LMFDB - Embedded newform 273.2.bh.a.131.4

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			131.4
Character	$\chi$	$=$	273.131
Dual form			273.2.bh.a.248.4

$q$-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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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	−0.999933	−	0.0115644i	$-0.996319\pi$
$2$	−2.13534	−	1.23284i	−1.50991	−	0.871750i	−0.509982	−	0.860185i	$-0.670348\pi$
$3$	−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	0.325892	+	0.945407i	$0.394335\pi$
$5$	−1.46641	+	2.53990i	−0.655800	+	1.13588i	−0.981693	+	0.190472i	$0.938998\pi$
$6$	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	−0.601541	−	0.798842i	$-0.705447\pi$
$11$	−0.698133	+	0.403067i	−0.210495	+	0.121529i	0.391046	+	0.920371i	$0.372113\pi$
$12$	−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	−0.993580	−	0.113128i	$-0.963913\pi$
$17$	−2.45226	−	4.24745i	−0.594762	−	1.03016i	0.398819	−	0.917030i	$-0.369420\pi$
$18$	5.90848	+	4.45041i	1.39264	+	1.04897i
$19$	−5.66648	−	3.27154i	−1.29998	−	0.750544i	−0.319580	−	0.947559i	$-0.603542\pi$
$19$	−5.66648	−	3.27154i	−1.29998	−	0.750544i	−0.980400	+	0.197016i	$0.936875\pi$
$20$	−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	0.915423	+	0.402494i	$0.131857\pi$
$23$	8.25700	+	4.76718i	1.72170	+	0.994026i	0.806281	+	0.591532i	$0.201477\pi$
$24$	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	$0.0584324\pi$
$29$			1.96603i			0.365083i	−0.983198	+	0.182542i	$0.941568\pi$
$30$	5.58989	+	11.2086i	1.02057	+	2.04641i
$31$	−5.03226	+	2.90538i	−0.903821	+	0.521821i	−0.878438	−	0.477857i	$-0.841414\pi$
$31$	−5.03226	+	2.90538i	−0.903821	+	0.521821i	−0.0253831	+	0.999678i	$0.508081\pi$
$32$	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	−0.958548	−	0.284931i	$-0.908029\pi$
$37$	−1.41434	+	2.44971i	−0.232516	+	0.402730i	0.726032	+	0.687661i	$0.241363\pi$
$38$	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	−0.924402	−	0.381420i	$-0.875435\pi$
$47$	−0.904136	+	1.56601i	−0.131882	+	0.228426i	0.792520	+	0.609846i	$0.208769\pi$
$48$	−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	−0.722484	−	0.691388i	$-0.756999\pi$
$53$	−3.53060	+	2.03839i	−0.484966	+	0.279995i	0.237518	+	0.971383i	$0.423666\pi$
$54$	−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	−0.996400	−	0.0847780i	$-0.972982\pi$
$59$	−4.39070	−	7.60491i	−0.571620	−	0.990075i	0.424780	−	0.905297i	$-0.360351\pi$
$60$	1.26296	−	20.6850i	0.163048	−	2.67042i
$61$	−8.96446	−	5.17563i	−1.14778	−	0.662672i	−0.199436	−	0.979911i	$-0.563911\pi$
$61$	−8.96446	−	5.17563i	−1.14778	−	0.662672i	−0.948346	+	0.317239i	$0.897244\pi$
$62$	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	0.888929	−	0.458045i	$-0.151450\pi$
$67$	0.391145	+	0.677483i	0.0477859	+	0.0827677i	−0.841143	+	0.540813i	$0.818117\pi$
$68$	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	$0.0429961\pi$
$71$			2.26943i			0.269332i	−0.990891	+	0.134666i	$0.957004\pi$
$72$	−1.87148	+	15.2685i	−0.220555	+	1.79941i
$73$	4.80065	−	2.77165i	0.561873	−	0.324398i	−0.192024	−	0.981390i	$-0.561505\pi$
$73$	4.80065	−	2.77165i	0.561873	−	0.324398i	0.753897	+	0.656993i	$0.228172\pi$
$74$	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	0.482212	+	0.876054i	$0.339833\pi$
