.2382i	−0.152714	+	0.470005i
$679$	−0.783499	+	2.41136i	−0.0300680	+	0.0925396i
$680$	−31.8128	−	6.59838i	−1.21997	−	0.253036i
$681$	−0.405793	−	1.24890i	−0.0155500	−	0.0478581i
$682$	39.0909			1.49687
$683$	−13.0507	−	40.1661i	−0.499373	−	1.53691i	−0.810029	−	0.586389i	$-0.800549\pi$
$683$	−13.0507	−	40.1661i	−0.499373	−	1.53691i	0.310657	−	0.950522i	$-0.399451\pi$
$684$	−0.881780	−	0.640651i	−0.0337157	−	0.0244959i
$685$	−2.27891	−	20.7008i	−0.0870726	−	0.790937i
$686$	1.24444	−	0.904140i	0.0475130	−	0.0345202i
$687$	19.7829	+	14.3731i	0.754765	+	0.548369i
$688$	20.2303	+	14.6982i	0.771272	+	0.560362i
$689$	−23.6908	+	17.2124i	−0.902548	+	0.655739i
$690$	−3.01259	−	27.3654i	−0.114688	−	1.04178i
$691$	−29.7619	−	21.6233i	−1.13219	−	0.822588i	−0.146182	−	0.989258i	$-0.546698\pi$
$691$	−29.7619	−	21.6233i	−1.13219	−	0.822588i	−0.986013	+	0.166670i	$0.946698\pi$
$692$	2.50981	+	7.72440i	0.0954086	+	0.293638i
$693$	−3.79946			−0.144329
$694$	16.6050	+	51.1050i	0.630318	+	1.93992i
$695$	20.5821	+	4.26900i	0.780725	+	0.161932i
$696$	1.12561	−	3.46428i	0.0426662	−	0.131313i
$697$	6.14681	−	18.9179i	0.232827	−	0.716568i
$698$	18.9840	−	13.7927i	0.718556	−	0.522061i
$699$	30.2352			1.14360
$700$	−1.67952	−	0.728029i	−0.0634800	−	0.0275169i
$701$	−44.5516			−1.68269			−0.841346	−	0.540497i	$-0.818236\pi$
$701$	−44.5516			−1.68269			−0.841346	+	0.540497i	$0.818236\pi$
$702$	3.53109	−	2.56548i	0.133272	−	0.0968279i
$703$	−1.89349	+	5.82757i	−0.0714144	+	0.219791i
$704$	7.10155	−	21.8563i	0.267650	−	0.823741i
$705$	0.268355	+	2.43764i	0.0101068	+	0.0918068i
$706$	−4.98416	−	15.3397i	−0.187581	−	0.577316i
$707$	−6.72468			−0.252907
$708$	0.909894	+	2.80037i	0.0341959	+	0.105244i
$709$	20.1558	+	14.6441i	0.756967	+	0.549969i	0.897979	−	0.440039i	$-0.145035\pi$
$709$	20.1558	+	14.6441i	0.756967	+	0.549969i	−0.141011	+	0.990008i	$0.545035\pi$
$710$	−25.0159	+	43.8260i	−0.938829	+	1.64476i
$711$	−1.06530	+	0.773984i	−0.0399518	+	0.0290267i
$712$	19.6276	+	14.2603i	0.735577	+	0.534428i
$713$	43.3122	+	31.4681i	1.62205	+	1.17849i
$714$	7.19443	−	5.22706i	0.269245	−	0.195618i
$715$	16.2187	+	17.8352i	0.606544	+	0.666998i
$716$	6.07228	+	4.41177i	0.226932	+	0.164876i
$717$	7.44693	+	22.9193i	0.278111	+	0.855937i
$718$	−50.1468			−1.87146
$719$	−3.39774	−	10.4572i	−0.126714	−	0.389987i	0.867495	−	0.497446i	$-0.165729\pi$
$719$	−3.39774	−	10.4572i	−0.126714	−	0.389987i	−0.994210	+	0.107459i	$0.965729\pi$
$720$	−5.09699	+	8.92955i	−0.189954	+	0.332785i
$721$	−2.52121	+	7.75948i	−0.0938947	+	0.288978i
$722$	−4.81834	+	14.8293i	−0.179320	+	0.551890i
$723$	6.71561	−	4.87918i	0.249756	−	0.181459i
$724$	3.72973			0.138614
$725$	−6.64883	−	2.88209i	−0.246932	−	0.107038i
$726$	5.28513			0.196149
$727$	−10.3414	+	7.51350i	−0.383543	+	0.278660i	−0.762804	−	0.646629i	$-0.776178\pi$
$727$	−10.3414	+	7.51350i	−0.383543	+	0.278660i	0.379261	+	0.925290i	$0.376178\pi$
$728$	−2.20372	+	6.78236i	−0.0816754	+	0.251371i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	−16.7483	+	7.55593i	−0.619884	+	0.279658i
$731$	9.71545	+	29.9011i	0.359339	+	1.10593i
$732$	1.15662			0.0427500
