LMFDB - Embedded newform 840.2.e.d.491.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [840,2,Mod(491,840)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(840, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1, 0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("840.491"); 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.e (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44,2] 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			491.23
Character	$\chi$	$=$	840.491
Dual form			840.2.e.d.491.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.252227 - 1.39154i) q^{2} +(1.52280 - 0.825275i) q^{3} +(-1.87276 - 0.701969i) q^{4} -1.00000 q^{5} +(-0.764310 - 2.32719i) q^{6} -1.00000i q^{7} +(-1.44918 + 2.42897i) q^{8} +(1.63784 - 2.51346i) q^{9} +(-0.252227 + 1.39154i) q^{10} -3.18310i q^{11} +(-3.43116 + 0.476586i) q^{12} -0.611147i q^{13} +(-1.39154 - 0.252227i) q^{14} +(-1.52280 + 0.825275i) q^{15} +(3.01448 + 2.62924i) q^{16} -3.24419i q^{17} +(-3.08447 - 2.91309i) q^{18} -1.51894 q^{19} +(1.87276 + 0.701969i) q^{20} +(-0.825275 - 1.52280i) q^{21} +(-4.42941 - 0.802866i) q^{22} -3.27747 q^{23} +(-0.202245 + 4.89480i) q^{24} +1.00000 q^{25} +(-0.850435 - 0.154148i) q^{26} +(0.419813 - 5.17917i) q^{27} +(-0.701969 + 1.87276i) q^{28} -6.32996 q^{29} +(0.764310 + 2.32719i) q^{30} +5.58711i q^{31} +(4.41903 - 3.53160i) q^{32} +(-2.62694 - 4.84723i) q^{33} +(-4.51441 - 0.818273i) q^{34} +1.00000i q^{35} +(-4.83166 + 3.55740i) q^{36} +1.51137i q^{37} +(-0.383118 + 2.11366i) q^{38} +(-0.504364 - 0.930655i) q^{39} +(1.44918 - 2.42897i) q^{40} -4.12940i q^{41} +(-2.32719 + 0.764310i) q^{42} -0.874980 q^{43} +(-2.23444 + 5.96120i) q^{44} +(-1.63784 + 2.51346i) q^{45} +(-0.826669 + 4.56073i) q^{46} +0.289369 q^{47} +(6.76030 + 1.51604i) q^{48} -1.00000 q^{49} +(0.252227 - 1.39154i) q^{50} +(-2.67735 - 4.94025i) q^{51} +(-0.429006 + 1.14453i) q^{52} +3.74257 q^{53} +(-7.10112 - 1.89051i) q^{54} +3.18310i q^{55} +(2.42897 + 1.44918i) q^{56} +(-2.31304 + 1.25354i) q^{57} +(-1.59659 + 8.80839i) q^{58} +4.18632i q^{59} +(3.43116 - 0.476586i) q^{60} -11.4482i q^{61} +(7.77469 + 1.40922i) q^{62} +(-2.51346 - 1.63784i) q^{63} +(-3.79976 - 7.04002i) q^{64} +0.611147i q^{65} +(-7.40770 + 2.43288i) q^{66} +0.637748 q^{67} +(-2.27732 + 6.07559i) q^{68} +(-4.99094 + 2.70482i) q^{69} +(1.39154 + 0.252227i) q^{70} +13.8053 q^{71} +(3.73158 + 7.62072i) q^{72} +14.2348 q^{73} +(2.10314 + 0.381210i) q^{74} +(1.52280 - 0.825275i) q^{75} +(2.84461 + 1.06625i) q^{76} -3.18310 q^{77} +(-1.42226 + 0.467106i) q^{78} -12.9762i q^{79} +(-3.01448 - 2.62924i) q^{80} +(-3.63494 - 8.23330i) q^{81} +(-5.74622 - 1.04155i) q^{82} +2.55489i q^{83} +(0.476586 + 3.43116i) q^{84} +3.24419i q^{85} +(-0.220694 + 1.21757i) q^{86} +(-9.63927 + 5.22396i) q^{87} +(7.73165 + 4.61289i) q^{88} +8.07133i q^{89} +(3.08447 + 2.91309i) q^{90} -0.611147 q^{91} +(6.13793 + 2.30068i) q^{92} +(4.61091 + 8.50806i) q^{93} +(0.0729867 - 0.402668i) q^{94} +1.51894 q^{95} +(3.81476 - 9.02483i) q^{96} +13.4141 q^{97} +(-0.252227 + 1.39154i) q^{98} +(-8.00060 - 5.21342i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} + 4 q^{3} - 2 q^{4} - 44 q^{5} - 6 q^{6} - 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} + 4 q^{14} - 4 q^{15} + 22 q^{16} + 2 q^{18} + 16 q^{19} + 2 q^{20} + 16 q^{23} + 10 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) $ 44 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 - 44 * q^5 - 6 * q^6 - 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 + 4 * q^14 - 4 * q^15 + 22 * q^16 + 2 * q^18 + 16 * q^19 + 2 * q^20 + 16 * q^23 + 10 * q^24 + 44 * q^25 - 16 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^30 - 18 * q^32 + 24 * q^33 + 20 * q^34 - 46 * q^36 + 8 * q^38 - 16 * q^39 + 22 * q^40 - 4 * q^42 + 24 * q^43 + 32 * q^44 - 4 * q^45 - 24 * q^47 + 18 * q^48 - 44 * q^49 + 2 * q^50 - 20 * q^52 - 32 * q^53 + 2 * q^54 + 8 * q^56 - 4 * q^58 - 6 * q^60 + 32 * q^62 - 50 * q^64 - 8 * q^66 + 24 * q^67 - 28 * q^68 - 8 * q^69 - 4 * q^70 + 8 * q^71 + 2 * q^72 + 8 * q^73 - 48 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^77 - 84 * q^78 - 22 * q^80 + 20 * q^81 - 8 * q^82 + 4 * q^84 - 4 * q^86 - 16 * q^87 - 28 * q^88 - 2 * q^90 - 16 * q^91 + 76 * q^92 + 16 * q^93 - 16 * q^95 + 38 * q^96 + 24 * q^97 - 2 * q^98 - 64 * q^99

Character values

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

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$1$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.252227	−	1.39154i	0.178352	−	0.983967i
$2$	0.252227	−	1.39154i	0.178352	−	0.983967i
$3$	1.52280	−	0.825275i	0.879189	−	0.476473i
$3$	1.52280	−	0.825275i	0.879189	−	0.476473i
$4$	−1.87276	−	0.701969i	−0.936381	−	0.350984i
$5$	−1.00000			−0.447214
$5$	−1.00000			−0.447214
$6$	−0.764310	−	2.32719i	−0.312028	−	0.950073i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	−1.44918	+	2.42897i	−0.512362	+	0.858769i
$9$	1.63784	−	2.51346i	0.545948	−	0.837819i
$10$	−0.252227	+	1.39154i	−0.0797613	+	0.440043i
$11$		−	3.18310i		−	0.959742i	−0.877339	−	0.479871i	$-0.840683\pi$
$11$		−	3.18310i		−	0.959742i	0.877339	−	0.479871i	$-0.159317\pi$
$12$	−3.43116	+	0.476586i	−0.990491	+	0.137578i
$13$		−	0.611147i		−	0.169502i	−0.996402	−	0.0847508i	$-0.972991\pi$
$13$		−	0.611147i		−	0.169502i	0.996402	−	0.0847508i	$-0.0270094\pi$
$14$	−1.39154	−	0.252227i	−0.371904	−	0.0674106i
$15$	−1.52280	+	0.825275i	−0.393185	+	0.213085i
$16$	3.01448	+	2.62924i	0.753620	+	0.657310i
$17$		−	3.24419i		−	0.786831i	−0.919361	−	0.393415i	$-0.871293\pi$
$17$		−	3.24419i		−	0.786831i	0.919361	−	0.393415i	$-0.128707\pi$
$18$	−3.08447	−	2.91309i	−0.727016	−	0.686621i
$19$	−1.51894			−0.348468			−0.174234	−	0.984704i	$-0.555745\pi$
$19$	−1.51894			−0.348468			−0.174234	+	0.984704i	$0.555745\pi$
$20$	1.87276	+	0.701969i	0.418762	+	0.156965i
$21$	−0.825275	−	1.52280i	−0.180090	−	0.332302i
$22$	−4.42941	−	0.802866i	−0.944354	−	0.171172i
$23$	−3.27747			−0.683401			−0.341700	−	0.939809i	$-0.611003\pi$
$23$	−3.27747			−0.683401			−0.341700	+	0.939809i	$0.611003\pi$
$24$	−0.202245	+	4.89480i	−0.0412831	+	0.999147i
$25$	1.00000			0.200000
$26$	−0.850435	−	0.154148i	−0.166784	−	0.0302309i
$27$	0.419813	−	5.17917i	0.0807931	−	0.996731i
$28$	−0.701969	+	1.87276i	−0.132660	+	0.353919i
$29$	−6.32996			−1.17544			−0.587722	−	0.809063i	$-0.699975\pi$
$29$	−6.32996			−1.17544			−0.587722	+	0.809063i	$0.699975\pi$
$30$	0.764310	+	2.32719i	0.139543	+	0.424885i
$31$			5.58711i			1.00348i	0.865020	+	0.501738i	$0.167306\pi$
$31$			5.58711i			1.00348i	−0.865020	+	0.501738i	$0.832694\pi$
$32$	4.41903	−	3.53160i	0.781181	−	0.624305i
$33$	−2.62694	−	4.84723i	−0.457291	−	0.843795i
$34$	−4.51441	−	0.818273i	−0.774215	−	0.140333i
$35$			1.00000i			0.169031i
$36$	−4.83166	+	3.55740i	−0.805277	+	0.592899i
$37$			1.51137i			0.248468i	0.992253	+	0.124234i	$0.0396474\pi$
$37$			1.51137i			0.248468i	−0.992253	+	0.124234i	$0.960353\pi$
$38$	−0.383118	+	2.11366i	−0.0621500	+	0.342881i
$39$	−0.504364	−	0.930655i	−0.0807629	−	0.149024i
$40$	1.44918	−	2.42897i	0.229135	−	0.384053i
$41$		−	4.12940i		−	0.644904i	−0.946586	−	0.322452i	$-0.895493\pi$
$41$		−	4.12940i		−	0.644904i	0.946586	−	0.322452i	$-0.104507\pi$
$42$	−2.32719	+	0.764310i	−0.359094	+	0.117936i
$43$	−0.874980			−0.133433			−0.0667166	−	0.997772i	$-0.521252\pi$
$43$	−0.874980			−0.133433			−0.0667166	+	0.997772i	$0.521252\pi$
$44$	−2.23444	+	5.96120i	−0.336854	+	0.898684i
$45$	−1.63784	+	2.51346i	−0.244155	+	0.374684i
$46$	−0.826669	+	4.56073i	−0.121886	+	0.672444i
$47$	0.289369			0.0422087			0.0211044	−	0.999777i	$-0.493282\pi$
$47$	0.289369			0.0422087			0.0211044	+	0.999777i	$0.493282\pi$
$48$	6.76030	+	1.51604i	0.975765	+	0.218821i
$49$	−1.00000			−0.142857
$50$	0.252227	−	1.39154i	0.0356703	−	0.196793i
$51$	−2.67735	−	4.94025i	−0.374903	−	0.691773i
$52$	−0.429006	+	1.14453i	−0.0594924	+	0.158718i
$53$	3.74257			0.514081			0.257041	−	0.966401i	$-0.417253\pi$
$53$	3.74257			0.514081			0.257041	+	0.966401i	$0.417253\pi$
$54$	−7.10112	−	1.89051i	−0.966341	−	0.257266i
$55$			3.18310i			0.429210i
$56$	2.42897	+	1.44918i	0.324584	+	0.193655i
$57$	−2.31304	+	1.25354i	−0.306370	+	0.166036i
$58$	−1.59659	+	8.80839i	−0.209643	+	1.15660i
$59$			4.18632i			0.545013i	0.962154	+	0.272507i	$0.0878526\pi$
$59$			4.18632i			0.545013i	−0.962154	+	0.272507i	$0.912147\pi$
$60$	3.43116	−	0.476586i	0.442961	−	0.0615270i
