LMFDB - Embedded newform 572.2.bn.a.283.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(95,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([15, 21, 5]))

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

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

chi := DirichletCharacter("572.95");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bn (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$640$
Relative dimension:	$80$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			283.24
Character	$\chi$	$=$	572.283
Dual form			572.2.bn.a.95.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.909706 - 1.08279i) q^{2} +(-1.01203 - 0.911240i) q^{3} +(-0.344870 + 1.97004i) q^{4} +(0.329599 - 0.453654i) q^{5} +(-0.0660280 + 1.92478i) q^{6} +(-0.622444 + 0.560451i) q^{7} +(2.44687 - 1.41874i) q^{8} +(-0.119730 - 1.13915i) q^{9} +O(q^{10})$	\(q+(-0.909706 - 1.08279i) q^{2} +(-1.01203 - 0.911240i) q^{3} +(-0.344870 + 1.97004i) q^{4} +(0.329599 - 0.453654i) q^{5} +(-0.0660280 + 1.92478i) q^{6} +(-0.622444 + 0.560451i) q^{7} +(2.44687 - 1.41874i) q^{8} +(-0.119730 - 1.13915i) q^{9} +(-0.791051 + 0.0558053i) q^{10} +(-3.27455 + 0.526616i) q^{11} +(2.14420 - 1.67949i) q^{12} +(0.844983 + 3.50514i) q^{13} +(1.17309 + 0.164131i) q^{14} +(-0.746954 + 0.158770i) q^{15} +(-3.76213 - 1.35882i) q^{16} +(-2.20978 - 4.96324i) q^{17} +(-1.12455 + 1.16594i) q^{18} +(-0.417349 + 1.96347i) q^{19} +(0.780049 + 0.805776i) q^{20} +1.14064 q^{21} +(3.54909 + 3.06659i) q^{22} +(-7.01090 + 4.04774i) q^{23} +(-3.76913 - 0.793877i) q^{24} +(1.44792 + 4.45623i) q^{25} +(3.02664 - 4.10359i) q^{26} +(-3.31826 + 4.56719i) q^{27} +(-0.889450 - 1.41952i) q^{28} +(0.378111 + 1.77887i) q^{29} +(0.851423 + 0.664360i) q^{30} +(4.78001 - 3.47288i) q^{31} +(1.95112 + 5.30972i) q^{32} +(3.79383 + 2.45095i) q^{33} +(-3.36390 + 6.90782i) q^{34} +(0.0490941 + 0.467099i) q^{35} +(2.28547 + 0.156987i) q^{36} +(-0.246286 - 1.15869i) q^{37} +(2.50569 - 1.33428i) q^{38} +(2.33887 - 4.31730i) q^{39} +(0.162871 - 1.57765i) q^{40} +(-5.15797 + 5.72850i) q^{41} +(-1.03765 - 1.23507i) q^{42} +(-3.10539 + 5.37869i) q^{43} +(0.0918385 - 6.63261i) q^{44} +(-0.556245 - 0.321148i) q^{45} +(10.7607 + 3.90908i) q^{46} +(0.292632 + 0.900628i) q^{47} +(2.56920 + 4.80337i) q^{48} +(-0.658368 + 6.26395i) q^{49} +(3.50799 - 5.62166i) q^{50} +(-2.28633 + 7.03661i) q^{51} +(-7.19668 + 0.455835i) q^{52} +(9.70361 - 7.05009i) q^{53} +(7.96394 - 0.561822i) q^{54} +(-0.840387 + 1.65909i) q^{55} +(-0.727909 + 2.25444i) q^{56} +(2.21156 - 1.60680i) q^{57} +(1.58218 - 2.02767i) q^{58} +(-0.0129921 - 0.0144292i) q^{59} +(-0.0551814 - 1.52629i) q^{60} +(4.96396 + 11.1492i) q^{61} +(-8.10881 - 2.01645i) q^{62} +(0.712965 + 0.641957i) q^{63} +(3.97437 - 6.94294i) q^{64} +(1.86863 + 0.771961i) q^{65} +(-0.797409 - 6.33756i) q^{66} +(-1.89884 - 3.28888i) q^{67} +(10.5399 - 2.64168i) q^{68} +(10.7837 + 2.29215i) q^{69} +(0.461109 - 0.478081i) q^{70} +(-8.93623 + 3.97867i) q^{71} +(-1.90912 - 2.61750i) q^{72} +(1.23344 - 3.79615i) q^{73} +(-1.03057 + 1.32074i) q^{74} +(2.59536 - 5.82926i) q^{75} +(-3.72419 - 1.49934i) q^{76} +(1.74308 - 2.16302i) q^{77} +(-6.80242 + 1.39497i) q^{78} +(3.38131 - 2.45667i) q^{79} +(-1.85643 + 1.25884i) q^{80} +(4.15880 - 0.883980i) q^{81} +(10.8950 + 0.373744i) q^{82} +(-1.83934 + 2.53163i) q^{83} +(-0.393373 + 2.24711i) q^{84} +(-2.97994 - 0.633405i) q^{85} +(8.64899 - 1.53054i) q^{86} +(1.23832 - 2.14483i) q^{87} +(-7.26528 + 5.93429i) q^{88} +(-6.41766 + 3.70524i) q^{89} +(0.158283 + 0.894447i) q^{90} +(-2.49042 - 1.70818i) q^{91} +(-5.55637 - 15.2077i) q^{92} +(-8.00217 - 0.841061i) q^{93} +(0.708982 - 1.13617i) q^{94} +(0.753179 + 0.836491i) q^{95} +(2.86383 - 7.15156i) q^{96} +(-18.1917 + 1.91202i) q^{97} +(7.38147 - 4.98548i) q^{98} +(0.991958 + 3.66716i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	$ 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) $ 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.909706	−	1.08279i	−0.643259	−	0.765648i
$2$	−0.909706	−	1.08279i	−0.643259	−	0.765648i
$3$	−1.01203	−	0.911240i	−0.584298	−	0.526105i	0.323106	−	0.946363i	$-0.395273\pi$
$3$	−1.01203	−	0.911240i	−0.584298	−	0.526105i	−0.907405	+	0.420258i	$0.861940\pi$
$4$	−0.344870	+	1.97004i	−0.172435	+	0.985021i
$5$	0.329599	−	0.453654i	0.147401	−	0.202880i	−0.728932	−	0.684587i	$-0.759983\pi$
$5$	0.329599	−	0.453654i	0.147401	−	0.202880i	0.876333	+	0.481706i	$0.159983\pi$
$6$	−0.0660280	+	1.92478i	−0.0269558	+	0.785789i
$7$	−0.622444	+	0.560451i	−0.235262	+	0.211831i	−0.778326	−	0.627861i	$-0.783931\pi$
$7$	−0.622444	+	0.560451i	−0.235262	+	0.211831i	0.543064	+	0.839691i	$0.317264\pi$
$8$	2.44687	−	1.41874i	0.865100	−	0.501599i
$9$	−0.119730	−	1.13915i	−0.0399100	−	0.379718i
$10$	−0.791051	+	0.0558053i	−0.250152	+	0.0176472i
$11$	−3.27455	+	0.526616i	−0.987314	+	0.158781i
$11$	−3.27455	+	0.526616i	−0.987314	+	0.158781i
$12$	2.14420	−	1.67949i	0.618977	−	0.484827i
$13$	0.844983	+	3.50514i	0.234356	+	0.972151i
$13$	0.844983	+	3.50514i	0.234356	+	0.972151i
$14$	1.17309	+	0.164131i	0.313522	+	0.0438658i
$15$	−0.746954	+	0.158770i	−0.192863	+	0.0409942i
$16$	−3.76213	−	1.35882i	−0.940532	−	0.339704i
$17$	−2.20978	−	4.96324i	−0.535950	−	1.20376i	−0.955219	−	0.295901i	$-0.904380\pi$
$17$	−2.20978	−	4.96324i	−0.535950	−	1.20376i	0.419269	−	0.907862i	$-0.362287\pi$
$18$	−1.12455	+	1.16594i	−0.265058	+	0.274814i
$19$	−0.417349	+	1.96347i	−0.0957463	+	0.450451i	0.903991	+	0.427551i	$0.140623\pi$
$19$	−0.417349	+	1.96347i	−0.0957463	+	0.450451i	−0.999738	+	0.0229005i	$0.992710\pi$
$20$	0.780049	+	0.805776i	0.174424	+	0.180177i
$21$	1.14064			0.248908
$22$	3.54909	+	3.06659i	0.756669	+	0.653798i
$23$	−7.01090	+	4.04774i	−1.46187	+	0.844013i	−0.999098	−	0.0424630i	$-0.986480\pi$
$23$	−7.01090	+	4.04774i	−1.46187	+	0.844013i	−0.462775	+	0.886476i	$0.653146\pi$
$24$	−3.76913	−	0.793877i	−0.769370	−	0.162050i
$25$	1.44792	+	4.45623i	0.289584	+	0.891247i
$26$	3.02664	−	4.10359i	0.593574	−	0.804779i
$27$	−3.31826	+	4.56719i	−0.638599	+	0.878956i
$28$	−0.889450	−	1.41952i	−0.168090	−	0.268265i
$29$	0.378111	+	1.77887i	0.0702135	+	0.330329i	0.999209	−	0.0397620i	$-0.0126600\pi$
$29$	0.378111	+	1.77887i	0.0702135	+	0.330329i	−0.928996	+	0.370091i	$0.879327\pi$
$30$	0.851423	+	0.664360i	0.155448	+	0.121295i
$31$	4.78001	−	3.47288i	0.858516	−	0.623748i	−0.0689651	−	0.997619i	$-0.521970\pi$
$31$	4.78001	−	3.47288i	0.858516	−	0.623748i	0.927481	+	0.373871i	$0.121970\pi$
$32$	1.95112	+	5.30972i	0.344912	+	0.938635i
$33$	3.79383	+	2.45095i	0.660421	+	0.426655i
$34$	−3.36390	+	6.90782i	−0.576905	+	1.18468i
$35$	0.0490941	+	0.467099i	0.00829841	+	0.0789541i
$36$	2.28547	+	0.156987i	0.380912	+	0.0261645i
$37$	−0.246286	−	1.15869i	−0.0404892	−	0.190487i	0.953255	−	0.302167i	$-0.0977101\pi$
$37$	−0.246286	−	1.15869i	−0.0404892	−	0.190487i	−0.993744	+	0.111680i	$0.964377\pi$
$38$	2.50569	−	1.33428i	0.406477	−	0.216449i
$39$	2.33887	−	4.31730i	0.374519	−	0.691322i
$40$	0.162871	−	1.57765i	0.0257522	−	0.249448i
$41$	−5.15797	+	5.72850i	−0.805539	+	0.894642i	−0.996207	−	0.0870128i	$-0.972268\pi$
$41$	−5.15797	+	5.72850i	−0.805539	+	0.894642i	0.190668	+	0.981655i	$0.438935\pi$
$42$	−1.03765	−	1.23507i	−0.160113	−	0.190576i
$43$	−3.10539	+	5.37869i	−0.473568	+	0.820243i	−0.999542	−	0.0302573i	$-0.990367\pi$
$43$	−3.10539	+	5.37869i	−0.473568	+	0.820243i	0.525975	+	0.850500i	$0.323701\pi$
$44$	0.0918385	−	6.63261i	0.0138452	−	0.999904i
$45$	−0.556245	−	0.321148i	−0.0829201	−	0.0478739i
$46$	10.7607	+	3.90908i	1.58658	+	0.576362i
$47$	0.292632	+	0.900628i	0.0426847	+	0.131370i	0.970128	−	0.242594i	$-0.0779983\pi$
$47$	0.292632	+	0.900628i	0.0426847	+	0.131370i	−0.927443	+	0.373964i	$0.877998\pi$
$48$	2.56920	+	4.80337i	0.370832	+	0.693307i
$49$	−0.658368	+	6.26395i	−0.0940526	+	0.894851i
$50$	3.50799	−	5.62166i	0.496104	−	0.795022i
$51$	−2.28633	+	7.03661i	−0.320151	+	0.985323i
$52$	−7.19668	+	0.455835i	−0.998000	+	0.0632129i
$53$	9.70361	−	7.05009i	1.33289	−	0.968404i	0.333220	−	0.942849i	$-0.391865\pi$
$53$	9.70361	−	7.05009i	1.33289	−	0.968404i	0.999673	−	0.0255546i	$-0.00813517\pi$
$54$	7.96394	−	0.561822i	1.08376	−	0.0764543i
$55$	−0.840387	+	1.65909i	−0.113318	+	0.223711i
$56$	−0.727909	+	2.25444i	−0.0972709	+	0.301262i
$57$	2.21156	−	1.60680i	0.292929	−	0.212825i
$58$	1.58218	−	2.02767i	0.207750	−	0.266246i
$59$	−0.0129921	−	0.0144292i	−0.00169142	−	0.00187852i	0.742299	−	0.670069i	$-0.233736\pi$
$59$	−0.0129921	−	0.0144292i	−0.00169142	−	0.00187852i	−0.743990	+	0.668191i	$0.767069\pi$
$60$	−0.0551814	−	1.52629i	−0.00712389	−	0.197043i
$61$	4.96396	+	11.1492i	0.635570	+	1.42751i	0.887975	+	0.459892i	$0.152112\pi$
$61$	4.96396	+	11.1492i	0.635570	+	1.42751i	−0.252405	+	0.967622i	$0.581221\pi$
$62$	−8.10881	−	2.01645i	−1.02982	−	0.256089i
$63$	0.712965	+	0.641957i	0.0898252	+	0.0808790i
$64$	3.97437	−	6.94294i	0.496796	−	0.867867i
$65$	1.86863	+	0.771961i	0.231775	+	0.0957500i
$66$	−0.797409	−	6.33756i	−0.0981542	−	0.780100i
$67$	−1.89884	−	3.28888i	−0.231980	−	0.401801i	0.726411	−	0.687261i	$-0.241187\pi$
$67$	−1.89884	−	3.28888i	−0.231980	−	0.401801i	−0.958391	+	0.285460i	$0.907854\pi$
$68$	10.5399	−	2.64168i	1.27815	−	0.320351i
$69$	10.7837	+	2.29215i	1.29821	+	0.275943i
$70$	0.461109	−	0.478081i	0.0551131	−	0.0571416i
$71$	−8.93623	+	3.97867i	−1.06054	+	0.472181i	−0.861472	−	0.507806i	$-0.830457\pi$
$71$	−8.93623	+	3.97867i	−1.06054	+	0.472181i	−0.199064	+	0.979987i	$0.563790\pi$
$72$	−1.90912	−	2.61750i	−0.224992	−	0.308475i
$73$	1.23344	−	3.79615i	0.144364	−	0.444306i	−0.852565	−	0.522621i	$-0.824954\pi$