$79$	−4.60034	+	7.96803i	−0.517579	+	0.896473i	−0.999792	+	0.0204190i	$0.993500\pi$
$80$	−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	0.338474	+	0.940976i	$0.390089\pi$
$89$	−6.09126	+	10.5504i	−0.645672	+	1.11834i	−0.984146	+	0.177361i	$0.943244\pi$
$90$	−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	$0.167915\pi$
$97$			9.91566i			1.00678i	−0.864058	+	0.503392i	$0.832085\pi$
$98$	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	0.791560	−	0.611092i	$-0.209269\pi$
$101$	−1.34106	−	2.32279i	−0.133441	−	0.231126i	−0.925001	+	0.379965i	$0.875936\pi$
$102$	−20.9068	−	1.27651i	−2.07008	−	0.126393i
$103$	9.04672	+	5.22313i	0.891400	+	0.514650i	0.874400	−	0.485205i	$-0.161255\pi$
$103$	9.04672	+	5.22313i	0.891400	+	0.514650i	0.0169999	+	0.999855i	$0.494588\pi$
$104$	−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	0.388621	−	0.921398i	$-0.372952\pi$
$107$	−2.22421	−	1.28415i	−0.215022	−	0.124143i	−0.603643	+	0.797255i	$0.706285\pi$
$108$	19.9800	−	7.08238i	1.92258	−	0.681502i
$109$	5.79331	+	10.0343i	0.554898	+	0.961112i	0.997911	+	0.0645969i	$0.0205762\pi$
$109$	5.79331	+	10.0343i	0.554898	+	0.961112i	−0.443013	+	0.896515i	$0.646090\pi$
$110$	−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	$0.218571\pi$
$113$			13.4782i			1.26792i	−0.773366	+	0.633959i	$0.781429\pi$
$114$	−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	−0.638441	−	0.769671i	$-0.720420\pi$
$131$	3.97542	−	6.88562i	0.347334	−	0.601600i	0.985775	+	0.168071i	$0.0537538\pi$
$132$	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	−0.854051	−	0.520189i	$-0.825861\pi$
$137$	−9.72168	+	5.61282i	−0.830579	+	0.479535i	0.0234717	+	0.999725i	$0.492528\pi$
$138$	36.4383	−	18.1722i	3.10183	−	1.54692i
$139$		−	4.17599i		−	0.354203i	−0.984193	−	0.177101i	$-0.943328\pi$
$139$		−	4.17599i		−	0.354203i	0.984193	−	0.177101i	$-0.0566721\pi$
$140$	−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	0.854892	−	0.518806i	$-0.173623\pi$
$149$	10.1685	+	5.87080i	0.833039	+	0.480955i	−0.0218533	+	0.999761i	$0.506957\pi$
$150$	−15.3522	−	0.937360i	−1.25350	−	0.0765351i
$151$	0.0492351	+	0.0852776i	0.00400669	+	0.00693979i	0.868022	−	0.496526i	$-0.165391\pi$
$151$	0.0492351	+	0.0852776i	0.00400669	+	0.00693979i	−0.864015	+	0.503466i	$0.832058\pi$
$152$	−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	−0.224274	−	0.974526i	$-0.572001\pi$
$157$	6.35962	−	3.67173i	0.507553	−	0.293036i	0.731827	+	0.681490i	$0.238668\pi$
$158$	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	−0.140469	−	0.990085i	$-0.544861\pi$
$163$	10.0504	−	17.4077i	0.787205	−	1.36348i	0.927673	−	0.373393i	$-0.121806\pi$
$164$	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	−0.999892	−	0.0146919i	$-0.995323\pi$
$173$	−6.40841	+	11.0997i	−0.487222	+	0.843894i	0.512670	+	0.858586i	$0.328657\pi$
$174$	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	−0.849716	−	0.527241i	$-0.823227\pi$
$179$	−10.9437	+	6.31834i	−0.817970	+	0.472255i	0.0317462	+	0.999496i	$0.489893\pi$
$180$	35.6275	+	4.36690i	2.65552	+	0.325490i
$181$			19.0550i			1.41635i	0.706037	+	0.708175i	$0.250481\pi$
$181$			19.0550i			1.41635i	−0.706037	+	0.708175i	$0.749519\pi$
