LMFDB - Embedded newform 276.2.c.b.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(47,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("276.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			47.7
Character	$\chi$	$=$	276.47
Dual form			276.2.c.b.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.725653 - 1.21385i) q^{2} +(-0.173813 - 1.72331i) q^{3} +(-0.946854 + 1.76167i) q^{4} +1.59003i q^{5} +(-1.96571 + 1.46151i) q^{6} -4.71351i q^{7} +(2.82548 - 0.129022i) q^{8} +(-2.93958 + 0.599066i) q^{9} +O(q^{10})$	\(q+(-0.725653 - 1.21385i) q^{2} +(-0.173813 - 1.72331i) q^{3} +(-0.946854 + 1.76167i) q^{4} +1.59003i q^{5} +(-1.96571 + 1.46151i) q^{6} -4.71351i q^{7} +(2.82548 - 0.129022i) q^{8} +(-2.93958 + 0.599066i) q^{9} +(1.93005 - 1.15381i) q^{10} -5.82512 q^{11} +(3.20047 + 1.32552i) q^{12} -1.61546 q^{13} +(-5.72148 + 3.42037i) q^{14} +(2.74011 - 0.276367i) q^{15} +(-2.20693 - 3.33608i) q^{16} -3.60195i q^{17} +(2.86029 + 3.13349i) q^{18} +3.18817i q^{19} +(-2.80110 - 1.50553i) q^{20} +(-8.12283 + 0.819269i) q^{21} +(4.22702 + 7.07081i) q^{22} -1.00000 q^{23} +(-0.713450 - 4.84675i) q^{24} +2.47181 q^{25} +(1.17226 + 1.96092i) q^{26} +(1.54331 + 4.96167i) q^{27} +(8.30363 + 4.46301i) q^{28} +0.123751i q^{29} +(-2.32384 - 3.12553i) q^{30} -2.32972i q^{31} +(-2.44803 + 5.09972i) q^{32} +(1.01248 + 10.0385i) q^{33} +(-4.37222 + 2.61377i) q^{34} +7.49462 q^{35} +(1.72800 - 5.74578i) q^{36} +1.69076 q^{37} +(3.86995 - 2.31351i) q^{38} +(0.280788 + 2.78393i) q^{39} +(0.205149 + 4.49260i) q^{40} -8.92645i q^{41} +(6.88882 + 9.26537i) q^{42} -3.88980i q^{43} +(5.51554 - 10.2619i) q^{44} +(-0.952532 - 4.67401i) q^{45} +(0.725653 + 1.21385i) q^{46} -4.75555 q^{47} +(-5.36550 + 4.38308i) q^{48} -15.2172 q^{49} +(-1.79368 - 3.00040i) q^{50} +(-6.20727 + 0.626065i) q^{51} +(1.52960 - 2.84590i) q^{52} -8.35826i q^{53} +(4.90281 - 5.47380i) q^{54} -9.26211i q^{55} +(-0.608147 - 13.3179i) q^{56} +(5.49420 - 0.554145i) q^{57} +(0.150215 - 0.0898002i) q^{58} +7.00860 q^{59} +(-2.10762 + 5.08884i) q^{60} +2.05472 q^{61} +(-2.82793 + 1.69057i) q^{62} +(2.82370 + 13.8557i) q^{63} +(7.96671 - 0.729099i) q^{64} -2.56863i q^{65} +(11.4505 - 8.51345i) q^{66} -11.0554i q^{67} +(6.34543 + 3.41052i) q^{68} +(0.173813 + 1.72331i) q^{69} +(-5.43849 - 9.09732i) q^{70} -1.48951 q^{71} +(-8.22843 + 2.07192i) q^{72} +7.31498 q^{73} +(-1.22691 - 2.05233i) q^{74} +(-0.429632 - 4.25969i) q^{75} +(-5.61649 - 3.01873i) q^{76} +27.4568i q^{77} +(3.17552 - 2.36100i) q^{78} +11.3669i q^{79} +(5.30447 - 3.50909i) q^{80} +(8.28224 - 3.52200i) q^{81} +(-10.8353 + 6.47751i) q^{82} +16.1489 q^{83} +(6.24785 - 15.0854i) q^{84} +5.72720 q^{85} +(-4.72163 + 2.82265i) q^{86} +(0.213261 - 0.0215095i) q^{87} +(-16.4588 + 0.751569i) q^{88} -10.1497i q^{89} +(-4.98233 + 4.54794i) q^{90} +7.61448i q^{91} +(0.946854 - 1.76167i) q^{92} +(-4.01483 + 0.404936i) q^{93} +(3.45088 + 5.77252i) q^{94} -5.06928 q^{95} +(9.21389 + 3.33230i) q^{96} +2.76260 q^{97} +(11.0424 + 18.4713i) q^{98} +(17.1234 - 3.48963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q + 9 * q^8 - 2 * q^9	$ 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) $ 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$-1$

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 $

$2$	−0.725653	−	1.21385i	−0.513114	−	0.858320i
$2$	−0.725653	−	1.21385i	−0.513114	−	0.858320i
$3$	−0.173813	−	1.72331i	−0.100351	−	0.994952i
$3$	−0.173813	−	1.72331i	−0.100351	−	0.994952i
$4$	−0.946854	+	1.76167i	−0.473427	+	0.880833i
$5$			1.59003i			0.711082i	0.934661	+	0.355541i	$0.115703\pi$
$5$			1.59003i			0.711082i	−0.934661	+	0.355541i	$0.884297\pi$
$6$	−1.96571	+	1.46151i	−0.802496	+	0.596658i
$7$		−	4.71351i		−	1.78154i	−0.454455	−	0.890770i	$-0.650166\pi$
$7$		−	4.71351i		−	1.78154i	0.454455	−	0.890770i	$-0.349834\pi$
$8$	2.82548	−	0.129022i	0.998959	−	0.0456162i
$9$	−2.93958	+	0.599066i	−0.979859	+	0.199689i
$10$	1.93005	−	1.15381i	0.610336	−	0.364867i
$11$	−5.82512			−1.75634			−0.878170	−	0.478349i	$-0.841235\pi$
$11$	−5.82512			−1.75634			−0.878170	+	0.478349i	$0.841235\pi$
$12$	3.20047	+	1.32552i	0.923896	+	0.382645i
$13$	−1.61546			−0.448048			−0.224024	−	0.974584i	$-0.571919\pi$
$13$	−1.61546			−0.448048			−0.224024	+	0.974584i	$0.571919\pi$
$14$	−5.72148	+	3.42037i	−1.52913	+	0.914134i
$15$	2.74011	−	0.276367i	0.707493	−	0.0713578i
$16$	−2.20693	−	3.33608i	−0.551734	−	0.834020i
$17$		−	3.60195i		−	0.873601i	−0.899558	−	0.436800i	$-0.856112\pi$
$17$		−	3.60195i		−	0.873601i	0.899558	−	0.436800i	$-0.143888\pi$
$18$	2.86029	+	3.13349i	0.674177	+	0.738570i
$19$			3.18817i			0.731416i	0.930730	+	0.365708i	$0.119173\pi$
$19$			3.18817i			0.731416i	−0.930730	+	0.365708i	$0.880827\pi$
$20$	−2.80110	−	1.50553i	−0.626345	−	0.336646i
$21$	−8.12283	+	0.819269i	−1.77255	+	0.178779i
$22$	4.22702	+	7.07081i	0.901203	+	1.50750i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$	−0.713450	−	4.84675i	−0.145632	−	0.989339i
$25$	2.47181			0.494362
$26$	1.17226	+	1.96092i	0.229900	+	0.384568i
$27$	1.54331	+	4.96167i	0.297010	+	0.954874i
$28$	8.30363	+	4.46301i	1.56924	+	0.843429i
$29$			0.123751i			0.0229799i	0.999934	+	0.0114900i	$0.00365745\pi$
$29$			0.123751i			0.0229799i	−0.999934	+	0.0114900i	$0.996343\pi$
$30$	−2.32384	−	3.12553i	−0.424273	−	0.570641i
$31$		−	2.32972i		−	0.418431i	−0.977870	−	0.209215i	$-0.932909\pi$
$31$		−	2.32972i		−	0.418431i	0.977870	−	0.209215i	$-0.0670910\pi$
$32$	−2.44803	+	5.09972i	−0.432754	+	0.901512i
$33$	1.01248	+	10.0385i	0.176250	+	1.74747i
$34$	−4.37222	+	2.61377i	−0.749829	+	0.448257i
$35$	7.49462			1.26682
$36$	1.72800	−	5.74578i	0.288000	−	0.957631i
$37$	1.69076			0.277959			0.138980	−	0.990295i	$-0.455618\pi$
$37$	1.69076			0.277959			0.138980	+	0.990295i	$0.455618\pi$
$38$	3.86995	−	2.31351i	0.627789	−	0.375300i
$39$	0.280788	+	2.78393i	0.0449620	+	0.445786i
$40$	0.205149	+	4.49260i	0.0324369	+	0.710342i
$41$		−	8.92645i		−	1.39408i	−0.717034	−	0.697038i	$-0.754501\pi$
$41$		−	8.92645i		−	1.39408i	0.717034	−	0.697038i	$-0.245499\pi$
$42$	6.88882	+	9.26537i	1.06297	+	1.42968i
$43$		−	3.88980i		−	0.593189i	−0.955003	−	0.296595i	$-0.904149\pi$
$43$		−	3.88980i		−	0.593189i	0.955003	−	0.296595i	$-0.0958510\pi$
$44$	5.51554	−	10.2619i	0.831499	−	1.54704i
$45$	−0.952532	−	4.67401i	−0.141995	−	0.696761i
$46$	0.725653	+	1.21385i	0.106992	+	0.178972i
$47$	−4.75555			−0.693668			−0.346834	−	0.937926i	$-0.612743\pi$
$47$	−4.75555			−0.693668			−0.346834	+	0.937926i	$0.612743\pi$
$48$	−5.36550	+	4.38308i	−0.774443	+	0.632643i
$49$	−15.2172			−2.17388
$50$	−1.79368	−	3.00040i	−0.253664	−	0.424321i
$51$	−6.20727	+	0.626065i	−0.869191	+	0.0876666i
$52$	1.52960	−	2.84590i	0.212118	−	0.394655i
$53$		−	8.35826i		−	1.14810i	−0.818822	−	0.574048i	$-0.805372\pi$
$53$		−	8.35826i		−	1.14810i	0.818822	−	0.574048i	$-0.194628\pi$
$54$	4.90281	−	5.47380i	0.667187	−	0.744890i
$55$		−	9.26211i		−	1.24890i
$56$	−0.608147	−	13.3179i	−0.0812670	−	1.77968i
$57$	5.49420	−	0.554145i	0.727724	−	0.0733983i
$58$	0.150215	−	0.0898002i	0.0197242	−	0.0117913i
$59$	7.00860			0.912442			0.456221	−	0.889867i	$-0.349203\pi$
$59$	7.00860			0.912442			0.456221	+	0.889867i	$0.349203\pi$
$60$	−2.10762	+	5.08884i	−0.272092	+	0.656966i
$61$	2.05472			0.263080			0.131540	−	0.991311i	$-0.458008\pi$
$61$	2.05472			0.263080			0.131540	+	0.991311i	$0.458008\pi$
$62$	−2.82793	+	1.69057i	−0.359148	+	0.214703i
$63$	2.82370	+	13.8557i	0.355753	+	1.74566i
$64$	7.96671	−	0.729099i	0.995838	−	0.0911374i
$65$		−	2.56863i		−	0.318599i
$66$	11.4505	−	8.51345i	1.40946	−	1.04793i
$67$		−	11.0554i		−	1.35064i	−0.737527	−	0.675318i	$-0.764007\pi$
$67$		−	11.0554i		−	1.35064i	0.737527	−	0.675318i	$-0.235993\pi$
$68$	6.34543	+	3.41052i	0.769497	+	0.413586i
$69$	0.173813	+	1.72331i	0.0209246	+	0.207462i
$70$	−5.43849	−	9.09732i	−0.650024	−	1.08734i
$71$	−1.48951			−0.176772			−0.0883861	−	0.996086i	$-0.528171\pi$
$71$	−1.48951			−0.176772			−0.0883861	+	0.996086i	$0.528171\pi$
$72$	−8.22843	+	2.07192i	−0.969730	+	0.244178i
$73$	7.31498			0.856154			0.428077	−	0.903742i	$-0.359191\pi$
$73$	7.31498			0.856154			0.428077	+	0.903742i	$0.359191\pi$
$74$	−1.22691	−	2.05233i	−0.142625	−	0.238578i
$75$	−0.429632	−	4.25969i	−0.0496096	−	0.491866i
$76$	−5.61649	−	3.01873i	−0.644256	−	0.346272i
