LMFDB - Embedded newform 224.2.be.a.3.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(3,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(24))

chi = DirichletCharacter(H, H._module([12, 9, 4]))

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

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

chi := DirichletCharacter("224.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.be (of order $24$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			3.13
Character	$\chi$	$=$	224.3
Dual form			224.2.be.a.75.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.210188 - 1.39851i) q^{2} +(-2.33910 + 1.79485i) q^{3} +(-1.91164 + 0.587899i) q^{4} +(-1.19071 - 0.913663i) q^{5} +(3.00177 + 2.89399i) q^{6} +(2.51525 - 0.820673i) q^{7} +(1.22399 + 2.54987i) q^{8} +(1.47343 - 5.49891i) q^{9} +O(q^{10})$	\(q+(-0.210188 - 1.39851i) q^{2} +(-2.33910 + 1.79485i) q^{3} +(-1.91164 + 0.587899i) q^{4} +(-1.19071 - 0.913663i) q^{5} +(3.00177 + 2.89399i) q^{6} +(2.51525 - 0.820673i) q^{7} +(1.22399 + 2.54987i) q^{8} +(1.47343 - 5.49891i) q^{9} +(-1.02749 + 1.85726i) q^{10} +(4.90123 + 0.645259i) q^{11} +(3.41633 - 4.80627i) q^{12} +(-1.27169 - 0.526752i) q^{13} +(-1.67639 - 3.34510i) q^{14} +4.42508 q^{15} +(3.30875 - 2.24771i) q^{16} +(1.74895 - 3.02927i) q^{17} +(-7.99996 - 0.904794i) q^{18} +(0.841939 - 0.110843i) q^{19} +(2.81335 + 1.04658i) q^{20} +(-4.41044 + 6.43415i) q^{21} +(-0.127781 - 6.99003i) q^{22} +(5.24348 + 1.40498i) q^{23} +(-7.43968 - 3.76754i) q^{24} +(-0.711087 - 2.65381i) q^{25} +(-0.469371 + 1.88918i) q^{26} +(3.03837 + 7.33528i) q^{27} +(-4.32579 + 3.04755i) q^{28} +(5.11353 + 2.11809i) q^{29} +(-0.930100 - 6.18851i) q^{30} +(-3.42344 + 5.92957i) q^{31} +(-3.83889 - 4.15487i) q^{32} +(-12.6226 + 7.28767i) q^{33} +(-4.60407 - 1.80920i) q^{34} +(-3.74475 - 1.32091i) q^{35} +(0.416137 + 11.3782i) q^{36} +(-4.56522 + 5.94951i) q^{37} +(-0.331981 - 1.15416i) q^{38} +(3.92005 - 1.05038i) q^{39} +(0.872316 - 4.15447i) q^{40} +(8.83893 - 8.83893i) q^{41} +(9.92522 + 4.81565i) q^{42} +(-1.03800 - 2.50595i) q^{43} +(-9.74875 + 1.64793i) q^{44} +(-6.77858 + 5.20139i) q^{45} +(0.862764 - 7.62835i) q^{46} +(-1.90815 + 1.10167i) q^{47} +(-3.70519 + 11.1963i) q^{48} +(5.65299 - 4.12840i) q^{49} +(-3.56191 + 1.55226i) q^{50} +(1.34613 + 10.2249i) q^{51} +(2.74069 + 0.259334i) q^{52} +(0.942862 - 7.16175i) q^{53} +(9.61981 - 5.79097i) q^{54} +(-5.24639 - 5.24639i) q^{55} +(5.17125 + 5.40909i) q^{56} +(-1.77043 + 1.77043i) q^{57} +(1.88736 - 7.59650i) q^{58} +(6.33282 + 0.833732i) q^{59} +(-8.45917 + 2.60150i) q^{60} +(2.38043 - 0.313389i) q^{61} +(9.01211 + 3.54138i) q^{62} +(-0.806763 - 15.0404i) q^{63} +(-5.00372 + 6.24202i) q^{64} +(1.03294 + 1.78911i) q^{65} +(12.8450 + 16.1210i) q^{66} +(-6.91866 - 9.01657i) q^{67} +(-1.56246 + 6.81909i) q^{68} +(-14.7868 + 6.12488i) q^{69} +(-1.06020 + 5.51470i) q^{70} +(-2.31844 - 2.31844i) q^{71} +(15.8250 - 2.97353i) q^{72} +(3.20298 + 11.9537i) q^{73} +(9.27998 + 5.13397i) q^{74} +(6.42651 + 4.93124i) q^{75} +(-1.54432 + 0.706868i) q^{76} +(12.8574 - 2.39932i) q^{77} +(-2.29291 - 5.26145i) q^{78} +(2.08038 + 3.60332i) q^{79} +(-5.99341 - 0.346719i) q^{80} +(-5.48225 - 3.16518i) q^{81} +(-14.2191 - 10.5035i) q^{82} +(2.34140 - 5.65265i) q^{83} +(4.64855 - 14.8927i) q^{84} +(-4.85023 + 2.00903i) q^{85} +(-3.28641 + 1.97837i) q^{86} +(-15.7627 + 4.22361i) q^{87} +(4.35371 + 13.2873i) q^{88} +(-1.20130 + 4.48330i) q^{89} +(8.69896 + 8.38662i) q^{90} +(-3.63091 - 0.281271i) q^{91} +(-10.8496 + 0.396807i) q^{92} +(-2.63495 - 20.0144i) q^{93} +(1.94176 + 2.43700i) q^{94} +(-1.10378 - 0.637267i) q^{95} +(16.4369 + 2.82840i) q^{96} -0.343262i q^{97} +(-6.96179 - 7.03801i) q^{98} +(10.7698 - 26.0007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	$ 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.210188	−	1.39851i	−0.148626	−	0.988894i
$2$	−0.210188	−	1.39851i	−0.148626	−	0.988894i
$3$	−2.33910	+	1.79485i	−1.35048	+	1.03626i	−0.355659	+	0.934616i	$0.615744\pi$
$3$	−2.33910	+	1.79485i	−1.35048	+	1.03626i	−0.994821	+	0.101644i	$0.967590\pi$
$4$	−1.91164	+	0.587899i	−0.955821	+	0.293950i
$5$	−1.19071	−	0.913663i	−0.532501	−	0.408603i	0.307205	−	0.951643i	$-0.400606\pi$
$5$	−1.19071	−	0.913663i	−0.532501	−	0.408603i	−0.839706	+	0.543041i	$0.817273\pi$
$6$	3.00177	+	2.89399i	1.22547	+	1.18147i
$7$	2.51525	−	0.820673i	0.950676	−	0.310185i
$7$	2.51525	−	0.820673i	0.950676	−	0.310185i
$8$	1.22399	+	2.54987i	0.432744	+	0.901517i
$9$	1.47343	−	5.49891i	0.491143	−	1.83297i
$10$	−1.02749	+	1.85726i	−0.324921	+	0.587316i
$11$	4.90123	+	0.645259i	1.47778	+	0.194553i	0.825919	−	0.563788i	$-0.190657\pi$
$11$	4.90123	+	0.645259i	1.47778	+	0.194553i	0.651858	+	0.758341i	$0.273990\pi$
$12$	3.41633	−	4.80627i	0.986209	−	1.38745i
$13$	−1.27169	−	0.526752i	−0.352704	−	0.146095i	0.199295	−	0.979939i	$-0.436135\pi$
$13$	−1.27169	−	0.526752i	−0.352704	−	0.146095i	−0.551999	+	0.833845i	$0.686135\pi$
$14$	−1.67639	−	3.34510i	−0.448035	−	0.894016i
$15$	4.42508			1.14255
$16$	3.30875	−	2.24771i	0.827187	−	0.561926i
$17$	1.74895	−	3.02927i	0.424183	−	0.734706i	−0.572161	−	0.820141i	$-0.693895\pi$
$17$	1.74895	−	3.02927i	0.424183	−	0.734706i	0.996344	+	0.0854350i	$0.0272280\pi$
$18$	−7.99996	−	0.904794i	−1.88561	−	0.213262i
$19$	0.841939	−	0.110843i	0.193154	−	0.0254292i	−0.0333284	−	0.999444i	$-0.510611\pi$
$19$	0.841939	−	0.110843i	0.193154	−	0.0254292i	0.226482	+	0.974015i	$0.427277\pi$
$20$	2.81335	+	1.04658i	0.629085	+	0.234022i
$21$	−4.41044	+	6.43415i	−0.962437	+	1.40405i
$22$	−0.127781	−	6.99003i	−0.0272431	−	1.49028i
$23$	5.24348	+	1.40498i	1.09334	+	0.292960i	0.760050	−	0.649865i	$-0.225174\pi$
$23$	5.24348	+	1.40498i	1.09334	+	0.292960i	0.333290	+	0.942824i	$0.391841\pi$
$24$	−7.43968	−	3.76754i	−1.51862	−	0.769045i
$25$	−0.711087	−	2.65381i	−0.142217	−	0.530763i
$26$	−0.469371	+	1.88918i	−0.0920513	+	0.370500i
$27$	3.03837	+	7.33528i	0.584735	+	1.41168i
$28$	−4.32579	+	3.04755i	−0.817497	+	0.575932i
$29$	5.11353	+	2.11809i	0.949558	+	0.393320i	0.803065	−	0.595892i	$-0.203201\pi$
$29$	5.11353	+	2.11809i	0.949558	+	0.393320i	0.146494	+	0.989212i	$0.453201\pi$
$30$	−0.930100	−	6.18851i	−0.169812	−	1.12986i
$31$	−3.42344	+	5.92957i	−0.614868	+	1.06498i	0.375540	+	0.926806i	$0.377457\pi$
$31$	−3.42344	+	5.92957i	−0.614868	+	1.06498i	−0.990408	+	0.138176i	$0.955876\pi$
$32$	−3.83889	−	4.15487i	−0.678626	−	0.734484i
$33$	−12.6226	+	7.28767i	−2.19732	+	1.26862i
$34$	−4.60407	−	1.80920i	−0.789591	−	0.310276i
$35$	−3.74475	−	1.32091i	−0.632979	−	0.223275i
$36$	0.416137	+	11.3782i	0.0693562	+	1.89636i
$37$	−4.56522	+	5.94951i	−0.750517	+	0.978093i	0.249436	+	0.968391i	$0.419755\pi$
$37$	−4.56522	+	5.94951i	−0.750517	+	0.978093i	−0.999953	+	0.00970167i	$0.996912\pi$
$38$	−0.331981	−	1.15416i	−0.0538544	−	0.187229i
$39$	3.92005	−	1.05038i	0.627711	−	0.168195i
$40$	0.872316	−	4.15447i	0.137925	−	0.656879i
$41$	8.83893	−	8.83893i	1.38041	−	1.38041i	0.536522	−	0.843886i	$-0.319738\pi$
$41$	8.83893	−	8.83893i	1.38041	−	1.38041i	0.843886	−	0.536522i	$-0.180262\pi$
$42$	9.92522	+	4.81565i	1.53150	+	0.743070i
$43$	−1.03800	−	2.50595i	−0.158293	−	0.382153i	0.824758	−	0.565486i	$-0.191311\pi$
$43$	−1.03800	−	2.50595i	−0.158293	−	0.382153i	−0.983051	+	0.183333i	$0.941311\pi$
$44$	−9.74875	+	1.64793i	−1.46968	+	0.248434i
$45$	−6.77858	+	5.20139i	−1.01049	+	0.775377i
$46$	0.862764	−	7.62835i	0.127208	−	1.12474i
$47$	−1.90815	+	1.10167i	−0.278332	+	0.160695i	−0.632668	−	0.774423i	$-0.718040\pi$
$47$	−1.90815	+	1.10167i	−0.278332	+	0.160695i	0.354336	+	0.935118i	$0.384707\pi$
$48$	−3.70519	+	11.1963i	−0.534798	+	1.61605i
$49$	5.65299	−	4.12840i	0.807570	−	0.589771i
$50$	−3.56191	+	1.55226i	−0.503731	+	0.219523i
$51$	1.34613	+	10.2249i	0.188496	+	1.43177i
$52$	2.74069	+	0.259334i	0.380066	+	0.0359632i
$53$	0.942862	−	7.16175i	0.129512	−	0.983742i	−0.796073	−	0.605201i	$-0.793093\pi$
$53$	0.942862	−	7.16175i	0.129512	−	0.983742i	0.925585	−	0.378541i	$-0.123574\pi$
$54$	9.61981	−	5.79097i	1.30909	−	0.788052i
$55$	−5.24639	−	5.24639i	−0.707423	−	0.707423i
$56$	5.17125	+	5.40909i	0.691037	+	0.722820i
$57$	−1.77043	+	1.77043i	−0.234499	+	0.234499i
$58$	1.88736	−	7.59650i	0.247823	−	0.997470i
$59$	6.33282	+	0.833732i	0.824463	+	0.108543i	0.530940	−	0.847409i	$-0.321839\pi$
$59$	6.33282	+	0.833732i	0.824463	+	0.108543i	0.293523	+	0.955952i	$0.405172\pi$
$60$	−8.45917	+	2.60150i	−1.09207	+	0.335852i
$61$	2.38043	−	0.313389i	0.304783	−	0.0401254i	0.0234162	−	0.999726i	$-0.492546\pi$
$61$	2.38043	−	0.313389i	0.304783	−	0.0401254i	0.281366	+	0.959600i	$0.409212\pi$
$62$	9.01211	+	3.54138i	1.14454	+	0.449755i
$63$	−0.806763	−	15.0404i	−0.101643	−	1.89491i
$64$	−5.00372	+	6.24202i	−0.625465	+	0.780252i
$65$	1.03294	+	1.78911i	0.128120	+	0.221911i
$66$	12.8450	+	16.1210i	1.58111	+	1.98436i
$67$	−6.91866	−	9.01657i	−0.845249	−	1.10155i	−0.993638	−	0.112621i	$-0.964075\pi$
$67$	−6.91866	−	9.01657i	−0.845249	−	1.10155i	0.148389	−	0.988929i	$-0.452591\pi$
$68$	−1.56246	+	6.81909i	−0.189476	+	0.826936i
$69$	−14.7868	+	6.12488i	−1.78012	+	0.737348i
$70$	−1.06020	+	5.51470i	−0.126718	+	0.659133i
$71$	−2.31844	−	2.31844i	−0.275148	−	0.275148i	0.556020	−	0.831169i	$-0.312328\pi$
$71$	−2.31844	−	2.31844i	−0.275148	−	0.275148i	−0.831169	+	0.556020i	$0.812328\pi$
$72$	15.8250	−	2.97353i	1.86499	−	0.350434i
$73$	3.20298	+	11.9537i	0.374880	+	1.39907i	0.853520	+	0.521060i	$0.174463\pi$
$73$	3.20298	+	11.9537i	0.374880	+	1.39907i	−0.478640	+	0.878011i	$0.658870\pi$
$74$	9.27998	+	5.13397i	1.07878	+	0.596812i