$733$	1.69603	+	5.21985i	0.0626443	+	0.192799i	0.977480	−	0.211026i	$-0.0676804\pi$
$733$	1.69603	+	5.21985i	0.0626443	+	0.192799i	−0.914836	+	0.403825i	$0.867680\pi$
$734$	−37.7876	−	27.4543i	−1.39477	−	1.01336i
$735$	−2.03824	+	0.919544i	−0.0751818	+	0.0339179i
$736$	−13.2516	+	9.62784i	−0.488460	+	0.354887i
$737$	−10.4629	−	7.60175i	−0.385406	−	0.280014i
$738$	−4.28174	−	3.11086i	−0.157613	−	0.114513i
$739$	3.42167	−	2.48599i	0.125868	−	0.0914486i	−0.523070	−	0.852290i	$-0.675213\pi$
$739$	3.42167	−	2.48599i	0.125868	−	0.0914486i	0.648938	+	0.760841i	$0.275213\pi$
$740$	−1.64979	−	0.342187i	−0.0606474	−	0.0125790i
$741$	6.83421	+	4.96534i	0.251061	+	0.182406i
$742$	4.90555	+	15.0977i	0.180089	+	0.554255i
$743$	27.9080			1.02385			0.511923	−	0.859031i	$-0.328933\pi$
$743$	27.9080			1.02385			0.511923	+	0.859031i	$0.328933\pi$
$744$	−5.19471	−	15.9877i	−0.190447	−	0.586136i
$745$	−36.2756	−	39.8911i	−1.32903	−	1.46150i
$746$	−0.828067	+	2.54853i	−0.0303177	+	0.0933083i
$747$	−1.96304	+	6.04162i	−0.0718240	+	0.221051i
$748$	−6.50589	+	4.72681i	−0.237879	+	0.172829i
$749$	−7.32410			−0.267617
$750$	14.0612	+	9.90186i	0.513441	+	0.361565i
$751$	14.7888			0.539650			0.269825	−	0.962909i	$-0.413034\pi$
$751$	14.7888			0.539650			0.269825	+	0.962909i	$0.413034\pi$
$752$	4.07985	−	2.96418i	0.148777	−	0.108093i
$753$	−3.76638	+	11.5917i	−0.137254	+	0.422426i
$754$	1.95478	−	6.01620i	0.0711889	−	0.219097i
$755$	−23.0219	−	25.3165i	−0.837853	−	0.921361i
$756$	−0.113133	−	0.348187i	−0.00411460	−	0.0126634i
$757$	38.9941			1.41727			0.708633	−	0.705578i	$-0.249312\pi$
$757$	38.9941			1.41727			0.708633	+	0.705578i	$0.249312\pi$
$758$	1.25005	+	3.84727i	0.0454040	+	0.139739i
$759$	24.6034	+	17.8754i	0.893045	+	0.648835i
$760$	−16.3824	−	3.39791i	−0.594251	−	0.123255i
$761$	4.29553	−	3.12089i	0.155713	−	0.113132i	−0.507201	−	0.861828i	$-0.669320\pi$
$761$	4.29553	−	3.12089i	0.155713	−	0.113132i	0.662914	+	0.748696i	$0.269320\pi$
$762$	17.2525	+	12.5347i	0.624991	+	0.454083i
$763$	10.6048	+	7.70485i	0.383920	+	0.278934i
$764$	−5.41531	+	3.93446i	−0.195919	+	0.142344i
$765$	−11.7836	+	5.31611i	−0.426037	+	0.192205i
$766$	32.0285	+	23.2700i	1.15724	+	0.840781i
$767$	−7.05210	−	21.7041i	−0.254637	−	0.783691i
$768$	8.51006			0.307080
$769$	−0.563745	−	1.73503i	−0.0203292	−	0.0625668i	0.940377	−	0.340133i	$-0.110472\pi$
$769$	−0.563745	−	1.73503i	−0.0203292	−	0.0625668i	−0.960706	+	0.277566i	$0.910472\pi$
$770$	11.9123	−	5.37416i	0.429289	−	0.193671i
$771$	1.35576	−	4.17259i	0.0488264	−	0.150272i
$772$	−0.747925	+	2.30188i	−0.0269184	+	0.0828463i
$773$	21.0661	−	15.3054i	0.757694	−	0.550497i	−0.140508	−	0.990080i	$-0.544874\pi$
$773$	21.0661	−	15.3054i	0.757694	−	0.550497i	0.898202	+	0.439583i	$0.144874\pi$
$774$	8.36519			0.300680
$775$	−32.6423	+	7.27521i	−1.17254	+	0.261333i
$776$	−6.37232			−0.228753
$777$	−1.66510	+	1.20977i	−0.0597353	+	0.0434002i
$778$	−2.86861	+	8.82866i	−0.102845	+	0.316523i
$779$	3.16537	−	9.74202i	0.113411	−	0.349044i
$780$	−1.15151	+	2.01736i	−0.0412306	+	0.0722330i
$781$	−17.2256	−	53.0150i	−0.616381	−	1.89703i
$782$	−71.1793			−2.54537
$783$	−0.447866	−	1.37839i	−0.0160054	−	0.0492596i
$784$	3.72000	+	2.70274i	0.132857	+	0.0965265i
