LMFDB - Embedded newform 418.2.n.a.201.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(49,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([12, 20]))

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

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

chi := DirichletCharacter("418.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.n (of order $15$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{15})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + x^{5} - x^{4} + x^{3} - x + 1 $ x^8 - x^7 + x^5 - x^4 + x^3 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			201.1
Root			$0.913545 + 0.406737i$ of defining polynomial
Character	$\chi$	$=$	418.201
Dual form			418.2.n.a.235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.104528 + 0.994522i) q^{2} +(1.20906 + 0.256993i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(2.60735 - 1.16087i) q^{5} +(-0.129204 + 1.22930i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.34486 - 0.598772i) q^{9} +O(q^{10})$	\(q+(0.104528 + 0.994522i) q^{2} +(1.20906 + 0.256993i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(2.60735 - 1.16087i) q^{5} +(-0.129204 + 1.22930i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.34486 - 0.598772i) q^{9} +(1.42705 + 2.47172i) q^{10} +(0.309017 + 3.30220i) q^{11} -1.23607 q^{12} +(3.52090 + 1.56760i) q^{13} +(0.978148 + 0.207912i) q^{14} +(3.45077 - 0.733484i) q^{15} +(0.913545 - 0.406737i) q^{16} +(1.26249 - 0.562096i) q^{17} +(0.454915 - 1.40008i) q^{18} +(3.06539 - 3.09893i) q^{19} +(-2.30902 + 1.67760i) q^{20} +(0.618034 - 1.07047i) q^{21} +(-3.25181 + 0.652498i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.129204 - 1.22930i) q^{24} +(2.10502 - 2.33786i) q^{25} +(-1.19098 + 3.66547i) q^{26} +(-4.47214 - 3.24920i) q^{27} +(-0.104528 + 0.994522i) q^{28} +(0.978148 - 0.207912i) q^{29} +(1.09017 + 3.35520i) q^{30} +(-8.97214 + 6.51864i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.475022 + 4.07196i) q^{33} +(0.690983 + 1.19682i) q^{34} +(-0.298335 - 2.83847i) q^{35} +(1.43997 + 0.306074i) q^{36} +(-0.427051 + 1.31433i) q^{37} +(3.40238 + 2.72467i) q^{38} +(3.85410 + 2.80017i) q^{39} +(-1.90977 - 2.12101i) q^{40} +(-0.230909 - 0.0490813i) q^{41} +(1.12920 + 0.502754i) q^{42} +(-1.26393 + 2.18919i) q^{43} +(-0.988830 - 3.16579i) q^{44} -4.20163 q^{45} +(0.809017 - 0.587785i) q^{46} +(-0.669131 + 0.743145i) q^{47} +(1.20906 - 0.256993i) q^{48} +(4.85410 + 3.52671i) q^{49} +(2.54508 + 1.84911i) q^{50} +(1.67088 - 0.355156i) q^{51} +(-3.76988 - 0.801313i) q^{52} +(-10.2647 - 4.57012i) q^{53} +(2.76393 - 4.78727i) q^{54} +(4.63913 + 8.25126i) q^{55} -1.00000 q^{56} +(4.50264 - 2.95900i) q^{57} +(0.309017 + 0.951057i) q^{58} +(-2.63923 - 2.93117i) q^{59} +(-3.22286 + 1.43491i) q^{60} +(1.13456 - 10.7946i) q^{61} +(-7.42077 - 8.24160i) q^{62} +(-0.985051 + 1.09401i) q^{63} +(-0.809017 + 0.587785i) q^{64} +11.0000 q^{65} +(-4.09931 - 0.0467845i) q^{66} +(-1.16312 - 2.01458i) q^{67} +(-1.11803 + 0.812299i) q^{68} +(-0.381966 - 1.17557i) q^{69} +(2.79173 - 0.593401i) q^{70} +(-12.2250 + 5.44294i) q^{71} +(-0.153880 + 1.46407i) q^{72} +(-7.32315 - 8.13318i) q^{73} +(-1.35177 - 0.287327i) q^{74} +(3.14590 - 2.28563i) q^{75} +(-2.35410 + 3.66854i) q^{76} +(3.23607 + 0.726543i) q^{77} +(-2.38197 + 4.12569i) q^{78} +(0.577819 + 5.49758i) q^{79} +(1.90977 - 2.12101i) q^{80} +(-1.61689 - 1.79574i) q^{81} +(0.0246758 - 0.234775i) q^{82} +(-4.04508 - 2.93893i) q^{83} +(-0.381966 + 1.17557i) q^{84} +(2.63923 - 2.93117i) q^{85} +(-2.30932 - 1.02817i) q^{86} +1.23607 q^{87} +(3.04508 - 1.31433i) q^{88} +(5.97214 + 10.3440i) q^{89} +(-0.439190 - 4.17861i) q^{90} +(2.57890 - 2.86416i) q^{91} +(0.669131 + 0.743145i) q^{92} +(-12.5231 + 5.57563i) q^{93} +(-0.809017 - 0.587785i) q^{94} +(4.39511 - 11.6385i) q^{95} +(0.381966 + 1.17557i) q^{96} +(-1.38355 - 13.1636i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(1.56168 - 4.62603i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - q^{2} + 6 q^{3} + q^{4} + 7 q^{5} + 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) $ 8 * q - q^2 + 6 * q^3 + q^4 + 7 * q^5 + 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9	\( 8 q - q^{2} + 6 q^{3} + q^{4} + 7 q^{5} + 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} - 2 q^{10} - 2 q^{11} + 8 q^{12} + 8 q^{13} - q^{14} - 18 q^{15} + q^{16} + 26 q^{18} + 4 q^{19} - 14 q^{20} - 4 q^{21} - 11 q^{22} - 4 q^{23} + 4 q^{24} + 14 q^{25} - 14 q^{26} + q^{28} - q^{29} - 36 q^{30} - 36 q^{31} + 4 q^{32} - 24 q^{33} + 10 q^{34} + 7 q^{35} + 13 q^{36} + 10 q^{37} + 17 q^{38} + 4 q^{39} + 8 q^{40} - 7 q^{41} + 4 q^{42} - 28 q^{43} - 4 q^{44} - 132 q^{45} + 2 q^{46} - q^{47} + 6 q^{48} + 12 q^{49} - 2 q^{50} + 20 q^{51} - 7 q^{52} - 14 q^{53} + 40 q^{54} + 12 q^{55} - 8 q^{56} + 8 q^{57} - 2 q^{58} + 25 q^{59} + 2 q^{60} - 15 q^{61} + 7 q^{62} + 13 q^{63} - 2 q^{64} + 88 q^{65} + 14 q^{66} + 22 q^{67} - 12 q^{69} + 8 q^{70} - 12 q^{71} + 7 q^{72} + 18 q^{73} + 5 q^{74} + 52 q^{75} + 8 q^{76} + 8 q^{77} - 28 q^{78} - 8 q^{80} + 41 q^{81} - 3 q^{82} - 10 q^{83} - 12 q^{84} - 25 q^{85} + 3 q^{86} - 8 q^{87} + 2 q^{88} + 12 q^{89} - 11 q^{90} - 7 q^{91} + q^{92} - 22 q^{93} - 2 q^{94} - 14 q^{95} + 12 q^{96} + 16 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 8 * q - q^2 + 6 * q^3 + q^4 + 7 * q^5 + 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 - 2 * q^10 - 2 * q^11 + 8 * q^12 + 8 * q^13 - q^14 - 18 * q^15 + q^16 + 26 * q^18 + 4 * q^19 - 14 * q^20 - 4 * q^21 - 11 * q^22 - 4 * q^23 + 4 * q^24 + 14 * q^25 - 14 * q^26 + q^28 - q^29 - 36 * q^30 - 36 * q^31 + 4 * q^32 - 24 * q^33 + 10 * q^34 + 7 * q^35 + 13 * q^36 + 10 * q^37 + 17 * q^38 + 4 * q^39 + 8 * q^40 - 7 * q^41 + 4 * q^42 - 28 * q^43 - 4 * q^44 - 132 * q^45 + 2 * q^46 - q^47 + 6 * q^48 + 12 * q^49 - 2 * q^50 + 20 * q^51 - 7 * q^52 - 14 * q^53 + 40 * q^54 + 12 * q^55 - 8 * q^56 + 8 * q^57 - 2 * q^58 + 25 * q^59 + 2 * q^60 - 15 * q^61 + 7 * q^62 + 13 * q^63 - 2 * q^64 + 88 * q^65 + 14 * q^66 + 22 * q^67 - 12 * q^69 + 8 * q^70 - 12 * q^71 + 7 * q^72 + 18 * q^73 + 5 * q^74 + 52 * q^75 + 8 * q^76 + 8 * q^77 - 28 * q^78 - 8 * q^80 + 41 * q^81 - 3 * q^82 - 10 * q^83 - 12 * q^84 - 25 * q^85 + 3 * q^86 - 8 * q^87 + 2 * q^88 + 12 * q^89 - 11 * q^90 - 7 * q^91 + q^92 - 22 * q^93 - 2 * q^94 - 14 * q^95 + 12 * q^96 + 16 * q^97 - 24 * q^98 + 43 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$2$	0.104528	+	0.994522i	0.0739128	+	0.703233i
