LMFDB - Embedded newform 273.2.bh.a.248.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (of order $6$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			248.4
Character	$\chi$	$=$	273.248
Dual form			273.2.bh.a.131.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.13534 + 1.23284i) q^{2} +(-0.105557 - 1.72883i) q^{3} +(2.03979 - 3.53302i) q^{4} +(-1.46641 - 2.53990i) q^{5} +(2.35677 + 3.56151i) q^{6} +(0.805632 - 2.52011i) q^{7} +5.12758i q^{8} +(-2.97772 + 0.364982i) q^{9} +O(q^{10})$	\(q+(-2.13534 + 1.23284i) q^{2} +(-0.105557 - 1.72883i) q^{3} +(2.03979 - 3.53302i) q^{4} +(-1.46641 - 2.53990i) q^{5} +(2.35677 + 3.56151i) q^{6} +(0.805632 - 2.52011i) q^{7} +5.12758i q^{8} +(-2.97772 + 0.364982i) q^{9} +(6.26259 + 3.61571i) q^{10} +(-0.698133 - 0.403067i) q^{11} +(-6.32331 - 3.15352i) q^{12} +1.00000i q^{13} +(1.38659 + 6.37451i) q^{14} +(-4.23627 + 2.80329i) q^{15} +(-2.24191 - 3.88310i) q^{16} +(-2.45226 + 4.24745i) q^{17} +(5.90848 - 4.45041i) q^{18} +(-5.66648 + 3.27154i) q^{19} -11.9647 q^{20} +(-4.44189 - 1.12679i) q^{21} +1.98767 q^{22} +(8.25700 - 4.76718i) q^{23} +(8.86472 - 0.541254i) q^{24} +(-1.80074 + 3.11897i) q^{25} +(-1.23284 - 2.13534i) q^{26} +(0.945312 + 5.10944i) q^{27} +(-7.26028 - 7.98681i) q^{28} -1.96603i q^{29} +(5.58989 - 11.2086i) q^{30} +(-5.03226 - 2.90538i) q^{31} +(0.693249 + 0.400248i) q^{32} +(-0.623142 + 1.24950i) q^{33} -12.0930i q^{34} +(-7.58223 + 1.64930i) q^{35} +(-4.78443 + 11.2648i) q^{36} +(-1.41434 - 2.44971i) q^{37} +(8.06658 - 13.9717i) q^{38} +(1.72883 - 0.105557i) q^{39} +(13.0236 - 7.51916i) q^{40} +1.98882 q^{41} +(10.8741 - 3.07006i) q^{42} +4.59323 q^{43} +(-2.84809 + 1.64435i) q^{44} +(5.29358 + 7.02789i) q^{45} +(-11.7543 + 20.3591i) q^{46} +(-0.904136 - 1.56601i) q^{47} +(-6.47657 + 4.28577i) q^{48} +(-5.70191 - 4.06056i) q^{49} -8.88010i q^{50} +(7.60197 + 3.79120i) q^{51} +(3.53302 + 2.03979i) q^{52} +(-3.53060 - 2.03839i) q^{53} +(-8.31769 - 9.74498i) q^{54} +2.36425i q^{55} +(12.9221 + 4.13094i) q^{56} +(6.25409 + 9.45105i) q^{57} +(2.42380 + 4.19815i) q^{58} +(-4.39070 + 7.60491i) q^{59} +(1.26296 + 20.6850i) q^{60} +(-8.96446 + 5.17563i) q^{61} +14.3275 q^{62} +(-1.47915 + 7.79821i) q^{63} +6.99387 q^{64} +(2.53990 - 1.46641i) q^{65} +(-0.209813 - 3.43635i) q^{66} +(0.391145 - 0.677483i) q^{67} +(10.0042 + 17.3278i) q^{68} +(-9.11324 - 13.7718i) q^{69} +(14.1573 - 12.8695i) q^{70} -2.26943i q^{71} +(-1.87148 - 15.2685i) q^{72} +(4.80065 + 2.77165i) q^{73} +(6.04021 + 3.48732i) q^{74} +(5.58226 + 2.78394i) q^{75} +26.6931i q^{76} +(-1.57821 + 1.43465i) q^{77} +(-3.56151 + 2.35677i) q^{78} +(-4.60034 - 7.96803i) q^{79} +(-6.57513 + 11.3885i) q^{80} +(8.73358 - 2.17363i) q^{81} +(-4.24682 + 2.45190i) q^{82} +1.72902 q^{83} +(-13.0415 + 13.3949i) q^{84} +14.3841 q^{85} +(-9.80812 + 5.66272i) q^{86} +(-3.39894 + 0.207529i) q^{87} +(2.06676 - 3.57973i) q^{88} +(-6.09126 - 10.5504i) q^{89} +(-19.9679 - 8.48082i) q^{90} +(2.52011 + 0.805632i) q^{91} -38.8962i q^{92} +(-4.49172 + 9.00662i) q^{93} +(3.86128 + 2.22931i) q^{94} +(16.6188 + 9.59488i) q^{95} +(0.618783 - 1.24076i) q^{96} -9.91566i q^{97} +(17.1816 + 1.64114i) q^{98} +(2.22595 + 0.945414i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.13534	+	1.23284i	−1.50991	+	0.871750i	−0.509982	+	0.860185i	$0.670348\pi$
$2$	−2.13534	+	1.23284i	−1.50991	+	0.871750i	−0.999933	+	0.0115644i	$0.996319\pi$
$3$	−0.105557	−	1.72883i	−0.0609436	−	0.998141i
$3$	−0.105557	−	1.72883i	−0.0609436	−	0.998141i
$4$	2.03979	−	3.53302i	1.01990	−	1.76651i
$5$	−1.46641	−	2.53990i	−0.655800	−	1.13588i	−0.981693	−	0.190472i	$-0.938998\pi$
$5$	−1.46641	−	2.53990i	−0.655800	−	1.13588i	0.325892	−	0.945407i	$-0.394335\pi$
$6$	2.35677	+	3.56151i	0.962149	+	1.45398i
$7$	0.805632	−	2.52011i	0.304500	−	0.952512i
$7$	0.805632	−	2.52011i	0.304500	−	0.952512i
$8$			5.12758i			1.81287i
$9$	−2.97772	+	0.364982i	−0.992572	+	0.121661i
$10$	6.26259	+	3.61571i	1.98040	+	1.14339i
$11$	−0.698133	−	0.403067i	−0.210495	−	0.121529i	0.391046	−	0.920371i	$-0.372113\pi$
$11$	−0.698133	−	0.403067i	−0.210495	−	0.121529i	−0.601541	+	0.798842i	$0.705447\pi$
$12$	−6.32331	−	3.15352i	−1.82538	−	0.910342i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	1.38659	+	6.37451i	0.370583	+	1.70366i
$15$	−4.23627	+	2.80329i	−1.09380	+	0.723806i
$16$	−2.24191	−	3.88310i	−0.560477	−	0.970775i
$17$	−2.45226	+	4.24745i	−0.594762	+	1.03016i	0.398819	+	0.917030i	$0.369420\pi$
$17$	−2.45226	+	4.24745i	−0.594762	+	1.03016i	−0.993580	+	0.113128i	$0.963913\pi$
$18$	5.90848	−	4.45041i	1.39264	−	1.04897i
$19$	−5.66648	+	3.27154i	−1.29998	+	0.750544i	−0.980400	−	0.197016i	$-0.936875\pi$
$19$	−5.66648	+	3.27154i	−1.29998	+	0.750544i	−0.319580	+	0.947559i	$0.603542\pi$
$20$	−11.9647			−2.67539
$21$	−4.44189	−	1.12679i	−0.969299	−	0.245885i
$22$	1.98767			0.423773
$23$	8.25700	−	4.76718i	1.72170	−	0.994026i	0.806281	−	0.591532i	$-0.201477\pi$
$23$	8.25700	−	4.76718i	1.72170	−	0.994026i	0.915423	−	0.402494i	$-0.131857\pi$
$24$	8.86472	−	0.541254i	1.80950	−	0.110483i
$25$	−1.80074	+	3.11897i	−0.360148	+	0.623794i
$26$	−1.23284	−	2.13534i	−0.241780	−	0.418775i
$27$	0.945312	+	5.10944i	0.181925	+	0.983312i
$28$	−7.26028	−	7.98681i	−1.37206	−	1.50937i
$29$		−	1.96603i		−	0.365083i	−0.983198	−	0.182542i	$-0.941568\pi$
$29$		−	1.96603i		−	0.365083i	0.983198	−	0.182542i	$-0.0584324\pi$
$30$	5.58989	−	11.2086i	1.02057	−	2.04641i
$31$	−5.03226	−	2.90538i	−0.903821	−	0.521821i	−0.0253831	−	0.999678i	$-0.508081\pi$
$31$	−5.03226	−	2.90538i	−0.903821	−	0.521821i	−0.878438	+	0.477857i	$0.841414\pi$
$32$	0.693249	+	0.400248i	0.122550	+	0.0707545i
$33$	−0.623142	+	1.24950i	−0.108475	+	0.217510i
$34$		−	12.0930i		−	2.07393i
$35$	−7.58223	+	1.64930i	−1.28163	+	0.278782i
$36$	−4.78443	+	11.2648i	−0.797404	+	1.87747i
$37$	−1.41434	−	2.44971i	−0.232516	−	0.402730i	0.726032	−	0.687661i	$-0.241363\pi$
$37$	−1.41434	−	2.44971i	−0.232516	−	0.402730i	−0.958548	+	0.284931i	$0.908029\pi$
$38$	8.06658	−	13.9717i	1.30857	−	2.26651i
$39$	1.72883	−	0.105557i	0.276835	−	0.0169027i
$40$	13.0236	−	7.51916i	2.05921	−	1.18888i
$41$	1.98882			0.310602			0.155301	−	0.987867i	$-0.450365\pi$
$41$	1.98882			0.310602			0.155301	+	0.987867i	$0.450365\pi$
$42$	10.8741	−	3.07006i	1.67791	−	0.473721i
$43$	4.59323			0.700461			0.350230	−	0.936664i	$-0.386103\pi$
$43$	4.59323			0.700461			0.350230	+	0.936664i	$0.386103\pi$
$44$	−2.84809	+	1.64435i	−0.429366	+	0.247894i
$45$	5.29358	+	7.02789i	0.789121	+	1.04766i
$46$	−11.7543	+	20.3591i	−1.73308	+	3.00179i
$47$	−0.904136	−	1.56601i	−0.131882	−	0.228426i	0.792520	−	0.609846i	$-0.208769\pi$
$47$	−0.904136	−	1.56601i	−0.131882	−	0.228426i	−0.924402	+	0.381420i	$0.875435\pi$
$48$	−6.47657	+	4.28577i	−0.934813	+	0.618598i
$49$	−5.70191	−	4.06056i	−0.814559	−	0.580080i
$50$		−	8.88010i		−	1.25584i
$51$	7.60197	+	3.79120i	1.06449	+	0.530875i
$52$	3.53302	+	2.03979i	0.489942	+	0.282868i
$53$	−3.53060	−	2.03839i	−0.484966	−	0.279995i	0.237518	−	0.971383i	$-0.423666\pi$
$53$	−3.53060	−	2.03839i	−0.484966	−	0.279995i	−0.722484	+	0.691388i	$0.756999\pi$
$54$	−8.31769	−	9.74498i	−1.13189	−	1.32612i
$55$			2.36425i			0.318796i
$56$	12.9221	+	4.13094i	1.72678	+	0.552021i
$57$	6.25409	+	9.45105i	0.828374	+	1.25182i
$58$	2.42380	+	4.19815i	0.318261	+	0.551244i
$59$	−4.39070	+	7.60491i	−0.571620	+	0.990075i	0.424780	+	0.905297i	$0.360351\pi$
$59$	−4.39070	+	7.60491i	−0.571620	+	0.990075i	−0.996400	+	0.0847780i	$0.972982\pi$
$60$	1.26296	+	20.6850i	0.163048	+	2.67042i
$61$	−8.96446	+	5.17563i	−1.14778	+	0.662672i	−0.948346	−	0.317239i	$-0.897244\pi$
$61$	−8.96446	+	5.17563i	−1.14778	+	0.662672i	−0.199436	+	0.979911i	$0.563911\pi$
$62$	14.3275			1.81959
$63$	−1.47915	+	7.79821i	−0.186355	+	0.982482i
$64$	6.99387			0.874233
$65$	2.53990	−	1.46641i	0.315036	−	0.181886i
$66$	−0.209813	−	3.43635i	−0.0258262	−	0.422985i
$67$	0.391145	−	0.677483i	0.0477859	−	0.0827677i	−0.841143	−	0.540813i	$-0.818117\pi$
$67$	0.391145	−	0.677483i	0.0477859	−	0.0827677i	0.888929	+	0.458045i	$0.151450\pi$
$68$	10.0042	+	17.3278i	1.21319	+	2.10130i
$69$	−9.11324	−	13.7718i	−1.09711	−	1.65792i
$70$	14.1573	−	12.8695i	1.69212	−	1.53820i
$71$		−	2.26943i		−	0.269332i	−0.990891	−	0.134666i	$-0.957004\pi$
$71$		−	2.26943i		−	0.269332i	0.990891	−	0.134666i	$-0.0429961\pi$
$72$	−1.87148	−	15.2685i	−0.220555	−	1.79941i
$73$	4.80065	+	2.77165i	0.561873	+	0.324398i	0.753897	−	0.656993i	$-0.228172\pi$
$73$	4.80065	+	2.77165i	0.561873	+	0.324398i	−0.192024	+	0.981390i	$0.561505\pi$
$74$	6.04021	+	3.48732i	0.702160	+	0.405392i
$75$	5.58226	+	2.78394i	0.644584	+	0.321462i
$76$			26.6931i			3.06190i
