LMFDB - Embedded newform 361.2.e.i.54.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [361,2,Mod(28,361)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(361, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("361.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 361 = 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	361.e (of order $9$, degree $6$, not 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:	$2.88259951297$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	12.0.6053445140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4x^{9} + 17x^{6} + 4x^{3} + 1 $ x^12 - 4x^9 + 17x^6 + 4*x^3 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			54.1
Root			$1.52045 - 0.553400i$ of defining polynomial
Character	$\chi$	$=$	361.54
Dual form			361.2.e.i.234.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.23949 - 1.04005i) q^{2} +(0.358931 - 0.130640i) q^{3} +(0.107320 + 0.608645i) q^{4} +(0.561937 - 3.18690i) q^{5} +(-0.580762 - 0.211380i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-2.18637 + 1.83458i) q^{9} +O(q^{10})$	\(q+(-1.23949 - 1.04005i) q^{2} +(0.358931 - 0.130640i) q^{3} +(0.107320 + 0.608645i) q^{4} +(0.561937 - 3.18690i) q^{5} +(-0.580762 - 0.211380i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-2.18637 + 1.83458i) q^{9} +(-4.01106 + 3.36568i) q^{10} +(0.809017 - 1.40126i) q^{11} +(0.118034 + 0.204441i) q^{12} +(-0.939693 - 0.342020i) q^{13} +(-0.842906 + 4.78036i) q^{14} +(-0.214641 - 1.21729i) q^{15} +(4.56136 - 1.66020i) q^{16} +(0.585206 + 0.491046i) q^{17} +4.61803 q^{18} +2.00000 q^{20} +(-0.877809 - 0.736569i) q^{21} +(-2.46015 + 0.895420i) q^{22} +(0.934569 + 5.30020i) q^{23} +(-0.148313 + 0.841126i) q^{24} +(-5.14213 - 1.87158i) q^{25} +(0.809017 + 1.40126i) q^{26} +(-1.11803 + 1.93649i) q^{27} +(1.42032 - 1.19179i) q^{28} +(2.77157 - 2.32563i) q^{29} +(-1.00000 + 1.73205i) q^{30} +(-4.42705 - 7.66788i) q^{31} +(-3.17801 - 1.15670i) q^{32} +(0.107320 - 0.608645i) q^{33} +(-0.214641 - 1.21729i) q^{34} +(-9.12273 + 3.32040i) q^{35} +(-1.35125 - 1.13383i) q^{36} -8.85410 q^{37} -0.381966 q^{39} +(5.54315 + 4.65125i) q^{40} +(-2.81908 + 1.02606i) q^{41} +(0.321961 + 1.82593i) q^{42} +(-0.0253349 + 0.143682i) q^{43} +(0.939693 + 0.342020i) q^{44} +(4.61803 + 7.99867i) q^{45} +(4.35410 - 7.54153i) q^{46} +(2.29813 - 1.92836i) q^{47} +(1.42032 - 1.19179i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(4.42705 + 7.66788i) q^{50} +(0.274199 + 0.0998001i) q^{51} +(0.107320 - 0.608645i) q^{52} +(1.09854 + 6.23013i) q^{53} +(3.39984 - 1.23744i) q^{54} +(-4.01106 - 3.36568i) q^{55} +6.70820 q^{56} -5.85410 q^{58} +(-0.249913 - 0.209702i) q^{59} +(0.717861 - 0.261280i) q^{60} +(-1.77747 - 10.0806i) q^{61} +(-2.48773 + 14.1086i) q^{62} +(8.04594 + 2.92848i) q^{63} +(-2.11803 - 3.66854i) q^{64} +(-1.61803 + 2.80252i) q^{65} +(-0.766044 + 0.642788i) q^{66} +(5.36231 - 4.49951i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(1.02786 + 1.78031i) q^{69} +(14.7609 + 5.37252i) q^{70} +(1.29752 - 7.35862i) q^{71} +(-1.10822 - 6.28501i) q^{72} +(2.54488 - 0.926260i) q^{73} +(10.9745 + 9.20873i) q^{74} -2.09017 q^{75} -4.85410 q^{77} +(0.473442 + 0.397265i) q^{78} +(12.6073 - 4.58868i) q^{79} +(-2.72770 - 15.4696i) q^{80} +(1.33852 - 7.59110i) q^{81} +(4.56136 + 1.66020i) q^{82} +(-4.23607 - 7.33708i) q^{83} +(0.354102 - 0.613323i) q^{84} +(1.89377 - 1.58906i) q^{85} +(0.180839 - 0.151742i) q^{86} +(0.690983 - 1.19682i) q^{87} +(1.80902 + 3.13331i) q^{88} +(-7.29571 - 2.65542i) q^{89} +(2.59505 - 14.7172i) q^{90} +(0.520945 + 2.95442i) q^{91} +(-3.12564 + 1.13764i) q^{92} +(-2.59074 - 2.17389i) q^{93} -4.85410 q^{94} -1.29180 q^{96} +(-10.6129 - 8.90525i) q^{97} +(3.04091 - 1.10680i) q^{98} +(0.801913 + 4.54788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 18 q^{7}+O(q^{10}) $ 12 * q - 18 * q^7	$ 12 q - 18 q^{7} + 3 q^{11} - 12 q^{12} + 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} - 33 q^{31} - 66 q^{37} - 18 q^{39} + 42 q^{45} + 12 q^{46} - 12 q^{49} + 33 q^{50} - 30 q^{58} - 12 q^{64} - 6 q^{65} + 24 q^{68} + 66 q^{69} + 42 q^{75} - 18 q^{77} - 24 q^{83} - 36 q^{84} + 15 q^{87} + 15 q^{88} - 18 q^{94} - 96 q^{96}+O(q^{100}) $ 12 * q - 18 * q^7 + 3 * q^11 - 12 * q^12 + 42 * q^18 + 24 * q^20 + 3 * q^26 - 12 * q^30 - 33 * q^31 - 66 * q^37 - 18 * q^39 + 42 * q^45 + 12 * q^46 - 12 * q^49 + 33 * q^50 - 30 * q^58 - 12 * q^64 - 6 * q^65 + 24 * q^68 + 66 * q^69 + 42 * q^75 - 18 * q^77 - 24 * q^83 - 36 * q^84 + 15 * q^87 + 15 * q^88 - 18 * q^94 - 96 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/361\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	−1.23949	−	1.04005i	−0.876449	−	0.735428i	0.0889969	−	0.996032i	$-0.471634\pi$
$2$	−1.23949	−	1.04005i	−0.876449	−	0.735428i	−0.965446	+	0.260604i	$0.916078\pi$
$3$	0.358931	−	0.130640i	0.207229	−	0.0754251i	−0.236320	−	0.971675i	$-0.575941\pi$
$3$	0.358931	−	0.130640i	0.207229	−	0.0754251i	0.443549	+	0.896250i	$0.353719\pi$
$4$	0.107320	+	0.608645i	0.0536602	+	0.304322i
$5$	0.561937	−	3.18690i	0.251306	−	1.42523i	−0.554074	−	0.832468i	$-0.686927\pi$
$5$	0.561937	−	3.18690i	0.251306	−	1.42523i	0.805380	−	0.592759i	$-0.201962\pi$
$6$	−0.580762	−	0.211380i	−0.237095	−	0.0862956i
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−1.50000	−	2.59808i	−0.566947	−	0.981981i	0.429919	−	0.902867i	$-0.358542\pi$
$8$	−1.11803	+	1.93649i	−0.395285	+	0.684653i
$9$	−2.18637	+	1.83458i	−0.728790	+	0.611527i
$10$	−4.01106	+	3.36568i	−1.26841	+	1.06432i
$11$	0.809017	−	1.40126i	0.243928	−	0.422495i	−0.717902	−	0.696144i	$-0.754897\pi$
$11$	0.809017	−	1.40126i	0.243928	−	0.422495i	0.961830	+	0.273649i	$0.0882307\pi$
$12$	0.118034	+	0.204441i	0.0340735	+	0.0590170i
$13$	−0.939693	−	0.342020i	−0.260624	−	0.0948593i	0.208404	−	0.978043i	$-0.433173\pi$
$13$	−0.939693	−	0.342020i	−0.260624	−	0.0948593i	−0.469027	+	0.883184i	$0.655395\pi$
$14$	−0.842906	+	4.78036i	−0.225276	+	1.27760i
$15$	−0.214641	−	1.21729i	−0.0554201	−	0.314303i
$16$	4.56136	−	1.66020i	1.14034	−	0.415050i
$17$	0.585206	+	0.491046i	0.141933	+	0.119096i	0.710990	−	0.703202i	$-0.248247\pi$
$17$	0.585206	+	0.491046i	0.141933	+	0.119096i	−0.569057	+	0.822298i	$0.692692\pi$
$18$	4.61803			1.08848
$19$		0			0
$19$		0			0
$20$	2.00000			0.447214
$21$	−0.877809	−	0.736569i	−0.191554	−	0.160733i
$22$	−2.46015	+	0.895420i	−0.524505	+	0.190904i
$23$	0.934569	+	5.30020i	0.194871	+	1.10517i	0.912602	+	0.408848i	$0.134069\pi$
$23$	0.934569	+	5.30020i	0.194871	+	1.10517i	−0.717731	+	0.696320i	$0.754819\pi$
$24$	−0.148313	+	0.841126i	−0.0302743	+	0.171694i
$25$	−5.14213	−	1.87158i	−1.02843	−	0.374316i
$26$	0.809017	+	1.40126i	0.158661	+	0.274809i
$27$	−1.11803	+	1.93649i	−0.215166	+	0.372678i
$28$	1.42032	−	1.19179i	0.268416	−	0.225228i
$29$	2.77157	−	2.32563i	0.514669	−	0.431858i	−0.348100	−	0.937457i	$-0.613173\pi$
$29$	2.77157	−	2.32563i	0.514669	−	0.431858i	0.862768	+	0.505599i	$0.168729\pi$
$30$	−1.00000	+	1.73205i	−0.182574	+	0.316228i
$31$	−4.42705	−	7.66788i	−0.795122	−	1.37719i	−0.922762	−	0.385371i	$-0.874074\pi$
$31$	−4.42705	−	7.66788i	−0.795122	−	1.37719i	0.127640	−	0.991821i	$-0.459260\pi$
$32$	−3.17801	−	1.15670i	−0.561798	−	0.204478i
$33$	0.107320	−	0.608645i	0.0186821	−	0.105951i
$34$	−0.214641	−	1.21729i	−0.0368106	−	0.208763i
$35$	−9.12273	+	3.32040i	−1.54202	+	0.561250i
$36$	−1.35125	−	1.13383i	−0.225208	−	0.188972i
$37$	−8.85410			−1.45561			−0.727803	−	0.685787i	$-0.759458\pi$
$37$	−8.85410			−1.45561			−0.727803	+	0.685787i	$0.759458\pi$
$38$		0			0
$39$	−0.381966			−0.0611635
$40$	5.54315	+	4.65125i	0.876449	+	0.735428i
$41$	−2.81908	+	1.02606i	−0.440266	+	0.160244i	−0.552636	−	0.833423i	$-0.686378\pi$
$41$	−2.81908	+	1.02606i	−0.440266	+	0.160244i	0.112370	+	0.993666i	$0.464156\pi$
$42$	0.321961	+	1.82593i	0.0496797	+	0.281748i
$43$	−0.0253349	+	0.143682i	−0.00386354	+	0.0219112i	−0.986679	−	0.162682i	$-0.947986\pi$
$43$	−0.0253349	+	0.143682i	−0.00386354	+	0.0219112i	0.982815	+	0.184593i	$0.0590967\pi$
$44$	0.939693	+	0.342020i	0.141664	+	0.0515615i
$45$	4.61803	+	7.99867i	0.688416	+	1.19237i
$46$	4.35410	−	7.54153i	0.641977	−	1.11194i
$47$	2.29813	−	1.92836i	0.335217	−	0.281281i	−0.459604	−	0.888124i	$-0.652009\pi$
$47$	2.29813	−	1.92836i	0.335217	−	0.281281i	0.794822	+	0.606843i	$0.207564\pi$
$48$	1.42032	−	1.19179i	0.205006	−	0.172021i
$49$	−1.00000	+	1.73205i	−0.142857	+	0.247436i
$50$	4.42705	+	7.66788i	0.626080	+	1.08440i
$51$	0.274199	+	0.0998001i	0.0383955	+	0.0139748i
$52$	0.107320	−	0.608645i	0.0148827	−	0.0844038i
$53$	1.09854	+	6.23013i	0.150896	+	0.855774i	0.962442	+	0.271486i	$0.0875150\pi$
$53$	1.09854	+	6.23013i	0.150896	+	0.855774i	−0.811546	+	0.584288i	$0.801374\pi$
$54$	3.39984	−	1.23744i	0.462660	−	0.168394i
$55$	−4.01106	−	3.36568i	−0.540851	−	0.453828i
$56$	6.70820			0.896421
$57$		0			0
$58$	−5.85410			−0.768681
$59$	−0.249913	−	0.209702i	−0.0325359	−	0.0273008i	0.626375	−	0.779522i	$-0.284538\pi$
$59$	−0.249913	−	0.209702i	−0.0325359	−	0.0273008i	−0.658911	+	0.752221i	$0.728982\pi$
$60$	0.717861	−	0.261280i	0.0926755	−	0.0337311i
$61$	−1.77747	−	10.0806i	−0.227582	−	1.29068i	−0.857687	−	0.514173i	$-0.828099\pi$
$61$	−1.77747	−	10.0806i	−0.227582	−	1.29068i	0.630104	−	0.776511i	$-0.283012\pi$
