LMFDB - Embedded newform 525.2.bp.a.59.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(59,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, 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("525.59");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bp (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$608$
Relative dimension:	$76$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			59.14
Character	$\chi$	$=$	525.59
Dual form			525.2.bp.a.89.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.211264 + 2.01005i) q^{2} +(-0.544642 - 1.64419i) q^{3} +(-2.03936 - 0.433479i) q^{4} +(1.73522 - 1.41032i) q^{5} +(3.41996 - 0.747397i) q^{6} +(0.844505 - 2.50735i) q^{7} +(0.0530372 - 0.163232i) q^{8} +(-2.40673 + 1.79099i) q^{9} +O(q^{10})$	\(q+(-0.211264 + 2.01005i) q^{2} +(-0.544642 - 1.64419i) q^{3} +(-2.03936 - 0.433479i) q^{4} +(1.73522 - 1.41032i) q^{5} +(3.41996 - 0.747397i) q^{6} +(0.844505 - 2.50735i) q^{7} +(0.0530372 - 0.163232i) q^{8} +(-2.40673 + 1.79099i) q^{9} +(2.46822 + 3.78582i) q^{10} +(-0.919382 - 2.06497i) q^{11} +(0.397999 + 3.58919i) q^{12} +(-3.78830 + 2.75236i) q^{13} +(4.86148 + 2.22721i) q^{14} +(-3.26391 - 2.08491i) q^{15} +(-3.49244 - 1.55493i) q^{16} +(5.92929 - 5.33876i) q^{17} +(-3.09152 - 5.21601i) q^{18} +(-0.480508 - 2.26061i) q^{19} +(-4.15008 + 2.12397i) q^{20} +(-4.58252 - 0.0229181i) q^{21} +(4.34491 - 1.41175i) q^{22} +(0.802062 - 7.63111i) q^{23} +(-0.297270 + 0.00169960i) q^{24} +(1.02198 - 4.89444i) q^{25} +(-4.73205 - 8.19615i) q^{26} +(4.25554 + 2.98167i) q^{27} +(-2.80913 + 4.74731i) q^{28} +(0.0480758 - 0.0156208i) q^{29} +(4.88032 - 6.12015i) q^{30} +(-2.74380 + 2.47053i) q^{31} +(4.03495 - 6.98874i) q^{32} +(-2.89446 + 2.63631i) q^{33} +(9.47851 + 13.0460i) q^{34} +(-2.07077 - 5.54183i) q^{35} +(5.68454 - 2.60921i) q^{36} +(-2.21979 + 4.98572i) q^{37} +(4.64545 - 0.488257i) q^{38} +(6.58868 + 4.72964i) q^{39} +(-0.138178 - 0.358042i) q^{40} +(-1.61437 + 1.17291i) q^{41} +(1.01419 - 9.20623i) q^{42} -3.43941i q^{43} +(0.979830 + 4.60974i) q^{44} +(-1.65033 + 6.50203i) q^{45} +(15.1694 + 3.22437i) q^{46} +(9.33825 + 8.40820i) q^{47} +(-0.654479 + 6.58912i) q^{48} +(-5.57362 - 4.23494i) q^{49} +(9.62215 + 3.08825i) q^{50} +(-12.0073 - 6.84118i) q^{51} +(8.91881 - 3.97091i) q^{52} +(4.37065 + 0.929010i) q^{53} +(-6.89235 + 7.92391i) q^{54} +(-4.50760 - 2.28655i) q^{55} +(-0.364489 - 0.270833i) q^{56} +(-3.45517 + 2.02127i) q^{57} +(0.0212418 + 0.0999348i) q^{58} +(-1.10635 - 10.5263i) q^{59} +(5.75253 + 5.66672i) q^{60} +(4.71146 + 0.495194i) q^{61} +(-4.38621 - 6.03710i) q^{62} +(2.45815 + 7.54702i) q^{63} +(7.00958 + 5.09276i) q^{64} +(-2.69182 + 10.1187i) q^{65} +(-4.68760 - 6.37496i) q^{66} +(5.39652 - 4.85905i) q^{67} +(-14.4062 + 8.31742i) q^{68} +(-12.9838 + 2.83748i) q^{69} +(11.5768 - 2.99156i) q^{70} +(-0.365054 + 0.118613i) q^{71} +(0.164700 + 0.487844i) q^{72} +(-0.278813 + 0.124135i) q^{73} +(-9.55257 - 5.51518i) q^{74} +(-8.60401 + 0.985388i) q^{75} +4.81849i q^{76} +(-5.95402 + 0.561340i) q^{77} +(-10.8988 + 12.2444i) q^{78} +(-3.38816 + 3.76294i) q^{79} +(-8.25311 + 2.22731i) q^{80} +(2.58469 - 8.62087i) q^{81} +(-2.01655 - 3.49276i) q^{82} +(6.20004 + 2.01452i) q^{83} +(9.33546 + 2.03316i) q^{84} +(2.75926 - 17.6261i) q^{85} +(6.91338 + 0.726625i) q^{86} +(-0.0518677 - 0.0705381i) q^{87} +(-0.385829 + 0.0405523i) q^{88} +(-1.48334 + 14.1131i) q^{89} +(-12.7207 - 4.69089i) q^{90} +(3.70190 + 11.8230i) q^{91} +(-4.94362 + 15.2149i) q^{92} +(5.55641 + 3.16578i) q^{93} +(-18.8737 + 16.9940i) q^{94} +(-4.02198 - 3.24499i) q^{95} +(-13.6884 - 2.82787i) q^{96} +(1.40292 + 4.31773i) q^{97} +(9.68994 - 10.3085i) q^{98} +(5.91104 + 3.32321i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	$ 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) $ 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.211264	+	2.01005i	−0.149386	+	1.42132i	0.621035	+	0.783783i	$0.286712\pi$
$2$	−0.211264	+	2.01005i	−0.149386	+	1.42132i	−0.770422	+	0.637535i	$0.779954\pi$
$3$	−0.544642	−	1.64419i	−0.314449	−	0.949274i
$3$	−0.544642	−	1.64419i	−0.314449	−	0.949274i
$4$	−2.03936	−	0.433479i	−1.01968	−	0.216740i
$5$	1.73522	−	1.41032i	0.776014	−	0.630715i
$5$	1.73522	−	1.41032i	0.776014	−	0.630715i
$6$	3.41996	−	0.747397i	1.39619	−	0.305124i
$7$	0.844505	−	2.50735i	0.319193	−	0.947690i
$7$	0.844505	−	2.50735i	0.319193	−	0.947690i
$8$	0.0530372	−	0.163232i	0.0187515	−	0.0577111i
$9$	−2.40673	+	1.79099i	−0.802243	+	0.596997i
$10$	2.46822	+	3.78582i	0.780521	+	1.19718i
$11$	−0.919382	−	2.06497i	−0.277204	−	0.622611i	0.720266	−	0.693698i	$-0.244020\pi$
$11$	−0.919382	−	2.06497i	−0.277204	−	0.622611i	−0.997470	+	0.0710874i	$0.977353\pi$
$12$	0.397999	+	3.58919i	0.114892	+	1.03611i
$13$	−3.78830	+	2.75236i	−1.05069	+	0.763369i	−0.972343	−	0.233558i	$-0.924963\pi$
$13$	−3.78830	+	2.75236i	−1.05069	+	0.763369i	−0.0783438	+	0.996926i	$0.524963\pi$
$14$	4.86148	+	2.22721i	1.29928	+	0.595246i
$15$	−3.26391	−	2.08491i	−0.842739	−	0.538322i
$16$	−3.49244	−	1.55493i	−0.873110	−	0.388733i
$17$	5.92929	−	5.33876i	1.43807	−	1.29484i	0.549967	−	0.835187i	$-0.314640\pi$
$17$	5.92929	−	5.33876i	1.43807	−	1.29484i	0.888099	−	0.459653i	$-0.152026\pi$
$18$	−3.09152	−	5.21601i	−0.728679	−	1.22943i
$19$	−0.480508	−	2.26061i	−0.110236	−	0.518620i	−0.998268	−	0.0588374i	$-0.981261\pi$
$19$	−0.480508	−	2.26061i	−0.110236	−	0.518620i	0.888031	−	0.459783i	$-0.152073\pi$
$20$	−4.15008	+	2.12397i	−0.927987	+	0.474935i
$21$	−4.58252	−	0.0229181i	−0.999987	−	0.00500113i
$22$	4.34491	−	1.41175i	0.926338	−	0.300985i
$23$	0.802062	−	7.63111i	0.167242	−	1.59120i	−0.513117	−	0.858318i	$-0.671509\pi$
$23$	0.802062	−	7.63111i	0.167242	−	1.59120i	0.680359	−	0.732879i	$-0.261824\pi$
$24$	−0.297270	+	0.00169960i	−0.0606800	+	0.000346930i
$25$	1.02198	−	4.89444i	0.204396	−	0.978888i
$26$	−4.73205	−	8.19615i	−0.928031	−	1.60740i
$27$	4.25554	+	2.98167i	0.818979	+	0.573823i
$28$	−2.80913	+	4.74731i	−0.530876	+	0.897158i
$29$	0.0480758	−	0.0156208i	0.00892746	−	0.00290071i	−0.304550	−	0.952496i	$-0.598506\pi$
$29$	0.0480758	−	0.0156208i	0.00892746	−	0.00290071i	0.313477	+	0.949596i	$0.398506\pi$
$30$	4.88032	−	6.12015i	0.891021	−	1.11738i
$31$	−2.74380	+	2.47053i	−0.492801	+	0.443720i	−0.877680	−	0.479247i	$-0.840910\pi$
$31$	−2.74380	+	2.47053i	−0.492801	+	0.443720i	0.384879	+	0.922967i	$0.374243\pi$
$32$	4.03495	−	6.98874i	0.713285	−	1.23545i
$33$	−2.89446	+	2.63631i	−0.503862	+	0.458922i
$34$	9.47851	+	13.0460i	1.62555	+	2.23738i
$35$	−2.07077	−	5.54183i	−0.350024	−	0.936741i
$36$	5.68454	−	2.60921i	0.947424	−	0.434868i
$37$	−2.21979	+	4.98572i	−0.364931	+	0.819647i	0.633996	+	0.773336i	$0.281413\pi$
$37$	−2.21979	+	4.98572i	−0.364931	+	0.819647i	−0.998927	+	0.0463115i	$0.985253\pi$
$38$	4.64545	−	0.488257i	0.753592	−	0.0792057i
$39$	6.58868	+	4.72964i	1.05503	+	0.757349i
$40$	−0.138178	−	0.358042i	−0.0218479	−	0.0566115i
$41$	−1.61437	+	1.17291i	−0.252123	+	0.183178i	−0.706667	−	0.707546i	$-0.749802\pi$
$41$	−1.61437	+	1.17291i	−0.252123	+	0.183178i	0.454544	+	0.890724i	$0.349802\pi$
$42$	1.01419	−	9.20623i	0.156493	−	1.42055i
$43$		−	3.43941i		−	0.524505i	−0.964999	−	0.262253i	$-0.915535\pi$
$43$		−	3.43941i		−	0.524505i	0.964999	−	0.262253i	$-0.0844654\pi$
$44$	0.979830	+	4.60974i	0.147715	+	0.694944i
$45$	−1.65033	+	6.50203i	−0.246017	+	0.969266i
$46$	15.1694	+	3.22437i	2.23661	+	0.475407i
$47$	9.33825	+	8.40820i	1.36212	+	1.22646i	0.948800	+	0.315878i	$0.102299\pi$
$47$	9.33825	+	8.40820i	1.36212	+	1.22646i	0.413324	+	0.910584i	$0.364368\pi$
$48$	−0.654479	+	6.58912i	−0.0944659	+	0.951058i
$49$	−5.57362	−	4.23494i	−0.796232	−	0.604992i
$50$	9.62215	+	3.08825i	1.36078	+	0.436745i
$51$	−12.0073	−	6.84118i	−1.68136	−	0.957957i
$52$	8.91881	−	3.97091i	1.23682	−	0.550666i
$53$	4.37065	+	0.929010i	0.600355	+	0.127609i	0.498057	−	0.867144i	$-0.334047\pi$
$53$	4.37065	+	0.929010i	0.600355	+	0.127609i	0.102298	+	0.994754i	$0.467380\pi$
$54$	−6.89235	+	7.92391i	−0.937929	+	1.07831i
$55$	−4.50760	−	2.28655i	−0.607804	−	0.308318i
$56$	−0.364489	−	0.270833i	−0.0487069	−	0.0361916i
$57$	−3.45517	+	2.02127i	−0.457649	+	0.267724i
$58$	0.0212418	+	0.0999348i	0.00278918	+	0.0131221i
$59$	−1.10635	−	10.5263i	−0.144035	−	1.37040i	−0.792832	−	0.609440i	$-0.791394\pi$
$59$	−1.10635	−	10.5263i	−0.144035	−	1.37040i	0.648797	−	0.760962i	$-0.275273\pi$
$60$	5.75253	+	5.66672i	0.742648	+	0.731571i
$61$	4.71146	+	0.495194i	0.603240	+	0.0634031i	0.401225	−	0.915979i	$-0.368584\pi$
$61$	4.71146	+	0.495194i	0.603240	+	0.0634031i	0.202015	+	0.979382i	$0.435251\pi$
$62$	−4.38621	−	6.03710i	−0.557049	−	0.766713i
$63$	2.45815	+	7.54702i	0.309698	+	0.950835i
$64$	7.00958	+	5.09276i	0.876198	+	0.636595i
$65$	−2.69182	+	10.1187i	−0.333880	+	1.25507i
$66$	−4.68760	−	6.37496i	−0.577004	−	0.784704i
$67$	5.39652	−	4.85905i	0.659290	−	0.593627i	−0.270053	−	0.962845i	$-0.587041\pi$
$67$	5.39652	−	4.85905i	0.659290	−	0.593627i	0.929343	+	0.369218i	$0.120375\pi$
$68$	−14.4062	+	8.31742i	−1.74701	+	1.00864i
$69$	−12.9838	+	2.83748i	−1.56307	+	0.341593i
$70$	11.5768	−	2.99156i	1.38369	−	0.357559i
$71$	−0.365054	+	0.118613i	−0.0433239	+	0.0140768i	−0.330599	−	0.943771i	$-0.607251\pi$
$71$	−0.365054	+	0.118613i	−0.0433239	+	0.0140768i	0.287275	+	0.957848i	$0.407251\pi$
$72$	0.164700	+	0.487844i	0.0194101	+	0.0574929i
$73$	−0.278813	+	0.124135i	−0.0326325	+	0.0145289i	−0.422988	−	0.906135i	$-0.639019\pi$
$73$	−0.278813	+	0.124135i	−0.0326325	+	0.0145289i	0.390355	+	0.920664i	$0.372352\pi$
$74$	−9.55257	−	5.51518i	−1.11046	−	0.641126i
