LMFDB - Embedded newform 132.2.o.b.119.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [132,2,Mod(47,132)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(132, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 8])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("132.47"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 132 = 2^{2} \cdot 3 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	132.o (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.05402530668$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	$\Q(\zeta_{20})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} + x^{4} - x^{2} + 1 $ x^8 - x^6 + x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			119.1
Root			$0.587785 - 0.809017i$ of defining polynomial
Character	$\chi$	$=$	132.119
Dual form			132.2.o.b.71.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.26007 + 0.642040i) q^{2} +(-1.45106 - 0.945746i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-0.587785 + 0.190983i) q^{5} +(2.43564 + 0.260074i) q^{6} +(-2.48990 + 3.42705i) q^{7} +(-0.442463 + 2.79360i) q^{8} +(1.21113 + 2.74466i) q^{9} +(0.618034 - 0.618034i) q^{10} +(-3.30902 - 0.224514i) q^{11} +(-3.23607 + 1.23607i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(0.937153 - 5.91695i) q^{14} +(1.03353 + 0.278768i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-5.79210 + 1.88197i) q^{17} +(-3.28829 - 2.68088i) q^{18} +(1.08981 + 1.50000i) q^{19} +(-0.381966 + 1.17557i) q^{20} +(6.85410 - 2.61803i) q^{21} +(4.31375 - 1.84162i) q^{22} +6.23607 q^{23} +(3.28408 - 3.63522i) q^{24} +(-3.73607 + 2.71441i) q^{25} +(-0.221232 - 1.39680i) q^{26} +(0.838333 - 5.12808i) q^{27} +(2.61803 + 8.05748i) q^{28} +(2.35114 - 3.23607i) q^{29} +(-1.48131 + 0.312299i) q^{30} +(-0.812299 - 0.263932i) q^{31} +(4.00000 + 4.00000i) q^{32} +(4.58924 + 3.45527i) q^{33} +(6.09017 - 6.09017i) q^{34} +(0.809017 - 2.48990i) q^{35} +(5.86472 + 1.26689i) q^{36} +(-4.66312 - 3.38795i) q^{37} +(-2.33630 - 1.19041i) q^{38} +(1.34786 - 1.08779i) q^{39} +(-0.273457 - 1.72654i) q^{40} +(0.310271 + 0.427051i) q^{41} +(-6.95579 + 7.69952i) q^{42} -1.76393i q^{43} +(-4.25325 + 5.09017i) q^{44} +(-1.23607 - 1.38197i) q^{45} +(-7.85790 + 4.00380i) q^{46} +(-3.54508 + 2.57565i) q^{47} +(-1.80423 + 6.68915i) q^{48} +(-3.38197 - 10.4086i) q^{49} +(2.96496 - 5.81906i) q^{50} +(10.1845 + 2.74701i) q^{51} +(1.17557 + 1.61803i) q^{52} +(4.89404 + 1.59017i) q^{53} +(2.23607 + 7.00000i) q^{54} +(1.98787 - 0.500000i) q^{55} +(-8.47214 - 8.47214i) q^{56} +(-0.162763 - 3.20727i) q^{57} +(-0.884927 + 5.58721i) q^{58} +(-4.73607 - 3.44095i) q^{59} +(1.66605 - 1.34458i) q^{60} +(1.57295 + 4.84104i) q^{61} +(1.19301 - 0.188954i) q^{62} +(-12.4217 - 2.68332i) q^{63} +(-7.60845 - 2.47214i) q^{64} -0.618034i q^{65} +(-8.00120 - 1.40742i) q^{66} +3.85410i q^{67} +(-3.76393 + 11.5842i) q^{68} +(-9.04889 - 5.89773i) q^{69} +(0.579192 + 3.65688i) q^{70} +(1.57295 + 4.84104i) q^{71} +(-8.20338 + 2.16901i) q^{72} +(-4.61803 - 3.35520i) q^{73} +(8.05107 + 1.27516i) q^{74} +(7.98839 - 0.405395i) q^{75} +3.70820 q^{76} +(9.00854 - 10.7812i) q^{77} +(-1.00000 + 2.23607i) q^{78} +(4.92680 + 1.60081i) q^{79} +(1.45309 + 2.00000i) q^{80} +(-6.06633 + 6.64828i) q^{81} +(-0.665148 - 0.338910i) q^{82} +(4.16312 + 12.8128i) q^{83} +(3.82141 - 14.1679i) q^{84} +(3.04508 - 2.21238i) q^{85} +(1.13251 + 2.22268i) q^{86} +(-6.47214 + 2.47214i) q^{87} +(2.09132 - 9.14475i) q^{88} +15.1803i q^{89} +(2.44481 + 0.947774i) q^{90} +(-2.48990 - 3.42705i) q^{91} +(7.33094 - 10.0902i) q^{92} +(0.929080 + 1.15121i) q^{93} +(2.81340 - 5.52160i) q^{94} +(-0.927051 - 0.673542i) q^{95} +(-2.02124 - 9.58721i) q^{96} +(-3.80902 + 11.7229i) q^{97} +(10.9443 + 10.9443i) q^{98} +(-3.39144 - 9.35405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9} - 4 q^{10} - 22 q^{11} - 8 q^{12} + 2 q^{13} + 14 q^{14} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 12 q^{20} + 28 q^{21} - 8 q^{22} + 32 q^{23} + 20 q^{24}+ \cdots + 40 q^{99}+O(q^{100}) $ 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9 - 4 * q^10 - 22 * q^11 - 8 * q^12 + 2 * q^13 + 14 * q^14 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 12 * q^20 + 28 * q^21 - 8 * q^22 + 32 * q^23 + 20 * q^24 - 12 * q^25 - 2 * q^26 + 2 * q^27 + 12 * q^28 + 32 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^35 + 8 * q^36 - 6 * q^37 - 18 * q^38 - 6 * q^39 - 8 * q^40 - 10 * q^42 + 8 * q^45 - 2 * q^46 - 6 * q^47 + 16 * q^48 - 36 * q^49 + 2 * q^50 + 28 * q^51 - 32 * q^56 - 6 * q^57 - 8 * q^58 - 20 * q^59 + 16 * q^60 + 26 * q^61 + 10 * q^62 - 28 * q^63 - 2 * q^66 - 48 * q^68 - 16 * q^69 + 8 * q^70 + 26 * q^71 - 28 * q^72 - 28 * q^73 + 6 * q^74 + 16 * q^75 - 24 * q^76 - 8 * q^78 - 2 * q^81 + 30 * q^82 + 2 * q^83 - 16 * q^84 + 2 * q^85 + 18 * q^86 - 16 * q^87 + 36 * q^88 + 22 * q^90 - 10 * q^93 + 16 * q^94 + 6 * q^95 + 8 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/132\mathbb{Z}\right)^\times$.

$n$	$13$	$67$	$89$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$-1$

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 $

$2$	−1.26007	+	0.642040i	−0.891007	+	0.453990i
$2$	−1.26007	+	0.642040i	−0.891007	+	0.453990i
$3$	−1.45106	−	0.945746i	−0.837768	−	0.546027i
$3$	−1.45106	−	0.945746i	−0.837768	−	0.546027i
$4$	1.17557	−	1.61803i	0.587785	−	0.809017i
$5$	−0.587785	+	0.190983i	−0.262866	+	0.0854102i	−0.437485	−	0.899226i	$-0.644131\pi$
$5$	−0.587785	+	0.190983i	−0.262866	+	0.0854102i	0.174619	+	0.984636i	$0.444131\pi$
$6$	2.43564	+	0.260074i	0.994348	+	0.106175i
$7$	−2.48990	+	3.42705i	−0.941093	+	1.29530i	0.0142789	+	0.999898i	$0.495455\pi$
$7$	−2.48990	+	3.42705i	−0.941093	+	1.29530i	−0.955372	+	0.295405i	$0.904545\pi$
$8$	−0.442463	+	2.79360i	−0.156434	+	0.987688i
$9$	1.21113	+	2.74466i	0.403710	+	0.914887i
$10$	0.618034	−	0.618034i	0.195440	−	0.195440i
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$11$	−3.30902	−	0.224514i	−0.997706	−	0.0676935i
$12$	−3.23607	+	1.23607i	−0.934172	+	0.356822i
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	−0.984720	−	0.174143i	$-0.944284\pi$
$13$	−0.309017	+	0.951057i	−0.0857059	+	0.263776i	0.899014	+	0.437919i	$0.144284\pi$
$14$	0.937153	−	5.91695i	0.250465	−	1.58137i
$15$	1.03353	+	0.278768i	0.266857	+	0.0719777i
$16$	−1.23607	−	3.80423i	−0.309017	−	0.951057i
$17$	−5.79210	+	1.88197i	−1.40479	+	0.456444i	−0.910736	−	0.412988i	$-0.864485\pi$
$17$	−5.79210	+	1.88197i	−1.40479	+	0.456444i	−0.494053	+	0.869432i	$0.664485\pi$
$18$	−3.28829	−	2.68088i	−0.775058	−	0.631890i
$19$	1.08981	+	1.50000i	0.250020	+	0.344124i	0.915518	−	0.402276i	$-0.131781\pi$
$19$	1.08981	+	1.50000i	0.250020	+	0.344124i	−0.665498	+	0.746400i	$0.731781\pi$
$20$	−0.381966	+	1.17557i	−0.0854102	+	0.262866i
$21$	6.85410	−	2.61803i	1.49569	−	0.571302i
$22$	4.31375	−	1.84162i	0.919695	−	0.392634i
$23$	6.23607			1.30031			0.650155	−	0.759802i	$-0.274704\pi$
$23$	6.23607			1.30031			0.650155	+	0.759802i	$0.274704\pi$
$24$	3.28408	−	3.63522i	0.670360	−	0.742036i
$25$	−3.73607	+	2.71441i	−0.747214	+	0.542882i
$26$	−0.221232	−	1.39680i	−0.0433871	−	0.273935i
$27$	0.838333	−	5.12808i	0.161337	−	0.986899i
$28$	2.61803	+	8.05748i	0.494762	+	1.52272i
$29$	2.35114	−	3.23607i	0.436596	−	0.600923i	−0.532855	−	0.846206i	$-0.678881\pi$
$29$	2.35114	−	3.23607i	0.436596	−	0.600923i	0.969451	+	0.245284i	$0.0788811\pi$
$30$	−1.48131	+	0.312299i	−0.270448	+	0.0570178i
$31$	−0.812299	−	0.263932i	−0.145893	−	0.0474036i	0.235160	−	0.971957i	$-0.424439\pi$
$31$	−0.812299	−	0.263932i	−0.145893	−	0.0474036i	−0.381053	+	0.924553i	$0.624439\pi$
$32$	4.00000	+	4.00000i	0.707107	+	0.707107i
$33$	4.58924	+	3.45527i	0.798884	+	0.601486i
$34$	6.09017	−	6.09017i	1.04446	−	1.04446i
$35$	0.809017	−	2.48990i	0.136749	−	0.420870i
$36$	5.86472	+	1.26689i	0.977454	+	0.211149i
$37$	−4.66312	−	3.38795i	−0.766612	−	0.556976i	0.134319	−	0.990938i	$-0.457115\pi$
$37$	−4.66312	−	3.38795i	−0.766612	−	0.556976i	−0.900931	+	0.433962i	$0.857115\pi$
$38$	−2.33630	−	1.19041i	−0.378999	−	0.193109i
$39$	1.34786	−	1.08779i	0.215830	−	0.174185i
$40$	−0.273457	−	1.72654i	−0.0432374	−	0.272990i
$41$	0.310271	+	0.427051i	0.0484561	+	0.0666942i	0.832558	−	0.553939i	$-0.186876\pi$
$41$	0.310271	+	0.427051i	0.0484561	+	0.0666942i	−0.784101	+	0.620633i	$0.786876\pi$
$42$	−6.95579	+	7.69952i	−1.07330	+	1.18806i
$43$		−	1.76393i		−	0.268997i	−0.990914	−	0.134499i	$-0.957058\pi$
$43$		−	1.76393i		−	0.268997i	0.990914	−	0.134499i	$-0.0429424\pi$
$44$	−4.25325	+	5.09017i	−0.641202	+	0.767372i
$45$	−1.23607	−	1.38197i	−0.184262	−	0.206011i
$46$	−7.85790	+	4.00380i	−1.15858	+	0.590328i
$47$	−3.54508	+	2.57565i	−0.517104	+	0.375698i	−0.815512	−	0.578741i	$-0.803544\pi$
$47$	−3.54508	+	2.57565i	−0.517104	+	0.375698i	0.298408	+	0.954438i	$0.403544\pi$
$48$	−1.80423	+	6.68915i	−0.260418	+	0.965496i
$49$	−3.38197	−	10.4086i	−0.483138	−	1.48695i
$50$	2.96496	−	5.81906i	0.419309	−	0.822940i
$51$	10.1845	+	2.74701i	1.42612	+	0.384658i
$52$	1.17557	+	1.61803i	0.163022	+	0.224381i
$53$	4.89404	+	1.59017i	0.672248	+	0.218427i	0.625198	−	0.780466i	$-0.285018\pi$
$53$	4.89404	+	1.59017i	0.672248	+	0.218427i	0.0470497	+	0.998893i	$0.485018\pi$
$54$	2.23607	+	7.00000i	0.304290	+	0.952579i
$55$	1.98787	−	0.500000i	0.268044	−	0.0674200i
$56$	−8.47214	−	8.47214i	−1.13214	−	1.13214i
$57$	−0.162763	−	3.20727i	−0.0215585	−	0.424813i
$58$	−0.884927	+	5.58721i	−0.116197	+	0.733636i
