LMFDB - Embedded newform 546.2.bb.a.269.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(269,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 4]))

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

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

chi := DirichletCharacter("546.269");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bb (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.22
Character	$\chi$	$=$	546.269
Dual form			546.2.bb.a.341.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.70567 - 0.301159i) q^{3} -1.00000 q^{4} +(-2.12998 - 3.68924i) q^{5} +(0.301159 - 1.70567i) q^{6} +(2.63074 + 0.281454i) q^{7} -1.00000i q^{8} +(2.81861 + 1.02735i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.70567 - 0.301159i) q^{3} -1.00000 q^{4} +(-2.12998 - 3.68924i) q^{5} +(0.301159 - 1.70567i) q^{6} +(2.63074 + 0.281454i) q^{7} -1.00000i q^{8} +(2.81861 + 1.02735i) q^{9} +(3.68924 - 2.12998i) q^{10} +(-1.28788 + 0.743556i) q^{11} +(1.70567 + 0.301159i) q^{12} +(-2.41401 + 2.67816i) q^{13} +(-0.281454 + 2.63074i) q^{14} +(2.52200 + 6.93408i) q^{15} +1.00000 q^{16} -2.66507 q^{17} +(-1.02735 + 2.81861i) q^{18} +(-3.55819 - 2.05432i) q^{19} +(2.12998 + 3.68924i) q^{20} +(-4.40240 - 1.27234i) q^{21} +(-0.743556 - 1.28788i) q^{22} +0.158431i q^{23} +(-0.301159 + 1.70567i) q^{24} +(-6.57365 + 11.3859i) q^{25} +(-2.67816 - 2.41401i) q^{26} +(-4.49821 - 2.60117i) q^{27} +(-2.63074 - 0.281454i) q^{28} +(0.413684 + 0.238841i) q^{29} +(-6.93408 + 2.52200i) q^{30} +(3.04646 + 1.75887i) q^{31} +1.00000i q^{32} +(2.42062 - 0.880404i) q^{33} -2.66507i q^{34} +(-4.56508 - 10.3049i) q^{35} +(-2.81861 - 1.02735i) q^{36} -10.4771 q^{37} +(2.05432 - 3.55819i) q^{38} +(4.92406 - 3.84105i) q^{39} +(-3.68924 + 2.12998i) q^{40} +(-5.13995 + 8.90266i) q^{41} +(1.27234 - 4.40240i) q^{42} +(4.00148 + 6.93077i) q^{43} +(1.28788 - 0.743556i) q^{44} +(-2.21343 - 12.5868i) q^{45} -0.158431 q^{46} +(-2.27135 - 3.93409i) q^{47} +(-1.70567 - 0.301159i) q^{48} +(6.84157 + 1.48086i) q^{49} +(-11.3859 - 6.57365i) q^{50} +(4.54572 + 0.802608i) q^{51} +(2.41401 - 2.67816i) q^{52} +(3.23858 + 1.86979i) q^{53} +(2.60117 - 4.49821i) q^{54} +(5.48631 + 3.16752i) q^{55} +(0.281454 - 2.63074i) q^{56} +(5.45041 + 4.57557i) q^{57} +(-0.238841 + 0.413684i) q^{58} -4.78769 q^{59} +(-2.52200 - 6.93408i) q^{60} +(2.28652 + 1.32012i) q^{61} +(-1.75887 + 3.04646i) q^{62} +(7.12586 + 3.49601i) q^{63} -1.00000 q^{64} +(15.0222 + 3.20144i) q^{65} +(0.880404 + 2.42062i) q^{66} +(1.63445 + 2.83094i) q^{67} +2.66507 q^{68} +(0.0477129 - 0.270231i) q^{69} +(10.3049 - 4.56508i) q^{70} +(-7.70265 + 4.44713i) q^{71} +(1.02735 - 2.81861i) q^{72} +(-6.03059 - 3.48176i) q^{73} -10.4771i q^{74} +(14.6414 - 17.4408i) q^{75} +(3.55819 + 2.05432i) q^{76} +(-3.59734 + 1.59362i) q^{77} +(3.84105 + 4.92406i) q^{78} +(-8.20543 - 14.2122i) q^{79} +(-2.12998 - 3.68924i) q^{80} +(6.88909 + 5.79141i) q^{81} +(-8.90266 - 5.13995i) q^{82} -8.37013 q^{83} +(4.40240 + 1.27234i) q^{84} +(5.67655 + 9.83207i) q^{85} +(-6.93077 + 4.00148i) q^{86} +(-0.633679 - 0.531968i) q^{87} +(0.743556 + 1.28788i) q^{88} +11.8904 q^{89} +(12.5868 - 2.21343i) q^{90} +(-7.10442 + 6.36610i) q^{91} -0.158431i q^{92} +(-4.66655 - 3.91752i) q^{93} +(3.93409 - 2.27135i) q^{94} +17.5027i q^{95} +(0.301159 - 1.70567i) q^{96} +(-3.13800 + 1.81173i) q^{97} +(-1.48086 + 6.84157i) q^{98} +(-4.39391 + 0.772687i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	$ 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) $ 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.70567	−	0.301159i	−0.984768	−	0.173874i
$3$	−1.70567	−	0.301159i	−0.984768	−	0.173874i
$4$	−1.00000			−0.500000
$5$	−2.12998	−	3.68924i	−0.952557	−	1.64988i	−0.739862	−	0.672759i	$-0.765109\pi$
$5$	−2.12998	−	3.68924i	−0.952557	−	1.64988i	−0.212695	−	0.977119i	$-0.568224\pi$
$6$	0.301159	−	1.70567i	0.122948	−	0.696336i
$7$	2.63074	+	0.281454i	0.994326	+	0.106380i
$7$	2.63074	+	0.281454i	0.994326	+	0.106380i
$8$		−	1.00000i		−	0.353553i
$9$	2.81861	+	1.02735i	0.939536	+	0.342451i
$10$	3.68924	−	2.12998i	1.16664	−	0.673560i
$11$	−1.28788	+	0.743556i	−0.388309	+	0.224191i	−0.681427	−	0.731886i	$-0.738640\pi$
$11$	−1.28788	+	0.743556i	−0.388309	+	0.224191i	0.293118	+	0.956076i	$0.405307\pi$
$12$	1.70567	+	0.301159i	0.492384	+	0.0869370i
$13$	−2.41401	+	2.67816i	−0.669527	+	0.742788i
$13$	−2.41401	+	2.67816i	−0.669527	+	0.742788i
$14$	−0.281454	+	2.63074i	−0.0752217	+	0.703094i
$15$	2.52200	+	6.93408i	0.651177	+	1.79037i
$16$	1.00000			0.250000
$17$	−2.66507			−0.646374			−0.323187	−	0.946335i	$-0.604754\pi$
$17$	−2.66507			−0.646374			−0.323187	+	0.946335i	$0.604754\pi$
$18$	−1.02735	+	2.81861i	−0.242150	+	0.664352i
$19$	−3.55819	−	2.05432i	−0.816305	−	0.471294i	0.0328359	−	0.999461i	$-0.489546\pi$
$19$	−3.55819	−	2.05432i	−0.816305	−	0.471294i	−0.849140	+	0.528167i	$0.822879\pi$
$20$	2.12998	+	3.68924i	0.476279	+	0.824939i
$21$	−4.40240	−	1.27234i	−0.960683	−	0.277647i
$22$	−0.743556	−	1.28788i	−0.158527	−	0.274576i
$23$			0.158431i			0.0330352i	0.999864	+	0.0165176i	$0.00525795\pi$
$23$			0.158431i			0.0330352i	−0.999864	+	0.0165176i	$0.994742\pi$
$24$	−0.301159	+	1.70567i	−0.0614738	+	0.348168i
$25$	−6.57365	+	11.3859i	−1.31473	+	2.27718i
$26$	−2.67816	−	2.41401i	−0.525230	−	0.473427i
$27$	−4.49821	−	2.60117i	−0.865681	−	0.500596i
$28$	−2.63074	−	0.281454i	−0.497163	−	0.0531898i
$29$	0.413684	+	0.238841i	0.0768193	+	0.0443516i	0.537918	−	0.842997i	$-0.319211\pi$
$29$	0.413684	+	0.238841i	0.0768193	+	0.0443516i	−0.461098	+	0.887349i	$0.652544\pi$
$30$	−6.93408	+	2.52200i	−1.26598	+	0.460452i
$31$	3.04646	+	1.75887i	0.547160	+	0.315903i	0.747976	−	0.663726i	$-0.231026\pi$
$31$	3.04646	+	1.75887i	0.547160	+	0.315903i	−0.200816	+	0.979629i	$0.564359\pi$
$32$			1.00000i			0.176777i
$33$	2.42062	−	0.880404i	0.421376	−	0.153259i
$34$		−	2.66507i		−	0.457055i
$35$	−4.56508	−	10.3049i	−0.771639	−	1.74185i
$36$	−2.81861	−	1.02735i	−0.469768	−	0.171226i
$37$	−10.4771			−1.72242			−0.861211	−	0.508248i	$-0.830293\pi$
$37$	−10.4771			−1.72242			−0.861211	+	0.508248i	$0.830293\pi$
$38$	2.05432	−	3.55819i	0.333255	−	0.577215i
$39$	4.92406	−	3.84105i	0.788480	−	0.615060i
$40$	−3.68924	+	2.12998i	−0.583320	+	0.336780i
$41$	−5.13995	+	8.90266i	−0.802726	+	1.39036i	0.115090	+	0.993355i	$0.463284\pi$
$41$	−5.13995	+	8.90266i	−0.802726	+	1.39036i	−0.917816	+	0.397007i	$0.870049\pi$
$42$	1.27234	−	4.40240i	0.196326	−	0.679306i
$43$	4.00148	+	6.93077i	0.610221	+	1.05693i	0.991203	+	0.132351i	$0.0422526\pi$
$43$	4.00148	+	6.93077i	0.610221	+	1.05693i	−0.380982	+	0.924582i	$0.624414\pi$
$44$	1.28788	−	0.743556i	0.194155	−	0.112095i
$45$	−2.21343	−	12.5868i	−0.329959	−	1.87632i
$46$	−0.158431			−0.0233594
$47$	−2.27135	−	3.93409i	−0.331310	−	0.573846i	0.651459	−	0.758684i	$-0.274157\pi$
$47$	−2.27135	−	3.93409i	−0.331310	−	0.573846i	−0.982769	+	0.184838i	$0.940824\pi$
$48$	−1.70567	−	0.301159i	−0.246192	−	0.0434685i
$49$	6.84157	+	1.48086i	0.977367	+	0.211552i
$50$	−11.3859	−	6.57365i	−1.61021	−	0.929654i
$51$	4.54572	+	0.802608i	0.636528	+	0.112388i
$52$	2.41401	−	2.67816i	0.334763	−	0.371394i
$53$	3.23858	+	1.86979i	0.444853	+	0.256836i	0.705654	−	0.708557i	$-0.250653\pi$
$53$	3.23858	+	1.86979i	0.444853	+	0.256836i	−0.260801	+	0.965393i	$0.583987\pi$
$54$	2.60117	−	4.49821i	0.353975	−	0.612129i
$55$	5.48631	+	3.16752i	0.739774	+	0.427109i
$56$	0.281454	−	2.63074i	0.0376108	−	0.351547i
$57$	5.45041	+	4.57557i	0.721925	+	0.606049i
$58$	−0.238841	+	0.413684i	−0.0313613	+	0.0543194i
$59$	−4.78769			−0.623304			−0.311652	−	0.950196i	$-0.600882\pi$
$59$	−4.78769			−0.623304			−0.311652	+	0.950196i	$0.600882\pi$
$60$	−2.52200	−	6.93408i	−0.325588	−	0.895186i
$61$	2.28652	+	1.32012i	0.292759	+	0.169025i	0.639186	−	0.769053i	$-0.279272\pi$
$61$	2.28652	+	1.32012i	0.292759	+	0.169025i	−0.346426	+	0.938077i	$0.612605\pi$
$62$	−1.75887	+	3.04646i	−0.223377	+	0.386900i
$63$	7.12586	+	3.49601i	0.897775	+	0.440455i
$64$	−1.00000			−0.125000
$65$	15.0222	+	3.20144i	1.86327	+	0.397089i
$66$	0.880404	+	2.42062i	0.108370	+	0.297957i
$67$	1.63445	+	2.83094i	0.199679	+	0.345855i	0.948424	−	0.317003i	$-0.102677\pi$
$67$	1.63445	+	2.83094i	0.199679	+	0.345855i	−0.748745	+	0.662858i	$0.769343\pi$
$68$	2.66507			0.323187
$69$	0.0477129	−	0.270231i	0.00574396	−	0.0325320i
$70$	10.3049	−	4.56508i	1.23167	−	0.545631i
$71$	−7.70265	+	4.44713i	−0.914136	+	0.527777i	−0.881760	−	0.471699i	$-0.843641\pi$
$71$	−7.70265	+	4.44713i	−0.914136	+	0.527777i	−0.0323767	+	0.999476i	$0.510308\pi$
$72$	1.02735	−	2.81861i	0.121075	−	0.332176i
$73$	−6.03059	−	3.48176i	−0.705828	−	0.407510i	0.103687	−	0.994610i	$-0.466936\pi$
$73$	−6.03059	−	3.48176i	−0.705828	−	0.407510i	−0.809514	+	0.587100i	$0.800269\pi$
$74$		−	10.4771i		−	1.21794i
$75$	14.6414	−	17.4408i	1.69065	−	2.01390i
$76$	3.55819	+	2.05432i	0.408152	+	0.235647i
$77$	−3.59734	+	1.59362i	−0.409955	+	0.181610i
$78$	3.84105	+	4.92406i	0.434913	+	0.557540i