$75$	−8.60401	+	0.985388i	−0.993506	+	0.113783i
$76$			4.81849i			0.552719i
$77$	−5.95402	+	0.561340i	−0.678523	+	0.0639706i
$78$	−10.8988	+	12.2444i	−1.23404	+	1.38640i
$79$	−3.38816	+	3.76294i	−0.381198	+	0.423363i	−0.902958	−	0.429729i	$-0.858609\pi$
$79$	−3.38816	+	3.76294i	−0.381198	+	0.423363i	0.521760	+	0.853092i	$0.325276\pi$
$80$	−8.25311	+	2.22731i	−0.922726	+	0.249021i
$81$	2.58469	−	8.62087i	0.287188	−	0.957874i
$82$	−2.01655	−	3.49276i	−0.222690	−	0.385711i
$83$	6.20004	+	2.01452i	0.680543	+	0.221122i	0.628833	−	0.777540i	$-0.283533\pi$
$83$	6.20004	+	2.01452i	0.680543	+	0.221122i	0.0517101	+	0.998662i	$0.483533\pi$
$84$	9.33546	+	2.03316i	1.01858	+	0.221836i
$85$	2.75926	−	17.6261i	0.299284	−	1.91182i
$86$	6.91338	+	0.726625i	0.745488	+	0.0783540i
$87$	−0.0518677	−	0.0705381i	−0.00556080	−	0.00756248i
$88$	−0.385829	+	0.0405523i	−0.0411295	+	0.00432289i
$89$	−1.48334	+	14.1131i	−0.157234	+	1.49598i	0.576809	+	0.816879i	$0.304298\pi$
$89$	−1.48334	+	14.1131i	−0.157234	+	1.49598i	−0.734043	+	0.679103i	$0.762369\pi$
$90$	−12.7207	−	4.69089i	−1.34088	−	0.494463i
$91$	3.70190	+	11.8230i	0.388065	+	1.23939i
$92$	−4.94362	+	15.2149i	−0.515408	+	1.58626i
$93$	5.55641	+	3.16578i	0.576173	+	0.328276i
$94$	−18.8737	+	16.9940i	−1.94667	+	1.75279i
$95$	−4.02198	−	3.24499i	−0.412646	−	0.332929i
$96$	−13.6884	−	2.82787i	−1.39707	−	0.288618i
$97$	1.40292	+	4.31773i	0.142444	+	0.438399i	0.996674	−	0.0814978i	$-0.0259704\pi$
$97$	1.40292	+	4.31773i	0.142444	+	0.438399i	−0.854229	+	0.519897i	$0.825970\pi$
$98$	9.68994	−	10.3085i	0.978832	−	1.04132i
$99$	5.91104	+	3.32321i	0.594082	+	0.333995i
$100$	−4.20582	+	9.53851i	−0.420582	+	0.953851i
$101$	−8.05111	+	13.9449i	−0.801116	+	1.38757i	0.117767	+	0.993041i	$0.462426\pi$
$101$	−8.05111	+	13.9449i	−0.801116	+	1.38757i	−0.918882	+	0.394532i	$0.870907\pi$
$102$	16.2878	−	22.6899i	1.61273	−	2.24664i
$103$	7.29012	−	8.09650i	0.718317	−	0.797772i	−0.267861	−	0.963457i	$-0.586317\pi$
$103$	7.29012	−	8.09650i	0.718317	−	0.797772i	0.986179	+	0.165685i	$0.0529836\pi$
$104$	0.248352	+	0.764349i	0.0243529	+	0.0749506i
$105$	−7.98400	+	6.42306i	−0.779159	+	0.626827i
$106$	−2.79072	+	8.58894i	−0.271058	+	0.834232i
$107$	−0.701774	−	1.21551i	−0.0678430	−	0.117508i	0.830109	−	0.557602i	$-0.188278\pi$
$107$	−0.701774	−	1.21551i	−0.0678430	−	0.117508i	−0.897952	+	0.440094i	$0.854945\pi$
$108$	−7.38608	−	7.92539i	−0.710726	−	0.762621i
$109$	1.00967	+	9.60640i	0.0967092	+	0.920126i	0.930066	+	0.367392i	$0.119749\pi$
$109$	1.00967	+	9.60640i	0.0967092	+	0.920126i	−0.833357	+	0.552735i	$0.813584\pi$
$110$	5.54836	−	8.57742i	0.529015	−	0.817824i
$111$	9.40647	+	0.934318i	0.892822	+	0.0886815i
$112$	−6.84815	+	7.44362i	−0.647089	+	0.703356i
$113$	3.30596	−	2.40192i	0.310999	−	0.225954i	−0.421326	−	0.906909i	$-0.638435\pi$
$113$	3.30596	−	2.40192i	0.310999	−	0.225954i	0.732325	+	0.680955i	$0.238435\pi$
$114$	−3.33290	−	7.37208i	−0.312154	−	0.690459i
$115$	−9.37058	−	14.3728i	−0.873811	−	1.34027i
$116$	−0.104815	+	0.0110165i	−0.00973184	+	0.00102286i
$117$	4.18796	−	13.4090i	0.387177	−	1.23966i
$118$	21.3920			1.96929
$119$	−8.37883	−	19.3754i	−0.768086	−	1.77614i
$120$	−0.513433	+	0.422196i	−0.0468698	+	0.0385411i
$121$	3.94162	−	4.37761i	0.358329	−	0.397964i
$122$	−1.99073	+	9.36563i	−0.180232	+	0.847924i
$123$	2.80775	+	2.01552i	0.253166	+	0.181734i
$124$	6.66652	−	3.84892i	0.598671	−	0.345643i
$125$	−5.12938	−	9.93426i	−0.458786	−	0.888547i
$126$	−15.6892	+	3.34658i	−1.39770	+	0.298137i
$127$	−8.74696	+	12.0392i	−0.776167	+	1.06830i	0.219527	+	0.975606i	$0.429548\pi$
$127$	−8.74696	+	12.0392i	−0.776167	+	1.06830i	−0.995694	+	0.0926960i	$0.970452\pi$
$128$	−0.917925	+	1.01946i	−0.0811339	+	0.0901083i
$129$	−5.65505	+	1.87325i	−0.497899	+	0.164930i
$130$	−19.7704	−	7.54841i	−1.73397	−	0.662039i
$131$	−2.23155	+	0.474330i	−0.194971	+	0.0414424i	−0.304362	−	0.952556i	$-0.598443\pi$
$131$	−2.23155	+	0.474330i	−0.194971	+	0.0414424i	0.109391	+	0.993999i	$0.465110\pi$
$132$	7.04563	−	4.12169i	0.613244	−	0.358747i
$133$	−6.07394	−	0.704296i	−0.526678	−	0.0610702i
$134$	8.62682	+	11.8738i	0.745244	+	1.02574i
$135$	11.5894	−	0.827823i	0.997459	−	0.0712477i
$136$	−0.556982	−	1.25100i	−0.0477608	−	0.107272i
$137$	0.320071	+	3.04527i	0.0273455	+	0.260175i	0.999650	+	0.0264571i	$0.00842254\pi$
$137$	0.320071	+	3.04527i	0.0273455	+	0.260175i	−0.972304	+	0.233718i	$0.924911\pi$
$138$	−2.96045	−	26.6976i	−0.252010	−	2.27265i
$139$	−3.34990	+	4.61074i	−0.284135	+	0.391078i	−0.927098	−	0.374819i	$-0.877705\pi$
$139$	−3.34990	+	4.61074i	−0.284135	+	0.391078i	0.642963	+	0.765897i	$0.277705\pi$
$140$	1.82078	+	12.1994i	0.153884	+	1.03104i
$141$	8.73868	−	19.9333i	0.735930	−	1.67869i
$142$	−0.161295	−	0.758834i	−0.0135356	−	0.0636799i
$143$	9.16644	+	5.29224i	0.766536	+	0.442560i
$144$	11.1902	−	2.51263i	0.932519	−	0.209385i
$145$	0.0613918	−	0.0949079i	0.00509831	−	0.00788168i
$146$	−0.190615	−	0.586652i	−0.0157754	−	0.0485516i
$147$	−3.92742	+	11.4706i	−0.323928	+	0.946082i
$148$	6.68815	−	9.20544i	0.549762	−	0.756683i
$149$	−4.80599	+	2.77474i	−0.393722	+	0.227316i	−0.683772	−	0.729696i	$-0.739662\pi$
$149$	−4.80599	+	2.77474i	−0.393722	+	0.227316i	0.290049	+	0.957012i	$0.406328\pi$
$150$	−0.162954	−	17.5026i	−0.0133051	−	1.42908i
$151$	−2.95783	+	5.12311i	−0.240705	+	0.416913i	−0.960915	−	0.276843i	$-0.910712\pi$
$151$	−2.95783	+	5.12311i	−0.240705	+	0.416913i	0.720210	+	0.693756i	$0.244045\pi$
$152$	−0.394488	−	0.0414624i	−0.0319972	−	0.00336304i
$153$	−4.70853	+	23.4683i	−0.380662	+	1.89730i
$154$	0.129553	−	12.0864i	0.0104397	−	0.973953i
$155$	−1.27686	+	8.15656i	−0.102560	+	0.655150i
$156$	−11.3865	−	12.5015i	−0.911649	−	1.00092i
$157$	9.04203	−	15.6613i	0.721632	−	1.24990i	−0.238713	−	0.971090i	$-0.576725\pi$
$157$	9.04203	−	15.6613i	0.721632	−	1.24990i	0.960345	−	0.278814i	$-0.0899413\pi$
$158$	−6.84788	−	7.60534i	−0.544788	−	0.605048i
$159$	−0.852970	−	7.69216i	−0.0676449	−	0.610028i
$160$	−2.85485	−	17.8176i	−0.225695	−	1.40860i
$161$	−18.4565	−	8.45557i	−1.45458	−	0.666392i
$162$	16.7823	+	7.01664i	1.31854	+	0.551279i
$163$	−4.92822	+	11.0690i	−0.386008	+	0.866988i	0.611140	+	0.791522i	$0.290711\pi$
$163$	−4.92822	+	11.0690i	−0.386008	+	0.866988i	−0.997148	+	0.0754658i	$0.975956\pi$
$164$	3.80072	−	1.69219i	0.296786	−	0.132138i
$165$	−1.30449	+	8.65670i	−0.101554	+	0.673923i
$166$	−5.35912	+	12.0368i	−0.415948	+	0.934236i
$167$	23.0421	+	7.48682i	1.78305	+	0.579348i	0.999138	−	0.0415241i	$-0.0132213\pi$
$167$	23.0421	+	7.48682i	1.78305	+	0.579348i	0.783912	+	0.620872i	$0.213221\pi$
$168$	−0.246785	+	0.746796i	−0.0190399	+	0.0576166i
$169$	2.75852	−	8.48986i	0.212194	−	0.653066i
$170$	34.8464	+	9.27002i	2.67260	+	0.710978i
$171$	5.20519	+	4.58010i	0.398051	+	0.350249i
$172$	−1.49091	+	7.01419i	−0.113681	+	0.534827i
$173$	−11.4540	−	1.20386i	−0.870832	−	0.0915281i	−0.341438	−	0.939904i	$-0.610914\pi$
$173$	−11.4540	−	1.20386i	−0.870832	−	0.0915281i	−0.529394	+	0.848376i	$0.677581\pi$
$174$	0.152743	−	0.0893543i	0.0115794	−	0.00677393i
$175$	−11.4090	−	6.69585i	−0.862441	−	0.506158i
$176$			8.64134i			0.651366i
$177$	−16.7046	+	7.55210i	−1.25560	+	0.567651i
$178$	−28.0545	−	5.96318i	−2.10278	−	0.446959i
$179$	−0.685124	+	3.22326i	−0.0512086	+	0.240917i	−0.996306	−	0.0858704i	$-0.972633\pi$
$179$	−0.685124	+	3.22326i	−0.0512086	+	0.240917i	0.945098	+	0.326788i	$0.105966\pi$
$180$	6.18411	−	12.5446i	0.460936	−	0.935019i
$181$	−10.2541	−	3.33175i	−0.762178	−	0.247647i	−0.0979651	−	0.995190i	$-0.531233\pi$
$181$	−10.2541	−	3.33175i	−0.762178	−	0.247647i	−0.664213	+	0.747543i	$0.731233\pi$
$182$	−24.5469	+	4.94322i	−1.81953	+	0.366416i
$183$	−1.75187	−	8.01624i	−0.129502	−	0.592578i
$184$	−1.20310	−	0.535655i	−0.0886937	−	0.0394890i
$185$	3.17966	+	11.7819i	0.233773	+	0.866225i
$186$	−7.53723	+	10.4998i	−0.552657	+	0.769885i
$187$	−16.4756	−	7.33543i	−1.20482	−	0.536420i
$188$	−15.3993	−	21.1953i	−1.12311	−	1.54582i
$189$	11.0699	−	8.15210i	0.805219	−	0.592978i
$190$	7.37228	−	7.39882i	0.534842	−	0.536767i
$191$	−0.496906	+	1.11607i	−0.0359548	+	0.0807559i	−0.930630	−	0.365961i	$-0.880740\pi$
$191$	−0.496906	+	1.11607i	−0.0359548	+	0.0807559i	0.894675	+	0.446717i	$0.147407\pi$
$192$	4.55575	−	14.2988i	0.328783	−	1.03193i
$193$	−11.6457	−	6.72364i	−0.838275	−	0.483978i	0.0184025	−	0.999831i	$-0.494142\pi$
$193$	−11.6457	−	6.72364i	−0.838275	−	0.483978i	−0.856678	+	0.515852i	$0.827475\pi$
$194$	−8.97522	+	1.90774i	−0.644383	+	0.136968i
$195$	18.1031	−	1.08520i	1.29639	−	0.0777125i
$196$	9.53086	+	11.0526i	0.680776	+	0.789472i
$197$	−0.154170	−	0.474487i	−0.0109842	−	0.0338058i	0.945414	−	0.325871i	$-0.105658\pi$
$197$	−0.154170	−	0.474487i	−0.0109842	−	0.0338058i	−0.956398	+	0.292065i	$0.905658\pi$
$198$	−7.92859	+	11.1794i	−0.563461	+	0.794485i
$199$	14.4462	+	8.34054i	1.02407	+	0.591245i	0.915279	−	0.402820i	$-0.131970\pi$
$199$	14.4462	+	8.34054i	1.02407	+	0.591245i	0.108787	+	0.994065i	$0.465303\pi$
$200$	−0.744725	−	0.426407i	−0.0526600	−	0.0301515i
$201$	−10.9284	−	6.22647i	−0.770828	−	0.439181i
$202$	−26.3291	−	19.1292i	−1.85251	−	1.34592i
$203$	0.00143349	−	0.133735i	0.000100611	−	0.00938635i
$204$	21.5217	+	19.1565i	1.50682	+	1.34123i
$205$	−1.14711	+	4.31205i	−0.0801177	+	0.301166i
$206$	14.7342	+	16.3640i	1.02658	+	1.14013i
$207$	11.7369	+	19.8025i	0.815772	+	1.37637i
$208$	17.5102	−	3.72190i	1.21411	−	0.258067i
$209$	−4.22632	+	3.07060i	−0.292340	+	0.212398i
$210$	−11.2239	−	17.4052i	−0.774524	−	1.20107i