$785$	23.2956	+	25.6174i	0.831454	+	0.914324i
$786$	−11.7359	+	8.52661i	−0.418605	+	0.304134i
$787$	−34.8305	−	25.3059i	−1.24157	−	0.902056i	−0.243872	−	0.969807i	$-0.578418\pi$
$787$	−34.8305	−	25.3059i	−1.24157	−	0.902056i	−0.997702	+	0.0677511i	$0.978418\pi$
$788$	−6.30373	−	4.57993i	−0.224561	−	0.163153i
$789$	8.75952	−	6.36416i	0.311847	−	0.226570i
$790$	2.24522	−	3.93346i	0.0798812	−	0.139946i
$791$	−6.76786	−	4.91714i	−0.240637	−	0.174833i
$792$	−2.95084	−	9.08174i	−0.104853	−	0.322706i
$793$	−8.96436			−0.318334
$794$	−3.84583	−	11.8362i	−0.136483	−	0.420053i
$795$	−2.52521	−	22.9381i	−0.0895599	−	0.813531i
$796$	2.72813	−	8.39632i	0.0966960	−	0.297600i
$797$	−12.9846	+	39.9626i	−0.459939	+	1.41555i	0.405298	+	0.914185i	$0.367168\pi$
$797$	−12.9846	+	39.9626i	−0.459939	+	1.41555i	−0.865237	+	0.501363i	$0.832832\pi$
$798$	3.70486	−	2.69174i	0.131151	−	0.0952865i
$799$	6.34048			0.224310
$800$	0.969229	−	10.1861i	0.0342674	−	0.360133i
$801$	9.65315			0.341077
$802$	−15.0863	+	10.9608i	−0.532715	+	0.387040i
$803$	6.27195	−	19.3031i	0.221332	−	0.681191i
$804$	0.385089	−	1.18518i	0.0135810	−	0.0417982i
$805$	17.5248	+	3.63487i	0.617669	+	0.128112i
$806$	−9.02133	−	27.7648i	−0.317763	−	0.977973i
$807$	20.3183			0.715239
$808$	−5.22270	−	16.0738i	−0.183734	−	0.565475i
$809$	−30.0365	−	21.8228i	−1.05603	−	0.767249i	−0.0826781	−	0.996576i	$-0.526347\pi$
$809$	−30.0365	−	21.8228i	−1.05603	−	0.767249i	−0.973349	+	0.229327i	$0.926347\pi$
$810$	0.376379	+	3.41890i	0.0132246	+	0.120128i
$811$	13.1371	−	9.54463i	0.461305	−	0.335157i	−0.332738	−	0.943019i	$-0.607973\pi$
$811$	13.1371	−	9.54463i	0.461305	−	0.335157i	0.794043	+	0.607862i	$0.207973\pi$
$812$	−0.429268	−	0.311882i	−0.0150644	−	0.0109449i
$813$	−5.58334	−	4.05654i	−0.195816	−	0.142269i
$814$	9.73151	−	7.07036i	0.341089	−	0.247816i
$815$	2.77744	+	25.2293i	0.0972893	+	0.883742i
$816$	21.5063	+	15.6252i	0.752871	+	0.546992i
$817$	5.00309	+	15.3979i	0.175036	+	0.538705i
$818$	5.35343			0.187178
$819$	0.876831	+	2.69861i	0.0306390	+	0.0942970i
$820$	2.75797	+	0.572038i	0.0963125	+	0.0199764i
$821$	4.55922	−	14.0318i	0.159118	−	0.489714i	−0.839437	−	0.543457i	$-0.817115\pi$
$821$	4.55922	−	14.0318i	0.159118	−	0.489714i	0.998555	+	0.0537429i	$0.0171151\pi$
$822$	−4.42708	+	13.6252i	−0.154412	+	0.475232i
$823$	10.1821	−	7.39772i	0.354925	−	0.257868i	−0.396007	−	0.918247i	$-0.629604\pi$
$823$	10.1821	−	7.39772i	0.354925	−	0.257868i	0.750932	+	0.660379i	$0.229604\pi$
$824$	−20.5054			−0.714338
$825$	−18.5423	+	4.13266i	−0.645561	+	0.143881i
$826$	−12.3714			−0.430457
$827$	22.3178	−	16.2148i	0.776067	−	0.563845i	−0.127729	−	0.991809i	$-0.540769\pi$
$827$	22.3178	−	16.2148i	0.776067	−	0.563845i	0.903796	+	0.427964i	$0.140769\pi$
$828$	−0.905530	+	2.78694i	−0.0314694	+	0.0968527i
$829$	−1.49145	+	4.59022i	−0.0518003	+	0.159425i	−0.973610	−	0.228217i	$-0.926710\pi$
$829$	−1.49145	+	4.59022i	−0.0518003	+	0.159425i	0.921810	+	0.387642i	$0.126710\pi$
$830$	−2.39096	−	21.7187i	−0.0829916	−	0.753866i
$831$	0.684932	+	2.10800i	0.0237600	+	0.0731258i
$832$	−17.1626			−0.595005
$833$	1.78651	+	5.49830i	0.0618988	+	0.190505i