$77$	−1.57821	+	1.43465i	−0.179854	+	0.163493i
$78$	−3.56151	+	2.35677i	−0.403262	+	0.266852i
$79$	−4.60034	−	7.96803i	−0.517579	−	0.896473i	−0.999792	−	0.0204190i	$-0.993500\pi$
$79$	−4.60034	−	7.96803i	−0.517579	−	0.896473i	0.482212	−	0.876054i	$-0.339833\pi$
$80$	−6.57513	+	11.3885i	−0.735122	+	1.27327i
$81$	8.73358	−	2.17363i	0.970397	−	0.241514i
$82$	−4.24682	+	2.45190i	−0.468983	+	0.270767i
$83$	1.72902			0.189785			0.0948924	−	0.995488i	$-0.469749\pi$
$83$	1.72902			0.189785			0.0948924	+	0.995488i	$0.469749\pi$
$84$	−13.0415	+	13.3949i	−1.42294	+	1.46150i
$85$	14.3841			1.56018
$86$	−9.80812	+	5.66272i	−1.05764	+	0.610627i
$87$	−3.39894	+	0.207529i	−0.364404	+	0.0222495i
$88$	2.06676	−	3.57973i	0.220317	−	0.381601i
$89$	−6.09126	−	10.5504i	−0.645672	−	1.11834i	−0.984146	−	0.177361i	$-0.943244\pi$
$89$	−6.09126	−	10.5504i	−0.645672	−	1.11834i	0.338474	−	0.940976i	$-0.390089\pi$
$90$	−19.9679	−	8.48082i	−2.10480	−	0.893957i
$91$	2.52011	+	0.805632i	0.264179	+	0.0844532i
$92$		−	38.8962i		−	4.05521i
$93$	−4.49172	+	9.00662i	−0.465769	+	0.933943i
$94$	3.86128	+	2.22931i	0.398261	+	0.229936i
$95$	16.6188	+	9.59488i	1.70505	+	0.984414i
$96$	0.618783	−	1.24076i	0.0631543	−	0.126635i
$97$		−	9.91566i		−	1.00678i	−0.864058	−	0.503392i	$-0.832085\pi$
$97$		−	9.91566i		−	1.00678i	0.864058	−	0.503392i	$-0.167915\pi$
$98$	17.1816	+	1.64114i	1.73560	+	0.165780i
$99$	2.22595	+	0.945414i	0.223717	+	0.0950176i
$100$	7.34626	+	12.7241i	0.734626	+	1.27241i
$101$	−1.34106	+	2.32279i	−0.133441	+	0.231126i	−0.925001	−	0.379965i	$-0.875936\pi$
$101$	−1.34106	+	2.32279i	−0.133441	+	0.231126i	0.791560	+	0.611092i	$0.209269\pi$
$102$	−20.9068	+	1.27651i	−2.07008	+	0.126393i
$103$	9.04672	−	5.22313i	0.891400	−	0.514650i	0.0169999	−	0.999855i	$-0.494588\pi$
$103$	9.04672	−	5.22313i	0.891400	−	0.514650i	0.874400	+	0.485205i	$0.161255\pi$
$104$	−5.12758			−0.502801
$105$	3.65172	+	12.9343i	0.356371	+	1.26226i
$106$	10.0521			0.976342
$107$	−2.22421	+	1.28415i	−0.215022	+	0.124143i	−0.603643	−	0.797255i	$-0.706285\pi$
$107$	−2.22421	+	1.28415i	−0.215022	+	0.124143i	0.388621	+	0.921398i	$0.372952\pi$
$108$	19.9800	+	7.08238i	1.92258	+	0.681502i
$109$	5.79331	−	10.0343i	0.554898	−	0.961112i	−0.443013	−	0.896515i	$-0.646090\pi$
$109$	5.79331	−	10.0343i	0.554898	−	0.961112i	0.997911	−	0.0645969i	$-0.0205762\pi$
$110$	−2.91475	−	5.04849i	−0.277910	−	0.481355i
$111$	−4.08585	+	2.70374i	−0.387811	+	0.256628i
$112$	−11.5920	+	2.52151i	−1.09534	+	0.238260i
$113$		−	13.4782i		−	1.26792i	−0.773366	−	0.633959i	$-0.781429\pi$
$113$		−	13.4782i		−	1.26792i	0.773366	−	0.633959i	$-0.218571\pi$
$114$	−25.0063	−	12.4709i	−2.34205	−	1.16801i
$115$	−24.2164	−	13.9813i	−2.25819	−	1.30377i
$116$	−6.94603	−	4.01029i	−0.644923	−	0.372346i
$117$	−0.364982	−	2.97772i	−0.0337426	−	0.275290i
$118$		−	21.6521i		−	1.99324i
$119$	8.72841	+	9.60186i	0.800132	+	0.880201i
$120$	−14.3741	−	21.7218i	−1.31217	−	1.98292i
$121$	−5.17507	−	8.96349i	−0.470461	−	0.814863i
$122$	12.7615	−	22.1035i	1.15537	−	2.00116i
$123$	−0.209935	−	3.43834i	−0.0189292	−	0.310025i
$124$	−20.5295	+	11.8527i	−1.84361	+	1.06441i
$125$	−4.10162			−0.366860
$126$	−6.45547	−	18.4754i	−0.575099	−	1.64592i
$127$	−3.34872			−0.297151			−0.148575	−	0.988901i	$-0.547469\pi$
$127$	−3.34872			−0.297151			−0.148575	+	0.988901i	$0.547469\pi$
$128$	−16.3208	+	9.42281i	−1.44257	+	0.832867i
$129$	−0.484850	−	7.94092i	−0.0426886	−	0.699159i
$130$	−3.61571	+	6.26259i	−0.317119	+	0.549265i
$131$	3.97542	+	6.88562i	0.347334	+	0.601600i	0.985775	−	0.168071i	$-0.0537538\pi$
$131$	3.97542	+	6.88562i	0.347334	+	0.601600i	−0.638441	+	0.769671i	$0.720420\pi$
$132$	3.14343	+	4.75029i	0.273601	+	0.413460i
$133$	3.67956	+	16.9158i	0.319058	+	1.46679i
$134$			1.92888i			0.166630i
$135$	11.5913	−	9.89356i	0.997617	−	0.851502i
$136$	−21.7791	−	12.5742i	−1.86755	−	1.07823i
$137$	−9.72168	−	5.61282i	−0.830579	−	0.479535i	0.0234717	−	0.999725i	$-0.492528\pi$
$137$	−9.72168	−	5.61282i	−0.830579	−	0.479535i	−0.854051	+	0.520189i	$0.825861\pi$
$138$	36.4383	+	18.1722i	3.10183	+	1.54692i
$139$			4.17599i			0.354203i	0.984193	+	0.177101i	$0.0566721\pi$
$139$			4.17599i			0.354203i	−0.984193	+	0.177101i	$0.943328\pi$
$140$	−9.63915	+	30.1524i	−0.814657	+	2.54834i
$141$	−2.61193	+	1.72840i	−0.219964	+	0.145558i
$142$	2.79784	+	4.84601i	0.234790	+	0.406668i
$143$	0.403067	−	0.698133i	0.0337062	−	0.0583808i
$144$	8.09302	+	10.7445i	0.674419	+	0.895375i
$145$	−4.99353	+	2.88302i	−0.414690	+	0.239422i
$146$	−13.6680			−1.13117
$147$	−6.41815	+	10.2863i	−0.529360	+	0.848397i
$148$	−11.5398			−0.948570
$149$	10.1685	−	5.87080i	0.833039	−	0.480955i	−0.0218533	−	0.999761i	$-0.506957\pi$
$149$	10.1685	−	5.87080i	0.833039	−	0.480955i	0.854892	+	0.518806i	$0.173623\pi$
$150$	−15.3522	+	0.937360i	−1.25350	+	0.0765351i
$151$	0.0492351	−	0.0852776i	0.00400669	−	0.00693979i	−0.864015	−	0.503466i	$-0.832058\pi$
$151$	0.0492351	−	0.0852776i	0.00400669	−	0.00693979i	0.868022	+	0.496526i	$0.165391\pi$
$152$	−16.7751	−	29.0553i	−1.36064	−	2.35670i
$153$	5.75190	−	13.5427i	0.465014	−	1.09486i
$154$	1.60133	−	5.00915i	0.129039	−	0.403649i
$155$			17.0419i			1.36884i
$156$	3.15352	−	6.32331i	0.252483	−	0.506270i
$157$	6.35962	+	3.67173i	0.507553	+	0.293036i	0.731827	−	0.681490i	$-0.238668\pi$
$157$	6.35962	+	3.67173i	0.507553	+	0.293036i	−0.224274	+	0.974526i	$0.572001\pi$
$158$	19.6466	+	11.3430i	1.56300	+	0.902399i
$159$	−3.15136	+	6.31898i	−0.249919	+	0.501128i
$160$		−	2.34772i		−	0.185603i
$161$	−5.36172	−	24.6492i	−0.422563	−	1.94263i
$162$	−15.9694	+	15.4085i	−1.25468	+	1.21061i
$163$	10.0504	+	17.4077i	0.787205	+	1.36348i	0.927673	+	0.373393i	$0.121806\pi$
$163$	10.0504	+	17.4077i	0.787205	+	1.36348i	−0.140469	+	0.990085i	$0.544861\pi$
$164$	4.05678	−	7.02655i	0.316782	−	0.548682i
$165$	4.08740	−	0.249565i	0.318203	−	0.0194286i
$166$	−3.69205	+	2.13161i	−0.286559	+	0.165445i
$167$	24.4093			1.88885			0.944424	−	0.328731i	$-0.106621\pi$
$167$	24.4093			1.88885			0.944424	+	0.328731i	$0.106621\pi$
$168$	5.77768	−	22.7761i	0.445758	−	1.75722i
$169$	−1.00000			−0.0769231
$170$	−30.7151	+	17.7333i	−2.35574	+	1.36009i
$171$	15.6791	−	11.8099i	1.19901	−	0.903125i
$172$	9.36922	−	16.2280i	0.714397	−	1.23737i
$173$	−6.40841	−	11.0997i	−0.487222	−	0.843894i	0.512670	−	0.858586i	$-0.328657\pi$
$173$	−6.40841	−	11.0997i	−0.487222	−	0.843894i	−0.999892	+	0.0146919i	$0.995323\pi$
$174$	7.00205	−	4.63349i	0.530824	−	0.351264i
$175$	6.40942	+	7.05081i	0.484507	+	0.532991i
$176$			3.61456i			0.272458i
$177$	13.6111	+	6.78802i	1.02307	+	0.510219i
$178$	26.0138	+	15.0191i	1.94982	+	1.12573i
$179$	−10.9437	−	6.31834i	−0.817970	−	0.472255i	0.0317462	−	0.999496i	$-0.489893\pi$
$179$	−10.9437	−	6.31834i	−0.817970	−	0.472255i	−0.849716	+	0.527241i	$0.823227\pi$
$180$	35.6275	−	4.36690i	2.65552	−	0.325490i
$181$		−	19.0550i		−	1.41635i	−0.706037	−	0.708175i	$-0.749519\pi$
$181$		−	19.0550i		−	1.41635i	0.706037	−	0.708175i	$-0.250481\pi$
$182$	−6.37451	+	1.38659i	−0.472510	+	0.102781i
$183$	9.89406	+	14.9517i	0.731390	+	1.10526i
$184$	24.4441	+	42.3384i	1.80204	+	3.12123i
$185$	−4.14802	+	7.18459i	−0.304969	+	0.528221i
$186$	−1.51237	−	24.7698i	−0.110892	−	1.81621i
$187$	3.42401	−	1.97686i	0.250389	−	0.144562i
$188$	−7.37699			−0.538023
$189$	13.6379	+	1.73404i	0.992013	+	0.126133i
$190$	−47.3158			−3.43265
$191$	−19.9851	+	11.5384i	−1.44607	+	0.834890i	−0.998244	−	0.0592301i	$-0.981135\pi$
$191$	−19.9851	+	11.5384i	−1.44607	+	0.834890i	−0.447827	+	0.894120i	$0.647802\pi$
$192$	−0.738255	−	12.0912i	−0.0532789	−	0.872608i
$193$	4.58543	−	7.94220i	0.330067	−	0.571692i	−0.652458	−	0.757825i	$-0.726262\pi$
$193$	4.58543	−	7.94220i	0.330067	−	0.571692i	0.982525	+	0.186133i	$0.0595954\pi$
$194$	12.2244	+	21.1733i	0.877663	+	1.52016i
$195$	−2.80329	−	4.23627i	−0.200748	−	0.303366i
$196$	−25.9768	+	11.8623i	−1.85548	+	0.847306i
$197$		−	2.77957i		−	0.198036i	−0.995086	−	0.0990180i	$-0.968430\pi$
$197$		−	2.77957i		−	0.198036i	0.995086	−	0.0990180i	$-0.0315701\pi$
$198$	−5.91872	+	0.725464i	−0.420625	+	0.0515565i
$199$	18.9718	+	10.9534i	1.34488	+	0.776464i	0.987518	−	0.157503i	$-0.0503445\pi$
$199$	18.9718	+	10.9534i	1.34488	+	0.776464i	0.357357	+	0.933968i	$0.383678\pi$
$200$	−15.9928	−	9.23344i	−1.13086	−	0.652903i
$201$	−1.21254	−	0.604710i	−0.0855261	−	0.0426530i
$202$		−	6.61327i		−	0.465308i
$203$	−4.95462	−	1.58390i	−0.347746	−	0.111168i
$204$	28.9008	−	19.1247i	2.02346	−	1.33899i
$205$	−2.91644	−	5.05142i	−0.203693	−	0.352806i
$206$	−12.8786	+	22.3063i	−0.897292	+	1.55416i
$207$	−22.8471	+	17.2090i	−1.58798	+	1.19611i
$208$	3.88310	−	2.24191i	0.269244	−	0.155448i
