LMFDB - Embedded newform 418.2.v.b.249.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(13,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.v (of order $90$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$10$ over $\Q(\zeta_{90})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{90}]$

Embedding invariants

Embedding label			249.7
Character	$\chi$	$=$	418.249
Dual form			418.2.v.b.371.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.719340 + 0.694658i) q^{2} +(0.522279 + 0.835822i) q^{3} +(0.0348995 - 0.999391i) q^{4} +(0.198762 - 0.294676i) q^{5} +(-0.956307 - 0.238434i) q^{6} +(-2.40481 - 2.16530i) q^{7} +(0.669131 + 0.743145i) q^{8} +(0.889291 - 1.82332i) q^{9} +O(q^{10})$	\(q+(-0.719340 + 0.694658i) q^{2} +(0.522279 + 0.835822i) q^{3} +(0.0348995 - 0.999391i) q^{4} +(0.198762 - 0.294676i) q^{5} +(-0.956307 - 0.238434i) q^{6} +(-2.40481 - 2.16530i) q^{7} +(0.669131 + 0.743145i) q^{8} +(0.889291 - 1.82332i) q^{9} +(0.0617222 + 0.350044i) q^{10} +(-1.77542 - 2.80141i) q^{11} +(0.853540 - 0.492791i) q^{12} +(4.37621 - 0.306014i) q^{13} +(3.23402 - 0.112934i) q^{14} +(0.350106 + 0.0122260i) q^{15} +(-0.997564 - 0.0697565i) q^{16} +(3.52111 - 1.71736i) q^{17} +(0.626880 + 1.92934i) q^{18} +(-2.02301 - 3.86101i) q^{19} +(-0.287560 - 0.208925i) q^{20} +(0.553822 - 3.14088i) q^{21} +(3.22315 + 0.781850i) q^{22} +(-4.84646 - 1.76397i) q^{23} +(-0.271663 + 0.947403i) q^{24} +(1.82571 + 4.51878i) q^{25} +(-2.93540 + 3.26010i) q^{26} +(4.92898 - 0.518056i) q^{27} +(-2.24791 + 2.32778i) q^{28} +(-5.07745 + 2.69973i) q^{29} +(-0.260338 + 0.234409i) q^{30} +(6.31758 + 0.664005i) q^{31} +(0.766044 - 0.642788i) q^{32} +(1.41421 - 2.94705i) q^{33} +(-1.33990 + 3.68134i) q^{34} +(-1.11605 + 0.278262i) q^{35} +(-1.79117 - 0.952383i) q^{36} +(2.69884 - 0.876907i) q^{37} +(4.13732 + 1.37208i) q^{38} +(2.54138 + 3.49790i) q^{39} +(0.351985 - 0.0494682i) q^{40} +(-1.02797 + 0.642345i) q^{41} +(1.78345 + 2.64408i) q^{42} +(-3.93241 - 10.8042i) q^{43} +(-2.86166 + 1.67657i) q^{44} +(-0.360532 - 0.624459i) q^{45} +(4.71160 - 2.09774i) q^{46} +(7.75379 + 1.08972i) q^{47} +(-0.462703 - 0.870218i) q^{48} +(0.362884 + 3.45261i) q^{49} +(-4.45231 - 1.98230i) q^{50} +(3.27441 + 2.04608i) q^{51} +(-0.153100 - 4.38422i) q^{52} +(-0.279200 + 0.188323i) q^{53} +(-3.18574 + 3.79661i) q^{54} +(-1.17839 - 0.0336368i) q^{55} -3.23599i q^{56} +(2.17054 - 3.70740i) q^{57} +(1.77702 - 5.46912i) q^{58} +(1.83508 + 13.0573i) q^{59} +(0.0244370 - 0.349466i) q^{60} +(2.27912 + 7.94823i) q^{61} +(-5.00574 + 3.91092i) q^{62} +(-6.08661 + 2.45915i) q^{63} +(-0.104528 + 0.994522i) q^{64} +(0.779647 - 1.35039i) q^{65} +(1.02990 + 3.10232i) q^{66} +(12.6985 - 2.23909i) q^{67} +(-1.59343 - 3.57890i) q^{68} +(-1.05684 - 4.97205i) q^{69} +(0.609520 - 0.975436i) q^{70} +(-6.13857 - 4.14052i) q^{71} +(1.95004 - 0.559165i) q^{72} +(-13.4425 - 5.43111i) q^{73} +(-1.33223 + 2.50557i) q^{74} +(-2.82336 + 3.88603i) q^{75} +(-3.92926 + 1.88703i) q^{76} +(-1.79633 + 10.5812i) q^{77} +(-4.25796 - 0.750793i) q^{78} +(-3.32374 - 13.3308i) q^{79} +(-0.218833 + 0.280094i) q^{80} +(-0.739537 - 0.946564i) q^{81} +(0.293247 - 1.17615i) q^{82} +(0.608420 - 1.36653i) q^{83} +(-3.11964 - 0.663100i) q^{84} +(0.193797 - 1.37893i) q^{85} +(10.3340 + 5.04022i) q^{86} +(-4.90834 - 2.83383i) q^{87} +(0.893860 - 3.19390i) q^{88} +(1.34985 + 1.60868i) q^{89} +(0.693130 + 0.198752i) q^{90} +(-11.1866 - 8.73989i) q^{91} +(-1.93203 + 4.78194i) q^{92} +(2.74455 + 5.62717i) q^{93} +(-6.33460 + 4.60236i) q^{94} +(-1.53985 - 0.171289i) q^{95} +(0.937345 + 0.304562i) q^{96} +(-2.73911 - 2.83643i) q^{97} +(-2.65942 - 2.23152i) q^{98} +(-6.68672 + 0.745895i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	$ 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) $ 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.719340	+	0.694658i	−0.508650	+	0.491198i
$2$	−0.719340	+	0.694658i	−0.508650	+	0.491198i
$3$	0.522279	+	0.835822i	0.301538	+	0.482562i	0.963769	−	0.266738i	$-0.0859458\pi$
$3$	0.522279	+	0.835822i	0.301538	+	0.482562i	−0.662231	+	0.749300i	$0.730390\pi$
$4$	0.0348995	−	0.999391i	0.0174497	−	0.499695i
$5$	0.198762	−	0.294676i	0.0888890	−	0.131783i	−0.781970	−	0.623316i	$-0.785785\pi$
$5$	0.198762	−	0.294676i	0.0888890	−	0.131783i	0.870859	+	0.491532i	$0.163563\pi$
$6$	−0.956307	−	0.238434i	−0.390411	−	0.0973403i
$7$	−2.40481	−	2.16530i	−0.908932	−	0.818406i	0.0749565	−	0.997187i	$-0.476118\pi$
$7$	−2.40481	−	2.16530i	−0.908932	−	0.818406i	−0.983889	+	0.178780i	$0.942785\pi$
$8$	0.669131	+	0.743145i	0.236573	+	0.262741i
$9$	0.889291	−	1.82332i	0.296430	−	0.607773i
$10$	0.0617222	+	0.350044i	0.0195183	+	0.110694i
$11$	−1.77542	−	2.80141i	−0.535310	−	0.844655i
$11$	−1.77542	−	2.80141i	−0.535310	−	0.844655i
$12$	0.853540	−	0.492791i	0.246396	−	0.142257i
$13$	4.37621	−	0.306014i	1.21374	−	0.0848731i	0.551507	−	0.834170i	$-0.314053\pi$
$13$	4.37621	−	0.306014i	1.21374	−	0.0848731i	0.662234	+	0.749297i	$0.269608\pi$
$14$	3.23402	−	0.112934i	0.864328	−	0.0301830i
$15$	0.350106	+	0.0122260i	0.0903970	+	0.00315673i
$16$	−0.997564	−	0.0697565i	−0.249391	−	0.0174391i
$17$	3.52111	−	1.71736i	0.853995	−	0.416521i	0.0412556	−	0.999149i	$-0.486864\pi$
$17$	3.52111	−	1.71736i	0.853995	−	0.416521i	0.812739	+	0.582627i	$0.197975\pi$
$18$	0.626880	+	1.92934i	0.147757	+	0.454749i
$19$	−2.02301	−	3.86101i	−0.464110	−	0.885777i
$19$	−2.02301	−	3.86101i	−0.464110	−	0.885777i
$20$	−0.287560	−	0.208925i	−0.0643004	−	0.0467170i
$21$	0.553822	−	3.14088i	0.120854	−	0.685397i
$22$	3.22315	+	0.781850i	0.687178	+	0.166691i
$23$	−4.84646	−	1.76397i	−1.01056	−	0.367812i	−0.216910	−	0.976192i	$-0.569598\pi$
$23$	−4.84646	−	1.76397i	−1.01056	−	0.367812i	−0.793646	+	0.608379i	$0.791820\pi$
$24$	−0.271663	+	0.947403i	−0.0554531	+	0.193388i
$25$	1.82571	+	4.51878i	0.365141	+	0.903756i
$26$	−2.93540	+	3.26010i	−0.575680	+	0.639358i
$27$	4.92898	−	0.518056i	0.948582	−	0.0997000i
$28$	−2.24791	+	2.32778i	−0.424815	+	0.439908i
$29$	−5.07745	+	2.69973i	−0.942860	+	0.501327i	−0.868382	−	0.495895i	$-0.834840\pi$
$29$	−5.07745	+	2.69973i	−0.942860	+	0.501327i	−0.0744773	+	0.997223i	$0.523729\pi$
$30$	−0.260338	+	0.234409i	−0.0475310	+	0.0427971i
$31$	6.31758	+	0.664005i	1.13467	+	0.119259i	0.653187	−	0.757196i	$-0.273431\pi$
$31$	6.31758	+	0.664005i	1.13467	+	0.119259i	0.481484	+	0.876455i	$0.340098\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	1.41421	−	2.94705i	0.246182	−	0.513016i
$34$	−1.33990	+	3.68134i	−0.229790	+	0.631344i
$35$	−1.11605	+	0.278262i	−0.188646	+	0.0470348i
$36$	−1.79117	−	0.952383i	−0.298529	−	0.158730i
$37$	2.69884	−	0.876907i	0.443687	−	0.144163i	−0.0786490	−	0.996902i	$-0.525061\pi$
$37$	2.69884	−	0.876907i	0.443687	−	0.144163i	0.522336	+	0.852740i	$0.325061\pi$
$38$	4.13732	+	1.37208i	0.671161	+	0.222581i
$39$	2.54138	+	3.49790i	0.406946	+	0.560113i
$40$	0.351985	−	0.0494682i	0.0556537	−	0.00782162i
$41$	−1.02797	+	0.642345i	−0.160541	+	0.100317i	−0.607811	−	0.794082i	$-0.707952\pi$
$41$	−1.02797	+	0.642345i	−0.160541	+	0.100317i	0.447269	+	0.894399i	$0.352397\pi$
$42$	1.78345	+	2.64408i	0.275193	+	0.407990i
$43$	−3.93241	−	10.8042i	−0.599688	−	1.64763i	−0.751898	−	0.659280i	$-0.770861\pi$
$43$	−3.93241	−	10.8042i	−0.599688	−	1.64763i	0.152210	−	0.988348i	$-0.451361\pi$
$44$	−2.86166	+	1.67657i	−0.431412	+	0.252753i
$45$	−0.360532	−	0.624459i	−0.0537449	−	0.0930889i
$46$	4.71160	−	2.09774i	0.694688	−	0.309295i
$47$	7.75379	+	1.08972i	1.13101	+	0.158953i	0.679752	−	0.733442i	$-0.262088\pi$
$47$	7.75379	+	1.08972i	1.13101	+	0.158953i	0.451255	+	0.892395i	$0.350976\pi$
$48$	−0.462703	−	0.870218i	−0.0667854	−	0.125605i
$49$	0.362884	+	3.45261i	0.0518406	+	0.493231i
$50$	−4.45231	−	1.98230i	−0.629652	−	0.280339i
$51$	3.27441	+	2.04608i	0.458509	+	0.286508i
$52$	−0.153100	−	4.38422i	−0.0212312	−	0.607982i
$53$	−0.279200	+	0.188323i	−0.0383511	+	0.0258681i	−0.578219	−	0.815882i	$-0.696252\pi$
$53$	−0.279200	+	0.188323i	−0.0383511	+	0.0258681i	0.539868	+	0.841750i	$0.318474\pi$
$54$	−3.18574	+	3.79661i	−0.433524	+	0.516654i
$55$	−1.17839	−	0.0336368i	−0.158895	−	0.00453559i
$56$		−	3.23599i		−	0.432427i
$57$	2.17054	−	3.70740i	0.287495	−	0.491057i
$58$	1.77702	−	5.46912i	0.233335	−	0.718131i
$59$	1.83508	+	13.0573i	0.238907	+	1.69991i	0.627594	+	0.778541i	$0.284040\pi$
$59$	1.83508	+	13.0573i	0.238907	+	1.69991i	−0.388687	+	0.921370i	$0.627071\pi$
$60$	0.0244370	−	0.349466i	0.00315481	−	0.0451159i
$61$	2.27912	+	7.94823i	0.291811	+	1.01767i	0.961450	+	0.274980i	$0.0886711\pi$
$61$	2.27912	+	7.94823i	0.291811	+	1.01767i	−0.669639	+	0.742687i	$0.733551\pi$
$62$	−5.00574	+	3.91092i	−0.635730	+	0.496687i
$63$	−6.08661	+	2.45915i	−0.766840	+	0.309824i
$64$	−0.104528	+	0.994522i	−0.0130661	+	0.124315i
$65$	0.779647	−	1.35039i	0.0967034	−	0.167495i
$66$	1.02990	+	3.10232i	0.126772	+	0.381870i
$67$	12.6985	−	2.23909i	1.55137	−	0.273549i	0.668698	−	0.743534i	$-0.266852\pi$
$67$	12.6985	−	2.23909i	1.55137	−	0.273549i	0.882674	+	0.469985i	$0.155741\pi$
$68$	−1.59343	−	3.57890i	−0.193232	−	0.434006i
$69$	−1.05684	−	4.97205i	−0.127229	−	0.598565i
$70$	0.609520	−	0.975436i	0.0728516	−	0.116587i
$71$	−6.13857	−	4.14052i	−0.728514	−	0.491389i	0.138068	−	0.990423i	$-0.455911\pi$
$71$	−6.13857	−	4.14052i	−0.728514	−	0.491389i	−0.866583	+	0.499034i	$0.833688\pi$
$72$	1.95004	−	0.559165i	0.229815	−	0.0658983i
$73$	−13.4425	−	5.43111i	−1.57332	−	0.635663i	−0.588385	−	0.808581i	$-0.700236\pi$
$73$	−13.4425	−	5.43111i	−1.57332	−	0.635663i	−0.984936	+	0.172918i	$0.944681\pi$
$74$	−1.33223	+	2.50557i	−0.154869	+	0.291266i
$75$	−2.82336	+	3.88603i	−0.326014	+	0.448720i
$76$	−3.92926	+	1.88703i	−0.450718	+	0.216457i