$211$	−0.351478	−	0.255364i	−0.0241968	−	0.0175800i	0.575621	−	0.817717i	$-0.304760\pi$
$211$	−0.351478	−	0.255364i	−0.0241968	−	0.0175800i	−0.599818	+	0.800137i	$0.704760\pi$
$212$	−8.51062	−	3.78917i	−0.584512	−	0.260241i
$213$	0.393846	+	0.535617i	0.0269859	+	0.0366998i
$214$	2.59149	−	1.15380i	0.177150	−	0.0788725i
$215$	−4.85068	−	5.96814i	−0.330814	−	0.407024i
$216$	0.712405	−	0.536499i	0.0484730	−	0.0365042i
$217$	3.87733	+	8.96605i	0.263210	+	0.608655i
$218$	−19.5226			−1.32224
$219$	0.355955	+	0.390812i	0.0240532	+	0.0264086i
$220$	8.20144	+	6.61704i	0.552941	+	0.446121i
$221$	−7.76776	+	36.5444i	−0.522516	+	2.45824i
$222$	−3.86527	+	18.7100i	−0.259420	+	1.25574i
$223$	5.53658	+	4.02256i	0.370757	+	0.269371i	0.757525	−	0.652807i	$-0.226409\pi$
$223$	5.53658	+	4.02256i	0.370757	+	0.269371i	−0.386768	+	0.922177i	$0.626409\pi$
$224$	−14.1157	−	16.0191i	−0.943144	−	1.07032i
$225$	6.30627	+	13.6100i	0.420418	+	0.907330i
$226$	4.12955	+	7.15258i	0.274693	+	0.475783i
$227$	4.12177	+	9.25764i	0.273571	+	0.614451i	0.997121	−	0.0758205i	$-0.0241576\pi$
$227$	4.12177	+	9.25764i	0.273571	+	0.614451i	−0.723550	+	0.690272i	$0.757491\pi$
$228$	7.92252	−	2.62435i	0.524682	−	0.173802i
$229$	17.3886	+	15.6568i	1.14907	+	1.03463i	0.998943	+	0.0459611i	$0.0146350\pi$
$229$	17.3886	+	15.6568i	1.14907	+	1.03463i	0.150127	+	0.988667i	$0.452032\pi$
$230$	30.8697	−	15.7988i	2.03549	−	1.04174i
$231$	4.16576	+	9.48381i	0.274087	+	0.623989i
$232$		−	0.00867598i		−	0.000569606i
$233$	10.5272	−	2.23762i	0.689657	−	0.146591i	0.150265	−	0.988646i	$-0.451987\pi$
$233$	10.5272	−	2.23762i	0.689657	−	0.146591i	0.539392	+	0.842055i	$0.318654\pi$
$234$	26.0680	+	11.2508i	1.70412	+	0.735491i
$235$	28.0622	+	1.42013i	1.83058	+	0.0926394i
$236$	−2.30666	+	21.9464i	−0.150151	+	1.42859i
$237$	8.03232	+	3.52133i	0.521755	+	0.228735i
$238$	40.7157	−	12.7485i	2.63921	−	0.826362i
$239$	18.0816	−	24.8871i	1.16960	−	1.60981i	0.503355	−	0.864080i	$-0.332099\pi$
$239$	18.0816	−	24.8871i	1.16960	−	1.60981i	0.666243	−	0.745735i	$-0.267901\pi$
$240$	8.15712	+	12.3566i	0.526540	+	0.797615i
$241$	−12.4415	+	1.30766i	−0.801429	+	0.0842336i	−0.496383	−	0.868104i	$-0.665339\pi$
$241$	−12.4415	+	1.30766i	−0.801429	+	0.0842336i	−0.305047	+	0.952337i	$0.598672\pi$
$242$	7.96647	+	8.84767i	0.512104	+	0.568749i
$243$	−15.5821	+	0.445559i	−0.999591	+	0.0285826i
$244$	−9.39370	−	3.05220i	−0.601370	−	0.195397i
$245$	−15.6441	+	0.512047i	−0.999465	+	0.0327135i
$246$	−4.64447	+	5.21789i	−0.296121	+	0.332681i
$247$	8.04234	+	7.24136i	0.511722	+	0.460756i
$248$	0.257745	+	0.578905i	0.0163668	+	0.0367605i
$249$	−0.0645562	−	11.2913i	−0.00409108	−	0.715554i
$250$	21.0520	−	8.21153i	1.33144	−	0.519343i
$251$	23.7020			1.49606			0.748028	−	0.663667i	$-0.231001\pi$
$251$	23.7020			1.49606			0.748028	+	0.663667i	$0.231001\pi$
$252$	−1.74158	−	16.4566i	−0.109709	−	1.03667i
$253$	−16.4954	+	5.35968i	−1.03706	+	0.336960i
$254$	−22.3513	−	20.1252i	−1.40245	−	1.26277i
$255$	−30.4836	+	5.06319i	−1.90895	+	0.317070i
$256$	9.73989	+	10.8172i	0.608743	+	0.676078i
$257$	3.83334	−	2.21318i	0.239117	−	0.138054i	−0.375654	−	0.926760i	$-0.622582\pi$
$257$	3.83334	−	2.21318i	0.239117	−	0.138054i	0.614771	+	0.788706i	$0.289248\pi$
$258$	−2.57061	−	11.7627i	−0.160039	−	0.732311i
$259$	10.6263	+	9.77625i	0.660288	+	0.607467i
$260$	9.87583	−	19.4688i	0.612473	−	1.20740i
$261$	−0.0877288	+	0.123698i	−0.00543028	+	0.00765674i
$262$	−0.481979	−	4.58572i	−0.0297767	−	0.283307i
$263$	−2.56464	−	24.4010i	−0.158143	−	1.50463i	−0.729531	−	0.683948i	$-0.760262\pi$
$263$	−2.56464	−	24.4010i	−0.158143	−	1.50463i	0.571388	−	0.820680i	$-0.306405\pi$
$264$	0.276815	+	0.612290i	0.0170368	+	0.0376839i
$265$	8.89425	−	4.55199i	0.546369	−	0.279626i
$266$	2.69888	−	12.0601i	0.165479	−	0.739453i
$267$	24.0125	−	5.24767i	1.46954	−	0.321152i
$268$	−13.1117	+	7.57006i	−0.800926	+	0.462415i
$269$	−6.53742	−	7.26054i	−0.398594	−	0.442683i	0.510120	−	0.860103i	$-0.329601\pi$
$269$	−6.53742	−	7.26054i	−0.398594	−	0.442683i	−0.908714	+	0.417420i	$0.862934\pi$
$270$	−0.784469	+	23.4702i	−0.0477412	+	1.42835i
$271$	−13.5361	−	12.1880i	−0.822260	−	0.740366i	0.146275	−	0.989244i	$-0.453272\pi$
$271$	−13.5361	−	12.1880i	−0.822260	−	0.740366i	−0.968535	+	0.248878i	$0.919938\pi$
$272$	−29.0091	+	9.42563i	−1.75894	+	0.571513i
$273$	17.4231	−	12.5259i	1.05449	−	0.758104i
$274$	−6.18875			−0.373876
$275$	−11.0464	+	2.38951i	−0.666126	+	0.144093i
$276$	27.7087	−	0.158421i	1.66787	−	0.00953581i
$277$	4.44694	+	9.98800i	0.267191	+	0.600121i	0.996456	−	0.0841102i	$-0.0268048\pi$
$277$	4.44694	+	9.98800i	0.267191	+	0.600121i	−0.729266	+	0.684231i	$0.760138\pi$
$278$	−8.56008	−	7.70753i	−0.513400	−	0.462267i
$279$	2.17889	−	10.8600i	0.130447	−	0.650173i
$280$	−1.01443	+	0.0440923i	−0.0606238	+	0.00263502i
$281$	18.2470	+	5.92881i	1.08852	+	0.353683i	0.797676	−	0.603086i	$-0.206062\pi$
$281$	18.2470	+	5.92881i	1.08852	+	0.353683i	0.290848	+	0.956769i	$0.406062\pi$
$282$	38.2208	+	21.7764i	2.27601	+	1.29676i
$283$	14.7463	+	16.3774i	0.876577	+	0.973537i	0.999823	−	0.0188392i	$-0.00599707\pi$
$283$	14.7463	+	16.3774i	0.876577	+	0.973537i	−0.123246	+	0.992376i	$0.539330\pi$
$284$	0.795892	−	0.0836516i	0.0472275	−	0.00496381i
$285$	−3.14484	+	8.38026i	−0.186284	+	0.496404i
$286$	−12.5742	+	17.3069i	−0.743528	+	1.02338i
$287$	1.57755	+	5.03833i	0.0931201	+	0.297403i
$288$	2.80574	+	24.0466i	0.165330	+	1.41696i
$289$	4.87718	−	46.4033i	0.286893	−	2.72961i
$290$	0.177799	+	0.143451i	0.0104407	+	0.00842374i
$291$	6.33509	−	4.65828i	0.371369	−	0.273073i
$292$	0.622409	−	0.132297i	0.0364237	−	0.00774210i
$293$		−	8.81235i		−	0.514823i	−0.966302	−	0.257411i	$-0.917130\pi$
$293$		−	8.81235i		−	0.514823i	0.966302	−	0.257411i	$-0.0828696\pi$
$294$	−22.2268	−	10.3176i	−1.29629	−	0.601737i
$295$	−16.7652	−	16.7051i	−0.976107	−	0.972607i
$296$	0.696096	+	0.626768i	0.0404598	+	0.0364301i
$297$	2.24459	−	11.5288i	0.130244	−	0.668971i
$298$	−4.56202	−	10.2465i	−0.264271	−	0.593562i
$299$	17.9652	+	31.1166i	1.03895	+	1.79952i
$300$	17.9738	+	1.72010i	1.03772	+	0.0993100i
$301$	−8.62381	−	2.90460i	−0.497068	−	0.167418i
$302$	−9.67281	−	7.02771i	−0.556608	−	0.404399i
$303$	27.3131	+	5.64257i	1.56910	+	0.324157i
$304$	−1.83696	+	8.64221i	−0.105357	+	0.495665i
$305$	8.87380	−	5.78540i	0.508112	−	0.331271i
$306$	−46.1776	−	14.4224i	−2.63980	−	0.824472i
$307$	2.97944			0.170045			0.0850227	−	0.996379i	$-0.472904\pi$
$307$	2.97944			0.170045			0.0850227	+	0.996379i	$0.472904\pi$
$308$	12.3857	+	1.43617i	0.705741	+	0.0818333i
$309$	−17.2827	−	7.57666i	−0.983179	−	0.431021i
$310$	−16.1253	−	4.28973i	−0.915856	−	0.243640i
$311$	8.14880	−	3.62808i	0.462076	−	0.205729i	−0.162476	−	0.986712i	$-0.551948\pi$
$311$	8.14880	−	3.62808i	0.462076	−	0.205729i	0.624552	+	0.780983i	$0.285281\pi$
$312$	1.12147	−	0.824635i	0.0634909	−	0.0466858i
$313$	3.73792	+	1.66423i	0.211280	+	0.0940678i	0.509648	−	0.860383i	$-0.329776\pi$
$313$	3.73792	+	1.66423i	0.211280	+	0.0940678i	−0.298368	+	0.954451i	$0.596442\pi$
$314$	29.5696	+	21.4836i	1.66871	+	1.21239i
$315$	14.9092	+	9.62896i	0.840036	+	0.542530i
$316$	8.54083	−	6.20528i	0.480459	−	0.349074i
$317$	−21.1953	+	4.50520i	−1.19045	+	0.253037i	−0.760209	−	0.649679i	$-0.774903\pi$
$317$	−21.1953	+	4.50520i	−1.19045	+	0.253037i	−0.430237	+	0.902716i	$0.641570\pi$
$318$	15.6418	−	0.0894299i	0.877149	−	0.00501498i
$319$	−0.0764564	−	0.0849135i	−0.00428074	−	0.00475424i
$320$	19.3456	−	1.04871i	1.08145	−	0.0586247i
$321$	−1.61631	+	1.81587i	−0.0902137	+	0.101352i
$322$	20.8953	−	35.3121i	1.16445	−	1.96787i
$323$	−14.9179	−	10.8385i	−0.830057	−	0.603071i
$324$	−9.00808	+	16.4606i	−0.500449	+	0.914480i
$325$	9.59971	+	21.3545i	0.532496	+	1.18453i
$326$	−21.2080	−	12.2444i	−1.17460	−	0.678156i
$327$	15.2448	−	6.89215i	0.843042	−	0.381137i
$328$	0.105834	+	0.325725i	0.00584373	+	0.0179851i
$329$	28.9685	−	16.3135i	1.59709	−	0.899393i
$330$	−17.1248	−	4.45094i	−0.942688	−	0.245016i
$331$	−1.29392	+	0.275031i	−0.0711204	+	0.0151171i	−0.243334	−	0.969942i	$-0.578241\pi$
$331$	−1.29392	+	0.275031i	−0.0711204	+	0.0151171i	0.172214	+	0.985060i	$0.444908\pi$
$332$	−11.7709	−	6.79591i	−0.646010	−	0.372974i
$333$	−3.58696	−	15.9749i	−0.196564	−	0.875419i
$334$	−19.9168	+	44.7339i	−1.08980	+	2.44773i
$335$	2.51133	−	16.0423i	0.137208	−	0.876487i
$336$	15.9685	+	7.20555i	0.871155	+	0.393095i
$337$	−3.31247	−	4.55923i	−0.180442	−	0.248357i	0.709209	−	0.704998i	$-0.249052\pi$
$337$	−3.31247	−	4.55923i	−0.180442	−	0.248357i	−0.889651	+	0.456641i	$0.849052\pi$
$338$	16.4822	+	7.33836i	0.896515	+	0.399154i
$339$	−5.74979	−	4.12745i	−0.312286	−	0.224172i
$340$	−13.2677	+	34.7500i	−0.719541	+	1.88458i
$341$	7.62416	+	3.39449i	0.412871	+	0.183822i
$342$	−10.3059	+	9.49507i	−0.557278	+	0.513434i
$343$	−15.3254	+	10.3986i	−0.827496	+	0.561472i
$344$	−0.561421	−	0.182417i	−0.0302698	−	0.00983525i
$345$	−18.5281	+	23.2351i	−0.997518	+	1.25093i
$346$	4.83965	−	22.7688i	0.260181	−	1.22406i
$347$	−15.9183	−	3.38354i	−0.854539	−	0.181638i	−0.240242	−	0.970713i	$-0.577227\pi$
$347$	−15.9183	−	3.38354i	−0.854539	−	0.181638i	−0.614297	+	0.789075i	$0.710560\pi$
$348$	0.0752000	+	0.166336i	0.00403114	+	0.00891655i
$349$			11.0079i			0.589240i	0.955614	+	0.294620i	$0.0951931\pi$
$349$			11.0079i			0.589240i	−0.955614	+	0.294620i	$0.904807\pi$
$350$	15.8693	−	21.5181i	0.848249	−	1.15019i
$351$	−24.3279	+	0.417311i	−1.29853	+	0.0222744i
$352$	−18.1412	−	1.90671i	−0.966927	−	0.101628i
$353$	−3.79243	+	17.8420i	−0.201851	+	0.949632i	0.754249	+	0.656589i	$0.228001\pi$