$182$	−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	−0.447827	−	0.894120i	$-0.647802\pi$
$191$	−19.9851	−	11.5384i	−1.44607	−	0.834890i	−0.998244	+	0.0592301i	$0.981135\pi$
$192$	−0.738255	+	12.0912i	−0.0532789	+	0.872608i
$193$	4.58543	+	7.94220i	0.330067	+	0.571692i	0.982525	−	0.186133i	$-0.0595954\pi$
$193$	4.58543	+	7.94220i	0.330067	+	0.571692i	−0.652458	+	0.757825i	$0.726262\pi$
$194$	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	$0.0315701\pi$
$197$			2.77957i			0.198036i	−0.995086	+	0.0990180i	$0.968430\pi$
$198$	−5.91872	−	0.725464i	−0.420625	−	0.0515565i
$199$	18.9718	−	10.9534i	1.34488	−	0.776464i	0.357357	−	0.933968i	$-0.383678\pi$
$199$	18.9718	−	10.9534i	1.34488	−	0.776464i	0.987518	+	0.157503i	$0.0503445\pi$
$200$	−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	$0.172518\pi$
$223$			15.4061i			1.03167i	−0.856688	+	0.515834i	$0.827482\pi$
$224$	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	0.769148	−	0.639071i	$-0.220681\pi$
$227$	−2.54440	−	4.40703i	−0.168878	−	0.292505i	−0.938026	+	0.346566i	$0.887348\pi$
$228$	46.1478	+	2.81765i	3.05621	+	0.186604i
$229$	−12.2357	−	7.06429i	−0.808559	−	0.466822i	0.0378962	−	0.999282i	$-0.487934\pi$
$229$	−12.2357	−	7.06429i	−0.808559	−	0.466822i	−0.846455	+	0.532460i	$0.821268\pi$
$230$	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	0.730664	−	0.682737i	$-0.239210\pi$
$233$	7.70435	+	4.44811i	0.504729	+	0.291405i	−0.225935	+	0.974142i	$0.572544\pi$
$234$	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	$-0.856845\pi$
$239$		−	13.4414i		−	0.869452i	0.900563	−	0.434726i	$-0.143155\pi$
$240$	20.3828	−	10.1652i	1.31570	−	0.656158i
$241$	−4.54772	+	2.62563i	−0.292944	+	0.169131i	−0.639269	−	0.768983i	$-0.720763\pi$
$241$	−4.54772	+	2.62563i	−0.292944	+	0.169131i	0.346325	+	0.938115i	$0.387430\pi$
$242$	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	−0.999176	−	0.0405920i	$-0.987076\pi$
$257$	−7.44545	+	12.8959i	−0.464434	+	0.804424i	0.534742	+	0.845016i	$0.320409\pi$
$258$	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	−0.870711	−	0.491794i	$-0.836341\pi$
$263$	−14.2738	+	8.24099i	−0.880161	+	0.508161i	−0.00944918	+	0.999955i	$0.503008\pi$
$264$	−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	0.825682	−	0.564136i	$-0.190791\pi$
$269$	−1.24183	−	2.15091i	−0.0757156	−	0.131143i	−0.901397	+	0.432993i	$0.857457\pi$
$270$	−12.5541	−	35.4163i	−0.764021	−	2.15537i
$271$	15.1860	+	8.76763i	0.922483	+	0.532596i	0.884426	−	0.466680i	$-0.154550\pi$
$271$	15.1860	+	8.76763i	0.922483	+	0.532596i	0.0380564	+	0.999276i	$0.487883\pi$
$272$	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	−0.863030	−	0.505153i	$-0.831436\pi$
$277$	−14.4629	−	25.0504i	−0.868990	−	1.50513i	−0.00595989	−	0.999982i	$-0.501897\pi$
$278$	−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	$-0.892744\pi$
$281$		−	11.0843i		−	0.661231i	0.943765	−	0.330616i	$-0.107256\pi$
$282$	3.44652	+	6.91082i	0.205237	+	0.411534i
$283$	−18.2010	+	10.5083i	−1.08193	+	0.624655i	−0.931418	−	0.363952i	$-0.881427\pi$
$283$	−18.2010	+	10.5083i	−1.08193	+	0.624655i	−0.150517	+	0.988607i	$0.548094\pi$
$284$	−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	$0.126768\pi$
$307$			13.5899i			0.775618i	−0.921740	+	0.387809i	$0.873232\pi$