$3$	1.20906	+	0.256993i	0.698049	+	0.148375i	0.543250	−	0.839571i	$-0.317194\pi$
$3$	1.20906	+	0.256993i	0.698049	+	0.148375i	0.154799	+	0.987946i	$0.450527\pi$
$4$	−0.978148	+	0.207912i	−0.489074	+	0.103956i
$5$	2.60735	−	1.16087i	1.16604	−	0.519156i	0.269886	−	0.962892i	$-0.413014\pi$
$5$	2.60735	−	1.16087i	1.16604	−	0.519156i	0.896157	+	0.443736i	$0.146347\pi$
$6$	−0.129204	+	1.22930i	−0.0527474	+	0.501858i
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i	−0.875520	−	0.483181i	$-0.839481\pi$
$7$	0.309017	−	0.951057i	0.116797	−	0.359466i	0.992318	+	0.123716i	$0.0394811\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−1.34486	−	0.598772i	−0.448288	−	0.199591i
$10$	1.42705	+	2.47172i	0.451273	+	0.781628i
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$11$	0.309017	+	3.30220i	0.0931721	+	0.995650i
$12$	−1.23607			−0.356822
$13$	3.52090	+	1.56760i	0.976521	+	0.434775i	0.832030	−	0.554731i	$-0.187179\pi$
$13$	3.52090	+	1.56760i	0.976521	+	0.434775i	0.144491	+	0.989506i	$0.453845\pi$
$14$	0.978148	+	0.207912i	0.261421	+	0.0555667i
$15$	3.45077	−	0.733484i	0.890985	−	0.189385i
$16$	0.913545	−	0.406737i	0.228386	−	0.101684i
$17$	1.26249	−	0.562096i	0.306199	−	0.136328i	−0.247885	−	0.968789i	$-0.579736\pi$
$17$	1.26249	−	0.562096i	0.306199	−	0.136328i	0.554083	+	0.832461i	$0.313069\pi$
$18$	0.454915	−	1.40008i	0.107225	−	0.330003i
$19$	3.06539	−	3.09893i	0.703249	−	0.710943i
$19$	3.06539	−	3.09893i	0.703249	−	0.710943i
$20$	−2.30902	+	1.67760i	−0.516312	+	0.375123i
$21$	0.618034	−	1.07047i	0.134866	−	0.233595i
$22$	−3.25181	+	0.652498i	−0.693288	+	0.139113i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$	−0.129204	−	1.22930i	−0.0263737	−	0.250929i
$25$	2.10502	−	2.33786i	0.421003	−	0.467572i
$26$	−1.19098	+	3.66547i	−0.233571	+	0.718858i
$27$	−4.47214	−	3.24920i	−0.860663	−	0.625308i
$28$	−0.104528	+	0.994522i	−0.0197540	+	0.187947i
$29$	0.978148	−	0.207912i	0.181637	−	0.0386082i	−0.116195	−	0.993226i	$-0.537070\pi$
$29$	0.978148	−	0.207912i	0.181637	−	0.0386082i	0.297832	+	0.954618i	$0.403736\pi$
$30$	1.09017	+	3.35520i	0.199037	+	0.612573i
$31$	−8.97214	+	6.51864i	−1.61144	+	1.17078i	−0.752723	+	0.658338i	$0.771260\pi$
$31$	−8.97214	+	6.51864i	−1.61144	+	1.17078i	−0.858720	+	0.512444i	$0.828740\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.475022	+	4.07196i	−0.0826908	+	0.708837i
$34$	0.690983	+	1.19682i	0.118503	+	0.205253i
$35$	−0.298335	−	2.83847i	−0.0504278	−	0.479788i
$36$	1.43997	+	0.306074i	0.239994	+	0.0510124i
$37$	−0.427051	+	1.31433i	−0.0702067	+	0.216074i	−0.980004	−	0.198980i	$-0.936237\pi$
