LMFDB - Embedded newform 840.2.bj.b.13.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(13,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.13"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.bj (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [184] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$184$
Relative dimension:	$92$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.1
Character	$\chi$	$=$	840.13
Dual form			840.2.bj.b.517.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.40929 + 0.117921i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.97219 - 0.332370i) q^{4} +(0.361094 + 2.20672i) q^{5} +(1.07990 + 0.913135i) q^{6} +(2.47159 + 0.944062i) q^{7} +(-2.74019 + 0.700969i) q^{8} +1.00000i q^{9} +(-0.769104 - 3.06732i) q^{10} +3.00292i q^{11} +(-1.62957 - 1.15953i) q^{12} +(2.37833 + 2.37833i) q^{13} +(-3.59451 - 1.03900i) q^{14} +(1.30505 - 1.81572i) q^{15} +(3.77906 - 1.31099i) q^{16} +(-3.17167 - 3.17167i) q^{17} +(-0.117921 - 1.40929i) q^{18} +7.49985i q^{19} +(1.44559 + 4.23205i) q^{20} +(-1.08012 - 2.41523i) q^{21} +(-0.354109 - 4.23199i) q^{22} +(-2.48231 - 2.48231i) q^{23} +(2.43327 + 1.44195i) q^{24} +(-4.73922 + 1.59366i) q^{25} +(-3.63222 - 3.07130i) q^{26} +(0.707107 - 0.707107i) q^{27} +(5.18822 + 1.04039i) q^{28} -2.42536 q^{29} +(-1.62509 + 2.71276i) q^{30} -1.92561i q^{31} +(-5.17119 + 2.29320i) q^{32} +(2.12339 - 2.12339i) q^{33} +(4.84381 + 4.09580i) q^{34} +(-1.19081 + 5.79500i) q^{35} +(0.332370 + 1.97219i) q^{36} +(-7.03701 - 7.03701i) q^{37} +(-0.884392 - 10.5695i) q^{38} -3.36347i q^{39} +(-2.53631 - 5.79372i) q^{40} -2.62677i q^{41} +(1.80701 + 3.27639i) q^{42} +(2.67688 - 2.67688i) q^{43} +(0.998083 + 5.92234i) q^{44} +(-2.20672 + 0.361094i) q^{45} +(3.79102 + 3.20558i) q^{46} +(5.83940 + 5.83940i) q^{47} +(-3.59921 - 1.74519i) q^{48} +(5.21749 + 4.66667i) q^{49} +(6.49101 - 2.80479i) q^{50} +4.48542i q^{51} +(5.48101 + 3.90004i) q^{52} +(-3.92370 + 3.92370i) q^{53} +(-0.913135 + 1.07990i) q^{54} +(-6.62661 + 1.08434i) q^{55} +(-7.43438 - 0.854404i) q^{56} +(5.30319 - 5.30319i) q^{57} +(3.41804 - 0.286002i) q^{58} +12.1091i q^{59} +(1.97032 - 4.01470i) q^{60} -3.11135 q^{61} +(0.227070 + 2.71373i) q^{62} +(-0.944062 + 2.47159i) q^{63} +(7.01729 - 3.84158i) q^{64} +(-4.38952 + 6.10712i) q^{65} +(-2.74207 + 3.24286i) q^{66} +(-5.83002 - 5.83002i) q^{67} +(-7.30931 - 5.20097i) q^{68} +3.51052i q^{69} +(0.994836 - 8.30724i) q^{70} +1.88481 q^{71} +(-0.700969 - 2.74019i) q^{72} +(-1.14816 + 1.14816i) q^{73} +(10.7470 + 9.08736i) q^{74} +(4.47803 + 2.22425i) q^{75} +(2.49273 + 14.7911i) q^{76} +(-2.83495 + 7.42199i) q^{77} +(0.396625 + 4.74010i) q^{78} +14.4613i q^{79} +(4.25759 + 7.86593i) q^{80} -1.00000 q^{81} +(0.309752 + 3.70188i) q^{82} +(8.44650 + 8.44650i) q^{83} +(-2.93296 - 4.40429i) q^{84} +(5.85372 - 8.14426i) q^{85} +(-3.45683 + 4.08815i) q^{86} +(1.71499 + 1.71499i) q^{87} +(-2.10496 - 8.22859i) q^{88} +3.40001 q^{89} +(3.06732 - 0.769104i) q^{90} +(3.63297 + 8.12356i) q^{91} +(-5.72064 - 4.07055i) q^{92} +(-1.36161 + 1.36161i) q^{93} +(-8.91799 - 7.54081i) q^{94} +(-16.5501 + 2.70815i) q^{95} +(5.27812 + 2.03505i) q^{96} +(-0.895923 - 0.895923i) q^{97} +(-7.90325 - 5.96143i) q^{98} -3.00292 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) $ 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−1.40929	+	0.117921i	−0.996518	+	0.0833830i
$2$	−1.40929	+	0.117921i	−0.996518	+	0.0833830i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$3$	−0.707107	−	0.707107i	−0.408248	−	0.408248i
$4$	1.97219	−	0.332370i	0.986095	−	0.166185i
$5$	0.361094	+	2.20672i	0.161486	+	0.986875i
$5$	0.361094	+	2.20672i	0.161486	+	0.986875i
$6$	1.07990	+	0.913135i	0.440868	+	0.372786i
$7$	2.47159	+	0.944062i	0.934172	+	0.356822i
$7$	2.47159	+	0.944062i	0.934172	+	0.356822i
$8$	−2.74019	+	0.700969i	−0.968804	+	0.247830i
$9$			1.00000i			0.333333i
$10$	−0.769104	−	3.06732i	−0.243212	−	0.969973i
$11$			3.00292i			0.905416i	0.891659	+	0.452708i	$0.149542\pi$
$11$			3.00292i			0.905416i	−0.891659	+	0.452708i	$0.850458\pi$
$12$	−1.62957	−	1.15953i	−0.470416	−	0.334727i
$13$	2.37833	+	2.37833i	0.659631	+	0.659631i	0.955293	−	0.295662i	$-0.0955401\pi$
$13$	2.37833	+	2.37833i	0.659631	+	0.659631i	−0.295662	+	0.955293i	$0.595540\pi$
$14$	−3.59451	−	1.03900i	−0.960672	−	0.277685i
$15$	1.30505	−	1.81572i	0.336964	−	0.468816i
$16$	3.77906	−	1.31099i	0.944765	−	0.327749i
$17$	−3.17167	−	3.17167i	−0.769244	−	0.769244i	0.208730	−	0.977973i	$-0.433067\pi$
$17$	−3.17167	−	3.17167i	−0.769244	−	0.769244i	−0.977973	+	0.208730i	$0.933067\pi$
$18$	−0.117921	−	1.40929i	−0.0277943	−	0.332173i
$19$			7.49985i			1.72058i	0.509802	+	0.860292i	$0.329719\pi$
$19$			7.49985i			1.72058i	−0.509802	+	0.860292i	$0.670281\pi$
$20$	1.44559	+	4.23205i	0.323244	+	0.946316i
$21$	−1.08012	−	2.41523i	−0.235702	−	0.527046i
$22$	−0.354109	−	4.23199i	−0.0754962	−	0.902263i
$23$	−2.48231	−	2.48231i	−0.517598	−	0.517598i	0.399246	−	0.916844i	$-0.369272\pi$
$23$	−2.48231	−	2.48231i	−0.517598	−	0.517598i	−0.916844	+	0.399246i	$0.869272\pi$
$24$	2.43327	+	1.44195i	0.496689	+	0.294336i
$25$	−4.73922	+	1.59366i	−0.947845	+	0.318733i
$26$	−3.63222	−	3.07130i	−0.712336	−	0.602332i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	5.18822	+	1.04039i	0.980481	+	0.196615i
$29$	−2.42536			−0.450379			−0.225189	−	0.974315i	$-0.572300\pi$
$29$	−2.42536			−0.450379			−0.225189	+	0.974315i	$0.572300\pi$
$30$	−1.62509	+	2.71276i	−0.296699	+	0.495281i
$31$		−	1.92561i		−	0.345849i	−0.984935	−	0.172924i	$-0.944678\pi$
$31$		−	1.92561i		−	0.345849i	0.984935	−	0.172924i	$-0.0553216\pi$
$32$	−5.17119	+	2.29320i	−0.914146	+	0.405384i
$33$	2.12339	−	2.12339i	0.369634	−	0.369634i
$34$	4.84381	+	4.09580i	0.830707	+	0.702423i
$35$	−1.19081	+	5.79500i	−0.201283	+	0.979533i
$36$	0.332370	+	1.97219i	0.0553951	+	0.328698i
$37$	−7.03701	−	7.03701i	−1.15688	−	1.15688i	−0.985144	−	0.171733i	$-0.945063\pi$
$37$	−7.03701	−	7.03701i	−1.15688	−	1.15688i	−0.171733	−	0.985144i	$-0.554937\pi$
$38$	−0.884392	−	10.5695i	−0.143467	−	1.71459i
$39$		−	3.36347i		−	0.538587i
$40$	−2.53631	−	5.79372i	−0.401025	−	0.916067i
$41$		−	2.62677i		−	0.410233i	−0.978738	−	0.205116i	$-0.934243\pi$
$41$		−	2.62677i		−	0.410233i	0.978738	−	0.205116i	$-0.0657573\pi$
$42$	1.80701	+	3.27639i	0.278828	+	0.505557i
$43$	2.67688	−	2.67688i	0.408220	−	0.408220i	−0.472897	−	0.881117i	$-0.656792\pi$
$43$	2.67688	−	2.67688i	0.408220	−	0.408220i	0.881117	+	0.472897i	$0.156792\pi$
$44$	0.998083	+	5.92234i	0.150467	+	0.892826i
$45$	−2.20672	+	0.361094i	−0.328958	+	0.0538287i
$46$	3.79102	+	3.20558i	0.558955	+	0.472637i
$47$	5.83940	+	5.83940i	0.851764	+	0.851764i	0.990350	−	0.138586i	$-0.0442559\pi$
$47$	5.83940	+	5.83940i	0.851764	+	0.851764i	−0.138586	+	0.990350i	$0.544256\pi$
$48$	−3.59921	−	1.74519i	−0.519501	−	0.251896i
$49$	5.21749	+	4.66667i	0.745356	+	0.666667i
$50$	6.49101	−	2.80479i	0.917967	−	0.396657i
$51$			4.48542i			0.628085i
$52$	5.48101	+	3.90004i	0.760080	+	0.540838i
$53$	−3.92370	+	3.92370i	−0.538962	+	0.538962i	−0.923224	−	0.384262i	$-0.874456\pi$
$53$	−3.92370	+	3.92370i	−0.538962	+	0.538962i	0.384262	+	0.923224i	$0.374456\pi$
$54$	−0.913135	+	1.07990i	−0.124262	+	0.146956i
$55$	−6.62661	+	1.08434i	−0.893532	+	0.146212i
$56$	−7.43438	−	0.854404i	−0.993461	−	0.114175i
$57$	5.30319	−	5.30319i	0.702425	−	0.702425i
$58$	3.41804	−	0.286002i	0.448810	−	0.0375539i
$59$			12.1091i			1.57647i	0.615373	+	0.788236i	$0.289005\pi$
$59$			12.1091i			1.57647i	−0.615373	+	0.788236i	$0.710995\pi$
$60$	1.97032	−	4.01470i	0.254368	−	0.518296i
$61$	−3.11135			−0.398367			−0.199184	−	0.979962i	$-0.563829\pi$
$61$	−3.11135			−0.398367			−0.199184	+	0.979962i	$0.563829\pi$
$62$	0.227070	+	2.71373i	0.0288379	+	0.344644i
$63$	−0.944062	+	2.47159i	−0.118941	+	0.311391i
$64$	7.01729	−	3.84158i	0.877161	−	0.480197i
$65$	−4.38952	+	6.10712i	−0.544452	+	0.757495i
$66$	−2.74207	+	3.24286i	−0.337526	+	0.399168i
$67$	−5.83002	−	5.83002i	−0.712250	−	0.712250i	0.254756	−	0.967005i	$-0.418005\pi$
$67$	−5.83002	−	5.83002i	−0.712250	−	0.712250i	−0.967005	+	0.254756i	$0.918005\pi$
$68$	−7.30931	−	5.20097i	−0.886384	−	0.630710i
$69$			3.51052i			0.422617i
$70$	0.994836	−	8.30724i	0.118906	−	0.992906i
$71$	1.88481			0.223685			0.111843	−	0.993726i	$-0.464325\pi$
$71$	1.88481			0.223685			0.111843	+	0.993726i	$0.464325\pi$
$72$	−0.700969	−	2.74019i	−0.0826100	−	0.322935i
$73$	−1.14816	+	1.14816i	−0.134382	+	0.134382i	−0.771098	−	0.636716i	$-0.780292\pi$
$73$	−1.14816	+	1.14816i	−0.134382	+	0.134382i	0.636716	+	0.771098i	$0.280292\pi$
$74$	10.7470	+	9.08736i	1.24931	+	1.05638i
$75$	4.47803	+	2.22425i	0.517078	+	0.256834i
$76$	2.49273	+	14.7911i	0.285935	+	1.69666i
$77$	−2.83495	+	7.42199i	−0.323072	+	0.845815i
$78$	0.396625	+	4.74010i	0.0449089	+	0.536711i
