LMFDB - Embedded newform 276.2.c.a.47.16

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			47.16
Character	$\chi$	$=$	276.47
Dual form			276.2.c.a.47.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.725653 + 1.21385i) q^{2} +(0.173813 - 1.72331i) q^{3} +(-0.946854 + 1.76167i) q^{4} -1.59003i q^{5} +(2.21796 - 1.03954i) q^{6} -4.71351i q^{7} +(-2.82548 + 0.129022i) q^{8} +(-2.93958 - 0.599066i) q^{9} +O(q^{10})$	\(q+(0.725653 + 1.21385i) q^{2} +(0.173813 - 1.72331i) q^{3} +(-0.946854 + 1.76167i) q^{4} -1.59003i q^{5} +(2.21796 - 1.03954i) 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} +(2.87132 + 1.93792i) 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} +(-1.40594 - 4.00292i) 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} +(-0.268761 + 4.89160i) 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} +(-1.65290 - 3.52662i) 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} +(3.83871 - 4.61133i) 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} +(-4.89989 - 10.4544i) 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} +(-6.13269 + 3.22337i) 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} +(-7.14263 + 1.72711i) 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} +(3.08135 - 4.56548i) 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} +(12.9199 - 6.05545i) 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} +(8.38302 + 1.31338i) 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} +(-3.58303 + 1.67934i) 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} +(9.13441 - 13.5340i) 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} +(-6.36475 + 2.23548i) 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} +(-8.36289 - 5.10510i) 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 - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	$ 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) $ 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * 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	$-0.884297\pi$
$5$		−	1.59003i		−	0.711082i	0.934661	−	0.355541i	$-0.115703\pi$
$6$	2.21796	−	1.03954i	0.905479	−	0.424391i
$7$		−	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	$-0.158765\pi$
$11$	5.82512			1.75634			0.878170	+	0.478349i	$0.158765\pi$
$12$	2.87132	+	1.93792i	0.828878	+	0.559430i
$13$	−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	$0.143888\pi$
$17$			3.60195i			0.873601i	−0.899558	+	0.436800i	$0.856112\pi$
$18$	−1.40594	−	4.00292i	−0.331383	−	0.943496i
$19$			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
$24$	−0.268761	+	4.89160i	−0.0548605	+	0.998494i
$25$	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	$-0.996343\pi$
$29$		−	0.123751i		−	0.0229799i	0.999934	−	0.0114900i	$-0.00365745\pi$
$30$	−1.65290	−	3.52662i	−0.301777	−	0.643870i
$31$		−	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
$36$	3.83871	−	4.61133i	0.639784	−	0.768554i
$37$	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	$0.245499\pi$
$41$			8.92645i			1.39408i	−0.717034	+	0.697038i	$0.754501\pi$
$42$	−4.89989	−	10.4544i	−0.756069	−	1.61315i
$43$		−	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	$-0.387257\pi$
$47$	4.75555			0.693668			0.346834	+	0.937926i	$0.387257\pi$
$48$	−6.13269	+	3.22337i	−0.885177	+	0.465254i
$49$	−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	$0.194628\pi$
$53$			8.35826i			1.14810i	−0.818822	+	0.574048i	$0.805372\pi$
$54$	−7.14263	+	1.72711i	−0.971988	+	0.235030i
$55$		−	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	$-0.650797\pi$
$59$	−7.00860			−0.912442			−0.456221	+	0.889867i	$0.650797\pi$
$60$	3.08135	−	4.56548i	0.397801	−	0.589401i
$61$	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
$66$	12.9199	−	6.05545i	1.59033	−	0.745375i
$67$		−	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	$-0.471829\pi$