$79$	−8.20543	−	14.2122i	−0.923183	−	1.59900i	−0.794458	−	0.607320i	$-0.792245\pi$
$79$	−8.20543	−	14.2122i	−0.923183	−	1.59900i	−0.128725	−	0.991680i	$-0.541089\pi$
$80$	−2.12998	−	3.68924i	−0.238139	−	0.412469i
$81$	6.88909	+	5.79141i	0.765454	+	0.643490i
$82$	−8.90266	−	5.13995i	−0.983134	−	0.567613i
$83$	−8.37013			−0.918741			−0.459370	−	0.888245i	$-0.651925\pi$
$83$	−8.37013			−0.918741			−0.459370	+	0.888245i	$0.651925\pi$
$84$	4.40240	+	1.27234i	0.480342	+	0.138823i
$85$	5.67655	+	9.83207i	0.615708	+	1.06644i
$86$	−6.93077	+	4.00148i	−0.747365	+	0.431491i
$87$	−0.633679	−	0.531968i	−0.0679375	−	0.0570329i
$88$	0.743556	+	1.28788i	0.0792633	+	0.137288i
$89$	11.8904			1.26038			0.630190	−	0.776441i	$-0.282977\pi$
$89$	11.8904			1.26038			0.630190	+	0.776441i	$0.282977\pi$
$90$	12.5868	−	2.21343i	1.32676	−	0.233316i
$91$	−7.10442	+	6.36610i	−0.744745	+	0.667349i
$92$		−	0.158431i		−	0.0165176i
$93$	−4.66655	−	3.91752i	−0.483898	−	0.406228i
$94$	3.93409	−	2.27135i	0.405770	−	0.234271i
$95$			17.5027i			1.79574i
$96$	0.301159	−	1.70567i	0.0307369	−	0.174084i
$97$	−3.13800	+	1.81173i	−0.318616	+	0.183953i	−0.650775	−	0.759270i	$-0.725556\pi$
$97$	−3.13800	+	1.81173i	−0.318616	+	0.183953i	0.332160	+	0.943223i	$0.392223\pi$
$98$	−1.48086	+	6.84157i	−0.149590	+	0.691103i
$99$	−4.39391	+	0.772687i	−0.441605	+	0.0776580i
$100$	6.57365	−	11.3859i	0.657365	−	1.13859i
$101$	2.40953	+	4.17343i	0.239757	+	0.415272i	0.960645	−	0.277781i	$-0.0895988\pi$
$101$	2.40953	+	4.17343i	0.239757	+	0.415272i	−0.720887	+	0.693052i	$0.756265\pi$
$102$	−0.802608	+	4.54572i	−0.0794700	+	0.450093i
$103$	2.15332	−	1.24322i	0.212173	−	0.122498i	−0.390148	−	0.920752i	$-0.627576\pi$
$103$	2.15332	−	1.24322i	0.212173	−	0.122498i	0.602321	+	0.798254i	$0.294243\pi$
$104$	2.67816	+	2.41401i	0.262615	+	0.236713i
$105$	4.68309	+	18.9516i	0.457023	+	1.84948i
$106$	−1.86979	+	3.23858i	−0.181611	+	0.314559i
$107$		−	9.19824i		−	0.889227i	−0.895722	−	0.444614i	$-0.853341\pi$
$107$		−	9.19824i		−	0.889227i	0.895722	−	0.444614i	$-0.146659\pi$
$108$	4.49821	+	2.60117i	0.432841	+	0.250298i
$109$	3.36845	−	5.83432i	0.322639	−	0.558827i	−0.658393	−	0.752675i	$-0.728763\pi$
$109$	3.36845	−	5.83432i	0.322639	−	0.558827i	0.981032	+	0.193848i	$0.0620967\pi$
$110$	−3.16752	+	5.48631i	−0.302011	+	0.523099i
$111$	17.8704	+	3.15526i	1.69619	+	0.299484i
$112$	2.63074	+	0.281454i	0.248581	+	0.0265949i
$113$	−14.7950	+	8.54191i	−1.39180	+	0.803556i	−0.993514	−	0.113706i	$-0.963728\pi$
$113$	−14.7950	+	8.54191i	−1.39180	+	0.803556i	−0.398285	+	0.917262i	$0.630394\pi$
$114$	−4.57557	+	5.45041i	−0.428541	+	0.510478i
$115$	0.584490	−	0.337456i	0.0545040	−	0.0314679i
$116$	−0.413684	−	0.238841i	−0.0384096	−	0.0221758i
$117$	−9.55557	+	5.06863i	−0.883413	+	0.468595i
$118$		−	4.78769i		−	0.440742i
$119$	−7.01109	−	0.750093i	−0.642706	−	0.0687609i
$120$	6.93408	−	2.52200i	0.632992	−	0.230226i
$121$	−4.39425	+	7.61106i	−0.399477	+	0.691915i
$122$	−1.32012	+	2.28652i	−0.119518	+	0.207012i
$123$	11.4482	−	13.6370i	1.03225	−	1.22961i
$124$	−3.04646	−	1.75887i	−0.273580	−	0.157951i
$125$	34.7072			3.10431
$126$	−3.49601	+	7.12586i	−0.311449	+	0.634822i
$127$	2.85690	−	4.94830i	0.253509	−	0.439091i	−0.710980	−	0.703212i	$-0.751749\pi$
$127$	2.85690	−	4.94830i	0.253509	−	0.439091i	0.964490	+	0.264121i	$0.0850819\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−4.73794	−	13.0267i	−0.417152	−	1.14694i
$130$	−3.20144	+	15.0222i	−0.280785	+	1.31753i
$131$	−7.49454	−	12.9809i	−0.654801	−	1.13415i	−0.981944	−	0.189173i	$-0.939419\pi$
$131$	−7.49454	−	12.9809i	−0.654801	−	1.13415i	0.327143	−	0.944975i	$-0.393914\pi$
$132$	−2.42062	+	0.880404i	−0.210688	+	0.0766294i
$133$	−8.78247	−	6.40585i	−0.761537	−	0.555457i
$134$	−2.83094	+	1.63445i	−0.244556	+	0.141195i
$135$	−0.0152294	+	22.1354i	−0.00131074	+	1.90511i
$136$			2.66507i			0.228528i
$137$		−	10.6670i		−	0.911342i	−0.890148	−	0.455671i	$-0.849399\pi$
$137$		−	10.6670i		−	0.911342i	0.890148	−	0.455671i	$-0.150601\pi$
$138$	0.270231	+	0.0477129i	0.0230036	+	0.00406159i
$139$	9.57332	−	5.52716i	0.811998	−	0.468807i	−0.0356511	−	0.999364i	$-0.511351\pi$
$139$	9.57332	−	5.52716i	0.811998	−	0.468807i	0.847649	+	0.530557i	$0.178017\pi$
$140$	4.56508	+	10.3049i	0.385819	+	0.870924i
$141$	2.68938	+	7.39428i	0.226487	+	0.622711i
$142$	−4.44713	−	7.70265i	−0.373195	−	0.646392i
$143$	1.11759	−	5.24409i	0.0934576	−	0.438533i
$144$	2.81861	+	1.02735i	0.234884	+	0.0856128i
$145$		−	2.03491i		−	0.168990i
$146$	3.48176	−	6.03059i	0.288153	−	0.499095i
$147$	−11.2235	−	4.58626i	−0.925696	−	0.378268i
$148$	10.4771			0.861211
$149$	−7.27861	−	4.20231i	−0.596287	−	0.344266i	0.171292	−	0.985220i	$-0.445206\pi$
$149$	−7.27861	−	4.20231i	−0.596287	−	0.344266i	−0.767580	+	0.640954i	$0.778539\pi$
$150$	17.4408	+	14.6414i	1.42404	+	1.19547i
$151$	11.2766	−	19.5317i	0.917679	−	1.58947i	0.114748	−	0.993395i	$-0.463394\pi$
$151$	11.2766	−	19.5317i	0.917679	−	1.58947i	0.802931	−	0.596072i	$-0.203273\pi$
$152$	−2.05432	+	3.55819i	−0.166627	+	0.288607i
$153$	−7.51178	−	2.73797i	−0.607291	−	0.221351i
$154$	−1.59362	−	3.59734i	−0.128418	−	0.289882i
$155$		−	14.9855i		−	1.20366i
$156$	−4.92406	+	3.84105i	−0.394240	+	0.307530i
$157$	14.0883	+	8.13386i	1.12437	+	0.649153i	0.942512	−	0.334173i	$-0.108457\pi$
$157$	14.0883	+	8.13386i	1.12437	+	0.649153i	0.181854	+	0.983326i	$0.441790\pi$
$158$	14.2122	−	8.20543i	1.13066	−	0.652789i
$159$	−4.96084	−	4.16457i	−0.393420	−	0.330272i
$160$	3.68924	−	2.12998i	0.291660	−	0.168390i
$161$	−0.0445910	+	0.416791i	−0.00351427	+	0.0328477i
$162$	−5.79141	+	6.88909i	−0.455016	+	0.541258i
$163$	3.49025	−	6.04529i	0.273377	−	0.473503i	−0.696347	−	0.717705i	$-0.745193\pi$
$163$	3.49025	−	6.04529i	0.273377	−	0.473503i	0.969724	+	0.244202i	$0.0785259\pi$
$164$	5.13995	−	8.90266i	0.401363	−	0.695181i
$165$	−8.40389	−	7.05499i	−0.654242	−	0.549230i
$166$		−	8.37013i		−	0.649648i
$167$	−4.12054	+	7.13698i	−0.318857	+	0.552276i	−0.980250	−	0.197764i	$-0.936632\pi$
$167$	−4.12054	+	7.13698i	−0.318857	+	0.552276i	0.661393	+	0.750039i	$0.269965\pi$
$168$	−1.27234	+	4.40240i	−0.0981629	+	0.339653i
$169$	−1.34508	−	12.9302i	−0.103468	−	0.994633i
$170$	−9.83207	+	5.67655i	−0.754085	+	0.435371i
$171$	−7.91862	−	9.44584i	−0.605552	−	0.722342i
$172$	−4.00148	−	6.93077i	−0.305110	−	0.528467i
$173$	−7.88311	+	13.6540i	−0.599342	+	1.03809i	0.393576	+	0.919292i	$0.371238\pi$
$173$	−7.88311	+	13.6540i	−0.599342	+	1.03809i	−0.992918	+	0.118799i	$0.962096\pi$
$174$	0.531968	−	0.633679i	0.0403284	−	0.0480391i
$175$	−20.4982	+	28.1031i	−1.54951	+	2.12440i
$176$	−1.28788	+	0.743556i	−0.0970773	+	0.0560476i
$177$	8.16620	+	1.44185i	0.613809	+	0.108376i
$178$			11.8904i			0.891224i
$179$	−6.51608	+	3.76206i	−0.487035	+	0.281190i	−0.723343	−	0.690488i	$-0.757396\pi$
$179$	−6.51608	+	3.76206i	−0.487035	+	0.281190i	0.236309	+	0.971678i	$0.424062\pi$
$180$	2.21343	+	12.5868i	0.164980	+	0.938161i
$181$		−	3.30682i		−	0.245794i	−0.992419	−	0.122897i	$-0.960781\pi$
$181$		−	3.30682i		−	0.245794i	0.992419	−	0.122897i	$-0.0392185\pi$
$182$	−6.36610	−	7.10442i	−0.471887	−	0.526614i
$183$	−3.50248	−	2.94030i	−0.258911	−	0.217353i
$184$	0.158431			0.0116797
$185$	22.3160	+	38.6524i	1.64071	+	2.84178i
$186$	3.91752	−	4.66655i	0.287247	−	0.342168i
$187$	3.43228	−	1.98163i	0.250993	−	0.144911i
$188$	2.27135	+	3.93409i	0.165655	+	0.286923i
$189$	−11.1015	−	8.10904i	−0.807516	−	0.589846i
$190$	−17.5027			−1.26978
$191$	22.5097	+	12.9960i	1.62875	+	0.940358i	0.984467	+	0.175569i	$0.0561766\pi$
$191$	22.5097	+	12.9960i	1.62875	+	0.940358i	0.644281	+	0.764789i	$0.277157\pi$
$192$	1.70567	+	0.301159i	0.123096	+	0.0217343i
$193$	−6.03765	−	10.4575i	−0.434600	−	0.752749i	0.562663	−	0.826686i	$-0.309777\pi$
$193$	−6.03765	−	10.4575i	−0.434600	−	0.752749i	−0.997263	+	0.0739372i	$0.976444\pi$
$194$	−1.81173	−	3.13800i	−0.130074	−	0.225295i
$195$	−24.6587	−	9.98465i	−1.76585	−	0.715015i
$196$	−6.84157	−	1.48086i	−0.488683	−	0.105776i
$197$	2.02572	+	1.16955i	0.144326	+	0.0833268i	0.570424	−	0.821350i	$-0.306779\pi$
$197$	2.02572	+	1.16955i	0.144326	+	0.0833268i	−0.426098	+	0.904677i	$0.640112\pi$
$198$	−0.772687	−	4.39391i	−0.0549125	−	0.312262i
$199$		−	10.6892i		−	0.757736i	−0.925451	−	0.378868i	$-0.876313\pi$
$199$		−	10.6892i		−	0.757736i	0.925451	−	0.378868i	$-0.123687\pi$
$200$	11.3859	+	6.57365i	0.805104	+	0.464827i
$201$	−1.93526	−	5.32087i	−0.136503	−	0.375306i
$202$	−4.17343	+	2.40953i	−0.293641	+	0.169534i
$203$	1.02107	+	0.744761i	0.0716652	+	0.0522719i
$204$	−4.54572	−	0.802608i	−0.318264	−	0.0561938i
$205$	43.7920			3.05857
$206$	1.24322	+	2.15332i	0.0866192	+	0.150029i
$207$	−0.162765	+	0.446555i	−0.0113129	+	0.0310377i
$208$	−2.41401	+	2.67816i	−0.167382	+	0.185697i
$209$	6.11001			0.422638
$210$	−18.9516	+	4.68309i	−1.30778	+	0.323164i
$211$	2.22580	−	3.85520i	0.153230	−	0.265403i	−0.779183	−	0.626797i	$-0.784366\pi$