$75$	6.42651	+	4.93124i	0.742070	+	0.569410i
$76$	−1.54432	+	0.706868i	−0.177146	+	0.0810833i
$77$	12.8574	−	2.39932i	1.46523	−	0.273428i
$78$	−2.29291	−	5.26145i	−0.259621	−	0.595741i
$79$	2.08038	+	3.60332i	0.234061	+	0.405405i	0.958999	−	0.283408i	$-0.0914652\pi$
$79$	2.08038	+	3.60332i	0.234061	+	0.405405i	−0.724939	+	0.688814i	$0.758132\pi$
$80$	−5.99341	−	0.346719i	−0.670083	−	0.0387644i
$81$	−5.48225	−	3.16518i	−0.609139	−	0.351687i
$82$	−14.2191	−	10.5035i	−1.57024	−	1.15991i
$83$	2.34140	−	5.65265i	0.257003	−	0.620459i	−0.741735	−	0.670693i	$-0.765997\pi$
$83$	2.34140	−	5.65265i	0.257003	−	0.620459i	0.998737	+	0.0502341i	$0.0159967\pi$
$84$	4.64855	−	14.8927i	0.507198	−	1.62492i
$85$	−4.85023	+	2.00903i	−0.526081	+	0.217910i
$86$	−3.28641	+	1.97837i	−0.354382	+	0.213333i
$87$	−15.7627	+	4.22361i	−1.68994	+	0.452818i
$88$	4.35371	+	13.2873i	0.464107	+	1.41643i
$89$	−1.20130	+	4.48330i	−0.127337	+	0.475229i	−0.999912	−	0.0132514i	$-0.995782\pi$
$89$	−1.20130	+	4.48330i	−0.127337	+	0.475229i	0.872575	+	0.488480i	$0.162448\pi$
$90$	8.69896	+	8.38662i	0.916950	+	0.884028i
$91$	−3.63091	−	0.281271i	−0.380623	−	0.0294852i
$92$	−10.8496	+	0.396807i	−1.13115	+	0.0413700i
$93$	−2.63495	−	20.0144i	−0.273232	−	2.07540i
$94$	1.94176	+	2.43700i	0.200277	+	0.251357i
$95$	−1.10378	−	0.637267i	−0.113245	−	0.0653822i
$96$	16.4369	+	2.82840i	1.67759	+	0.288672i
$97$		−	0.343262i		−	0.0348530i	−0.999848	−	0.0174265i	$-0.994453\pi$
$97$		−	0.343262i		−	0.0348530i	0.999848	−	0.0174265i	$-0.00554730\pi$
$98$	−6.96179	−	7.03801i	−0.703247	−	0.710946i
$99$	10.7698	−	26.0007i	1.08241	−	2.61317i
$100$	2.91952	+	4.65509i	0.291952	+	0.465509i
$101$	0.989594	−	7.51671i	0.0984683	−	0.747941i	−0.868976	−	0.494855i	$-0.835221\pi$
$101$	0.989594	−	7.51671i	0.0984683	−	0.747941i	0.967444	−	0.253086i	$-0.0814455\pi$
$102$	14.0166	−	4.03172i	1.38785	−	0.399200i
$103$	−5.15713	−	1.38185i	−0.508147	−	0.136158i	−0.00436844	−	0.999990i	$-0.501391\pi$
$103$	−5.15713	−	1.38185i	−0.508147	−	0.136158i	−0.503778	+	0.863833i	$0.668057\pi$
$104$	−0.213381	−	3.88739i	−0.0209237	−	0.381190i
$105$	11.1302	−	3.63155i	1.08620	−	0.354403i
$106$	−10.2139	+	0.186716i	−0.992065	+	0.0181355i
$107$	−9.65099	+	12.5774i	−0.932997	+	1.21590i	0.0432108	+	0.999066i	$0.486241\pi$
$107$	−9.65099	+	12.5774i	−0.932997	+	1.21590i	−0.976207	+	0.216839i	$0.930425\pi$
$108$	−10.1207	−	12.2362i	−0.973864	−	1.17743i
$109$	−9.72865	−	12.6786i	−0.931836	−	1.21439i	−0.976528	−	0.215392i	$-0.930897\pi$
$109$	−9.72865	−	12.6786i	−0.931836	−	1.21439i	0.0446917	−	0.999001i	$-0.485769\pi$
$110$	−6.23439	+	8.43985i	−0.594425	+	0.804708i
$111$		−	22.1104i		−	2.09863i
$112$	6.47771	−	8.36895i	0.612086	−	0.790791i
$113$			0.324670i			0.0305424i	0.999883	+	0.0152712i	$0.00486116\pi$
$113$			0.324670i			0.0305424i	−0.999883	+	0.0152712i	$0.995139\pi$
$114$	2.84808	+	2.10384i	0.266748	+	0.197042i
$115$	−4.95977	−	6.46370i	−0.462501	−	0.602743i
$116$	−11.0205	−	1.04280i	−1.02322	−	0.0968211i
$117$	−4.77031	+	6.21679i	−0.441015	+	0.574742i
$118$	−0.165105	−	9.03173i	−0.0151991	−	0.831438i
$119$	1.91301	−	9.05470i	0.175366	−	0.830043i
$120$	5.41624	+	11.2834i	0.494432	+	1.03003i
$121$	12.9805	+	3.47812i	1.18005	+	0.316193i
$122$	−0.938615	−	3.26317i	−0.0849782	−	0.295434i
$123$	−4.81055	+	36.5397i	−0.433752	+	3.29468i
$124$	3.05840	−	13.3478i	0.274652	−	1.19867i
$125$	−4.44976	+	10.7427i	−0.397999	+	0.960853i
$126$	−20.8645	+	4.28957i	−1.85875	+	0.382145i
$127$			9.53682i			0.846256i	0.906070	+	0.423128i	$0.139068\pi$
$127$			9.53682i			0.846256i	−0.906070	+	0.423128i	$0.860932\pi$
$128$	9.78123	+	5.68574i	0.864547	+	0.502553i
$129$	6.92579	+	3.99861i	0.609782	+	0.352058i
$130$	2.28496	−	1.82062i	0.200405	−	0.159679i
$131$	1.56922	+	11.9194i	0.137104	+	1.04141i	0.912253	+	0.409628i	$0.134342\pi$
$131$	1.56922	+	11.9194i	0.137104	+	1.04141i	−0.775149	+	0.631779i	$0.782325\pi$
$132$	19.8455	−	21.3522i	1.72733	−	1.85847i
$133$	2.02672	−	0.969756i	0.175739	−	0.0840885i
$134$	−11.1555	+	11.5710i	−0.963690	+	0.999580i
$135$	3.08416	−	11.5102i	0.265442	−	0.990644i
$136$	9.86495	+	0.751820i	0.845913	+	0.0644681i
$137$	−12.3233	+	3.30202i	−1.05285	+	0.282110i	−0.743429	−	0.668815i	$-0.766802\pi$
$137$	−12.3233	+	3.30202i	−1.05285	+	0.282110i	−0.309421	+	0.950925i	$0.600135\pi$
$138$	11.6737	+	19.3920i	0.993730	+	1.65076i
$139$	14.9948	−	6.21105i	1.27184	−	0.526815i	0.358319	−	0.933599i	$-0.383350\pi$
$139$	14.9948	−	6.21105i	1.27184	−	0.526815i	0.913524	+	0.406784i	$0.133350\pi$
$140$	7.93519	+	0.323571i	0.670646	+	0.0273468i
$141$	2.48601	−	6.00176i	0.209360	−	0.505439i
$142$	−2.75504	+	3.72966i	−0.231198	+	0.312986i
$143$	−5.89296	−	3.40230i	−0.492794	−	0.284515i
$144$	−7.48473	−	21.5064i	−0.623727	−	1.79220i
$145$	−4.15350	−	7.19408i	−0.344930	−	0.597436i
$146$	16.0441	−	6.99190i	1.32782	−	0.578654i
$147$	−5.81304	+	19.8030i	−0.479451	+	1.63333i
$148$	5.22935	−	14.0572i	0.429850	−	1.15550i
$149$	5.70869	+	4.38043i	0.467674	+	0.358859i	0.815555	−	0.578680i	$-0.196432\pi$
$149$	5.70869	+	4.38043i	0.467674	+	0.358859i	−0.347881	+	0.937539i	$0.613099\pi$
$150$	5.54559	−	10.0240i	0.452796	−	0.818457i
$151$	4.70797	+	17.5704i	0.383129	+	1.42986i	0.841095	+	0.540888i	$0.181912\pi$
$151$	4.70797	+	17.5704i	0.383129	+	1.42986i	−0.457965	+	0.888970i	$0.651422\pi$
$152$	1.31316	+	2.01117i	0.106511	+	0.163127i
$153$	−14.0807	−	14.0807i	−1.13836	−	1.13836i
$154$	−6.05793	−	17.4768i	−0.488162	−	1.40832i
$155$	9.49395	−	3.93252i	0.762572	−	0.315868i
$156$	−6.87623	+	4.31254i	−0.550539	+	0.345279i
$157$	−3.45587	−	4.50378i	−0.275808	−	0.359441i	0.634825	−	0.772656i	$-0.281072\pi$
$157$	−3.45587	−	4.50378i	−0.275808	−	0.359441i	−0.910633	+	0.413216i	$0.864406\pi$
$158$	4.60200	−	3.66680i	0.366115	−	0.291715i
$159$	10.6489	+	18.4443i	0.844509	+	1.46273i
$160$	0.774854	+	8.45469i	0.0612576	+	0.668402i
$161$	14.3417	−	0.769287i	1.13028	−	0.0606283i
$162$	−3.27422	+	8.33225i	−0.257247	+	0.654643i
$163$	5.77392	−	0.760151i	0.452248	−	0.0595396i	0.0990382	−	0.995084i	$-0.468423\pi$
$163$	5.77392	−	0.760151i	0.452248	−	0.0595396i	0.353210	+	0.935544i	$0.385090\pi$
$164$	−11.7005	+	22.0933i	−0.913653	+	1.72519i
$165$	21.6884	+	2.85533i	1.68844	+	0.222287i
$166$	−8.39741	−	2.08635i	−0.651765	−	0.161932i
$167$	−15.2297	+	15.2297i	−1.17851	+	1.17851i	−0.198381	+	0.980125i	$0.563568\pi$
$167$	−15.2297	+	15.2297i	−1.17851	+	1.17851i	−0.980125	+	0.198381i	$0.936432\pi$
$168$	−21.8046	−	3.37076i	−1.68226	−	0.260060i
$169$	−7.85266	−	7.85266i	−0.604051	−	0.604051i
$170$	3.82910	+	6.36080i	0.293679	+	0.487851i
$171$	0.631020	−	4.79307i	0.0482553	−	0.366535i
$172$	3.45752	+	4.18023i	0.263634	+	0.318740i
$173$	−1.45212	−	11.0299i	−0.110403	−	0.838591i	−0.953619	−	0.301017i	$-0.902674\pi$
$173$	−1.45212	−	11.0299i	−0.110403	−	0.838591i	0.843216	−	0.537575i	$-0.180659\pi$
$174$	9.21988	+	21.1565i	0.698958	+	1.60387i
$175$	−3.96648	−	6.09144i	−0.299838	−	0.460470i
$176$	17.6673	−	8.88152i	1.33172	−	0.669470i
$177$	−16.3095	+	9.41631i	−1.22590	+	0.707773i
$178$	6.52242	+	0.737684i	0.488876	+	0.0552918i
$179$	1.51202	−	1.16021i	0.113014	−	0.0867184i	−0.550709	−	0.834698i	$-0.685642\pi$
$179$	1.51202	−	1.16021i	0.113014	−	0.0867184i	0.663722	+	0.747979i	$0.268976\pi$
$180$	9.90033	−	13.9283i	0.737927	−	1.03816i
$181$	5.95379	+	14.3737i	0.442542	+	1.06839i	0.975054	+	0.221968i	$0.0712481\pi$
$181$	5.95379	+	14.3737i	0.442542	+	1.06839i	−0.532512	+	0.846422i	$0.678752\pi$
$182$	0.369816	+	5.13698i	0.0274126	+	0.380778i
$183$	−5.00557	+	5.00557i	−0.370023	+	0.370023i
$184$	2.83540	+	15.0899i	0.209029	+	1.11244i
$185$	10.8717	−	2.91306i	0.799303	−	0.214173i
$186$	−27.4365	+	7.89179i	−2.01174	+	0.578654i
$187$	10.5267	−	13.7186i	0.769787	−	1.00321i
$188$	3.00002	−	3.22779i	0.218799	−	0.235411i
$189$	13.6621	+	15.9566i	0.993775	+	1.16067i
$190$	−0.659221	+	1.67759i	−0.0478249	+	0.121705i
$191$	−10.0366	+	5.79461i	−0.726221	+	0.419284i	−0.817038	−	0.576584i	$-0.804385\pi$
$191$	−10.0366	+	5.79461i	−0.726221	+	0.419284i	0.0908174	+	0.995868i	$0.471052\pi$
$192$	0.500684	−	23.5817i	0.0361337	−	1.70186i
$193$	−0.848395	+	1.46946i	−0.0610688	+	0.105774i	−0.894943	−	0.446180i	$-0.852784\pi$
$193$	−0.848395	+	1.46946i	−0.0610688	+	0.105774i	0.833875	+	0.551954i	$0.186118\pi$
$194$	−0.480054	+	0.0721496i	−0.0344659	+	0.00518004i
$195$	−5.62734	−	2.33092i	−0.402982	−	0.166921i
$196$	−8.37941	+	11.2154i	−0.598529	+	0.801101i
$197$	4.94415	+	11.9362i	0.352256	+	0.850422i	0.996341	+	0.0854679i	$0.0272385\pi$
$197$	4.94415	+	11.9362i	0.352256	+	0.850422i	−0.644084	+	0.764954i	$0.722761\pi$
$198$	−38.6259	−	9.59666i	−2.74502	−	0.682005i
$199$	−6.43001	−	23.9971i	−0.455812	−	1.70111i	−0.685691	−	0.727893i	$-0.740500\pi$
$199$	−6.43001	−	23.9971i	−0.455812	−	1.70111i	0.229880	−	0.973219i	$-0.426167\pi$
$200$	5.89653	−	5.06141i	0.416948	−	0.357896i
$201$	32.3669	+	8.67268i	2.28298	+	0.611724i
$202$	−10.7202	+	0.195970i	−0.754269	+	0.0137884i
$203$	14.6001	+	1.13100i	1.02472	+	0.0793809i
$204$	−8.58452	−	18.7549i	−0.601037	−	1.31311i
$205$	−18.6004	+	2.44879i	−1.29911	+	0.171031i
$206$	−0.848556	+	7.50273i	−0.0591217	+	0.522740i
$207$	15.4518	−	26.7633i	1.07397	−	1.86018i
$208$	−5.39169	+	1.11550i	−0.373846	+	0.0773458i
$209$	4.19806			0.290386
$210$	−7.41818	−	14.8023i	−0.511903	−	1.02146i
$211$	−3.91303	−	1.62083i	−0.269384	−	0.111582i	0.243903	−	0.969800i	$-0.421572\pi$
$211$	−3.91303	−	1.62083i	−0.269384	−	0.111582i	−0.513287	+	0.858217i	$0.671572\pi$
$212$	2.40797	+	14.2450i	0.165380	+	0.978351i