$77$			27.4568i			3.12899i
$78$	3.17552	−	2.36100i	0.359557	−	0.267331i
$79$			11.3669i			1.27888i	0.768842	+	0.639439i	$0.220833\pi$
$79$			11.3669i			1.27888i	−0.768842	+	0.639439i	$0.779167\pi$
$80$	5.30447	−	3.50909i	0.593057	−	0.392328i
$81$	8.28224	−	3.52200i	0.920249	−	0.391334i
$82$	−10.8353	+	6.47751i	−1.19656	+	0.715321i
$83$	16.1489			1.77257			0.886286	−	0.463139i	$-0.153277\pi$
$83$	16.1489			1.77257			0.886286	+	0.463139i	$0.153277\pi$
$84$	6.24785	−	15.0854i	0.681697	−	1.64596i
$85$	5.72720			0.621202
$86$	−4.72163	+	2.82265i	−0.509146	+	0.304374i
$87$	0.213261	−	0.0215095i	0.0228639	−	0.00230606i
$88$	−16.4588	+	0.751569i	−1.75451	+	0.0801175i
$89$		−	10.1497i		−	1.07586i	−0.842988	−	0.537932i	$-0.819206\pi$
$89$		−	10.1497i		−	1.07586i	0.842988	−	0.537932i	$-0.180794\pi$
$90$	−4.98233	+	4.54794i	−0.525184	+	0.479395i
$91$			7.61448i			0.798215i
$92$	0.946854	−	1.76167i	0.0987164	−	0.183666i
$93$	−4.01483	+	0.404936i	−0.416319	+	0.0419899i
$94$	3.45088	+	5.77252i	0.355931	+	0.595390i
$95$	−5.06928			−0.520097
$96$	9.21389	+	3.33230i	0.940389	+	0.340102i
$97$	2.76260			0.280500			0.140250	−	0.990116i	$-0.455209\pi$
$97$	2.76260			0.280500			0.140250	+	0.990116i	$0.455209\pi$
$98$	11.0424	+	18.4713i	1.11545	+	1.86589i
$99$	17.1234	−	3.48963i	1.72097	−	0.350721i
$100$	−2.34044	+	4.35450i	−0.234044	+	0.435450i
$101$			8.06147i			0.802146i	0.916046	+	0.401073i	$0.131363\pi$
$101$			8.06147i			0.802146i	−0.916046	+	0.401073i	$0.868637\pi$
$102$	5.26427	+	7.08037i	0.521241	+	0.701061i
$103$		−	5.26379i		−	0.518656i	−0.965789	−	0.259328i	$-0.916499\pi$
$103$		−	5.26379i		−	0.518656i	0.965789	−	0.259328i	$-0.0835011\pi$
$104$	−4.56445	+	0.208430i	−0.447581	+	0.0204382i
$105$	−1.30266	−	12.9155i	−0.127127	−	1.26043i
$106$	−10.1457	+	6.06520i	−0.985434	+	0.589105i
$107$	−15.9961			−1.54640			−0.773199	−	0.634163i	$-0.781345\pi$
$107$	−15.9961			−1.54640			−0.773199	+	0.634163i	$0.781345\pi$
$108$	−10.2021	−	1.97918i	−0.981698	−	0.190447i
$109$	3.17515			0.304125			0.152062	−	0.988371i	$-0.451409\pi$
$109$	3.17515			0.304125			0.152062	+	0.988371i	$0.451409\pi$
$110$	−11.2428	+	6.72108i	−1.07196	+	0.640830i
$111$	−0.293876	−	2.91370i	−0.0278935	−	0.276556i
$112$	−15.7247	+	10.4024i	−1.48584	+	0.982935i
$113$		−	3.05167i		−	0.287077i	−0.989645	−	0.143538i	$-0.954152\pi$
$113$		−	3.05167i		−	0.287077i	0.989645	−	0.143538i	$-0.0458481\pi$
$114$	−4.65953	−	6.26700i	−0.436405	−	0.586959i
$115$		−	1.59003i		−	0.148271i
$116$	−0.218008	−	0.117174i	−0.0202415	−	0.0108793i
$117$	4.74877	−	0.967767i	0.439024	−	0.0894701i
$118$	−5.08581	−	8.50737i	−0.468187	−	0.783167i
$119$	−16.9778			−1.55635
$120$	7.70647	−	1.13441i	0.703501	−	0.103557i
$121$	22.9320			2.08473
$122$	−1.49101	−	2.49412i	−0.134990	−	0.225807i
$123$	−15.3830	+	1.55153i	−1.38704	+	0.139897i
$124$	4.10420	+	2.20591i	0.368568	+	0.198096i
$125$			11.8804i			1.06261i
$126$	14.7697	−	13.4820i	1.31579	−	1.20107i
$127$		−	7.26174i		−	0.644375i	−0.946676	−	0.322188i	$-0.895582\pi$
$127$		−	7.26174i		−	0.644375i	0.946676	−	0.322188i	$-0.104418\pi$
$128$	−6.66608	−	9.14130i	−0.589204	−	0.807984i
$129$	−6.70333	+	0.676098i	−0.590195	+	0.0595271i
$130$	−3.11792	+	1.86393i	−0.273460	+	0.163478i
$131$	9.25091			0.808256			0.404128	−	0.914703i	$-0.367575\pi$
$131$	9.25091			0.808256			0.404128	+	0.914703i	$0.367575\pi$
$132$	−18.6431	−	7.72132i	−1.62267	−	0.672054i
$133$	15.0275			1.30305
$134$	−13.4196	+	8.02241i	−1.15928	+	0.693030i
$135$	−7.88920	+	2.45391i	−0.678994	+	0.211199i
$136$	−0.464731	−	10.1772i	−0.0398503	−	0.872692i
$137$		−	10.5742i		−	0.903412i	−0.892167	−	0.451706i	$-0.850816\pi$
$137$		−	10.5742i		−	0.903412i	0.892167	−	0.451706i	$-0.149184\pi$
$138$	1.96571	−	1.46151i	0.167332	−	0.124412i
$139$			0.657922i			0.0558042i	0.999611	+	0.0279021i	$0.00888267\pi$
$139$			0.657922i			0.0558042i	−0.999611	+	0.0279021i	$0.991117\pi$
$140$	−7.09631	+	13.2030i	−0.599747	+	1.11586i
$141$	0.826576	+	8.19528i	0.0696102	+	0.690167i
$142$	1.08087	+	1.80804i	0.0907044	+	0.151727i
$143$	9.41024			0.786924
$144$	8.48599	+	8.48457i	0.707166	+	0.707048i
$145$	−0.196767			−0.0163406
$146$	−5.30814	−	8.87928i	−0.439305	−	0.734854i
$147$	2.64494	+	26.2239i	0.218151	+	2.16291i
$148$	−1.60090	+	2.97856i	−0.131594	+	0.244836i
$149$		−	5.02881i		−	0.411976i	−0.978555	−	0.205988i	$-0.933959\pi$
$149$		−	5.02881i		−	0.411976i	0.978555	−	0.205988i	$-0.0660408\pi$
$150$	−4.85885	+	3.61256i	−0.396723	+	0.294965i
$151$			20.7363i			1.68749i	0.536740	+	0.843747i	$0.319655\pi$
$151$			20.7363i			1.68749i	−0.536740	+	0.843747i	$0.680345\pi$
$152$	0.411344	+	9.00812i	0.0333644	+	0.730655i
$153$	2.15781	+	10.5882i	0.174448	+	0.856006i
$154$	33.3283	−	19.9241i	2.68567	−	1.60553i
$155$	3.70433			0.297539
$156$	−5.17023	−	2.14132i	−0.413949	−	0.171443i
$157$	−18.5129			−1.47749			−0.738744	−	0.673986i	$-0.764581\pi$
$157$	−18.5129			−1.47749			−0.738744	+	0.673986i	$0.764581\pi$
$158$	13.7977	−	8.24844i	1.09769	−	0.656210i
$159$	−14.4039	+	1.45277i	−1.14230	+	0.115212i
$160$	−8.10871	−	3.89243i	−0.641049	−	0.307724i
$161$			4.71351i			0.371477i
$162$	−10.2852	−	7.49763i	−0.808083	−	0.589069i
$163$			10.0303i			0.785637i	0.919616	+	0.392818i	$0.128500\pi$
$163$			10.0303i			0.785637i	−0.919616	+	0.392818i	$0.871500\pi$
$164$	15.7254	+	8.45204i	1.22795	+	0.659994i
$165$	−15.9615	+	1.60987i	−1.24260	+	0.125328i
$166$	−11.7185	−	19.6023i	−0.909532	−	1.52143i
$167$	−14.9741			−1.15873			−0.579365	−	0.815068i	$-0.696699\pi$
$167$	−14.9741			−1.15873			−0.579365	+	0.815068i	$0.696699\pi$
$168$	−22.8452	+	3.36285i	−1.76255	+	0.259450i
$169$	−10.3903			−0.799253
$170$	−4.15596	−	6.95195i	−0.318748	−	0.533190i
$171$	−1.90992	−	9.37187i	−0.146056	−	0.716685i
$172$	6.85253	+	3.68308i	0.522501	+	0.280832i
$173$			14.3282i			1.08935i	0.838646	+	0.544676i	$0.183347\pi$
$173$			14.3282i			1.08935i	−0.838646	+	0.544676i	$0.816653\pi$
$174$	−0.180863	−	0.243258i	−0.0137112	−	0.0184413i
$175$		−	11.6509i		−	0.880725i
$176$	12.8557	+	19.4331i	0.969032	+	1.46482i
$177$	−1.21818	−	12.0780i	−0.0915643	−	0.907836i
$178$	−12.3202	+	7.36515i	−0.923435	+	0.552041i
$179$	5.23034			0.390934			0.195467	−	0.980710i	$-0.437378\pi$
$179$	5.23034			0.390934			0.195467	+	0.980710i	$0.437378\pi$
$180$	9.13596	+	2.74757i	0.680954	+	0.204791i
$181$	−2.35805			−0.175273			−0.0876363	−	0.996153i	$-0.527931\pi$
$181$	−2.35805			−0.175273			−0.0876363	+	0.996153i	$0.527931\pi$
$182$	9.24282	−	5.52548i	0.685124	−	0.409576i
$183$	−0.357137	−	3.54091i	−0.0264003	−	0.261752i
$184$	−2.82548	+	0.129022i	−0.208297	+	0.00951163i
$185$			2.68836i			0.197652i
$186$	3.40491	+	4.57955i	0.249660	+	0.335789i
$187$			20.9818i			1.53434i
$188$	4.50281	−	8.37769i	0.328401	−	0.611006i
$189$	23.3869	−	7.27441i	1.70115	−	0.529136i
$190$	3.67854	+	6.15334i	0.266869	+	0.446410i
$191$	−5.10821			−0.369617			−0.184808	−	0.982775i	$-0.559166\pi$
$191$	−5.10821			−0.369617			−0.184808	+	0.982775i	$0.559166\pi$
$192$	−2.64118	−	13.6024i	−0.190611	−	0.981666i
$193$	10.1807			0.732826			0.366413	−	0.930452i	$-0.380586\pi$
$193$	10.1807			0.732826			0.366413	+	0.930452i	$0.380586\pi$
$194$	−2.00469	−	3.35338i	−0.143929	−	0.240759i
$195$	−4.42653	+	0.446460i	−0.316991	+	0.0319717i
$196$	14.4084	−	26.8076i	1.02917	−	1.91483i
$197$			7.11940i			0.507236i	0.967304	+	0.253618i	$0.0816206\pi$
$197$			7.11940i			0.507236i	−0.967304	+	0.253618i	$0.918379\pi$
$198$	−16.6615	−	18.2529i	−1.18408	−	1.29718i
$199$		−	5.76508i		−	0.408675i	−0.978900	−	0.204338i	$-0.934496\pi$
$199$		−	5.76508i		−	0.408675i	0.978900	−	0.204338i	$-0.0655041\pi$
$200$	6.98405	−	0.318918i	0.493847	−	0.0225509i
$201$	−19.0519	+	1.92158i	−1.34382	+	0.135537i
$202$	9.78540	−	5.84983i	0.688498	−	0.411593i
$203$	0.583301			0.0409397
$204$	4.77446	−	11.5279i	0.334279	−	0.807116i
$205$	14.1933			0.991304
$206$	−6.38944	+	3.81969i	−0.445173	+	0.266130i
$207$	2.93958	−	0.599066i	0.204315	−	0.0416380i
$208$	3.56521	+	5.38930i	0.247203	+	0.373681i
$209$		−	18.5715i		−	1.28462i
$210$	−14.7322	+	10.9534i	−1.01662	+	0.755858i
$211$		−	11.7428i		−	0.808404i	−0.914670	−	0.404202i	$-0.867549\pi$
$211$		−	11.7428i		−	0.808404i	0.914670	−	0.404202i	$-0.132451\pi$
$212$	14.7245	+	7.91406i	1.01128	+	0.543540i
$213$	0.258896	+	2.56688i	0.0177393	+	0.175880i