$61$		−	11.4482i		−	1.46580i	−0.680338	−	0.732898i	$-0.738167\pi$
$61$		−	11.4482i		−	1.46580i	0.680338	−	0.732898i	$-0.261833\pi$
$62$	7.77469	+	1.40922i	0.987387	+	0.178972i
$63$	−2.51346	−	1.63784i	−0.316666	−	0.206349i
$64$	−3.79976	−	7.04002i	−0.474970	−	0.880002i
$65$			0.611147i			0.0758034i
$66$	−7.40770	+	2.43288i	−0.911825	+	0.299467i
$67$	0.637748			0.0779133			0.0389567	−	0.999241i	$-0.487597\pi$
$67$	0.637748			0.0779133			0.0389567	+	0.999241i	$0.487597\pi$
$68$	−2.27732	+	6.07559i	−0.276165	+	0.736774i
$69$	−4.99094	+	2.70482i	−0.600839	+	0.325622i
$70$	1.39154	+	0.252227i	0.166321	+	0.0301469i
$71$	13.8053			1.63839			0.819194	−	0.573516i	$-0.194421\pi$
$71$	13.8053			1.63839			0.819194	+	0.573516i	$0.194421\pi$
$72$	3.73158	+	7.62072i	0.439771	+	0.898110i
$73$	14.2348			1.66605			0.833027	−	0.553233i	$-0.186606\pi$
$73$	14.2348			1.66605			0.833027	+	0.553233i	$0.186606\pi$
$74$	2.10314	+	0.381210i	0.244485	+	0.0443148i
$75$	1.52280	−	0.825275i	0.175838	−	0.0952945i
$76$	2.84461	+	1.06625i	0.326299	+	0.122307i
$77$	−3.18310			−0.362748
$78$	−1.42226	+	0.467106i	−0.161039	+	0.0528893i
$79$		−	12.9762i		−	1.45993i	−0.683483	−	0.729966i	$-0.739536\pi$
$79$		−	12.9762i		−	1.45993i	0.683483	−	0.729966i	$-0.260464\pi$
$80$	−3.01448	−	2.62924i	−0.337029	−	0.293958i
$81$	−3.63494	−	8.23330i	−0.403883	−	0.914811i
$82$	−5.74622	−	1.04155i	−0.634564	−	0.115020i
$83$			2.55489i			0.280436i	0.990121	+	0.140218i	$0.0447803\pi$
$83$			2.55489i			0.280436i	−0.990121	+	0.140218i	$0.955220\pi$
$84$	0.476586	+	3.43116i	0.0519998	+	0.374370i
$85$			3.24419i			0.351881i
$86$	−0.220694	+	1.21757i	−0.0237980	+	0.131294i
$87$	−9.63927	+	5.22396i	−1.03344	+	0.560067i
$88$	7.73165	+	4.61289i	0.824197	+	0.491736i
$89$			8.07133i			0.855559i	0.903883	+	0.427780i	$0.140704\pi$
$89$			8.07133i			0.855559i	−0.903883	+	0.427780i	$0.859296\pi$
$90$	3.08447	+	2.91309i	0.325131	+	0.307066i
$91$	−0.611147			−0.0640656
$92$	6.13793	+	2.30068i	0.639924	+	0.239863i
$93$	4.61091	+	8.50806i	0.478129	+	0.882245i
$94$	0.0729867	−	0.402668i	0.00752800	−	0.0415320i
$95$	1.51894			0.155840
$96$	3.81476	−	9.02483i	0.389342	−	0.921093i
$97$	13.4141			1.36199			0.680997	−	0.732286i	$-0.261546\pi$
$97$	13.4141			1.36199			0.680997	+	0.732286i	$0.261546\pi$
$98$	−0.252227	+	1.39154i	−0.0254788	+	0.140567i
$99$	−8.00060	−	5.21342i	−0.804090	−	0.523969i
$100$	−1.87276	−	0.701969i	−0.187276	−	0.0701969i
$101$	19.4589			1.93623			0.968115	−	0.250507i	$-0.0805974\pi$
$101$	19.4589			1.93623			0.968115	+	0.250507i	$0.0805974\pi$
$102$	−7.54985	+	2.47956i	−0.747546	+	0.245514i
$103$		−	6.25210i		−	0.616038i	−0.951380	−	0.308019i	$-0.900334\pi$
$103$		−	6.25210i		−	0.616038i	0.951380	−	0.308019i	$-0.0996660\pi$
$104$	1.48446	+	0.885661i	0.145563	+	0.0868462i
$105$	0.825275	+	1.52280i	0.0805386	+	0.148610i
$106$	0.943978	−	5.20793i	0.0916872	−	0.505839i
$107$			5.85213i			0.565747i	0.959157	+	0.282873i	$0.0912876\pi$
$107$			5.85213i			0.565747i	−0.959157	+	0.282873i	$0.908712\pi$
$108$	−4.42182	+	9.40465i	−0.425490	+	0.904963i
$109$		−	9.96334i		−	0.954315i	−0.878818	−	0.477157i	$-0.841667\pi$
$109$		−	9.96334i		−	0.954315i	0.878818	−	0.477157i	$-0.158333\pi$
$110$	4.42941	+	0.802866i	0.422328	+	0.0765503i
$111$	1.24730	+	2.30152i	0.118388	+	0.218451i
$112$	2.62924	−	3.01448i	0.248440	−	0.284842i
$113$		−	0.131393i		−	0.0123604i	−0.999981	−	0.00618021i	$-0.998033\pi$
$113$		−	0.131393i		−	0.0123604i	0.999981	−	0.00618021i	$-0.00196724\pi$
$114$	1.16094	+	3.53486i	0.108732	+	0.331070i
$115$	3.27747			0.305626
$116$	11.8545	+	4.44344i	1.10066	+	0.412563i
$117$	−1.53609	−	1.00096i	−0.142012	−	0.0925390i
$118$	5.82543	+	1.05591i	0.536275	+	0.0972040i
$119$	−3.24419			−0.297394
$120$	0.202245	−	4.89480i	0.0184624	−	0.446832i
$121$	0.867849			0.0788953
$122$	−15.9307	−	2.88756i	−1.44230	−	0.261427i
$123$	−3.40789	−	6.28825i	−0.307279	−	0.566992i
$124$	3.92198	−	10.4633i	0.352204	−	0.939636i
$125$	−1.00000			−0.0894427
$126$	−2.91309	+	3.08447i	−0.259518	+	0.274786i
$127$			2.32125i			0.205978i	0.994682	+	0.102989i	$0.0328406\pi$
$127$			2.32125i			0.205978i	−0.994682	+	0.102989i	$0.967159\pi$
$128$	−10.7549	+	3.51183i	−0.950604	+	0.310405i
$129$	−1.33242	+	0.722099i	−0.117313	+	0.0635773i
$130$	0.850435	+	0.154148i	0.0745881	+	0.0135197i
$131$		−	9.68475i		−	0.846161i	−0.906092	−	0.423080i	$-0.860949\pi$
$131$		−	9.68475i		−	0.846161i	0.906092	−	0.423080i	$-0.139051\pi$
$132$	1.51702	+	10.9217i	0.132040	+	0.950616i
$133$			1.51894i			0.131709i
$134$	0.160858	−	0.887451i	0.0138960	−	0.0766641i
$135$	−0.419813	+	5.17917i	−0.0361318	+	0.445752i
$136$	7.88002	+	4.70141i	0.675706	+	0.403142i
$137$			14.6389i			1.25069i	0.780350	+	0.625343i	$0.215041\pi$
$137$			14.6389i			1.25069i	−0.780350	+	0.625343i	$0.784959\pi$
$138$	2.50501	+	7.62732i	0.213240	+	0.649280i
$139$	−12.3779			−1.04988			−0.524938	−	0.851141i	$-0.675911\pi$
$139$	−12.3779			−1.04988			−0.524938	+	0.851141i	$0.675911\pi$
$140$	0.701969	−	1.87276i	0.0593272	−	0.158277i
$141$	0.440651	−	0.238809i	0.0371095	−	0.0201113i
$142$	3.48208	−	19.2106i	0.292209	−	1.61212i
$143$	−1.94534			−0.162678
$144$	11.5457	−	3.27048i	0.962144	−	0.272540i
$145$	6.32996			0.525675
$146$	3.59040	−	19.8082i	0.297144	−	1.63934i
$147$	−1.52280	+	0.825275i	−0.125598	+	0.0680675i
$148$	1.06094	−	2.83045i	0.0872085	−	0.232661i
$149$	−16.7175			−1.36955			−0.684777	−	0.728753i	$-0.740100\pi$
$149$	−16.7175			−1.36955			−0.684777	+	0.728753i	$0.740100\pi$
$150$	−0.764310	−	2.32719i	−0.0624057	−	0.190015i
$151$			7.45900i			0.607005i	0.952831	+	0.303502i	$0.0981561\pi$
$151$			7.45900i			0.607005i	−0.952831	+	0.303502i	$0.901844\pi$
$152$	2.20121	−	3.68945i	0.178542	−	0.299254i
$153$	−8.15413	−	5.31347i	−0.659222	−	0.429568i
$154$	−0.802866	+	4.42941i	−0.0646968	+	0.356932i
$155$		−	5.58711i		−	0.448768i
$156$	0.291264	+	2.09694i	0.0233198	+	0.167890i
$157$			13.9858i			1.11619i	0.829777	+	0.558095i	$0.188468\pi$
$157$			13.9858i			1.11619i	−0.829777	+	0.558095i	$0.811532\pi$
$158$	−18.0568	−	3.27294i	−1.43653	−	0.260382i
$159$	5.69918	−	3.08865i	0.451975	−	0.244946i
$160$	−4.41903	+	3.53160i	−0.349355	+	0.279197i
$161$			3.27747i			0.258301i
$162$	−12.3738	+	2.98150i	−0.972177	+	0.234249i
$163$	−15.1310			−1.18515			−0.592576	−	0.805515i	$-0.701889\pi$
$163$	−15.1310			−1.18515			−0.592576	+	0.805515i	$0.701889\pi$
$164$	−2.89871	+	7.73338i	−0.226351	+	0.603876i
$165$	2.62694	+	4.84723i	0.204507	+	0.377357i
$166$	3.55523	+	0.644414i	0.275939	+	0.0500162i
$167$	−3.06283			−0.237009			−0.118504	−	0.992954i	$-0.537810\pi$
$167$	−3.06283			−0.237009			−0.118504	+	0.992954i	$0.537810\pi$
$168$	4.89480	+	0.202245i	0.377642	+	0.0156036i
$169$	12.6265			0.971269
$170$	4.51441	+	0.818273i	0.346240	+	0.0627587i
$171$	−2.48778	+	3.81779i	−0.190245	+	0.291954i
$172$	1.63863	+	0.614208i	0.124944	+	0.0468330i
$173$	12.0690			0.917591			0.458795	−	0.888542i	$-0.348281\pi$
$173$	12.0690			0.917591			0.458795	+	0.888542i	$0.348281\pi$
$174$	4.83805	+	14.7310i	0.366772	+	1.11676i
$175$		−	1.00000i		−	0.0755929i
$176$	8.36915	−	9.59540i	0.630848	−	0.723281i
$177$	3.45487	+	6.37494i	0.259684	+	0.479170i
$178$	11.2316	+	2.03581i	0.841842	+	0.152590i
$179$		−	1.52974i		−	0.114338i	−0.998365	−	0.0571692i	$-0.981793\pi$
$179$		−	1.52974i		−	0.114338i	0.998365	−	0.0571692i	$-0.0182074\pi$
$180$	4.83166	−	3.55740i	0.360131	−	0.265153i
$181$		−	14.8089i		−	1.10074i	−0.834922	−	0.550368i	$-0.814488\pi$
$181$		−	14.8089i		−	1.10074i	0.834922	−	0.550368i	$-0.185512\pi$
$182$	−0.154148	+	0.850435i	−0.0114262	+	0.0630384i
$183$	−9.44794	−	17.4334i	−0.698412	−	1.28871i
$184$	4.74965	−	7.96088i	0.350149	−	0.586884i
$185$		−	1.51137i		−	0.111118i
$186$	13.0023	−	4.27029i	0.953375	−	0.313113i
$187$	−10.3266			−0.755154
$188$	−0.541919	−	0.203128i	−0.0395235	−	0.0148146i
$189$	−5.17917	−	0.419813i	−0.376729	−	0.0305369i
$190$	0.383118	−	2.11366i	0.0277943	−	0.153341i
$191$	1.22855			0.0888950			0.0444475	−	0.999012i	$-0.485847\pi$
$191$	1.22855			0.0888950			0.0444475	+	0.999012i	$0.485847\pi$
$192$	−11.5962	−	7.58469i	−0.836885	−	0.547378i
$193$	26.0157			1.87265			0.936327	−	0.351129i	$-0.114202\pi$
$193$	26.0157			1.87265			0.936327	+	0.351129i	$0.114202\pi$
$194$	3.38340	−	18.6662i	0.242914	−	1.34016i
$195$	0.504364	+	0.930655i	0.0361183	+	0.0666456i
$196$	1.87276	+	0.701969i	0.133769	+	0.0501406i