$73$	1.23344	−	3.79615i	0.144364	−	0.444306i	0.996929	+	0.0783154i	$0.0249541\pi$
$74$	−1.03057	+	1.32074i	−0.119801	+	0.153533i
$75$	2.59536	−	5.82926i	0.299686	−	0.673105i
$76$	−3.72419	−	1.49934i	−0.427194	−	0.171986i
$77$	1.74308	−	2.16302i	0.198643	−	0.246498i
$78$	−6.80242	+	1.39497i	−0.770222	+	0.157949i
$79$	3.38131	−	2.45667i	0.380427	−	0.276396i	−0.381094	−	0.924536i	$-0.624453\pi$
$79$	3.38131	−	2.45667i	0.380427	−	0.276396i	0.761521	+	0.648140i	$0.224453\pi$
$80$	−1.85643	+	1.25884i	−0.207555	+	0.140743i
$81$	4.15880	−	0.883980i	0.462089	−	0.0982200i
$82$	10.8950	+	0.373744i	1.20315	+	0.0412731i
$83$	−1.83934	+	2.53163i	−0.201893	+	0.277882i	−0.897943	−	0.440111i	$-0.854939\pi$
$83$	−1.83934	+	2.53163i	−0.201893	+	0.277882i	0.696050	+	0.717993i	$0.254939\pi$
$84$	−0.393373	+	2.24711i	−0.0429205	+	0.245180i
$85$	−2.97994	−	0.633405i	−0.323220	−	0.0687025i
$86$	8.64899	−	1.53054i	0.932644	−	0.165043i
$87$	1.23832	−	2.14483i	0.132762	−	0.229950i
$88$	−7.26528	+	5.93429i	−0.774481	+	0.632597i
$89$	−6.41766	+	3.70524i	−0.680271	+	0.392754i	−0.799957	−	0.600057i	$-0.795144\pi$
$89$	−6.41766	+	3.70524i	−0.680271	+	0.392754i	0.119686	+	0.992812i	$0.461811\pi$
$90$	0.158283	+	0.894447i	0.0166845	+	0.0942830i
$91$	−2.49042	−	1.70818i	−0.261066	−	0.179066i
$92$	−5.55637	−	15.2077i	−0.579292	−	1.58551i
$93$	−8.00217	−	0.841061i	−0.829786	−	0.0872140i
$94$	0.708982	−	1.13617i	0.0731259	−	0.117186i
$95$	0.753179	+	0.836491i	0.0772746	+	0.0858221i
$96$	2.86383	−	7.15156i	0.292289	−	0.729903i
$97$	−18.1917	+	1.91202i	−1.84709	+	0.194137i	−0.962324	−	0.271906i	$-0.912346\pi$
$97$	−18.1917	+	1.91202i	−1.84709	+	0.194137i	−0.884762	+	0.466043i	$0.845679\pi$
$98$	7.38147	−	4.98548i	0.745641	−	0.503610i
$99$	0.991958	+	3.66716i	0.0996955	+	0.368564i
$100$	−9.27831	+	1.31564i	−0.927831	+	0.131564i
$101$	−1.62883	+	3.65841i	−0.162075	+	0.364026i	−0.976267	−	0.216569i	$-0.930513\pi$
$101$	−1.62883	+	3.65841i	−0.162075	+	0.364026i	0.814193	+	0.580595i	$0.197180\pi$
$102$	9.69907	−	3.92563i	0.960351	−	0.388695i
$103$	−19.1859	−	6.23386i	−1.89044	−	0.614241i	−0.979403	−	0.201913i	$-0.935284\pi$
$103$	−19.1859	−	6.23386i	−1.89044	−	0.614241i	−0.911036	−	0.412328i	$-0.864716\pi$
$104$	7.04044	+	7.37782i	0.690372	+	0.723455i
$105$	0.375954	−	0.517457i	0.0366894	−	0.0504986i
$106$	−16.4612	−	4.09347i	−1.59885	−	0.397593i
$107$	9.31538	−	10.3458i	0.900552	−	1.00016i	−0.0994349	−	0.995044i	$-0.531703\pi$
$107$	9.31538	−	10.3458i	0.900552	−	1.00016i	0.999987	−	0.00512028i	$-0.00162984\pi$
$108$	−7.85318	−	8.11219i	−0.755673	−	0.780596i
$109$	−14.6283			−1.40114			−0.700569	−	0.713585i	$-0.747070\pi$
$109$	−14.6283			−1.40114			−0.700569	+	0.713585i	$0.747070\pi$
$110$	2.56095	−	0.599317i	0.244177	−	0.0571427i
$111$	−0.806590	+	1.39706i	−0.0765582	+	0.132603i
$112$	3.10327	−	1.26270i	0.293231	−	0.119314i
$113$	−14.9047	−	3.16809i	−1.40211	−	0.298028i	−0.556067	−	0.831137i	$-0.687690\pi$
$113$	−14.9047	−	3.16809i	−1.40211	−	0.298028i	−0.846047	+	0.533109i	$0.821024\pi$
$114$	−3.75170	−	0.932949i	−0.351379	−	0.0873787i
$115$	−0.474510	+	4.51466i	−0.0442482	+	0.420994i
$116$	−3.63486	+	0.131415i	−0.337488	+	0.0122016i
$117$	3.89172	−	1.38224i	0.359790	−	0.127788i
$118$	−0.00380479	+	0.0271940i	−0.000350259	+	0.00250341i
$119$	4.15712	+	1.85087i	0.381083	+	0.169669i
$120$	−1.60245	+	1.44822i	−0.146283	+	0.132204i
$121$	10.4454	−	3.44886i	0.949577	−	0.313533i
$122$	7.55655	−	15.5175i	0.684137	−	1.40488i
$123$	10.4401	−	1.09730i	0.941350	−	0.0989399i
$124$	5.19324	+	10.6145i	0.466367	+	0.953212i
$125$	5.16534	+	1.67832i	0.462002	+	0.150113i
$126$	0.0465159	−	1.35598i	0.00414397	−	0.120801i
$127$	−1.17991	+	11.2261i	−0.104700	+	0.996156i	0.808459	+	0.588553i	$0.200302\pi$
$127$	−1.17991	+	11.2261i	−0.104700	+	0.996156i	−0.913159	+	0.407603i	$0.866365\pi$
$128$	−11.1333	+	2.01262i	−0.984050	+	0.177892i
$129$	8.04404	−	2.61367i	0.708238	−	0.230121i
$130$	−0.864030	−	2.72559i	−0.0757805	−	0.239050i
$131$	19.8413			1.73354			0.866770	−	0.498708i	$-0.166192\pi$
$131$	19.8413			1.73354			0.866770	+	0.498708i	$0.166192\pi$
$132$	−6.13685	+	6.62875i	−0.534144	+	0.576958i
$133$	−0.840654	−	1.45606i	−0.0728939	−	0.126256i
$134$	−1.83379	+	5.04796i	−0.158415	+	0.436077i
$135$	0.978230	+	3.01068i	0.0841927	+	0.259118i
$136$	−12.4486	−	9.00933i	−1.06746	−	0.772544i
$137$	−8.23334	−	18.4924i	−0.703422	−	1.57991i	−0.810552	−	0.585666i	$-0.800833\pi$
$137$	−8.23334	−	18.4924i	−0.703422	−	1.57991i	0.107131	−	0.994245i	$-0.465834\pi$
$138$	−7.32811	−	13.7617i	−0.623810	−	1.17147i
$139$	5.82074	+	6.46458i	0.493709	+	0.548319i	0.937579	−	0.347772i	$-0.113062\pi$
$139$	5.82074	+	6.46458i	0.493709	+	0.548319i	−0.443871	+	0.896091i	$0.646395\pi$
$140$	−0.937136	−	0.0643711i	−0.0792024	−	0.00544035i
$141$	0.524535	−	1.17812i	0.0441738	−	0.0992159i
$142$	12.4374	+	6.05665i	1.04372	+	0.508263i
$143$	−4.61280	−	11.0328i	−0.385742	−	0.922607i
$144$	−1.09746	+	4.44833i	−0.0914552	+	0.370695i
$145$	0.931619	+	0.414784i	0.0773668	+	0.0344459i
$146$	−5.23251	+	2.11782i	−0.433046	+	0.175272i
$147$	6.37426	−	5.73941i	0.525740	−	0.473378i
$148$	2.36760	−	0.0855982i	0.194615	−	0.00703613i
$149$	−3.67180	+	1.63479i	−0.300805	+	0.133927i	−0.551589	−	0.834116i	$-0.685978\pi$
$149$	−3.67180	+	1.63479i	−0.300805	+	0.133927i	0.250784	+	0.968043i	$0.419312\pi$
$150$	−8.67288	+	2.49269i	−0.708138	+	0.203527i
$151$	−8.00230	+	2.60010i	−0.651218	+	0.211593i	−0.615951	−	0.787785i	$-0.711228\pi$
$151$	−8.00230	+	2.60010i	−0.651218	+	0.211593i	−0.0352666	+	0.999378i	$0.511228\pi$
$152$	1.76445	+	5.39647i	0.143116	+	0.437712i
$153$	−5.38932	+	3.11153i	−0.435701	+	0.251552i
$154$	−3.92778	+	0.0803152i	−0.316510	+	0.00647198i
$155$		−	3.31313i		−	0.266117i
$156$	7.69866	+	6.09658i	0.616386	+	0.488117i
$157$	−0.138568	−	0.426468i	−0.0110589	−	0.0340358i	0.945375	−	0.325985i	$-0.105696\pi$
$157$	−0.138568	−	0.426468i	−0.0110589	−	0.0340358i	−0.956434	+	0.291950i	$0.905696\pi$
$158$	−5.73605	−	1.42641i	−0.456336	−	0.113479i
$159$	−16.2447	−	1.70739i	−1.28829	−	0.135405i
$160$	3.05187	+	0.864947i	0.241271	+	0.0683801i
$161$	2.09533	−	6.44876i	0.165135	−	0.508234i
$162$	−4.74045	−	3.69895i	−0.372445	−	0.290617i
$163$	−1.66335	−	15.8257i	−0.130283	−	1.23956i	−0.842923	−	0.538034i	$-0.819167\pi$
$163$	−1.66335	−	15.8257i	−0.130283	−	1.23956i	0.712640	−	0.701530i	$-0.247499\pi$
$164$	−9.50656	−	12.1370i	−0.742338	−	0.947740i
$165$	2.36233	−	0.913258i	0.183907	−	0.0710970i
$166$	4.41448	−	0.311422i	0.342630	−	0.0241711i
$167$	6.47911	−	14.5523i	0.501369	−	1.12609i	−0.468721	−	0.883346i	$-0.655285\pi$
$167$	6.47911	−	14.5523i	0.501369	−	1.12609i	0.970090	−	0.242746i	$-0.0780483\pi$
$168$	2.79100	−	1.61827i	0.215331	−	0.124852i
$169$	−11.5720	+	5.92357i	−0.890154	+	0.455659i
$170$	2.02502	+	3.80286i	0.155312	+	0.291666i
$171$	2.28666	+	0.240338i	0.174866	+	0.0183791i
$172$	−9.52529	−	7.97270i	−0.726297	−	0.607913i
$173$	1.40841	−	6.62604i	0.107079	−	0.503769i	−0.891620	−	0.452784i	$-0.850431\pi$
$173$	1.40841	−	6.62604i	0.107079	−	0.503769i	0.998699	−	0.0509845i	$-0.0162359\pi$
$174$	−3.44891	+	0.610326i	−0.261461	+	0.0462687i
$175$	−3.39875	−	1.96227i	−0.256921	−	0.148334i
$176$	13.0349	+	2.46832i	0.982539	+	0.186056i
$177$			0.0264417i			0.00198748i
$178$	9.85018	+	3.57830i	0.738302	+	0.268205i
$179$	4.61711	+	4.15726i	0.345099	+	0.310728i	0.823393	−	0.567471i	$-0.192078\pi$
$179$	4.61711	+	4.15726i	0.345099	+	0.310728i	−0.478295	+	0.878199i	$0.658745\pi$
$180$	0.824508	−	0.985071i	0.0614552	−	0.0734229i
$181$	−11.1470	−	8.09874i	−0.828547	−	0.601975i	0.0906009	−	0.995887i	$-0.471121\pi$
$181$	−11.1470	−	8.09874i	−0.828547	−	0.601975i	−0.919148	+	0.393913i	$0.871121\pi$
$182$	0.415943	+	4.25054i	0.0308317	+	0.315071i
$183$	5.13593	−	15.8068i	0.379659	−	1.16847i
$184$	−11.4121	+	19.8509i	−0.841310	+	1.46343i
$185$	−0.606819	−	0.270173i	−0.0446142	−	0.0198635i
$186$	6.36892	+	9.42979i	0.466992	+	0.691425i
$187$	9.84975	+	15.0887i	0.720285	+	1.10339i
$188$	−1.87519	+	0.265897i	−0.136763	+	0.0193925i
$189$	−0.494257	−	4.70254i	−0.0359519	−	0.342060i
$190$	0.220572	−	1.57650i	0.0160020	−	0.114371i
$191$	6.66337	−	5.99973i	0.482145	−	0.434125i	−0.391873	−	0.920019i	$-0.628173\pi$
$191$	6.66337	−	5.99973i	0.482145	−	0.434125i	0.874018	+	0.485894i	$0.161506\pi$
$192$	−10.3489	+	3.40488i	−0.746866	+	0.245726i
$193$	−1.43575	+	13.6602i	−0.103347	+	0.983285i	0.812827	+	0.582505i	$0.197927\pi$
$193$	−1.43575	+	13.6602i	−0.103347	+	0.983285i	−0.916174	+	0.400780i	$0.868739\pi$
$194$	18.6194	+	17.9584i	1.33680	+	1.28934i
$195$	−1.18767	−	2.48402i	−0.0850511	−	0.177884i
$196$	−12.1132	−	3.45726i	−0.865229	−	0.246947i
$197$	−9.00373	−	15.5949i	−0.641489	−	1.11109i	−0.985100	−	0.171980i	$-0.944984\pi$
$197$	−9.00373	−	15.5949i	−0.641489	−	1.11109i	0.343611	−	0.939112i	$-0.388350\pi$
$198$	3.06838	−	4.41012i	0.218060	−	0.313414i
$199$	1.78009	+	1.02774i	0.126187	+	0.0728543i	0.561765	−	0.827297i	$-0.310123\pi$
$199$	1.78009	+	1.02774i	0.126187	+	0.0728543i	−0.435578	+	0.900151i	$0.643456\pi$
$200$	9.86510	+	8.84962i	0.697568	+	0.625763i
$201$	−1.07527	+	5.05876i	−0.0758439	+	0.356817i
$202$	5.44305	−	1.56440i	0.382972	−	0.110071i
$203$	−1.23233	−	0.895337i	−0.0864923	−	0.0628403i
$204$	−13.0739	−	6.93089i	−0.915358	−	0.485259i
$205$	0.898699	+	4.22804i	0.0627678	+	0.295299i
$206$	10.7035	+	26.4452i	0.745750	+	1.84253i
$207$	5.45042	+	7.50185i	0.378830	+	0.521415i
$208$	1.58391	−	14.3350i	0.109824	−	0.993951i
$209$	0.332633	−	6.64927i	0.0230087	−	0.459939i
$210$	−0.902305	+	0.0636538i	−0.0622650	+	0.00439253i