$214$	11.6076	+	19.4168i	0.793479	+	1.32730i
$215$	6.18490			0.421807
$216$	5.00077	+	13.8200i	0.340259	+	0.940332i
$217$	−10.9812			−0.745451
$218$	−2.30406	−	3.85415i	−0.156051	−	0.261036i
$219$	−1.27144	−	12.6060i	−0.0859158	−	0.851832i
$220$	16.3167	+	8.76986i	1.10007	+	0.591264i
$221$			5.81880i			0.391415i
$222$	−3.32354	+	2.47106i	−0.223061	+	0.165847i
$223$		−	19.2029i		−	1.28592i	−0.765899	−	0.642960i	$-0.777706\pi$
$223$		−	19.2029i		−	1.28592i	0.765899	−	0.642960i	$-0.222294\pi$
$224$	24.0376	+	11.5388i	1.60608	+	0.770968i
$225$	−7.26607	+	1.48078i	−0.484405	+	0.0987184i
$226$	−3.70426	+	2.21445i	−0.246404	+	0.147303i
$227$	10.9685			0.728005			0.364003	−	0.931398i	$-0.381410\pi$
$227$	10.9685			0.728005			0.364003	+	0.931398i	$0.381410\pi$
$228$	−4.22599	+	10.2036i	−0.279873	+	0.675752i
$229$	−14.5456			−0.961200			−0.480600	−	0.876940i	$-0.659581\pi$
$229$	−14.5456			−0.961200			−0.480600	+	0.876940i	$0.659581\pi$
$230$	−1.93005	+	1.15381i	−0.127264	+	0.0760800i
$231$	47.3164	−	4.77234i	3.11319	−	0.313997i
$232$	0.0159666	+	0.349656i	0.00104826	+	0.0229560i
$233$			16.0184i			1.04940i	0.851288	+	0.524699i	$0.175822\pi$
$233$			16.0184i			1.04940i	−0.851288	+	0.524699i	$0.824178\pi$
$234$	−4.62068	−	5.06202i	−0.302063	−	0.330915i
$235$		−	7.56146i		−	0.493255i
$236$	−6.63612	+	12.3468i	−0.431975	+	0.803709i
$237$	19.5887	−	1.97572i	1.27242	−	0.128336i
$238$	12.3200	+	20.6085i	0.798588	+	1.33585i
$239$	25.3265			1.63823			0.819117	−	0.573627i	$-0.194464\pi$
$239$	25.3265			1.63823			0.819117	+	0.573627i	$0.194464\pi$
$240$	−6.96922	−	8.53130i	−0.449862	−	0.550693i
$241$	−25.0758			−1.61527			−0.807636	−	0.589682i	$-0.799253\pi$
$241$	−25.0758			−1.61527			−0.807636	+	0.589682i	$0.799253\pi$
$242$	−16.6407	−	27.8360i	−1.06970	−	1.78936i
$243$	−7.50905	−	13.6607i	−0.481706	−	0.876333i
$244$	−1.94552	+	3.61973i	−0.124549	+	0.231729i
$245$		−	24.1957i		−	1.54581i
$246$	13.0461	+	17.5468i	0.831786	+	1.11874i
$247$		−	5.15036i		−	0.327709i
$248$	−0.300586	−	6.58260i	−0.0190872	−	0.417995i
$249$	−2.80689	−	27.8295i	−0.177879	−	1.76362i
$250$	14.4210	−	8.62105i	0.912063	−	0.545243i
$251$	−7.30711			−0.461220			−0.230610	−	0.973046i	$-0.574072\pi$
$251$	−7.30711			−0.461220			−0.230610	+	0.973046i	$0.574072\pi$
$252$	−27.0828	−	8.14493i	−1.70606	−	0.513082i
$253$	5.82512			0.366222
$254$	−8.81465	+	5.26951i	−0.553080	+	0.330638i
$255$	−0.995461	−	9.86973i	−0.0623382	−	0.618067i
$256$	−6.25888	+	14.7250i	−0.391180	+	0.920314i
$257$			15.5116i			0.967585i	0.875183	+	0.483793i	$0.160741\pi$
$257$			15.5116i			0.967585i	−0.875183	+	0.483793i	$0.839259\pi$
$258$	5.68497	+	7.64621i	0.353931	+	0.476032i
$259$		−	7.96942i		−	0.495196i
$260$	4.52506	+	2.43211i	0.280632	+	0.150833i
$261$	−0.0741349	−	0.363775i	−0.00458884	−	0.0225171i
$262$	−6.71295	−	11.2292i	−0.414728	−	0.693742i
$263$	21.9697			1.35471			0.677355	−	0.735656i	$-0.263126\pi$
$263$	21.9697			1.35471			0.677355	+	0.735656i	$0.263126\pi$
$264$	4.15593	+	28.2329i	0.255780	+	1.73761i
$265$	13.2899			0.816391
$266$	−10.9047	−	18.2411i	−0.668612	−	1.11843i
$267$	−17.4910	+	1.76414i	−1.07043	+	0.107964i
$268$	19.4760	+	10.4679i	1.18968	+	0.639427i
$269$			8.85430i			0.539856i	0.962880	+	0.269928i	$0.0870000\pi$
$269$			8.85430i			0.539856i	−0.962880	+	0.269928i	$0.913000\pi$
$270$	8.70350	+	7.79560i	0.529678	+	0.474425i
$271$			14.0767i			0.855096i	0.903993	+	0.427548i	$0.140623\pi$
$271$			14.0767i			0.855096i	−0.903993	+	0.427548i	$0.859377\pi$
$272$	−12.0164	+	7.94927i	−0.728601	+	0.481995i
$273$	13.1221	−	1.32350i	0.794185	−	0.0801016i
$274$	−12.8354	+	7.67318i	−0.775417	+	0.463554i
$275$	−14.3986			−0.868267
$276$	−3.20047	−	1.32552i	−0.192646	−	0.0797870i
$277$	−24.2427			−1.45660			−0.728301	−	0.685257i	$-0.759690\pi$
$277$	−24.2427			−1.45660			−0.728301	+	0.685257i	$0.759690\pi$
$278$	0.798617	−	0.477423i	0.0478979	−	0.0286339i
$279$	1.39566	+	6.84841i	0.0835559	+	0.410003i
$280$	21.1759	−	0.966971i	1.26550	−	0.0577876i
$281$		−	29.0638i		−	1.73380i	−0.498479	−	0.866902i	$-0.666108\pi$
$281$		−	29.0638i		−	1.73380i	0.498479	−	0.866902i	$-0.333892\pi$
$282$	9.34801	−	6.95027i	0.556666	−	0.413882i
$283$			11.1372i			0.662038i	0.943624	+	0.331019i	$0.107392\pi$
$283$			11.1372i			0.662038i	−0.943624	+	0.331019i	$0.892608\pi$
$284$	1.41035	−	2.62402i	0.0836888	−	0.155707i
$285$	0.881106	+	8.73593i	0.0521922	+	0.517472i
$286$	−6.82858	−	11.4226i	−0.403782	−	0.675433i
$287$	−42.0749			−2.48360
$288$	4.14109	−	16.4576i	0.244016	−	0.969771i
$289$	4.02596			0.236821
$290$	0.142785	+	0.238846i	0.00838462	+	0.0140255i
$291$	−0.480176	−	4.76082i	−0.0281484	−	0.279084i
$292$	−6.92622	+	12.8866i	−0.405326	+	0.754129i
$293$		−	18.2693i		−	1.06731i	−0.845704	−	0.533653i	$-0.820819\pi$
$293$		−	18.2693i		−	1.06731i	0.845704	−	0.533653i	$-0.179181\pi$
$294$	29.9125	−	22.2400i	1.74453	−	1.29706i
$295$			11.1439i			0.648821i
$296$	4.77722	−	0.218146i	0.277670	−	0.0126795i
$297$	−8.98997	−	28.9023i	−0.521651	−	1.67708i
$298$	−6.10421	+	3.64917i	−0.353607	+	0.211391i
$299$	1.61546			0.0934244
$300$	7.91094	+	3.27643i	0.456739	+	0.189165i
$301$	−18.3346			−1.05679
$302$	25.1707	−	15.0474i	1.44841	−	0.865878i
$303$	13.8924	−	1.40119i	0.798097	−	0.0804961i
$304$	10.6360	−	7.03608i	0.610016	−	0.403547i
$305$			3.26706i			0.187071i
$306$	11.2867	−	10.3026i	0.645215	−	0.588962i
$307$			6.35510i			0.362705i	0.983418	+	0.181352i	$0.0580474\pi$
$307$			6.35510i			0.362705i	−0.983418	+	0.181352i	$0.941953\pi$
$308$	−48.3696	−	25.9975i	−2.75612	−	1.48135i
$309$	−9.07113	+	0.914914i	−0.516038	+	0.0520476i
$310$	−2.68806	−	4.49649i	−0.152671	−	0.255384i
$311$	17.0809			0.968568			0.484284	−	0.874911i	$-0.339080\pi$
$311$	17.0809			0.968568			0.484284	+	0.874911i	$0.339080\pi$
$312$	1.15255	+	7.82973i	0.0652503	+	0.443271i
$313$	−12.1741			−0.688120			−0.344060	−	0.938948i	$-0.611802\pi$
$313$	−12.1741			−0.688120			−0.344060	+	0.938948i	$0.611802\pi$
$314$	13.4339	+	22.4718i	0.758121	+	1.26816i
$315$	−22.0310	+	4.48977i	−1.24131	+	0.252970i
$316$	−20.0247	−	10.7628i	−1.12648	−	0.605455i
$317$			13.9955i			0.786068i	0.919524	+	0.393034i	$0.128574\pi$
$317$			13.9955i			0.786068i	−0.919524	+	0.393034i	$0.871426\pi$
$318$	12.2157	+	16.4299i	0.685020	+	0.921342i
$319$		−	0.720863i		−	0.0403606i
$320$	1.15929	+	12.6673i	0.0648062	+	0.708123i
$321$	2.78032	+	27.5661i	0.155182	+	1.53859i
$322$	5.72148	−	3.42037i	0.318846	−	0.190610i
$323$	11.4836			0.638966
$324$	−1.63748	+	17.9254i	−0.0909711	+	0.995854i
$325$	−3.99311			−0.221498
$326$	12.1753	−	7.27855i	0.674328	−	0.403121i
$327$	−0.551883	−	5.47177i	−0.0305192	−	0.302589i
$328$	−1.15171	−	25.2215i	−0.0635925	−	1.39263i
$329$			22.4153i			1.23580i
$330$	13.5366	+	18.2066i	0.745167	+	1.00224i
$331$		−	16.8569i		−	0.926541i	−0.886217	−	0.463271i	$-0.846676\pi$
$331$		−	16.8569i		−	0.926541i	0.886217	−	0.463271i	$-0.153324\pi$
$332$	−15.2906	+	28.4490i	−0.839183	+	1.56134i
$333$	−4.97013	+	1.01288i	−0.272361	+	0.0555054i
$334$	10.8660	+	18.1763i	0.594561	+	0.994561i
$335$	17.5784			0.960413
$336$	20.6597	+	25.2903i	1.12708	+	1.37970i
$337$	21.1061			1.14972			0.574861	−	0.818251i	$-0.305056\pi$
$337$	21.1061			1.14972			0.574861	+	0.818251i	$0.305056\pi$
$338$	7.53975	+	12.6122i	0.410108	+	0.686015i
$339$	−5.25897	+	0.530419i	−0.285628	+	0.0288084i
$340$	−5.42282	+	10.0894i	−0.294094	+	0.547175i
$341$			13.5709i			0.734907i
$342$	−9.99009	+	9.11909i	−0.540202	+	0.493104i
$343$			38.7317i			2.09132i
$344$	−0.501870	−	10.9906i	−0.0270590	−	0.592572i
$345$	−2.74011	+	0.276367i	−0.147522	+	0.0148791i
$346$	17.3923	−	10.3973i	0.935013	−	0.558963i
$347$	22.6326			1.21498			0.607490	−	0.794327i	$-0.292177\pi$
$347$	22.6326			1.21498			0.607490	+	0.794327i	$0.292177\pi$
$348$	−0.164034	+	0.396061i	−0.00879316	+	0.0212311i
$349$	−16.6899			−0.893392			−0.446696	−	0.894686i	$-0.647399\pi$
$349$	−16.6899			−0.893392			−0.446696	+	0.894686i	$0.647399\pi$
$350$	−14.1424	+	8.45451i	−0.755944	+	0.451913i
$351$	−2.49316	−	8.01538i	−0.133075	−	0.427829i
$352$	14.2600	−	29.7065i	0.760063	−	1.58336i
$353$		−	31.7089i		−	1.68769i	−0.536583	−	0.843847i	$-0.680285\pi$
$353$		−	31.7089i		−	1.68769i	0.536583	−	0.843847i	$-0.319715\pi$
$354$	−13.7768	+	10.2431i	−0.732231	+	0.544415i
$355$		−	2.36836i		−	0.125700i