$834$	−11.6984	−	8.49938i	−0.405082	−	0.294310i
$835$	−0.0403436	+	0.0706790i	−0.00139615	+	0.00244595i
$836$	−3.35029	+	2.43413i	−0.115872	+	0.0841860i
$837$	−5.41122	−	3.93148i	−0.187039	−	0.135892i
$838$	47.6555	+	34.6238i	1.64623	+	1.19606i
$839$	19.6492	−	14.2760i	0.678364	−	0.492861i	−0.194450	−	0.980912i	$-0.562292\pi$
$839$	19.6492	−	14.2760i	0.678364	−	0.492861i	0.872815	+	0.488052i	$0.162292\pi$
$840$	−3.78096	−	4.15780i	−0.130455	−	0.143458i
$841$	21.7621	+	15.8111i	0.750418	+	0.545211i
$842$	−8.57247	−	26.3833i	−0.295427	−	0.909230i
$843$	6.78494			0.233686
$844$	−1.58661	−	4.88309i	−0.0546134	−	0.168083i
$845$	−5.48551	+	9.61022i	−0.188707	+	0.330602i
$846$	0.521314	−	1.60444i	0.0179232	−	0.0551618i
$847$	−1.06175	+	3.26772i	−0.0364820	+	0.112280i
$848$	−38.3912	+	27.8929i	−1.31836	+	0.957845i
$849$	−23.9832			−0.823101
$850$	29.4252	−	33.3348i	1.00928	−	1.14337i
$851$	16.4740			0.564721
$852$	4.34544	−	3.15715i	0.148872	−	0.108162i
$853$	14.5880	−	44.8973i	0.499484	−	1.53725i	−0.310366	−	0.950617i	$-0.600452\pi$
$853$	14.5880	−	44.8973i	0.499484	−	1.53725i	0.809850	−	0.586637i	$-0.199548\pi$
$854$	−1.50171	+	4.62178i	−0.0513874	+	0.158154i
$855$	−6.06811	+	2.73760i	−0.207525	+	0.0936238i
$856$	−5.68824	−	17.5066i	−0.194420	−	0.598363i
$857$	−6.64636			−0.227035			−0.113518	−	0.993536i	$-0.536212\pi$
$857$	−6.64636			−0.227035			−0.113518	+	0.993536i	$0.536212\pi$
$858$	−5.12454	−	15.7717i	−0.174949	−	0.538437i
$859$	10.6417	+	7.73165i	0.363090	+	0.263801i	0.754340	−	0.656484i	$-0.227957\pi$
$859$	10.6417	+	7.73165i	0.363090	+	0.263801i	−0.391250	+	0.920285i	$0.627957\pi$
$860$	−4.05808	+	1.83078i	−0.138379	+	0.0624292i
$861$	2.78358	−	2.02239i	0.0948640	−	0.0689227i
$862$	−10.5243	−	7.64632i	−0.358458	−	0.260435i
$863$	44.4632	+	32.3044i	1.51355	+	1.09966i	0.964573	+	0.263815i	$0.0849808\pi$
$863$	44.4632	+	32.3044i	1.51355	+	1.09966i	0.548972	+	0.835841i	$0.315019\pi$
$864$	1.65559	−	1.20286i	0.0563243	−	0.0409220i
$865$	48.5726	+	10.0746i	1.65152	+	0.342546i
$866$	23.8417	+	17.3220i	0.810175	+	0.588627i
$867$	5.07495	+	15.6191i	0.172354	+	0.530452i
$868$	−2.44874			−0.0831158
$869$	1.54603	+	4.75818i	0.0524454	+	0.161410i
$870$	3.35384	+	3.68812i	0.113706	+	0.125039i
$871$	−2.98462	+	9.18572i	−0.101130	+	0.311246i
$872$	−10.1805	+	31.3323i	−0.344755	+	1.06105i
$873$	−2.05123	+	1.49030i	−0.0694236	+	0.0504392i
$874$	−36.6547			−1.23986
$875$	−8.94697	+	6.70460i	−0.302463	+	0.226657i
$876$	1.95571			0.0660773
$877$	45.0774	−	32.7507i	1.52216	−	1.10591i	0.561750	−	0.827307i	$-0.310128\pi$
$877$	45.0774	−	32.7507i	1.52216	−	1.10591i	0.960406	−	0.278604i	$-0.0898716\pi$
$878$	−16.7286	+	51.4854i	−0.564564	+	1.73755i
$879$	−9.29798	+	28.6162i	−0.313613	+	0.965202i
$880$	26.2826	+	28.9021i	0.885985	+	0.974290i
$881$	3.01688	+	9.28500i	0.101641	+	0.312820i	0.988927	−	0.148400i	$-0.0474122\pi$
$881$	3.01688	+	9.28500i	0.101641	+	0.312820i	−0.887286	+	0.461219i	$0.847412\pi$
$882$	1.53821			0.0517944
$883$	−10.4920	−	32.2910i	−0.353083	−	1.08668i	−0.957113	−	0.289716i	$-0.906439\pi$
$883$	−10.4920	−	32.2910i	−0.353083	−	1.08668i	0.604030	−	0.796962i	$-0.293561\pi$