$211$	6.87524	+	3.06105i	0.473311	+	0.210732i	0.629507	−	0.776994i	$-0.283257\pi$
$211$	6.87524	+	3.06105i	0.473311	+	0.210732i	−0.156197	+	0.987726i	$0.549923\pi$
$212$	10.5425	+	21.5479i	0.724060	+	1.47991i
$213$	12.6693	+	4.11650i	0.868086	+	0.282058i
$214$	−19.6766	−	0.674988i	−1.34506	−	0.0461413i
$215$	1.41653	+	3.18159i	0.0966068	+	0.216982i
$216$	−1.63971	+	15.8831i	−0.111568	+	1.08071i
$217$	−1.02891	+	4.84064i	−0.0698470	+	0.328604i
$218$	13.3075	+	15.8394i	0.901295	+	1.07278i
$219$	−4.70749	+	2.71787i	−0.318103	+	0.183657i
$220$	−2.97864	−	2.22777i	−0.200820	−	0.150196i
$221$	15.5296	−	11.9394i	1.04464	−	0.803134i
$222$	2.24648	−	0.397541i	0.150774	−	0.0266812i
$223$	17.8687	−	19.8452i	1.19658	−	1.32893i	0.265500	−	0.964111i	$-0.414463\pi$
$223$	17.8687	−	19.8452i	1.19658	−	1.32893i	0.931077	−	0.364822i	$-0.118870\pi$
$224$	−4.19030	−	2.21150i	−0.279976	−	0.147762i
$225$	4.90298	−	2.18295i	0.326865	−	0.145530i
$226$	10.1285	+	19.0207i	0.673738	+	1.26524i
$227$	−6.36237	+	5.72871i	−0.422286	+	0.380228i	−0.852698	−	0.522405i	$-0.825035\pi$
$227$	−6.36237	+	5.72871i	−0.422286	+	0.380228i	0.430412	+	0.902633i	$0.358368\pi$
$228$	2.40275	+	4.91101i	0.159126	+	0.325240i
$229$	1.41199	+	1.94343i	0.0933066	+	0.128426i	0.853118	−	0.521718i	$-0.174709\pi$
$229$	1.41199	+	1.94343i	0.0933066	+	0.128426i	−0.759811	+	0.650144i	$0.774709\pi$
$230$	5.32009	−	3.59322i	0.350796	−	0.236930i
$231$	−3.73508	+	0.600680i	−0.245751	+	0.0395218i
$232$	3.44894	+	3.81624i	0.226434	+	0.250548i
$233$	12.5086	+	17.2167i	0.819468	+	1.12790i	0.989793	+	0.142513i	$0.0455183\pi$
$233$	12.5086	+	17.2167i	0.819468	+	1.12790i	−0.170325	+	0.985388i	$0.554482\pi$
$234$	−5.03700	−	2.95649i	−0.329279	−	0.193272i
$235$	0.505025	+	0.164093i	0.0329442	+	0.0107042i
$236$	0.0329066	−	0.0206188i	0.00214204	−	0.00134217i
$237$	−5.66061	−	0.594954i	−0.367696	−	0.0386464i
$238$	−1.77765	−	6.18504i	−0.115228	−	0.400916i
$239$	−15.3375	+	4.98346i	−0.992102	+	0.322353i	−0.759705	−	0.650268i	$-0.774657\pi$
$239$	−15.3375	+	4.98346i	−0.992102	+	0.322353i	−0.232397	+	0.972621i	$0.574657\pi$
$240$	3.02588	+	0.417660i	0.195319	+	0.0269599i
$241$	11.1246	−	19.2684i	0.716600	−	1.24119i	−0.245739	−	0.969336i	$-0.579031\pi$
$241$	11.1246	−	19.2684i	0.716600	−	1.24119i	0.962339	−	0.271852i	$-0.0876361\pi$
$242$	−13.2366	−	8.17268i	−0.850880	−	0.525360i
$243$	9.65270	+	5.57299i	0.619221	+	0.357507i
$244$	−23.6764	+	5.93417i	−1.51573	+	0.379897i
$245$	2.62467	+	2.36327i	0.167684	+	0.150984i
$246$	−10.6855	−	10.3062i	−0.681285	−	0.657099i
$247$	−7.23489	+	0.196235i	−0.460345	+	0.0124861i
$248$	6.76898	−	15.2793i	0.429830	−	0.970235i
$249$	4.16839	−	0.886019i	0.264161	−	0.0561492i
$250$	−2.88167	−	7.11975i	−0.182253	−	0.450293i
$251$	−1.86487	+	0.196006i	−0.117710	+	0.0123718i	−0.163200	−	0.986593i	$-0.552182\pi$
$251$	−1.86487	+	0.196006i	−0.117710	+	0.0123718i	0.0454905	+	0.998965i	$0.485515\pi$
$252$	−1.51056	+	1.18318i	−0.0951565	+	0.0745333i
$253$	20.8259	−	16.9466i	1.30931	−	1.06542i
$254$	13.2289	−	8.93486i	0.830055	−	0.560623i
$255$	2.43862	+	3.35647i	0.152712	+	0.210190i
$256$	12.3072	+	10.2241i	0.769202	+	0.639006i
$257$	4.63312	−	0.984800i	0.289006	−	0.0614301i	−0.0611273	−	0.998130i	$-0.519470\pi$
$257$	4.63312	−	0.984800i	0.289006	−	0.0614301i	0.350133	+	0.936700i	$0.386136\pi$
$258$	−10.1478	−	6.33234i	−0.631772	−	0.394234i
$259$	0.802686	+	0.583186i	0.0498765	+	0.0362374i
$260$	−2.16523	+	3.41505i	−0.134282	+	0.211792i
$261$	1.98114	−	0.643711i	0.122629	−	0.0398447i
$262$	−18.0497	−	21.4839i	−1.11512	−	1.32728i
$263$	10.4803	+	18.1523i	0.646240	+	1.11932i	0.984014	+	0.178093i	$0.0569928\pi$
$263$	10.4803	+	18.1523i	0.646240	+	1.11932i	−0.337774	+	0.941227i	$0.609674\pi$
$264$	12.7603	+	0.614707i	0.785340	+	0.0378326i
$265$		−	6.72579i		−	0.413162i
$266$	−0.811855	+	2.23483i	−0.0497780	+	0.137026i
$267$	9.87125	+	2.09820i	0.604111	+	0.128408i
$268$	7.13409	−	2.60655i	0.435784	−	0.159221i
$269$	−25.0401	+	11.1486i	−1.52672	+	0.679740i	−0.986795	−	0.161973i	$-0.948214\pi$
$269$	−25.0401	+	11.1486i	−1.52672	+	0.679740i	−0.539925	+	0.841713i	$0.681548\pi$
$270$	2.37004	−	3.79805i	0.144236	−	0.231142i
$271$	−1.61713	−	7.60801i	−0.0982338	−	0.462154i	−0.999578	−	0.0290501i	$-0.990752\pi$
$271$	−1.61713	−	7.60801i	−0.0982338	−	0.462154i	0.901344	−	0.433104i	$-0.142582\pi$
$272$	1.56933	+	21.6750i	0.0951548	+	1.31424i
$273$	0.963822	+	3.99810i	0.0583332	+	0.241976i
$274$	−12.5335	+	25.7376i	−0.757174	+	1.55487i
$275$	−7.08800	−	13.8297i	−0.427423	−	0.833960i
$276$	−8.23462	+	20.4539i	−0.495666	+	1.23118i
$277$	6.40858	−	0.673569i	0.385054	−	0.0404709i	0.0899761	−	0.995944i	$-0.471321\pi$
$277$	6.40858	−	0.673569i	0.385054	−	0.0404709i	0.295078	+	0.955473i	$0.404654\pi$
$278$	1.70463	−	12.1835i	0.102237	−	0.730718i
$279$	−4.52846	−	5.02936i	−0.271112	−	0.301100i
$280$	0.782817	+	1.07328i	0.0467823	+	0.0641408i
$281$	15.1460	+	11.0042i	0.903535	+	0.656457i	0.939372	−	0.342901i	$-0.111409\pi$
$281$	15.1460	+	11.0042i	0.903535	+	0.656457i	−0.0358362	+	0.999358i	$0.511409\pi$
$282$	−1.75283	+	0.503785i	−0.104380	+	0.0300000i
$283$	−6.34493	+	7.04676i	−0.377167	+	0.418886i	−0.901604	−	0.432563i	$-0.857609\pi$
$283$	−6.34493	+	7.04676i	−0.377167	+	0.418886i	0.524437	+	0.851449i	$0.324276\pi$
$284$	−4.75630	−	18.9769i	−0.282235	−	1.12607i
$285$		−	1.53288i		−	0.0908002i
$286$	−7.74988	+	15.0313i	−0.458260	+	0.888818i
$287$		−	6.45646i		−	0.381113i
$288$	5.81498	−	2.85836i	0.342651	−	0.168430i
$289$	−8.37544	+	9.30187i	−0.492673	+	0.547169i
$290$	−0.398376	−	1.38608i	−0.0233934	−	0.0813934i
$291$	20.1529	+	14.6420i	1.18139	+	0.858327i
$292$	7.05320	+	3.73912i	0.412757	+	0.218815i
$293$	3.34260	+	3.71233i	0.195277	+	0.216877i	0.832829	−	0.553530i	$-0.186720\pi$
$293$	3.34260	+	3.71233i	0.195277	+	0.216877i	−0.637552	+	0.770407i	$0.720053\pi$
$294$	−12.0133	−	1.68081i	−0.700628	−	0.0980269i
$295$	−0.0108280	+	0.00113807i	−0.000630432	+	6.62611e-5i
$296$	−2.24650	−	2.48574i	−0.130575	−	0.144481i
$297$	8.46064	−	16.7029i	0.490936	−	0.969202i
$298$	5.11039	+	2.48861i	0.296037	+	0.144161i
$299$	−20.1120	−	21.1539i	−1.16311	−	1.22336i
$300$	10.5888	+	7.12330i	0.611346	+	0.411264i
$301$	−1.08156	−	5.08836i	−0.0623403	−	0.293288i
$302$	10.0951	+	6.29948i	0.580908	+	0.362494i
$303$	4.98213	−	2.21819i	0.286216	−	0.127431i
$304$	4.23812	−	6.81973i	0.243073	−	0.391138i
$305$	6.69402	+	1.42286i	0.383299	+	0.0814726i
$306$	8.27183	+	3.00493i	0.472869	+	0.171780i
$307$			26.8687i			1.53348i	0.641958	+	0.766740i	$0.278123\pi$
$307$			26.8687i			1.53348i	−0.641958	+	0.766740i	$0.721877\pi$
$308$	3.66009	+	4.17990i	0.208553	+	0.238172i
$309$	13.7362	+	23.7918i	0.781425	+	1.35347i
$310$	−3.58743	+	3.01398i	−0.203752	+	0.171182i
$311$	8.74538	−	2.84155i	0.495905	−	0.161129i	−0.0503776	−	0.998730i	$-0.516042\pi$
$311$	8.74538	−	2.84155i	0.495905	−	0.161129i	0.546283	+	0.837601i	$0.316042\pi$
$312$	−0.402200	−	13.8821i	−0.0227701	−	0.785921i
$313$	−15.8563	−	11.5203i	−0.896250	−	0.651164i	0.0412499	−	0.999149i	$-0.486866\pi$
$313$	−15.8563	−	11.5203i	−0.896250	−	0.651164i	−0.937500	+	0.347985i	$0.886866\pi$
$314$	−0.335719	+	0.538000i	−0.0189457	+	0.0303611i
$315$	0.526219	−	0.111851i	0.0296491	−	0.00630211i
$316$	3.67362	+	7.50855i	0.206657	+	0.422389i
$317$	6.94100	+	9.55347i	0.389846	+	0.536576i	0.958159	−	0.286236i	$-0.0924040\pi$
$317$	6.94100	+	9.55347i	0.389846	+	0.536576i	−0.568314	+	0.822812i	$0.692404\pi$
$318$	12.9292	+	19.1428i	0.725031	+	1.07348i
$319$	−2.17493	−	5.62589i	−0.121773	−	0.314989i
$320$	−1.83974	−	4.09138i	−0.102845	−	0.228715i
$321$	−18.8550	+	1.98174i	−1.05238	+	0.110610i
$322$	−8.88879	+	3.59767i	−0.495353	+	0.200491i
$323$	10.6674	−	2.26743i	0.593552	−	0.126163i
$324$	0.307232	+	8.49786i	0.0170685	+	0.472104i
$325$	−14.3963	+	8.84060i	−0.798561	+	0.490388i
$326$	−15.6228	+	16.1978i	−0.865264	+	0.897112i
$327$	14.8043	+	13.3299i	0.818682	+	0.737145i
$328$	−4.49365	+	21.3347i	−0.248120	+	1.17801i
$329$	−0.686905	−	0.396585i	−0.0378703	−	0.0218644i
$330$	−3.13789	−	1.72711i	−0.172735	−	0.0950742i
$331$	4.72156	−	8.17798i	0.259520	−	0.449503i	−0.706593	−	0.707620i	$-0.749769\pi$
$331$	4.72156	−	8.17798i	0.259520	−	0.449503i	0.966114	+	0.258117i	$0.0831022\pi$
$332$	−4.35308	−	4.49665i	−0.238906	−	0.246786i
$333$	−1.29043	+	0.419287i	−0.0707153	+	0.0229768i
$334$	−21.6512	+	6.22282i	−1.18470	+	0.340497i
$335$	−2.11787	−	0.222597i	−0.115712	−	0.0121618i
$336$	−4.29124	−	1.54992i	−0.234106	−	0.0845552i
$337$	−4.83008	−	1.56939i	−0.263111	−	0.0854900i	0.174491	−	0.984659i	$-0.444172\pi$
$337$	−4.83008	−	1.56939i	−0.263111	−	0.0854900i	−0.437602	+	0.899169i	$0.644172\pi$
$338$	16.9411	+	7.14135i	0.921475	+	0.388438i
$339$	12.1972	+	16.7879i	0.662459	+	0.911796i
$340$	2.27553	−	5.65216i	0.123408	−	0.306531i
$341$	−13.8235	+	13.8894i	−0.748585	+	0.752151i
$342$	−1.81996	−	2.69462i	−0.0984120	−	0.145708i
$343$	−6.54707	−	9.01127i	−0.353509	−	0.486563i
$344$	0.0324562	+	17.5667i	0.00174992	+	0.947133i
$345$	4.59416	−	4.13660i	0.247341	−	0.222707i
$346$	−8.45586	+	4.50274i	−0.454590	+	0.242069i
$347$	−3.16529	+	1.40928i	−0.169922	+	0.0756540i	−0.489935	−	0.871759i	$-0.662979\pi$
$347$	−3.16529	+	1.40928i	−0.169922	+	0.0756540i	0.320013	+	0.947413i	$0.396313\pi$
$348$	3.79835	+	3.17923i	0.203613	+	0.170425i
$349$	−0.852548	+	0.946850i	−0.0456358	+	0.0506837i	−0.765531	−	0.643400i	$-0.777523\pi$
$349$	−0.852548	+	0.946850i	−0.0456358	+	0.0506837i	0.719895	+	0.694083i	$0.244190\pi$
$350$	0.967137	+	5.46522i	0.0516957	+	0.292129i
$351$	−18.8125	−	7.77175i	−1.00414	−	0.414825i
$352$	−9.18522	−	16.3595i	−0.489574	−	0.871962i