$308$	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	0.923654	−	0.383227i	$-0.125187\pi$
$311$	2.29156	+	3.96910i	0.129943	+	0.225067i	−0.793712	+	0.608294i	$0.791854\pi$
$312$	0.541254	−	8.86472i	0.0306425	−	0.501866i
$313$	9.12611	+	5.26896i	0.515838	+	0.297819i	0.735230	−	0.677817i	$-0.237074\pi$
$313$	9.12611	+	5.26896i	0.515838	+	0.297819i	−0.219392	+	0.975637i	$0.570407\pi$
$314$	−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	0.552286	−	0.833655i	$-0.313756\pi$
$317$	1.89550	+	1.09437i	0.106462	+	0.0614658i	−0.445824	+	0.895121i	$0.647089\pi$
$318$	−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	−0.517189	−	0.855871i	$-0.673022\pi$
$331$	8.78035	−	15.2080i	0.482612	−	0.835908i	0.999801	+	0.0199634i	$0.00635496\pi$
$332$	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	−0.719818	−	0.694163i	$-0.755775\pi$
$347$	−8.91465	+	5.14687i	−0.478563	+	0.276299i	0.241254	+	0.970462i	$0.422441\pi$
$348$	−6.19992	−	12.4318i	−0.332350	−	0.666416i
$349$		−	0.183075i		−	0.00979978i	−0.999988	−	0.00489989i	$-0.998440\pi$
$349$		−	0.183075i		−	0.00979978i	0.999988	−	0.00489989i	$-0.00155969\pi$
$350$	−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	0.798299	−	0.602262i	$-0.205734\pi$
$353$	−2.30015	−	3.98397i	−0.122425	−	0.212046i	−0.920723	+	0.390216i	$0.872400\pi$
$354$	−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	0.988505	−	0.151188i	$-0.0483098\pi$
$359$	25.6134	+	14.7879i	1.35183	+	0.780477i	0.363320	+	0.931664i	$0.381643\pi$
$360$	−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	0.166321	−	0.986072i	$-0.446811\pi$
$367$	21.1390	−	12.2046i	1.10344	−	0.637074i	0.937124	+	0.348997i	$0.113478\pi$
$368$	−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	0.297327	+	0.954776i	$0.403905\pi$
$373$	−13.0981	+	22.6867i	−0.678196	+	1.17467i	−0.975524	+	0.219895i	$0.929429\pi$
$374$	−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	−0.532378	−	0.846507i	$-0.678702\pi$
$383$	9.13755	−	15.8267i	0.466907	−	0.808707i	0.999285	+	0.0377998i	$0.0120349\pi$
$384$	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	0.713267	−	0.700892i	$-0.247215\pi$
$389$	33.0735	−	19.0950i	1.67689	−	0.968154i	0.963624	−	0.267261i	$-0.0861186\pi$
$390$	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	0.963737	−	0.266856i	$-0.0859847\pi$
$397$	24.1988	+	13.9712i	1.21450	+	0.701193i	0.250765	+	0.968048i	$0.419318\pi$
$398$	−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	0.999723	−	0.0235147i	$-0.00748565\pi$
$401$	29.6214	+	17.1019i	1.47922	+	0.854029i	0.479497	+	0.877543i	$0.340819\pi$
$402$	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	−0.899650	−	0.436613i	$-0.856178\pi$
$409$	−19.6445	+	11.3417i	−0.971357	+	0.560813i	−0.0717072	+	0.997426i	$0.522845\pi$
$410$	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	0.298586	−	0.954383i	$-0.403485\pi$
$431$	26.4572	−	15.2751i	1.27440	−	0.735774i	0.975813	+	0.218609i	$0.0701518\pi$
$432$	17.7212	+	15.1256i	0.852610	+	0.727733i
$433$			16.2968i			0.783173i	0.920141	+	0.391587i	$0.128074\pi$
$433$			16.2968i			0.783173i	−0.920141	+	0.391587i	$0.871926\pi$
$434$	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	0.276686	−	0.960960i	$-0.410764\pi$