$884$	4.85869	+	3.53004i	0.163415	+	0.118728i
$885$	17.6093	+	3.65239i	0.591929	+	0.122774i
$886$	−28.8167	+	20.9365i	−0.968115	+	0.703377i
$887$	1.23260	+	0.895536i	0.0413866	+	0.0300691i	0.608286	−	0.793718i	$-0.291857\pi$
$887$	1.23260	+	0.895536i	0.0413866	+	0.0300691i	−0.566900	+	0.823787i	$0.691857\pi$
$888$	−4.18488	−	3.04049i	−0.140435	−	0.102032i
$889$	−11.2159	+	8.14883i	−0.376169	+	0.273303i
$890$	−30.2651	+	13.6540i	−1.01449	+	0.457682i
$891$	−3.07383	−	2.23327i	−0.102977	−	0.0748172i
$892$	1.23645	+	3.80541i	0.0413996	+	0.127415i
$893$	3.26511			0.109263
$894$	11.4618	+	35.2758i	0.383340	+	1.17980i
$895$	41.7873	−	18.8521i	1.39680	−	0.630158i
$896$	−4.13983	+	12.7411i	−0.138302	+	0.425650i
$897$	7.01828	−	21.6001i	0.234334	−	0.721205i
$898$	−40.8575	+	29.6847i	−1.36343	+	0.990591i
$899$	−9.69400			−0.323313
$900$	−0.930838	−	1.57619i	−0.0310279	−	0.0525395i
$901$	−59.6638			−1.98769
$902$	−16.2683	+	11.8196i	−0.541675	+	0.393550i
$903$	−1.68051	+	5.17208i	−0.0559239	+	0.172116i
$904$	6.49706	−	19.9959i	0.216089	−	0.665054i
$905$	11.2927	−	19.7841i	0.375384	−	0.657645i
$906$	7.27412	+	22.3874i	0.241666	+	0.743772i
$907$	8.89436			0.295332			0.147666	−	0.989037i	$-0.452824\pi$
$907$	8.89436			0.295332			0.147666	+	0.989037i	$0.452824\pi$
$908$	−0.148563	−	0.457230i	−0.00493024	−	0.0151737i
$909$	−5.44038	−	3.95266i	−0.180446	−	0.131102i
$910$	−6.56615	−	7.22059i	−0.217666	−	0.239360i
$911$	−24.2790	+	17.6398i	−0.804400	+	0.584431i	−0.912202	−	0.409741i	$-0.865619\pi$
$911$	−24.2790	+	17.6398i	−0.804400	+	0.584431i	0.107801	+	0.994172i	$0.465619\pi$
$912$	11.0749	+	8.04640i	0.366727	+	0.266443i
$913$	19.5266	+	14.1869i	0.646236	+	0.469518i
$914$	−8.58798	+	6.23953i	−0.284065	+	0.206385i
$915$	3.50198	−	6.13521i	0.115772	−	0.202824i
$916$	7.24262	+	5.26207i	0.239303	+	0.173864i
$917$	−2.91422	−	8.96906i	−0.0962361	−	0.296184i
$918$	8.89281			0.293506
$919$	7.78549	+	23.9613i	0.256820	+	0.790410i	0.993466	+	0.114131i	$0.0364084\pi$
$919$	7.78549	+	23.9613i	0.256820	+	0.790410i	−0.736646	+	0.676279i	$0.763592\pi$
$920$	4.92226	+	44.7121i	0.162282	+	1.47411i
$921$	7.11799	−	21.9069i	0.234546	−	0.721858i
$922$	13.8056	−	42.4893i	0.454663	−	1.39931i
$923$	−33.6792	+	24.4694i	−1.10856	+	0.805419i
$924$	−1.39100			−0.0457606
$925$	−6.81028	+	7.71512i	−0.223921	+	0.253671i
$926$	−15.4207			−0.506754
$927$	−6.60061	+	4.79562i	−0.216792	+	0.157509i
$928$	0.916522	−	2.82076i	0.0300863	−	0.0925961i
$929$	−11.9167	+	36.6759i	−0.390975	+	1.20330i	0.541077	+	0.840973i	$0.318017\pi$
$929$	−11.9167	+	36.6759i	−0.390975	+	1.20330i	−0.932052	+	0.362325i	$0.881983\pi$
$930$	22.5265	+	4.67228i	0.738672	+	0.153210i
$931$	0.919982	+	2.83141i	0.0301512	+	0.0927959i
$932$	11.0693			0.362585
$933$	−5.61646	−	17.2857i	−0.183875	−	0.565908i
$934$	−2.97360	−	2.16044i	−0.0972990	−	0.0706919i
$935$	5.37468	+	48.8217i	0.175771	+	1.59664i
$936$	−5.76942	+	4.19173i	−0.188579	+	0.137011i
$937$	3.01446	+	2.19013i	0.0984780	+	0.0715485i	0.635935	−	0.771743i	$-0.280615\pi$
$937$	3.01446	+	2.19013i	0.0984780	+	0.0715485i	−0.537457	+	0.843291i	$0.680615\pi$
$938$	4.23592	+	3.07758i	0.138308	+	0.100486i