$59$	−4.73607	−	3.44095i	−0.616584	−	0.447974i	0.235143	−	0.971961i	$-0.424444\pi$
$59$	−4.73607	−	3.44095i	−0.616584	−	0.447974i	−0.851726	+	0.523987i	$0.824444\pi$
$60$	1.66605	−	1.34458i	0.215085	−	0.173584i
$61$	1.57295	+	4.84104i	0.201395	+	0.619832i	0.999842	+	0.0177660i	$0.00565541\pi$
$61$	1.57295	+	4.84104i	0.201395	+	0.619832i	−0.798447	+	0.602066i	$0.794345\pi$
$62$	1.19301	−	0.188954i	0.151513	−	0.0239972i
$63$	−12.4217	−	2.68332i	−1.56499	−	0.338067i
$64$	−7.60845	−	2.47214i	−0.951057	−	0.309017i
$65$		−	0.618034i		−	0.0766577i
$66$	−8.00120	−	1.40742i	−0.984879	−	0.173242i
$67$			3.85410i			0.470853i	0.971892	+	0.235427i	$0.0756488\pi$
$67$			3.85410i			0.470853i	−0.971892	+	0.235427i	$0.924351\pi$
$68$	−3.76393	+	11.5842i	−0.456444	+	1.40479i
$69$	−9.04889	−	5.89773i	−1.08936	−	0.710004i
$70$	0.579192	+	3.65688i	0.0692267	+	0.437080i
$71$	1.57295	+	4.84104i	0.186675	+	0.574526i	0.999973	−	0.00732101i	$-0.00233037\pi$
$71$	1.57295	+	4.84104i	0.186675	+	0.574526i	−0.813298	+	0.581847i	$0.802330\pi$
$72$	−8.20338	+	2.16901i	−0.966777	+	0.255620i
$73$	−4.61803	−	3.35520i	−0.540500	−	0.392696i	0.283771	−	0.958892i	$-0.408415\pi$
$73$	−4.61803	−	3.35520i	−0.540500	−	0.392696i	−0.824271	+	0.566196i	$0.808415\pi$
$74$	8.05107	+	1.27516i	0.935918	+	0.148235i
$75$	7.98839	−	0.405395i	0.922420	−	0.0468110i
$76$	3.70820			0.425360
$77$	9.00854	−	10.7812i	1.02662	−	1.22863i
$78$	−1.00000	+	2.23607i	−0.113228	+	0.253185i
$79$	4.92680	+	1.60081i	0.554308	+	0.180106i	0.572758	−	0.819724i	$-0.305873\pi$
$79$	4.92680	+	1.60081i	0.554308	+	0.180106i	−0.0184505	+	0.999830i	$0.505873\pi$
$80$	1.45309	+	2.00000i	0.162460	+	0.223607i
$81$	−6.06633	+	6.64828i	−0.674036	+	0.738698i
$82$	−0.665148	−	0.338910i	−0.0734533	−	0.0374263i
$83$	4.16312	+	12.8128i	0.456962	+	1.40638i	0.868817	+	0.495134i	$0.164881\pi$
$83$	4.16312	+	12.8128i	0.456962	+	1.40638i	−0.411855	+	0.911249i	$0.635119\pi$
$84$	3.82141	−	14.1679i	0.416950	−	1.54584i
$85$	3.04508	−	2.21238i	0.330286	−	0.239967i
$86$	1.13251	+	2.22268i	0.122122	+	0.239678i
$87$	−6.47214	+	2.47214i	−0.693886	+	0.265041i
$88$	2.09132	−	9.14475i	0.222936	−	0.974833i
$89$			15.1803i			1.60911i	0.593876	+	0.804556i	$0.297597\pi$
$89$			15.1803i			1.60911i	−0.593876	+	0.804556i	$0.702403\pi$
$90$	2.44481	+	0.947774i	0.257706	+	0.0999042i
$91$	−2.48990	−	3.42705i	−0.261012	−	0.359253i
$92$	7.33094	−	10.0902i	0.764303	−	1.05197i
$93$	0.929080	+	1.15121i	0.0963411	+	0.119375i
$94$	2.81340	−	5.52160i	0.290180	−	0.569509i
$95$	−0.927051	−	0.673542i	−0.0951134	−	0.0691039i
$96$	−2.02124	−	9.58721i	−0.206292	−	0.978490i
$97$	−3.80902	+	11.7229i	−0.386747	+	1.19029i	0.548458	+	0.836178i	$0.315215\pi$
$97$	−3.80902	+	11.7229i	−0.386747	+	1.19029i	−0.935205	+	0.354107i	$0.884785\pi$
$98$	10.9443	+	10.9443i	1.10554	+	1.10554i
$99$	−3.39144	−	9.35405i	−0.340852	−	0.940117i
$100$			9.23607i			0.923607i
$101$	−4.75528	−	1.54508i	−0.473168	−	0.153742i	0.0627190	−	0.998031i	$-0.480023\pi$
$101$	−4.75528	−	1.54508i	−0.473168	−	0.153742i	−0.535887	+	0.844290i	$0.680023\pi$
$102$	−14.5969	+	3.07743i	−1.44531	+	0.304711i
$103$	5.53483	−	7.61803i	0.545363	−	0.750627i	−0.444011	−	0.896021i	$-0.646445\pi$
$103$	5.53483	−	7.61803i	0.545363	−	0.750627i	0.989374	+	0.145394i	$0.0464450\pi$
$104$	−2.52015	−	1.28408i	−0.247121	−	0.125914i
$105$	−3.52874	+	2.84786i	−0.344370	+	0.277923i
$106$	−7.18780	+	1.13844i	−0.698141	+	0.110575i
$107$	3.42705	−	2.48990i	0.331306	−	0.240708i	−0.409679	−	0.912230i	$-0.634359\pi$
$107$	3.42705	−	2.48990i	0.331306	−	0.240708i	0.740984	+	0.671522i	$0.234359\pi$
$108$	−7.31189	−	7.38487i	−0.703587	−	0.710610i
$109$	17.2361			1.65092			0.825458	−	0.564464i	$-0.190917\pi$
$109$	17.2361			1.65092			0.825458	+	0.564464i	$0.190917\pi$
$110$	−2.18384	+	1.90633i	−0.208221	+	0.181761i
$111$	3.56231	+	9.32624i	0.338119	+	0.885207i
$112$	16.1150	+	5.23607i	1.52272	+	0.494762i
$113$	−0.587785	−	0.809017i	−0.0552942	−	0.0761059i	0.780474	−	0.625188i	$-0.214978\pi$
$113$	−0.587785	−	0.809017i	−0.0552942	−	0.0761059i	−0.835769	+	0.549082i	$0.814978\pi$
$114$	2.26429	+	3.93690i	0.212070	+	0.368724i
$115$	−3.66547	+	1.19098i	−0.341807	+	0.111060i
$116$	−2.47214	−	7.60845i	−0.229532	−	0.706427i
$117$	−2.98459	+	0.303706i	−0.275925	+	0.0280776i
$118$	8.17702	+	1.29511i	0.752756	+	0.119225i
$119$	7.97214	−	24.5357i	0.730805	−	2.24918i
$120$	−1.23607	+	2.76393i	−0.112837	+	0.252311i
$121$	10.8992	+	1.48584i	0.990835	+	0.135076i
$122$	−5.09017	−	5.09017i	−0.460842	−	0.460842i
$123$	−0.0463387	−	0.913112i	−0.00417822	−	0.0823326i
$124$	−1.38197	+	1.00406i	−0.124104	+	0.0901670i
$125$	3.49396	−	4.80902i	0.312509	−	0.430132i
$126$	17.3750	−	4.59403i	1.54789	−	0.409269i
$127$	−13.4863	+	4.38197i	−1.19672	+	0.388837i	−0.838552	−	0.544822i	$-0.816597\pi$
$127$	−13.4863	+	4.38197i	−1.19672	+	0.388837i	−0.358164	+	0.933659i	$0.616597\pi$
$128$	11.1744	−	1.76985i	0.987688	−	0.156434i
$129$	−1.66823	+	2.55957i	−0.146880	+	0.225357i
$130$	0.396802	+	0.778768i	0.0348019	+	0.0683025i
$131$	−14.3820			−1.25656			−0.628279	−	0.777988i	$-0.716240\pi$
$131$	−14.3820			−1.25656			−0.628279	+	0.777988i	$0.716240\pi$
$132$	10.9857	−	3.36363i	0.956184	−	0.292766i
$133$	−7.85410			−0.681037
$134$	−2.47449	−	4.85645i	−0.213763	−	0.419534i
$135$	0.486616	+	3.17432i	0.0418812	+	0.273202i
$136$	−2.69468	−	17.0135i	−0.231067	−	1.45890i
$137$	13.5393	−	4.39919i	1.15674	−	0.375848i	0.333062	−	0.942905i	$-0.391918\pi$
$137$	13.5393	−	4.39919i	1.15674	−	0.375848i	0.823679	+	0.567057i	$0.191918\pi$
$138$	15.1888	+	1.62184i	1.29296	+	0.138060i
$139$	−2.40414	+	3.30902i	−0.203917	+	0.280667i	−0.898711	−	0.438541i	$-0.855495\pi$
$139$	−2.40414	+	3.30902i	−0.203917	+	0.280667i	0.694794	+	0.719208i	$0.255495\pi$
$140$	−3.07768	−	4.23607i	−0.260112	−	0.358013i
$141$	7.58003	−	0.384672i	0.638354	−	0.0323952i
$142$	−5.09017	−	5.09017i	−0.427158	−	0.427158i
$143$	1.23607	−	3.07768i	0.103365	−	0.257369i
$144$	8.94427	−	8.00000i	0.745356	−	0.666667i
$145$	−0.763932	+	2.35114i	−0.0634411	+	0.195252i
$146$	7.97323	+	1.26284i	0.659869	+	0.104513i
$147$	−4.93649	+	18.3020i	−0.407154	+	1.50952i
$148$	−10.9637	+	3.56231i	−0.901206	+	0.292820i
$149$	−10.1841	+	3.30902i	−0.834315	+	0.271085i	−0.694862	−	0.719143i	$-0.744534\pi$
$149$	−10.1841	+	3.30902i	−0.834315	+	0.271085i	−0.139453	+	0.990229i	$0.544534\pi$
$150$	−9.80568	+	5.63969i	−0.800630	+	0.460479i
$151$	8.50651	+	11.7082i	0.692250	+	0.952800i	0.999999	+	0.00133264i	$0.000424193\pi$
$151$	8.50651	+	11.7082i	0.692250	+	0.952800i	−0.307749	+	0.951467i	$0.599576\pi$
$152$	−4.67261	+	2.38081i	−0.378999	+	0.193109i
$153$	−12.1803	−	13.6180i	−0.984722	−	1.10095i
$154$	−4.42949	+	19.3689i	−0.356939	+	1.56079i
$155$	0.527864			0.0423991
$156$	−0.175571	−	3.45965i	−0.0140569	−	0.276994i
$157$	5.23607	−	3.80423i	0.417884	−	0.303610i	−0.358902	−	0.933375i	$-0.616849\pi$
$157$	5.23607	−	3.80423i	0.417884	−	0.303610i	0.776786	+	0.629765i	$0.216849\pi$
$158$	−7.23591	+	1.14606i	−0.575658	+	0.0911753i
$159$	−5.59763	−	6.93594i	−0.443921	−	0.550056i
$160$	−3.11507	−	1.58721i	−0.246268	−	0.125480i
$161$	−15.5272	+	21.3713i	−1.22371	+	1.68430i
$162$	3.37556	−	12.2721i	0.265209	−	0.964191i
$163$	−7.24518	−	2.35410i	−0.567486	−	0.184387i	0.0112006	−	0.999937i	$-0.496435\pi$
$163$	−7.24518	−	2.35410i	−0.567486	−	0.184387i	−0.578687	+	0.815550i	$0.696435\pi$
$164$	1.05573			0.0824385
$165$	−3.35738	−	1.15449i	−0.261372	−	0.0898770i
$166$	−13.4721	−	13.4721i	−1.04564	−	1.04564i
$167$	−1.04508	+	3.21644i	−0.0808711	+	0.248896i	−0.983315	−	0.181912i	$-0.941771\pi$
$167$	−1.04508	+	3.21644i	−0.0808711	+	0.248896i	0.902444	+	0.430808i	$0.141771\pi$
$168$	4.28106	+	20.3060i	0.330291	+	1.56664i
$169$	9.70820	+	7.05342i	0.746785	+	0.542571i
$170$	−2.41659	+	4.74283i	−0.185344	+	0.363759i
$171$	−2.79709	+	4.80786i	−0.213898	+	0.367667i
$172$	−2.85410	−	2.07363i	−0.217623	−	0.158113i
$173$	−12.2250	−	16.8262i	−0.929448	−	1.27928i	−0.960075	−	0.279744i	$-0.909750\pi$
$173$	−12.2250	−	16.8262i	−0.929448	−	1.27928i	0.0306267	−	0.999531i	$-0.490250\pi$
$174$	6.56816	−	7.27044i	0.497931	−	0.551171i
$175$		−	19.5623i		−	1.47877i
$176$	3.23607	+	12.8658i	0.243928	+	0.969793i
$177$	3.61803	+	9.47214i	0.271948	+	0.711969i
$178$	−9.74638	−	19.1283i	−0.730522	−	1.43373i
$179$	−14.8992	+	10.8249i	−1.11362	+	0.809090i	−0.983230	−	0.182373i	$-0.941622\pi$
$179$	−14.8992	+	10.8249i	−1.11362	+	0.809090i	−0.130388	+	0.991463i	$0.541622\pi$
$180$	−3.68915	+	0.375402i	−0.274973	+	0.0279808i
$181$	6.63525	+	20.4212i	0.493195	+	1.51790i	0.819751	+	0.572719i	$0.194112\pi$
$181$	6.63525	+	20.4212i	0.493195	+	1.51790i	−0.326557	+	0.945178i	$0.605888\pi$
$182$	5.33776	+	2.71972i	0.395661	+	0.201599i
$183$	2.29595	−	8.51223i	0.169722	−	0.629242i
$184$	−2.75923	+	17.4211i	−0.203413	+	1.28430i
$185$	3.38795	+	1.10081i	0.249087	+	0.0809334i
$186$	−1.90983	−	0.854102i	−0.140036	−	0.0626258i
$187$	19.5887	−	4.92705i	1.43247	−	0.360302i
$188$			8.76393i			0.639175i
$189$	15.4868	+	15.6414i	1.12650	+	1.13774i
$190$	1.60059	+	0.253509i	0.116119	+	0.0183915i
$191$	13.2812	+	9.64932i	0.960991	+	0.698200i	0.953381	−	0.301771i	$-0.0975777\pi$
$191$	13.2812	+	9.64932i	0.960991	+	0.698200i	0.00760993	+	0.999971i	$0.497578\pi$
$192$	8.70228	+	10.7829i	0.628033	+	0.778187i
$193$	−4.02786	−	12.3965i	−0.289932	−	0.892319i	−0.984877	−	0.173256i	$-0.944571\pi$
$193$	−4.02786	−	12.3965i	−0.289932	−	0.892319i	0.694945	−	0.719063i	$-0.255429\pi$