$356$	17.8803	+	9.61026i	0.947656	+	0.509343i
$357$	2.95096	+	29.2580i	0.156182	+	1.54850i
$358$	−3.79541	−	6.34884i	−0.200594	−	0.335547i
$359$	8.49888			0.448554			0.224277	−	0.974525i	$-0.427998\pi$
$359$	8.49888			0.448554			0.224277	+	0.974525i	$0.427998\pi$
$360$	−3.29441	−	13.0834i	−0.173631	−	0.689558i
$361$	8.83557			0.465030
$362$	1.71113	+	2.86232i	0.0899349	+	0.150440i
$363$	−3.98588	−	39.5189i	−0.209204	−	2.07421i
$364$	−13.4142	−	7.20980i	−0.703094	−	0.377896i
$365$			11.6310i			0.608796i
$366$	−4.03897	+	3.00298i	−0.211120	+	0.156969i
$367$			9.70568i			0.506632i	0.967384	+	0.253316i	$0.0815213\pi$
$367$			9.70568i			0.506632i	−0.967384	+	0.253316i	$0.918479\pi$
$368$	2.20693	+	3.33608i	0.115044	+	0.173905i
$369$	5.34753	+	26.2400i	0.278381	+	1.36600i
$370$	3.26326	−	1.95082i	0.169649	−	0.101418i
$371$	−39.3968			−2.04538
$372$	3.08810	−	7.45621i	0.160110	−	0.386586i
$373$	21.5847			1.11762			0.558808	−	0.829297i	$-0.311259\pi$
$373$	21.5847			1.11762			0.558808	+	0.829297i	$0.311259\pi$
$374$	25.4687	−	15.2255i	1.31695	−	0.787292i
$375$	20.4736	−	2.06496i	1.05725	−	0.106634i
$376$	−13.4367	+	0.613571i	−0.692946	+	0.0316425i
$377$		−	0.199914i		−	0.0102961i
$378$	−25.8008	−	23.1094i	−1.32705	−	1.18862i
$379$		−	17.5731i		−	0.902672i	−0.892354	−	0.451336i	$-0.850948\pi$
$379$		−	17.5731i		−	0.902672i	0.892354	−	0.451336i	$-0.149052\pi$
$380$	4.79987	−	8.93038i	0.246228	−	0.458119i
$381$	−12.5142	+	1.26218i	−0.641122	+	0.0646636i
$382$	3.70679	+	6.20059i	0.189656	+	0.317250i
$383$	−8.84200			−0.451805			−0.225902	−	0.974150i	$-0.572533\pi$
$383$	−8.84200			−0.451805			−0.225902	+	0.974150i	$0.572533\pi$
$384$	−14.5946	+	13.0766i	−0.744778	+	0.667312i
$385$	−43.6570			−2.22497
$386$	−7.38769	−	12.3579i	−0.376023	−	0.628999i
$387$	2.33025	+	11.4344i	0.118453	+	0.581242i
$388$	−2.61578	+	4.86679i	−0.132796	+	0.247074i
$389$		−	9.08929i		−	0.460845i	−0.973091	−	0.230423i	$-0.925989\pi$
$389$		−	9.08929i		−	0.460845i	0.973091	−	0.230423i	$-0.0740108\pi$
$390$	3.75406	+	5.04916i	0.190094	+	0.255674i
$391$			3.60195i			0.182158i
$392$	−42.9959	+	1.96335i	−2.17162	+	0.0991642i
$393$	−1.60793	−	15.9422i	−0.0811092	−	0.804176i
$394$	8.64187	−	5.16622i	0.435371	−	0.260270i
$395$	−18.0737			−0.909387
$396$	−10.0658	+	33.4699i	−0.505825	+	1.68192i
$397$	−17.2537			−0.865940			−0.432970	−	0.901408i	$-0.642534\pi$
$397$	−17.2537			−0.865940			−0.432970	+	0.901408i	$0.642534\pi$
$398$	−6.99793	+	4.18345i	−0.350774	+	0.209697i
$399$	−2.61197	−	25.8970i	−0.130762	−	1.29647i
$400$	−5.45512	−	8.24615i	−0.272756	−	0.412308i
$401$		−	1.20505i		−	0.0601774i	−0.999547	−	0.0300887i	$-0.990421\pi$
$401$		−	1.20505i		−	0.0601774i	0.999547	−	0.0300887i	$-0.00957897\pi$
$402$	16.1576	+	21.7317i	0.805867	+	1.08388i
$403$			3.76357i			0.187477i
$404$	−14.2016	−	7.63304i	−0.706557	−	0.379758i
$405$	5.60009	+	13.1690i	0.278271	+	0.654373i
$406$	−0.423274	−	0.708038i	−0.0210067	−	0.0351394i
$407$	−9.84889			−0.488191
$408$	−17.4577	+	2.56981i	−0.864287	+	0.127225i
$409$	1.68033			0.0830871			0.0415436	−	0.999137i	$-0.486772\pi$
$409$	1.68033			0.0830871			0.0415436	+	0.999137i	$0.486772\pi$
$410$	−10.2994	−	17.2285i	−0.508652	−	0.850856i
$411$	−18.2225	+	1.83793i	−0.898852	+	0.0906582i
$412$	9.27304	+	4.98404i	0.456850	+	0.245546i
$413$		−	33.0351i		−	1.62555i
$414$	−2.86029	−	3.13349i	−0.140576	−	0.154002i
$415$			25.6772i			1.26044i
$416$	3.95469	−	8.23839i	0.193894	−	0.403920i
$417$	1.13380	−	0.114355i	0.0555225	−	0.00560000i
$418$	−22.5429	+	13.4765i	−1.10261	+	0.659155i
$419$	−13.1658			−0.643193			−0.321596	−	0.946877i	$-0.604219\pi$
$419$	−13.1658			−0.643193			−0.321596	+	0.946877i	$0.604219\pi$
$420$	23.9863	+	9.93427i	1.17041	+	0.484743i
$421$	12.1317			0.591264			0.295632	−	0.955302i	$-0.404470\pi$
$421$	12.1317			0.591264			0.295632	+	0.955302i	$0.404470\pi$
$422$	−14.2539	+	8.52117i	−0.693870	+	0.414804i
$423$	13.9793	−	2.84889i	0.679697	−	0.138518i
$424$	−1.07840	−	23.6161i	−0.0523718	−	1.14690i
$425$		−	8.90333i		−	0.431875i
$426$	2.92794	−	2.17693i	0.141859	−	0.105473i
$427$		−	9.68494i		−	0.468687i
$428$	15.1459	−	28.1797i	0.732107	−	1.36212i
$429$	−1.63562	−	16.2167i	−0.0789685	−	0.782952i
$430$	−4.48809	−	7.50753i	−0.216435	−	0.362045i
$431$	1.65853			0.0798884			0.0399442	−	0.999202i	$-0.487282\pi$
$431$	1.65853			0.0798884			0.0399442	+	0.999202i	$0.487282\pi$
$432$	13.1466	−	16.0987i	0.632514	−	0.774549i
$433$	22.2218			1.06791			0.533956	−	0.845512i	$-0.320705\pi$
$433$	22.2218			1.06791			0.533956	+	0.845512i	$0.320705\pi$
$434$	7.96853	+	13.3295i	0.382502	+	0.639836i
$435$	0.0342007	+	0.339091i	0.00163980	+	0.0162582i
$436$	−3.00641	+	5.59356i	−0.143981	+	0.267883i
$437$		−	3.18817i		−	0.152511i
$438$	−14.3791	+	10.6909i	−0.687060	+	0.510831i
$439$		−	7.58986i		−	0.362244i	−0.983461	−	0.181122i	$-0.942027\pi$
$439$		−	7.58986i		−	0.362244i	0.983461	−	0.181122i	$-0.0579730\pi$
$440$	−1.19502	−	26.1699i	−0.0569702	−	1.24760i
$441$	44.7321	−	9.11609i	2.13010	−	0.434100i
$442$	7.06314	−	4.22243i	0.335959	−	0.200841i
$443$	−33.2024			−1.57749			−0.788747	−	0.614717i	$-0.789270\pi$
$443$	−33.2024			−1.57749			−0.788747	+	0.614717i	$0.789270\pi$
$444$	5.41123	+	2.24114i	0.256805	+	0.106360i
$445$	16.1383			0.765028
$446$	−23.3094	+	13.9346i	−1.10373	+	0.659825i
$447$	−8.66618	+	0.874072i	−0.409896	+	0.0413422i
$448$	−3.43662	−	37.5511i	−0.162365	−	1.77412i
$449$			18.6239i			0.878918i	0.898263	+	0.439459i	$0.144830\pi$
$449$			18.6239i			0.878918i	−0.898263	+	0.439459i	$0.855170\pi$
$450$	7.07009	+	7.74538i	0.333287	+	0.365121i
$451$			51.9976i			2.44847i
$452$	5.37602	+	2.88949i	0.252867	+	0.135910i
$453$	35.7350	−	3.60423i	1.67898	−	0.169342i
$454$	−7.95933	−	13.3141i	−0.373550	−	0.624861i
$455$	−12.1072			−0.567596
$456$	15.4523	−	2.27460i	0.723619	−	0.106518i
$457$	4.64391			0.217233			0.108616	−	0.994084i	$-0.465358\pi$
$457$	4.64391			0.217233			0.108616	+	0.994084i	$0.465358\pi$
$458$	10.5551	+	17.6561i	0.493205	+	0.825017i
$459$	17.8717	−	5.55893i	0.834179	−	0.259469i
$460$	2.80110	+	1.50553i	0.130602	+	0.0701955i
$461$		−	20.6179i		−	0.960273i	−0.877194	−	0.480136i	$-0.840587\pi$
$461$		−	20.6179i		−	0.960273i	0.877194	−	0.480136i	$-0.159413\pi$
$462$	−40.1282	−	53.9719i	−1.86693	−	2.51100i
$463$		−	27.4269i		−	1.27463i	−0.770602	−	0.637317i	$-0.780044\pi$
$463$		−	27.4269i		−	1.27463i	0.770602	−	0.637317i	$-0.219956\pi$
$464$	0.412843	−	0.273110i	0.0191657	−	0.0126788i
$465$	−0.643860	−	6.38370i	−0.0298583	−	0.296037i
$466$	19.4439	−	11.6238i	0.900719	−	0.538461i
$467$	16.4512			0.761273			0.380636	−	0.924725i	$-0.375705\pi$
$467$	16.4512			0.761273			0.380636	+	0.924725i	$0.375705\pi$
$468$	−2.79151	+	9.28208i	−0.129038	+	0.429064i
$469$	−52.1099			−2.40621
$470$	−9.17847	+	5.48700i	−0.423371	+	0.253096i
$471$	3.21778	+	31.9034i	0.148267	+	1.47003i
$472$	19.8027	−	0.904264i	0.911492	−	0.0416221i
$473$			22.6586i			1.04184i
$474$	−16.6128	−	22.3440i	−0.763052	−	1.02629i
$475$			7.88055i			0.361584i
$476$	16.0755	−	29.9092i	0.736820	−	1.37089i
$477$	5.00715	+	24.5698i	0.229262	+	1.12497i
$478$	−18.3782	−	30.7425i	−0.840602	−	1.40613i
$479$	−27.0376			−1.23538			−0.617690	−	0.786421i	$-0.711931\pi$
$479$	−27.0376			−1.23538			−0.617690	+	0.786421i	$0.711931\pi$
$480$	−5.29846	+	14.6503i	−0.241841	+	0.668694i
$481$	−2.73136			−0.124539
$482$	18.1963	+	30.4382i	0.828819	+	1.38642i
$483$	8.12283	−	0.819269i	0.369601	−	0.0372780i
$484$	−21.7133	+	40.3986i	−0.986967	+	1.83630i
$485$			4.39262i			0.199459i
$486$	−11.1330	+	19.0278i	−0.505004	+	0.863117i
$487$			20.2652i			0.918304i	0.888358	+	0.459152i	$0.151847\pi$
$487$			20.2652i			0.918304i	−0.888358	+	0.459152i	$0.848153\pi$
$488$	5.80557	−	0.265104i	0.262806	−	0.0120007i
$489$	17.2854	−	1.74340i	0.781671	−	0.0788393i
$490$	−29.3700	+	17.5577i	−1.32680	+	0.793177i
$491$	23.1339			1.04402			0.522010	−	0.852939i	$-0.325182\pi$
$491$	23.1339			1.04402			0.522010	+	0.852939i	$0.325182\pi$
$492$	11.8322	−	28.5688i	0.533436	−	1.28798i
$493$	0.445744			0.0200753
$494$	−6.25175	+	3.73738i	−0.281280	+	0.168152i
$495$	5.54861	+	27.2267i	0.249392	+	1.22375i
$496$	−7.77215	+	5.14155i	−0.348980	+	0.230862i
$497$			7.02082i			0.314927i
$498$	−31.7440	+	23.6017i	−1.42248	+	1.05762i
$499$			0.361191i			0.0161691i	0.999967	+	0.00808457i	$0.00257343\pi$