$353$	−13.0387	+	7.52788i	−0.693978	+	0.400668i	−0.805101	−	0.593138i	$-0.797889\pi$
$353$	−13.0387	+	7.52788i	−0.693978	+	0.400668i	0.111123	+	0.993807i	$0.464555\pi$
$354$	0.0286308	−	0.0240542i	0.00152171	−	0.00127847i
$355$	−1.14044	+	5.36533i	−0.0605280	+	0.284762i
$356$	−5.08621	−	13.9209i	−0.269569	−	0.737805i
$357$	−2.52056	−	5.66128i	−0.133402	−	0.299627i
$358$	0.301233	−	8.78124i	0.0159207	−	0.464103i
$359$	−21.7267	−	7.05944i	−1.14669	−	0.372583i	−0.326796	−	0.945095i	$-0.605969\pi$
$359$	−21.7267	−	7.05944i	−1.14669	−	0.372583i	−0.819896	+	0.572512i	$0.805969\pi$
$360$	−1.81669	+	0.00335650i	−0.0957477	+	0.000176903i
$361$	13.6763	+	6.08909i	0.719807	+	0.320479i
$362$	1.37122	+	19.4373i	0.0720696	+	1.02160i
$363$	−13.7138	−	6.02785i	−0.719787	−	0.316380i
$364$	4.22406	−	4.31712i	0.221401	−	0.226279i
$365$	−1.31560	−	1.81077i	−0.0688616	−	0.0947799i
$366$	−21.7876	+	8.81838i	−1.13886	+	0.460944i
$367$	−5.12086	−	24.0918i	−0.267307	−	1.25758i	−0.882917	−	0.469529i	$-0.844424\pi$
$367$	−5.12086	−	24.0918i	−0.267307	−	1.25758i	0.615610	−	0.788051i	$-0.288910\pi$
$368$	31.8760	−	5.70161i	1.66165	−	0.297217i
$369$	7.14321	+	5.18984i	0.371861	+	0.270172i
$370$	0.259486	+	0.902835i	0.0134900	+	0.0469362i
$371$	−2.08873	+	9.82669i	−0.108441	+	0.510176i
$372$	4.41663	−	15.4745i	0.228992	−	0.802318i
$373$	16.8491	+	9.72785i	0.872415	+	0.503689i	0.868150	−	0.496302i	$-0.165309\pi$
$373$	16.8491	+	9.72785i	0.872415	+	0.503689i	0.00426520	+	0.999991i	$0.498642\pi$
$374$	7.37750	−	24.3915i	0.381481	−	1.26125i
$375$	−3.69815	−	6.40538i	−0.190971	−	0.330772i
$376$	1.99379	+	1.78855i	0.102822	+	0.0922376i
$377$	−5.91570	+	2.82845i	−0.304674	+	0.145673i
$378$	−4.64224	+	4.81311i	−0.238771	+	0.247560i
$379$	−1.30103	+	12.3784i	−0.0668293	+	0.635838i	0.908924	+	0.416963i	$0.136905\pi$
$379$	−1.30103	+	12.3784i	−0.0668293	+	0.635838i	−0.975753	+	0.218875i	$0.929761\pi$
$380$	−1.90767	+	1.19531i	−0.0978614	+	0.0613183i
$381$	11.4238	−	10.2860i	0.585258	−	0.526969i
$382$	−12.5582	−	1.75705i	−0.642531	−	0.0898984i
$383$	−2.45663	−	23.3733i	−0.125528	−	1.19432i	−0.858046	−	0.513572i	$-0.828322\pi$
$383$	−2.45663	−	23.3733i	−0.125528	−	1.19432i	0.732518	−	0.680747i	$-0.238345\pi$
$384$	13.1012	+	8.10823i	0.668569	+	0.413771i
$385$	−0.406743	−	1.50369i	−0.0207295	−	0.0766349i
$386$	16.0973	−	10.8722i	0.819330	−	0.553379i
$387$	6.49897	+	2.89353i	0.330361	+	0.147086i
$388$	2.50700	−	36.4978i	0.127274	−	1.85289i
$389$	−9.35014	+	28.7768i	−0.474071	+	1.45904i	0.373136	+	0.927777i	$0.378283\pi$
$389$	−9.35014	+	28.7768i	−0.474071	+	1.45904i	−0.847207	+	0.531264i	$0.821717\pi$
$390$	−1.60924	+	3.54573i	−0.0814869	+	0.179545i
$391$	35.5825	+	25.8522i	1.79948	+	1.30740i
$392$	7.27596	+	16.2611i	0.367491	+	0.821312i
$393$	−20.0801	−	18.0802i	−1.01290	−	0.912023i
$394$	−8.69528	+	23.9359i	−0.438062	+	1.20588i
$395$		−	2.34366i		−	0.117922i
$396$	−7.56656	+	0.689504i	−0.380234	+	0.0346489i
$397$	−20.5488	−	11.8639i	−1.03132	−	0.595430i	−0.113954	−	0.993486i	$-0.536352\pi$
$397$	−20.5488	−	11.8639i	−1.03132	−	0.595430i	−0.917361	+	0.398056i	$0.869685\pi$
$398$	−0.506537	−	2.86240i	−0.0253904	−	0.143479i
$399$	−0.476045	+	2.23961i	−0.0238321	+	0.112121i
$400$	0.607950	−	18.7324i	0.0303975	−	0.936619i
$401$	−18.8469	−	1.98089i	−0.941169	−	0.0989208i	−0.378498	−	0.925602i	$-0.623559\pi$
$401$	−18.8469	−	1.98089i	−0.941169	−	0.0989208i	−0.562671	+	0.826681i	$0.690226\pi$
$402$	6.45576	−	3.43769i	0.321984	−	0.171456i
$403$	16.2120	+	13.8201i	0.807576	+	0.688427i
$404$	−6.64549	−	4.47054i	−0.330626	−	0.222418i
$405$	0.969715	−	2.17802i	0.0481855	−	0.108227i
$406$	0.151592	+	2.14884i	0.00752337	+	0.106645i
$407$	1.41666	+	3.66447i	0.0702212	+	0.181641i
$408$	4.38873	+	20.4614i	0.217275	+	1.01299i
$409$	2.56967	+	24.4488i	0.127062	+	1.20891i	0.853281	+	0.521451i	$0.174609\pi$
$409$	2.56967	+	24.4488i	0.127062	+	1.20891i	−0.726219	+	0.687463i	$0.758724\pi$
$410$	3.76053	−	4.81938i	0.185720	−	0.238012i
$411$	−8.51857	+	26.2175i	−0.420190	+	1.29321i
$412$	18.8976	−	35.6471i	0.931018	−	1.75621i
$413$	0.0161737	+	0.00169992i	0.000795855	+	8.36478e-5i
$414$	3.16466	−	12.7261i	0.155535	−	0.625456i
$415$	0.542241	+	1.66885i	0.0266176	+	0.0819204i
$416$	−16.9627	+	11.3256i	−0.831662	+	0.555282i
$417$		−	11.8465i		−	0.580124i
$418$	−7.50236	+	5.68870i	−0.366952	+	0.278244i
$419$	−1.61212	+	0.930759i	−0.0787573	+	0.0454705i	−0.538861	−	0.842394i	$-0.681145\pi$
$419$	−1.61212	+	0.930759i	−0.0787573	+	0.0454705i	0.460104	+	0.887865i	$0.347812\pi$
$420$	0.889756	+	0.919101i	0.0434156	+	0.0448475i
$421$	16.1262	−	5.23972i	0.785943	−	0.255368i	0.111567	−	0.993757i	$-0.464413\pi$
$421$	16.1262	−	5.23972i	0.785943	−	0.255368i	0.674375	+	0.738389i	$0.264413\pi$
$422$	−2.93997	−	10.2291i	−0.143115	−	0.497945i
$423$	0.990917	−	0.441185i	0.0481800	−	0.0214511i
$424$	13.7413	−	31.0175i	0.667336	−	1.50634i
$425$	18.9178	−	17.0337i	0.917648	−	0.826254i
$426$	−7.06802	−	17.4630i	−0.342447	−	0.846085i
$427$	−9.33840	−	4.15772i	−0.451917	−	0.201206i
$428$	17.1690	+	21.9196i	0.829896	+	1.05953i
$429$	−5.38519	+	15.3689i	−0.259999	+	0.742018i
$430$	2.15636	−	4.42812i	0.103989	−	0.213543i
$431$	10.4498	−	23.4705i	0.503347	−	1.13054i	−0.465987	−	0.884791i	$-0.654301\pi$
$431$	10.4498	−	23.4705i	0.503347	−	1.13054i	0.969335	−	0.245745i	$-0.0790326\pi$
$432$	18.6897	−	12.6734i	0.899208	−	0.609752i
$433$	0.239441	+	0.265926i	0.0115068	+	0.0127796i	0.748871	−	0.662716i	$-0.230596\pi$
$433$	0.239441	+	0.265926i	0.0115068	+	0.0127796i	−0.737364	+	0.675496i	$0.763930\pi$
$434$	6.17740	−	3.28947i	0.296525	−	0.157899i
$435$	−0.564863	−	1.26870i	−0.0270831	−	0.0608297i
$436$	5.04486	−	28.8184i	0.241605	−	1.38015i
$437$	−5.02164	−	15.4550i	−0.240218	−	0.739314i
$438$	7.22532	+	2.62476i	0.345239	+	0.125416i
$439$	−6.79221	−	11.7645i	−0.324175	−	0.561487i	0.657170	−	0.753742i	$-0.271753\pi$
$439$	−6.79221	−	11.7645i	−0.324175	−	0.561487i	−0.981345	+	0.192255i	$0.938420\pi$
$440$	0.297486	+	5.25186i	0.0141821	+	0.250373i
$441$	7.21443			0.343544
$442$	−27.0553	−	5.95396i	−1.28689	−	0.283201i
$443$	9.26341	−	3.00987i	0.440118	−	0.143003i	−0.0805721	−	0.996749i	$-0.525675\pi$
$443$	9.26341	−	3.00987i	0.440118	−	0.143003i	0.520690	+	0.853746i	$0.325675\pi$
$444$	−2.47409	−	2.07082i	−0.117415	−	0.0982767i
$445$	−0.434358	+	4.13264i	−0.0205906	+	0.195906i
$446$	−37.7435	−	1.29476i	−1.78720	−	0.0613086i
$447$	5.20567	+	1.69143i	0.246220	+	0.0800017i
$448$	1.41735	+	6.54903i	0.0669637	+	0.309413i
$449$	−5.46343	+	0.574230i	−0.257835	+	0.0270996i	−0.232564	−	0.972581i	$-0.574712\pi$
$449$	−5.46343	+	0.574230i	−0.257835	+	0.0270996i	−0.0252711	+	0.999681i	$0.508045\pi$
$450$	−6.82394	−	3.32306i	−0.321684	−	0.156650i
$451$	13.8733	−	21.4745i	0.653268	−	1.01120i
$452$	11.3814	−	28.2703i	0.535338	−	1.32972i
$453$	10.4679	+	4.66062i	0.491826	+	0.218975i
$454$	11.9909	+	1.67768i	0.562760	+	0.0787373i
$455$	−1.59576	+	0.566772i	−0.0748105	+	0.0265707i
$456$	3.13180	−	7.06925i	0.146660	−	0.331048i
$457$	−0.838777	+	7.98043i	−0.0392363	+	0.373309i	0.957231	+	0.289325i	$0.0934309\pi$
$457$	−0.838777	+	7.98043i	−0.0392363	+	0.373309i	−0.996467	+	0.0839834i	$0.973236\pi$
$458$	0.819837	−	3.29683i	0.0383085	−	0.154051i
$459$	30.0007	+	6.37684i	1.40031	+	0.297645i
$460$	−8.73042	−	2.49177i	−0.407058	−	0.116180i
$461$	−1.81373	+	3.14148i	−0.0844740	+	0.146313i	−0.905167	−	0.425056i	$-0.860254\pi$
$461$	−1.81373	+	3.14148i	−0.0844740	+	0.146313i	0.820693	+	0.571369i	$0.193588\pi$
$462$	4.04824	+	3.49787i	0.188341	+	0.162736i
$463$	0.0234358			0.00108915			0.000544576	−	1.00000i	$-0.499827\pi$
$463$	0.0234358			0.00108915			0.000544576		1.00000i	$0.499827\pi$
$464$	0.994660	−	7.20614i	0.0461759	−	0.334537i
$465$	−3.01906	+	3.35300i	−0.140005	+	0.155492i
$466$	7.26285	−	29.2063i	0.336445	−	1.35296i
$467$	−14.3397	+	19.7369i	−0.663562	+	0.913315i	−0.999593	−	0.0285360i	$-0.990915\pi$
$467$	−14.3397	+	19.7369i	−0.663562	+	0.913315i	0.336030	+	0.941851i	$0.390915\pi$
$468$	1.38092	+	8.14355i	0.0638332	+	0.376436i
$469$	3.02518	+	0.982941i	0.139690	+	0.0453880i
$470$	−0.281746	−	0.696112i	−0.0129960	−	0.0321093i
$471$	−0.248379	+	0.557868i	−0.0114447	+	0.0257052i
$472$	−0.0522612	−	0.0168740i	−0.00240551	−	0.000776688i
$473$	7.33625	−	19.2481i	0.337321	−	0.885031i
$474$	4.50528	+	6.67049i	0.206934	+	0.306386i
$475$	−9.35397	+	0.983142i	−0.429190	+	0.0451097i
$476$	−5.07996	+	7.55139i	−0.232839	+	0.346117i
$477$	−9.19294	−	10.2098i	−0.420916	−	0.467475i
$478$	19.3487	+	12.0738i	0.884988	+	0.552244i
$479$	−32.1589	−	3.38003i	−1.46938	−	0.154438i	−0.664237	−	0.747522i	$-0.731243\pi$
$479$	−32.1589	−	3.38003i	−1.46938	−	0.154438i	−0.805140	+	0.593085i	$0.797910\pi$
$480$	−2.30042	−	3.65634i	−0.104999	−	0.166888i
$481$	3.85325	−	1.84234i	0.175693	−	0.0840034i
$482$	−30.9838	+	5.48296i	−1.41127	+	0.249742i
$483$	−7.99691	+	4.61702i	−0.363872	+	0.210082i
$484$	3.19211	+	21.7672i	0.145096	+	0.989418i
$485$	−5.12857	+	8.88294i	−0.232876	+	0.403354i
$486$	−2.74674	−	15.5216i	−0.124595	−	0.704075i
$487$	0.748539	+	0.159107i	0.0339196	+	0.00720982i	0.224840	−	0.974396i	$-0.427814\pi$
$487$	0.748539	+	0.159107i	0.0339196	+	0.00720982i	−0.190921	+	0.981605i	$0.561147\pi$
$488$	27.9640	+	20.2382i	1.26587	+	0.916141i
$489$	−12.7376	+	17.5319i	−0.576016	+	0.792818i
$490$	0.171241	−	4.99185i	0.00773589	−	0.225509i
$491$	13.4910	−	2.86760i	0.608839	−	0.129413i	0.106833	−	0.994277i	$-0.465929\pi$
$491$	13.4910	−	2.86760i	0.608839	−	0.129413i	0.502006	+	0.864864i	$0.332596\pi$
$492$	−1.43875	+	20.9458i	−0.0648639	+	0.944310i
$493$	7.99344	−	5.80758i	0.360007	−	0.261560i
$494$	6.79411	+	7.65536i	0.305681	+	0.344431i