$194$	−2.72696	−	17.2173i	−0.195784	−	1.23613i
$195$	−0.584503	+	0.896802i	−0.0418571	+	0.0642213i
$196$	−20.8172	−	6.76393i	−1.48695	−	0.483138i
$197$			4.38197i			0.312202i	0.987741	+	0.156101i	$0.0498926\pi$
$197$			4.38197i			0.312202i	−0.987741	+	0.156101i	$0.950107\pi$
$198$	10.2791	+	9.60935i	0.730506	+	0.682907i
$199$		−	19.9443i		−	1.41381i	−0.707308	−	0.706906i	$-0.750090\pi$
$199$		−	19.9443i		−	1.41381i	0.707308	−	0.706906i	$-0.249910\pi$
$200$	−5.92992	−	11.6381i	−0.419309	−	0.822940i
$201$	3.64500	−	5.59252i	0.257099	−	0.394466i
$202$	6.98401	−	1.10616i	0.491393	−	0.0778291i
$203$	5.23607	+	16.1150i	0.367500	+	1.13105i
$204$	16.4174	−	13.2496i	1.14945	−	0.927657i
$205$	−0.263932	−	0.191758i	−0.0184338	−	0.0133929i
$206$	−2.08321	+	13.1529i	−0.145144	+	0.916403i
$207$	7.55269	+	17.1159i	0.524948	+	1.18964i
$208$	4.00000			0.277350
$209$	−3.26944	−	5.20820i	−0.226152	−	0.360259i
$210$	2.61803	−	5.85410i	0.180662	−	0.403971i
$211$	−12.9515	−	4.20820i	−0.891619	−	0.289705i	−0.172846	−	0.984949i	$-0.555296\pi$
$211$	−12.9515	−	4.20820i	−0.891619	−	0.289705i	−0.718774	+	0.695244i	$0.755296\pi$
$212$	8.32624	−	6.04937i	0.571848	−	0.415472i
$213$	2.29595	−	8.51223i	0.157316	−	0.583248i
$214$	−2.71972	+	5.33776i	−0.185916	+	0.364882i
$215$	0.336881	+	1.03681i	0.0229751	+	0.0707101i
$216$	13.9549	+	4.61096i	0.949510	+	0.313736i
$217$	2.92705	−	2.12663i	0.198701	−	0.144365i
$218$	−21.7187	+	11.0662i	−1.47098	+	0.749500i
$219$	3.52786	+	9.23607i	0.238391	+	0.624116i
$220$	1.52786	−	3.80423i	0.103009	−	0.256481i
$221$		−	6.09017i		−	0.409669i
$222$	−10.4766	−	9.46460i	−0.703142	−	0.635223i
$223$	4.28601	+	5.89919i	0.287012	+	0.395039i	0.928041	−	0.372478i	$-0.121492\pi$
$223$	4.28601	+	5.89919i	0.287012	+	0.395039i	−0.641028	+	0.767517i	$0.721492\pi$
$224$	−23.6678	+	3.74861i	−1.58137	+	0.250465i
$225$	−11.9750	−	6.96673i	−0.798334	−	0.464449i
$226$	1.26007	+	0.642040i	0.0838188	+	0.0427078i
$227$	−13.2812	−	9.64932i	−0.881501	−	0.640448i	0.0521471	−	0.998639i	$-0.483394\pi$
$227$	−13.2812	−	9.64932i	−0.881501	−	0.640448i	−0.933648	+	0.358191i	$0.883394\pi$
$228$	−5.38081	−	3.50702i	−0.356353	−	0.232258i
$229$	4.14590	−	12.7598i	0.273969	−	0.843189i	−0.715522	−	0.698590i	$-0.753811\pi$
$229$	4.14590	−	12.7598i	0.273969	−	0.843189i	0.989490	−	0.144598i	$-0.0461890\pi$
$230$	3.85410	−	3.85410i	0.254132	−	0.254132i
$231$	−23.2681	+	7.12428i	−1.53093	+	0.468743i
$232$	8.00000	+	8.00000i	0.525226	+	0.525226i
$233$	−1.48584	−	0.482779i	−0.0973407	−	0.0316279i	0.259942	−	0.965624i	$-0.416297\pi$
$233$	−1.48584	−	0.482779i	−0.0973407	−	0.0316279i	−0.357282	+	0.933996i	$0.616297\pi$
$234$	3.56581	−	2.29892i	0.233104	−	0.150285i
$235$	1.59184	−	2.19098i	0.103840	−	0.142924i
$236$	−11.1352	+	3.61803i	−0.724837	+	0.235514i
$237$	−5.63510	−	6.98237i	−0.366039	−	0.453553i
$238$	5.70742	+	36.0352i	0.369957	+	2.33582i
$239$	11.5451	−	8.38800i	0.746789	−	0.542574i	−0.148041	−	0.988981i	$-0.547297\pi$
$239$	11.5451	−	8.38800i	0.746789	−	0.542574i	0.894830	+	0.446407i	$0.147297\pi$
$240$	−0.217017	−	4.27636i	−0.0140084	−	0.276038i
$241$	−21.4164			−1.37955			−0.689776	−	0.724023i	$-0.742291\pi$
$241$	−21.4164			−1.37955			−0.689776	+	0.724023i	$0.742291\pi$
$242$	−14.6877	+	5.12544i	−0.944164	+	0.329476i
$243$	15.0902	−	3.90983i	0.968035	−	0.250816i
$244$	9.68208	+	3.14590i	0.619832	+	0.201395i
$245$	3.97574	+	5.47214i	0.254001	+	0.349602i
$246$	0.644644	+	1.12084i	0.0411010	+	0.0714620i
$247$	−1.76336	+	0.572949i	−0.112200	+	0.0364559i
$248$	1.09673	−	2.15246i	0.0696427	−	0.136682i
$249$	6.07669	−	22.5293i	0.385095	−	1.42774i
$250$	−1.31506	+	8.30297i	−0.0831718	+	0.525126i
$251$	2.06231	−	6.34712i	0.130172	−	0.400627i	−0.864636	−	0.502398i	$-0.832451\pi$
$251$	2.06231	−	6.34712i	0.130172	−	0.400627i	0.994808	+	0.101772i	$0.0324511\pi$
$252$	−18.9443	+	16.9443i	−1.19338	+	1.06739i
$253$	−20.6353	−	1.40008i	−1.29733	−	0.0880226i
$254$	14.1803	−	14.1803i	0.889754	−	0.889754i
$255$	−6.51094	+	0.330418i	−0.407731	+	0.0206916i
$256$	−12.9443	+	9.40456i	−0.809017	+	0.587785i
$257$	3.26944	−	4.50000i	0.203942	−	0.280702i	−0.694779	−	0.719224i	$-0.744498\pi$
$257$	3.26944	−	4.50000i	0.203942	−	0.280702i	0.898721	+	0.438521i	$0.144498\pi$
$258$	0.458752	−	4.29631i	0.0285607	−	0.267477i
$259$	23.2214	−	7.54508i	1.44291	−	0.468829i
$260$	−1.00000	−	0.726543i	−0.0620174	−	0.0450583i
$261$	11.7294	+	2.53379i	0.726035	+	0.156837i
$262$	18.1223	−	9.23379i	1.11960	−	0.570465i
$263$	−1.85410			−0.114329			−0.0571644	−	0.998365i	$-0.518206\pi$
$263$	−1.85410			−0.114329			−0.0571644	+	0.998365i	$0.518206\pi$
$264$	−11.6832	+	11.2917i	−0.719053	+	0.694955i
$265$	−3.18034			−0.195367
$266$	9.89675	−	5.04264i	0.606808	−	0.309184i
$267$	14.3567	−	22.0275i	0.878618	−	1.34806i
$268$	6.23607	+	4.53077i	0.380928	+	0.276761i
$269$	2.07363	−	0.673762i	0.126431	−	0.0410800i	−0.245118	−	0.969493i	$-0.578827\pi$
$269$	2.07363	−	0.673762i	0.126431	−	0.0410800i	0.371549	+	0.928413i	$0.378827\pi$
$270$	−2.65121	−	3.68745i	−0.161347	−	0.224411i
$271$	−6.69015	+	9.20820i	−0.406398	+	0.559359i	−0.962335	−	0.271866i	$-0.912359\pi$
$271$	−6.69015	+	9.20820i	−0.406398	+	0.559359i	0.555937	+	0.831224i	$0.312359\pi$
$272$	14.3188	+	19.7082i	0.868208	+	1.19499i
$273$	0.371864	+	7.32766i	0.0225063	+	0.443490i
$274$	−14.2361	+	14.2361i	−0.860032	+	0.860032i
$275$	12.9721	−	8.14324i	0.782249	−	0.491056i
$276$	−20.1803	+	7.70820i	−1.21471	+	0.463979i
$277$	4.44427	−	13.6781i	0.267030	−	0.821835i	−0.724188	−	0.689602i	$-0.757785\pi$
$277$	4.44427	−	13.6781i	0.267030	−	0.821835i	0.991219	−	0.132233i	$-0.0422146\pi$
$278$	0.904875	−	5.71316i	0.0542708	−	0.342652i
$279$	−0.259396	−	2.54914i	−0.0155296	−	0.152613i
$280$	6.59783	+	3.36176i	0.394296	+	0.200904i
$281$	15.3884	−	5.00000i	0.917996	−	0.298275i	0.188352	−	0.982102i	$-0.439686\pi$
$281$	15.3884	−	5.00000i	0.917996	−	0.298275i	0.729644	+	0.683827i	$0.239686\pi$
$282$	−9.30442	+	5.35140i	−0.554070	+	0.318671i
$283$	0.106001	+	0.145898i	0.00630111	+	0.00867274i	0.812156	−	0.583440i	$-0.198294\pi$
$283$	0.106001	+	0.145898i	0.00630111	+	0.00867274i	−0.805855	+	0.592113i	$0.798294\pi$
$284$	9.68208	+	3.14590i	0.574526	+	0.186675i
$285$	0.708204	+	1.85410i	0.0419504	+	0.109828i
$286$	0.418458	+	4.67171i	0.0247439	+	0.276244i
$287$	−2.23607			−0.131991
$288$	−6.13412	+	15.8232i	−0.361457	+	0.932389i
$289$	16.2533	−	11.8087i	0.956076	−	0.694630i
$290$	−0.546915	−	3.45309i	−0.0321160	−	0.202772i
$291$	16.6140	−	13.4083i	0.973932	−	0.786008i
$292$	−10.8576	+	3.52786i	−0.635396	+	0.206453i
$293$	−13.1760	+	18.1353i	−0.769752	+	1.05947i	0.226588	+	0.973991i	$0.427243\pi$
$293$	−13.1760	+	18.1353i	−0.769752	+	1.05947i	−0.996340	+	0.0854821i	$0.972757\pi$
$294$	−5.53026	−	26.2313i	−0.322531	−	1.52984i
$295$	3.44095	+	1.11803i	0.200340	+	0.0650945i
$296$	11.5279	−	11.5279i	0.670043	−	0.670043i
$297$	−3.92538	+	16.7807i	−0.227774	+	0.973714i
$298$	10.7082	−	10.7082i	0.620310	−	0.620310i
$299$	−1.92705	+	5.93085i	−0.111444	+	0.342990i
$300$	8.73497	−	13.4021i	0.504314	−	0.773768i
$301$	6.04508	+	4.39201i	0.348433	+	0.253151i
$302$	−18.2360	−	9.29168i	−1.04936	−	0.534676i
$303$	5.43893	+	6.73929i	0.312458	+	0.387162i
$304$	4.35926	−	6.00000i	0.250020	−	0.344124i
$305$	−1.84911	−	2.54508i	−0.105880	−	0.145731i
$306$	24.0914	+	9.33946i	1.37722	+	0.533902i
$307$			1.61803i			0.0923461i	0.998933	+	0.0461730i	$0.0147026\pi$
$307$			1.61803i			0.0923461i	−0.998933	+	0.0461730i	$0.985297\pi$
$308$	−6.85410	−	27.2501i	−0.390549	−	1.55272i
$309$	−15.2361	+	5.81966i	−0.866750	+	0.331069i
$310$	−0.665148	+	0.338910i	−0.0377778	+	0.0192488i
$311$	2.95492	−	2.14687i	0.167558	−	0.121738i	−0.500846	−	0.865536i	$-0.666978\pi$
$311$	2.95492	−	2.14687i	0.167558	−	0.121738i	0.668404	+	0.743798i	$0.266978\pi$
$312$	2.44246	+	4.24669i	0.138277	+	0.240421i
$313$	2.45492	+	7.55545i	0.138760	+	0.427059i	0.996156	−	0.0875981i	$-0.0279191\pi$
$313$	2.45492	+	7.55545i	0.138760	+	0.427059i	−0.857396	+	0.514657i	$0.827919\pi$
$314$	−4.15537	+	8.15537i	−0.234501	+	0.460234i
$315$	7.81375	−	0.795113i	0.440255	−	0.0447996i
$316$	8.38197	−	6.08985i	0.471522	−	0.342581i
$317$	8.73102	+	2.83688i	0.490383	+	0.159335i	0.543762	−	0.839239i	$-0.316999\pi$
$317$	8.73102	+	2.83688i	0.490383	+	0.159335i	−0.0533794	+	0.998574i	$0.516999\pi$
$318$	11.5066	+	5.14590i	0.645257	+	0.288568i
$319$	−8.50651	+	10.1803i	−0.476273	+	0.569990i
$320$	4.94427			0.276393
$321$	−7.32766	+	0.371864i	−0.408990	+	0.0207554i
$322$	5.84415	−	36.8985i	0.325682	−	2.05627i
$323$	−9.13525	−	6.63715i	−0.508299	−	0.369301i
$324$	3.62575	+	17.6311i	0.201431	+	0.979503i
$325$	−1.42705	−	4.39201i	−0.0791585	−	0.243625i
$326$	10.6409	−	1.68535i	0.589344	−	0.0933430i
$327$	−25.0105	−	16.3009i	−1.38308	−	0.901444i
$328$	−1.33030	+	0.677819i	−0.0734533	+	0.0374263i
$329$		−	18.5623i		−	1.02337i
$330$	4.97178	−	0.700830i	0.273687	−	0.0385794i
$331$			26.7082i			1.46802i	0.679141	+	0.734008i	$0.262352\pi$
$331$			26.7082i			1.46802i	−0.679141	+	0.734008i	$0.737648\pi$
$332$	25.6255	+	8.32624i	1.40638	+	0.456962i
$333$	3.65114	−	16.9019i	0.200081	−	0.926220i
$334$	−0.748198	−	4.72394i	−0.0409396	−	0.258482i
$335$	−0.736068	−	2.26538i	−0.0402157	−	0.123771i
$336$	−18.4317	−	22.8385i	−1.00553	−	1.24594i
$337$	21.0902	+	15.3229i	1.14885	+	0.834692i	0.988328	−	0.152340i	$-0.0486808\pi$
$337$	21.0902	+	15.3229i	1.14885	+	0.834692i	0.160527	+	0.987032i	$0.448681\pi$