$197$	−9.99215			−0.711912			−0.355956	−	0.934503i	$-0.615845\pi$
$197$	−9.99215			−0.711912			−0.355956	+	0.934503i	$0.615845\pi$
$198$	−9.27265	+	9.81818i	−0.658979	+	0.697748i
$199$			19.9327i			1.41299i	0.707716	+	0.706497i	$0.249725\pi$
$199$			19.9327i			1.41299i	−0.707716	+	0.706497i	$0.750275\pi$
$200$	−1.44918	+	2.42897i	−0.102472	+	0.171754i
$201$	0.971163	−	0.526317i	0.0685005	−	0.0371236i
$202$	4.90806	−	27.0778i	0.345330	−	1.90519i
$203$			6.32996i			0.444276i
$204$	1.54613	+	11.1313i	0.108251	+	0.779349i
$205$			4.12940i			0.288410i
$206$	−8.70004	−	1.57695i	−0.606161	−	0.109871i
$207$	−5.36799	+	8.23780i	−0.373101	+	0.572566i
$208$	1.60685	−	1.84229i	0.111415	−	0.127740i
$209$			4.83494i			0.334440i
$210$	2.32719	−	0.764310i	0.160592	−	0.0527424i
$211$	−4.55116			−0.313315			−0.156658	−	0.987653i	$-0.550072\pi$
$211$	−4.55116			−0.313315			−0.156658	+	0.987653i	$0.550072\pi$
$212$	−7.00894	−	2.62716i	−0.481376	−	0.180434i
$213$	21.0227	−	11.3932i	1.44045	−	0.780647i
$214$	8.14347	+	1.47607i	0.556676	+	0.100902i
$215$	0.874980			0.0596731
$216$	11.9716	+	8.52525i	0.814567	+	0.580070i
$217$	5.58711			0.379278
$218$	−13.8644	−	2.51303i	−0.939014	−	0.170204i
$219$	21.6767	−	11.7476i	1.46478	−	0.793829i
$220$	2.23444	−	5.96120i	0.150646	−	0.401904i
$221$	−1.98267			−0.133369
$222$	3.51726	−	1.15516i	0.236063	−	0.0775292i
$223$		−	16.4614i		−	1.10234i	−0.834395	−	0.551168i	$-0.814182\pi$
$223$		−	16.4614i		−	1.10234i	0.834395	−	0.551168i	$-0.185818\pi$
$224$	−3.53160	−	4.41903i	−0.235965	−	0.295259i
$225$	1.63784	−	2.51346i	0.109190	−	0.167564i
$226$	−0.182839	−	0.0331409i	−0.0121622	−	0.00220450i
$227$		−	24.3134i		−	1.61373i	−0.590733	−	0.806867i	$-0.701161\pi$
$227$		−	24.3134i		−	1.61373i	0.590733	−	0.806867i	$-0.298839\pi$
$228$	5.21172	−	0.723905i	0.345155	−	0.0479417i
$229$		−	24.3515i		−	1.60919i	−0.593821	−	0.804597i	$-0.702381\pi$
$229$		−	24.3515i		−	1.60919i	0.593821	−	0.804597i	$-0.297619\pi$
$230$	0.826669	−	4.56073i	0.0545089	−	0.300726i
$231$	−4.84723	+	2.62694i	−0.318924	+	0.172840i
$232$	9.17325	−	15.3753i	0.602253	−	1.00944i
$233$			28.2542i			1.85099i	0.378757	+	0.925496i	$0.376352\pi$
$233$			28.2542i			1.85099i	−0.378757	+	0.925496i	$0.623648\pi$
$234$	−1.78032	+	1.88506i	−0.116383	+	0.123230i
$235$	−0.289369			−0.0188763
$236$	2.93867	−	7.83999i	0.191291	−	0.510340i
$237$	−10.7089	−	19.7601i	−0.695618	−	1.28356i
$238$	−0.818273	+	4.51441i	−0.0530407	+	0.292626i
$239$	2.63400			0.170379			0.0851897	−	0.996365i	$-0.472850\pi$
$239$	2.63400			0.170379			0.0851897	+	0.996365i	$0.472850\pi$
$240$	−6.76030	−	1.51604i	−0.436375	−	0.0978597i
$241$	29.6819			1.91198			0.955991	−	0.293398i	$-0.0947860\pi$
$241$	29.6819			1.91198			0.955991	+	0.293398i	$0.0947860\pi$
$242$	0.218895	−	1.20765i	0.0140711	−	0.0776304i
$243$	−12.3300	−	9.53784i	−0.790972	−	0.611853i
$244$	−8.03630	+	21.4398i	−0.514472	+	1.37254i
$245$	1.00000			0.0638877
$246$	−9.60991	+	3.15614i	−0.612705	+	0.201228i
$247$			0.928295i			0.0590660i
$248$	−13.5709	−	8.09673i	−0.861754	−	0.514143i
$249$	2.10849	+	3.89059i	0.133620	+	0.246556i
$250$	−0.252227	+	1.39154i	−0.0159523	+	0.0880087i
$251$		−	0.525155i		−	0.0331475i	−0.999863	−	0.0165737i	$-0.994724\pi$
$251$		−	0.525155i		−	0.0331475i	0.999863	−	0.0165737i	$-0.00527583\pi$
$252$	3.55740	+	4.83166i	0.224095	+	0.304366i
$253$			10.4325i			0.655888i
$254$	3.23012	+	0.585484i	0.202675	+	0.0367365i
$255$	2.67735	+	4.94025i	0.167662	+	0.309370i
$256$	2.17418	+	15.8516i	0.135886	+	0.990724i
$257$			8.87096i			0.553355i	0.960963	+	0.276678i	$0.0892335\pi$
$257$			8.87096i			0.553355i	−0.960963	+	0.276678i	$0.910767\pi$
$258$	0.668756	+	2.03625i	0.0416349	+	0.126771i
$259$	1.51137			0.0939122
$260$	0.429006	−	1.14453i	0.0266058	−	0.0709809i
$261$	−10.3675	+	15.9101i	−0.641731	+	0.984810i
$262$	−13.4767	−	2.44276i	−0.832594	−	0.150914i
$263$	−28.5258			−1.75897			−0.879487	−	0.475922i	$-0.842114\pi$
$263$	−28.5258			−1.75897			−0.879487	+	0.475922i	$0.842114\pi$
$264$	15.5807	+	0.643768i	0.958924	+	0.0396212i
$265$	−3.74257			−0.229904
$266$	2.11366	+	0.383118i	0.129597	+	0.0234905i
$267$	6.66107	+	12.2910i	0.407651	+	0.752198i
$268$	−1.19435	−	0.447679i	−0.0729566	−	0.0273464i
$269$	27.8415			1.69753			0.848764	−	0.528771i	$-0.177347\pi$
$269$	27.8415			1.69753			0.848764	+	0.528771i	$0.177347\pi$
$270$	7.10112	+	1.89051i	0.432161	+	0.115053i
$271$		−	11.3907i		−	0.691935i	−0.938247	−	0.345967i	$-0.887551\pi$
$271$		−	11.3907i		−	0.691935i	0.938247	−	0.345967i	$-0.112449\pi$
$272$	8.52975	−	9.77953i	0.517192	−	0.592971i
$273$	−0.930655	+	0.504364i	−0.0563258	+	0.0305255i
$274$	20.3706	+	3.69233i	1.23063	+	0.223062i
$275$		−	3.18310i		−	0.191948i
$276$	11.2455	−	1.56200i	0.676902	−	0.0940212i
$277$			7.15528i			0.429919i	0.976623	+	0.214959i	$0.0689619\pi$
$277$			7.15528i			0.429919i	−0.976623	+	0.214959i	$0.931038\pi$
$278$	−3.12203	+	17.2243i	−0.187247	+	1.03304i
$279$	14.0430	+	9.15081i	0.840731	+	0.547845i
$280$	−2.42897	−	1.44918i	−0.145159	−	0.0866050i
$281$			23.5148i			1.40277i	0.712781	+	0.701387i	$0.247435\pi$
$281$			23.5148i			1.40277i	−0.712781	+	0.701387i	$0.752565\pi$
$282$	−0.221167	−	0.673417i	−0.0131703	−	0.0401014i
$283$	4.23414			0.251694			0.125847	−	0.992050i	$-0.459835\pi$
$283$	4.23414			0.251694			0.125847	+	0.992050i	$0.459835\pi$
$284$	−25.8541	−	9.69089i	−1.53416	−	0.575049i
$285$	2.31304	−	1.25354i	0.137013	−	0.0742534i
$286$	−0.490669	+	2.70702i	−0.0290139	+	0.160070i
$287$	−4.12940			−0.243751
$288$	−1.63886	−	16.8912i	−0.0965706	−	0.995326i
$289$	6.47526			0.380897
$290$	1.59659	−	8.80839i	0.0937550	−	0.517246i
$291$	20.4270	−	11.0703i	1.19745	−	0.648953i
$292$	−26.6583	−	9.99236i	−1.56006	−	0.584759i
$293$	16.6676			0.973732			0.486866	−	0.873477i	$-0.338140\pi$
$293$	16.6676			0.973732			0.486866	+	0.873477i	$0.338140\pi$
$294$	0.764310	+	2.32719i	0.0445755	+	0.135725i
$295$		−	4.18632i		−	0.243737i
$296$	−3.67108	−	2.19025i	−0.213377	−	0.127306i
$297$	−16.4858	−	1.33631i	−0.956604	−	0.0775405i
$298$	−4.21662	+	23.2631i	−0.244262	+	1.34760i
$299$			2.00302i			0.115838i
$300$	−3.43116	+	0.476586i	−0.198098	+	0.0275157i
$301$			0.874980i			0.0504330i
$302$	10.3795	+	1.88136i	0.597273	+	0.108260i
$303$	29.6320	−	16.0589i	1.70231	−	0.922560i
$304$	−4.57881	−	3.99366i	−0.262613	−	0.229052i
$305$			11.4482i			0.655524i
$306$	−9.45059	+	10.0066i	−0.540254	+	0.572038i
$307$	−5.46542			−0.311928			−0.155964	−	0.987763i	$-0.549848\pi$
$307$	−5.46542			−0.311928			−0.155964	+	0.987763i	$0.549848\pi$
$308$	5.96120	+	2.23444i	0.339671	+	0.127319i
$309$	−5.15970	−	9.52070i	−0.293525	−	0.541614i
$310$	−7.77469	−	1.40922i	−0.441573	−	0.0800385i
$311$	18.8900			1.07115			0.535576	−	0.844487i	$-0.320095\pi$
$311$	18.8900			1.07115			0.535576	+	0.844487i	$0.320095\pi$
$312$	2.99144	+	0.123602i	0.169357	+	0.00699756i
$313$	−18.5316			−1.04747			−0.523735	−	0.851881i	$-0.675462\pi$
$313$	−18.5316			−1.04747			−0.523735	+	0.851881i	$0.675462\pi$
$314$	19.4618	+	3.52761i	1.09829	+	0.199075i
$315$	2.51346	+	1.63784i	0.141617	+	0.0922820i
$316$	−9.10886	+	24.3013i	−0.512414	+	1.36705i
$317$	−20.6294			−1.15866			−0.579330	−	0.815093i	$-0.696686\pi$
$317$	−20.6294			−1.15866			−0.579330	+	0.815093i	$0.696686\pi$
$318$	−2.86048	−	8.70968i	−0.160408	−	0.488414i
$319$			20.1489i			1.12812i
$320$	3.79976	+	7.04002i	0.212413	+	0.393549i
$321$	4.82962	+	8.91162i	0.269563	+	0.497398i
$322$	4.56073	+	0.826669i	0.254160	+	0.0460685i
$323$			4.92772i			0.274186i
$324$	1.02787	+	17.9706i	0.0571039	+	0.998368i
$325$		−	0.611147i		−	0.0339003i
$326$	−3.81645	+	21.0554i	−0.211374	+	1.16615i
$327$	−8.22249	−	15.1722i	−0.454705	−	0.839023i
$328$	10.0302	+	5.98424i	0.553823	+	0.330424i
$329$		−	0.289369i		−	0.0159534i
$330$	7.40770	−	2.43288i	0.407780	−	0.133926i
$331$	−26.6014			−1.46215			−0.731073	−	0.682299i	$-0.760980\pi$
$331$	−26.6014			−1.46215			−0.731073	+	0.682299i	$0.760980\pi$
$332$	1.79345	−	4.78470i	0.0984286	−	0.262595i
$333$	3.79878	+	2.47539i	0.208172	+	0.135651i
$334$	−0.772530	+	4.26205i	−0.0422709	+	0.233209i
$335$	−0.637748			−0.0348439
$336$	1.51604	−	6.76030i	0.0827065	−	0.368805i
$337$	6.17287			0.336258			0.168129	−	0.985765i	$-0.446228\pi$
$337$	6.17287			0.336258			0.168129	+	0.985765i	$0.446228\pi$
$338$	3.18475	−	17.5703i	0.173228	−	0.955697i
$339$	−0.108435	−	0.200085i	−0.00588940	−	0.0108672i
$340$	2.27732	−	6.07559i	0.123505	−	0.329495i
$341$	17.7844			0.963078