$37$	−0.427051	+	1.31433i	−0.0702067	+	0.216074i	0.909797	+	0.415054i	$0.136237\pi$
$38$	3.40238	+	2.72467i	0.551938	+	0.442000i
$39$	3.85410	+	2.80017i	0.617150	+	0.448386i
$40$	−1.90977	−	2.12101i	−0.301961	−	0.335361i
$41$	−0.230909	−	0.0490813i	−0.0360620	−	0.00766521i	0.189845	−	0.981814i	$-0.439201\pi$
$41$	−0.230909	−	0.0490813i	−0.0360620	−	0.00766521i	−0.225907	+	0.974149i	$0.572535\pi$
$42$	1.12920	+	0.502754i	0.174240	+	0.0775766i
$43$	−1.26393	+	2.18919i	−0.192748	+	0.333849i	−0.946160	−	0.323700i	$-0.895073\pi$
$43$	−1.26393	+	2.18919i	−0.192748	+	0.333849i	0.753412	+	0.657549i	$0.228407\pi$
$44$	−0.988830	−	3.16579i	−0.149072	−	0.477261i
$45$	−4.20163			−0.626341
$46$	0.809017	−	0.587785i	0.119283	−	0.0866642i
$47$	−0.669131	+	0.743145i	−0.0976027	+	0.108399i	−0.789967	−	0.613149i	$-0.789902\pi$
$47$	−0.669131	+	0.743145i	−0.0976027	+	0.108399i	0.692364	+	0.721548i	$0.256569\pi$
$48$	1.20906	−	0.256993i	0.174512	−	0.0370937i
$49$	4.85410	+	3.52671i	0.693443	+	0.503816i
$50$	2.54508	+	1.84911i	0.359929	+	0.261504i
$51$	1.67088	−	0.355156i	0.233969	−	0.0497317i
$52$	−3.76988	−	0.801313i	−0.522788	−	0.111122i
$53$	−10.2647	−	4.57012i	−1.40996	−	0.627754i	−0.446299	−	0.894884i	$-0.647258\pi$
$53$	−10.2647	−	4.57012i	−1.40996	−	0.627754i	−0.963661	+	0.267130i	$0.913925\pi$
$54$	2.76393	−	4.78727i	0.376124	−	0.651465i
$55$	4.63913	+	8.25126i	0.625540	+	1.11260i
$56$	−1.00000			−0.133631
$57$	4.50264	−	2.95900i	0.596389	−	0.391929i
$58$	0.309017	+	0.951057i	0.0405759	+	0.124880i
$59$	−2.63923	−	2.93117i	−0.343599	−	0.381605i	0.546434	−	0.837502i	$-0.315985\pi$
$59$	−2.63923	−	2.93117i	−0.343599	−	0.381605i	−0.890032	+	0.455897i	$0.849318\pi$
$60$	−3.22286	+	1.43491i	−0.416070	+	0.185246i
$61$	1.13456	−	10.7946i	0.145266	−	1.38211i	−0.642570	−	0.766227i	$-0.722132\pi$
$61$	1.13456	−	10.7946i	0.145266	−	1.38211i	0.787836	−	0.615885i	$-0.211202\pi$
$62$	−7.42077	−	8.24160i	−0.942439	−	1.04668i
$63$	−0.985051	+	1.09401i	−0.124105	+	0.137832i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	11.0000			1.36438
$66$	−4.09931	−	0.0467845i	−0.504590	−	0.00575878i
$67$	−1.16312	−	2.01458i	−0.142098	−	0.246120i	0.786189	−	0.617986i	$-0.212051\pi$
$67$	−1.16312	−	2.01458i	−0.142098	−	0.246120i	−0.928286	+	0.371866i	$0.878718\pi$
$68$	−1.11803	+	0.812299i	−0.135582	+	0.0985058i
$69$	−0.381966	−	1.17557i	−0.0459833	−	0.141522i
$70$	2.79173	−	0.593401i	0.333676	−	0.0709250i
$71$	−12.2250	+	5.44294i	−1.45084	+	0.645958i	−0.972646	−	0.232294i	$-0.925377\pi$
$71$	−12.2250	+	5.44294i	−1.45084	+	0.645958i	−0.478199	+	0.878252i	$0.658710\pi$
$72$	−0.153880	+	1.46407i	−0.0181349	+	0.172542i
$73$	−7.32315	−	8.13318i	−0.857110	−	0.951917i	0.142171	−	0.989842i	$-0.454592\pi$
$73$	−7.32315	−	8.13318i	−0.857110	−	0.951917i	−0.999281	+	0.0379255i	$0.987925\pi$
$74$	−1.35177	−	0.287327i	−0.157140	−	0.0334011i
$75$	3.14590	−	2.28563i	0.363257	−	0.263922i
$76$	−2.35410	+	3.66854i	−0.270034	+	0.420811i
$77$	3.23607	+	0.726543i	0.368784	+	0.0827972i