$338$	−16.7616	−	2.65478i	−0.911712	−	0.144401i
$339$	0.0877853	+	1.72982i	0.00476784	+	0.0939512i
$340$		−	7.52786i		−	0.408256i
$341$	2.62866	+	1.05573i	0.142350	+	0.0571709i
$342$	0.437694	−	7.85410i	0.0236678	−	0.424701i
$343$	15.8904	+	5.16312i	0.858003	+	0.278782i
$344$	4.92773	+	0.780476i	0.265685	+	0.0420804i
$345$	6.44517	+	1.73842i	0.346996	+	0.0935933i
$346$	26.2075	+	13.3534i	1.40892	+	0.717882i
$347$	−2.20163	−	6.77591i	−0.118189	−	0.363750i	0.874409	−	0.485189i	$-0.161249\pi$
$347$	−2.20163	−	6.77591i	−0.118189	−	0.363750i	−0.992599	+	0.121439i	$0.961249\pi$
$348$	−3.60845	+	13.3783i	−0.193433	+	0.717152i
$349$	−20.2254	+	14.6946i	−1.08264	+	0.786586i	−0.978142	−	0.207939i	$-0.933324\pi$
$349$	−20.2254	+	14.6946i	−1.08264	+	0.786586i	−0.104500	+	0.994525i	$0.533324\pi$
$350$	12.5598	+	24.6499i	0.671348	+	1.31759i
$351$	4.61803	+	2.38197i	0.246492	+	0.127140i
$352$	−12.3380	−	14.1341i	−0.657618	−	0.753351i
$353$		−	2.29180i		−	0.121980i	−0.998138	−	0.0609900i	$-0.980574\pi$
$353$		−	2.29180i		−	0.121980i	0.998138	−	0.0609900i	$-0.0194258\pi$
$354$	−10.6405	−	9.61267i	−0.565535	−	0.510907i
$355$	−1.84911	−	2.54508i	−0.0981407	−	0.135079i
$356$	24.5623	+	17.8456i	1.30180	+	0.945813i
$357$	−34.7726	+	28.0631i	−1.84036	+	1.48526i
$358$	11.8241	−	23.2060i	0.624921	−	1.22648i
$359$	14.4721	+	10.5146i	0.763810	+	0.554941i	0.900077	−	0.435732i	$-0.143510\pi$
$359$	14.4721	+	10.5146i	0.763810	+	0.554941i	−0.136266	+	0.990672i	$0.543510\pi$
$360$	4.40758	−	2.84162i	0.232300	−	0.149766i
$361$	4.80902	−	14.8006i	0.253106	−	0.778981i
$362$	−21.4721	−	21.4721i	−1.12855	−	1.12855i
$363$	−14.4101	−	12.4639i	−0.756335	−	0.654185i
$364$	−8.47214			−0.444061
$365$	3.35520	+	1.09017i	0.175619	+	0.0570621i
$366$	2.57212	+	12.2001i	0.134447	+	0.637711i
$367$	−1.36733	+	1.88197i	−0.0713740	+	0.0982378i	−0.843211	−	0.537582i	$-0.819338\pi$
$367$	−1.36733	+	1.88197i	−0.0713740	+	0.0982378i	0.771838	+	0.635820i	$0.219338\pi$
$368$	−7.70820	−	23.7234i	−0.401818	−	1.23667i
$369$	−0.796332	+	1.36880i	−0.0414554	+	0.0712570i
$370$	−4.97584	+	0.788095i	−0.258681	+	0.0409711i
$371$	−17.6353	+	12.8128i	−0.915577	+	0.665205i
$372$	2.95489	−	0.149955i	0.153204	−	0.00777481i
$373$	−16.5279			−0.855780			−0.427890	−	0.903831i	$-0.640743\pi$
$373$	−16.5279			−0.855780			−0.427890	+	0.903831i	$0.640743\pi$
$374$	−21.5198	+	18.7851i	−1.11276	+	0.971357i
$375$	−9.61803	+	3.67376i	−0.496673	+	0.189712i
$376$	−5.62679	−	11.0432i	−0.290180	−	0.569509i
$377$	2.35114	+	3.23607i	0.121090	+	0.166666i
$378$	−29.5569	−	9.76617i	−1.52024	−	0.502318i
$379$	−13.8168	+	4.48936i	−0.709722	+	0.230603i	−0.641562	−	0.767072i	$-0.721713\pi$
$379$	−13.8168	+	4.48936i	−0.709722	+	0.230603i	−0.0681608	+	0.997674i	$0.521713\pi$
$380$	−2.17963	+	0.708204i	−0.111813	+	0.0363301i
$381$	23.7136	+	6.39613i	1.21489	+	0.327684i
$382$	−22.9305	−	3.63183i	−1.17323	−	0.185821i
$383$	−5.10739	+	15.7189i	−0.260975	+	0.803200i	0.731618	+	0.681715i	$0.238766\pi$
$383$	−5.10739	+	15.7189i	−0.260975	+	0.803200i	−0.992593	+	0.121485i	$0.961234\pi$
$384$	−17.8885	−	8.00000i	−0.912871	−	0.408248i
$385$	−3.23607	+	8.05748i	−0.164925	+	0.410647i
$386$	13.0344	+	13.0344i	0.663436	+	0.663436i
$387$	4.84140	−	2.13635i	0.246102	−	0.108597i
$388$	14.4904	+	19.9443i	0.735637	+	1.01252i
$389$	−21.6623	+	29.8156i	−1.09832	+	1.51171i	−0.260732	+	0.965411i	$0.583964\pi$
$389$	−21.6623	+	29.8156i	−1.09832	+	1.51171i	−0.837590	+	0.546299i	$0.816036\pi$
$390$	0.160734	−	1.50531i	0.00813910	−	0.0762244i
$391$	−36.1199	+	11.7361i	−1.82666	+	0.593518i
$392$	30.5740	−	4.84244i	1.54422	−	0.244580i
$393$	20.8690	+	13.6017i	1.05270	+	0.686114i
$394$	−2.81340	−	5.52160i	−0.141737	−	0.278174i
$395$	−3.20163			−0.161091
$396$	−19.1220	−	5.50888i	−0.960918	−	0.276832i
$397$	7.47214			0.375016			0.187508	−	0.982263i	$-0.439959\pi$
$397$	7.47214			0.375016			0.187508	+	0.982263i	$0.439959\pi$
$398$	12.8050	+	25.1312i	0.641857	+	1.25972i
$399$	11.3967	+	7.42798i	0.570551	+	0.371864i
$400$	14.9443	+	10.8576i	0.747214	+	0.542882i
$401$	16.2007	−	5.26393i	0.809025	−	0.262868i	0.124840	−	0.992177i	$-0.460158\pi$
$401$	16.2007	−	5.26393i	0.809025	−	0.262868i	0.684185	+	0.729309i	$0.260158\pi$
$402$	−1.00235	+	9.38722i	−0.0499927	+	0.468192i
$403$	0.502029	−	0.690983i	0.0250078	−	0.0344203i
$404$	−8.09017	+	5.87785i	−0.402501	+	0.292434i
$405$	2.29599	−	5.06633i	0.114089	−	0.251748i
$406$	−16.9443	−	16.9443i	−0.840930	−	0.840930i
$407$	14.6697	+	12.2577i	0.727150	+	0.607593i
$408$	−12.1803	+	27.2361i	−0.603017	+	1.34839i
$409$	−5.65248	+	17.3965i	−0.279497	+	0.860203i	0.708497	+	0.705713i	$0.249373\pi$
$409$	−5.65248	+	17.3965i	−0.279497	+	0.860203i	−0.987994	+	0.154490i	$0.950627\pi$
$410$	0.455690	+	0.0721742i	0.0225049	+	0.00356443i
$411$	−23.8068	−	6.42127i	−1.17430	−	0.316738i
$412$	−5.81966	−	17.9111i	−0.286714	−	0.882415i
$413$	23.5847	−	7.66312i	1.16053	−	0.377077i
$414$	−20.5060	−	16.7182i	−1.00782	−	0.821653i
$415$	−4.89404	−	6.73607i	−0.240239	−	0.330661i
$416$	−5.04029	+	2.56816i	−0.247121	+	0.125914i
$417$	6.61803	−	2.52786i	0.324087	−	0.123790i
$418$	7.46361	+	4.46361i	0.365057	+	0.218322i
$419$	−22.0344			−1.07645			−0.538226	−	0.842800i	$-0.680905\pi$
$419$	−22.0344			−1.07645			−0.538226	+	0.842800i	$0.680905\pi$
$420$	0.459650	+	9.05748i	0.0224286	+	0.441960i
$421$	−9.97214	+	7.24518i	−0.486012	+	0.353109i	−0.803649	−	0.595104i	$-0.797111\pi$
$421$	−9.97214	+	7.24518i	−0.486012	+	0.353109i	0.317636	+	0.948213i	$0.397111\pi$
$422$	19.0217	−	3.01274i	0.925962	−	0.146658i
$423$	−11.3629	−	6.61060i	−0.552481	−	0.321419i
$424$	−6.60774	+	12.9684i	−0.320900	+	0.629802i
$425$	16.5312	−	22.7533i	0.801883	−	1.10370i
$426$	2.57212	+	12.2001i	0.124620	+	0.591098i
$427$	−20.5070	−	6.66312i	−0.992402	−	0.322451i
$428$		−	8.47214i		−	0.409516i
$429$	−4.70431	+	3.29689i	−0.227126	+	0.159175i
$430$	−1.09017	−	1.09017i	−0.0525727	−	0.0525727i
$431$	7.26393	−	22.3561i	0.349891	−	1.07685i	−0.609022	−	0.793154i	$-0.708438\pi$
$431$	7.26393	−	22.3561i	0.349891	−	1.07685i	0.958913	−	0.283701i	$-0.0915623\pi$
$432$	−20.5446	+	3.14945i	−0.988453	+	0.151528i
$433$	−20.7984	−	15.1109i	−0.999506	−	0.726184i	−0.0375238	−	0.999296i	$-0.511947\pi$
$433$	−20.7984	−	15.1109i	−0.999506	−	0.726184i	−0.961982	+	0.273112i	$0.911947\pi$
$434$	−2.32292	+	4.55899i	−0.111504	+	0.218838i
$435$	3.33209	−	2.68915i	0.159761	−	0.128935i
$436$	20.2622	−	27.8885i	0.970384	−	1.33562i
$437$	6.79615	+	9.35410i	0.325104	+	0.447467i
$438$	−10.3753	−	9.37310i	−0.495750	−	0.447864i
$439$			21.3607i			1.01949i	0.860326	+	0.509745i	$0.170260\pi$
$439$			21.3607i			1.01949i	−0.860326	+	0.509745i	$0.829740\pi$
$440$	0.517242	+	5.77455i	0.0246586	+	0.275291i
$441$	24.4721	−	21.8885i	1.16534	−	1.04231i
$442$	3.91013	+	7.67406i	0.185986	+	0.365018i
$443$	−2.38197	+	1.73060i	−0.113171	+	0.0822233i	−0.642931	−	0.765924i	$-0.722282\pi$
$443$	−2.38197	+	1.73060i	−0.113171	+	0.0822233i	0.529760	+	0.848147i	$0.322282\pi$
$444$	19.2779	+	5.19972i	0.914889	+	0.246768i
$445$	−2.89919	−	8.92278i	−0.137435	−	0.422980i
$446$	−9.18820	−	4.68162i	−0.435074	−	0.221681i
$447$	17.9072	+	4.83001i	0.846982	+	0.228451i
$448$	27.4164	−	19.9192i	1.29530	−	0.941093i
$449$	−36.4832	−	11.8541i	−1.72175	−	0.559430i	−0.729530	−	0.683949i	$-0.760261\pi$
$449$	−36.4832	−	11.8541i	−1.72175	−	0.559430i	−0.992217	+	0.124519i	$0.960261\pi$
$450$	19.5623	+	1.09017i	0.922176	+	0.0513911i
$451$	−0.930812	−	1.48278i	−0.0438302	−	0.0698213i
$452$	−2.00000			−0.0940721
$453$	−1.27044	−	25.0343i	−0.0596905	−	1.17621i
$454$	22.9305	+	3.63183i	1.07618	+	0.170450i
$455$	2.11803	+	1.53884i	0.0992950	+	0.0721420i
$456$	9.03186	+	0.964406i	0.422956	+	0.0451624i
$457$	−0.354102	−	1.08981i	−0.0165642	−	0.0509793i	0.942433	−	0.334396i	$-0.108532\pi$
$457$	−0.354102	−	1.08981i	−0.0165642	−	0.0509793i	−0.958997	+	0.283416i	$0.908532\pi$
$458$	2.96814	+	18.7401i	0.138692	+	0.875666i
$459$	4.79516	+	31.2800i	0.223819	+	1.46003i
$460$	−2.38197	+	7.33094i	−0.111060	+	0.341807i
$461$			25.8541i			1.20415i	0.798441	+	0.602073i	$0.205658\pi$
$461$			25.8541i			1.20415i	−0.798441	+	0.602073i	$0.794342\pi$
$462$	24.7455	−	23.9162i	1.15126	−	1.11268i
$463$		−	16.5623i		−	0.769716i	−0.922976	−	0.384858i	$-0.874250\pi$
$463$		−	16.5623i		−	0.769716i	0.922976	−	0.384858i	$-0.125750\pi$
$464$	−15.2169	−	4.94427i	−0.706427	−	0.229532i
$465$	−0.765961	−	0.499225i	−0.0355206	−	0.0231510i
$466$	2.18223	−	0.345632i	0.101090	−	0.0160111i
$467$	−3.54508	−	10.9106i	−0.164047	−	0.504885i	0.834918	−	0.550375i	$-0.185515\pi$
$467$	−3.54508	−	10.9106i	−0.164047	−	0.504885i	−0.998965	+	0.0454900i	$0.985515\pi$
$468$	−3.01719	+	5.18619i	−0.139469	+	0.239732i
$469$	−13.2082	−	9.59632i	−0.609898	−	0.443117i
$470$	−0.599141	+	3.78283i	−0.0276363	+	0.174489i
$471$	−11.1957	+	0.568158i	−0.515869	+	0.0261793i
$472$	11.7082	−	11.7082i	0.538914	−	0.538914i
$473$	−0.396027	+	5.83688i	−0.0182094	+	0.268380i
$474$	11.5836	+	5.18034i	0.532052	+	0.237941i
$475$	−8.14324	−	2.64590i	−0.373637	−	0.121402i
$476$	−30.3278	−	41.7426i	−1.39007	−	1.91327i
$477$	1.56284	+	15.3584i	0.0715576	+	0.703212i
$478$	−9.16223	+	17.9819i	−0.419071	+	0.822473i
$479$	−6.97214	−	21.4580i	−0.318565	−	0.980442i	−0.974262	−	0.225418i	$-0.927625\pi$
$479$	−6.97214	−	21.4580i	−0.318565	−	0.980442i	0.655697	−	0.755024i	$-0.272375\pi$
$480$	3.01905	+	5.24920i	0.137800	+	0.239592i
$481$	4.66312	−	3.38795i	0.212620	−	0.154477i
$482$	26.9862	−	13.7502i	1.22919	−	0.626304i