$79$			14.4613i			1.62702i	0.581549	+	0.813512i	$0.302447\pi$
$79$			14.4613i			1.62702i	−0.581549	+	0.813512i	$0.697553\pi$
$80$	4.25759	+	7.86593i	0.476013	+	0.879438i
$81$	−1.00000			−0.111111
$82$	0.309752	+	3.70188i	0.0342064	+	0.408804i
$83$	8.44650	+	8.44650i	0.927124	+	0.927124i	0.997519	−	0.0703954i	$-0.0224261\pi$
$83$	8.44650	+	8.44650i	0.927124	+	0.927124i	−0.0703954	+	0.997519i	$0.522426\pi$
$84$	−2.93296	−	4.40429i	−0.320012	−	0.480547i
$85$	5.85372	−	8.14426i	0.634925	−	0.883370i
$86$	−3.45683	+	4.08815i	−0.372760	+	0.440837i
$87$	1.71499	+	1.71499i	0.183866	+	0.183866i
$88$	−2.10496	−	8.22859i	−0.224389	−	0.877170i
$89$	3.40001			0.360400			0.180200	−	0.983630i	$-0.442325\pi$
$89$	3.40001			0.360400			0.180200	+	0.983630i	$0.442325\pi$
$90$	3.06732	−	0.769104i	0.323324	−	0.0810707i
$91$	3.63297	+	8.12356i	0.380838	+	0.851580i
$92$	−5.72064	−	4.07055i	−0.596418	−	0.424384i
$93$	−1.36161	+	1.36161i	−0.141192	+	0.141192i
$94$	−8.91799	−	7.54081i	−0.919820	−	0.777775i
$95$	−16.5501	+	2.70815i	−1.69800	+	0.277850i
$96$	5.27812	+	2.03505i	0.538696	+	0.207701i
$97$	−0.895923	−	0.895923i	−0.0909672	−	0.0909672i	0.660159	−	0.751126i	$-0.270489\pi$
$97$	−0.895923	−	0.895923i	−0.0909672	−	0.0909672i	−0.751126	+	0.660159i	$0.770489\pi$
$98$	−7.90325	−	5.96143i	−0.798349	−	0.602195i
$99$	−3.00292			−0.301805
$100$	−8.81696	+	4.71818i	−0.881696	+	0.471818i
$101$	3.27179			0.325556			0.162778	−	0.986663i	$-0.447955\pi$
$101$	3.27179			0.325556			0.162778	+	0.986663i	$0.447955\pi$
$102$	−0.528927	−	6.32126i	−0.0523716	−	0.625898i
$103$	−10.5912	+	10.5912i	−1.04359	+	1.04359i	−0.0445799	+	0.999006i	$0.514195\pi$
$103$	−10.5912	+	10.5912i	−1.04359	+	1.04359i	−0.999006	+	0.0445799i	$0.985805\pi$
$104$	−8.18423	−	4.84995i	−0.802529	−	0.475577i
$105$	4.93971	−	3.25565i	0.482066	−	0.317719i
$106$	5.06694	−	5.99232i	0.492145	−	0.582025i
$107$	−0.666115	−	0.666115i	−0.0643957	−	0.0643957i	0.674175	−	0.738571i	$-0.264499\pi$
$107$	−0.666115	−	0.666115i	−0.0643957	−	0.0643957i	−0.738571	+	0.674175i	$0.764499\pi$
$108$	1.15953	−	1.62957i	0.111576	−	0.156805i
$109$	11.7431			1.12479			0.562394	−	0.826869i	$-0.309880\pi$
$109$	11.7431			1.12479			0.562394	+	0.826869i	$0.309880\pi$
$110$	9.21094	−	2.30956i	0.878229	−	0.220208i
$111$			9.95183i			0.944586i
$112$	10.5779	+	0.327431i	0.999521	+	0.0309393i
$113$	0.890203	+	0.890203i	0.0837432	+	0.0837432i	0.747738	−	0.663994i	$-0.231140\pi$
$113$	0.890203	+	0.890203i	0.0837432	+	0.0837432i	−0.663994	+	0.747738i	$0.731140\pi$
$114$	−6.84837	+	8.09909i	−0.641409	+	0.758549i
$115$	4.58142	−	6.37412i	0.427220	−	0.594390i
$116$	−4.78328	+	0.806119i	−0.444116	+	0.0748463i
$117$	−2.37833	+	2.37833i	−0.219877	+	0.219877i
$118$	−1.42792	−	17.0652i	−0.131451	−	1.57098i
$119$	−4.84481	−	10.8333i	−0.444123	−	0.993089i
$120$	−2.30334	+	5.89022i	−0.210265	+	0.537701i
$121$	1.98244			0.180222
$122$	4.38479	−	0.366894i	0.396980	−	0.0332170i
$123$	−1.85741	+	1.85741i	−0.167477	+	0.167477i
$124$	−0.640014	−	3.79766i	−0.0574749	−	0.341040i
$125$	−5.22807	−	9.88267i	−0.467613	−	0.883933i
$126$	1.03900	−	3.59451i	0.0925618	−	0.320224i
$127$	7.20293	−	7.20293i	0.639157	−	0.639157i	−0.311191	−	0.950347i	$-0.600728\pi$
$127$	7.20293	−	7.20293i	0.639157	−	0.639157i	0.950347	+	0.311191i	$0.100728\pi$
$128$	−9.43638	+	6.24138i	−0.834066	+	0.551665i
$129$	−3.78568			−0.333310
$130$	5.46593	−	9.12431i	0.479394	−	0.800255i
$131$	−0.273205			−0.0238700			−0.0119350	−	0.999929i	$-0.503799\pi$
$131$	−0.273205			−0.0238700			−0.0119350	+	0.999929i	$0.503799\pi$
$132$	3.48197	−	4.89347i	0.303067	−	0.425922i
$133$	−7.08033	+	18.5365i	−0.613942	+	1.60732i
$134$	8.90366	+	7.52869i	0.769159	+	0.650380i
$135$	1.81572	+	1.30505i	0.156272	+	0.112321i
$136$	10.9142	+	6.46774i	0.935888	+	0.554605i
$137$	12.4496	−	12.4496i	1.06364	−	1.06364i	0.0658125	−	0.997832i	$-0.479036\pi$
$137$	12.4496	−	12.4496i	1.06364	−	1.06364i	0.997832	−	0.0658125i	$-0.0209639\pi$
$138$	−0.413965	−	4.94734i	−0.0352391	−	0.421146i
$139$			6.67967i			0.566562i	0.959037	+	0.283281i	$0.0914229\pi$
$139$			6.67967i			0.566562i	−0.959037	+	0.283281i	$0.908577\pi$
$140$	−0.422411	+	11.8246i	−0.0357002	+	0.999363i
$141$		−	8.25816i		−	0.695462i
$142$	−2.65624	+	0.222259i	−0.222906	+	0.0186515i
$143$	−7.14196	+	7.14196i	−0.597241	+	0.597241i
$144$	1.31099	+	3.77906i	0.109250	+	0.314922i
$145$	−0.875784	−	5.35210i	−0.0727299	−	0.444468i
$146$	1.48269	−	1.75348i	0.122709	−	0.145119i
$147$	−0.389493	−	6.98916i	−0.0321249	−	0.576456i
$148$	−16.2172	−	11.5394i	−1.33305	−	0.948534i
$149$	−5.54020			−0.453871			−0.226935	−	0.973910i	$-0.572871\pi$
$149$	−5.54020			−0.453871			−0.226935	+	0.973910i	$0.572871\pi$
$150$	−6.57312	−	2.60655i	−0.536693	−	0.212824i
$151$	0.135366			0.0110159			0.00550796	−	0.999985i	$-0.498247\pi$
$151$	0.135366			0.0110159			0.00550796	+	0.999985i	$0.498247\pi$
$152$	−5.25716	−	20.5510i	−0.426412	−	1.66691i
$153$	3.17167	−	3.17167i	0.256415	−	0.256415i
$154$	3.12005	−	10.7940i	0.251421	−	0.869808i
$155$	4.24927	−	0.695324i	0.341310	−	0.0558497i
$156$	−1.11792	−	6.63340i	−0.0895051	−	0.531097i
$157$	2.85632	−	2.85632i	0.227959	−	0.227959i	−0.583881	−	0.811840i	$-0.698466\pi$
$157$	2.85632	−	2.85632i	0.227959	−	0.227959i	0.811840	+	0.583881i	$0.198466\pi$
$158$	−1.70529	−	20.3801i	−0.135666	−	1.62136i
$159$	5.54895			0.440061
$160$	−6.92774	−	10.5833i	−0.547686	−	0.836684i
$161$	−3.79180	−	8.47872i	−0.298836	−	0.668217i
$162$	1.40929	−	0.117921i	0.110724	−	0.00926477i
$163$	−13.0658	+	13.0658i	−1.02339	+	1.02339i	−0.0236748	+	0.999720i	$0.507537\pi$
$163$	−13.0658	+	13.0658i	−1.02339	+	1.02339i	−0.999720	+	0.0236748i	$0.992463\pi$
$164$	−0.873060	−	5.18049i	−0.0681746	−	0.404528i
$165$	5.45246	+	3.91898i	0.424474	+	0.305092i
$166$	−12.8996	−	10.9075i	−1.00120	−	0.846589i
$167$	0.369628	+	0.369628i	0.0286027	+	0.0286027i	0.721263	−	0.692661i	$-0.243562\pi$
$167$	0.369628	+	0.369628i	0.0286027	+	0.0286027i	−0.692661	+	0.721263i	$0.743562\pi$
$168$	4.65274	+	5.86106i	0.358967	+	0.452190i
$169$		−	1.68705i		−	0.129773i
$170$	−7.28920	+	12.1679i	−0.559056	+	0.933235i
$171$	−7.49985			−0.573528
$172$	4.38959	−	6.16902i	0.334703	−	0.470384i
$173$	−11.3541	−	11.3541i	−0.863233	−	0.863233i	0.128479	−	0.991712i	$-0.458990\pi$
$173$	−11.3541	−	11.3541i	−0.863233	−	0.863233i	−0.991712	+	0.128479i	$0.958990\pi$
$174$	−2.61915	−	2.21468i	−0.198557	−	0.167895i
$175$	−13.2179	−	0.535240i	−0.999181	−	0.0404603i
$176$	3.93682	+	11.3482i	0.296749	+	0.855405i
$177$	8.56243	−	8.56243i	0.643592	−	0.643592i
$178$	−4.79160	+	0.400934i	−0.359145	+	0.0300512i
$179$	24.1089			1.80199			0.900994	−	0.433832i	$-0.142839\pi$
$179$	24.1089			1.80199			0.900994	+	0.433832i	$0.142839\pi$
$180$	−4.23205	+	1.44559i	−0.315439	+	0.107748i
$181$	−8.93271			−0.663963			−0.331981	−	0.943286i	$-0.607717\pi$
$181$	−8.93271			−0.663963			−0.331981	+	0.943286i	$0.607717\pi$
$182$	−6.07784	−	11.0200i	−0.450519	−	0.816859i
$183$	2.20005	+	2.20005i	0.162633	+	0.162633i
$184$	8.54204	+	5.06199i	0.629728	+	0.373175i
$185$	12.9877	−	18.0697i	0.954873	−	1.32851i
$186$	1.75834	−	2.07946i	0.128927	−	0.152474i
$187$	9.52430	−	9.52430i	0.696486	−	0.696486i
$188$	13.4572	+	9.57556i	0.981470	+	0.698369i
$189$	2.41523	−	1.08012i	0.175682	−	0.0785674i
$190$	23.0045	−	5.76817i	1.66892	−	0.418467i
$191$	−2.58414			−0.186982			−0.0934908	−	0.995620i	$-0.529803\pi$
$191$	−2.58414			−0.186982			−0.0934908	+	0.995620i	$0.529803\pi$
$192$	−7.67837	−	2.24557i	−0.554139	−	0.162060i
$193$	12.7542	+	12.7542i	0.918070	+	0.918070i	0.996889	−	0.0788185i	$-0.0251148\pi$
$193$	12.7542	+	12.7542i	0.918070	+	0.918070i	−0.0788185	+	0.996889i	$0.525115\pi$
$194$	1.36826	+	1.15697i	0.0982355	+	0.0830653i
$195$	7.42224	−	1.21453i	0.531518	−	0.0869742i
$196$	11.8409	+	7.46941i	0.845782	+	0.533529i
$197$	12.5295	+	12.5295i	0.892687	+	0.892687i	0.994775	−	0.102088i	$-0.0325523\pi$
$197$	12.5295	+	12.5295i	0.892687	+	0.892687i	−0.102088	+	0.994775i	$0.532552\pi$
$198$	4.23199	−	0.354109i	0.300754	−	0.0251654i
$199$	−11.5976			−0.822129			−0.411065	−	0.911606i	$-0.634843\pi$
$199$	−11.5976			−0.822129			−0.411065	+	0.911606i	$0.634843\pi$
$200$	11.8693	−	7.68899i	0.839284	−	0.543694i
$201$			8.24489i			0.581550i
$202$	−4.61090	+	0.385814i	−0.324422	+	0.0271458i
$203$	−5.99450	−	2.28970i	−0.420732	−	0.160705i
$204$	1.49082	+	8.84610i	0.104378	+	0.619351i
$205$	5.79655	−	0.948510i	0.404848	−	0.0662468i
$206$	13.6772	−	16.1750i	0.952934	−	1.12697i
$207$	2.48231	−	2.48231i	0.172533	−	0.172533i
$208$	12.1058	+	5.86988i	0.839390	+	0.407003i
$209$	−22.5215			−1.55784
$210$	−6.57756	+	5.17065i	−0.453895	+	0.356809i
$211$		−	25.5145i		−	1.75649i	−0.478213	−	0.878244i	$-0.658715\pi$
$211$		−	25.5145i		−	1.75649i	0.478213	−	0.878244i	$-0.341285\pi$