$342$	4.68512	+	4.42480i	0.253342	+	0.239266i
$343$			1.00000i			0.0539949i
$344$	1.26800	−	2.12530i	0.0683661	−	0.114588i
$345$	4.99094	−	2.70482i	0.268703	−	0.145622i
$346$	3.04414	−	16.7945i	0.163654	−	0.902879i
$347$			33.9389i			1.82194i	0.412477	+	0.910968i	$0.364664\pi$
$347$			33.9389i			1.82194i	−0.412477	+	0.910968i	$0.635336\pi$
$348$	21.7191	−	3.01677i	1.16427	−	0.161716i
$349$		−	29.0093i		−	1.55283i	−0.630222	−	0.776415i	$-0.717036\pi$
$349$		−	29.0093i		−	1.55283i	0.630222	−	0.776415i	$-0.282964\pi$
$350$	−1.39154	−	0.252227i	−0.0743809	−	0.0134821i
$351$	−3.16523	−	0.256568i	−0.168948	−	0.0136946i
$352$	−11.2414	−	14.0662i	−0.599171	−	0.749732i
$353$		−	14.8212i		−	0.788851i	−0.918928	−	0.394425i	$-0.870944\pi$
$353$		−	14.8212i		−	0.788851i	0.918928	−	0.394425i	$-0.129056\pi$
$354$	9.74239	−	3.19965i	0.517802	−	0.170060i
$355$	−13.8053			−0.732709
$356$	5.66582	−	15.1157i	0.300288	−	0.801130i
$357$	−4.94025	+	2.67735i	−0.261466	+	0.141700i
$358$	−2.12870	−	0.385843i	−0.112505	−	0.0203924i
$359$	33.2076			1.75263			0.876316	−	0.481737i	$-0.159994\pi$
$359$	33.2076			1.75263			0.876316	+	0.481737i	$0.159994\pi$
$360$	−3.73158	−	7.62072i	−0.196671	−	0.401647i
$361$	−16.6928			−0.878570
$362$	−20.6071	−	3.73521i	−1.08309	−	0.196318i
$363$	1.32156	−	0.716214i	0.0693639	−	0.0375915i
$364$	1.14453	+	0.429006i	0.0599898	+	0.0224860i
$365$	−14.2348			−0.745082
$366$	−26.6423	+	8.75001i	−1.39261	+	0.457370i
$367$			28.3135i			1.47795i	0.673732	+	0.738976i	$0.264690\pi$
$367$			28.3135i			1.47795i	−0.673732	+	0.738976i	$0.735310\pi$
$368$	−9.87988	−	8.61727i	−0.515024	−	0.449206i
$369$	−10.3791	−	6.76330i	−0.540313	−	0.352083i
$370$	−2.10314	−	0.381210i	−0.109337	−	0.0198182i
$371$		−	3.74257i		−	0.194304i
$372$	−2.66274	−	19.1703i	−0.138057	−	0.993933i
$373$			26.4429i			1.36916i	0.728938	+	0.684580i	$0.240014\pi$
$373$			26.4429i			1.36916i	−0.728938	+	0.684580i	$0.759986\pi$
$374$	−2.60465	+	14.3698i	−0.134683	+	0.743047i
$375$	−1.52280	+	0.825275i	−0.0786371	+	0.0426170i
$376$	−0.419347	+	0.702867i	−0.0216262	+	0.0362476i
$377$			3.86854i			0.199240i
$378$	−1.89051	+	7.10112i	−0.0972376	+	0.365242i
$379$	−35.0973			−1.80283			−0.901413	−	0.432960i	$-0.857469\pi$
$379$	−35.0973			−1.80283			−0.901413	+	0.432960i	$0.857469\pi$
$380$	−2.84461	−	1.06625i	−0.145926	−	0.0546973i
$381$	1.91567	+	3.53481i	0.0981429	+	0.181094i
$382$	0.309875	−	1.70958i	0.0158546	−	0.0874697i
$383$	−14.4373			−0.737710			−0.368855	−	0.929487i	$-0.620250\pi$
$383$	−14.4373			−0.737710			−0.368855	+	0.929487i	$0.620250\pi$
$384$	−13.4793	+	14.2235i	−0.687862	+	0.725842i
$385$	3.18310			0.162226
$386$	6.56188	−	36.2019i	0.333991	−	1.84263i
$387$	−1.43308	+	2.19922i	−0.0728475	+	0.111793i
$388$	−25.1214	−	9.41628i	−1.27535	−	0.478039i
$389$	−17.0620			−0.865076			−0.432538	−	0.901616i	$-0.642382\pi$
$389$	−17.0620			−0.865076			−0.432538	+	0.901616i	$0.642382\pi$
$390$	1.42226	−	0.467106i	0.0720188	−	0.0236528i
$391$			10.6327i			0.537721i
$392$	1.44918	−	2.42897i	0.0731946	−	0.122681i
$393$	−7.99258	−	14.7479i	−0.403172	−	0.743935i
$394$	−2.52030	+	13.9045i	−0.126971	+	0.700497i
$395$			12.9762i			0.652902i
$396$	11.3236	+	15.3797i	0.569030	+	0.772858i
$397$			16.7656i			0.841443i	0.907190	+	0.420721i	$0.138223\pi$
$397$			16.7656i			0.841443i	−0.907190	+	0.420721i	$0.861777\pi$
$398$	27.7372	+	5.02758i	1.39034	+	0.252010i
$399$	1.25354	+	2.31304i	0.0627556	+	0.115797i
$400$	3.01448	+	2.62924i	0.150724	+	0.131462i
$401$		−	25.5862i		−	1.27772i	−0.769325	−	0.638858i	$-0.779407\pi$
$401$		−	25.5862i		−	1.27772i	0.769325	−	0.638858i	$-0.220593\pi$
$402$	−0.487437	−	1.48416i	−0.0243112	−	0.0740233i
$403$	3.41455			0.170091
$404$	−36.4418	−	13.6595i	−1.81305	−	0.679586i
$405$	3.63494	+	8.23330i	0.180622	+	0.409116i
$406$	8.80839	+	1.59659i	0.437153	+	0.0792374i
$407$	4.81086			0.238466
$408$	15.8797	+	0.656121i	0.786160	+	0.0324828i
$409$	−34.0307			−1.68271			−0.841355	−	0.540482i	$-0.818242\pi$
$409$	−34.0307			−1.68271			−0.841355	+	0.540482i	$0.818242\pi$
$410$	5.74622	+	1.04155i	0.283785	+	0.0514384i
$411$	12.0811	+	22.2921i	0.595918	+	1.09959i
$412$	−4.38878	+	11.7087i	−0.216220	+	0.576846i
$413$	4.18632			0.205996
$414$	10.1093	+	9.54756i	0.496843	+	0.469237i
$415$		−	2.55489i		−	0.125415i
$416$	−2.15833	−	2.70067i	−0.105821	−	0.132411i
$417$	−18.8490	+	10.2151i	−0.923039	+	0.500237i
$418$	6.72801	+	1.21950i	0.329078	+	0.0596479i
$419$			3.50519i			0.171240i	0.996328	+	0.0856199i	$0.0272871\pi$
$419$			3.50519i			0.171240i	−0.996328	+	0.0856199i	$0.972713\pi$
$420$	−0.476586	−	3.43116i	−0.0232550	−	0.167424i
$421$			20.7225i			1.00996i	0.863132	+	0.504978i	$0.168499\pi$
$421$			20.7225i			1.00996i	−0.863132	+	0.504978i	$0.831501\pi$
$422$	−1.14793	+	6.33312i	−0.0558803	+	0.308292i
$423$	0.473940	−	0.727316i	0.0230438	−	0.0353633i
$424$	−5.42365	+	9.09057i	−0.263396	+	0.441477i
$425$		−	3.24419i		−	0.157366i
$426$	−10.5515	−	32.1276i	−0.511224	−	1.55659i
$427$	−11.4482			−0.554019
$428$	4.10801	−	10.9596i	0.198568	−	0.529755i
$429$	−2.96237	+	1.60544i	−0.143025	+	0.0775116i
$430$	0.220694	−	1.21757i	0.0106428	−	0.0587164i
$431$	−20.2688			−0.976313			−0.488156	−	0.872756i	$-0.662330\pi$
$431$	−20.2688			−0.976313			−0.488156	+	0.872756i	$0.662330\pi$
$432$	14.8828	−	14.5087i	0.716049	−	0.698050i
$433$	−13.7333			−0.659979			−0.329989	−	0.943985i	$-0.607045\pi$
$433$	−13.7333			−0.659979			−0.329989	+	0.943985i	$0.607045\pi$
$434$	1.40922	−	7.77469i	0.0676449	−	0.373197i
$435$	9.63927	−	5.22396i	0.462168	−	0.250470i
$436$	−6.99395	+	18.6590i	−0.334949	+	0.893602i
$437$	4.97828			0.238144
$438$	−10.8798	−	33.1271i	−0.519856	−	1.58287i
$439$		−	19.9303i		−	0.951219i	−0.879656	−	0.475610i	$-0.842228\pi$
$439$		−	19.9303i		−	0.951219i	0.879656	−	0.475610i	$-0.157772\pi$
$440$	−7.73165	−	4.61289i	−0.368592	−	0.219911i
$441$	−1.63784	+	2.51346i	−0.0779925	+	0.119688i
$442$	−0.500085	+	2.75897i	−0.0237866	+	0.131231i
$443$			7.34323i			0.348887i	0.984667	+	0.174444i	$0.0558127\pi$
$443$			7.34323i			0.348887i	−0.984667	+	0.174444i	$0.944187\pi$
$444$	−0.720299	−	5.18577i	−0.0341839	−	0.246106i
$445$		−	8.07133i		−	0.382618i
$446$	−22.9066	−	4.15201i	−1.08466	−	0.196603i
$447$	−25.4575	+	13.7966i	−1.20410	+	0.652555i
$448$	−7.04002	+	3.79976i	−0.332610	+	0.179522i
$449$		−	5.65278i		−	0.266771i	−0.991064	−	0.133386i	$-0.957415\pi$
$449$		−	5.65278i		−	0.266771i	0.991064	−	0.133386i	$-0.0425849\pi$
$450$	−3.08447	−	2.91309i	−0.145403	−	0.137324i
$451$	−13.1443			−0.618941
$452$	−0.0922339	+	0.246068i	−0.00433832	+	0.0115741i
$453$	6.15573	+	11.3586i	0.289221	+	0.533672i
$454$	−33.8330	−	6.13250i	−1.58786	−	0.287812i
$455$	0.611147			0.0286510
$456$	0.307198	−	7.43491i	0.0143859	−	0.348171i
$457$	18.3259			0.857250			0.428625	−	0.903483i	$-0.358998\pi$
$457$	18.3259			0.857250			0.428625	+	0.903483i	$0.358998\pi$
$458$	−33.8861	−	6.14212i	−1.58339	−	0.287002i
$459$	−16.8022	−	1.36195i	−0.784258	−	0.0635705i
$460$	−6.13793	−	2.30068i	−0.286183	−	0.107270i
$461$	−1.96787			−0.0916527			−0.0458263	−	0.998949i	$-0.514592\pi$
$461$	−1.96787			−0.0916527			−0.0458263	+	0.998949i	$0.514592\pi$
$462$	2.43288	+	7.40770i	0.113188	+	0.344637i
$463$		−	14.0960i		−	0.655098i	−0.944834	−	0.327549i	$-0.893777\pi$
$463$		−	14.0960i		−	0.655098i	0.944834	−	0.327549i	$-0.106223\pi$
$464$	−19.0815	−	16.6430i	−0.885838	−	0.772632i
$465$	−4.61091	−	8.50806i	−0.213826	−	0.394552i
$466$	39.3168	+	7.12648i	1.82132	+	0.330128i
$467$			13.5412i			0.626612i	0.949652	+	0.313306i	$0.101437\pi$
$467$			13.5412i			0.626612i	−0.949652	+	0.313306i	$0.898563\pi$
$468$	2.17409	+	2.95285i	0.100497	+	0.136496i
$469$		−	0.637748i		−	0.0294485i
$470$	−0.0729867	+	0.402668i	−0.00336663	+	0.0185737i
$471$	11.5422	+	21.2976i	0.531834	+	0.981343i
$472$	−10.1684	−	6.06673i	−0.468041	−	0.279244i
$473$			2.78515i			0.128061i
$474$	−30.1980	+	9.91782i	−1.38704	+	0.455540i
$475$	−1.51894			−0.0696937
$476$	6.07559	+	2.27732i	0.278474	+	0.104381i
$477$	6.12973	−	9.40678i	0.280661	−	0.430707i
$478$	0.664367	−	3.66532i	0.0303875	−	0.167648i
$479$	41.0871			1.87732			0.938658	−	0.344849i	$-0.112070\pi$
$479$	41.0871			1.87732			0.938658	+	0.344849i	$0.112070\pi$
$480$	−3.81476	+	9.02483i	−0.174119	+	0.411925i
$481$	0.923672			0.0421158
$482$	7.48660	−	41.3036i	0.341005	−	1.88133i
$483$	2.70482	+	4.99094i	0.123073	+	0.227096i