$483$	42.7426	−	16.3262i	1.94486	−	0.742870i
$484$	15.2169	−	15.8885i	0.691677	−	0.722207i
$485$		−	7.61803i		−	0.345917i
$486$	−16.5045	+	14.6152i	−0.748657	+	0.662957i
$487$	10.3759	+	14.2812i	0.470175	+	0.647141i	0.976580	−	0.215155i	$-0.0690257\pi$
$487$	10.3759	+	14.2812i	0.470175	+	0.647141i	−0.506405	+	0.862296i	$0.669026\pi$
$488$	−14.2199	+	2.25221i	−0.643706	+	0.101953i
$489$	8.28679	+	10.2680i	0.374741	+	0.464337i
$490$	−8.52305	−	4.34271i	−0.385032	−	0.196184i
$491$	−6.45492	−	4.68977i	−0.291306	−	0.211646i	0.432528	−	0.901621i	$-0.357622\pi$
$491$	−6.45492	−	4.68977i	−0.291306	−	0.211646i	−0.723834	+	0.689974i	$0.757622\pi$
$492$	−1.53192	−	0.998450i	−0.0690643	−	0.0450136i
$493$	−7.52786	+	23.1684i	−0.339038	+	1.04345i
$494$	1.85410	−	1.85410i	0.0834200	−	0.0834200i
$495$	3.77990	+	4.85046i	0.169894	+	0.218012i
$496$			3.41641i			0.153401i
$497$	−20.5070	−	6.66312i	−0.919863	−	0.298882i
$498$	6.80762	+	32.2900i	0.305057	+	1.44695i
$499$	5.79210	−	7.97214i	0.259290	−	0.356882i	−0.659448	−	0.751750i	$-0.729210\pi$
$499$	5.79210	−	7.97214i	0.259290	−	0.356882i	0.918738	+	0.394869i	$0.129210\pi$
$500$	−3.67376	−	11.3067i	−0.164296	−	0.505650i
$501$	4.55841	−	3.67885i	0.203655	−	0.164359i
$502$	1.47645	+	9.32193i	0.0658971	+	0.416058i
$503$	33.7984	−	24.5560i	1.50700	−	1.09490i	0.539506	−	0.841982i	$-0.318611\pi$
$503$	33.7984	−	24.5560i	1.50700	−	1.09490i	0.967489	−	0.252914i	$-0.0813891\pi$
$504$	12.9923	−	33.5140i	0.578722	−	1.49283i
$505$	3.09017			0.137511
$506$	26.9008	−	11.4844i	1.19589	−	0.510546i
$507$	−7.41641	−	19.4164i	−0.329374	−	0.862313i
$508$	−8.76393	+	26.9726i	−0.388837	+	1.19672i
$509$	19.0336	+	26.1976i	0.843651	+	1.16119i	0.985226	+	0.171259i	$0.0547835\pi$
$509$	19.0336	+	26.1976i	0.843651	+	1.16119i	−0.141575	+	0.989928i	$0.545217\pi$
$510$	7.99213	−	4.59663i	0.353897	−	0.203542i
$511$	22.9969	−	7.47214i	1.01732	−	0.330548i
$512$	10.2726	−	20.1612i	0.453990	−	0.891007i
$513$	8.60575	−	4.33115i	0.379953	−	0.191225i
$514$	−1.23056	+	7.76944i	−0.0542776	+	0.342695i
$515$	−1.79837	+	5.53483i	−0.0792458	+	0.243894i
$516$	2.18034	+	5.70820i	0.0959841	+	0.251290i
$517$	12.3090	−	7.72696i	0.541350	−	0.339832i
$518$	−24.4164	+	24.4164i	−1.07280	+	1.07280i
$519$	1.82579	+	35.9775i	0.0801433	+	1.57924i
$520$	1.72654	+	0.273457i	0.0757139	+	0.0119919i
$521$	15.0049	−	20.6525i	0.657377	−	0.904801i	−0.342014	−	0.939695i	$-0.611109\pi$
$521$	15.0049	−	20.6525i	0.657377	−	0.904801i	0.999391	+	0.0348933i	$0.0111091\pi$
$522$	−16.4068	+	4.33801i	−0.718104	+	0.189870i
$523$	34.7728	−	11.2984i	1.52051	−	0.494043i	0.574589	−	0.818442i	$-0.305162\pi$
$523$	34.7728	−	11.2984i	1.52051	−	0.494043i	0.945920	+	0.324399i	$0.105162\pi$
$524$	−16.9070	+	23.2705i	−0.738586	+	1.01658i
$525$	−18.5010	+	28.3860i	−0.807448	+	1.23887i
$526$	2.33630	−	1.19041i	0.101868	−	0.0519042i
$527$	5.20163			0.226586
$528$	7.47202	−	21.7294i	0.325178	−	0.945653i
$529$	15.8885			0.690806
$530$	4.00746	−	2.04190i	0.174073	−	0.0886946i
$531$	3.70826	−	17.1663i	0.160925	−	0.744956i
$532$	−9.23305	+	12.7082i	−0.400304	+	0.550971i
$533$	−0.502029	+	0.163119i	−0.0217453	+	0.00706547i
$534$	−3.94800	+	36.9739i	−0.170847	+	1.60002i
$535$	−1.53884	+	2.11803i	−0.0665299	+	0.0915706i
$536$	−10.7668	−	1.70530i	−0.465057	−	0.0736577i
$537$	31.8572	−	1.61669i	1.37474	−	0.0697653i
$538$	−2.18034	+	2.18034i	−0.0940011	+	0.0940011i
$539$	8.85410	+	35.2016i	0.381373	+	1.51624i
$540$	5.70820	+	2.94427i	0.245642	+	0.126701i
$541$	6.89919	−	21.2335i	0.296619	−	0.912900i	−0.686054	−	0.727551i	$-0.740658\pi$
$541$	6.89919	−	21.2335i	0.296619	−	0.912900i	0.982673	−	0.185349i	$-0.0593416\pi$
$542$	2.51805	−	15.8984i	0.108160	−	0.682893i
$543$	9.68515	−	35.9076i	0.415629	−	1.54094i
$544$	−30.6962	−	15.6405i	−1.31609	−	0.670582i
$545$	−10.1311	+	3.29180i	−0.433969	+	0.141005i
$546$	−5.17322	−	8.99463i	−0.221393	−	0.384935i
$547$	19.3112	+	26.5795i	0.825685	+	1.13646i	0.988711	+	0.149837i	$0.0478748\pi$
$547$	19.3112	+	26.5795i	0.825685	+	1.13646i	−0.163025	+	0.986622i	$0.552125\pi$
$548$	8.79837	−	27.0786i	0.375848	−	1.15674i
$549$	−11.3820	+	10.1803i	−0.485770	+	0.434486i
$550$	−11.1176	+	18.5897i	−0.474055	+	0.792668i
$551$	7.41641			0.315950
$552$	20.4797	−	22.6695i	0.871676	−	0.964877i
$553$	−17.7533	+	12.8985i	−0.754947	+	0.548501i
$554$	3.18175	+	20.0888i	0.135179	+	0.853490i
$555$	−3.87502	−	4.80149i	−0.164486	−	0.203812i
$556$	2.52786	+	7.77997i	0.107205	+	0.329944i
$557$	1.26133	−	1.73607i	0.0534441	−	0.0735596i	−0.781458	−	0.623957i	$-0.785524\pi$
$557$	1.26133	−	1.73607i	0.0534441	−	0.0735596i	0.834903	+	0.550398i	$0.185524\pi$
$558$	1.96351	+	3.04556i	0.0831219	+	0.128929i
$559$	1.67760	+	0.545085i	0.0709549	+	0.0230546i
$560$	−10.4721			−0.442529
$561$	−33.0840	−	11.3765i	−1.39681	−	0.480315i
$562$	−16.1803	+	16.1803i	−0.682526	+	0.682526i
$563$	4.69098	−	14.4374i	0.197701	−	0.608462i	−0.802233	−	0.597011i	$-0.796355\pi$
$563$	4.69098	−	14.4374i	0.197701	−	0.608462i	0.999934	−	0.0114513i	$-0.00364513\pi$
$564$	8.28845	−	12.7170i	0.349007	−	0.535481i
$565$	0.500000	+	0.363271i	0.0210352	+	0.0152829i
$566$	−0.227242	−	0.115785i	−0.00955167	−	0.00486682i
$567$	−7.67946	−	37.3432i	−0.322507	−	1.56827i
$568$	−14.2199	+	2.25221i	−0.596655	+	0.0945008i
$569$	−15.4944	−	21.3262i	−0.649560	−	0.894042i	0.349520	−	0.936929i	$-0.386345\pi$
$569$	−15.4944	−	21.3262i	−0.649560	−	0.894042i	−0.999080	+	0.0428865i	$0.986345\pi$
$570$	−2.08280	−	1.88161i	−0.0872387	−	0.0788120i
$571$			12.4377i			0.520501i	0.965541	+	0.260251i	$0.0838052\pi$
$571$			12.4377i			0.520501i	−0.965541	+	0.260251i	$0.916195\pi$
$572$	−3.52671	−	5.61803i	−0.147459	−	0.234902i
$573$	−10.1459	−	26.5623i	−0.423851	−	1.10966i
$574$	2.81761	−	1.43564i	0.117605	−	0.0599226i
$575$	−23.2984	+	16.9273i	−0.971609	+	0.705916i
$576$	−2.42965	−	23.8767i	−0.101235	−	0.994862i
$577$	−7.32624	−	22.5478i	−0.304995	−	0.938679i	−0.979679	−	0.200572i	$-0.935720\pi$
$577$	−7.32624	−	22.5478i	−0.304995	−	0.938679i	0.674684	−	0.738107i	$-0.264280\pi$
$578$	−12.8987	+	25.3151i	−0.536514	+	1.05297i
$579$	−5.87927	+	21.7973i	−0.244334	+	0.905867i
$580$	2.90617	+	4.00000i	0.120672	+	0.166091i
$581$	−54.2757	−	17.6353i	−2.25174	−	0.731634i
$582$	−12.3262	+	27.5623i	−0.510939	+	1.14249i
$583$	−15.8374	−	6.36068i	−0.655920	−	0.263432i
$584$	11.4164	−	11.4164i	0.472414	−	0.472414i
$585$	1.69629	−	0.748520i	0.0701331	−	0.0309475i
$586$	4.95922	−	31.3113i	0.204864	−	1.29346i
$587$	22.3713	+	16.2537i	0.923363	+	0.670863i	0.944359	−	0.328917i	$-0.106684\pi$
$587$	22.3713	+	16.2537i	0.923363	+	0.670863i	−0.0209956	+	0.999780i	$0.506684\pi$
$588$	23.8100	+	29.5027i	0.981909	+	1.21667i
$589$	−0.489357	−	1.50609i	−0.0201636	−	0.0620572i
$590$	−5.05368	+	0.800424i	−0.208057	+	0.0329529i
$591$	4.14423	−	6.35848i	0.170471	−	0.261553i
$592$	−7.12461	+	21.9273i	−0.292820	+	0.901206i
$593$			7.38197i			0.303141i	0.988446	+	0.151571i	$0.0484331\pi$
$593$			7.38197i			0.303141i	−0.988446	+	0.151571i	$0.951567\pi$
$594$	−5.82759	−	23.6651i	−0.239109	−	0.970993i
$595$			15.9443i			0.653651i
$596$	−6.61803	+	20.3682i	−0.271085	+	0.834315i
$597$	−18.8622	+	28.9403i	−0.771979	+	1.18445i
$598$	−1.37962	−	8.71055i	−0.0564167	−	0.356201i
$599$	12.0344	+	37.0382i	0.491714	+	1.51334i	0.822016	+	0.569465i	$0.192849\pi$
$599$	12.0344	+	37.0382i	0.491714	+	1.51334i	−0.330302	+	0.943875i	$0.607151\pi$
$600$	−2.40206	+	22.4958i	−0.0980636	+	0.918386i
$601$	−7.89919	−	5.73910i	−0.322215	−	0.234103i	0.414905	−	0.909865i	$-0.363815\pi$
$601$	−7.89919	−	5.73910i	−0.322215	−	0.234103i	−0.737120	+	0.675762i	$0.763815\pi$
$602$	−10.4371	−	1.65307i	−0.425384	−	0.0673743i
$603$	−10.5782	+	4.66782i	−0.430778	+	0.190088i
$604$	28.9443			1.17773
$605$	−6.69015	+	1.20820i	−0.271993	+	0.0491205i
$606$	−11.1803	−	5.00000i	−0.454170	−	0.203111i
$607$	18.9354	+	6.15248i	0.768563	+	0.249721i	0.666950	−	0.745103i	$-0.267600\pi$
$607$	18.9354	+	6.15248i	0.768563	+	0.249721i	0.101613	+	0.994824i	$0.467600\pi$
$608$	−1.64074	+	10.3593i	−0.0665410	+	0.420123i
$609$	7.64282	−	28.3357i	0.309703	−	1.14822i
$610$	3.96406	+	2.01979i	0.160500	+	0.0817789i
$611$	−1.35410	−	4.16750i	−0.0547811	−	0.168599i
$612$	−36.3533	+	3.69924i	−1.46949	+	0.149533i
$613$	21.5623	−	15.6659i	0.870893	−	0.632741i	−0.0599332	−	0.998202i	$-0.519089\pi$
$613$	21.5623	−	15.6659i	0.870893	−	0.632741i	0.930827	+	0.365461i	$0.119089\pi$
$614$	−1.03884	−	2.03884i	−0.0419242	−	0.0822810i
$615$	0.201626	+	0.527864i	0.00813035	+	0.0212855i
$616$	26.1323	+	29.9366i	1.05290	+	1.20618i
$617$		−	19.7639i		−	0.795666i	−0.917458	−	0.397833i	$-0.869762\pi$
$617$		−	19.7639i		−	0.795666i	0.917458	−	0.397833i	$-0.130238\pi$
$618$	15.4621	−	17.1154i	0.621977	−	0.688481i
$619$	−26.3193	−	36.2254i	−1.05786	−	1.45602i	−0.881788	−	0.471646i	$-0.843660\pi$
$619$	−26.3193	−	36.2254i	−1.05786	−	1.45602i	−0.176074	−	0.984377i	$-0.556340\pi$
$620$	0.620541	−	0.854102i	0.0249215	−	0.0343016i
$621$	5.22790	−	31.9791i	0.209789	−	1.28328i
$622$	−2.34503	+	4.60239i	−0.0940273	+	0.184539i
$623$	−52.0238	−	37.7975i	−2.08429	−	1.51432i
$624$	−5.80423	−	3.78298i	−0.232355	−	0.151441i
$625$	6.00000	−	18.4661i	0.240000	−	0.738644i
$626$	−7.94427	−	7.94427i	−0.317517	−	0.317517i
$627$	−0.181492	+	10.6495i	−0.00724811	+	0.425298i
$628$		−	12.9443i		−	0.516533i
$629$	33.3852	+	10.8475i	1.33116	+	0.432519i
$630$	−9.33541	+	6.01864i	−0.371932	+	0.239788i