$353$	−3.79243	+	17.8420i	−0.201851	+	0.949632i	−0.956099	+	0.293043i	$0.905332\pi$
$354$	−11.6510	−	35.1725i	−0.619243	−	1.86940i
$355$	−0.466166	+	0.720664i	−0.0247415	+	0.0382489i
$356$	9.14279	−	28.1386i	0.484567	−	1.49134i
$357$	−27.2935	+	24.3291i	−1.44452	+	1.28763i
$358$	−6.33415	−	2.05809i	−0.334770	−	0.108773i
$359$	−5.71121	+	12.8276i	−0.301426	+	0.677014i	−0.999228	−	0.0392765i	$-0.987495\pi$
$359$	−5.71121	+	12.8276i	−0.301426	+	0.677014i	0.697802	+	0.716290i	$0.254161\pi$
$360$	0.973808	+	0.614235i	0.0513242	+	0.0323730i
$361$	12.4779	−	5.55551i	0.656731	−	0.292395i
$362$	8.86328	−	19.9073i	0.465844	−	1.04630i
$363$	−9.34440	−	4.09654i	−0.490454	−	0.215013i
$364$	−2.42449	−	25.7160i	−0.127078	−	1.34789i
$365$	−0.308730	+	0.608618i	−0.0161597	+	0.0318565i
$366$	16.4831	−	1.82778i	0.861587	−	0.0955398i
$367$	1.47221	+	1.63506i	0.0768489	+	0.0853494i	0.780343	−	0.625352i	$-0.215045\pi$
$367$	1.47221	+	1.63506i	0.0768489	+	0.0853494i	−0.703494	+	0.710701i	$0.748378\pi$
$368$	−14.6670	+	25.4040i	−0.764572	+	1.32428i
$369$	1.78469	−	5.71421i	0.0929071	−	0.297470i
$370$	−24.3540	+	3.90215i	−1.26610	+	0.202863i
$371$	6.02039	−	10.1742i	0.312563	−	0.528218i
$372$	−9.95922	−	8.86475i	−0.516362	−	0.459616i
$373$	−9.32013	−	0.979585i	−0.482578	−	0.0507210i	−0.139884	−	0.990168i	$-0.544673\pi$
$373$	−9.32013	−	0.979585i	−0.482578	−	0.0507210i	−0.342694	+	0.939447i	$0.611339\pi$
$374$	18.2253	−	31.5671i	0.942406	−	1.63230i
$375$	−13.5401	+	13.8443i	−0.699210	+	0.714916i
$376$	1.86776	−	1.07835i	0.0963223	−	0.0556117i
$377$	−0.139132	+	0.191499i	−0.00716565	+	0.00986268i
$378$	14.0474	+	23.9733i	0.722521	+	1.23305i
$379$	−4.45239	−	13.7030i	−0.228704	−	0.703878i	−0.997894	−	0.0648587i	$-0.979340\pi$
$379$	−4.45239	−	13.7030i	−0.228704	−	0.703878i	0.769191	−	0.639019i	$-0.220660\pi$
$380$	6.79563	+	8.36114i	0.348608	+	0.428918i
$381$	24.5586	+	7.82464i	1.25818	+	0.400868i
$382$	−2.13837	−	1.23459i	−0.109409	−	0.0631671i
$383$	−5.25283	−	24.7126i	−0.268407	−	1.26276i	−0.881287	−	0.472581i	$-0.843323\pi$
$383$	−5.25283	−	24.7126i	−0.268407	−	1.26276i	0.612880	−	0.790176i	$-0.290011\pi$
$384$	2.17613	+	0.954004i	0.111050	+	0.0486838i
$385$	−9.53986	+	9.37113i	−0.486196	+	0.477597i
$386$	15.9752	−	21.9879i	0.813114	−	1.11916i
$387$	6.15996	+	8.27773i	0.313128	+	0.420781i
$388$	−0.989402	−	9.41353i	−0.0502293	−	0.477900i
$389$	2.32804	+	5.22886i	0.118036	+	0.265114i	0.962895	−	0.269875i	$-0.0869824\pi$
$389$	2.32804	+	5.22886i	0.118036	+	0.265114i	−0.844859	+	0.534989i	$0.820316\pi$
$390$	−1.64326	+	36.6174i	−0.0832095	+	1.85420i
$391$	−35.9850	−	49.5291i	−1.81984	−	2.50480i
$392$	−0.986886	+	0.685182i	−0.0498453	+	0.0346069i
$393$	1.99528	+	3.41075i	0.100649	+	0.172049i
$394$	0.986311	−	0.209647i	0.0496897	−	0.0105619i
$395$	−0.572257	+	11.3079i	−0.0287934	+	0.568963i
$396$	−10.6142	−	9.33953i	−0.533383	−	0.469329i
$397$	−7.37885	+	8.19504i	−0.370334	+	0.411297i	−0.899291	−	0.437351i	$-0.855917\pi$
$397$	−7.37885	+	8.19504i	−0.370334	+	0.411297i	0.528957	+	0.848649i	$0.322583\pi$
$398$	−19.8168	+	27.2755i	−0.993328	+	1.36720i
$399$	2.15013	+	10.3703i	0.107641	+	0.519165i
$400$	−11.1797	+	15.5044i	−0.558987	+	0.775221i
$401$	7.38275	−	4.26243i	0.368677	−	0.212856i	−0.304203	−	0.952607i	$-0.598390\pi$
$401$	7.38275	−	4.26243i	0.368677	−	0.212856i	0.672880	+	0.739751i	$0.265057\pi$
$402$	14.8243	−	20.6511i	0.739367	−	1.02998i
$403$	3.59456	−	16.9111i	0.179058	−	0.842400i
$404$	22.4639	−	24.9487i	1.11762	−	1.24125i
$405$	−7.67319	−	18.6044i	−0.381284	−	0.924458i
$406$	0.268510	+	0.0311348i	0.0133259	+	0.00154519i
$407$	12.3362			0.611481
$408$	−1.75353	+	1.59713i	−0.0868126	+	0.0790698i
$409$	5.93083	−	0.623355i	0.293261	−	0.0308229i	0.0432442	−	0.999065i	$-0.486231\pi$
$409$	5.93083	−	0.623355i	0.293261	−	0.0308229i	0.250016	+	0.968242i	$0.419564\pi$
$410$	−8.42507	−	3.21673i	−0.416085	−	0.158863i
$411$	4.83268	−	2.18484i	0.238379	−	0.107770i
$412$	−18.3768	+	13.3516i	−0.905362	+	0.657784i
$413$	−27.3274	−	6.11546i	−1.34469	−	0.300922i
$414$	−42.2836	+	19.4082i	−2.07812	+	0.953860i
$415$	13.5996	−	5.24843i	0.667576	−	0.257635i
$416$	3.94993	+	37.5811i	0.193661	+	1.84257i
$417$	9.40543	+	2.99667i	0.460586	+	0.146747i
$418$	−5.27918	−	9.14380i	−0.258213	−	0.447238i
$419$	7.55700	−	23.2580i	0.369184	−	1.13623i	−0.578136	−	0.815940i	$-0.696220\pi$
$419$	7.55700	−	23.2580i	0.369184	−	1.13623i	0.947320	−	0.320290i	$-0.103780\pi$
$420$	19.0665	−	9.63803i	0.930350	−	0.470288i
$421$	7.20953	+	22.1887i	0.351371	+	1.08141i	0.958084	+	0.286488i	$0.0924879\pi$
$421$	7.20953	+	22.1887i	0.351371	+	1.08141i	−0.606713	+	0.794921i	$0.707512\pi$
$422$	0.587549	−	0.652539i	0.0286014	−	0.0317651i
$423$	−37.5337	−	3.51153i	−1.82495	−	0.170736i
$424$	0.383451	−	0.664156i	0.0186220	−	0.0322543i
$425$	−20.0706	−	34.4767i	−0.973568	−	1.67237i
$426$	−1.15982	+	0.678493i	−0.0561935	+	0.0328731i
$427$	5.22048	−	11.3951i	0.252637	−	0.551447i
$428$	0.904271	+	2.78306i	0.0437096	+	0.134524i
$429$	3.70903	−	17.9538i	0.179074	−	0.866815i
$430$	13.0210	−	8.48923i	0.627929	−	0.409387i
$431$	10.5621	−	9.51012i	0.508757	−	0.458087i	−0.374331	−	0.927295i	$-0.622127\pi$
$431$	10.5621	−	9.51012i	0.508757	−	0.458087i	0.883087	+	0.469209i	$0.155461\pi$
$432$	−10.2259	−	17.0304i	−0.491994	−	0.819375i
$433$	5.06052	−	15.5747i	0.243193	−	0.748471i	−0.752735	−	0.658323i	$-0.771266\pi$
$433$	5.06052	−	15.5747i	0.243193	−	0.748471i	0.995928	−	0.0901481i	$-0.0287340\pi$
$434$	−18.8413	+	5.89941i	−0.904412	+	0.283181i
$435$	−0.189483	−	0.0492490i	−0.00908503	−	0.00236131i
$436$	2.10509	−	20.0286i	0.100815	−	0.959195i
$437$	−17.6364	+	1.85366i	−0.843663	+	0.0886726i
$438$	−0.860751	+	0.632922i	−0.0411283	+	0.0302422i
$439$	1.48601	+	0.156185i	0.0709232	+	0.00745433i	0.139924	−	0.990162i	$-0.455314\pi$
$439$	1.48601	+	0.156185i	0.0709232	+	0.00745433i	−0.0690004	+	0.997617i	$0.521981\pi$
$440$	−0.612307	+	0.614511i	−0.0291906	+	0.0292956i
$441$	20.9989	+	0.210045i	0.999950	+	0.0100021i
$442$	−71.8150	−	23.3341i	−3.41589	−	1.10989i
$443$	−1.98827	−	3.44379i	−0.0944657	−	0.163619i	0.814920	−	0.579574i	$-0.196781\pi$
$443$	−1.98827	−	3.44379i	−0.0944657	−	0.163619i	−0.909385	+	0.415954i	$0.863448\pi$
$444$	−18.7782	−	5.98292i	−0.891172	−	0.283937i
$445$	17.3300	+	26.5813i	0.821523	+	1.26007i
$446$	−9.25521	+	10.2790i	−0.438247	+	0.486723i
$447$	7.17975	+	6.39073i	0.339591	+	0.302271i
$448$	18.6890	−	13.2746i	0.882971	−	0.627167i
$449$		−	36.6631i		−	1.73024i	−0.501564	−	0.865120i	$-0.667242\pi$
$449$		−	36.6631i		−	1.73024i	0.501564	−	0.865120i	$-0.332758\pi$
$450$	−28.6889	+	9.80061i	−1.35241	+	0.462005i
$451$	3.90625	+	2.25527i	0.183938	+	0.106197i
$452$	−7.78323	+	3.46532i	−0.366092	+	0.162995i
$453$	10.0343	+	2.07297i	0.471454	+	0.0973968i
$454$	−19.4791	+	6.32914i	−0.914198	+	0.297041i
$455$	23.0979	+	15.2946i	1.08284	+	0.717023i
$456$	0.146683	+	0.671196i	0.00686906	+	0.0314316i
$457$	10.8789	−	6.28095i	0.508895	−	0.293811i	−0.223484	−	0.974708i	$-0.571743\pi$
$457$	10.8789	−	6.28095i	0.508895	−	0.293811i	0.732379	+	0.680897i	$0.238410\pi$
$458$	−35.1444	+	31.6442i	−1.64219	+	1.47863i
$459$	41.1508	−	5.04009i	1.92075	−	0.235251i
$460$	12.8796	+	33.3733i	0.600517	+	1.55604i
$461$	7.58703	+	5.51230i	0.353363	+	0.256734i	0.750279	−	0.661122i	$-0.229919\pi$
$461$	7.58703	+	5.51230i	0.353363	+	0.256734i	−0.396915	+	0.917855i	$0.629919\pi$
$462$	−19.9430	+	6.36978i	−0.927831	+	0.296349i
$463$	−14.2149	−	19.5652i	−0.660624	−	0.909271i	0.338878	−	0.940830i	$-0.389953\pi$
$463$	−14.2149	−	19.5652i	−0.660624	−	0.909271i	−0.999502	+	0.0315595i	$0.989953\pi$
$464$	−0.192191	−	0.0202001i	−0.00892225	−	0.000937766i
$465$	14.1064	−	2.34301i	0.654167	−	0.108654i
$466$	2.27370	+	21.6328i	0.105327	+	1.00212i
$467$	3.98484	+	18.7472i	0.184397	+	0.867518i	0.968911	+	0.247408i	$0.0795787\pi$
$467$	3.98484	+	18.7472i	0.184397	+	0.867518i	−0.784515	+	0.620110i	$0.787088\pi$
$468$	−14.3533	+	25.5304i	−0.663481	+	1.18014i
$469$	−7.62595	−	17.6345i	−0.352134	−	0.814284i
$470$	−8.78308	+	56.1063i	−0.405133	+	2.58799i
$471$	−30.6748	−	6.33704i	−1.41342	−	0.291996i
$472$	−1.77690	−	0.377691i	−0.0817883	−	0.0173846i
$473$	−7.10227	+	3.16213i	−0.326563	+	0.145395i
$474$	−8.77499	+	15.4014i	−0.403048	+	0.707410i
$475$	−11.5555	+	0.0415153i	−0.530203	+	0.00190485i
$476$	8.68860	+	43.1455i	0.398241	+	1.97757i
$477$	−12.1828	+	5.59192i	−0.557813	+	0.256037i
$478$	46.2043	+	41.6025i	2.11333	+	1.90286i
$479$	13.7853	+	2.93015i	0.629865	+	0.133882i	0.511773	−	0.859121i	$-0.328989\pi$
$479$	13.7853	+	2.93015i	0.629865	+	0.133882i	0.118092	+	0.993003i	$0.462322\pi$
$480$	−27.7406	+	14.3981i	−1.26618	+	0.657181i
$481$	−5.31330	−	24.9971i	−0.242265	−	1.13977i
$482$		−	25.2843i		−	1.15167i
$483$	−3.85036	+	34.9513i	−0.175197	+	1.59034i
$484$	−9.93597	+	7.21891i	−0.451635	+	0.328132i
$485$	8.52376	+	5.51365i	0.387044	+	0.250362i
$486$	2.39635	−	31.4149i	0.108700	−	1.42501i
$487$	18.5430	−	1.94895i	0.840264	−	0.0883153i	0.325388	−	0.945580i	$-0.394505\pi$
$487$	18.5430	−	1.94895i	0.840264	−	0.0883153i	0.514875	+	0.857265i	$0.327838\pi$
$488$	0.330714	−	0.742795i	0.0149707	−	0.0336248i
$489$	20.8836	+	2.07431i	0.944389	+	0.0938035i
$490$	2.27580	−	31.5535i	0.102810	−	1.42544i
$491$	0.577718	+	0.795160i	0.0260720	+	0.0358851i	0.821854	−	0.569698i	$-0.192940\pi$
$491$	0.577718	+	0.795160i	0.0260720	+	0.0358851i	−0.795782	+	0.605583i	$0.792940\pi$
$492$	−4.85232	−	5.32747i	−0.218759	−	0.240181i
$493$	0.201660	−	0.349286i	0.00908232	−	0.0157310i
$494$	−16.2545	+	14.6356i	−0.731326	+	0.658489i