$71$	1.48951			0.176772			0.0883861	+	0.996086i	$0.471829\pi$
$72$	8.38302	+	1.31338i	0.987948	+	0.154783i
$73$	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
$78$	−3.58303	+	1.67934i	−0.405698	+	0.190148i
$79$			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	$-0.846723\pi$
$83$	−16.1489			−1.77257			−0.886286	+	0.463139i	$0.846723\pi$
$84$	9.13441	−	13.5340i	0.996646	−	1.47668i
$85$	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	$0.180794\pi$
$89$			10.1497i			1.07586i	−0.842988	+	0.537932i	$0.819206\pi$
$90$	−6.36475	+	2.23548i	−0.670904	+	0.235641i
$91$			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
$96$	−8.36289	−	5.10510i	−0.853534	−	0.521037i
$97$	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	$-0.868637\pi$
$101$		−	8.06147i		−	0.802146i	0.916046	−	0.401073i	$-0.131363\pi$
$102$	3.74438	+	7.98898i	0.370748	+	0.791027i
$103$		−	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	$-0.218655\pi$
$107$	15.9961			1.54640			0.773199	+	0.634163i	$0.218655\pi$
$108$	−7.27952	−	7.41678i	−0.700472	−	0.713680i
$109$	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	$0.0458481\pi$
$113$			3.05167i			0.287077i	−0.989645	+	0.143538i	$0.954152\pi$
$114$	3.31424	+	7.07124i	0.310407	+	0.662282i
$115$		−	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
$120$	7.77779	+	0.427337i	0.710012	+	0.0390103i
$121$	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
$126$	−18.8678	+	6.62691i	−1.68088	+	0.590372i
$127$		−	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	$-0.632425\pi$
$131$	−9.25091			−0.808256			−0.404128	+	0.914703i	$0.632425\pi$
$132$	16.7258	+	11.2886i	1.45579	+	0.982548i
$133$	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	$0.149184\pi$
$137$			10.5742i			0.903412i	−0.892167	+	0.451706i	$0.850816\pi$
$138$	2.21796	−	1.03954i	0.188805	−	0.0884917i
$139$			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
$144$	4.48892	+	11.1288i	0.374077	+	0.927398i
$145$	−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	$0.0660408\pi$
$149$			5.02881i			0.411976i	−0.978555	+	0.205988i	$0.933959\pi$
$150$	5.48238	−	2.56955i	0.447634	−	0.209803i
$151$			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
$156$	−4.63850	−	3.13063i	−0.371377	−	0.250651i
$157$	−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
$162$	1.73486	+	12.6091i	0.136303	+	0.990667i
$163$			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	$-0.303301\pi$
$167$	14.9741			1.15873			0.579365	+	0.815068i	$0.303301\pi$
$168$	23.0566	+	1.26681i	1.77886	+	0.0977362i
$169$	−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	$-0.816653\pi$
$173$		−	14.3282i		−	1.08935i	0.838646	−	0.544676i	$-0.183347\pi$
$174$	−0.128644	−	0.274475i	−0.00975249	−	0.0208079i
$175$		−	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	$-0.562622\pi$
$179$	−5.23034			−0.390934			−0.195467	+	0.980710i	$0.562622\pi$
$180$	−7.33214	−	6.10365i	−0.546506	−	0.454939i
$181$	−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
$186$	−2.42185	−	5.16724i	−0.177578	−	0.378880i
$187$			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	$-0.440834\pi$
$191$	5.10821			0.369617			0.184808	+	0.982775i	$0.440834\pi$
$192$	0.128254	−	13.8558i	0.00925591	−	0.999957i
$193$	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	$-0.918379\pi$
$197$		−	7.11940i		−	0.507236i	0.967304	−	0.253618i	$-0.0816206\pi$
$198$	−8.18977	−	23.3175i	−0.582021	−	1.65710i
$199$		−	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
$204$	−6.98029	+	10.3423i	−0.488718	+	0.724108i
$205$	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
$210$	−16.6228	+	7.79097i	−1.14708	+	0.537628i
$211$		−	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
$216$	3.72044	−	14.2182i	0.253144	−	0.967429i
$217$	−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