$213$	9.58432	+	1.26180i	0.656707	+	0.0864571i
$214$	19.6181	+	10.8534i	1.34107	+	0.741920i
$215$	−1.05364	+	3.93223i	−0.0718576	+	0.268176i
$216$	−14.9851	+	16.7257i	−1.01961	+	1.13804i
$217$	−3.74457	+	17.7239i	−0.254198	+	1.20318i
$218$	−15.6863	+	16.2705i	−1.06241	+	1.10198i
$219$	−28.9472	−	22.2120i	−1.95607	−	1.50094i
$220$	13.1136	+	6.94487i	0.884117	+	0.468223i
$221$	−3.81980	+	2.93103i	−0.256947	+	0.197163i
$222$	−30.9215	+	4.64734i	−2.07532	+	0.311909i
$223$	−0.286013			−0.0191529			−0.00957644	−	0.999954i	$-0.503048\pi$
$223$	−0.286013			−0.0191529			−0.00957644	+	0.999954i	$0.503048\pi$
$224$	−13.0656	−	7.30006i	−0.872980	−	0.487756i
$225$	−15.6408			−1.04272
$226$	0.454053	−	0.0682418i	0.0302032	−	0.00453938i
$227$	−1.20688	+	0.926070i	−0.0801033	+	0.0614654i	−0.648037	−	0.761609i	$-0.724410\pi$
$227$	−1.20688	+	0.926070i	−0.0801033	+	0.0614654i	0.567934	+	0.823074i	$0.307743\pi$
$228$	2.34360	−	4.42527i	0.155208	−	0.293070i
$229$	−3.34087	−	2.56354i	−0.220771	−	0.169404i	0.492454	−	0.870338i	$-0.336100\pi$
$229$	−3.34087	−	2.56354i	−0.220771	−	0.169404i	−0.713226	+	0.700935i	$0.752766\pi$
$230$	−7.99704	+	8.29487i	−0.527309	+	0.546947i
$231$	−25.7683	+	28.6894i	−1.69543	+	1.88762i
$232$	0.858014	+	15.6314i	0.0563314	+	1.02625i
$233$	4.96509	−	18.5300i	0.325274	−	1.21394i	−0.588763	−	0.808306i	$-0.700385\pi$
$233$	4.96509	−	18.5300i	0.325274	−	1.21394i	0.914036	−	0.405632i	$-0.132949\pi$
$234$	9.69688	+	5.36461i	0.633905	+	0.350696i
$235$	3.27860	+	0.431636i	0.213872	+	0.0281568i
$236$	−12.5962	+	2.12926i	−0.819945	+	0.138603i
$237$	−11.3336	−	4.69455i	−0.736200	−	0.304944i
$238$	−13.0652	−	0.772168i	−0.846888	−	0.0500522i
$239$	3.86638			0.250096			0.125048	−	0.992151i	$-0.460092\pi$
$239$	3.86638			0.250096			0.125048	+	0.992151i	$0.460092\pi$
$240$	14.6415	−	9.94628i	0.945104	−	0.642030i
$241$	−3.41543	+	5.91569i	−0.220007	+	0.381063i	−0.954810	−	0.297218i	$-0.903941\pi$
$241$	−3.41543	+	5.91569i	−0.220007	+	0.381063i	0.734803	+	0.678281i	$0.237275\pi$
$242$	2.13582	−	18.8844i	0.137296	−	1.21394i
$243$	−5.11061	+	0.672824i	−0.327846	+	0.0431617i
$244$	−4.36629	+	1.99854i	−0.279523	+	0.127943i
$245$	−10.5030	−	0.249207i	−0.671015	−	0.0159212i
$246$	52.1122	−	0.952638i	3.32255	−	0.0607380i
$247$	−1.12907	−	0.302534i	−0.0718412	−	0.0192498i
$248$	−19.3099	−	1.47163i	−1.22618	−	0.0934487i
$249$	4.66891	+	17.4246i	0.295880	+	1.10424i
$250$	15.9590	+	3.96504i	1.00933	+	0.250771i
$251$	−3.29723	−	7.96021i	−0.208119	−	0.502444i	0.785008	−	0.619486i	$-0.212659\pi$
$251$	−3.29723	−	7.96021i	−0.208119	−	0.502444i	−0.993127	+	0.117042i	$0.962659\pi$
$252$	10.3845	+	28.2775i	0.654159	+	1.78131i
$253$	24.7929	+	10.2696i	1.55872	+	0.645642i
$254$	13.3373	−	2.00453i	0.836857	−	0.125775i
$255$	7.73925	−	13.4048i	0.484651	−	0.839440i
$256$	5.89564	−	14.8742i	0.368478	−	0.929637i
$257$	2.71789	−	1.56917i	0.169537	−	0.0978824i	−0.412830	−	0.910808i	$-0.635460\pi$
$257$	2.71789	−	1.56917i	0.169537	−	0.0978824i	0.582368	+	0.812926i	$0.302126\pi$
$258$	4.13636	−	10.5262i	0.257518	−	0.655334i
$259$	−6.60008	+	18.7111i	−0.410109	+	1.16265i
$260$	−3.02643	−	2.81286i	−0.187691	−	0.174446i
$261$	19.1816	−	24.9980i	1.18731	−	1.54734i
$262$	16.3396	−	4.69990i	1.00946	−	0.290361i
$263$	−27.4701	+	7.36058i	−1.69388	+	0.453873i	−0.971386	−	0.237507i	$-0.923670\pi$
$263$	−27.4701	+	7.36058i	−1.69388	+	0.453873i	−0.722491	+	0.691380i	$0.757003\pi$
$264$	−34.0326	−	23.2661i	−2.09456	−	1.43193i
$265$	−7.66610	+	7.66610i	−0.470925	+	0.470925i
$266$	−1.78220	−	2.63055i	−0.109274	−	0.161290i
$267$	−5.23692	−	12.6430i	−0.320494	−	0.773741i
$268$	18.5268	+	13.1690i	1.13171	+	0.804424i
$269$	−8.01541	+	6.15044i	−0.488708	+	0.374999i	−0.823521	−	0.567286i	$-0.807993\pi$
$269$	−8.01541	+	6.15044i	−0.488708	+	0.374999i	0.334813	+	0.942285i	$0.391327\pi$
$270$	−16.7454	−	1.89390i	−1.01909	−	0.115259i
$271$	2.05656	−	1.18736i	0.124927	−	0.0721267i	−0.436234	−	0.899833i	$-0.643688\pi$
$271$	2.05656	−	1.18736i	0.124927	−	0.0721267i	0.561161	+	0.827706i	$0.310355\pi$
$272$	−1.02207	−	13.9542i	−0.0619722	−	0.846099i
$273$	8.99791	−	5.85904i	0.544578	−	0.354605i
$274$	7.20810	+	16.5402i	0.435457	+	0.999228i
$275$	−1.77281	−	13.4658i	−0.106904	−	0.812018i
$276$	24.6662	−	20.4017i	1.48473	−	1.22804i
$277$	0.00534527	−	0.0406014i	0.000321166	−	0.00243950i	−0.991284	−	0.131746i	$-0.957942\pi$
$277$	0.00534527	−	0.0406014i	0.000321166	−	0.00243950i	0.991605	+	0.129306i	$0.0412751\pi$
$278$	−11.8379	−	19.6649i	−0.709992	−	1.17942i
$279$	27.5620	+	27.5620i	1.65009	+	1.65009i
$280$	−1.21537	−	11.1654i	−0.0726321	−	0.667262i
$281$	12.9709	−	12.9709i	0.773777	−	0.773777i	−0.204987	−	0.978765i	$-0.565715\pi$
$281$	12.9709	−	12.9709i	0.773777	−	0.773777i	0.978765	+	0.204987i	$0.0657153\pi$
$282$	−8.91603	−	2.21520i	−0.530942	−	0.131913i
$283$	−11.6686	−	1.53620i	−0.693627	−	0.0913177i	−0.224534	−	0.974466i	$-0.572086\pi$
$283$	−11.6686	−	1.53620i	−0.693627	−	0.0913177i	−0.469093	+	0.883149i	$0.655419\pi$
$284$	5.79503	+	3.06902i	0.343872	+	0.182113i
$285$	3.72565	−	0.490491i	0.220688	−	0.0290542i
$286$	−3.51951	+	8.95647i	−0.208113	+	0.529607i
$287$	14.9783	−	29.4860i	0.884139	−	1.74050i
$288$	−28.5036	+	14.9878i	−1.67959	+	0.883166i
$289$	2.38234	+	4.12633i	0.140138	+	0.242725i
$290$	−9.18795	+	7.32081i	−0.539535	+	0.429893i
$291$	0.616105	+	0.802924i	0.0361167	+	0.0470682i
$292$	−13.1505	−	20.9681i	−0.769574	−	1.22707i
$293$	9.61588	−	3.98303i	0.561766	−	0.232691i	−0.0836859	−	0.996492i	$-0.526669\pi$
$293$	9.61588	−	3.98303i	0.561766	−	0.232691i	0.645451	+	0.763801i	$0.276669\pi$
$294$	28.9165	+	3.96720i	1.68645	+	0.231372i
$295$	−6.77880	−	6.77880i	−0.394677	−	0.394677i
$296$	−20.7583	−	4.35862i	−1.20655	−	0.253340i
$297$	10.1586	+	37.9124i	0.589462	+	2.19990i
$298$	4.92616	−	8.90435i	0.285365	−	0.515815i
$299$	−5.92800	−	4.54871i	−0.342825	−	0.263059i
$300$	−15.1843	−	5.64862i	−0.876664	−	0.326123i
$301$	−4.66739	−	5.45123i	−0.269024	−	0.314204i
$302$	23.5827	−	10.2772i	1.35703	−	0.591387i
$303$	11.1766	+	19.3585i	0.642082	+	1.11212i
$304$	2.53662	−	2.25918i	0.145485	−	0.129573i
$305$	−3.12073	−	1.80175i	−0.178693	−	0.103168i
$306$	−16.7324	+	22.6516i	−0.956528	+	1.29491i
$307$	3.40029	−	8.20902i	0.194065	−	0.468514i	−0.796655	−	0.604434i	$-0.793399\pi$
$307$	3.40029	−	8.20902i	0.194065	−	0.468514i	0.990720	+	0.135921i	$0.0433992\pi$
$308$	−23.1682	+	12.1455i	−1.32013	+	0.692053i
$309$	14.5433	−	6.02401i	0.827337	−	0.342694i
$310$	−7.49518	−	12.4508i	−0.425697	−	0.707157i
$311$	15.9588	−	4.27614i	0.904939	−	0.242478i	0.223803	−	0.974634i	$-0.428153\pi$
$311$	15.9588	−	4.27614i	0.904939	−	0.242478i	0.681136	+	0.732157i	$0.261486\pi$
$312$	7.47642	+	8.71000i	0.423269	+	0.493107i
$313$	−3.63367	+	13.5610i	−0.205387	+	0.766516i	0.783944	+	0.620832i	$0.213205\pi$
$313$	−3.63367	+	13.5610i	−0.205387	+	0.766516i	−0.989331	+	0.145684i	$0.953462\pi$
$314$	−5.57218	+	5.77970i	−0.314456	+	0.326167i
$315$	−12.7812	+	18.6458i	−0.720139	+	1.05057i
$316$	−6.09533	−	5.66520i	−0.342889	−	0.318693i
$317$	−2.71767	−	20.6428i	−0.152640	−	1.15941i	−0.880623	−	0.473818i	$-0.842875\pi$
$317$	−2.71767	−	20.6428i	−0.152640	−	1.15941i	0.727983	−	0.685595i	$-0.240458\pi$
$318$	23.5563	−	18.7693i	1.32097	−	1.05253i
$319$	23.6959	+	13.6808i	1.32671	+	0.765979i
$320$	11.6611	−	2.86072i	0.651874	−	0.159919i
$321$		−	46.7420i		−	2.60888i
$322$	−4.09031	−	19.8953i	−0.227944	−	1.10872i
$323$	1.13674	−	2.74432i	0.0632497	−	0.152698i
$324$	12.3409	+	2.82768i	0.685606	+	0.157093i
$325$	−0.493617	+	3.74940i	−0.0273810	+	0.207979i
$326$	−2.27669	−	7.91509i	−0.126094	−	0.438376i
$327$	45.5126	+	12.1951i	2.51685	+	0.674389i
$328$	33.3569	+	11.7194i	1.84182	+	0.647097i
$329$	−3.89536	+	4.33694i	−0.214758	+	0.239103i
$330$	−0.565444	−	30.9315i	−0.0311266	−	1.70272i
$331$	−7.95965	+	10.3732i	−0.437502	+	0.570164i	−0.959114	−	0.283019i	$-0.908664\pi$
$331$	−7.95965	+	10.3732i	−0.437502	+	0.570164i	0.521612	+	0.853183i	$0.325331\pi$
$332$	−1.15274	+	12.1824i	−0.0632647	+	0.668594i
$333$	25.9893	+	33.8699i	1.42420	+	1.85606i
$334$	24.4999	+	18.0977i	1.34057	+	0.990261i
$335$			17.0574i			0.931948i
$336$	−0.130963	+	31.2024i	−0.00714462	+	1.70223i
$337$			23.9661i			1.30551i	0.757567	+	0.652757i	$0.226388\pi$
$337$			23.9661i			1.30551i	−0.757567	+	0.652757i	$0.773612\pi$
$338$	−9.33146	+	12.6325i	−0.507564	+	0.687119i
$339$	−0.582735	−	0.759435i	−0.0316498	−	0.0412469i
$340$	8.09079	−	6.69199i	0.438785	−	0.362924i
$341$	−20.6052	+	26.8532i	−1.11583	+	1.45418i
$342$	−6.83577	+	0.124962i	−0.369636	+	0.00675715i
$343$	10.8306	−	15.0232i	0.584799	−	0.811178i
$344$	5.11935	−	5.71400i	0.276017	−	0.308078i
$345$	23.2028	+	6.21717i	1.24920	+	0.334721i
$346$	−15.1202	+	4.34916i	−0.812869	+	0.233813i
$347$	3.77291	−	28.6581i	0.202540	−	1.53845i	−0.524237	−	0.851572i	$-0.675649\pi$
$347$	3.77291	−	28.6581i	0.202540	−	1.53845i	0.726777	−	0.686873i	$-0.241017\pi$
$348$	27.6496	−	17.3409i	1.48218	−	0.929571i
$349$	−9.76697	+	23.5796i	−0.522814	+	1.26218i	0.413334	+	0.910579i	$0.364364\pi$
$349$	−9.76697	+	23.5796i	−0.522814	+	1.26218i	−0.936148	+	0.351606i	$0.885636\pi$
$350$	−7.68522	+	6.82749i	−0.410792	+	0.364945i
$351$		−	10.9287i		−	0.583330i
$352$	−16.1343	−	22.8410i	−0.859963	−	1.21743i
$353$	−11.3277	−	6.54003i	−0.602910	−	0.348090i	0.167275	−	0.985910i	$-0.446503\pi$
$353$	−11.3277	−	6.54003i	−0.602910	−	0.348090i	−0.770186	+	0.637820i	$0.779836\pi$
$354$	16.5968	+	20.8298i	0.882112	+	1.10709i
$355$	0.642314	+	4.87886i	0.0340905	+	0.258943i
$356$	−0.339279	−	9.27670i	−0.0179818	−	0.491664i