$77$	−1.79633	+	10.5812i	−0.204711	+	1.20584i
$78$	−4.25796	−	0.750793i	−0.482119	−	0.0850106i
$79$	−3.32374	−	13.3308i	−0.373950	−	1.49983i	−0.802687	−	0.596401i	$-0.796597\pi$
$79$	−3.32374	−	13.3308i	−0.373950	−	1.49983i	0.428737	−	0.903429i	$-0.358959\pi$
$80$	−0.218833	+	0.280094i	−0.0244663	+	0.0313154i
$81$	−0.739537	−	0.946564i	−0.0821708	−	0.105174i
$82$	0.293247	−	1.17615i	0.0323837	−	0.129884i
$83$	0.608420	−	1.36653i	0.0667828	−	0.149997i	−0.877070	−	0.480362i	$-0.840505\pi$
$83$	0.608420	−	1.36653i	0.0667828	−	0.149997i	0.943853	+	0.330365i	$0.107172\pi$
$84$	−3.11964	−	0.663100i	−0.340381	−	0.0723502i
$85$	0.193797	−	1.37893i	0.0210202	−	0.149566i
$86$	10.3340	+	5.04022i	1.11434	+	0.543501i
$87$	−4.90834	−	2.83383i	−0.526229	−	0.303819i
$88$	0.893860	−	3.19390i	0.0952858	−	0.340471i
$89$	1.34985	+	1.60868i	0.143083	+	0.170520i	0.832827	−	0.553534i	$-0.186721\pi$
$89$	1.34985	+	1.60868i	0.143083	+	0.170520i	−0.689743	+	0.724054i	$0.742277\pi$
$90$	0.693130	+	0.198752i	0.0730624	+	0.0209503i
$91$	−11.1866	−	8.73989i	−1.17267	−	0.916190i
$92$	−1.93203	+	4.78194i	−0.201428	+	0.498552i
$93$	2.74455	+	5.62717i	0.284597	+	0.583510i
$94$	−6.33460	+	4.60236i	−0.653364	+	0.474697i
$95$	−1.53985	−	0.171289i	−0.157985	−	0.0175739i
$96$	0.937345	+	0.304562i	0.0956674	+	0.0310842i
$97$	−2.73911	−	2.83643i	−0.278114	−	0.287996i	0.565723	−	0.824596i	$-0.308597\pi$
$97$	−2.73911	−	2.83643i	−0.278114	−	0.287996i	−0.843837	+	0.536600i	$0.819708\pi$
$98$	−2.65942	−	2.23152i	−0.268642	−	0.225418i
$99$	−6.68672	+	0.745895i	−0.672041	+	0.0749653i
$100$	4.57974	−	1.66689i	0.457974	−	0.166689i
$101$	1.03761	+	14.8385i	0.103246	+	1.47648i	0.722543	+	0.691325i	$0.242973\pi$
$101$	1.03761	+	14.8385i	0.103246	+	1.47648i	−0.619298	+	0.785156i	$0.712583\pi$
$102$	−3.77674	+	0.802771i	−0.373953	+	0.0794861i
$103$	−2.40975	+	11.3370i	−0.237440	+	1.11707i	0.684283	+	0.729217i	$0.260115\pi$
$103$	−2.40975	+	11.3370i	−0.237440	+	1.11707i	−0.921723	+	0.387850i	$0.873218\pi$
$104$	3.15567	+	3.04739i	0.309439	+	0.298821i
$105$	−0.815465	−	0.787486i	−0.0795813	−	0.0768507i
$106$	0.0700197	−	0.329417i	0.00680092	−	0.0319958i
$107$	−16.2250	+	3.44873i	−1.56853	+	0.333402i	−0.908516	−	0.417850i	$-0.862784\pi$
$107$	−16.2250	+	3.44873i	−1.56853	+	0.333402i	−0.660015	+	0.751252i	$0.729450\pi$
$108$	−0.345722	−	4.94405i	−0.0332671	−	0.475742i
$109$	6.80611	−	2.47722i	0.651907	−	0.237275i	0.00516843	−	0.999987i	$-0.498355\pi$
$109$	6.80611	−	2.47722i	0.651907	−	0.237275i	0.646738	+	0.762712i	$0.276133\pi$
$110$	0.871032	−	0.794385i	0.0830496	−	0.0757417i
$111$	2.14249	+	1.79776i	0.203356	+	0.170636i
$112$	2.24791	+	2.32778i	0.212407	+	0.219954i
$113$	−8.98924	−	2.92078i	−0.845637	−	0.274764i	−0.146019	−	0.989282i	$-0.546646\pi$
$113$	−8.98924	−	2.92078i	−0.845637	−	0.274764i	−0.699617	+	0.714518i	$0.746646\pi$
$114$	1.01402	+	4.17467i	0.0949717	+	0.390993i
$115$	−1.48309	+	1.07753i	−0.138299	+	0.100480i
$116$	2.52089	+	5.16858i	0.234058	+	0.479891i
$117$	3.33376	−	8.25135i	0.308206	−	0.762838i
$118$	−10.3904	−	8.11785i	−0.956512	−	0.747309i
$119$	−12.1862	−	3.49434i	−1.11711	−	0.320325i
$120$	0.225181	+	0.268360i	0.0205561	+	0.0244978i
$121$	−4.69574	+	9.94736i	−0.426886	+	0.904306i
$122$	−7.16076	−	4.13427i	−0.648305	−	0.374299i
$123$	−1.07377	−	0.523713i	−0.0968187	−	0.0472216i
$124$	0.884081	−	6.29056i	0.0793928	−	0.564909i
$125$	3.43284	+	0.729673i	0.307043	+	0.0652639i
$126$	2.67007	−	5.99708i	0.237869	−	0.534262i
$127$	−3.09385	+	12.4087i	−0.274534	+	1.10110i	0.661713	+	0.749757i	$0.269830\pi$
$127$	−3.09385	+	12.4087i	−0.274534	+	1.10110i	−0.936248	+	0.351340i	$0.885726\pi$
$128$	−0.615661	−	0.788011i	−0.0544173	−	0.0696510i
$129$	6.97658	−	8.92962i	0.614254	−	0.786209i
$130$	0.377228	+	1.51298i	0.0330850	+	0.132697i
$131$	14.4776	+	2.55279i	1.26491	+	0.223038i	0.765561	−	0.643363i	$-0.222461\pi$
$131$	14.4776	+	2.55279i	1.26491	+	0.223038i	0.499349	+	0.866401i	$0.333572\pi$
$132$	−2.89590	−	1.51620i	−0.252056	−	0.131968i
$133$	−3.49530	+	13.6654i	−0.303081	+	1.18494i
$134$	−7.57915	+	10.4318i	−0.654739	+	0.901171i
$135$	0.827033	−	1.55542i	0.0711797	−	0.133870i
$136$	3.63233	+	1.46756i	0.311470	+	0.125842i
$137$	5.66908	−	1.62558i	0.484342	−	0.138883i	−0.0245758	−	0.999698i	$-0.507824\pi$
$137$	5.66908	−	1.62558i	0.484342	−	0.138883i	0.508918	+	0.860815i	$0.330046\pi$
$138$	4.21411	+	2.84245i	0.358729	+	0.241966i
$139$	8.53463	−	13.6583i	0.723898	−	1.15848i	−0.257460	−	0.966289i	$-0.582885\pi$
$139$	8.53463	−	13.6583i	0.723898	−	1.15848i	0.981358	−	0.192190i	$-0.0615590\pi$
$140$	0.239143	+	1.12508i	0.0202113	+	0.0950865i
$141$	3.13883	+	7.04993i	0.264337	+	0.593711i
$142$	7.29196	−	1.28577i	0.611928	−	0.107899i
$143$	−8.62689	−	11.7162i	−0.721417	−	0.979760i
$144$	−1.01431	+	1.75684i	−0.0845261	+	0.146404i
$145$	−0.213657	+	2.03281i	−0.0177432	+	0.168816i
$146$	13.4425	−	5.43111i	1.11251	−	0.449482i
$147$	−2.69624	+	2.10654i	−0.222382	+	0.173744i
$148$	−0.782185	−	2.72780i	−0.0642952	−	0.224224i
$149$	−0.581024	+	8.30903i	−0.0475993	+	0.680702i	0.913908	+	0.405922i	$0.133050\pi$
$149$	−0.581024	+	8.30903i	−0.0475993	+	0.680702i	−0.961507	+	0.274780i	$0.911395\pi$
$150$	−0.668503	−	4.75665i	−0.0545831	−	0.388379i
$151$	−1.80720	+	5.56199i	−0.147068	+	0.452629i	−0.997271	−	0.0738261i	$-0.976479\pi$
$151$	−1.80720	+	5.56199i	−0.147068	+	0.452629i	0.850203	+	0.526455i	$0.176479\pi$
$152$	1.51564	−	4.08691i	0.122934	−	0.331492i
$153$		−	7.94734i		−	0.642504i
$154$	−6.05813	−	8.85929i	−0.488178	−	0.713902i
$155$	1.45136	−	1.72966i	0.116576	−	0.138930i
$156$	3.58446	−	2.41775i	0.286987	−	0.193575i
$157$	−0.403253	−	11.5477i	−0.0321831	−	0.921603i	−0.902908	−	0.429833i	$-0.858572\pi$
$157$	−0.403253	−	11.5477i	−0.0321831	−	0.921603i	0.870725	−	0.491770i	$-0.163650\pi$
$158$	11.6512	+	7.28050i	0.926923	+	0.579206i
$159$	−0.303225	−	0.135004i	−0.0240473	−	0.0107065i
$160$	−0.0371540	−	0.353497i	−0.00293728	−	0.0279464i
$161$	7.83529	+	14.7360i	0.617507	+	1.16136i
$162$	1.18952	+	0.167176i	0.0934573	+	0.0131346i
$163$	8.73285	−	3.88812i	0.684010	−	0.304541i	−0.0351536	−	0.999382i	$-0.511192\pi$
$163$	8.73285	−	3.88812i	0.684010	−	0.304541i	0.719163	+	0.694841i	$0.244525\pi$
$164$	0.606078	+	1.04976i	0.0473267	+	0.0819723i
$165$	−0.587336	−	1.00250i	−0.0457241	−	0.0780441i
$166$	0.511614	+	1.40565i	0.0397089	+	0.109099i
$167$	9.05343	+	13.4223i	0.700576	+	1.03865i	0.996513	+	0.0834388i	$0.0265903\pi$
$167$	9.05343	+	13.4223i	0.700576	+	1.03865i	−0.295937	+	0.955207i	$0.595632\pi$
$168$	2.70471	−	1.69009i	0.208673	−	0.130393i
$169$	6.18406	−	0.869112i	0.475697	−	0.0668548i
$170$	0.818482	+	1.12654i	0.0627747	+	0.0864020i
$171$	−8.83890	+	0.255022i	−0.675928	+	0.0195020i
$172$	−10.9349	+	3.55296i	−0.833776	+	0.270910i
$173$	6.79446	+	3.61268i	0.516573	+	0.274667i	0.707222	−	0.706991i	$-0.249948\pi$
$173$	6.79446	+	3.61268i	0.516573	+	0.274667i	−0.190649	+	0.981658i	$0.561059\pi$
$174$	5.49931	−	1.37113i	0.416902	−	0.103945i
$175$	5.39404	−	14.8200i	0.407751	−	1.12029i
$176$	1.57568	+	2.91843i	0.118772	+	0.219985i
$177$	−9.95512	+	8.35333i	−0.748272	+	0.627875i
$178$	−2.08848	−	0.219508i	−0.156538	−	0.0164528i
$179$	−14.4507	+	13.0115i	−1.08010	+	0.972523i	−0.999706	−	0.0242401i	$-0.992283\pi$
$179$	−14.4507	+	13.0115i	−1.08010	+	0.972523i	−0.0803905	+	0.996763i	$0.525617\pi$
$180$	−0.636661	+	0.338519i	−0.0474539	+	0.0252317i
$181$	6.20652	−	6.42704i	0.461327	−	0.477718i	−0.447861	−	0.894103i	$-0.647814\pi$
$181$	6.20652	−	6.42704i	0.461327	−	0.477718i	0.909189	+	0.416385i	$0.136703\pi$
$182$	14.1182	−	1.48388i	1.04651	−	0.109993i
$183$	−5.45296	+	6.05613i	−0.403095	+	0.447682i
$184$	−1.93203	−	4.78194i	−0.142431	−	0.352529i
$185$	0.278023	−	0.969581i	0.0204407	−	0.0712850i
$186$	−5.88322	−	2.14132i	−0.431379	−	0.157009i
$187$	−11.0625	−	6.81502i	−0.808969	−	0.498363i
$188$	1.35966	−	7.71104i	0.0991637	−	0.562385i
$189$	−12.9750	−	9.42689i	−0.943792	−	0.685705i
$190$	1.22666	−	0.946453i	0.0889913	−	0.0686629i
$191$	3.89712	+	11.9941i	0.281986	+	0.867862i	0.987286	+	0.158954i	$0.0508121\pi$
$191$	3.89712	+	11.9941i	0.281986	+	0.867862i	−0.705300	+	0.708908i	$0.749188\pi$
$192$	−0.885836	+	0.432051i	−0.0639297	+	0.0311806i
$193$	17.9190	+	1.25302i	1.28984	+	0.0901942i	0.698137	−	0.715964i	$-0.254013\pi$
$193$	17.9190	+	1.25302i	1.28984	+	0.0901942i	0.591700	+	0.806159i	$0.298457\pi$
$194$	3.94070	+	0.137612i	0.282926	+	0.00987998i
$195$	1.53588	−	0.0536340i	0.109986	−	0.00384081i
$196$	3.46318	−	0.242169i	0.247370	−	0.0172978i
$197$	20.1389	−	11.6272i	1.43484	−	0.828403i	0.437352	−	0.899290i	$-0.355916\pi$
$197$	20.1389	−	11.6272i	1.43484	−	0.828403i	0.997484	+	0.0708868i	$0.0225829\pi$
$198$	4.29188	−	5.18154i	0.305011	−	0.368236i
$199$	2.80996	+	15.9361i	0.199193	+	1.12968i	0.906320	+	0.422591i	$0.138879\pi$
$199$	2.80996	+	15.9361i	0.199193	+	1.12968i	−0.707128	+	0.707086i	$0.750009\pi$
$200$	−2.13647	+	4.38042i	−0.151071	+	0.309742i
$201$	8.50366	+	9.44427i	0.599802	+	0.666148i
$202$	−11.0540	−	9.95311i	−0.777760	−	0.700298i
$203$	18.0560	+	4.50188i	1.26729	+	0.315970i
$204$	2.15911	−	3.20101i	0.151168	−	0.224115i
$205$	−0.0150366	+	0.430591i	−0.00105020	+	0.0300738i
$206$	−6.14190	−	9.82910i	−0.427927	−	0.684826i
$207$	−7.52618	+	7.26795i	−0.523106	+	0.505157i
$208$	−4.38689			−0.304176
$209$	−7.22457	+	12.5222i	−0.499734	+	0.866179i
$210$	1.13363			0.0782279
$211$	−2.70891	+	2.61597i	−0.186489	+	0.180090i	−0.782042	−	0.623226i	$-0.785822\pi$
$211$	−2.70891	+	2.61597i	−0.186489	+	0.180090i	0.595553	+	0.803316i	$0.296933\pi$
$212$	0.178464	+	0.285602i	0.0122570	+	0.0196153i
$213$	0.254686	−	7.29325i	0.0174508	−	0.499726i
$214$	9.27561	−	13.7517i	0.634067	−	0.940044i