$222$	3.75004	−	1.75762i	0.251686	−	0.117964i
$223$		−	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	$-0.618590\pi$
$227$	−10.9685			−0.728005			−0.364003	+	0.931398i	$0.618590\pi$
$228$	−6.17842	+	9.15425i	−0.409176	+	0.606255i
$229$	−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	$-0.824178\pi$
$233$		−	16.0184i		−	1.04940i	0.851288	−	0.524699i	$-0.175822\pi$
$234$	2.27124	+	6.46655i	0.148476	+	0.422731i
$235$		−	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	$-0.805536\pi$
$239$	−25.3265			−1.63823			−0.819117	+	0.573627i	$0.805536\pi$
$240$	5.12526	+	9.75115i	0.330834	+	0.629434i
$241$	−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
$246$	9.27941	+	19.7985i	0.591634	+	1.26231i
$247$		−	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	$-0.425928\pi$
$251$	7.30711			0.461220			0.230610	+	0.973046i	$0.425928\pi$
$252$	−21.7355	−	18.0938i	−1.36921	−	1.13980i
$253$	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	$-0.839259\pi$
$257$		−	15.5116i		−	0.967585i	0.875183	−	0.483793i	$-0.160741\pi$
$258$	−4.04361	−	8.62743i	−0.251744	−	0.537120i
$259$		−	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	$-0.736874\pi$
$263$	−21.9697			−1.35471			−0.677355	+	0.735656i	$0.736874\pi$
$264$	−1.56556	+	28.4942i	−0.0963537	+	1.75369i
$265$	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	$-0.913000\pi$
$269$		−	8.85430i		−	0.539856i	0.962880	−	0.269928i	$-0.0870000\pi$
$270$	2.74615	+	11.3570i	0.167126	+	0.691164i
$271$			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
$276$	2.87132	+	1.93792i	0.172833	+	0.116649i
$277$	−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	$0.333892\pi$
$281$			29.0638i			1.73380i	−0.498479	+	0.866902i	$0.666108\pi$
$282$	10.5476	−	4.94359i	0.628102	−	0.294387i
$283$			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
$288$	−10.2512	+	13.5245i	−0.604060	+	0.796939i
$289$	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	$0.179181\pi$
$293$			18.2693i			1.06731i	−0.845704	+	0.533653i	$0.820819\pi$
$294$	−33.7511	+	15.8189i	−1.96840	+	0.922576i
$295$			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
$300$	7.09735	+	4.79017i	0.409765	+	0.276561i
$301$	−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
$306$	14.4183	−	5.06412i	0.824239	−	0.289497i
$307$			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	$-0.660920\pi$
$311$	−17.0809			−0.968568			−0.484284	+	0.874911i	$0.660920\pi$
$312$	0.434172	−	7.90218i	0.0245801	−	0.447373i
$313$	−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	$-0.871426\pi$
$317$		−	13.9955i		−	0.786068i	0.919524	−	0.393034i	$-0.128574\pi$
$318$	8.68877	+	18.5383i	0.487242	+	1.03958i
$319$		−	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
$324$	−14.0467	+	11.2557i	−0.780370	+	0.625318i
$325$	−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
$330$	−9.62835	−	20.5430i	−0.530023	−	1.13085i
$331$		−	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
$336$	15.1934	+	28.9065i	0.828868	+	1.57698i
$337$	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
$342$	12.7620	−	4.48238i	0.690089	−	0.242379i
$343$			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	$-0.707823\pi$
$347$	−22.6326			−1.21498			−0.607490	+	0.794327i	$0.707823\pi$
$348$	0.239819	−	0.355328i	0.0128557	−	0.0190476i
$349$	−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	$0.319715\pi$
$353$			31.7089i			1.68769i	−0.536583	+	0.843847i	$0.680285\pi$
$354$	−15.5448	+	7.28573i	−0.826197	+	0.387232i
$355$		−	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	$-0.572002\pi$
$359$	−8.49888			−0.448554			−0.224277	+	0.974525i	$0.572002\pi$
$360$	2.08831	−	13.3292i	0.110064	−	0.702513i
$361$	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
$366$	4.55729	−	2.13597i	0.238213	−	0.111649i
$367$			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