$357$	11.7771	+	24.6134i	0.623313	+	1.30268i
$358$	−1.94037	−	1.87071i	−0.102552	−	0.0988699i
$359$	−3.33820	+	12.4583i	−0.176184	+	0.657526i	0.820163	+	0.572129i	$0.193883\pi$
$359$	−3.33820	+	12.4583i	−0.176184	+	0.657526i	−0.996347	+	0.0853970i	$0.972784\pi$
$360$	−21.5598	−	10.9181i	−1.13630	−	0.575435i
$361$	−17.6560	+	4.73092i	−0.929264	+	0.248996i
$362$	18.8503	−	11.3476i	0.990752	−	0.596417i
$363$	−36.6055	+	15.1625i	−1.92129	+	0.795824i
$364$	7.10637	−	1.59692i	0.372475	−	0.0837015i
$365$	7.10782	−	17.1598i	0.372040	−	0.898184i
$366$	8.05244	+	5.94821i	0.420908	+	0.310918i
$367$	18.9447	+	10.9377i	0.988906	+	0.570945i	0.904947	−	0.425524i	$-0.139910\pi$
$367$	18.9447	+	10.9377i	0.988906	+	0.570945i	0.0839589	+	0.996469i	$0.473244\pi$
$368$	20.5073	−	7.13704i	1.06902	−	0.372044i
$369$	−35.5810	−	61.6280i	−1.85227	−	3.20823i
$370$	−6.35904	−	14.5918i	−0.330591	−	0.758594i
$371$	−3.50592	−	18.7874i	−0.182018	−	0.975393i
$372$	16.8035	+	36.7113i	0.871223	+	1.90339i
$373$	−4.07573	−	3.12742i	−0.211034	−	0.161932i	0.497836	−	0.867271i	$-0.334128\pi$
$373$	−4.07573	−	3.12742i	−0.211034	−	0.161932i	−0.708870	+	0.705339i	$0.750795\pi$
$374$	−21.3982	−	11.8381i	−1.10647	−	0.612136i
$375$	−8.87310	−	33.1148i	−0.458205	−	1.71004i
$376$	−5.14466	−	3.51710i	−0.265315	−	0.181381i
$377$	−5.38712	−	5.38712i	−0.277451	−	0.277451i
$378$	19.4438	−	22.4605i	1.00008	−	1.15524i
$379$	−21.0845	+	8.73348i	−1.08304	+	0.448609i	−0.851574	−	0.524234i	$-0.824352\pi$
$379$	−21.0845	+	8.73348i	−1.08304	+	0.448609i	−0.231464	+	0.972843i	$0.574352\pi$
$380$	2.48468	+	0.569315i	0.127461	+	0.0292053i
$381$	−17.1172	−	22.3076i	−0.876941	−	1.14285i
$382$	10.2134	+	12.8182i	0.522562	+	0.655839i
$383$	0.784463	+	1.35873i	0.0400842	+	0.0694278i	0.885371	−	0.464884i	$-0.153904\pi$
$383$	0.784463	+	1.35873i	0.0400842	+	0.0694278i	−0.845287	+	0.534312i	$0.820571\pi$
$384$	−33.0843	+	4.25638i	−1.68833	+	0.217207i
$385$	−17.5016	−	8.89043i	−0.891963	−	0.453098i
$386$	2.23338	+	0.877622i	0.113676	+	0.0446698i
$387$	−15.3094	+	2.01552i	−0.778220	+	0.102455i
$388$	0.201803	+	0.656194i	0.0102450	+	0.0333132i
$389$	1.70553	+	0.224538i	0.0864739	+	0.0113845i	0.173639	−	0.984809i	$-0.444447\pi$
$389$	1.70553	+	0.224538i	0.0864739	+	0.0113845i	−0.0871650	+	0.996194i	$0.527781\pi$
$390$	−2.07701	+	8.35980i	−0.105173	+	0.423315i
$391$	13.4267	−	13.4267i	0.679016	−	0.679016i
$392$	17.4461	+	9.36132i	0.881160	+	0.472818i
$393$	−25.0642	−	25.0642i	−1.26432	−	1.26432i
$394$	15.6537	−	9.42329i	0.788623	−	0.474739i
$395$	0.815096	−	6.19127i	0.0410120	−	0.311517i
$396$	−5.30229	+	56.0356i	−0.266450	+	2.81590i
$397$	−3.06526	−	23.2829i	−0.153841	−	1.16854i	−0.877916	−	0.478816i	$-0.841066\pi$
$397$	−3.06526	−	23.2829i	−0.153841	−	1.16854i	0.724075	−	0.689722i	$-0.242267\pi$
$398$	−32.2086	+	14.0363i	−1.61447	+	0.703578i
$399$	−3.00014	+	5.90603i	−0.150195	+	0.295671i
$400$	−8.31780	−	7.18249i	−0.415890	−	0.359124i
$401$	5.51052	−	3.18150i	0.275182	−	0.158876i	−0.356058	−	0.934464i	$-0.615880\pi$
$401$	5.51052	−	3.18150i	0.275182	−	0.158876i	0.631240	+	0.775587i	$0.282546\pi$
$402$	5.32566	−	47.0882i	0.265620	−	2.34855i
$403$	7.47696	−	5.73728i	0.372454	−	0.285794i
$404$	2.52732	+	14.9510i	0.125739	+	0.743842i
$405$	3.63586	+	8.77774i	0.180667	+	0.436169i
$406$	−1.48705	−	20.6560i	−0.0738010	−	1.02514i
$407$	−26.2142	+	26.2142i	−1.29939	+	1.29939i
$408$	−24.4245	+	15.9476i	−1.20919	+	0.789523i
$409$	−34.4146	+	9.22136i	−1.70169	+	0.455967i	−0.973365	−	0.229262i	$-0.926369\pi$
$409$	−34.4146	+	9.22136i	−1.70169	+	0.455967i	−0.728328	+	0.685229i	$0.759702\pi$
$410$	7.33423	+	25.4981i	0.362212	+	1.25926i
$411$	22.8988	−	29.8423i	1.12951	−	1.47201i
$412$	10.6710	−	0.390272i	0.525721	−	0.0192273i
$413$	16.6129	−	3.10013i	0.817466	−	0.152547i
$414$	−40.6764	−	15.9841i	−1.99914	−	0.785575i
$415$	−7.95255	+	4.59141i	−0.390376	+	0.225383i
$416$	2.69330	+	7.30585i	0.132050	+	0.358199i
$417$	−23.9264	+	41.4418i	−1.17168	+	2.02941i
$418$	−0.882383	−	5.87102i	−0.0431588	−	0.287161i
$419$	−9.16968	−	3.79821i	−0.447968	−	0.185555i	0.147283	−	0.989094i	$-0.452947\pi$
$419$	−9.16968	−	3.79821i	−0.447968	−	0.185555i	−0.595251	+	0.803540i	$0.702947\pi$
$420$	−19.1420	+	13.4856i	−0.934033	+	0.658032i
$421$	−1.85843	−	4.48665i	−0.0905743	−	0.218666i	0.872100	−	0.489327i	$-0.162758\pi$
$421$	−1.85843	−	4.48665i	−0.0905743	−	0.218666i	−0.962675	+	0.270661i	$0.912758\pi$
$422$	−1.44427	+	5.81307i	−0.0703058	+	0.282976i
$423$	3.24646	+	12.1160i	0.157848	+	0.589098i
$424$	19.4156	−	6.36170i	0.942905	−	0.308951i
$425$	−9.28278	−	2.48731i	−0.450281	−	0.120652i
$426$	−0.249876	−	13.6690i	−0.0121065	−	0.662263i
$427$	5.73019	−	2.74181i	0.277303	−	0.132685i
$428$	11.0550	−	29.7173i	0.534363	−	1.43644i
$429$	19.8909	−	2.61868i	0.960340	−	0.126431i
$430$	5.72072	+	0.647012i	0.275877	+	0.0312017i
$431$	1.73151	−	2.99907i	0.0834041	−	0.144460i	−0.821306	−	0.570488i	$-0.806754\pi$
$431$	1.73151	−	2.99907i	0.0834041	−	0.144460i	0.904710	+	0.426028i	$0.140087\pi$
$432$	26.5408	+	17.4412i	1.27694	+	0.839142i
$433$	10.6976			0.514093			0.257047	−	0.966399i	$-0.417251\pi$
$433$	10.6976			0.514093			0.257047	+	0.966399i	$0.417251\pi$
$434$	25.5740	+	1.51146i	1.22759	+	0.0725524i
$435$	22.6278	+	9.37273i	1.08492	+	0.449388i
$436$	26.0515	+	18.5175i	1.24764	+	0.886829i
$437$	4.57042	+	0.601707i	0.218633	+	0.0287836i
$438$	−24.9792	+	45.1515i	−1.19355	+	2.15742i
$439$	0.721069	−	2.69107i	0.0344147	−	0.128438i	−0.946581	−	0.322465i	$-0.895488\pi$
$439$	0.721069	−	2.69107i	0.0344147	−	0.128438i	0.980996	+	0.194028i	$0.0621551\pi$
$440$	6.95613	−	19.7992i	0.331621	−	0.943888i
$441$	−14.3724	−	37.1682i	−0.684401	−	1.76991i
$442$	4.90195	+	4.72594i	0.233162	+	0.224790i
$443$	11.8334	+	9.08012i	0.562224	+	0.431409i	0.850376	−	0.526175i	$-0.176374\pi$
$443$	11.8334	+	9.08012i	0.562224	+	0.431409i	−0.288153	+	0.957585i	$0.593041\pi$
$444$	12.9987	+	42.2672i	0.616890	+	2.00591i
$445$	5.52662	−	4.24073i	0.261987	−	0.201030i
$446$	0.0601167	+	0.399992i	0.00284661	+	0.0189402i
$447$	−21.2154			−1.00346
$448$	−7.46296	+	19.8067i	−0.352592	+	0.935777i
$449$	37.9240			1.78974			0.894872	−	0.446324i	$-0.147267\pi$
$449$	37.9240			1.78974			0.894872	+	0.446324i	$0.147267\pi$
$450$	3.28752	+	21.8738i	0.154975	+	1.03114i
$451$	49.0250	−	37.6182i	2.30850	−	1.77137i
$452$	−0.190873	−	0.620653i	−0.00897792	−	0.0291930i
$453$	−42.5487	−	32.6488i	−1.99911	−	1.53397i
$454$	1.54879	+	1.49318i	0.0726882	+	0.0700783i
$455$	4.06638	+	3.65235i	0.190635	+	0.171225i
$456$	−6.68136	−	2.34740i	−0.312883	−	0.109927i
$457$	1.09935	−	4.10284i	0.0514255	−	0.191923i	−0.935435	−	0.353500i	$-0.884991\pi$
$457$	1.09935	−	4.10284i	0.0514255	−	0.191923i	0.986860	+	0.161577i	$0.0516581\pi$
$458$	−2.88292	+	5.21106i	−0.134710	+	0.243497i
$459$	27.5345	+	3.62499i	1.28520	+	0.169200i
$460$	13.2813	+	9.44043i	0.619244	+	0.440163i
$461$	−12.5317	−	5.19080i	−0.583660	−	0.241760i	0.0712607	−	0.997458i	$-0.477298\pi$
$461$	−12.5317	−	5.19080i	−0.583660	−	0.241760i	−0.654920	+	0.755698i	$0.727298\pi$
$462$	45.5385	+	30.0069i	2.11864	+	1.39605i
$463$	−3.79596			−0.176413			−0.0882065	−	0.996102i	$-0.528114\pi$
$463$	−3.79596			−0.176413			−0.0882065	+	0.996102i	$0.528114\pi$
$464$	21.6802	−	4.48547i	1.00648	−	0.208233i
$465$	−15.1490	+	26.2388i	−0.702518	+	1.21680i
$466$	−26.9579	−	3.04893i	−1.24880	−	0.141239i
$467$	−25.4938	+	3.35632i	−1.17971	+	0.155312i	−0.694769	−	0.719233i	$-0.744493\pi$
$467$	−25.4938	+	3.35632i	−1.17971	+	0.155312i	−0.484944	+	0.874545i	$0.661160\pi$
$468$	5.46428	−	14.6887i	0.252586	−	0.678987i
$469$	−24.8018	−	17.0010i	−1.14524	−	0.785033i
$470$	−0.0854774	−	4.67587i	−0.00394278	−	0.215682i
$471$	16.1673	+	4.33200i	0.744948	+	0.199608i
$472$	5.62537	+	17.1684i	0.258929	+	0.790238i
$473$	−3.47048	−	12.9520i	−0.159573	−	0.595534i
$474$	−4.18316	+	16.8369i	−0.192139	+	0.773345i
$475$	−0.892850	−	2.15553i	−0.0409668	−	0.0989025i
$476$	1.66626	+	18.4340i	0.0763728	+	0.844921i
$477$	−37.9926	−	15.7370i	−1.73956	−	0.720550i
$478$	−0.812668	−	5.40716i	−0.0371706	−	0.247318i
$479$	−14.5524	+	25.2055i	−0.664916	+	1.15167i	0.314392	+	0.949293i	$0.398199\pi$
$479$	−14.5524	+	25.2055i	−0.664916	+	1.15167i	−0.979308	+	0.202375i	$0.935134\pi$
$480$	−16.9874	−	18.3856i	−0.775366	−	0.839185i
$481$	8.93946	−	5.16120i	0.407604	−	0.235330i
$482$	8.99101	+	3.53309i	0.409530	+	0.160928i
$483$	−32.1659	+	27.5407i	−1.46360	+	1.25315i
$484$	−26.8589	+	0.982318i	−1.22086	+	0.0446508i
$485$	−0.313626	+	0.408725i	−0.0142410	+	0.0185593i
$486$	2.01514	+	7.00580i	0.0914085	+	0.317789i
$487$	−22.0281	+	5.90240i	−0.998186	+	0.267463i	−0.720686	−	0.693262i	$-0.756173\pi$
$487$	−22.0281	+	5.90240i	−0.998186	+	0.267463i	−0.277501	+	0.960725i	$0.589506\pi$
$488$	3.71271	+	5.68621i	0.168067	+	0.257403i
$489$	−12.1414	+	12.1414i	−0.549054	+	0.549054i
$490$	1.85910	+	14.7409i	0.0839855	+	0.665928i
$491$	3.66716	+	8.85330i	0.165497	+	0.399544i	0.984771	−	0.173858i	$-0.0556234\pi$
$491$	3.66716	+	8.85330i	0.165497	+	0.399544i	−0.819274	+	0.573402i	$0.805623\pi$
$492$	−12.2856	−	72.6790i	−0.553879	−	3.27662i
$493$	15.3596	−	11.7858i	0.691761	−	0.530807i
$494$	−0.185778	+	1.64261i	−0.00835856	+	0.0739043i
$495$	−36.5796	+	21.1193i	−1.64413	+	0.949241i
$496$	2.00063	+	27.3143i	0.0898308	+	1.22645i
$497$	−7.73414	−	3.92878i	−0.346924	−	0.176230i
$498$	23.3871	−	10.1919i	1.04800	−	0.456712i
$499$	2.14422	+	16.2870i	0.0959885	+	0.729105i	0.969984	+	0.243170i	$0.0781874\pi$
$499$	2.14422	+	16.2870i	0.0959885	+	0.729105i	−0.873995	+	0.485935i	$0.838479\pi$