$62$	−2.48773	+	14.1086i	−0.315941	+	1.79179i
$63$	8.04594	+	2.92848i	1.01369	+	0.368954i
$64$	−2.11803	−	3.66854i	−0.264754	−	0.458568i
$65$	−1.61803	+	2.80252i	−0.200692	+	0.347609i
$66$	−0.766044	+	0.642788i	−0.0942936	+	0.0791217i
$67$	5.36231	−	4.49951i	0.655111	−	0.549703i	−0.253506	−	0.967334i	$-0.581584\pi$
$67$	5.36231	−	4.49951i	0.655111	−	0.549703i	0.908617	+	0.417631i	$0.137139\pi$
$68$	−0.236068	+	0.408882i	−0.0286274	+	0.0495842i
$69$	1.02786	+	1.78031i	0.123740	+	0.214324i
$70$	14.7609	+	5.37252i	1.76426	+	0.642139i
$71$	1.29752	−	7.35862i	0.153988	−	0.873307i	−0.805718	−	0.592299i	$-0.798220\pi$
$71$	1.29752	−	7.35862i	0.153988	−	0.873307i	0.959706	−	0.281008i	$-0.0906687\pi$
$72$	−1.10822	−	6.28501i	−0.130605	−	0.740695i
$73$	2.54488	−	0.926260i	0.297856	−	0.108411i	−0.188770	−	0.982021i	$-0.560450\pi$
$73$	2.54488	−	0.926260i	0.297856	−	0.108411i	0.486625	+	0.873611i	$0.338228\pi$
$74$	10.9745	+	9.20873i	1.27576	+	1.07049i
$75$	−2.09017			−0.241352
$76$		0			0
$77$	−4.85410			−0.553176
$78$	0.473442	+	0.397265i	0.0536067	+	0.0449814i
$79$	12.6073	−	4.58868i	1.41843	−	0.516267i	0.484839	−	0.874603i	$-0.338878\pi$
$79$	12.6073	−	4.58868i	1.41843	−	0.516267i	0.933593	+	0.358336i	$0.116656\pi$
$80$	−2.72770	−	15.4696i	−0.304966	−	1.72955i
$81$	1.33852	−	7.59110i	0.148724	−	0.843455i
$82$	4.56136	+	1.66020i	0.503718	+	0.183338i
$83$	−4.23607	−	7.33708i	−0.464969	−	0.805350i	0.534231	−	0.845338i	$-0.320601\pi$
$83$	−4.23607	−	7.33708i	−0.464969	−	0.805350i	−0.999200	+	0.0399887i	$0.987268\pi$
$84$	0.354102	−	0.613323i	0.0386357	−	0.0669190i
$85$	1.89377	−	1.58906i	0.205408	−	0.172358i
$86$	0.180839	−	0.151742i	0.0195003	−	0.0163627i
$87$	0.690983	−	1.19682i	0.0740812	−	0.128312i
$88$	1.80902	+	3.13331i	0.192842	+	0.334012i
$89$	−7.29571	−	2.65542i	−0.773344	−	0.281474i	−0.0749494	−	0.997187i	$-0.523880\pi$
$89$	−7.29571	−	2.65542i	−0.773344	−	0.281474i	−0.698394	+	0.715713i	$0.746102\pi$
$90$	2.59505	−	14.7172i	0.273542	−	1.55133i
$91$	0.520945	+	2.95442i	0.0546098	+	0.309708i
$92$	−3.12564	+	1.13764i	−0.325871	+	0.118607i
$93$	−2.59074	−	2.17389i	−0.268647	−	0.225421i
$94$	−4.85410			−0.500662
$95$		0			0
$96$	−1.29180			−0.131843
$97$	−10.6129	−	8.90525i	−1.07757	−	0.904191i	−0.0818555	−	0.996644i	$-0.526085\pi$
$97$	−10.6129	−	8.90525i	−1.07757	−	0.904191i	−0.995717	+	0.0924536i	$0.970529\pi$
$98$	3.04091	−	1.10680i	0.307178	−	0.111804i
$99$	0.801913	+	4.54788i	0.0805953	+	0.457079i
$100$	0.587272	−	3.33059i	0.0587272	−	0.333059i
$101$	8.62670	+	3.13986i	0.858388	+	0.312428i	0.733456	−	0.679737i	$-0.237906\pi$
$101$	8.62670	+	3.13986i	0.858388	+	0.312428i	0.124933	+	0.992165i	$0.460128\pi$
$102$	−0.236068	−	0.408882i	−0.0233742	−	0.0404853i
$103$	7.16312	−	12.4069i	0.705803	−	1.22249i	−0.260598	−	0.965447i	$-0.583920\pi$
$103$	7.16312	−	12.4069i	0.705803	−	1.22249i	0.966401	−	0.257039i	$-0.0827470\pi$
$104$	1.71293	−	1.43732i	0.167966	−	0.140941i
$105$	−2.84065	+	2.38359i	−0.277219	+	0.232614i
$106$	5.11803	−	8.86469i	0.497107	−	0.861015i
$107$	8.20820	+	14.2170i	0.793517	+	1.37441i	0.923777	+	0.382932i	$0.125086\pi$
$107$	8.20820	+	14.2170i	0.793517	+	1.37441i	−0.130260	+	0.991480i	$0.541581\pi$
$108$	−1.29862	−	0.472660i	−0.124960	−	0.0454818i
$109$	0.571614	−	3.24179i	0.0547507	−	0.310507i	−0.945118	−	0.326730i	$-0.894053\pi$
$109$	0.571614	−	3.24179i	0.0547507	−	0.310507i	0.999868	+	0.0162234i	$0.00516428\pi$
$110$	1.47117	+	8.34343i	0.140271	+	0.795514i
$111$	−3.17801	+	1.15670i	−0.301643	+	0.109789i
$112$	−11.1554	−	9.36047i	−1.05408	−	0.884481i
$113$	−6.76393			−0.636297			−0.318149	−	0.948041i	$-0.603061\pi$
$113$	−6.76393			−0.636297			−0.318149	+	0.948041i	$0.603061\pi$
$114$		0			0
$115$	17.4164			1.62409
$116$	1.71293	+	1.43732i	0.159041	+	0.133452i
$117$	2.68198	−	0.976160i	0.247949	−	0.0902461i
$118$	0.0916626	+	0.519845i	0.00843823	+	0.0478556i
$119$	0.397966	−	2.25698i	0.0364815	−	0.206897i
$120$	2.59725	+	0.945320i	0.237095	+	0.0862956i
$121$	4.19098	+	7.25900i	0.380998	+	0.659909i
$122$	−8.28115	+	14.3434i	−0.749740	+	1.29859i
$123$	−0.877809	+	0.736569i	−0.0791494	+	0.0664142i
$124$	4.19190	−	3.51742i	0.376444	−	0.315874i
$125$	−0.763932	+	1.32317i	−0.0683282	+	0.118348i
$126$	−6.92705	−	11.9980i	−0.617111	−	1.06887i
$127$	5.41632	+	1.97138i	0.480621	+	0.174932i	0.570958	−	0.820980i	$-0.306572\pi$
$127$	5.41632	+	1.97138i	0.480621	+	0.174932i	−0.0903366	+	0.995911i	$0.528794\pi$
$128$	−2.36475	+	13.4111i	−0.209016	+	1.18539i
$129$	0.00967708	+	0.0548815i	0.000852019	+	0.00483204i
$130$	4.92029	−	1.79084i	0.431538	−	0.157067i
$131$	11.5597	+	9.69977i	1.00998	+	0.847473i	0.988335	−	0.152293i	$-0.0486656\pi$
$131$	11.5597	+	9.69977i	1.00998	+	0.847473i	0.0216438	+	0.999766i	$0.493110\pi$
$132$	0.381966			0.0332459
$133$		0			0
$134$	−11.3262			−0.978438
$135$	5.54315	+	4.65125i	0.477078	+	0.400316i
$136$	−1.60519	+	0.584240i	−0.137644	+	0.0500982i
$137$	1.29752	+	7.35862i	0.110855	+	0.628689i	0.988719	+	0.149780i	$0.0478565\pi$
$137$	1.29752	+	7.35862i	0.110855	+	0.628689i	−0.877864	+	0.478909i	$0.841032\pi$
$138$	0.577595	−	3.27570i	0.0491682	−	0.278847i
$139$	−13.9059	−	5.06134i	−1.17948	−	0.429297i	−0.323465	−	0.946240i	$-0.604848\pi$
$139$	−13.9059	−	5.06134i	−1.17948	−	0.429297i	−0.856020	+	0.516943i	$0.827070\pi$
$140$	−3.00000	−	5.19615i	−0.253546	−	0.439155i
$141$	0.572949	−	0.992377i	0.0482510	−	0.0835732i
$142$	−9.26161	+	7.77141i	−0.777217	+	0.652162i
$143$	−1.23949	+	1.04005i	−0.103651	+	0.0869735i
$144$	−6.92705	+	11.9980i	−0.577254	+	0.999834i
$145$	−5.85410	−	10.1396i	−0.486157	−	0.842048i
$146$	−4.11770	−	1.49872i	−0.340783	−	0.124035i
$147$	−0.132655	+	0.752326i	−0.0109412	+	0.0620508i
$148$	−0.950226	−	5.38900i	−0.0781081	−	0.442973i
$149$	1.79465	−	0.653200i	0.147024	−	0.0535123i	−0.267460	−	0.963569i	$-0.586184\pi$
$149$	1.79465	−	0.653200i	0.147024	−	0.0535123i	0.414484	+	0.910057i	$0.363962\pi$
$150$	2.59074	+	2.17389i	0.211533	+	0.177497i
$151$	21.0902			1.71629			0.858147	−	0.513404i	$-0.171616\pi$
$151$	21.0902			1.71629			0.858147	+	0.513404i	$0.171616\pi$
$152$		0			0
$153$	−2.18034			−0.176270
$154$	6.01659	+	5.04852i	0.484831	+	0.406821i
$155$	−26.9245	+	9.79972i	−2.16263	+	0.787133i
$156$	−0.0409928	−	0.232482i	−0.00328205	−	0.0186134i
$157$	−3.10033	+	17.5829i	−0.247433	+	1.40326i	0.567339	+	0.823484i	$0.307973\pi$
$157$	−3.10033	+	17.5829i	−0.247433	+	1.40326i	−0.814773	+	0.579781i	$0.803138\pi$
$158$	−20.3990	−	7.42464i	−1.62286	−	0.590673i
$159$	1.20820	+	2.09267i	0.0958168	+	0.165960i
$160$	−5.47214	+	9.47802i	−0.432610	+	0.749303i
$161$	12.3685	−	10.3784i	0.974772	−	0.817931i
$162$	−9.55421	+	8.01693i	−0.750650	+	0.629870i
$163$	−0.881966	+	1.52761i	−0.0690809	+	0.119652i	−0.898497	−	0.438980i	$-0.855340\pi$
$163$	−0.881966	+	1.52761i	−0.0690809	+	0.119652i	0.829416	+	0.558631i	$0.188673\pi$
$164$	−0.927051	−	1.60570i	−0.0723905	−	0.125384i
$165$	−1.87939	−	0.684040i	−0.146310	−	0.0532525i
$166$	−2.38040	+	13.4999i	−0.184755	+	1.04780i
$167$	−3.51396	−	19.9286i	−0.271918	−	1.54212i	−0.748584	−	0.663040i	$-0.769266\pi$
$167$	−3.51396	−	19.9286i	−0.271918	−	1.54212i	0.476666	−	0.879084i	$-0.341845\pi$
$168$	2.40778	−	0.876360i	0.185764	−	0.0676127i
$169$	−9.19253	−	7.71345i	−0.707118	−	0.593342i
$170$	−4.00000			−0.306786
$171$		0			0
$172$	−0.0901699			−0.00687539
$173$	0.361677	+	0.303483i	0.0274978	+	0.0230734i	0.656433	−	0.754384i	$-0.272064\pi$
$173$	0.361677	+	0.303483i	0.0274978	+	0.0230734i	−0.628935	+	0.777458i	$0.716509\pi$
$174$	−2.10122	+	0.764780i	−0.159293	+	0.0579778i
$175$	2.85068	+	16.1670i	0.215491	+	1.22211i
$176$	1.36385	−	7.73478i	0.102804	−	0.583031i
$177$	−0.117097	−	0.0426197i	−0.00880153	−	0.00320350i
$178$	6.28115	+	10.8793i	0.470792	+	0.815436i
$179$	6.11803	−	10.5967i	0.457283	−	0.792038i	−0.541533	−	0.840680i	$-0.682156\pi$
$179$	6.11803	−	10.5967i	0.457283	−	0.792038i	0.998816	+	0.0486416i	$0.0154892\pi$
$180$	−4.37274	+	3.66916i	−0.325925	+	0.273483i
$181$	−9.19253	+	7.71345i	−0.683276	+	0.573336i	−0.916961	−	0.398976i	$-0.869366\pi$
$181$	−9.19253	+	7.71345i	−0.683276	+	0.573336i	0.233686	+	0.972312i	$0.424921\pi$
$182$	2.42705	−	4.20378i	0.179905	−	0.311605i
$183$	−1.95492	−	3.38601i	−0.144511	−	0.250301i
$184$	−11.3087	−	4.11602i	−0.833687	−	0.303437i
$185$	−4.97545	+	28.2172i	−0.365802	+	2.07457i
$186$	0.950226	+	5.38900i	0.0696740	+	0.395141i
$187$	1.16152	−	0.422760i	0.0849390	−	0.0309153i
$188$	1.42032	+	1.19179i	0.103588	+	0.0869205i
$189$	6.70820			0.487950
$190$		0			0
$191$	14.2361			1.03009			0.515043	−	0.857164i	$-0.327776\pi$
$191$	14.2361			1.03009			0.515043	+	0.857164i	$0.327776\pi$
$192$	−1.23949	−	1.04005i	−0.0894522	−	0.0750593i
$193$	4.75083	−	1.72916i	0.341972	−	0.124468i	−0.165324	−	0.986239i	$-0.552867\pi$
$193$	4.75083	−	1.72916i	0.341972	−	0.124468i	0.507297	+	0.861772i	$0.330645\pi$
$194$	3.89257	+	22.0759i	0.279470	+	1.58495i
$195$	−0.214641	+	1.21729i	−0.0153708	+	0.0871719i
$196$	−1.16152	−	0.422760i	−0.0829660	−	0.0301972i
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	0.807630	−	0.589689i	$-0.200750\pi$
$197$	−1.50000	−	2.59808i	−0.106871	−	0.185105i	−0.914501	+	0.404584i	$0.867416\pi$
$198$	3.73607	−	6.47106i	0.265511	−	0.459878i