$215$	−3.96536	−	0.988676i	−0.270435	−	0.0674271i
$216$	3.68312	+	3.31630i	0.250605	+	0.225645i
$217$	−13.7548	−	15.2763i	−0.933737	−	1.03702i
$218$	−3.17508	+	6.50988i	−0.215044	+	0.440905i
$219$	−2.48128	−	14.0721i	−0.167670	−	0.950901i
$220$	−0.0747417	+	1.17650i	−0.00503909	+	0.0793198i
$221$	14.8836	−	8.59304i	1.00118	−	0.578030i
$222$	−2.79001	+	0.195096i	−0.187253	+	0.0130940i
$223$	20.2183	−	0.706040i	1.35392	−	0.0472799i	0.651287	−	0.758832i	$-0.274229\pi$
$223$	20.2183	−	0.706040i	1.35392	−	0.0472799i	0.702634	+	0.711552i	$0.252007\pi$
$224$	−3.23402	−	0.112934i	−0.216082	−	0.00754575i
$225$	9.86275	+	0.689671i	0.657517	+	0.0459781i
$226$	8.49527	−	4.14342i	0.565097	−	0.275616i
$227$	−4.46891	−	13.7539i	−0.296612	−	0.912878i	−0.982675	−	0.185336i	$-0.940663\pi$
$227$	−4.46891	−	13.7539i	−0.296612	−	0.912878i	0.686063	−	0.727542i	$-0.259337\pi$
$228$	−3.62939	−	2.29861i	−0.240362	−	0.152229i
$229$	12.8878	+	9.36351i	0.851647	+	0.618758i	0.925600	−	0.378504i	$-0.123561\pi$
$229$	12.8878	+	9.36351i	0.851647	+	0.618758i	−0.0739525	+	0.997262i	$0.523561\pi$
$230$	0.318332	−	1.80535i	0.0209902	−	0.119041i
$231$	−9.78215	+	4.02492i	−0.643619	+	0.264820i
$232$	−5.40377	−	1.96681i	−0.354775	−	0.129128i
$233$	3.93562	−	13.7251i	0.257831	−	0.899163i	−0.720732	−	0.693214i	$-0.756194\pi$
$233$	3.93562	−	13.7251i	0.257831	−	0.899163i	0.978563	−	0.205949i	$-0.0660282\pi$
$234$	3.33376	+	8.25135i	0.217935	+	0.539408i
$235$	1.86227	−	2.06826i	0.121481	−	0.134919i
$236$	13.1133	−	1.37827i	0.853606	−	0.0897176i
$237$	9.40624	−	9.74044i	0.611001	−	0.632710i
$238$	11.1934	−	5.95163i	0.725560	−	0.385787i
$239$	−0.326439	+	0.293927i	−0.0211156	+	0.0190126i	−0.679621	−	0.733564i	$-0.737856\pi$
$239$	−0.326439	+	0.293927i	−0.0211156	+	0.0190126i	0.658505	+	0.752576i	$0.271189\pi$
$240$	−0.348400	−	0.0366184i	−0.0224891	−	0.00236370i
$241$	14.4965	−	12.1640i	0.933798	−	0.783550i	−0.0426970	−	0.999088i	$-0.513595\pi$
$241$	14.4965	−	12.1640i	0.933798	−	0.783550i	0.976495	+	0.215538i	$0.0691506\pi$
$242$	−3.53218	−	10.4175i	−0.227057	−	0.669660i
$243$	5.49020	−	15.0842i	0.352196	−	0.967652i
$244$	8.02293	−	2.00034i	0.513615	−	0.128059i
$245$	1.08953	+	0.579314i	0.0696076	+	0.0370110i
$246$	1.13621	−	0.369176i	0.0724420	−	0.0235378i
$247$	−10.0346	−	16.2775i	−0.638488	−	1.03571i
$248$	3.73384	+	5.13918i	0.237099	+	0.326339i
$249$	1.45994	−	0.205182i	0.0925202	−	0.0130029i
$250$	−2.97625	+	1.85977i	−0.188235	+	0.117622i
$251$	3.93419	+	5.83268i	0.248324	+	0.368156i	0.932505	−	0.361157i	$-0.117618\pi$
$251$	3.93419	+	5.83268i	0.248324	+	0.368156i	−0.684181	+	0.729312i	$0.739840\pi$
$252$	2.24523	+	6.16872i	0.141436	+	0.388593i
$253$	3.66293	+	16.7087i	0.230286	+	1.05047i
$254$	−6.39431	−	11.0753i	−0.401214	−	0.694924i
$255$	1.25376	−	0.558209i	0.0785134	−	0.0349564i
$256$	0.990268	+	0.139173i	0.0618918	+	0.00869832i
$257$	−2.41883	−	4.54917i	−0.150883	−	0.283769i	0.796032	−	0.605255i	$-0.206929\pi$
$257$	−2.41883	−	4.54917i	−0.150883	−	0.283769i	−0.946914	+	0.321486i	$0.895818\pi$
$258$	1.18450	+	11.2698i	0.0737438	+	0.701625i
$259$	−8.38897	−	3.73501i	−0.521265	−	0.232082i
$260$	−1.32236	−	0.826300i	−0.0820091	−	0.0512450i
$261$	0.407129	+	11.6587i	0.0252007	+	0.721653i
$262$	−12.1876	+	8.22064i	−0.752953	+	0.507873i
$263$	−19.6993	+	23.4768i	−1.21471	+	1.44764i	−0.356539	+	0.934280i	$0.616043\pi$
$263$	−19.6993	+	23.4768i	−1.21471	+	1.44764i	−0.858174	+	0.513359i	$0.828401\pi$
$264$	3.13638	−	0.921002i	0.193031	−	0.0566837i
$265$			0.119705i			0.00735342i
$266$	−6.97849	−	12.2581i	−0.427879	−	0.751594i
$267$	−0.639576	+	1.96841i	−0.0391414	+	0.120465i
$268$	−1.79456	−	12.7689i	−0.109620	−	0.779987i
$269$	−0.930093	+	13.3010i	−0.0567088	+	0.810973i	0.883081	+	0.469220i	$0.155465\pi$
$269$	−0.930093	+	13.3010i	−0.0567088	+	0.810973i	−0.939790	+	0.341753i	$0.888979\pi$
$270$	0.485570	+	1.69338i	0.0295508	+	0.103056i
$271$	−14.8538	+	11.6051i	−0.902304	+	0.704957i	−0.955927	−	0.293604i	$-0.905145\pi$
$271$	−14.8538	+	11.6051i	−0.902304	+	0.704957i	0.0536231	+	0.998561i	$0.482923\pi$
$272$	−3.63233	+	1.46756i	−0.220242	+	0.0889837i
$273$	1.46249	−	13.9146i	0.0885137	−	0.842152i
$274$	−2.94877	+	5.10742i	−0.178142	+	0.308550i
$275$	9.41753	−	13.1373i	0.567898	−	0.792208i
$276$	−5.00591	+	0.882677i	−0.301320	+	0.0531309i
$277$	12.2365	+	27.4837i	0.735221	+	1.65133i	0.758558	+	0.651606i	$0.225904\pi$
$277$	12.2365	+	27.4837i	0.735221	+	1.65133i	−0.0233366	+	0.999728i	$0.507429\pi$
$278$	3.34853	+	15.7536i	0.200831	+	0.944837i
$279$	6.82886	−	10.9285i	0.408833	−	0.654270i
$280$	−0.953570	−	0.643191i	−0.0569867	−	0.0384380i
$281$	−1.31515	+	0.377112i	−0.0784550	+	0.0224966i	−0.314635	−	0.949213i	$-0.601882\pi$
$281$	−1.31515	+	0.377112i	−0.0784550	+	0.0224966i	0.236180	+	0.971709i	$0.424104\pi$
$282$	−7.15518	−	2.89088i	−0.426085	−	0.172149i
$283$	2.01306	−	3.78602i	0.119664	−	0.225056i	−0.815916	−	0.578171i	$-0.803767\pi$
$283$	2.01306	−	3.78602i	0.119664	−	0.225056i	0.935580	+	0.353115i	$0.114878\pi$
$284$	−4.35223	+	5.99033i	−0.258257	+	0.355461i
$285$	−0.661063	−	1.37650i	−0.0391580	−	0.0815367i
$286$	14.3444	+	2.43521i	0.848204	+	0.143997i
$287$	3.86293	+	0.681139i	0.228022	+	0.0402064i
$288$	−0.490769	−	1.96837i	−0.0289189	−	0.115987i
$289$	−1.01735	+	1.30215i	−0.0598440	+	0.0765969i
$290$	−1.25842	−	1.61070i	−0.0738967	−	0.0945835i
$291$	0.940169	−	3.77081i	0.0551137	−	0.221049i
$292$	−5.89693	+	13.2447i	−0.345092	+	0.775089i
$293$	−8.67277	−	1.84346i	−0.506669	−	0.107696i	−0.0525169	−	0.998620i	$-0.516724\pi$
$293$	−8.67277	−	1.84346i	−0.506669	−	0.107696i	−0.454152	+	0.890924i	$0.650058\pi$
$294$	0.476192	−	3.38828i	0.0277721	−	0.197609i
$295$	4.21241	+	2.05453i	0.245256	+	0.119619i
$296$	2.45755	+	1.41887i	0.142842	+	0.0824699i
$297$	−10.2023	−	12.8883i	−0.591998	−	0.747855i
$298$	−5.35398	−	6.38063i	−0.310148	−	0.369620i
$299$	−21.7489	−	6.23639i	−1.25777	−	0.360660i
$300$	3.78513	+	2.95726i	0.218534	+	0.170738i
$301$	−13.9377	+	34.4969i	−0.803354	+	1.98837i
$302$	−2.56369	−	5.25635i	−0.147524	−	0.302469i
$303$	−11.8604	+	8.61707i	−0.681361	+	0.495038i
$304$	1.74875	+	3.99273i	0.100298	+	0.228999i
$305$	2.79516	+	0.908202i	0.160050	+	0.0520035i
$306$	5.52069	+	5.71684i	0.315597	+	0.326810i
$307$	−1.84299	−	1.54646i	−0.105185	−	0.0882609i	0.588678	−	0.808367i	$-0.299648\pi$
$307$	−1.84299	−	1.54646i	−0.105185	−	0.0882609i	−0.693864	+	0.720106i	$0.744093\pi$
$308$	10.5120	+	2.16451i	0.598979	+	0.123334i
$309$	−10.7343	+	3.90695i	−0.610651	+	0.222259i
$310$	0.157504	+	2.25242i	0.00894564	+	0.127929i
$311$	−6.87213	+	1.46072i	−0.389683	+	0.0828297i	−0.398587	−	0.917131i	$-0.630499\pi$
$311$	−6.87213	+	1.46072i	−0.389683	+	0.0828297i	0.00890368	+	0.999960i	$0.497166\pi$
$312$	−0.898937	+	4.22916i	−0.0508923	+	0.239429i
$313$	1.02171	+	0.986650i	0.0577502	+	0.0557688i	0.722974	−	0.690876i	$-0.242775\pi$
$313$	1.02171	+	0.986650i	0.0577502	+	0.0557688i	−0.665223	+	0.746644i	$0.731664\pi$
$314$	8.31175	+	8.02656i	0.469059	+	0.452965i
$315$	−0.485131	+	2.28236i	−0.0273341	+	0.128597i
$316$	−13.4387	+	2.85648i	−0.755984	+	0.160689i
$317$	−0.758415	−	10.8458i	−0.0425968	−	0.609163i	−0.971227	−	0.238156i	$-0.923457\pi$
$317$	−0.758415	−	10.8458i	−0.0425968	−	0.609163i	0.928630	−	0.371007i	$-0.120987\pi$
$318$	0.311904	−	0.113524i	0.0174907	−	0.00636609i
$319$	16.5777	+	9.43084i	0.928171	+	0.528026i
$320$	0.272286	+	0.228475i	0.0152212	+	0.0127721i
$321$	−11.3565	−	11.7600i	−0.633859	−	0.656380i
$322$	−15.8727	−	5.15737i	−0.884553	−	0.287409i
$323$	−13.7540	−	10.1208i	−0.765293	−	0.563138i
$324$	−0.971797	+	0.706052i	−0.0539887	+	0.0392251i
$325$	9.37247	+	19.2164i	0.519891	+	1.06594i
$326$	−3.58097	+	8.86322i	−0.198332	+	0.490889i
$327$	5.62520	+	4.39489i	0.311074	+	0.243038i
$328$	−1.16520	−	0.334115i	−0.0643374	−	0.0184484i
$329$	−16.2868	−	19.4099i	−0.897921	−	1.07010i
$330$	1.11889	+	0.313136i	0.0615927	+	0.0172376i
$331$	30.3083	+	17.4985i	1.66589	+	0.961803i	0.969817	+	0.243835i	$0.0784055\pi$
$331$	30.3083	+	17.4985i	1.66589	+	0.961803i	0.696076	+	0.717969i	$0.254928\pi$
$332$	−1.34447	−	0.655741i	−0.0737873	−	0.0359885i
$333$	0.801178	−	5.70068i	0.0439043	−	0.312395i
$334$	−15.8364	−	3.36613i	−0.866528	−	0.184186i
$335$	1.86417	−	4.18700i	0.101851	−	0.228760i
$336$	−0.771570	+	3.09460i	−0.0420926	+	0.168824i
$337$	11.3503	+	14.5278i	0.618292	+	0.791378i	0.990609	−	0.136728i	$-0.0436587\pi$
$337$	11.3503	+	14.5278i	0.618292	+	0.791378i	−0.372317	+	0.928106i	$0.621436\pi$
$338$	−3.84470	+	4.92099i	−0.209124	+	0.267667i
$339$	−2.25364	−	9.03887i	−0.122401	−	0.490924i
$340$	−1.37133	−	0.241803i	−0.0743708	−	0.0131136i
$341$	−9.35624	−	18.8770i	−0.506669	−	1.02225i
$342$	6.18102	−	6.32346i	0.334231	−	0.341934i
$343$	−6.71119	+	9.23717i	−0.362370	+	0.498760i
$344$	5.39780	−	10.1518i	0.291030	−	0.547348i
$345$	−1.67521	−	0.676828i	−0.0901901	−	0.0364392i
$346$	−7.39711	+	2.12109i	−0.397671	+	0.114030i
$347$	7.09809	+	4.78772i	0.381045	+	0.257018i	0.734749	−	0.678339i	$-0.237300\pi$
$347$	7.09809	+	4.78772i	0.381045	+	0.257018i	−0.353703	+	0.935358i	$0.615078\pi$
$348$	−3.00340	+	4.80645i	−0.160999	+	0.257653i
$349$	−3.09058	−	14.5401i	−0.165435	−	0.778311i	−0.980120	−	0.198407i	$-0.936423\pi$
$349$	−3.09058	−	14.5401i	−0.165435	−	0.778311i	0.814685	−	0.579904i	$-0.196910\pi$
$350$	6.41469	+	14.4076i	0.342880	+	0.770120i
$351$	21.4117	−	3.77546i	1.14287	−	0.201519i
$352$	−3.16076	−	1.00478i	−0.168469	−	0.0535550i
$353$	8.80143	−	15.2445i	0.468453	−	0.811384i	−0.530897	−	0.847436i	$-0.678145\pi$
$353$	8.80143	−	15.2445i	0.468453	−	0.811384i	0.999350	+	0.0360521i	$0.0114782\pi$
$354$	1.35840	−	12.9243i	0.0721980	−	0.686918i