$499$			0.361191i			0.0161691i	−0.999967	+	0.00808457i	$0.997427\pi$
$500$	−20.9293	−	11.2490i	−0.935986	−	0.503070i
$501$	2.60269	+	25.8050i	0.116280	+	1.15288i
$502$	5.30243	+	8.86972i	0.236659	+	0.395875i
$503$	−29.5066			−1.31563			−0.657817	−	0.753177i	$-0.728520\pi$
$503$	−29.5066			−1.31563			−0.657817	+	0.753177i	$0.728520\pi$
$504$	9.76602	+	38.7848i	0.435013	+	1.72761i
$505$	−12.8180			−0.570392
$506$	−4.22702	−	7.07081i	−0.187914	−	0.314336i
$507$	1.80597	+	17.9057i	0.0802058	+	0.795219i
$508$	12.7928	+	6.87581i	0.567587	+	0.305065i
$509$		−	5.79948i		−	0.257057i	−0.991706	−	0.128529i	$-0.958975\pi$
$509$		−	5.79948i		−	0.257057i	0.991706	−	0.128529i	$-0.0410254\pi$
$510$	−11.2580	+	8.37034i	−0.498512	+	0.370645i
$511$		−	34.4792i		−	1.52527i
$512$	22.4157	−	3.08794i	0.990644	−	0.136469i
$513$	−15.8187	+	4.92034i	−0.698411	+	0.217238i
$514$	18.8287	−	11.2560i	0.830498	−	0.496482i
$515$	8.36957			0.368808
$516$	5.15601	−	12.4492i	0.226981	−	0.548045i
$517$	27.7016			1.21832
$518$	−9.67366	+	5.78304i	−0.425036	+	0.254092i
$519$	24.6919	−	2.49042i	1.08385	−	0.109318i
$520$	−0.331410	−	7.25761i	−0.0145333	−	0.318267i
$521$		−	17.3884i		−	0.761800i	−0.924616	−	0.380900i	$-0.875614\pi$
$521$		−	17.3884i		−	0.761800i	0.924616	−	0.380900i	$-0.124386\pi$
$522$	−0.387772	+	0.353963i	−0.0169723	+	0.0154926i
$523$			6.03381i			0.263840i	0.991260	+	0.131920i	$0.0421142\pi$
$523$			6.03381i			0.263840i	−0.991260	+	0.131920i	$0.957886\pi$
$524$	−8.75926	+	16.2970i	−0.382650	+	0.711938i
$525$	−20.0781	+	2.02508i	−0.876279	+	0.0883815i
$526$	−15.9424	−	26.6679i	−0.695121	−	1.16277i
$527$	−8.39155			−0.365542
$528$	31.2547	−	25.5320i	1.36019	−	1.11114i
$529$	1.00000			0.0434783
$530$	−9.64385	−	16.1319i	−0.418902	−	0.700725i
$531$	−20.6023	+	4.19861i	−0.894065	+	0.182204i
$532$	−14.2288	+	26.4734i	−0.616898	+	1.14777i
$533$			14.4203i			0.624613i
$534$	14.8338	+	19.9513i	0.641922	+	0.863376i
$535$		−	25.4342i		−	1.09962i
$536$	−1.42639	−	31.2369i	−0.0616108	−	1.34923i
$537$	−0.909100	−	9.01349i	−0.0392306	−	0.388961i
$538$	10.7478	−	6.42516i	0.463370	−	0.277008i
$539$	88.6418			3.81807
$540$	3.14695	−	16.2216i	0.135423	−	0.698068i
$541$	8.29951			0.356824			0.178412	−	0.983956i	$-0.442904\pi$
$541$	8.29951			0.356824			0.178412	+	0.983956i	$0.442904\pi$
$542$	17.0869	−	10.2148i	0.733946	−	0.438762i
$543$	0.409860	+	4.06365i	0.0175888	+	0.174388i
$544$	18.3689	+	8.81767i	0.787562	+	0.378054i
$545$			5.04859i			0.216258i
$546$	−11.1286	−	14.9678i	−0.476261	−	0.640564i
$547$			11.1722i			0.477687i	0.971058	+	0.238844i	$0.0767684\pi$
$547$			11.1722i			0.477687i	−0.971058	+	0.238844i	$0.923232\pi$
$548$	18.6282	+	10.0122i	0.795755	+	0.427700i
$549$	−6.04001	+	1.23091i	−0.257781	+	0.0525341i
$550$	10.4484	+	17.4777i	0.445520	+	0.745251i
$551$	−0.394539			−0.0168079
$552$	0.713450	+	4.84675i	0.0303664	+	0.206291i
$553$	53.5780			2.27837
$554$	17.5918	+	29.4269i	0.747404	+	1.25023i
$555$	4.63287	−	0.467271i	0.196654	−	0.0198346i
$556$	−1.15904	−	0.622956i	−0.0491542	−	0.0264192i
$557$			15.3463i			0.650243i	0.945672	+	0.325121i	$0.105405\pi$
$557$			15.3463i			0.650243i	−0.945672	+	0.325121i	$0.894595\pi$
$558$	7.30016	−	6.66369i	0.309040	−	0.282096i
$559$			6.28382i			0.265777i
$560$	−16.5401	−	25.0026i	−0.698948	−	1.05655i
$561$	36.1581	−	3.64690i	1.52659	−	0.153972i
$562$	−35.2791	+	21.0903i	−1.48816	+	0.889639i
$563$	−1.52294			−0.0641844			−0.0320922	−	0.999485i	$-0.510217\pi$
$563$	−1.52294			−0.0641844			−0.0320922	+	0.999485i	$0.510217\pi$
$564$	−15.2200	−	6.30358i	−0.640877	−	0.265429i
$565$	4.85224			0.204135
$566$	13.5189	−	8.08175i	0.568240	−	0.339701i
$567$	−16.6010	−	39.0384i	−0.697176	−	1.63946i
$568$	−4.20858	+	0.192180i	−0.176588	+	0.00806368i
$569$			12.3265i			0.516756i	0.966044	+	0.258378i	$0.0831880\pi$
$569$			12.3265i			0.516756i	−0.966044	+	0.258378i	$0.916812\pi$
$570$	9.96472	−	7.40879i	0.417376	−	0.310320i
$571$			11.2084i			0.469056i	0.972109	+	0.234528i	$0.0753544\pi$
$571$			11.2084i			0.469056i	−0.972109	+	0.234528i	$0.924646\pi$
$572$	−8.91013	+	16.5777i	−0.372551	+	0.693149i
$573$	0.887872	+	8.80301i	0.0370914	+	0.367751i
$574$	30.5318	+	51.0725i	1.27437	+	2.13173i
$575$	−2.47181			−0.103082
$576$	−22.9820	+	6.91583i	−0.957582	+	0.288160i
$577$	15.6586			0.651877			0.325938	−	0.945391i	$-0.394320\pi$
$577$	15.6586			0.651877			0.325938	+	0.945391i	$0.394320\pi$
$578$	−2.92146	−	4.88691i	−0.121517	−	0.203269i
$579$	−1.76954	−	17.5445i	−0.0735397	−	0.729126i
$580$	0.186310	−	0.346638i	0.00773610	−	0.0143934i
$581$		−	76.1180i		−	3.15790i
$582$	−5.43047	+	4.03756i	−0.225100	+	0.167362i
$583$			48.6879i			2.01645i
$584$	20.6684	−	0.943794i	0.855263	−	0.0390545i
$585$	1.53878	+	7.55068i	0.0636206	+	0.312182i
$586$	−22.1762	+	13.2572i	−0.916090	+	0.547650i
$587$	25.1744			1.03906			0.519528	−	0.854453i	$-0.326108\pi$
$587$	25.1744			1.03906			0.519528	+	0.854453i	$0.326108\pi$
$588$	−48.7021	−	20.1707i	−2.00844	−	0.831825i
$589$	7.42756			0.306047
$590$	13.5270	−	8.08659i	0.556896	−	0.332920i
$591$	12.2689	−	1.23744i	0.504676	−	0.0509016i
$592$	−3.73140	−	5.64052i	−0.153360	−	0.231824i
$593$		−	3.72999i		−	0.153172i	−0.997063	−	0.0765862i	$-0.975598\pi$
$593$		−	3.72999i		−	0.153172i	0.997063	−	0.0765862i	$-0.0244020\pi$
$594$	−28.5594	+	31.8855i	−1.17181	+	1.30828i
$595$		−	26.9952i		−	1.10670i
$596$	8.85908	+	4.76155i	0.362882	+	0.195041i
$597$	−9.93500	+	1.00204i	−0.406613	+	0.0410110i
$598$	−1.17226	−	1.96092i	−0.0479374	−	0.0801881i
$599$	−15.0630			−0.615456			−0.307728	−	0.951474i	$-0.599569\pi$
$599$	−15.0630			−0.615456			−0.307728	+	0.951474i	$0.599569\pi$
$600$	−1.76351	−	11.9802i	−0.0719951	−	0.489091i
$601$	−19.9651			−0.814393			−0.407197	−	0.913340i	$-0.633494\pi$
$601$	−19.9651			−0.814393			−0.407197	+	0.913340i	$0.633494\pi$
$602$	13.3046	+	22.2554i	0.542254	+	0.907064i
$603$	6.62293	+	32.4983i	0.269707	+	1.32343i
$604$	−36.5304	−	19.6342i	−1.48640	−	0.798906i
$605$			36.4626i			1.48241i
$606$	−11.7819	−	15.8465i	−0.478607	−	0.643719i
$607$		−	7.83568i		−	0.318040i	−0.987275	−	0.159020i	$-0.949167\pi$
$607$		−	7.83568i		−	0.318040i	0.987275	−	0.159020i	$-0.0508335\pi$
$608$	−16.2588	−	7.80472i	−0.659381	−	0.316523i
$609$	−0.101385	−	1.00521i	−0.00410833	−	0.0407330i
$610$	3.96572	−	2.37075i	0.160567	−	0.0959891i
$611$	7.68240			0.310797
$612$	−20.6960	−	6.22416i	−0.836587	−	0.251597i
$613$	35.7879			1.44546			0.722729	−	0.691131i	$-0.242887\pi$
$613$	35.7879			1.44546			0.722729	+	0.691131i	$0.242887\pi$
$614$	7.71412	−	4.61160i	0.311317	−	0.186109i
$615$	−2.46698	−	24.4594i	−0.0994782	−	0.986300i
$616$	3.54253	+	77.5786i	0.142733	+	3.12573i
$617$		−	29.1094i		−	1.17190i	−0.810346	−	0.585951i	$-0.800721\pi$
$617$		−	29.1094i		−	1.17190i	0.810346	−	0.585951i	$-0.199279\pi$
$618$	7.69306	+	10.3471i	0.309460	+	0.416220i
$619$		−	4.99308i		−	0.200689i	−0.994953	−	0.100344i	$-0.968006\pi$
$619$		−	4.99308i		−	0.200689i	0.994953	−	0.100344i	$-0.0319945\pi$
$620$	−3.50746	+	6.52579i	−0.140863	+	0.262082i
$621$	−1.54331	−	4.96167i	−0.0619310	−	0.199105i
$622$	−12.3948	−	20.7336i	−0.496986	−	0.831341i
$623$	−47.8406			−1.91669
$624$	8.66775	−	7.08069i	0.346988	−	0.283454i
$625$	−6.53112			−0.261245
$626$	8.83417	+	14.7775i	0.353084	+	0.590627i
$627$	−32.0044	+	3.22796i	−1.27813	+	0.128912i
$628$	17.5290	−	32.6135i	0.699483	−	1.30142i
$629$		−	6.09004i		−	0.242826i
$630$	21.4368	+	23.4843i	0.854062	+	0.935636i
$631$		−	18.0503i		−	0.718571i	−0.933228	−	0.359286i	$-0.883020\pi$
$631$		−	18.0503i		−	0.718571i	0.933228	−	0.359286i	$-0.116980\pi$
$632$	1.46658	+	32.1170i	0.0583375	+	1.27755i
$633$	−20.2364	+	2.04104i	−0.804324	+	0.0811241i
$634$	16.9885	−	10.1559i	0.674698	−	0.403343i
$635$	11.5464			0.458204
$636$	11.0791	−	26.7504i	0.439313	−	1.06072i
$637$	24.5827			0.974003
$638$	−0.875018	+	0.523097i	−0.0346423	+	0.0207096i
$639$	4.37853	−	0.892315i	0.173212	−	0.0352994i
$640$	14.5349	−	10.5993i	0.574543	−	0.418973i
$641$			12.0996i			0.477907i	0.971031	+	0.238953i	$0.0768043\pi$
$641$			12.0996i			0.477907i	−0.971031	+	0.238953i	$0.923196\pi$
$642$	31.4436	−	23.3784i	1.24098	−	0.922670i
$643$		−	6.78783i		−	0.267686i	−0.991003	−	0.133843i	$-0.957268\pi$
$643$		−	6.78783i		−	0.267686i	0.991003	−	0.133843i	$-0.0427317\pi$