$78$	−2.38197	+	4.12569i	−0.269705	+	0.467142i
$79$	0.577819	+	5.49758i	0.0650097	+	0.618526i	0.977719	+	0.209917i	$0.0673194\pi$
$79$	0.577819	+	5.49758i	0.0650097	+	0.618526i	−0.912709	+	0.408609i	$0.866014\pi$
$80$	1.90977	−	2.12101i	0.213518	−	0.237136i
$81$	−1.61689	−	1.79574i	−0.179655	−	0.199527i
$82$	0.0246758	−	0.234775i	0.00272499	−	0.0259265i
$83$	−4.04508	−	2.93893i	−0.444006	−	0.322589i	0.343219	−	0.939255i	$-0.388483\pi$
$83$	−4.04508	−	2.93893i	−0.444006	−	0.322589i	−0.787225	+	0.616666i	$0.788483\pi$
$84$	−0.381966	+	1.17557i	−0.0416759	+	0.128265i
$85$	2.63923	−	2.93117i	0.286265	−	0.317930i
$86$	−2.30932	−	1.02817i	−0.249020	−	0.110871i
$87$	1.23607			0.132520
$88$	3.04508	−	1.31433i	0.324607	−	0.140108i
$89$	5.97214	+	10.3440i	0.633045	+	1.09647i	0.986926	+	0.161176i	$0.0515286\pi$
$89$	5.97214	+	10.3440i	0.633045	+	1.09647i	−0.353881	+	0.935291i	$0.615138\pi$
$90$	−0.439190	−	4.17861i	−0.0462946	−	0.440464i
$91$	2.57890	−	2.86416i	0.270342	−	0.300245i
$92$	0.669131	+	0.743145i	0.0697617	+	0.0774782i
$93$	−12.5231	+	5.57563i	−1.29858	+	0.578166i
$94$	−0.809017	−	0.587785i	−0.0834437	−	0.0606254i
$95$	4.39511	−	11.6385i	0.450928	−	1.19409i
$96$	0.381966	+	1.17557i	0.0389842	+	0.119981i
$97$	−1.38355	−	13.1636i	−0.140478	−	1.33656i	−0.806770	−	0.590866i	$-0.798786\pi$
$97$	−1.38355	−	13.1636i	−0.140478	−	1.33656i	0.666292	−	0.745691i	$-0.267880\pi$
$98$	−3.00000	+	5.19615i	−0.303046	+	0.524891i
$99$	1.56168	−	4.62603i	0.156954	−	0.464934i
$100$	−1.57295	+	2.72443i	−0.157295	+	0.272443i
$101$	−3.65418	−	1.62695i	−0.363605	−	0.161887i	0.216799	−	0.976216i	$-0.430438\pi$
$101$	−3.65418	−	1.62695i	−0.363605	−	0.161887i	−0.580403	+	0.814329i	$0.697105\pi$
$102$	0.527864	+	1.62460i	0.0522663	+	0.160859i
$103$	5.70820	−	17.5680i	0.562446	−	1.73103i	−0.112974	−	0.993598i	$-0.536038\pi$
$103$	5.70820	−	17.5680i	0.562446	−	1.73103i	0.675420	−	0.737433i	$-0.263962\pi$
$104$	0.402863	−	3.83299i	0.0395040	−	0.375855i
$105$	0.368762	−	3.50854i	0.0359875	−	0.342398i
$106$	3.47214	−	10.6861i	0.337244	−	1.03793i
$107$	4.82624	+	14.8536i	0.466570	+	1.43595i	0.856997	+	0.515321i	$0.172327\pi$
$107$	4.82624	+	14.8536i	0.466570	+	1.43595i	−0.390427	+	0.920634i	$0.627673\pi$
$108$	5.04996	+	2.24838i	0.485932	+	0.216351i
$109$	5.66312	−	9.80881i	0.542428	−	0.939514i	−0.456335	−	0.889808i	$-0.650838\pi$
$109$	5.66312	−	9.80881i	0.542428	−	0.939514i	0.998764	−	0.0497058i	$-0.0158284\pi$
$110$	−7.72114	+	5.47621i	−0.736182	+	0.522136i
$111$	−0.854102	+	1.47935i	−0.0810678	+	0.140413i
$112$	−0.104528	−	0.994522i	−0.00987701	−	0.0939735i
$113$	4.26393	+	13.1230i	0.401117	+	1.23451i	0.924094	+	0.382165i	$0.124821\pi$
$113$	4.26393	+	13.1230i	0.401117	+	1.23451i	−0.522977	+	0.852347i	$0.675179\pi$
$114$	3.41344	+	4.16867i	0.319698	+	0.390432i
$115$	−2.30902	−	1.67760i	−0.215317	−	0.156437i
$116$	−0.913545	+	0.406737i	−0.0848206	+	0.0377645i
$117$	−3.79649	−	4.21643i	−0.350985	−	0.389809i
$118$	2.63923	−	2.93117i	0.242961	−	0.269836i
$119$	−0.144455	−	1.37440i	−0.0132421	−	0.125991i