$211$	2.22580	−	3.85520i	0.153230	−	0.265403i	0.932413	+	0.361394i	$0.117699\pi$
$212$	−3.23858	−	1.86979i	−0.222427	−	0.128418i
$213$	14.4775	−	5.26560i	0.991979	−	0.360793i
$214$	9.19824			0.628779
$215$	17.0462	−	29.5249i	1.16254	−	2.01358i
$216$	−2.60117	+	4.49821i	−0.176987	+	0.306065i
$217$	7.51939	+	5.48457i	0.510450	+	0.372317i
$218$	5.83432	+	3.36845i	0.395150	+	0.228140i
$219$	9.23763	+	7.75490i	0.624221	+	0.524028i
$220$	−5.48631	−	3.16752i	−0.369887	−	0.213554i
$221$	6.43351	−	7.13748i	0.432765	−	0.480119i
$222$	−3.15526	+	17.8704i	−0.211767	+	1.19938i
$223$	−3.82172	−	2.20647i	−0.255921	−	0.147756i	0.366551	−	0.930398i	$-0.380538\pi$
$223$	−3.82172	−	2.20647i	−0.255921	−	0.147756i	−0.622473	+	0.782642i	$0.713872\pi$
$224$	−0.281454	+	2.63074i	−0.0188054	+	0.175774i
$225$	−30.2259	+	25.3389i	−2.01506	+	1.68926i
$226$	−8.54191	−	14.7950i	−0.568200	−	0.984151i
$227$	−19.6477			−1.30407			−0.652033	−	0.758190i	$-0.726084\pi$
$227$	−19.6477			−1.30407			−0.652033	+	0.758190i	$0.726084\pi$
$228$	−5.45041	−	4.57557i	−0.360962	−	0.303025i
$229$	−11.0523	+	6.38106i	−0.730358	+	0.421672i	−0.818553	−	0.574431i	$-0.805223\pi$
$229$	−11.0523	+	6.38106i	−0.730358	+	0.421672i	0.0881953	+	0.996103i	$0.471890\pi$
$230$	0.337456	+	0.584490i	0.0222512	+	0.0385401i
$231$	6.61581	−	1.63482i	0.435288	−	0.107563i
$232$	0.238841	−	0.413684i	0.0156807	−	0.0271597i
$233$	−19.0288	+	10.9863i	−1.24662	+	0.719734i	−0.970433	−	0.241371i	$-0.922403\pi$
$233$	−19.0288	+	10.9863i	−1.24662	+	0.719734i	−0.276183	+	0.961105i	$0.589070\pi$
$234$	−5.06863	−	9.55557i	−0.331347	−	0.624667i
$235$	−9.67586	+	16.7591i	−0.631183	+	1.09324i
$236$	4.78769			0.311652
$237$	9.71561	+	26.7125i	0.631096	+	1.73516i
$238$	0.750093	−	7.01109i	0.0486213	−	0.454462i
$239$		−	17.9466i		−	1.16087i	−0.814306	−	0.580436i	$-0.802882\pi$
$239$		−	17.9466i		−	1.16087i	0.814306	−	0.580436i	$-0.197118\pi$
$240$	2.52200	+	6.93408i	0.162794	+	0.447593i
$241$			16.4325i			1.05851i	0.848463	+	0.529254i	$0.177528\pi$
$241$			16.4325i			1.05851i	−0.848463	+	0.529254i	$0.822472\pi$
$242$	−7.61106	−	4.39425i	−0.489258	−	0.282473i
$243$	−10.0064	−	11.9529i	−0.641909	−	0.766781i
$244$	−2.28652	−	1.32012i	−0.146380	−	0.0845123i
$245$	−9.10916	−	28.3944i	−0.581963	−	1.81405i
$246$	13.6370	+	11.4482i	0.869466	+	0.729909i
$247$	14.0913	−	4.57024i	0.896609	−	0.290797i
$248$	1.75887	−	3.04646i	0.111689	−	0.193450i
$249$	14.2767	+	2.52074i	0.904746	+	0.159745i
$250$			34.7072i			2.19508i
$251$	−5.60540	−	9.70884i	−0.353810	−	0.612816i	0.633104	−	0.774067i	$-0.281781\pi$
$251$	−5.60540	−	9.70884i	−0.353810	−	0.612816i	−0.986913	+	0.161251i	$0.948447\pi$
$252$	−7.12586	−	3.49601i	−0.448887	−	0.220228i
$253$	−0.117802	−	0.204040i	−0.00740617	−	0.0128279i
$254$	4.94830	+	2.85690i	0.310484	+	0.179258i
$255$	−6.72129	−	18.4798i	−0.420904	−	1.15725i
$256$	1.00000			0.0625000
$257$	−2.46735			−0.153909			−0.0769546	−	0.997035i	$-0.524520\pi$
$257$	−2.46735			−0.153909			−0.0769546	+	0.997035i	$0.524520\pi$
$258$	13.0267	−	4.73794i	0.811006	−	0.294971i
$259$	−27.5625	−	2.94881i	−1.71265	−	0.183230i
$260$	−15.0222	−	3.20144i	−0.931636	−	0.198545i
$261$	0.920640	+	1.09820i	0.0569862	+	0.0679768i
$262$	12.9809	−	7.49454i	0.801964	−	0.463014i
$263$	−14.4808	+	8.36047i	−0.892922	+	0.515529i	−0.874897	−	0.484309i	$-0.839071\pi$
$263$	−14.4808	+	8.36047i	−0.892922	+	0.515529i	−0.0180250	+	0.999838i	$0.505738\pi$
$264$	−0.880404	−	2.42062i	−0.0541851	−	0.148979i
$265$		−	15.9305i		−	0.978604i
$266$	6.40585	−	8.78247i	0.392768	−	0.538488i
$267$	−20.2811	−	3.58090i	−1.24118	−	0.219147i
$268$	−1.63445	−	2.83094i	−0.0998396	−	0.172927i
$269$	2.62459			0.160024			0.0800121	−	0.996794i	$-0.474504\pi$
$269$	2.62459			0.160024			0.0800121	+	0.996794i	$0.474504\pi$
$270$	−22.1354	−	0.0152294i	−1.34712	−	0.000926832i
$271$			8.91429i			0.541505i	0.962649	+	0.270752i	$0.0872725\pi$
$271$			8.91429i			0.541505i	−0.962649	+	0.270752i	$0.912728\pi$
$272$	−2.66507			−0.161593
$273$	14.0350	−	8.71890i	0.849436	−	0.527692i
$274$	10.6670			0.644416
$275$		−	19.5515i		−	1.17900i
$276$	−0.0477129	+	0.270231i	−0.00287198	+	0.0162660i
$277$	−29.2308			−1.75631			−0.878156	−	0.478375i	$-0.841226\pi$
$277$	−29.2308			−1.75631			−0.878156	+	0.478375i	$0.841226\pi$
$278$	5.52716	+	9.57332i	0.331497	+	0.574169i
$279$	6.77978	+	8.08736i	0.405895	+	0.484178i
$280$	−10.3049	+	4.56508i	−0.615836	+	0.272815i
$281$		−	18.8564i		−	1.12488i	−0.826839	−	0.562439i	$-0.809863\pi$
$281$		−	18.8564i		−	1.12488i	0.826839	−	0.562439i	$-0.190137\pi$
$282$	−7.39428	+	2.68938i	−0.440323	+	0.160150i
$283$	−0.302847	+	0.174849i	−0.0180024	+	0.0103937i	−0.508974	−	0.860782i	$-0.669975\pi$
$283$	−0.302847	+	0.174849i	−0.0180024	+	0.0103937i	0.490972	+	0.871175i	$0.336642\pi$
$284$	7.70265	−	4.44713i	0.457068	−	0.263888i
$285$	5.27108	−	29.8538i	0.312232	−	1.76838i
$286$	5.24409	+	1.11759i	0.310090	+	0.0660845i
$287$	−16.0276	+	21.9739i	−0.946077	+	1.29708i
$288$	−1.02735	+	2.81861i	−0.0605374	+	0.166088i
$289$	−9.89742			−0.582201
$290$	2.03491			0.119494
$291$	5.89801	−	2.14517i	0.345747	−	0.125752i
$292$	6.03059	+	3.48176i	0.352914	+	0.203755i
$293$	−5.35220	−	9.27029i	−0.312679	−	0.541576i	0.666262	−	0.745717i	$-0.267893\pi$
$293$	−5.35220	−	9.27029i	−0.312679	−	0.541576i	−0.978941	+	0.204141i	$0.934560\pi$
$294$	4.58626	−	11.2235i	0.267476	−	0.654566i
$295$	10.1977	+	17.6629i	0.593732	+	1.02837i
$296$			10.4771i			0.608968i
$297$	7.72726	+	0.00531643i	0.448381	+	0.000308491i
$298$	4.20231	−	7.27861i	0.243433	−	0.421639i
$299$	−0.424304	−	0.382455i	−0.0245381	−	0.0221179i
$300$	−14.6414	+	17.4408i	−0.845323	+	1.00695i
$301$	8.57617	+	19.3593i	0.494322	+	1.11585i
$302$	19.5317	+	11.2766i	1.12392	+	0.648897i
$303$	−2.85299	−	7.84414i	−0.163900	−	0.450634i
$304$	−3.55819	−	2.05432i	−0.204076	−	0.117823i
$305$		−	11.2474i		−	0.644022i
$306$	2.73797	−	7.51178i	0.156519	−	0.429420i
$307$			4.04677i			0.230961i	0.993310	+	0.115481i	$0.0368408\pi$
$307$			4.04677i			0.230961i	−0.993310	+	0.115481i	$0.963159\pi$
$308$	3.59734	−	1.59362i	0.204978	−	0.0908051i
$309$	−4.04726	+	1.47203i	−0.230240	+	0.0837408i
$310$	14.9855			0.851118
$311$	−8.19728	+	14.1981i	−0.464825	+	0.805101i	−0.999194	−	0.0401509i	$-0.987216\pi$
$311$	−8.19728	+	14.1981i	−0.464825	+	0.805101i	0.534369	+	0.845252i	$0.320549\pi$
$312$	−3.84105	−	4.92406i	−0.217457	−	0.278770i
$313$	17.1202	−	9.88433i	0.967689	−	0.558696i	0.0691582	−	0.997606i	$-0.477969\pi$
$313$	17.1202	−	9.88433i	0.967689	−	0.558696i	0.898531	+	0.438910i	$0.144635\pi$
$314$	−8.13386	+	14.0883i	−0.459020	+	0.795047i
$315$	−2.28037	−	33.7354i	−0.128484	−	1.90078i
$316$	8.20543	+	14.2122i	0.461591	+	0.799500i
$317$	−6.98551	+	4.03309i	−0.392345	+	0.226521i	−0.683176	−	0.730254i	$-0.739402\pi$
$317$	−6.98551	+	4.03309i	−0.392345	+	0.226521i	0.290830	+	0.956775i	$0.406068\pi$
$318$	4.16457	−	4.96084i	0.233538	−	0.278190i
$319$	−0.710366			−0.0397729
$320$	2.12998	+	3.68924i	0.119070	+	0.206235i
$321$	−2.77013	+	15.6891i	−0.154614	+	0.875682i
$322$	−0.416791	−	0.0445910i	−0.0232268	−	0.00248496i
$323$	9.48281	+	5.47490i	0.527638	+	0.304632i
$324$	−6.88909	−	5.79141i	−0.382727	−	0.321745i
$325$	−14.6244	−	45.0910i	−0.811214	−	2.50120i
$326$	6.04529	+	3.49025i	0.334818	+	0.193307i
$327$	−7.50251	+	8.93698i	−0.414890	+	0.494216i
$328$	8.90266	+	5.13995i	0.491567	+	0.283806i
$329$	−4.86805	−	10.9888i	−0.268385	−	0.605834i
$330$	7.05499	−	8.40389i	0.388364	−	0.462619i
$331$	−9.20927	+	15.9509i	−0.506188	+	0.876742i	0.493787	+	0.869583i	$0.335612\pi$
$331$	−9.20927	+	15.9509i	−0.506188	+	0.876742i	−0.999974	+	0.00715951i	$0.997721\pi$
$332$	8.37013			0.459370
$333$	−29.5308	−	10.7637i	−1.61828	−	0.589845i
$334$	−7.13698	−	4.12054i	−0.390518	−	0.225466i
$335$	6.96268	−	12.0597i	0.380412	−	0.658893i
$336$	−4.40240	−	1.27234i	−0.240171	−	0.0694116i
$337$	−16.8561			−0.918208			−0.459104	−	0.888383i	$-0.651829\pi$
$337$	−16.8561			−0.918208			−0.459104	+	0.888383i	$0.651829\pi$
$338$	12.9302	−	1.34508i	0.703312	−	0.0731626i
$339$	27.8079	−	10.1140i	1.51032	−	0.549318i
$340$	−5.67655	−	9.83207i	−0.307854	−	0.533219i
$341$	−5.23128			−0.283290
$342$	9.44584	−	7.91862i	0.510773	−	0.428190i
$343$	17.5816	+	5.82135i	0.949316	+	0.314323i
$344$	6.93077	−	4.00148i	0.373682	−	0.215746i
$345$	−1.09857	+	0.399563i	−0.0591452	+	0.0215117i
$346$	−13.6540	−	7.88311i	−0.734041	−	0.423799i
$347$			15.6755i			0.841507i	0.907175	+	0.420754i	$0.138234\pi$
$347$			15.6755i			0.841507i	−0.907175	+	0.420754i	$0.861766\pi$
$348$	0.633679	+	0.531968i	0.0339688	+	0.0285165i
$349$	16.3312	+	9.42880i	0.874187	+	0.504712i	0.868737	−	0.495273i	$-0.164932\pi$
$349$	16.3312	+	9.42880i	0.874187	+	0.504712i	0.00544978	+	0.999985i	$0.498265\pi$
$350$	−28.1031	−	20.4982i	−1.50218	−	1.09567i
$351$	17.8251	−	5.76767i	0.951433	−	0.307855i
$352$	−0.743556	−	1.28788i	−0.0396317	−	0.0686441i
$353$	−9.20379	−	15.9414i	−0.489868	−	0.848477i	0.510064	−	0.860137i	$-0.329622\pi$