$484$	−1.62527	−	0.609203i	−0.0738761	−	0.0276910i
$485$	−13.4141			−0.609103
$486$	−16.3823	+	14.7520i	−0.743114	+	0.669165i
$487$			33.5339i			1.51956i	0.650178	+	0.759782i	$0.274694\pi$
$487$			33.5339i			1.51956i	−0.650178	+	0.759782i	$0.725306\pi$
$488$	27.8074	+	16.5905i	1.25878	+	0.751019i
$489$	−23.0415	+	12.4872i	−1.04197	+	0.564692i
$490$	0.252227	−	1.39154i	0.0113945	−	0.0628633i
$491$			18.6783i			0.842940i	0.906842	+	0.421470i	$0.138486\pi$
$491$			18.6783i			0.842940i	−0.906842	+	0.421470i	$0.861514\pi$
$492$	1.96801	+	14.1686i	0.0887248	+	0.638771i
$493$			20.5356i			0.924876i
$494$	1.29176	+	0.234141i	0.0581190	+	0.0105345i
$495$	8.00060	+	5.21342i	0.359600	+	0.234326i
$496$	−14.6899	+	16.8422i	−0.659595	+	0.756239i
$497$		−	13.8053i		−	0.619252i
$498$	5.94573	−	1.95273i	0.266434	−	0.0875039i
$499$	21.3606			0.956233			0.478116	−	0.878296i	$-0.341320\pi$
$499$	21.3606			0.956233			0.478116	+	0.878296i	$0.341320\pi$
$500$	1.87276	+	0.701969i	0.0837525	+	0.0313930i
$501$	−4.66408	+	2.52768i	−0.208376	+	0.112928i
$502$	−0.730774	−	0.132458i	−0.0326160	−	0.00591191i
$503$	−33.0495			−1.47360			−0.736802	−	0.676109i	$-0.763665\pi$
$503$	−33.0495			−1.47360			−0.736802	+	0.676109i	$0.763665\pi$
$504$	7.62072	−	3.73158i	0.339454	−	0.166218i
$505$	−19.4589			−0.865908
$506$	14.5173	+	2.63137i	0.645372	+	0.116979i
$507$	19.2276	−	10.4203i	0.853929	−	0.462783i
$508$	1.62945	−	4.34716i	0.0722950	−	0.192874i
$509$	13.9071			0.616420			0.308210	−	0.951318i	$-0.400270\pi$
$509$	13.9071			0.616420			0.308210	+	0.951318i	$0.400270\pi$
$510$	7.54985	−	2.47956i	0.334313	−	0.109797i
$511$		−	14.2348i		−	0.629709i
$512$	22.6065	+	0.972756i	0.999075	+	0.0429901i
$513$	−0.637671	+	7.86684i	−0.0281538	+	0.347329i
$514$	12.3443	+	2.23750i	0.544483	+	0.0986919i
$515$			6.25210i			0.275500i
$516$	3.00220	−	0.417003i	0.132164	−	0.0183575i
$517$		−	0.921090i		−	0.0405095i
$518$	0.381210	−	2.10314i	0.0167494	−	0.0924065i
$519$	18.3787	−	9.96026i	0.806736	−	0.437207i
$520$	−1.48446	−	0.885661i	−0.0650977	−	0.0388388i
$521$		−	4.23868i		−	0.185700i	−0.995680	−	0.0928501i	$-0.970402\pi$
$521$		−	4.23868i		−	0.185700i	0.995680	−	0.0928501i	$-0.0295977\pi$
$522$	19.5246	+	18.4397i	0.854567	+	0.807084i
$523$	−33.8757			−1.48128			−0.740641	−	0.671901i	$-0.765478\pi$
$523$	−33.8757			−1.48128			−0.740641	+	0.671901i	$0.765478\pi$
$524$	−6.79839	+	18.1372i	−0.296989	+	0.792329i
$525$	−0.825275	−	1.52280i	−0.0360180	−	0.0664605i
$526$	−7.19498	+	39.6947i	−0.313716	+	1.73077i
$527$	18.1256			0.789565
$528$	4.82570	−	21.5187i	0.210012	−	0.936483i
$529$	−12.2582			−0.532963
$530$	−0.943978	+	5.20793i	−0.0410038	+	0.226218i
$531$	10.5222	+	6.85654i	0.456623	+	0.297549i
$532$	1.06625	−	2.84461i	0.0462277	−	0.123330i
$533$	−2.52367			−0.109312
$534$	18.7835	−	6.16900i	0.812843	−	0.266959i
$535$		−	5.85213i		−	0.253010i
$536$	−0.924211	+	1.54907i	−0.0399198	+	0.0669096i
$537$	−1.26246	−	2.32949i	−0.0544791	−	0.100525i
$538$	7.02240	−	38.7426i	0.302757	−	1.67031i
$539$			3.18310i			0.137106i
$540$	4.42182	−	9.40465i	0.190285	−	0.404712i
$541$			28.4229i			1.22200i	0.791632	+	0.610998i	$0.209232\pi$
$541$			28.4229i			1.22200i	−0.791632	+	0.610998i	$0.790768\pi$
$542$	−15.8506	−	2.87304i	−0.680841	−	0.123408i
$543$	−12.2214	−	22.5510i	−0.524470	−	0.967755i
$544$	−11.4572	−	14.3361i	−0.491222	−	0.614657i
$545$			9.96334i			0.426782i
$546$	0.467106	+	1.42226i	0.0199903	+	0.0608670i
$547$	23.5245			1.00584			0.502918	−	0.864334i	$-0.332260\pi$
$547$	23.5245			1.00584			0.502918	+	0.864334i	$0.332260\pi$
$548$	10.2761	−	27.4152i	0.438971	−	1.17112i
$549$	−28.7747	−	18.7504i	−1.22807	−	0.800248i
$550$	−4.42941	−	0.802866i	−0.188871	−	0.0342343i
$551$	9.61482			0.409605
$552$	0.662854	−	16.0426i	0.0282129	−	0.682818i
$553$	−12.9762			−0.551803
$554$	9.95685	+	1.80476i	0.423026	+	0.0766768i
$555$	−1.24730	−	2.30152i	−0.0529449	−	0.0976942i
$556$	23.1808	+	8.68887i	0.983084	+	0.368490i
$557$	−4.60175			−0.194982			−0.0974912	−	0.995236i	$-0.531082\pi$
$557$	−4.60175			−0.194982			−0.0974912	+	0.995236i	$0.531082\pi$
$558$	16.2757	−	17.2333i	0.689007	−	0.729542i
$559$			0.534741i			0.0226171i
$560$	−2.62924	+	3.01448i	−0.111106	+	0.127385i
$561$	−15.7253	+	8.52227i	−0.663924	+	0.359810i
$562$	32.7217	+	5.93107i	1.38028	+	0.250187i
$563$			13.8201i			0.582450i	0.956655	+	0.291225i	$0.0940628\pi$
$563$			13.8201i			0.582450i	−0.956655	+	0.291225i	$0.905937\pi$
$564$	−0.992870	+	0.137909i	−0.0418074	+	0.00580701i
$565$			0.131393i			0.00552775i
$566$	1.06797	−	5.89197i	0.0448900	−	0.247658i
$567$	−8.23330	+	3.63494i	−0.345766	+	0.152653i
$568$	−20.0064	+	33.5326i	−0.839448	+	1.40700i
$569$			3.61438i			0.151523i	0.997126	+	0.0757614i	$0.0241387\pi$
$569$			3.61438i			0.151523i	−0.997126	+	0.0757614i	$0.975861\pi$
$570$	−1.16094	−	3.53486i	−0.0486265	−	0.148059i
$571$	20.0146			0.837584			0.418792	−	0.908082i	$-0.362454\pi$
$571$	20.0146			0.837584			0.418792	+	0.908082i	$0.362454\pi$
$572$	3.64317	+	1.36557i	0.152328	+	0.0570974i
$573$	1.87084	−	1.01389i	0.0781555	−	0.0423560i
$574$	−1.04155	+	5.74622i	−0.0434733	+	0.239843i
$575$	−3.27747			−0.136680
$576$	−23.9182	−	1.97990i	−0.996591	−	0.0824959i
$577$	−3.16309			−0.131681			−0.0658406	−	0.997830i	$-0.520973\pi$
$577$	−3.16309			−0.131681			−0.0658406	+	0.997830i	$0.520973\pi$
$578$	1.63324	−	9.01057i	0.0679337	−	0.374790i
$579$	39.6168	−	21.4701i	1.64642	−	0.892269i
$580$	−11.8545	−	4.44344i	−0.492232	−	0.184504i
$581$	2.55489			0.105995
$582$	−10.2525	−	31.2172i	−0.424981	−	1.29399i
$583$		−	11.9130i		−	0.493385i
$584$	−20.6287	+	34.5758i	−0.853623	+	1.43076i
$585$	1.53609	+	1.00096i	0.0635096	+	0.0413847i
$586$	4.20403	−	23.1936i	0.173667	−	0.958120i
$587$			13.3591i			0.551391i	0.961245	+	0.275695i	$0.0889081\pi$
$587$			13.3591i			0.551391i	−0.961245	+	0.275695i	$0.911092\pi$
$588$	3.43116	−	0.476586i	0.141499	−	0.0196541i
$589$		−	8.48649i		−	0.349680i
$590$	−5.82543	−	1.05591i	−0.239829	−	0.0434710i
$591$	−15.2161	+	8.24627i	−0.625905	+	0.339206i
$592$	−3.97377	+	4.55601i	−0.163321	+	0.187251i
$593$		−	28.7133i		−	1.17911i	−0.807727	−	0.589556i	$-0.799303\pi$
$593$		−	28.7133i		−	1.17911i	0.807727	−	0.589556i	$-0.200697\pi$
$594$	−6.01770	+	22.6036i	−0.246909	+	0.927438i
$595$	3.24419			0.132999
$596$	31.3080	+	11.7352i	1.28242	+	0.480692i
$597$	16.4500	+	30.3536i	0.673253	+	1.24229i
$598$	2.78728	+	0.505216i	0.113980	+	0.0206598i
$599$	−21.3190			−0.871070			−0.435535	−	0.900172i	$-0.643441\pi$
$599$	−21.3190			−0.871070			−0.435535	+	0.900172i	$0.643441\pi$
$600$	−0.202245	+	4.89480i	−0.00825663	+	0.199829i
$601$	−21.1769			−0.863823			−0.431912	−	0.901916i	$-0.642161\pi$
$601$	−21.1769			−0.863823			−0.431912	+	0.901916i	$0.642161\pi$
$602$	1.21757	+	0.220694i	0.0496244	+	0.00899481i
$603$	1.04453	−	1.60295i	0.0425366	−	0.0652773i
$604$	5.23599	−	13.9689i	0.213049	−	0.568388i
$605$	−0.867849			−0.0352831
$606$	−14.8726	−	45.2845i	−0.604159	−	1.83956i
$607$			41.2524i			1.67438i	0.546909	+	0.837192i	$0.315804\pi$
$607$			41.2524i			1.67438i	−0.546909	+	0.837192i	$0.684196\pi$
$608$	−6.71223	+	5.36428i	−0.272217	+	0.217550i
$609$	5.22396	+	9.63927i	0.211685	+	0.390603i
$610$	15.9307	+	2.88756i	0.645014	+	0.116914i
$611$		−	0.176847i		−	0.00715445i
$612$	11.5409	+	15.6748i	0.466511	+	0.633616i
$613$		−	44.7492i		−	1.80740i	−0.428164	−	0.903701i	$-0.640840\pi$
$613$		−	44.7492i		−	1.80740i	0.428164	−	0.903701i	$-0.359160\pi$
$614$	−1.37853	+	7.60534i	−0.0556329	+	0.306927i
$615$	3.40789	+	6.28825i	0.137419	+	0.253567i
$616$	4.61289	−	7.73165i	0.185859	−	0.311517i
$617$		−	7.18138i		−	0.289112i	−0.989497	−	0.144556i	$-0.953825\pi$
$617$		−	7.18138i		−	0.289112i	0.989497	−	0.144556i	$-0.0461753\pi$
$618$	−14.5498	+	4.77855i	−0.585281	+	0.192221i
$619$	−14.9728			−0.601806			−0.300903	−	0.953655i	$-0.597288\pi$
$619$	−14.9728			−0.601806			−0.300903	+	0.953655i	$0.597288\pi$
$620$	−3.92198	+	10.4633i	−0.157511	+	0.420218i
$621$	−1.37593	+	16.9746i	−0.0552141	+	0.681167i
$622$	4.76457	−	26.2861i	0.191042	−	1.05398i
$623$	8.07133			0.323371
$624$	0.926521	−	4.13154i	0.0370905	−	0.165394i
$625$	1.00000			0.0400000
$626$	−4.67419	+	25.7875i	−0.186818	+	1.03068i
$627$	3.99015	+	7.36265i	0.159351	+	0.294036i
$628$	9.81761	−	26.1921i	0.391765	−	1.04518i
$629$	4.90318			0.195503
$630$	2.91309	−	3.08447i	0.116060	−	0.122888i
$631$		−	37.5150i		−	1.49345i	−0.665134	−	0.746724i	$-0.731626\pi$