$199$	−10.2776	+	8.62390i	−0.728557	+	0.611332i	−0.929738	−	0.368222i	$-0.879967\pi$
$199$	−10.2776	+	8.62390i	−0.728557	+	0.611332i	0.201181	+	0.979554i	$0.435522\pi$
$200$	9.37337	−	7.86519i	0.662797	−	0.556153i
$201$	1.33688	−	2.31555i	0.0942963	−	0.163326i
$202$	−7.42705	−	12.8640i	−0.522565	−	0.905110i
$203$	−10.1995	−	3.71232i	−0.715866	−	0.260554i
$204$	−0.0313157	+	0.177600i	−0.00219254	+	0.0124345i
$205$	1.68581	+	9.56071i	0.117742	+	0.667749i
$206$	−21.7824	+	7.92814i	−1.51765	+	0.552380i
$207$	−11.7670	−	9.87365i	−0.817860	−	0.686266i
$208$	−4.85410			−0.336571
$209$		0			0
$210$	6.00000			0.414039
$211$	2.95241	+	2.47737i	0.203253	+	0.170549i	0.738732	−	0.673999i	$-0.235425\pi$
$211$	2.95241	+	2.47737i	0.203253	+	0.170549i	−0.535480	+	0.844548i	$0.679869\pi$
$212$	−3.67404	+	1.33724i	−0.252334	+	0.0918421i
$213$	−0.495610	−	2.81074i	−0.0339586	−	0.192589i
$214$	4.61250	−	26.1588i	0.315304	−	1.78818i
$215$	0.443663	+	0.161480i	0.0302575	+	0.0110128i
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	−13.2812	+	23.0036i	−0.901583	+	1.56159i
$218$	−4.08013	+	3.42364i	−0.276342	+	0.231878i
$219$	0.792428	−	0.664926i	0.0535474	−	0.0449316i
$220$	1.61803	−	2.80252i	0.109088	−	0.188946i
$221$	−0.381966	−	0.661585i	−0.0256938	−	0.0445030i
$222$	5.14213	+	1.87158i	0.345117	+	0.125612i
$223$	2.02343	−	11.4754i	0.135499	−	0.768453i	−0.839012	−	0.544113i	$-0.816866\pi$
$223$	2.02343	−	11.4754i	0.135499	−	0.768453i	0.974511	−	0.224340i	$-0.0720226\pi$
$224$	1.76182	+	9.99176i	0.117716	+	0.667602i
$225$	14.6762	−	5.34168i	0.978410	−	0.356112i
$226$	8.38380	+	7.03484i	0.557682	+	0.467951i
$227$	−16.4164			−1.08960			−0.544798	−	0.838568i	$-0.683394\pi$
$227$	−16.4164			−1.08960			−0.544798	+	0.838568i	$0.683394\pi$
$228$		0			0
$229$	−13.6180			−0.899905			−0.449953	−	0.893052i	$-0.648559\pi$
$229$	−13.6180			−0.899905			−0.449953	+	0.893052i	$0.648559\pi$
$230$	−21.5874	−	18.1140i	−1.42343	−	1.19440i
$231$	−1.74229	+	0.634140i	−0.114634	+	0.0417234i
$232$	1.40484	+	7.96726i	0.0922325	+	0.523076i
$233$	0.786255	−	4.45908i	0.0515093	−	0.292124i	−0.948161	−	0.317790i	$-0.897059\pi$
$233$	0.786255	−	4.45908i	0.0515093	−	0.292124i	0.999671	+	0.0256658i	$0.00817057\pi$
$234$	−4.33953	−	1.57946i	−0.283684	−	0.103253i
$235$	−4.85410	−	8.40755i	−0.316647	−	0.548448i
$236$	0.100813	−	0.174613i	0.00656237	−	0.0113664i
$237$	3.92568	−	3.29404i	0.255000	−	0.213971i
$238$	−2.84065	+	2.38359i	−0.184132	+	0.154505i
$239$	0.163119	−	0.282530i	0.0105513	−	0.0182754i	−0.860702	−	0.509110i	$-0.829975\pi$
$239$	0.163119	−	0.282530i	0.0105513	−	0.0182754i	0.871253	+	0.490834i	$0.163308\pi$
$240$	−3.00000	−	5.19615i	−0.193649	−	0.335410i
$241$	2.98854	+	1.08774i	0.192509	+	0.0700675i	0.436476	−	0.899716i	$-0.356227\pi$
$241$	2.98854	+	1.08774i	0.192509	+	0.0700675i	−0.243967	+	0.969784i	$0.578449\pi$
$242$	2.35507	−	13.3563i	0.151390	−	0.858573i
$243$	−1.67613	−	9.50583i	−0.107524	−	0.609799i
$244$	5.94472	−	2.16370i	0.380572	−	0.138517i
$245$	4.95794	+	4.16021i	0.316751	+	0.265786i
$246$	1.85410			0.118213
$247$		0			0
$248$	19.7984			1.25720
$249$	−2.47897	−	2.08010i	−0.157098	−	0.131821i
$250$	2.32305	−	0.845520i	0.146922	−	0.0534754i
$251$	−4.40384	−	24.9754i	−0.277968	−	1.57643i	−0.729374	−	0.684115i	$-0.760189\pi$
$251$	−4.40384	−	24.9754i	−0.277968	−	1.57643i	0.451407	−	0.892318i	$-0.350922\pi$
$252$	−0.918911	+	5.21140i	−0.0578859	+	0.328287i
$253$	8.18303	+	2.97838i	0.514463	+	0.187249i
$254$	−4.66312	−	8.07676i	−0.292590	−	0.506781i
$255$	0.472136	−	0.817763i	0.0295663	−	0.0512103i
$256$	10.3893	−	8.71768i	0.649333	−	0.544855i
$257$	−15.5972	+	13.0876i	−0.972926	+	0.816382i	−0.983007	−	0.183568i	$-0.941235\pi$
$257$	−15.5972	+	13.0876i	−0.972926	+	0.816382i	0.0100814	+	0.999949i	$0.496791\pi$
$258$	0.0450850	−	0.0780895i	0.00280687	−	0.00486164i
$259$	13.2812	+	23.0036i	0.825251	+	1.42938i
$260$	−1.87939	−	0.684040i	−0.116555	−	0.0424224i
$261$	−1.79313	+	10.1694i	−0.110992	+	0.629468i
$262$	−4.23986	−	24.0455i	−0.261940	−	1.48553i
$263$	14.0430	−	5.11124i	0.865930	−	0.315173i	0.129412	−	0.991591i	$-0.458691\pi$
$263$	14.0430	−	5.11124i	0.865930	−	0.315173i	0.736518	+	0.676418i	$0.236469\pi$
$264$	1.05865	+	0.888311i	0.0651552	+	0.0546717i
$265$	20.4721			1.25759
$266$		0			0
$267$	−2.96556			−0.181489
$268$	3.31409	+	2.78085i	0.202440	+	0.169868i
$269$	28.4973	−	10.3722i	1.73751	−	0.632403i	0.738395	−	0.674369i	$-0.235584\pi$
$269$	28.4973	−	10.3722i	1.73751	−	0.632403i	0.999119	+	0.0419657i	$0.0133620\pi$
$270$	−2.03311	−	11.5303i	−0.123731	−	0.701714i
$271$	0.198983	−	1.12849i	0.0120874	−	0.0685508i	−0.978167	−	0.207818i	$-0.933364\pi$
$271$	0.198983	−	1.12849i	0.0120874	−	0.0685508i	0.990255	+	0.139268i	$0.0444748\pi$
$272$	3.48457	+	1.26828i	0.211283	+	0.0769008i
$273$	0.572949	+	0.992377i	0.0346765	+	0.0600614i
$274$	6.04508	−	10.4704i	0.365197	−	0.632540i
$275$	−6.78264	+	5.69131i	−0.409008	+	0.343199i
$276$	−0.973267	+	0.816668i	−0.0585838	+	0.0491576i
$277$	−5.70820	+	9.88690i	−0.342973	+	0.594046i	−0.984983	−	0.172650i	$-0.944767\pi$
$277$	−5.70820	+	9.88690i	−0.342973	+	0.594046i	0.642011	+	0.766696i	$0.278101\pi$
$278$	11.9721	+	20.7363i	0.718041	+	1.24368i
$279$	23.7465	+	8.64302i	1.42167	+	0.517444i
$280$	3.76959	−	21.3784i	0.225276	−	1.27760i
$281$	5.12376	+	29.0583i	0.305658	+	1.73347i	0.620391	+	0.784293i	$0.286974\pi$
$281$	5.12376	+	29.0583i	0.305658	+	1.73347i	−0.314733	+	0.949180i	$0.601915\pi$
$282$	−1.74229	+	0.634140i	−0.103752	+	0.0377625i
$283$	19.9435	+	16.7346i	1.18552	+	0.994770i	0.999926	+	0.0121432i	$0.00386540\pi$
$283$	19.9435	+	16.7346i	1.18552	+	0.994770i	0.185594	+	0.982626i	$0.440579\pi$
$284$	4.61803			0.274030
$285$		0			0
$286$	2.61803			0.154808
$287$	6.89440	+	5.78509i	0.406964	+	0.341483i
$288$	9.07036	−	3.30134i	0.534476	−	0.194533i
$289$	−2.85068	−	16.1670i	−0.167687	−	0.951000i
$290$	−3.28964	+	18.6565i	−0.193174	+	1.09555i
$291$	−4.97266	−	1.80990i	−0.291503	−	0.106098i
$292$	0.836881	+	1.44952i	0.0489748	+	0.0848268i
$293$	−5.07295	+	8.78661i	−0.296365	+	0.513319i	−0.975301	−	0.220878i	$-0.929108\pi$
$293$	−5.07295	+	8.78661i	−0.296365	+	0.513319i	0.678937	+	0.734197i	$0.262441\pi$
$294$	0.946883	−	0.794529i	0.0552233	−	0.0463379i
$295$	−0.808735	+	0.678609i	−0.0470864	+	0.0395101i
$296$	9.89919	−	17.1459i	0.575379	−	0.996585i
$297$	1.80902	+	3.13331i	0.104970	+	0.181813i
$298$	−2.90381	−	1.05690i	−0.168213	−	0.0612246i
$299$	0.934569	−	5.30020i	0.0540475	−	0.306519i
$300$	−0.224318	−	1.27217i	−0.0129510	−	0.0734488i
$301$	0.411298	−	0.149700i	0.0237068	−	0.00862858i
$302$	−26.1410	−	21.9349i	−1.50424	−	1.26221i
$303$	3.50658			0.201448
$304$		0			0
$305$	−33.1246			−1.89671
$306$	2.70250	+	2.26767i	0.154492	+	0.129634i
$307$	−16.2813	+	5.92592i	−0.929225	+	0.338210i	−0.761902	−	0.647692i	$-0.775734\pi$
$307$	−16.2813	+	5.92592i	−0.929225	+	0.338210i	−0.167323	+	0.985902i	$0.553512\pi$
$308$	−0.520945	−	2.95442i	−0.0296836	−	0.168344i
$309$	0.950226	−	5.38900i	0.0540565	−	0.306570i
$310$	43.5648	+	15.8563i	2.47431	+	0.900577i
$311$	−6.32624	−	10.9574i	−0.358728	−	0.621335i	0.629021	−	0.777389i	$-0.283456\pi$
$311$	−6.32624	−	10.9574i	−0.358728	−	0.621335i	−0.987749	+	0.156053i	$0.950123\pi$
$312$	0.427051	−	0.739674i	0.0241770	−	0.0418758i
$313$	−8.67640	+	7.28037i	−0.490419	+	0.411511i	−0.854176	−	0.519983i	$-0.825938\pi$
$313$	−8.67640	+	7.28037i	−0.490419	+	0.411511i	0.363757	+	0.931494i	$0.381494\pi$
$314$	22.1299	−	18.5692i	1.24886	−	1.04792i
$315$	13.8541	−	23.9960i	0.780590	−	1.35202i
$316$	4.14590	+	7.18091i	0.233225	+	0.403958i
$317$	16.9145	+	6.15636i	0.950011	+	0.345776i	0.770112	−	0.637909i	$-0.220201\pi$
$317$	16.9145	+	6.15636i	0.950011	+	0.345776i	0.179900	+	0.983685i	$0.442423\pi$
$318$	0.678935	−	3.85043i	0.0380728	−	0.215921i
$319$	−1.01655	−	5.76517i	−0.0569161	−	0.322787i
$320$	−12.8815	+	4.68848i	−0.720098	+	0.262094i
$321$	4.80349	+	4.03061i	0.268105	+	0.224966i
$322$	−26.1246			−1.45587
$323$		0			0
$324$	4.76393			0.264663
$325$	4.19190	+	3.51742i	0.232525	+	0.195111i
$326$	2.68198	−	0.976160i	0.148541	−	0.0540645i
$327$	−0.218337	−	1.23825i	−0.0120741	−	0.0684755i
$328$	1.16487	−	6.60629i	0.0643190	−	0.364771i
$329$	−8.45723	−	3.07818i	−0.466262	−	0.169706i
$330$	1.61803	+	2.80252i	0.0890698	+	0.154273i
$331$	5.47214	−	9.47802i	0.300776	−	0.520959i	−0.675536	−	0.737327i	$-0.736088\pi$
$331$	5.47214	−	9.47802i	0.300776	−	0.520959i	0.976312	+	0.216368i	$0.0694211\pi$
$332$	4.01106	−	3.36568i	0.220136	−	0.184716i
$333$	19.3583	−	16.2436i	1.06083	−	0.890142i
$334$	−16.3713	+	28.3560i	−0.895799	+	1.55157i
$335$	−11.3262	−	19.6176i	−0.618818	−	1.07183i
$336$	−5.22686	−	1.90242i	−0.285148	−	0.103786i
$337$	2.97366	−	16.8645i	0.161985	−	0.918665i	−0.790133	−	0.612936i	$-0.789989\pi$
$337$	2.97366	−	16.8645i	0.161985	−	0.918665i	0.952118	−	0.305730i	$-0.0989004\pi$
$338$	3.37162	+	19.1214i	0.183392	+	1.04007i
$339$	−2.42778	+	0.883641i	−0.131859	+	0.0479928i
$340$	1.17041	+	0.982092i	0.0634745	+	0.0532614i
$341$	−14.3262			−0.775809
$342$		0			0
$343$	−15.0000			−0.809924
$344$	−0.249913	−	0.209702i	−0.0134744	−	0.0113064i
$345$	6.25128	−	2.27528i	0.336558	−	0.122497i
$346$	−0.132655	−	0.752326i	−0.00713160	−	0.0404453i