$353$	−9.20379	−	15.9414i	−0.489868	−	0.848477i	−0.999932	+	0.0116598i	$0.996288\pi$
$354$	−1.44185	+	8.16620i	−0.0766336	+	0.434029i
$355$	32.8130	+	18.9446i	1.74153	+	1.00548i
$356$	−11.8904			−0.630190
$357$	11.7327	+	3.39086i	0.620960	+	0.179463i
$358$	−3.76206	−	6.51608i	−0.198831	−	0.344385i
$359$	29.2230	−	16.8719i	1.54233	−	0.890465i	0.543639	−	0.839319i	$-0.317046\pi$
$359$	29.2230	−	16.8719i	1.54233	−	0.890465i	0.998691	−	0.0511459i	$-0.0162873\pi$
$360$	−12.5868	+	2.21343i	−0.663380	+	0.116658i
$361$	−1.05953	−	1.83515i	−0.0557645	−	0.0965870i
$362$	3.30682			0.173803
$363$	9.78727	−	11.6586i	0.513698	−	0.611917i
$364$	7.10442	−	6.36610i	0.372373	−	0.333675i
$365$			29.6644i			1.55271i
$366$	2.94030	−	3.50248i	0.153692	−	0.183078i
$367$	−29.4842	+	17.0227i	−1.53906	+	0.888579i	−0.540171	+	0.841555i	$0.681640\pi$
$367$	−29.4842	+	17.0227i	−1.53906	+	0.888579i	−0.998894	+	0.0470240i	$0.985026\pi$
$368$			0.158431i			0.00825879i
$369$	−23.6337	+	19.8126i	−1.23032	+	1.03140i
$370$	−38.6524	+	22.3160i	−2.00945	+	1.16015i
$371$	7.99359	+	5.83045i	0.415007	+	0.302702i
$372$	4.66655	+	3.91752i	0.241949	+	0.203114i
$373$	−15.4251	+	26.7171i	−0.798682	+	1.38336i	0.121792	+	0.992556i	$0.461136\pi$
$373$	−15.4251	+	26.7171i	−0.798682	+	1.38336i	−0.920474	+	0.390803i	$0.872197\pi$
$374$	1.98163	+	3.43228i	0.102467	+	0.177479i
$375$	−59.1990	−	10.4524i	−3.05702	−	0.539758i
$376$	−3.93409	+	2.27135i	−0.202885	+	0.117136i
$377$	−1.63829	+	0.531348i	−0.0843764	+	0.0273658i
$378$	8.10904	−	11.1015i	0.417084	−	0.571000i
$379$	3.11757	−	5.39979i	0.160139	−	0.277368i	−0.774780	−	0.632231i	$-0.782139\pi$
$379$	3.11757	−	5.39979i	0.160139	−	0.277368i	0.934918	+	0.354863i	$0.115473\pi$
$380$		−	17.5027i		−	0.897868i
$381$	−6.36315	+	7.57978i	−0.325994	+	0.388324i
$382$	−12.9960	+	22.5097i	−0.664934	+	1.15170i
$383$	−2.72642	+	4.72231i	−0.139314	+	0.241299i	−0.927237	−	0.374475i	$-0.877823\pi$
$383$	−2.72642	+	4.72231i	−0.139314	+	0.241299i	0.787923	+	0.615773i	$0.211156\pi$
$384$	−0.301159	+	1.70567i	−0.0153684	+	0.0870420i
$385$	13.5415	+	9.87706i	0.690140	+	0.503382i
$386$	10.4575	−	6.03765i	0.532274	−	0.307309i
$387$	4.15826	+	23.6461i	0.211376	+	1.20200i
$388$	3.13800	−	1.81173i	0.159308	−	0.0919765i
$389$	33.4019	+	19.2846i	1.69354	+	0.977768i	0.951616	+	0.307290i	$0.0994221\pi$
$389$	33.4019	+	19.2846i	1.69354	+	0.977768i	0.741929	+	0.670479i	$0.233911\pi$
$390$	9.98465	−	24.6587i	0.505592	−	1.24864i
$391$		−	0.422230i		−	0.0213531i
$392$	1.48086	−	6.84157i	0.0747948	−	0.345551i
$393$	8.87388	+	24.3982i	0.447628	+	1.23073i
$394$	−1.16955	+	2.02572i	−0.0589209	+	0.102054i
$395$	−34.9548	+	60.5436i	−1.75877	+	3.04628i
$396$	4.39391	−	0.772687i	0.220802	−	0.0388290i
$397$	−23.3251	−	13.4667i	−1.17065	−	0.675876i	−0.216819	−	0.976212i	$-0.569568\pi$
$397$	−23.3251	−	13.4667i	−1.17065	−	0.675876i	−0.953834	+	0.300336i	$0.902901\pi$
$398$	10.6892			0.535801
$399$	13.0508	+	13.5712i	0.653357	+	0.679408i
$400$	−6.57365	+	11.3859i	−0.328682	+	0.569295i
$401$		−	9.26244i		−	0.462544i	−0.972889	−	0.231272i	$-0.925711\pi$
$401$		−	9.26244i		−	0.462544i	0.972889	−	0.231272i	$-0.0742888\pi$
$402$	5.32087	−	1.93526i	0.265381	−	0.0965219i
$403$	−12.0647	+	3.91296i	−0.600987	+	0.194918i
$404$	−2.40953	−	4.17343i	−0.119879	−	0.207636i
$405$	6.69225	−	37.7511i	0.332541	−	1.87587i
$406$	−0.744761	+	1.02107i	−0.0369618	+	0.0506750i
$407$	13.4932	−	7.79030i	0.668833	−	0.386151i
$408$	0.802608	−	4.54572i	0.0397350	−	0.225047i
$409$		−	15.2524i		−	0.754184i	−0.926176	−	0.377092i	$-0.876924\pi$
$409$		−	15.2524i		−	0.754184i	0.926176	−	0.377092i	$-0.123076\pi$
$410$			43.7920i			2.16273i
$411$	−3.21245	+	18.1943i	−0.158459	+	0.897460i
$412$	−2.15332	+	1.24322i	−0.106086	+	0.0612490i
$413$	−12.5952	−	1.34751i	−0.619767	−	0.0663068i
$414$	−0.446555	−	0.162765i	−0.0219470	−	0.00799945i
$415$	17.8282	+	30.8794i	0.875153	+	1.51581i
$416$	−2.67816	−	2.41401i	−0.131308	−	0.118357i
$417$	−17.9935	+	6.54441i	−0.881143	+	0.320481i
$418$			6.11001i			0.298850i
$419$	10.7855	−	18.6811i	0.526908	−	0.912631i	−0.472600	−	0.881277i	$-0.656685\pi$
$419$	10.7855	−	18.6811i	0.526908	−	0.912631i	0.999508	−	0.0313545i	$-0.00998208\pi$
$420$	−4.68309	−	18.9516i	−0.228511	−	0.924742i
$421$	−25.8262			−1.25869			−0.629345	−	0.777126i	$-0.716677\pi$
$421$	−25.8262			−1.25869			−0.629345	+	0.777126i	$0.716677\pi$
$422$	3.85520	+	2.22580i	0.187668	+	0.108350i
$423$	−2.36033	−	13.4221i	−0.114763	−	0.652606i
$424$	1.86979	−	3.23858i	0.0908053	−	0.157279i
$425$	17.5192	−	30.3442i	0.849807	−	1.47191i
$426$	5.26560	+	14.4775i	0.255119	+	0.701435i
$427$	5.64369	+	4.11645i	0.273117	+	0.199209i
$428$			9.19824i			0.444614i
$429$	−3.48554	+	8.60811i	−0.168284	+	0.415603i
$430$	29.5249	+	17.0462i	1.42381	+	0.822040i
$431$	9.38332	−	5.41746i	0.451979	−	0.260950i	−0.256687	−	0.966495i	$-0.582631\pi$
$431$	9.38332	−	5.41746i	0.451979	−	0.260950i	0.708666	+	0.705545i	$0.249298\pi$
$432$	−4.49821	−	2.60117i	−0.216420	−	0.125149i
$433$	−15.5101	+	8.95476i	−0.745368	+	0.430338i	−0.824018	−	0.566564i	$-0.808272\pi$
$433$	−15.5101	+	8.95476i	−0.745368	+	0.430338i	0.0786500	+	0.996902i	$0.474939\pi$
$434$	−5.48457	+	7.51939i	−0.263268	+	0.360942i
$435$	−0.612830	+	3.47087i	−0.0293829	+	0.166416i
$436$	−3.36845	+	5.83432i	−0.161319	+	0.279413i
$437$	0.325469	−	0.563728i	0.0155693	−	0.0269668i
$438$	−7.75490	+	9.23763i	−0.370543	+	0.441391i
$439$		−	7.13870i		−	0.340711i	−0.985383	−	0.170356i	$-0.945508\pi$
$439$		−	7.13870i		−	0.340711i	0.985383	−	0.170356i	$-0.0544917\pi$
$440$	3.16752	−	5.48631i	0.151006	−	0.261550i
$441$	17.7623	+	11.2027i	0.845825	+	0.533461i
$442$	7.13748	+	6.43351i	0.339495	+	0.306011i
$443$	15.1527	−	8.74841i	0.719926	−	0.415650i	−0.0947992	−	0.995496i	$-0.530221\pi$
$443$	15.1527	−	8.74841i	0.719926	−	0.415650i	0.814726	+	0.579847i	$0.196888\pi$
$444$	−17.8704	−	3.15526i	−0.848093	−	0.149742i
$445$	−25.3264	−	43.8665i	−1.20058	−	2.07947i
$446$	2.20647	−	3.82172i	0.104479	−	0.180964i
$447$	11.1493	+	9.35976i	0.527345	+	0.442701i
$448$	−2.63074	−	0.281454i	−0.124291	−	0.0132974i
$449$	3.24523	−	1.87364i	0.153152	−	0.0884224i	−0.421466	−	0.906844i	$-0.638484\pi$
$449$	3.24523	−	1.87364i	0.153152	−	0.0884224i	0.574618	+	0.818422i	$0.305151\pi$
$450$	−25.3389	−	30.2259i	−1.19449	−	1.42486i
$451$		−	15.2874i		−	0.719854i
$452$	14.7950	−	8.54191i	0.695900	−	0.401778i
$453$	−25.1163	+	29.9185i	−1.18007	+	1.40569i
$454$		−	19.6477i		−	0.922114i
$455$	38.6184	+	12.6502i	1.81046	+	0.593050i
$456$	4.57557	−	5.45041i	0.214271	−	0.255239i
$457$	12.5530			0.587205			0.293603	−	0.955928i	$-0.405146\pi$
$457$	12.5530			0.587205			0.293603	+	0.955928i	$0.405146\pi$
$458$	−6.38106	−	11.0523i	−0.298167	−	0.516441i
$459$	11.9880	+	6.93230i	0.559554	+	0.323572i
$460$	−0.584490	+	0.337456i	−0.0272520	+	0.0157339i
$461$	3.57386	+	6.19010i	0.166451	+	0.288302i	0.937170	−	0.348874i	$-0.113436\pi$
$461$	3.57386	+	6.19010i	0.166451	+	0.288302i	−0.770719	+	0.637176i	$0.780103\pi$
$462$	1.63482	+	6.61581i	0.0760588	+	0.307795i
$463$	−6.57780			−0.305696			−0.152848	−	0.988250i	$-0.548845\pi$
$463$	−6.57780			−0.305696			−0.152848	+	0.988250i	$0.548845\pi$
$464$	0.413684	+	0.238841i	0.0192048	+	0.0110879i
$465$	−4.51301	+	25.5602i	−0.209286	+	1.18533i
$466$	−10.9863	−	19.0288i	−0.508929	−	0.881490i
$467$	10.6728	+	18.4857i	0.493876	+	0.855418i	0.999975	−	0.00705702i	$-0.00224634\pi$
$467$	10.6728	+	18.4857i	0.493876	+	0.855418i	−0.506099	+	0.862475i	$0.668913\pi$
$468$	9.55557	−	5.06863i	0.441706	−	0.234298i
$469$	3.50302	+	7.90749i	0.161754	+	0.365134i
$470$	−16.7591	−	9.67586i	−0.773038	−	0.446314i
$471$	−21.5803	−	18.1165i	−0.994369	−	0.834763i
$472$			4.78769i			0.220371i
$473$	−10.3068	−	5.95065i	−0.473909	−	0.273611i
$474$	−26.7125	+	9.71561i	−1.22694	+	0.446253i
$475$	46.7806	−	27.0088i	2.14644	−	1.23925i
$476$	7.01109	+	0.750093i	0.321353	+	0.0343805i
$477$	7.20734	+	8.59738i	0.330002	+	0.393647i
$478$	17.9466			0.820860
$479$	12.5227	+	21.6900i	0.572177	+	0.991040i	0.996342	+	0.0854548i	$0.0272343\pi$
$479$	12.5227	+	21.6900i	0.572177	+	0.991040i	−0.424165	+	0.905585i	$0.639432\pi$
$480$	−6.93408	+	2.52200i	−0.316496	+	0.115113i
$481$	25.2918	−	28.0593i	1.15321	−	1.27939i
$482$	−16.4325			−0.748478
$483$	0.201578	−	0.697478i	0.00917210	−	0.0317363i
$484$	4.39425	−	7.61106i	0.199739	−	0.345957i
$485$	13.3678	+	7.71789i	0.607000	+	0.350451i
$486$	11.9529	−	10.0064i	0.542196	−	0.453898i
$487$	35.1851			1.59439			0.797195	−	0.603722i	$-0.206316\pi$
$487$	35.1851			1.59439			0.797195	+	0.603722i	$0.206316\pi$
$488$	1.32012	−	2.28652i	0.0597592	−	0.103506i
$489$	−7.77380	+	9.26014i	−0.351543	+	0.418758i
$490$	28.3944	−	9.10916i	1.28273	−	0.411510i
$491$	27.3749	+	15.8049i	1.23541	+	0.713265i	0.968153	−	0.250360i	$-0.0805490\pi$
$491$	27.3749	+	15.8049i	1.23541	+	0.713265i	0.267258	+	0.963625i	$0.413882\pi$
$492$	−11.4482	+	13.6370i	−0.516123	+	0.614805i
$493$	−1.10250	−	0.636527i	−0.0496539	−	0.0286677i
$494$	4.57024	+	14.0913i	0.205625	+	0.633998i