$500$	2.19074	−	23.1521i	0.0979728	−	1.03540i
$501$	8.28867	−	62.9587i	0.370310	−	2.81279i
$502$	−10.4394	+	6.28434i	−0.465932	+	0.280484i
$503$	−4.01354	−	4.01354i	−0.178955	−	0.178955i	0.611945	−	0.790900i	$-0.290387\pi$
$503$	−4.01354	−	4.01354i	−0.178955	−	0.178955i	−0.790900	+	0.611945i	$0.790387\pi$
$504$	37.3636	−	20.4663i	1.66431	−	0.911643i
$505$	−8.04607	+	8.04607i	−0.358045	+	0.358045i
$506$	9.15087	−	36.8316i	0.406806	−	1.63736i
$507$	32.4625	+	4.27377i	1.44171	+	0.189805i
$508$	−5.60669	−	18.2310i	−0.248757	−	0.808869i
$509$	−15.4047	+	2.02807i	−0.682801	+	0.0898925i	−0.463944	−	0.885864i	$-0.653566\pi$
$509$	−15.4047	+	2.02807i	−0.682801	+	0.0898925i	−0.218857	+	0.975757i	$0.570233\pi$
$510$	−20.3734	−	8.00587i	−0.902148	−	0.354506i
$511$	17.8663	+	27.4379i	0.790361	+	1.21378i
$512$	−22.0408	−	5.11871i	−0.974077	−	0.226217i
$513$	3.37119	+	5.83908i	0.148842	+	0.257801i
$514$	−2.76577	−	3.47117i	−0.121993	−	0.153107i
$515$	4.87810	+	6.35726i	0.214955	+	0.280134i
$516$	−15.5904	−	3.57224i	−0.686329	−	0.157259i
$517$	−10.0631	+	4.16828i	−0.442576	+	0.183321i
$518$	27.5548	+	5.29740i	1.21069	+	0.232755i
$519$	23.1938	+	23.1938i	1.01810	+	1.01810i
$520$	−3.29769	+	4.82371i	−0.144613	+	0.211534i
$521$	−4.94922	−	18.4707i	−0.216829	−	0.809217i	−0.985515	−	0.169590i	$-0.945755\pi$
$521$	−4.94922	−	18.4707i	−0.216829	−	0.809217i	0.768685	−	0.639627i	$-0.220911\pi$
$522$	−38.9916	−	21.5714i	−1.70662	−	0.944153i
$523$	9.52683	+	7.31019i	0.416579	+	0.319652i	0.795696	−	0.605696i	$-0.207105\pi$
$523$	9.52683	+	7.31019i	0.416579	+	0.319652i	−0.379117	+	0.925349i	$0.623772\pi$
$524$	−10.0072	−	21.8632i	−0.437168	−	0.955097i
$525$	20.2112	+	7.12924i	0.882091	+	0.311146i
$526$	16.0677	+	36.8700i	0.700585	+	1.60761i
$527$	11.9749	+	20.7411i	0.521633	+	0.903494i
$528$	−25.3845	+	52.4850i	−1.10472	+	2.28412i
$529$	5.60147	+	3.23401i	0.243542	+	0.140609i
$530$	12.3324	+	9.10977i	0.535686	+	0.395703i
$531$	13.9156	−	33.5952i	0.603885	−	1.45791i
$532$	−3.30425	+	3.04533i	−0.143257	+	0.132032i
$533$	−15.8963	+	6.58446i	−0.688545	+	0.285205i
$534$	−16.5806	+	9.98128i	−0.717514	+	0.431932i
$535$	22.9831	−	6.15829i	0.993644	−	0.266246i
$536$	14.5228	−	28.6779i	0.627289	−	1.23870i
$537$	−1.45435	+	5.42771i	−0.0627599	+	0.234223i
$538$	10.2862	+	9.91685i	0.443468	+	0.427546i
$539$	30.3705	−	16.5866i	1.30815	−	0.714435i
$540$	0.871052	+	23.8166i	0.0374841	+	1.02490i
$541$	2.33326	+	17.7229i	0.100315	+	0.761966i	0.965480	+	0.260478i	$0.0838803\pi$
$541$	2.33326	+	17.7229i	0.100315	+	0.761966i	−0.865165	+	0.501487i	$0.832786\pi$
$542$	−2.09279	−	2.62655i	−0.0898930	−	0.112820i
$543$	−39.7253	−	22.9354i	−1.70477	−	0.984252i
$544$	−19.3003	+	4.36239i	−0.827492	+	0.187036i
$545$			23.9853i			1.02742i
$546$	−10.0852	−	11.3521i	−0.431605	−	0.485827i
$547$	−5.09466	+	12.2996i	−0.217832	+	0.525893i	−0.994587	−	0.103911i	$-0.966864\pi$
$547$	−5.09466	+	12.2996i	−0.217832	+	0.525893i	0.776755	+	0.629803i	$0.216864\pi$
$548$	21.6165	−	13.5571i	0.923410	−	0.579132i
$549$	1.78409	−	13.5515i	0.0761432	−	0.578365i
$550$	−18.4594	+	5.30963i	−0.787110	+	0.226403i
$551$	4.54006	+	1.21650i	0.193413	+	0.0518248i
$552$	−33.7164	−	30.2076i	−1.43507	−	1.28572i
$553$	8.18982	+	7.35595i	0.348267	+	0.312807i
$554$	−0.0579048	+	0.00105853i	−0.00246014	+	4.49727e-5i
$555$	−20.2015	+	26.3271i	−0.857504	+	1.11752i
$556$	−25.0132	+	20.6887i	−1.06080	+	0.877398i
$557$	27.6581	+	36.0447i	1.17191	+	1.52726i	0.801075	+	0.598564i	$0.204262\pi$
$557$	27.6581	+	36.0447i	1.17191	+	1.52726i	0.370835	+	0.928699i	$0.379072\pi$
$558$	32.7524	−	44.3388i	1.38652	−	1.87701i
$559$			3.73355i			0.157913i
$560$	−15.3595	+	4.04654i	−0.649056	+	0.170998i
$561$			50.9831i			2.15251i
$562$	−20.8662	−	15.4135i	−0.880186	−	0.650180i
$563$	19.4629	+	25.3645i	0.820263	+	1.06899i	0.996413	+	0.0846240i	$0.0269689\pi$
$563$	19.4629	+	25.3645i	0.820263	+	1.06899i	−0.176150	+	0.984363i	$0.556364\pi$
$564$	−1.22393	+	12.9347i	−0.0515368	+	0.544650i
$565$	0.296639	−	0.386587i	0.0124797	−	0.0162639i
$566$	0.304216	+	16.6415i	0.0127871	+	0.699495i
$567$	−16.3868	−	3.46209i	−0.688182	−	0.145394i
$568$	3.07399	−	8.74946i	0.128982	−	0.367119i
$569$	−41.6623	−	11.1634i	−1.74658	−	0.467993i	−0.762686	−	0.646769i	$-0.776120\pi$
$569$	−41.6623	−	11.1634i	−1.74658	−	0.467993i	−0.983890	+	0.178776i	$0.942786\pi$
$570$	−1.46904	−	5.10725i	−0.0615314	−	0.213919i
$571$	−3.07362	+	23.3464i	−0.128627	+	0.977017i	0.798428	+	0.602091i	$0.205665\pi$
$571$	−3.07362	+	23.3464i	−0.128627	+	0.977017i	−0.927054	+	0.374927i	$0.877668\pi$
$572$	13.2654	+	3.03952i	0.554656	+	0.127089i
$573$	13.0760	−	31.5684i	0.546260	−	1.31879i
$574$	−44.3846	−	14.7496i	−1.85258	−	0.615636i
$575$		−	14.9143i		−	0.621968i
$576$	26.9517	+	36.7122i	1.12299	+	1.52967i
$577$	36.8512	+	21.2761i	1.53414	+	0.885734i	0.999165	+	0.0408643i	$0.0130111\pi$
$577$	36.8512	+	21.2761i	1.53414	+	0.885734i	0.534972	+	0.844870i	$0.320322\pi$
$578$	5.26996	−	4.19902i	0.219202	−	0.174656i
$579$	−0.652992	−	4.95997i	−0.0271374	−	0.206129i
$580$	12.1694	+	11.3107i	0.505307	+	0.469650i
$581$	1.25025	−	16.1394i	0.0518689	−	0.669574i
$582$	0.993396	−	1.03039i	0.0411776	−	0.0427111i
$583$	9.24237	−	34.4930i	0.382780	−	1.42855i
$584$	−26.5600	+	22.7983i	−1.09906	+	0.943400i
$585$	11.3601	−	3.04393i	0.469682	−	0.125851i
$586$	−7.59143	−	12.6107i	−0.313599	−	0.520943i
$587$	33.7846	−	13.9940i	1.39444	−	0.577595i	0.446137	−	0.894965i	$-0.352800\pi$
$587$	33.7846	−	13.9940i	1.39444	−	0.577595i	0.948302	+	0.317370i	$0.102800\pi$
$588$	−0.529751	−	41.2738i	−0.0218465	−	1.70210i
$589$	−2.22507	+	5.37180i	−0.0916825	+	0.221341i
$590$	−8.05537	+	10.9050i	−0.331634	+	0.448953i
$591$	−32.9887	−	19.0460i	−1.35697	−	0.783449i
$592$	−1.73242	+	29.9467i	−0.0712020	+	1.23080i
$593$	7.13265	+	12.3541i	0.292903	+	0.507323i	0.974495	−	0.224410i	$-0.0720454\pi$
$593$	7.13265	+	12.3541i	0.292903	+	0.507323i	−0.681592	+	0.731732i	$0.738712\pi$
$594$	50.8856	−	22.1756i	2.08786	−	0.909877i
$595$	−10.5508	+	9.03367i	−0.432540	+	0.370344i
$596$	−13.4882	−	5.01768i	−0.552499	−	0.205532i
$597$	58.1118	+	44.5908i	2.37836	+	1.82498i
$598$	−5.11541	+	9.24643i	−0.209185	+	0.378115i
$599$	−3.66763	−	13.6878i	−0.149855	−	0.559268i	−0.999491	−	0.0318980i	$-0.989845\pi$
$599$	−3.66763	−	13.6878i	−0.149855	−	0.559268i	0.849636	−	0.527370i	$-0.176822\pi$
$600$	−4.70808	+	22.4226i	−0.192206	+	0.915398i
$601$	17.9216	+	17.9216i	0.731036	+	0.731036i	0.970825	−	0.239789i	$-0.0770783\pi$
$601$	17.9216	+	17.9216i	0.731036	+	0.731036i	−0.239789	+	0.970825i	$0.577078\pi$
$602$	−6.64255	+	7.67316i	−0.270730	+	0.312735i
$603$	−59.7755	+	24.7598i	−2.43425	+	1.00830i
$604$	−19.3296	−	30.8205i	−0.786509	−	1.25407i
$605$	−12.2782	−	16.0013i	−0.499180	−	0.650544i
$606$	24.7238	−	19.6996i	1.00434	−	0.800240i
$607$	−7.41114	−	12.8365i	−0.300809	−	0.521017i	0.675510	−	0.737350i	$-0.263923\pi$
$607$	−7.41114	−	12.8365i	−0.300809	−	0.521017i	−0.976319	+	0.216334i	$0.930590\pi$
$608$	−3.69265	−	3.07263i	−0.149757	−	0.124612i
$609$	−36.1810	+	23.5595i	−1.46613	+	0.954679i
$610$	−1.86383	+	4.74307i	−0.0754641	+	0.192041i
$611$	3.00688	−	0.395863i	0.121645	−	0.0160149i
$612$	35.1954	+	18.6393i	1.42269	+	0.753449i
$613$	7.37294	+	0.970666i	0.297790	+	0.0392048i	0.277941	−	0.960598i	$-0.410348\pi$
$613$	7.37294	+	0.970666i	0.297790	+	0.0392048i	0.0198493	+	0.999803i	$0.493681\pi$
$614$	−12.1951	−	3.02989i	−0.492153	−	0.122276i
$615$	39.1130	−	39.1130i	1.57719	−	1.57719i
$616$	21.8552	+	29.8480i	0.880572	+	1.20261i
$617$	8.55719	+	8.55719i	0.344500	+	0.344500i	0.858056	−	0.513556i	$-0.171672\pi$
$617$	8.55719	+	8.55719i	0.344500	+	0.344500i	−0.513556	+	0.858056i	$0.671672\pi$
$618$	−11.4814	−	19.0727i	−0.461851	−	0.767215i
$619$	5.00780	−	38.0380i	0.201280	−	1.52888i	−0.530705	−	0.847557i	$-0.678073\pi$
$619$	5.00780	−	38.0380i	0.201280	−	1.52888i	0.731985	−	0.681320i	$-0.238594\pi$
$620$	−15.8371	+	13.0991i	−0.636033	+	0.526071i
$621$	5.62567	+	42.7312i	0.225750	+	1.71475i
$622$	−9.33456	−	21.4197i	−0.374282	−	0.858850i
$623$	0.657759	+	12.2625i	0.0263526	+	0.491287i
$624$	10.6095	−	12.2866i	0.424722	−	0.491856i
$625$	3.21683	−	1.85724i	0.128673	−	0.0742895i
$626$	19.7290	+	2.23134i	0.788528	+	0.0891824i
$627$	−9.81968	+	7.53491i	−0.392160	+	0.300915i
$628$	9.25415	+	6.57791i	0.369281	+	0.262487i
$629$	10.0383	+	24.2347i	0.400255	+	0.966300i
$630$	28.7627	+	13.9555i	1.14594	+	0.555999i
$631$	8.59879	−	8.59879i	0.342312	−	0.342312i	−0.514924	−	0.857236i	$-0.672180\pi$
$631$	8.59879	−	8.59879i	0.342312	−	0.342312i	0.857236	+	0.514924i	$0.172180\pi$
$632$	−6.64166	+	9.71511i	−0.264191	+	0.386446i
$633$	12.0621	−	3.23203i	0.479426	−	0.128462i
$634$	−28.2978	+	8.13955i	−1.12385	+	0.323263i
$635$	8.71345	−	11.3556i	0.345783	−	0.450633i
$636$	−31.2002	−	28.9985i	−1.23717	−	1.14987i
$637$	−9.36350	+	2.27233i	−0.370995	+	0.0900328i
$638$	14.1521	−	36.0144i	0.560288	−	1.42582i
$639$	−16.1650	+	9.33284i	−0.639476	+	0.369201i
$640$	−6.45175	−	15.7068i	−0.255028	−	0.620866i
$641$	5.73713	−	9.93700i	0.226603	−	0.392488i	−0.730196	−	0.683238i	$-0.760571\pi$
$641$	5.73713	−	9.93700i	0.226603	−	0.392488i	0.956799	+	0.290750i	$0.0939047\pi$
$642$	−65.3690	+	9.82461i	−2.57991	+	0.387746i
$643$	−24.5492	−	10.1686i	−0.968127	−	0.401011i	−0.158113	−	0.987421i	$-0.550541\pi$
$643$	−24.5492	−	10.1686i	−0.968127	−	0.401011i	−0.810015	+	0.586410i	$0.800541\pi$
$644$	−26.9639	+	9.90207i	−1.06253	+	0.390196i
$645$	−4.59322	−	11.0890i	−0.180858	−	0.436630i
$646$	−4.07688	−	1.01291i	−0.160403	−	0.0398523i