$209$	5.27461			0.364852
$210$	−23.7436	−	23.1172i	−1.63846	−	1.59524i
$211$	−1.97243			−0.135788			−0.0678938	−	0.997693i	$-0.521628\pi$
$211$	−1.97243			−0.135788			−0.0678938	+	0.997693i	$0.521628\pi$
$212$	−14.4034	+	8.31579i	−0.989228	+	0.571131i
$213$	−3.92346	+	0.239555i	−0.268831	+	0.0164140i
$214$	3.16630	−	5.48418i	0.216444	−	0.374891i
$215$	−6.73558	−	11.6664i	−0.459362	−	0.795639i
$216$	−26.1991	+	4.84717i	−1.78262	+	0.329808i
$217$	−11.3760	+	10.3412i	−0.772255	+	0.702006i
$218$			28.5689i			1.93493i
$219$	4.28498	−	8.59208i	0.289552	−	0.580599i
$220$	8.35296	+	4.82258i	0.563156	+	0.325138i
$221$	−4.24745	−	2.45226i	−0.285714	−	0.164957i
$222$	5.39139	−	10.8106i	0.361847	−	0.725561i
$223$		−	15.4061i		−	1.03167i	−0.856688	−	0.515834i	$-0.827482\pi$
$223$		−	15.4061i		−	1.03167i	0.856688	−	0.515834i	$-0.172518\pi$
$224$	1.56717	−	1.42461i	0.104711	−	0.0951859i
$225$	4.22372	−	9.94465i	0.281581	−	0.662976i
$226$	16.6164	+	28.7805i	1.10531	+	1.91445i
$227$	−2.54440	+	4.40703i	−0.168878	+	0.292505i	−0.938026	−	0.346566i	$-0.887348\pi$
$227$	−2.54440	+	4.40703i	−0.168878	+	0.292505i	0.769148	+	0.639071i	$0.220681\pi$
$228$	46.1478	−	2.81765i	3.05621	−	0.186604i
$229$	−12.2357	+	7.06429i	−0.808559	+	0.466822i	−0.846455	−	0.532460i	$-0.821268\pi$
$229$	−12.2357	+	7.06429i	−0.808559	+	0.466822i	0.0378962	+	0.999282i	$0.487934\pi$
$230$	68.9470			4.54623
$231$	2.64686	+	2.57703i	0.174150	+	0.169556i
$232$	10.0810			0.661850
$233$	7.70435	−	4.44811i	0.504729	−	0.291405i	−0.225935	−	0.974142i	$-0.572544\pi$
$233$	7.70435	−	4.44811i	0.504729	−	0.291405i	0.730664	+	0.682737i	$0.239210\pi$
$234$	4.45041	+	5.90848i	0.290932	+	0.386249i
$235$	−2.65168	+	4.59284i	−0.172976	+	0.299604i
$236$	17.9122	+	31.0248i	1.16598	+	2.01954i
$237$	−13.2898	+	8.79430i	−0.863264	+	0.571251i
$238$	−30.4757	−	9.74251i	−1.97545	−	0.631513i
$239$			13.4414i			0.869452i	0.900563	+	0.434726i	$0.143155\pi$
$239$			13.4414i			0.869452i	−0.900563	+	0.434726i	$0.856845\pi$
$240$	20.3828	+	10.1652i	1.31570	+	0.656158i
$241$	−4.54772	−	2.62563i	−0.292944	−	0.169131i	0.346325	−	0.938115i	$-0.387430\pi$
$241$	−4.54772	−	2.62563i	−0.292944	−	0.169131i	−0.639269	+	0.768983i	$0.720763\pi$
$242$	22.1011	+	12.7601i	1.42071	+	0.820249i
$243$	−4.67973	−	14.8694i	−0.300205	−	0.953875i
$244$			42.2288i			2.70342i
$245$	−1.95207	+	20.4368i	−0.124713	+	1.30566i
$246$	4.68721	+	7.08322i	0.298845	+	0.451609i
$247$	−3.27154	−	5.66648i	−0.208163	−	0.360550i
$248$	14.8976	−	25.8033i	0.945996	−	1.63851i
$249$	−0.182511	−	2.98919i	−0.0115662	−	0.189432i
$250$	8.75837	−	5.05665i	0.553928	−	0.319810i
$251$	11.0481			0.697348			0.348674	−	0.937244i	$-0.386632\pi$
$251$	11.0481			0.697348			0.348674	+	0.937244i	$0.386632\pi$
$252$	24.5341	+	21.1326i	1.54550	+	1.33123i
$253$	−7.68598			−0.483214
$254$	7.15066	−	4.12844i	0.448673	−	0.259041i
$255$	−1.51835	−	24.8678i	−0.0950830	−	1.55728i
$256$	16.2398	−	28.1281i	1.01499	−	1.75801i
$257$	−7.44545	−	12.8959i	−0.464434	−	0.804424i	0.534742	−	0.845016i	$-0.320409\pi$
$257$	−7.44545	−	12.8959i	−0.464434	−	0.804424i	−0.999176	+	0.0405920i	$0.987076\pi$
$258$	10.8252	+	16.3588i	0.673948	+	1.01846i
$259$	−7.31299	+	1.59073i	−0.454407	+	0.0988433i
$260$		−	11.9647i		−	0.742020i
$261$	0.717567	+	5.85429i	0.0444163	+	0.362371i
$262$	−16.9777	−	9.80211i	−1.04889	−	0.605576i
$263$	−14.2738	−	8.24099i	−0.880161	−	0.508161i	−0.00944918	−	0.999955i	$-0.503008\pi$
$263$	−14.2738	−	8.24099i	−0.880161	−	0.508161i	−0.870711	+	0.491794i	$0.836341\pi$
$264$	−6.40692	−	3.19521i	−0.394319	−	0.196652i
$265$			11.9565i			0.734483i
$266$	−28.7116	−	31.5848i	−1.76042	−	1.93659i
$267$	−17.5968	+	11.6444i	−1.07691	+	0.712628i
$268$	−1.59571	−	2.76385i	−0.0974733	−	0.168829i
$269$	−1.24183	+	2.15091i	−0.0757156	+	0.131143i	−0.901397	−	0.432993i	$-0.857457\pi$
$269$	−1.24183	+	2.15091i	−0.0757156	+	0.131143i	0.825682	+	0.564136i	$0.190791\pi$
$270$	−12.5541	+	35.4163i	−0.764021	+	2.15537i
$271$	15.1860	−	8.76763i	0.922483	−	0.532596i	0.0380564	−	0.999276i	$-0.487883\pi$
$271$	15.1860	−	8.76763i	0.922483	−	0.532596i	0.884426	+	0.466680i	$0.154550\pi$
$272$	21.9910			1.33340
$273$	1.12679	−	4.44189i	0.0681961	−	0.268835i
$274$	27.6788			1.67214
$275$	2.51431	−	1.45164i	0.151619	−	0.0875371i
$276$	−67.2450	+	4.10578i	−4.04767	+	0.247139i
$277$	−14.4629	+	25.0504i	−0.868990	+	1.50513i	−0.00595989	+	0.999982i	$0.501897\pi$
$277$	−14.4629	+	25.0504i	−0.868990	+	1.50513i	−0.863030	+	0.505153i	$0.831436\pi$
$278$	−5.14833	−	8.91717i	−0.308776	−	0.534816i
$279$	16.0451	+	6.81470i	0.960592	+	0.407986i
$280$	−8.45691	−	38.8785i	−0.505397	−	2.32343i
$281$			11.0843i			0.661231i	0.943765	+	0.330616i	$0.107256\pi$
$281$			11.0843i			0.661231i	−0.943765	+	0.330616i	$0.892744\pi$
$282$	3.44652	−	6.91082i	0.205237	−	0.411534i
$283$	−18.2010	−	10.5083i	−1.08193	−	0.624655i	−0.150517	−	0.988607i	$-0.548094\pi$
$283$	−18.2010	−	10.5083i	−1.08193	−	0.624655i	−0.931418	+	0.363952i	$0.881427\pi$
$284$	−8.01794	−	4.62916i	−0.475777	−	0.274690i
$285$	14.8337	−	29.7439i	0.878672	−	1.76188i
$286$			1.98767i			0.117533i
$287$	1.60226	−	5.01205i	0.0945784	−	0.295852i
$288$	−2.21038	−	0.938800i	−0.130248	−	0.0553193i
$289$	−3.52721	−	6.10930i	−0.207483	−	0.359371i
$290$	7.10860	−	12.3125i	0.417431	−	0.723012i
$291$	−17.1425	+	1.04667i	−1.00491	+	0.0613570i
$292$	19.5846	−	11.3072i	1.14610	−	0.661703i
$293$	5.98434			0.349609			0.174804	−	0.984603i	$-0.444071\pi$
$293$	5.98434			0.349609			0.174804	+	0.984603i	$0.444071\pi$
$294$	1.02361	−	29.8773i	0.0596984	−	1.74248i
$295$	25.7543			1.49947
$296$	12.5611	−	7.25216i	0.730099	−	0.421523i
$297$	1.39949	−	3.94809i	0.0812069	−	0.229092i
$298$	−14.4755	+	25.0724i	−0.838545	+	1.45240i
$299$	4.76718	+	8.25700i	0.275693	+	0.477515i
$300$	21.2224	−	14.0436i	1.22527	−	0.810806i
$301$	3.70045	−	11.5754i	0.213291	−	0.667198i
$302$			0.242796i			0.0139713i
$303$	4.15727	+	2.07328i	0.238829	+	0.119107i
$304$	25.4075	+	14.6690i	1.45722	+	0.841325i
$305$	26.2912	+	15.1792i	1.50543	+	0.869161i
$306$	4.41373	+	36.0095i	0.252316	+	2.05853i
$307$		−	13.5899i		−	0.775618i	−0.921740	−	0.387809i	$-0.873232\pi$
$307$		−	13.5899i		−	0.775618i	0.921740	−	0.387809i	$-0.126768\pi$
$308$	1.84942	+	8.50224i	0.105380	+	0.484460i
$309$	−9.98486	−	15.0889i	−0.568019	−	0.858379i
$310$	−21.0100	−	36.3904i	−1.19329	−	2.06683i
$311$	2.29156	−	3.96910i	0.129943	−	0.225067i	−0.793712	−	0.608294i	$-0.791854\pi$
$311$	2.29156	−	3.96910i	0.129943	−	0.225067i	0.923654	+	0.383227i	$0.125187\pi$
$312$	0.541254	+	8.86472i	0.0306425	+	0.501866i
$313$	9.12611	−	5.26896i	0.515838	−	0.297819i	−0.219392	−	0.975637i	$-0.570407\pi$
$313$	9.12611	−	5.26896i	0.515838	−	0.297819i	0.735230	+	0.677817i	$0.237074\pi$
$314$	−18.1066			−1.02181
$315$	21.9757	−	7.67852i	1.23819	−	0.432635i
$316$	−37.5349			−2.11151
$317$	1.89550	−	1.09437i	0.106462	−	0.0614658i	−0.445824	−	0.895121i	$-0.647089\pi$
$317$	1.89550	−	1.09437i	0.106462	−	0.0614658i	0.552286	+	0.833655i	$0.313756\pi$
$318$	−1.06107	−	17.3783i	−0.0595018	−	0.974527i
$319$	−0.792443	+	1.37255i	−0.0443683	+	0.0768482i
$320$	−10.2559	−	17.7637i	−0.573322	−	0.993023i
$321$	2.45485	+	3.70973i	0.137017	+	0.207057i
$322$	41.8376	+	46.0242i	2.33152	+	2.56483i
$323$		−	32.0908i		−	1.78558i
$324$	10.1352	−	35.2896i	0.563067	−	1.96054i
$325$	−3.11897	−	1.80074i	−0.173009	−	0.0998870i
$326$	−42.9219	−	24.7810i	−2.37722	−	1.37249i
$327$	−17.9591	−	8.95646i	−0.993143	−	0.495293i
$328$			10.1979i			0.563082i
$329$	−4.67492	+	1.01690i	−0.257737	+	0.0560633i
$330$	−8.42032	+	5.57201i	−0.463523	+	0.306729i
$331$	8.78035	+	15.2080i	0.482612	+	0.835908i	0.999801	−	0.0199634i	$-0.00635496\pi$
$331$	8.78035	+	15.2080i	0.482612	+	0.835908i	−0.517189	+	0.855871i	$0.673022\pi$
$332$	3.52684	−	6.10867i	0.193561	−	0.335257i
$333$	5.10561	+	6.77834i	0.279786	+	0.371451i
$334$	−52.1222	+	30.0928i	−2.85200	+	1.64660i
$335$	−2.29432			−0.125352
$336$	5.58288	+	19.7744i	0.304571	+	1.07878i
$337$	−6.56950			−0.357864			−0.178932	−	0.983861i	$-0.557264\pi$
$337$	−6.56950			−0.357864			−0.178932	+	0.983861i	$0.557264\pi$
$338$	2.13534	−	1.23284i	0.116147	−	0.0670577i
$339$	−23.3015	+	1.42272i	−1.26556	+	0.0772716i
$340$	29.3406	−	50.8195i	1.59122	−	2.75607i
$341$	2.34213	+	4.05668i	0.126833	+	0.219682i
$342$	−18.9206	+	44.5480i	−1.02311	+	2.40888i
$343$	−14.8267	+	11.0981i	−0.800567	+	0.599243i
$344$			23.5522i			1.26985i
$345$	−21.6151	+	43.3418i	−1.16372	+	2.33345i
$346$	27.3683	+	15.8011i	1.47133	+	0.849472i
$347$	−8.91465	−	5.14687i	−0.478563	−	0.276299i	0.241254	−	0.970462i	$-0.422441\pi$
$347$	−8.91465	−	5.14687i	−0.478563	−	0.276299i	−0.719818	+	0.694163i	$0.755775\pi$