$495$	12.2096	+	14.5644i	0.548780	+	0.654620i
$496$	3.04646	+	1.75887i	0.136790	+	0.0789757i
$497$	−21.5153	+	9.53129i	−0.965094	+	0.427537i
$498$	−2.52074	+	14.2767i	−0.112957	+	0.639752i
$499$	−8.10265	−	14.0342i	−0.362725	−	0.628257i	0.625684	−	0.780077i	$-0.284820\pi$
$499$	−8.10265	−	14.0342i	−0.362725	−	0.628257i	−0.988408	+	0.151819i	$0.951487\pi$
$500$	−34.7072			−1.55215
$501$	9.17763	−	10.9324i	0.410026	−	0.488423i
$502$	9.70884	−	5.60540i	0.433327	−	0.250181i
$503$	16.5718	+	28.7032i	0.738900	+	1.27981i	0.952991	+	0.302999i	$0.0979879\pi$
$503$	16.5718	+	28.7032i	0.738900	+	1.27981i	−0.214091	+	0.976814i	$0.568679\pi$
$504$	3.49601	−	7.12586i	0.155724	−	0.317411i
$505$	10.2645	−	17.7787i	0.456765	−	0.791140i
$506$	0.204040	−	0.117802i	0.00907067	−	0.00523696i
$507$	−1.59979	+	22.4598i	−0.0710493	+	0.997473i
$508$	−2.85690	+	4.94830i	−0.126755	+	0.219545i
$509$	−10.5327			−0.466855			−0.233427	−	0.972374i	$-0.574994\pi$
$509$	−10.5327			−0.466855			−0.233427	+	0.972374i	$0.574994\pi$
$510$	18.4798	−	6.72129i	0.818299	−	0.297624i
$511$	−14.8850	−	10.8569i	−0.658472	−	0.480283i
$512$			1.00000i			0.0441942i
$513$	10.6618	+	18.4962i	0.470732	+	0.816629i
$514$		−	2.46735i		−	0.108830i
$515$	−9.17307	−	5.29607i	−0.404214	−	0.233373i
$516$	4.73794	+	13.0267i	0.208576	+	0.573468i
$517$	5.85043	+	3.37775i	0.257302	+	0.148553i
$518$	2.94881	−	27.5625i	0.129563	−	1.21103i
$519$	17.5580	−	20.9150i	0.770710	−	0.918068i
$520$	3.20144	−	15.0222i	0.140392	−	0.658766i
$521$	9.84785	−	17.0570i	0.431442	−	0.747279i	−0.565556	−	0.824710i	$-0.691338\pi$
$521$	9.84785	−	17.0570i	0.431442	−	0.747279i	0.996998	+	0.0774306i	$0.0246716\pi$
$522$	−1.09820	+	0.920640i	−0.0480668	+	0.0402953i
$523$		−	3.30184i		−	0.144379i	−0.997391	−	0.0721896i	$-0.977001\pi$
$523$		−	3.30184i		−	0.144379i	0.997391	−	0.0721896i	$-0.0229987\pi$
$524$	7.49454	+	12.9809i	0.327400	+	0.567074i
$525$	43.4265	−	41.7614i	1.89529	−	1.82262i
$526$	−8.36047	−	14.4808i	−0.364534	−	0.631391i
$527$	−8.11901	−	4.68751i	−0.353670	−	0.204191i
$528$	2.42062	−	0.880404i	0.105344	−	0.0383147i
$529$	22.9749			0.998909
$530$	15.9305			0.691977
$531$	−13.4946	−	4.91865i	−0.585616	−	0.213451i
$532$	8.78247	+	6.40585i	0.380768	+	0.277729i
$533$	−11.4348	−	35.2568i	−0.495297	−	1.52714i
$534$	3.58090	−	20.2811i	0.154961	−	0.877648i
$535$	−33.9345	+	19.5921i	−1.46712	+	0.847040i
$536$	2.83094	−	1.63445i	0.122278	−	0.0705973i
$537$	12.2472	−	4.45445i	0.528508	−	0.192224i
$538$			2.62459i			0.113154i
$539$	−9.91220	+	3.17992i	−0.426949	+	0.136969i
$540$	0.0152294	−	22.1354i	0.000655369	−	0.952557i
$541$	14.3963	+	24.9351i	0.618944	+	1.07204i	0.989679	+	0.143304i	$0.0457726\pi$
$541$	14.3963	+	24.9351i	0.618944	+	1.07204i	−0.370735	+	0.928739i	$0.620894\pi$
$542$	−8.91429			−0.382902
$543$	−0.995878	+	5.64034i	−0.0427372	+	0.242050i
$544$		−	2.66507i		−	0.114264i
$545$	−28.6989			−1.22933
$546$	8.71890	+	14.0350i	0.373135	+	0.600642i
$547$	19.4820			0.832989			0.416495	−	0.909138i	$-0.363258\pi$
$547$	19.4820			0.832989			0.416495	+	0.909138i	$0.363258\pi$
$548$			10.6670i			0.455671i
$549$	5.08857	+	6.06998i	0.217175	+	0.259060i
$550$	19.5515			0.833679
$551$	−0.981311	−	1.69968i	−0.0418053	−	0.0724089i
$552$	−0.270231	−	0.0477129i	−0.0115018	−	0.00203080i
$553$	−17.5863	−	39.6981i	−0.747844	−	1.68813i
$554$		−	29.2308i		−	1.24190i
$555$	−26.4232	−	72.6489i	−1.12160	−	3.08377i
$556$	−9.57332	+	5.52716i	−0.405999	+	0.234404i
$557$	32.8823	−	18.9846i	1.39327	−	0.804403i	0.399592	−	0.916693i	$-0.369152\pi$
$557$	32.8823	−	18.9846i	1.39327	−	0.804403i	0.993676	+	0.112290i	$0.0358184\pi$
$558$	−8.08736	+	6.77978i	−0.342365	+	0.287011i
$559$	−28.2214	−	6.01437i	−1.19364	−	0.254381i
$560$	−4.56508	−	10.3049i	−0.192910	−	0.435462i
$561$	−6.45111	+	2.34634i	−0.272366	+	0.0990624i
$562$	18.8564			0.795409
$563$	10.9234			0.460365			0.230183	−	0.973147i	$-0.426068\pi$
$563$	10.9234			0.460365			0.230183	+	0.973147i	$0.426068\pi$
$564$	−2.68938	−	7.39428i	−0.113243	−	0.311355i
$565$	63.0263	+	36.3883i	2.65154	+	1.53087i
$566$	−0.174849	−	0.302847i	−0.00734944	−	0.0127296i
$567$	16.4934	+	17.1746i	0.692657	+	0.721267i
$568$	4.44713	+	7.70265i	0.186597	+	0.323196i
$569$		−	10.5599i		−	0.442696i	−0.975195	−	0.221348i	$-0.928954\pi$
$569$		−	10.5599i		−	0.442696i	0.975195	−	0.221348i	$-0.0710456\pi$
$570$	29.8538	+	5.27108i	1.25044	+	0.220781i
$571$	8.25387	−	14.2961i	0.345414	−	0.598274i	−0.640015	−	0.768362i	$-0.721072\pi$
$571$	8.25387	−	14.2961i	0.345414	−	0.598274i	0.985429	+	0.170088i	$0.0544053\pi$
$572$	−1.11759	+	5.24409i	−0.0467288	+	0.219267i
$573$	−34.4803	−	28.9459i	−1.44043	−	1.20923i
$574$	−21.9739	−	16.0276i	−0.917173	−	0.668977i
$575$	−1.80388	−	1.04147i	−0.0752270	−	0.0434323i
$576$	−2.81861	−	1.02735i	−0.117442	−	0.0428064i
$577$	5.28817	+	3.05312i	0.220149	+	0.127103i	0.606019	−	0.795450i	$-0.292765\pi$
$577$	5.28817	+	3.05312i	0.220149	+	0.127103i	−0.385870	+	0.922553i	$0.626099\pi$
$578$		−	9.89742i		−	0.411678i
$579$	7.14886	+	19.6554i	0.297097	+	0.816849i
$580$			2.03491i			0.0844949i
$581$	−22.0196	−	2.35580i	−0.913527	−	0.0977352i
$582$	2.14517	+	5.89801i	0.0889200	+	0.244480i
$583$	−5.56119			−0.230321
$584$	−3.48176	+	6.03059i	−0.144076	+	0.249548i
$585$	39.0526	+	24.4567i	1.61463	+	1.01116i
$586$	9.27029	−	5.35220i	0.382952	−	0.221098i
$587$	1.08728	−	1.88323i	0.0448769	−	0.0777291i	−0.842714	−	0.538361i	$-0.819044\pi$
$587$	1.08728	−	1.88323i	0.0448769	−	0.0777291i	0.887591	+	0.460632i	$0.152377\pi$
$588$	11.2235	+	4.58626i	0.462848	+	0.189134i
$589$	−7.22658	−	12.5168i	−0.297766	−	0.515746i
$590$	−17.6629	+	10.1977i	−0.727171	+	0.419832i
$591$	−3.10298	−	2.60492i	−0.127639	−	0.107152i
$592$	−10.4771			−0.430605
$593$	0.707096	+	1.22473i	0.0290370	+	0.0502935i	0.880179	−	0.474642i	$-0.157423\pi$
$593$	0.707096	+	1.22473i	0.0290370	+	0.0502935i	−0.851142	+	0.524936i	$0.824089\pi$
$594$	−0.00531643	+	7.72726i	−0.000218136	+	0.317053i
$595$	12.1662	+	27.4633i	0.498767	+	1.12588i
$596$	7.27861	+	4.20231i	0.298144	+	0.172133i
$597$	−3.21914	+	18.2322i	−0.131751	+	0.746195i
$598$	0.382455	−	0.424304i	0.0156397	−	0.0173511i
$599$	13.9159	+	8.03436i	0.568589	+	0.328275i	0.756586	−	0.653894i	$-0.226866\pi$
$599$	13.9159	+	8.03436i	0.568589	+	0.328275i	−0.187996	+	0.982170i	$0.560199\pi$
$600$	−17.4408	−	14.6414i	−0.712020	−	0.597734i
$601$	26.6115	+	15.3641i	1.08550	+	0.626716i	0.932376	−	0.361490i	$-0.117732\pi$
$601$	26.6115	+	15.3641i	1.08550	+	0.626716i	0.153128	+	0.988206i	$0.451065\pi$
$602$	−19.3593	+	8.57617i	−0.789026	+	0.349538i
$603$	1.69848	+	9.65847i	0.0691675	+	0.393323i
$604$	−11.2766	+	19.5317i	−0.458839	+	0.794733i
$605$	37.4387			1.52210
$606$	7.84414	−	2.85299i	0.318646	−	0.115895i
$607$	−28.1452	−	16.2496i	−1.14238	−	0.659552i	−0.195360	−	0.980732i	$-0.562587\pi$
$607$	−28.1452	−	16.2496i	−1.14238	−	0.659552i	−0.947018	+	0.321180i	$0.895921\pi$
$608$	2.05432	−	3.55819i	0.0833137	−	0.144304i
$609$	−1.51732	−	1.57782i	−0.0614849	−	0.0639365i
$610$	11.2474			0.455393
$611$	16.0192	+	3.41391i	0.648066	+	0.138112i
$612$	7.51178	+	2.73797i	0.303646	+	0.110676i
$613$	4.35349	+	7.54046i	0.175836	+	0.304556i	0.940450	−	0.339932i	$-0.110404\pi$
$613$	4.35349	+	7.54046i	0.175836	+	0.304556i	−0.764614	+	0.644488i	$0.777071\pi$
$614$	−4.04677			−0.163314
$615$	−74.6947	−	13.1884i	−3.01198	−	0.531806i
$616$	1.59362	+	3.59734i	0.0642089	+	0.144941i
$617$	−29.1565	+	16.8335i	−1.17380	+	0.677691i	−0.954571	−	0.297983i	$-0.903686\pi$
$617$	−29.1565	+	16.8335i	−1.17380	+	0.677691i	−0.219225	+	0.975674i	$0.570353\pi$
$618$	−1.47203	−	4.04726i	−0.0592137	−	0.162804i
$619$	−15.4503	−	8.92024i	−0.621001	−	0.358535i	0.156258	−	0.987716i	$-0.450057\pi$
$619$	−15.4503	−	8.92024i	−0.621001	−	0.358535i	−0.777259	+	0.629181i	$0.783390\pi$
$620$			14.9855i			0.601831i
$621$	0.412107	−	0.712657i	0.0165373	−	0.0285979i
$622$	−14.1981	−	8.19728i	−0.569292	−	0.328681i
$623$	31.2805	+	3.34660i	1.25323	+	0.134079i
$624$	4.92406	−	3.84105i	0.197120	−	0.153765i
$625$	−41.0575	−	71.1137i	−1.64230	−	2.84455i
$626$	9.88433	+	17.1202i	0.395057	+	0.684260i
$627$	−10.4217	−	1.84008i	−0.416201	−	0.0734858i
$628$	−14.0883	−	8.13386i	−0.562183	−	0.324576i
$629$	27.9221			1.11333
$630$	33.7354	−	2.28037i	1.34405	−	0.0908522i
$631$	−16.4881	−	28.5582i	−0.656380	−	1.13688i	−0.981546	−	0.191227i	$-0.938753\pi$
$631$	−16.4881	−	28.5582i	−0.656380	−	1.13688i	0.325166	−	0.945657i	$-0.394580\pi$
$632$	−14.2122	+	8.20543i	−0.565332	+	0.326394i
$633$	−4.95750	+	5.90537i	−0.197043	+	0.234717i
$634$	−4.03309	−	6.98551i	−0.160174	−	0.277430i
$635$	−24.3406			−0.965928
$636$	4.96084	+	4.16457i	0.196710	+	0.165136i
$637$	−20.4816	+	14.7480i	−0.811511	+	0.584337i
$638$		−	0.710366i		−	0.0281237i
$639$	−26.2795	+	4.62136i	−1.03960	+	0.182818i
$640$	−3.68924	+	2.12998i	−0.145830	+	0.0841949i
$641$			16.1872i			0.639356i	0.947526	+	0.319678i	$0.103575\pi$
$641$			16.1872i			0.639356i	−0.947526	+	0.319678i	$0.896425\pi$