$120$	−1.76393	−	3.05522i	−0.161024	−	0.278902i
$121$	−10.8090	+	2.04087i	−0.982638	+	0.185534i
$122$	10.8541			0.982684
$123$	−0.266569	−	0.118684i	−0.0240357	−	0.0107014i
$124$	7.42077	−	8.24160i	0.666405	−	0.740118i
$125$	−1.63525	+	5.03280i	−0.146262	+	0.450147i
$126$	−1.19098	−	0.865300i	−0.106101	−	0.0770870i
$127$	−1.13456	+	10.7946i	−0.100676	+	0.957870i	0.821267	+	0.570544i	$0.193268\pi$
$127$	−1.13456	+	10.7946i	−0.100676	+	0.957870i	−0.921943	+	0.387325i	$0.873399\pi$
$128$	−0.669131	−	0.743145i	−0.0591433	−	0.0656853i
$129$	−2.09077	+	2.32204i	−0.184082	+	0.204444i
$130$	1.14981	+	10.9397i	0.100845	+	0.959479i
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	−0.599699	−	0.800226i	$-0.704713\pi$
$131$	4.50000	−	7.79423i	0.393167	−	0.680985i	0.992865	+	0.119241i	$0.0380462\pi$
$132$	−0.381966	−	4.08174i	−0.0332459	−	0.355270i
$133$	−2.00000	−	3.87298i	−0.173422	−	0.335830i
$134$	1.88197	−	1.36733i	0.162577	−	0.118119i
$135$	−15.4323	−	3.28024i	−1.32820	−	0.282318i
$136$	−0.924716	−	1.02700i	−0.0792937	−	0.0880646i
$137$	0.328836	−	3.12866i	0.0280943	−	0.267300i	−0.971453	−	0.237230i	$-0.923760\pi$
$137$	0.328836	−	3.12866i	0.0280943	−	0.267300i	0.999548	−	0.0300696i	$-0.00957290\pi$
$138$	1.12920	−	0.502754i	0.0961243	−	0.0427973i
$139$	−3.85808	+	0.820060i	−0.327238	+	0.0695566i	−0.368601	−	0.929588i	$-0.620163\pi$
$139$	−3.85808	+	0.820060i	−0.327238	+	0.0695566i	0.0413633	+	0.999144i	$0.486830\pi$
$140$	0.881966	+	2.71441i	0.0745397	+	0.229410i
$141$	−1.00000	+	0.726543i	−0.0842152	+	0.0611859i
$142$	−6.69098	−	11.5891i	−0.561495	−	0.972538i
$143$	−4.08852	+	12.1111i	−0.341899	+	1.01278i
$144$	−1.47214			−0.122678
$145$	2.30902	−	1.67760i	0.191753	−	0.139317i
$146$	7.32315	−	8.13318i	0.606068	−	0.673107i
$147$	4.96255	+	5.51147i	0.409304	+	0.454578i
$148$	0.144455	−	1.37440i	0.0118741	−	0.112975i
$149$	11.6919	−	5.20557i	0.957837	−	0.426457i	0.132554	−	0.991176i	$-0.457682\pi$
$149$	11.6919	−	5.20557i	0.957837	−	0.426457i	0.825283	+	0.564719i	$0.191015\pi$
$150$	2.60194	+	2.88975i	0.212448	+	0.235947i
$151$	2.01722	+	6.20837i	0.164159	+	0.505230i	0.998973	−	0.0453020i	$-0.0144250\pi$
$151$	2.01722	+	6.20837i	0.164159	+	0.505230i	−0.834814	+	0.550532i	$0.814425\pi$
$152$	−3.89452	−	1.95774i	−0.315887	−	0.158794i
$153$	−2.03444			−0.164475
$154$	−0.384301	+	3.29428i	−0.0309679	+	0.265461i
$155$	−15.8262	+	27.4118i	−1.27119	+	2.20177i
$156$	−4.35207	−	1.93767i	−0.348444	−	0.155137i
$157$	−5.26436	−	1.11897i	−0.420141	−	0.0893038i	−0.00701044	−	0.999975i	$-0.502232\pi$
$157$	−5.26436	−	1.11897i	−0.420141	−	0.0893038i	−0.413131	+	0.910672i	$0.635565\pi$
$158$	−5.40707	+	1.14931i	−0.430163	+	0.0914340i
$159$	−11.2361	−	8.16348i	−0.891078	−	0.647406i
$160$	2.30902	+	1.67760i	0.182544	+	0.132626i
$161$	−0.978148	+	0.207912i	−0.0770888	+	0.0163857i
$162$	1.61689	−	1.79574i	0.127035	−	0.141087i
$163$	5.09017	−	3.69822i	0.398693	−	0.289667i	−0.370315	−	0.928906i	$-0.620750\pi$
$163$	5.09017	−	3.69822i	0.398693	−	0.289667i	0.769008	+	0.639239i	$0.220750\pi$