$495$	1.99057	+	0.758688i	0.0894696	+	0.0341005i
$496$	−22.7020	+	6.57027i	−1.01935	+	0.295014i
$497$	3.33246	−	7.48482i	0.149481	−	0.335740i
$498$	−4.75138	−	3.70748i	−0.212915	−	0.166136i
$499$	−1.58678	+	4.88362i	−0.0710342	+	0.218621i	−0.980271	−	0.197659i	$-0.936666\pi$
$499$	−1.58678	+	4.88362i	−0.0710342	+	0.218621i	0.909237	+	0.416280i	$0.136666\pi$
$500$	−5.08773	+	9.59713i	−0.227530	+	0.429197i
$501$	−19.8177	+	8.82343i	−0.885391	+	0.394202i
$502$	1.90872	+	1.84096i	0.0851902	+	0.0821659i
$503$	−20.7813	−	4.41720i	−0.926592	−	0.196953i	−0.280185	−	0.959946i	$-0.590396\pi$
$503$	−20.7813	−	4.41720i	−0.926592	−	0.196953i	−0.646407	+	0.762993i	$0.723729\pi$
$504$	2.65530	+	0.559277i	0.118277	+	0.0249122i
$505$	1.12279	+	1.94474i	0.0499637	+	0.0865397i
$506$	−37.2951	−	7.13370i	−1.65797	−	0.317132i
$507$	17.1091	+	4.55002i	0.759840	+	0.202073i
$508$	−21.7090	−	6.19602i	−0.963180	−	0.274904i
$509$	0.449373	+	0.404618i	0.0199181	+	0.0179344i	0.679030	−	0.734111i	$-0.262401\pi$
$509$	0.449373	+	0.404618i	0.0199181	+	0.0179344i	−0.659111	+	0.752045i	$0.729067\pi$
$510$	1.41593	−	5.69391i	0.0626983	−	0.252130i
$511$	1.35981	+	3.05418i	0.0601544	+	0.135109i
$512$	−0.125418	−	22.6271i	−0.00554276	−	0.999985i
$513$	−7.58267	−	8.42141i	−0.334783	−	0.371814i
$514$	−5.28111	−	4.12082i	−0.232940	−	0.181762i
$515$	−9.15166	+	6.64907i	−0.403271	+	0.292993i
$516$	2.37488	+	16.7485i	0.104548	+	0.737310i
$517$	−1.43252	−	2.79505i	−0.0630022	−	0.122926i
$518$	−0.0987406	−	1.39967i	−0.00433841	−	0.0614979i
$519$	−7.46327	+	5.42239i	−0.327601	+	0.238016i
$520$	5.66750	−	0.762201i	0.248536	−	0.0334247i
$521$	−0.657985	+	2.02507i	−0.0288269	+	0.0887199i	−0.964435	−	0.264321i	$-0.914852\pi$
$521$	−0.657985	+	2.02507i	−0.0288269	+	0.0887199i	0.935608	+	0.353041i	$0.114852\pi$
$522$	−2.49926	−	1.55957i	−0.109390	−	0.0682606i
$523$	2.15368	−	20.4909i	0.0941740	−	0.896006i	−0.840813	−	0.541325i	$-0.817923\pi$
$523$	2.15368	−	20.4909i	0.0941740	−	0.896006i	0.934987	−	0.354681i	$-0.115411\pi$
$524$	−6.84266	+	39.0881i	−0.298923	+	1.70757i
$525$	1.65155	+	5.08296i	0.0720797	+	0.221839i
$526$	10.1212	−	27.8612i	0.441306	−	1.21481i
$527$	−27.7995	−	16.0501i	−1.21097	−	0.699152i
$528$	−10.9425	−	14.3759i	−0.476211	−	0.625631i
$529$	21.2684	−	36.8380i	0.924715	−	1.60165i
$530$	−7.28262	+	6.11849i	−0.316337	+	0.265770i
$531$	−0.0148815	+	0.0165276i	−0.000645802	+	0.000717236i
$532$	3.15841	−	1.15397i	0.136934	−	0.0500311i
$533$	−24.4376	−	13.2389i	−1.05851	−	0.573441i
$534$	−6.70803	−	12.5972i	−0.290285	−	0.545136i
$535$	−1.62307	−	7.63593i	−0.0701713	−	0.330130i
$536$	−9.31228	−	5.35353i	−0.402229	−	0.231237i
$537$	−0.884408	−	8.41458i	−0.0381650	−	0.363116i
$538$	34.8507	+	16.9712i	1.50252	+	0.731682i
$539$	−1.14284	−	20.8583i	−0.0492256	−	0.898432i
$540$	−6.26853	+	0.888860i	−0.269755	+	0.0382504i
$541$	12.6753	−	9.20915i	0.544954	−	0.395932i	−0.280967	−	0.959717i	$-0.590655\pi$
$541$	12.6753	−	9.20915i	0.544954	−	0.395932i	0.825922	+	0.563785i	$0.190655\pi$
$542$	−6.76677	+	8.67207i	−0.290657	+	0.372497i
$543$	3.90121	+	18.3538i	0.167417	+	0.787635i
$544$	22.0419	−	21.4172i	0.945039	−	0.918254i
$545$	−4.82148	+	6.63620i	−0.206529	+	0.284263i
$546$	3.45231	−	4.68072i	0.147745	−	0.200316i
$547$	−2.50988	−	7.72462i	−0.107315	−	0.330281i	0.882952	−	0.469463i	$-0.155553\pi$
$547$	−2.50988	−	7.72462i	−0.107315	−	0.330281i	−0.990267	+	0.139182i	$0.955553\pi$
$548$	39.2702	−	9.84255i	1.67754	−	0.420453i
$549$	12.1064	−	6.98961i	0.516687	−	0.298309i
$550$	−8.52663	+	20.2558i	−0.363577	+	0.863708i
$551$	−3.65057			−0.155520
$552$	29.6384	−	9.69067i	1.26149	−	0.412462i
$553$	−0.727835	+	3.42420i	−0.0309507	+	0.145612i
$554$	−6.55926	−	6.32640i	−0.278676	−	0.268783i
$555$	0.367929	+	0.826382i	0.0156177	+	0.0350779i
$556$	−14.7429	+	9.23766i	−0.625238	+	0.391764i
$557$	−5.01778	+	1.06656i	−0.212610	+	0.0451917i	−0.312985	−	0.949758i	$-0.601329\pi$
$557$	−5.01778	+	1.06656i	−0.212610	+	0.0451917i	0.100375	+	0.994950i	$0.467996\pi$
$558$	−1.32618	+	9.47861i	−0.0561416	+	0.401262i
$559$	−21.4771	−	6.33992i	−0.908383	−	0.268150i
$560$	0.450004	−	1.82400i	0.0190161	−	0.0770779i
$561$	3.78112	−	24.2458i	0.159639	−	1.02366i
$562$	−1.86315	−	26.4106i	−0.0785923	−	1.11406i
$563$	2.37841	+	22.6291i	0.100238	+	0.953702i	0.922866	+	0.385122i	$0.125841\pi$
$563$	2.37841	+	22.6291i	0.100238	+	0.953702i	−0.822628	+	0.568581i	$0.807493\pi$
$564$	2.14006	+	1.43965i	0.0901127	+	0.0606204i
$565$	−6.34979	+	5.71737i	−0.267137	+	0.240532i
$566$	13.4022	+	0.459751i	0.563336	+	0.0193248i
$567$	−2.09319	+	2.88103i	−0.0879058	+	0.120992i
$568$	−16.2211	+	22.4135i	−0.680624	+	0.940448i
$569$	15.6164	+	14.0610i	0.654671	+	0.589469i	0.928058	−	0.372435i	$-0.121477\pi$
$569$	15.6164	+	14.0610i	0.654671	+	0.589469i	−0.273387	+	0.961904i	$0.588144\pi$
$570$	−1.65979	+	1.39447i	−0.0695211	+	0.0584081i
$571$	−18.4563			−0.772371			−0.386186	−	0.922421i	$-0.626208\pi$
$571$	−18.4563			−0.772371			−0.386186	+	0.922421i	$0.626208\pi$
$572$	23.3258	−	5.28254i	0.975302	−	0.220874i
$573$	−12.2108			−0.510112
$574$	−6.99100	+	5.87348i	−0.291799	+	0.245154i
$575$	−28.1889	−	25.3814i	−1.17556	−	1.05848i
$576$	−8.38492	−	3.69614i	−0.349372	−	0.154006i
$577$	−10.6171	+	14.6132i	−0.441996	+	0.608356i	−0.970654	−	0.240479i	$-0.922695\pi$
$577$	−10.6171	+	14.6132i	−0.441996	+	0.608356i	0.528658	+	0.848835i	$0.322695\pi$
$578$	17.6912	+	0.606881i	0.735856	+	0.0252429i
$579$	13.9008	−	12.5163i	0.577696	−	0.520160i
$580$	−1.13843	+	1.69228i	−0.0472707	+	0.0702682i
$581$	−0.273971	−	2.60666i	−0.0113662	−	0.108142i
$582$	−2.47907	−	35.1413i	−0.102761	−	1.45665i
$583$	−28.0623	+	28.1959i	−1.16222	+	1.16776i
$584$	−2.36766	−	11.0386i	−0.0979745	−	0.456782i
$585$	0.655651	−	2.22108i	0.0271078	−	0.0918304i
$586$	0.978895	−	6.99646i	0.0404378	−	0.289021i
$587$	13.4459	−	2.85802i	0.554973	−	0.117963i	0.0781163	−	0.996944i	$-0.475109\pi$
$587$	13.4459	−	2.85802i	0.554973	−	0.117963i	0.476857	+	0.878981i	$0.341776\pi$
$588$	9.10858	+	14.5369i	0.375631	+	0.599492i
$589$	4.82397	+	10.8348i	0.198768	+	0.446441i
$590$	0.0110826	+	0.0106892i	0.000456264	+	0.000440067i
$591$	−5.09863	+	23.9872i	−0.209729	+	0.986700i
$592$	−0.647881	+	4.69378i	−0.0266277	+	0.192913i
$593$	−7.14772			−0.293522			−0.146761	−	0.989172i	$-0.546885\pi$
$593$	−7.14772			−0.293522			−0.146761	+	0.989172i	$0.546885\pi$
$594$	−25.7825	+	6.03366i	−1.05787	+	0.247564i
$595$	2.20984	−	1.27585i	0.0905946	−	0.0523048i
$596$	−1.95431	−	7.79739i	−0.0800517	−	0.319393i
$597$	−0.865000	−	2.66219i	−0.0354021	−	0.108956i
$598$	−4.60923	+	41.0209i	−0.188486	+	1.67747i
$599$	1.83713	−	2.52860i	0.0750632	−	0.103316i	−0.769834	−	0.638244i	$-0.779661\pi$
$599$	1.83713	−	2.52860i	0.0750632	−	0.103316i	0.844898	+	0.534928i	$0.179661\pi$
$600$	−1.91969	−	17.9456i	−0.0783709	−	0.732626i
$601$	8.33604	+	39.2180i	0.340034	+	1.59973i	0.733031	+	0.680195i	$0.238105\pi$
$601$	8.33604	+	39.2180i	0.340034	+	1.59973i	−0.392997	+	0.919540i	$0.628562\pi$
$602$	−4.52572	+	5.80002i	−0.184455	+	0.236391i
$603$	−3.51920	+	2.55685i	−0.143313	+	0.104123i
$604$	−2.36256	−	16.6616i	−0.0961312	−	0.677949i
$605$	1.87819	−	5.87532i	0.0763592	−	0.238866i
$606$	−6.93410	−	3.37670i	−0.281679	−	0.137169i
$607$	0.915307	+	8.70856i	0.0371512	+	0.353470i	0.997268	+	0.0738702i	$0.0235350\pi$
$607$	0.915307	+	8.70856i	0.0371512	+	0.353470i	−0.960117	+	0.279600i	$0.909798\pi$
$608$	−11.2398	+	1.61496i	−0.455833	+	0.0654952i
$609$	0.431289	+	2.02906i	0.0174767	+	0.0822215i
$610$	−4.54893	−	8.54260i	−0.184181	−	0.345880i
$611$	−2.90956	+	1.78673i	−0.117708	+	0.0722834i
$612$	−4.27122	−	11.6903i	−0.172654	−	0.472551i
$613$	13.7543	−	15.2757i	0.555530	−	0.616978i	−0.398326	−	0.917244i	$-0.630409\pi$
$613$	13.7543	−	15.2757i	0.555530	−	0.616978i	0.953856	+	0.300266i	$0.0970754\pi$
$614$	29.0932	−	24.4427i	1.17411	−	0.986425i
$615$	2.94325	−	5.09786i	0.118683	−	0.205565i
$616$	1.19635	−	7.76560i	0.0482024	−	0.312885i
$617$	33.2490	+	19.1963i	1.33855	+	0.772814i	0.986593	−	0.163201i	$-0.0521818\pi$
$617$	33.2490	+	19.1963i	1.33855	+	0.772814i	0.351961	+	0.936015i	$0.385515\pi$
$618$	13.2656	−	36.5170i	0.533622	−	1.46893i
$619$	7.49375	+	23.0634i	0.301199	+	0.926997i	0.981068	+	0.193663i	$0.0620367\pi$
$619$	7.49375	+	23.0634i	0.301199	+	0.926997i	−0.679869	+	0.733334i	$0.737963\pi$
$620$	6.52701	+	1.14260i	0.262131	+	0.0458879i
$621$	4.77715	−	45.4515i	0.191700	−	1.82391i
$622$	−11.0325	−	6.88444i	−0.442364	−	0.276041i
$623$	1.91803	−	5.90309i	0.0768443	−	0.236502i
$624$	−14.6656	+	13.0642i	−0.587092	+	0.522985i
$625$	−16.4896	+	11.9804i	−0.659585	+	0.479217i
$626$	1.95052	+	27.6491i	0.0779586	+	1.10508i
$627$	−6.39571	+	6.42618i	−0.255420	+	0.256637i
$628$	0.887947	−	0.125908i	0.0354329	−	0.00502429i
$629$	−5.20660	+	3.78282i	−0.207601	+	0.150831i
$630$	−0.599817	−	0.468033i	−0.0238973	−	0.0186469i
$631$	22.3533	+	24.8258i	0.889870	+	0.988301i	0.999984	−	0.00561825i	$-0.00178835\pi$
$631$	22.3533	+	24.8258i	0.889870	+	0.988301i	−0.110114	+	0.993919i	$0.535122\pi$
$632$	4.78827	−	10.8083i	0.190467	−	0.429932i
$633$	−4.16862	−	9.36288i	−0.165688	−	0.372141i
$634$	4.03014	−	16.2065i	0.160057	−	0.643642i
$635$	4.70387	+	4.23539i	0.186668	+	0.168076i
$636$	8.96594	−	31.4139i	0.355523	−	1.24564i
$637$	−22.5123	+	2.98526i	−0.891971	+	0.118281i
$638$	−4.11312	+	7.47290i	−0.162840	+	0.295855i
$639$	5.60225	+	9.70338i	0.221621	+	0.383860i
$640$	−2.75648	+	5.71401i	−0.108959	+	0.225866i
$641$	28.5825	+	6.07539i	1.12894	+	0.239964i	0.734269	−	0.678859i	$-0.237525\pi$
$641$	28.5825	+	6.07539i	1.12894	+	0.239964i	0.394671	+	0.918822i	$0.370858\pi$