$642$	−15.6891	−	2.77013i	−0.619201	−	0.109328i
$643$	31.2120	−	18.0203i	1.23088	−	0.710650i	0.263668	−	0.964613i	$-0.415068\pi$
$643$	31.2120	−	18.0203i	1.23088	−	0.710650i	0.967214	+	0.253963i	$0.0817342\pi$
$644$	0.0445910	−	0.416791i	0.00175713	−	0.0164239i
$645$	−37.9668	+	45.2260i	−1.49494	+	1.78077i
$646$	−5.47490	+	9.48281i	−0.215407	+	0.373096i
$647$	−5.58047	−	9.66565i	−0.219391	−	0.379996i	0.735231	−	0.677817i	$-0.237074\pi$
$647$	−5.58047	−	9.66565i	−0.219391	−	0.379996i	−0.954622	+	0.297821i	$0.903740\pi$
$648$	5.79141	−	6.88909i	0.227508	−	0.270629i
$649$	6.16595	−	3.55991i	0.242035	−	0.139739i
$650$	45.0910	−	14.6244i	1.76861	−	0.573615i
$651$	−11.1739	−	11.6194i	−0.437938	−	0.455400i
$652$	−3.49025	+	6.04529i	−0.136689	+	0.236752i
$653$			29.9947i			1.17378i	0.809666	+	0.586892i	$0.199649\pi$
$653$			29.9947i			1.17378i	−0.809666	+	0.586892i	$0.800351\pi$
$654$	−8.93698	−	7.50251i	−0.349464	−	0.293371i
$655$	−31.9265	+	55.2982i	−1.24747	+	2.16068i
$656$	−5.13995	+	8.90266i	−0.200681	+	0.347591i
$657$	−13.4209	−	16.0093i	−0.523598	−	0.624581i
$658$	10.9888	−	4.86805i	0.428389	−	0.189777i
$659$	10.5441	−	6.08763i	0.410739	−	0.237141i	−0.280368	−	0.959893i	$-0.590456\pi$
$659$	10.5441	−	6.08763i	0.410739	−	0.237141i	0.691107	+	0.722752i	$0.257123\pi$
$660$	8.40389	+	7.05499i	0.327121	+	0.274615i
$661$	−22.6422	+	13.0725i	−0.880678	+	0.508460i	−0.870882	−	0.491492i	$-0.836452\pi$
$661$	−22.6422	+	13.0725i	−0.880678	+	0.508460i	−0.00979596	+	0.999952i	$0.503118\pi$
$662$	−15.9509	−	9.20927i	−0.619951	−	0.357929i
$663$	−13.1229	+	10.2367i	−0.509653	+	0.397559i
$664$			8.37013i			0.324824i
$665$	−4.92619	+	46.0450i	−0.191030	+	1.78555i
$666$	10.7637	−	29.5308i	0.417084	−	1.14429i
$667$	−0.0378398	+	0.0655405i	−0.00146516	+	0.00253774i
$668$	4.12054	−	7.13698i	0.159428	−	0.276138i
$669$	5.85409	+	4.91445i	0.226332	+	0.190004i
$670$	12.0597	+	6.96268i	0.465907	+	0.268992i
$671$	−3.92635			−0.151575
$672$	1.27234	−	4.40240i	0.0490814	−	0.169826i
$673$	−10.0870	+	17.4712i	−0.388825	+	0.673464i	−0.992292	−	0.123924i	$-0.960452\pi$
$673$	−10.0870	+	17.4712i	−0.388825	+	0.673464i	0.603467	+	0.797388i	$0.293785\pi$
$674$		−	16.8561i		−	0.649271i
$675$	59.1863	−	34.1170i	2.27808	−	1.31316i
$676$	1.34508	+	12.9302i	0.0517338	+	0.497316i
$677$	−0.365307	−	0.632731i	−0.0140399	−	0.0243178i	0.858920	−	0.512110i	$-0.171136\pi$
$677$	−0.365307	−	0.632731i	−0.0140399	−	0.0243178i	−0.872960	+	0.487792i	$0.837803\pi$
$678$	10.1140	+	27.8079i	0.388427	+	1.06796i
$679$	−8.76518	+	3.88298i	−0.336377	+	0.149015i
$680$	9.83207	−	5.67655i	0.377043	−	0.217686i
$681$	33.5125	+	5.91709i	1.28420	+	0.226743i
$682$		−	5.23128i		−	0.200316i
$683$		−	8.23447i		−	0.315083i	−0.987512	−	0.157542i	$-0.949643\pi$
$683$		−	8.23447i		−	0.315083i	0.987512	−	0.157542i	$-0.0503569\pi$
$684$	7.91862	+	9.44584i	0.302776	+	0.361171i
$685$	−39.3530	+	22.7205i	−1.50360	+	0.868105i
$686$	−5.82135	+	17.5816i	−0.222260	+	0.671268i
$687$	20.7733	−	7.55547i	0.792551	−	0.288259i
$688$	4.00148	+	6.93077i	0.152555	+	0.264233i
$689$	−12.8256	+	4.15972i	−0.488616	+	0.158473i
$690$	−0.399563	−	1.09857i	−0.0152111	−	0.0418220i
$691$		−	29.9099i		−	1.13783i	−0.822397	−	0.568914i	$-0.807364\pi$
$691$		−	29.9099i		−	1.13783i	0.822397	−	0.568914i	$-0.192636\pi$
$692$	7.88311	−	13.6540i	0.299671	−	0.519045i
$693$	−11.7767	+	0.796055i	−0.447360	+	0.0302396i
$694$	−15.6755			−0.595035
$695$	−40.7820	−	23.5455i	−1.54695	−	0.893132i
$696$	−0.531968	+	0.633679i	−0.0201642	+	0.0240195i
$697$	13.6983	−	23.7262i	0.518861	−	0.898694i
$698$	−9.42880	+	16.3312i	−0.356885	+	0.618144i
$699$	35.7654	−	13.0082i	1.35277	−	0.492017i
$700$	20.4982	−	28.1031i	0.774757	−	1.06220i
$701$			11.4510i			0.432498i	0.976338	+	0.216249i	$0.0693824\pi$
$701$			11.4510i			0.432498i	−0.976338	+	0.216249i	$0.930618\pi$
$702$	5.76767	+	17.8251i	0.217686	+	0.672765i
$703$	37.2794	+	21.5233i	1.40602	+	0.811767i
$704$	1.28788	−	0.743556i	0.0485387	−	0.0280238i
$705$	21.5509	−	25.6714i	0.811655	−	0.966843i
$706$	15.9414	−	9.20379i	0.599964	−	0.346389i
$707$	5.16422	+	11.6574i	0.194220	+	0.438421i
$708$	−8.16620	−	1.44185i	−0.306905	−	0.0541882i
$709$	−8.51576	+	14.7497i	−0.319816	+	0.553938i	−0.980449	−	0.196771i	$-0.936954\pi$
$709$	−8.51576	+	14.7497i	−0.319816	+	0.553938i	0.660633	+	0.750709i	$0.270288\pi$
$710$	−18.9446	+	32.8130i	−0.710978	+	1.23145i
$711$	−8.52691	−	48.4885i	−0.319784	−	1.81846i
$712$		−	11.8904i		−	0.445612i
$713$	−0.278660	+	0.482654i	−0.0104359	+	0.0180755i
$714$	−3.39086	+	11.7327i	−0.126900	+	0.439085i
$715$	−21.7272	+	7.04677i	−0.812549	+	0.263534i
$716$	6.51608	−	3.76206i	0.243517	−	0.140595i
$717$	−5.40478	+	30.6110i	−0.201845	+	1.14319i
$718$	16.8719	+	29.2230i	0.629654	+	1.09059i
$719$	8.48150	−	14.6904i	0.316306	−	0.547859i	−0.663408	−	0.748258i	$-0.730891\pi$
$719$	8.48150	−	14.6904i	0.316306	−	0.547859i	0.979714	+	0.200399i	$0.0642239\pi$
$720$	−2.21343	−	12.5868i	−0.0824898	−	0.469081i
$721$	6.01473	−	2.66453i	0.224000	−	0.0992321i
$722$	1.83515	−	1.05953i	0.0682973	−	0.0394315i
$723$	4.94878	−	28.0283i	0.184047	−	1.04238i
$724$			3.30682i			0.122897i
$725$	−5.43883	+	3.14011i	−0.201993	+	0.116621i
$726$	11.6586	+	9.78727i	0.432691	+	0.363240i
$727$			35.4828i			1.31598i	0.753025	+	0.657992i	$0.228594\pi$
$727$			35.4828i			1.31598i	−0.753025	+	0.657992i	$0.771406\pi$
$728$	6.36610	+	7.10442i	0.235944	+	0.263307i
$729$	13.4678	+	23.4012i	0.498808	+	0.866713i
$730$	−29.6644			−1.09793
$731$	−10.6642	−	18.4710i	−0.394431	−	0.683174i
$732$	3.50248	+	2.94030i	0.129455	+	0.108677i
$733$	7.97236	−	4.60284i	0.294466	−	0.170010i	−0.345488	−	0.938423i	$-0.612287\pi$
$733$	7.97236	−	4.60284i	0.294466	−	0.170010i	0.639954	+	0.768413i	$0.278953\pi$
$734$	−17.0227	−	29.4842i	−0.628320	−	1.08828i
$735$	6.98600	+	51.1747i	0.257682	+	1.88761i
$736$	−0.158431			−0.00583985
$737$	−4.20993	−	2.43060i	−0.155075	−	0.0895324i
$738$	−19.8126	−	23.6337i	−0.729310	−	0.869968i
$739$	17.8808	+	30.9704i	0.657754	+	1.13926i	0.981196	+	0.193016i	$0.0618269\pi$
$739$	17.8808	+	30.9704i	0.657754	+	1.13926i	−0.323441	+	0.946248i	$0.604840\pi$
$740$	−22.3160	−	38.6524i	−0.820353	−	1.42089i
$741$	−25.4115	+	3.55159i	−0.933514	+	0.130471i
$742$	−5.83045	+	7.99359i	−0.214043	+	0.293454i
$743$	−3.57295	−	2.06284i	−0.131079	−	0.0756783i	0.433027	−	0.901381i	$-0.357446\pi$
$743$	−3.57295	−	2.06284i	−0.131079	−	0.0756783i	−0.564106	+	0.825703i	$0.690779\pi$
$744$	−3.91752	+	4.66655i	−0.143623	+	0.171084i
$745$			35.8034i			1.31173i
$746$	−26.7171	−	15.4251i	−0.978182	−	0.564754i
$747$	−23.5921	−	8.59908i	−0.863190	−	0.314624i
$748$	−3.43228	+	1.98163i	−0.125496	+	0.0724554i
$749$	2.58888	−	24.1982i	0.0945956	−	0.884181i
$750$	10.4524	−	59.1990i	0.381667	−	2.16164i
$751$	−28.8707			−1.05351			−0.526753	−	0.850018i	$-0.676591\pi$
$751$	−28.8707			−1.05351			−0.526753	+	0.850018i	$0.676591\pi$
$752$	−2.27135	−	3.93409i	−0.0828275	−	0.143461i
$753$	6.63705	+	18.2482i	0.241868	+	0.665000i
$754$	−0.531348	−	1.63829i	−0.0193505	−	0.0596631i
$755$	−96.0761			−3.49657
$756$	11.1015	+	8.10904i	0.403758	+	0.294923i
$757$	17.6464	−	30.5645i	0.641371	−	1.11089i	−0.343756	−	0.939059i	$-0.611699\pi$
$757$	17.6464	−	30.5645i	0.641371	−	1.11089i	0.985127	−	0.171828i	$-0.0549673\pi$
$758$	5.39979	+	3.11757i	0.196129	+	0.113235i
$759$	0.139483	+	0.383501i	0.00506293	+	0.0139202i
$760$	17.5027			0.634889
$761$	−15.5145	+	26.8720i	−0.562402	+	0.974108i	0.434885	+	0.900486i	$0.356789\pi$
$761$	−15.5145	+	26.8720i	−0.562402	+	0.974108i	−0.997286	+	0.0736221i	$0.976544\pi$
$762$	−7.57978	−	6.36315i	−0.274586	−	0.230513i
$763$	10.5036	−	14.4005i	0.380256	−	0.521334i
$764$	−22.5097	−	12.9960i	−0.814374	−	0.470179i
$765$	5.89895	+	33.5445i	0.213277	+	1.21281i
$766$	−4.72231	−	2.72642i	−0.170624	−	0.0985097i
$767$	11.5575	−	12.8222i	0.417319	−	0.462982i
$768$	−1.70567	−	0.301159i	−0.0615480	−	0.0108671i
$769$	−23.8845	−	13.7897i	−0.861297	−	0.497270i	0.00314940	−	0.999995i	$-0.498998\pi$
$769$	−23.8845	−	13.7897i	−0.861297	−	0.497270i	−0.864446	+	0.502725i	$0.832331\pi$
$770$	−9.87706	+	13.5415i	−0.355945	+	0.488003i
$771$	4.20849	+	0.743065i	0.151565	+	0.0267608i
$772$	6.03765	+	10.4575i	0.217300	+	0.376375i
$773$	0.713668			0.0256689			0.0128344	−	0.999918i	$-0.495915\pi$
$773$	0.713668			0.0256689			0.0128344	+	0.999918i	$0.495915\pi$
$774$	−23.6461	+	4.15826i	−0.849940	+	0.149465i
$775$	−40.0527	+	23.1244i	−1.43874	+	0.830654i
$776$	1.81173	+	3.13800i	0.0650372	+	0.112648i
$777$	46.1244	+	13.3304i	1.65470	+	0.478224i
$778$	−19.2846	+	33.4019i	−0.691387	+	1.19752i
$779$	36.5779	−	21.1182i	1.31054	−	0.756639i
$780$	24.6587	+	9.98465i	0.882923	+	0.357508i
$781$	6.61337	−	11.4547i	0.236645	−	0.409881i
$782$	0.422230			0.0150989
$783$	−1.23957	−	2.15042i	−0.0442988	−	0.0768498i
$784$	6.84157	+	1.48086i	0.244342	+	0.0528879i
$785$		−	69.2999i		−	2.47342i
$786$	−24.3982	+	8.87388i	−0.870254	+	0.316521i