$355$	−2.44023	+	0.985915i	−0.129514	+	0.0523269i
$356$	1.65481	−	1.29288i	0.0877049	−	0.0685226i
$357$	−3.44396	−	12.0105i	−0.182274	−	0.635664i
$358$	1.35644	−	19.3980i	0.0716900	−	1.02521i
$359$	1.79349	+	12.7614i	0.0946569	+	0.673519i	0.978577	+	0.205881i	$0.0660060\pi$
$359$	1.79349	+	12.7614i	0.0946569	+	0.673519i	−0.883920	+	0.467638i	$0.845105\pi$
$360$	0.222821	−	0.685772i	0.0117437	−	0.0361433i
$361$	−10.8149	+	15.6217i	−0.569203	+	0.822197i
$362$			8.93464i			0.469594i
$363$	−10.7667	+	1.27050i	−0.565106	+	0.0666838i
$364$	−9.12498	+	10.8747i	−0.478279	+	0.569990i
$365$	−4.27227	+	2.88168i	−0.223621	+	0.150834i
$366$	−0.284407	−	8.14436i	−0.0148662	−	0.425713i
$367$	14.4935	+	9.05651i	0.756552	+	0.472746i	0.852557	−	0.522635i	$-0.175051\pi$
$367$	14.4935	+	9.05651i	0.756552	+	0.472746i	−0.0960048	+	0.995381i	$0.530606\pi$
$368$	4.71160	+	2.09774i	0.245609	+	0.109352i
$369$	0.257037	+	2.44554i	0.0133808	+	0.127310i
$370$	0.473535	+	0.890589i	0.0246179	+	0.0462995i
$371$	1.07920	+	0.151671i	0.0560292	+	0.00787439i
$372$	5.71952	−	2.54650i	0.296543	−	0.132030i
$373$	−10.9923	−	19.0393i	−0.569162	−	0.985818i	−0.996649	−	0.0817962i	$-0.973934\pi$
$373$	−10.9923	−	19.0393i	−0.569162	−	0.985818i	0.427487	−	0.904022i	$-0.359399\pi$
$374$	12.6918	−	2.78234i	0.656277	−	0.143871i
$375$	1.18303	+	3.25034i	0.0610912	+	0.167847i
$376$	4.37848	+	6.49136i	0.225803	+	0.334766i
$377$	−21.3938	+	13.3684i	−1.10184	+	0.688505i
$378$	15.8819	−	2.23206i	0.816877	−	0.114805i
$379$	−14.4919	−	19.9464i	−0.744398	−	1.02458i	−0.998354	−	0.0573603i	$-0.981732\pi$
$379$	−14.4919	−	19.9464i	−0.744398	−	1.02458i	0.253955	−	0.967216i	$-0.418268\pi$
$380$	−0.224924	+	1.53293i	−0.0115384	+	0.0786377i
$381$	−11.9873	+	3.89492i	−0.614130	+	0.199543i
$382$	−11.1352	−	5.92066i	−0.569724	−	0.302928i
$383$	−15.1252	+	3.77114i	−0.772862	+	0.192696i	−0.608339	−	0.793677i	$-0.708164\pi$
$383$	−15.1252	+	3.77114i	−0.772862	+	0.192696i	−0.164523	+	0.986373i	$0.552608\pi$
$384$	0.337089	−	0.926145i	0.0172020	−	0.0472621i
$385$	2.76098	+	2.63247i	0.140713	+	0.134163i
$386$	−13.7603	+	11.5462i	−0.700379	+	0.587687i
$387$	−23.1966	−	2.43806i	−1.17915	−	0.123934i
$388$	−2.93029	+	2.63845i	−0.148763	+	0.133947i
$389$	−2.81008	+	1.49414i	−0.142476	+	0.0757561i	−0.539179	−	0.842191i	$-0.681265\pi$
$389$	−2.81008	+	1.49414i	−0.142476	+	0.0757561i	0.396703	+	0.917947i	$0.370154\pi$
$390$	−1.06756	+	1.10549i	−0.0540580	+	0.0559787i
$391$	−20.0943	+	2.11199i	−1.01621	+	0.106808i
$392$	−2.32298	+	2.57993i	−0.117328	+	0.130306i
$393$	5.42766	+	13.4339i	0.273789	+	0.677652i
$394$	−6.40978	+	22.3536i	−0.322920	+	1.12616i
$395$	−4.58890	−	1.67022i	−0.230893	−	0.0840380i
$396$	0.512077	+	6.70868i	0.0257329	+	0.337124i
$397$	2.42850	−	13.7727i	0.121883	−	0.691233i	−0.861228	−	0.508220i	$-0.830304\pi$
$397$	2.42850	−	13.7727i	0.121883	−	0.691233i	0.983110	−	0.183013i	$-0.0585850\pi$
$398$	−13.0914	−	9.51148i	−0.656214	−	0.476767i
$399$	−13.2474	+	4.21572i	−0.663199	+	0.211050i
$400$	−1.50604	−	4.63513i	−0.0753022	−	0.231756i
$401$	5.41287	−	2.64003i	0.270306	−	0.131837i	−0.298234	−	0.954493i	$-0.596398\pi$
$401$	5.41287	−	2.64003i	0.270306	−	0.131837i	0.568540	+	0.822656i	$0.307509\pi$
$402$	−12.6776	−	0.886502i	−0.632299	−	0.0442147i
$403$	27.8502	+	0.972552i	1.38732	+	0.0484463i
$404$	14.8656	−	0.519119i	0.739593	−	0.0258271i
$405$	−0.425922	+	0.0297833i	−0.0211642	+	0.00147995i
$406$	−16.1157	+	9.30440i	−0.799808	+	0.461770i
$407$	−7.24816	−	6.00367i	−0.359278	−	0.297591i
$408$	0.670475	+	3.80246i	0.0331935	+	0.188250i
$409$	−9.66057	+	19.8071i	−0.477684	+	0.979398i	0.514833	+	0.857291i	$0.327854\pi$
$409$	−9.66057	+	19.8071i	−0.477684	+	0.979398i	−0.992517	+	0.122107i	$0.961035\pi$
$410$	−0.288297	−	0.320187i	−0.0142380	−	0.0158129i
$411$	4.31954	+	3.88933i	0.213067	+	0.191846i
$412$	11.2460	+	2.80394i	0.554050	+	0.138140i
$413$	23.8599	−	35.3737i	1.17407	−	1.74063i
$414$	0.365140	−	10.4563i	0.0179457	−	0.513897i
$415$	−0.281755	−	0.450902i	−0.0138308	−	0.0221339i
$416$	3.15567	−	3.04739i	0.154719	−	0.149411i
$417$	15.8733			0.777320
$418$	−3.50173	−	14.0263i	−0.171275	−	0.686050i
$419$	−20.7142			−1.01195			−0.505977	−	0.862547i	$-0.668868\pi$
$419$	−20.7142			−1.01195			−0.505977	+	0.862547i	$0.668868\pi$
$420$	−0.815465	+	0.787486i	−0.0397906	+	0.0384254i
$421$	−7.86348	−	12.5842i	−0.383242	−	0.613316i	0.599041	−	0.800718i	$-0.295549\pi$
$421$	−7.86348	−	12.5842i	−0.383242	−	0.613316i	−0.982283	+	0.187402i	$0.939993\pi$
$422$	0.131426	−	3.76354i	0.00639770	−	0.183206i
$423$	8.88230	−	13.1685i	0.431872	−	0.640277i
$424$	−0.326773	−	0.0814735i	−0.0158695	−	0.00395670i
$425$	14.1889	+	12.7757i	0.688262	+	0.619714i
$426$	4.88311	+	5.42325i	0.236588	+	0.262757i
$427$	11.7295	−	24.0489i	0.567628	−	1.16381i
$428$	2.88039	+	16.3355i	0.139229	+	0.789606i
$429$	5.28703	−	13.3297i	0.255260	−	0.643563i
$430$	3.53923	−	2.04338i	0.170677	−	0.0985404i
$431$	24.0715	−	1.68324i	1.15948	−	0.0810789i	0.522974	−	0.852349i	$-0.324823\pi$
$431$	24.0715	−	1.68324i	1.15948	−	0.0810789i	0.636508	+	0.771270i	$0.280378\pi$
$432$	−4.95311	+	0.172966i	−0.238307	+	0.00832185i
$433$	−17.6662	−	0.616919i	−0.848986	−	0.0296472i	−0.392898	−	0.919582i	$-0.628527\pi$
$433$	−17.6662	−	0.616919i	−0.848986	−	0.0296472i	−0.456088	+	0.889935i	$0.650750\pi$
$434$	20.5062	+	1.43393i	0.984328	+	0.0688309i
$435$	−1.81065	+	0.883115i	−0.0868142	+	0.0423421i
$436$	−2.23818	−	6.88841i	−0.107189	−	0.329895i
$437$	2.99373	+	22.2808i	0.143209	+	1.06583i
$438$	11.5602	+	8.39895i	0.552366	+	0.401317i
$439$	0.00650147	−	0.0368717i	0.000310298	−	0.00175979i	−0.984652	−	0.174528i	$-0.944160\pi$
$439$	0.00650147	−	0.0368717i	0.000310298	−	0.00175979i	0.984963	+	0.172768i	$0.0552712\pi$
$440$	−0.763503	−	0.898225i	−0.0363986	−	0.0428212i
$441$	6.61792	+	2.40873i	0.315139	+	0.114701i
$442$	−4.73712	+	16.5203i	−0.225322	+	0.785791i
$443$	3.51210	+	8.69275i	0.166865	+	0.413005i	0.987328	−	0.158695i	$-0.0507286\pi$
$443$	3.51210	+	8.69275i	0.166865	+	0.413005i	−0.820463	+	0.571700i	$0.806284\pi$
$444$	1.87144	−	2.07844i	0.0888145	−	0.0986385i
$445$	0.742339	−	0.0780229i	0.0351902	−	0.00369864i
$446$	−14.0534	+	14.5527i	−0.665448	+	0.689092i
$447$	−7.24832	+	3.85400i	−0.342834	+	0.182288i
$448$	2.40481	−	2.16530i	0.113617	−	0.102301i
$449$	14.4870	+	1.52264i	0.683684	+	0.0718581i	0.440001	−	0.897997i	$-0.354978\pi$
$449$	14.4870	+	1.52264i	0.683684	+	0.0718581i	0.243682	+	0.969855i	$0.421645\pi$
$450$	−7.57376	+	6.35514i	−0.357030	+	0.299584i
$451$	3.62454	+	1.73932i	0.170673	+	0.0819012i
$452$	−3.23272	+	8.88183i	−0.152054	+	0.417766i
$453$	−5.59270	+	1.39442i	−0.262768	+	0.0655154i
$454$	12.7689	+	6.78936i	0.599275	+	0.318640i
$455$	−4.79890	+	1.55926i	−0.224976	+	0.0730991i
$456$	4.20751	−	0.867709i	0.197035	−	0.0406342i
$457$	4.24745	+	5.84611i	0.198687	+	0.273469i	0.896722	−	0.442594i	$-0.145942\pi$
$457$	4.24745	+	5.84611i	0.198687	+	0.273469i	−0.698035	+	0.716064i	$0.745942\pi$
$458$	−15.7751	+	2.21705i	−0.737123	+	0.103596i
$459$	16.4658	−	10.2890i	0.768557	−	0.480248i
$460$	1.02511	+	1.51979i	0.0477961	+	0.0708606i
$461$	−9.90297	−	27.2082i	−0.461227	−	1.26721i	−0.924563	−	0.381029i	$-0.875570\pi$
$461$	−9.90297	−	27.2082i	−0.461227	−	1.26721i	0.463336	−	0.886183i	$-0.346652\pi$
$462$	4.24075	−	9.69054i	0.197298	−	0.450845i
$463$	−14.2800	−	24.7336i	−0.663646	−	1.14947i	−0.979650	−	0.200711i	$-0.935675\pi$
$463$	−14.2800	−	24.7336i	−0.663646	−	1.14947i	0.316004	−	0.948758i	$-0.397659\pi$
$464$	5.25341	−	2.33897i	0.243883	−	0.108584i
$465$	2.20371	+	0.309711i	0.102194	+	0.0143625i
$466$	6.70323	+	12.6069i	0.310521	+	0.584006i
$467$	−1.89586	−	18.0379i	−0.0877301	−	0.834696i	−0.946580	−	0.322469i	$-0.895487\pi$
$467$	−1.89586	−	18.0379i	−0.0877301	−	0.834696i	0.858850	−	0.512227i	$-0.171179\pi$
$468$	−8.12998	−	3.61970i	−0.375808	−	0.167321i
$469$	−35.3859	−	22.1115i	−1.63397	−	1.02102i
$470$	0.0971296	+	2.78143i	0.00448026	+	0.128298i
$471$	9.44117	−	6.36815i	0.435026	−	0.293429i
$472$	−8.47553	+	10.1007i	−0.390118	+	0.464924i
$473$	−23.2853	+	30.1983i	−1.07066	+	1.38852i
$474$			13.5408i			0.621950i
$475$	13.7537	−	16.1906i	0.631061	−	0.742876i
$476$	−3.91750	+	12.0568i	−0.179558	+	0.552624i
$477$	0.0950821	+	0.676544i	0.00435351	+	0.0309768i
$478$	0.0306417	−	0.438197i	0.00140152	−	0.0200427i
$479$	−2.03215	−	7.08694i	−0.0928512	−	0.323811i	0.901103	−	0.433605i	$-0.142759\pi$
$479$	−2.03215	−	7.08694i	−0.0928512	−	0.323811i	−0.993954	+	0.109794i	$0.964981\pi$
$480$	0.276055	−	0.215678i	0.0126002	−	0.00984432i
$481$	11.5424	−	4.66341i	0.526286	−	0.212633i
$482$	−1.97807	+	18.8201i	−0.0900987	+	0.857232i
$483$	−8.22448	+	14.2452i	−0.374227	+	0.648180i
$484$	9.77742	+	5.04004i	0.444428	+	0.229093i
$485$	−1.38026	+	0.243377i	−0.0626743	+	0.0110512i
$486$	6.52905	+	14.6645i	0.296164	+	0.665194i
$487$	1.49089	+	7.01408i	0.0675586	+	0.317838i	0.998931	−	0.0462302i	$-0.0147208\pi$
$487$	1.49089	+	7.01408i	0.0675586	+	0.317838i	−0.931372	+	0.364068i	$0.881387\pi$
$488$	−4.38166	+	7.01212i	−0.198348	+	0.317424i
$489$	7.81076	+	5.26842i	0.353215	+	0.238246i
$490$	−1.18617	+	0.340128i	−0.0535856	+	0.0153654i
$491$	29.5593	+	11.9427i	1.33399	+	0.538967i	0.927204	−	0.374556i	$-0.122205\pi$
$491$	29.5593	+	11.9427i	1.33399	+	0.538967i	0.406786	+	0.913523i	$0.366649\pi$
$492$	−0.560868	+	1.05484i	−0.0252859	+	0.0475558i
$493$	−13.2419	+	18.2259i	−0.596384	+	0.820852i
$494$	18.5256	+	4.73843i	0.833508	+	0.213192i
$495$	−1.10927	+	2.11867i	−0.0498578	+	0.0952273i
$496$	−6.25587	−	1.10308i	−0.280897	−	0.0495297i
$497$	5.79663	+	23.2490i	0.260014	+	1.04286i
$498$	−0.907665	+	1.16176i	−0.0406734	+	0.0520596i
$499$	−12.9190	−	16.5356i	−0.578334	−	0.740234i	0.406516	−	0.913644i	$-0.366744\pi$