$212$	−6.43416	+	9.04241i	−0.441900	+	0.621035i
$213$	−1.33276	−	1.33276i	−0.0913192	−	0.0913192i
$214$	1.01730	+	0.860199i	0.0695410	+	0.0588020i
$215$	6.87372	+	4.94051i	0.468784	+	0.336940i
$216$	−1.44195	+	2.43327i	−0.0981121	+	0.165563i
$217$	1.81789	−	4.75930i	0.123406	−	0.323082i
$218$	−16.5495	+	1.38477i	−1.12087	+	0.0937881i
$219$	1.62374			0.109722
$220$	−12.7085	+	4.34101i	−0.856809	+	0.292671i
$221$		−	15.0866i		−	1.01483i
$222$	−1.17353	−	14.0250i	−0.0787624	−	0.941296i
$223$	17.1885	−	17.1885i	1.15102	−	1.15102i	0.164676	−	0.986348i	$-0.447342\pi$
$223$	17.1885	−	17.1885i	1.15102	−	1.15102i	0.986348	−	0.164676i	$-0.0526580\pi$
$224$	−14.9460	+	0.785920i	−0.998620	+	0.0525115i
$225$	−1.59366	−	4.73922i	−0.106244	−	0.315948i
$226$	−1.35953	−	1.14958i	−0.0904343	−	0.0764688i
$227$	13.5914	−	13.5914i	0.902094	−	0.902094i	−0.0935233	−	0.995617i	$-0.529813\pi$
$227$	13.5914	−	13.5914i	0.902094	−	0.902094i	0.995617	+	0.0935233i	$0.0298130\pi$
$228$	8.69628	−	12.2215i	0.575925	−	0.809390i
$229$		−	7.88853i		−	0.521289i	−0.965435	−	0.260644i	$-0.916065\pi$
$229$		−	7.88853i		−	0.521289i	0.965435	−	0.260644i	$-0.0839350\pi$
$230$	−5.70491	+	9.52322i	−0.376170	+	0.627943i
$231$	7.25275	−	3.24353i	0.477196	−	0.213409i
$232$	6.64596	−	1.70010i	0.436329	−	0.111617i
$233$	20.9449	+	20.9449i	1.37214	+	1.37214i	0.857260	+	0.514884i	$0.172165\pi$
$233$	20.9449	+	20.9449i	1.37214	+	1.37214i	0.514884	+	0.857260i	$0.327835\pi$
$234$	3.07130	−	3.63222i	0.200777	−	0.237445i
$235$	−10.7773	+	14.9945i	−0.703037	+	0.978132i
$236$	4.02471	+	23.8815i	0.261986	+	1.55455i
$237$	10.2257	−	10.2257i	0.664229	−	0.664229i
$238$	8.10522	+	14.6960i	0.525383	+	0.952599i
$239$		−	11.3812i		−	0.736186i	−0.929789	−	0.368093i	$-0.880011\pi$
$239$		−	11.3812i		−	0.736186i	0.929789	−	0.368093i	$-0.119989\pi$
$240$	2.55148	−	8.57263i	0.164698	−	0.553361i
$241$		−	15.4129i		−	0.992834i	−0.868084	−	0.496417i	$-0.834649\pi$
$241$		−	15.4129i		−	0.992834i	0.868084	−	0.496417i	$-0.165351\pi$
$242$	−2.79383	+	0.233772i	−0.179594	+	0.0150274i
$243$	0.707107	+	0.707107i	0.0453609	+	0.0453609i
$244$	−6.13617	+	1.03412i	−0.392828	+	0.0662027i
$245$	−8.41402	+	13.1986i	−0.537552	+	0.843231i
$246$	2.39859	−	2.83665i	0.152929	−	0.180858i
$247$	−17.8371	+	17.8371i	−1.13495	+	1.13495i
$248$	1.34979	+	5.27652i	0.0857117	+	0.335060i
$249$		−	11.9452i		−	0.756993i
$250$	8.53324	+	13.3110i	0.539690	+	0.841864i
$251$	12.7592			0.805356			0.402678	−	0.915342i	$-0.368079\pi$
$251$	12.7592			0.805356			0.402678	+	0.915342i	$0.368079\pi$
$252$	−1.04039	+	5.18822i	−0.0655382	+	0.326827i
$253$	7.45420	−	7.45420i	0.468642	−	0.468642i
$254$	−9.30163	+	11.0004i	−0.583636	+	0.690226i
$255$	−9.89807	+	1.61966i	−0.619841	+	0.101427i
$256$	12.5626	−	9.90865i	0.785162	−	0.619291i
$257$	15.0108	+	15.0108i	0.936348	+	0.936348i	0.998092	−	0.0617442i	$-0.0196663\pi$
$257$	15.0108	+	15.0108i	0.936348	+	0.936348i	−0.0617442	+	0.998092i	$0.519666\pi$
$258$	5.33511	−	0.446412i	0.332149	−	0.0277924i
$259$	−10.7492	−	24.0360i	−0.667923	−	1.49352i
$260$	−6.62713	+	13.5033i	−0.410997	+	0.837441i
$261$		−	2.42536i		−	0.150126i
$262$	0.385024	−	0.0322166i	0.0237869	−	0.00199035i
$263$	−11.0013	−	11.0013i	−0.678369	−	0.678369i	0.281262	−	0.959631i	$-0.409247\pi$
$263$	−11.0013	−	11.0013i	−0.678369	−	0.678369i	−0.959631	+	0.281262i	$0.909247\pi$
$264$	−4.33006	+	7.30692i	−0.266497	+	0.449710i
$265$	−10.0753	−	7.24169i	−0.618923	−	0.444853i
$266$	7.79237	−	26.9583i	0.477781	−	1.65292i
$267$	−2.40417	−	2.40417i	−0.147133	−	0.147133i
$268$	−13.4356	−	9.56017i	−0.820711	−	0.583980i
$269$			8.37372i			0.510555i	0.966868	+	0.255277i	$0.0821668\pi$
$269$			8.37372i			0.510555i	−0.966868	+	0.255277i	$0.917833\pi$
$270$	−2.71276	−	1.62509i	−0.165094	−	0.0988996i
$271$			5.26514i			0.319834i	0.987130	+	0.159917i	$0.0511227\pi$
$271$			5.26514i			0.319834i	−0.987130	+	0.159917i	$0.948877\pi$
$272$	−16.1440	−	7.82790i	−0.978873	−	0.474636i
$273$	3.17533	−	8.31312i	0.192180	−	0.503133i
$274$	−16.0771	+	19.0132i	−0.971251	+	1.14863i
$275$	−4.78565	−	14.2315i	−0.288586	−	0.858194i
$276$	1.16679	+	6.92342i	0.0702327	+	0.416741i
$277$	11.6013	+	11.6013i	0.697055	+	0.697055i	0.963774	−	0.266719i	$-0.0859396\pi$
$277$	11.6013	+	11.6013i	0.697055	+	0.697055i	−0.266719	+	0.963774i	$0.585940\pi$
$278$	−0.787675	−	9.41358i	−0.0472416	−	0.564589i
$279$	1.92561			0.115283
$280$	−0.799076	−	16.7141i	−0.0477539	−	0.998859i
$281$	−12.0023			−0.715997			−0.357998	−	0.933722i	$-0.616541\pi$
$281$	−12.0023			−0.715997			−0.357998	+	0.933722i	$0.616541\pi$
$282$	0.973813	+	11.6381i	0.0579897	+	0.693040i
$283$	3.99550	+	3.99550i	0.237508	+	0.237508i	0.815817	−	0.578309i	$-0.196287\pi$
$283$	3.99550	+	3.99550i	0.237508	+	0.237508i	−0.578309	+	0.815817i	$0.696287\pi$
$284$	3.71719	−	0.626454i	0.220575	−	0.0371732i
$285$	13.6176	+	9.78771i	0.806638	+	0.579774i
$286$	9.22289	−	10.9073i	0.545361	−	0.644960i
$287$	2.47983	−	6.49229i	0.146380	−	0.383228i
$288$	−2.29320	−	5.17119i	−0.135128	−	0.304715i
$289$			3.11903i			0.183472i
$290$	1.86536	+	7.43938i	0.109538	+	0.436855i
$291$			1.26703i			0.0742744i
$292$	−1.88277	+	2.64600i	−0.110181	+	0.154845i
$293$	−21.8942	−	21.8942i	−1.27907	−	1.27907i	−0.941186	−	0.337888i	$-0.890287\pi$
$293$	−21.8942	−	21.8942i	−1.27907	−	1.27907i	−0.337888	−	0.941186i	$-0.609713\pi$
$294$	1.37308	+	9.80381i	0.0800796	+	0.571770i
$295$	−26.7214	+	4.37252i	−1.55578	+	0.254578i
$296$	24.2155	+	14.3500i	1.40749	+	0.834078i
$297$	2.12339	+	2.12339i	0.123211	+	0.123211i
$298$	7.80773	−	0.653307i	0.452290	−	0.0378451i
$299$		−	11.8075i		−	0.682848i
$300$	9.57079	+	2.89827i	0.552570	+	0.167332i
$301$	9.14328	−	4.08900i	0.527010	−	0.235686i
$302$	−0.190770	+	0.0159625i	−0.0109776	+	0.000918540i
$303$	−2.31351	−	2.31351i	−0.132908	−	0.132908i
$304$	9.83226	+	28.3424i	0.563919	+	1.62555i
$305$	−1.12349	−	6.86587i	−0.0643307	−	0.393139i
$306$	−4.09580	+	4.84381i	−0.234141	+	0.276902i
$307$	−20.0439	+	20.0439i	−1.14397	+	1.14397i	−0.156251	+	0.987717i	$0.549941\pi$
$307$	−20.0439	+	20.0439i	−1.14397	+	1.14397i	−0.987717	+	0.156251i	$0.950059\pi$
$308$	−3.12420	+	15.5798i	−0.178018	+	0.887743i
$309$	14.9783			0.852084
$310$	−5.90646	+	1.48099i	−0.335464	+	0.0841146i
$311$			2.95009i			0.167284i	0.996496	+	0.0836421i	$0.0266552\pi$
$311$			2.95009i			0.167284i	−0.996496	+	0.0836421i	$0.973345\pi$
$312$	2.35769	+	9.21655i	0.133478	+	0.521785i
$313$	−8.39886	+	8.39886i	−0.474732	+	0.474732i	−0.903442	−	0.428710i	$-0.858968\pi$
$313$	−8.39886	+	8.39886i	−0.474732	+	0.474732i	0.428710	+	0.903442i	$0.358968\pi$
$314$	−3.68855	+	4.36220i	−0.208157	+	0.246173i
$315$	−5.79500	−	1.19081i	−0.326511	−	0.0670943i
$316$	4.80651	+	28.5204i	0.270387	+	1.60440i
$317$	−24.0231	−	24.0231i	−1.34927	−	1.34927i	−0.886455	−	0.462815i	$-0.846840\pi$
$317$	−24.0231	−	24.0231i	−1.34927	−	1.34927i	−0.462815	−	0.886455i	$-0.653160\pi$
$318$	−7.82008	+	0.654340i	−0.438528	+	0.0366936i
$319$		−	7.28319i		−	0.407780i
$320$	11.0112	+	14.0980i	0.615544	+	0.788103i
$321$			0.942028i			0.0525789i
$322$	6.34356	+	11.5018i	0.353513	+	0.640972i
$323$	23.7871	−	23.7871i	1.32355	−	1.32355i
$324$	−1.97219	+	0.332370i	−0.109566	+	0.0184650i
$325$	−15.0617	−	7.48119i	−0.835474	−	0.414982i
$326$	16.8728	−	19.9543i	0.934497	−	1.10516i
$327$	−8.30365	−	8.30365i	−0.459193	−	0.459193i
$328$	1.84128	+	7.19785i	0.101668	+	0.397435i
$329$	8.91983	+	19.9453i	0.491766	+	1.09962i
$330$	−8.14623	−	4.88001i	−0.448435	−	0.268636i
$331$			23.5363i			1.29367i	0.762628	+	0.646837i	$0.223909\pi$
$331$			23.5363i			1.29367i	−0.762628	+	0.646837i	$0.776091\pi$
$332$	19.4655	+	13.8507i	1.06831	+	0.760157i
$333$	7.03701	−	7.03701i	0.385626	−	0.385626i
$334$	−0.564499	−	0.477325i	−0.0308880	−	0.0261181i
$335$	10.7600	−	14.9704i	0.587883	−	0.817920i
$336$	−7.24820	−	7.71126i	−0.395422	−	0.420684i
$337$	−18.0931	+	18.0931i	−0.985592	+	0.985592i	−0.999898	−	0.0143053i	$-0.995446\pi$
$337$	−18.0931	+	18.0931i	−0.985592	+	0.985592i	0.0143053	+	0.999898i	$0.495446\pi$
$338$	0.198940	+	2.37755i	0.0108209	+	0.129321i
$339$		−	1.25894i		−	0.0683761i
$340$	8.83774	−	18.0076i	0.479294	−	0.976601i
$341$	5.78245			0.313137
$342$	10.5695	−	0.884392i	0.571531	−	0.0478224i
$343$	8.48987	+	16.4597i	0.458410	+	0.888741i
$344$	−5.45875	+	9.21156i	−0.294316	+	0.496654i
$345$	−7.74674	+	1.26763i	−0.417070	+	0.0682468i
$346$	17.3400	+	14.6623i	0.932205	+	0.788248i
$347$	23.5853	+	23.5853i	1.26613	+	1.26613i	0.948072	+	0.318055i	$0.103030\pi$
$347$	23.5853	+	23.5853i	1.26613	+	1.26613i	0.318055	+	0.948072i	$0.396970\pi$
$348$	3.95230	+	2.81228i	0.211866	+	0.150754i
$349$		−	23.3192i		−	1.24825i	−0.781324	−	0.624125i	$-0.785456\pi$
$349$		−	23.3192i		−	1.24825i	0.781324	−	0.624125i	$-0.214544\pi$
$350$	18.6910	−	0.804367i	0.999075	−	0.0429952i
$351$	3.36347			0.179529