$647$	−1.90637	−	7.11466i	−0.0749471	−	0.279706i	0.918274	−	0.395945i	$-0.129583\pi$
$647$	−1.90637	−	7.11466i	−0.0749471	−	0.279706i	−0.993221	+	0.116239i	$0.962916\pi$
$648$	1.36061	−	17.8532i	0.0534499	−	0.701339i
$649$	30.5006	+	8.17262i	1.19726	+	0.320804i
$650$	5.34731	−	0.0977516i	0.209739	−	0.00383413i
$651$	−23.0529	−	48.1789i	−0.903513	−	1.88828i
$652$	−10.5908	+	4.84762i	−0.414767	+	0.189847i
$653$	−11.7045	+	1.54093i	−0.458034	+	0.0603013i	−0.356013	−	0.934481i	$-0.615864\pi$
$653$	−11.7045	+	1.54093i	−0.458034	+	0.0603013i	−0.102021	+	0.994782i	$0.532531\pi$
$654$	7.48867	−	66.2129i	0.292830	−	2.58913i
$655$	9.02187	−	15.6263i	0.352514	−	0.610572i
$656$	9.37849	−	49.1131i	0.366168	−	1.91754i
$657$	70.4515			2.74858
$658$	6.88399	+	4.53611i	0.268366	+	0.176836i
$659$	29.6740	+	12.2914i	1.15594	+	0.478804i	0.876520	−	0.481366i	$-0.159859\pi$
$659$	29.6740	+	12.2914i	1.15594	+	0.478804i	0.279416	+	0.960170i	$0.409859\pi$
$660$	−43.1390	+	7.29220i	−1.67918	+	0.283849i
$661$	−35.0447	−	4.61372i	−1.36308	−	0.179453i	−0.586744	−	0.809773i	$-0.699590\pi$
$661$	−35.0447	−	4.61372i	−1.36308	−	0.179453i	−0.776335	+	0.630320i	$0.782924\pi$
$662$	16.1800	+	8.95130i	0.628855	+	0.347902i
$663$	3.67411	−	13.7120i	0.142691	−	0.532529i
$664$	17.2794	−	0.948475i	0.670571	−	0.0368080i
$665$	−3.29927	−	0.697046i	−0.127940	−	0.0270303i
$666$	41.9047	−	43.4653i	1.62377	−	1.68424i
$667$	23.8368	+	18.2906i	0.922963	+	0.708215i
$668$	20.1601	−	38.0671i	0.780019	−	1.47286i
$669$	0.669014	−	0.513353i	0.0258656	−	0.0198474i
$670$	23.8550	−	3.58527i	0.921597	−	0.138511i
$671$	11.8692			0.458207
$672$	43.6642	−	6.37521i	1.68438	−	0.245929i
$673$	18.3928			0.708991			0.354496	−	0.935058i	$-0.384653\pi$
$673$	18.3928			0.708991			0.354496	+	0.935058i	$0.384653\pi$
$674$	33.5167	−	5.03738i	1.29102	−	0.194033i
$675$	17.3059	−	13.2793i	0.666105	−	0.511120i
$676$	19.6280	+	10.3949i	0.754925	+	0.399804i
$677$	24.4013	+	18.7238i	0.937818	+	0.719613i	0.959959	−	0.280141i	$-0.0903814\pi$
$677$	24.4013	+	18.7238i	0.937818	+	0.719613i	−0.0221403	+	0.999755i	$0.507048\pi$
$678$	−0.939591	+	0.974584i	−0.0360848	+	0.0374287i
$679$	−0.281706	−	0.863390i	−0.0108109	−	0.0331339i
$680$	−11.0594	−	9.90845i	−0.424108	−	0.379972i
$681$	1.16085	−	4.33234i	0.0444838	−	0.166016i
$682$	41.8853	+	23.1722i	1.60387	+	0.887311i
$683$	8.24507	+	1.08548i	0.315489	+	0.0415349i	0.286608	−	0.958048i	$-0.407472\pi$
$683$	8.24507	+	1.08548i	0.315489	+	0.0415349i	0.0288809	+	0.999583i	$0.490806\pi$
$684$	1.61156	+	9.53361i	0.0616195	+	0.364527i
$685$	17.6904	+	7.32760i	0.675915	+	0.279973i
$686$	−23.2866	−	11.9890i	−0.889085	−	0.457743i
$687$	12.4158			0.473693
$688$	−9.06710	−	5.95844i	−0.345680	−	0.227163i
$689$	−4.97149	+	8.61087i	−0.189399	+	0.328048i
$690$	3.81780	−	33.7561i	0.145341	−	1.28507i
$691$	2.96521	−	0.390377i	0.112802	−	0.0148506i	−0.0739140	−	0.997265i	$-0.523549\pi$
$691$	2.96521	−	0.390377i	0.112802	−	0.0148506i	0.186716	+	0.982414i	$0.440216\pi$
$692$	9.26043	+	20.2316i	0.352029	+	0.769090i
$693$	5.75080	−	74.2369i	0.218455	−	2.82002i
$694$	−40.8715	+	0.747153i	−1.55146	+	0.0283615i
$695$	−23.5293	−	6.30465i	−0.892516	−	0.239149i
$696$	−30.0630	−	35.0233i	−1.13954	−	1.32756i
$697$	−11.3167	−	42.2344i	−0.428649	−	1.59974i
$698$	35.0291	+	8.70303i	1.32587	+	0.329415i
$699$	21.6448	+	52.2551i	0.818680	+	1.97647i
$700$	11.1636	+	9.31277i	0.421946	+	0.351989i
$701$	−7.89119	−	3.26864i	−0.298046	−	0.123455i	0.228649	−	0.973509i	$-0.426569\pi$
$701$	−7.89119	−	3.26864i	−0.298046	−	0.123455i	−0.526695	+	0.850054i	$0.676569\pi$
$702$	−15.2838	+	2.29708i	−0.576851	+	0.0866976i
$703$	−3.18417	+	5.51515i	−0.120093	+	0.208008i
$704$	−28.5521	+	27.3649i	−1.07610	+	1.03135i
$705$	−8.44370	+	4.87497i	−0.318008	+	0.183602i
$706$	−6.76533	+	17.2164i	−0.254617	+	0.647949i
$707$	−3.67969	−	19.7186i	−0.138389	−	0.741593i
$708$	25.6421	−	27.5890i	0.963690	−	1.03686i
$709$	−19.1695	+	24.9822i	−0.719926	+	0.938225i	−0.999762	−	0.0218225i	$-0.993053\pi$
$709$	−19.1695	+	24.9822i	−0.719926	+	0.938225i	0.279836	+	0.960048i	$0.409720\pi$
$710$	6.68811	−	1.92376i	0.251000	−	0.0721974i
$711$	22.8796	−	6.13058i	0.858053	−	0.229915i
$712$	−12.9022	+	2.42434i	−0.483531	+	0.0908559i
$713$	−26.2817	+	26.2817i	−0.984256	+	0.984256i
$714$	31.9466	−	21.6439i	1.19557	−	0.810002i
$715$	3.90824	+	9.43533i	0.146160	+	0.352861i
$716$	−2.20835	+	3.10683i	−0.0825299	+	0.116108i
$717$	−9.04386	+	6.93960i	−0.337749	+	0.259164i
$718$	18.1247	+	2.04990i	0.676409	+	0.0765017i
$719$	−43.7894	+	25.2818i	−1.63307	+	0.942853i	−0.649931	+	0.759994i	$0.725202\pi$
$719$	−43.7894	+	25.2818i	−1.63307	+	0.942853i	−0.983139	+	0.182860i	$0.941465\pi$
$720$	−10.7374	+	32.4463i	−0.400161	+	1.20920i
$721$	−14.1055	+	0.756618i	−0.525317	+	0.0281779i
$722$	10.3273	+	23.6977i	0.384342	+	0.881936i
$723$	−2.62878	−	19.9676i	−0.0977655	−	0.742603i
$724$	−19.8318	−	23.9772i	−0.737044	−	0.891105i
$725$	1.98486	−	15.0765i	0.0737158	−	0.559927i
$726$	28.8989	+	48.0060i	1.07254	+	1.78167i
$727$	30.1412	+	30.1412i	1.11788	+	1.11788i	0.992053	+	0.125823i	$0.0401572\pi$
$727$	30.1412	+	30.1412i	1.11788	+	1.11788i	0.125823	+	0.992053i	$0.459843\pi$
$728$	−3.72698	−	9.60265i	−0.138131	−	0.355898i
$729$	24.1753	−	24.1753i	0.895382	−	0.895382i
$730$	−25.4921	−	6.33354i	−0.943503	−	0.234415i
$731$	−9.40660	−	1.23840i	−0.347916	−	0.0458040i
$732$	6.62609	−	12.5116i	0.244907	−	0.462443i
$733$	41.2876	−	5.43562i	1.52499	−	0.200769i	0.679070	−	0.734074i	$-0.262383\pi$
$733$	41.2876	−	5.43562i	1.52499	−	0.200769i	0.845923	+	0.533305i	$0.179050\pi$
$734$	11.3145	−	28.7933i	0.417627	−	1.06278i
$735$	25.0150	−	18.2685i	0.922690	−	0.673844i
$736$	−14.2916	−	27.1795i	−0.526796	−	1.00185i
$737$	−28.0919	−	48.6567i	−1.03478	−	1.79229i
$738$	−78.7085	+	62.7137i	−2.89730	+	2.30852i
$739$	6.36159	+	8.29059i	0.234015	+	0.304974i	0.895568	−	0.444924i	$-0.146769\pi$
$739$	6.36159	+	8.29059i	0.234015	+	0.304974i	−0.661553	+	0.749898i	$0.730103\pi$
$740$	−19.0702	+	11.9602i	−0.701035	+	0.439665i
$741$	3.18402	−	1.31886i	0.116968	−	0.0484497i
$742$	−25.5374	+	8.85194i	−0.937507	+	0.324965i
$743$	−2.47749	−	2.47749i	−0.0908904	−	0.0908904i	0.660200	−	0.751090i	$-0.270472\pi$
$743$	−2.47749	−	2.47749i	−0.0908904	−	0.0908904i	−0.751090	+	0.660200i	$0.770472\pi$
$744$	47.8091	−	31.2162i	1.75277	−	1.14444i
$745$	−2.79515	−	10.4316i	−0.102406	−	0.382186i
$746$	−3.51705	+	6.35729i	−0.128768	+	0.232757i
$747$	−27.6335	−	21.2040i	−1.01106	−	0.775812i
$748$	−12.0581	+	32.4137i	−0.440887	+	1.18516i
$749$	−13.9527	+	39.5557i	−0.509822	+	1.44533i
$750$	−44.4463	+	19.3694i	−1.62295	+	0.707272i
$751$	−3.97345	−	6.88221i	−0.144993	−	0.251135i	0.784377	−	0.620284i	$-0.212983\pi$
$751$	−3.97345	−	6.88221i	−0.144993	−	0.251135i	−0.929370	+	0.369149i	$0.879649\pi$
$752$	−3.83735	+	7.93409i	−0.139934	+	0.289327i
$753$	22.0000	+	12.7017i	0.801724	+	0.462875i
$754$	−6.40161	+	8.66623i	−0.233133	+	0.315605i
$755$	10.4476	−	25.2227i	0.380227	−	0.917949i
$756$	−35.4980	−	22.4713i	−1.29105	−	0.817273i
$757$	−16.3063	+	6.75428i	−0.592662	+	0.245488i	−0.658795	−	0.752322i	$-0.728934\pi$
$757$	−16.3063	+	6.75428i	−0.592662	+	0.245488i	0.0661336	+	0.997811i	$0.478934\pi$
$758$	16.6455	+	27.6511i	0.604594	+	1.00433i
$759$	−76.4255	+	20.4781i	−2.77407	+	0.743309i
$760$	0.273941	−	3.59450i	0.00993690	−	0.130386i
$761$	2.46855	−	9.21275i	0.0894849	−	0.333962i	−0.906641	−	0.421903i	$-0.861362\pi$
$761$	2.46855	−	9.21275i	0.0894849	−	0.333962i	0.996126	+	0.0879413i	$0.0280288\pi$
$762$	−27.5995	+	28.6273i	−0.999823	+	1.03706i
$763$	−34.8750	−	23.9059i	−1.26256	−	0.865452i
$764$	15.7797	−	16.9777i	0.570889	−	0.614232i
$765$	3.90101	+	29.6311i	0.141041	+	1.07132i
$766$	1.73531	−	1.38266i	0.0626992	−	0.0499577i
$767$	−7.61422	−	4.39607i	−0.274934	−	0.158733i
$768$	12.9065	+	45.3740i	0.465724	+	1.63729i
$769$		−	8.73801i		−	0.315101i	−0.987511	−	0.157550i	$-0.949640\pi$
$769$		−	8.73801i		−	0.315101i	0.987511	−	0.157550i	$-0.0503597\pi$
$770$	−8.75470	+	26.3447i	−0.315498	+	0.949398i
$771$	−3.54098	+	8.54867i	−0.127525	+	0.307873i
$772$	0.757931	−	3.30786i	0.0272785	−	0.119052i
$773$	−5.84328	+	44.3841i	−0.210168	+	1.59639i	0.483007	+	0.875617i	$0.339545\pi$
$773$	−5.84328	+	44.3841i	−0.210168	+	1.59639i	−0.693175	+	0.720769i	$0.743789\pi$
$774$	6.03657	+	20.9867i	0.216980	+	0.754350i
$775$	18.1703	+	4.86873i	0.652698	+	0.174890i
$776$	0.875275	−	0.420148i	0.0314205	−	0.0150824i
$777$	−18.1454	−	55.6132i	−0.650963	−	1.99511i
$778$	−0.0444655	−	2.43239i	−0.00159416	−	0.0872056i
$779$	6.46210	−	8.42157i	0.231529	−	0.301734i
$780$	12.1278	+	1.14758i	0.434245	+	0.0410898i
$781$	−9.86721	−	12.8592i	−0.353077	−	0.460138i
$782$	−21.5994	−	15.9552i	−0.772393	−	0.570555i
$783$			43.9447i			1.57046i
$784$	9.42490	−	26.3661i	0.336604	−	0.941646i
$785$			8.52019i			0.304099i
$786$	−29.7843	+	40.3207i	−1.06237	+	1.43819i
$787$	−6.74898	−	8.79544i	−0.240575	−	0.313524i	0.657424	−	0.753521i	$-0.271646\pi$
$787$	−6.74898	−	8.79544i	−0.240575	−	0.313524i	−0.897999	+	0.439997i	$0.854979\pi$
$788$	−16.4688	−	19.9112i	−0.586675	−	0.709306i
$789$	51.0441	−	66.5219i	1.81722	−	2.36824i
$790$	−8.82986	+	0.161415i	−0.314152	+	0.00574287i
$791$	0.266448	+	0.816627i	0.00947379	+	0.0290359i
$792$	79.4807	−	4.36273i	2.82422	−	0.155023i
$793$	−3.19225	−	0.855360i	−0.113360	−	0.0303747i
$794$	−31.9171	+	9.18058i	−1.13269	+	0.325807i
$795$	4.17224	−	31.6913i	0.147974	−	1.12398i
$796$	26.3998	+	42.0937i	0.935715	+	1.49197i
$797$	−4.90280	+	11.8364i	−0.173666	+	0.419267i	−0.986615	−	0.163068i	$-0.947861\pi$