$347$	−4.41351	+	25.0303i	−0.236930	+	1.34370i	0.601582	+	0.798811i	$0.294537\pi$
$347$	−4.41351	+	25.0303i	−0.236930	+	1.34370i	−0.838511	+	0.544884i	$0.816574\pi$
$348$	0.802593	+	0.292120i	0.0430235	+	0.0156593i
$349$	10.4894	+	18.1681i	0.561482	+	0.972516i	0.997367	+	0.0725137i	$0.0231021\pi$
$349$	10.4894	+	18.1681i	0.561482	+	0.972516i	−0.435885	+	0.900002i	$0.643565\pi$
$350$	13.2812	−	23.0036i	0.709907	−	1.22960i
$351$	1.71293	−	1.43732i	0.0914293	−	0.0767183i
$352$	−4.19190	+	3.51742i	−0.223429	+	0.187479i
$353$	−12.2254	+	21.1751i	−0.650694	+	1.12703i	0.332261	+	0.943187i	$0.392188\pi$
$353$	−12.2254	+	21.1751i	−0.650694	+	1.12703i	−0.982955	+	0.183847i	$0.941145\pi$
$354$	0.100813	+	0.174613i	0.00535815	+	0.00928059i
$355$	−22.7221	−	8.27016i	−1.20596	−	0.438935i
$356$	0.833229	−	4.72548i	0.0441610	−	0.250450i
$357$	−0.152010	−	0.862089i	−0.00804520	−	0.0456266i
$358$	−18.6044	+	6.77144i	−0.983272	+	0.357882i
$359$	5.38870	+	4.52165i	0.284404	+	0.238644i	0.773818	−	0.633408i	$-0.218345\pi$
$359$	5.38870	+	4.52165i	0.284404	+	0.238644i	−0.489413	+	0.872052i	$0.662789\pi$
$360$	−20.6525			−1.08848
$361$		0			0
$362$	19.4164			1.02050
$363$	2.45259	+	2.05797i	0.128727	+	0.108015i
$364$	−1.74229	+	0.634140i	−0.0913206	+	0.0332380i
$365$	−1.52184	−	8.63079i	−0.0796568	−	0.451756i
$366$	−1.09854	+	6.23013i	−0.0574216	+	0.325654i
$367$	14.9827	+	5.45326i	0.782091	+	0.284658i	0.702044	−	0.712133i	$-0.252271\pi$
$367$	14.9827	+	5.45326i	0.782091	+	0.284658i	0.0800469	+	0.996791i	$0.474493\pi$
$368$	13.0623	+	22.6246i	0.680920	+	1.17939i
$369$	4.28115	−	7.41517i	0.222868	−	0.386019i
$370$	35.5143	−	29.8001i	1.84630	−	1.54923i
$371$	14.5385	−	12.1993i	0.754803	−	0.633355i
$372$	1.04508	−	1.81014i	0.0541851	−	0.0938514i
$373$	−2.73607	−	4.73901i	−0.141668	−	0.245377i	0.786457	−	0.617645i	$-0.211913\pi$
$373$	−2.73607	−	4.73901i	−0.141668	−	0.245377i	−0.928125	+	0.372269i	$0.878580\pi$
$374$	−1.87939	−	0.684040i	−0.0971807	−	0.0353709i
$375$	−0.101340	+	0.574726i	−0.00523316	+	0.0296787i
$376$	1.16487	+	6.60629i	0.0600734	+	0.340693i
$377$	−3.39984	+	1.23744i	−0.175101	+	0.0637314i
$378$	−8.31472	−	6.97688i	−0.427663	−	0.358852i
$379$	15.1246			0.776899			0.388450	−	0.921470i	$-0.373011\pi$
$379$	15.1246			0.776899			0.388450	+	0.921470i	$0.373011\pi$
$380$		0			0
$381$	2.20163			0.112793
$382$	−17.6454	−	14.8063i	−0.902818	−	0.757554i
$383$	0.358931	−	0.130640i	0.0183405	−	0.00667540i	−0.332834	−	0.942986i	$-0.608005\pi$
$383$	0.358931	−	0.130640i	0.0183405	−	0.00667540i	0.351174	+	0.936310i	$0.385783\pi$
$384$	0.903253	+	5.12260i	0.0460939	+	0.261412i
$385$	−2.72770	+	15.4696i	−0.139017	+	0.788402i
$386$	−7.68701	−	2.79784i	−0.391258	−	0.142406i
$387$	−0.208204	−	0.360620i	−0.0105836	−	0.0183313i
$388$	4.28115	−	7.41517i	0.217343	−	0.376448i
$389$	7.10162	−	5.95897i	0.360067	−	0.302132i	−0.444751	−	0.895654i	$-0.646708\pi$
$389$	7.10162	−	5.95897i	0.360067	−	0.302132i	0.804817	+	0.593523i	$0.202263\pi$
$390$	1.53209	−	1.28558i	0.0775803	−	0.0650976i
$391$	−2.05573	+	3.56063i	−0.103963	+	0.180069i
$392$	−2.23607	−	3.87298i	−0.112938	−	0.195615i
$393$	5.41632	+	1.97138i	0.273217	+	0.0994430i
$394$	−0.842906	+	4.78036i	−0.0424650	+	0.240831i
$395$	−7.53918	−	42.7568i	−0.379337	−	2.15133i
$396$	−2.68198	+	0.976160i	−0.134774	+	0.0490539i
$397$	−8.78817	−	7.37415i	−0.441065	−	0.370098i	0.395042	−	0.918663i	$-0.370730\pi$
$397$	−8.78817	−	7.37415i	−0.441065	−	0.370098i	−0.836108	+	0.548565i	$0.815174\pi$
$398$	21.7082			1.08813
$399$		0			0
$400$	−26.5623			−1.32812
$401$	27.4922	+	23.0687i	1.37290	+	1.15200i	0.971758	+	0.235979i	$0.0758296\pi$
$401$	27.4922	+	23.0687i	1.37290	+	1.15200i	0.401138	+	0.916018i	$0.368615\pi$
$402$	−4.06533	+	1.47966i	−0.202760	+	0.0737988i
$403$	1.53750	+	8.71959i	0.0765883	+	0.434354i
$404$	−0.985238	+	5.58756i	−0.0490174	+	0.277992i
$405$	−23.4399	−	8.53144i	−1.16474	−	0.423931i
$406$	8.78115	+	15.2094i	0.435801	+	0.754830i
$407$	−7.16312	+	12.4069i	−0.355063	+	0.614987i
$408$	−0.499825	+	0.419403i	−0.0247450	+	0.0207636i
$409$	6.35188	−	5.32986i	0.314080	−	0.263545i	−0.472096	−	0.881547i	$-0.656502\pi$
$409$	6.35188	−	5.32986i	0.314080	−	0.263545i	0.786176	+	0.618003i	$0.212058\pi$
$410$	7.85410	−	13.6037i	0.387886	−	0.671839i
$411$	1.42705	+	2.47172i	0.0703912	+	0.121921i
$412$	8.32013	+	3.02828i	0.409904	+	0.149193i
$413$	−0.169952	+	0.963845i	−0.00836278	+	0.0474277i
$414$	4.31587	+	24.4765i	0.212113	+	1.20295i
$415$	−25.7630	+	9.37696i	−1.26466	+	0.460297i
$416$	2.59074	+	2.17389i	0.127021	+	0.106584i
$417$	−5.65248			−0.276803
$418$		0			0
$419$	−8.94427			−0.436956			−0.218478	−	0.975842i	$-0.570109\pi$
$419$	−8.94427			−0.436956			−0.218478	+	0.975842i	$0.570109\pi$
$420$	−1.75562	−	1.47314i	−0.0856654	−	0.0718818i
$421$	−25.8154	+	9.39602i	−1.25816	+	0.457934i	−0.883152	−	0.469086i	$-0.844583\pi$
$421$	−25.8154	+	9.39602i	−1.25816	+	0.457934i	−0.375011	+	0.927020i	$0.622361\pi$
$422$	−1.08288	−	6.14133i	−0.0527139	−	0.298955i
$423$	−1.48683	+	8.43223i	−0.0722921	+	0.409989i
$424$	−13.2928	−	4.83818i	−0.645555	−	0.234963i
$425$	−2.09017	−	3.62028i	−0.101388	−	0.175609i
$426$	−2.30902	+	3.99933i	−0.111872	+	0.193768i
$427$	−23.5238	+	19.7389i	−1.13840	+	0.955230i
$428$	−7.77221	+	6.52166i	−0.375684	+	0.315236i
$429$	−0.309017	+	0.535233i	−0.0149195	+	0.0258413i
$430$	−0.381966	−	0.661585i	−0.0184200	−	0.0319044i
$431$	25.9848	+	9.45770i	1.25165	+	0.455562i	0.880957	−	0.473196i	$-0.156900\pi$
$431$	25.9848	+	9.45770i	1.25165	+	0.455562i	0.370688	+	0.928757i	$0.379122\pi$
$432$	−1.88480	+	10.6892i	−0.0906822	+	0.514285i
$433$	0.596949	+	3.38547i	0.0286876	+	0.162695i	0.995786	−	0.0917071i	$-0.0292324\pi$
$433$	0.596949	+	3.38547i	0.0286876	+	0.162695i	−0.967098	+	0.254402i	$0.918121\pi$
$434$	40.3868	−	14.6996i	1.93863	−	0.705603i
$435$	−3.42585	−	2.87463i	−0.164257	−	0.137828i
$436$	2.03444			0.0974321
$437$		0			0
$438$	−1.67376			−0.0799754
$439$	26.5026	+	22.2384i	1.26490	+	1.06138i	0.995142	+	0.0984516i	$0.0313890\pi$
$439$	26.5026	+	22.2384i	1.26490	+	1.06138i	0.269760	+	0.962927i	$0.413055\pi$
$440$	11.0021	−	4.00444i	0.524505	−	0.190904i
$441$	−0.991219	−	5.62148i	−0.0472009	−	0.267690i
$442$	−0.214641	+	1.21729i	−0.0102094	+	0.0579005i
$443$	7.12625	+	2.59374i	0.338578	+	0.123232i	0.505713	−	0.862702i	$-0.331229\pi$
$443$	7.12625	+	2.59374i	0.338578	+	0.123232i	−0.167135	+	0.985934i	$0.553452\pi$
$444$	−1.04508	−	1.81014i	−0.0495975	−	0.0859055i
$445$	−12.5623	+	21.7586i	−0.595510	+	1.03145i
$446$	−14.4431	+	12.1192i	−0.683900	+	0.573860i
$447$	0.558822	−	0.468907i	0.0264314	−	0.0221786i
$448$	−6.35410	+	11.0056i	−0.300203	+	0.519967i
$449$	1.44427	+	2.50155i	0.0681594	+	0.118056i	0.898091	−	0.439809i	$-0.144954\pi$
$449$	1.44427	+	2.50155i	0.0681594	+	0.118056i	−0.829932	+	0.557865i	$0.811621\pi$
$450$	−23.7465	−	8.64302i	−1.11942	−	0.407436i
$451$	−0.842906	+	4.78036i	−0.0396909	+	0.225098i
$452$	−0.725908	−	4.11683i	−0.0341439	−	0.193639i
$453$	7.56991	−	2.75522i	0.355665	−	0.129452i
$454$	20.3479	+	17.0739i	0.954975	+	0.801319i
$455$	9.70820			0.455128
$456$		0			0
$457$	19.7082			0.921911			0.460955	−	0.887423i	$-0.347507\pi$
$457$	19.7082			0.921911			0.460955	+	0.887423i	$0.347507\pi$
$458$	16.8794	+	14.1635i	0.788721	+	0.661815i
$459$	−1.60519	+	0.584240i	−0.0749237	+	0.0272700i
$460$	1.86914	+	10.6004i	0.0871490	+	0.494246i
$461$	3.63693	−	20.6261i	0.169389	−	0.960652i	−0.775034	−	0.631920i	$-0.782267\pi$
$461$	3.63693	−	20.6261i	0.169389	−	0.960652i	0.944423	−	0.328733i	$-0.106622\pi$
$462$	2.81908	+	1.02606i	0.131155	+	0.0477367i
$463$	−14.1353	−	24.4830i	−0.656921	−	1.13782i	−0.981409	−	0.191931i	$-0.938525\pi$
$463$	−14.1353	−	24.4830i	−0.656921	−	1.13782i	0.324487	−	0.945890i	$-0.394808\pi$
$464$	8.78115	−	15.2094i	0.407655	−	0.706079i
$465$	−8.38380	+	7.03484i	−0.388789	+	0.326233i
$466$	−5.61222	+	4.70921i	−0.259981	+	0.218150i
$467$	7.97214	−	13.8081i	0.368906	−	0.638965i	−0.620488	−	0.784216i	$-0.713066\pi$
$467$	7.97214	−	13.8081i	0.368906	−	0.638965i	0.989395	+	0.145251i	$0.0463989\pi$
$468$	0.881966	+	1.52761i	0.0407689	+	0.0706138i
$469$	−19.7335	−	7.18242i	−0.911210	−	0.331653i
$470$	−2.72770	+	15.4696i	−0.125819	+	0.713558i
$471$	1.18422	+	6.71605i	0.0545660	+	0.309459i
$472$	0.685497	−	0.249500i	0.0315525	−	0.0114842i
$473$	0.180839	+	0.151742i	0.00831497	+	0.00697708i
$474$	−8.29180			−0.380855
$475$		0			0
$476$	1.41641			0.0649209
$477$	−13.8315	−	11.6060i	−0.633300	−	0.531402i
$478$	−0.496030	+	0.180540i	−0.0226879	+	0.00825771i
$479$	4.00957	+	22.7394i	0.183202	+	1.03899i	0.928244	+	0.371972i	$0.121318\pi$
$479$	4.00957	+	22.7394i	0.183202	+	1.03899i	−0.745042	+	0.667017i	$0.767571\pi$
$480$	−0.725908	+	4.11683i	−0.0331330	+	0.187907i
$481$	8.32013	+	3.02828i	0.379365	+	0.138078i
$482$	−2.57295	−	4.45648i	−0.117195	−	0.202987i
$483$	3.08359	−	5.34094i	0.140308	−	0.243021i
$484$	−3.96837	+	3.32986i	−0.180380	+	0.151357i
$485$	−34.3439	+	28.8180i	−1.55948	+	1.30856i
$486$	−7.80902	+	13.5256i	−0.354224	+	0.613534i
$487$	2.09017	+	3.62028i	0.0947146	+	0.164051i	0.909489	−	0.415727i	$-0.136473\pi$
$487$	2.09017	+	3.62028i	0.0947146	+	0.164051i	−0.814775	+	0.579778i	$0.803139\pi$
$488$	21.5082	+	7.82834i	0.973630	+	0.354372i