$352$	−6.88631	−	15.5287i	−0.367042	−	0.827683i
$353$	−18.0172	+	18.0172i	−0.958959	+	0.958959i	−0.999190	−	0.0402313i	$-0.987191\pi$
$353$	−18.0172	+	18.0172i	−0.958959	+	0.958959i	0.0402313	+	0.999190i	$0.487191\pi$
$354$	−11.0572	+	13.0766i	−0.587686	+	0.695015i
$355$	0.680591	+	4.15924i	0.0361220	+	0.220749i
$356$	6.70546	−	1.13006i	0.355389	−	0.0598932i
$357$	−4.23452	+	11.0861i	−0.224115	+	0.586740i
$358$	−33.9765	+	2.84296i	−1.79571	+	0.150255i
$359$		−	21.4705i		−	1.13317i	−0.824003	−	0.566586i	$-0.808264\pi$
$359$		−	21.4705i		−	1.13317i	0.824003	−	0.566586i	$-0.191736\pi$
$360$	5.79372	−	2.53631i	0.305356	−	0.133675i
$361$	−37.2477			−1.96041
$362$	12.5888	−	1.05336i	0.661651	−	0.0553632i
$363$	−1.40180	−	1.40180i	−0.0735753	−	0.0735753i
$364$	9.86493	+	14.8137i	0.517063	+	0.776449i
$365$	−2.94826	−	2.11907i	−0.154319	−	0.110917i
$366$	−3.35995	−	2.84108i	−0.175627	−	0.148506i
$367$	25.6709	+	25.6709i	1.34001	+	1.34001i	0.896043	+	0.443967i	$0.146429\pi$
$367$	25.6709	+	25.6709i	1.34001	+	1.34001i	0.443967	+	0.896043i	$0.353571\pi$
$368$	−12.6351	−	6.12652i	−0.658651	−	0.319367i
$369$	2.62677			0.136744
$370$	−16.1726	+	26.9970i	−0.840773	+	1.40351i
$371$	−13.4020	+	5.99356i	−0.695797	+	0.311170i
$372$	−2.23279	+	3.13791i	−0.115765	+	0.162693i
$373$	1.68540	−	1.68540i	0.0872665	−	0.0872665i	−0.662126	−	0.749393i	$-0.730346\pi$
$373$	1.68540	−	1.68540i	0.0872665	−	0.0872665i	0.749393	+	0.662126i	$0.230346\pi$
$374$	−12.2994	+	14.5456i	−0.635985	+	0.752135i
$375$	−3.29130	+	10.6849i	−0.169962	+	0.551766i
$376$	−20.0943	−	11.9078i	−1.03628	−	0.614099i
$377$	−5.76833	−	5.76833i	−0.297084	−	0.297084i
$378$	−3.27639	+	1.80701i	−0.168519	+	0.0929427i
$379$	11.0290			0.566523			0.283262	−	0.959043i	$-0.408584\pi$
$379$	11.0290			0.566523			0.283262	+	0.959043i	$0.408584\pi$
$380$	−31.7398	+	10.8417i	−1.62821	+	0.556169i
$381$	−10.1865			−0.521869
$382$	3.64180	−	0.304725i	0.186330	−	0.0155911i
$383$	12.6130	−	12.6130i	0.644495	−	0.644495i	−0.307162	−	0.951657i	$-0.599379\pi$
$383$	12.6130	−	12.6130i	0.644495	−	0.644495i	0.951657	+	0.307162i	$0.0993795\pi$
$384$	11.0858	+	2.25921i	0.565722	+	0.115290i
$385$	−17.4019	−	3.57590i	−0.886885	−	0.182245i
$386$	−19.4784	−	16.4704i	−0.991425	−	0.838322i
$387$	2.67688	+	2.67688i	0.136073	+	0.136073i
$388$	−2.06471	−	1.46915i	−0.104820	−	0.0745848i
$389$	−34.1653			−1.73225			−0.866125	−	0.499828i	$-0.833397\pi$
$389$	−34.1653			−1.73225			−0.866125	+	0.499828i	$0.833397\pi$
$390$	−10.3169	+	2.58686i	−0.522415	+	0.130991i
$391$			15.7462i			0.796319i
$392$	−17.5681	−	9.13025i	−0.887324	−	0.461147i
$393$	0.193185	+	0.193185i	0.00974488	+	0.00974488i
$394$	−19.1351	−	16.1801i	−0.964014	−	0.815144i
$395$	−31.9120	+	5.22188i	−1.60567	+	0.262741i
$396$	−5.92234	+	0.998083i	−0.297609	+	0.0501556i
$397$	−23.7065	+	23.7065i	−1.18979	+	1.18979i	−0.212670	+	0.977124i	$0.568216\pi$
$397$	−23.7065	+	23.7065i	−1.18979	+	1.18979i	−0.977124	+	0.212670i	$0.931784\pi$
$398$	16.3443	−	1.36760i	0.819266	−	0.0685515i
$399$	18.1139	−	8.10077i	0.906827	−	0.405546i
$400$	−15.8205	+	12.2356i	−0.791026	+	0.611782i
$401$	16.9872			0.848302			0.424151	−	0.905592i	$-0.360573\pi$
$401$	16.9872			0.848302			0.424151	+	0.905592i	$0.360573\pi$
$402$	−0.972248	−	11.6194i	−0.0484913	−	0.579524i
$403$	4.57973	−	4.57973i	0.228133	−	0.228133i
$404$	6.45260	−	1.08745i	0.321029	−	0.0541025i
$405$	−0.361094	−	2.20672i	−0.0179429	−	0.109653i
$406$	8.71799	+	2.51996i	0.432666	+	0.125064i
$407$	21.1316	−	21.1316i	1.04745	−	1.04745i
$408$	−3.14414	−	12.2909i	−0.155658	−	0.608491i
$409$	28.8479			1.42644			0.713218	−	0.700942i	$-0.247237\pi$
$409$	28.8479			1.42644			0.713218	+	0.700942i	$0.247237\pi$
$410$	−8.05716	+	2.02026i	−0.397915	+	0.0997735i
$411$	−17.6064			−0.868462
$412$	−17.3677	+	24.4081i	−0.855646	+	1.20250i
$413$	−11.4318	+	29.9287i	−0.562520	+	1.47270i
$414$	−3.20558	+	3.79102i	−0.157546	+	0.186318i
$415$	−15.5891	+	21.6890i	−0.765238	+	1.06467i
$416$	−17.7528	−	6.84482i	−0.870404	−	0.335595i
$417$	4.72324	−	4.72324i	0.231298	−	0.231298i
$418$	31.7393	−	2.65576i	1.55242	−	0.129898i
$419$			24.0295i			1.17392i	0.809617	+	0.586958i	$0.199675\pi$
$419$			24.0295i			1.17392i	−0.809617	+	0.586958i	$0.800325\pi$
$420$	8.65996	−	8.06258i	0.422563	−	0.393413i
$421$		−	17.2247i		−	0.839481i	−0.907644	−	0.419741i	$-0.862121\pi$
$421$		−	17.2247i		−	0.839481i	0.907644	−	0.419741i	$-0.137879\pi$
$422$	3.00870	+	35.9572i	0.146461	+	1.75037i
$423$	−5.83940	+	5.83940i	−0.283921	+	0.283921i
$424$	8.00130	−	13.5021i	0.388577	−	0.655719i
$425$	20.0859	+	9.97668i	0.974307	+	0.483940i
$426$	2.03540	+	1.72108i	0.0986156	+	0.0833867i
$427$	−7.68997	−	2.93731i	−0.372144	−	0.142146i
$428$	−1.53510	−	1.09231i	−0.0742019	−	0.0527987i
$429$	10.1003			0.487645
$430$	−10.2696	−	6.15205i	−0.495246	−	0.296678i
$431$	20.3538			0.980408			0.490204	−	0.871608i	$-0.336922\pi$
$431$	20.3538			0.980408			0.490204	+	0.871608i	$0.336922\pi$
$432$	1.74519	−	3.59921i	0.0839653	−	0.173167i
$433$	13.7548	−	13.7548i	0.661014	−	0.661014i	−0.294605	−	0.955619i	$-0.595188\pi$
$433$	13.7548	−	13.7548i	0.661014	−	0.661014i	0.955619	+	0.294605i	$0.0951881\pi$
$434$	−2.00071	+	6.92160i	−0.0960372	+	0.332247i
$435$	−3.16523	+	4.40378i	−0.151761	+	0.211145i
$436$	23.1597	−	3.90307i	1.10915	−	0.186923i
$437$	18.6170	−	18.6170i	0.890571	−	0.890571i
$438$	−2.28832	+	0.191474i	−0.109340	+	0.00914896i
$439$	−24.3515			−1.16223			−0.581116	−	0.813821i	$-0.697384\pi$
$439$	−24.3515			−1.16223			−0.581116	+	0.813821i	$0.697384\pi$
$440$	17.3981	−	7.61634i	0.829422	−	0.363095i
$441$	−4.66667	+	5.21749i	−0.222222	+	0.248452i
$442$	1.77903	+	21.2614i	0.0846199	+	1.01130i
$443$	15.8768	−	15.8768i	0.754330	−	0.754330i	−0.220954	−	0.975284i	$-0.570917\pi$
$443$	15.8768	−	15.8768i	0.754330	−	0.754330i	0.975284	+	0.220954i	$0.0709170\pi$
$444$	3.30769	+	19.6269i	0.156976	+	0.931451i
$445$	1.22772	+	7.50287i	0.0581996	+	0.355670i
$446$	−22.1966	+	26.2504i	−1.05104	+	1.24299i
$447$	3.91751	+	3.91751i	0.185292	+	0.185292i
$448$	20.9705	−	2.87004i	0.990764	−	0.135597i
$449$			12.7243i			0.600497i	0.953861	+	0.300248i	$0.0970696\pi$
$449$			12.7243i			0.600497i	−0.953861	+	0.300248i	$0.902930\pi$
$450$	2.80479	+	6.49101i	0.132219	+	0.305989i
$451$	7.88799			0.371431
$452$	2.05152	+	1.45977i	0.0964956	+	0.0686619i
$453$	−0.0957181	−	0.0957181i	−0.00449723	−	0.00449723i
$454$	−17.5515	+	20.7569i	−0.823733	+	0.974172i
$455$	−16.6146	+	10.9503i	−0.778903	+	0.513358i
$456$	−10.8144	+	18.2491i	−0.506430	+	0.854594i
$457$	27.6729	−	27.6729i	1.29449	−	1.29449i	0.362503	−	0.931983i	$-0.381922\pi$
$457$	27.6729	−	27.6729i	1.29449	−	1.29449i	0.931983	−	0.362503i	$-0.118078\pi$
$458$	0.930226	+	11.1172i	0.0434666	+	0.519473i
$459$	−4.48542			−0.209362
$460$	6.91687	−	14.0937i	0.322501	−	0.657122i
$461$	22.9930			1.07089			0.535445	−	0.844570i	$-0.320144\pi$
$461$	22.9930			1.07089			0.535445	+	0.844570i	$0.320144\pi$
$462$	−9.83874	+	5.42632i	−0.457740	+	0.252455i
$463$	27.3905	+	27.3905i	1.27294	+	1.27294i	0.944537	+	0.328406i	$0.106511\pi$
$463$	27.3905	+	27.3905i	1.27294	+	1.27294i	0.328406	+	0.944537i	$0.393489\pi$
$464$	−9.16560	+	3.17964i	−0.425502	+	0.147611i
$465$	−3.49636	−	2.51302i	−0.162140	−	0.116539i
$466$	−31.9872	−	27.0475i	−1.48178	−	1.25295i
$467$	8.94233	−	8.94233i	0.413802	−	0.413802i	−0.469259	−	0.883061i	$-0.655479\pi$
$467$	8.94233	−	8.94233i	0.413802	−	0.413802i	0.883061	+	0.469259i	$0.155479\pi$
$468$	−3.90004	+	5.48101i	−0.180279	+	0.253360i
$469$	−8.90550	−	19.9133i	−0.411218	−	0.919511i
$470$	13.4202	−	22.4024i	0.619029	−	1.03335i
$471$	−4.03944			−0.186128
$472$	−8.48811	−	33.1813i	−0.390697	−	1.52729i
$473$	8.03846	+	8.03846i	0.369609	+	0.369609i
$474$	−13.2051	+	15.6168i	−0.606531	+	0.717302i
$475$	−11.9522	−	35.5435i	−0.548407	−	1.63085i
$476$	−13.1556	−	19.7551i	−0.602984	−	0.905473i
$477$	−3.92370	−	3.92370i	−0.179654	−	0.179654i
$478$	1.34208	+	16.0393i	0.0613853	+	0.733622i
$479$	31.1231			1.42205			0.711026	−	0.703166i	$-0.248231\pi$
$479$	31.1231			1.42205			0.711026	+	0.703166i	$0.248231\pi$
$480$	−2.58488	+	12.3822i	−0.117983	+	0.565167i
$481$		−	33.4727i		−	1.52622i
$482$	1.81751	+	21.7213i	0.0827854	+	0.989377i
$483$	−3.31415	+	8.67657i	−0.150799	+	0.394797i
$484$	3.90975	−	0.658905i	0.177716	−	0.0299502i
$485$	1.65354	−	2.30056i	0.0750833	−	0.104463i
$486$	−1.07990	−	0.913135i	−0.0489853	−	0.0414206i
$487$	5.05709	−	5.05709i	0.229159	−	0.229159i	−0.583183	−	0.812341i	$-0.698193\pi$
$487$	5.05709	−	5.05709i	0.229159	−	0.229159i	0.812341	+	0.583183i	$0.198193\pi$
$488$	8.52568	−	2.18096i	0.385940	−	0.0987273i
$489$	18.4779			0.835598
$490$	10.3014	−	19.5929i	0.465369	−	0.885117i
$491$		−	22.2881i		−	1.00585i	−0.864331	−	0.502923i	$-0.832258\pi$