$644$	−8.30363	−	4.46301i	−0.327209	−	0.175867i
$645$	−1.07501	−	10.6585i	−0.0423287	−	0.419677i
$646$	−8.33313	−	13.9394i	−0.327863	−	0.548437i
$647$	23.5484			0.925783			0.462892	−	0.886415i	$-0.346812\pi$
$647$	23.5484			0.925783			0.462892	+	0.886415i	$0.346812\pi$
$648$	22.9469	−	11.0200i	0.901440	−	0.432905i
$649$	−40.8259			−1.60256
$650$	2.89761	+	4.84702i	0.113654	+	0.190116i
$651$	1.90867	+	18.9239i	0.0748067	+	0.741688i
$652$	−17.6701	−	9.49726i	−0.692015	−	0.371942i
$653$			16.7517i			0.655544i	0.944757	+	0.327772i	$0.106298\pi$
$653$			16.7517i			0.655544i	−0.944757	+	0.327772i	$0.893702\pi$
$654$	−6.24142	+	4.64051i	−0.244059	+	0.181458i
$655$			14.7092i			0.574736i
$656$	−29.7794	+	19.7001i	−1.16269	+	0.769159i
$657$	−21.5030	+	4.38216i	−0.838911	+	0.170964i
$658$	27.2088	−	16.2658i	1.06071	−	0.634105i
$659$	−0.538650			−0.0209828			−0.0104914	−	0.999945i	$-0.503340\pi$
$659$	−0.538650			−0.0209828			−0.0104914	+	0.999945i	$0.503340\pi$
$660$	12.2771	−	29.6431i	0.477886	−	1.15386i
$661$	43.5108			1.69238			0.846188	−	0.532885i	$-0.178892\pi$
$661$	43.5108			1.69238			0.846188	+	0.532885i	$0.178892\pi$
$662$	−20.4618	+	12.2323i	−0.795269	+	0.475422i
$663$	10.0276	−	1.01138i	0.389439	−	0.0392788i
$664$	45.6284	−	2.08356i	1.77073	−	0.0808580i
$665$			23.8941i			0.926574i
$666$	4.83607	+	5.29798i	0.187394	+	0.205292i
$667$		−	0.123751i		−	0.00479165i
$668$	14.1783	−	26.3794i	0.548574	−	1.02065i
$669$	−33.0925	+	3.33771i	−1.27943	+	0.129043i
$670$	−12.7559	−	21.3376i	−0.492802	−	0.824342i
$671$	−11.9690			−0.462057
$672$	15.7069	−	43.4298i	0.605905	−	1.67534i
$673$	24.4913			0.944072			0.472036	−	0.881579i	$-0.343519\pi$
$673$	24.4913			0.944072			0.472036	+	0.881579i	$0.343519\pi$
$674$	−15.3157	−	25.6196i	−0.589939	−	0.986830i
$675$	3.81477	+	12.2643i	0.146831	+	0.472053i
$676$	9.83809	−	18.3042i	0.378388	−	0.704009i
$677$		−	26.5951i		−	1.02213i	−0.859542	−	0.511066i	$-0.829251\pi$
$677$		−	26.5951i		−	1.02213i	0.859542	−	0.511066i	$-0.170749\pi$
$678$	4.46004	+	5.99868i	0.171287	+	0.230378i
$679$		−	13.0216i		−	0.499722i
$680$	16.1821	−	0.738936i	0.620556	−	0.0283369i
$681$	−1.90647	−	18.9021i	−0.0730560	−	0.724330i
$682$	16.4730	−	9.84779i	0.630785	−	0.377091i
$683$	32.8706			1.25776			0.628878	−	0.777504i	$-0.283514\pi$
$683$	32.8706			1.25776			0.628878	+	0.777504i	$0.283514\pi$
$684$	18.3185	+	5.50915i	0.700427	+	0.210648i
$685$	16.8132			0.642401
$686$	47.0144	−	28.1058i	1.79502	−	1.07308i
$687$	2.52821	+	25.0665i	0.0964572	+	0.956348i
$688$	−12.9767	+	8.58454i	−0.494732	+	0.327283i
$689$			13.5024i			0.514402i
$690$	2.32384	+	3.12553i	0.0884670	+	0.118987i
$691$		−	24.9097i		−	0.947608i	−0.880630	−	0.473804i	$-0.842881\pi$
$691$		−	24.9097i		−	0.947608i	0.880630	−	0.473804i	$-0.157119\pi$
$692$	−25.2415	−	13.5667i	−0.959538	−	0.515729i
$693$	−16.4484	−	80.7113i	−0.624823	−	3.06597i
$694$	−16.4234	−	27.4725i	−0.623424	−	1.04284i
$695$	−1.04611			−0.0396814
$696$	0.599789	−	0.0882900i	0.0227350	−	0.00334662i
$697$	−32.1526			−1.21787
$698$	12.1111	+	20.2591i	0.458412	+	0.766816i
$699$	27.6046	−	2.78420i	1.04410	−	0.105308i
$700$	20.5250	+	11.0317i	0.775771	+	0.416959i
$701$		−	36.9927i		−	1.39719i	−0.715515	−	0.698597i	$-0.753808\pi$
$701$		−	36.9927i		−	1.39719i	0.715515	−	0.698597i	$-0.246192\pi$
$702$	−7.92028	+	8.84270i	−0.298932	+	0.333746i
$703$			5.39043i			0.203304i
$704$	−46.4070	+	4.24709i	−1.74903	+	0.160068i
$705$	−13.0307	+	1.31428i	−0.490765	+	0.0494986i
$706$	−38.4898	+	23.0097i	−1.44858	+	0.865981i
$707$	37.9978			1.42905
$708$	22.4308	+	9.29004i	0.843001	+	0.349141i
$709$	4.68972			0.176126			0.0880631	−	0.996115i	$-0.471932\pi$
$709$	4.68972			0.176126			0.0880631	+	0.996115i	$0.471932\pi$
$710$	−2.87483	+	1.71861i	−0.107891	+	0.0644983i
$711$	−6.80953	−	33.4139i	−0.255377	−	1.25312i
$712$	−1.30953	−	28.6777i	−0.0490768	−	1.07474i
$713$			2.32972i			0.0872489i
$714$	33.3734	−	24.8132i	1.24897	−	0.928610i
$715$			14.9626i			0.559568i
$716$	−4.95237	+	9.21411i	−0.185079	+	0.344348i
$717$	−4.40207	−	43.6453i	−0.164398	−	1.62996i
$718$	−6.16724	−	10.3164i	−0.230160	−	0.385003i
$719$	9.69447			0.361543			0.180771	−	0.983525i	$-0.442141\pi$
$719$	9.69447			0.361543			0.180771	+	0.983525i	$0.442141\pi$
$720$	−13.4907	+	13.4930i	−0.502769	+	0.502853i
$721$	−24.8109			−0.924007
$722$	−6.41156	−	10.7250i	−0.238614	−	0.399145i
$723$	4.35849	+	43.2132i	0.162094	+	1.60712i
$724$	2.23273	−	4.15410i	0.0829788	−	0.154386i
$725$			0.305888i			0.0113604i
$726$	−45.0776	+	33.5153i	−1.67299	+	1.24387i
$727$		−	11.2233i		−	0.416248i	−0.978102	−	0.208124i	$-0.933264\pi$
$727$		−	11.2233i		−	0.416248i	0.978102	−	0.208124i	$-0.0667358\pi$
$728$	0.982436	+	21.5146i	0.0364115	+	0.797384i
$729$	−22.2364	+	15.3148i	−0.823570	+	0.567215i
$730$	14.1183	−	8.44010i	0.522542	−	0.312382i
$731$	−14.0109			−0.518211
$732$	6.57606	+	2.72357i	0.243058	+	0.100666i
$733$	−38.4431			−1.41993			−0.709965	−	0.704237i	$-0.751289\pi$
$733$	−38.4431			−1.41993			−0.709965	+	0.704237i	$0.751289\pi$
$734$	11.7812	−	7.04296i	0.434853	−	0.259960i
$735$	−41.6967	+	4.20553i	−1.53801	+	0.155123i
$736$	2.44803	−	5.09972i	0.0902354	−	0.187978i
$737$			64.3992i			2.37217i
$738$	27.9709	−	25.5322i	1.02962	−	0.939854i
$739$		−	32.3424i		−	1.18973i	−0.803825	−	0.594866i	$-0.797205\pi$
$739$		−	32.3424i		−	1.18973i	0.803825	−	0.594866i	$-0.202795\pi$
$740$	−4.73599	−	2.54548i	−0.174098	−	0.0935738i
$741$	−8.87565	+	0.895199i	−0.326055	+	0.0328859i
$742$	28.5884	+	47.8217i	1.04951	+	1.75559i
$743$	−7.90090			−0.289856			−0.144928	−	0.989442i	$-0.546295\pi$
$743$	−7.90090			−0.289856			−0.144928	+	0.989442i	$0.546295\pi$
$744$	−11.2916	+	1.66214i	−0.413970	+	0.0609371i
$745$	7.99595			0.292949
$746$	−15.6630	−	26.2006i	−0.573465	−	0.959272i
$747$	−47.4709	+	9.67425i	−1.73687	+	0.353962i
$748$	−36.9629	−	19.8667i	−1.35150	−	0.726398i
$749$			75.3976i			2.75497i
$750$	−17.3633	−	23.3534i	−0.634017	−	0.852744i
$751$			42.9148i			1.56598i	0.622032	+	0.782992i	$0.286307\pi$
$751$			42.9148i			1.56598i	−0.622032	+	0.782992i	$0.713693\pi$
$752$	10.4952	+	15.8649i	0.382720	+	0.578533i
$753$	1.27007	+	12.5924i	0.0462839	+	0.458892i
$754$	−0.242666	+	0.145069i	−0.00883736	+	0.00528309i
$755$	−32.9713			−1.19995
$756$	−9.32888	+	48.0877i	−0.339288	+	1.74893i
$757$	−36.4035			−1.32311			−0.661553	−	0.749898i	$-0.730102\pi$
$757$	−36.4035			−1.32311			−0.661553	+	0.749898i	$0.730102\pi$
$758$	−21.3311	+	12.7520i	−0.774782	+	0.463174i
$759$	−1.01248	−	10.0385i	−0.0367507	−	0.364373i
$760$	−14.3232	+	0.654049i	−0.519556	+	0.0237249i
$761$			31.5511i			1.14373i	0.820349	+	0.571863i	$0.193779\pi$
$761$			31.5511i			1.14373i	−0.820349	+	0.571863i	$0.806221\pi$
$762$	10.6131	+	14.2744i	0.384471	+	0.517108i
$763$		−	14.9661i		−	0.541810i
$764$	4.83673	−	8.99895i	0.174987	−	0.325571i
$765$	−16.8356	+	3.43097i	−0.608691	+	0.124047i
$766$	6.41622	+	10.7328i	0.231828	+	0.387793i
$767$	−11.3221			−0.408817
$768$	26.4636	+	8.22657i	0.954924	+	0.296851i
$769$	15.9321			0.574527			0.287264	−	0.957852i	$-0.407254\pi$
$769$	15.9321			0.574527			0.287264	+	0.957852i	$0.407254\pi$
$770$	31.6799	+	52.9930i	1.14166	+	1.90974i
$771$	26.7312	−	2.69611i	0.962701	−	0.0970981i
$772$	−9.63967	+	17.9351i	−0.346939	+	0.645497i
$773$		−	11.8269i		−	0.425382i	−0.977119	−	0.212691i	$-0.931777\pi$
$773$		−	11.8269i		−	0.425382i	0.977119	−	0.212691i	$-0.0682228\pi$
$774$	12.1886	−	11.1260i	0.438112	−	0.399915i
$775$		−	5.75863i		−	0.206856i
$776$	7.80569	−	0.356437i	0.280208	−	0.0127953i
$777$	−13.7338	+	1.38519i	−0.492696	+	0.0496933i
$778$	−11.0330	+	6.59567i	−0.395553	+	0.236466i
$779$	28.4590			1.01965
$780$	3.40477	−	8.22081i	0.121910	−	0.294352i
$781$	8.67657			0.310472
$782$	4.37222	−	2.61377i	0.156350	−	0.0934681i
$783$	−0.614011	+	0.190986i	−0.0219430	+	0.00682529i
$784$	33.5833	+	50.7657i	1.19940	+	1.81306i
$785$		−	29.4360i		−	1.05062i
$786$	−18.1846	+	13.5203i	−0.648622	+	0.482252i
$787$		−	35.9134i		−	1.28018i	−0.768302	−	0.640088i	$-0.778898\pi$
$787$		−	35.9134i		−	1.28018i	0.768302	−	0.640088i	$-0.221102\pi$
$788$	−12.5420	−	6.74103i	−0.446790	−	0.240139i
$789$	−3.81862	−	37.8606i	−0.135946	−	1.34787i
$790$	13.1153	+	21.9387i	0.466620	+	0.780545i
$791$	−14.3841			−0.511439
$792$	47.9316	−	12.0692i	1.70318	−	0.428860i