$348$	−6.19992	+	12.4318i	−0.332350	+	0.666416i
$349$			0.183075i			0.00979978i	0.999988	+	0.00489989i	$0.00155969\pi$
$349$			0.183075i			0.00979978i	−0.999988	+	0.00489989i	$0.998440\pi$
$350$	−22.3788	−	7.15409i	−1.19620	−	0.382402i
$351$	−5.10944	+	0.945312i	−0.272722	+	0.0504570i
$352$	−0.322654	−	0.558852i	−0.0171975	−	0.0297869i
$353$	−2.30015	+	3.98397i	−0.122425	+	0.212046i	−0.920723	−	0.390216i	$-0.872400\pi$
$353$	−2.30015	+	3.98397i	−0.122425	+	0.212046i	0.798299	+	0.602262i	$0.205734\pi$
$354$	−37.4328	+	2.28554i	−1.98953	+	0.121475i
$355$	−5.76413	+	3.32792i	−0.305928	+	0.176628i
$356$	−49.6996			−2.63407
$357$	15.6786	−	16.1035i	0.829802	−	0.852288i
$358$	31.1580			1.64675
$359$	25.6134	−	14.7879i	1.35183	−	0.780477i	0.363320	−	0.931664i	$-0.381643\pi$
$359$	25.6134	−	14.7879i	1.35183	−	0.780477i	0.988505	+	0.151188i	$0.0483098\pi$
$360$	−36.0361	+	27.1433i	−1.89927	+	1.43058i
$361$	11.9060	−	20.6218i	0.626632	−	1.08536i
$362$	23.4918	+	40.6890i	1.23470	+	2.13857i
$363$	−14.9501	+	9.89299i	−0.784676	+	0.519247i
$364$	7.98681	−	7.26028i	0.418623	−	0.380542i
$365$		−	16.2576i		−	0.850960i
$366$	−39.5603	−	19.7292i	−2.06785	−	1.03126i
$367$	21.1390	+	12.2046i	1.10344	+	0.637074i	0.937124	−	0.348997i	$-0.113478\pi$
$367$	21.1390	+	12.2046i	1.10344	+	0.637074i	0.166321	+	0.986072i	$0.446811\pi$
$368$	−37.0229	−	21.3752i	−1.92995	−	1.11426i
$369$	−5.92215	+	0.725885i	−0.308295	+	0.0377881i
$370$		−	20.4554i		−	1.06343i
$371$	−7.98135	+	7.25531i	−0.414371	+	0.376677i
$372$	22.6584	+	34.2409i	1.17478	+	1.77531i
$373$	−13.0981	−	22.6867i	−0.678196	−	1.17467i	−0.975524	−	0.219895i	$-0.929429\pi$
$373$	−13.0981	−	22.6867i	−0.678196	−	1.17467i	0.297327	−	0.954776i	$-0.403905\pi$
$374$	−4.87429	+	8.44253i	−0.252044	+	0.436553i
$375$	0.432957	+	7.09101i	0.0223578	+	0.366178i
$376$	8.02984	−	4.63603i	0.414108	−	0.239085i
$377$	1.96603			0.101256
$378$	−31.2594	+	13.1106i	−1.60781	+	0.674338i
$379$	−20.7850			−1.06765			−0.533827	−	0.845594i	$-0.679247\pi$
$379$	−20.7850			−1.06765			−0.533827	+	0.845594i	$0.679247\pi$
$380$	67.7978	−	39.1431i	3.47795	−	2.00800i
$381$	0.353482	+	5.78937i	0.0181095	+	0.296599i
$382$	28.4500	−	49.2769i	1.45563	−	2.52123i
$383$	9.13755	+	15.8267i	0.466907	+	0.808707i	0.999285	−	0.0377998i	$-0.0120349\pi$
$383$	9.13755	+	15.8267i	0.466907	+	0.808707i	−0.532378	+	0.846507i	$0.678702\pi$
$384$	18.0132	+	27.2213i	0.919234	+	1.38913i
$385$	5.95818	+	1.90472i	0.303657	+	0.0970734i
$386$			22.6124i			1.15094i
$387$	−13.6773	+	1.67645i	−0.695258	+	0.0852186i
$388$	−35.0322	−	20.2259i	−1.77849	−	1.02681i
$389$	33.0735	+	19.0950i	1.67689	+	0.968154i	0.963624	+	0.267261i	$0.0861186\pi$
$389$	33.0735	+	19.0950i	1.67689	+	0.968154i	0.713267	+	0.700892i	$0.247215\pi$
$390$	11.2086	+	5.58989i	0.567571	+	0.283055i
$391$			46.7616i			2.36483i
$392$	20.8209	−	29.2370i	1.05161	−	1.47669i
$393$	11.4844	−	7.59965i	0.579314	−	0.383352i
$394$	3.42676	+	5.93533i	0.172638	+	0.299017i
$395$	−13.4920	+	23.3689i	−0.678857	+	1.17581i
$396$	7.88064	−	5.93589i	0.396017	−	0.298290i
$397$	24.1988	−	13.9712i	1.21450	−	0.701193i	0.250765	−	0.968048i	$-0.419318\pi$
$397$	24.1988	−	13.9712i	1.21450	−	0.701193i	0.963737	+	0.266856i	$0.0859847\pi$
$398$	−54.0151			−2.70753
$399$	28.8562	−	8.14692i	1.44462	−	0.407856i
$400$	16.1484			0.807418
$401$	29.6214	−	17.1019i	1.47922	−	0.854029i	0.479497	−	0.877543i	$-0.340819\pi$
$401$	29.6214	−	17.1019i	1.47922	−	0.854029i	0.999723	+	0.0235147i	$0.00748565\pi$
$402$	3.33470	−	0.203607i	0.166320	−	0.0101550i
$403$	2.90538	−	5.03226i	0.144727	−	0.250675i
$404$	5.47098	+	9.47601i	0.272191	+	0.471449i
$405$	−18.3278	−	18.9950i	−0.910717	−	0.943869i
$406$	12.5325	−	2.72609i	0.621978	−	0.135294i
$407$			2.28030i			0.113030i
$408$	−19.4397	+	38.9797i	−0.962408	+	1.92978i
$409$	−19.6445	−	11.3417i	−0.971357	−	0.560813i	−0.0717072	−	0.997426i	$-0.522845\pi$
$409$	−19.6445	−	11.3417i	−0.971357	−	0.560813i	−0.899650	+	0.436613i	$0.856178\pi$
$410$	12.4552	+	7.19100i	0.615118	+	0.355138i
$411$	−8.67742	+	17.3996i	−0.428025	+	0.858260i
$412$		−	42.6163i		−	2.09956i
$413$	15.6279	+	17.1918i	0.769000	+	0.845953i
$414$	27.5704	−	64.9138i	1.35501	−	3.19034i
$415$	−2.53546	−	4.39155i	−0.124461	−	0.215573i
$416$	−0.400248	+	0.693249i	−0.0196238	+	0.0339893i
$417$	7.21958	−	0.440807i	0.353545	−	0.0215864i
$418$	−11.2631	+	6.50275i	−0.550896	+	0.318060i
$419$	−3.77782			−0.184559			−0.0922793	−	0.995733i	$-0.529415\pi$
$419$	−3.77782			−0.184559			−0.0922793	+	0.995733i	$0.529415\pi$
$420$	53.1459	+	13.4817i	2.59325	+	0.657837i
$421$	−15.4562			−0.753288			−0.376644	−	0.926358i	$-0.622922\pi$
$421$	−15.4562			−0.753288			−0.376644	+	0.926358i	$0.622922\pi$
$422$	4.21181	−	2.43169i	0.205028	−	0.118373i
$423$	3.26383	+	4.33314i	0.158693	+	0.210684i
$424$	10.4520	−	18.1035i	0.507596	−	0.879181i
$425$	−8.83178	−	15.2971i	−0.428404	−	0.742018i
$426$	8.08259	−	5.34853i	0.391603	−	0.259137i
$427$	5.82111	+	26.7611i	0.281703	+	1.29506i
$428$			10.4776i			0.506452i
$429$	−1.24950	−	0.623142i	−0.0603265	−	0.0300856i
$430$	28.7655	+	16.6078i	1.38720	+	0.800898i
$431$	26.4572	+	15.2751i	1.27440	+	0.735774i	0.975813	−	0.218609i	$-0.0701518\pi$
$431$	26.4572	+	15.2751i	1.27440	+	0.735774i	0.298586	+	0.954383i	$0.403485\pi$
$432$	17.7212	−	15.1256i	0.852610	−	0.727733i
$433$		−	16.2968i		−	0.783173i	−0.920141	−	0.391587i	$-0.871926\pi$
$433$		−	16.2968i		−	0.783173i	0.920141	−	0.391587i	$-0.128074\pi$
$434$	11.5427	−	36.1068i	0.554066	−	1.73318i
$435$	5.51136	+	8.32865i	0.264249	+	0.399328i
$436$	−23.6343	−	40.9358i	−1.13188	−	1.96047i
$437$	−31.1921	+	54.0263i	−1.49212	+	2.58443i
$438$	1.44276	+	23.6297i	0.0689378	+	1.12907i
$439$	−8.74102	+	5.04663i	−0.417186	+	0.240863i	−0.693873	−	0.720098i	$-0.744097\pi$
$439$	−8.74102	+	5.04663i	−0.417186	+	0.240863i	0.276686	+	0.960960i	$0.410764\pi$
$440$	−12.1229			−0.577937
$441$	18.4607	+	10.0101i	0.879081	+	0.476672i
$442$	12.0930			0.575206
$443$	−6.17202	+	3.56342i	−0.293241	+	0.169303i	−0.639403	−	0.768872i	$-0.720818\pi$
$443$	−6.17202	+	3.56342i	−0.293241	+	0.169303i	0.346161	+	0.938175i	$0.387485\pi$
$444$	1.21812	+	19.9504i	0.0578093	+	0.946806i
$445$	−17.8646	+	30.9424i	−0.846864	+	1.46681i
$446$	18.9933	+	32.8973i	0.899357	+	1.55773i
$447$	−11.2230	−	16.9600i	−0.530829	−	0.802179i
$448$	5.63448	−	17.6253i	0.266204	−	0.832718i
$449$			20.4959i			0.967262i	0.875272	+	0.483631i	$0.160682\pi$
$449$			20.4959i			0.967262i	−0.875272	+	0.483631i	$0.839318\pi$
$450$	3.24108	+	26.4424i	0.152786	+	1.24651i
$451$	−1.38846	−	0.801630i	−0.0653802	−	0.0377473i
$452$	−47.6186	−	27.4926i	−2.23979	−	1.29314i
$453$	−0.152628	−	0.0761174i	−0.00717108	−	0.00357631i
$454$		−	12.5473i		−	0.588876i
$455$	−1.64930	−	7.58223i	−0.0773203	−	0.355460i
$456$	−48.4610	+	32.0683i	−2.26940	+	1.50174i
$457$	19.4091	+	33.6176i	0.907922	+	1.57257i	0.816947	+	0.576713i	$0.195665\pi$
$457$	19.4091	+	33.6176i	0.907922	+	1.57257i	0.0909749	+	0.995853i	$0.471002\pi$
$458$	17.4183	−	30.1694i	0.813903	−	1.40972i
$459$	−24.0202	−	8.51454i	−1.12117	−	0.397425i
$460$	−98.7926	+	57.0379i	−4.60623	+	2.65941i
$461$	−4.74598			−0.221042			−0.110521	−	0.993874i	$-0.535252\pi$
$461$	−4.74598			−0.221042			−0.110521	+	0.993874i	$0.535252\pi$
$462$	−8.82901	−	2.23968i	−0.410763	−	0.104199i
$463$	14.6578			0.681206			0.340603	−	0.940207i	$-0.389369\pi$
$463$	14.6578			0.681206			0.340603	+	0.940207i	$0.389369\pi$
$464$	−7.63430	+	4.40766i	−0.354413	+	0.204621i
$465$	29.4626	−	1.79890i	1.36630	−	0.0834222i
$466$	−10.9676	+	18.9965i	−0.508065	+	0.879995i
$467$	−2.21279	−	3.83267i	−0.102396	−	0.177355i	0.810275	−	0.586049i	$-0.199318\pi$
$467$	−2.21279	−	3.83267i	−0.102396	−	0.177355i	−0.912671	+	0.408694i	$0.865984\pi$
$468$	−11.2648	−	4.78443i	−0.520716	−	0.221160i
$469$	−1.39221	−	1.53153i	−0.0642864	−	0.0707195i
$470$		−	13.0764i		−	0.603168i
$471$	5.67649	−	11.3823i	0.261559	−	0.524468i
$472$	−38.9948	−	22.5136i	−1.79488	−	1.03627i
$473$	−3.20669	−	1.85138i	−0.147444	−	0.0851266i
$474$	17.5362	−	35.1630i	0.805467	−	1.61509i
$475$		−	23.5648i		−	1.08123i
$476$	51.7277	−	11.2519i	2.37093	−	0.515729i
$477$	11.2571	+	4.78115i	0.515428	+	0.218914i
$478$	−16.5711	−	28.7020i	−0.757944	−	1.31280i
$479$	5.89055	−	10.2027i	0.269146	−	0.466175i	−0.699496	−	0.714637i	$-0.746592\pi$
$479$	5.89055	−	10.2027i	0.269146	−	0.466175i	0.968642	+	0.248462i	$0.0799253\pi$
$480$	−4.05880	+	0.247819i	−0.185258	+	0.0113113i
$481$	2.44971	−	1.41434i	0.111697	−	0.0644885i
$482$	12.9479			0.589761
$483$	−42.0483	+	11.8714i	−1.91326	+	0.540168i
$484$	−42.2243			−1.91928
$485$	−25.1848	+	14.5405i	−1.14358	+	0.660249i