$491$		−	22.2881i		−	1.00585i	0.864331	−	0.502923i	$-0.167742\pi$
$492$	−3.04581	+	4.28050i	−0.137316	+	0.192980i
$493$	7.69246	+	7.69246i	0.346451	+	0.346451i
$494$	23.0343	−	27.2411i	1.03636	−	1.22563i
$495$	−1.08434	−	6.62661i	−0.0487373	−	0.297844i
$496$	−2.52446	−	7.27698i	−0.113351	−	0.326746i
$497$	4.65846	+	1.77937i	0.208961	+	0.0798159i
$498$	1.40859	+	16.8342i	0.0631203	+	0.754357i
$499$	32.3756			1.44933			0.724665	−	0.689102i	$-0.241995\pi$
$499$	32.3756			1.44933			0.724665	+	0.689102i	$0.241995\pi$
$500$	−13.5955	−	17.7528i	−0.608007	−	0.793931i
$501$		−	0.522733i		−	0.0233540i
$502$	−17.9814	+	1.50459i	−0.802551	+	0.0671529i
$503$	−4.12684	+	4.12684i	−0.184007	+	0.184007i	−0.793099	−	0.609093i	$-0.791534\pi$
$503$	−4.12684	+	4.12684i	−0.184007	+	0.184007i	0.609093	+	0.793099i	$0.291534\pi$
$504$	0.854404	−	7.43438i	0.0380582	−	0.331154i
$505$	1.18142	+	7.21993i	0.0525727	+	0.321283i
$506$	−9.62612	+	11.3841i	−0.427933	+	0.506087i
$507$	−1.19293	+	1.19293i	−0.0529798	+	0.0529798i
$508$	11.8115	−	16.5996i	0.524050	−	0.736487i
$509$		−	7.83443i		−	0.347255i	−0.984811	−	0.173627i	$-0.944451\pi$
$509$		−	7.83443i		−	0.347255i	0.984811	−	0.173627i	$-0.0555488\pi$
$510$	13.7582	−	3.44976i	0.609226	−	0.152758i
$511$	−3.92171	+	1.75384i	−0.173486	+	0.0775854i
$512$	−16.5359	+	15.4455i	−0.730789	+	0.682603i
$513$	5.30319	+	5.30319i	0.234142	+	0.234142i
$514$	−22.9246	−	19.3845i	−1.01116	−	0.855012i
$515$	−27.1963	−	19.5475i	−1.19841	−	0.861364i
$516$	−7.46607	+	1.25825i	−0.328675	+	0.0553912i
$517$	−17.5353	+	17.5353i	−0.771201	+	0.771201i
$518$	17.9831	+	32.6060i	0.790131	+	1.43263i
$519$			16.0571i			0.704827i
$520$	7.74721	−	19.8116i	0.339738	−	0.868795i
$521$			25.5002i			1.11718i	0.829442	+	0.558592i	$0.188658\pi$
$521$			25.5002i			1.11718i	−0.829442	+	0.558592i	$0.811342\pi$
$522$	0.286002	+	3.41804i	0.0125180	+	0.149603i
$523$	−10.4193	−	10.4193i	−0.455604	−	0.455604i	0.441605	−	0.897209i	$-0.354409\pi$
$523$	−10.4193	−	10.4193i	−0.455604	−	0.455604i	−0.897209	+	0.441605i	$0.854409\pi$
$524$	−0.538811	+	0.0908051i	−0.0235381	+	0.00396684i
$525$	8.96801	+	9.72496i	0.391396	+	0.424432i
$526$	16.8013	+	14.2067i	0.732571	+	0.619442i
$527$	−6.10739	+	6.10739i	−0.266042	+	0.266042i
$528$	5.24066	−	10.8082i	0.228071	−	0.470365i
$529$		−	10.6762i		−	0.464184i
$530$	15.0530	+	9.01753i	0.653861	+	0.391697i
$531$	−12.1091			−0.525491
$532$	−7.80275	+	38.9108i	−0.338292	+	1.68700i
$533$	6.24734	−	6.24734i	0.270602	−	0.270602i
$534$	3.67167	+	3.10467i	0.158889	+	0.134352i
$535$	1.22940	−	1.71046i	0.0531515	−	0.0739495i
$536$	20.0620	+	11.8887i	0.866547	+	0.513513i
$537$	−17.0476	−	17.0476i	−0.735658	−	0.735658i
$538$	−0.987440	−	11.8010i	−0.0425716	−	0.508777i
$539$	−14.0136	+	15.6677i	−0.603610	+	0.674857i
$540$	4.01470	+	1.97032i	0.172765	+	0.0847892i
$541$		−	25.1730i		−	1.08227i	−0.840935	−	0.541136i	$-0.817994\pi$
$541$		−	25.1730i		−	1.08227i	0.840935	−	0.541136i	$-0.182006\pi$
$542$	−0.620872	−	7.42010i	−0.0266687	−	0.318720i
$543$	6.31638	+	6.31638i	0.271062	+	0.271062i
$544$	23.6746	+	9.12805i	1.01504	+	0.391362i
$545$	4.24037	+	25.9138i	0.181637	+	1.11003i
$546$	−3.49466	+	12.0900i	−0.149558	+	0.517405i
$547$	−22.1918	−	22.1918i	−0.948853	−	0.948853i	0.0499010	−	0.998754i	$-0.484109\pi$
$547$	−22.1918	−	22.1918i	−0.948853	−	0.948853i	−0.998754	+	0.0499010i	$0.984109\pi$
$548$	20.4152	−	28.6909i	0.872092	−	1.22562i
$549$		−	3.11135i		−	0.132789i
$550$	8.42257	+	19.4920i	0.359140	+	0.831142i
$551$		−	18.1899i		−	0.774915i
$552$	−2.46077	−	9.61950i	−0.104737	−	0.409433i
$553$	−13.6524	+	35.7424i	−0.580558	+	1.51992i
$554$	−17.7176	−	14.9816i	−0.752750	−	0.636505i
$555$	−21.9609	+	3.59354i	−0.932188	+	0.152537i
$556$	2.22012	+	13.1736i	0.0941542	+	0.558684i
$557$	13.9795	+	13.9795i	0.592331	+	0.592331i	0.938260	−	0.345930i	$-0.112436\pi$
$557$	13.9795	+	13.9795i	0.592331	+	0.592331i	−0.345930	+	0.938260i	$0.612436\pi$
$558$	−2.71373	+	0.227070i	−0.114881	+	0.00961263i
$559$	12.7330			0.538549
$560$	3.09708	+	23.4608i	0.130875	+	0.991399i
$561$	−13.4694			−0.568678
$562$	16.9147	−	1.41533i	0.713503	−	0.0597019i
$563$	−3.59971	−	3.59971i	−0.151710	−	0.151710i	0.627172	−	0.778881i	$-0.284212\pi$
$563$	−3.59971	−	3.59971i	−0.151710	−	0.151710i	−0.778881	+	0.627172i	$0.784212\pi$
$564$	−2.74477	−	16.2866i	−0.115576	−	0.685792i
$565$	−1.64298	+	2.28587i	−0.0691207	+	0.0961674i
$566$	−6.10197	−	5.15966i	−0.256485	−	0.216877i
$567$	−2.47159	−	0.944062i	−0.103797	−	0.0396469i
$568$	−5.16473	+	1.32119i	−0.216707	+	0.0554359i
$569$		−	28.0941i		−	1.17777i	−0.808218	−	0.588883i	$-0.799568\pi$
$569$		−	28.0941i		−	1.17777i	0.808218	−	0.588883i	$-0.200432\pi$
$570$	−20.3453	−	12.1879i	−0.852172	−	0.510495i
$571$			31.8090i			1.33117i	0.746323	+	0.665584i	$0.231817\pi$
$571$			31.8090i			1.33117i	−0.746323	+	0.665584i	$0.768183\pi$
$572$	−11.7115	+	16.4591i	−0.489683	+	0.688188i
$573$	1.82726	+	1.82726i	0.0763349	+	0.0763349i
$574$	−2.72922	+	9.44194i	−0.113916	+	0.394099i
$575$	15.7202	+	7.80827i	0.655578	+	0.325627i
$576$	3.84158	+	7.01729i	0.160066	+	0.292387i
$577$	12.2550	+	12.2550i	0.510183	+	0.510183i	0.914582	−	0.404400i	$-0.132519\pi$
$577$	12.2550	+	12.2550i	0.510183	+	0.510183i	−0.404400	+	0.914582i	$0.632519\pi$
$578$	−0.367799	−	4.39561i	−0.0152984	−	0.182833i
$579$		−	18.0372i		−	0.749601i
$580$	−3.50609	−	10.2643i	−0.145582	−	0.426201i
$581$	12.9022	+	28.8503i	0.535275	+	1.19691i
$582$	−0.149409	−	1.78561i	−0.00619322	−	0.0740157i
$583$	−11.7826	−	11.7826i	−0.487985	−	0.487985i
$584$	2.34135	−	3.95100i	0.0968857	−	0.163493i
$585$	−6.10712	−	4.38952i	−0.252498	−	0.181484i
$586$	33.4371	+	28.2735i	1.38127	+	1.16797i
$587$	2.65901	−	2.65901i	0.109749	−	0.109749i	−0.650100	−	0.759849i	$-0.725273\pi$
$587$	2.65901	−	2.65901i	0.109749	−	0.109749i	0.759849	+	0.650100i	$0.225273\pi$
$588$	−3.09114	−	13.6545i	−0.127477	−	0.563101i
$589$	14.4417			0.595062
$590$	37.1426	−	9.31317i	1.52914	−	0.383417i
$591$		−	17.7193i		−	0.728876i
$592$	−35.8187	−	17.3678i	−1.47214	−	0.713812i
$593$	−17.3614	+	17.3614i	−0.712947	+	0.712947i	−0.967151	−	0.254204i	$-0.918187\pi$
$593$	−17.3614	+	17.3614i	−0.712947	+	0.712947i	0.254204	+	0.967151i	$0.418187\pi$
$594$	−3.24286	−	2.74207i	−0.133056	−	0.112509i
$595$	22.1567	−	14.6030i	0.908335	−	0.598664i
$596$	−10.9263	+	1.84140i	−0.447559	+	0.0754265i
$597$	8.20071	+	8.20071i	0.335633	+	0.335633i
$598$	1.39236	+	16.6402i	0.0569379	+	0.680470i
$599$		−	29.4726i		−	1.20422i	−0.798414	−	0.602109i	$-0.794327\pi$
$599$		−	29.4726i		−	1.20422i	0.798414	−	0.602109i	$-0.205673\pi$
$600$	−13.8298	−	2.95590i	−0.564598	−	0.120674i
$601$			9.91955i			0.404627i	0.979321	+	0.202313i	$0.0648460\pi$
$601$			9.91955i			0.404627i	−0.979321	+	0.202313i	$0.935154\pi$
$602$	−12.4033	+	6.84077i	−0.505522	+	0.278809i
$603$	5.83002	−	5.83002i	0.237417	−	0.237417i
$604$	0.266967	−	0.0449916i	0.0108627	−	0.00183068i
$605$	0.715847	+	4.37469i	0.0291033	+	0.177857i
$606$	3.53321	+	2.98759i	0.143527	+	0.121362i
$607$	−33.7122	−	33.7122i	−1.36834	−	1.36834i	−0.862811	−	0.505526i	$-0.831298\pi$
$607$	−33.7122	−	33.7122i	−1.36834	−	1.36834i	−0.505526	−	0.862811i	$-0.668702\pi$
$608$	−17.1987	−	38.7832i	−0.697498	−	1.57287i
$609$	2.61969	+	5.85781i	0.106155	+	0.237371i
$610$	2.39295	+	9.54351i	0.0968877	+	0.386405i
$611$			27.7761i			1.12370i
$612$	5.20097	−	7.30931i	0.210237	−	0.295461i
$613$	−4.44443	+	4.44443i	−0.179509	+	0.179509i	−0.791142	−	0.611633i	$-0.790513\pi$
$613$	−4.44443	+	4.44443i	−0.179509	+	0.179509i	0.611633	+	0.791142i	$0.290513\pi$
$614$	25.8841	−	30.6113i	1.04460	−	1.23537i
$615$	−4.76947	−	3.42808i	−0.192324	−	0.138233i
$616$	2.56571	−	22.3249i	0.103375	−	0.899495i
$617$	−5.98081	+	5.98081i	−0.240778	+	0.240778i	−0.817172	−	0.576394i	$-0.804459\pi$
$617$	−5.98081	+	5.98081i	−0.240778	+	0.240778i	0.576394	+	0.817172i	$0.304459\pi$
$618$	−21.1087	+	1.76626i	−0.849117	+	0.0710493i
$619$			17.2047i			0.691516i	0.938324	+	0.345758i	$0.112378\pi$
$619$			17.2047i			0.691516i	−0.938324	+	0.345758i	$0.887622\pi$
$620$	8.14926	−	2.78364i	0.327282	−	0.111794i
$621$	−3.51052			−0.140872
$622$	−0.347878	−	4.15753i	−0.0139486	−	0.166702i
$623$	8.40342	+	3.20982i	0.336676	+	0.128599i
$624$	−4.40949	−	12.7108i	−0.176521	−	0.508838i
$625$	19.9205	−	15.1055i	0.796819	−	0.604219i
$626$	10.8460	−	12.8268i	0.433494	−	0.512663i
$627$	15.9251	+	15.9251i	0.635987	+	0.635987i
$628$	4.68384	−	6.58255i	0.186906	−	0.262672i
$629$			44.6382i			1.77984i
$630$	8.30724	+	0.994836i	0.330969	+	0.0396352i
$631$	41.5855			1.65549			0.827747	−	0.561101i	$-0.189622\pi$
$631$	41.5855			1.65549			0.827747	+	0.561101i	$0.189622\pi$
$632$	−10.1369	−	39.6267i	−0.403225	−	1.57627i
$633$	−18.0414	+	18.0414i	−0.717083	+	0.717083i
$634$	36.6883	+	31.0226i	1.45708	+	1.23206i
$635$	18.4958	+	13.2939i	0.733982	+	0.527553i