$939$	−24.4998	+	17.8001i	−0.799520	+	0.580886i
$940$	0.0982460	+	0.892432i	0.00320443	+	0.0291079i
$941$	−21.1197	−	15.3444i	−0.688483	−	0.500212i	0.187678	−	0.982231i	$-0.439904\pi$
$941$	−21.1197	−	15.3444i	−0.688483	−	0.500212i	−0.876161	+	0.482018i	$0.839904\pi$
$942$	−7.36058	−	22.6535i	−0.239821	−	0.738092i
$943$	−27.5398			−0.896818
$944$	−11.4280	−	35.1718i	−0.371950	−	1.14475i
$945$	−2.18947	−	0.454124i	−0.0712234	−	0.0147726i
$946$	9.82154	−	30.2276i	0.319326	−	0.982784i
$947$	14.6337	−	45.0380i	0.475532	−	1.46354i	−0.369707	−	0.929148i	$-0.620542\pi$
$947$	14.6337	−	45.0380i	0.475532	−	1.46354i	0.845239	−	0.534389i	$-0.179458\pi$
$948$	−0.390011	+	0.283359i	−0.0126670	+	0.00920309i
$949$	−15.1577			−0.492039
$950$	15.1529	−	17.1661i	0.491624	−	0.556943i
$951$	23.5812			0.764672
$952$	−11.7550	+	8.54047i	−0.380980	+	0.276798i
$953$	1.96708	−	6.05405i	0.0637200	−	0.196110i	−0.914128	−	0.405425i	$-0.867123\pi$
$953$	1.96708	−	6.05405i	0.0637200	−	0.196110i	0.977848	+	0.209315i	$0.0671235\pi$
$954$	−4.90555	+	15.0977i	−0.158823	+	0.488807i
$955$	4.47372	+	40.6377i	0.144766	+	1.31501i
$956$	2.72636	+	8.39087i	0.0881768	+	0.271380i
$957$	−5.50664			−0.178005
$958$	17.6451	+	54.3061i	0.570088	+	1.75455i
$959$	−7.53487	−	5.47440i	−0.243314	−	0.176778i
$960$	6.70466	−	11.7461i	0.216392	−	0.379103i
$961$	−11.1141	+	8.07490i	−0.358521	+	0.260481i
$962$	−7.26762	−	5.28023i	−0.234317	−	0.170242i
$963$	−5.92532	−	4.30500i	−0.190941	−	0.138727i
$964$	2.45862	−	1.78629i	0.0791868	−	0.0575326i
$965$	9.94558	+	10.9369i	0.320160	+	0.352070i
$966$	−9.96069	−	7.23687i	−0.320480	−	0.232842i
$967$	2.96565	+	9.12733i	0.0953688	+	0.293515i	0.987350	−	0.158558i	$-0.0506845\pi$
$967$	2.96565	+	9.12733i	0.0953688	+	0.293515i	−0.891981	+	0.452073i	$0.850685\pi$
$968$	−8.63534			−0.277550
$969$	5.31865	+	16.3691i	0.170860	+	0.525852i
$970$	4.32316	−	7.57386i	0.138808	−	0.243182i
$971$	1.51633	−	4.66680i	0.0486615	−	0.149765i	−0.923773	−	0.382940i	$-0.874912\pi$
$971$	1.51633	−	4.66680i	0.0486615	−	0.149765i	0.972435	+	0.233175i	$0.0749116\pi$
$972$	0.113133	−	0.348187i	0.00362873	−	0.0111681i
$973$	7.60518	−	5.52549i	0.243811	−	0.177139i
$974$	32.7929			1.05075
$975$	7.21443	+	12.2162i	0.231047	+	0.391231i
$976$	−14.5269			−0.464993
$977$	4.02130	−	2.92164i	0.128653	−	0.0934717i	−0.521598	−	0.853191i	$-0.674664\pi$
$977$	4.02130	−	2.92164i	0.128653	−	0.0934717i	0.650251	+	0.759720i	$0.274664\pi$
$978$	5.39554	−	16.6058i	0.172530	−	0.530994i
$979$	11.3337	−	34.8817i	0.362228	−	1.11482i
$980$	−0.746211	+	0.336649i	−0.0238368	+	0.0107539i
$981$	4.05068	+	12.4667i	0.129328	+	0.398031i
$982$	41.5850			1.32703
$983$	−10.2397	−	31.5147i	−0.326597	−	1.00516i	−0.970715	−	0.240235i	$-0.922775\pi$
$983$	−10.2397	−	31.5147i	−0.326597	−	1.00516i	0.644118	−	0.764926i	$-0.277225\pi$
$984$	6.99591	+	5.08283i	0.223021	+	0.162035i
$985$	−43.3801	+	19.5707i	−1.38221	+	0.623575i
$986$	10.4271	−	7.57570i	0.332065	−	0.241260i
$987$	0.887274	+	0.644643i	0.0282423	+	0.0205192i
$988$	2.50204	+	1.81784i	0.0796004	+	0.0578331i
$989$	35.2153	−	25.5854i	1.11978	−	0.813569i
$990$	12.7961	+	2.65407i	0.406687	+	0.0843520i