$372$	4.51482	−	6.68938i	0.234083	−	0.346828i
$373$	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
$378$	8.14074	+	33.6668i	0.418715	+	1.73163i
$379$		−	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	$-0.427467\pi$
$383$	8.84200			0.451805			0.225902	+	0.974150i	$0.427467\pi$
$384$	16.9119	−	9.89884i	0.863033	−	0.505148i
$385$	−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	$0.0740108\pi$
$389$			9.08929i			0.460845i	−0.973091	+	0.230423i	$0.925989\pi$
$390$	2.67019	+	5.69711i	0.135211	+	0.288485i
$391$			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
$396$	22.3609	−	26.8615i	1.12368	−	1.34984i
$397$	−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	$0.00957897\pi$
$401$			1.20505i			0.0601774i	−0.999547	+	0.0300887i	$0.990421\pi$
$402$	−11.4926	−	24.5205i	−0.573198	−	1.22297i
$403$			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
$408$	−17.6193	−	0.968062i	−0.872285	−	0.0479262i
$409$	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
$414$	−1.40594	−	4.00292i	−0.0690982	−	0.196733i
$415$			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	$-0.395781\pi$
$419$	13.1658			0.643193			0.321596	+	0.946877i	$0.395781\pi$
$420$	−21.5194	−	14.5240i	−1.05004	−	0.708697i
$421$	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
$426$	3.30368	−	1.54841i	0.160064	−	0.0750206i
$427$		−	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	$-0.512718\pi$
$431$	−1.65853			−0.0798884			−0.0399442	+	0.999202i	$0.512718\pi$
$432$	19.9585	−	5.80147i	0.960255	−	0.279123i
$433$	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
$438$	16.2244	−	7.60423i	0.775229	−	0.363344i
$439$		−	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	$-0.210730\pi$
$443$	33.2024			1.57749			0.788747	+	0.614717i	$0.210730\pi$
$444$	4.85471	+	3.27656i	0.230394	+	0.155499i
$445$	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	$-0.855170\pi$
$449$		−	18.6239i		−	0.878918i	0.898263	−	0.439459i	$-0.144830\pi$
$450$	−3.47521	−	9.89444i	−0.163823	−	0.466428i
$451$			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
$456$	−15.5953	−	0.856854i	−0.730315	−	0.0401259i
$457$	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	$0.159413\pi$
$461$			20.6179i			0.960273i	−0.877194	+	0.480136i	$0.840587\pi$
$462$	−28.5424	−	60.8980i	−1.32791	−	2.83323i
$463$		−	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	$-0.624295\pi$
$467$	−16.4512			−0.761273			−0.380636	+	0.924725i	$0.624295\pi$
$468$	−6.20127	+	7.44941i	−0.286654	+	0.344349i
$469$	−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
$474$	11.8164	+	25.2114i	0.542744	+	1.15800i
$475$			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	$-0.288069\pi$
$479$	27.0376			1.23538			0.617690	+	0.786421i	$0.288069\pi$
$480$	−8.11725	+	13.2972i	−0.370500	+	0.606933i
$481$	−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
$486$	22.0310	−	0.798067i	0.999345	−	0.0362010i
$487$			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	$-0.674818\pi$
$491$	−23.1339			−1.04402			−0.522010	+	0.852939i	$0.674818\pi$
$492$	−17.2987	+	25.6307i	−0.779888	+	1.15552i
$493$	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
$498$	−35.8176	+	16.7874i	−1.60503	+	0.752263i
$499$			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	$-0.271480\pi$
$503$	29.5066			1.31563			0.657817	+	0.753177i	$0.271480\pi$
$504$	6.19063	−	39.5134i	0.275753	−	1.76007i
$505$	−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	$0.0410254\pi$
$509$			5.79948i			0.257057i	−0.991706	+	0.128529i	$0.958975\pi$
$510$	12.7027	−	5.95367i	0.562486	−	0.263633i
$511$		−	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
$516$	7.53813	−	11.1689i	0.331848	−	0.491682i
$517$	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	$0.124386\pi$
$521$			17.3884i			0.761800i	−0.924616	+	0.380900i	$0.875614\pi$