$636$	10.9436	−	1.84431i	0.433941	−	0.0731315i
$637$	1.31005	+	23.5078i	0.0519061	+	0.931414i
$638$	0.858843	+	10.2641i	0.0340019	+	0.406360i
$639$			1.88481i			0.0745618i
$640$	−17.1804	−	18.5697i	−0.679114	−	0.734033i
$641$	0.326576			0.0128990			0.00644949	−	0.999979i	$-0.497947\pi$
$641$	0.326576			0.0128990			0.00644949	+	0.999979i	$0.497947\pi$
$642$	−0.111085	−	1.32759i	−0.00438418	−	0.0523958i
$643$	−18.8040	−	18.8040i	−0.741557	−	0.741557i	0.231321	−	0.972878i	$-0.425695\pi$
$643$	−18.8040	−	18.8040i	−0.741557	−	0.741557i	−0.972878	+	0.231321i	$0.925695\pi$
$644$	−10.2962	−	15.4614i	−0.405728	−	0.609263i
$645$	−1.36698	−	8.35393i	−0.0538249	−	0.328936i
$646$	−30.7179	+	36.3279i	−1.20858	+	1.42930i
$647$	12.7976	+	12.7976i	0.503127	+	0.503127i	0.912408	−	0.409281i	$-0.134220\pi$
$647$	12.7976	+	12.7976i	0.503127	+	0.503127i	−0.409281	+	0.912408i	$0.634220\pi$
$648$	2.74019	−	0.700969i	0.107645	−	0.0275367i
$649$	−36.3627			−1.42736
$650$	22.1085	+	8.76706i	0.867167	+	0.343872i
$651$	−4.65078	+	2.07989i	−0.182278	+	0.0815174i
$652$	−21.4256	+	30.1110i	−0.839091	+	1.17924i
$653$	4.45533	−	4.45533i	0.174351	−	0.174351i	−0.614537	−	0.788888i	$-0.710657\pi$
$653$	4.45533	−	4.45533i	0.174351	−	0.174351i	0.788888	+	0.614537i	$0.210657\pi$
$654$	12.6814	+	10.7231i	0.495882	+	0.419305i
$655$	−0.0986524	−	0.602886i	−0.00385467	−	0.0235567i
$656$	−3.44368	−	9.92672i	−0.134453	−	0.387573i
$657$	−1.14816	−	1.14816i	−0.0447939	−	0.0447939i
$658$	−14.9226	−	27.0569i	−0.581743	−	1.05479i
$659$	16.7657			0.653099			0.326549	−	0.945180i	$-0.394114\pi$
$659$	16.7657			0.653099			0.326549	+	0.945180i	$0.394114\pi$
$660$	12.0558	+	5.91673i	0.469273	+	0.230309i
$661$	42.9946			1.67229			0.836147	−	0.548505i	$-0.184803\pi$
$661$	42.9946			1.67229			0.836147	+	0.548505i	$0.184803\pi$
$662$	−2.77544	−	33.1695i	−0.107870	−	1.28917i
$663$	−10.6678	+	10.6678i	−0.414304	+	0.414304i
$664$	−29.0657	−	17.2243i	−1.12797	−	0.668432i
$665$	−43.4616	−	8.93087i	−1.68537	−	0.346324i
$666$	−9.08736	+	10.7470i	−0.352128	+	0.416437i
$667$	6.02052	+	6.02052i	0.233115	+	0.233115i
$668$	0.851830	+	0.606123i	0.0329583	+	0.0234516i
$669$	−24.3081			−0.939807
$670$	−13.3987	+	22.3664i	−0.517635	+	0.864091i
$671$		−	9.34314i		−	0.360688i
$672$	11.1241	+	10.0127i	0.429123	+	0.386247i
$673$	−2.34468	−	2.34468i	−0.0903808	−	0.0903808i	0.660471	−	0.750852i	$-0.270357\pi$
$673$	−2.34468	−	2.34468i	−0.0903808	−	0.0903808i	−0.750852	+	0.660471i	$0.770357\pi$
$674$	23.3648	−	27.6319i	0.899979	−	1.06434i
$675$	−2.22425	+	4.47803i	−0.0856113	+	0.172359i
$676$	−0.560727	−	3.32719i	−0.0215664	−	0.127969i
$677$	15.9212	−	15.9212i	0.611900	−	0.611900i	−0.331541	−	0.943441i	$-0.607568\pi$
$677$	15.9212	−	15.9212i	0.611900	−	0.611900i	0.943441	+	0.331541i	$0.107568\pi$
$678$	0.148455	+	1.77421i	0.00570140	+	0.0681379i
$679$	−1.36854	−	3.06016i	−0.0525199	−	0.117438i
$680$	−10.3314	+	26.4201i	−0.396193	+	1.01317i
$681$	−19.2212			−0.736556
$682$	−8.14914	+	0.681874i	−0.312047	+	0.0261103i
$683$	8.37740	−	8.37740i	0.320552	−	0.320552i	−0.528427	−	0.848979i	$-0.677218\pi$
$683$	8.37740	−	8.37740i	0.320552	−	0.320552i	0.848979	+	0.528427i	$0.177218\pi$
$684$	−14.7911	+	2.49273i	−0.565553	+	0.0953118i
$685$	31.9683	+	22.9774i	1.22145	+	0.877921i
$686$	−13.9056	−	22.1954i	−0.530919	−	0.847422i
$687$	−5.57803	+	5.57803i	−0.212815	+	0.212815i
$688$	6.60671	−	13.6255i	0.251878	−	0.519465i
$689$	−18.6638			−0.711032
$690$	10.7679	−	2.69996i	0.409927	−	0.102786i
$691$	−14.2845			−0.543408			−0.271704	−	0.962381i	$-0.587587\pi$
$691$	−14.2845			−0.543408			−0.271704	+	0.962381i	$0.587587\pi$
$692$	−26.1661	−	18.6186i	−0.994686	−	0.707773i
$693$	−7.42199	−	2.83495i	−0.281938	−	0.107691i
$694$	−36.0198	−	30.4573i	−1.36729	−	1.15614i
$695$	−14.7402	+	2.41198i	−0.559126	+	0.0914918i
$696$	−5.90156	−	3.49725i	−0.223698	−	0.132563i
$697$	−8.33126	+	8.33126i	−0.315569	+	0.315569i
$698$	2.74984	+	32.8635i	0.104083	+	1.24390i
$699$		−	29.6205i		−	1.12035i
$700$	−26.2461	+	3.33765i	−0.992011	+	0.126151i
$701$		−	10.0346i		−	0.379001i	−0.981881	−	0.189500i	$-0.939313\pi$
$701$		−	10.0346i		−	0.379001i	0.981881	−	0.189500i	$-0.0606868\pi$
$702$	−4.74010	+	0.396625i	−0.178904	+	0.0149696i
$703$	52.7765	−	52.7765i	1.99050	−	1.99050i
$704$	11.5360	+	21.0724i	0.434778	+	0.794195i
$705$	18.2234	−	2.98197i	0.686334	−	0.112307i
$706$	23.2668	−	27.5161i	0.875659	−	1.03558i
$707$	8.08652	+	3.08878i	0.304125	+	0.116165i
$708$	14.0408	−	19.7326i	0.527687	−	0.741598i
$709$	−27.1322			−1.01897			−0.509486	−	0.860479i	$-0.670165\pi$
$709$	−27.1322			−1.01897			−0.509486	+	0.860479i	$0.670165\pi$
$710$	−1.44961	−	5.78131i	−0.0544030	−	0.216969i
$711$	−14.4613			−0.542341
$712$	−9.31668	+	2.38330i	−0.349157	+	0.0893180i
$713$	−4.77996	+	4.77996i	−0.179011	+	0.179011i
$714$	4.66037	−	16.1229i	0.174410	−	0.603384i
$715$	−18.3392	−	13.1814i	−0.685848	−	0.492956i
$716$	47.5474	−	8.01310i	1.77693	−	0.299464i
$717$	−8.04769	+	8.04769i	−0.300547	+	0.300547i
$718$	2.53183	+	30.2582i	0.0944872	+	1.12923i
$719$	27.6938			1.03280			0.516401	−	0.856347i	$-0.327271\pi$
$719$	27.6938			1.03280			0.516401	+	0.856347i	$0.327271\pi$
$720$	−7.86593	+	4.25759i	−0.293146	+	0.158671i
$721$	−36.1760	+	16.1784i	−1.34726	+	0.602515i
$722$	52.4928	−	4.39230i	1.95358	−	0.163465i
$723$	−10.8986	+	10.8986i	−0.405323	+	0.405323i
$724$	−17.6170	+	2.96897i	−0.654730	+	0.110341i
$725$	11.4943	−	3.86522i	0.426889	−	0.143551i
$726$	2.14084	+	1.81024i	0.0794541	+	0.0671842i
$727$	−21.3358	−	21.3358i	−0.791301	−	0.791301i	0.190405	−	0.981706i	$-0.439020\pi$
$727$	−21.3358	−	21.3358i	−0.791301	−	0.791301i	−0.981706	+	0.190405i	$0.939020\pi$
$728$	−15.6494	−	19.7135i	−0.580005	−	0.730631i
$729$		−	1.00000i		−	0.0370370i
$730$	4.40483	+	2.63872i	0.163030	+	0.0976634i
$731$	−16.9804			−0.628041
$732$	5.07016	+	3.60769i	0.187398	+	0.133344i
$733$	19.5514	+	19.5514i	0.722148	+	0.722148i	0.969042	−	0.246895i	$-0.0794102\pi$
$733$	19.5514	+	19.5514i	0.722148	+	0.722148i	−0.246895	+	0.969042i	$0.579410\pi$
$734$	−39.2049	−	33.1506i	−1.44708	−	1.22361i
$735$	15.2825	−	3.38324i	0.563702	−	0.124793i
$736$	18.5290	+	7.14408i	0.682987	+	0.263334i
$737$	17.5071	−	17.5071i	0.644882	−	0.644882i
$738$	−3.70188	+	0.309752i	−0.136268	+	0.0114021i
$739$	−4.97856			−0.183139			−0.0915696	−	0.995799i	$-0.529188\pi$
$739$	−4.97856			−0.183139			−0.0915696	+	0.995799i	$0.529188\pi$
$740$	19.6083	−	39.9536i	0.720816	−	1.46872i
$741$	25.2255			0.926683
$742$	18.1805	−	10.0270i	0.667428	−	0.368104i
$743$	−12.8240	−	12.8240i	−0.470468	−	0.470468i	0.431598	−	0.902066i	$-0.357950\pi$
$743$	−12.8240	−	12.8240i	−0.470468	−	0.470468i	−0.902066	+	0.431598i	$0.857950\pi$
$744$	2.77662	−	4.68551i	0.101796	−	0.171779i
$745$	−2.00053	−	12.2257i	−0.0732937	−	0.447913i
$746$	−2.17647	+	2.57395i	−0.0796861	+	0.0942392i
$747$	−8.44650	+	8.44650i	−0.309041	+	0.309041i
$748$	15.6181	−	21.9493i	0.571055	−	0.802546i
$749$	−1.01751	−	2.27521i	−0.0371789	−	0.0831345i
$750$	3.37841	−	15.4462i	0.123362	−	0.564017i
$751$	10.0477			0.366645			0.183322	−	0.983053i	$-0.441315\pi$
$751$	10.0477			0.366645			0.183322	+	0.983053i	$0.441315\pi$
$752$	29.7229	+	14.4120i	1.08388	+	0.525552i
$753$	−9.02214	−	9.02214i	−0.328785	−	0.328785i
$754$	8.80945	+	7.44903i	0.320821	+	0.271278i
$755$	0.0488797	+	0.298715i	0.00177892	+	0.0108713i
$756$	4.40429	−	2.93296i	0.160182	−	0.106671i
$757$	7.44806	+	7.44806i	0.270704	+	0.270704i	0.829384	−	0.558679i	$-0.188692\pi$
$757$	7.44806	+	7.44806i	0.270704	+	0.270704i	−0.558679	+	0.829384i	$0.688692\pi$
$758$	−15.5431	+	1.30056i	−0.564550	+	0.0472384i
$759$	−10.5418			−0.382644
$760$	43.4520	−	19.0219i	1.57617	−	0.689998i
$761$		−	32.7237i		−	1.18623i	−0.805117	−	0.593116i	$-0.797897\pi$
$761$		−	32.7237i		−	1.18623i	0.805117	−	0.593116i	$-0.202103\pi$
$762$	14.3557	−	1.20120i	0.520052	−	0.0435150i
$763$	29.0242	+	11.0862i	1.05075	+	0.401349i
$764$	−5.09641	+	0.858890i	−0.184382	+	0.0310736i
$765$	8.14426	+	5.85372i	0.294457	+	0.211642i
$766$	−16.2880	+	19.2627i	−0.588510	+	0.695990i
$767$	−28.7995	+	28.7995i	−1.03989	+	1.03989i
$768$	−15.8896	−	1.87662i	−0.573365	−	0.0677166i
$769$	4.58984			0.165514			0.0827569	−	0.996570i	$-0.473627\pi$
$769$	4.58984			0.165514			0.0827569	+	0.996570i	$0.473627\pi$
$770$	24.9460	+	2.98742i	0.898992	+	0.107659i
$771$		−	21.2285i		−	0.764525i
$772$	29.3929	+	20.9146i	1.05787	+	0.752735i
$773$	−31.4846	−	31.4846i	−1.13242	−	1.13242i	−0.989773	−	0.142648i	$-0.954438\pi$
$773$	−31.4846	−	31.4846i	−1.13242	−	1.13242i	−0.142648	−	0.989773i	$-0.545562\pi$
$774$	−4.08815	−	3.45683i	−0.146946	−	0.124253i
$775$	3.06877	+	9.12587i	0.110233	+	0.327811i
$776$	3.08301	+	1.82698i	0.110674	+	0.0655849i
$777$	−9.39515	+	24.5968i	−0.337049	+	0.882406i
$778$	48.1488	−	4.02882i	1.72622	−	0.144440i