$486$	28.3245	+	25.9820i	1.28482	+	1.17857i
$487$	−11.3049	+	19.5806i	−0.512273	+	0.887283i	0.487625	+	0.873053i	$0.337863\pi$
$487$	−11.3049	+	19.5806i	−0.512273	+	0.887283i	−0.999899	+	0.0142305i	$0.995470\pi$
$488$	−26.5385	−	45.9660i	−1.20134	−	2.08078i
$489$	29.0341	−	19.2129i	1.31297	−	0.868837i
$490$	−21.0269	−	46.0461i	−0.949900	−	2.08015i
$491$		−	20.7577i		−	0.936782i	−0.883521	−	0.468391i	$-0.844834\pi$
$491$		−	20.7577i		−	0.936782i	0.883521	−	0.468391i	$-0.155166\pi$
$492$	−12.5759	−	6.27179i	−0.566968	−	0.282754i
$493$	8.35062	+	4.82123i	0.376093	+	0.217137i
$494$	13.9717	+	8.06658i	0.628618	+	0.362933i
$495$	−0.862910	−	7.04007i	−0.0387849	−	0.316428i
$496$			26.0544i			1.16988i
$497$	−5.71921	−	1.82832i	−0.256542	−	0.0820115i
$498$	4.07491	+	6.15793i	0.182601	+	0.275943i
$499$	4.16181	+	7.20846i	0.186308	+	0.322695i	0.944017	−	0.329898i	$-0.107014\pi$
$499$	4.16181	+	7.20846i	0.186308	+	0.322695i	−0.757708	+	0.652593i	$0.773681\pi$
$500$	−8.36645	+	14.4911i	−0.374159	+	0.648062i
$501$	−2.57658	−	42.1995i	−0.115113	−	1.88534i
$502$	−23.5914	+	13.6205i	−1.05294	+	0.607913i
$503$	−40.5206			−1.80672			−0.903361	−	0.428880i	$-0.858908\pi$
$503$	−40.5206			−1.80672			−0.903361	+	0.428880i	$0.858908\pi$
$504$	−39.9860	−	7.58445i	−1.78112	−	0.337838i
$505$	7.86622			0.350042
$506$	16.4122	−	9.47559i	0.729611	−	0.421241i
$507$	0.105557	+	1.72883i	0.00468797	+	0.0767801i
$508$	−6.83069	+	11.8311i	−0.303063	+	0.524920i
$509$	2.09254	+	3.62439i	0.0927504	+	0.160648i	0.908668	−	0.417520i	$-0.137101\pi$
$509$	2.09254	+	3.62439i	0.0927504	+	0.160648i	−0.815917	+	0.578169i	$0.803767\pi$
$510$	33.9002	+	51.2293i	1.50112	+	2.26847i
$511$	10.8524	−	9.86523i	0.480083	−	0.436412i
$512$			42.3930i			1.87352i
$513$	−22.0724	−	25.8599i	−0.974518	−	1.14174i
$514$	31.7971	+	18.3581i	1.40251	+	0.809741i
$515$	−26.5325	−	15.3185i	−1.16916	−	0.675015i
$516$	−29.0444	−	14.4848i	−1.27861	−	0.637659i
$517$			1.45771i			0.0641101i
$518$	13.6546	−	12.4125i	0.599949	−	0.545374i
$519$	−18.5130	+	12.2507i	−0.812632	+	0.537747i
$520$	7.51916	+	13.0236i	0.329737	+	0.571121i
$521$	−4.76939	+	8.26082i	−0.208951	+	0.361913i	−0.951384	−	0.308007i	$-0.900338\pi$
$521$	−4.76939	+	8.26082i	−0.208951	+	0.361913i	0.742434	+	0.669920i	$0.233671\pi$
$522$	−8.74965	−	11.6163i	−0.382962	−	0.508430i
$523$	39.1907	−	22.6268i	1.71369	−	0.989399i	0.784233	−	0.620466i	$-0.213056\pi$
$523$	39.1907	−	22.6268i	1.71369	−	0.989399i	0.929456	−	0.368933i	$-0.120277\pi$
$524$	32.4361			1.41698
$525$	11.5131	−	11.8251i	0.502472	−	0.516088i
$526$	40.6393			1.77196
$527$	24.6809	−	14.2495i	1.07512	−	0.620719i
$528$	6.24896	−	0.381544i	0.271951	−	0.0166046i
$529$	33.9521	−	58.8067i	1.47618	−	2.55681i
$530$	−14.7405	−	25.5313i	−0.640285	−	1.10901i
$531$	10.2986	−	24.2478i	0.446921	−	1.05226i
$532$	67.2695	+	21.5048i	2.91650	+	0.932351i
$533$			1.98882i			0.0861455i
$534$	23.2195	−	46.5589i	1.00481	−	2.01480i
$535$	6.52322	+	3.76618i	0.282023	+	0.162826i
$536$	3.47385	+	2.00563i	0.150047	+	0.0866299i
$537$	−9.76816	+	19.5867i	−0.421527	+	0.845230i
$538$		−	6.12391i		−	0.264020i
$539$	2.34401	+	5.13307i	0.100964	+	0.221097i
$540$	−11.3104	−	61.1330i	−0.486721	−	2.63074i
$541$	−2.48712	−	4.30782i	−0.106930	−	0.185207i	0.807595	−	0.589737i	$-0.200769\pi$
$541$	−2.48712	−	4.30782i	−0.106930	−	0.185207i	−0.914525	+	0.404530i	$0.867435\pi$
$542$	−21.6182	+	37.4438i	−0.928580	+	1.60835i
$543$	−32.9430	+	2.01140i	−1.41372	+	0.0863175i
$544$	−3.40006	+	1.96303i	−0.145776	+	0.0841641i
$545$	−33.9816			−1.45561
$546$	3.07006	+	10.8741i	0.131387	+	0.465368i
$547$	8.47425			0.362333			0.181166	−	0.983452i	$-0.442013\pi$
$547$	8.47425			0.362333			0.181166	+	0.983452i	$0.442013\pi$
$548$	−39.6604	+	22.8979i	−1.69421	+	0.978151i
$549$	24.8046	−	18.6834i	1.05863	−	0.797389i
$550$	−3.57928	+	6.19949i	−0.152621	+	0.264347i
$551$	6.43196	+	11.1405i	0.274011	+	0.474601i
$552$	70.6158	−	46.7289i	3.00561	−	1.98891i
$553$	−23.7865	+	5.17408i	−1.01150	+	0.220024i
$554$		−	71.3217i		−	3.03017i
$555$	12.8588	+	6.41284i	0.545825	+	0.272210i
$556$	14.7539	+	8.51815i	0.625703	+	0.361250i
$557$	5.53943	+	3.19819i	0.234713	+	0.135512i	0.612745	−	0.790281i	$-0.290065\pi$
$557$	5.53943	+	3.19819i	0.234713	+	0.135512i	−0.378031	+	0.925793i	$0.623399\pi$
$558$	−42.6631	+	5.22927i	−1.80607	+	0.221373i
$559$			4.59323i			0.194273i
$560$	23.4030	+	25.7450i	0.988959	+	1.08792i
$561$	−3.77908	−	5.71087i	−0.159553	−	0.241113i
$562$	−13.6651	−	23.6687i	−0.576428	−	0.998403i
$563$	19.2825	−	33.3983i	0.812661	−	1.40757i	−0.0983345	−	0.995153i	$-0.531352\pi$
$563$	19.2825	−	33.3983i	0.812661	−	1.40757i	0.910995	−	0.412417i	$-0.135315\pi$
$564$	0.778697	+	12.7536i	0.0327890	+	0.537023i
$565$	−34.2332	+	19.7646i	−1.44020	+	0.831501i
$566$	51.8203			2.17817
$567$	1.55827	−	23.7607i	0.0654413	−	0.997856i
$568$	11.6367			0.488264
$569$	1.85590	−	1.07151i	0.0778035	−	0.0449199i	−0.460594	−	0.887611i	$-0.652363\pi$
$569$	1.85590	−	1.07151i	0.0778035	−	0.0449199i	0.538397	+	0.842691i	$0.319030\pi$
$570$	4.99454	+	81.8010i	0.209198	+	3.42627i
$571$	17.8324	−	30.8866i	0.746263	−	1.29257i	−0.203339	−	0.979108i	$-0.565179\pi$
$571$	17.8324	−	30.8866i	0.746263	−	1.29257i	0.949602	−	0.313457i	$-0.101487\pi$
$572$	−1.64435	−	2.84809i	−0.0687535	−	0.119085i
$573$	22.0575	+	33.3329i	0.921467	+	1.39250i
$574$	2.75769	+	12.6778i	0.115104	+	0.529160i
$575$			34.3378i			1.43199i
$576$	−20.8257	+	2.55264i	−0.867739	+	0.106360i
$577$	−24.8934	−	14.3722i	−1.03633	−	0.598323i	−0.117536	−	0.993069i	$-0.537499\pi$
$577$	−24.8934	−	14.3722i	−1.03633	−	0.598323i	−0.918791	+	0.394745i	$0.870833\pi$
$578$	15.0636	+	8.69696i	0.626562	+	0.361746i
$579$	−14.2148	−	7.08908i	−0.590745	−	0.294612i
$580$			23.5230i			0.976740i
$581$	1.39296	−	4.35733i	0.0577895	−	0.180772i
$582$	35.3147	−	23.3690i	1.46384	−	0.968675i
$583$	1.64322	+	2.84614i	0.0680552	+	0.117875i
$584$	−14.2119	+	24.6157i	−0.588092	+	1.01860i
$585$	−7.02789	+	5.29358i	−0.290568	+	0.218863i
$586$	−12.7786	+	7.37774i	−0.527880	+	0.304771i
$587$	10.8303			0.447015			0.223507	−	0.974702i	$-0.428249\pi$
$587$	10.8303			0.447015			0.223507	+	0.974702i	$0.428249\pi$
$588$	23.2499	+	43.6573i	0.958811	+	1.80040i
$589$	38.0203			1.56660
$590$	−54.9942	+	31.7509i	−2.26408	+	1.30717i
$591$	−4.80540	+	0.293404i	−0.197668	+	0.0120690i
$592$	−6.34165	+	10.9841i	−0.260640	+	0.451442i
$593$	1.35983	+	2.35529i	0.0558415	+	0.0967203i	0.892595	−	0.450860i	$-0.148883\pi$
$593$	1.35983	+	2.35529i	0.0558415	+	0.0967203i	−0.836753	+	0.547580i	$0.815549\pi$
$594$	1.87897	+	10.1559i	0.0770951	+	0.416701i
$595$	11.5883	−	36.2496i	0.475075	−	1.48609i
$596$		−	47.9008i		−	1.96209i
$597$	16.9339	−	33.9553i	0.693060	−	1.38970i
$598$	−20.3591	−	11.7543i	−0.832547	−	0.480671i
$599$	17.1120	+	9.87963i	0.699179	+	0.403671i	0.807041	−	0.590495i	$-0.201067\pi$
$599$	17.1120	+	9.87963i	0.699179	+	0.403671i	−0.107863	+	0.994166i	$0.534401\pi$
$600$	−14.2749	+	28.6235i	−0.582770	+	1.16855i
$601$			25.1855i			1.02734i	0.857989	+	0.513668i	$0.171714\pi$
$601$			25.1855i			1.02734i	−0.857989	+	0.513668i	$0.828286\pi$
$602$	6.36894	+	29.2796i	0.259579	+	1.19335i
$603$	−0.917449	+	2.16011i	−0.0373614	+	0.0879665i
$604$	−0.200858	−	0.347897i	−0.00817281	−	0.0141557i
$605$	−15.1776	+	26.2884i	−0.617057	+	1.06877i
$606$	−11.4332	+	0.698080i	−0.464443	+	0.0283575i
$607$	9.19098	−	5.30641i	0.373050	−	0.215381i	−0.301740	−	0.953390i	$-0.597567\pi$
$607$	9.19098	−	5.30641i	0.373050	−	0.215381i	0.674790	+	0.738010i	$0.264234\pi$
$608$	−5.23771			−0.212417
$609$	−2.21530	+	8.73289i	−0.0897683	+	0.353875i
$610$	−74.8543			−3.03076
$611$	1.56601	−	0.904136i	0.0633540	−	0.0365774i
$612$	−36.1140	−	47.9459i	−1.45982	−	1.93810i
$613$	−18.9373	+	32.8004i	−0.764870	+	1.32479i	0.175445	+	0.984489i	$0.443863\pi$
$613$	−18.9373	+	32.8004i	−0.764870	+	1.32479i	−0.940315	+	0.340304i	$0.889470\pi$
$614$	16.7542	+	29.0191i	0.676145	+	1.17112i
$615$	−8.42520	+	5.57524i	−0.339737	+	0.224816i
$616$	−7.35628	−	8.09241i	−0.296393	−	0.326053i
$617$			4.29321i			0.172838i	0.996259	+	0.0864191i	$0.0275424\pi$
$617$			4.29321i			0.172838i	−0.996259	+	0.0864191i	$0.972458\pi$
$618$	39.9233	+	19.9103i	1.60595	+	0.800908i
$619$	−13.2571	−	7.65401i	−0.532849	−	0.307641i	0.209327	−	0.977846i	$-0.432873\pi$
$619$	−13.2571	−	7.65401i	−0.532849	−	0.307641i	−0.742176	+	0.670205i	$0.766206\pi$
$620$	60.2095	+	34.7620i	2.41807	+	1.39608i
$621$	32.1631	+	37.6822i	1.29066	+	1.51213i
$622$			11.3005i			0.453110i
$623$	−31.4954	+	6.85093i	−1.26184	+	0.274477i
$624$	−4.28577	−	6.47657i	−0.171568	−	0.259270i
$625$	15.0184	+	26.0126i	0.600735	+	1.04050i