$642$	19.2983	+	18.6132i	0.761643	+	0.734604i
$643$	−44.2185	+	19.6874i	−1.74381	+	0.776394i	−0.750505	+	0.660865i	$0.770190\pi$
$643$	−44.2185	+	19.6874i	−1.74381	+	0.776394i	−0.993304	+	0.115529i	$0.963144\pi$
$644$	11.9817	+	6.35187i	0.472146	+	0.250299i
$645$	1.46561	−	4.51068i	0.0577083	−	0.177608i
$646$	−12.1594	−	9.48790i	−0.478404	−	0.373296i
$647$	−12.2405	+	27.4927i	−0.481225	+	1.08085i	0.495939	+	0.868358i	$0.334824\pi$
$647$	−12.2405	+	27.4927i	−0.481225	+	1.08085i	−0.977163	+	0.212490i	$0.931843\pi$
$648$	8.92192	−	8.06323i	0.350486	−	0.316753i
$649$	0.0501418	+	0.0404072i	0.00196824	+	0.00158612i
$650$	22.6689	+	7.54578i	0.889146	+	0.295970i
$651$	5.45228	−	3.96131i	0.213692	−	0.155256i
$652$	31.7509	+	2.18094i	1.24346	+	0.0854123i
$653$	−2.98278	+	0.634010i	−0.116725	+	0.0248107i	−0.265904	−	0.964000i	$-0.585670\pi$
$653$	−2.98278	+	0.634010i	−0.116725	+	0.0248107i	0.149179	+	0.988810i	$0.452337\pi$
$654$	0.965878	−	28.1563i	0.0377688	−	1.10100i
$655$	6.53967	−	9.00108i	0.255526	−	0.351701i
$656$	27.1889	−	14.5426i	1.06155	−	0.567795i
$657$	−4.47208	−	0.950570i	−0.174473	−	0.0370853i
$658$	0.195463	+	1.10455i	0.00761996	+	0.0430598i
$659$	−3.22623	+	5.58800i	−0.125676	+	0.217677i	−0.921997	−	0.387197i	$-0.873443\pi$
$659$	−3.22623	+	5.58800i	−0.125676	+	0.217677i	0.796321	+	0.604874i	$0.206777\pi$
$660$	0.984460	+	4.96884i	0.0383201	+	0.193412i
$661$	30.9679	−	17.8793i	1.20451	−	0.695426i	0.242957	−	0.970037i	$-0.421883\pi$
$661$	30.9679	−	17.8793i	1.20451	−	0.695426i	0.961555	+	0.274611i	$0.0885492\pi$
$662$	−13.1503	+	2.32710i	−0.511100	+	0.0904453i
$663$	−26.5962	−	2.06810i	−1.03291	−	0.0803183i
$664$	−0.908906	+	8.80411i	−0.0352724	+	0.341666i
$665$	−0.937625	−	0.0985483i	−0.0363595	−	0.00382154i
$666$	1.62791	+	1.01584i	0.0630804	+	0.0393630i
$667$	−9.85133	−	10.9410i	−0.381445	−	0.423637i
$668$	26.4342	+	17.7828i	1.02277	+	0.688036i
$669$	−36.1675	+	3.80136i	−1.39832	+	0.146969i
$670$	1.68561	+	2.49571i	0.0651210	+	0.0964177i
$671$	−22.1261	−	33.8946i	−0.854169	−	1.30849i
$672$	2.22552	+	6.05648i	0.0858515	+	0.233634i
$673$	4.74106	−	10.6486i	0.182755	−	0.410473i	−0.798816	−	0.601576i	$-0.794540\pi$
$673$	4.74106	−	10.6486i	0.182755	−	0.410473i	0.981570	+	0.191103i	$0.0612063\pi$
$674$	2.69463	+	6.65764i	0.103793	+	0.256443i
$675$	−25.1570	−	8.17401i	−0.968294	−	0.314618i
$676$	−7.67884	−	24.8402i	−0.295340	−	0.955392i
$677$	−1.27242	+	1.75133i	−0.0489030	+	0.0673092i	−0.832768	−	0.553622i	$-0.813245\pi$
$677$	−1.27242	+	1.75133i	−0.0489030	+	0.0673092i	0.783865	+	0.620931i	$0.213245\pi$
$678$	7.08200	−	28.4791i	0.271983	−	1.09373i
$679$	10.2517	−	11.3857i	0.393425	−	0.436942i
$680$	−8.19017	+	2.67789i	−0.314079	+	0.102692i
$681$	11.6592			0.446780
$682$	27.6146	+	2.33274i	1.05742	+	0.0893251i
$683$	13.2275	−	22.9108i	0.506138	−	0.876656i	−0.493837	−	0.869555i	$-0.664406\pi$
$683$	13.2275	−	22.9108i	0.506138	−	0.876656i	0.999975	−	0.00710192i	$-0.00226063\pi$
$684$	−1.26208	+	4.42194i	−0.0482568	+	0.169077i
$685$	−11.1029	−	2.35998i	−0.424218	−	0.0901704i
$686$	−3.80141	+	15.2867i	−0.145138	+	0.583649i
$687$	0.341954	−	3.25348i	0.0130464	−	0.124128i
$688$	18.9915	−	16.0157i	0.724046	−	0.610592i
$689$	32.9109	+	28.0553i	1.25381	+	1.06882i
$690$	−8.65840	−	1.21142i	−0.329620	−	0.0461180i
$691$	44.9464	+	20.0114i	1.70984	+	0.761270i	0.998279	+	0.0586469i	$0.0186786\pi$
$691$	44.9464	+	20.0114i	1.70984	+	0.761270i	0.711562	+	0.702623i	$0.247988\pi$
$692$	12.5679	+	5.05975i	0.477759	+	0.192343i
$693$	−2.67271	−	1.72666i	−0.101528	−	0.0655904i
$694$	4.40544	+	2.14532i	0.167228	+	0.0814352i
$695$	4.85120	−	0.509881i	0.184016	−	0.0193409i
$696$	−0.0129424	−	7.00498i	−0.000490580	−	0.265523i
$697$	39.8299	+	12.9415i	1.50867	+	0.490195i
$698$	1.80081	+	0.0617752i	0.0681616	+	0.00233823i
$699$	3.02934	−	28.8222i	0.114580	−	1.09016i
$700$	5.03788	−	6.01895i	0.190414	−	0.227495i
$701$	−36.1739	+	11.7536i	−1.36627	+	0.443927i	−0.898131	−	0.439729i	$-0.855075\pi$
$701$	−36.1739	+	11.7536i	−1.36627	+	0.443927i	−0.468137	+	0.883656i	$0.655075\pi$
$702$	8.69867	+	27.4400i	0.328310	+	1.03566i
$703$	2.37783			0.0896817
$704$	−9.35802	+	24.8280i	−0.352693	+	0.935739i
$705$	−0.361575	−	0.626266i	−0.0136177	−	0.0235865i
$706$	20.0125	+	7.26999i	0.753179	+	0.273610i
$707$	−1.03651	−	3.19004i	−0.0389819	−	0.119974i
$708$	−0.0520913	−	0.00911895i	−0.00195771	−	0.000342711i
$709$	8.90557	+	20.0022i	0.334456	+	0.751199i	0.999988	+	0.00483080i	$0.00153770\pi$
$709$	8.90557	+	20.0022i	0.334456	+	0.751199i	−0.665533	+	0.746369i	$0.731796\pi$
$710$	6.84698	−	3.64602i	0.256963	−	0.136833i
$711$	−3.20336	−	3.55769i	−0.120135	−	0.133424i
$712$	−10.4464	+	18.1712i	−0.391497	+	0.680995i
$713$	−19.4548	+	43.6963i	−0.728589	+	1.63644i
$714$	−3.83701	+	7.87934i	−0.143596	+	0.294877i
$715$	−6.52544	−	1.54377i	−0.244038	−	0.0577339i
$716$	−9.78228	+	7.66218i	−0.365581	+	0.286349i
$717$	20.0632	+	8.93273i	0.749275	+	0.333599i
$718$	12.1210	+	29.9475i	0.452353	+	1.11763i
$719$	23.0892	−	20.7896i	0.861083	−	0.775322i	−0.114853	−	0.993383i	$-0.536640\pi$
$719$	23.0892	−	20.7896i	0.861083	−	0.775322i	0.975935	+	0.218060i	$0.0699729\pi$
$720$	1.65628	+	1.96404i	0.0617261	+	0.0731953i
$721$	15.4359	−	6.87251i	0.574863	−	0.255946i
$722$	−5.84822	−	20.3479i	−0.217648	−	0.757270i
$723$	−28.8167	+	9.36310i	−1.07170	+	0.348217i
$724$	19.7991	−	19.1670i	0.735828	−	0.712335i
$725$	−7.37961	+	4.26062i	−0.274072	+	0.158235i
$726$	5.94862	+	20.3327i	0.220774	+	0.754619i
$727$			8.43605i			0.312876i	0.987688	+	0.156438i	$0.0500011\pi$
$727$			8.43605i			0.312876i	−0.987688	+	0.156438i	$0.949999\pi$
$728$	−8.51719	−	0.646460i	−0.315668	−	0.0239594i
$729$	−8.63208	−	26.5668i	−0.319707	−	0.983956i
$730$	−0.763873	+	3.07178i	−0.0282722	+	0.113692i
$731$	33.5580	+	3.52709i	1.24119	+	0.130454i
$732$	29.3688	+	15.5693i	1.08550	+	0.575457i
$733$	2.81930	−	8.67692i	0.104133	−	0.320489i	−0.885393	−	0.464844i	$-0.846111\pi$
$733$	2.81930	−	8.67692i	0.104133	−	0.320489i	0.989526	+	0.144354i	$0.0461105\pi$
$734$	−21.4279	+	27.4612i	−0.790917	+	1.01361i
$735$	−0.502757	−	4.78341i	−0.0185445	−	0.176439i
$736$	−35.1715	−	29.3283i	−1.29644	−	1.08105i
$737$	7.94982	+	9.76965i	0.292835	+	0.359870i
$738$	−0.878705	−	12.4558i	−0.0323456	−	0.458505i
$739$	−16.3220	+	36.6599i	−0.600416	+	1.34856i	0.316164	+	0.948705i	$0.397605\pi$
$739$	−16.3220	+	36.6599i	−0.600416	+	1.34856i	−0.916580	+	0.399852i	$0.869062\pi$
$740$	0.741526	−	1.10228i	0.0272590	−	0.0405207i
$741$	7.50078	+	6.39413i	0.275548	+	0.234894i
$742$	12.5404	−	6.67774i	0.460371	−	0.245148i
$743$	27.0640	+	2.84455i	0.992883	+	0.104356i	0.587016	−	0.809576i	$-0.300303\pi$
$743$	27.0640	+	2.84455i	0.992883	+	0.104356i	0.405868	+	0.913932i	$0.366969\pi$
$744$	−20.7735	+	9.29500i	−0.761594	+	0.340771i
$745$	−0.468592	+	2.20455i	−0.0171679	+	0.0807686i
$746$	−4.79453	−	27.0936i	−0.175540	−	0.991966i
$747$	3.10414	+	1.79217i	0.113574	+	0.0655722i
$748$	−33.1222	+	14.2008i	−1.21107	+	0.519232i
$749$			11.6605i			0.426065i
$750$	−3.57146	+	9.83133i	−0.130411	+	0.358989i
$751$	15.6979	+	14.1344i	0.572823	+	0.515772i	0.903850	−	0.427849i	$-0.140729\pi$
$751$	15.6979	+	14.1344i	0.572823	+	0.515772i	−0.331027	+	0.943621i	$0.607395\pi$
$752$	0.122870	−	3.78591i	0.00448060	−	0.138058i
$753$	2.06592	+	1.50098i	0.0752864	+	0.0546988i
$754$	8.44417	+	3.83241i	0.307519	+	0.139568i
$755$	−1.45800	+	4.48727i	−0.0530621	+	0.163308i
$756$	9.43466	+	0.648059i	0.343135	+	0.0235697i
$757$	28.6623	+	12.7613i	1.04175	+	0.463817i	0.855021	−	0.518594i	$-0.173544\pi$
$757$	28.6623	+	12.7613i	1.04175	+	0.463817i	0.186730	+	0.982411i	$0.440211\pi$
$758$	14.5868	−	9.85201i	0.529817	−	0.357841i
$759$	−36.5190	−	1.82688i	−1.32555	−	0.0663116i
$760$	3.02969	+	0.978222i	0.109899	+	0.0354839i
$761$	1.50143	+	14.2851i	0.0544267	+	0.517836i	0.987440	+	0.157994i	$0.0505027\pi$
$761$	1.50143	+	14.2851i	0.0544267	+	0.517836i	−0.933013	+	0.359842i	$0.882831\pi$
$762$	−21.5299	−	3.01231i	−0.779946	−	0.109124i
$763$	9.10531	−	8.19845i	0.329634	−	0.296804i
$764$	9.52172	+	15.1963i	0.344484	+	0.549781i
$765$	−0.364758	+	3.47045i	−0.0131879	+	0.125474i
$766$	−23.0736	+	23.9228i	−0.833682	+	0.864367i
$767$	0.0395981	−	0.0577315i	0.00142981	−	0.00208456i
$768$	−3.13875	−	21.5620i	−0.113260	−	0.778051i
$769$	−20.0193	−	34.6745i	−0.721916	−	1.25039i	−0.960231	−	0.279207i	$-0.909929\pi$
$769$	−20.0193	−	34.6745i	−0.721916	−	1.25039i	0.238315	−	0.971188i	$-0.423405\pi$
$770$	−1.25816	+	1.80833i	−0.0453409	+	0.0651676i
$771$	−5.58627	−	3.22523i	−0.201184	−	0.116154i
$772$	−26.4161	−	7.53949i	−0.950735	−	0.271352i
$773$	−1.30590	+	6.14376i	−0.0469698	+	0.220976i	−0.995372	−	0.0960932i	$-0.969365\pi$
$773$	−1.30590	+	6.14376i	−0.0469698	+	0.220976i	0.948403	+	0.317069i	$0.102699\pi$
$774$	−2.77907	−	9.66928i	−0.0998915	−	0.347555i
$775$	22.3970	+	16.2724i	0.804526	+	0.584522i
$776$	−41.8001	+	30.4877i	−1.50054	+	1.09444i
$777$	−0.280924	−	1.32164i	−0.0100781	−	0.0474137i
$778$	39.6651	−	16.0542i	1.42206	−	0.575570i
$779$	−9.09508	−	12.5183i	−0.325865	−	0.448515i
$780$	5.30321	−	1.48310i	0.189886	−	0.0531036i
$781$	27.1669	−	17.7343i	0.972108	−	0.634583i
$782$	−4.37709	−	62.0462i	−0.156525	−	2.21877i
$783$	−9.37912	−	4.17585i	−0.335183	−	0.149233i
$784$	10.9884	−	22.6712i	0.392444	−	0.809686i
$785$	−0.239141	−	0.0777015i	−0.00853530	−	0.00277329i
$786$	−1.31008	+	38.1901i	−0.0467290	+	1.36220i
$787$	1.08642	+	2.44014i	0.0387267	+	0.0869815i	0.931873	−	0.362785i	$-0.118174\pi$
$787$	1.08642	+	2.44014i	0.0387267	+	0.0869815i	−0.893146	+	0.449766i	$0.851507\pi$
$788$	33.8278	−	12.3595i	1.20506	−	0.440289i