$495$	14.9438	−	2.56998i	0.671672	−	0.115512i
$496$	13.4241	−	4.36174i	0.602758	−	0.195848i
$497$	−0.0108849	+	1.01549i	−0.000488253	+	0.0455508i
$498$	22.7096	+	2.25568i	1.01764	+	0.101079i
$499$	1.52558	+	2.64239i	0.0682946	+	0.118290i	0.898151	−	0.439688i	$-0.144911\pi$
$499$	1.52558	+	2.64239i	0.0682946	+	0.118290i	−0.829856	+	0.557977i	$0.811578\pi$
$500$	6.15435	+	22.4830i	0.275231	+	1.00547i
$501$	−0.239919	−	41.9632i	−0.0107188	−	1.87478i
$502$	−5.00738	+	47.6421i	−0.223490	+	2.12637i
$503$	20.5893	−	6.68987i	0.918031	−	0.298286i	0.188372	−	0.982098i	$-0.439679\pi$
$503$	20.5893	−	6.68987i	0.918031	−	0.298286i	0.729659	+	0.683811i	$0.239679\pi$
$504$	1.36229		0.000975595i	0.0606810		4.34565e-5i
$505$	5.69640	+	35.5522i	0.253486	+	1.58205i
$506$	−7.28831	−	34.2888i	−0.324005	−	1.52432i
$507$	−15.4614	+	0.0883982i	−0.686663	+	0.00392590i
$508$	23.0569	−	20.7605i	1.02298	−	0.921100i
$509$	14.8373	+	6.60600i	0.657652	+	0.292806i	0.708301	−	0.705911i	$-0.249462\pi$
$509$	14.8373	+	6.60600i	0.657652	+	0.292806i	−0.0506483	+	0.998717i	$0.516129\pi$
$510$	−3.73716	−	62.3430i	−0.165484	−	2.76060i
$511$	0.0757923	+	0.803914i	0.00335286	+	0.0355631i
$512$	−26.0205	+	18.9050i	−1.14995	+	0.835491i
$513$	4.69559	−	11.0528i	0.207315	−	0.487995i
$514$	3.63875	+	8.17276i	0.160498	+	0.360485i
$515$	1.23129	−	24.3306i	0.0542573	−	1.07214i
$516$	12.3447	−	1.36888i	0.543445	−	0.0602616i
$517$	8.77722	−	27.0135i	0.386022	−	1.18805i
$518$	−21.8957	+	19.2941i	−0.962041	+	0.847732i
$519$	4.25895	+	19.4883i	0.186947	+	0.855439i
$520$	1.50892	+	0.976057i	0.0661707	+	0.0428029i
$521$	17.1556	+	3.64653i	0.751599	+	0.159757i	0.567754	−	0.823198i	$-0.307812\pi$
$521$	17.1556	+	3.64653i	0.751599	+	0.159757i	0.183844	+	0.982955i	$0.441146\pi$
$522$	−0.230106	−	0.202472i	−0.0100715	−	0.00886196i
$523$	0.131626	−	1.25234i	0.00575560	−	0.0547609i	−0.991267	−	0.131869i	$-0.957902\pi$
$523$	0.131626	−	1.25234i	0.00575560	−	0.0547609i	0.997023	+	0.0771084i	$0.0245688\pi$
$524$	4.75653			0.207790
$525$	−4.79542	+	22.4054i	−0.209289	+	0.977854i
$526$	49.5889			2.16218
$527$	−3.07924	+	29.2970i	−0.134134	+	1.27620i
$528$	14.2080	−	4.70644i	0.618325	−	0.204822i
$529$	−35.0932	−	7.45929i	−1.52579	−	0.324317i
$530$	7.27067	+	18.8395i	0.315818	+	0.818337i
$531$	21.5151	+	23.3524i	0.933678	+	1.01341i
$532$	12.0816	+	4.06924i	0.523806	+	0.176424i
$533$	2.88746	−	8.88669i	0.125070	−	0.384925i
$534$	5.47509	+	49.3748i	0.236930	+	2.13666i
$535$	−2.93199	−	1.11945i	−0.126761	−	0.0483979i
$536$	−0.506934	−	1.13859i	−0.0218962	−	0.0491797i
$537$	5.67280	−	0.629046i	0.244799	−	0.0271454i
$538$	15.9752	−	11.6066i	0.688738	−	0.500397i
$539$	−3.62072	+	15.4029i	−0.155956	+	0.663448i
$540$	−23.9938	−	3.33554i	−1.03253	−	0.143539i
$541$	9.43684	+	4.20155i	0.405721	+	0.180639i	0.599442	−	0.800418i	$-0.295389\pi$
$541$	9.43684	+	4.20155i	0.405721	+	0.180639i	−0.193721	+	0.981057i	$0.562056\pi$
$542$	27.3581	−	24.6333i	1.17513	−	1.05809i
$543$	0.106767	+	18.6742i	0.00458183	+	0.801389i
$544$	−13.3868	−	62.9799i	−0.573954	−	2.70024i
$545$	15.3001	+	15.2453i	0.655386	+	0.653035i
$546$	21.4969	+	37.6674i	0.919980	+	1.61202i
$547$	4.13464	−	1.34343i	0.176785	−	0.0574408i	−0.219287	−	0.975660i	$-0.570373\pi$
$547$	4.13464	−	1.34343i	0.176785	−	0.0574408i	0.396072	+	0.918220i	$0.370373\pi$
$548$	0.667322	−	6.34914i	0.0285066	−	0.271222i
$549$	−12.2261	+	7.24639i	−0.521797	+	0.309268i
$550$	−2.46930	−	22.7087i	−0.105291	−	0.968301i
$551$	−0.0584134	−	0.101175i	−0.00248849	−	0.00431020i
$552$	−0.225459	+	2.26987i	−0.00959619	+	0.0966120i
$553$	6.57368	+	11.6731i	0.279541	+	0.496392i
$554$	−21.0158	+	6.82845i	−0.892877	+	0.290113i
$555$	17.6400	−	11.6449i	0.748776	−	0.494299i
$556$	8.83030	−	7.95084i	0.374488	−	0.337191i
$557$	−3.97248	+	6.88054i	−0.168319	+	0.291538i	−0.937829	−	0.347097i	$-0.887167\pi$
$557$	−3.97248	+	6.88054i	−0.168319	+	0.291538i	0.769510	+	0.638635i	$0.220501\pi$
$558$	21.3688	+	6.67400i	0.904615	+	0.282533i
$559$	9.46651	+	13.0295i	0.400391	+	0.551091i
$560$	−1.38514	+	22.5744i	−0.0585329	+	0.953943i
$561$	−3.08752	+	31.0843i	−0.130355	+	1.31238i
$562$	−15.7721	+	35.4248i	−0.665307	+	1.49430i
$563$	−3.03735	+	0.319238i	−0.128009	+	0.0134543i	−0.168316	−	0.985733i	$-0.553833\pi$
$563$	−3.03735	+	0.319238i	−0.128009	+	0.0134543i	0.0403073	+	0.999187i	$0.487166\pi$
$564$	−26.4620	+	36.8632i	−1.11425	+	1.55222i
$565$	2.34909	−	8.83034i	0.0988270	−	0.371495i
$566$	−36.0348	+	26.1808i	−1.51465	+	1.10046i
$567$	−19.4328	−	13.7611i	−0.816099	−	0.577912i
$568$			0.0658792i			0.00276423i
$569$	2.77227	+	13.0425i	0.116220	+	0.546770i	0.997276	+	0.0737592i	$0.0234996\pi$
$569$	2.77227	+	13.0425i	0.116220	+	0.546770i	−0.881056	+	0.473011i	$0.843167\pi$
$570$	−16.1803	−	8.09173i	−0.677719	−	0.338925i
$571$	−14.8041	−	3.14671i	−0.619533	−	0.131686i	−0.112556	−	0.993645i	$-0.535904\pi$
$571$	−14.8041	−	3.14671i	−0.619533	−	0.131686i	−0.506977	+	0.861960i	$0.669237\pi$
$572$	−16.3996	−	14.7662i	−0.685701	−	0.617408i
$573$	2.10567	+	0.209150i	0.0879655	+	0.00873736i
$574$	−10.4606	+	2.10654i	−0.436615	+	0.0879251i
$575$	−36.5303	−	11.7245i	−1.52342	−	0.488946i
$576$	−25.9913	+	0.297213i	−1.08297	+	0.0123839i
$577$	−21.9447	+	9.77040i	−0.913569	+	0.406747i	−0.809026	−	0.587773i	$-0.800005\pi$
$577$	−21.9447	+	9.77040i	−0.913569	+	0.406747i	−0.104543	+	0.994520i	$0.533338\pi$
$578$	92.2424	+	19.6067i	3.83678	+	0.815532i
$579$	−4.71222	+	22.8097i	−0.195833	+	0.947940i
$580$	−0.166341	+	0.166939i	−0.00690692	+	0.00693178i
$581$	10.2871	−	13.8444i	0.426780	−	0.574363i
$582$	8.02498	+	13.7179i	0.332646	+	0.568627i
$583$	−2.09992	−	9.87936i	−0.0869699	−	0.409161i
$584$	0.00547539	+	0.0520948i	0.000226573	+	0.00215570i
$585$	−11.6440	−	29.1740i	−0.481420	−	1.20620i
$586$	17.7132	+	1.86174i	0.731727	+	0.0769076i
$587$	−24.2393	−	33.3625i	−1.00046	−	1.37702i	−0.925042	−	0.379865i	$-0.875971\pi$
$587$	−24.2393	−	33.3625i	−1.00046	−	1.37702i	−0.0754189	−	0.997152i	$-0.524029\pi$
$588$	12.9817	−	21.6903i	0.535356	−	0.894492i
$589$	6.90333	+	5.01556i	0.284447	+	0.206663i
$590$	37.1198	−	30.1696i	1.52820	−	1.24206i
$591$	−0.696180	+	0.511911i	−0.0286370	+	0.0210572i
$592$	15.5049	−	13.9607i	0.637249	−	0.573781i
$593$	−8.88298	+	5.12859i	−0.364780	+	0.210606i	−0.671176	−	0.741298i	$-0.734210\pi$
$593$	−8.88298	+	5.12859i	−0.364780	+	0.210606i	0.306395	+	0.951904i	$0.400877\pi$
$594$	22.6993	+	6.94736i	0.931364	+	0.285053i
$595$	−41.8647	−	21.8038i	−1.71629	−	0.893869i
$596$	11.0039	−	3.57540i	0.450739	−	0.146454i
$597$	5.84541	−	28.2950i	0.239237	−	1.15804i
$598$	−66.3411	+	29.5370i	−2.71289	+	1.20786i
$599$	−33.8615	−	19.5499i	−1.38354	−	0.798789i	−0.390966	−	0.920405i	$-0.627859\pi$
$599$	−33.8615	−	19.5499i	−1.38354	−	0.798789i	−0.992577	+	0.121616i	$0.961192\pi$
$600$	−0.295486	+	1.45671i	−0.0120632	+	0.0594699i
$601$			26.0196i			1.06136i	0.847572	+	0.530680i	$0.178063\pi$
$601$			26.0196i			1.06136i	−0.847572	+	0.530680i	$0.821937\pi$
$602$	7.66028	−	16.7206i	0.312210	−	0.681482i
$603$	−4.28544	+	21.3595i	−0.174517	+	0.869827i
$604$	8.25284	−	9.16571i	0.335803	−	0.372947i
$605$	0.665734	−	13.1551i	0.0270659	−	0.534830i
$606$	−17.1121	+	53.7086i	−0.695132	+	2.18176i
$607$	16.9776	+	29.4061i	0.689101	+	1.19356i	0.972129	+	0.234446i	$0.0753275\pi$
$607$	16.9776	+	29.4061i	0.689101	+	1.19356i	−0.283029	+	0.959111i	$0.591339\pi$
$608$	−17.7377	−	5.76331i	−0.719357	−	0.233733i
$609$	−0.220666	+	0.0704807i	−0.00894185	+	0.00285602i
$610$	9.75421	+	19.0590i	0.394936	+	0.771677i
$611$	−58.5186	−	6.15055i	−2.36741	−	0.248825i
$612$	19.7754	−	45.8192i	0.799373	−	1.85213i
$613$	−11.6736	+	1.22694i	−0.471491	+	0.0495557i	−0.337295	−	0.941399i	$-0.609512\pi$
$613$	−11.6736	+	1.22694i	−0.471491	+	0.0495557i	−0.134196	+	0.990955i	$0.542845\pi$
$614$	−0.629449	+	5.98880i	−0.0254025	+	0.241688i
$615$	7.71460	−	0.462453i	0.311083	−	0.0186479i
$616$	−0.224156	+	1.00166i	−0.00903150	+	0.0403579i
$617$	−1.12365	+	3.45824i	−0.0452364	+	0.139223i	−0.971124	−	0.238576i	$-0.923319\pi$
$617$	−1.12365	+	3.45824i	−0.0452364	+	0.139223i	0.925887	+	0.377800i	$0.123319\pi$
$618$	18.8807	−	33.1384i	0.759491	−	1.33302i
$619$	−21.0857	+	18.9856i	−0.847504	+	0.763096i	−0.973440	−	0.228942i	$-0.926473\pi$
$619$	−21.0857	+	18.9856i	−0.847504	+	0.763096i	0.125936	+	0.992038i	$0.459807\pi$
$620$	6.13967	−	16.0807i	0.246575	−	0.645815i
$621$	26.1667	−	30.0830i	1.05003	−	1.20719i
$622$	5.57105	+	17.1459i	0.223379	+	0.687490i
$623$	34.1337	+	15.6378i	1.36754	+	0.626516i
$624$	−15.6563	−	26.7630i	−0.626753	−	1.07138i
$625$	−22.9111	−	10.0041i	−0.916444	−	0.400162i
$626$	−4.13487	+	7.16180i	−0.165263	+	0.286243i
$627$	7.35048	+	5.27650i	0.293550	+	0.210723i
$628$	−25.2288	+	28.0194i	−1.00674	+	1.11810i
$629$	13.4558	+	41.4127i	0.536518	+	1.65123i
$630$	−22.5044	+	27.9339i	−0.896598	+	1.11291i
$631$	8.92223	−	27.4598i	0.355189	−	1.09316i	−0.600712	−	0.799466i	$-0.705116\pi$
$631$	8.92223	−	27.4598i	0.355189	−	1.09316i	0.955900	−	0.293692i	$-0.0948840\pi$
$632$	0.434532	+	0.752631i	0.0172847	+	0.0299380i
$633$	−0.228437	+	0.716980i	−0.00907957	+	0.0284974i
$634$	−4.57785	−	43.5553i	−0.181810	−	1.72980i
$635$	1.80119	+	33.2266i	0.0714780	+	1.31856i
$636$	−1.59488	+	16.0568i	−0.0632411	+	0.636695i
$637$	32.7707	+	0.702610i	1.29842	+	0.0278384i
$638$	0.186833	−	0.135742i	0.00739677	−	0.00537407i
$639$	0.666151	−	0.939278i	0.0263525	−	0.0371573i
$640$	−0.155036	+	3.06356i	−0.00612835	+	0.121098i
$641$	−39.3317	+	4.13393i	−1.55351	+	0.163280i	−0.842031	−	0.539429i	$-0.818640\pi$