$626$	−12.9916	+	22.5021i	−0.519248	+	0.899364i
$627$	−0.556774	−	9.11891i	−0.0222354	−	0.364174i
$628$	25.9446	−	14.9791i	1.03530	−	0.597731i
$629$	13.8734			0.553167
$630$	−37.4594	+	43.4888i	−1.49242	+	1.73264i
$631$	−44.9784			−1.79056			−0.895280	−	0.445503i	$-0.853025\pi$
$631$	−44.9784			−1.79056			−0.895280	+	0.445503i	$0.853025\pi$
$632$	40.8567	−	23.5886i	1.62519	−	0.938306i
$633$	0.208205	+	3.41000i	0.00827539	+	0.135535i
$634$	−2.69836	+	4.67370i	−0.107166	+	0.185616i
$635$	4.91061	+	8.50543i	0.194872	+	0.337528i
$636$	15.8970	+	24.0232i	0.630357	+	0.952583i
$637$	4.06056	−	5.70191i	0.160885	−	0.225918i
$638$		−	3.90782i		−	0.154712i
$639$	0.828301	+	6.75771i	0.0327671	+	0.267331i
$640$	47.8661	+	27.6355i	1.89207	+	1.09239i
$641$	−14.5890	−	8.42299i	−0.576232	−	0.332688i	0.183402	−	0.983038i	$-0.441289\pi$
$641$	−14.5890	−	8.42299i	−0.576232	−	0.332688i	−0.759635	+	0.650350i	$0.774622\pi$
$642$	−9.81546	−	4.89509i	−0.387385	−	0.193194i
$643$			20.9545i			0.826366i	0.910648	+	0.413183i	$0.135583\pi$
$643$			20.9545i			0.826366i	−0.910648	+	0.413183i	$0.864417\pi$
$644$	−98.0227	−	31.3360i	−3.86264	−	1.23481i
$645$	−19.4582	+	12.8761i	−0.766165	+	0.506998i
$646$	39.5628	+	68.5248i	1.55658	+	2.69607i
$647$	3.68349	−	6.38000i	0.144813	−	0.250824i	−0.784490	−	0.620141i	$-0.787075\pi$
$647$	3.68349	−	6.38000i	0.144813	−	0.250824i	0.929303	+	0.369318i	$0.120409\pi$
$648$	11.1454	+	44.7821i	0.437834	+	1.75921i
$649$	6.13058	−	3.53949i	0.240646	−	0.138937i
$650$	8.88010			0.348306
$651$	19.0790	+	18.5756i	0.747765	+	0.728037i
$652$	82.0025			3.21146
$653$	−21.7548	+	12.5601i	−0.851330	+	0.491515i	−0.861099	−	0.508437i	$-0.830224\pi$
$653$	−21.7548	+	12.5601i	−0.851330	+	0.491515i	0.00976961	+	0.999952i	$0.496890\pi$
$654$	49.3908	−	3.01566i	1.93133	−	0.117922i
$655$	11.6592	−	20.1943i	0.455563	−	0.789058i
$656$	−4.45876	−	7.72280i	−0.174085	−	0.301525i
$657$	−15.3066	−	6.50105i	−0.597166	−	0.253630i
$658$	8.72888	−	7.93485i	0.340287	−	0.309333i
$659$			35.6744i			1.38968i	0.719165	+	0.694839i	$0.244524\pi$
$659$			35.6744i			1.38968i	−0.719165	+	0.694839i	$0.755476\pi$
$660$	7.45571	−	14.9499i	0.290213	−	0.581925i
$661$	−14.5858	−	8.42113i	−0.567323	−	0.327544i	0.188757	−	0.982024i	$-0.439554\pi$
$661$	−14.5858	−	8.42113i	−0.567323	−	0.327544i	−0.756079	+	0.654480i	$0.772888\pi$
$662$	−37.4981	−	21.6495i	−1.45740	−	0.841433i
$663$	−3.79120	+	7.60197i	−0.147238	+	0.295236i
$664$			8.86570i			0.344056i
$665$	37.5688	−	34.1513i	1.45686	−	1.32433i
$666$	−19.2588	−	8.17967i	−0.746265	−	0.316956i
$667$	−9.37244	−	16.2335i	−0.362902	−	0.628565i
$668$	49.7898	−	86.2385i	1.92643	−	3.33667i
$669$	−26.6345	+	1.62623i	−1.02975	+	0.0628736i
$670$	4.89916	−	2.82853i	0.189271	−	0.109276i
$671$	8.34451			0.322136
$672$	−2.62834	−	2.55900i	−0.101390	−	0.0987155i
$673$	−7.72201			−0.297661			−0.148831	−	0.988863i	$-0.547551\pi$
$673$	−7.72201			−0.297661			−0.148831	+	0.988863i	$0.547551\pi$
$674$	14.0281	−	8.09915i	0.540344	−	0.311968i
$675$	−17.6385	−	6.25237i	−0.678905	−	0.240654i
$676$	−2.03979	+	3.53302i	−0.0784535	+	0.135885i
$677$	2.65076	+	4.59125i	0.101877	+	0.176456i	0.912458	−	0.409170i	$-0.134182\pi$
$677$	2.65076	+	4.59125i	0.101877	+	0.176456i	−0.810581	+	0.585627i	$0.800849\pi$
$678$	48.0026	−	31.7650i	1.84353	−	1.21993i
$679$	−24.9886	−	7.98837i	−0.958973	−	0.306566i
$680$			73.7558i			2.82841i
$681$	7.88759	+	3.93364i	0.302253	+	0.150737i
$682$	−10.0025	−	5.77493i	−0.383015	−	0.221134i
$683$	−2.05816	−	1.18828i	−0.0787532	−	0.0454682i	0.460106	−	0.887864i	$-0.347811\pi$
$683$	−2.05816	−	1.18828i	−0.0787532	−	0.0454682i	−0.538859	+	0.842396i	$0.681145\pi$
$684$	−9.74249	−	79.4843i	−0.372513	−	3.03916i
$685$			32.9228i			1.25792i
$686$	17.9779	−	41.9773i	0.686398	−	1.60270i
$687$	13.5045	+	20.4078i	0.515231	+	0.778606i
$688$	−10.2976	−	17.8360i	−0.392592	−	0.679990i
$689$	2.03839	−	3.53060i	0.0776566	−	0.134505i
$690$	−7.27787	−	119.198i	−0.277064	−	4.53778i
$691$	24.4869	−	14.1375i	0.931524	−	0.537815i	0.0442306	−	0.999021i	$-0.485916\pi$
$691$	24.4869	−	14.1375i	0.931524	−	0.537815i	0.887293	+	0.461206i	$0.152583\pi$
$692$	−52.2873			−1.98766
$693$	4.17585	−	4.84799i	0.158627	−	0.184160i
$694$	25.3811			0.963453
$695$	10.6066	−	6.12373i	0.402332	−	0.232286i
$696$	−1.06412	−	17.4283i	−0.0403355	−	0.660619i
$697$	−4.87712	+	8.44742i	−0.184734	+	0.319969i
$698$	−0.225702	−	0.390928i	−0.00854296	−	0.0147968i
$699$	−8.50328	−	12.8500i	−0.321624	−	0.486031i
$700$	37.9845	−	8.26245i	1.43568	−	0.312291i
$701$		−	17.6262i		−	0.665733i	−0.942974	−	0.332867i	$-0.891984\pi$
$701$		−	17.6262i		−	0.665733i	0.942974	−	0.332867i	$-0.108016\pi$
$702$	9.74498	−	8.31769i	0.367801	−	0.313931i
$703$	16.0287	+	9.25417i	0.604533	+	0.349028i
$704$	−4.88265	−	2.81900i	−0.184022	−	0.106245i
$705$	8.22015	+	4.09949i	0.309589	+	0.154396i
$706$		−	11.3429i		−	0.426894i
$707$	4.77328	+	5.25094i	0.179518	+	0.197482i
$708$	51.7459	−	34.2421i	1.94473	−	1.28690i
$709$	14.9460	+	25.8871i	0.561307	+	0.972212i	0.997383	+	0.0723023i	$0.0230346\pi$
$709$	14.9460	+	25.8871i	0.561307	+	0.972212i	−0.436076	+	0.899910i	$0.643632\pi$
$710$	8.20559	−	14.2125i	0.307950	−	0.533386i
$711$	16.6067	+	22.0475i	0.622800	+	0.826845i
$712$	54.0979	−	31.2334i	2.02740	−	1.17052i
$713$	−55.4019			−2.07482
$714$	−13.6262	+	53.7157i	−0.509948	+	2.01026i
$715$	−2.36425			−0.0884181
$716$	−44.6457	+	25.7762i	−1.66849	+	0.963301i
$717$	23.2379	−	1.41884i	0.867835	−	0.0529875i
$718$	−36.4623	+	63.1545i	−1.36076	+	2.35691i
$719$	−11.9755	−	20.7422i	−0.446612	−	0.773554i	0.551551	−	0.834141i	$-0.314036\pi$
$719$	−11.9755	−	20.7422i	−0.446612	−	0.773554i	−0.998163	+	0.0605870i	$0.980703\pi$
$720$	15.4223	−	36.3114i	0.574754	−	1.35325i
$721$	−5.87453	−	27.0067i	−0.218779	−	1.00578i
$722$			58.7128i			2.18506i
$723$	−4.05922	+	8.13939i	−0.150964	+	0.302707i
$724$	−67.3219	−	38.8683i	−2.50200	−	1.44453i
$725$	6.13200	+	3.54031i	0.227737	+	0.131484i
$726$	19.7271	−	39.5560i	0.732141	−	1.46806i
$727$			39.4447i			1.46292i	0.681882	+	0.731462i	$0.261162\pi$
$727$			39.4447i			1.46292i	−0.681882	+	0.731462i	$0.738838\pi$
$728$	−4.13094	+	12.9221i	−0.153103	+	0.478924i
$729$	−25.2128	+	9.66004i	−0.933806	+	0.357779i
$730$	20.0430	+	34.7155i	0.741824	+	1.28488i
$731$	−11.2638	+	19.5095i	−0.416607	+	0.721585i
$732$	73.0065	−	4.45757i	2.69840	−	0.164756i
$733$	−22.3960	+	12.9303i	−0.827216	+	0.477593i	−0.852898	−	0.522077i	$-0.825157\pi$
$733$	−22.3960	+	12.9303i	−0.827216	+	0.477593i	0.0256826	+	0.999670i	$0.491824\pi$
$734$	−60.1852			−2.22148
$735$	35.5378	+	1.21755i	1.31083	+	0.0449100i
$736$	7.63222			0.281327
$737$	−0.546142	+	0.315315i	−0.0201174	+	0.0116148i
$738$	11.7509	−	8.85108i	0.432557	−	0.325813i
$739$	10.8244	−	18.7484i	0.398182	−	0.689672i	−0.595319	−	0.803489i	$-0.702974\pi$
$739$	10.8244	−	18.7484i	0.398182	−	0.689672i	0.993502	+	0.113817i	$0.0363078\pi$
$740$	16.9222	+	29.3101i	0.622072	+	1.07746i
$741$	−9.45105	+	6.25409i	−0.347193	+	0.229750i
$742$	8.09826	−	25.3323i	0.297296	−	0.929978i
$743$		−	31.9647i		−	1.17267i	−0.810068	−	0.586336i	$-0.800570\pi$
$743$		−	31.9647i		−	1.17267i	0.810068	−	0.586336i	$-0.199430\pi$
$744$	−46.1822	−	23.0316i	−1.69312	−	0.844381i
$745$	−29.8226	−	17.2181i	−1.09261	−	0.630821i
$746$	55.9380	+	32.2958i	2.04804	+	1.18243i
$747$	−5.14853	+	0.631062i	−0.188375	+	0.0230893i
$748$		−	16.1295i		−	0.589752i
$749$	1.44430	+	6.63980i	0.0527735	+	0.242613i
$750$	−9.66660	−	14.6080i	−0.352974	−	0.533408i
$751$	21.7753	+	37.7159i	0.794592	+	1.37627i	0.923098	+	0.384566i	$0.125649\pi$
$751$	21.7753	+	37.7159i	0.794592	+	1.37627i	−0.128505	+	0.991709i	$0.541018\pi$
$752$	−4.05398	+	7.02170i	−0.147833	+	0.256055i
$753$	−1.16621	−	19.1003i	−0.0424989	−	0.696052i
$754$	−4.19815	+	2.42380i	−0.152888	+	0.0882697i
$755$	−0.288796			−0.0105104
$756$	33.9449	−	44.6460i	1.23456	−	1.62376i
$757$	−2.70361			−0.0982643			−0.0491321	−	0.998792i	$-0.515646\pi$
$757$	−2.70361			−0.0982643			−0.0491321	+	0.998792i	$0.515646\pi$
$758$	44.3831	−	25.6246i	1.61207	−	0.930727i
$759$	0.811313	+	13.2878i	0.0294488	+	0.482315i
$760$	−49.1985	+	85.2143i	−1.78462	+	3.09105i
$761$	−17.1006	−	29.6191i	−0.619897	−	1.07369i	−0.989504	−	0.144505i	$-0.953841\pi$
$761$	−17.1006	−	29.6191i	−0.619897	−	1.07369i	0.369607	−	0.929188i	$-0.379492\pi$
$762$	−7.89218	−	11.9265i	−0.285903	−	0.432052i
$763$	−20.6203	−	22.6837i	−0.746504	−	0.821206i
$764$			94.1437i			3.40600i
$765$	−42.8319	+	5.24995i	−1.54859	+	0.189812i
$766$	−39.0236	−	22.5303i	−1.40998	−	0.814052i
$767$	−7.60491	−	4.39070i	−0.274597	−	0.158539i
$768$	−50.3430	−	25.1067i	−1.81660	−	0.905961i