$439$	−8.74102	−	5.04663i	−0.417186	−	0.240863i	−0.693873	+	0.720098i	$0.744097\pi$
$440$	−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	0.346161	−	0.938175i	$-0.387485\pi$
$443$	−6.17202	−	3.56342i	−0.293241	−	0.169303i	−0.639403	+	0.768872i	$0.720818\pi$
$444$	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	$-0.839318\pi$
$449$		−	20.4959i		−	0.967262i	0.875272	−	0.483631i	$-0.160682\pi$
$450$	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	0.0909749	−	0.995853i	$-0.471002\pi$
$457$	19.4091	−	33.6176i	0.907922	−	1.57257i	0.816947	−	0.576713i	$-0.195665\pi$
$458$	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	−0.912671	−	0.408694i	$-0.865984\pi$
$467$	−2.21279	+	3.83267i	−0.102396	+	0.177355i	0.810275	+	0.586049i	$0.199318\pi$
$468$	−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	0.968642	−	0.248462i	$-0.0799253\pi$
$479$	5.89055	+	10.2027i	0.269146	+	0.466175i	−0.699496	+	0.714637i	$0.746592\pi$
$480$	−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	−0.999899	−	0.0142305i	$-0.995470\pi$
$487$	−11.3049	−	19.5806i	−0.512273	−	0.887283i	0.487625	−	0.873053i	$-0.337863\pi$
$488$	−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	$0.155166\pi$
$491$			20.7577i			0.936782i	−0.883521	+	0.468391i	$0.844834\pi$
$492$	−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	−0.757708	−	0.652593i	$-0.773681\pi$
$499$	4.16181	−	7.20846i	0.186308	−	0.322695i	0.944017	+	0.329898i	$0.107014\pi$
$500$	−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	−0.815917	−	0.578169i	$-0.803767\pi$
$509$	2.09254	−	3.62439i	0.0927504	−	0.160648i	0.908668	+	0.417520i	$0.137101\pi$
$510$	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	0.742434	−	0.669920i	$-0.233671\pi$
$521$	−4.76939	−	8.26082i	−0.208951	−	0.361913i	−0.951384	+	0.308007i	$0.900338\pi$
$522$	−8.74965	+	11.6163i	−0.382962	+	0.508430i
$523$	39.1907	+	22.6268i	1.71369	+	0.989399i	0.929456	+	0.368933i	$0.120277\pi$
$523$	39.1907	+	22.6268i	1.71369	+	0.989399i	0.784233	+	0.620466i	$0.213056\pi$
$524$	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	−0.914525	−	0.404530i	$-0.867435\pi$
$541$	−2.48712	+	4.30782i	−0.106930	+	0.185207i	0.807595	+	0.589737i	$0.200769\pi$
$542$	−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	−0.378031	−	0.925793i	$-0.623399\pi$
$557$	5.53943	−	3.19819i	0.234713	−	0.135512i	0.612745	+	0.790281i	$0.290065\pi$
$558$	−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	0.910995	+	0.412417i	$0.135315\pi$
$563$	19.2825	+	33.3983i	0.812661	+	1.40757i	−0.0983345	+	0.995153i	$0.531352\pi$
$564$	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	0.538397	−	0.842691i	$-0.319030\pi$
$569$	1.85590	+	1.07151i	0.0778035	+	0.0449199i	−0.460594	+	0.887611i	$0.652363\pi$
$570$	4.99454	−	81.8010i	0.209198	−	3.42627i
$571$	17.8324	+	30.8866i	0.746263	+	1.29257i	0.949602	+	0.313457i	$0.101487\pi$
$571$	17.8324	+	30.8866i	0.746263	+	1.29257i	−0.203339	+	0.979108i	$0.565179\pi$
$572$	−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	−0.918791	−	0.394745i	$-0.870833\pi$
$577$	−24.8934	+	14.3722i	−1.03633	+	0.598323i	−0.117536	+	0.993069i	$0.537499\pi$
$578$	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	−0.836753	−	0.547580i	$-0.815549\pi$