$787$			2.24914i			0.0801732i	0.999196	+	0.0400866i	$0.0127634\pi$
$787$			2.24914i			0.0801732i	−0.999196	+	0.0400866i	$0.987237\pi$
$788$	−2.02572	−	1.16955i	−0.0721631	−	0.0416634i
$789$	27.2172	−	9.89918i	0.968958	−	0.352420i
$790$	−60.5436	−	34.9548i	−2.15404	−	1.24364i
$791$	−41.3260	+	18.3074i	−1.46938	+	0.650937i
$792$	0.772687	+	4.39391i	0.0274563	+	0.156131i
$793$	−9.05520	+	2.93687i	−0.321560	+	0.104291i
$794$	13.4667	−	23.3251i	0.477917	−	0.827776i
$795$	−4.79761	+	27.1722i	−0.170154	+	0.963698i
$796$			10.6892i			0.378868i
$797$	0.0987658	+	0.171067i	0.00349846	+	0.00605952i	0.867769	−	0.496967i	$-0.165553\pi$
$797$	0.0987658	+	0.171067i	0.00349846	+	0.00605952i	−0.864271	+	0.503027i	$0.832220\pi$
$798$	−13.5712	+	13.0508i	−0.480414	+	0.461993i
$799$	6.05329	+	10.4846i	0.214150	+	0.370919i
$800$	−11.3859	−	6.57365i	−0.402552	−	0.232414i
$801$	33.5144	+	12.2156i	1.18417	+	0.431619i
$802$	9.26244			0.327068
$803$	10.3555			0.365439
$804$	1.93526	+	5.32087i	0.0682513	+	0.187653i
$805$	1.63262	−	0.723250i	0.0575423	−	0.0254912i
$806$	−3.91296	−	12.0647i	−0.137828	−	0.424962i
$807$	−4.47668	−	0.790419i	−0.157587	−	0.0278241i
$808$	4.17343	−	2.40953i	0.146821	−	0.0847670i
$809$	−10.2467	+	5.91593i	−0.360255	+	0.207993i	−0.669192	−	0.743089i	$-0.733360\pi$
$809$	−10.2467	+	5.91593i	−0.360255	+	0.207993i	0.308938	+	0.951082i	$0.400027\pi$
$810$	37.7511	+	6.69225i	1.32644	+	0.235142i
$811$			25.6241i			0.899785i	0.893083	+	0.449893i	$0.148538\pi$
$811$			25.6241i			0.899785i	−0.893083	+	0.449893i	$0.851462\pi$
$812$	−1.02107	−	0.744761i	−0.0358326	−	0.0261360i
$813$	2.68462	−	15.2048i	0.0941536	−	0.533256i
$814$	7.79030	+	13.4932i	0.273050	+	0.472936i
$815$	−29.7367			−1.04163
$816$	4.54572	+	0.802608i	0.159132	+	0.0280969i
$817$		−	32.8813i		−	1.15037i
$818$	15.2524			0.533288
$819$	−26.5648	+	10.6448i	−0.928249	+	0.371959i
$820$	−43.7920			−1.52928
$821$		−	3.09796i		−	0.108120i	−0.998538	−	0.0540598i	$-0.982784\pi$
$821$		−	3.09796i		−	0.108120i	0.998538	−	0.0540598i	$-0.0172162\pi$
$822$	−18.1943	−	3.21245i	−0.634600	−	0.112047i
$823$	0.467584			0.0162990			0.00814948	−	0.999967i	$-0.497406\pi$
$823$	0.467584			0.0162990			0.00814948	+	0.999967i	$0.497406\pi$
$824$	−1.24322	−	2.15332i	−0.0433096	−	0.0750145i
$825$	−5.88810	+	33.3484i	−0.204997	+	1.16104i
$826$	1.34751	−	12.5952i	0.0468860	−	0.438241i
$827$			0.459061i			0.0159631i	0.999968	+	0.00798156i	$0.00254064\pi$
$827$			0.459061i			0.0159631i	−0.999968	+	0.00798156i	$0.997459\pi$
$828$	0.162765	−	0.446555i	0.00565647	−	0.0155189i
$829$	−2.85932	+	1.65083i	−0.0993084	+	0.0573357i	−0.548832	−	0.835933i	$-0.684927\pi$
$829$	−2.85932	+	1.65083i	−0.0993084	+	0.0573357i	0.449523	+	0.893269i	$0.351594\pi$
$830$	−30.8794	+	17.8282i	−1.07184	+	0.618827i
$831$	49.8581	+	8.80312i	1.72956	+	0.305377i
$832$	2.41401	−	2.67816i	0.0836909	−	0.0928485i
$833$	−18.2332	−	3.94660i	−0.631744	−	0.136742i
$834$	−6.54441	−	17.9935i	−0.226614	−	0.623062i
$835$	35.1067			1.21492
$836$	−6.11001			−0.211319
$837$	−9.12848	−	15.8361i	−0.315526	−	0.547377i
$838$	18.6811	+	10.7855i	0.645328	+	0.372580i
$839$	−0.978193	−	1.69428i	−0.0337710	−	0.0584930i	0.848646	−	0.528961i	$-0.177418\pi$
$839$	−0.978193	−	1.69428i	−0.0337710	−	0.0584930i	−0.882417	+	0.470468i	$0.844085\pi$
$840$	18.9516	−	4.68309i	0.653891	−	0.161582i
$841$	−14.3859	−	24.9171i	−0.496066	−	0.859211i
$842$		−	25.8262i		−	0.890028i
$843$	−5.67877	+	32.1628i	−0.195587	+	1.10774i
$844$	−2.22580	+	3.85520i	−0.0766152	+	0.132701i
$845$	−44.8377	+	32.5035i	−1.54246	+	1.11815i
$846$	13.4221	−	2.36033i	0.461462	−	0.0811500i
$847$	−13.7023	+	18.7859i	−0.470816	+	0.645492i
$848$	3.23858	+	1.86979i	0.111213	+	0.0642090i
$849$	0.569214	−	0.207029i	0.0195354	−	0.00710522i
$850$	30.3442	+	17.5192i	1.04080	+	0.600904i
$851$		−	1.65990i		−	0.0569005i
$852$	−14.4775	+	5.26560i	−0.495989	+	0.180397i
$853$		−	26.7743i		−	0.916734i	−0.888763	−	0.458367i	$-0.848434\pi$
$853$		−	26.7743i		−	0.916734i	0.888763	−	0.458367i	$-0.151566\pi$
$854$	−4.11645	+	5.64369i	−0.140862	+	0.193123i
$855$	−17.9814	+	49.3332i	−0.614952	+	1.68716i
$856$	−9.19824			−0.314389
$857$	−1.29961	+	2.25099i	−0.0443938	+	0.0768923i	−0.887369	−	0.461061i	$-0.847469\pi$
$857$	−1.29961	+	2.25099i	−0.0443938	+	0.0768923i	0.842975	+	0.537953i	$0.180802\pi$
$858$	−8.60811	−	3.48554i	−0.293876	−	0.118994i
$859$	−11.5553	+	6.67144i	−0.394261	+	0.227626i	−0.684005	−	0.729478i	$-0.739763\pi$
$859$	−11.5553	+	6.67144i	−0.394261	+	0.227626i	0.289744	+	0.957104i	$0.406430\pi$
$860$	−17.0462	+	29.5249i	−0.581270	+	1.00679i
$861$	33.9553	−	32.6534i	1.15719	−	1.11282i
$862$	5.41746	+	9.38332i	0.184520	+	0.319597i
$863$	−29.7858	+	17.1968i	−1.01392	+	0.585387i	−0.912337	−	0.409440i	$-0.865724\pi$
$863$	−29.7858	+	17.1968i	−1.01392	+	0.585387i	−0.101583	+	0.994827i	$0.532391\pi$
$864$	2.60117	−	4.49821i	0.0884937	−	0.153032i
$865$	67.1636			2.28363
$866$	−8.95476	−	15.5101i	−0.304295	−	0.527055i
$867$	16.8817	+	2.98069i	0.573333	+	0.101230i
$868$	−7.51939	−	5.48457i	−0.255225	−	0.186158i
$869$	21.1352	+	12.2024i	0.716961	+	0.413938i
$870$	−3.47087	−	0.612830i	−0.117674	−	0.0207769i
$871$	−11.5273	−	2.45663i	−0.390587	−	0.0832396i
$872$	−5.83432	−	3.36845i	−0.197575	−	0.114070i
$873$	−10.7061	+	1.88271i	−0.362346	+	0.0637200i
$874$	0.563728	+	0.325469i	0.0190684	+	0.0110091i
$875$	91.3056	+	9.76848i	3.08669	+	0.330235i
$876$	−9.23763	−	7.75490i	−0.312111	−	0.262014i
$877$	−5.65982	+	9.80310i	−0.191119	+	0.331027i	−0.945621	−	0.325270i	$-0.894545\pi$
$877$	−5.65982	+	9.80310i	−0.191119	+	0.331027i	0.754503	+	0.656297i	$0.227878\pi$
$878$	7.13870			0.240919
$879$	6.33726	+	17.4239i	0.213750	+	0.587694i
$880$	5.48631	+	3.16752i	0.184943	+	0.106777i
$881$	−6.87833	+	11.9136i	−0.231737	+	0.401380i	−0.958319	−	0.285699i	$-0.907774\pi$
$881$	−6.87833	+	11.9136i	−0.231737	+	0.401380i	0.726583	+	0.687079i	$0.241107\pi$
$882$	−11.2027	+	17.7623i	−0.377214	+	0.598088i
$883$	−22.8717			−0.769694			−0.384847	−	0.922980i	$-0.625746\pi$
$883$	−22.8717			−0.769694			−0.384847	+	0.922980i	$0.625746\pi$
$884$	−6.43351	+	7.13748i	−0.216382	+	0.240059i
$885$	−12.0745	−	33.1982i	−0.405881	−	1.11594i
$886$	8.74841	+	15.1527i	0.293909	+	0.509065i
$887$	−22.8297			−0.766545			−0.383273	−	0.923635i	$-0.625203\pi$
$887$	−22.8297			−0.766545			−0.383273	+	0.923635i	$0.625203\pi$
$888$	3.15526	−	17.8704i	0.105884	−	0.599692i
$889$	8.90848	−	12.2136i	0.298781	−	0.409631i
$890$	43.8665	−	25.3264i	1.47041	−	0.848941i
$891$	−13.1785	−	2.33620i	−0.441498	−	0.0782656i
$892$	3.82172	+	2.20647i	0.127961	+	0.0738781i
$893$			18.6643i			0.624577i
$894$	−9.35976	+	11.1493i	−0.313037	+	0.372889i
$895$	27.7583	+	16.0262i	0.927856	+	0.535698i
$896$	0.281454	−	2.63074i	0.00940271	−	0.0878868i
$897$	0.608542	+	0.780124i	0.0203186	+	0.0260476i
$898$	1.87364	+	3.24523i	0.0625241	+	0.108295i
$899$	0.840181	+	1.45524i	0.0280216	+	0.0485349i
$900$	30.2259	−	25.3389i	1.00753	−	0.844630i
$901$	−8.63103	−	4.98313i	−0.287541	−	0.166012i
$902$	15.2874			0.509014
$903$	−8.79788	−	35.6033i	−0.292775	−	1.18480i
$904$	8.54191	+	14.7950i	0.284100	+	0.492075i
$905$	−12.1997	+	7.04347i	−0.405530	+	0.234133i
$906$	−29.9185	−	25.1163i	−0.993976	−	0.834434i
$907$	1.87545	+	3.24838i	0.0622734	+	0.107861i	0.895481	−	0.445099i	$-0.146832\pi$
$907$	1.87545	+	3.24838i	0.0622734	+	0.107861i	−0.833208	+	0.552960i	$0.813498\pi$
$908$	19.6477			0.652033
$909$	2.50393	+	14.2387i	0.0830502	+	0.472268i
$910$	−12.6502	+	38.6184i	−0.419350	+	1.28019i
$911$		−	9.38466i		−	0.310927i	−0.987842	−	0.155464i	$-0.950313\pi$
$911$		−	9.38466i		−	0.310927i	0.987842	−	0.155464i	$-0.0496872\pi$
$912$	5.45041	+	4.57557i	0.180481	+	0.151512i
$913$	10.7797	−	6.22366i	0.356756	−	0.205973i
$914$			12.5530i			0.415217i
$915$	−3.38724	+	19.1843i	−0.111979	+	0.634213i
$916$	11.0523	−	6.38106i	0.365179	−	0.210836i
$917$	−16.0626	−	36.2588i	−0.530435	−	1.19737i
$918$	−6.93230	+	11.9880i	−0.228800	+	0.395664i
$919$	−6.57566	+	11.3894i	−0.216911	+	0.375701i	−0.953862	−	0.300245i	$-0.902932\pi$
$919$	−6.57566	+	11.3894i	−0.216911	+	0.375701i	0.736951	+	0.675946i	$0.236265\pi$
$920$	−0.337456	−	0.584490i	−0.0111256	−	0.0192701i
$921$	1.21872	−	6.90245i	0.0401582	−	0.227443i
$922$	−6.19010	+	3.57386i	−0.203860	+	0.117699i
$923$	6.68418	−	31.3644i	0.220013	−	1.03237i
$924$	−6.61581	+	1.63482i	−0.217644	+	0.0537817i
$925$	68.8727	−	119.291i	2.26452	−	3.92226i
$926$		−	6.57780i		−	0.216160i
$927$	7.34659	−	1.29193i	0.241294	−	0.0424325i
$928$	−0.238841	+	0.413684i	−0.00784033	+	0.0135799i
$929$	12.8094	−	22.1866i	0.420263	−	0.727917i	−0.575702	−	0.817660i	$-0.695271\pi$
$929$	12.8094	−	22.1866i	0.420263	−	0.727917i	0.995965	+	0.0897426i	$0.0286044\pi$
$930$	−25.5602	−	4.51301i	−0.838153	−	0.147987i
$931$	−21.3014	−	19.3240i	−0.698126	−	0.633317i
$932$	19.0288	−	10.9863i	0.623308	−	0.359867i
$933$	18.2577	−	21.7486i	0.597731	−	0.712016i
$934$	−18.4857	+	10.6728i	−0.604872	+	0.349223i