$489$	−0.116998	+	0.663526i	−0.00529081	+	0.0300057i
$490$	−1.81847	−	10.3130i	−0.0821500	−	0.465896i
$491$	19.9354	−	7.25588i	0.899671	−	0.327453i	0.149550	−	0.988754i	$-0.452218\pi$
$491$	19.9354	−	7.25588i	0.899671	−	0.327453i	0.750121	+	0.661301i	$0.229995\pi$
$492$	−0.542516	−	0.455225i	−0.0244585	−	0.0205231i
$493$	2.76393			0.124481
$494$		0			0
$495$	14.9443			0.671695
$496$	−32.9236	−	27.6262i	−1.47831	−	1.24045i
$497$	−21.0645	+	7.66686i	−0.944873	+	0.343906i
$498$	0.909234	+	5.15652i	0.0407437	+	0.231069i
$499$	4.36284	−	24.7429i	0.195308	−	1.10764i	−0.716672	−	0.697410i	$-0.754336\pi$
$499$	4.36284	−	24.7429i	0.195308	−	1.10764i	0.911980	−	0.410235i	$-0.134553\pi$
$500$	−0.887325	−	0.322960i	−0.0396824	−	0.0144432i
$501$	−3.86475	−	6.69393i	−0.172664	−	0.299063i
$502$	−20.5172	+	35.5369i	−0.915728	+	1.58609i
$503$	27.4495	−	23.0329i	1.22391	−	1.02699i	0.225303	−	0.974289i	$-0.427663\pi$
$503$	27.4495	−	23.0329i	1.22391	−	1.02699i	0.998611	−	0.0526972i	$-0.0167818\pi$
$504$	−14.6666	+	12.3067i	−0.653303	+	0.548186i
$505$	14.8541	−	25.7281i	0.660999	−	1.14488i
$506$	−7.04508	−	12.2024i	−0.313192	−	0.542465i
$507$	−4.30717	−	1.56768i	−0.191288	−	0.0696232i
$508$	−0.618588	+	3.50819i	−0.0274454	+	0.155651i
$509$	−0.353277	−	2.00353i	−0.0156587	−	0.0888051i	0.975977	−	0.217874i	$-0.0699122\pi$
$509$	−0.353277	−	2.00353i	−0.0156587	−	0.0888051i	−0.991636	+	0.129069i	$0.958801\pi$
$510$	−1.43572	+	0.522560i	−0.0635749	+	0.0231394i
$511$	−6.22381	−	5.22240i	−0.275325	−	0.231025i
$512$	5.29180			0.233867
$513$		0			0
$514$	32.9443			1.45311
$515$	−35.5143	−	29.8001i	−1.56495	−	1.31315i
$516$	−0.0323648	+	0.0117798i	−0.00142478	+	0.000518577i
$517$	−0.842906	−	4.78036i	−0.0370710	−	0.210240i
$518$	7.46318	−	42.3258i	0.327913	−	1.85969i
$519$	0.169464	+	0.0616799i	0.00743865	+	0.00270745i
$520$	−3.61803	−	6.26662i	−0.158661	−	0.274809i
$521$	3.13525	−	5.43042i	0.137358	−	0.237911i	−0.789138	−	0.614216i	$-0.789472\pi$
$521$	3.13525	−	5.43042i	0.137358	−	0.237911i	0.926496	+	0.376305i	$0.122806\pi$
$522$	12.7992	−	10.7398i	0.560207	−	0.470069i
$523$	3.38316	−	2.83881i	0.147935	−	0.124133i	−0.565816	−	0.824531i	$-0.691439\pi$
$523$	3.38316	−	2.83881i	0.147935	−	0.124133i	0.713752	+	0.700399i	$0.246994\pi$
$524$	−4.66312	+	8.07676i	−0.203709	+	0.352835i
$525$	3.13525	+	5.43042i	0.136834	+	0.237003i
$526$	−22.7221	−	8.27016i	−0.990730	−	0.360596i
$527$	1.17454	−	6.66117i	0.0511640	−	0.290165i
$528$	−0.520945	−	2.95442i	−0.0226712	−	0.128575i
$529$	−5.60579	+	2.04034i	−0.243730	+	0.0887105i
$530$	−25.3749	−	21.2921i	−1.10222	−	0.924869i
$531$	0.931116			0.0404070
$532$		0			0
$533$	3.00000			0.129944
$534$	3.67577	+	3.08434i	0.159066	+	0.133472i
$535$	49.9208	−	18.1697i	2.15826	−	0.785544i
$536$	2.71802	+	15.4147i	0.117401	+	0.665813i
$537$	0.811590	−	4.60276i	0.0350227	−	0.198624i
$538$	−46.1097	−	16.7825i	−1.98793	−	0.723547i
$539$	1.61803	+	2.80252i	0.0696937	+	0.120713i
$540$	−2.23607	+	3.87298i	−0.0962250	+	0.166667i
$541$	−22.8533	+	19.1762i	−0.982539	+	0.824448i	−0.984470	−	0.175550i	$-0.943829\pi$
$541$	−22.8533	+	19.1762i	−0.982539	+	0.824448i	0.00193193	+	0.999998i	$0.499385\pi$
$542$	−1.42032	+	1.19179i	−0.0610082	+	0.0511919i
$543$	−2.29180	+	3.96951i	−0.0983504	+	0.170348i
$544$	−1.29180	−	2.23746i	−0.0553853	−	0.0959302i
$545$	−10.0101	−	3.64336i	−0.428784	−	0.156064i
$546$	0.321961	−	1.82593i	0.0137787	−	0.0781428i
$547$	4.67513	+	26.5140i	0.199894	+	1.13366i	0.905275	+	0.424827i	$0.139665\pi$
$547$	4.67513	+	26.5140i	0.199894	+	1.13366i	−0.705381	+	0.708829i	$0.749224\pi$
$548$	−4.33953	+	1.57946i	−0.185376	+	0.0674712i
$549$	22.3798	+	18.7789i	0.955147	+	0.801464i
$550$	14.3262			0.610873
$551$		0			0
$552$	−4.59675			−0.195651
$553$	−30.8327	−	25.8717i	−1.31114	−	1.10018i
$554$	17.3581	−	6.31784i	0.737476	−	0.268419i
$555$	1.90045	+	10.7780i	0.0806697	+	0.457501i
$556$	1.58817	−	9.00695i	0.0673533	−	0.381980i
$557$	0.770229	+	0.280340i	0.0326356	+	0.0118784i	0.358286	−	0.933612i	$-0.383361\pi$
$557$	0.770229	+	0.280340i	0.0326356	+	0.0118784i	−0.325651	+	0.945490i	$0.605583\pi$
$558$	−20.4443	−	35.4105i	−0.865475	−	1.49905i
$559$	0.0729490	−	0.126351i	0.00308541	−	0.00534409i
$560$	−36.0995	+	30.2911i	−1.52548	+	1.28003i
$561$	0.361677	−	0.303483i	0.0152700	−	0.0128131i
$562$	23.8713	−	41.3463i	1.00695	−	1.74409i
$563$	−16.4164	−	28.4341i	−0.691869	−	1.19835i	−0.971225	−	0.238165i	$-0.923454\pi$
$563$	−16.4164	−	28.4341i	−0.691869	−	1.19835i	0.279356	−	0.960188i	$-0.409879\pi$
$564$	0.665494	+	0.242220i	0.0280224	+	0.0101993i
$565$	−3.80091	+	21.5560i	−0.159905	+	0.906868i
$566$	−7.31486	−	41.4846i	−0.307467	−	1.74373i
$567$	−21.7300	+	7.90908i	−0.912575	+	0.332150i
$568$	12.7992	+	10.7398i	0.537044	+	0.450633i
$569$	−16.9098			−0.708897			−0.354448	−	0.935076i	$-0.615331\pi$
$569$	−16.9098			−0.708897			−0.354448	+	0.935076i	$0.615331\pi$
$570$		0			0
$571$	6.67376			0.279288			0.139644	−	0.990202i	$-0.455404\pi$
$571$	6.67376			0.279288			0.139644	+	0.990202i	$0.455404\pi$
$572$	−0.766044	−	0.642788i	−0.0320299	−	0.0268763i
$573$	5.10976	−	1.85980i	0.213463	−	0.0776943i
$574$	−2.52872	−	14.3411i	−0.105547	−	0.598585i
$575$	5.11409	−	29.0034i	0.213272	−	1.20953i
$576$	11.3610	+	4.13508i	0.473377	+	0.172295i
$577$	6.06231	+	10.5002i	0.252377	+	0.437130i	0.964180	−	0.265250i	$-0.0854543\pi$
$577$	6.06231	+	10.5002i	0.252377	+	0.437130i	−0.711803	+	0.702379i	$0.752121\pi$
$578$	−13.2812	+	23.0036i	−0.552423	+	0.956825i
$579$	1.47932	−	1.24130i	0.0614785	−	0.0515866i
$580$	5.54315	−	4.65125i	0.230167	−	0.193133i
$581$	−12.7082	+	22.0113i	−0.527225	+	0.913181i
$582$	4.28115	+	7.41517i	0.177459	+	0.307369i
$583$	9.61876	+	3.50094i	0.398368	+	0.144994i
$584$	−1.05157	+	5.96373i	−0.0435141	+	0.246781i
$585$	−1.60383	−	9.09575i	−0.0663101	−	0.376063i
$586$	15.4264	−	5.61474i	0.637258	−	0.231943i
$587$	−1.62755	−	1.36567i	−0.0671761	−	0.0563674i	0.608581	−	0.793491i	$-0.291739\pi$
$587$	−1.62755	−	1.36567i	−0.0671761	−	0.0563674i	−0.675757	+	0.737124i	$0.736183\pi$
$588$	−0.472136			−0.0194706
$589$		0			0
$590$	1.70820			0.0703256
$591$	−0.877809	−	0.736569i	−0.0361082	−	0.0302984i
$592$	−40.3868	+	14.6996i	−1.65989	+	0.604149i
$593$	0.122978	+	0.697445i	0.00505011	+	0.0286406i	0.987229	−	0.159310i	$-0.0509268\pi$
$593$	0.122978	+	0.697445i	0.00505011	+	0.0286406i	−0.982179	+	0.187950i	$0.939816\pi$
$594$	1.01655	−	5.76517i	0.0417097	−	0.236548i
$595$	−6.96914	−	2.53656i	−0.285707	−	0.103989i
$596$	0.590170	+	1.02220i	0.0241743	+	0.0418711i
$597$	−2.56231	+	4.43804i	−0.104868	+	0.181637i
$598$	−6.67087	+	5.59753i	−0.272792	+	0.228900i
$599$	−21.7682	+	18.2657i	−0.889426	+	0.746317i	−0.968095	−	0.250584i	$-0.919377\pi$
$599$	−21.7682	+	18.2657i	−0.889426	+	0.746317i	0.0786691	+	0.996901i	$0.474933\pi$
$600$	2.33688	−	4.04760i	0.0954028	−	0.165242i
$601$	10.1459	+	17.5732i	0.413860	+	0.716826i	0.995308	−	0.0967572i	$-0.0308470\pi$
$601$	10.1459	+	17.5732i	0.413860	+	0.716826i	−0.581448	+	0.813583i	$0.697514\pi$
$602$	−0.665494	−	0.242220i	−0.0271235	−	0.00987215i
$603$	−3.46927	+	19.6752i	−0.141279	+	0.801236i
$604$	2.26341	+	12.8364i	0.0920967	+	0.522306i
$605$	25.4888	−	9.27716i	1.03627	−	0.377170i
$606$	−4.34635	−	3.64702i	−0.176559	−	0.148150i
$607$	6.27051			0.254512			0.127256	−	0.991870i	$-0.459383\pi$
$607$	6.27051			0.254512			0.127256	+	0.991870i	$0.459383\pi$
$608$		0			0
$609$	−4.14590			−0.168000
$610$	41.0575	+	34.4513i	1.66237	+	1.39489i
$611$	−2.81908	+	1.02606i	−0.114048	+	0.0415100i
$612$	−0.233995	−	1.32705i	−0.00945869	−	0.0536429i
$613$	−3.46329	+	19.6413i	−0.139881	+	0.793304i	0.831455	+	0.555592i	$0.187508\pi$
$613$	−3.46329	+	19.6413i	−0.139881	+	0.793304i	−0.971336	+	0.237711i	$0.923603\pi$
$614$	26.3438	+	9.58834i	1.06315	+	0.386954i
$615$	1.85410	+	3.21140i	0.0747646	+	0.129496i
$616$	5.42705	−	9.39993i	0.218662	−	0.378734i
$617$	5.87844	−	4.93260i	0.236657	−	0.198579i	−0.516744	−	0.856140i	$-0.672856\pi$
$617$	5.87844	−	4.93260i	0.236657	−	0.198579i	0.753401	+	0.657561i	$0.228412\pi$
$618$	−6.78264	+	5.69131i	−0.272838	+	0.228938i
$619$	−5.06231	+	8.76817i	−0.203471	+	0.352423i	−0.949645	−	0.313329i	$-0.898556\pi$
$619$	−5.06231	+	8.76817i	−0.203471	+	0.352423i	0.746173	+	0.665752i	$0.231889\pi$
$620$	−8.85410	−	15.3358i	−0.355589	−	0.615899i
$621$	−11.3087	−	4.11602i	−0.453802	−	0.165170i
$622$	−3.55495	+	20.1611i	−0.142540	+	0.808387i
$623$	4.04458	+	22.9379i	0.162043	+	0.918989i
$624$	−1.74229	+	0.634140i	−0.0697473	+	0.0253859i
$625$	−17.1720	−	14.4090i	−0.686879	−	0.576360i
$626$	18.3262			0.732464
$627$		0			0
$628$	−11.0344			−0.440322
$629$	−5.18147	−	4.34777i	−0.206599	−	0.173357i
$630$	−42.1291	+	15.3337i	−1.67846	+	0.610910i
$631$	5.09843	+	28.9146i	0.202965	+	1.15107i	0.900610	+	0.434629i	$0.143120\pi$
$631$	5.09843	+	28.9146i	0.202965	+	1.15107i	−0.697644	+	0.716444i	$0.745768\pi$
$632$	−5.20945	+	29.5442i	−0.207221	+	1.17521i
$633$	1.38336	+	0.503500i	0.0549834	+	0.0200123i
$634$	−14.5623	−	25.2227i	−0.578343	−	1.00172i
$635$	9.32624	−	16.1535i	0.370100	−	0.641033i
$636$	−1.14403	+	0.959953i	−0.0453637	+	0.0380646i
$637$	1.53209	−	1.28558i	0.0607036	−	0.0509363i
$638$	−4.73607	+	8.20311i	−0.187503	+	0.324764i
$639$	10.6631	+	18.4691i	0.421826	+	0.730625i