$991$	18.8823	+	13.7188i	0.599815	+	0.435791i	0.845813	−	0.533479i	$-0.179116\pi$
$991$	18.8823	+	13.7188i	0.599815	+	0.435791i	−0.245998	+	0.969270i	$0.579116\pi$
$992$	−4.22975	−	13.0178i	−0.134295	−	0.413317i
$993$	−31.6460			−1.00426
$994$	6.97381	+	21.4632i	0.221196	+	0.680771i
$995$	−36.2775	−	39.8932i	−1.15007	−	1.26470i
$996$	−0.718680	+	2.21187i	−0.0227722	+	0.0700857i
$997$	−11.2721	+	34.6921i	−0.356993	+	1.09871i	0.597853	+	0.801606i	$0.296021\pi$
$997$	−11.2721	+	34.6921i	−0.356993	+	1.09871i	−0.954845	+	0.297104i	$0.903979\pi$
$998$	13.4959	−	9.80531i	0.427204	−	0.310382i
$999$	−2.05818			−0.0651180

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.d.211.2	✓	32
25.16	even	5	inner	525.2.n.d.316.2	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.d.211.2	✓	32	1.1	even	1	trivial
525.2.n.d.316.2	yes	32	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.24444 + 0.904140i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.113133 - 0.348187i) q^{4} +(-1.50439 - 1.65433i) q^{5} +(0.475335 + 1.46293i) q^{6} -1.00000 q^{7} +(-0.776647 - 2.39027i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-1.24444 + 0.904140i) q^{2} +(0.309017 - 0.951057i) q^{3} +(0.113133 - 0.348187i) q^{4} +(-1.50439 - 1.65433i) q^{5} +(0.475335 + 1.46293i) q^{6} -1.00000 q^{7} +(-0.776647 - 2.39027i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(3.36787 + 0.698540i) q^{10} +(-3.07383 + 2.23327i) q^{11} +(-0.296185 - 0.215191i) q^{12} +(2.29557 + 1.66783i) q^{13} +(1.24444 - 0.904140i) q^{14} +(-2.03824 + 0.919544i) q^{15} +(3.72000 + 2.70274i) q^{16} +(1.78651 + 5.49830i) q^{17} +1.53821 q^{18} +(0.919982 + 2.83141i) q^{19} +(-0.746211 + 0.336649i) q^{20} +(-0.309017 + 0.951057i) q^{21} +(1.80601 - 5.55834i) q^{22} +(6.47549 - 4.70472i) q^{23} -2.51328 q^{24} +(-0.473621 + 4.97752i) q^{25} -4.36466 q^{26} +(-0.809017 + 0.587785i) q^{27} +(-0.113133 + 0.348187i) q^{28} +(-0.447866 + 1.37839i) q^{29} +(1.70508 - 2.98718i) q^{30} +(2.06690 + 6.36127i) q^{31} -2.04642 q^{32} +(1.17410 + 3.61350i) q^{33} +(-7.19443 - 5.22706i) q^{34} +(1.50439 + 1.65433i) q^{35} +(-0.296185 + 0.215191i) q^{36} +(1.66510 + 1.20977i) q^{37} +(-3.70486 - 2.69174i) q^{38} +(2.29557 - 1.66783i) q^{39} +(-2.78592 + 4.88073i) q^{40} +(-2.78358 - 2.02239i) q^{41} +(-0.475335 - 1.46293i) q^{42} +5.43824 q^{43} +(0.429843 + 1.32292i) q^{44} +(0.244686 + 2.22264i) q^{45} +(-3.80465 + 11.7095i) q^{46} +(0.338909 - 1.04305i) q^{47} +(3.72000 - 2.70274i) q^{48} +1.00000 q^{49} +(-3.91098 - 6.62245i) q^{50} +5.78125 q^{51} +(0.840421 - 0.610602i) q^{52} +(-3.18912 + 9.81510i) q^{53} +(0.475335 - 1.46293i) q^{54} +(8.31879 + 1.72542i) q^{55} +(0.776647 + 2.39027i) q^{56} +2.97713 q^{57} +(-0.688914 - 2.12026i) q^{58} +(-6.50669 - 4.72739i) q^{59} +(0.0895807 + 0.813720i) q^{60} +(-2.55590 + 1.85697i) q^{61} +(-8.32362 - 6.04746i) q^{62} +(0.809017 + 0.587785i) q^{63} +(-4.89335 + 3.55523i) q^{64} +(-0.694292 - 6.30671i) q^{65} +(-4.72821 - 3.43524i) q^{66} +(1.05185 + 3.23727i) q^{67} +2.11655 q^{68} +(-2.47342 - 7.61239i) q^{69} +(-3.36787 - 0.698540i) q^{70} +(-4.53370 + 13.9533i) q^{71} +(-0.776647 + 2.39027i) q^{72} +(-4.32172 + 3.13991i) q^{73} -3.16593 