$631$		−	37.5150i		−	1.49345i	0.665134	−	0.746724i	$-0.268374\pi$
$632$	31.5187	+	18.8048i	1.25375	+	0.748014i
$633$	−6.93051	+	3.75596i	−0.275463	+	0.149286i
$634$	−5.20329	+	28.7066i	−0.206649	+	1.14008i
$635$		−	2.32125i		−	0.0921161i
$636$	−12.8413	+	1.78365i	−0.509193	+	0.0707265i
$637$			0.611147i			0.0242145i
$638$	28.0380	+	5.08211i	1.11004	+	0.201203i
$639$	22.6109	−	34.6991i	0.894474	−	1.37267i
$640$	10.7549	−	3.51183i	0.425123	−	0.138817i
$641$		−	3.16867i		−	0.125155i	−0.998040	−	0.0625775i	$-0.980068\pi$
$641$		−	3.16867i		−	0.125155i	0.998040	−	0.0625775i	$-0.0199321\pi$
$642$	13.6190	−	4.47284i	0.537500	−	0.176529i
$643$	25.1374			0.991321			0.495660	−	0.868516i	$-0.334926\pi$
$643$	25.1374			0.991321			0.495660	+	0.868516i	$0.334926\pi$
$644$	2.30068	−	6.13793i	0.0906597	−	0.241868i
$645$	1.33242	−	0.722099i	0.0524640	−	0.0284326i
$646$	6.85712	+	1.24291i	0.269790	+	0.0489015i
$647$	4.95837			0.194934			0.0974668	−	0.995239i	$-0.468926\pi$
$647$	4.95837			0.194934			0.0974668	+	0.995239i	$0.468926\pi$
$648$	25.2661	+	3.10237i	0.992546	+	0.121872i
$649$	13.3255			0.523072
$650$	−0.850435	−	0.154148i	−0.0333568	−	0.00604618i
$651$	8.50806	−	4.61091i	0.333457	−	0.180716i
$652$	28.3368	+	10.6215i	1.10975	+	0.415970i
$653$	12.5298			0.490331			0.245165	−	0.969481i	$-0.421158\pi$
$653$	12.5298			0.490331			0.245165	+	0.969481i	$0.421158\pi$
$654$	−23.1866	+	7.61508i	−0.906668	+	0.297773i
$655$			9.68475i			0.378415i
$656$	10.8572	−	12.4480i	0.423902	−	0.486012i
$657$	23.3143	−	35.7785i	0.909578	−	1.39585i
$658$	−0.402668	−	0.0729867i	−0.0156976	−	0.00284532i
$659$		−	18.8673i		−	0.734964i	−0.930031	−	0.367482i	$-0.880220\pi$
$659$		−	18.8673i		−	0.734964i	0.930031	−	0.367482i	$-0.119780\pi$
$660$	−1.51702	−	10.9217i	−0.0590500	−	0.425128i
$661$		−	29.0940i		−	1.13163i	−0.824533	−	0.565814i	$-0.808562\pi$
$661$		−	29.0940i		−	1.13163i	0.824533	−	0.565814i	$-0.191438\pi$
$662$	−6.70961	+	37.0169i	−0.260776	+	1.43870i
$663$	−3.01922	+	1.63625i	−0.117257	+	0.0635467i
$664$	−6.20575	−	3.70249i	−0.240830	−	0.143685i
$665$		−	1.51894i		−	0.0589019i
$666$	4.40276	−	4.66178i	0.170604	−	0.180640i
$667$	20.7463			0.803299
$668$	5.73595	+	2.15001i	0.221931	+	0.0831864i
$669$	−13.5852	−	25.0674i	−0.525233	−	0.969161i
$670$	−0.160858	+	0.887451i	−0.00621447	+	0.0342852i
$671$	−36.4409			−1.40679
$672$	−9.02483	−	3.81476i	−0.348141	−	0.147157i
$673$	16.9244			0.652389			0.326194	−	0.945303i	$-0.394234\pi$
$673$	16.9244			0.652389			0.326194	+	0.945303i	$0.394234\pi$
$674$	1.55697	−	8.58979i	0.0599721	−	0.330866i
$675$	0.419813	−	5.17917i	0.0161586	−	0.199346i
$676$	−23.6464	−	8.86341i	−0.909478	−	0.340900i
$677$	15.8627			0.609654			0.304827	−	0.952408i	$-0.401401\pi$
$677$	15.8627			0.609654			0.304827	+	0.952408i	$0.401401\pi$
$678$	−0.305777	+	0.100425i	−0.0117433	+	0.00385680i
$679$		−	13.4141i		−	0.514786i
$680$	−7.88002	−	4.70141i	−0.302185	−	0.180291i
$681$	−20.0652	−	37.0244i	−0.768901	−	1.41878i
$682$	4.48571	−	24.7476i	0.171767	−	0.947636i
$683$			35.9075i			1.37396i	0.726675	+	0.686981i	$0.241065\pi$
$683$			35.9075i			1.37396i	−0.726675	+	0.686981i	$0.758935\pi$
$684$	7.33899	−	5.40347i	0.280613	−	0.206607i
$685$		−	14.6389i		−	0.559324i
$686$	1.39154	+	0.252227i	0.0531292	+	0.00963009i
$687$	−20.0967	−	37.0825i	−0.766737	−	1.41479i
$688$	−2.63761	−	2.30053i	−0.100558	−	0.0877070i
$689$		−	2.28726i		−	0.0871376i
$690$	−2.50501	−	7.62732i	−0.0953640	−	0.290367i
$691$	29.5157			1.12283			0.561414	−	0.827535i	$-0.310257\pi$
$691$	29.5157			1.12283			0.561414	+	0.827535i	$0.310257\pi$
$692$	−22.6024	−	8.47208i	−0.859215	−	0.322060i
$693$	−5.21342	+	8.00060i	−0.198042	+	0.303918i
$694$	47.2273	+	8.56032i	1.79272	+	0.324945i
$695$	12.3779			0.469519
$696$	1.28020	−	30.9839i	0.0485260	−	1.17444i
$697$	−13.3965			−0.507430
$698$	−40.3675	−	7.31693i	−1.52793	−	0.276950i
$699$	23.3175	+	43.0255i	0.881947	+	1.62737i
$700$	−0.701969	+	1.87276i	−0.0265319	+	0.0707838i
$701$	11.6157			0.438720			0.219360	−	0.975644i	$-0.429603\pi$
$701$	11.6157			0.438720			0.219360	+	0.975644i	$0.429603\pi$
$702$	−1.15538	+	4.33983i	−0.0436071	+	0.163796i
$703$		−	2.29569i		−	0.0865834i
$704$	−22.4091	+	12.0950i	−0.844575	+	0.455849i
$705$	−0.440651	+	0.238809i	−0.0165959	+	0.00899405i
$706$	−20.6242	−	3.73830i	−0.776203	−	0.140693i
$707$		−	19.4589i		−	0.731826i
$708$	−1.99514	−	14.3640i	−0.0749821	−	0.539830i
$709$		−	11.6247i		−	0.436575i	−0.975884	−	0.218288i	$-0.929953\pi$
$709$		−	11.6247i		−	0.436575i	0.975884	−	0.218288i	$-0.0700471\pi$
$710$	−3.48208	+	19.2106i	−0.130680	+	0.720962i
$711$	−32.6150	−	21.2529i	−1.22316	−	0.797047i
$712$	−19.6050	−	11.6968i	−0.734728	−	0.438356i
$713$		−	18.3116i		−	0.685776i
$714$	2.47956	+	7.54985i	0.0927954	+	0.282546i
$715$	1.94534			0.0727517
$716$	−1.07383	+	2.86484i	−0.0401310	+	0.107064i
$717$	4.01106	−	2.17377i	0.149796	−	0.0811811i
$718$	8.37588	−	46.2097i	0.312585	−	1.72453i
$719$	26.3029			0.980934			0.490467	−	0.871460i	$-0.336826\pi$
$719$	26.3029			0.980934			0.490467	+	0.871460i	$0.336826\pi$
$720$	−11.5457	+	3.27048i	−0.430284	+	0.121884i
$721$	−6.25210			−0.232840
$722$	−4.21039	+	23.2287i	−0.156694	+	0.864483i
$723$	45.1997	−	24.4958i	1.68099	−	0.911007i
$724$	−10.3954	+	27.7335i	−0.386341	+	1.03071i
$725$	−6.32996			−0.235089
$726$	−0.663306	−	2.01965i	−0.0246176	−	0.0749563i
$727$			4.00280i			0.148456i	0.997241	+	0.0742279i	$0.0236492\pi$
$727$			4.00280i			0.148456i	−0.997241	+	0.0742279i	$0.976351\pi$
$728$	0.885661	−	1.48446i	0.0328248	−	0.0550176i
$729$	−26.6475	−	4.34857i	−0.986945	−	0.161058i
$730$	−3.59040	+	19.8082i	−0.132887	+	0.733136i
$731$			2.83860i			0.104989i
$732$	5.45607	+	39.2807i	0.201662	+	1.45186i
$733$			28.5005i			1.05269i	0.850271	+	0.526346i	$0.176438\pi$
$733$			28.5005i			1.05269i	−0.850271	+	0.526346i	$0.823562\pi$
$734$	39.3993	+	7.14144i	1.45426	+	0.263595i
$735$	1.52280	−	0.825275i	0.0561693	−	0.0304407i
$736$	−14.4833	+	11.5747i	−0.533860	+	0.426650i
$737$		−	2.03002i		−	0.0747767i
$738$	−12.0293	+	12.7370i	−0.442804	+	0.468855i
$739$	−5.16559			−0.190019			−0.0950096	−	0.995476i	$-0.530288\pi$
$739$	−5.16559			−0.190019			−0.0950096	+	0.995476i	$0.530288\pi$
$740$	−1.06094	+	2.83045i	−0.0390008	+	0.104049i
$741$	0.766098	+	1.41361i	0.0281433	+	0.0519302i
$742$	−5.20793	−	0.943978i	−0.191189	−	0.0346545i
$743$	−26.3582			−0.966989			−0.483495	−	0.875347i	$-0.660633\pi$
$743$	−26.3582			−0.966989			−0.483495	+	0.875347i	$0.660633\pi$
$744$	−27.3478	−	1.12997i	−1.00262	−	0.0414266i
$745$	16.7175			0.612483
$746$	36.7963	+	6.66962i	1.34721	+	0.244192i
$747$	6.42161	+	4.18451i	0.234954	+	0.153103i
$748$	19.3392	+	7.24894i	0.707113	+	0.265047i
$749$	5.85213			0.213832
$750$	0.764310	+	2.32719i	0.0279087	+	0.0849771i
$751$		−	20.3767i		−	0.743556i	−0.928322	−	0.371778i	$-0.878748\pi$
$751$		−	20.3767i		−	0.743556i	0.928322	−	0.371778i	$-0.121252\pi$
$752$	0.872296	+	0.760820i	0.0318093	+	0.0277442i
$753$	−0.433397	−	0.799706i	−0.0157939	−	0.0291429i
$754$	5.38322	+	0.975751i	0.196045	+	0.0355348i
$755$		−	7.45900i		−	0.271461i
$756$	9.40465	+	4.42182i	0.342044	+	0.160820i
$757$			42.6839i			1.55137i	0.631118	+	0.775687i	$0.282597\pi$
$757$			42.6839i			1.55137i	−0.631118	+	0.775687i	$0.717403\pi$
$758$	−8.85250	+	48.8392i	−0.321537	+	1.77392i
$759$	8.60972	+	15.8867i	0.312513	+	0.576650i
$760$	−2.20121	+	3.68945i	−0.0798464	+	0.133830i
$761$			1.09083i			0.0395426i	0.999805	+	0.0197713i	$0.00629381\pi$
$761$			1.09083i			0.0395426i	−0.999805	+	0.0197713i	$0.993706\pi$
$762$	5.40201	−	1.77416i	0.195694	−	0.0642710i
$763$	−9.96334			−0.360697
$764$	−2.30079	−	0.862406i	−0.0832396	−	0.0312008i
$765$	8.15413	+	5.31347i	0.294813	+	0.192109i
$766$	−3.64147	+	20.0900i	−0.131572	+	0.725882i
$767$	2.55846			0.0923806
$768$	16.3928	+	22.3445i	0.591523	+	0.806288i
$769$	4.69263			0.169221			0.0846104	−	0.996414i	$-0.473035\pi$
$769$	4.69263			0.169221			0.0846104	+	0.996414i	$0.473035\pi$
$770$	0.802866	−	4.42941i	0.0289333	−	0.159625i
$771$	7.32098	+	13.5087i	0.263659	+	0.486504i
$772$	−48.7213	−	18.2622i	−1.75352	−	0.657272i
$773$	32.2310			1.15927			0.579635	−	0.814876i	$-0.303195\pi$
$773$	32.2310			1.15927			0.579635	+	0.814876i	$0.303195\pi$
$774$	2.69885	+	2.54889i	0.0970080	+	0.0916180i
$775$			5.58711i			0.200695i
$776$	−19.4394	+	32.5824i	−0.697835	+	1.16964i
$777$	2.30152	−	1.24730i	0.0825666	−	0.0447466i