$935$	−14.6214	−	8.44166i	−0.478170	−	0.276072i
$936$	5.06863	+	9.55557i	0.165674	+	0.312334i
$937$			44.0425i			1.43881i	0.694593	+	0.719403i	$0.255585\pi$
$937$			44.0425i			1.43881i	−0.694593	+	0.719403i	$0.744415\pi$
$938$	−7.90749	+	3.50302i	−0.258189	+	0.114378i
$939$	−32.1781	+	11.7035i	−1.05009	+	0.381929i
$940$	9.67586	−	16.7591i	0.315592	−	0.546621i
$941$	−14.6395	+	25.3563i	−0.477234	+	0.826593i	−0.999660	−	0.0260916i	$-0.991694\pi$
$941$	−14.6395	+	25.3563i	−0.477234	+	0.826593i	0.522426	+	0.852685i	$0.325027\pi$
$942$	18.1165	−	21.5803i	0.590267	−	0.703125i
$943$	−1.41046	−	0.814329i	−0.0459309	−	0.0265182i
$944$	−4.78769			−0.155826
$945$	−6.27016	+	58.2282i	−0.203968	+	1.89416i
$946$	5.95065	−	10.3068i	0.193472	−	0.335104i
$947$		−	58.8404i		−	1.91206i	−0.293274	−	0.956028i	$-0.594745\pi$
$947$		−	58.8404i		−	1.91206i	0.293274	−	0.956028i	$-0.405255\pi$
$948$	−9.71561	−	26.7125i	−0.315548	−	0.867581i
$949$	23.8827	−	7.74587i	0.775264	−	0.251441i
$950$	27.0088	+	46.7806i	0.876281	+	1.51776i
$951$	13.1296	−	4.77536i	0.425755	−	0.154852i
$952$	−0.750093	+	7.01109i	−0.0243107	+	0.227231i
$953$	0.646257	−	0.373117i	0.0209343	−	0.0120864i	−0.489496	−	0.872005i	$-0.662819\pi$
$953$	0.646257	−	0.373117i	0.0209343	−	0.0120864i	0.510431	+	0.859919i	$0.329486\pi$
$954$	−8.59738	+	7.20734i	−0.278350	+	0.233346i
$955$		−	110.725i		−	3.58298i
$956$			17.9466i			0.580436i
$957$	1.21165	+	0.213933i	0.0391670	+	0.00691547i
$958$	−21.6900	+	12.5227i	−0.700771	+	0.404590i
$959$	3.00226	−	28.0620i	0.0969481	−	0.906170i
$960$	−2.52200	−	6.93408i	−0.0813971	−	0.223796i
$961$	−9.31273	−	16.1301i	−0.300411	−	0.520327i
$962$	28.0593	+	25.2918i	0.904668	+	0.815441i
$963$	9.44984	−	25.9262i	0.304517	−	0.835461i
$964$		−	16.4325i		−	0.529254i
$965$	−25.7202	+	44.5487i	−0.827962	+	1.43407i
$966$	0.697478	+	0.201578i	0.0224410	+	0.00648566i
$967$	6.94251			0.223256			0.111628	−	0.993750i	$-0.464393\pi$
$967$	6.94251			0.223256			0.111628	+	0.993750i	$0.464393\pi$
$968$	7.61106	+	4.39425i	0.244629	+	0.141237i
$969$	−14.5257	−	12.1942i	−0.466633	−	0.391734i
$970$	−7.71789	+	13.3678i	−0.247807	+	0.429213i
$971$	−29.0679	+	50.3471i	−0.932834	+	1.61572i	−0.154382	+	0.988011i	$0.549339\pi$
$971$	−29.0679	+	50.3471i	−0.932834	+	1.61572i	−0.778452	+	0.627704i	$0.783995\pi$
$972$	10.0064	+	11.9529i	0.320954	+	0.383391i
$973$	26.7405	−	11.8461i	0.857262	−	0.379767i
$974$			35.1851i			1.12740i
$975$	11.3648	+	81.3145i	0.363964	+	2.60415i
$976$	2.28652	+	1.32012i	0.0731898	+	0.0422562i
$977$	1.80040	−	1.03946i	0.0575998	−	0.0332552i	−0.470924	−	0.882174i	$-0.656079\pi$
$977$	1.80040	−	1.03946i	0.0575998	−	0.0332552i	0.528523	+	0.848919i	$0.322746\pi$
$978$	−9.26014	−	7.77380i	−0.296106	−	0.248579i
$979$	−15.3134	+	8.84118i	−0.489418	+	0.282565i
$980$	9.10916	+	28.3944i	0.290982	+	0.907025i
$981$	15.4882	−	12.9841i	0.494502	−	0.414550i
$982$	−15.8049	+	27.3749i	−0.504354	+	0.873568i
$983$	−6.74253	+	11.6784i	−0.215053	+	0.372483i	−0.953289	−	0.302060i	$-0.902326\pi$
$983$	−6.74253	+	11.6784i	−0.215053	+	0.372483i	0.738236	+	0.674543i	$0.235659\pi$
$984$	−13.6370	−	11.4482i	−0.434733	−	0.364954i
$985$		−	9.96446i		−	0.317494i
$986$	0.636527	−	1.10250i	0.0202711	−	0.0351106i
$987$	4.99390	+	20.2094i	0.158958	+	0.643271i
$988$	−14.0913	+	4.57024i	−0.448305	+	0.145399i
$989$	−1.09805	+	0.633960i	−0.0349160	+	0.0201587i
$990$	−14.5644	+	12.2096i	−0.462886	+	0.388046i
$991$	−11.3699	−	19.6932i	−0.361176	−	0.625576i	0.626978	−	0.779037i	$-0.284291\pi$
$991$	−11.3699	−	19.6932i	−0.361176	−	0.625576i	−0.988155	+	0.153461i	$0.950958\pi$
$992$	−1.75887	+	3.04646i	−0.0558443	+	0.0967251i
$993$	20.5117	−	24.4335i	0.650920	−	0.775375i
$994$	−9.53129	−	21.5153i	−0.302314	−	0.682424i
$995$	−39.4350	+	22.7678i	−1.25017	+	0.721787i
$996$	−14.2767	−	2.52074i	−0.452373	−	0.0798726i
$997$			7.47992i			0.236891i	0.992961	+	0.118446i	$0.0377912\pi$
$997$			7.47992i			0.236891i	−0.992961	+	0.118446i	$0.962209\pi$
$998$	14.0342	−	8.10265i	0.444245	−	0.256485i
$999$	47.1281	+	27.2527i	1.49107	+	0.862237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bb.a.269.22	yes	76
3.2	odd	2	inner	546.2.bb.a.269.8	yes	76
7.5	odd	6		546.2.u.a.425.24	yes	76
13.3	even	3		546.2.u.a.185.15	✓	76
21.5	even	6		546.2.u.a.425.15	yes	76
39.29	odd	6		546.2.u.a.185.24	yes	76
91.68	odd	6	inner	546.2.bb.a.341.27	yes	76
273.68	even	6	inner	546.2.bb.a.341.3	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.u.a.185.15	✓	76	13.3	even	3
546.2.u.a.185.24	yes	76	39.29	odd	6
546.2.u.a.425.15	yes	76	21.5	even	6
546.2.u.a.425.24	yes	76	7.5	odd	6
546.2.bb.a.269.8	yes	76	3.2	odd	2	inner
546.2.bb.a.269.22	yes	76	1.1	even	1	trivial
546.2.bb.a.341.3	yes	76	273.68	even	6	inner
546.2.bb.a.341.27	yes	76	91.68	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bb (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.70567 - 0.301159i) q^{3} -1.00000 q^{4} +(-2.12998 - 3.68924i) q^{5} +(0.301159 - 1.70567i) q^{6} +(2.63074 + 0.281454i) q^{7} -1.00000i q^{8} +(2.81861 + 1.02735i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.70567 - 0.301159i) q^{3} -1.00000 q^{4} +(-2.12998 - 3.68924i) q^{5} +(0.301159 - 1.70567i) q^{6} +(2.63074 + 0.281454i) q^{7} -1.00000i q^{8} +(2.81861 + 1.02735i) q^{9} +(3.68924 - 2.12998i) q^{10} +(-1.28788 + 0.743556i) q^{11} +(1.70567 + 0.301159i) q^{12} +(-2.41401 + 2.67816i) q^{13} +(-0.281454 + 2.63074i) q^{14} +(2.52200 + 6.93408i) q^{15} +1.00000 q^{16} -2.66507 q^{17} +(-1.02735 + 2.81861i) q^{18} +(-3.55819 - 2.05432i) q^{19} +(2.12998 + 3.68924i) q^{20} +(-4.40240 - 1.27234i) q^{21} +(-0.743556 - 1.28788i) q^{22} +0.158431i q^{23} +(-0.301159 + 1.70567i) q^{24} +(-6.57365 + 11.3859i) q^{25} +(-2.67816 - 2.41401i) q^{26} +(-4.49821 - 2.60117i) q^{27} +(-2.63074 - 0.281454i) q^{28} +(0.413684 + 0.238841i) q^{29} +(-6.93408 + 2.52200i) q^{30} +(3.04646 + 1.75887i) q^{31} +1.00000i q^{32} +(2.42062 - 0.880404i) q^{33} -2.66507i q^{34} +(-4.56508 - 10.3049i) q^{35} +(-2.81861 - 1.02735i) q^{36} -10.4771 q^{37} +(2.05432 - 3.55819i) q^{38} +(4.92406 - 3.84105i) q^{39} +(-3.68924 + 2.12998i) q^{40} +(-5.13995 + 8.90266i) q^{41} +(1.27234 - 4.40240i) q^{42} +(4.00148 + 6.93077i) q^{43} +(1.28788 - 0.743556i) q^{44} +(-2.21343 - 12.5868i) q^{45} -0.158431 q^{46} +(-2.27135 - 3.93409i) q^{47} +(-1.70567 - 0.301159i) q^{48} +(6.84157 + 1.48086i) q^{49} +(-11.3859 - 6.57365i) q^{50} +(4.54572 + 0.802608i) q^{51} +(2.41401 - 2.67816i) q^{52} +(3.23858 + 1.86979i) q^{53} +(2.60117 - 4.49821i) q^{54} +(5.48631 + 3.16752i) q^{55} +(0.281454 - 2.63074i) q^{56} +(5.45041 + 4.57557i) q^{57} +(-0.238841 + 0.413684i) q^{58} -4.78769 q^{59} +(-2.52200 - 6.93408i) q^{60} +(2.28652 + 1.32012i) q^{61} +(-1.75887 + 3.04646i) q^{62} +(7.12586 + 3.49601i) q^{63} -1.00000 q^{64} +(15.0222 + 3.20144i) q^{65} +(0.880404 + 2.42062i) q^{66} +(1.63445 + 2.83094i) q^{67} +2.66507 q^{68} +(0.0477129 - 0.270231i) q^{69} +(10.3049 - 4.56508i) q^{70} +(-7.70265 + 4.44713i) q^{71} +(1.02735 - 2.81861i) q^{72} +(-6.03059 - 3.48176i) q^{73} -10.4771i q^{74} +(14.6414 - 17.4408i) q^{75} +(3.55819 + 2.05432i) q^{76} +(-3.59734 + 1.59362i) q^{77} +(3.84105 + 4.92406i) q^{78} +(-8.20543 - 14.2122i) q^{79} +(-2.12998 - 3.68924i) q^{80} +(6.88909 + 5.79141i) q^{81} +(-8.90266 - 5.13995i) q^{82} -8.37013 q^{83} +(4.40240 + 1.27234i) q^{84} +(5.67655 + 9.83207i) q^{85} +(-6.93077 + 4.00148i) q^{86} +(-0.633679 - 0.531968i) q^{87} +(0.743556 + 1.28788i) q^{88} +11.8904 q^{89} +(12.5868 - 2.21343i) q^{90} +(-7.10442 + 6.36610i) q^{91} -0.158431i q^{92} +(-4.66655 - 3.91752i) q^{93} +(3.93409 - 2.27135i) q^{94} +17.5027i q^{95} +(0.301159 - 1.70567i) q^{96} +(-3.13800 + 1.81173i) q^{97} +(-1.48086 + 6.84157i) q^{98} +(-4.39391 + 0.772687i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9}+O(q^{10}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9	\( 76 q - 76 q^{4} + 10 q^{7} + 4 q^{9} - 2 q^{13} + 12 q^{15} + 76 q^{16} + 18 q^{19} - 8 q^{21} - 42 q^{25} - 10 q^{28} - 10 q^{30} + 12 q^{31} + 72 q^{33} - 4 q^{36} + 12 q^{37} - 42 q^{39} + 2 q^{42} - 2 q^{43} + 8 q^{46} - 10 q^{49} + 10 q^{51} + 2 q^{52} - 24 q^{55} + 8 q^{57} - 8 q^{58} - 12 q^{60} + 78 q^{61} + 2 q^{63} - 76 q^{64} - 24 q^{66} - 48 q^{67} + 30 q^{69} - 54 q^{73} - 18 q^{76} - 12 q^{78} - 60 q^{79} - 4 q^{81} - 24 q^{82} + 8 q^{84} + 8 q^{85} - 8 q^{91} - 32 q^{93} - 24 q^{94} + 66 q^{97}+O(q^{100}) \) 76 * q - 76 * q^4 + 10 * q^7 + 4 * q^9 - 2 * q^13 + 12 * q^15 + 76 * q^16 + 18 * q^19 - 8 * q^21 - 42 * q^25 - 10 * q^28 - 10 * q^30 + 12 * q^31 + 72 * q^33 - 4 * q^36 + 12 * q^37 - 42 * q^39 + 2 * q^42 - 2 * q^43 + 8 * q^46 - 10 * q^49 + 10 * q^51 + 2 * q^52 - 24 * q^55 + 8 * q^57 - 8 * q^58 - 12 * q^60 + 78 * q^61 + 2 * q^63 - 76 * q^64 - 24 * q^66 - 48 * q^67 + 30 * q^69 - 54 * q^73 - 18 * q^76 - 12 * q^78 - 60 * q^79 - 4 * q^81 - 24 * q^82 + 8 * q^84 + 8 * q^85 - 8 * q^91 - 32 * q^93 - 24 * q^94 + 66 * q^97

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