$789$	5.93475	−	27.9208i	0.211283	−	0.994007i
$790$	−2.53769	+	2.13204i	−0.0902871	+	0.0758547i
$791$	11.0529	−	6.38139i	0.392995	−	0.226896i
$792$	7.62993	+	7.56575i	0.271118	+	0.268837i
$793$	−34.8852	+	26.8203i	−1.23881	+	0.952417i
$794$	5.84730	+	33.0427i	0.207513	+	1.17264i
$795$	−6.12881	+	6.80673i	−0.217366	+	0.241410i
$796$	−2.63858	+	3.15242i	−0.0935221	+	0.111735i
$797$	−19.4011	+	8.63794i	−0.687223	+	0.305971i	−0.720480	−	0.693475i	$-0.756079\pi$
$797$	−19.4011	+	8.63794i	−0.687223	+	0.305971i	0.0332572	+	0.999447i	$0.489412\pi$
$798$	2.85809	−	1.52193i	0.101175	−	0.0538759i
$799$	3.82338	−	3.44259i	0.135262	−	0.121790i
$800$	−20.8363	+	16.3827i	−0.736675	+	0.579215i
$801$	4.98922	+	6.86707i	0.176285	+	0.242636i
$802$	15.0002	+	22.2093i	0.529677	+	0.784236i
$803$	−2.03986	+	13.0802i	−0.0719851	+	0.461592i
$804$	−9.59514	−	3.86295i	−0.338394	−	0.136236i
$805$	−2.23489	−	3.07606i	−0.0787695	−	0.108417i
$806$	0.216128	−	30.1264i	0.00761279	−	1.06116i
$807$	35.5004	+	11.5348i	1.24967	+	0.406044i
$808$	1.20479	+	11.2626i	0.0423842	+	0.396215i
$809$	−12.7058	−	1.33543i	−0.446713	−	0.0469514i	−0.121498	−	0.992592i	$-0.538770\pi$
$809$	−12.7058	−	1.33543i	−0.446713	−	0.0469514i	−0.325215	+	0.945640i	$0.605437\pi$
$810$	−3.24049	+	0.931356i	−0.113859	+	0.0327245i
$811$	−14.0431	+	4.56287i	−0.493119	+	0.160224i	−0.545011	−	0.838429i	$-0.683475\pi$
$811$	−14.0431	+	4.56287i	−0.493119	+	0.160224i	0.0518925	+	0.998653i	$0.483475\pi$
$812$	2.18884	−	2.11896i	0.0768134	−	0.0743609i
$813$	−5.29613	+	9.17316i	−0.185743	+	0.321717i
$814$	2.67912	−	4.86754i	0.0939029	−	0.170607i
$815$	−7.72763	−	4.46155i	−0.270687	−	0.156281i
$816$	18.1629	−	23.3659i	0.635830	−	0.817971i
$817$	−9.26488	−	8.34213i	−0.324137	−	0.291854i
$818$	24.1353	−	25.0236i	0.843870	−	0.874930i
$819$	−1.64770	+	3.04149i	−0.0575755	+	0.106278i
$820$	−8.63936	+	0.312348i	−0.301699	+	0.0109077i
$821$	4.10134	−	0.871767i	0.143138	−	0.0304249i	−0.135785	−	0.990738i	$-0.543356\pi$
$821$	4.10134	−	0.871767i	0.143138	−	0.0304249i	0.278923	+	0.960313i	$0.410022\pi$
$822$	36.1374	−	14.6264i	1.26044	−	0.510153i
$823$	−18.5186	+	1.94638i	−0.645517	+	0.0678466i	−0.421629	−	0.906768i	$-0.638542\pi$
$823$	−18.5186	+	1.94638i	−0.645517	+	0.0678466i	−0.223888	+	0.974615i	$0.571875\pi$
$824$	−55.7896	+	11.9662i	−1.94352	+	0.416863i
$825$	−5.42884	+	20.4550i	−0.189008	+	0.712151i
$826$	−0.0128726	−	0.0190591i	−0.000447897	−	0.000663153i
$827$	24.4557	+	33.6604i	0.850407	+	1.17049i	0.983773	+	0.179418i	$0.0574216\pi$
$827$	24.4557	+	33.6604i	0.850407	+	1.17049i	−0.133365	+	0.991067i	$0.542578\pi$
$828$	−16.6586	+	8.15038i	−0.578928	+	0.283245i
$829$	−39.0417	+	8.29857i	−1.35597	+	0.288221i	−0.827852	−	0.560947i	$-0.810437\pi$
$829$	−39.0417	+	8.29857i	−1.35597	+	0.288221i	−0.528123	+	0.849168i	$0.677104\pi$
$830$	1.31373	−	2.10529i	0.0456002	−	0.0730757i
$831$	−7.09949	−	5.15808i	−0.246279	−	0.178932i
$832$	27.6942	+	8.06406i	0.960125	+	0.279571i
$833$	32.5444	−	10.5743i	1.12760	−	0.366378i
$834$	−12.8272	+	10.7768i	−0.444171	+	0.373170i
$835$	−4.46622	−	7.73571i	−0.154560	−	0.267705i
$836$	12.9846	+	2.94843i	0.449082	+	0.101974i
$837$			33.3551i			1.15292i
$838$	2.47437	+	0.898873i	0.0854758	+	0.0310510i
$839$	−54.9452	−	11.6790i	−1.89692	−	0.403202i	−0.897623	−	0.440763i	$-0.854708\pi$
$839$	−54.9452	−	11.6790i	−1.89692	−	0.403202i	−0.999294	+	0.0375608i	$0.988041\pi$
$840$	0.185777	−	1.79953i	0.00640993	−	0.0620897i
$841$	23.4714	−	10.4501i	0.809358	−	0.360350i
$842$	−20.3436	−	12.6947i	−0.701087	−	0.437488i
$843$	−5.30080	−	24.9383i	−0.182569	−	0.858921i
$844$	−8.40146	+	12.4888i	−0.289190	+	0.429883i
$845$	−1.12687	+	7.20210i	−0.0387655	+	0.247760i
$846$	−1.37915	−	0.671607i	−0.0474163	−	0.0230903i
$847$	−4.56873	+	8.00084i	−0.156983	+	0.274912i
$848$	−46.0860	+	13.3379i	−1.58260	+	0.458026i
$849$	12.8426	−	1.34981i	0.440756	−	0.0463253i
$850$	−35.6535	−	4.98839i	−1.22291	−	0.171100i
$851$	6.41675	+	7.12652i	0.219963	+	0.244294i
$852$	−12.4789	+	23.5394i	−0.427522	+	0.806446i
$853$	2.23271	+	1.62216i	0.0764467	+	0.0555418i	0.625352	−	0.780343i	$-0.284955\pi$
$853$	2.23271	+	1.62216i	0.0764467	+	0.0555418i	−0.548906	+	0.835884i	$0.684955\pi$
$854$	3.99325	+	13.8938i	0.136646	+	0.475437i
$855$	0.862713	−	0.958140i	0.0295042	−	0.0327677i
$856$	8.11562	−	38.5309i	0.277386	−	1.31696i
$857$		−	7.19831i		−	0.245889i	−0.992414	−	0.122945i	$-0.960766\pi$
$857$		−	7.19831i		−	0.245889i	0.992414	−	0.122945i	$-0.0392338\pi$
$858$	21.5402	−	8.15017i	0.735372	−	0.278242i
$859$			28.4529i			0.970801i	0.874292	+	0.485401i	$0.161326\pi$
$859$			28.4529i			0.970801i	−0.874292	+	0.485401i	$0.838674\pi$
$860$	−6.75638	+	1.69340i	−0.230391	+	0.0577443i
$861$	−5.88339	+	6.53416i	−0.200505	+	0.222684i
$862$	−34.9199	+	10.0364i	−1.18938	+	0.341841i
$863$	32.0274	+	23.2693i	1.09023	+	0.792096i	0.979438	−	0.201748i	$-0.0646621\pi$
$863$	32.0274	+	23.2693i	1.09023	+	0.792096i	0.110789	+	0.993844i	$0.464662\pi$
$864$	−30.7248	−	8.70789i	−1.04528	−	0.296249i
$865$	−2.54172	−	2.82287i	−0.0864212	−	0.0959805i
$866$	0.0701214	−	0.501179i	0.00238282	−	0.0170308i
$867$	16.9525	−	1.78178i	0.575736	−	0.0605123i
$868$	−9.18142	−	3.69639i	−0.311638	−	0.125464i
$869$	−9.77855	+	9.82512i	−0.331714	+	0.333294i
$870$	−0.859881	+	1.76578i	−0.0291527	+	0.0598654i
$871$	9.92351	−	9.43474i	0.336245	−	0.319684i
$872$	−35.7936	+	20.7537i	−1.21212	+	0.702810i
$873$	4.35618	+	20.4942i	0.147434	+	0.693624i
$874$	−12.1663	+	19.4969i	−0.411532	+	0.659492i
$875$	−4.15575	+	1.85026i	−0.140490	+	0.0625502i
$876$	−3.73085	−	10.2113i	−0.126054	−	0.345007i
$877$	16.7314	+	3.55636i	0.564978	+	0.120090i	0.481542	−	0.876423i	$-0.340077\pi$
$877$	16.7314	+	3.55636i	0.564978	+	0.120090i	0.0834367	+	0.996513i	$0.473410\pi$
$878$	−6.55952	+	18.0567i	−0.221373	+	0.609385i
$879$		−	6.80291i		−	0.229457i
$880$	5.41604	−	5.09976i	0.182575	−	0.171913i
$881$	−15.5930	−	27.0078i	−0.525340	−	0.909916i	−0.999564	−	0.0295121i	$-0.990605\pi$
$881$	−15.5930	−	27.0078i	−0.525340	−	0.909916i	0.474224	−	0.880404i	$-0.342729\pi$
$882$	−6.56301	−	7.81172i	−0.220988	−	0.263034i
$883$	49.7033	−	16.1496i	1.67265	−	0.543476i	0.689185	−	0.724585i	$-0.257969\pi$
$883$	49.7033	−	16.1496i	1.67265	−	0.543476i	0.983463	+	0.181109i	$0.0579686\pi$
$884$	18.1655	+	34.7116i	0.610971	+	1.16748i
$885$	0.0119954	+	0.00871517i	0.000403221	+	0.000292957i
$886$	−11.6860	−	7.29224i	−0.392600	−	0.244988i
$887$	−41.3330	+	8.78561i	−1.38783	+	0.294992i	−0.840448	−	0.541893i	$-0.817708\pi$
$887$	−41.3330	+	8.78561i	−1.38783	+	0.294992i	−0.547380	+	0.836885i	$0.684375\pi$
$888$	0.00843013	+	4.56276i	0.000282897	+	0.153116i
$889$	−5.55726	−	7.64891i	−0.186384	−	0.256536i
$890$	4.86992	−	3.28917i	0.163240	−	0.110253i
$891$	−13.1527	+	5.08473i	−0.440631	+	0.170345i
$892$	32.9335	+	42.0461i	1.10270	+	1.40781i
$893$	−1.89049	+	0.198698i	−0.0632627	+	0.00664918i
$894$	−2.90417	−	7.17535i	−0.0971300	−	0.239980i
$895$	3.40775	−	0.724340i	0.113909	−	0.0242120i
$896$	5.80186	−	7.49239i	0.193826	−	0.250303i
$897$	1.07776	+	39.7353i	0.0359853	+	1.32672i
$898$	5.59189	+	5.39337i	0.186604	+	0.179979i
$899$	7.98520	+	7.18990i	0.266321	+	0.239797i
$900$	2.60960	+	10.4119i	0.0869868	+	0.347063i
$901$	−56.4341	−	32.5823i	−1.88009	−	1.08547i
$902$	−35.8730	+	4.51364i	−1.19444	+	0.150288i
$903$	−3.54213	+	6.13516i	−0.117875	+	0.204165i
$904$	−40.9645	+	13.3939i	−1.36246	+	0.445475i
$905$	−7.34806	+	2.38753i	−0.244258	+	0.0793642i
$906$	−4.47625	−	15.5743i	−0.148714	−	0.517423i
$907$	−1.74751	−	0.183671i	−0.0580252	−	0.00609869i	0.0754714	−	0.997148i	$-0.475954\pi$
$907$	−1.74751	−	0.183671i	−0.0580252	−	0.00609869i	−0.133497	+	0.991049i	$0.542621\pi$
$908$	−9.09160	−	14.5098i	−0.301715	−	0.481525i
$909$	4.36252	+	1.41747i	0.144696	+	0.0470144i
$910$	2.06537	+	1.21228i	0.0684664	+	0.0401867i
$911$	2.29890	+	3.16417i	0.0761661	+	0.104834i	0.845400	−	0.534133i	$-0.179362\pi$
$911$	2.29890	+	3.16417i	0.0761661	+	0.104834i	−0.769234	+	0.638967i	$0.779362\pi$
$912$	−10.5035	+	3.03986i	−0.347807	+	0.100660i
$913$	4.68980	−	9.25857i	0.155210	−	0.306414i
$914$	9.40417	−	6.35162i	0.311062	−	0.210093i
$915$	−5.47801	−	7.53984i	−0.181098	−	0.249259i
$916$	−4.31559	+	2.11144i	−0.142591	+	0.0697639i
$917$	−12.3501	+	11.1201i	−0.407836	+	0.367217i
$918$	−20.3870	−	38.2855i	−0.672872	−	1.26361i
$919$	48.7984	−	21.7264i	1.60971	−	0.716689i	0.612439	−	0.790518i	$-0.290189\pi$
$919$	48.7984	−	21.7264i	1.60971	−	0.716689i	0.997271	+	0.0738289i	$0.0235219\pi$
$920$	5.24405	+	11.7200i	0.172891	+	0.386397i
$921$	24.4839	−	27.1921i	0.806771	−	0.896010i
$922$	5.05153	−	0.893929i	0.166363	−	0.0294400i
$923$	−21.4967	−	27.9608i	−0.707574	−	0.920342i
$924$	0.104755	−	7.56543i	0.00344618	−	0.248884i
$925$	4.80677	−	2.77519i	0.158046	−	0.0912477i
$926$	−0.0213196	−	0.0253760i	−0.000700607	−	0.000833907i
$927$	−4.80421	+	22.6020i	−0.157791	+	0.742348i
$928$	−8.70759	+	5.47846i	−0.285841	+	0.179839i
$929$	−4.21979	−	9.47779i	−0.138447	−	0.310956i	0.830994	−	0.556281i	$-0.187772\pi$
$929$	−4.21979	−	9.47779i	−0.138447	−	0.310956i	−0.969441	+	0.245325i	$0.921105\pi$
$930$	6.37706	+	0.218760i	0.209112	+	0.00717341i
$931$	−12.0243	−	3.90694i	−0.394081	−	0.128045i
$932$	−38.2314	+	18.7050i	−1.25231	+	0.612704i
$933$	−11.4400	−	5.09340i	−0.374527	−	0.166750i
$934$	34.4158	−	2.42789i	1.12612	−	0.0794430i
$935$	10.0915	+	0.504834i	0.330028	+	0.0165098i
$936$	7.56152	−	8.90349i	0.247156	−	0.291020i
$937$	−2.89738	−	3.98790i	−0.0946532	−	0.130279i	0.759064	−	0.651016i	$-0.225657\pi$
$937$	−2.89738	−	3.98790i	−0.0946532	−	0.130279i	−0.853717	+	0.520737i	$0.825657\pi$