$641$	−39.3317	+	4.13393i	−1.55351	+	0.163280i	−0.711477	+	0.702709i	$0.751974\pi$
$642$	−3.30851	−	3.63249i	−0.130576	−	0.143363i
$643$	−15.2966			−0.603240			−0.301620	−	0.953428i	$-0.597527\pi$
$643$	−15.2966			−0.603240			−0.301620	+	0.953428i	$0.597527\pi$
$644$	33.9742	+	25.2445i	1.33877	+	0.994771i
$645$	−7.17087	+	11.2259i	−0.282353	+	0.442021i
$646$	24.9376	−	27.6960i	0.981155	−	1.08968i
$647$	7.28264	−	34.2621i	0.286310	−	1.34698i	−0.566198	−	0.824269i	$-0.691586\pi$
$647$	7.28264	−	34.2621i	0.286310	−	1.34698i	0.852508	−	0.522714i	$-0.175080\pi$
$648$	−1.27011	−	0.879130i	−0.0498948	−	0.0345355i
$649$	−20.7192	+	11.9622i	−0.813300	+	0.469559i
$650$	−44.9516	+	14.7844i	−1.76315	+	0.579893i
$651$	12.6301	−	11.2584i	0.495014	−	0.441250i
$652$	14.8486	−	20.4373i	0.581515	−	0.800387i
$653$	14.6846	−	16.3089i	0.574651	−	0.638215i	−0.383819	−	0.923409i	$-0.625391\pi$
$653$	14.6846	−	16.3089i	0.574651	−	0.638215i	0.958470	+	0.285194i	$0.0920579\pi$
$654$	10.6328	+	32.0989i	0.415777	+	1.25517i
$655$	−3.20327	+	3.97027i	−0.125162	+	0.155131i
$656$	7.46190	−	1.58608i	0.291338	−	0.0619259i
$657$	0.448701	−	0.798111i	0.0175055	−	0.0311373i
$658$	26.6709	+	61.6745i	1.03974	+	2.40432i
$659$	−11.7298	−	16.1447i	−0.456930	−	0.628910i	0.516939	−	0.856022i	$-0.327071\pi$
$659$	−11.7298	−	16.1447i	−0.456930	−	0.628910i	−0.973869	+	0.227113i	$0.927071\pi$
$660$	6.41282	−	17.0887i	0.249619	−	0.665175i
$661$	13.1605	+	29.5590i	0.511884	+	1.14971i	0.965947	+	0.258741i	$0.0833076\pi$
$661$	13.1605	+	29.5590i	0.511884	+	1.14971i	−0.454063	+	0.890970i	$0.650026\pi$
$662$	−0.279467	−	2.65895i	−0.0108618	−	0.103343i
$663$	64.3167	−	7.13196i	2.49785	−	0.276983i
$664$	0.657666	−	0.905199i	0.0255224	−	0.0351285i
$665$	−11.5329	+	7.34411i	−0.447227	+	0.284792i
$666$	32.8681	−	3.83503i	1.27361	−	0.148605i
$667$	−0.0806442	−	0.379401i	−0.00312256	−	0.0146905i
$668$	−43.7457	−	25.2566i	−1.69257	−	0.977206i
$669$	3.59840	−	11.2941i	0.139122	−	0.436653i
$670$	31.7153	+	8.43706i	1.22527	+	0.325952i
$671$	−3.30907	−	10.1843i	−0.127745	−	0.393159i
$672$	−18.6504	+	31.9335i	−0.719455	+	1.23186i
$673$	18.4661	−	25.4164i	0.711815	−	0.979729i	−0.287942	−	0.957648i	$-0.592971\pi$
$673$	18.4661	−	25.4164i	0.711815	−	0.979729i	0.999756	−	0.0220807i	$-0.00702908\pi$
$674$	9.86407	−	5.69503i	0.379950	−	0.219364i
$675$	18.9427	−	17.7813i	0.729105	−	0.684402i
$676$	−9.30579	+	16.1181i	−0.357915	+	0.619927i
$677$	4.17199	+	0.438494i	0.160343	+	0.0168527i	0.184360	−	0.982859i	$-0.440979\pi$
$677$	4.17199	+	0.438494i	0.160343	+	0.0168527i	−0.0240169	+	0.999712i	$0.507646\pi$
$678$	9.51109	−	10.6854i	0.365271	−	0.410369i
$679$	12.0108	+	0.128743i	0.460934	+	0.00494068i
$680$	−2.73080	−	1.38524i	−0.104721	−	0.0531215i
$681$	12.9764	−	11.8191i	0.497258	−	0.452908i
$682$	−8.43380	+	14.6078i	−0.322947	+	0.559361i
$683$	19.1365	+	21.2533i	0.732239	+	0.813234i	0.988154	−	0.153465i	$-0.0490433\pi$
$683$	19.1365	+	21.2533i	0.732239	+	0.813234i	−0.255915	+	0.966699i	$0.582377\pi$
$684$	−8.62988	−	11.5968i	−0.329972	−	0.443415i
$685$	4.85021	+	4.83281i	0.185317	+	0.184652i
$686$	−17.6639	−	33.0017i	−0.674413	−	1.26001i
$687$	16.2721	−	37.1175i	0.620821	−	1.41612i
$688$	−5.34806	+	12.0119i	−0.203893	+	0.457951i
$689$	−19.1143	+	8.51025i	−0.728198	+	0.324215i
$690$	−42.7893	−	42.1510i	−1.62896	−	1.60466i
$691$	1.43565	−	3.22453i	0.0546148	−	0.122667i	−0.884177	−	0.467152i	$-0.845280\pi$
$691$	1.43565	−	3.22453i	0.0546148	−	0.122667i	0.938792	+	0.344485i	$0.111947\pi$
$692$	22.8370	+	7.42018i	0.868132	+	0.282073i
$693$	13.3244	−	12.0146i	0.506150	−	0.456397i
$694$	10.1640	−	31.2817i	0.385822	−	1.18744i
$695$	0.689817	+	12.7251i	0.0261662	+	0.482690i
$696$	−0.0142650	+	0.00472531i	−0.000540712	+	0.000179112i
$697$	−3.31021	+	15.5733i	−0.125383	+	0.589881i
$698$	−22.1264	−	2.32558i	−0.837498	−	0.0880245i
$699$	−9.41261	−	16.0900i	−0.356017	−	0.608578i
$700$	20.3646	+	18.6008i	0.769708	+	0.703044i
$701$		−	7.74587i		−	0.292557i	−0.989243	−	0.146279i	$-0.953270\pi$
$701$		−	7.74587i		−	0.292557i	0.989243	−	0.146279i	$-0.0467296\pi$
$702$	4.30081	−	48.9884i	0.162324	−	1.84895i
$703$	12.3374	+	2.62240i	0.465314	+	0.0989056i
$704$	4.07189	−	19.1567i	0.153465	−	0.721997i
$705$	−12.9489	−	46.9131i	−0.487683	−	1.76685i
$706$	−35.0620	−	11.3923i	−1.31958	−	0.428756i
$707$	28.1656	+	31.9635i	1.05928	+	1.20211i
$708$	37.3404	−	8.16035i	1.40334	−	0.306685i
$709$	−46.0287	−	20.4933i	−1.72864	−	0.769642i	−0.996032	−	0.0889959i	$-0.971634\pi$
$709$	−46.0287	−	20.4933i	−1.72864	−	0.769642i	−0.732612	−	0.680646i	$-0.761699\pi$
$710$	−1.35008	−	1.08927i	−0.0506677	−	0.0408794i
$711$	1.41500	−	15.1245i	0.0530667	−	0.567215i
$712$	2.22503	+	0.990646i	0.0833864	+	0.0371260i
$713$	16.6522	+	22.9198i	0.623630	+	0.858352i
$714$	−43.1364	−	60.0010i	−1.61434	−	2.24548i
$715$	23.3696	−	3.74442i	0.873972	−	0.140033i
$716$	2.79443	−	6.27639i	0.104433	−	0.234560i
$717$	−50.7672	−	16.1750i	−1.89593	−	0.604065i
$718$	−24.5775	−	14.1898i	−0.917222	−	0.529559i
$719$	−48.1842	+	10.2419i	−1.79697	+	0.381957i	−0.980669	−	0.195672i	$-0.937311\pi$
$719$	−48.1842	+	10.2419i	−1.79697	+	0.381957i	−0.816299	+	0.577629i	$0.803978\pi$
$720$	15.8739	−	20.1418i	0.591586	−	0.750640i
$721$	−14.1442	−	25.1164i	−0.526759	−	0.935385i
$722$	8.53070	+	26.2548i	0.317480	+	0.977103i
$723$	8.92622	+	19.7440i	0.331970	+	0.734289i
$724$	19.4675	+	11.2395i	0.723503	+	0.417715i
$725$	−0.0273224	−	0.251268i	−0.00101473	−	0.00933188i
$726$	10.2084	−	17.9172i	0.378868	−	0.664970i
$727$	28.6170	+	20.7915i	1.06135	+	0.771114i	0.974337	−	0.225093i	$-0.0722687\pi$
$727$	28.6170	+	20.7915i	1.06135	+	0.771114i	0.0870103	+	0.996207i	$0.472269\pi$
$728$	2.12623	+	0.0227907i	0.0788032	+	0.000844680i
$729$	9.21925	+	25.3773i	0.341454	+	0.939899i
$730$	−1.15813	−	0.749142i	−0.0428642	−	0.0277270i
$731$	−18.3622	−	20.3933i	−0.679150	−	0.754273i
$732$	0.0978091	+	17.1074i	0.00361513	+	0.632307i
$733$	−45.4036	+	9.65083i	−1.67702	+	0.356462i	−0.945566	−	0.325430i	$-0.894491\pi$
$733$	−45.4036	+	9.65083i	−1.67702	+	0.356462i	−0.731453	+	0.681891i	$0.761158\pi$
$734$	−3.59757	+	2.61379i	−0.132789	+	0.0964767i
$735$	9.36234	+	25.4430i	0.345335	+	0.938479i
$736$	−50.0956	−	36.3966i	−1.84655	−	1.34160i
$737$	−14.9952	−	6.67630i	−0.552356	−	0.245925i
$738$	11.1088	+	4.79451i	0.408920	+	0.176488i
$739$	−4.08251	+	1.81765i	−0.150178	+	0.0668633i	−0.480449	−	0.877023i	$-0.659526\pi$
$739$	−4.08251	+	1.81765i	−0.150178	+	0.0668633i	0.330272	+	0.943886i	$0.392860\pi$
$740$	−1.37723	−	25.4059i	−0.0506282	−	0.933940i
$741$	7.52598	−	17.1671i	0.276474	−	0.630649i
$742$	19.1787	+	14.2507i	0.704073	+	0.523160i
$743$	27.1224			0.995024			0.497512	−	0.867457i	$-0.334247\pi$
$743$	27.1224			0.995024			0.497512	+	0.867457i	$0.334247\pi$
$744$	0.811452	−	0.739078i	0.0297493	−	0.0270959i
$745$	−4.42618	+	11.5928i	−0.162163	+	0.424727i
$746$	3.93802	−	18.5269i	0.144181	−	0.678319i
$747$	−18.5298	+	6.25584i	−0.677970	+	0.228889i
$748$	30.4200	+	22.1014i	1.11227	+	0.808108i
$749$	−3.64036	+	0.733091i	−0.133016	+	0.0267866i
$750$	−24.9671	−	30.1411i	−0.911671	−	1.10060i
$751$	0.238080	+	0.412366i	0.00868765	+	0.0150474i	0.870337	−	0.492457i	$-0.163901\pi$
$751$	0.238080	+	0.412366i	0.00868765	+	0.0150474i	−0.861649	+	0.507505i	$0.830568\pi$
$752$	−19.5391	−	43.8855i	−0.712517	−	1.60034i
$753$	−12.9091	−	38.9706i	−0.470434	−	1.42017i
$754$	−0.355527	−	0.320118i	−0.0129475	−	0.0116580i
$755$	2.09275	+	13.0612i	0.0761631	+	0.475347i
$756$	−26.1093	+	11.8265i	−0.949587	+	0.430125i
$757$		−	16.2539i		−	0.590757i	−0.955380	−	0.295378i	$-0.904554\pi$
$757$		−	16.2539i		−	0.590757i	0.955380	−	0.295378i	$-0.0954457\pi$
$758$	28.4844	−	6.05454i	1.03460	−	0.219911i
$759$	17.7964	+	24.2025i	0.645969	+	0.878494i
$760$	−0.743000	+	0.484409i	−0.0269514	+	0.0175714i
$761$	−0.741987	+	7.05954i	−0.0268970	+	0.255908i	0.972808	+	0.231614i	$0.0744005\pi$
$761$	−0.741987	+	7.05954i	−0.0268970	+	0.255908i	−0.999705	+	0.0242943i	$0.992266\pi$
$762$	−20.9163	+	47.7109i	−0.757716	+	1.72838i
$763$	24.9393	+	5.58105i	0.902863	+	0.202048i
$764$	1.49716	−	2.06067i	0.0541654	−	0.0745523i
$765$	24.9275	+	47.3632i	0.901256	+	1.71242i
$766$	50.7833	−	5.33754i	1.83487	−	0.192853i
$767$	33.1633	+	36.8316i	1.19746	+	1.32991i
$768$	12.4809	−	21.9058i	0.450364	−	0.790456i
$769$	26.9591	+	8.75956i	0.972172	+	0.315878i	0.751692	−	0.659514i	$-0.229238\pi$
$769$	26.9591	+	8.75956i	0.972172	+	0.315878i	0.220479	+	0.975392i	$0.429238\pi$
$770$	−16.8210	−	21.1554i	−0.606186	−	0.762386i
$771$	−5.72669	−	5.09735i	−0.206242	−	0.183577i
$772$	20.8352	+	18.7601i	0.749875	+	0.675190i
$773$	−4.31323	−	9.68768i	−0.155136	−	0.348442i	0.819211	−	0.573493i	$-0.194412\pi$
$773$	−4.31323	−	9.68768i	−0.155136	−	0.348442i	−0.974347	+	0.225051i	$0.927745\pi$
$774$	−17.9400	+	10.6330i	−0.644840	+	0.382196i
$775$	9.28775	+	15.9542i	0.333626	+	0.573092i
$776$	0.779197			0.0279715
$777$	10.2865	−	22.7963i	0.369025	−	0.817812i
$778$	−11.0021	+	3.57480i	−0.394444	+	0.128163i
$779$	3.42722	+	3.08588i	0.122793	+	0.110563i
$780$	−37.3892	−	5.63423i	−1.33875	−	0.201738i
$781$	0.580556	+	0.644773i	0.0207739	+	0.0230718i
$782$	107.158	−	61.8678i	3.83197	−	2.21239i
$783$	0.251165	+	0.0768715i	0.00897590	+	0.00274716i
$784$	12.8805	+	23.4569i	0.460017	+	0.837746i
$785$	−6.39750	−	39.9279i	−0.228337	−	1.42509i
$786$	−7.27729	+	3.29004i	−0.259573	+	0.117352i
$787$	−2.63219	−	25.0436i	−0.0938274	−	0.892708i	−0.935644	−	0.352945i	$-0.885180\pi$
$787$	−2.63219	−	25.0436i	−0.0938274	−	0.892708i	0.841817	−	0.539763i	$-0.181486\pi$