$797$	−4.90280	+	11.8364i	−0.173666	+	0.419267i	0.812949	+	0.582335i	$0.197861\pi$
$798$	8.89022	+	2.95434i	0.314710	+	0.104582i
$799$			7.70706i			0.272656i
$800$	−8.29646	+	13.1422i	−0.293324	+	0.464646i
$801$	22.8832	+	13.2116i	0.808540	+	0.466811i
$802$	−5.60759	−	7.03778i	−0.198011	−	0.248513i
$803$	7.98531	+	60.6544i	0.281795	+	2.14045i
$804$	−66.9726	+	2.44941i	−2.36194	+	0.0863839i
$805$	−17.7797	−	12.1875i	−0.626651	−	0.429553i
$806$	−9.59519	−	9.25068i	−0.337976	−	0.325841i
$807$	7.70970	−	28.7730i	0.271394	−	1.01286i
$808$	20.3779	−	6.67701i	0.716893	−	0.234896i
$809$	−36.5097	+	9.78275i	−1.28361	+	0.343943i	−0.835231	−	0.549899i	$-0.814666\pi$
$809$	−36.5097	+	9.78275i	−1.28361	+	0.343943i	−0.448382	+	0.893842i	$0.648000\pi$
$810$	11.5115	−	6.92975i	0.404473	−	0.243487i
$811$	−43.6183	+	18.0673i	−1.53165	+	0.634428i	−0.979883	−	0.199573i	$-0.936045\pi$
$811$	−43.6183	+	18.0673i	−1.53165	+	0.634428i	−0.551763	+	0.834001i	$0.686045\pi$
$812$	−28.5750	+	6.42130i	−1.00279	+	0.225343i
$813$	−2.67937	+	6.46857i	−0.0939696	+	0.226863i
$814$	42.1706	+	31.1508i	1.47808	+	1.09183i
$815$	−7.56958	−	4.37030i	−0.265151	−	0.153085i
$816$	27.4365	+	30.8059i	0.960471	+	1.07842i
$817$	−1.15170	−	1.99480i	−0.0402928	−	0.0697892i
$818$	20.1297	+	46.1908i	0.703818	+	1.61502i
$819$	−6.89658	+	19.5516i	−0.240986	+	0.683190i
$820$	34.1177	−	15.6164i	1.19144	−	0.545347i
$821$	−7.46854	−	5.73081i	−0.260654	−	0.200007i	0.470164	−	0.882579i	$-0.344195\pi$
$821$	−7.46854	−	5.73081i	−0.260654	−	0.200007i	−0.730818	+	0.682572i	$0.760861\pi$
$822$	−46.5477	−	25.7516i	−1.62354	−	0.898190i
$823$	−10.8947	−	40.6596i	−0.379766	−	1.41730i	−0.846255	−	0.532778i	$-0.821148\pi$
$823$	−10.8947	−	40.6596i	−0.379766	−	1.41730i	0.466490	−	0.884527i	$-0.345519\pi$
$824$	−2.78871	−	14.8414i	−0.0971493	−	0.517024i
$825$	28.3159	+	28.3159i	0.985833	+	0.985833i
$826$	−7.82738	−	22.5816i	−0.272349	−	0.785714i
$827$	16.3168	−	6.75863i	0.567390	−	0.235020i	−0.0805002	−	0.996755i	$-0.525652\pi$
$827$	16.3168	−	6.75863i	0.567390	−	0.235020i	0.647890	+	0.761734i	$0.275652\pi$
$828$	−13.8042	+	60.2459i	−0.479728	+	2.09369i
$829$	1.38987	+	1.81132i	0.0482722	+	0.0629096i	0.816866	−	0.576828i	$-0.195710\pi$
$829$	1.38987	+	1.81132i	0.0482722	+	0.0629096i	−0.768593	+	0.639738i	$0.779043\pi$
$830$	8.09265	+	10.1566i	0.280900	+	0.352542i
$831$	0.0603705	+	0.104565i	0.00209423	+	0.00362731i
$832$	9.65118	−	5.30220i	0.334594	−	0.183821i
$833$	−2.61924	−	24.3448i	−0.0907514	−	0.843498i
$834$	62.9857	+	24.7507i	2.18102	+	0.857046i
$835$	32.0489	−	4.21931i	1.10910	−	0.146015i
$836$	−8.02519	+	2.46804i	−0.277557	+	0.0853588i
$837$	−53.8967	−	7.09564i	−1.86294	−	0.245261i
$838$	−3.38446	+	13.6222i	−0.116914	+	0.470571i
$839$	10.4186	−	10.4186i	0.359690	−	0.359690i	−0.504009	−	0.863699i	$-0.668142\pi$
$839$	10.4186	−	10.4186i	0.359690	−	0.359690i	0.863699	+	0.504009i	$0.168142\pi$
$840$	22.8832	+	23.9357i	0.789545	+	0.825858i
$841$	1.15576	+	1.15576i	0.0398537	+	0.0398537i
$842$	−5.88399	+	3.54207i	−0.202776	+	0.122068i
$843$	−7.05934	+	53.6210i	−0.243137	+	1.84681i
$844$	8.43319	+	0.797979i	0.290282	+	0.0274676i
$845$	2.17555	+	16.5249i	0.0748411	+	0.568475i
$846$	16.2619	−	7.08683i	0.559095	−	0.243650i
$847$	35.5037	−	1.90441i	1.21992	−	0.0654364i
$848$	−12.9778	−	25.8157i	−0.445660	−	0.886515i
$849$	30.0513	−	17.3501i	1.03136	−	0.595455i
$850$	−1.52739	+	13.5048i	−0.0523892	+	0.463212i
$851$	−32.2966	+	24.7820i	−1.10711	+	0.849517i
$852$	−19.0636	+	3.22251i	−0.653108	+	0.110401i
$853$	2.32005	+	5.60110i	0.0794371	+	0.191778i	0.958608	−	0.284728i	$-0.0919031\pi$
$853$	2.32005	+	5.60110i	0.0794371	+	0.191778i	−0.879171	+	0.476506i	$0.841903\pi$
$854$	−5.03885	−	7.43741i	−0.172426	−	0.254503i
$855$	−5.13061	+	5.13061i	−0.175463	+	0.175463i
$856$	−43.8835	−	9.21424i	−1.49991	−	0.314936i
$857$	43.9119	−	11.7662i	1.50000	−	0.401925i	0.586902	−	0.809658i	$-0.300347\pi$
$857$	43.9119	−	11.7662i	1.50000	−	0.401925i	0.913101	+	0.407734i	$0.133681\pi$
$858$	−7.84307	−	27.2671i	−0.267758	−	0.930883i
$859$	3.44057	−	4.48384i	0.117391	−	0.152987i	−0.730962	−	0.682418i	$-0.760928\pi$
$859$	3.44057	−	4.48384i	0.117391	−	0.152987i	0.848352	+	0.529432i	$0.177595\pi$
$860$	−0.297577	−	8.13646i	−0.0101473	−	0.277451i
$861$	17.8874	+	95.8545i	0.609602	+	3.26671i
$862$	−4.55816	−	1.79117i	−0.155252	−	0.0610073i
$863$	25.0707	−	14.4746i	0.853417	−	0.492720i	−0.00838563	−	0.999965i	$-0.502669\pi$
$863$	25.0707	−	14.4746i	0.853417	−	0.492720i	0.861802	+	0.507245i	$0.169336\pi$
$864$	18.8131	−	40.7834i	0.640036	−	1.38748i
$865$	−8.34861	+	14.4602i	−0.283861	+	0.491662i
$866$	−2.24851	−	14.9607i	−0.0764074	−	0.508384i
$867$	−12.9787	−	5.37595i	−0.440780	−	0.182577i
$868$	−3.26157	−	36.0832i	−0.110705	−	1.22474i
$869$	7.87134	+	19.0031i	0.267017	+	0.644636i
$870$	8.35174	−	33.6151i	0.283150	−	1.13966i
$871$	4.04890	+	15.1107i	0.137192	+	0.512007i
$872$	20.4212	−	40.3253i	0.691548	−	1.36559i
$873$	−1.88757	−	0.505772i	−0.0638845	−	0.0171178i
$874$	−0.119157	−	6.51823i	−0.00403054	−	0.220483i
$875$	−2.37605	+	30.6723i	−0.0803251	+	1.03691i
$876$	68.3950	+	25.4433i	2.31085	+	0.859649i
$877$	11.9013	−	1.56683i	0.401877	−	0.0529081i	0.0731211	−	0.997323i	$-0.476704\pi$
$877$	11.9013	−	1.56683i	0.401877	−	0.0529081i	0.328756	+	0.944415i	$0.393371\pi$
$878$	−3.91503	−	0.442790i	−0.132126	−	0.0149434i
$879$	−15.3435	+	26.5758i	−0.517525	+	0.896380i
$880$	−29.1513	−	5.56665i	−0.982692	−	0.187652i
$881$	17.9606			0.605109			0.302554	−	0.953132i	$-0.402161\pi$
$881$	17.9606			0.605109			0.302554	+	0.953132i	$0.402161\pi$
$882$	−48.9591	+	27.9123i	−1.64854	+	0.939855i
$883$	−22.5227	−	9.32921i	−0.757949	−	0.313953i	−0.0299688	−	0.999551i	$-0.509541\pi$
$883$	−22.5227	−	9.32921i	−0.757949	−	0.313953i	−0.727980	+	0.685598i	$0.759541\pi$
$884$	5.57893	−	7.84874i	0.187640	−	0.263982i
$885$	28.0232	+	3.68933i	0.941991	+	0.124015i
$886$	10.2114	−	18.4577i	0.343057	−	0.620098i
$887$	8.06523	−	30.0999i	0.270804	−	1.01065i	−0.687797	−	0.725903i	$-0.741422\pi$
$887$	8.06523	−	30.0999i	0.270804	−	1.01065i	0.958601	−	0.284752i	$-0.0919112\pi$
$888$	56.3787	−	27.0628i	1.89195	−	0.908168i
$889$	7.82661	+	23.9875i	0.262496	+	0.804515i
$890$	−7.09231	−	6.83767i	−0.237735	−	0.229199i
$891$	−24.8274	−	19.0507i	−0.831750	−	0.638224i
$892$	0.546755	−	0.168147i	0.0183067	−	0.00562998i
$893$	−1.48443	+	1.13904i	−0.0496745	+	0.0381166i
$894$	4.45923	+	29.6699i	0.149139	+	0.992310i
$895$	−2.86042			−0.0956133
$896$	29.2684	+	6.27387i	0.977788	+	0.209595i
$897$	22.0305			0.735576
$898$	−7.97117	−	53.0369i	−0.266001	−	1.76987i
$899$	−30.0652	+	23.0699i	−1.00273	+	0.769423i
$900$	29.8997	−	9.19523i	0.996655	−	0.306508i
$901$	−20.0459	−	15.3817i	−0.667825	−	0.512440i
$902$	−62.9138	−	60.6549i	−2.09480	−	2.01959i
$903$	20.7017	+	4.37370i	0.688908	+	0.145547i
$904$	−0.827867	+	0.397391i	−0.0275345	+	0.0132170i
$905$	6.04351	−	22.5547i	0.200893	−	0.749743i
$906$	−36.7163	+	66.3670i	−1.21982	+	2.20490i
$907$	−28.1046	−	3.70004i	−0.933197	−	0.122858i	−0.351431	−	0.936214i	$-0.614305\pi$
$907$	−28.1046	−	3.70004i	−0.933197	−	0.122858i	−0.581766	+	0.813356i	$0.697638\pi$
$908$	1.76268	−	2.47984i	0.0584967	−	0.0822963i
$909$	−39.8757	−	16.5170i	−1.32259	−	0.547836i
$910$	4.25312	−	6.45453i	0.140990	−	0.213966i
$911$	−40.9636			−1.35719			−0.678593	−	0.734515i	$-0.737410\pi$
$911$	−40.9636			−1.35719			−0.678593	+	0.734515i	$0.737410\pi$
$912$	−1.87851	+	9.83732i	−0.0622035	+	0.325746i
$913$	15.1232	−	26.1941i	0.500505	−	0.866899i
$914$	−5.96891	−	0.675083i	−0.197434	−	0.0223298i
$915$	10.5336	−	1.38677i	0.348230	−	0.0458453i
$916$	7.89366	+	2.93648i	0.260814	+	0.0970240i
$917$	13.7290	+	28.6926i	0.453370	+	0.947513i
$918$	−0.717861	−	39.2692i	−0.0236929	−	1.29608i
$919$	−19.0869	−	5.11433i	−0.629620	−	0.168706i	−0.0701228	−	0.997538i	$-0.522339\pi$
$919$	−19.0869	−	5.11433i	−0.629620	−	0.168706i	−0.559497	+	0.828832i	$0.689006\pi$
$920$	10.4109	−	20.5583i	0.343238	−	0.677786i
$921$	6.78039	+	25.3047i	0.223421	+	0.833820i
$922$	−4.62535	+	18.6167i	−0.152328	+	0.613109i
$923$	1.72710	+	4.16958i	0.0568481	+	0.137243i
$924$	32.3933	−	69.9930i	1.06566	−	2.30260i
$925$	19.0352	+	7.88462i	0.625872	+	0.259245i
$926$	0.797865	+	5.30867i	0.0262195	+	0.174454i
$927$	−15.1973	+	26.3225i	−0.499146	+	0.864546i
$928$	−10.8299	−	29.3772i	−0.355508	−	0.964352i
$929$	20.2209	−	11.6745i	0.663426	−	0.383029i	−0.130155	−	0.991494i	$-0.541548\pi$
$929$	20.2209	−	11.6745i	0.663426	−	0.383029i	0.793581	+	0.608465i	$0.208214\pi$
$930$	39.8793	+	15.6709i	1.30769	+	0.513868i
$931$	4.30187	−	4.10246i	0.140988	−	0.134453i
$932$	1.40228	+	38.3416i	0.0459332	+	1.25592i
$933$	−29.6541	+	38.6460i	−0.970833	+	1.26521i
$934$	10.0523	+	34.9478i	0.328923	+	1.14353i
$935$	−25.0684	+	6.71707i	−0.819826	+	0.219672i
$936$	−21.6908	−	4.55443i	−0.708986	−	0.148866i
$937$	−24.5895	+	24.5895i	−0.803303	+	0.803303i	−0.983610	−	0.180307i	$-0.942291\pi$
$937$	−24.5895	+	24.5895i	−0.803303	+	0.803303i	0.180307	+	0.983610i	$0.442291\pi$
$938$	−18.5630	+	38.2589i	−0.606102	+	1.24920i
$939$	−15.8406	−	38.2426i	−0.516938	−	1.24800i
$940$	−6.52127	+	1.10235i	−0.212700	+	0.0359548i
$941$	12.2757	−	9.41947i	0.400176	−	0.307066i	−0.388994	−	0.921240i	$-0.627177\pi$
$941$	12.2757	−	9.41947i	0.400176	−	0.307066i	0.789170	+	0.614174i	$0.210511\pi$
$942$	2.66017	−	23.5205i	0.0866730	−	0.766341i
$943$	58.7652	−	33.9281i	1.91366	−	1.10485i
$944$	22.8277	−	11.4757i	0.742978	−	0.373502i
$945$	−1.68870	−	31.4822i	−0.0549335	−	1.02412i