$779$	19.7004			0.705839
$780$	14.2344	−	4.86221i	0.509673	−	0.174095i
$781$			5.65993i			0.202528i
$782$	−1.85681	−	22.1909i	−0.0663994	−	0.793546i
$783$	−1.71499	+	1.71499i	−0.0612888	+	0.0612888i
$784$	25.8352	+	10.7955i	0.922685	+	0.385554i
$785$	7.33449	+	5.27169i	0.261779	+	0.188155i
$786$	−0.295034	−	0.249473i	−0.0105235	−	0.00889839i
$787$	−12.2368	+	12.2368i	−0.436194	+	0.436194i	−0.890729	−	0.454535i	$-0.849805\pi$
$787$	−12.2368	+	12.2368i	−0.436194	+	0.436194i	0.454535	+	0.890729i	$0.349805\pi$
$788$	28.8749	+	20.5461i	1.02863	+	0.731923i
$789$			15.5582i			0.553886i
$790$	44.3575	−	11.1222i	1.57817	−	0.395712i
$791$	1.35981	+	3.04062i	0.0483492	+	0.108112i
$792$	8.22859	−	2.10496i	0.292390	−	0.0747964i
$793$	−7.39982	−	7.39982i	−0.262775	−	0.262775i
$794$	30.6138	−	36.2048i	1.08644	−	1.28486i
$795$	2.00369	+	12.2450i	0.0710636	+	0.434285i
$796$	−22.8726	+	3.85468i	−0.810697	+	0.136626i
$797$	10.3322	−	10.3322i	0.365985	−	0.365985i	−0.500026	−	0.866011i	$-0.666676\pi$
$797$	10.3322	−	10.3322i	0.365985	−	0.365985i	0.866011	+	0.500026i	$0.166676\pi$
$798$	−24.5724	+	13.5523i	−0.869854	+	0.479747i
$799$		−	37.0413i		−	1.31043i
$800$	20.8528	−	19.1091i	0.737259	−	0.675610i
$801$			3.40001i			0.120133i
$802$	−23.9399	+	2.00316i	−0.845348	+	0.0707339i
$803$	−3.44783	−	3.44783i	−0.121671	−	0.121671i
$804$	2.74036	+	16.2605i	0.0966449	+	0.573463i
$805$	17.3410	−	11.4290i	0.611189	−	0.402821i
$806$	−5.91412	+	6.99421i	−0.208316	+	0.246361i
$807$	5.92111	−	5.92111i	0.208433	−	0.208433i
$808$	−8.96534	+	2.29343i	−0.315399	+	0.0806824i
$809$			16.8518i			0.592478i	0.955114	+	0.296239i	$0.0957325\pi$
$809$			16.8518i			0.592478i	−0.955114	+	0.296239i	$0.904267\pi$
$810$	0.769104	+	3.06732i	0.0270236	+	0.107775i
$811$	11.0683			0.388660			0.194330	−	0.980936i	$-0.437747\pi$
$811$	11.0683			0.388660			0.194330	+	0.980936i	$0.437747\pi$
$812$	−12.5833	−	2.52332i	−0.441588	−	0.0885511i
$813$	3.72301	−	3.72301i	0.130572	−	0.130572i
$814$	−27.2887	+	32.2724i	−0.956467	+	1.13115i
$815$	−33.5506	−	24.1146i	−1.17523	−	0.844699i
$816$	5.88036	+	16.9507i	0.205854	+	0.593393i
$817$	20.0762	+	20.0762i	0.702377	+	0.702377i
$818$	−40.6550	+	3.40178i	−1.42147	+	0.118940i
$819$	−8.12356	+	3.63297i	−0.283860	+	0.126946i
$820$	11.1166	−	3.79724i	0.388209	−	0.132605i
$821$		−	15.7536i		−	0.549805i	−0.961472	−	0.274903i	$-0.911354\pi$
$821$		−	15.7536i		−	0.549805i	0.961472	−	0.274903i	$-0.0886456\pi$
$822$	24.8126	−	2.07618i	0.865438	−	0.0724149i
$823$	0.973603	+	0.973603i	0.0339377	+	0.0339377i	0.723872	−	0.689934i	$-0.242361\pi$
$823$	0.973603	+	0.973603i	0.0339377	+	0.0339377i	−0.689934	+	0.723872i	$0.742361\pi$
$824$	21.5979	−	36.4461i	0.752398	−	1.26966i
$825$	−6.67924	+	13.4472i	−0.232541	+	0.468171i
$826$	12.5814	−	43.5263i	0.437763	−	1.51447i
$827$	−28.8134	−	28.8134i	−1.00194	−	1.00194i	−0.999998	−	0.00194243i	$-0.999382\pi$
$827$	−28.8134	−	28.8134i	−1.00194	−	1.00194i	−0.00194243	−	0.999998i	$-0.500618\pi$
$828$	4.07055	−	5.72064i	0.141461	−	0.198806i
$829$			4.04194i			0.140382i	0.997534	+	0.0701911i	$0.0223609\pi$
$829$			4.04194i			0.140382i	−0.997534	+	0.0701911i	$0.977639\pi$
$830$	19.4119	−	32.4044i	0.673797	−	1.12477i
$831$		−	16.4067i		−	0.569143i
$832$	25.8260	+	7.55290i	0.895355	+	0.261850i
$833$	−1.74704	−	31.3493i	−0.0605315	−	1.08619i
$834$	−6.09943	+	7.21337i	−0.211206	+	0.249779i
$835$	−0.682195	+	0.949136i	−0.0236083	+	0.0328462i
$836$	−44.4166	+	7.48547i	−1.53618	+	0.258890i
$837$	−1.36161	−	1.36161i	−0.0470641	−	0.0470641i
$838$	−2.83359	−	33.8645i	−0.0978846	−	1.16983i
$839$	−17.0360			−0.588150			−0.294075	−	0.955782i	$-0.595011\pi$
$839$	−17.0360			−0.588150			−0.294075	+	0.955782i	$0.595011\pi$
$840$	−11.2536	+	12.3837i	−0.388287	+	0.427278i
$841$	−23.1176			−0.797159
$842$	2.03116	+	24.2746i	0.0699984	+	0.836558i
$843$	8.48690	+	8.48690i	0.292304	+	0.292304i
$844$	−8.48025	−	50.3193i	−0.291902	−	1.73206i
$845$	3.72286	−	0.609184i	0.128070	−	0.0209566i
$846$	7.54081	−	8.91799i	0.259258	−	0.306607i
$847$	4.89978	+	1.87155i	0.168358	+	0.0643072i
$848$	−9.68396	+	19.9719i	−0.332548	+	0.685836i
$849$		−	5.65050i		−	0.193925i
$850$	−29.4832	−	11.6915i	−1.01127	−	0.401014i
$851$			34.9361i			1.19759i
$852$	−3.07142	−	2.18548i	−0.105225	−	0.0748734i
$853$	19.9463	+	19.9463i	0.682950	+	0.682950i	0.960664	−	0.277714i	$-0.0895767\pi$
$853$	19.9463	+	19.9463i	0.682950	+	0.682950i	−0.277714	+	0.960664i	$0.589577\pi$
$854$	11.1838	+	3.23270i	0.382700	+	0.110621i
$855$	−2.70815	−	16.5501i	−0.0926167	−	0.566000i
$856$	2.29221	+	1.35836i	0.0783460	+	0.0464276i
$857$	−22.8565	−	22.8565i	−0.780762	−	0.780762i	0.199198	−	0.979959i	$-0.436166\pi$
$857$	−22.8565	−	22.8565i	−0.780762	−	0.780762i	−0.979959	+	0.199198i	$0.936166\pi$
$858$	−14.2342	+	1.19104i	−0.485947	+	0.0406613i
$859$		−	15.2669i		−	0.520901i	−0.965487	−	0.260451i	$-0.916129\pi$
$859$		−	15.2669i		−	0.520901i	0.965487	−	0.260451i	$-0.0838711\pi$
$860$	15.1984	+	7.45901i	0.518260	+	0.254350i
$861$	−6.34425	+	2.83724i	−0.216212	+	0.0966928i
$862$	−28.6844	+	2.40015i	−0.976994	+	0.0817493i
$863$	10.9563	+	10.9563i	0.372955	+	0.372955i	0.868553	−	0.495597i	$-0.165051\pi$
$863$	10.9563	+	10.9563i	0.372955	+	0.372955i	−0.495597	+	0.868553i	$0.665051\pi$
$864$	−2.03505	+	5.27812i	−0.0692337	+	0.179565i
$865$	20.9553	−	29.1551i	0.712503	−	0.991303i
$866$	−17.7625	+	21.0065i	−0.603595	+	0.713829i
$867$	2.20548	−	2.20548i	0.0749022	−	0.0749022i
$868$	2.00337	−	9.99046i	0.0679990	−	0.339098i
$869$	−43.4262			−1.47313
$870$	3.94143	−	6.57944i	0.133627	−	0.223064i
$871$		−	27.7315i		−	0.939645i
$872$	−32.1784	+	8.23157i	−1.08970	+	0.278756i
$873$	0.895923	−	0.895923i	0.0303224	−	0.0303224i
$874$	−24.0414	+	28.4320i	−0.813211	+	0.961728i
$875$	−3.59178	−	29.3615i	−0.121424	−	0.992601i
$876$	3.20232	−	0.539683i	0.108197	−	0.0182342i
$877$	1.79847	+	1.79847i	0.0607299	+	0.0607299i	0.736819	−	0.676090i	$-0.236327\pi$
$877$	1.79847	+	1.79847i	0.0607299	+	0.0607299i	−0.676090	+	0.736819i	$0.736327\pi$
$878$	34.3182	−	2.87155i	1.15818	−	0.0969103i
$879$			30.9631i			1.04436i
$880$	−23.6208	+	12.7852i	−0.796257	+	0.430990i
$881$			41.8013i			1.40832i	0.710041	+	0.704160i	$0.248676\pi$
$881$			41.8013i			1.40832i	−0.710041	+	0.704160i	$0.751324\pi$
$882$	5.96143	−	7.90325i	0.200732	−	0.266116i
$883$	−7.93799	+	7.93799i	−0.267134	+	0.267134i	−0.827945	−	0.560810i	$-0.810490\pi$
$883$	−7.93799	+	7.93799i	−0.267134	+	0.267134i	0.560810	+	0.827945i	$0.310490\pi$
$884$	−5.01434	−	29.7536i	−0.168650	−	1.00072i
$885$	21.9867	+	15.8030i	0.739076	+	0.531214i
$886$	−20.5028	+	24.2472i	−0.688805	+	0.814602i
$887$	8.49831	+	8.49831i	0.285345	+	0.285345i	0.835236	−	0.549891i	$-0.185331\pi$
$887$	8.49831	+	8.49831i	0.285345	+	0.285345i	−0.549891	+	0.835236i	$0.685331\pi$
$888$	−6.97592	−	27.2699i	−0.234097	−	0.915118i
$889$	24.6027	−	11.0027i	0.825148	−	0.369017i
$890$	−2.61496	−	10.4289i	−0.0876538	−	0.349579i
$891$		−	3.00292i		−	0.100602i
$892$	28.1860	−	39.6118i	0.943736	−	1.32630i
$893$	−43.7946	+	43.7946i	−1.46553	+	1.46553i
$894$	−5.98286	−	5.05894i	−0.200097	−	0.169196i
$895$	8.70559	+	53.2017i	0.290996	+	1.77834i
$896$	−29.2151	+	6.51758i	−0.976007	+	0.217737i
$897$	−8.34920	+	8.34920i	−0.278772	+	0.278772i
$898$	−1.50047	−	17.9322i	−0.0500712	−	0.598406i
$899$			4.67029i			0.155763i
$900$	−4.71818	−	8.81696i	−0.157273	−	0.293899i
$901$	24.8894			0.829186
$902$	−11.1165	+	0.930162i	−0.370138	+	0.0309710i
$903$	−9.35663	−	3.57391i	−0.311369	−	0.118932i
$904$	−3.06333	−	1.81532i	−0.101885	−	0.0603767i
$905$	−3.22554	−	19.7120i	−0.107221	−	0.655248i
$906$	0.146182	+	0.123607i	0.00485656	+	0.00410658i
$907$	−21.8046	−	21.8046i	−0.724011	−	0.724011i	0.245409	−	0.969420i	$-0.421078\pi$
$907$	−21.8046	−	21.8046i	−0.724011	−	0.724011i	−0.969420	+	0.245409i	$0.921078\pi$
$908$	22.2875	−	31.3222i	0.739635	−	1.03946i
$909$			3.27179i			0.108519i
$910$	22.1235	−	17.3913i	0.733385	−	0.576518i
$911$	−0.414643			−0.0137377			−0.00686887	−	0.999976i	$-0.502186\pi$
$911$	−0.414643			−0.0137377			−0.00686887	+	0.999976i	$0.502186\pi$
$912$	13.0886	−	26.9935i	0.433408	−	0.893846i
$913$	−25.3642	+	25.3642i	−0.839433	+	0.839433i
$914$	−35.7359	+	42.2624i	−1.18204	+	1.39792i
$915$	−4.06048	+	5.64933i	−0.134235	+	0.186761i
$916$	−2.62191	−	15.5577i	−0.0866304	−	0.514040i
$917$	−0.675249	−	0.257922i	−0.0222987	−	0.00851734i
$918$	6.32126	−	0.528927i	0.208633	−	0.0174572i
$919$		−	40.3280i		−	1.33030i	−0.746711	−	0.665149i	$-0.768368\pi$
$919$		−	40.3280i		−	1.33030i	0.746711	−	0.665149i	$-0.231632\pi$
$920$	−8.08592	+	20.6777i	−0.266585	+	0.681725i
$921$	28.3464			0.934046
$922$	−32.4038	+	2.71136i	−1.06716	+	0.0892940i
$923$	4.48270	+	4.48270i	0.147550	+	0.147550i
$924$	13.2257	−	8.80745i	0.435095	−	0.289744i
$925$	44.5646	+	22.1353i	1.46527	+	0.727805i