$593$	1.35983	−	2.35529i	0.0558415	−	0.0967203i	0.892595	+	0.450860i	$0.148883\pi$
$594$	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	−0.107863	−	0.994166i	$-0.534401\pi$
$599$	17.1120	−	9.87963i	0.699179	−	0.403671i	0.807041	+	0.590495i	$0.201067\pi$
$600$	−14.2749	−	28.6235i	−0.582770	−	1.16855i
$601$		−	25.1855i		−	1.02734i	−0.857989	−	0.513668i	$-0.828286\pi$
$601$		−	25.1855i		−	1.02734i	0.857989	−	0.513668i	$-0.171714\pi$
$602$	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	0.674790	−	0.738010i	$-0.264234\pi$
$607$	9.19098	+	5.30641i	0.373050	+	0.215381i	−0.301740	+	0.953390i	$0.597567\pi$
$608$	−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	−0.940315	−	0.340304i	$-0.889470\pi$
$613$	−18.9373	−	32.8004i	−0.764870	−	1.32479i	0.175445	−	0.984489i	$-0.443863\pi$
$614$	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	$-0.972458\pi$
$617$		−	4.29321i		−	0.172838i	0.996259	−	0.0864191i	$-0.0275424\pi$
$618$	39.9233	−	19.9103i	1.60595	−	0.800908i
$619$	−13.2571	+	7.65401i	−0.532849	+	0.307641i	−0.742176	−	0.670205i	$-0.766206\pi$
$619$	−13.2571	+	7.65401i	−0.532849	+	0.307641i	0.209327	+	0.977846i	$0.432873\pi$
$620$	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	−0.759635	−	0.650350i	$-0.774622\pi$
$641$	−14.5890	+	8.42299i	−0.576232	+	0.332688i	0.183402	+	0.983038i	$0.441289\pi$
$642$	−9.81546	+	4.89509i	−0.387385	+	0.193194i
$643$		−	20.9545i		−	0.826366i	−0.910648	−	0.413183i	$-0.864417\pi$
$643$		−	20.9545i		−	0.826366i	0.910648	−	0.413183i	$-0.135583\pi$
$644$	−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	0.929303	−	0.369318i	$-0.120409\pi$
$647$	3.68349	+	6.38000i	0.144813	+	0.250824i	−0.784490	+	0.620141i	$0.787075\pi$
$648$	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	0.00976961	−	0.999952i	$-0.496890\pi$
$653$	−21.7548	−	12.5601i	−0.851330	−	0.491515i	−0.861099	+	0.508437i	$0.830224\pi$
$654$	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	$-0.755476\pi$
$659$		−	35.6744i		−	1.38968i	0.719165	−	0.694839i	$-0.244524\pi$
$660$	7.45571	+	14.9499i	0.290213	+	0.581925i
$661$	−14.5858	+	8.42113i	−0.567323	+	0.327544i	−0.756079	−	0.654480i	$-0.772888\pi$
$661$	−14.5858	+	8.42113i	−0.567323	+	0.327544i	0.188757	+	0.982024i	$0.439554\pi$
$662$	−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	−0.810581	−	0.585627i	$-0.800849\pi$
$677$	2.65076	−	4.59125i	0.101877	−	0.176456i	0.912458	+	0.409170i	$0.134182\pi$
$678$	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	−0.538859	−	0.842396i	$-0.681145\pi$
$683$	−2.05816	+	1.18828i	−0.0787532	+	0.0454682i	0.460106	+	0.887864i	$0.347811\pi$
$684$	−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	0.887293	−	0.461206i	$-0.152583\pi$
$691$	24.4869	+	14.1375i	0.931524	+	0.537815i	0.0442306	+	0.999021i	$0.485916\pi$
$692$	−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	$0.108016\pi$
$701$			17.6262i			0.665733i	−0.942974	+	0.332867i	$0.891984\pi$
$702$	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	−0.436076	−	0.899910i	$-0.643632\pi$
$709$	14.9460	−	25.8871i	0.561307	−	0.972212i	0.997383	−	0.0723023i	$-0.0230346\pi$
$710$	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	−0.998163	−	0.0605870i	$-0.980703\pi$
$719$	−11.9755	+	20.7422i	−0.446612	+	0.773554i	0.551551	+	0.834141i	$0.314036\pi$