$522$	−0.495364	+	0.173986i	−0.0216815	+	0.00761517i
$523$			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
$528$	−35.7236	+	18.7765i	−1.55467	+	0.817144i
$529$	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
$534$	10.5510	+	22.5116i	0.456587	+	0.974172i
$535$		−	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
$540$	−11.7929	+	11.5746i	−0.507485	+	0.498093i
$541$	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
$546$	7.91557	+	16.8886i	0.338755	+	0.722767i
$547$			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
$552$	−0.268761	+	4.89160i	−0.0114392	+	0.208200i
$553$	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	$-0.894595\pi$
$557$		−	15.3463i		−	0.650243i	0.945672	−	0.325121i	$-0.105405\pi$
$558$	−9.32569	+	3.27545i	−0.394788	+	0.138661i
$559$			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	$-0.489783\pi$
$563$	1.52294			0.0641844			0.0320922	+	0.999485i	$0.489783\pi$
$564$	13.6547	+	9.21588i	0.574966	+	0.388059i
$565$	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	$-0.916812\pi$
$569$		−	12.3265i		−	0.516756i	0.966044	−	0.258378i	$-0.0831880\pi$
$570$	11.2435	−	5.26973i	0.470937	−	0.220725i
$571$			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
$576$	−23.8555	−	2.62934i	−0.993981	−	0.109556i
$577$	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
$582$	6.12735	−	2.87184i	0.253987	−	0.119042i
$583$			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	$-0.673892\pi$
$587$	−25.1744			−1.03906			−0.519528	+	0.854453i	$0.673892\pi$
$588$	−43.6933	−	29.4897i	−1.80188	−	1.21613i
$589$	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	$0.0244020\pi$
$593$			3.72999i			0.153172i	−0.997063	+	0.0765862i	$0.975598\pi$
$594$	−41.6066	+	10.0606i	−1.70714	+	0.412792i
$595$		−	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	$-0.400431\pi$
$599$	15.0630			0.615456			0.307728	+	0.951474i	$0.400431\pi$
$600$	−0.664325	+	12.0911i	−0.0271209	+	0.493617i
$601$	−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
$606$	−8.38023	−	17.8800i	−0.340424	−	0.726326i
$607$		−	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
$612$	16.6098	+	13.8268i	0.671410	+	0.558916i
$613$	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	$0.199279\pi$
$617$			29.1094i			1.17190i	−0.810346	+	0.585951i	$0.800721\pi$
$618$	−5.47193	−	11.6749i	−0.220113	−	0.469633i
$619$		−	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
$624$	9.90711	−	5.20723i	0.396602	−	0.208456i
$625$	−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
$630$	10.5370	+	30.0003i	0.419803	+	1.19524i
$631$		−	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
$636$	−16.1977	+	23.9992i	−0.642279	+	0.951631i
$637$	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	$-0.923196\pi$
$641$		−	12.0996i		−	0.477907i	0.971031	−	0.238953i	$-0.0768043\pi$
$642$	35.4787	−	16.6286i	1.40023	−	0.656278i
$643$		−	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	$-0.653188\pi$
$647$	−23.5484			−0.925783			−0.462892	+	0.886415i	$0.653188\pi$
$648$	−23.8557	−	8.88277i	−0.937142	−	0.348948i
$649$	−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	$-0.893702\pi$
$653$		−	16.7517i		−	0.655544i	0.944757	−	0.327772i	$-0.106298\pi$
$654$	7.04237	−	3.30071i	0.275378	−	0.129068i
$655$			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	$-0.496660\pi$
$659$	0.538650			0.0209828			0.0104914	+	0.999945i	$0.496660\pi$
$660$	17.9492	−	26.5944i	0.698673	−	1.03519i
$661$	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
$666$	−2.37711	−	6.76797i	−0.0921111	−	0.262254i
$667$		−	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
$672$	−24.0629	+	39.4186i	−0.928248	+	1.52060i
$673$	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	$0.170749\pi$
$677$			26.5951i			1.02213i	−0.859542	+	0.511066i	$0.829251\pi$