$631$	10.2496	−	14.1074i	0.408031	−	0.561606i	−0.554706	−	0.832047i	$-0.687169\pi$
$631$	10.2496	−	14.1074i	0.408031	−	0.561606i	0.962737	+	0.270440i	$0.0871692\pi$
$632$	−6.65197	+	13.0552i	−0.264601	+	0.519309i
$633$	14.8135	+	18.3552i	0.588784	+	0.729553i
$634$	−12.8231	+	2.03098i	−0.509271	+	0.0806606i
$635$	7.09017	−	5.15131i	0.281365	−	0.204424i
$636$	−17.8030	+	0.903468i	−0.705935	+	0.0358248i
$637$	10.9443			0.433628
$638$	4.18264	−	18.2895i	0.165592	−	0.724088i
$639$	−11.3820	+	10.1803i	−0.450264	+	0.402728i
$640$	−6.23015	+	3.17442i	−0.246268	+	0.125480i
$641$	27.7194	+	38.1525i	1.09485	+	1.50693i	0.842039	+	0.539417i	$0.181355\pi$
$641$	27.7194	+	38.1525i	1.09485	+	1.50693i	0.252811	+	0.967516i	$0.418645\pi$
$642$	8.99463	−	5.17322i	0.354990	−	0.204171i
$643$	−10.1514	+	3.29837i	−0.400330	+	0.130075i	−0.502260	−	0.864716i	$-0.667498\pi$
$643$	−10.1514	+	3.29837i	−0.400330	+	0.130075i	0.101930	+	0.994792i	$0.467498\pi$
$644$	16.3262	+	50.2470i	0.643344	+	1.98001i
$645$	0.491728	−	1.82308i	0.0193618	−	0.0717836i
$646$	15.7724	+	2.49810i	0.620557	+	0.0982866i
$647$	−13.9721	+	43.0018i	−0.549301	+	1.69058i	0.161236	+	0.986916i	$0.448452\pi$
$647$	−13.9721	+	43.0018i	−0.549301	+	1.69058i	−0.710537	+	0.703660i	$0.751548\pi$
$648$	−15.8885	−	19.8885i	−0.624161	−	0.781296i
$649$	14.8992	+	12.4495i	0.584844	+	0.488685i
$650$	4.61803	+	4.61803i	0.181134	+	0.181134i
$651$	−6.25856	+	0.317610i	−0.245292	+	0.0124481i
$652$	−12.3262	+	8.95554i	−0.482733	+	0.350726i
$653$	−2.85317	+	3.92705i	−0.111653	+	0.153677i	−0.861186	−	0.508289i	$-0.830278\pi$
$653$	−2.85317	+	3.92705i	−0.111653	+	0.153677i	0.749533	+	0.661967i	$0.230278\pi$
$654$	41.9809	+	4.48264i	1.64158	+	0.175285i
$655$	8.45351	−	2.74671i	0.330306	−	0.107323i
$656$	1.24108	−	1.70820i	0.0484561	−	0.0666942i
$657$	3.61584	−	16.7385i	0.141067	−	0.653032i
$658$	11.9177	+	23.3899i	0.464602	+	0.911832i
$659$	13.4164			0.522629			0.261315	−	0.965254i	$-0.415844\pi$
$659$	13.4164			0.522629			0.261315	+	0.965254i	$0.415844\pi$
$660$	−5.81485	+	4.07518i	−0.226343	+	0.158626i
$661$	5.21478			0.202832			0.101416	−	0.994844i	$-0.467663\pi$
$661$	5.21478			0.202832			0.101416	+	0.994844i	$0.467663\pi$
$662$	−17.1477	−	33.6543i	−0.666465	−	1.30801i
$663$	−5.75975	+	8.83718i	−0.223690	+	0.343208i
$664$	−37.6358	+	5.96093i	−1.46055	+	0.231329i
$665$	4.61653	−	1.50000i	0.179021	−	0.0581675i
$666$	6.25100	+	23.6419i	0.242221	+	0.916103i
$667$	14.6619	−	20.1803i	0.567710	−	0.781386i
$668$	3.97574	+	5.47214i	0.153826	+	0.211723i
$669$	−0.640112	−	12.6135i	−0.0247482	−	0.487667i
$670$	2.38197	+	2.38197i	0.0920234	+	0.0920234i
$671$	−4.11803	−	16.3722i	−0.158975	−	0.632043i
$672$	37.8885	+	16.9443i	1.46158	+	0.653639i
$673$	−10.6353	+	32.7319i	−0.409959	+	1.26172i	0.506724	+	0.862108i	$0.330856\pi$
$673$	−10.6353	+	32.7319i	−0.409959	+	1.26172i	−0.916683	+	0.399616i	$0.869144\pi$
$674$	−36.4131	−	5.76726i	−1.40258	−	0.222147i
$675$	10.7877	+	21.4344i	0.415217	+	0.825012i
$676$	22.8254	−	7.41641i	0.877898	−	0.285246i
$677$	−9.23305	+	3.00000i	−0.354855	+	0.115299i	−0.481019	−	0.876710i	$-0.659733\pi$
$677$	−9.23305	+	3.00000i	−0.354855	+	0.115299i	0.126164	+	0.992009i	$0.459733\pi$
$678$	−1.22123	−	2.12334i	−0.0469011	−	0.0815466i
$679$	−30.6911	−	42.2426i	−1.17782	−	1.62112i
$680$	4.83319	+	9.48566i	0.185344	+	0.363759i
$681$	10.1459	+	26.5623i	0.388792	+	1.01787i
$682$	−3.99012	+	0.357406i	−0.152790	+	0.0136858i
$683$	−4.41641			−0.168989			−0.0844946	−	0.996424i	$-0.526928\pi$
$683$	−4.41641			−0.168989			−0.0844946	+	0.996424i	$0.526928\pi$
$684$	4.49112	+	10.1778i	0.171722	+	0.389156i
$685$	−7.11803	+	5.17155i	−0.271966	+	0.197595i
$686$	−23.3381	+	3.69639i	−0.891051	+	0.141129i
$687$	−18.0834	+	14.5942i	−0.689926	+	0.556802i
$688$	−6.71040	+	2.18034i	−0.255831	+	0.0831247i
$689$	−3.02468	+	4.16312i	−0.115231	+	0.158602i
$690$	−9.23752	+	1.94752i	−0.351666	+	0.0741408i
$691$	11.1352	+	3.61803i	0.423602	+	0.137636i	0.513057	−	0.858354i	$-0.328513\pi$
$691$	11.1352	+	3.61803i	0.423602	+	0.137636i	−0.0894558	+	0.995991i	$0.528513\pi$
$692$	−41.5967			−1.58127
$693$	40.5011	+	11.6680i	1.53851	+	0.443231i
$694$	7.12461	+	7.12461i	0.270447	+	0.270447i
$695$	0.781153	−	2.40414i	0.0296308	−	0.0911943i
$696$	−4.04249	−	19.1744i	−0.153230	−	0.726804i
$697$	−2.60081	−	1.88960i	−0.0985128	−	0.0715738i
$698$	16.0510	−	31.5018i	0.607539	−	1.19236i
$699$	1.69945	+	2.10577i	0.0642792	+	0.0796474i
$700$	−31.6525	−	22.9969i	−1.19635	−	0.869200i
$701$	−16.5842	−	22.8262i	−0.626378	−	0.862135i	0.371420	−	0.928465i	$-0.378871\pi$
$701$	−16.5842	−	22.8262i	−0.626378	−	0.862135i	−0.997798	+	0.0663299i	$0.978871\pi$
$702$	−7.34838	−	0.0364919i	−0.277347	−	0.00137730i
$703$		−	10.6869i		−	0.403065i
$704$	24.6215	+	9.88854i	0.927957	+	0.372689i
$705$	−4.38197	+	1.67376i	−0.165034	+	0.0630375i
$706$	1.47142	+	2.88783i	0.0553778	+	0.108685i
$707$	17.1353	−	12.4495i	0.644438	−	0.468211i
$708$	19.5795	+	5.28106i	0.735842	+	0.198474i
$709$	−1.77051	−	5.44907i	−0.0664929	−	0.204644i	0.912290	−	0.409545i	$-0.134313\pi$
$709$	−1.77051	−	5.44907i	−0.0664929	−	0.204644i	−0.978783	+	0.204901i	$0.934313\pi$
$710$	3.96406	+	2.01979i	0.148769	+	0.0758014i
$711$	1.57330	+	15.4612i	0.0590034	+	0.579839i
$712$	−42.4079	−	6.71675i	−1.58930	−	0.251721i
$713$	−5.06555	−	1.64590i	−0.189706	−	0.0616394i
$714$	25.7984	−	57.6869i	0.965480	−	2.15888i
$715$	−0.138757	+	2.04508i	−0.00518923	+	0.0764818i
$716$			36.8328i			1.37651i
$717$	−24.6855	+	1.25274i	−0.921896	+	0.0467844i
$718$	−24.9868	−	3.95751i	−0.932498	−	0.147693i
$719$	−16.6074	−	12.0660i	−0.619351	−	0.449985i	0.233344	−	0.972394i	$-0.425033\pi$
$719$	−16.6074	−	12.0660i	−0.619351	−	0.449985i	−0.852695	+	0.522409i	$0.825033\pi$
$720$	−3.72945	+	6.41049i	−0.138988	+	0.238905i
$721$	12.3262	+	37.9363i	0.459053	+	1.41282i
$722$	3.44288	+	21.7375i	0.128131	+	0.808985i
$723$	31.0764	+	20.2545i	1.15574	+	0.753272i
$724$	40.8424	+	13.2705i	1.51790	+	0.493195i
$725$			18.4721i			0.686038i
$726$	26.1601	+	6.45357i	0.970893	+	0.239514i
$727$		−	25.2148i		−	0.935164i	−0.883950	−	0.467582i	$-0.845125\pi$
$727$		−	25.2148i		−	0.935164i	0.883950	−	0.467582i	$-0.154875\pi$
$728$	10.6755	−	5.43945i	0.395661	−	0.201599i
$729$	−25.5944	−	8.59808i	−0.947941	−	0.318447i
$730$	−4.92773	+	0.780476i	−0.182383	+	0.0288867i
$731$	3.31966	+	10.2169i	0.122782	+	0.377884i
$732$	−11.0740	−	13.7217i	−0.409308	−	0.507167i
$733$	1.23607	+	0.898056i	0.0456552	+	0.0331705i	0.610379	−	0.792110i	$-0.291017\pi$
$733$	1.23607	+	0.898056i	0.0456552	+	0.0331705i	−0.564724	+	0.825280i	$0.691017\pi$
$734$	0.514638	−	3.24929i	0.0189956	−	0.119934i
$735$	−0.593773	−	11.7004i	−0.0219017	−	0.431576i
$736$	24.9443	+	24.9443i	0.919458	+	0.919458i
$737$	0.865300	−	12.7533i	0.0318737	−	0.469773i
$738$	0.124612	−	2.23607i	0.00458702	−	0.0823108i
$739$	−35.9811	−	11.6910i	−1.32359	−	0.430060i	−0.439862	−	0.898065i	$-0.644973\pi$
$739$	−35.9811	−	11.6910i	−1.32359	−	0.430060i	−0.883726	+	0.468005i	$0.844973\pi$
$740$	5.76393	−	4.18774i	0.211886	−	0.153944i
$741$	3.10059	+	0.836305i	0.113903	+	0.0307224i
$742$	13.9954	−	27.4676i	0.513788	−	1.00837i
$743$	−3.60081	−	11.0822i	−0.132101	−	0.406565i	0.863027	−	0.505158i	$-0.168566\pi$
$743$	−3.60081	−	11.0822i	−0.132101	−	0.406565i	−0.995128	+	0.0985930i	$0.968566\pi$
$744$	−3.62711	+	2.08611i	−0.132976	+	0.0764806i
$745$	5.35410	−	3.88998i	0.196159	−	0.142518i
$746$	20.8263	−	10.6115i	0.762506	−	0.388516i
$747$	−30.1246	+	26.9443i	−1.10220	+	0.985839i
$748$	15.0557	−	37.4872i	0.550492	−	1.37067i
$749$			17.9443i			0.655669i
$750$	9.76073	−	10.8044i	0.356411	−	0.394520i
$751$	20.8375	+	28.6803i	0.760371	+	1.04656i	0.997183	+	0.0750051i	$0.0238973\pi$
$751$	20.8375	+	28.6803i	0.760371	+	1.04656i	−0.236812	+	0.971555i	$0.576103\pi$
$752$	14.1803	+	10.3026i	0.517104	+	0.375698i
$753$	−8.99529	+	7.25962i	−0.327807	+	0.264555i
$754$	−5.04029	−	2.56816i	−0.183557	−	0.0935268i
$755$	−7.23607	−	5.25731i	−0.263347	−	0.191333i
$756$	43.5142	−	6.67063i	1.58260	−	0.242609i
$757$	−11.8369	+	36.4302i	−0.430219	+	1.32408i	0.467689	+	0.883893i	$0.345087\pi$
$757$	−11.8369	+	36.4302i	−0.430219	+	1.32408i	−0.897908	+	0.440184i	$0.854913\pi$
$758$	14.5279	−	14.5279i	0.527676	−	0.527676i
$759$	28.6188	+	21.5473i	1.03880	+	0.782118i
$760$	2.29180	−	2.29180i	0.0831322	−	0.0831322i
$761$	−9.62908	−	3.12868i	−0.349054	−	0.113414i	0.129242	−	0.991613i	$-0.458745\pi$
$761$	−9.62908	−	3.12868i	−0.349054	−	0.113414i	−0.478296	+	0.878199i	$0.658745\pi$
$762$	−33.9875	+	7.16548i	−1.23124	+	0.259578i
$763$	−42.9161	+	59.0689i	−1.55367	+	2.13844i
$764$	31.2259	−	10.1459i	1.12971	−	0.367066i
$765$	9.76024	+	5.67824i	0.352882	+	0.205297i
$766$	−3.65649	−	23.0862i	−0.132114	−	0.834137i
$767$	4.73607	−	3.44095i	0.171010	−	0.124246i
$768$	27.6772	−	1.40456i	0.998715	−	0.0506828i
$769$	39.9230			1.43966			0.719830	−	0.694151i	$-0.244220\pi$
$769$	39.9230			1.43966			0.719830	+	0.694151i	$0.244220\pi$
$770$	−1.09554	−	12.2307i	−0.0394804	−	0.440764i
$771$	−9.00000	+	3.43769i	−0.324127	+	0.123806i
$772$	−24.7930	−	8.05573i	−0.892319	−	0.289932i
$773$	−21.8541	−	30.0795i	−0.786036	−	1.08189i	−0.994590	−	0.103875i	$-0.966876\pi$
$773$	−21.8541	−	30.0795i	−0.786036	−	1.08189i	0.208555	−	0.978011i	$-0.433124\pi$
$774$	−4.72889	+	5.80033i	−0.169977	+	0.208488i
$775$	3.75123	−	1.21885i	0.134748	−	0.0437823i
$776$	−31.0639	−	15.8279i	−1.11513	−	0.568187i
$777$	−40.8313	−	11.0132i	−1.46481	−	0.395096i