$769$			31.1068i			1.12174i	0.827904	+	0.560869i	$0.189533\pi$
$769$			31.1068i			1.12174i	−0.827904	+	0.560869i	$0.810467\pi$
$770$	−15.0710	+	3.27826i	−0.543120	+	0.118140i
$771$	−21.5089	+	14.2332i	−0.774624	+	0.512595i
$772$	−18.7066	−	32.4009i	−0.673267	−	1.16613i
$773$	18.9636	−	32.8459i	0.682073	−	1.18138i	−0.292274	−	0.956335i	$-0.594412\pi$
$773$	18.9636	−	32.8459i	0.682073	−	1.18138i	0.974347	−	0.225050i	$-0.0722546\pi$
$774$	27.1390	−	20.4417i	0.975491	−	0.734763i
$775$	18.1236	−	10.4637i	0.651018	−	0.375866i
$776$	50.8434			1.82517
$777$	3.52205	+	12.4750i	0.126353	+	0.447538i
$778$	−94.1642			−3.37595
$779$	−11.2696	+	6.50652i	−0.403776	+	0.233120i
$780$	−20.6850	+	1.26296i	−0.740640	+	0.0452214i
$781$	−0.914732	+	1.58436i	−0.0327317	+	0.0566930i
$782$	−57.6496	−	99.8520i	−2.06154	−	3.57070i
$783$	10.0453	−	1.85851i	0.358991	−	0.0664179i
$784$	−2.98440	+	31.2445i	−0.106586	+	1.11588i
$785$		−	21.5371i		−	0.768691i
$786$	−15.1541	+	30.3863i	−0.540527	+	1.08384i
$787$	24.3261	+	14.0447i	0.867134	+	0.500640i	0.866395	−	0.499360i	$-0.166431\pi$
$787$	24.3261	+	14.0447i	0.867134	+	0.500640i	0.000738919		1.00000i	$0.499765\pi$
$788$	−9.82027	−	5.66973i	−0.349832	−	0.201976i
$789$	−12.7406	+	25.5469i	−0.453576	+	0.909494i
$790$		−	66.5340i		−	2.36717i
$791$	−33.9665	−	10.8584i	−1.20771	−	0.386082i
$792$	−4.84769	+	11.4138i	−0.172255	+	0.405570i
$793$	−5.17563	−	8.96446i	−0.183792	−	0.318337i
$794$	−34.4484	+	59.6664i	−1.22253	+	2.11748i
$795$	20.6708	−	1.26210i	0.733118	−	0.0447621i
$796$	77.3970	−	44.6852i	2.74326	−	1.58382i
$797$	−6.44578			−0.228321			−0.114161	−	0.993462i	$-0.536418\pi$
$797$	−6.44578			−0.228321			−0.114161	+	0.993462i	$0.536418\pi$
$798$	−51.5740	+	52.9715i	−1.82570	+	1.87517i
$799$	8.86873			0.313753
$800$	−2.49672	+	1.44148i	−0.0882725	+	0.0509641i
$801$	21.9887	+	29.1928i	0.776934	+	1.03148i
$802$	−42.1678	+	73.0368i	−1.48900	+	2.57902i
$803$	−2.23433	−	3.86997i	−0.0788477	−	0.136568i
$804$	−4.60978	+	3.05045i	−0.162575	+	0.107581i
$805$	−54.7440	+	49.7641i	−1.92947	+	1.75395i
$806$			14.3275i			0.504664i
$807$	3.84965	+	1.91987i	0.135514	+	0.0675825i
$808$	−11.9103	−	6.87641i	−0.419003	−	0.241911i
$809$	24.7651	+	14.2982i	0.870696	+	0.502697i	0.867580	−	0.497298i	$-0.165675\pi$
$809$	24.7651	+	14.2982i	0.870696	+	0.502697i	0.00311670	+	0.999995i	$0.499008\pi$
$810$	62.5540	+	17.9655i	2.19792	+	0.631245i
$811$		−	4.66778i		−	0.163908i	−0.996636	−	0.0819539i	$-0.973884\pi$
$811$		−	4.66778i		−	0.163908i	0.996636	−	0.0819539i	$-0.0261160\pi$
$812$	−15.7023	+	14.2739i	−0.551044	+	0.500917i
$813$	−16.7607	−	25.3285i	−0.587825	−	0.888310i
$814$	−2.81125	−	4.86922i	−0.0985341	−	0.170666i
$815$	29.4760	−	51.0539i	1.03250	−	1.78834i
$816$	−2.32131	−	38.0187i	−0.0812623	−	1.33092i
$817$	−26.0274	+	15.0270i	−0.910585	+	0.525727i
$818$	55.9302			1.95555
$819$	−7.79821	−	1.47915i	−0.272492	−	0.0516856i
$820$	−23.7957			−0.830981
$821$	17.5732	−	10.1459i	0.613308	−	0.354094i	−0.160951	−	0.986962i	$-0.551456\pi$
$821$	17.5732	−	10.1459i	0.613308	−	0.354094i	0.774259	+	0.632869i	$0.218123\pi$
$822$	−2.92171	−	47.8520i	−0.101906	−	1.66903i
$823$	9.66510	−	16.7404i	0.336904	−	0.583535i	−0.646945	−	0.762537i	$-0.723953\pi$
$823$	9.66510	−	16.7404i	0.336904	−	0.583535i	0.983849	+	0.179002i	$0.0572868\pi$
$824$	26.7820	+	46.3878i	0.932996	+	1.61600i
$825$	−2.77504	−	4.19359i	−0.0966146	−	0.146002i
$826$	−54.5657	−	17.4436i	−1.89858	−	0.606941i
$827$		−	7.79466i		−	0.271047i	−0.990774	−	0.135523i	$-0.956728\pi$
$827$		−	7.79466i		−	0.271047i	0.990774	−	0.135523i	$-0.0432716\pi$
$828$	14.1964	+	115.822i	0.493360	+	4.02509i
$829$	9.49976	+	5.48469i	0.329940	+	0.190491i	0.655815	−	0.754922i	$-0.272325\pi$
$829$	9.49976	+	5.48469i	0.329940	+	0.190491i	−0.325874	+	0.945413i	$0.605659\pi$
$830$	10.8282	+	6.25164i	0.375851	+	0.216998i
$831$	44.8346	+	22.3596i	1.55530	+	0.775646i
$832$			6.99387i			0.242469i
$833$	31.2296	−	14.2610i	1.08204	−	0.494115i
$834$	−14.8728	+	9.84187i	−0.515004	+	0.340796i
$835$	−35.7941	−	61.9972i	−1.23871	−	2.14550i
$836$	10.7591	−	18.6353i	0.372111	−	0.644516i
$837$	10.0878	−	28.4585i	0.348685	−	0.983671i
$838$	8.06694	−	4.65745i	0.278668	−	0.160889i
$839$	14.4865			0.500129			0.250064	−	0.968229i	$-0.419548\pi$
$839$	14.4865			0.500129			0.250064	+	0.968229i	$0.419548\pi$
$840$	−66.3216	+	18.7245i	−2.28831	+	0.646056i
$841$	25.1347			0.866714
$842$	33.0042	−	19.0550i	1.13740	−	0.656679i
$843$	19.1628	−	1.17003i	0.660002	−	0.0402978i
$844$	−4.02334	+	6.96863i	−0.138489	+	0.239870i
$845$	1.46641	+	2.53990i	0.0504462	+	0.0873753i
$846$	−12.3115	−	5.22896i	−0.423277	−	0.179775i
$847$	−26.7582	+	5.82048i	−0.919422	+	0.199994i
$848$			18.2796i			0.627723i
$849$	−16.2459	+	32.5756i	−0.557557	+	1.11799i
$850$	37.7177	+	21.7763i	1.29371	+	0.746922i
$851$	−23.3565	−	13.4849i	−0.800649	−	0.462255i
$852$	−7.15668	+	14.3503i	−0.245184	+	0.491633i
$853$		−	6.09429i		−	0.208664i	−0.994543	−	0.104332i	$-0.966729\pi$
$853$		−	6.09429i		−	0.208664i	0.994543	−	0.104332i	$-0.0332705\pi$
$854$	−45.4222	−	49.9676i	−1.55432	−	1.70985i
$855$	−52.9881	−	22.5052i	−1.81215	−	0.769663i
$856$	−6.58457	−	11.4048i	−0.225056	−	0.389808i
$857$	−8.65979	+	14.9992i	−0.295813	+	0.512363i	−0.975174	−	0.221442i	$-0.928924\pi$
$857$	−8.65979	+	14.9992i	−0.295813	+	0.512363i	0.679361	+	0.733804i	$0.262257\pi$
$858$	3.43635	−	0.209813i	0.117315	−	0.00716291i
$859$	0.410631	−	0.237078i	0.0140105	−	0.00808898i	−0.492978	−	0.870042i	$-0.664092\pi$
$859$	0.410631	−	0.237078i	0.0140105	−	0.00808898i	0.506989	+	0.861953i	$0.330759\pi$
$860$	−54.9566			−1.87401
$861$	−8.83413	−	2.24098i	−0.301066	−	0.0763723i
$862$	−75.3269			−2.56564
$863$	28.3350	−	16.3592i	0.964533	−	0.556873i	0.0669678	−	0.997755i	$-0.478668\pi$
$863$	28.3350	−	16.3592i	0.964533	−	0.556873i	0.897565	+	0.440882i	$0.145334\pi$
$864$	−1.38970	+	3.92048i	−0.0472787	+	0.133377i
$865$	−18.7948	+	32.5535i	−0.639041	+	1.10685i
$866$	20.0913	+	34.7992i	0.682731	+	1.18252i
$867$	−10.1896	+	6.74283i	−0.346058	+	0.228998i
$868$	13.3309	+	61.2856i	0.452481	+	2.08017i
$869$			7.41699i			0.251604i
$870$	−22.0365	−	10.9899i	−0.747108	−	0.372592i
$871$	0.677483	+	0.391145i	0.0229556	+	0.0132534i
$872$	51.4517	+	29.7057i	1.74237	+	1.00596i
$873$	3.61904	+	29.5260i	0.122486	+	0.999304i
$874$		−	153.820i		−	5.20302i
$875$	−3.30440	+	10.3365i	−0.111709	+	0.349439i
$876$	−21.6155	−	32.6649i	−0.730321	−	1.10365i
$877$	7.16116	+	12.4035i	0.241815	+	0.418836i	0.961231	−	0.275743i	$-0.0889239\pi$
$877$	7.16116	+	12.4035i	0.241815	+	0.418836i	−0.719416	+	0.694579i	$0.755591\pi$
$878$	12.4434	−	21.5526i	0.419944	−	0.727364i
$879$	−0.631692	−	10.3459i	−0.0213064	−	0.348959i
$880$	9.18063	−	5.30044i	0.309479	−	0.178678i
$881$	−19.6297			−0.661342			−0.330671	−	0.943746i	$-0.607275\pi$
$881$	−19.6297			−0.661342			−0.330671	+	0.943746i	$0.607275\pi$
$882$	−51.7608	+	1.38411i	−1.74288	+	0.0466054i
$883$	51.7695			1.74218			0.871091	−	0.491121i	$-0.163413\pi$
$883$	51.7695			1.74218			0.871091	+	0.491121i	$0.163413\pi$
$884$	−17.3278	+	10.0042i	−0.582797	+	0.336478i
$885$	−2.71856	−	44.5248i	−0.0913833	−	1.49669i
$886$	8.78625	−	15.2182i	0.295180	−	0.511266i
$887$	−6.74797	−	11.6878i	−0.226575	−	0.392439i	0.730216	−	0.683216i	$-0.239419\pi$
$887$	−6.74797	−	11.6878i	−0.226575	−	0.392439i	−0.956791	+	0.290777i	$0.906086\pi$
$888$	−13.8637	−	20.9505i	−0.465234	−	0.703053i
$889$	−2.69784	+	8.43915i	−0.0904825	+	0.283040i
$890$		−	88.0969i		−	2.95301i
$891$	−6.97332	−	2.00274i	−0.233615	−	0.0670943i
$892$	−54.4300	−	31.4252i	−1.82245	−	1.05219i
$893$	10.2465	+	5.91585i	0.342888	+	0.197966i
$894$	44.8739	+	22.3792i	1.50081	+	0.748472i
$895$			37.0612i			1.23882i
$896$	10.5980	+	48.7215i	0.354054	+	1.62767i
$897$	13.7718	−	9.11324i	0.459825	−	0.304282i
$898$	−25.2682	−	43.7658i	−0.843211	−	1.46048i
$899$	−5.71207	+	9.89359i	−0.190508	+	0.329970i
$900$	−26.5191	−	35.2075i	−0.883971	−	1.17358i
$901$	17.3159	−	9.99737i	0.576878	−	0.333061i
$902$	3.95313			0.131625
$903$	−20.4026	−	5.17558i	−0.678956	−	0.172233i
$904$	69.1104			2.29858
$905$	−48.3980	+	27.9426i	−1.60880	+	0.928843i
$906$	0.419753	−	0.0256289i	0.0139454	−	0.000851463i
$907$	6.51295	−	11.2808i	0.216259	−	0.374571i	−0.737402	−	0.675454i	$-0.763948\pi$
$907$	6.51295	−	11.2808i	0.216259	−	0.374571i	0.953661	+	0.300882i	$0.0972812\pi$
$908$	10.3801	+	17.9788i	0.344475	+	0.596648i
$909$	3.14553	−	7.40607i	0.104331	−	0.245644i
$910$	12.8695	+	14.1573i	0.426619	+	0.469311i
$911$		−	2.33168i		−	0.0772521i	−0.999254	−	0.0386260i	$-0.987702\pi$
$911$		−	2.33168i		−	0.0772521i	0.999254	−	0.0386260i	$-0.0122981\pi$