$946$	−17.3840	+	7.57584i	−0.565203	+	0.246312i
$947$	−2.14255	−	16.2743i	−0.0696234	−	0.528843i	−0.990345	−	0.138623i	$-0.955732\pi$
$947$	−2.14255	−	16.2743i	−0.0696234	−	0.528843i	0.920722	−	0.390220i	$-0.127601\pi$
$948$	24.4258	+	2.31126i	0.793313	+	0.0750661i
$949$	2.22342	−	16.8885i	0.0721752	−	0.548225i
$950$	−2.82686	+	1.70172i	−0.0917153	+	0.0552112i
$951$	43.4077	+	43.4077i	1.40759	+	1.40759i
$952$	25.4299	−	6.20488i	0.824186	−	0.201101i
$953$	−6.55425	+	6.55425i	−0.212313	+	0.212313i	−0.805249	−	0.592936i	$-0.797969\pi$
$953$	−6.55425	+	6.55425i	−0.212313	+	0.212313i	0.592936	+	0.805249i	$0.297969\pi$
$954$	−14.0228	+	56.4406i	−0.454004	+	1.82733i
$955$	17.2450	+	2.27034i	0.558034	+	0.0734666i
$956$	−7.39114	+	2.27304i	−0.239047	+	0.0735155i
$957$	−79.9821	+	10.5298i	−2.58545	+	0.340381i
$958$	38.3088	+	15.0537i	1.23770	+	0.486364i
$959$	−28.2863	+	18.4188i	−0.913413	+	0.594774i
$960$	−22.1419	+	27.6214i	−0.714626	+	0.891478i
$961$	−7.93986	−	13.7522i	−0.256124	−	0.443620i
$962$	−9.09694	−	11.4171i	−0.293297	−	0.368101i
$963$	54.9421	+	71.6019i	1.77048	+	2.30734i
$964$	3.05124	−	13.3166i	0.0982738	−	0.428899i
$965$	2.35279	−	0.974556i	0.0757389	−	0.0313721i
$966$	45.2768	+	39.1955i	1.45676	+	1.26109i
$967$	−25.9948	−	25.9948i	−0.835935	−	0.835935i	0.152386	−	0.988321i	$-0.451304\pi$
$967$	−25.9948	−	25.9948i	−0.835935	−	0.835935i	−0.988321	+	0.152386i	$0.951304\pi$
$968$	7.01920	+	37.3559i	0.225606	+	1.20066i
$969$	2.26672	+	8.45952i	0.0728176	+	0.271759i
$970$	0.637525	+	0.352699i	0.0204697	+	0.0113245i
$971$	3.59490	+	2.75846i	0.115366	+	0.0885233i	0.664833	−	0.746992i	$-0.268503\pi$
$971$	3.59490	+	2.75846i	0.115366	+	0.0885233i	−0.549467	+	0.835515i	$0.685169\pi$
$972$	9.37410	−	4.29072i	0.300674	−	0.137625i
$973$	32.6185	−	27.9282i	1.04570	−	0.895337i
$974$	12.8846	+	29.5658i	0.412849	+	0.947348i
$975$	−5.57500	−	9.65619i	−0.178543	−	0.309245i
$976$	7.17183	−	6.38743i	0.229565	−	0.204457i
$977$	−19.3942	−	11.1973i	−0.620476	−	0.358232i	0.156578	−	0.987666i	$-0.449954\pi$
$977$	−19.3942	−	11.1973i	−0.620476	−	0.358232i	−0.777054	+	0.629433i	$0.783287\pi$
$978$	19.5318	+	14.4279i	0.624559	+	0.461353i
$979$	−8.78072	+	21.1985i	−0.280633	+	0.677508i
$980$	20.2246	−	5.69833i	0.646050	−	0.182027i
$981$	−84.0532	+	34.8160i	−2.68361	+	1.11159i
$982$	11.6106	−	6.98940i	0.370509	−	0.223041i
$983$	26.1730	−	7.01303i	0.834789	−	0.223681i	0.183987	−	0.982929i	$-0.441100\pi$
$983$	26.1730	−	7.01303i	0.834789	−	0.223681i	0.650802	+	0.759248i	$0.274433\pi$
$984$	−99.0597	+	32.4578i	−3.15791	+	1.03472i
$985$	5.01866	−	18.7299i	0.159908	−	0.596784i
$986$	−19.7110	−	19.0032i	−0.627725	−	0.605187i
$987$	1.32746	−	17.1361i	0.0422535	−	0.545449i
$988$	2.33624	−	0.0854441i	0.0743258	−	0.00271834i
$989$	−1.92189	−	14.5982i	−0.0611127	−	0.464197i
$990$	37.2240	+	46.7179i	1.18306	+	1.48479i
$991$	40.5476	+	23.4101i	1.28804	+	0.743648i	0.978304	−	0.207176i	$-0.0664273\pi$
$991$	40.5476	+	23.4101i	1.28804	+	0.743648i	0.309732	+	0.950824i	$0.399761\pi$
$992$	37.7788	−	8.53904i	1.19948	−	0.271115i
$993$		−	38.5504i		−	1.22336i
$994$	−3.86880	+	11.6420i	−0.122711	+	0.369263i
$995$	−14.2690	+	34.4485i	−0.452359	+	1.09209i
$996$	−19.1692	−	30.5647i	−0.607399	−	0.968481i
$997$	3.52993	−	26.8125i	0.111794	−	0.849159i	−0.840036	−	0.542531i	$-0.817466\pi$
$997$	3.52993	−	26.8125i	0.111794	−	0.849159i	0.951830	−	0.306628i	$-0.0992006\pi$
$998$	22.3268	−	6.42204i	0.706741	−	0.203286i
$999$	−57.5121	−	15.4103i	−1.81960	−	0.487561i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.be.a.3.13	✓	240
4.3	odd	2		896.2.bi.a.815.29		240
7.5	odd	6	inner	224.2.be.a.131.9	yes	240
28.19	even	6		896.2.bi.a.47.2		240
32.11	odd	8	inner	224.2.be.a.171.9	yes	240
32.21	even	8		896.2.bi.a.591.2		240
224.75	even	24	inner	224.2.be.a.75.13	yes	240
224.117	odd	24		896.2.bi.a.719.29		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.be.a.3.13	✓	240	1.1	even	1	trivial
224.2.be.a.75.13	yes	240	224.75	even	24	inner
224.2.be.a.131.9	yes	240	7.5	odd	6	inner
224.2.be.a.171.9	yes	240	32.11	odd	8	inner
896.2.bi.a.47.2		240	28.19	even	6
896.2.bi.a.591.2		240	32.21	even	8
896.2.bi.a.719.29		240	224.117	odd	24
896.2.bi.a.815.29		240	4.3	odd	2

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.be (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.210188 - 1.39851i) q^{2} +(-2.33910 + 1.79485i) q^{3} +(-1.91164 + 0.587899i) q^{4} +(-1.19071 - 0.913663i) q^{5} +(3.00177 + 2.89399i) q^{6} +(2.51525 - 0.820673i) q^{7} +(1.22399 + 2.54987i) q^{8} +(1.47343 - 5.49891i) q^{9} +O(q^{10})\)	\(q+(-0.210188 - 1.39851i) q^{2} +(-2.33910 + 1.79485i) q^{3} +(-1.91164 + 0.587899i) q^{4} +(-1.19071 - 0.913663i) q^{5} +(3.00177 + 2.89399i) q^{6} +(2.51525 - 0.820673i) q^{7} +(1.22399 + 2.54987i) q^{8} +(1.47343 - 5.49891i) q^{9} +(-1.02749 + 1.85726i) q^{10} +(4.90123 + 0.645259i) q^{11} +(3.41633 - 4.80627i) q^{12} +(-1.27169 - 0.526752i) q^{13} +(-1.67639 - 3.34510i) q^{14} +4.42508 q^{15} +(3.30875 - 2.24771i) q^{16} +(1.74895 - 3.02927i) q^{17} +(-7.99996 - 0.904794i) q^{18} +(0.841939 - 0.110843i) q^{19} +(2.81335 + 1.04658i) q^{20} +(-4.41044 + 6.43415i) q^{21} +(-0.127781 - 6.99003i) q^{22} +(5.24348 + 1.40498i) q^{23} +(-7.43968 - 3.76754i) q^{24} +(-0.711087 - 2.65381i) q^{25} +(-0.469371 + 1.88918i) q^{26} +(3.03837 + 7.33528i) q^{27} +(-4.32579 + 3.04755i) q^{28} +(5.11353 + 2.11809i) q^{29} +(-0.930100 - 6.18851i) q^{30} +(-3.42344 + 5.92957i) q^{31} +(-3.83889 - 4.15487i) q^{32} +(-12.6226 + 7.28767i) q^{33} +(-4.60407 - 1.80920i) q^{34} +(-3.74475 - 1.32091i) q^{35} +(0.416137 + 11.3782i) q^{36} +(-4.56522 + 5.94951i) q^{37} +(-0.331981 - 1.15416i) q^{38} +(3.92005 - 1.05038i) q^{39} +(0.872316 - 4.15447i) q^{40} +(8.83893 - 8.83893i) q^{41} +(9.92522 + 4.81565i) q^{42} +(-1.03800 - 2.50595i) q^{43} +(-9.74875 + 1.64793i) q^{44} +(-6.77858 + 5.20139i) q^{45} +(0.862764 - 7.62835i) q^{46} +(-1.90815 + 1.10167i) q^{47} +(-3.70519 + 11.1963i) q^{48} +(5.65299 - 4.12840i) q^{49} +(-3.56191 + 1.55226i) q^{50} +(1.34613 + 10.2249i) q^{51} +(2.74069 + 0.259334i) q^{52} +(0.942862 - 7.16175i) q^{53} +(9.61981 - 5.79097i) q^{54} +(-5.24639 - 5.24639i) q^{55} +(5.17125 + 5.40909i) q^{56} +(-1.77043 + 1.77043i) q^{57} +(1.88736 - 7.59650i) q^{58} +(6.33282 + 0.833732i) q^{59} +(-8.45917 + 2.60150i) q^{60} +(2.38043 - 0.313389i) q^{61} +(9.01211 + 3.54138i) q^{62} +(-0.806763 - 15.0404i) q^{63} +(-5.00372 + 6.24202i) q^{64} +(1.03294 + 1.78911i) q^{65} +(12.8450 + 16.1210i) q^{66} +(-6.91866 - 9.01657i) q^{67} +(-1.56246 + 6.81909i) q^{68} +(-14.7868 + 6.12488i) q^{69} +(-1.06020 + 5.51470i) q^{70} +(-2.31844 - 2.31844i) q^{71} +(15.8250 - 2.97353i) q^{72} +(3.20298 + 11.9537i) q^{73} +(9.27998 + 5.13397i) q^{74} +(6.42651 + 4.93124i) q^{75} +(-1.54432 + 0.706868i) q^{76} +(12.8574 - 2.39932i) q^{77} +(-2.29291 - 5.26145i) q^{78} +(2.08038 + 3.60332i) q^{79} +(-5.99341 - 0.346719i) q^{80} +(-5.48225 - 3.16518i) q^{81} +(-14.2191 - 10.5035i) q^{82} +(2.34140 - 5.65265i) q^{83} +(4.64855 - 14.8927i) q^{84} +(-4.85023 + 2.00903i) q^{85} +(-3.28641 + 1.97837i) q^{86} +(-15.7627 + 4.22361i) q^{87} +(4.35371 + 13.2873i) q^{88} +(-1.20130 + 4.48330i) q^{89} +(8.69896 + 8.38662i) q^{90} +(-3.63091 - 0.281271i) q^{91} +(-10.8496 + 0.396807i) q^{92} +(-2.63495 - 20.0144i) q^{93} +(1.94176 + 2.43700i) q^{94} +(-1.10378 - 0.637267i) q^{95} +(16.4369 + 2.82840i) q^{96} -0.343262i q^{97} +(-6.96179 - 7.03801i) q^{98} +(10.7698 - 26.0007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9	\( 240 q - 4 q^{2} - 12 q^{3} - 4 q^{4} - 12 q^{5} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 12 q^{10} - 4 q^{11} - 12 q^{12} - 40 q^{14} - 32 q^{15} - 24 q^{16} + 16 q^{18} - 12 q^{19} - 8 q^{21} - 8 q^{22} + 4 q^{23} - 12 q^{24} - 4 q^{25} - 12 q^{26} + 12 q^{28} - 16 q^{29} - 52 q^{30} - 4 q^{32} - 24 q^{33} - 32 q^{35} + 64 q^{36} - 4 q^{37} - 12 q^{38} - 4 q^{39} - 12 q^{40} - 28 q^{42} - 32 q^{43} - 52 q^{44} - 48 q^{45} - 4 q^{46} - 24 q^{47} - 40 q^{50} + 20 q^{51} + 60 q^{52} - 20 q^{53} - 12 q^{54} - 48 q^{56} - 16 q^{57} - 36 q^{58} + 84 q^{59} + 28 q^{60} - 12 q^{61} - 136 q^{64} - 8 q^{65} + 132 q^{66} + 36 q^{67} - 12 q^{68} + 28 q^{70} - 80 q^{71} - 4 q^{72} - 12 q^{73} - 20 q^{74} - 72 q^{75} - 8 q^{77} - 216 q^{78} - 8 q^{79} + 24 q^{80} + 108 q^{82} + 12 q^{84} + 24 q^{85} - 4 q^{86} - 12 q^{87} - 48 q^{88} - 12 q^{89} + 40 q^{91} - 80 q^{92} + 20 q^{93} + 60 q^{94} + 312 q^{96} - 16 q^{98} - 40 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 12 * q^3 - 4 * q^4 - 12 * q^5 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 12 * q^10 - 4 * q^11 - 12 * q^12 - 40 * q^14 - 32 * q^15 - 24 * q^16 + 16 * q^18 - 12 * q^19 - 8 * q^21 - 8 * q^22 + 4 * q^23 - 12 * q^24 - 4 * q^25 - 12 * q^26 + 12 * q^28 - 16 * q^29 - 52 * q^30 - 4 * q^32 - 24 * q^33 - 32 * q^35 + 64 * q^36 - 4 * q^37 - 12 * q^38 - 4 * q^39 - 12 * q^40 - 28 * q^42 - 32 * q^43 - 52 * q^44 - 48 * q^45 - 4 * q^46 - 24 * q^47 - 40 * q^50 + 20 * q^51 + 60 * q^52 - 20 * q^53 - 12 * q^54 - 48 * q^56 - 16 * q^57 - 36 * q^58 + 84 * q^59 + 28 * q^60 - 12 * q^61 - 136 * q^64 - 8 * q^65 + 132 * q^66 + 36 * q^67 - 12 * q^68 + 28 * q^70 - 80 * q^71 - 4 * q^72 - 12 * q^73 - 20 * q^74 - 72 * q^75 - 8 * q^77 - 216 * q^78 - 8 * q^79 + 24 * q^80 + 108 * q^82 + 12 * q^84 + 24 * q^85 - 4 * q^86 - 12 * q^87 - 48 * q^88 - 12 * q^89 + 40 * q^91 - 80 * q^92 + 20 * q^93 + 60 * q^94 + 312 * q^96 - 16 * q^98 - 40 * q^99

Introduction

L-functions

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