$778$	8.15330	−	51.4779i	0.292310	−	1.84557i
$779$	−0.302439	+	0.930812i	−0.0108360	+	0.0333498i
$780$	0.763932	+	2.00000i	0.0273532	+	0.0716115i
$781$	−4.11803	−	16.3722i	−0.147355	−	0.585844i
$782$	37.9787	−	37.9787i	1.35812	−	1.35812i
$783$	−14.6238	−	14.7697i	−0.522611	−	0.527827i
$784$	−35.4164	+	25.7315i	−1.26487	+	0.918983i
$785$	−2.35114	+	3.23607i	−0.0839158	+	0.115500i
$786$	−35.0293	−	3.74037i	−1.24946	−	0.133415i
$787$	19.9192	−	6.47214i	0.710042	−	0.230707i	0.0683417	−	0.997662i	$-0.478229\pi$
$787$	19.9192	−	6.47214i	0.710042	−	0.230707i	0.641701	+	0.766955i	$0.278229\pi$
$788$	7.09017	+	5.15131i	0.252577	+	0.183508i
$789$	2.69041	+	1.75351i	0.0957810	+	0.0624266i
$790$	4.03428	−	2.05557i	0.143533	−	0.0731339i
$791$	4.23607			0.150617
$792$	27.6321	−	5.33550i	0.981864	−	0.189589i
$793$	−5.09017			−0.180757
$794$	−9.41544	+	4.79741i	−0.334141	+	0.170254i
$795$	4.61485	+	3.00779i	0.163672	+	0.106675i
$796$	−32.2705	−	23.4459i	−1.14380	−	0.831018i
$797$	35.6911	−	11.5967i	1.26424	−	0.410778i	0.401239	−	0.915973i	$-0.368580\pi$
$797$	35.6911	−	11.5967i	1.26424	−	0.410778i	0.863005	+	0.505195i	$0.168580\pi$
$798$	−19.1298	−	2.04264i	−0.677187	−	0.0723088i
$799$	15.6862	−	21.5902i	0.554937	−	0.763805i
$800$	−25.8019	−	4.08662i	−0.912236	−	0.144484i
$801$	−41.6649	+	18.3854i	−1.47216	+	0.649615i
$802$	−17.0344	+	17.0344i	−0.601507	+	0.601507i
$803$	14.5279	+	12.1392i	0.512677	+	0.428384i
$804$	−4.76393	−	12.4721i	−0.168011	−	0.439858i
$805$	5.04508	−	15.5272i	0.177816	−	0.547261i
$806$	−0.188954	+	1.19301i	−0.00665564	+	0.0420220i
$807$	−3.64616	−	0.983457i	−0.128351	−	0.0346193i
$808$	6.42040	−	12.6007i	0.225869	−	0.443292i
$809$	23.4131	−	7.60739i	0.823162	−	0.267462i	0.133000	−	0.991116i	$-0.457539\pi$
$809$	23.4131	−	7.60739i	0.823162	−	0.267462i	0.690162	+	0.723654i	$0.257539\pi$
$810$	0.359668	+	7.85806i	0.0126374	+	0.276104i
$811$	−11.6372	−	16.0172i	−0.408637	−	0.562441i	0.554248	−	0.832351i	$-0.313006\pi$
$811$	−11.6372	−	16.0172i	−0.408637	−	0.562441i	−0.962885	+	0.269911i	$0.913006\pi$
$812$	32.2299	+	10.4721i	1.13105	+	0.367500i
$813$	18.4164	−	7.03444i	0.645892	−	0.246709i
$814$	−26.3548	−	6.02712i	−0.923737	−	0.211250i
$815$	4.70820			0.164921
$816$	−2.13851	−	42.1397i	−0.0748628	−	1.47518i
$817$	2.64590	−	1.92236i	0.0925683	−	0.0672548i
$818$	−4.04673	−	25.5500i	−0.141490	−	0.893336i
$819$	6.39050	−	10.9845i	0.223302	−	0.383831i
$820$	−0.620541	+	0.201626i	−0.0216702	+	0.00704109i
$821$	6.95515	−	9.57295i	0.242737	−	0.334098i	−0.670214	−	0.742168i	$-0.733798\pi$
$821$	6.95515	−	9.57295i	0.242737	−	0.334098i	0.912951	+	0.408069i	$0.133798\pi$
$822$	34.1210	−	7.19364i	1.19011	−	0.250907i
$823$	46.1123	+	14.9828i	1.60737	+	0.522267i	0.968916	−	0.247391i	$-0.0795733\pi$
$823$	46.1123	+	14.9828i	1.60737	+	0.522267i	0.638456	+	0.769658i	$0.279573\pi$
$824$	18.8328	+	18.8328i	0.656072	+	0.656072i
$825$	−26.5247	−	0.452045i	−0.923473	−	0.0157382i
$826$	−24.7984	+	24.7984i	−0.862846	+	0.862846i
$827$	5.56231	−	17.1190i	0.193420	−	0.595287i	−0.806571	−	0.591137i	$-0.798679\pi$
$827$	5.56231	−	17.1190i	0.193420	−	0.595287i	0.999991	−	0.00414942i	$-0.00132080\pi$
$828$	36.5728	+	7.90043i	1.27099	+	0.274559i
$829$	35.8156	+	26.0216i	1.24393	+	0.903766i	0.997854	−	0.0654853i	$-0.0208595\pi$
$829$	35.8156	+	26.0216i	1.24393	+	0.903766i	0.246073	+	0.969251i	$0.420860\pi$
$830$	10.4917	+	5.34577i	0.364171	+	0.185555i
$831$	−19.3849	+	15.6445i	−0.672453	+	0.542701i
$832$	4.70228	−	6.47214i	0.163022	−	0.224381i
$833$	39.1773	+	53.9230i	1.35741	+	1.86832i
$834$	−6.71622	+	7.43433i	−0.232564	+	0.257430i
$835$		−	2.09017i		−	0.0723333i
$836$	−12.2705	−	0.832544i	−0.424384	−	0.0287941i
$837$	−2.03444	+	3.94427i	−0.0703206	+	0.136334i
$838$	27.7650	−	14.1470i	0.959127	−	0.488699i
$839$	27.9894	−	20.3355i	0.966300	−	0.702058i	0.0116946	−	0.999932i	$-0.496277\pi$
$839$	27.9894	−	20.3355i	0.966300	−	0.702058i	0.954605	+	0.297874i	$0.0962774\pi$
$840$	−6.39445	−	11.1180i	−0.220630	−	0.383607i
$841$	4.01722	+	12.3637i	0.138525	+	0.426336i
$842$	7.91393	−	15.5320i	0.272732	−	0.535267i
$843$	−27.0582	−	7.29825i	−0.931934	−	0.251365i
$844$	−22.0344	+	16.0090i	−0.758457	+	0.551051i
$845$	−7.05342	−	2.29180i	−0.242645	−	0.0788402i
$846$	18.5623	+	1.03444i	0.638185	+	0.0355648i
$847$	−32.2299	+	33.6525i	−1.10743	+	1.15631i
$848$		−	20.5836i		−	0.706843i
$849$	−0.0158312	−	0.311956i	−0.000543325	−	0.0107063i
$850$	−6.22206	+	39.2845i	−0.213415	+	1.34745i
$851$	−29.0795	−	21.1275i	−0.996833	−	0.724242i
$852$	−11.0740	−	13.7217i	−0.379390	−	0.470096i
$853$	12.0517	+	37.0912i	0.412641	+	1.26998i	0.914344	+	0.404939i	$0.132707\pi$
$853$	12.0517	+	37.0912i	0.412641	+	1.26998i	−0.501703	+	0.865040i	$0.667293\pi$
$854$	30.1183	−	4.77027i	1.03063	−	0.163235i
$855$	0.725865	−	3.36019i	0.0248241	−	0.114916i
$856$	5.43945	+	10.6755i	0.185916	+	0.364882i
$857$			40.8885i			1.39673i	0.715744	+	0.698363i	$0.246088\pi$
$857$			40.8885i			1.39673i	−0.715744	+	0.698363i	$0.753912\pi$
$858$	3.81105	−	7.17467i	0.130107	−	0.244939i
$859$		−	20.3475i		−	0.694249i	−0.937819	−	0.347124i	$-0.887158\pi$
$859$		−	20.3475i		−	0.694249i	0.937819	−	0.347124i	$-0.112842\pi$
$860$	2.07363	+	0.673762i	0.0707101	+	0.0229751i
$861$	3.24466	+	2.11475i	0.110578	+	0.0720705i
$862$	5.20040	+	32.8340i	0.177126	+	1.11833i
$863$	−0.347524	−	1.06957i	−0.0118299	−	0.0364086i	0.944967	−	0.327165i	$-0.106093\pi$
$863$	−0.347524	−	1.06957i	−0.0118299	−	0.0364086i	−0.956797	+	0.290756i	$0.906093\pi$
$864$	23.8657	−	17.1590i	0.811926	−	0.583760i
$865$	10.3992	+	7.55545i	0.353583	+	0.256893i
$866$	35.9093	+	5.68747i	1.22025	+	0.193268i
$867$	−34.7525	+	1.76362i	−1.18026	+	0.0598957i
$868$		−	7.23607i		−	0.245608i
$869$	−15.9434	−	6.40325i	−0.540844	−	0.217215i
$870$	−2.47214	+	5.52786i	−0.0838133	+	0.187412i
$871$	−3.66547	−	1.19098i	−0.124200	−	0.0403549i
$872$	−7.62633	+	48.1508i	−0.258260	+	1.63059i
$873$	−36.7887	+	3.74355i	−1.24511	+	0.126700i
$874$	−14.5694	−	7.42346i	−0.492816	−	0.251102i
$875$	7.78115	+	23.9479i	0.263051	+	0.809588i
$876$	19.0915	+	5.14945i	0.645043	+	0.173984i
$877$	−19.1353	+	13.9026i	−0.646152	+	0.469457i	−0.861958	−	0.506980i	$-0.830762\pi$
$877$	−19.1353	+	13.9026i	−0.646152	+	0.469457i	0.215806	+	0.976436i	$0.430762\pi$
$878$	−13.7144	−	26.9160i	−0.462839	−	0.908372i
$879$	36.2705	−	13.8541i	1.22337	−	0.467287i
$880$	−4.35926	−	6.94427i	−0.146950	−	0.234091i
$881$			9.14590i			0.308133i	0.988060	+	0.154067i	$0.0492370\pi$
$881$			9.14590i			0.308133i	−0.988060	+	0.154067i	$0.950763\pi$
$882$	−16.7834	+	43.2933i	−0.565126	+	1.45776i
$883$	5.36331	+	7.38197i	0.180490	+	0.248423i	0.889670	−	0.456605i	$-0.150935\pi$
$883$	5.36331	+	7.38197i	0.180490	+	0.248423i	−0.709180	+	0.705028i	$0.750935\pi$
$884$	−9.85410	−	7.15942i	−0.331429	−	0.240797i
$885$	−3.93564	−	4.87660i	−0.132295	−	0.163925i
$886$	1.89034	−	3.71000i	0.0635072	−	0.124640i
$887$	0.336881	+	0.244758i	0.0113114	+	0.00821818i	0.593427	−	0.804888i	$-0.297775\pi$
$887$	0.336881	+	0.244758i	0.0113114	+	0.00821818i	−0.582115	+	0.813106i	$0.697775\pi$
$888$	−27.6300	+	5.82515i	−0.927202	+	0.195479i
$889$	18.5623	−	57.1289i	0.622560	−	1.91604i
$890$	9.38197	+	9.38197i	0.314484	+	0.314484i
$891$	21.5662	−	20.6373i	0.722495	−	0.691376i
$892$	14.5836			0.488295
$893$	−7.72696	−	2.51064i	−0.258573	−	0.0840155i
$894$	−25.6654	+	5.41097i	−0.858381	+	0.180970i
$895$	6.69015	−	9.20820i	0.223627	−	0.307796i
$896$	−21.7578	+	42.7021i	−0.726877	+	1.42658i
$897$	8.40534	−	6.78350i	0.280646	−	0.226495i
$898$	53.5823	−	8.48660i	1.78806	−	0.283202i
$899$	−2.76393	+	2.00811i	−0.0921823	+	0.0669744i
$900$	−25.3499	+	11.1861i	−0.844996	+	0.372869i
$901$	−31.3394			−1.04407
$902$	2.12489	+	1.27079i	0.0707512	+	0.0423128i
$903$	−4.61803	−	12.0902i	−0.153679	−	0.402336i
$904$	2.52015	−	1.28408i	0.0838188	−	0.0427078i
$905$	−7.80021	−	10.7361i	−0.259288	−	0.356879i
$906$	17.6738	+	30.7293i	0.587174	+	1.02091i
$907$	14.7351	−	4.78773i	0.489272	−	0.158974i	−0.0539832	−	0.998542i	$-0.517192\pi$
$907$	14.7351	−	4.78773i	0.489272	−	0.158974i	0.543255	+	0.839568i	$0.317192\pi$
$908$	−31.2259	+	10.1459i	−1.03627	+	0.336703i
$909$	−1.51853	−	14.9229i	−0.0503665	−	0.494963i
$910$	−3.65688	−	0.579192i	−0.121224	−	0.0192000i
$911$	4.07295	−	12.5352i	0.134943	−	0.415311i	−0.860638	−	0.509217i	$-0.829935\pi$
$911$	4.07295	−	12.5352i	0.134943	−	0.415311i	0.995581	+	0.0939055i	$0.0299351\pi$
$912$	−12.0000	+	4.58359i	−0.397360	+	0.151778i
$913$	−10.8992	−	43.3323i	−0.360710	−	1.43409i
$914$	1.14590	+	1.14590i	0.0379029	+	0.0379029i
$915$	0.276163	+	5.44185i	0.00912968	+	0.179902i
$916$	−15.7719	−	21.7082i	−0.521119	−	0.717259i
$917$	35.8096	−	49.2877i	1.18254	−	1.62762i
$918$	−26.1253	−	36.3365i	−0.862263	−	1.19928i
$919$	−46.6018	+	15.1418i	−1.53725	+	0.499483i	−0.950616	−	0.310369i	$-0.899547\pi$
$919$	−46.6018	+	15.1418i	−1.53725	+	0.499483i	−0.586634	+	0.809852i	$0.699547\pi$
$920$	−1.70530	−	10.7668i	−0.0562221	−	0.354972i
$921$	1.53025	−	2.34786i	0.0504234	−	0.0773646i
$922$	−16.5994	−	32.5781i	−0.546671	−	1.07290i
$923$	−5.09017			−0.167545
$924$	−15.8260	+	46.0237i	−0.520637	+	1.51407i
$925$	26.6180			0.875196
$926$	10.6337	+	20.8697i	0.349444	+	0.685822i
$927$	27.6123	+	5.96479i	0.906907	+	0.195909i
$928$	22.3488	−	3.53971i	0.733636	−	0.116197i
$929$	−12.8128	+	4.16312i	−0.420373	+	0.136588i	−0.511563	−	0.859246i	$-0.670933\pi$
$929$	−12.8128	+	4.16312i	−0.420373	+	0.136588i	0.0911894	+	0.995834i	$0.470933\pi$