$678$	3.17234	+	6.76849i	0.121833	+	0.259942i
$679$		−	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	$-0.716486\pi$
$683$	−32.8706			−1.25776			−0.628878	+	0.777504i	$0.716486\pi$
$684$	14.7017	+	12.2384i	0.562133	+	0.467949i
$685$	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
$690$	−1.65290	−	3.52662i	−0.0629249	−	0.134256i
$691$		−	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
$696$	0.605340	+	0.0332593i	0.0229453	+	0.00126069i
$697$	−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	$0.246192\pi$
$701$			36.9927i			1.39719i	−0.715515	+	0.698597i	$0.753808\pi$
$702$	11.5386	−	2.79007i	0.435497	−	0.105305i
$703$			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
$708$	−20.1239	−	13.5821i	−0.756303	−	0.510447i
$709$	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
$714$	37.6562	−	17.6492i	1.40925	−	0.660503i
$715$			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	$-0.557859\pi$
$719$	−9.69447			−0.361543			−0.180771	+	0.983525i	$0.557859\pi$
$720$	17.6951	−	7.13752i	0.659456	−	0.266000i
$721$	−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
$726$	50.8623	−	23.8388i	1.88768	−	0.884740i
$727$		−	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
$732$	5.89975	+	3.98188i	0.218061	+	0.147175i
$733$	−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
$738$	35.7318	−	12.5500i	1.31531	−	0.461974i
$739$		−	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	$-0.453705\pi$
$743$	7.90090			0.289856			0.144928	+	0.989442i	$0.453705\pi$
$744$	11.3961	+	0.626138i	0.417801	+	0.0229553i
$745$	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
$750$	−12.3502	−	26.3502i	−0.450964	−	0.962175i
$751$			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
$756$	−34.9591	+	34.3121i	−1.27145	+	1.24792i
$757$	−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	$-0.806221\pi$
$761$		−	31.5511i		−	1.14373i	0.820349	−	0.571863i	$-0.193779\pi$
$762$	−7.54888	−	16.1063i	−0.273467	−	0.583468i
$763$		−	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
$768$	24.2879	+	13.3454i	0.876413	+	0.481560i
$769$	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	$0.0682228\pi$
$773$			11.8269i			0.425382i	−0.977119	+	0.212691i	$0.931777\pi$
$774$	−15.5706	+	5.46883i	−0.559672	+	0.196573i
$775$		−	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
$780$	−4.97780	+	7.37534i	−0.178234	+	0.264080i
$781$	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
$786$	−20.5182	+	9.61671i	−0.731859	+	0.343017i
$787$		−	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
$792$	48.8321	+	7.65060i	1.73517	+	0.271852i
$793$	−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	$-0.957967\pi$
$797$		−	7.43422i		−	0.263334i	0.991294	−	0.131667i	$-0.0420329\pi$
$798$	33.3303	−	15.6217i	1.17988	−	0.553002i
$799$			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
$804$	21.4245	−	31.7436i	0.755585	−	1.11951i
$805$	−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	$0.204820\pi$
$809$			34.1297i			1.19993i	−0.800025	+	0.599967i	$0.795180\pi$
$810$	20.0489	−	2.75848i	0.704446	−	0.0969230i
$811$			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
$816$	−11.6104	−	22.0896i	−0.406446	−	0.773292i
$817$	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	$-0.920000\pi$
$821$		−	14.2515i		−	0.497382i	0.968583	−	0.248691i	$-0.0800003\pi$
$822$	10.9923	+	23.4531i	0.383400	+	0.818021i
$823$		−	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	$-0.389536\pi$
$827$	19.5614			0.680217			0.340108	+	0.940386i	$0.389536\pi$
$828$	3.83871	−	4.61133i	0.133404	−	0.160255i
$829$	−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
$834$	0.683937	+	1.45925i	0.0236828	+	0.0505295i
$835$		−	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	$-0.424141\pi$
$839$	13.6757			0.472136			0.236068	+	0.971737i	$0.424141\pi$