$720$	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	$-0.738838\pi$
$727$		−	39.4447i		−	1.46292i	0.681882	−	0.731462i	$-0.261162\pi$
$728$	−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	0.0256826	−	0.999670i	$-0.491824\pi$
$733$	−22.3960	−	12.9303i	−0.827216	−	0.477593i	−0.852898	+	0.522077i	$0.825157\pi$
$734$	−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	0.993502	−	0.113817i	$-0.0363078\pi$
$739$	10.8244	+	18.7484i	0.398182	+	0.689672i	−0.595319	+	0.803489i	$0.702974\pi$
$740$	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	$0.199430\pi$
$743$			31.9647i			1.17267i	−0.810068	+	0.586336i	$0.800570\pi$
$744$	−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	−0.128505	−	0.991709i	$-0.541018\pi$
$751$	21.7753	−	37.7159i	0.794592	−	1.37627i	0.923098	−	0.384566i	$-0.125649\pi$
$752$	−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	0.369607	+	0.929188i	$0.379492\pi$
$761$	−17.1006	+	29.6191i	−0.619897	+	1.07369i	−0.989504	+	0.144505i	$0.953841\pi$
$762$	−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	$-0.810467\pi$
$769$		−	31.1068i		−	1.12174i	0.827904	−	0.560869i	$-0.189533\pi$
$770$	−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	0.974347	+	0.225050i	$0.0722546\pi$
$773$	18.9636	+	32.8459i	0.682073	+	1.18138i	−0.292274	+	0.956335i	$0.594412\pi$
$774$	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	0.000738919	−	1.00000i	$-0.499765\pi$
$787$	24.3261	−	14.0447i	0.867134	−	0.500640i	0.866395	+	0.499360i	$0.166431\pi$
$788$	−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	0.00311670	−	0.999995i	$-0.499008\pi$
$809$	24.7651	−	14.2982i	0.870696	−	0.502697i	0.867580	+	0.497298i	$0.165675\pi$
$810$	62.5540	−	17.9655i	2.19792	−	0.631245i
$811$			4.66778i			0.163908i	0.996636	+	0.0819539i	$0.0261160\pi$
$811$			4.66778i			0.163908i	−0.996636	+	0.0819539i	$0.973884\pi$
$812$	−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	0.774259	−	0.632869i	$-0.218123\pi$
$821$	17.5732	+	10.1459i	0.613308	+	0.354094i	−0.160951	+	0.986962i	$0.551456\pi$
$822$	−2.92171	+	47.8520i	−0.101906	+	1.66903i
$823$	9.66510	+	16.7404i	0.336904	+	0.583535i	0.983849	−	0.179002i	$-0.0572868\pi$
$823$	9.66510	+	16.7404i	0.336904	+	0.583535i	−0.646945	+	0.762537i	$0.723953\pi$
$824$	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	$0.0432716\pi$
$827$			7.79466i			0.271047i	−0.990774	+	0.135523i	$0.956728\pi$
$828$	14.1964	−	115.822i	0.493360	−	4.02509i
$829$	9.49976	−	5.48469i	0.329940	−	0.190491i	−0.325874	−	0.945413i	$-0.605659\pi$
$829$	9.49976	−	5.48469i	0.329940	−	0.190491i	0.655815	+	0.754922i	$0.272325\pi$
$830$	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	$0.0332705\pi$
$853$			6.09429i			0.208664i	−0.994543	+	0.104332i	$0.966729\pi$
$854$	−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	0.679361	−	0.733804i	$-0.262257\pi$
$857$	−8.65979	−	14.9992i	−0.295813	−	0.512363i	−0.975174	+	0.221442i	$0.928924\pi$
$858$	3.43635	+	0.209813i	0.117315	+	0.00716291i
$859$	0.410631	+	0.237078i	0.0140105	+	0.00808898i	0.506989	−	0.861953i	$-0.330759\pi$
$859$	0.410631	+	0.237078i	0.0140105	+	0.00808898i	−0.492978	+	0.870042i	$0.664092\pi$