$640$	41.4112	+	15.0724i	1.63692	+	0.595791i
$641$	6.86025	−	38.9064i	0.270963	−	1.53671i	−0.480535	−	0.876975i	$-0.659558\pi$
$641$	6.86025	−	38.9064i	0.270963	−	1.53671i	0.751499	−	0.659734i	$-0.229331\pi$
$642$	−1.76182	−	9.99176i	−0.0695334	−	0.394343i
$643$	22.8268	−	8.30828i	0.900202	−	0.327647i	0.149868	−	0.988706i	$-0.452115\pi$
$643$	22.8268	−	8.30828i	0.900202	−	0.327647i	0.750334	+	0.661059i	$0.229893\pi$
$644$	7.64414	+	6.41419i	0.301221	+	0.252755i
$645$	0.180340			0.00710088
$646$		0			0
$647$	7.47214			0.293760			0.146880	−	0.989154i	$-0.453077\pi$
$647$	7.47214			0.293760			0.146880	+	0.989154i	$0.453077\pi$
$648$	13.2036	+	11.0791i	0.518686	+	0.435229i
$649$	−0.496030	+	0.180540i	−0.0194709	+	0.00708682i
$650$	−1.53750	−	8.71959i	−0.0603057	−	0.342010i
$651$	−1.76182	+	9.99176i	−0.0690510	+	0.391608i
$652$	−1.02442	−	0.372860i	−0.0401196	−	0.0146023i
$653$	11.7812	+	20.4056i	0.461032	+	0.798531i	0.999013	−	0.0444262i	$-0.0141459\pi$
$653$	11.7812	+	20.4056i	0.461032	+	0.798531i	−0.537981	+	0.842957i	$0.680813\pi$
$654$	−1.01722	+	1.76188i	−0.0397765	+	0.0688949i
$655$	37.4081	−	31.3891i	1.46166	−	1.22647i
$656$	−11.1554	+	9.36047i	−0.435544	+	0.365465i
$657$	−3.86475	+	6.69393i	−0.150778	+	0.261155i
$658$	7.28115	+	12.6113i	0.283849	+	0.491641i
$659$	−24.2225	−	8.81628i	−0.943576	−	0.343434i	−0.175999	−	0.984390i	$-0.556316\pi$
$659$	−24.2225	−	8.81628i	−0.943576	−	0.343434i	−0.767577	+	0.640957i	$0.778538\pi$
$660$	0.214641	−	1.21729i	0.00835489	−	0.0473829i
$661$	−0.940549	−	5.33412i	−0.0365831	−	0.207473i	0.961037	−	0.276419i	$-0.0891477\pi$
$661$	−0.940549	−	5.33412i	−0.0365831	−	0.207473i	−0.997620	+	0.0689455i	$0.978037\pi$
$662$	−16.6403	+	6.05656i	−0.646742	+	0.235395i
$663$	−0.223529	−	0.187563i	−0.00868114	−	0.00728434i
$664$	18.9443			0.735180
$665$		0			0
$666$	−40.8885			−1.58440
$667$	14.9165	+	12.5164i	0.577570	+	0.484639i
$668$	11.7523	−	4.27750i	0.454712	−	0.165502i
$669$	−0.772882	−	4.38323i	−0.0298813	−	0.169466i
$670$	−6.36464	+	36.0956i	−0.245887	+	1.39450i
$671$	−15.5635	−	5.66464i	−0.600821	−	0.218681i
$672$	1.93769	+	3.35618i	0.0747482	+	0.129468i
$673$	17.0623	−	29.5528i	0.657704	−	1.13918i	−0.323505	−	0.946226i	$-0.604861\pi$
$673$	17.0623	−	29.5528i	0.657704	−	1.13918i	0.981209	−	0.192950i	$-0.0618054\pi$
$674$	−21.2257	+	17.8105i	−0.817584	+	0.686034i
$675$	9.37337	−	7.86519i	0.360781	−	0.302731i
$676$	3.70820	−	6.42280i	0.142623	−	0.247031i
$677$	−15.3713	−	26.6239i	−0.590768	−	1.02324i	−0.994129	−	0.108199i	$-0.965492\pi$
$677$	−15.3713	−	26.6239i	−0.590768	−	1.02324i	0.403361	−	0.915041i	$-0.367842\pi$
$678$	3.92823	+	1.42976i	0.150863	+	0.0549096i
$679$	−7.21722	+	40.9309i	−0.276971	+	1.57078i
$680$	0.959904	+	5.44388i	0.0368106	+	0.208763i
$681$	−5.89235	+	2.14464i	−0.225795	+	0.0821828i
$682$	17.7572	+	14.9000i	0.679957	+	0.570552i
$683$	−9.65248			−0.369342			−0.184671	−	0.982800i	$-0.559122\pi$
$683$	−9.65248			−0.369342			−0.184671	+	0.982800i	$0.559122\pi$
$684$		0			0
$685$	24.1803			0.923883
$686$	18.5923	+	15.6008i	0.709857	+	0.595641i
$687$	−4.88793	+	1.77906i	−0.186486	+	0.0678754i
$688$	0.122978	+	0.697445i	0.00468850	+	0.0265898i
$689$	1.09854	−	6.23013i	0.0418510	−	0.237349i
$690$	−10.1148	−	3.68148i	−0.385063	−	0.140152i
$691$	19.5902	+	33.9312i	0.745245	+	1.29080i	0.950080	+	0.312006i	$0.101001\pi$
$691$	19.5902	+	33.9312i	0.745245	+	1.29080i	−0.204835	+	0.978797i	$0.565666\pi$
$692$	−0.145898	+	0.252703i	−0.00554621	+	0.00960632i
$693$	10.6129	−	8.90525i	0.403149	−	0.338282i
$694$	31.5033	−	26.4344i	1.19585	−	1.00344i
$695$	−23.9443	+	41.4727i	−0.908258	+	1.57315i
$696$	1.54508	+	2.67617i	0.0585663	+	0.101440i
$697$	−2.15358	−	0.783840i	−0.0815728	−	0.0296901i
$698$	5.89436	−	33.4286i	0.223105	−	1.26529i
$699$	−0.300323	−	1.70322i	−0.0113593	−	0.0644215i
$700$	−9.53403	+	3.47010i	−0.360352	+	0.131158i
$701$	−30.3593	−	25.4744i	−1.14665	−	0.962156i	−0.147017	−	0.989134i	$-0.546967\pi$
$701$	−30.3593	−	25.4744i	−1.14665	−	0.962156i	−0.999636	+	0.0269777i	$0.991412\pi$
$702$	−3.61803			−0.136554
$703$		0			0
$704$	−6.85410			−0.258324
$705$	−2.84065	−	2.38359i	−0.106985	−	0.0897711i
$706$	37.1764	−	13.5311i	1.39915	−	0.509250i
$707$	−4.78245	−	27.1226i	−0.179862	−	1.02005i
$708$	0.0133734	−	0.0758443i	0.000502603	−	0.00285040i
$709$	−15.5835	−	5.67192i	−0.585250	−	0.213014i	0.0323891	−	0.999475i	$-0.489688\pi$
$709$	−15.5835	−	5.67192i	−0.585250	−	0.213014i	−0.617639	+	0.786462i	$0.711911\pi$
$710$	19.5623	+	33.8829i	0.734160	+	1.27160i
$711$	−19.1459	+	33.1617i	−0.718027	+	1.24366i
$712$	13.2991	−	11.1592i	0.498403	−	0.418210i
$713$	36.5039	−	30.6304i	1.36708	−	1.14712i
$714$	−0.708204	+	1.22665i	−0.0265039	+	0.0459060i
$715$	2.61803	+	4.53457i	0.0979089	+	0.169583i
$716$	7.10624	+	2.58646i	0.265573	+	0.0966606i
$717$	0.0216386	−	0.122719i	0.000808109	−	0.00458301i
$718$	−1.97646	−	11.2090i	−0.0737607	−	0.418318i
$719$	−44.1979	+	16.0867i	−1.64830	+	0.599934i	−0.988462	−	0.151470i	$-0.951599\pi$
$719$	−44.1979	+	16.0867i	−1.64830	+	0.599934i	−0.659842	+	0.751404i	$0.729377\pi$
$720$	34.3439	+	28.8180i	1.27992	+	1.07398i
$721$	−42.9787			−1.60061
$722$		0			0
$723$	1.21478			0.0451782
$724$	−5.68130	−	4.76718i	−0.211144	−	0.177171i
$725$	−18.6044	+	6.77144i	−0.690950	+	0.251485i
$726$	−0.899557	−	5.10164i	−0.0333857	−	0.189340i
$727$	−2.79033	+	15.8248i	−0.103488	+	0.586908i	0.888326	+	0.459214i	$0.151869\pi$
$727$	−2.79033	+	15.8248i	−0.103488	+	0.586908i	−0.991814	+	0.127694i	$0.959242\pi$
$728$	−6.30365	−	2.29434i	−0.233629	−	0.0850339i
$729$	9.71885	+	16.8335i	0.359957	+	0.623464i
$730$	−7.09017	+	12.2805i	−0.262419	+	0.454523i
$731$	−0.0853804	+	0.0716427i	−0.00315791	+	0.00264980i
$732$	1.85108	−	1.55324i	0.0684177	−	0.0574093i
$733$	26.4787	−	45.8625i	0.978014	−	1.69397i	0.308405	−	0.951255i	$-0.400205\pi$
$733$	26.4787	−	45.8625i	0.978014	−	1.69397i	0.669609	−	0.742714i	$-0.266462\pi$
$734$	−12.8992	−	22.3420i	−0.476118	−	0.824660i
$735$	2.32305	+	0.845520i	0.0856869	+	0.0311875i
$736$	3.16068	−	17.9251i	0.116504	−	0.660728i
$737$	−1.96678	−	11.1542i	−0.0724473	−	0.410869i
$738$	−13.0186	+	4.73838i	−0.479221	+	0.174422i
$739$	−19.1511	−	16.0697i	−0.704485	−	0.591133i	0.218561	−	0.975823i	$-0.429864\pi$
$739$	−19.1511	−	16.0697i	−0.704485	−	0.591133i	−0.923046	+	0.384690i	$0.874308\pi$
$740$	−17.7082			−0.650967
$741$		0			0
$742$	−30.7082			−1.12733
$743$	2.57443	+	2.16020i	0.0944467	+	0.0792502i	0.688788	−	0.724962i	$-0.258143\pi$
$743$	2.57443	+	2.16020i	0.0944467	+	0.0792502i	−0.594342	+	0.804213i	$0.702587\pi$
$744$	7.10624	−	2.58646i	0.260528	−	0.0948243i
$745$	−1.07320	−	6.08645i	−0.0393192	−	0.222990i
$746$	−1.53750	+	8.71959i	−0.0562918	+	0.319247i
$747$	22.7221	+	8.27016i	0.831358	+	0.302589i
$748$	0.381966	+	0.661585i	0.0139661	+	0.0241899i
$749$	24.6246	−	42.6511i	0.899764	−	1.55844i
$750$	0.723354	−	0.606966i	0.0264132	−	0.0221633i
$751$	13.1345	−	11.0212i	0.479285	−	0.402168i	−0.370883	−	0.928680i	$-0.620945\pi$
$751$	13.1345	−	11.0212i	0.479285	−	0.402168i	0.850168	+	0.526512i	$0.176500\pi$
$752$	7.28115	−	12.6113i	0.265516	−	0.459888i
$753$	−4.84346	−	8.38912i	−0.176505	−	0.305716i
$754$	5.50106	+	2.00222i	0.200337	+	0.0729166i
$755$	11.8514	−	67.2124i	0.431315	−	2.44611i
$756$	0.719928	+	4.08291i	0.0261835	+	0.148494i
$757$	−25.1299	+	9.14652i	−0.913361	+	0.332436i	−0.755594	−	0.655040i	$-0.772652\pi$
$757$	−25.1299	+	9.14652i	−0.913361	+	0.332436i	−0.157767	+	0.987476i	$0.550429\pi$
$758$	−18.7467	−	15.7304i	−0.680912	−	0.571353i
$759$	3.32624			0.120735
$760$		0			0
$761$	4.88854			0.177210			0.0886048	−	0.996067i	$-0.471759\pi$
$761$	4.88854			0.177210			0.0886048	+	0.996067i	$0.471759\pi$
$762$	−2.72888	−	2.28981i	−0.0988571	−	0.0829509i
$763$	−9.27983	+	3.37758i	−0.335952	+	0.122277i
$764$	1.52782	+	8.66471i	0.0552746	+	0.313478i
$765$	−1.22521	+	6.94854i	−0.0442977	+	0.251225i
$766$	−0.580762	−	0.211380i	−0.0209838	−	0.00763747i
$767$	0.163119	+	0.282530i	0.00588988	+	0.0102016i
$768$	2.59017	−	4.48631i	0.0934647	−	0.161886i
$769$	28.0611	−	23.5461i	1.01191	−	0.849093i	0.0233204	−	0.999728i	$-0.492576\pi$
$769$	28.0611	−	23.5461i	1.01191	−	0.849093i	0.988589	+	0.150635i	$0.0481318\pi$
$770$	19.4701	−	16.3374i	0.701654	−	0.588757i
$771$	−3.88854	+	6.73516i	−0.140042	+	0.242561i
$772$	1.56231	+	2.70599i	0.0562286	+	0.0973908i
$773$	−33.7566	−	12.2864i	−1.21414	−	0.441911i	−0.346002	−	0.938234i	$-0.612461\pi$
$773$	−33.7566	−	12.2864i	−1.21414	−	0.441911i	−0.868138	+	0.496323i	$0.834683\pi$
$774$	−0.116998	+	0.663526i	−0.00420539	+	0.0238500i
$775$	8.41340	+	47.7148i	0.302218	+	1.71397i
$776$	29.1105	−	10.5953i	1.04500	−	0.380351i
$777$	7.77221	+	6.52166i	0.278826	+	0.233963i
$778$	−15.0000			−0.537776
$779$		0			0
$780$	−0.763932			−0.0273532
$781$	−9.26161	−	7.77141i	−0.331406	−	0.278083i
$782$	6.25128	−	2.27528i	0.223545	−	0.0813639i
$783$	1.40484	+	7.96726i	0.0502050	+	0.284727i
$784$	−1.68581	+	9.56071i	−0.0602076	+	0.341454i
$785$	54.2927	+	19.7609i	1.93779	+	0.705298i
$786$	−4.66312	−	8.07676i	−0.166328	−	0.288088i
$787$	19.0000	−	32.9090i	0.677277	−	1.17308i	−0.298521	−	0.954403i	$-0.596493\pi$
$787$	19.0000	−	32.9090i	0.677277	−	1.17308i	0.975798	−	0.218675i	$-0.0701734\pi$