$778$	−4.30349	+	23.7424i	−0.154288	+	0.851206i
$779$			6.27230i			0.224729i
$780$	−0.291264	−	2.09694i	−0.0104289	−	0.0750826i
$781$		−	43.9437i		−	1.57243i
$782$	14.7959	+	2.68187i	0.529099	+	0.0959034i
$783$	−2.65740	+	32.7839i	−0.0949678	+	1.17160i
$784$	−3.01448	−	2.62924i	−0.107660	−	0.0939015i
$785$		−	13.9858i		−	0.499176i
$786$	−22.5383	+	7.40216i	−0.803914	+	0.264026i
$787$	53.1288			1.89384			0.946918	−	0.321474i	$-0.104178\pi$
$787$	53.1288			1.89384			0.946918	+	0.321474i	$0.104178\pi$
$788$	18.7129	+	7.01418i	0.666621	+	0.249870i
$789$	−43.4391	+	23.5416i	−1.54647	+	0.838103i
$790$	18.0568	+	3.27294i	0.642434	+	0.116446i
$791$	−0.131393			−0.00467180
$792$	24.2575	−	11.8780i	0.861954	−	0.422067i
$793$	−6.99655			−0.248455
$794$	23.3300	+	4.22875i	0.827952	+	0.150073i
$795$	−5.69918	+	3.08865i	−0.202129	+	0.109543i
$796$	13.9921	−	37.3293i	0.495939	−	1.32310i
$797$	−15.1206			−0.535600			−0.267800	−	0.963475i	$-0.586297\pi$
$797$	−15.1206			−0.535600			−0.267800	+	0.963475i	$0.586297\pi$
$798$	3.53486	−	1.16094i	0.125133	−	0.0410969i
$799$		−	0.938765i		−	0.0332111i
$800$	4.41903	−	3.53160i	0.156236	−	0.124861i
$801$	20.2869	+	13.2196i	0.716804	+	0.467090i
$802$	−35.6043	−	6.45355i	−1.25723	−	0.227883i
$803$		−	45.3108i		−	1.59898i
$804$	−2.18822	+	0.303942i	−0.0771724	+	0.0107192i
$805$		−	3.27747i		−	0.115516i
$806$	0.861243	−	4.75148i	0.0303360	−	0.167364i
$807$	42.3971	−	22.9769i	1.49245	−	0.808826i
$808$	−28.1994	+	47.2649i	−0.992051	+	1.66277i
$809$		−	53.4286i		−	1.87845i	−0.343304	−	0.939224i	$-0.611546\pi$
$809$		−	53.4286i		−	1.87845i	0.343304	−	0.939224i	$-0.388454\pi$
$810$	12.3738	−	2.98150i	0.434771	−	0.104759i
$811$	−34.7634			−1.22071			−0.610354	−	0.792129i	$-0.708973\pi$
$811$	−34.7634			−1.22071			−0.610354	+	0.792129i	$0.708973\pi$
$812$	4.44344	−	11.8545i	0.155934	−	0.416012i
$813$	−9.40044	−	17.3457i	−0.329688	−	0.608341i
$814$	1.21343	−	6.69450i	0.0425308	−	0.234642i
$815$	15.1310			0.530016
$816$	4.91830	−	21.9317i	0.172175	−	0.767762i
$817$	1.32904			0.0464972
$818$	−8.58348	+	47.3551i	−0.300114	+	1.65573i
$819$	−1.00096	+	1.53609i	−0.0349765	+	0.0536754i
$820$	2.89871	−	7.73338i	0.101227	−	0.270061i
$821$	−40.0191			−1.39668			−0.698338	−	0.715768i	$-0.746077\pi$
$821$	−40.0191			−1.39668			−0.698338	+	0.715768i	$0.746077\pi$
$822$	34.0676	−	11.1887i	1.18824	−	0.390250i
$823$			11.1838i			0.389843i	0.980819	+	0.194922i	$0.0624453\pi$
$823$			11.1838i			0.389843i	−0.980819	+	0.194922i	$0.937555\pi$
$824$	15.1861	+	9.06041i	0.529034	+	0.315635i
$825$	−2.62694	−	4.84723i	−0.0914582	−	0.168759i
$826$	1.05591	−	5.82543i	0.0367397	−	0.202693i
$827$		−	4.10171i		−	0.142630i	−0.997454	−	0.0713152i	$-0.977280\pi$
$827$		−	4.10171i		−	0.142630i	0.997454	−	0.0713152i	$-0.0227196\pi$
$828$	15.8356	−	11.6593i	0.550327	−	0.405188i
$829$			31.7388i			1.10233i	0.834395	+	0.551166i	$0.185817\pi$
$829$			31.7388i			1.10233i	−0.834395	+	0.551166i	$0.814183\pi$
$830$	−3.55523	−	0.644414i	−0.123404	−	0.0223679i
$831$	5.90507	+	10.8961i	0.204845	+	0.377980i
$832$	−4.30248	+	2.32221i	−0.149162	+	0.0805082i
$833$			3.24419i			0.112404i
$834$	9.46052	+	28.8057i	0.327591	+	0.997458i
$835$	3.06283			0.105994
$836$	3.39398	−	9.05469i	0.117383	−	0.313163i
$837$	28.9366	+	2.34555i	1.00020	+	0.0810739i
$838$	4.87761	+	0.884105i	0.168494	+	0.0305409i
$839$	8.47189			0.292482			0.146241	−	0.989249i	$-0.453282\pi$
$839$	8.47189			0.292482			0.146241	+	0.989249i	$0.453282\pi$
$840$	−4.89480	−	0.202245i	−0.168887	−	0.00697813i
$841$	11.0684			0.381669
$842$	28.8362	+	5.22680i	0.993762	+	0.180127i
$843$	19.4062	+	35.8083i	0.668384	+	1.23330i
$844$	8.52325	+	3.19477i	0.293382	+	0.109969i
$845$	−12.6265			−0.434365
$846$	−0.892548	−	0.842955i	−0.0306864	−	0.0289814i
$847$		−	0.867849i		−	0.0298196i
$848$	11.2819	+	9.84011i	0.387422	+	0.337911i
$849$	6.44775	−	3.49433i	0.221286	−	0.119925i
$850$	−4.51441	−	0.818273i	−0.154843	−	0.0280665i
$851$		−	4.95349i		−	0.169804i
$852$	−47.3682	+	6.57941i	−1.62281	+	0.225407i
$853$		−	31.6458i		−	1.08353i	−0.840530	−	0.541766i	$-0.817756\pi$
$853$		−	31.6458i		−	1.08353i	0.840530	−	0.541766i	$-0.182244\pi$
$854$	−2.88756	+	15.9307i	−0.0988103	+	0.545136i
$855$	2.48778	−	3.81779i	0.0850804	−	0.130566i
$856$	−14.2146	−	8.48078i	−0.485846	−	0.289867i
$857$		−	19.0608i		−	0.651106i	−0.945524	−	0.325553i	$-0.894450\pi$
$857$		−	19.0608i		−	0.651106i	0.945524	−	0.325553i	$-0.105550\pi$
$858$	1.48685	+	4.52719i	0.0507601	+	0.154556i
$859$	41.3435			1.41062			0.705311	−	0.708898i	$-0.250808\pi$
$859$	41.3435			1.41062			0.705311	+	0.708898i	$0.250808\pi$
$860$	−1.63863	−	0.614208i	−0.0558768	−	0.0209443i
$861$	−6.28825	+	3.40789i	−0.214303	+	0.116141i
$862$	−5.11234	+	28.2048i	−0.174127	+	0.960659i
$863$	−42.3631			−1.44206			−0.721028	−	0.692906i	$-0.756330\pi$
$863$	−42.3631			−1.44206			−0.721028	+	0.692906i	$0.756330\pi$
$864$	−16.4356	−	24.3695i	−0.559150	−	0.829067i
$865$	−12.0690			−0.410359
$866$	−3.46391	+	19.1104i	−0.117708	+	0.649397i
$867$	9.86052	−	5.34387i	0.334881	−	0.181487i
$868$	−10.4633	−	3.92198i	−0.355149	−	0.133121i
$869$	−41.3045			−1.40116
$870$	−4.83805	−	14.7310i	−0.164025	−	0.499429i
$871$		−	0.389758i		−	0.0132064i
$872$	24.2006	+	14.4387i	0.819536	+	0.488955i
$873$	21.9702	−	33.7158i	0.743578	−	1.14111i
$874$	1.25566	−	6.92748i	0.0424733	−	0.234325i
$875$			1.00000i			0.0338062i
$876$	−48.8418	+	6.78409i	−1.65021	+	0.229213i
$877$			20.0882i			0.678330i	0.940727	+	0.339165i	$0.110145\pi$
$877$			20.0882i			0.678330i	−0.940727	+	0.339165i	$0.889855\pi$
$878$	−27.7337	−	5.02696i	−0.935968	−	0.169652i
$879$	25.3814	−	13.7554i	0.856094	−	0.463957i
$880$	−8.36915	+	9.59540i	−0.282124	+	0.323461i
$881$		−	5.98528i		−	0.201649i	−0.994904	−	0.100825i	$-0.967852\pi$
$881$		−	5.98528i		−	0.201649i	0.994904	−	0.100825i	$-0.0321481\pi$
$882$	3.08447	+	2.91309i	0.103859	+	0.0980887i
$883$	5.05387			0.170076			0.0850382	−	0.996378i	$-0.472899\pi$
$883$	5.05387			0.170076			0.0850382	+	0.996378i	$0.472899\pi$
$884$	3.71308	+	1.39178i	0.124884	+	0.0468105i
$885$	−3.45487	−	6.37494i	−0.116134	−	0.214291i
$886$	10.2184	+	1.85216i	0.343293	+	0.0622246i
$887$	45.6946			1.53427			0.767137	−	0.641484i	$-0.221681\pi$
$887$	45.6946			1.53427			0.767137	+	0.641484i	$0.221681\pi$
$888$	−7.39788	−	0.305668i	−0.248257	−	0.0102576i
$889$	2.32125			0.0778523
$890$	−11.2316	−	2.03581i	−0.376483	−	0.0682405i
$891$	−26.2074	+	11.5704i	−0.877982	+	0.387623i
$892$	−11.5554	+	30.8282i	−0.386902	+	1.03221i
$893$	−0.439533			−0.0147084
$894$	12.7774	+	38.9049i	0.427340	+	1.30118i
$895$			1.52974i			0.0511337i
$896$	3.51183	+	10.7549i	0.117322	+	0.359295i
$897$	1.65304	+	3.05020i	0.0551934	+	0.101843i
$898$	−7.86607	−	1.42579i	−0.262494	−	0.0475791i
$899$		−	35.3662i		−	1.17953i
$900$	−4.83166	+	3.55740i	−0.161055	+	0.118580i
$901$		−	12.1416i		−	0.404495i
$902$	−3.31535	+	18.2908i	−0.110389	+	0.609017i
$903$	0.722099	+	1.33242i	0.0240299	+	0.0443401i
$904$	0.319149	+	0.190412i	0.0106148	+	0.00633301i
$905$			14.8089i			0.492264i
$906$	17.3585	−	5.70099i	0.576699	−	0.189403i
$907$	−36.5992			−1.21526			−0.607629	−	0.794221i	$-0.707879\pi$
$907$	−36.5992			−1.21526			−0.607629	+	0.794221i	$0.707879\pi$
$908$	−17.0672	+	45.5332i	−0.566396	+	1.51107i
$909$	31.8706	−	48.9090i	1.05708	−	1.62221i
$910$	0.154148	−	0.850435i	0.00510996	−	0.0281916i
$911$	−41.7072			−1.38182			−0.690911	−	0.722940i	$-0.742790\pi$
$911$	−41.7072			−1.38182			−0.690911	+	0.722940i	$0.742790\pi$
$912$	−10.2685	−	2.30277i	−0.340023	−	0.0762522i
$913$	8.13248			0.269146
$914$	4.62230	−	25.5012i	0.152892	−	0.843505i
$915$	9.44794	+	17.4334i	0.312339	+	0.576330i
$916$	−17.0940	+	45.6046i	−0.564802	+	1.50682i
$917$	−9.68475			−0.319819
$918$	−6.13318	+	23.0374i	−0.202425	+	0.760346i
$919$			32.0158i			1.05610i	0.849212	+	0.528051i	$0.177077\pi$
$919$			32.0158i			1.05610i	−0.849212	+	0.528051i	$0.822923\pi$
$920$	−4.74965	+	7.96088i	−0.156591	+	0.262462i
$921$	−8.32274	+	4.51047i	−0.274244	+	0.148625i
$922$	−0.496350	+	2.73836i	−0.0163464	+	0.0901832i
$923$		−	8.43707i		−	0.277709i
$924$	10.9217	−	1.51702i	0.359299	−	0.0499064i
$925$			1.51137i			0.0496937i
$926$	−19.6152	−	3.55541i	−0.644595	−	0.116838i
$927$	−15.7144	−	10.2400i	−0.516128	−	0.336324i
$928$	−27.9723	+	22.3549i	−0.918235	+	0.733835i
$929$		−	19.9602i		−	0.654874i	−0.944873	−	0.327437i	$-0.893815\pi$
$929$		−	19.9602i		−	0.654874i	0.944873	−	0.327437i	$-0.106185\pi$