$164$	0.236068			0.0184338
$165$	3.48846	+	11.1685i	0.271576	+	0.869464i
$166$	2.50000	−	4.33013i	0.194038	−	0.336083i
$167$	−3.00721	−	1.33889i	−0.232705	−	0.103607i	0.287072	−	0.957909i	$-0.407318\pi$
$167$	−3.00721	−	1.33889i	−0.232705	−	0.103607i	−0.519776	+	0.854302i	$0.673985\pi$
$168$	−1.20906	−	0.256993i	−0.0932808	−	0.0198274i
$169$	1.24064	+	1.37787i	0.0954336	+	0.105990i
$170$	3.19098	+	2.31838i	0.244737	+	0.177812i
$171$	−5.97808	+	2.33217i	−0.457156	+	0.178345i
$172$	0.781153	−	2.40414i	0.0595624	−	0.183314i
$173$	5.29805	+	1.12613i	0.402803	+	0.0856184i	0.404858	−	0.914379i	$-0.367321\pi$
$173$	5.29805	+	1.12613i	0.402803	+	0.0856184i	−0.00205523	+	0.999998i	$0.500654\pi$
$174$	0.129204	+	1.22930i	0.00979495	+	0.0931927i
$175$	−1.57295	−	2.72443i	−0.118904	−	0.205947i
$176$	1.62543	+	2.89102i	0.122521	+	0.217919i
$177$	−2.43769	−	4.22221i	−0.183228	−	0.317361i
$178$	−9.66312	+	7.02067i	−0.724281	+	0.526221i
$179$	4.23607	+	13.0373i	0.316619	+	0.974452i	0.975083	+	0.221840i	$0.0712063\pi$
$179$	4.23607	+	13.0373i	0.316619	+	0.974452i	−0.658464	+	0.752612i	$0.728794\pi$
$180$	4.10981	−	0.873567i	0.306327	−	0.0651119i
$181$	1.43290	−	13.6331i	0.106506	−	1.01334i	−0.802526	−	0.596617i	$-0.796511\pi$
$181$	1.43290	−	13.6331i	0.106506	−	1.01334i	0.909033	−	0.416724i	$-0.136822\pi$
$182$	3.11803	+	2.26538i	0.231124	+	0.167921i
$183$	4.14590	−	12.7598i	0.306474	−	0.943229i
$184$	−0.669131	+	0.743145i	−0.0493290	+	0.0547854i
$185$	0.412289	+	3.92266i	0.0303121	+	0.288400i
$186$	−6.85410	−	11.8717i	−0.502567	−	0.870472i
$187$	2.24628	+	3.99529i	0.164264	+	0.292165i
$188$	0.500000	−	0.866025i	0.0364662	−	0.0631614i
$189$	−4.47214	+	3.24920i	−0.325300	+	0.236344i
$190$	12.0342	+	3.15447i	0.873051	+	0.228850i
$191$	−3.85410	+	11.8617i	−0.278873	+	0.858283i	0.709296	+	0.704911i	$0.249013\pi$
$191$	−3.85410	+	11.8617i	−0.278873	+	0.858283i	−0.988169	+	0.153372i	$0.950987\pi$
$192$	−1.12920	+	0.502754i	−0.0814933	+	0.0362832i
$193$	5.69693	−	2.53644i	0.410074	−	0.182577i	−0.191323	−	0.981527i	$-0.561278\pi$
$193$	5.69693	−	2.53644i	0.410074	−	0.182577i	0.601397	+	0.798950i	$0.294611\pi$
$194$	12.9468	−	2.75193i	0.929528	−	0.197577i
$195$	13.2996	+	2.82692i	0.952406	+	0.202440i
$196$	−5.48127	−	2.44042i	−0.391519	−	0.174316i
$197$	7.67376			0.546733			0.273366	−	0.961910i	$-0.411863\pi$
$197$	7.67376			0.546733			0.273366	+	0.961910i	$0.411863\pi$
$198$	4.76393	+	1.06957i	0.338558	+	0.0760110i
$199$	−0.517221	−	0.895853i	−0.0366648	−	0.0635053i	0.847111	−	0.531416i	$-0.178340\pi$
$199$	−0.517221	−	0.895853i	−0.0366648	−	0.0635053i	−0.883776	+	0.467911i	$0.845007\pi$
$200$	−2.87392	−	1.27955i	−0.203217	−	0.0904780i
$201$	−0.888544	−	2.73466i	−0.0626730	−	0.192888i
$202$	1.23607	−	3.80423i	0.0869694	−	0.267664i
$203$	0.104528	−	0.994522i	0.00733646	−	0.0698018i
$204$	−1.56052	+	0.694789i	−0.109258	+	0.0486450i
$205$	−0.659039	+	0.140083i	−0.0460293	+	0.00978382i
$206$	18.0685	+	3.84057i	1.25889	+	0.267585i