$793$	−3.31931			−0.117872
$794$	12.5202	+	20.9434i	0.444326	+	0.743254i
$795$	−2.30995	−	22.9026i	−0.0819256	−	0.812270i
$796$	10.1561	+	5.45869i	0.359975	+	0.193478i
$797$			7.43422i			0.263334i	0.991294	+	0.131667i	$0.0420329\pi$
$797$			7.43422i			0.263334i	−0.991294	+	0.131667i	$0.957967\pi$
$798$	−29.5396	+	21.9627i	−1.04569	+	0.777473i
$799$			17.1292i			0.605989i
$800$	−6.05105	+	12.6055i	−0.213937	+	0.445673i
$801$	6.08033	+	29.8358i	0.214838	+	1.05419i
$802$	−1.46275	+	0.874449i	−0.0516514	+	0.0308779i
$803$	−42.6106			−1.50370
$804$	14.6542	−	35.3825i	0.516814	−	1.24785i
$805$	−7.49462			−0.264150
$806$	4.56841	−	2.73105i	0.160915	−	0.0961972i
$807$	15.2587	−	1.53899i	0.537131	−	0.0541751i
$808$	1.04011	+	22.7775i	0.0365909	+	0.801311i
$809$		−	34.1297i		−	1.19993i	−0.800025	−	0.599967i	$-0.795180\pi$
$809$		−	34.1297i		−	1.19993i	0.800025	−	0.599967i	$-0.204820\pi$
$810$	11.9214	−	16.3538i	0.418877	−	0.574613i
$811$			53.0427i			1.86258i	0.364278	+	0.931290i	$0.381316\pi$
$811$			53.0427i			1.86258i	−0.364278	+	0.931290i	$0.618684\pi$
$812$	−0.552301	+	1.02758i	−0.0193820	+	0.0360610i
$813$	24.2584	−	2.44670i	0.850780	−	0.0858097i
$814$	7.14688	+	11.9551i	0.250498	+	0.419024i
$815$	−15.9485			−0.558652
$816$	15.7876	+	19.3263i	0.552678	+	0.676554i
$817$	12.4014			0.433868
$818$	−1.21934	−	2.03967i	−0.0426332	−	0.0713154i
$819$	−4.56158	−	22.3834i	−0.159394	−	0.782138i
$820$	−13.4390	+	25.0039i	−0.469310	+	0.873173i
$821$			14.2515i			0.497382i	0.968583	+	0.248691i	$0.0800003\pi$
$821$			14.2515i			0.497382i	−0.968583	+	0.248691i	$0.920000\pi$
$822$	15.4542	+	20.7857i	0.539028	+	0.724985i
$823$		−	16.0153i		−	0.558258i	−0.960254	−	0.279129i	$-0.909954\pi$
$823$		−	16.0153i		−	0.558258i	0.960254	−	0.279129i	$-0.0900457\pi$
$824$	−0.679145	−	14.8727i	−0.0236591	−	0.518117i
$825$	2.50266	+	24.8132i	0.0871314	+	0.863884i
$826$	−40.0996	+	23.9720i	−1.39524	+	0.834094i
$827$	−19.5614			−0.680217			−0.340108	−	0.940386i	$-0.610464\pi$
$827$	−19.5614			−0.680217			−0.340108	+	0.940386i	$0.610464\pi$
$828$	−1.72800	+	5.74578i	−0.0600521	+	0.199680i
$829$	−53.0745			−1.84335			−0.921676	−	0.387960i	$-0.873180\pi$
$829$	−53.0745			−1.84335			−0.921676	+	0.387960i	$0.873180\pi$
$830$	31.1682	−	18.6328i	1.08186	−	0.646752i
$831$	4.21369	+	41.7776i	0.146171	+	1.44925i
$832$	−12.8699	+	1.17783i	−0.446183	+	0.0408339i
$833$			54.8115i			1.89911i
$834$	−0.961557	−	1.29328i	−0.0332960	−	0.0447826i
$835$		−	23.8092i		−	0.823953i
$836$	32.7167	+	17.5845i	1.13153	+	0.608172i
$837$	11.5593	−	3.59549i	0.399549	−	0.124278i
$838$	9.55383	+	15.9813i	0.330031	+	0.552065i
$839$	−13.6757			−0.472136			−0.236068	−	0.971737i	$-0.575859\pi$
$839$	−13.6757			−0.472136			−0.236068	+	0.971737i	$0.575859\pi$
$840$	−5.34703	−	36.3245i	−0.184490	−	1.25332i
$841$	28.9847			0.999472
$842$	−8.80343	−	14.7261i	−0.303386	−	0.507494i
$843$	−50.0859	+	5.05167i	−1.72505	+	0.173989i
$844$	20.6868	+	11.1187i	0.712069	+	0.382720i
$845$		−	16.5209i		−	0.568335i
$846$	−13.6023	−	14.9015i	−0.467655	−	0.512323i
$847$		−	108.090i		−	3.71403i
$848$	−27.8839	+	18.4461i	−0.957535	+	0.633443i
$849$	19.1928	−	1.93579i	0.658696	−	0.0664361i
$850$	−10.8073	+	6.46073i	−0.370687	+	0.221601i
$851$	−1.69076			−0.0579586
$852$	−4.76713	−	1.97438i	−0.163319	−	0.0676410i
$853$	12.5112			0.428375			0.214188	−	0.976793i	$-0.431290\pi$
$853$	12.5112			0.428375			0.214188	+	0.976793i	$0.431290\pi$
$854$	−11.7560	+	7.02791i	−0.402283	+	0.240490i
$855$	14.9015	−	3.03683i	0.509622	−	0.103858i
$856$	−45.1966	+	2.06385i	−1.54479	+	0.0705408i
$857$		−	3.82985i		−	0.130825i	−0.997858	−	0.0654126i	$-0.979164\pi$
$857$		−	3.82985i		−	0.130825i	0.997858	−	0.0654126i	$-0.0208364\pi$
$858$	−18.4978	+	13.7531i	−0.631503	+	0.469524i
$859$		−	50.8176i		−	1.73387i	−0.498419	−	0.866937i	$-0.666086\pi$
$859$		−	50.8176i		−	1.73387i	0.498419	−	0.866937i	$-0.333914\pi$
$860$	−5.85620	+	10.8957i	−0.199695	+	0.371541i
$861$	7.31316	+	72.5080i	0.249232	+	2.47107i
$862$	−1.20352	−	2.01320i	−0.0409919	−	0.0685699i
$863$	52.9727			1.80321			0.901606	−	0.432558i	$-0.142389\pi$
$863$	52.9727			1.80321			0.901606	+	0.432558i	$0.142389\pi$
$864$	−29.0812	−	4.27584i	−0.989363	−	0.145467i
$865$	−22.7822			−0.774619
$866$	−16.1253	−	26.9739i	−0.547961	−	0.916610i
$867$	−0.699764	−	6.93798i	−0.0237652	−	0.235626i
$868$	10.3976	−	19.3452i	0.352917	−	0.656618i
$869$		−	66.2136i		−	2.24614i
$870$	0.386787	−	0.287577i	0.0131133	−	0.00974977i
$871$			17.8596i			0.605149i
$872$	8.97134	−	0.409665i	0.303808	−	0.0138730i
$873$	−8.12089	+	1.65498i	−0.274851	+	0.0560127i
$874$	−3.86995	+	2.31351i	−0.130903	+	0.0782555i
$875$	55.9983			1.89309
$876$	23.4114	+	9.69616i	0.790997	+	0.327603i
$877$	58.4665			1.97427			0.987137	−	0.159876i	$-0.0511094\pi$
$877$	58.4665			1.97427			0.987137	+	0.159876i	$0.0511094\pi$
$878$	−9.21294	+	5.50761i	−0.310922	+	0.185873i
$879$	−31.4837	+	3.17545i	−1.06192	+	0.107105i
$880$	−30.8991	+	20.4409i	−1.04161	+	0.689061i
$881$			36.5203i			1.23040i	0.788371	+	0.615201i	$0.210925\pi$
$881$			36.5203i			1.23040i	−0.788371	+	0.615201i	$0.789075\pi$
$882$	−43.5255	−	47.6828i	−1.46558	−	1.60556i
$883$			34.9516i			1.17622i	0.808782	+	0.588108i	$0.200127\pi$
$883$			34.9516i			1.17622i	−0.808782	+	0.588108i	$0.799873\pi$
$884$	−10.2508	−	5.50956i	−0.344771	−	0.185306i
$885$	19.2043	−	1.93695i	0.645546	−	0.0651098i
$886$	24.0935	+	40.3027i	0.809436	+	1.35400i
$887$	−16.7953			−0.563933			−0.281966	−	0.959424i	$-0.590987\pi$
$887$	−16.7953			−0.563933			−0.281966	+	0.959424i	$0.590987\pi$
$888$	−1.20627	−	8.19470i	−0.0404799	−	0.274996i
$889$	−34.2283			−1.14798
$890$	−11.7108	−	19.5894i	−0.392547	−	0.656639i
$891$	−48.2450	+	20.5161i	−1.61627	+	0.687315i
$892$	33.8291	+	18.1823i	1.13268	+	0.608790i
$893$		−	15.1615i		−	0.507360i
$894$	7.34964	+	9.88516i	0.245809	+	0.330609i
$895$			8.31639i			0.277986i
$896$	−43.0876	+	31.4207i	−1.43946	+	1.04969i
$897$	−0.280788	−	2.78393i	−0.00937523	−	0.0929528i
$898$	22.6066	−	13.5145i	0.754393	−	0.450986i
$899$	0.288305			0.00961552
$900$	4.27128	−	14.2025i	0.142376	−	0.473416i
$901$	−30.1060			−1.00298
$902$	63.1172	−	37.7323i	2.10157	−	1.25635i
$903$	3.18679	+	31.5962i	0.106050	+	1.05146i
$904$	−0.393733	−	8.62244i	−0.0130954	−	0.286778i
$905$		−	3.74937i		−	0.124633i
$906$	−30.3062	−	40.7614i	−1.00686	−	1.35421i
$907$		−	25.0296i		−	0.831095i	−0.909572	−	0.415547i	$-0.863590\pi$
$907$		−	25.0296i		−	0.831095i	0.909572	−	0.415547i	$-0.136410\pi$
$908$	−10.3856	+	19.3228i	−0.344657	+	0.641251i
$909$	−4.82935	−	23.6973i	−0.160180	−	0.785990i
$910$	8.78567	+	14.6964i	0.291242	+	0.487179i
$911$	55.7281			1.84635			0.923177	−	0.384375i	$-0.125583\pi$
$911$	55.7281			1.84635			0.923177	+	0.384375i	$0.125583\pi$
$912$	−13.9740	−	17.1061i	−0.462726	−	0.566441i
$913$	−94.0692			−3.11324
$914$	−3.36987	−	5.63700i	−0.111465	−	0.186455i
$915$	5.63015	−	0.567857i	0.186127	−	0.0187728i
$916$	13.7726	−	25.6245i	0.455058	−	0.846656i
$917$		−	43.6043i		−	1.43994i
$918$	−19.7163	−	17.6597i	−0.650736	−	0.582856i
$919$			1.07860i			0.0355797i	0.999842	+	0.0177899i	$0.00566299\pi$
$919$			1.07860i			0.0355797i	−0.999842	+	0.0177899i	$0.994337\pi$
$920$	−0.205149	−	4.49260i	−0.00676356	−	0.148117i
$921$	10.9518	−	1.10460i	0.360874	−	0.0363977i
$922$	−25.0270	+	14.9615i	−0.824221	+	0.492730i
$923$	2.40624			0.0792024
$924$	−36.3945	+	87.8745i	−1.19729	+	2.89086i
$925$	4.17924			0.137413
$926$	−33.2920	+	19.9024i	−1.09404	+	0.654033i
$927$	3.15336	+	15.4733i	0.103570	+	0.508210i
$928$	−0.631095	−	0.302945i	−0.0207167	−	0.00994466i
$929$		−	6.81266i		−	0.223516i	−0.993735	−	0.111758i	$-0.964352\pi$
$929$		−	6.81266i		−	0.223516i	0.993735	−	0.111758i	$-0.0356482\pi$
$930$	−7.28162	+	5.41390i	−0.238774	+	0.177529i
$931$		−	48.5149i		−	1.59001i
$932$	−28.2190	−	15.1671i	−0.924344	−	0.496813i
$933$	−2.96888	−	29.4356i	−0.0971966	−	0.963678i
$934$	−11.9379	−	19.9693i	−0.390620	−	0.653416i
$935$	−33.3616			−1.09104
$936$	13.2927	−	3.34710i	0.434486	−	0.109404i
$937$	−34.7265			−1.13446			−0.567232	−	0.823558i	$-0.691986\pi$
$937$	−34.7265			−1.13446			−0.567232	+	0.823558i	$0.691986\pi$
$938$	37.8137	+	63.2534i	1.23466	+	2.06530i
$939$	2.11601	+	20.9797i	0.0690534	+	0.684646i
$940$	13.3208	+	7.15960i	0.434476	+	0.233520i