$938$	−1.68771	−	4.16982i	−0.0551056	−	0.136150i
$939$	5.54938	+	26.1078i	0.181097	+	0.851995i
$940$	−0.497437	+	0.938330i	−0.0162246	+	0.0306049i
$941$	1.15668	+	0.840379i	0.0377068	+	0.0273956i	0.606479	−	0.795099i	$-0.292581\pi$
$941$	1.15668	+	0.840379i	0.0377068	+	0.0273956i	−0.568772	+	0.822495i	$0.692581\pi$
$942$	0.830006	−	0.238554i	0.0270431	−	0.00777250i
$943$	12.9745	−	61.0401i	0.422507	−	1.98774i
$944$	0.0292713	+	0.0719382i	0.000952699	+	0.00234139i
$945$	−2.29624	−	1.32573i	−0.0746965	−	0.0431261i
$946$	−27.5155	+	9.56654i	−0.894607	+	0.311035i
$947$	−23.5408	−	40.7739i	−0.764974	−	1.32497i	−0.940260	−	0.340457i	$-0.889418\pi$
$947$	−23.5408	−	40.7739i	−0.764974	−	1.32497i	0.175286	−	0.984518i	$-0.443915\pi$
$948$	3.12426	−	10.9465i	0.101471	−	0.355525i
$949$	14.3483	+	1.11571i	0.465765	+	0.0362175i
$950$	9.57390	+	9.23402i	0.310618	+	0.299591i
$951$	1.68097	−	15.9934i	0.0545092	−	0.518620i
$952$	12.7978	−	1.36902i	0.414780	−	0.0443701i
$953$	−36.0322	+	32.4435i	−1.16720	+	1.05095i	−0.169337	+	0.985558i	$0.554163\pi$
$953$	−36.0322	+	32.4435i	−1.16720	+	1.05095i	−0.997860	+	0.0653909i	$0.979171\pi$
$954$	−2.69220	+	19.2419i	−0.0871630	+	0.622981i
$955$	−0.525561	−	5.00038i	−0.0170067	−	0.161808i
$956$	−4.52818	−	31.9342i	−0.146452	−	1.03283i
$957$	−2.92544	+	7.67548i	−0.0945659	+	0.248113i
$958$	25.5953	+	37.8962i	0.826945	+	1.22437i
$959$	15.4889	+	6.89609i	0.500162	+	0.222686i
$960$	−1.86634	+	5.81706i	−0.0602359	+	0.187745i
$961$	1.20808	−	3.71809i	0.0389703	−	0.119938i
$962$	−5.50019	−	2.49627i	−0.177333	−	0.0804831i
$963$	−12.9008	−	9.37295i	−0.415721	−	0.302039i
$964$	34.1230	+	28.5611i	1.09903	+	0.919891i
$965$	5.72380	+	5.15373i	0.184256	+	0.165905i
$966$	12.2741	+	4.45885i	0.394913	+	0.143461i
$967$			18.0860i			0.581606i	0.956783	+	0.290803i	$0.0939225\pi$
$967$			18.0860i			0.581606i	−0.956783	+	0.290803i	$0.906078\pi$
$968$	20.6654	−	23.2581i	0.664212	−	0.747545i
$969$	−12.8620	−	7.42587i	−0.413186	−	0.238553i
$970$	14.2839	−	2.52770i	0.458627	−	0.0811595i
$971$	−3.43697	+	16.1697i	−0.110298	+	0.518909i	0.887961	+	0.459919i	$0.152121\pi$
$971$	−3.43697	+	16.1697i	−0.110298	+	0.518909i	−0.998259	+	0.0589904i	$0.981212\pi$
$972$	−14.3079	+	17.0943i	−0.458928	+	0.548299i
$973$	−7.24617	−	0.761603i	−0.232302	−	0.0244159i
$974$	−0.508671	−	0.955252i	−0.0162989	−	0.0306082i
$975$	22.6254	+	4.17145i	0.724593	+	0.133593i
$976$	−3.52529	−	48.6900i	−0.112842	−	1.55853i
$977$	14.9835	−	33.6535i	0.479365	−	1.07667i	−0.498397	−	0.866949i	$-0.666078\pi$
$977$	14.9835	−	33.6535i	0.479365	−	1.07667i	0.977761	−	0.209721i	$-0.0672557\pi$
$978$	30.5708	−	2.15664i	0.977547	−	0.0689618i
$979$	19.0637	−	15.5126i	0.609279	−	0.495786i
$980$	−5.56090	+	4.35570i	−0.177637	+	0.139138i
$981$	1.75145	+	16.6639i	0.0559193	+	0.532037i
$982$	−15.3778	−	11.9992i	−0.490726	−	0.382911i
$983$	−13.8617	+	42.6620i	−0.442121	+	1.36071i	0.443490	+	0.896279i	$0.353740\pi$
$983$	−13.8617	+	42.6620i	−0.442121	+	1.36071i	−0.885611	+	0.464428i	$0.846260\pi$
$984$	23.9888	−	17.4967i	0.764734	−	0.557773i
$985$	−10.0423	−	1.05549i	−0.319975	−	0.0336307i
$986$	−13.5601	−	3.37204i	−0.431841	−	0.107388i
$987$	0.333788	+	1.02729i	0.0106246	+	0.0326991i
$988$	2.10851	−	14.3207i	0.0670805	−	0.455603i
$989$		−	50.2793i		−	1.59879i
$990$	−0.989336	−	2.84556i	−0.0314432	−	0.0904377i
$991$	−17.0788	+	9.86043i	−0.542525	+	0.313227i	−0.746102	−	0.665832i	$-0.768077\pi$
$991$	−17.0788	+	9.86043i	−0.542525	+	0.313227i	0.203577	+	0.979059i	$0.434743\pi$
$992$	27.7664	+	18.6045i	0.881584	+	0.590694i
$993$	−12.2305	+	3.97393i	−0.388123	+	0.126109i
$994$	−11.1360	+	3.20063i	−0.353214	+	0.101518i
$995$	1.05295	−	0.468805i	0.0333809	−	0.0148621i
$996$	0.307941	+	8.51747i	0.00975748	+	0.269886i
$997$	15.0238	−	13.5275i	0.475809	−	0.428421i	−0.396011	−	0.918246i	$-0.629606\pi$
$997$	15.0238	−	13.5275i	0.475809	−	0.428421i	0.871821	+	0.489825i	$0.162939\pi$
$998$	6.73145	−	2.72450i	0.213080	−	0.0862427i
$999$	6.10917	+	2.71998i	0.193286	+	0.0860564i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bn.a.283.24	yes	640
4.3	odd	2	inner	572.2.bn.a.283.2	yes	640
11.7	odd	10	inner	572.2.bn.a.491.27	yes	640
13.4	even	6	inner	572.2.bn.a.459.50	yes	640
44.7	even	10	inner	572.2.bn.a.491.50	yes	640
52.43	odd	6	inner	572.2.bn.a.459.27	yes	640
143.95	odd	30	inner	572.2.bn.a.95.2	✓	640
572.95	even	30	inner	572.2.bn.a.95.24	yes	640

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bn.a.95.2	✓	640	143.95	odd	30	inner
572.2.bn.a.95.24	yes	640	572.95	even	30	inner
572.2.bn.a.283.2	yes	640	4.3	odd	2	inner
572.2.bn.a.283.24	yes	640	1.1	even	1	trivial
572.2.bn.a.459.27	yes	640	52.43	odd	6	inner
572.2.bn.a.459.50	yes	640	13.4	even	6	inner
572.2.bn.a.491.27	yes	640	11.7	odd	10	inner
572.2.bn.a.491.50	yes	640	44.7	even	10	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.909706 - 1.08279i) q^{2} +(-1.01203 - 0.911240i) q^{3} +(-0.344870 + 1.97004i) q^{4} +(0.329599 - 0.453654i) q^{5} +(-0.0660280 + 1.92478i) q^{6} +(-0.622444 + 0.560451i) q^{7} +(2.44687 - 1.41874i) q^{8} +(-0.119730 - 1.13915i) q^{9} +O(q^{10})\)	\(q+(-0.909706 - 1.08279i) q^{2} +(-1.01203 - 0.911240i) q^{3} +(-0.344870 + 1.97004i) q^{4} +(0.329599 - 0.453654i) q^{5} +(-0.0660280 + 1.92478i) q^{6} +(-0.622444 + 0.560451i) q^{7} +(2.44687 - 1.41874i) q^{8} +(-0.119730 - 1.13915i) q^{9} +(-0.791051 + 0.0558053i) q^{10} +(-3.27455 + 0.526616i) q^{11} +(2.14420 - 1.67949i) q^{12} +(0.844983 + 3.50514i) q^{13} +(1.17309 + 0.164131i) q^{14} +(-0.746954 + 0.158770i) q^{15} +(-3.76213 - 1.35882i) q^{16} +(-2.20978 - 4.96324i) q^{17} +(-1.12455 + 1.16594i) q^{18} +(-0.417349 + 1.96347i) q^{19} +(0.780049 + 0.805776i) q^{20} +1.14064 q^{21} +(3.54909 + 3.06659i) q^{22} +(-7.01090 + 4.04774i) q^{23} +(-3.76913 - 0.793877i) q^{24} +(1.44792 + 4.45623i) q^{25} +(3.02664 - 4.10359i) q^{26} +(-3.31826 + 4.56719i) q^{27} +(-0.889450 - 1.41952i) q^{28} +(0.378111 + 1.77887i) q^{29} +(0.851423 + 0.664360i) q^{30} +(4.78001 - 3.47288i) q^{31} +(1.95112 + 5.30972i) q^{32} +(3.79383 + 2.45095i) q^{33} +(-3.36390 + 6.90782i) q^{34} +(0.0490941 + 0.467099i) q^{35} +(2.28547 + 0.156987i) q^{36} +(-0.246286 - 1.15869i) q^{37} +(2.50569 - 1.33428i) q^{38} +(2.33887 - 4.31730i) q^{39} +(0.162871 - 1.57765i) q^{40} +(-5.15797 + 5.72850i) q^{41} +(-1.03765 - 1.23507i) q^{42} +(-3.10539 + 5.37869i) q^{43} +(0.0918385 - 6.63261i) q^{44} +(-0.556245 - 0.321148i) q^{45} +(10.7607 + 3.90908i) q^{46} +(0.292632 + 0.900628i) q^{47} +(2.56920 + 4.80337i) q^{48} +(-0.658368 + 6.26395i) q^{49} +(3.50799 - 5.62166i) q^{50} +(-2.28633 + 7.03661i) q^{51} +(-7.19668 + 0.455835i) q^{52} +(9.70361 - 7.05009i) q^{53} +(7.96394 - 0.561822i) q^{54} +(-0.840387 + 1.65909i) q^{55} +(-0.727909 + 2.25444i) q^{56} +(2.21156 - 1.60680i) q^{57} +(1.58218 - 2.02767i) q^{58} +(-0.0129921 - 0.0144292i) q^{59} +(-0.0551814 - 1.52629i) q^{60} +(4.96396 + 11.1492i) q^{61} +(-8.10881 - 2.01645i) q^{62} +(0.712965 + 0.641957i) q^{63} +(3.97437 - 6.94294i) q^{64} +(1.86863 + 0.771961i) q^{65} +(-0.797409 - 6.33756i) q^{66} +(-1.89884 - 3.28888i) q^{67} +(10.5399 - 2.64168i) q^{68} +(10.7837 + 2.29215i) q^{69} +(0.461109 - 0.478081i) q^{70} +(-8.93623 + 3.97867i) q^{71} +(-1.90912 - 2.61750i) q^{72} +(1.23344 - 3.79615i) q^{73} +(-1.03057 + 1.32074i) q^{74} +(2.59536 - 5.82926i) q^{75} +(-3.72419 - 1.49934i) q^{76} +(1.74308 - 2.16302i) q^{77} +(-6.80242 + 1.39497i) q^{78} +(3.38131 - 2.45667i) q^{79} +(-1.85643 + 1.25884i) q^{80} +(4.15880 - 0.883980i) q^{81} +(10.8950 + 0.373744i) q^{82} +(-1.83934 + 2.53163i) q^{83} +(-0.393373 + 2.24711i) q^{84} +(-2.97994 - 0.633405i) q^{85} +(8.64899 - 1.53054i) q^{86} +(1.23832 - 2.14483i) q^{87} +(-7.26528 + 5.93429i) q^{88} +(-6.41766 + 3.70524i) q^{89} +(0.158283 + 0.894447i) q^{90} +(-2.49042 - 1.70818i) q^{91} +(-5.55637 - 15.2077i) q^{92} +(-8.00217 - 0.841061i) q^{93} +(0.708982 - 1.13617i) q^{94} +(0.753179 + 0.836491i) q^{95} +(2.86383 - 7.15156i) q^{96} +(-18.1917 + 1.91202i) q^{97} +(7.38147 - 4.98548i) q^{98} +(0.991958 + 3.66716i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9}+O(q^{10}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9	\( 640 q - 15 q^{2} - 3 q^{4} - 15 q^{6} - 78 q^{9} - 4 q^{12} - 20 q^{13} - 12 q^{14} - 19 q^{16} - 10 q^{17} - 45 q^{20} - 15 q^{22} - 15 q^{24} + 104 q^{25} - 20 q^{26} - 15 q^{28} - 10 q^{29} + 45 q^{30} - 24 q^{33} + 4 q^{36} - 18 q^{37} - 14 q^{38} - 20 q^{40} - 30 q^{41} - 13 q^{42} - 108 q^{45} - 15 q^{46} + 35 q^{48} - 74 q^{49} - 90 q^{50} + 15 q^{52} - 8 q^{53} + 50 q^{56} + 27 q^{58} - 10 q^{61} - 5 q^{62} - 84 q^{64} - 146 q^{66} - 70 q^{68} - 26 q^{69} - 15 q^{72} - 55 q^{74} + 44 q^{77} + 24 q^{78} - 39 q^{80} + 30 q^{81} - 29 q^{82} + 30 q^{84} - 30 q^{85} - 75 q^{88} - 24 q^{89} + 30 q^{90} + 14 q^{92} + 66 q^{93} - 5 q^{94} - 30 q^{97}+O(q^{100}) \) 640 * q - 15 * q^2 - 3 * q^4 - 15 * q^6 - 78 * q^9 - 4 * q^12 - 20 * q^13 - 12 * q^14 - 19 * q^16 - 10 * q^17 - 45 * q^20 - 15 * q^22 - 15 * q^24 + 104 * q^25 - 20 * q^26 - 15 * q^28 - 10 * q^29 + 45 * q^30 - 24 * q^33 + 4 * q^36 - 18 * q^37 - 14 * q^38 - 20 * q^40 - 30 * q^41 - 13 * q^42 - 108 * q^45 - 15 * q^46 + 35 * q^48 - 74 * q^49 - 90 * q^50 + 15 * q^52 - 8 * q^53 + 50 * q^56 + 27 * q^58 - 10 * q^61 - 5 * q^62 - 84 * q^64 - 146 * q^66 - 70 * q^68 - 26 * q^69 - 15 * q^72 - 55 * q^74 + 44 * q^77 + 24 * q^78 - 39 * q^80 + 30 * q^81 - 29 * q^82 + 30 * q^84 - 30 * q^85 - 75 * q^88 - 24 * q^89 + 30 * q^90 + 14 * q^92 + 66 * q^93 - 5 * q^94 - 30 * q^97

Introduction

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