$499$	−12.9190	−	16.5356i	−0.578334	−	0.740234i	−0.984850	+	0.173410i	$0.944521\pi$
$500$	0.849033	−	3.40528i	0.0379699	−	0.152289i
$501$	−6.49020	+	14.5772i	−0.289961	+	0.651262i
$502$	−6.88174	−	1.46276i	−0.307147	−	0.0652862i
$503$	2.00537	−	14.2689i	0.0894150	−	0.636221i	−0.893075	−	0.449907i	$-0.851457\pi$
$503$	2.00537	−	14.2689i	0.0894150	−	0.636221i	0.982490	−	0.186314i	$-0.0596540\pi$
$504$	−5.90024	−	2.87774i	−0.262817	−	0.128185i
$505$	4.57878	+	2.64356i	0.203753	+	0.117637i
$506$	−14.2417	−	9.47473i	−0.633121	−	0.421203i
$507$	3.95623	+	4.71485i	0.175702	+	0.209394i
$508$	12.2932	+	3.52502i	0.545423	+	0.156397i
$509$	3.94723	+	3.08391i	0.174958	+	0.136692i	0.699335	−	0.714794i	$-0.253480\pi$
$509$	3.94723	+	3.08391i	0.174958	+	0.136692i	−0.524377	+	0.851486i	$0.675702\pi$
$510$	−0.514114	+	1.27248i	−0.0227653	+	0.0563462i
$511$	20.5666	+	42.1677i	0.909812	+	1.86539i
$512$	−0.809017	+	0.587785i	−0.0357538	+	0.0259767i
$513$	−11.9716	−	17.9828i	−0.528559	−	0.793961i
$514$	4.90008	+	1.59213i	0.216133	+	0.0702259i
$515$	2.86178	+	2.96346i	0.126105	+	0.130585i
$516$	−8.68070	−	7.28397i	−0.382146	−	0.320659i
$517$	−10.7135	−	23.6562i	−0.471179	−	1.04040i
$518$	8.62908	−	3.14073i	0.379140	−	0.137996i
$519$	0.529051	+	7.56579i	0.0232228	+	0.332101i
$520$	1.52522	−	0.324196i	0.0668853	−	0.0142169i
$521$	5.22010	−	24.5586i	0.228697	−	1.07593i	−0.702575	−	0.711609i	$-0.747967\pi$
$521$	5.22010	−	24.5586i	0.228697	−	1.07593i	0.931272	−	0.364324i	$-0.118700\pi$
$522$	−8.39165	−	8.10372i	−0.367293	−	0.354690i
$523$	5.43079	+	5.24445i	0.237472	+	0.229324i	0.803866	−	0.594811i	$-0.202773\pi$
$523$	5.43079	+	5.24445i	0.237472	+	0.229324i	−0.566394	+	0.824135i	$0.691662\pi$
$524$	3.05649	−	14.3797i	0.133523	−	0.628178i
$525$	15.2041	−	3.23172i	0.663560	−	0.141044i
$526$	−2.13781	−	30.5721i	−0.0932129	−	1.33301i
$527$	23.3852	−	8.51153i	1.01868	−	0.370768i
$528$	−1.61634	+	2.84122i	−0.0703421	+	0.123648i
$529$	2.75754	+	2.31385i	0.119893	+	0.100602i
$530$	−0.0831541	−	0.0861086i	−0.00361198	−	0.00374032i
$531$	25.4395	+	8.26578i	1.10398	+	0.358704i
$532$	13.5351	+	3.97009i	0.586822	+	0.172125i
$533$	−4.30203	+	3.12561i	−0.186342	+	0.135385i
$534$	−0.907301	−	1.86024i	−0.0392628	−	0.0805006i
$535$	−2.20865	+	5.46661i	−0.0954883	+	0.236342i
$536$	10.1609	+	7.93860i	0.438886	+	0.342895i
$537$	−18.4226	−	5.28259i	−0.794993	−	0.227961i
$538$	−8.57056	−	10.2140i	−0.369503	−	0.440357i
$539$	9.02790	−	7.14644i	0.388859	−	0.307819i
$540$	−1.52561	−	0.880813i	−0.0656519	−	0.0379041i
$541$	−16.1499	−	7.87681i	−0.694337	−	0.338651i	0.0571808	−	0.998364i	$-0.481789\pi$
$541$	−16.1499	−	7.87681i	−0.694337	−	0.338651i	−0.751517	+	0.659713i	$0.770678\pi$
$542$	2.62338	−	18.6663i	0.112684	−	0.801786i
$543$	8.61340	+	1.83083i	0.369636	+	0.0785686i
$544$	1.59343	−	3.57890i	0.0683177	−	0.153444i
$545$	0.622815	−	2.49798i	0.0266785	−	0.107002i
$546$	8.61389	+	11.0253i	0.368640	+	0.471838i
$547$	6.34255	−	8.11810i	0.271188	−	0.347105i	−0.633068	−	0.774097i	$-0.718204\pi$
$547$	6.34255	−	8.11810i	0.271188	−	0.347105i	0.904255	+	0.426992i	$0.140427\pi$
$548$	−1.42674	−	5.72236i	−0.0609475	−	0.244447i
$549$	16.5189	+	2.91274i	0.705011	+	0.124313i
$550$	2.35152	+	15.9921i	0.100269	+	0.681907i
$551$	20.6954	+	14.1425i	0.881655	+	0.602493i
$552$	2.98779	−	4.11234i	0.127169	−	0.175033i
$553$	−20.8722	+	39.2549i	−0.887576	+	1.66929i
$554$	−27.8940	−	11.2699i	−1.18510	−	0.478812i
$555$	0.955602	−	0.274015i	0.0405631	−	0.0116313i
$556$	−13.3521	−	9.00610i	−0.566255	−	0.381944i
$557$	12.2878	−	19.6647i	0.520652	−	0.833218i	−0.478336	−	0.878177i	$-0.658760\pi$
$557$	12.2878	−	19.6647i	0.520652	−	0.833218i	0.998989	+	0.0449586i	$0.0143156\pi$
$558$	2.67928	+	12.6050i	0.113423	+	0.533613i
$559$	−20.5153	−	46.0781i	−0.867705	−	1.94890i
$560$	1.13274	−	0.199732i	0.0478670	−	0.00844024i
$561$	−0.0815689	−	12.8056i	−0.00344384	−	0.540653i
$562$	0.684073	−	1.18485i	0.0288559	−	0.0499798i
$563$	0.627049	−	5.96598i	0.0264270	−	0.251436i	−0.973330	−	0.229408i	$-0.926321\pi$
$563$	0.627049	−	5.96598i	0.0264270	−	0.251436i	0.999757	−	0.0220280i	$-0.00701230\pi$
$564$	7.15518	−	2.89088i	0.301287	−	0.121728i
$565$	−2.64740	+	2.06838i	−0.111377	+	0.0870173i
$566$	1.18192	+	4.12183i	0.0496796	+	0.173253i
$567$	−0.271150	+	3.87762i	−0.0113872	+	0.162845i
$568$	−1.03050	−	7.33239i	−0.0432388	−	0.307660i
$569$	−0.429735	+	1.32259i	−0.0180154	+	0.0554458i	−0.959660	−	0.281163i	$-0.909280\pi$
$569$	−0.429735	+	1.32259i	−0.0180154	+	0.0554458i	0.941645	+	0.336609i	$0.109280\pi$
$570$	1.43172	+	0.530957i	0.0599683	+	0.0222393i
$571$			37.6600i			1.57602i	0.615660	+	0.788012i	$0.288889\pi$
$571$			37.6600i			1.57602i	−0.615660	+	0.788012i	$0.711111\pi$
$572$	−12.0102	+	8.21274i	−0.502170	+	0.343392i
$573$	−7.98954	+	9.52156i	−0.333768	+	0.397769i
$574$	−3.25192	+	2.19345i	−0.135733	+	0.0915527i
$575$	−0.877229	−	25.1205i	−0.0365830	−	1.04760i
$576$	1.72037	+	1.07501i	0.0716822	+	0.0447920i
$577$	−3.32973	−	1.48249i	−0.138619	−	0.0617170i	0.336255	−	0.941771i	$-0.390840\pi$
$577$	−3.32973	−	1.48249i	−0.138619	−	0.0617170i	−0.474874	+	0.880054i	$0.657506\pi$
$578$	−0.172728	−	1.64340i	−0.00718453	−	0.0683562i
$579$	8.31141	+	15.6315i	0.345411	+	0.649623i
$580$	2.02411	+	0.284471i	0.0840468	+	0.0118120i
$581$	−4.42209	+	1.96884i	−0.183459	+	0.0816813i
$582$	1.94313	+	3.36559i	0.0805452	+	0.139508i
$583$	1.02327	+	0.447800i	0.0423794	+	0.0185460i
$584$	−4.95866	−	13.6238i	−0.205191	−	0.563758i
$585$	−1.76885	−	2.62243i	−0.0731331	−	0.108424i
$586$	7.51924	−	4.69854i	0.310617	−	0.194095i
$587$	10.0152	−	1.40755i	0.413373	−	0.0580958i	0.0705786	−	0.997506i	$-0.477515\pi$
$587$	10.0152	−	1.40755i	0.413373	−	0.0580958i	0.342794	+	0.939410i	$0.388627\pi$
$588$	2.01115	+	2.76812i	0.0829386	+	0.114155i
$589$	−10.2168	−	25.7356i	−0.420976	−	1.06042i
$590$	−4.45735	+	1.44828i	−0.183506	+	0.0596248i
$591$	20.2364	+	10.7599i	0.832414	+	0.442602i
$592$	−2.75344	+	0.686510i	−0.113166	+	0.0282154i
$593$	−11.1073	+	30.5171i	−0.456122	+	1.25319i	0.472227	+	0.881477i	$0.343450\pi$
$593$	−11.1073	+	30.5171i	−0.456122	+	1.25319i	−0.928349	+	0.371709i	$0.878772\pi$
$594$	16.2919	+	2.18394i	0.668464	+	0.0896083i
$595$	−3.45185	+	2.89645i	−0.141512	+	0.118743i
$596$	8.28369	+	0.870651i	0.339313	+	0.0356633i
$597$	−11.8521	+	10.6717i	−0.485075	+	0.436763i
$598$	19.9770	−	10.6220i	0.816921	−	0.434364i
$599$	−22.2941	+	23.0862i	−0.910913	+	0.943278i	−0.998601	−	0.0528700i	$-0.983163\pi$
$599$	−22.2941	+	23.0862i	−0.910913	+	0.943278i	0.0876885	+	0.996148i	$0.472052\pi$
$600$	−4.77708	+	0.502091i	−0.195024	+	0.0204978i
$601$	16.5285	−	18.3568i	0.674212	−	0.748788i	−0.304839	−	0.952404i	$-0.598603\pi$
$601$	16.5285	−	18.3568i	0.674212	−	0.748788i	0.979051	+	0.203616i	$0.0652694\pi$
$602$	−13.9377	−	34.4969i	−0.568057	−	1.40599i
$603$	7.21012	−	25.1447i	0.293619	−	1.02397i
$604$	5.49553	+	2.00021i	0.223610	+	0.0813874i
$605$	1.99792	+	3.36088i	0.0812269	+	0.136639i
$606$	2.54572	−	14.4375i	0.103413	−	0.586484i
$607$	13.3765	+	9.71859i	0.542935	+	0.394465i	0.825174	−	0.564879i	$-0.191077\pi$
$607$	13.3765	+	9.71859i	0.542935	+	0.394465i	−0.282239	+	0.959344i	$0.591077\pi$
$608$	−4.03153	−	1.65734i	−0.163500	−	0.0672141i
$609$	5.66753	+	17.4429i	0.229660	+	0.706820i
$610$	−2.64156	+	1.28837i	−0.106954	+	0.0521647i
$611$	34.2657	+	2.39609i	1.38624	+	0.0969354i
$612$	−7.94250	−	0.277358i	−0.321056	−	0.0112115i
$613$	15.7898	−	0.551391i	0.637743	−	0.0222705i	0.285796	−	0.958290i	$-0.407742\pi$
$613$	15.7898	−	0.551391i	0.637743	−	0.0222705i	0.351947	+	0.936020i	$0.385520\pi$
$614$	2.40000	−	0.167824i	0.0968560	−	0.00677283i
$615$	−0.367751	+	0.212321i	−0.0148291	+	0.00856160i
$616$	−9.06532	+	5.74525i	−0.365252	+	0.231483i
$617$	−4.06508	−	23.0542i	−0.163654	−	0.928127i	−0.950442	−	0.310903i	$-0.899368\pi$
$617$	−4.06508	−	23.0542i	−0.163654	−	0.928127i	0.786788	−	0.617224i	$-0.211743\pi$
$618$	5.00758	−	10.2671i	0.201435	−	0.413002i
$619$	4.88033	+	5.42016i	0.196157	+	0.217854i	0.833197	−	0.552976i	$-0.186508\pi$
$619$	4.88033	+	5.42016i	0.196157	+	0.217854i	−0.637040	+	0.770831i	$0.719841\pi$
$620$	−1.67796	−	1.51084i	−0.0673884	−	0.0606768i
$621$	−24.8019	−	6.18381i	−0.995266	−	0.248148i
$622$	3.92870	−	5.82454i	0.157527	−	0.233543i
$623$	0.237161	−	6.79140i	0.00950165	−	0.272092i
$624$	−2.29118	−	3.66666i	−0.0917207	−	0.146784i
$625$	−16.6318	+	16.0611i	−0.665270	+	0.642444i
$626$	−1.42034			−0.0567682
$627$	−14.2396	+	0.501638i	−0.568674	+	0.0200335i
$628$	−11.5547			−0.461082
$629$	7.99696	−	7.72258i	0.318860	−	0.307919i
$630$	−1.23649	−	1.97880i	−0.0492629	−	0.0788371i
$631$	−0.987223	+	28.2704i	−0.0393007	+	1.12543i	0.806265	+	0.591555i	$0.201486\pi$
$631$	−0.987223	+	28.2704i	−0.0393007	+	1.12543i	−0.845566	+	0.533871i	$0.820737\pi$
$632$	7.68269	−	11.3901i	0.305601	−	0.453072i
$633$	−3.60129	−	0.897902i	−0.143138	−	0.0356884i
$634$	8.07971	+	7.27500i	0.320886	+	0.288927i
$635$	3.04162	+	3.37806i	0.120703	+	0.134054i
$636$	−0.145505	+	0.298328i	−0.00576963	+	0.0118295i
$637$	2.64461	+	14.9983i	0.104783	+	0.594254i
$638$	−18.4762	+	4.73184i	−0.731479	+	0.187335i
$639$	−13.0085	+	7.51044i	−0.514607	+	0.297108i
$640$	−0.354578	+	0.0247945i	−0.0140159	+	0.000980089i
$641$	−19.5638	+	0.683184i	−0.772725	+	0.0269841i	−0.418548	−	0.908195i	$-0.637461\pi$
$641$	−19.5638	+	0.683184i	−0.772725	+	0.0269841i	−0.354176	+	0.935179i	$0.615239\pi$
$642$	16.3384	+	0.570549i	0.644825	+	0.0225178i
$643$	−10.6888	−	0.747437i	−0.421527	−	0.0294760i	−0.142582	−	0.989783i	$-0.545540\pi$
$643$	−10.6888	−	0.747437i	−0.421527	−	0.0294760i	−0.278945	+	0.960307i	$0.589985\pi$
$644$	15.0005	−	7.31623i	0.591103	−	0.288300i