$941$			29.0855i			0.948161i	0.880481	+	0.474081i	$0.157219\pi$
$941$			29.0855i			0.948161i	−0.880481	+	0.474081i	$0.842781\pi$
$942$	36.3909	−	27.0567i	1.18568	−	0.881555i
$943$			8.92645i			0.290685i
$944$	−15.4675	−	23.3813i	−0.503425	−	0.760995i
$945$	11.5665	+	37.1858i	0.376259	+	1.20965i
$946$	27.5041	−	16.4423i	0.894234	−	0.534584i
$947$	42.6576			1.38619			0.693093	−	0.720849i	$-0.256248\pi$
$947$	42.6576			1.38619			0.693093	+	0.720849i	$0.256248\pi$
$948$	−15.0671	+	36.3794i	−0.489356	+	1.18155i
$949$	−11.8171			−0.383598
$950$	9.56579	−	5.71855i	0.310355	−	0.185534i
$951$	24.1186	−	2.43260i	0.782100	−	0.0788826i
$952$	−47.9705	+	2.19051i	−1.55473	+	0.0709950i
$953$			8.20879i			0.265909i	0.991122	+	0.132954i	$0.0424464\pi$
$953$			8.20879i			0.265909i	−0.991122	+	0.132954i	$0.957554\pi$
$954$	26.1905	−	23.9071i	0.847949	−	0.774020i
$955$		−	8.12220i		−	0.262828i
$956$	−23.9805	+	44.6168i	−0.775584	+	1.44301i
$957$	−1.24227	+	0.125295i	−0.0401569	+	0.00405022i
$958$	19.6199	+	32.8196i	0.633892	+	1.06035i
$959$	−49.8415			−1.60946
$960$	21.6281	−	4.19955i	0.698045	−	0.135540i
$961$	25.5724			0.824916
$962$	1.98202	+	3.31545i	0.0639028	+	0.106894i
$963$	47.0217	−	9.58270i	1.51525	−	0.308798i
$964$	23.7431	−	44.1751i	0.764713	−	1.42278i
$965$			16.1877i			0.521099i
$966$	−6.88882	−	9.26537i	−0.221644	−	0.298108i
$967$		−	43.8279i		−	1.40941i	−0.709501	−	0.704704i	$-0.751080\pi$
$967$		−	43.8279i		−	1.40941i	0.709501	−	0.704704i	$-0.248920\pi$
$968$	64.7940	−	2.95874i	2.08256	−	0.0950974i
$969$	−1.99600	−	19.7898i	−0.0641208	−	0.635741i
$970$	5.33197	−	3.18752i	0.171199	−	0.102345i
$971$	−59.1732			−1.89896			−0.949478	−	0.313832i	$-0.898387\pi$
$971$	−59.1732			−1.89896			−0.949478	+	0.313832i	$0.898387\pi$
$972$	31.1755	−	0.293778i	0.999956	−	0.00942294i
$973$	3.10112			0.0994174
$974$	24.5989	−	14.7055i	0.788199	−	0.471195i
$975$	0.694053	+	6.88135i	0.0222275	+	0.220380i
$976$	−4.53463	−	6.85471i	−0.145150	−	0.219414i
$977$		−	26.0725i		−	0.834134i	−0.908876	−	0.417067i	$-0.863058\pi$
$977$		−	26.0725i		−	0.834134i	0.908876	−	0.417067i	$-0.136942\pi$
$978$	−14.6594	−	19.7167i	−0.468756	−	0.630470i
$979$			59.1231i			1.88958i
$980$	42.6248	+	22.9098i	1.36160	+	0.731828i
$981$	−9.33361	+	1.90213i	−0.297999	+	0.0607302i
$982$	−16.7872	−	28.0811i	−0.535702	−	0.896104i
$983$	37.2168			1.18703			0.593515	−	0.804823i	$-0.297740\pi$
$983$	37.2168			1.18703			0.593515	+	0.804823i	$0.297740\pi$
$984$	−43.2643	+	6.36857i	−1.37921	+	0.203023i
$985$	−11.3200			−0.360687
$986$	−0.323456	−	0.541066i	−0.0103009	−	0.0172310i
$987$	38.6285	−	3.89607i	1.22956	−	0.124013i
$988$	9.07321	+	4.87664i	0.288657	+	0.155147i
$989$			3.88980i			0.123689i
$990$	29.0227	−	26.4923i	0.922402	−	0.841981i
$991$			13.8323i			0.439398i	0.975568	+	0.219699i	$0.0705075\pi$
$991$			13.8323i			0.439398i	−0.975568	+	0.219699i	$0.929493\pi$
$992$	11.8809	+	5.70323i	0.377220	+	0.181078i
$993$	−29.0497	+	2.92995i	−0.921864	+	0.0929793i
$994$	8.52221	−	5.09468i	0.270308	−	0.161593i
$995$	9.16664			0.290602
$996$	51.6840	+	21.4057i	1.63767	+	0.678265i
$997$	43.7155			1.38448			0.692242	−	0.721665i	$-0.256623\pi$
$997$	43.7155			1.38448			0.692242	+	0.721665i	$0.256623\pi$
$998$	0.438431	−	0.262100i	0.0138783	−	0.00829662i
$999$	2.60937	+	8.38900i	0.0825569	+	0.265416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.c.b.47.7	yes	22
3.2	odd	2		276.2.c.a.47.16	yes	22
4.3	odd	2		276.2.c.a.47.15	✓	22
12.11	even	2	inner	276.2.c.b.47.8	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.c.a.47.15	✓	22	4.3	odd	2
276.2.c.a.47.16	yes	22	3.2	odd	2
276.2.c.b.47.7	yes	22	1.1	even	1	trivial
276.2.c.b.47.8	yes	22	12.11	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.725653 - 1.21385i) q^{2} +(-0.173813 - 1.72331i) q^{3} +(-0.946854 + 1.76167i) q^{4} +1.59003i q^{5} +(-1.96571 + 1.46151i) q^{6} -4.71351i q^{7} +(2.82548 - 0.129022i) q^{8} +(-2.93958 + 0.599066i) q^{9} +O(q^{10})\)	\(q+(-0.725653 - 1.21385i) q^{2} +(-0.173813 - 1.72331i) q^{3} +(-0.946854 + 1.76167i) q^{4} +1.59003i q^{5} +(-1.96571 + 1.46151i) q^{6} -4.71351i q^{7} +(2.82548 - 0.129022i) q^{8} +(-2.93958 + 0.599066i) q^{9} +(1.93005 - 1.15381i) q^{10} -5.82512 q^{11} +(3.20047 + 1.32552i) q^{12} -1.61546 q^{13} +(-5.72148 + 3.42037i) q^{14} +(2.74011 - 0.276367i) q^{15} +(-2.20693 - 3.33608i) q^{16} -3.60195i q^{17} +(2.86029 + 3.13349i) q^{18} +3.18817i q^{19} +(-2.80110 - 1.50553i) q^{20} +(-8.12283 + 0.819269i) q^{21} +(4.22702 + 7.07081i) q^{22} -1.00000 q^{23} +(-0.713450 - 4.84675i) q^{24} +2.47181 q^{25} +(1.17226 + 1.96092i) q^{26} +(1.54331 + 4.96167i) q^{27} +(8.30363 + 4.46301i) q^{28} +0.123751i q^{29} +(-2.32384 - 3.12553i) q^{30} -2.32972i q^{31} +(-2.44803 + 5.09972i) q^{32} +(1.01248 + 10.0385i) q^{33} +(-4.37222 + 2.61377i) q^{34} +7.49462 q^{35} +(1.72800 - 5.74578i) q^{36} +1.69076 q^{37} +(3.86995 - 2.31351i) q^{38} +(0.280788 + 2.78393i) q^{39} +(0.205149 + 4.49260i) q^{40} -8.92645i q^{41} +(6.88882 + 9.26537i) q^{42} -3.88980i q^{43} +(5.51554 - 10.2619i) q^{44} +(-0.952532 - 4.67401i) q^{45} +(0.725653 + 1.21385i) q^{46} -4.75555 q^{47} +(-5.36550 + 4.38308i) q^{48} -15.2172 q^{49} +(-1.79368 - 3.00040i) q^{50} +(-6.20727 + 0.626065i) q^{51} +(1.52960 - 2.84590i) q^{52} -8.35826i q^{53} +(4.90281 - 5.47380i) q^{54} -9.26211i q^{55} +(-0.608147 - 13.3179i) q^{56} +(5.49420 - 0.554145i) q^{57} +(0.150215 - 0.0898002i) q^{58} +7.00860 q^{59} +(-2.10762 + 5.08884i) q^{60} +2.05472 q^{61} +(-2.82793 + 1.69057i) q^{62} +(2.82370 + 13.8557i) q^{63} +(7.96671 - 0.729099i) q^{64} -2.56863i q^{65} +(11.4505 - 8.51345i) q^{66} -11.0554i q^{67} +(6.34543 + 3.41052i) q^{68} +(0.173813 + 1.72331i) q^{69} +(-5.43849 - 9.09732i) q^{70} -1.48951 q^{71} +(-8.22843 + 2.07192i) q^{72} +7.31498 q^{73} +(-1.22691 - 2.05233i) q^{74} +(-0.429632 - 4.25969i) q^{75} +(-5.61649 - 3.01873i) q^{76} +27.4568i q^{77} +(3.17552 - 2.36100i) q^{78} +11.3669i q^{79} +(5.30447 - 3.50909i) q^{80} +(8.28224 - 3.52200i) q^{81} +(-10.8353 + 6.47751i) q^{82} +16.1489 q^{83} +(6.24785 - 15.0854i) q^{84} +5.72720 q^{85} +(-4.72163 + 2.82265i) q^{86} +(0.213261 - 0.0215095i) q^{87} +(-16.4588 + 0.751569i) q^{88} -10.1497i q^{89} +(-4.98233 + 4.54794i) q^{90} +7.61448i q^{91} +(0.946854 - 1.76167i) q^{92} +(-4.01483 + 0.404936i) q^{93} +(3.45088 + 5.77252i) q^{94} -5.06928 q^{95} +(9.21389 + 3.33230i) q^{96} +2.76260 q^{97} +(11.0424 + 18.4713i) q^{98} +(17.1234 - 3.48963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q + 9 * q^8 - 2 * q^9	\( 22 q + 9 q^{8} - 2 q^{9} + 4 q^{10} - 7 q^{12} - 4 q^{13} - 12 q^{14} + 4 q^{16} + 13 q^{18} + 14 q^{20} + 2 q^{22} - 22 q^{23} - 30 q^{24} - 18 q^{25} - 27 q^{26} - 12 q^{27} + 6 q^{28} + 34 q^{30} + 20 q^{32} - 8 q^{33} - 6 q^{34} + 8 q^{35} - 36 q^{36} - 4 q^{37} - 22 q^{38} + 24 q^{39} - 4 q^{40} + 26 q^{42} + 56 q^{44} - 8 q^{47} - 22 q^{48} - 14 q^{49} - 20 q^{50} - 16 q^{51} - 19 q^{52} + 22 q^{54} + 18 q^{56} + 12 q^{57} + 3 q^{58} + 72 q^{59} - 28 q^{60} + 12 q^{61} - 63 q^{62} + 20 q^{63} + 3 q^{64} + 60 q^{66} + 20 q^{68} - 40 q^{71} - 36 q^{72} - 4 q^{73} - 28 q^{74} - 48 q^{75} + 26 q^{76} + 11 q^{78} + 84 q^{80} + 10 q^{81} - 29 q^{82} + 8 q^{83} - 38 q^{84} + 8 q^{85} - 28 q^{86} + 48 q^{87} - 30 q^{88} + 84 q^{90} + 12 q^{93} - 13 q^{94} - 32 q^{95} - 45 q^{96} - 4 q^{97} - 64 q^{98} - 20 q^{99}+O(q^{100}) \) 22 * q + 9 * q^8 - 2 * q^9 + 4 * q^10 - 7 * q^12 - 4 * q^13 - 12 * q^14 + 4 * q^16 + 13 * q^18 + 14 * q^20 + 2 * q^22 - 22 * q^23 - 30 * q^24 - 18 * q^25 - 27 * q^26 - 12 * q^27 + 6 * q^28 + 34 * q^30 + 20 * q^32 - 8 * q^33 - 6 * q^34 + 8 * q^35 - 36 * q^36 - 4 * q^37 - 22 * q^38 + 24 * q^39 - 4 * q^40 + 26 * q^42 + 56 * q^44 - 8 * q^47 - 22 * q^48 - 14 * q^49 - 20 * q^50 - 16 * q^51 - 19 * q^52 + 22 * q^54 + 18 * q^56 + 12 * q^57 + 3 * q^58 + 72 * q^59 - 28 * q^60 + 12 * q^61 - 63 * q^62 + 20 * q^63 + 3 * q^64 + 60 * q^66 + 20 * q^68 - 40 * q^71 - 36 * q^72 - 4 * q^73 - 28 * q^74 - 48 * q^75 + 26 * q^76 + 11 * q^78 + 84 * q^80 + 10 * q^81 - 29 * q^82 + 8 * q^83 - 38 * q^84 + 8 * q^85 - 28 * q^86 + 48 * q^87 - 30 * q^88 + 84 * q^90 + 12 * q^93 - 13 * q^94 - 32 * q^95 - 45 * q^96 - 4 * q^97 - 64 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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