$788$	1.42032	−	1.19179i	0.0505970	−	0.0424559i
$789$	4.37274	−	3.66916i	0.155674	−	0.130626i
$790$	−35.1246	+	60.8376i	−1.24968	+	2.16451i
$791$	10.1459	+	17.5732i	0.360747	+	0.624831i
$792$	−9.70349	−	3.53178i	−0.344798	−	0.125496i
$793$	−1.77747	+	10.0806i	−0.0631200	+	0.357971i
$794$	3.22331	+	18.2803i	0.114391	+	0.648744i
$795$	7.34808	−	2.67448i	0.260609	−	0.0948541i
$796$	−6.35188	−	5.32986i	−0.225137	−	0.188912i
$797$	20.2918			0.718772			0.359386	−	0.933189i	$-0.382986\pi$
$797$	20.2918			0.718772			0.359386	+	0.933189i	$0.382986\pi$
$798$		0			0
$799$	2.29180			0.0810779
$800$	14.1769	+	11.8958i	0.501228	+	0.420580i
$801$	20.8227	−	7.57884i	0.735734	−	0.267785i
$802$	−10.0836	−	57.1867i	−0.356063	−	2.01933i
$803$	0.760920	−	4.31539i	0.0268523	−	0.152287i
$804$	1.55282	+	0.565180i	0.0547637	+	0.0199324i
$805$	−26.1246	−	45.2492i	−0.920772	−	1.59482i
$806$	7.16312	−	12.4069i	0.252310	−	0.437014i
$807$	8.87355	−	7.44579i	0.312364	−	0.262104i
$808$	−15.7253	+	13.1951i	−0.553213	+	0.464200i
$809$	12.3992	−	21.4760i	0.435932	−	0.755057i	−0.561439	−	0.827518i	$-0.689752\pi$
$809$	12.3992	−	21.4760i	0.435932	−	0.755057i	0.997371	+	0.0724614i	$0.0230854\pi$
$810$	20.1803	+	34.9534i	0.709065	+	1.22814i
$811$	21.5929	+	7.85918i	0.758230	+	0.275973i	0.692065	−	0.721835i	$-0.256701\pi$
$811$	21.5929	+	7.85918i	0.758230	+	0.275973i	0.0661655	+	0.997809i	$0.478923\pi$
$812$	1.16487	−	6.60629i	0.0408788	−	0.231835i
$813$	−0.0760048	−	0.431045i	−0.00266560	−	0.0151174i
$814$	21.7824	−	7.92814i	0.763473	−	0.277881i
$815$	4.37274	+	3.66916i	0.153170	+	0.128525i
$816$	1.41641			0.0495842
$817$		0			0
$818$	−13.4164			−0.469094
$819$	−6.55911	−	5.50374i	−0.229194	−	0.192316i
$820$	−5.63816	+	2.05212i	−0.196893	+	0.0716632i
$821$	9.03797	+	51.2569i	0.315427	+	1.78888i	0.569813	+	0.821774i	$0.307016\pi$
$821$	9.03797	+	51.2569i	0.315427	+	1.78888i	−0.254386	+	0.967103i	$0.581873\pi$
$822$	0.801913	−	4.54788i	0.0279699	−	0.158625i
$823$	24.0531	+	8.75460i	0.838437	+	0.305166i	0.725317	−	0.688415i	$-0.241693\pi$
$823$	24.0531	+	8.75460i	0.838437	+	0.305166i	0.113120	+	0.993581i	$0.463915\pi$
$824$	16.0172	+	27.7426i	0.557986	+	0.966461i
$825$	−1.69098	+	2.92887i	−0.0588725	+	0.101970i
$826$	1.21310	−	1.01791i	0.0422092	−	0.0354177i
$827$	−24.9706	+	20.9528i	−0.868311	+	0.728600i	−0.963742	−	0.266836i	$-0.914022\pi$
$827$	−24.9706	+	20.9528i	−0.868311	+	0.728600i	0.0954305	+	0.995436i	$0.469577\pi$
$828$	4.74671	−	8.22154i	0.164960	−	0.285718i
$829$	2.33688	+	4.04760i	0.0811632	+	0.140579i	0.903750	−	0.428061i	$-0.140803\pi$
$829$	2.33688	+	4.04760i	0.0811632	+	0.140579i	−0.822587	+	0.568640i	$0.807470\pi$
$830$	41.6854	+	15.1722i	1.44692	+	0.526636i
$831$	−0.757224	+	4.29443i	−0.0262678	+	0.148972i
$832$	0.735585	+	4.17171i	0.0255018	+	0.144628i
$833$	−1.43572	+	0.522560i	−0.0497448	+	0.0181056i
$834$	7.00616	+	5.87887i	0.242604	+	0.203569i
$835$	−65.4853			−2.26621
$836$		0			0
$837$	19.7984			0.684332
$838$	11.0863	+	9.30251i	0.382970	+	0.321350i
$839$	14.2849	−	5.19926i	0.493168	−	0.179498i	−0.0834506	−	0.996512i	$-0.526594\pi$
$839$	14.2849	−	5.19926i	0.493168	−	0.179498i	0.576619	+	0.817013i	$0.304372\pi$
$840$	−1.43986	−	8.16583i	−0.0496797	−	0.281748i
$841$	−2.76271	+	15.6681i	−0.0952660	+	0.540280i
$842$	41.7701	+	15.2031i	1.43949	+	0.523933i
$843$	5.63525	+	9.76055i	0.194088	+	0.336171i
$844$	−1.19098	+	2.06284i	−0.0409953	+	0.0710060i
$845$	−29.7477	+	24.9613i	−1.02335	+	0.858693i
$846$	10.6129	−	8.90525i	0.364878	−	0.306169i
$847$	12.5729	−	21.7770i	0.432012	−	0.748266i
$848$	15.3541	+	26.5941i	0.527262	+	0.913245i
$849$	9.34456	+	3.40114i	0.320704	+	0.116727i
$850$	−1.17454	+	6.66117i	−0.0402865	+	0.228476i
$851$	−8.27477	−	46.9285i	−0.283655	−	1.60869i
$852$	1.65755	−	0.603300i	0.0567869	−	0.0206687i
$853$	23.5238	+	19.7389i	0.805441	+	0.675845i	0.949515	−	0.313721i	$-0.101576\pi$
$853$	23.5238	+	19.7389i	0.805441	+	0.675845i	−0.144074	+	0.989567i	$0.546020\pi$
$854$	49.6869			1.70025
$855$		0			0
$856$	−36.7082			−1.25466
$857$	8.13389	+	6.82514i	0.277848	+	0.233142i	0.771053	−	0.636771i	$-0.219730\pi$
$857$	8.13389	+	6.82514i	0.277848	+	0.233142i	−0.493205	+	0.869913i	$0.664175\pi$
$858$	0.939693	−	0.342020i	0.0320806	−	0.0116764i
$859$	−8.42906	−	47.8036i	−0.287596	−	1.63104i	−0.695863	−	0.718174i	$-0.744978\pi$
$859$	−8.42906	−	47.8036i	−0.287596	−	1.63104i	0.408267	−	0.912862i	$-0.366133\pi$
$860$	−0.0506699	+	0.287363i	−0.00172783	+	0.00979900i
$861$	3.23038	+	1.17576i	0.110091	+	0.0400698i
$862$	−22.3713	−	38.7483i	−0.761970	−	1.31977i
$863$	−13.5279	+	23.4309i	−0.460494	+	0.797599i	−0.998986	−	0.0450321i	$-0.985661\pi$
$863$	−13.5279	+	23.4309i	−0.460494	+	0.797599i	0.538492	+	0.842631i	$0.318994\pi$
$864$	5.79306	−	4.86096i	0.197084	−	0.165373i
$865$	1.17041	−	0.982092i	0.0397952	−	0.0333921i
$866$	2.78115	−	4.81710i	0.0945074	−	0.163692i
$867$	−3.13525	−	5.43042i	−0.106479	−	0.184427i
$868$	−15.4264	−	5.61474i	−0.523605	−	0.190577i
$869$	3.76959	−	21.3784i	0.127875	−	0.725213i
$870$	1.25653	+	7.12614i	0.0426004	+	0.241599i
$871$	−6.57785	+	2.39414i	−0.222882	+	0.0811224i
$872$	5.63861	+	4.73135i	0.190947	+	0.160224i
$873$	39.5410			1.33826
$874$		0			0
$875$	4.58359			0.154954
$876$	0.489748	+	0.410947i	0.0165470	+	0.0138846i
$877$	11.1068	−	4.04256i	0.375052	−	0.136508i	−0.147615	−	0.989045i	$-0.547160\pi$
$877$	11.1068	−	4.04256i	0.375052	−	0.136508i	0.522666	+	0.852537i	$0.324937\pi$
$878$	−9.72060	−	55.1283i	−0.328054	−	1.86049i
$879$	−0.672954	+	3.81651i	−0.0226982	+	0.128728i
$880$	−23.8836	−	8.69292i	−0.805116	−	0.293038i
$881$	−16.2254	−	28.1033i	−0.546648	−	0.946823i	−0.998501	−	0.0547303i	$-0.982570\pi$
$881$	−16.2254	−	28.1033i	−0.546648	−	0.946823i	0.451853	−	0.892093i	$-0.350763\pi$
$882$	−4.61803	+	7.99867i	−0.155497	+	0.269329i
$883$	−39.0093	+	32.7327i	−1.31277	+	1.10154i	−0.324981	+	0.945720i	$0.605358\pi$
$883$	−39.0093	+	32.7327i	−1.31277	+	1.10154i	−0.987785	+	0.155821i	$0.950198\pi$
$884$	0.361677	−	0.303483i	0.0121645	−	0.0102072i
$885$	−0.201626	+	0.349227i	−0.00677759	+	0.0117391i
$886$	−6.13525	−	10.6266i	−0.206118	−	0.357007i
$887$	25.6983	+	9.35340i	0.862863	+	0.314057i	0.735274	−	0.677770i	$-0.237054\pi$
$887$	25.6983	+	9.35340i	0.862863	+	0.314057i	0.127590	+	0.991827i	$0.459276\pi$
$888$	1.31318	−	7.44742i	0.0440675	−	0.249919i
$889$	−3.00269	−	17.0291i	−0.100707	−	0.571138i
$890$	38.2008	−	13.9040i	1.28049	−	0.466062i
$891$	−9.55421	−	8.01693i	−0.320078	−	0.268577i
$892$	7.20163			0.241128
$893$		0			0
$894$	−1.18034			−0.0394765
$895$	−30.3329	−	25.4523i	−1.01392	−	0.850777i
$896$	38.3903	−	13.9729i	1.28253	−	0.466803i
$897$	−0.356973	−	2.02450i	−0.0119190	−	0.0675960i
$898$	0.811590	−	4.60276i	0.0270831	−	0.153596i
$899$	−30.1025	−	10.9564i	−1.00398	−	0.365417i
$900$	4.82624	+	8.35929i	0.160875	+	0.278643i
$901$	−2.41641	+	4.18534i	−0.0805022	+	0.139434i
$902$	6.01659	−	5.04852i	0.200331	−	0.168097i
$903$	0.128071	−	0.107464i	0.00426192	−	0.00357618i
$904$	7.56231	−	13.0983i	0.251519	−	0.435643i
$905$	19.4164	+	33.6302i	0.645423	+	1.11791i
$906$	−12.2484	−	4.45804i	−0.406925	−	0.148109i
$907$	4.59684	−	26.0700i	0.152636	−	0.865639i	−0.808280	−	0.588798i	$-0.799601\pi$
$907$	4.59684	−	26.0700i	0.152636	−	0.865639i	0.960916	−	0.276841i	$-0.0892875\pi$
$908$	−1.76182	−	9.99176i	−0.0584679	−	0.331588i
$909$	−24.6215	+	8.96148i	−0.816643	+	0.297234i
$910$	−12.0332	−	10.0970i	−0.398896	−	0.334714i
$911$	−3.38197			−0.112050			−0.0560248	−	0.998429i	$-0.517843\pi$
$911$	−3.38197			−0.112050			−0.0560248	+	0.998429i	$0.517843\pi$
$912$		0			0
$913$	−13.7082			−0.453675
$914$	−24.4280	−	20.4976i	−0.808008	−	0.677999i
$915$	−11.8894	+	4.32740i	−0.393053	+	0.143059i
$916$	−1.46149	−	8.28854i	−0.0482891	−	0.273861i
$917$	7.86114	−	44.5827i	0.259598	−	1.47225i
$918$	2.59725	+	0.945320i	0.0857219	+	0.0312002i
$919$	−11.6459	−	20.1713i	−0.384163	−	0.665389i	0.607490	−	0.794327i	$-0.292177\pi$
$919$	−11.6459	−	20.1713i	−0.384163	−	0.665389i	−0.991653	+	0.128938i	$0.958843\pi$
$920$	−19.4721	+	33.7267i	−0.641977	+	1.11194i
$921$	−5.06971	+	4.25399i	−0.167053	+	0.140174i
$922$	−25.9601	+	21.7831i	−0.854951	+	0.717389i
$923$	−3.73607	+	6.47106i	−0.122974	+	0.212998i
$924$	−0.572949	−	0.992377i	−0.0188486	−	0.0326468i
$925$	45.5289	+	16.5712i	1.49698	+	0.544857i
$926$	−7.94313	+	45.0477i	−0.261027	+	1.48036i
$927$	7.10022	+	40.2674i	0.233202	+	1.32255i
$928$	−11.4981	+	4.18498i	−0.377445	+	0.137379i
$929$	12.5493	+	10.5301i	0.411730	+	0.345482i	0.825007	−	0.565123i	$-0.191171\pi$
$929$	12.5493	+	10.5301i	0.411730	+	0.345482i	−0.413277	+	0.910605i	$0.635616\pi$
$930$	17.7082			0.580675
$931$		0			0
$932$	2.79837			0.0916638
$933$	−3.70215	−	3.10647i	−0.121203	−	0.101701i
$934$	−24.2425	+	8.82356i	−0.793240	+	0.288716i
$935$	−0.694593	−	3.93923i	−0.0227156	−	0.128827i
$936$	−1.10822	+	6.28501i	−0.0362232	+	0.205432i
$937$	−38.1161	−	13.8731i	−1.24520	−	0.453215i	−0.366422	−	0.930449i	$-0.619417\pi$
$937$	−38.1161	−	13.8731i	−1.24520	−	0.453215i	−0.878777	+	0.477233i	$0.841640\pi$
$938$	16.9894	+	29.4264i	0.554722	+	0.960807i
$939$	−2.16312	+	3.74663i	−0.0705907	+	0.122267i
$940$	4.59627	−	3.85673i	0.149914	−	0.125793i
$941$	8.18665	−	6.86942i	0.266877	−	0.223937i	−0.499522	−	0.866301i	$-0.666491\pi$