$860$	−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	0.897565	−	0.440882i	$-0.145334\pi$
$863$	28.3350	+	16.3592i	0.964533	+	0.556873i	0.0669678	+	0.997755i	$0.478668\pi$
$864$	−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	−0.719416	−	0.694579i	$-0.755591\pi$
$877$	7.16116	−	12.4035i	0.241815	−	0.418836i	0.961231	+	0.275743i	$0.0889239\pi$
$878$	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	−0.956791	−	0.290777i	$-0.906086\pi$
$887$	−6.74797	+	11.6878i	−0.226575	+	0.392439i	0.730216	+	0.683216i	$0.239419\pi$
$888$	−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	0.953661	−	0.300882i	$-0.0972812\pi$
$907$	6.51295	+	11.2808i	0.216259	+	0.374571i	−0.737402	+	0.675454i	$0.763948\pi$
$908$	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	$0.0122981\pi$
$911$			2.33168i			0.0772521i	−0.999254	+	0.0386260i	$0.987702\pi$
$912$	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	−0.741574	−	0.670871i	$-0.765920\pi$
$919$	6.37235	−	11.0372i	0.210204	−	0.364085i	0.951778	+	0.306786i	$0.0992537\pi$
$920$	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	−0.242215	−	0.970223i	$-0.577874\pi$
$929$	21.9187	−	37.9644i	0.719130	−	1.24557i	0.961345	−	0.275347i	$-0.0887928\pi$
$930$	−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	$0.227841\pi$
$937$			40.1737i			1.31242i	−0.754580	+	0.656208i	$0.772159\pi$
$938$	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	0.902171	−	0.431379i	$-0.141973\pi$
$941$	2.37739	+	4.11776i	0.0775007	+	0.134235i	−0.824670	+	0.565614i	$0.808639\pi$
$942$	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	0.571592	−	0.820538i	$-0.306326\pi$
$947$	4.51696	+	2.60787i	0.146781	+	0.0847442i	−0.424811	+	0.905282i	$0.639659\pi$
$948$	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	$-0.874752\pi$
$953$		−	23.6718i		−	0.766805i	0.923581	−	0.383402i	$-0.125248\pi$
$954$	−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	−0.994520	−	0.104550i	$-0.966660\pi$
$971$	−12.6736	+	21.9514i	−0.406717	+	0.704454i	0.587803	+	0.809004i	$0.299993\pi$
$972$	−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	−0.0486869	−	0.998814i	$-0.515504\pi$
$977$	24.7545	−	14.2920i	0.791968	−	0.457243i	0.840655	+	0.541571i	$0.182170\pi$
$978$	−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	0.998430	+	0.0560165i	$0.0178399\pi$
$983$	17.1728	+	29.7441i	0.547727	+	0.948690i	−0.450703	+	0.892674i	$0.648827\pi$
$984$	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	−0.928092	−	0.372352i	$-0.878551\pi$
$991$	−24.7595	−	42.8847i	−0.786512	−	1.36228i	0.141580	−	0.989927i	$-0.454782\pi$
$992$	−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	−0.571516	−	0.820591i	$-0.693645\pi$
$997$	−4.62963	+	2.67292i	−0.146622	+	0.0846521i	0.424894	+	0.905243i	$0.360311\pi$
$998$	−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.131.4	✓	64
3.2	odd	2	inner	273.2.bh.a.131.29	yes	64
7.3	odd	6	inner	273.2.bh.a.248.29	yes	64
21.17	even	6	inner	273.2.bh.a.248.4	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.4	✓	64	1.1	even	1	trivial
273.2.bh.a.131.29	yes	64	3.2	odd	2	inner
273.2.bh.a.248.4	yes	64	21.17	even	6	inner
273.2.bh.a.248.29	yes	64	7.3	odd	6	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

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