$912$	22.6783	−	45.4736i	0.750953	−	1.50578i
$913$	−1.20709	−	0.696912i	−0.0399488	−	0.0230644i
$914$	−82.8903	−	47.8568i	−2.74177	−	1.58296i
$915$	23.4671	−	47.0554i	0.775799	−	1.55560i
$916$			57.6387i			1.90444i
$917$	20.5553	−	4.47121i	0.678794	−	0.147652i
$918$	61.7885	−	11.4317i	2.03932	−	0.377301i
$919$	6.37235	+	11.0372i	0.210204	+	0.364085i	0.951778	−	0.306786i	$-0.0992537\pi$
$919$	6.37235	+	11.0372i	0.210204	+	0.364085i	−0.741574	+	0.670871i	$0.765920\pi$
$920$	71.6904	−	124.171i	2.36356	−	4.09381i
$921$	−23.4947	+	1.43452i	−0.774176	+	0.0472690i
$922$	10.1343	−	5.85104i	0.333755	−	0.192694i
$923$	2.26943			0.0746991
$924$	14.5037	−	4.09481i	0.477137	−	0.134709i
$925$	10.1874			0.334961
$926$	−31.2994	+	18.0707i	−1.02856	+	0.593841i
$927$	−25.0322	+	18.8549i	−0.822166	+	0.619276i
$928$	0.786900	−	1.36295i	0.0258313	−	0.0447411i
$929$	21.9187	+	37.9644i	0.719130	+	1.24557i	0.961345	+	0.275347i	$0.0887928\pi$
$929$	21.9187	+	37.9644i	0.719130	+	1.24557i	−0.242215	+	0.970223i	$0.577874\pi$
$930$	−60.6951	+	40.1640i	−1.99027	+	1.31703i
$931$	45.5941	+	4.35504i	1.49429	+	0.142731i
$932$		−	36.2928i		−	1.18881i
$933$	−7.10380	−	3.54276i	−0.232568	−	0.115985i
$934$	9.45014	+	5.45604i	0.309218	+	0.178527i
$935$	−10.0420	−	5.79778i	−0.328410	−	0.189608i
$936$	15.2685	−	1.87148i	0.499066	−	0.0611711i
$937$		−	40.1737i		−	1.31242i	−0.754580	−	0.656208i	$-0.772159\pi$
$937$		−	40.1737i		−	1.31242i	0.754580	−	0.656208i	$-0.227841\pi$
$938$	4.86098	+	1.55396i	0.158717	+	0.0507387i
$939$	−10.0725	−	15.2213i	−0.328703	−	0.496729i
$940$	10.8177	+	18.7369i	0.352835	+	0.611129i
$941$	2.37739	−	4.11776i	0.0775007	−	0.134235i	−0.824670	−	0.565614i	$-0.808639\pi$
$941$	2.37739	−	4.11776i	0.0775007	−	0.134235i	0.902171	+	0.431379i	$0.141973\pi$
$942$	1.91129	+	31.3033i	0.0622731	+	1.01992i
$943$	16.4217	−	9.48108i	0.534765	−	0.308747i
$944$	39.3741			1.28152
$945$	−15.5946	−	37.1818i	−0.507291	−	1.20953i
$946$	9.12983			0.296836
$947$	4.51696	−	2.60787i	0.146781	−	0.0847442i	−0.424811	−	0.905282i	$-0.639659\pi$
$947$	4.51696	−	2.60787i	0.146781	−	0.0847442i	0.571592	+	0.820538i	$0.306326\pi$
$948$	3.96209	+	64.8916i	0.128683	+	2.10758i
$949$	−2.77165	+	4.80065i	−0.0899717	+	0.155836i
$950$	29.0516	+	50.3189i	0.942559	+	1.63256i
$951$	−2.09206	−	3.16148i	−0.0678397	−	0.102518i
$952$	−49.2343	+	44.7557i	−1.59569	+	1.45054i
$953$			23.6718i			0.766805i	0.923581	+	0.383402i	$0.125248\pi$
$953$			23.6718i			0.766805i	−0.923581	+	0.383402i	$0.874752\pi$
$954$	−29.9322	+	3.66882i	−0.969090	+	0.118782i
$955$	58.6129	+	33.8402i	1.89667	+	1.09504i
$956$	47.4887	+	27.4176i	1.53590	+	0.886749i
$957$	2.45656	+	1.22512i	0.0794093	+	0.0396024i
$958$			29.0484i			0.938512i
$959$	−21.9770	+	19.9778i	−0.709675	+	0.645118i
$960$	−29.6279	+	19.6058i	−0.956237	+	0.632775i
$961$	1.38244	+	2.39446i	0.0445949	+	0.0772406i
$962$	−3.48732	+	6.04021i	−0.112436	+	0.194744i
$963$	6.15437	−	4.63562i	0.198322	−	0.149381i
$964$	−18.5528	+	10.7115i	−0.597545	+	0.344993i
$965$	−26.8966			−0.865831
$966$	75.1519	−	77.1883i	2.41797	−	2.48349i
$967$	34.2346			1.10091			0.550455	−	0.834865i	$-0.314454\pi$
$967$	34.2346			1.10091			0.550455	+	0.834865i	$0.314454\pi$
$968$	45.9610	−	26.5356i	1.47724	−	0.852887i
$969$	−55.4795	+	3.38742i	−1.78226	+	0.108820i
$970$	35.8521	−	62.0977i	1.15114	−	1.99384i
$971$	−12.6736	−	21.9514i	−0.406717	−	0.704454i	0.587803	−	0.809004i	$-0.299993\pi$
$971$	−12.6736	−	21.9514i	−0.406717	−	0.704454i	−0.994520	+	0.104550i	$0.966660\pi$
$972$	−62.0797	−	13.7970i	−1.99121	−	0.442538i
$973$	10.5240	+	3.36431i	0.337383	+	0.107855i
$974$		−	55.7485i		−	1.78630i
$975$	−2.78394	+	5.58226i	−0.0891575	+	0.178775i
$976$	40.1950	+	23.2066i	1.28661	+	0.742825i
$977$	24.7545	+	14.2920i	0.791968	+	0.457243i	0.840655	−	0.541571i	$-0.182170\pi$
$977$	24.7545	+	14.2920i	0.791968	+	0.457243i	−0.0486869	+	0.998814i	$0.515504\pi$
$978$	−38.3114	+	76.8205i	−1.22506	+	2.45645i
$979$			9.82075i			0.313873i
$980$	68.2217	+	48.5834i	2.17926	+	1.55194i
$981$	−13.5885	+	31.9938i	−0.433847	+	1.02148i
$982$	25.5909	+	44.3248i	0.816639	+	1.41446i
$983$	17.1728	−	29.7441i	0.547727	−	0.948690i	−0.450703	−	0.892674i	$-0.648827\pi$
$983$	17.1728	−	29.7441i	0.547727	−	0.948690i	0.998430	−	0.0560165i	$-0.0178399\pi$
$984$	17.6304	−	1.07646i	0.562036	−	0.0343163i
$985$	−7.05983	+	4.07599i	−0.224945	+	0.129872i
$986$	−23.7752			−0.757158
$987$	2.25151	+	7.97481i	0.0716665	+	0.253841i
$988$	−26.6931			−0.849219
$989$	37.9263	−	21.8968i	1.20599	−	0.696277i
$990$	10.5219	+	13.9691i	0.334408	+	0.443968i
$991$	−24.7595	+	42.8847i	−0.786512	+	1.36228i	0.141580	+	0.989927i	$0.454782\pi$
$991$	−24.7595	+	42.8847i	−0.786512	+	1.36228i	−0.928092	+	0.372352i	$0.878551\pi$
$992$	−2.32574	−	4.02830i	−0.0738424	−	0.127899i
$993$	25.3653	−	16.7851i	0.804942	−	0.532658i
$994$	14.4665	−	3.14678i	0.458850	−	0.0998097i
$995$		−	64.2487i		−	2.03682i
$996$	−10.9331	−	5.45250i	−0.346430	−	0.172769i
$997$	−4.62963	−	2.67292i	−0.146622	−	0.0846521i	0.424894	−	0.905243i	$-0.360311\pi$
$997$	−4.62963	−	2.67292i	−0.146622	−	0.0846521i	−0.571516	+	0.820591i	$0.693645\pi$
$998$	−17.7738	−	10.2617i	−0.562619	−	0.324828i
$999$	11.1797	−	9.54224i	0.353709	−	0.301903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.248.4	yes	64
3.2	odd	2	inner	273.2.bh.a.248.29	yes	64
7.5	odd	6	inner	273.2.bh.a.131.29	yes	64
21.5	even	6	inner	273.2.bh.a.131.4	✓	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.4	✓	64	21.5	even	6	inner
273.2.bh.a.131.29	yes	64	7.5	odd	6	inner
273.2.bh.a.248.4	yes	64	1.1	even	1	trivial
273.2.bh.a.248.29	yes	64	3.2	odd	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.13534 + 1.23284i) q^{2} +(-0.105557 - 1.72883i) q^{3} +(2.03979 - 3.53302i) q^{4} +(-1.46641 - 2.53990i) q^{5} +(2.35677 + 3.56151i) q^{6} +(0.805632 - 2.52011i) q^{7} +5.12758i q^{8} +(-2.97772 + 0.364982i) q^{9} +O(q^{10})\)	\(q+(-2.13534 + 1.23284i) q^{2} +(-0.105557 - 1.72883i) q^{3} +(2.03979 - 3.53302i) q^{4} +(-1.46641 - 2.53990i) q^{5} +(2.35677 + 3.56151i) q^{6} +(0.805632 - 2.52011i) q^{7} +5.12758i q^{8} +(-2.97772 + 0.364982i) q^{9} +(6.26259 + 3.61571i) q^{10} +(-0.698133 - 0.403067i) q^{11} +(-6.32331 - 3.15352i) q^{12} +1.00000i q^{13} +(1.38659 + 6.37451i) q^{14} +(-4.23627 + 2.80329i) q^{15} +(-2.24191 - 3.88310i) q^{16} +(-2.45226 + 4.24745i) q^{17} +(5.90848 - 4.45041i) q^{18} +(-5.66648 + 3.27154i) q^{19} -11.9647 q^{20} +(-4.44189 - 1.12679i) q^{21} +1.98767 q^{22} +(8.25700 - 4.76718i) q^{23} +(8.86472 - 0.541254i) q^{24} +(-1.80074 + 3.11897i) q^{25} +(-1.23284 - 2.13534i) q^{26} +(0.945312 + 5.10944i) q^{27} +(-7.26028 - 7.98681i) q^{28} -1.96603i q^{29} +(5.58989 - 11.2086i) q^{30} +(-5.03226 - 2.90538i) q^{31} +(0.693249 + 0.400248i) q^{32} +(-0.623142 + 1.24950i) q^{33} -12.0930i q^{34} +(-7.58223 + 1.64930i) q^{35} +(-4.78443 + 11.2648i) q^{36} +(-1.41434 - 2.44971i) q^{37} +(8.06658 - 13.9717i) q^{38} +(1.72883 - 0.105557i) q^{39} +(13.0236 - 7.51916i) q^{40} +1.98882 q^{41} +(10.8741 - 3.07006i) q^{42} +4.59323 q^{43} +(-2.84809 + 1.64435i) q^{44} +(5.29358 + 7.02789i) q^{45} +(-11.7543 + 20.3591i) q^{46} +(-0.904136 - 1.56601i) q^{47} +(-6.47657 + 4.28577i) q^{48} +(-5.70191 - 4.06056i) q^{49} -8.88010i q^{50} +(7.60197 + 3.79120i) q^{51} +(3.53302 + 2.03979i) q^{52} +(-3.53060 - 2.03839i) q^{53} +(-8.31769 - 9.74498i) q^{54} +2.36425i q^{55} +(12.9221 + 4.13094i) q^{56} +(6.25409 + 9.45105i) q^{57} +(2.42380 + 4.19815i) q^{58} +(-4.39070 + 7.60491i) q^{59} +(1.26296 + 20.6850i) q^{60} +(-8.96446 + 5.17563i) q^{61} +14.3275 q^{62} +(-1.47915 + 7.79821i) q^{63} +6.99387 q^{64} +(2.53990 - 1.46641i) q^{65} +(-0.209813 - 3.43635i) q^{66} +(0.391145 - 0.677483i) q^{67} +(10.0042 + 17.3278i) q^{68} +(-9.11324 - 13.7718i) q^{69} +(14.1573 - 12.8695i) q^{70} -2.26943i q^{71} +(-1.87148 - 15.2685i) q^{72} +(4.80065 + 2.77165i) q^{73} +(6.04021 + 3.48732i) q^{74} +(5.58226 + 2.78394i) q^{75} +26.6931i q^{76} +(-1.57821 + 1.43465i) q^{77} +(-3.56151 + 2.35677i) q^{78} +(-4.60034 - 7.96803i) q^{79} +(-6.57513 + 11.3885i) q^{80} +(8.73358 - 2.17363i) q^{81} +(-4.24682 + 2.45190i) q^{82} +1.72902 q^{83} +(-13.0415 + 13.3949i) q^{84} +14.3841 q^{85} +(-9.80812 + 5.66272i) q^{86} +(-3.39894 + 0.207529i) q^{87} +(2.06676 - 3.57973i) q^{88} +(-6.09126 - 10.5504i) q^{89} +(-19.9679 - 8.48082i) q^{90} +(2.52011 + 0.805632i) q^{91} -38.8962i q^{92} +(-4.49172 + 9.00662i) q^{93} +(3.86128 + 2.22931i) q^{94} +(16.6188 + 9.59488i) q^{95} +(0.618783 - 1.24076i) q^{96} -9.91566i q^{97} +(17.1816 + 1.64114i) q^{98} +(2.22595 + 0.945414i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more