$645$	−1.24467	−	3.83070i	−0.0490088	−	0.150834i
$646$	16.9243	−	2.27402i	0.665878	−	0.0894700i
$647$	−35.6347	−	25.8901i	−1.40095	−	1.01785i	−0.994562	−	0.104143i	$-0.966790\pi$
$647$	−35.6347	−	25.8901i	−1.40095	−	1.01785i	−0.406383	−	0.913703i	$-0.633210\pi$
$648$	0.208587	−	1.18296i	0.00819409	−	0.0464710i
$649$	33.3206	−	28.3230i	1.30795	−	1.11177i
$650$	−20.0908	−	7.31247i	−0.788028	−	0.286819i
$651$	5.58438	−	19.4750i	0.218869	−	0.763287i
$652$	−3.58097	−	8.86322i	−0.140242	−	0.347111i
$653$	29.2531	−	32.4889i	1.14476	−	1.27139i	0.187469	−	0.982271i	$-0.439972\pi$
$653$	29.2531	−	32.4889i	1.14476	−	1.27139i	0.957294	−	0.289117i	$-0.0933617\pi$
$654$	−7.09938	+	0.746175i	−0.277608	+	0.0291777i
$655$	3.62983	−	3.75880i	0.141829	−	0.146869i
$656$	1.07027	−	0.569073i	0.0417870	−	0.0222186i
$657$	−21.8569	+	19.6800i	−0.852719	+	0.767792i
$658$	25.1990	+	2.64852i	0.982359	+	0.103250i
$659$	3.67090	−	3.08025i	0.142998	−	0.119989i	−0.568483	−	0.822695i	$-0.692469\pi$
$659$	3.67090	−	3.08025i	0.142998	−	0.119989i	0.711481	+	0.702706i	$0.248025\pi$
$660$	−1.02238	+	0.551992i	−0.0397962	+	0.0214863i
$661$	−11.1061	+	30.5137i	−0.431977	+	1.18685i	0.512620	+	0.858615i	$0.328675\pi$
$661$	−11.1061	+	30.5137i	−0.431977	+	1.18685i	−0.944597	+	0.328232i	$0.893547\pi$
$662$	−33.9574	+	8.46653i	−1.31979	+	0.329061i
$663$	14.9556	+	7.95205i	0.580828	+	0.308832i
$664$	1.42265	−	0.462246i	0.0552094	−	0.0179386i
$665$	3.33215	+	3.74615i	0.129215	+	0.145269i
$666$	3.38370	+	4.65727i	0.131116	+	0.180465i
$667$	29.3699	−	4.12767i	1.13721	−	0.159824i
$668$	13.7301	−	8.57949i	0.531232	−	0.331950i
$669$	11.1497	+	16.5302i	0.431074	+	0.639094i
$670$	1.56756	+	4.30684i	0.0605602	+	0.166388i
$671$	18.2198	−	20.4962i	0.703368	−	0.791247i
$672$	−1.59467	−	2.76205i	−0.0615156	−	0.106548i
$673$	23.0056	−	10.2428i	0.886802	−	0.394830i	0.0877858	−	0.996139i	$-0.472021\pi$
$673$	23.0056	−	10.2428i	0.886802	−	0.394830i	0.799016	+	0.601310i	$0.205354\pi$
$674$	−18.2566	−	2.56579i	−0.703217	−	0.0988307i
$675$	11.3398	+	21.3271i	0.436471	+	0.820882i
$676$	−0.652763	−	6.21062i	−0.0251063	−	0.238870i
$677$	−41.7308	−	18.5798i	−1.60385	−	0.714078i	−0.607095	−	0.794629i	$-0.707665\pi$
$677$	−41.7308	−	18.5798i	−1.60385	−	0.714078i	−0.996750	+	0.0805514i	$0.974332\pi$
$678$	7.90006	+	4.93650i	0.303400	+	0.189585i
$679$	0.445312	+	12.7521i	0.0170895	+	0.489379i
$680$	1.15442	−	0.778668i	0.0442701	−	0.0298606i
$681$	9.16178	−	10.9186i	0.351080	−	0.418401i
$682$	19.8434	+	7.07959i	0.759842	+	0.271091i
$683$		−	27.2653i		−	1.04328i	−0.853166	−	0.521639i	$-0.825321\pi$
$683$		−	27.2653i		−	1.04328i	0.853166	−	0.521639i	$-0.174679\pi$
$684$	−0.0536068	+	8.84242i	−0.00204971	+	0.338098i
$685$	0.647775	−	1.99365i	0.0247502	−	0.0761733i
$686$	−1.58905	−	11.3066i	−0.0606700	−	0.431690i
$687$	−1.09521	+	15.6622i	−0.0417849	+	0.597551i
$688$	3.16917	+	11.0522i	0.120823	+	0.421362i
$689$	−1.16421	+	0.909579i	−0.0443528	+	0.0346522i
$690$	1.67521	−	0.676828i	0.0637740	−	0.0257664i
$691$	0.658202	−	6.26237i	0.0250392	−	0.238232i	−0.974843	−	0.222892i	$-0.928450\pi$
$691$	0.658202	−	6.26237i	0.0250392	−	0.238232i	0.999882	−	0.0153399i	$-0.00488304\pi$
$692$	3.84760	−	6.66424i	0.146264	−	0.253337i
$693$	17.6954	+	12.6850i	0.672192	+	0.481864i
$694$	−8.43177	+	1.48675i	−0.320066	+	0.0564362i
$695$	−2.32841	−	5.22970i	−0.0883216	−	0.198374i
$696$	−1.17837	−	5.54381i	−0.0446661	−	0.210138i
$697$	−2.51645	+	4.02716i	−0.0953172	+	0.152539i
$698$	12.3236	+	8.31234i	0.466453	+	0.314627i
$699$	13.5273	−	3.87888i	0.511648	−	0.146713i
$700$	−14.6227	−	5.90796i	−0.552687	−	0.223300i
$701$	−2.63568	+	4.95699i	−0.0995482	+	0.187223i	−0.927745	−	0.373214i	$-0.878256\pi$
$701$	−2.63568	+	4.95699i	−0.0995482	+	0.187223i	0.828197	+	0.560437i	$0.189367\pi$
$702$	−12.7796	+	17.5896i	−0.482336	+	0.663879i
$703$	−8.84554	−	8.64628i	−0.333616	−	0.326101i
$704$	2.97164	−	1.47287i	0.111998	−	0.0555109i
$705$	2.70133	+	0.476317i	0.101738	+	0.0179391i
$706$	4.25852	+	17.0800i	0.160271	+	0.642814i
$707$	29.6345	−	37.9304i	1.11452	−	1.42652i
$708$	8.00082	+	10.2406i	0.300689	+	0.384865i
$709$	−0.0690047	+	0.276763i	−0.00259153	+	0.0103940i	−0.971578	−	0.236721i	$-0.923927\pi$
$709$	−0.0690047	+	0.276763i	−0.00259153	+	0.0103940i	0.968986	+	0.247115i	$0.0794827\pi$
$710$	1.07048	−	2.40433i	0.0401743	−	0.0902329i
$711$	−27.2620	−	5.79472i	−1.02241	−	0.217319i
$712$	−0.292262	+	2.07955i	−0.0109530	+	0.0779344i
$713$	−29.4466	−	14.3621i	−1.10278	−	0.537864i
$714$	10.8206	+	6.24726i	0.404950	+	0.233798i
$715$	−5.16719	+	0.213404i	−0.193242	+	0.00798084i
$716$	12.4992	+	14.8960i	0.467118	+	0.556690i
$717$	−0.416163	−	0.119333i	−0.0155419	−	0.00445657i
$718$	−10.1549	−	7.93389i	−0.378978	−	0.296090i
$719$	−4.18229	+	10.3515i	−0.155973	+	0.386047i	−0.984856	−	0.173376i	$-0.944533\pi$
$719$	−4.18229	+	10.3515i	−0.155973	+	0.386047i	0.828883	+	0.559422i	$0.188977\pi$
$720$	0.316093	+	0.648087i	0.0117801	+	0.0241528i
$721$	30.3430	−	22.0455i	1.13003	−	0.821015i
$722$	−3.07221	−	18.7500i	−0.114336	−	0.697802i
$723$	17.7381	+	5.76346i	0.659687	+	0.214345i
$724$	−6.20652	−	6.42704i	−0.230664	−	0.238859i
$725$	−21.4694	−	18.0150i	−0.797354	−	0.669060i
$726$	6.86236	−	8.39310i	0.254686	−	0.311497i
$727$	−28.5437	+	10.3891i	−1.05863	+	0.385309i	−0.811912	−	0.583779i	$-0.801573\pi$
$727$	−28.5437	+	10.3891i	−1.05863	+	0.385309i	−0.246715	+	0.969088i	$0.579351\pi$
$728$	−0.990259	−	14.1614i	−0.0367014	−	0.524855i
$729$	11.9502	−	2.54010i	0.442602	−	0.0940779i
$730$	1.07143	−	5.04067i	0.0396553	−	0.186564i
$731$	−32.4012	−	31.2895i	−1.19840	−	1.15728i
$732$	5.86214	+	5.66100i	0.216671	+	0.209237i
$733$	−7.64009	+	35.9438i	−0.282193	+	1.32761i	0.577327	+	0.816513i	$0.304096\pi$
$733$	−7.64009	+	35.9438i	−0.282193	+	1.32761i	−0.859520	+	0.511102i	$0.829238\pi$
$734$	−16.7169	+	3.55329i	−0.617032	+	0.131154i
$735$	0.0848364	+	1.21322i	0.00312924	+	0.0447502i
$736$	−4.84646	+	1.76397i	−0.178643	+	0.0650206i
$737$	−28.8179	−	31.5984i	−1.06152	−	1.16394i
$738$	−1.88371	−	1.58062i	−0.0693404	−	0.0581835i
$739$	−0.167871	−	0.173835i	−0.00617522	−	0.00639462i	0.716245	−	0.697849i	$-0.245859\pi$
$739$	−0.167871	−	0.173835i	−0.00617522	−	0.00639462i	−0.722420	+	0.691454i	$0.756970\pi$
$740$	−0.959288	−	0.311691i	−0.0352641	−	0.0114580i
$741$	8.36423	−	16.8886i	0.307268	−	0.620417i
$742$	−0.881670	+	0.640571i	−0.0323671	+	0.0235161i
$743$	−1.05252	−	2.15798i	−0.0386132	−	0.0791688i	0.878615	−	0.477530i	$-0.158468\pi$
$743$	−1.05252	−	2.15798i	−0.0386132	−	0.0791688i	−0.917229	+	0.398361i	$0.869579\pi$
$744$	−2.34534	+	5.80491i	−0.0859842	+	0.212818i
$745$	2.33299	+	1.82273i	0.0854741	+	0.0667797i
$746$	21.1330	+	6.05980i	0.773736	+	0.221865i
$747$	−1.95056	−	2.32459i	−0.0713674	−	0.0850523i
$748$	−7.19694	+	10.8179i	−0.263146	+	0.395542i
$749$	46.4856	+	26.8385i	1.69855	+	0.980657i
$750$	−3.10887	−	1.51630i	−0.113520	−	0.0553673i
$751$	0.654103	−	4.65418i	0.0238685	−	0.169833i	−0.974686	−	0.223577i	$-0.928227\pi$
$751$	0.654103	−	4.65418i	0.0238685	−	0.169833i	0.998555	+	0.0537437i	$0.0171154\pi$
$752$	−7.65889	−	1.62795i	−0.279291	−	0.0593651i
$753$	−2.82033	+	6.33457i	−0.102779	+	0.230845i
$754$	6.10300	−	24.4778i	0.222258	−	0.891429i
$755$	1.27979	+	1.63805i	0.0465762	+	0.0596148i
$756$	−9.87397	+	12.6381i	−0.359113	+	0.459643i
$757$	−3.84621	−	15.4263i	−0.139793	−	0.560678i	−0.998812	−	0.0487345i	$-0.984481\pi$
$757$	−3.84621	−	15.4263i	−0.139793	−	0.560678i	0.859019	−	0.511944i	$-0.171074\pi$
$758$	24.2805	+	4.28131i	0.881908	+	0.155504i
$759$	−12.0524	+	11.7881i	−0.437474	+	0.427883i
$760$	−0.903066	−	1.25894i	−0.0327577	−	0.0456667i
$761$	5.84107	−	8.03955i	0.211739	−	0.291433i	−0.689916	−	0.723889i	$-0.742353\pi$
$761$	5.84107	−	8.03955i	0.211739	−	0.291433i	0.901655	+	0.432456i	$0.142353\pi$
$762$	5.91733	−	11.1289i	0.214362	−	0.403157i
$763$	−21.7313	−	8.78002i	−0.786726	−	0.317858i
$764$	12.1228	−	3.47616i	0.438587	−	0.125763i
$765$	−2.34189	−	1.57963i	−0.0846713	−	0.0571115i
$766$	8.26051	−	13.2196i	0.298465	−	0.477643i
$767$	12.0264	+	56.5797i	0.434248	+	2.04297i
$768$	0.400873	+	0.900375i	0.0144652	+	0.0324895i
$769$	−11.0956	+	1.95645i	−0.400117	+	0.0705515i	−0.370086	−	0.928997i	$-0.620672\pi$
$769$	−11.0956	+	1.95645i	−0.400117	+	0.0705515i	−0.0300313	+	0.999549i	$0.509561\pi$
$770$	−3.81475	+	0.0242991i	−0.137474	+	0.000875679i
$771$	2.53898	−	4.39765i	0.0914392	−	0.158377i
$772$	1.87762	−	17.8643i	0.0675769	−	0.642951i
$773$	10.8807	−	4.39607i	0.391350	−	0.158116i	−0.170494	−	0.985359i	$-0.554536\pi$
$773$	10.8807	−	4.39607i	0.391350	−	0.158116i	0.561844	+	0.827243i	$0.310092\pi$
$774$	18.3798	−	14.3599i	0.660650	−	0.516156i
$775$	8.53355	+	29.7600i	0.306534	+	1.06901i
$776$	0.275057	−	3.93350i	0.00987396	−	0.141204i
$777$	−1.25958	−	8.96240i	−0.0451873	−	0.321524i
$778$	0.983480	−	3.02684i	0.0352595	−	0.108517i
$779$	4.55969	+	2.66952i	0.163368	+	0.0956456i
$780$		−	1.53681i		−	0.0550268i
$781$	−0.700708	+	24.5478i	−0.0250733	+	0.878389i
$782$	12.9875	−	15.4779i	0.464432	−	0.553489i
$783$	−23.6280	+	15.9373i	−0.844397	+	0.569553i
$784$	−0.121158	−	3.46952i	−0.00432708	−	0.123911i
$785$	−3.48297	−	2.17640i	−0.124313	−	0.0776791i
$786$	−13.2363	−	5.89319i	−0.472124	−	0.210203i
$787$	1.66872	+	15.8768i	0.0594833	+	0.565946i	0.983157	+	0.182765i	$0.0585047\pi$
$787$	1.66872	+	15.8768i	0.0594833	+	0.565946i	−0.923673	+	0.383181i	$0.874829\pi$
$788$	−10.9173	−	20.5324i	−0.388912	−	0.731437i
$789$	−29.9109	−	4.20371i	−1.06486	−	0.149656i
$790$	4.46121	−	1.98626i	0.158723	−	0.0706680i
$791$	15.2930	+	26.4883i	0.543758	+	0.941817i
$792$	−5.02860	−	4.47010i	−0.178683	−	0.158838i
$793$	12.4062	+	34.0857i	0.440556	+	1.21042i