$788$	0.108728	+	1.03448i	0.00387328	+	0.0368518i
$789$	−38.7230	+	17.5066i	−1.37858	+	0.623250i
$790$	−22.6086	−	3.53922i	−0.804376	−	0.125920i
$791$	−3.23056	−	10.3177i	−0.114866	−	0.366853i
$792$	0.855958	−	0.788615i	0.0304151	−	0.0280222i
$793$	−19.2114	+	11.0917i	−0.682217	+	0.393878i
$794$	−14.9135	−	16.5631i	−0.529261	−	0.587804i
$795$	−12.3285	−	12.1446i	−0.437248	−	0.430726i
$796$	−25.8456	−	23.2715i	−0.916073	−	0.824836i
$797$	8.72918	−	2.83628i	0.309203	−	0.100466i	−0.150305	−	0.988640i	$-0.548026\pi$
$797$	8.72918	−	2.83628i	0.309203	−	0.100466i	0.459508	+	0.888173i	$0.348026\pi$
$798$	−21.2991	+	2.13098i	−0.753978	+	0.0754359i
$799$	100.259			3.54689
$800$	−30.0823	−	26.8912i	−1.06357	−	0.950747i
$801$	−21.7064	−	36.6230i	−0.766958	−	1.29401i
$802$	7.00798	+	15.7402i	0.247460	+	0.555805i
$803$	0.512670	+	0.461611i	0.0180917	+	0.0162899i
$804$	19.5878	+	17.4352i	0.690810	+	0.614893i
$805$	−43.9512	+	11.3574i	−1.54908	+	0.400296i
$806$	33.2326	+	10.7979i	1.17057	+	0.380341i
$807$	−8.37716	+	14.7032i	−0.294890	+	0.517576i
$808$	1.84925	+	2.05380i	0.0650563	+	0.0722523i
$809$	30.2577	−	3.18021i	1.06380	−	0.111810i	0.443580	−	0.896235i	$-0.353708\pi$
$809$	30.2577	−	3.18021i	1.06380	−	0.111810i	0.620224	+	0.784425i	$0.287042\pi$
$810$	39.0167	−	11.4930i	1.37091	−	0.403824i
$811$	−29.9173	+	41.1776i	−1.05054	+	1.44594i	−0.162196	+	0.986759i	$0.551858\pi$
$811$	−29.9173	+	41.1776i	−1.05054	+	1.44594i	−0.888342	+	0.459183i	$0.848142\pi$
$812$	−0.0608946	+	0.272112i	−0.00213698	+	0.00954926i
$813$	−12.6670	+	28.8940i	−0.444251	+	1.01336i
$814$	−2.60619	+	24.7963i	−0.0913471	+	0.869109i
$815$	7.05926	+	26.1575i	0.247275	+	0.916256i
$816$	31.2971	+	42.5629i	1.09562	+	1.49000i
$817$	−7.77518	+	1.65266i	−0.272019	+	0.0578194i
$818$			12.0529i			0.421421i
$819$	−30.0844	−	21.8247i	−1.05123	−	0.762616i
$820$	4.20855	−	8.29656i	0.146969	−	0.289729i
$821$	30.7678	+	27.7035i	1.07380	+	0.966857i	0.999538	−	0.0303813i	$-0.00967215\pi$
$821$	30.7678	+	27.7035i	1.07380	+	0.966857i	0.0742654	+	0.997239i	$0.476339\pi$
$822$	3.37066	+	10.1755i	0.117565	+	0.354911i
$823$	1.73361	+	3.89375i	0.0604299	+	0.135728i	0.941236	−	0.337749i	$-0.109665\pi$
$823$	1.73361	+	3.89375i	0.0604299	+	0.135728i	−0.880806	+	0.473477i	$0.842999\pi$
$824$	−0.934958	−	1.61939i	−0.0325708	−	0.0564143i
$825$	9.94516	+	16.8610i	0.346246	+	0.587026i
$826$	18.0657	−	53.6373i	0.628585	−	1.86628i
$827$	−11.6185	−	8.44132i	−0.404014	−	0.293533i	0.367160	−	0.930158i	$-0.380330\pi$
$827$	−11.6185	−	8.44132i	−0.404014	−	0.293533i	−0.771174	+	0.636624i	$0.780330\pi$
$828$	−15.3518	−	45.4721i	−0.533512	−	1.58027i
$829$	10.8632	−	51.1074i	0.377295	−	1.77503i	−0.222555	−	0.974920i	$-0.571440\pi$
$829$	10.8632	−	51.1074i	0.377295	−	1.77503i	0.599850	−	0.800113i	$-0.295227\pi$
$830$	7.67649	+	28.4446i	0.266455	+	0.987325i
$831$	14.0002	−	12.7515i	0.485661	−	0.442345i
$832$	−40.5716			−1.40657
$833$	−55.6570	+	4.64602i	−1.92840	+	0.160975i
$834$	−8.01047	+	18.2723i	−0.277380	+	0.632717i
$835$	50.5419	−	19.5055i	1.74908	−	0.675015i
$836$	9.95002	−	4.43003i	0.344129	−	0.153216i
$837$	−19.0427	+	2.33232i	−0.658211	+	0.0806168i
$838$	45.1532	+	20.1035i	1.55979	+	0.694464i
$839$	−4.63444	−	3.36712i	−0.159999	−	0.116246i	0.504905	−	0.863175i	$-0.331527\pi$
$839$	−4.63444	−	3.36712i	−0.159999	−	0.116246i	−0.664904	+	0.746929i	$0.731527\pi$
$840$	0.624998	+	1.64390i	0.0215645	+	0.0567200i
$841$	−23.4594	+	17.0443i	−0.808946	+	0.587733i
$842$	−46.1234	+	9.80382i	−1.58952	+	0.337862i
$843$	−0.189992	−	33.2306i	−0.00654366	−	1.14452i
$844$	0.606096	+	0.673138i	0.0208627	+	0.0231703i
$845$	−7.18679	−	18.6222i	−0.247233	−	0.640622i
$846$	14.9879	−	74.7026i	0.515293	−	2.56833i
$847$	−7.64749	−	13.5799i	−0.262771	−	0.466612i
$848$	−13.8197	−	10.0406i	−0.474570	−	0.344795i
$849$	18.8962	−	33.1656i	0.648515	−	1.13824i
$850$	73.5400	−	33.0592i	2.52240	−	1.13392i
$851$	36.2662	+	20.9383i	1.24319	+	0.717756i
$852$	−0.571016	−	1.26304i	−0.0195627	−	0.0432710i
$853$	12.9406	+	39.8272i	0.443079	+	1.36366i	0.884577	+	0.466395i	$0.154447\pi$
$853$	12.9406	+	39.8272i	0.443079	+	1.36366i	−0.441498	+	0.897262i	$0.645553\pi$
$854$	21.8018	+	12.9008i	0.746041	+	0.441455i
$855$	15.4916	+	0.606478i	0.529801	+	0.0207411i
$856$	−0.235629	+	0.0500846i	−0.00805365	+	0.00171186i
$857$	−22.2092	−	12.8225i	−0.758651	−	0.438007i	0.0701603	−	0.997536i	$-0.477649\pi$
$857$	−22.2092	−	12.8225i	−0.758651	−	0.438007i	−0.828811	+	0.559528i	$0.810982\pi$
$858$	35.3043	+	11.2483i	1.20527	+	0.384011i
$859$	0.399495	−	0.897281i	0.0136306	−	0.0306148i	−0.906602	−	0.421987i	$-0.861333\pi$
$859$	0.399495	−	0.897281i	0.0136306	−	0.0306148i	0.920233	+	0.391372i	$0.127999\pi$
$860$	7.30521	+	14.2738i	0.249106	+	0.486734i
$861$	7.42478	−	5.33789i	0.253036	−	0.181915i
$862$	16.8844	+	23.2394i	0.575085	+	0.791537i
$863$	−11.5056	−	5.12263i	−0.391656	−	0.174376i	0.201454	−	0.979498i	$-0.435433\pi$
$863$	−11.5056	−	5.12263i	−0.391656	−	0.174376i	−0.593110	+	0.805122i	$0.702100\pi$
$864$	38.0090	−	17.7100i	1.29309	−	0.602505i
$865$	−21.5731	+	14.0649i	−0.733506	+	0.478220i
$866$	30.2367	+	13.4623i	1.02749	+	0.457466i
$867$	−78.9522	+	17.2542i	−2.68136	+	0.585983i
$868$	−4.02068	−	19.9657i	−0.136471	−	0.677681i
$869$	10.8853	+	3.53686i	0.369260	+	0.119980i
$870$	0.139024	−	0.370466i	0.00471335	−	0.0125600i
$871$	−7.06979	+	33.2607i	−0.239551	+	1.12700i
$872$	1.62162	+	0.344686i	0.0549149	+	0.0116725i
$873$	−11.1095	−	7.87900i	−0.375998	−	0.266664i
$874$		−	35.8416i		−	1.21236i
$875$	−29.2405	+	4.47162i	−0.988508	+	0.151168i
$876$	−0.556512	−	0.951305i	−0.0188028	−	0.0321416i
$877$	10.3614	+	1.08903i	0.349881	+	0.0367740i	0.277839	−	0.960628i	$-0.410382\pi$
$877$	10.3614	+	1.08903i	0.349881	+	0.0367740i	0.0720419	+	0.997402i	$0.477048\pi$
$878$	−0.627880	+	2.95394i	−0.0211899	+	0.0996908i
$879$	−14.4892	+	4.79958i	−0.488708	+	0.161886i
$880$	12.1871	+	14.9946i	0.410826	+	0.505469i
$881$	−12.7311	+	39.1823i	−0.428922	+	1.32008i	0.470267	+	0.882524i	$0.344158\pi$
$881$	−12.7311	+	39.1823i	−0.428922	+	1.32008i	−0.899189	+	0.437561i	$0.855842\pi$
$882$	−4.85853	+	42.1645i	−0.163595	+	1.41975i
$883$	−20.6297	−	6.70301i	−0.694246	−	0.225574i	−0.0594241	−	0.998233i	$-0.518926\pi$
$883$	−20.6297	−	6.70301i	−0.694246	−	0.225574i	−0.634822	+	0.772659i	$0.718926\pi$
$884$	31.6825	−	71.1601i	1.06560	−	2.39337i
$885$	−18.3353	+	36.6635i	−0.616334	+	1.23243i
$886$	7.34223	−	3.26897i	0.246667	−	0.109823i
$887$	−18.1309	+	40.7228i	−0.608777	+	1.36734i	0.301551	+	0.953450i	$0.402496\pi$
$887$	−18.1309	+	40.7228i	−0.608777	+	1.36734i	−0.910329	+	0.413886i	$0.864171\pi$
$888$	0.651403	−	1.48588i	0.0218596	−	0.0498629i
$889$	22.7995	+	32.0988i	0.764672	+	1.07656i
$890$	−57.0908	+	29.2185i	−1.91369	+	0.979407i
$891$	−20.1781	+	2.58857i	−0.675992	+	0.0867202i
$892$	−9.54738	−	10.6034i	−0.319670	−	0.355029i
$893$	14.5206	−	25.1504i	0.485913	−	0.841625i
$894$	−14.3625	+	13.0815i	−0.480353	+	0.437511i
$895$	3.35699	+	6.55931i	0.112212	+	0.219253i
$896$	1.78095	+	3.16250i	0.0594974	+	0.105652i
$897$	41.3770	−	46.4855i	1.38154	−	1.55211i
$898$	73.6946	+	7.74562i	2.45922	+	0.258475i
$899$	−0.0933189	+	0.161633i	−0.00311236	+	0.00539077i
$900$	−6.96112	−	30.4892i	−0.232037	−	1.01631i
$901$	30.8746	−	17.8255i	1.02858	−	0.593853i
$902$	−5.35845	+	7.37528i	−0.178417	+	0.245570i
$903$	−0.0788247	+	15.7612i	−0.00262312	+	0.524499i
$904$	−0.216731	−	0.667029i	−0.00720836	−	0.0221851i
$905$	−22.4919	+	8.68022i	−0.747656	+	0.288540i
$906$	−6.28667	+	19.7315i	−0.208861	+	0.655536i
$907$	7.53946	+	4.35291i	0.250344	+	0.144536i	0.619922	−	0.784664i	$-0.287164\pi$
$907$	7.53946	+	4.35291i	0.250344	+	0.144536i	−0.369578	+	0.929200i	$0.620498\pi$
$908$	−4.39277	−	20.6664i	−0.145779	−	0.685837i
$909$	−5.59842	−	47.9812i	−0.185688	−	1.59143i
$910$	−35.6227	+	43.1966i	−1.18088	+	1.43195i
$911$	−6.39615	+	8.80355i	−0.211914	+	0.291675i	−0.901721	−	0.432319i	$-0.857695\pi$
$911$	−6.39615	+	8.80355i	−0.211914	+	0.291675i	0.689807	+	0.723994i	$0.257695\pi$
$912$	15.2099	−	1.68660i	0.503651	−	0.0558490i
$913$	−1.54030	−	14.6550i	−0.0509765	−	0.485009i
$914$	10.3267	+	23.1941i	0.341576	+	0.767193i
$915$	−14.3454	−	11.4393i	−0.474243	−	0.378170i
$916$	−28.6747	−	39.4673i	−0.947439	−	1.30404i
$917$	−0.695240	+	5.99584i	−0.0229589	+	0.198000i
$918$	1.43712	+	83.7798i	0.0474321	+	2.76515i
$919$	4.05665	−	0.862267i	0.133816	−	0.0284436i	−0.140516	−	0.990078i	$-0.544876\pi$
$919$	4.05665	−	0.862267i	0.133816	−	0.0284436i	0.274333	+	0.961635i	$0.411543\pi$
$920$	−2.84309	+	0.767280i	−0.0937339	+	0.0252965i
$921$	−1.62273	−	4.89876i	−0.0534707	−	0.161420i
$922$	−12.6829	+	14.0857i	−0.417688	+	0.463889i
$923$	1.05647	−	1.45410i	0.0347741	−	0.0478624i
$924$	−4.38444	−	21.1467i	−0.144238	−	0.695674i
$925$	22.1337	+	15.9599i	0.727753	+	0.524759i
$926$	42.3300	−	24.4392i	1.39105	−	0.803124i
$927$	−3.04458	+	32.5426i	−0.0999972	+	1.06884i
$928$	0.0848140	−	0.399018i	0.00278416	−	0.0130984i
$929$	31.9303	−	35.4622i	1.04760	−	1.16348i	0.0613666	−	0.998115i	$-0.480454\pi$
$929$	31.9303	−	35.4622i	1.04760	−	1.16348i	0.986233	−	0.165362i	$-0.0528792\pi$
$930$	1.72939	+	28.8495i	0.0567088	+	0.946011i
$931$	−6.89539	+	14.6347i	−0.225987	+	0.479634i
$932$	−22.4386			−0.735001
$933$	−10.4034	−	11.4222i	−0.340593	−	0.373945i
$934$	−38.5246	+	4.04910i	−1.26056	+	0.132491i
$935$	−38.9342	+	10.5074i	−1.27328	+	0.343628i
$936$	−1.96666	−	1.39478i	−0.0642823	−	0.0455900i
$937$	31.0827	−	22.5829i	1.01543	−	0.737750i	0.0500858	−	0.998745i	$-0.484051\pi$