$930$	−13.0023	+	4.27029i	−0.426362	+	0.140028i
$931$	1.51894			0.0497812
$932$	19.8335	−	52.9134i	0.649669	−	1.73323i
$933$	28.7656	−	15.5894i	0.941745	−	0.510374i
$934$	18.8431	+	3.41546i	0.616566	+	0.111757i
$935$	10.3266			0.337715
$936$	4.65738	−	2.28054i	0.152231	−	0.0745419i
$937$	12.2298			0.399532			0.199766	−	0.979844i	$-0.435982\pi$
$937$	12.2298			0.399532			0.199766	+	0.979844i	$0.435982\pi$
$938$	−0.887451	−	0.160858i	−0.0289763	−	0.00525218i
$939$	−28.2200	+	15.2937i	−0.920924	+	0.499091i
$940$	0.541919	+	0.203128i	0.0176754	+	0.00662529i
$941$	9.69349			0.315999			0.157999	−	0.987439i	$-0.449496\pi$
$941$	9.69349			0.315999			0.157999	+	0.987439i	$0.449496\pi$
$942$	32.5477	−	10.6895i	1.06046	−	0.348283i
$943$			13.5340i			0.440728i
$944$	−11.0069	+	12.6196i	−0.358243	+	0.410733i
$945$	5.17917	+	0.419813i	0.168478	+	0.0136565i
$946$	3.87565	+	0.702492i	0.126008	+	0.0228400i
$947$		−	18.2317i		−	0.592449i	−0.955118	−	0.296225i	$-0.904272\pi$
$947$		−	18.2317i		−	0.592449i	0.955118	−	0.296225i	$-0.0957277\pi$
$948$	6.18425	+	44.5233i	0.200855	+	1.44605i
$949$		−	8.69953i		−	0.282399i
$950$	−0.383118	+	2.11366i	−0.0124300	+	0.0685763i
$951$	−31.4144	+	17.0249i	−1.01868	+	0.552070i
$952$	4.70141	−	7.88002i	0.152373	−	0.255393i
$953$			37.4130i			1.21193i	0.795493	+	0.605963i	$0.207212\pi$
$953$			37.4130i			1.21193i	−0.795493	+	0.605963i	$0.792788\pi$
$954$	−11.5438	−	10.9024i	−0.373745	−	0.352979i
$955$	−1.22855			−0.0397551
$956$	−4.93286	−	1.84899i	−0.159540	−	0.0598005i
$957$	16.6284	+	30.6828i	0.537520	+	0.991834i
$958$	10.3633	−	57.1743i	0.334823	−	1.84722i
$959$	14.6389			0.472715
$960$	11.5962	+	7.58469i	0.374267	+	0.244795i
$961$	−0.215854			−0.00696303
$962$	0.232975	−	1.28533i	0.00751143	−	0.0414406i
$963$	14.7091	+	9.58487i	0.473994	+	0.308868i
$964$	−55.5872	−	20.8358i	−1.79034	−	0.671075i
$965$	−26.0157			−0.837476
$966$	7.62732	−	2.50501i	0.245405	−	0.0805973i
$967$		−	14.1408i		−	0.454737i	−0.973809	−	0.227369i	$-0.926988\pi$
$967$		−	14.1408i		−	0.454737i	0.973809	−	0.227369i	$-0.0730122\pi$
$968$	−1.25767	+	2.10798i	−0.0404230	+	0.0677529i
$969$	4.06672	+	7.50393i	0.130642	+	0.241061i
$970$	−3.38340	+	18.6662i	−0.108635	+	0.599337i
$971$			7.81770i			0.250882i	0.992101	+	0.125441i	$0.0400346\pi$
$971$			7.81770i			0.250882i	−0.992101	+	0.125441i	$0.959965\pi$
$972$	16.3959	+	26.5174i	0.525900	+	0.850546i
$973$			12.3779i			0.396816i
$974$	46.6637	+	8.45816i	1.49520	+	0.271017i
$975$	−0.504364	−	0.930655i	−0.0161526	−	0.0298048i
$976$	30.1002	−	34.5105i	0.963483	−	1.10465i
$977$		−	42.9825i		−	1.37513i	−0.726122	−	0.687565i	$-0.758679\pi$
$977$		−	42.9825i		−	1.37513i	0.726122	−	0.687565i	$-0.241321\pi$
$978$	11.5648	+	35.2128i	0.369801	+	1.12598i
$979$	25.6919			0.821116
$980$	−1.87276	−	0.701969i	−0.0598232	−	0.0224236i
$981$	−25.0424	−	16.3184i	−0.799543	−	0.521006i
$982$	25.9916	+	4.71118i	0.829425	+	0.150340i
$983$	−10.2677			−0.327489			−0.163744	−	0.986503i	$-0.552357\pi$
$983$	−10.2677			−0.327489			−0.163744	+	0.986503i	$0.552357\pi$
$984$	20.2126	+	0.835151i	0.644354	+	0.0266236i
$985$	9.99215			0.318377
$986$	28.5761	+	5.17963i	0.910047	+	0.164953i
$987$	−0.238809	−	0.440651i	−0.00760136	−	0.0140261i
$988$	0.651634	−	1.73848i	0.0207312	−	0.0553083i
$989$	2.86772			0.0911883
$990$	9.27265	−	9.81818i	0.294704	−	0.312042i
$991$		−	19.1535i		−	0.608432i	−0.952603	−	0.304216i	$-0.901606\pi$
$991$		−	19.1535i		−	0.608432i	0.952603	−	0.304216i	$-0.0983945\pi$
$992$	19.7315	+	24.6896i	0.626474	+	0.783896i
$993$	−40.5087	+	21.9535i	−1.28550	+	0.696673i
$994$	−19.2106	−	3.48208i	−0.609324	−	0.110445i
$995$		−	19.9327i		−	0.631910i
$996$	−1.21762	−	8.76624i	−0.0385819	−	0.277769i
$997$			2.43858i			0.0772306i	0.999254	+	0.0386153i	$0.0122947\pi$
$997$			2.43858i			0.0772306i	−0.999254	+	0.0386153i	$0.987705\pi$
$998$	5.38774	−	29.7241i	0.170546	−	0.940901i
$999$	7.82766	+	0.634495i	0.247656	+	0.0200745i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.e.d.491.23	yes	44
3.2	odd	2		840.2.e.c.491.22	yes	44
4.3	odd	2		3360.2.e.c.911.8		44
8.3	odd	2		840.2.e.c.491.21	✓	44
8.5	even	2		3360.2.e.d.911.8		44
12.11	even	2		3360.2.e.d.911.7		44
24.5	odd	2		3360.2.e.c.911.7		44
24.11	even	2	inner	840.2.e.d.491.24	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.e.c.491.21	✓	44	8.3	odd	2
840.2.e.c.491.22	yes	44	3.2	odd	2
840.2.e.d.491.23	yes	44	1.1	even	1	trivial
840.2.e.d.491.24	yes	44	24.11	even	2	inner
3360.2.e.c.911.7		44	24.5	odd	2
3360.2.e.c.911.8		44	4.3	odd	2
3360.2.e.d.911.7		44	12.11	even	2
3360.2.e.d.911.8		44	8.5	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.252227 - 1.39154i) q^{2} +(1.52280 - 0.825275i) q^{3} +(-1.87276 - 0.701969i) q^{4} -1.00000 q^{5} +(-0.764310 - 2.32719i) q^{6} -1.00000i q^{7} +(-1.44918 + 2.42897i) q^{8} +(1.63784 - 2.51346i) q^{9} +(-0.252227 + 1.39154i) q^{10} -3.18310i q^{11} +(-3.43116 + 0.476586i) q^{12} -0.611147i q^{13} +(-1.39154 - 0.252227i) q^{14} +(-1.52280 + 0.825275i) q^{15} +(3.01448 + 2.62924i) q^{16} -3.24419i q^{17} +(-3.08447 - 2.91309i) q^{18} -1.51894 q^{19} +(1.87276 + 0.701969i) q^{20} +(-0.825275 - 1.52280i) q^{21} +(-4.42941 - 0.802866i) q^{22} -3.27747 q^{23} +(-0.202245 + 4.89480i) q^{24} +1.00000 q^{25} +(-0.850435 - 0.154148i) q^{26} +(0.419813 - 5.17917i) q^{27} +(-0.701969 + 1.87276i) q^{28} -6.32996 q^{29} +(0.764310 + 2.32719i) q^{30} +5.58711i q^{31} +(4.41903 - 3.53160i) q^{32} +(-2.62694 - 4.84723i) q^{33} +(-4.51441 - 0.818273i) q^{34} +1.00000i q^{35} +(-4.83166 + 3.55740i) q^{36} +1.51137i q^{37} +(-0.383118 + 2.11366i) q^{38} +(-0.504364 - 0.930655i) q^{39} +(1.44918 - 2.42897i) q^{40} -4.12940i q^{41} +(-2.32719 + 0.764310i) q^{42} -0.874980 q^{43} +(-2.23444 + 5.96120i) q^{44} +(-1.63784 + 2.51346i) q^{45} +(-0.826669 + 4.56073i) q^{46} +0.289369 q^{47} +(6.76030 + 1.51604i) q^{48} -1.00000 q^{49} +(0.252227 - 1.39154i) q^{50} +(-2.67735 - 4.94025i) q^{51} +(-0.429006 + 1.14453i) q^{52} +3.74257 q^{53} +(-7.10112 - 1.89051i) q^{54} +3.18310i q^{55} +(2.42897 + 1.44918i) q^{56} +(-2.31304 + 1.25354i) q^{57} +(-1.59659 + 8.80839i) q^{58} +4.18632i q^{59} +(3.43116 - 0.476586i) q^{60} -11.4482i q^{61} +(7.77469 + 1.40922i) q^{62} +(-2.51346 - 1.63784i) q^{63} +(-3.79976 - 7.04002i) q^{64} +0.611147i q^{65} +(-7.40770 + 2.43288i) q^{66} +0.637748 q^{67} +(-2.27732 + 6.07559i) q^{68} +(-4.99094 + 2.70482i) q^{69} +(1.39154 + 0.252227i) q^{70} +13.8053 q^{71} +(3.73158 + 7.62072i) q^{72} +14.2348 q^{73} +(2.10314 + 0.381210i) q^{74} +(1.52280 - 0.825275i) q^{75} +(2.84461 + 1.06625i) q^{76} -3.18310 q^{77} +(-1.42226 + 0.467106i) q^{78} -12.9762i q^{79} +(-3.01448 - 2.62924i) q^{80} +(-3.63494 - 8.23330i) q^{81} +(-5.74622 - 1.04155i) q^{82} +2.55489i q^{83} +(0.476586 + 3.43116i) q^{84} +3.24419i q^{85} +(-0.220694 + 1.21757i) q^{86} +(-9.63927 + 5.22396i) q^{87} +(7.73165 + 4.61289i) q^{88} +8.07133i q^{89} +(3.08447 + 2.91309i) q^{90} -0.611147 q^{91} +(6.13793 + 2.30068i) q^{92} +(4.61091 + 8.50806i) q^{93} +(0.0729867 - 0.402668i) q^{94} +1.51894 q^{95} +(3.81476 - 9.02483i) q^{96} +13.4141 q^{97} +(-0.252227 + 1.39154i) q^{98} +(-8.00060 - 5.21342i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} + 4 q^{3} - 2 q^{4} - 44 q^{5} - 6 q^{6} - 22 q^{8} + 4 q^{9} - 2 q^{10} + 6 q^{12} + 4 q^{14} - 4 q^{15} + 22 q^{16} + 2 q^{18} + 16 q^{19} + 2 q^{20} + 16 q^{23} + 10 q^{24} + 44 q^{25}+ \cdots - 64 q^{99}+O(q^{100}) \) 44 * q + 2 * q^2 + 4 * q^3 - 2 * q^4 - 44 * q^5 - 6 * q^6 - 22 * q^8 + 4 * q^9 - 2 * q^10 + 6 * q^12 + 4 * q^14 - 4 * q^15 + 22 * q^16 + 2 * q^18 + 16 * q^19 + 2 * q^20 + 16 * q^23 + 10 * q^24 + 44 * q^25 - 16 * q^26 + 4 * q^27 + 16 * q^29 + 6 * q^30 - 18 * q^32 + 24 * q^33 + 20 * q^34 - 46 * q^36 + 8 * q^38 - 16 * q^39 + 22 * q^40 - 4 * q^42 + 24 * q^43 + 32 * q^44 - 4 * q^45 - 24 * q^47 + 18 * q^48 - 44 * q^49 + 2 * q^50 - 20 * q^52 - 32 * q^53 + 2 * q^54 + 8 * q^56 - 4 * q^58 - 6 * q^60 + 32 * q^62 - 50 * q^64 - 8 * q^66 + 24 * q^67 - 28 * q^68 - 8 * q^69 - 4 * q^70 + 8 * q^71 + 2 * q^72 + 8 * q^73 - 48 * q^74 + 4 * q^75 + 12 * q^76 + 8 * q^77 - 84 * q^78 - 22 * q^80 + 20 * q^81 - 8 * q^82 + 4 * q^84 - 4 * q^86 - 16 * q^87 - 28 * q^88 - 2 * q^90 - 16 * q^91 + 76 * q^92 + 16 * q^93 - 16 * q^95 + 38 * q^96 + 24 * q^97 - 2 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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