$794$	7.82041	+	11.5942i	0.277536	+	0.411464i
$795$	−0.100052	+	0.0625195i	−0.00354848	+	0.00221734i
$796$	16.0244	−	2.25208i	0.567970	−	0.0798230i
$797$	16.6508	+	22.9179i	0.589802	+	0.811793i	0.994727	−	0.102557i	$-0.0327023\pi$
$797$	16.6508	+	22.9179i	0.589802	+	0.811793i	−0.404925	+	0.914350i	$0.632702\pi$
$798$	6.60088	−	12.2349i	0.233669	−	0.433112i
$799$	29.1734	−	9.47902i	1.03208	−	0.335344i
$800$	4.30319	+	2.28804i	0.152141	+	0.0808946i
$801$	4.13355	−	1.03061i	0.146052	−	0.0364148i
$802$	−2.05977	+	5.65917i	−0.0727330	+	0.199832i
$803$	8.65133	+	47.3003i	0.305299	+	1.66919i
$804$	9.73529	−	8.16888i	0.343337	−	0.288094i
$805$	5.89972	+	0.620085i	0.207938	+	0.0218551i
$806$	−20.7094	+	18.6468i	−0.729457	+	0.656806i
$807$	−11.6030	+	6.16942i	−0.408445	+	0.217174i
$808$	−10.3328	+	10.7000i	−0.363508	+	0.376423i
$809$	−30.3433	+	3.18921i	−1.06681	+	0.112127i	−0.621629	−	0.783312i	$-0.713529\pi$
$809$	−30.3433	+	3.18921i	−1.06681	+	0.112127i	−0.445185	+	0.895438i	$0.646862\pi$
$810$	0.285693	−	0.317294i	0.0100382	−	0.0111486i
$811$	2.46161	+	6.09270i	0.0864388	+	0.213944i	0.964212	−	0.265133i	$-0.0854160\pi$
$811$	2.46161	+	6.09270i	0.0864388	+	0.213944i	−0.877773	+	0.479077i	$0.840972\pi$
$812$	5.12928	−	17.8879i	0.180002	−	0.627743i
$813$	−17.4576	−	6.35404i	−0.612264	−	0.222846i
$814$	9.38439	−	0.716316i	0.328923	−	0.0251069i
$815$	0.590021	−	3.34617i	0.0206675	−	0.117211i
$816$	−3.12371	−	2.26951i	−0.109352	−	0.0794486i
$817$	−33.7599	+	37.0401i	−1.18111	+	1.29587i
$818$	−6.80994	−	20.9588i	−0.238104	−	0.732808i
$819$	−25.8837	+	12.6243i	−0.904450	+	0.441130i
$820$	0.429804	+	0.0300548i	0.0150094	+	0.00104956i
$821$	3.65955	+	0.127794i	0.127719	+	0.00446006i	0.0986878	−	0.995118i	$-0.468535\pi$
$821$	3.65955	+	0.127794i	0.127719	+	0.00446006i	0.0290315	+	0.999578i	$0.490758\pi$
$822$	−5.80897	+	0.202854i	−0.202611	+	0.00707534i
$823$	16.3412	−	1.14269i	0.569617	−	0.0398315i	0.217956	−	0.975959i	$-0.430061\pi$
$823$	16.3412	−	1.14269i	0.569617	−	0.0398315i	0.351662	+	0.936127i	$0.385617\pi$
$824$	−10.0375	+	5.79513i	−0.349671	+	0.201883i
$825$	15.8990	+	1.01004i	0.553532	+	0.0351652i
$826$	7.40929	+	42.0202i	0.257802	+	1.46207i
$827$	3.19221	−	6.54501i	0.111004	−	0.227592i	−0.836059	−	0.548639i	$-0.815146\pi$
$827$	3.19221	−	6.54501i	0.111004	−	0.227592i	0.947063	+	0.321047i	$0.104035\pi$
$828$	7.00086	+	7.77524i	0.243297	+	0.270208i
$829$	−9.42996	−	8.49077i	−0.327516	−	0.294897i	0.488925	−	0.872326i	$-0.337389\pi$
$829$	−9.42996	−	8.49077i	−0.327516	−	0.294897i	−0.816441	+	0.577429i	$0.804056\pi$
$830$	0.515900	+	0.128628i	0.0179072	+	0.00446476i
$831$	−16.5806	+	24.5817i	−0.575173	+	0.852730i
$832$	−0.153100	+	4.38422i	−0.00530780	+	0.151996i
$833$	7.20714	+	11.5338i	0.249713	+	0.399624i
$834$	−11.4183	+	11.0265i	−0.395384	+	0.381818i
$835$	5.75470			0.199150
$836$	12.2624	+	7.65719i	0.424105	+	0.264829i
$837$	31.4832			1.08822
$838$	14.9005	−	14.3893i	0.514730	−	0.497069i
$839$	20.0488	+	32.0848i	0.692161	+	1.10769i	0.988297	+	0.152543i	$0.0487463\pi$
$839$	20.0488	+	32.0848i	0.692161	+	1.10769i	−0.296136	+	0.955146i	$0.595698\pi$
$840$	0.0395631	−	1.13294i	0.00136506	−	0.0390901i
$841$	2.27540	−	3.37342i	0.0784622	−	0.116325i
$842$	14.3982	+	3.58988i	0.496196	+	0.123715i
$843$	−1.00207	−	0.902270i	−0.0345132	−	0.0310758i
$844$	2.51983	+	2.79856i	0.0867362	+	0.0963303i
$845$	0.973047	−	1.99504i	0.0334738	−	0.0686315i
$846$	2.75825	+	15.6428i	0.0948306	+	0.537811i
$847$	32.8314	−	13.7538i	1.12810	−	0.472587i
$848$	0.291657	−	0.168388i	0.0100155	−	0.00578247i
$849$	4.21582	−	0.294799i	0.144687	−	0.0101175i
$850$	−19.0814	+	0.666337i	−0.654486	+	0.0228552i
$851$	−14.6267	−	0.510774i	−0.501396	−	0.0175091i
$852$	−7.27992	−	0.509062i	−0.249406	−	0.0174402i
$853$	−39.4513	+	19.2417i	−1.35079	+	0.658822i	−0.964629	−	0.263611i	$-0.915086\pi$
$853$	−39.4513	+	19.2417i	−1.35079	+	0.658822i	−0.386157	+	0.922433i	$0.626198\pi$
$854$	8.26834	+	25.4473i	0.282937	+	0.870790i
$855$	−1.68169	+	2.65530i	−0.0575125	+	0.0908095i
$856$	−13.4196	−	9.74988i	−0.458671	−	0.333244i
$857$	−2.39193	+	13.5653i	−0.0817068	+	0.463383i	0.916312	+	0.400465i	$0.131152\pi$
$857$	−2.39193	+	13.5653i	−0.0817068	+	0.463383i	−0.998019	+	0.0629172i	$0.979960\pi$
$858$	5.45641	+	13.2612i	0.186279	+	0.452732i
$859$	−17.5504	−	6.38782i	−0.598812	−	0.217950i	0.0247889	−	0.999693i	$-0.492109\pi$
$859$	−17.5504	−	6.38782i	−0.598812	−	0.217950i	−0.623601	+	0.781743i	$0.714331\pi$
$860$	−1.12646	+	3.92844i	−0.0384121	+	0.133959i
$861$	1.44822	+	3.58447i	0.0493552	+	0.122158i
$862$	−16.1463	+	17.9323i	−0.549945	+	0.610776i
$863$	−33.3411	+	3.50429i	−1.13495	+	0.119288i	−0.653314	−	0.757087i	$-0.726622\pi$
$863$	−33.3411	+	3.50429i	−1.13495	+	0.119288i	−0.481631	+	0.876374i	$0.659955\pi$
$864$	3.44282	−	3.56514i	0.117127	−	0.121289i
$865$	2.41505	−	1.28411i	0.0821142	−	0.0436609i
$866$	13.1366	−	11.8282i	0.446399	−	0.401940i
$867$	−1.61970	−	0.170238i	−0.0550080	−	0.00578157i
$868$	−15.7470	+	13.2133i	−0.534488	+	0.448489i
$869$	−31.4439	+	32.9789i	−1.06666	+	1.11873i
$870$	0.689012	−	1.89305i	0.0233597	−	0.0641803i
$871$	54.8862	−	13.6847i	1.85975	−	0.463687i
$872$	6.39511	+	3.40034i	0.216566	+	0.115150i
$873$	−7.60758	+	2.47185i	−0.257477	+	0.0836595i
$874$	−17.6310	−	13.9478i	−0.596378	−	0.471792i
$875$	−6.67537	−	9.18785i	−0.225669	−	0.310606i
$876$	−14.1501	+	1.98866i	−0.478087	+	0.0671907i
$877$	−0.387337	+	0.242035i	−0.0130794	+	0.00817295i	−0.536443	−	0.843936i	$-0.680232\pi$
$877$	−0.387337	+	0.242035i	−0.0130794	+	0.00817295i	0.523364	+	0.852109i	$0.324677\pi$
$878$	0.0209365	+	0.0310396i	0.000706571	+	0.00104754i
$879$	−2.98881	−	8.21169i	−0.100810	−	0.276973i
$880$	1.17318	+	0.115756i	0.0395478	+	0.00390212i
$881$	−21.5221	−	37.2773i	−0.725097	−	1.25590i	−0.958934	−	0.283628i	$-0.908462\pi$
$881$	−21.5221	−	37.2773i	−0.725097	−	1.25590i	0.233838	−	0.972276i	$-0.424872\pi$
$882$	−6.43378	+	2.86450i	−0.216637	+	0.0964528i
$883$	4.55097	+	0.639597i	0.153152	+	0.0215241i	0.215332	−	0.976541i	$-0.430916\pi$
$883$	4.55097	+	0.639597i	0.153152	+	0.0215241i	−0.0621803	+	0.998065i	$0.519805\pi$
$884$	−8.06837	−	15.1744i	−0.271369	−	0.510370i
$885$	0.482834	+	4.59386i	0.0162303	+	0.154421i
$886$	−8.56488	−	3.81333i	−0.287743	−	0.128111i
$887$	26.8671	+	16.7884i	0.902108	+	0.563700i	0.899802	−	0.436298i	$-0.143710\pi$
$887$	26.8671	+	16.7884i	0.902108	+	0.563700i	0.00230578	+	0.999997i	$0.499266\pi$
$888$	0.0976076	+	2.79512i	0.00327550	+	0.0937980i
$889$	34.3087	−	23.1415i	1.15068	−	0.776142i
$890$	−0.479794	+	0.571797i	−0.0160827	+	0.0191667i
$891$	−1.33872	+	3.75229i	−0.0448488	+	0.125707i
$892$		−	20.2307i		−	0.677373i
$893$	−11.4786	−	32.1420i	−0.384115	−	1.07559i
$894$	2.53679	−	7.80744i	0.0848430	−	0.261120i
$895$	0.961927	+	6.84447i	0.0321537	+	0.228785i
$896$	−0.225731	+	3.22811i	−0.00754115	+	0.107843i
$897$	−6.14648	−	21.4353i	−0.205225	−	0.715705i
$898$	−11.4788	+	8.96822i	−0.383052	+	0.299273i
$899$	−33.8699	+	13.6843i	−1.12962	+	0.456397i
$900$	1.03346	−	9.83268i	0.0344485	−	0.327756i
$901$	−0.659676	+	1.14259i	−0.0219770	+	0.0380653i
$902$	−3.81551	+	1.26666i	−0.127043	+	0.0421752i
$903$	−36.1126	+	6.36763i	−1.20175	+	0.211902i
$904$	−3.84441	−	8.63469i	−0.127863	−	0.287186i
$905$	−0.660279	−	3.10637i	−0.0219484	−	0.103259i
$906$	3.05441	−	4.88807i	0.101476	−	0.162395i
$907$	20.1727	+	13.6066i	0.669823	+	0.451801i	0.846444	−	0.532478i	$-0.178739\pi$
$907$	20.1727	+	13.6066i	0.669823	+	0.451801i	−0.176621	+	0.984279i	$0.556517\pi$
$908$	−13.9015	+	3.98618i	−0.461337	+	0.132286i
$909$	27.9780	+	11.3038i	0.927970	+	0.374924i
$910$	2.36889	−	4.45523i	0.0785279	−	0.147689i
$911$	−16.2414	+	22.3544i	−0.538103	+	0.740635i	−0.988338	−	0.152275i	$-0.951340\pi$
$911$	−16.2414	+	22.3544i	−0.538103	+	0.740635i	0.450236	+	0.892910i	$0.351340\pi$
$912$	−2.42387	+	3.54696i	−0.0802624	+	0.117452i
$913$	−4.90842	+	0.721745i	−0.162445	+	0.0238863i
$914$	−7.11641	−	1.25481i	−0.235390	−	0.0415056i
$915$	0.700758	+	2.81059i	0.0231663	+	0.0929151i
$916$	9.80758	−	12.5531i	0.324052	−	0.414767i
$917$	−29.2882	−	37.4872i	−0.967183	−	1.23794i
$918$	−4.69718	+	18.8394i	−0.155030	+	0.621792i
$919$	10.7408	−	24.1243i	0.354308	−	0.795788i	−0.645188	−	0.764024i	$-0.723221\pi$
$919$	10.7408	−	24.1243i	0.354308	−	0.795788i	0.999495	−	0.0317640i	$-0.0101125\pi$
$920$	−1.79314	−	0.381143i	−0.0591180	−	0.0125659i
$921$	0.330003	−	2.34810i	0.0108740	−	0.0773724i
$922$	26.0240	+	12.6928i	0.857055	+	0.418014i
$923$	−28.1307	−	16.2413i	−0.925933	−	0.534588i
$924$	3.68107	+	9.91666i	0.121098	+	0.326234i
$925$	8.88984	+	10.5945i	0.292296	+	0.348345i
$926$	27.4536	+	7.87219i	0.902180	+	0.258696i
$927$	18.5280	+	14.4756i	0.608538	+	0.475442i
$928$	−2.15420	+	5.33184i	−0.0707152	+	0.175026i
$929$	−20.6873	−	42.4152i	−0.678727	−	1.39160i	−0.908306	−	0.418307i	$-0.862624\pi$
$929$	−20.6873	−	42.4152i	−0.678727	−	1.39160i	0.229578	−	0.973290i	$-0.426265\pi$
$930$	−1.80036	+	1.30804i	−0.0590360	+	0.0428922i
$931$	12.5965	−	8.38577i	0.412833	−	0.274833i
$932$	−13.5794	−	4.41222i	−0.444809	−	0.144527i
$933$	−4.81007	−	4.98097i	−0.157475	−	0.163070i
$934$	13.8940	+	11.6584i	0.454625	+	0.381475i
$935$	−4.20702	+	1.90529i	−0.137584	+	0.0623096i
$936$	8.36267	−	3.04376i	0.273342	−	0.0994885i
$937$	0.323214	+	4.62218i	0.0105589	+	0.151000i	0.999982	+	0.00594360i	$0.00189192\pi$
$937$	0.323214	+	4.62218i	0.0105589	+	0.151000i	−0.989423	+	0.145056i	$0.953664\pi$
$938$	40.8144	−	8.67537i	1.33264	−	0.283261i
$939$	−0.291048	+	1.36927i	−0.00949798	+	0.0446845i
$940$	−2.00201	−	1.93332i	−0.0652984	−	0.0630580i
$941$	1.97922	+	1.91132i	0.0645209	+	0.0623071i	0.726220	−	0.687462i	$-0.241275\pi$