$930$	1.28569	+	0.137283i	0.0421594	+	0.00450170i
$931$	11.9272	−	16.4164i	0.390899	−	0.538026i
$932$	−2.52786	+	1.83660i	−0.0828029	+	0.0601599i
$933$	−6.31814	+	0.320634i	−0.206847	+	0.0104971i
$934$	11.4721	+	11.4721i	0.375380	+	0.375380i
$935$	−10.5729	+	6.63715i	−0.345772	+	0.217058i
$936$	0.472136	−	8.47214i	0.0154322	−	0.276920i
$937$	−2.16312	+	6.65740i	−0.0706660	+	0.217488i	−0.980152	−	0.198247i	$-0.936475\pi$
$937$	−2.16312	+	6.65740i	−0.0706660	+	0.217488i	0.909486	+	0.415734i	$0.136475\pi$
$938$	22.8045	+	3.61188i	0.744594	+	0.117932i
$939$	3.58332	−	13.2851i	0.116937	−	0.433543i
$940$	−1.67376	−	5.15131i	−0.0545921	−	0.168017i
$941$	11.9475	−	3.88197i	0.389476	−	0.126548i	−0.107732	−	0.994180i	$-0.534359\pi$
$941$	11.9475	−	3.88197i	0.389476	−	0.126548i	0.497208	+	0.867632i	$0.334359\pi$
$942$	13.7426	−	7.90398i	0.447757	−	0.257526i
$943$	1.93487	+	2.66312i	0.0630080	+	0.0867231i
$944$	−7.23607	+	22.2703i	−0.235514	+	0.724837i
$945$	−12.0902	−	6.23607i	−0.393293	−	0.202859i
$946$	−3.24848	−	7.60916i	−0.105617	−	0.247395i
$947$	−49.8115			−1.61866			−0.809329	−	0.587356i	$-0.800169\pi$
$947$	−49.8115			−1.61866			−0.809329	+	0.587356i	$0.800169\pi$
$948$	−17.9222	+	0.909515i	−0.582085	+	0.0295397i
$949$	4.61803	−	3.35520i	0.149908	−	0.108914i
$950$	11.9598	−	1.89425i	0.388029	−	0.0614577i
$951$	−9.98624	−	12.3738i	−0.323826	−	0.401248i
$952$	65.0157	+	33.1272i	2.10717	+	1.07366i
$953$	−0.489517	+	0.673762i	−0.0158570	+	0.0218253i	−0.816872	−	0.576819i	$-0.804294\pi$
$953$	−0.489517	+	0.673762i	−0.0158570	+	0.0218253i	0.801015	+	0.598644i	$0.204294\pi$
$954$	−11.8300	−	18.3493i	−0.383010	−	0.594080i
$955$	−9.64932	−	3.13525i	−0.312245	−	0.101454i
$956$		−	28.5410i		−	0.923083i
$957$	21.9714	−	6.72725i	0.710236	−	0.217461i
$958$	22.5623	+	22.5623i	0.728955	+	0.728955i
$959$	−18.6353	+	57.3534i	−0.601764	+	1.85204i
$960$	−7.17442	−	4.67602i	−0.231553	−	0.150918i
$961$	−24.4894	−	17.7926i	−0.789979	−	0.573954i
$962$	−3.70067	+	7.26298i	−0.119314	+	0.234168i
$963$	10.9845	+	6.39050i	0.353972	+	0.205931i
$964$	−25.1765	+	34.6525i	−0.810880	+	1.11608i
$965$	4.73504	+	6.51722i	0.152426	+	0.209797i
$966$	−43.3768	+	48.0147i	−1.39563	+	1.54485i
$967$			20.6869i			0.665246i	0.943060	+	0.332623i	$0.107934\pi$
$967$			20.6869i			0.665246i	−0.943060	+	0.332623i	$0.892066\pi$
$968$	−8.97334	+	29.7906i	−0.288414	+	0.957506i
$969$	6.97871	+	18.2705i	0.224189	+	0.586933i
$970$	4.89108	+	9.59928i	0.157043	+	0.308214i
$971$	22.6525	−	16.4580i	0.726953	−	0.528162i	−0.161645	−	0.986849i	$-0.551680\pi$
$971$	22.6525	−	16.4580i	0.726953	−	0.528162i	0.888598	+	0.458687i	$0.151680\pi$
$972$	11.4133	−	29.0127i	0.366082	−	0.930582i
$973$	−5.35410	−	16.4782i	−0.171645	−	0.528268i
$974$	−22.2434	−	11.3336i	−0.712725	−	0.363152i
$975$	−2.08299	+	7.72268i	−0.0667092	+	0.247324i
$976$	16.4721	−	11.9677i	0.527260	−	0.383077i
$977$	26.7481	+	8.69098i	0.855747	+	0.278049i	0.703851	−	0.710347i	$-0.251462\pi$
$977$	26.7481	+	8.69098i	0.855747	+	0.278049i	0.151896	+	0.988396i	$0.451462\pi$
$978$	−17.0344	−	7.61803i	−0.544701	−	0.243598i
$979$	3.40820	−	50.2320i	0.108927	−	1.60542i
$980$	13.5279			0.432132
$981$	20.8751	+	47.3072i	0.666491	+	1.51040i
$982$	11.1447	+	1.76514i	0.355641	+	0.0563280i
$983$	27.7426	+	20.1562i	0.884853	+	0.642883i	0.934531	−	0.355882i	$-0.115819\pi$
$983$	27.7426	+	20.1562i	0.884853	+	0.642883i	−0.0496779	+	0.998765i	$0.515819\pi$
$984$	2.57138	+	0.274567i	0.0819725	+	0.00875287i
$985$	−0.836881	−	2.57565i	−0.0266652	−	0.0820672i
$986$	−5.38936	−	34.0271i	−0.171632	−	1.08364i
$987$	−17.5552	+	26.9350i	−0.558789	+	0.857349i
$988$	−1.14590	+	3.52671i	−0.0364559	+	0.112200i
$989$		−	11.0000i		−	0.349780i
$990$	−7.87714	−	3.68510i	−0.250352	−	0.117120i
$991$			9.67376i			0.307297i	0.988126	+	0.153649i	$0.0491024\pi$
$991$			9.67376i			0.307297i	−0.988126	+	0.153649i	$0.950898\pi$
$992$	−2.19347	−	4.30493i	−0.0696427	−	0.136682i
$993$	25.2592	−	38.7551i	0.801576	−	1.22986i
$994$	30.1183	−	4.77027i	0.955294	−	0.151304i
$995$	3.80902	+	11.7229i	0.120754	+	0.371642i
$996$	−29.3096	−	36.3171i	−0.928710	−	1.15075i
$997$	−14.2984	−	10.3884i	−0.452834	−	0.329003i	0.337880	−	0.941189i	$-0.390290\pi$
$997$	−14.2984	−	10.3884i	−0.452834	−	0.329003i	−0.790714	+	0.612186i	$0.790290\pi$
$998$	−2.18004	+	13.7642i	−0.0690080	+	0.435699i
$999$	−21.2829	+	21.0726i	−0.673363	+	0.666708i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	132.2.o.b.119.1	yes	8
3.2	odd	2		132.2.o.a.119.2	yes	8
4.3	odd	2		132.2.o.a.119.1	yes	8
11.5	even	5	inner	132.2.o.b.71.2	yes	8
12.11	even	2	inner	132.2.o.b.119.2	yes	8
33.5	odd	10		132.2.o.a.71.1	✓	8
44.27	odd	10		132.2.o.a.71.2	yes	8
132.71	even	10	inner	132.2.o.b.71.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
132.2.o.a.71.1	✓	8	33.5	odd	10
132.2.o.a.71.2	yes	8	44.27	odd	10
132.2.o.a.119.1	yes	8	4.3	odd	2
132.2.o.a.119.2	yes	8	3.2	odd	2
132.2.o.b.71.1	yes	8	132.71	even	10	inner
132.2.o.b.71.2	yes	8	11.5	even	5	inner
132.2.o.b.119.1	yes	8	1.1	even	1	trivial
132.2.o.b.119.2	yes	8	12.11	even	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 132 = 2^{2} \cdot 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	132.o (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26007 + 0.642040i) q^{2} +(-1.45106 - 0.945746i) q^{3} +(1.17557 - 1.61803i) q^{4} +(-0.587785 + 0.190983i) q^{5} +(2.43564 + 0.260074i) q^{6} +(-2.48990 + 3.42705i) q^{7} +(-0.442463 + 2.79360i) q^{8} +(1.21113 + 2.74466i) q^{9} +(0.618034 - 0.618034i) q^{10} +(-3.30902 - 0.224514i) q^{11} +(-3.23607 + 1.23607i) q^{12} +(-0.309017 + 0.951057i) q^{13} +(0.937153 - 5.91695i) q^{14} +(1.03353 + 0.278768i) q^{15} +(-1.23607 - 3.80423i) q^{16} +(-5.79210 + 1.88197i) q^{17} +(-3.28829 - 2.68088i) q^{18} +(1.08981 + 1.50000i) q^{19} +(-0.381966 + 1.17557i) q^{20} +(6.85410 - 2.61803i) q^{21} +(4.31375 - 1.84162i) q^{22} +6.23607 q^{23} +(3.28408 - 3.63522i) q^{24} +(-3.73607 + 2.71441i) q^{25} +(-0.221232 - 1.39680i) q^{26} +(0.838333 - 5.12808i) q^{27} +(2.61803 + 8.05748i) q^{28} +(2.35114 - 3.23607i) q^{29} +(-1.48131 + 0.312299i) q^{30} +(-0.812299 - 0.263932i) q^{31} +(4.00000 + 4.00000i) q^{32} +(4.58924 + 3.45527i) q^{33} +(6.09017 - 6.09017i) q^{34} +(0.809017 - 2.48990i) q^{35} +(5.86472 + 1.26689i) q^{36} +(-4.66312 - 3.38795i) q^{37} +(-2.33630 - 1.19041i) q^{38} +(1.34786 - 1.08779i) q^{39} +(-0.273457 - 1.72654i) q^{40} +(0.310271 + 0.427051i) q^{41} +(-6.95579 + 7.69952i) q^{42} -1.76393i q^{43} +(-4.25325 + 5.09017i) q^{44} +(-1.23607 - 1.38197i) q^{45} +(-7.85790 + 4.00380i) q^{46} +(-3.54508 + 2.57565i) q^{47} +(-1.80423 + 6.68915i) q^{48} +(-3.38197 - 10.4086i) q^{49} +(2.96496 - 5.81906i) q^{50} +(10.1845 + 2.74701i) q^{51} +(1.17557 + 1.61803i) q^{52} +(4.89404 + 1.59017i) q^{53} +(2.23607 + 7.00000i) q^{54} +(1.98787 - 0.500000i) q^{55} +(-8.47214 - 8.47214i) q^{56} +(-0.162763 - 3.20727i) q^{57} +(-0.884927 + 5.58721i) q^{58} +(-4.73607 - 3.44095i) q^{59} +(1.66605 - 1.34458i) q^{60} +(1.57295 + 4.84104i) q^{61} +(1.19301 - 0.188954i) q^{62} +(-12.4217 - 2.68332i) q^{63} +(-7.60845 - 2.47214i) q^{64} -0.618034i q^{65} +(-8.00120 - 1.40742i) q^{66} +3.85410i q^{67} +(-3.76393 + 11.5842i) q^{68} +(-9.04889 - 5.89773i) q^{69} +(0.579192 + 3.65688i) q^{70} +(1.57295 + 4.84104i) q^{71} +(-8.20338 + 2.16901i) q^{72} +(-4.61803 - 3.35520i) q^{73} +(8.05107 + 1.27516i) q^{74} +(7.98839 - 0.405395i) q^{75} +3.70820 q^{76} +(9.00854 - 10.7812i) q^{77} +(-1.00000 + 2.23607i) q^{78} +(4.92680 + 1.60081i) q^{79} +(1.45309 + 2.00000i) q^{80} +(-6.06633 + 6.64828i) q^{81} +(-0.665148 - 0.338910i) q^{82} +(4.16312 + 12.8128i) q^{83} +(3.82141 - 14.1679i) q^{84} +(3.04508 - 2.21238i) q^{85} +(1.13251 + 2.22268i) q^{86} +(-6.47214 + 2.47214i) q^{87} +(2.09132 - 9.14475i) q^{88} +15.1803i q^{89} +(2.44481 + 0.947774i) q^{90} +(-2.48990 - 3.42705i) q^{91} +(7.33094 - 10.0902i) q^{92} +(0.929080 + 1.15121i) q^{93} +(2.81340 - 5.52160i) q^{94} +(-0.927051 - 0.673542i) q^{95} +(-2.02124 - 9.58721i) q^{96} +(-3.80902 + 11.7229i) q^{97} +(10.9443 + 10.9443i) q^{98} +(-3.39144 - 9.35405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 4 q^{3} - 2 q^{6} - 4 q^{8} - 10 q^{9} - 4 q^{10} - 22 q^{11} - 8 q^{12} + 2 q^{13} + 14 q^{14} + 2 q^{15} + 8 q^{16} - 14 q^{18} - 12 q^{20} + 28 q^{21} - 8 q^{22} + 32 q^{23} + 20 q^{24}+ \cdots + 40 q^{99}+O(q^{100}) \) 8 * q + 2 * q^2 - 4 * q^3 - 2 * q^6 - 4 * q^8 - 10 * q^9 - 4 * q^10 - 22 * q^11 - 8 * q^12 + 2 * q^13 + 14 * q^14 + 2 * q^15 + 8 * q^16 - 14 * q^18 - 12 * q^20 + 28 * q^21 - 8 * q^22 + 32 * q^23 + 20 * q^24 - 12 * q^25 - 2 * q^26 + 2 * q^27 + 12 * q^28 + 32 * q^32 - 4 * q^33 + 4 * q^34 + 2 * q^35 + 8 * q^36 - 6 * q^37 - 18 * q^38 - 6 * q^39 - 8 * q^40 - 10 * q^42 + 8 * q^45 - 2 * q^46 - 6 * q^47 + 16 * q^48 - 36 * q^49 + 2 * q^50 + 28 * q^51 - 32 * q^56 - 6 * q^57 - 8 * q^58 - 20 * q^59 + 16 * q^60 + 26 * q^61 + 10 * q^62 - 28 * q^63 - 2 * q^66 - 48 * q^68 - 16 * q^69 + 8 * q^70 + 26 * q^71 - 28 * q^72 - 28 * q^73 + 6 * q^74 + 16 * q^75 - 24 * q^76 - 8 * q^78 - 2 * q^81 + 30 * q^82 + 2 * q^83 - 16 * q^84 + 2 * q^85 + 18 * q^86 - 16 * q^87 + 36 * q^88 + 22 * q^90 - 10 * q^93 + 16 * q^94 + 6 * q^95 + 8 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Introduction

L-functions

Modular forms

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Database

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