$840$	2.01426	−	36.6607i	0.0694985	−	1.26491i
$841$	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
$846$	−6.68602	−	19.0361i	−0.229870	−	0.654473i
$847$		−	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
$852$	4.27685	+	2.88655i	0.146523	+	0.0988917i
$853$	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	$0.0208364\pi$
$857$			3.82985i			0.130825i	−0.997858	+	0.0654126i	$0.979164\pi$
$858$	−20.8716	+	9.78234i	−0.712543	+	0.333964i
$859$		−	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	$-0.857611\pi$
$863$	−52.9727			−1.80321			−0.901606	+	0.432558i	$0.857611\pi$
$864$	21.5251	+	20.0168i	0.732298	+	0.680984i
$865$	−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
$870$	−0.436422	+	0.204548i	−0.0147961	+	0.00693482i
$871$			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
$876$	21.0036	+	14.1759i	0.709647	+	0.478958i
$877$	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	$-0.789075\pi$
$881$		−	36.5203i		−	1.23040i	0.788371	−	0.615201i	$-0.210925\pi$
$882$	21.3944	+	60.9131i	0.720388	+	2.05105i
$883$			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	$-0.409013\pi$
$887$	16.7953			0.563933			0.281966	+	0.959424i	$0.409013\pi$
$888$	−0.454410	+	8.27053i	−0.0152490	+	0.277541i
$889$	−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
$894$	5.22766	+	11.1537i	0.174839	+	0.373036i
$895$			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
$900$	9.48855	−	11.3983i	0.316285	−	0.379944i
$901$	−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
$906$	21.5562	+	45.9923i	0.716158	+	1.52799i
$907$		−	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	$-0.874417\pi$
$911$	−55.7281			−1.84635			−0.923177	+	0.384375i	$0.874417\pi$
$912$	−10.2767	−	19.5521i	−0.340294	−	0.647433i
$913$	−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
$918$	−6.22096	−	25.7274i	−0.205322	−	0.849130i
$919$			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
$924$	53.2090	−	78.8371i	1.75045	−	2.59355i
$925$	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	$0.0356482\pi$
$929$			6.81266i			0.223516i	−0.993735	+	0.111758i	$0.964352\pi$
$930$	−8.21606	+	3.85080i	−0.269415	+	0.126273i
$931$		−	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
$936$	−13.5424	−	2.12171i	−0.442648	−	0.0693503i
$937$	−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	$-0.842781\pi$
$941$		−	29.0855i		−	0.948161i	0.880481	−	0.474081i	$-0.157219\pi$
$942$	−41.0609	+	19.2449i	−1.33783	+	0.627033i
$943$			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	$-0.743752\pi$
$947$	−42.6576			−1.38619			−0.693093	+	0.720849i	$0.743752\pi$
$948$	−22.0282	+	32.6380i	−0.715442	+	1.06003i
$949$	−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	$-0.957554\pi$
$953$		−	8.20879i		−	0.265909i	0.991122	−	0.132954i	$-0.0424464\pi$
$954$	33.4574	−	11.7512i	1.08322	−	0.380460i
$955$		−	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
$960$	−22.0311	−	0.203927i	−0.711052	−	0.00658171i
$961$	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
$966$	−4.89989	−	10.4544i	−0.157651	−	0.336364i
$967$		−	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	$-0.101613\pi$
$971$	59.1732			1.89896			0.949478	+	0.313832i	$0.101613\pi$
$972$	16.9556	+	26.1631i	0.543850	+	0.839182i
$973$	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	$0.136942\pi$
$977$			26.0725i			0.834134i	−0.908876	+	0.417067i	$0.863058\pi$
$978$	10.4270	+	22.2469i	0.333417	+	0.711377i
$979$			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	$-0.702260\pi$
$983$	−37.2168			−1.18703			−0.593515	+	0.804823i	$0.702260\pi$
$984$	−43.6646	−	2.39908i	−1.39198	−	0.0764798i
$985$	−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
$990$	−37.0754	+	13.0220i	−1.17833	+	0.413865i
$991$			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