$937$	31.0827	−	22.5829i	1.01543	−	0.737750i	0.965340	+	0.260995i	$0.0840505\pi$
$938$	37.0572	−	11.6030i	1.20996	−	0.378851i
$939$	0.700482	−	7.05227i	0.0228594	−	0.230142i
$940$	−56.6133	−	15.0605i	−1.84652	−	0.491221i
$941$	−0.995049	−	9.46726i	−0.0324377	−	0.308624i	−0.998696	−	0.0510494i	$-0.983743\pi$
$941$	−0.995049	−	9.46726i	−0.0324377	−	0.308624i	0.966258	−	0.257574i	$-0.0829232\pi$
$942$	19.2182	−	60.3189i	0.626164	−	1.96530i
$943$	7.65579	+	13.2602i	0.249307	+	0.431812i
$944$	−12.5038	+	38.4826i	−0.406963	+	1.25250i
$945$	7.71168	−	29.7579i	0.250861	−	0.968023i
$946$	−4.85558	−	14.9439i	−0.157868	−	0.485869i
$947$	15.1099	−	16.7813i	0.491007	−	0.545318i	−0.445815	−	0.895125i	$-0.647086\pi$
$947$	15.1099	−	16.7813i	0.491007	−	0.545318i	0.936822	+	0.349807i	$0.113753\pi$
$948$	−14.8544	−	10.6631i	−0.482447	−	0.346322i
$949$	0.714561	−	1.23766i	0.0231956	−	0.0401760i
$950$	2.35782	−	23.2359i	0.0764978	−	0.753871i
$951$	18.9513	+	32.3954i	0.614537	+	1.05049i
$952$	−3.60707	+	0.340072i	−0.116906	+	0.0110218i
$953$	17.4048	+	53.5665i	0.563797	+	1.73519i	0.671498	+	0.741007i	$0.265651\pi$
$953$	17.4048	+	53.5665i	0.563797	+	1.73519i	−0.107700	+	0.994183i	$0.534349\pi$
$954$	−8.66623	−	25.6694i	−0.280580	−	0.831078i
$955$	0.711776	+	2.63742i	0.0230325	+	0.0853450i
$956$	−47.6628	+	42.9158i	−1.54153	+	1.38800i
$957$	−0.0979726	+	0.171956i	−0.00316700	+	0.00555856i
$958$	−8.80207	+	27.0900i	−0.284382	+	0.875237i
$959$	7.90586	+	1.76922i	0.255294	+	0.0571310i
$960$	−12.2607	−	31.2367i	−0.395713	−	1.00816i
$961$	−1.81545	+	17.2729i	−0.0585631	+	0.557190i
$962$	51.3678	−	5.39898i	1.65617	−	0.174070i
$963$	3.86595	+	1.66853i	0.124578	+	0.0537675i
$964$	25.9396	+	2.72636i	0.835458	+	0.0878101i
$965$	−29.6903	+	4.75718i	−0.955766	+	0.153139i
$966$	−69.4404	−	15.1234i	−2.23421	−	0.486586i
$967$	25.0743	+	8.14713i	0.806335	+	0.261994i	0.683045	−	0.730377i	$-0.260655\pi$
$967$	25.0743	+	8.14713i	0.806335	+	0.261994i	0.123290	+	0.992371i	$0.460655\pi$
$968$	−0.505512	−	0.875573i	−0.0162478	−	0.0281420i
$969$	−9.69566	+	30.4311i	−0.311469	+	0.977587i
$970$	−12.8835	+	15.9683i	−0.413663	+	0.512712i
$971$	−23.3475	+	25.9300i	−0.749257	+	0.832134i	−0.990382	−	0.138360i	$-0.955817\pi$
$971$	−23.3475	+	25.9300i	−0.749257	+	0.832134i	0.241125	+	0.970494i	$0.422484\pi$
$972$	31.9706	+	5.84586i	1.02546	+	0.187506i
$973$	8.73173	+	12.2932i	0.279927	+	0.394101i
$974$			37.6840i			1.20747i
$975$	29.8825	−	27.4143i	0.957005	−	0.877961i
$976$	−15.6845	−	9.05544i	−0.502048	−	0.289858i
$977$	−43.2433	+	19.2532i	−1.38348	+	0.615963i	−0.957411	−	0.288729i	$-0.906767\pi$
$977$	−43.2433	+	19.2532i	−1.38348	+	0.615963i	−0.426065	+	0.904692i	$0.640101\pi$
$978$	−8.58142	+	41.5388i	−0.274404	+	1.32826i
$979$	30.5068	−	9.91225i	0.975000	−	0.316797i
$980$	32.1259	+	5.73714i	1.02622	+	0.183266i
$981$	−19.6350	−	21.3117i	−0.626897	−	0.680430i
$982$	−1.72036	+	0.993251i	−0.0548989	+	0.0316959i
$983$	16.1115	−	14.5069i	0.513879	−	0.462698i	−0.370925	−	0.928663i	$-0.620959\pi$
$983$	16.1115	−	14.5069i	0.513879	−	0.462698i	0.884803	+	0.465965i	$0.154293\pi$
$984$	0.477912	−	0.351415i	0.0152353	−	0.0112027i
$985$	−0.936699	−	0.605910i	−0.0298457	−	0.0193059i
$986$	0.659477	+	0.479138i	0.0210020	+	0.0152589i
$987$	−42.6000	−	38.7447i	−1.35597	−	1.23326i
$988$	−13.2622	−	18.2539i	−0.421928	−	0.580734i
$989$	−26.2465	−	2.75862i	−0.834591	−	0.0877191i
$990$	2.00869	+	30.5806i	0.0638403	+	0.971915i
$991$	−0.651406	−	6.19772i	−0.0206926	−	0.196877i	0.979292	−	0.202454i	$-0.0648916\pi$
$991$	−0.651406	−	6.19772i	−0.0206926	−	0.196877i	−0.999984	+	0.00557666i	$0.998225\pi$
$992$	6.19478	+	29.1442i	0.196685	+	0.925328i
$993$	1.15693	+	1.97766i	0.0367140	+	0.0627592i
$994$	−2.03888	−	0.236415i	−0.0646693	−	0.00749864i
$995$	36.8302	−	5.90118i	1.16760	−	0.187080i
$996$	−4.76287	+	23.0549i	−0.150917	+	0.730522i
$997$	23.1730	+	4.92558i	0.733897	+	0.155995i	0.559675	−	0.828712i	$-0.310926\pi$
$997$	23.1730	+	4.92558i	0.733897	+	0.155995i	0.174221	+	0.984707i	$0.444259\pi$
$998$	−5.63363	+	2.50825i	−0.178329	+	0.0793974i
$999$	−24.3122	+	14.5983i	−0.769203	+	0.461869i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bp.a.59.14	✓	608
3.2	odd	2	inner	525.2.bp.a.59.63	yes	608
7.5	odd	6	inner	525.2.bp.a.509.63	yes	608
21.5	even	6	inner	525.2.bp.a.509.14	yes	608
25.14	even	10	inner	525.2.bp.a.164.14	yes	608
75.14	odd	10	inner	525.2.bp.a.164.63	yes	608
175.89	odd	30	inner	525.2.bp.a.89.63	yes	608
525.89	even	30	inner	525.2.bp.a.89.14	yes	608

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bp.a.59.14	✓	608	1.1	even	1	trivial
525.2.bp.a.59.63	yes	608	3.2	odd	2	inner
525.2.bp.a.89.14	yes	608	525.89	even	30	inner
525.2.bp.a.89.63	yes	608	175.89	odd	30	inner
525.2.bp.a.164.14	yes	608	25.14	even	10	inner
525.2.bp.a.164.63	yes	608	75.14	odd	10	inner
525.2.bp.a.509.14	yes	608	21.5	even	6	inner
525.2.bp.a.509.63	yes	608	7.5	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bp (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.211264 + 2.01005i) q^{2} +(-0.544642 - 1.64419i) q^{3} +(-2.03936 - 0.433479i) q^{4} +(1.73522 - 1.41032i) q^{5} +(3.41996 - 0.747397i) q^{6} +(0.844505 - 2.50735i) q^{7} +(0.0530372 - 0.163232i) q^{8} +(-2.40673 + 1.79099i) q^{9} +O(q^{10})\)	\(q+(-0.211264 + 2.01005i) q^{2} +(-0.544642 - 1.64419i) q^{3} +(-2.03936 - 0.433479i) q^{4} +(1.73522 - 1.41032i) q^{5} +(3.41996 - 0.747397i) q^{6} +(0.844505 - 2.50735i) q^{7} +(0.0530372 - 0.163232i) q^{8} +(-2.40673 + 1.79099i) q^{9} +(2.46822 + 3.78582i) q^{10} +(-0.919382 - 2.06497i) q^{11} +(0.397999 + 3.58919i) q^{12} +(-3.78830 + 2.75236i) q^{13} +(4.86148 + 2.22721i) q^{14} +(-3.26391 - 2.08491i) q^{15} +(-3.49244 - 1.55493i) q^{16} +(5.92929 - 5.33876i) q^{17} +(-3.09152 - 5.21601i) q^{18} +(-0.480508 - 2.26061i) q^{19} +(-4.15008 + 2.12397i) q^{20} +(-4.58252 - 0.0229181i) q^{21} +(4.34491 - 1.41175i) q^{22} +(0.802062 - 7.63111i) q^{23} +(-0.297270 + 0.00169960i) q^{24} +(1.02198 - 4.89444i) q^{25} +(-4.73205 - 8.19615i) q^{26} +(4.25554 + 2.98167i) q^{27} +(-2.80913 + 4.74731i) q^{28} +(0.0480758 - 0.0156208i) q^{29} +(4.88032 - 6.12015i) q^{30} +(-2.74380 + 2.47053i) q^{31} +(4.03495 - 6.98874i) q^{32} +(-2.89446 + 2.63631i) q^{33} +(9.47851 + 13.0460i) q^{34} +(-2.07077 - 5.54183i) q^{35} +(5.68454 - 2.60921i) q^{36} +(-2.21979 + 4.98572i) q^{37} +(4.64545 - 0.488257i) q^{38} +(6.58868 + 4.72964i) q^{39} +(-0.138178 - 0.358042i) q^{40} +(-1.61437 + 1.17291i) q^{41} +(1.01419 - 9.20623i) q^{42} -3.43941i q^{43} +(0.979830 + 4.60974i) q^{44} +(-1.65033 + 6.50203i) q^{45} +(15.1694 + 3.22437i) q^{46} +(9.33825 + 8.40820i) q^{47} +(-0.654479 + 6.58912i) q^{48} +(-5.57362 - 4.23494i) q^{49} +(9.62215 + 3.08825i) q^{50} +(-12.0073 - 6.84118i) q^{51} +(8.91881 - 3.97091i) q^{52} +(4.37065 + 0.929010i) q^{53} +(-6.89235 + 7.92391i) q^{54} +(-4.50760 - 2.28655i) q^{55} +(-0.364489 - 0.270833i) q^{56} +(-3.45517 + 2.02127i) q^{57} +(0.0212418 + 0.0999348i) q^{58} +(-1.10635 - 10.5263i) q^{59} +(5.75253 + 5.66672i) q^{60} +(4.71146 + 0.495194i) q^{61} +(-4.38621 - 6.03710i) q^{62} +(2.45815 + 7.54702i) q^{63} +(7.00958 + 5.09276i) q^{64} +(-2.69182 + 10.1187i) q^{65} +(-4.68760 - 6.37496i) q^{66} +(5.39652 - 4.85905i) q^{67} +(-14.4062 + 8.31742i) q^{68} +(-12.9838 + 2.83748i) q^{69} +(11.5768 - 2.99156i) q^{70} +(-0.365054 + 0.118613i) q^{71} +(0.164700 + 0.487844i) q^{72} +(-0.278813 + 0.124135i) q^{73} +(-9.55257 - 5.51518i) q^{74} +(-8.60401 + 0.985388i) q^{75} +4.81849i q^{76} +(-5.95402 + 0.561340i) q^{77} +(-10.8988 + 12.2444i) q^{78} +(-3.38816 + 3.76294i) q^{79} +(-8.25311 + 2.22731i) q^{80} +(2.58469 - 8.62087i) q^{81} +(-2.01655 - 3.49276i) q^{82} +(6.20004 + 2.01452i) q^{83} +(9.33546 + 2.03316i) q^{84} +(2.75926 - 17.6261i) q^{85} +(6.91338 + 0.726625i) q^{86} +(-0.0518677 - 0.0705381i) q^{87} +(-0.385829 + 0.0405523i) q^{88} +(-1.48334 + 14.1131i) q^{89} +(-12.7207 - 4.69089i) q^{90} +(3.70190 + 11.8230i) q^{91} +(-4.94362 + 15.2149i) q^{92} +(5.55641 + 3.16578i) q^{93} +(-18.8737 + 16.9940i) q^{94} +(-4.02198 - 3.24499i) q^{95} +(-13.6884 - 2.82787i) q^{96} +(1.40292 + 4.31773i) q^{97} +(9.68994 - 10.3085i) q^{98} +(5.91104 + 3.32321i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9}+O(q^{10}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9	\( 608 q - 15 q^{3} + 66 q^{4} - 3 q^{9} - 30 q^{10} - 15 q^{12} - 36 q^{15} + 66 q^{16} - 18 q^{19} + 9 q^{21} - 80 q^{22} - 30 q^{24} + 2 q^{25} - 90 q^{28} - 23 q^{30} - 90 q^{33} + 44 q^{36} - 10 q^{37} - 19 q^{39} + 42 q^{40} - 70 q^{42} - 117 q^{45} - 54 q^{46} - 28 q^{49} - 8 q^{51} - 30 q^{52} - 21 q^{54} + 50 q^{58} - 67 q^{60} - 18 q^{61} - 70 q^{63} - 176 q^{64} + 57 q^{66} - 10 q^{67} + 42 q^{70} - 45 q^{72} - 150 q^{73} + 33 q^{75} + 10 q^{78} - 34 q^{79} + 49 q^{81} - 53 q^{84} - 8 q^{85} - 15 q^{87} + 80 q^{88} - 62 q^{91} + 30 q^{94} - 9 q^{96} + 36 q^{99}+O(q^{100}) \) 608 * q - 15 * q^3 + 66 * q^4 - 3 * q^9 - 30 * q^10 - 15 * q^12 - 36 * q^15 + 66 * q^16 - 18 * q^19 + 9 * q^21 - 80 * q^22 - 30 * q^24 + 2 * q^25 - 90 * q^28 - 23 * q^30 - 90 * q^33 + 44 * q^36 - 10 * q^37 - 19 * q^39 + 42 * q^40 - 70 * q^42 - 117 * q^45 - 54 * q^46 - 28 * q^49 - 8 * q^51 - 30 * q^52 - 21 * q^54 + 50 * q^58 - 67 * q^60 - 18 * q^61 - 70 * q^63 - 176 * q^64 + 57 * q^66 - 10 * q^67 + 42 * q^70 - 45 * q^72 - 150 * q^73 + 33 * q^75 + 10 * q^78 - 34 * q^79 + 49 * q^81 - 53 * q^84 - 8 * q^85 - 15 * q^87 + 80 * q^88 - 62 * q^91 + 30 * q^94 - 9 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

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