$941$	8.18665	−	6.86942i	0.266877	−	0.223937i	0.766399	+	0.642365i	$0.222047\pi$
$942$	5.51722	−	9.55611i	0.179761	−	0.311355i
$943$	−8.07295	−	13.9828i	−0.262891	−	0.455341i
$944$	−1.48809	−	0.541620i	−0.0484332	−	0.0176282i
$945$	3.76959	−	21.3784i	0.122625	−	0.695440i
$946$	−0.0663277	−	0.376163i	−0.00215650	−	0.0122301i
$947$	30.6833	−	11.1678i	0.997073	−	0.362905i	0.208618	−	0.977997i	$-0.433104\pi$
$947$	30.6833	−	11.1678i	0.997073	−	0.362905i	0.788455	+	0.615092i	$0.210881\pi$
$948$	2.42620	+	2.03583i	0.0787994	+	0.0661206i
$949$	−2.70820			−0.0879120
$950$		0			0
$951$	6.87539			0.222950
$952$	3.92568	+	3.29404i	0.127232	+	0.106760i
$953$	16.2490	−	5.91414i	0.526356	−	0.191578i	−0.0651546	−	0.997875i	$-0.520754\pi$
$953$	16.2490	−	5.91414i	0.526356	−	0.191578i	0.591510	+	0.806297i	$0.298532\pi$
$954$	5.07309	+	28.7709i	0.164247	+	0.931494i
$955$	7.99978	−	45.3690i	0.258867	−	1.46811i
$956$	0.189467	+	0.0689602i	0.00612779	+	0.00223033i
$957$	−1.11803	−	1.93649i	−0.0361409	−	0.0625979i
$958$	18.6803	−	32.3553i	0.603534	−	1.04535i
$959$	17.1720	−	14.4090i	0.554512	−	0.465291i
$960$	−4.01106	+	3.36568i	−0.129456	+	0.108627i
$961$	−23.6976	+	41.0454i	−0.764437	+	1.32404i
$962$	−7.16312	−	12.4069i	−0.230948	−	0.400014i
$963$	−44.0285	−	16.0250i	−1.41880	−	0.516400i
$964$	−0.341316	+	1.93570i	−0.0109930	+	0.0623446i
$965$	−2.84100	−	16.1121i	−0.0914551	−	0.518668i
$966$	−9.37692	+	3.41292i	−0.301698	+	0.109809i
$967$	5.01071	+	4.20449i	0.161134	+	0.135207i	0.719790	−	0.694192i	$-0.244238\pi$
$967$	5.01071	+	4.20449i	0.161134	+	0.135207i	−0.558656	+	0.829400i	$0.688683\pi$
$968$	−18.7426			−0.602411
$969$		0			0
$970$	72.5410			2.32915
$971$	−18.0071	−	15.1097i	−0.577875	−	0.484895i	0.306374	−	0.951911i	$-0.400884\pi$
$971$	−18.0071	−	15.1097i	−0.577875	−	0.484895i	−0.884248	+	0.467017i	$0.845329\pi$
$972$	5.60579	−	2.04034i	0.179806	−	0.0654440i
$973$	7.70913	+	43.7207i	0.247143	+	1.40162i
$974$	1.17454	−	6.66117i	0.0376348	−	0.213438i
$975$	1.96412	+	0.714880i	0.0629021	+	0.0228945i
$976$	−24.8435	−	43.0301i	−0.795220	−	1.37736i
$977$	5.31966	−	9.21392i	0.170191	−	0.294779i	−0.768296	−	0.640095i	$-0.778895\pi$
$977$	5.31966	−	9.21392i	0.170191	−	0.294779i	0.938487	+	0.345316i	$0.112228\pi$
$978$	0.835119	−	0.700748i	0.0267041	−	0.0224074i
$979$	−9.62328	+	8.07489i	−0.307562	+	0.258075i
$980$	−2.00000	+	3.46410i	−0.0638877	+	0.110657i
$981$	4.69756	+	8.13641i	0.149982	+	0.259776i
$982$	−32.2561	−	11.7403i	−1.02933	−	0.374647i
$983$	−5.66406	+	32.1225i	−0.180656	+	1.02455i	0.750756	+	0.660580i	$0.229690\pi$
$983$	−5.66406	+	32.1225i	−0.180656	+	1.02455i	−0.931411	+	0.363968i	$0.881422\pi$
$984$	−0.444940	−	2.52338i	−0.0141842	−	0.0804424i
$985$	−9.12273	+	3.32040i	−0.290674	+	0.105797i
$986$	−3.42585	−	2.87463i	−0.109101	−	0.0915470i
$987$	−3.43769			−0.109423
$988$		0			0
$989$	−0.785218			−0.0249685
$990$	−18.5232	−	15.5428i	−0.588706	−	0.493983i
$991$	7.00151	−	2.54834i	0.222410	−	0.0809507i	−0.228412	−	0.973565i	$-0.573353\pi$
$991$	7.00151	−	2.54834i	0.222410	−	0.0809507i	0.450822	+	0.892614i	$0.351131\pi$
$992$	5.19977	+	29.4894i	0.165093	+	0.936288i
$993$	0.725908	−	4.11683i	0.0230360	−	0.130644i
$994$	34.0831	+	12.4052i	1.08105	+	0.393470i
$995$	21.7082	+	37.5997i	0.688196	+	1.19199i
$996$	1.00000	−	1.73205i	0.0316862	−	0.0548821i
$997$	30.4182	−	25.5239i	0.963356	−	0.808351i	−0.0181401	−	0.999835i	$-0.505774\pi$
$997$	30.4182	−	25.5239i	0.963356	−	0.808351i	0.981496	+	0.191484i	$0.0613300\pi$
$998$	−31.1416	+	26.1309i	−0.985770	+	0.827159i
$999$	9.89919	−	17.1459i	0.313196	−	0.542472i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	361.2.e.i.54.1		12
19.2	odd	18		361.2.c.d.292.1		4
19.3	odd	18		361.2.c.d.68.1		4
19.4	even	9	inner	361.2.e.i.28.1		12
19.5	even	9		361.2.a.c.1.1	✓	2
19.6	even	9	inner	361.2.e.i.234.1		12
19.7	even	3	inner	361.2.e.i.62.2		12
19.8	odd	6		361.2.e.j.245.2		12
19.9	even	9	inner	361.2.e.i.99.2		12
19.10	odd	18		361.2.e.j.99.1		12
19.11	even	3	inner	361.2.e.i.245.1		12
19.12	odd	6		361.2.e.j.62.1		12
19.13	odd	18		361.2.e.j.234.2		12
19.14	odd	18		361.2.a.f.1.2	yes	2
19.15	odd	18		361.2.e.j.28.2		12
19.16	even	9		361.2.c.g.68.2		4
19.17	even	9		361.2.c.g.292.2		4
19.18	odd	2		361.2.e.j.54.2		12
57.5	odd	18		3249.2.a.o.1.2		2
57.14	even	18		3249.2.a.i.1.1		2
76.43	odd	18		5776.2.a.bg.1.1		2
76.71	even	18		5776.2.a.s.1.2		2
95.14	odd	18		9025.2.a.n.1.1		2
95.24	even	18		9025.2.a.s.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
361.2.a.c.1.1	✓	2	19.5	even	9
361.2.a.f.1.2	yes	2	19.14	odd	18
361.2.c.d.68.1		4	19.3	odd	18
361.2.c.d.292.1		4	19.2	odd	18
361.2.c.g.68.2		4	19.16	even	9
361.2.c.g.292.2		4	19.17	even	9
361.2.e.i.28.1		12	19.4	even	9	inner
361.2.e.i.54.1		12	1.1	even	1	trivial
361.2.e.i.62.2		12	19.7	even	3	inner
361.2.e.i.99.2		12	19.9	even	9	inner
361.2.e.i.234.1		12	19.6	even	9	inner
361.2.e.i.245.1		12	19.11	even	3	inner
361.2.e.j.28.2		12	19.15	odd	18
361.2.e.j.54.2		12	19.18	odd	2
361.2.e.j.62.1		12	19.12	odd	6
361.2.e.j.99.1		12	19.10	odd	18
361.2.e.j.234.2		12	19.13	odd	18
361.2.e.j.245.2		12	19.8	odd	6
3249.2.a.i.1.1		2	57.14	even	18
3249.2.a.o.1.2		2	57.5	odd	18
5776.2.a.s.1.2		2	76.71	even	18
5776.2.a.bg.1.1		2	76.43	odd	18
9025.2.a.n.1.1		2	95.14	odd	18
9025.2.a.s.1.2		2	95.24	even	18

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:	\( N \)	\(=\)	\( 361 = 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	361.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.23949 - 1.04005i) q^{2} +(0.358931 - 0.130640i) q^{3} +(0.107320 + 0.608645i) q^{4} +(0.561937 - 3.18690i) q^{5} +(-0.580762 - 0.211380i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-2.18637 + 1.83458i) q^{9} +O(q^{10})\)	\(q+(-1.23949 - 1.04005i) q^{2} +(0.358931 - 0.130640i) q^{3} +(0.107320 + 0.608645i) q^{4} +(0.561937 - 3.18690i) q^{5} +(-0.580762 - 0.211380i) q^{6} +(-1.50000 - 2.59808i) q^{7} +(-1.11803 + 1.93649i) q^{8} +(-2.18637 + 1.83458i) q^{9} +(-4.01106 + 3.36568i) q^{10} +(0.809017 - 1.40126i) q^{11} +(0.118034 + 0.204441i) q^{12} +(-0.939693 - 0.342020i) q^{13} +(-0.842906 + 4.78036i) q^{14} +(-0.214641 - 1.21729i) q^{15} +(4.56136 - 1.66020i) q^{16} +(0.585206 + 0.491046i) q^{17} +4.61803 q^{18} +2.00000 q^{20} +(-0.877809 - 0.736569i) q^{21} +(-2.46015 + 0.895420i) q^{22} +(0.934569 + 5.30020i) q^{23} +(-0.148313 + 0.841126i) q^{24} +(-5.14213 - 1.87158i) q^{25} +(0.809017 + 1.40126i) q^{26} +(-1.11803 + 1.93649i) q^{27} +(1.42032 - 1.19179i) q^{28} +(2.77157 - 2.32563i) q^{29} +(-1.00000 + 1.73205i) q^{30} +(-4.42705 - 7.66788i) q^{31} +(-3.17801 - 1.15670i) q^{32} +(0.107320 - 0.608645i) q^{33} +(-0.214641 - 1.21729i) q^{34} +(-9.12273 + 3.32040i) q^{35} +(-1.35125 - 1.13383i) q^{36} -8.85410 q^{37} -0.381966 q^{39} +(5.54315 + 4.65125i) q^{40} +(-2.81908 + 1.02606i) q^{41} +(0.321961 + 1.82593i) q^{42} +(-0.0253349 + 0.143682i) q^{43} +(0.939693 + 0.342020i) q^{44} +(4.61803 + 7.99867i) q^{45} +(4.35410 - 7.54153i) q^{46} +(2.29813 - 1.92836i) q^{47} +(1.42032 - 1.19179i) q^{48} +(-1.00000 + 1.73205i) q^{49} +(4.42705 + 7.66788i) q^{50} +(0.274199 + 0.0998001i) q^{51} +(0.107320 - 0.608645i) q^{52} +(1.09854 + 6.23013i) q^{53} +(3.39984 - 1.23744i) q^{54} +(-4.01106 - 3.36568i) q^{55} +6.70820 q^{56} -5.85410 q^{58} +(-0.249913 - 0.209702i) q^{59} +(0.717861 - 0.261280i) q^{60} +(-1.77747 - 10.0806i) q^{61} +(-2.48773 + 14.1086i) q^{62} +(8.04594 + 2.92848i) q^{63} +(-2.11803 - 3.66854i) q^{64} +(-1.61803 + 2.80252i) q^{65} +(-0.766044 + 0.642788i) q^{66} +(5.36231 - 4.49951i) q^{67} +(-0.236068 + 0.408882i) q^{68} +(1.02786 + 1.78031i) q^{69} +(14.7609 + 5.37252i) q^{70} +(1.29752 - 7.35862i) q^{71} +(-1.10822 - 6.28501i) q^{72} +(2.54488 - 0.926260i) q^{73} +(10.9745 + 9.20873i) q^{74} -2.09017 q^{75} -4.85410 q^{77} +(0.473442 + 0.397265i) q^{78} +(12.6073 - 4.58868i) q^{79} +(-2.72770 - 15.4696i) q^{80} +(1.33852 - 7.59110i) q^{81} +(4.56136 + 1.66020i) q^{82} +(-4.23607 - 7.33708i) q^{83} +(0.354102 - 0.613323i) q^{84} +(1.89377 - 1.58906i) q^{85} +(0.180839 - 0.151742i) q^{86} +(0.690983 - 1.19682i) q^{87} +(1.80902 + 3.13331i) q^{88} +(-7.29571 - 2.65542i) q^{89} +(2.59505 - 14.7172i) q^{90} +(0.520945 + 2.95442i) q^{91} +(-3.12564 + 1.13764i) q^{92} +(-2.59074 - 2.17389i) q^{93} -4.85410 q^{94} -1.29180 q^{96} +(-10.6129 - 8.90525i) q^{97} +(3.04091 - 1.10680i) q^{98} +(0.801913 + 4.54788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 18 q^{7}+O(q^{10}) \) 12 * q - 18 * q^7	\( 12 q - 18 q^{7} + 3 q^{11} - 12 q^{12} + 42 q^{18} + 24 q^{20} + 3 q^{26} - 12 q^{30} - 33 q^{31} - 66 q^{37} - 18 q^{39} + 42 q^{45} + 12 q^{46} - 12 q^{49} + 33 q^{50} - 30 q^{58} - 12 q^{64} - 6 q^{65} + 24 q^{68} + 66 q^{69} + 42 q^{75} - 18 q^{77} - 24 q^{83} - 36 q^{84} + 15 q^{87} + 15 q^{88} - 18 q^{94} - 96 q^{96}+O(q^{100}) \) 12 * q - 18 * q^7 + 3 * q^11 - 12 * q^12 + 42 * q^18 + 24 * q^20 + 3 * q^26 - 12 * q^30 - 33 * q^31 - 66 * q^37 - 18 * q^39 + 42 * q^45 + 12 * q^46 - 12 * q^49 + 33 * q^50 - 30 * q^58 - 12 * q^64 - 6 * q^65 + 24 * q^68 + 66 * q^69 + 42 * q^75 - 18 * q^77 - 24 * q^83 - 36 * q^84 + 15 * q^87 + 15 * q^88 - 18 * q^94 - 96 * q^96

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