$996$	−46.3686	−	31.2953i	−1.46924	−	0.991629i
$997$	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.a.47.16	yes	22
3.2	odd	2		276.2.c.b.47.7	yes	22
4.3	odd	2		276.2.c.b.47.8	yes	22
12.11	even	2	inner	276.2.c.a.47.15	✓	22

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

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

\(f(q)\)	\(=\)	\(q+(0.725653 + 1.21385i) q^{2} +(0.173813 - 1.72331i) q^{3} +(-0.946854 + 1.76167i) q^{4} -1.59003i q^{5} +(2.21796 - 1.03954i) q^{6} -4.71351i q^{7} +(-2.82548 + 0.129022i) q^{8} +(-2.93958 - 0.599066i) q^{9} +O(q^{10})\)	\(q+(0.725653 + 1.21385i) q^{2} +(0.173813 - 1.72331i) q^{3} +(-0.946854 + 1.76167i) q^{4} -1.59003i q^{5} +(2.21796 - 1.03954i) 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} +(2.87132 + 1.93792i) 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} +(-1.40594 - 4.00292i) 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} +(-0.268761 + 4.89160i) 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} +(-1.65290 - 3.52662i) 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} +(3.83871 - 4.61133i) 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} +(-4.89989 - 10.4544i) 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} +(-6.13269 + 3.22337i) 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} +(-7.14263 + 1.72711i) 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} +(3.08135 - 4.56548i) 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} +(12.9199 - 6.05545i) 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} +(8.38302 + 1.31338i) 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} +(-3.58303 + 1.67934i) 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} +(9.13441 - 13.5340i) 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} +(-6.36475 + 2.23548i) 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} +(-8.36289 - 5.10510i) q^{96} +2.76260 q^{97} +(-11.0424 - 18.4713i) q^{98} +(-17.1234 - 3.48963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9}+O(q^{10}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9	\( 22 q - 3 q^{6} - 9 q^{8} - 2 q^{9} + 4 q^{10} + 14 q^{12} - 4 q^{13} + 12 q^{14} + 4 q^{16} - 14 q^{18} - 14 q^{20} + 2 q^{22} + 22 q^{23} + 22 q^{24} - 18 q^{25} + 27 q^{26} + 12 q^{27} + 6 q^{28} - 24 q^{30} - 20 q^{32} - 8 q^{33} - 6 q^{34} - 8 q^{35} + 3 q^{36} - 4 q^{37} + 22 q^{38} - 24 q^{39} - 4 q^{40} - 38 q^{42} - 56 q^{44} + 8 q^{47} + 17 q^{48} - 14 q^{49} + 20 q^{50} + 16 q^{51} - 19 q^{52} - 54 q^{54} - 18 q^{56} + 12 q^{57} + 3 q^{58} - 72 q^{59} + 64 q^{60} + 12 q^{61} + 63 q^{62} - 20 q^{63} + 3 q^{64} - 18 q^{66} - 20 q^{68} + 40 q^{71} + 48 q^{72} - 4 q^{73} + 28 q^{74} + 48 q^{75} + 26 q^{76} - 46 q^{78} - 84 q^{80} + 10 q^{81} - 29 q^{82} - 8 q^{83} + 76 q^{84} + 8 q^{85} + 28 q^{86} - 48 q^{87} - 30 q^{88} - 26 q^{90} + 12 q^{93} - 13 q^{94} + 32 q^{95} + 18 q^{96} - 4 q^{97} + 64 q^{98} + 20 q^{99}+O(q^{100}) \) 22 * q - 3 * q^6 - 9 * q^8 - 2 * q^9 + 4 * q^10 + 14 * q^12 - 4 * q^13 + 12 * q^14 + 4 * q^16 - 14 * q^18 - 14 * q^20 + 2 * q^22 + 22 * q^23 + 22 * q^24 - 18 * q^25 + 27 * q^26 + 12 * q^27 + 6 * q^28 - 24 * q^30 - 20 * q^32 - 8 * q^33 - 6 * q^34 - 8 * q^35 + 3 * q^36 - 4 * q^37 + 22 * q^38 - 24 * q^39 - 4 * q^40 - 38 * q^42 - 56 * q^44 + 8 * q^47 + 17 * q^48 - 14 * q^49 + 20 * q^50 + 16 * q^51 - 19 * q^52 - 54 * q^54 - 18 * q^56 + 12 * q^57 + 3 * q^58 - 72 * q^59 + 64 * q^60 + 12 * q^61 + 63 * q^62 - 20 * q^63 + 3 * q^64 - 18 * q^66 - 20 * q^68 + 40 * q^71 + 48 * q^72 - 4 * q^73 + 28 * q^74 + 48 * q^75 + 26 * q^76 - 46 * q^78 - 84 * q^80 + 10 * q^81 - 29 * q^82 - 8 * q^83 + 76 * q^84 + 8 * q^85 + 28 * q^86 - 48 * q^87 - 30 * q^88 - 26 * q^90 + 12 * q^93 - 13 * q^94 + 32 * q^95 + 18 * 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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