q^{74} +(4.58754 + 1.98858i) q^{75} +1.08994 q^{76} +(3.07383 - 2.23327i) q^{77} +(-1.34875 + 4.15104i) q^{78} +(0.406907 - 1.25233i) q^{79} +(-1.12511 - 10.2201i) q^{80} +(0.309017 + 0.951057i) q^{81} +5.29252 q^{82} +(-1.96304 - 6.04162i) q^{83} +(0.296185 + 0.215191i) q^{84} +(6.40840 - 11.2271i) q^{85} +(-6.76758 + 4.91693i) q^{86} +(1.17253 + 0.851891i) q^{87} +(7.72539 + 5.61283i) q^{88} +(-7.80956 + 5.67398i) q^{89} +(-2.31408 - 2.54472i) q^{90} +(-2.29557 - 1.66783i) q^{91} +(-0.905530 - 2.78694i) q^{92} +6.68864 q^{93} +(0.521314 + 1.60444i) q^{94} +(3.30008 - 5.78151i) q^{95} +(-0.632379 + 1.94626i) q^{96} +(0.783499 - 2.41136i) q^{97} +(-1.24444 + 0.904140i) q^{98} +3.79946 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9}+O(q^{10}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9	\( 32 q + q^{2} - 8 q^{3} - 15 q^{4} - 3 q^{5} + q^{6} - 32 q^{7} - 3 q^{8} - 8 q^{9} + 8 q^{10} + 2 q^{11} - 5 q^{12} + 12 q^{13} - q^{14} - 8 q^{15} - 17 q^{16} + 12 q^{17} - 4 q^{18} - 13 q^{19} - 27 q^{20} + 8 q^{21} - 21 q^{22} - 12 q^{23} - 18 q^{24} + 11 q^{25} - 2 q^{26} - 8 q^{27} + 15 q^{28} + 21 q^{29} - 12 q^{30} + 3 q^{31} - 50 q^{32} - 13 q^{33} - 41 q^{34} + 3 q^{35} - 5 q^{36} - 22 q^{37} + 44 q^{38} + 12 q^{39} - 39 q^{40} - 3 q^{41} - q^{42} + 24 q^{43} - 43 q^{44} + 2 q^{45} + 10 q^{46} + 8 q^{47} - 17 q^{48} + 32 q^{49} + 19 q^{50} - 8 q^{51} + 53 q^{52} + 18 q^{53} + q^{54} + 23 q^{55} + 3 q^{56} + 42 q^{57} - 32 q^{58} + 28 q^{59} + 73 q^{60} + 36 q^{61} + 10 q^{62} + 8 q^{63} + 9 q^{64} - 34 q^{65} + 4 q^{66} - 22 q^{67} - 78 q^{68} - 2 q^{69} - 8 q^{70} - 40 q^{71} - 3 q^{72} - 10 q^{73} - 34 q^{74} + 6 q^{75} + 132 q^{76} - 2 q^{77} + 28 q^{78} + 18 q^{79} + 148 q^{80} - 8 q^{81} + 102 q^{82} + 16 q^{83} + 5 q^{84} + 18 q^{85} + 16 q^{86} - 34 q^{87} + 13 q^{88} - 17 q^{89} - 2 q^{90} - 12 q^{91} - 106 q^{92} + 18 q^{93} - 20 q^{94} - 92 q^{95} - 15 q^{96} + 30 q^{97} + q^{98} + 22 q^{99}+O(q^{100}) \) 32 * q + q^2 - 8 * q^3 - 15 * q^4 - 3 * q^5 + q^6 - 32 * q^7 - 3 * q^8 - 8 * q^9 + 8 * q^10 + 2 * q^11 - 5 * q^12 + 12 * q^13 - q^14 - 8 * q^15 - 17 * q^16 + 12 * q^17 - 4 * q^18 - 13 * q^19 - 27 * q^20 + 8 * q^21 - 21 * q^22 - 12 * q^23 - 18 * q^24 + 11 * q^25 - 2 * q^26 - 8 * q^27 + 15 * q^28 + 21 * q^29 - 12 * q^30 + 3 * q^31 - 50 * q^32 - 13 * q^33 - 41 * q^34 + 3 * q^35 - 5 * q^36 - 22 * q^37 + 44 * q^38 + 12 * q^39 - 39 * q^40 - 3 * q^41 - q^42 + 24 * q^43 - 43 * q^44 + 2 * q^45 + 10 * q^46 + 8 * q^47 - 17 * q^48 + 32 * q^49 + 19 * q^50 - 8 * q^51 + 53 * q^52 + 18 * q^53 + q^54 + 23 * q^55 + 3 * q^56 + 42 * q^57 - 32 * q^58 + 28 * q^59 + 73 * q^60 + 36 * q^61 + 10 * q^62 + 8 * q^63 + 9 * q^64 - 34 * q^65 + 4 * q^66 - 22 * q^67 - 78 * q^68 - 2 * q^69 - 8 * q^70 - 40 * q^71 - 3 * q^72 - 10 * q^73 - 34 * q^74 + 6 * q^75 + 132 * q^76 - 2 * q^77 + 28 * q^78 + 18 * q^79 + 148 * q^80 - 8 * q^81 + 102 * q^82 + 16 * q^83 + 5 * q^84 + 18 * q^85 + 16 * q^86 - 34 * q^87 + 13 * q^88 - 17 * q^89 - 2 * q^90 - 12 * q^91 - 106 * q^92 + 18 * q^93 - 20 * q^94 - 92 * q^95 - 15 * q^96 + 30 * q^97 + q^98 + 22 * q^99

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