$926$	−41.8310	−	35.3711i	−1.37465	−	1.16237i
$927$	−10.5912	−	10.5912i	−0.347862	−	0.347862i
$928$	12.5420	−	5.56185i	0.411712	−	0.182577i
$929$	1.92282			0.0630856			0.0315428	−	0.999502i	$-0.489958\pi$
$929$	1.92282			0.0630856			0.0315428	+	0.999502i	$0.489958\pi$
$930$	5.22371	+	3.12928i	0.171292	+	0.102613i
$931$	−34.9993	+	39.1304i	−1.14706	+	1.28245i
$932$	48.2687	+	34.3458i	1.58109	+	1.12503i
$933$	2.08603	−	2.08603i	0.0682935	−	0.0682935i
$934$	−11.5478	+	13.6568i	−0.377857	+	0.446865i
$935$	24.4566	+	17.5783i	0.799817	+	0.574872i
$936$	4.84995	−	8.18423i	0.158526	−	0.267510i
$937$	28.0250	+	28.0250i	0.915537	+	0.915537i	0.996701	−	0.0811639i	$-0.0258637\pi$
$937$	28.0250	+	28.0250i	0.915537	+	0.915537i	−0.0811639	+	0.996701i	$0.525864\pi$
$938$	14.8986	+	27.0134i	0.486457	+	0.882020i
$939$	11.8778			0.387617
$940$	−16.2712	+	33.1540i	−0.530709	+	1.08137i
$941$	16.8454			0.549144			0.274572	−	0.961567i	$-0.411464\pi$
$941$	16.8454			0.549144			0.274572	+	0.961567i	$0.411464\pi$
$942$	5.69274	−	0.476336i	0.185479	−	0.0155199i
$943$	−6.52047	+	6.52047i	−0.212336	+	0.212336i
$944$	15.8750	+	45.7610i	0.516686	+	1.48940i
$945$	3.25565	+	4.93971i	0.105906	+	0.160689i
$946$	−12.2764	−	10.3806i	−0.399141	−	0.337503i
$947$	5.91437	+	5.91437i	0.192191	+	0.192191i	0.796642	−	0.604451i	$-0.206608\pi$
$947$	5.91437	+	5.91437i	0.192191	+	0.192191i	−0.604451	+	0.796642i	$0.706608\pi$
$948$	16.7683	−	23.5657i	0.544608	−	0.765378i
$949$	−5.46141			−0.177285
$950$	21.0355	+	48.6816i	0.682482	+	1.57944i
$951$			33.9737i			1.10167i
$952$	20.8695	+	26.2893i	0.676385	+	0.852042i
$953$	40.8799	+	40.8799i	1.32423	+	1.32423i	0.910317	+	0.413911i	$0.135838\pi$
$953$	40.8799	+	40.8799i	1.32423	+	1.32423i	0.413911	+	0.910317i	$0.364162\pi$
$954$	5.99232	+	5.06694i	0.194008	+	0.164048i
$955$	−0.933115	−	5.70247i	−0.0301949	−	0.184527i
$956$	−3.78276	−	22.4458i	−0.122343	−	0.725949i
$957$	−5.14999	+	5.14999i	−0.166476	+	0.166476i
$958$	−43.8615	+	3.67008i	−1.41710	+	0.118575i
$959$	42.5236	−	19.0171i	1.37316	−	0.614096i
$960$	2.18272	−	17.7549i	0.0704471	−	0.573036i
$961$	27.2920			0.880389
$962$	3.94714	+	47.1727i	0.127261	+	1.52091i
$963$	0.666115	−	0.666115i	0.0214652	−	0.0214652i
$964$	−5.12280	−	30.3972i	−0.164994	−	0.979028i
$965$	−23.5396	+	32.7505i	−0.757765	+	1.05428i
$966$	3.64745	−	12.6186i	0.117355	−	0.405997i
$967$	14.3480	−	14.3480i	0.461400	−	0.461400i	−0.437714	−	0.899114i	$-0.644212\pi$
$967$	14.3480	−	14.3480i	0.461400	−	0.461400i	0.899114	+	0.437714i	$0.144212\pi$
$968$	−5.43227	+	1.38963i	−0.174600	+	0.0446644i
$969$	−33.6400			−1.08067
$970$	−2.05903	+	3.43714i	−0.0661114	+	0.110360i
$971$	13.1969			0.423508			0.211754	−	0.977323i	$-0.432082\pi$
$971$	13.1969			0.423508			0.211754	+	0.977323i	$0.432082\pi$
$972$	1.62957	+	1.15953i	0.0522685	+	0.0371918i
$973$	−6.30602	+	16.5094i	−0.202162	+	0.529266i
$974$	−6.53056	+	7.72323i	−0.209253	+	0.247468i
$975$	5.36025	+	15.9402i	0.171665	+	0.510496i
$976$	−11.7580	+	4.07896i	−0.376363	+	0.130564i
$977$	−18.5822	+	18.5822i	−0.594497	+	0.594497i	−0.938843	−	0.344346i	$-0.888101\pi$
$977$	−18.5822	+	18.5822i	−0.594497	+	0.594497i	0.344346	+	0.938843i	$0.388101\pi$
$978$	−26.0407	+	2.17893i	−0.832688	+	0.0696746i
$979$			10.2100i			0.326312i
$980$	−12.2072	+	28.8268i	−0.389945	+	0.920838i
$981$			11.7431i			0.374929i
$982$	2.62824	+	31.4103i	0.0838705	+	1.00234i
$983$	−35.5328	+	35.5328i	−1.13332	+	1.13332i	−0.143697	+	0.989622i	$0.545899\pi$
$983$	−35.5328	+	35.5328i	−1.13332	+	1.13332i	−0.989622	+	0.143697i	$0.954101\pi$
$984$	3.78766	−	6.39163i	0.120746	−	0.203758i
$985$	−23.1247	+	32.1733i	−0.736814	+	1.02513i
$986$	−11.7480	−	9.93380i	−0.374133	−	0.316357i
$987$	7.79621	−	20.4108i	0.248156	−	0.649682i
$988$	−29.2497	+	41.1068i	−0.930557	+	1.30778i
$989$	−13.2897			−0.422588
$990$	2.30956	+	9.21094i	0.0734027	+	0.292743i
$991$	−12.1822			−0.386980			−0.193490	−	0.981102i	$-0.561981\pi$
$991$	−12.1822			−0.386980			−0.193490	+	0.981102i	$0.561981\pi$
$992$	4.41580	+	9.95767i	0.140202	+	0.316156i
$993$	16.6427	−	16.6427i	0.528140	−	0.528140i
$994$	−6.77495	−	1.95832i	−0.214888	−	0.0621141i
$995$	−4.18780	−	25.5926i	−0.132762	−	0.811339i
$996$	−3.97021	−	23.5581i	−0.125801	−	0.746467i
$997$	22.4809	−	22.4809i	0.711976	−	0.711976i	−0.254973	−	0.966948i	$-0.582066\pi$
$997$	22.4809	−	22.4809i	0.711976	−	0.711976i	0.966948	+	0.254973i	$0.0820664\pi$
$998$	−45.6265	+	3.81777i	−1.44428	+	0.120849i
$999$	−9.95183			−0.314862

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.bj.b.13.1	✓	184
5.2	odd	4	inner	840.2.bj.b.517.41	yes	184
7.6	odd	2	inner	840.2.bj.b.13.2	yes	184
8.5	even	2	inner	840.2.bj.b.13.42	yes	184
35.27	even	4	inner	840.2.bj.b.517.42	yes	184
40.37	odd	4	inner	840.2.bj.b.517.2	yes	184
56.13	odd	2	inner	840.2.bj.b.13.41	yes	184
280.237	even	4	inner	840.2.bj.b.517.1	yes	184

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.bj.b.13.1	✓	184	1.1	even	1	trivial
840.2.bj.b.13.2	yes	184	7.6	odd	2	inner
840.2.bj.b.13.41	yes	184	56.13	odd	2	inner
840.2.bj.b.13.42	yes	184	8.5	even	2	inner
840.2.bj.b.517.1	yes	184	280.237	even	4	inner
840.2.bj.b.517.2	yes	184	40.37	odd	4	inner
840.2.bj.b.517.41	yes	184	5.2	odd	4	inner
840.2.bj.b.517.42	yes	184	35.27	even	4	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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.40929 + 0.117921i) q^{2} +(-0.707107 - 0.707107i) q^{3} +(1.97219 - 0.332370i) q^{4} +(0.361094 + 2.20672i) q^{5} +(1.07990 + 0.913135i) q^{6} +(2.47159 + 0.944062i) q^{7} +(-2.74019 + 0.700969i) q^{8} +1.00000i q^{9} +(-0.769104 - 3.06732i) q^{10} +3.00292i q^{11} +(-1.62957 - 1.15953i) q^{12} +(2.37833 + 2.37833i) q^{13} +(-3.59451 - 1.03900i) q^{14} +(1.30505 - 1.81572i) q^{15} +(3.77906 - 1.31099i) q^{16} +(-3.17167 - 3.17167i) q^{17} +(-0.117921 - 1.40929i) q^{18} +7.49985i q^{19} +(1.44559 + 4.23205i) q^{20} +(-1.08012 - 2.41523i) q^{21} +(-0.354109 - 4.23199i) q^{22} +(-2.48231 - 2.48231i) q^{23} +(2.43327 + 1.44195i) q^{24} +(-4.73922 + 1.59366i) q^{25} +(-3.63222 - 3.07130i) q^{26} +(0.707107 - 0.707107i) q^{27} +(5.18822 + 1.04039i) q^{28} -2.42536 q^{29} +(-1.62509 + 2.71276i) q^{30} -1.92561i q^{31} +(-5.17119 + 2.29320i) q^{32} +(2.12339 - 2.12339i) q^{33} +(4.84381 + 4.09580i) q^{34} +(-1.19081 + 5.79500i) q^{35} +(0.332370 + 1.97219i) q^{36} +(-7.03701 - 7.03701i) q^{37} +(-0.884392 - 10.5695i) q^{38} -3.36347i q^{39} +(-2.53631 - 5.79372i) q^{40} -2.62677i q^{41} +(1.80701 + 3.27639i) q^{42} +(2.67688 - 2.67688i) q^{43} +(0.998083 + 5.92234i) q^{44} +(-2.20672 + 0.361094i) q^{45} +(3.79102 + 3.20558i) q^{46} +(5.83940 + 5.83940i) q^{47} +(-3.59921 - 1.74519i) q^{48} +(5.21749 + 4.66667i) q^{49} +(6.49101 - 2.80479i) q^{50} +4.48542i q^{51} +(5.48101 + 3.90004i) q^{52} +(-3.92370 + 3.92370i) q^{53} +(-0.913135 + 1.07990i) q^{54} +(-6.62661 + 1.08434i) q^{55} +(-7.43438 - 0.854404i) q^{56} +(5.30319 - 5.30319i) q^{57} +(3.41804 - 0.286002i) q^{58} +12.1091i q^{59} +(1.97032 - 4.01470i) q^{60} -3.11135 q^{61} +(0.227070 + 2.71373i) q^{62} +(-0.944062 + 2.47159i) q^{63} +(7.01729 - 3.84158i) q^{64} +(-4.38952 + 6.10712i) q^{65} +(-2.74207 + 3.24286i) q^{66} +(-5.83002 - 5.83002i) q^{67} +(-7.30931 - 5.20097i) q^{68} +3.51052i q^{69} +(0.994836 - 8.30724i) q^{70} +1.88481 q^{71} +(-0.700969 - 2.74019i) q^{72} +(-1.14816 + 1.14816i) q^{73} +(10.7470 + 9.08736i) q^{74} +(4.47803 + 2.22425i) q^{75} +(2.49273 + 14.7911i) q^{76} +(-2.83495 + 7.42199i) q^{77} +(0.396625 + 4.74010i) q^{78} +14.4613i q^{79} +(4.25759 + 7.86593i) q^{80} -1.00000 q^{81} +(0.309752 + 3.70188i) q^{82} +(8.44650 + 8.44650i) q^{83} +(-2.93296 - 4.40429i) q^{84} +(5.85372 - 8.14426i) q^{85} +(-3.45683 + 4.08815i) q^{86} +(1.71499 + 1.71499i) q^{87} +(-2.10496 - 8.22859i) q^{88} +3.40001 q^{89} +(3.06732 - 0.769104i) q^{90} +(3.63297 + 8.12356i) q^{91} +(-5.72064 - 4.07055i) q^{92} +(-1.36161 + 1.36161i) q^{93} +(-8.91799 - 7.54081i) q^{94} +(-16.5501 + 2.70815i) q^{95} +(5.27812 + 2.03505i) q^{96} +(-0.895923 - 0.895923i) q^{97} +(-7.90325 - 5.96143i) q^{98} -3.00292 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 184 q + 8 q^{2} + 4 q^{7} + 8 q^{8} - 16 q^{15} + 64 q^{16} + 8 q^{18} + 16 q^{23} - 32 q^{25} - 4 q^{28} + 24 q^{30} - 32 q^{32} - 16 q^{36} - 20 q^{42} - 80 q^{46} + 80 q^{50} + 56 q^{58} - 56 q^{60}+ \cdots + 48 q^{98}+O(q^{100}) \) 184 * q + 8 * q^2 + 4 * q^7 + 8 * q^8 - 16 * q^15 + 64 * q^16 + 8 * q^18 + 16 * q^23 - 32 * q^25 - 4 * q^28 + 24 * q^30 - 32 * q^32 - 16 * q^36 - 20 * q^42 - 80 * q^46 + 80 * q^50 + 56 * q^58 - 56 * q^60 + 4 * q^63 + 32 * q^65 - 44 * q^70 + 32 * q^71 - 8 * q^72 + 8 * q^78 - 184 * q^81 - 16 * q^86 - 64 * q^88 + 104 * q^92 - 96 * q^95 + 48 * q^98

Introduction

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