$941$	1.97922	+	1.91132i	0.0645209	+	0.0623071i	−0.661699	+	0.749770i	$0.730164\pi$
$942$	−2.36772	+	11.1392i	−0.0771445	+	0.362936i
$943$	6.11507	−	1.29980i	0.199134	−	0.0423272i
$944$	−0.919780	−	13.1535i	−0.0299363	−	0.428109i
$945$	−5.35681	+	1.94972i	−0.174257	+	0.0634244i
$946$	−4.22749	−	37.8982i	−0.137448	−	1.23218i
$947$	−13.3591	−	11.2097i	−0.434114	−	0.364265i	0.399387	−	0.916782i	$-0.369223\pi$
$947$	−13.3591	−	11.2097i	−0.434114	−	0.364265i	−0.833501	+	0.552517i	$0.813667\pi$
$948$	−9.40624	−	9.74044i	−0.305500	−	0.316355i
$949$	−60.4890	−	19.6541i	−1.96356	−	0.637998i
$950$	1.35339	+	21.2006i	0.0439098	+	0.687839i
$951$	8.66908	−	6.29846i	0.281114	−	0.204241i
$952$	−5.55736	−	11.3943i	−0.180115	−	0.369291i
$953$	5.80681	−	14.3723i	0.188101	−	0.465566i	−0.803436	−	0.595391i	$-0.796997\pi$
$953$	5.80681	−	14.3723i	0.188101	−	0.465566i	0.991537	+	0.129825i	$0.0414416\pi$
$954$	−0.538364	−	0.420616i	−0.0174302	−	0.0136179i
$955$	4.30897	+	1.23558i	0.139435	+	0.0399824i
$956$	0.282355	+	0.336498i	0.00913203	+	0.0108831i
$957$	0.775671	+	18.7815i	0.0250739	+	0.607120i
$958$	6.38481	+	3.68627i	0.206284	+	0.119098i
$959$	−17.1529	−	8.36604i	−0.553897	−	0.270153i
$960$	−0.0487550	+	0.346910i	−0.00157356	+	0.0111965i
$961$	9.14837	+	1.94455i	0.295109	+	0.0627273i
$962$	−5.06339	+	11.3726i	−0.163250	+	0.366666i
$963$	−8.14063	+	32.6503i	−0.262328	+	1.05214i
$964$	−11.6506	−	14.9121i	−0.375242	−	0.480288i
$965$	3.93084	−	5.03125i	0.126538	−	0.161962i
$966$	−3.97937	−	15.9604i	−0.128034	−	0.513516i
$967$	−49.8780	−	8.79484i	−1.60397	−	0.282823i	−0.701205	−	0.712960i	$-0.747354\pi$
$967$	−49.8780	−	8.79484i	−1.60397	−	0.282823i	−0.902764	+	0.430137i	$0.858465\pi$
$968$	−10.5344	+	3.16647i	−0.338588	+	0.101774i
$969$	1.27578	−	16.7818i	0.0409838	−	0.539109i
$970$	0.823811	−	1.13388i	0.0264510	−	0.0364067i
$971$	17.5039	−	32.9201i	0.561728	−	1.05646i	−0.426647	−	0.904418i	$-0.640305\pi$
$971$	17.5039	−	32.9201i	0.561728	−	1.05646i	0.988375	−	0.152038i	$-0.0485836\pi$
$972$	−14.8834	−	6.01329i	−0.477385	−	0.192876i
$973$	−50.0984	+	14.3655i	−1.60608	+	0.460536i
$974$	−5.94484	−	4.00985i	−0.190485	−	0.128484i
$975$	−11.1664	+	17.8701i	−0.357613	+	0.572300i
$976$	−1.71913	−	8.08785i	−0.0550279	−	0.258886i
$977$	8.87745	+	19.9391i	0.284015	+	0.637908i	0.998064	−	0.0621873i	$-0.0198076\pi$
$977$	8.87745	+	19.9391i	0.284015	+	0.637908i	−0.714050	+	0.700095i	$0.753141\pi$
$978$	−9.27834	+	1.63602i	−0.296689	+	0.0523142i
$979$	2.11003	−	6.63756i	0.0674367	−	0.212137i
$980$	0.616985	−	1.06865i	0.0197089	−	0.0341368i
$981$	1.53585	−	14.6127i	0.0490360	−	0.466546i
$982$	−29.5593	+	11.9427i	−0.943274	+	0.381107i
$983$	−9.85883	+	7.70256i	−0.314448	+	0.245674i	−0.760507	−	0.649330i	$-0.775049\pi$
$983$	−9.85883	+	7.70256i	−0.314448	+	0.245674i	0.446059	+	0.895004i	$0.352827\pi$
$984$	−0.329298	−	1.14840i	−0.0104977	−	0.0366097i
$985$	0.576581	−	8.24550i	0.0183714	−	0.262723i
$986$	−3.13535	−	22.3092i	−0.0998499	−	0.710469i
$987$	7.71692	−	23.7502i	0.245632	−	0.755979i
$988$	−16.6178	+	9.46044i	−0.528683	+	0.300977i
$989$			59.2988i			1.88559i
$990$	−0.673815	−	2.29461i	−0.0214153	−	0.0729274i
$991$	−20.7518	+	24.7310i	−0.659202	+	0.785606i	−0.987271	−	0.159048i	$-0.949158\pi$
$991$	−20.7518	+	24.7310i	−0.659202	+	0.785606i	0.328069	+	0.944654i	$0.393602\pi$
$992$	5.26636	−	3.55221i	0.167207	−	0.112783i
$993$	1.20377	+	34.4714i	0.0382004	+	1.09392i
$994$	−20.3199	−	12.6973i	−0.644507	−	0.402732i
$995$	5.25449	+	2.33945i	0.166579	+	0.0741656i
$996$	−0.154105	−	1.46622i	−0.00488302	−	0.0464588i
$997$	−4.78136	−	8.99244i	−0.151427	−	0.284793i	0.795676	−	0.605723i	$-0.207116\pi$
$997$	−4.78136	−	8.99244i	−0.151427	−	0.284793i	−0.947103	+	0.320929i	$0.896005\pi$
$998$	20.7797	+	2.92040i	0.657771	+	0.0924436i
$999$	12.8483	−	5.72041i	0.406501	−	0.180986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.v.b.249.7	yes	240
11.8	odd	10		418.2.v.a.173.4	yes	240
19.10	odd	18		418.2.v.a.29.4	✓	240
209.162	even	90	inner	418.2.v.b.371.7	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.v.a.29.4	✓	240	19.10	odd	18
418.2.v.a.173.4	yes	240	11.8	odd	10
418.2.v.b.249.7	yes	240	1.1	even	1	trivial
418.2.v.b.371.7	yes	240	209.162	even	90	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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.v (of order \(90\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.719340 + 0.694658i) q^{2} +(0.522279 + 0.835822i) q^{3} +(0.0348995 - 0.999391i) q^{4} +(0.198762 - 0.294676i) q^{5} +(-0.956307 - 0.238434i) q^{6} +(-2.40481 - 2.16530i) q^{7} +(0.669131 + 0.743145i) q^{8} +(0.889291 - 1.82332i) q^{9} +O(q^{10})\)	\(q+(-0.719340 + 0.694658i) q^{2} +(0.522279 + 0.835822i) q^{3} +(0.0348995 - 0.999391i) q^{4} +(0.198762 - 0.294676i) q^{5} +(-0.956307 - 0.238434i) q^{6} +(-2.40481 - 2.16530i) q^{7} +(0.669131 + 0.743145i) q^{8} +(0.889291 - 1.82332i) q^{9} +(0.0617222 + 0.350044i) q^{10} +(-1.77542 - 2.80141i) q^{11} +(0.853540 - 0.492791i) q^{12} +(4.37621 - 0.306014i) q^{13} +(3.23402 - 0.112934i) q^{14} +(0.350106 + 0.0122260i) q^{15} +(-0.997564 - 0.0697565i) q^{16} +(3.52111 - 1.71736i) q^{17} +(0.626880 + 1.92934i) q^{18} +(-2.02301 - 3.86101i) q^{19} +(-0.287560 - 0.208925i) q^{20} +(0.553822 - 3.14088i) q^{21} +(3.22315 + 0.781850i) q^{22} +(-4.84646 - 1.76397i) q^{23} +(-0.271663 + 0.947403i) q^{24} +(1.82571 + 4.51878i) q^{25} +(-2.93540 + 3.26010i) q^{26} +(4.92898 - 0.518056i) q^{27} +(-2.24791 + 2.32778i) q^{28} +(-5.07745 + 2.69973i) q^{29} +(-0.260338 + 0.234409i) q^{30} +(6.31758 + 0.664005i) q^{31} +(0.766044 - 0.642788i) q^{32} +(1.41421 - 2.94705i) q^{33} +(-1.33990 + 3.68134i) q^{34} +(-1.11605 + 0.278262i) q^{35} +(-1.79117 - 0.952383i) q^{36} +(2.69884 - 0.876907i) q^{37} +(4.13732 + 1.37208i) q^{38} +(2.54138 + 3.49790i) q^{39} +(0.351985 - 0.0494682i) q^{40} +(-1.02797 + 0.642345i) q^{41} +(1.78345 + 2.64408i) q^{42} +(-3.93241 - 10.8042i) q^{43} +(-2.86166 + 1.67657i) q^{44} +(-0.360532 - 0.624459i) q^{45} +(4.71160 - 2.09774i) q^{46} +(7.75379 + 1.08972i) q^{47} +(-0.462703 - 0.870218i) q^{48} +(0.362884 + 3.45261i) q^{49} +(-4.45231 - 1.98230i) q^{50} +(3.27441 + 2.04608i) q^{51} +(-0.153100 - 4.38422i) q^{52} +(-0.279200 + 0.188323i) q^{53} +(-3.18574 + 3.79661i) q^{54} +(-1.17839 - 0.0336368i) q^{55} -3.23599i q^{56} +(2.17054 - 3.70740i) q^{57} +(1.77702 - 5.46912i) q^{58} +(1.83508 + 13.0573i) q^{59} +(0.0244370 - 0.349466i) q^{60} +(2.27912 + 7.94823i) q^{61} +(-5.00574 + 3.91092i) q^{62} +(-6.08661 + 2.45915i) q^{63} +(-0.104528 + 0.994522i) q^{64} +(0.779647 - 1.35039i) q^{65} +(1.02990 + 3.10232i) q^{66} +(12.6985 - 2.23909i) q^{67} +(-1.59343 - 3.57890i) q^{68} +(-1.05684 - 4.97205i) q^{69} +(0.609520 - 0.975436i) q^{70} +(-6.13857 - 4.14052i) q^{71} +(1.95004 - 0.559165i) q^{72} +(-13.4425 - 5.43111i) q^{73} +(-1.33223 + 2.50557i) q^{74} +(-2.82336 + 3.88603i) q^{75} +(-3.92926 + 1.88703i) q^{76} +(-1.79633 + 10.5812i) q^{77} +(-4.25796 - 0.750793i) q^{78} +(-3.32374 - 13.3308i) q^{79} +(-0.218833 + 0.280094i) q^{80} +(-0.739537 - 0.946564i) q^{81} +(0.293247 - 1.17615i) q^{82} +(0.608420 - 1.36653i) q^{83} +(-3.11964 - 0.663100i) q^{84} +(0.193797 - 1.37893i) q^{85} +(10.3340 + 5.04022i) q^{86} +(-4.90834 - 2.83383i) q^{87} +(0.893860 - 3.19390i) q^{88} +(1.34985 + 1.60868i) q^{89} +(0.693130 + 0.198752i) q^{90} +(-11.1866 - 8.73989i) q^{91} +(-1.93203 + 4.78194i) q^{92} +(2.74455 + 5.62717i) q^{93} +(-6.33460 + 4.60236i) q^{94} +(-1.53985 - 0.171289i) q^{95} +(0.937345 + 0.304562i) q^{96} +(-2.73911 - 2.83643i) q^{97} +(-2.65942 - 2.23152i) q^{98} +(-6.68672 + 0.745895i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9}+O(q^{10}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9	\( 240 q + 3 q^{3} - 3 q^{6} - 3 q^{7} + 30 q^{8} + 3 q^{9} - 3 q^{11} + 6 q^{13} - 18 q^{14} - 69 q^{15} + 9 q^{17} + 60 q^{18} - 45 q^{19} + 12 q^{20} - 48 q^{21} - 12 q^{22} + 3 q^{24} - 18 q^{25} + 84 q^{26} - 9 q^{27} + 6 q^{28} + 12 q^{29} + 9 q^{31} - 69 q^{33} - 24 q^{34} + 36 q^{35} + 3 q^{36} + 24 q^{38} - 30 q^{41} - 6 q^{42} + 12 q^{43} - 48 q^{44} + 48 q^{45} - 12 q^{46} - 54 q^{47} + 6 q^{48} - 81 q^{49} + 21 q^{50} + 45 q^{51} - 3 q^{52} + 81 q^{53} - 27 q^{54} - 72 q^{55} - 30 q^{57} - 24 q^{58} + 114 q^{59} + 78 q^{60} - 66 q^{61} - 45 q^{62} + 9 q^{63} + 30 q^{64} - 135 q^{66} - 9 q^{67} - 42 q^{68} - 54 q^{69} + 39 q^{70} - 102 q^{71} - 6 q^{72} + 12 q^{74} + 72 q^{77} + 36 q^{79} - 117 q^{81} + 30 q^{82} - 36 q^{83} - 36 q^{84} - 90 q^{85} + 3 q^{86} - 216 q^{87} - 3 q^{88} + 18 q^{89} - 24 q^{90} + 102 q^{91} + 30 q^{92} + 147 q^{93} + 18 q^{94} - 66 q^{95} - 24 q^{97} + 12 q^{98} - 195 q^{99}+O(q^{100}) \) 240 * q + 3 * q^3 - 3 * q^6 - 3 * q^7 + 30 * q^8 + 3 * q^9 - 3 * q^11 + 6 * q^13 - 18 * q^14 - 69 * q^15 + 9 * q^17 + 60 * q^18 - 45 * q^19 + 12 * q^20 - 48 * q^21 - 12 * q^22 + 3 * q^24 - 18 * q^25 + 84 * q^26 - 9 * q^27 + 6 * q^28 + 12 * q^29 + 9 * q^31 - 69 * q^33 - 24 * q^34 + 36 * q^35 + 3 * q^36 + 24 * q^38 - 30 * q^41 - 6 * q^42 + 12 * q^43 - 48 * q^44 + 48 * q^45 - 12 * q^46 - 54 * q^47 + 6 * q^48 - 81 * q^49 + 21 * q^50 + 45 * q^51 - 3 * q^52 + 81 * q^53 - 27 * q^54 - 72 * q^55 - 30 * q^57 - 24 * q^58 + 114 * q^59 + 78 * q^60 - 66 * q^61 - 45 * q^62 + 9 * q^63 + 30 * q^64 - 135 * q^66 - 9 * q^67 - 42 * q^68 - 54 * q^69 + 39 * q^70 - 102 * q^71 - 6 * q^72 + 12 * q^74 + 72 * q^77 + 36 * q^79 - 117 * q^81 + 30 * q^82 - 36 * q^83 - 36 * q^84 - 90 * q^85 + 3 * q^86 - 216 * q^87 - 3 * q^88 + 18 * q^89 - 24 * q^90 + 102 * q^91 + 30 * q^92 + 147 * q^93 + 18 * q^94 - 66 * q^95 - 24 * q^97 + 12 * q^98 - 195 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more