$207$	0.153880	+	1.46407i	0.0106954	+	0.101760i
$208$	3.85410			0.267234
$209$	11.1805	+	9.16491i	0.773374	+	0.633950i
$210$	3.52786			0.243446
$211$	1.28844	+	12.2587i	0.0887001	+	0.843925i	0.944917	+	0.327309i	$0.106142\pi$
$211$	1.28844	+	12.2587i	0.0887001	+	0.843925i	−0.856217	+	0.516616i	$0.827192\pi$
$212$	10.9905	+	2.33611i	0.754833	+	0.160445i
$213$	−16.1796	+	3.43907i	−1.10861	+	0.235641i
$214$	−14.2678	+	6.35243i	−0.975326	+	0.434243i
$215$	−0.754150	+	7.17526i	−0.0514326	+	0.489349i
$216$	−1.70820	+	5.25731i	−0.116229	+	0.357715i
$217$	3.42705	+	10.5474i	0.232643	+	0.716003i
$218$	10.3470	+	4.60680i	0.700790	+	0.312012i
$219$	−6.76393	−	11.7155i	−0.457064	−	0.791658i
$220$	−6.25329	−	7.10642i	−0.421597	−	0.479115i
$221$	5.32624			0.358282
$222$	−1.56052	−	0.694789i	−0.104735	−	0.0466312i
$223$	12.6614	+	2.69127i	0.847871	+	0.180220i	0.611305	−	0.791395i	$-0.290645\pi$
$223$	12.6614	+	2.69127i	0.847871	+	0.180220i	0.236566	+	0.971616i	$0.423978\pi$
$224$	0.978148	−	0.207912i	0.0653552	−	0.0138917i
$225$	−4.23080	+	1.88367i	−0.282053	+	0.125578i
$226$	−12.6054	+	5.61230i	−0.838502	+	0.373325i
$227$	−4.39919	+	13.5393i	−0.291984	+	0.898635i	0.692233	+	0.721674i	$0.256627\pi$
$227$	−4.39919	+	13.5393i	−0.291984	+	0.898635i	−0.984218	+	0.176962i	$0.943373\pi$
$228$	−3.78903	+	3.83049i	−0.250935	+	0.253680i
$229$	19.9894	−	14.5231i	1.32093	−	0.959715i	0.321014	−	0.947075i	$-0.395976\pi$
$229$	19.9894	−	14.5231i	1.32093	−	0.959715i	0.999920	−	0.0126401i	$-0.00402358\pi$
$230$	1.42705	−	2.47172i	0.0940970	−	0.162981i
$231$	3.72587	+	1.71008i	0.245145	+	0.112515i
$232$	−0.500000	−	0.866025i	−0.0328266	−	0.0568574i
$233$	1.75591	+	16.7064i	0.115033	+	1.09447i	0.887943	+	0.459953i	$0.152134\pi$
$233$	1.75591	+	16.7064i	0.115033	+	1.09447i	−0.772910	+	0.634516i	$0.781199\pi$
$234$	3.79649	−	4.21643i	0.248184	−	0.275636i
$235$	−0.881966	+	2.71441i	−0.0575331	+	0.177069i
$236$	3.19098	+	2.31838i	0.207715	+	0.150914i
$237$	−0.714224	+	6.79538i	−0.0463938	+	0.441408i
$238$	1.35177	−	0.287327i	0.0876220	−	0.0186246i
$239$	5.88197	+	18.1028i	0.380473	+	1.17097i	0.939712	+	0.341968i	$0.111093\pi$
$239$	5.88197	+	18.1028i	0.380473	+	1.17097i	−0.559239	+	0.829007i	$0.688907\pi$
$240$	2.85410	−	2.07363i	0.184231	−	0.133852i
$241$	3.19098	+	5.52694i	0.205549	+	0.356022i	0.950308	−	0.311312i	$-0.100769\pi$
$241$	3.19098	+	5.52694i	0.205549	+	0.356022i	−0.744758	+	0.667334i	$0.767435\pi$
$242$	−3.15954	−	10.5365i	−0.203103	−	0.677310i
$243$	6.79837	+	11.7751i	0.436116	+	0.755375i
$244$	1.13456	+	10.7946i	0.0726329	+	0.691056i
$245$	16.7504	+	3.56041i	1.07014	+	0.227466i
$246$	0.0901699	−	0.277515i	0.00574903	−	0.0176937i
$247$	15.6508	−	6.10569i	0.995838	−	0.388496i
$248$	8.97214	+	6.51864i	0.569731	+	0.413934i
$249$	−4.13545	−	4.59289i	−0.262074	−	0.291062i
$250$	−5.17616	−	1.10023i	−0.327369	−	0.0695844i
$251$	−22.8701	−	10.1824i	−1.44355	−	0.642709i	−0.472443	−	0.881361i	$-0.656628\pi$
$251$	−22.8701	−	10.1824i	−1.44355	−	0.642709i	−0.971105	+	0.238652i	$0.923294\pi$
$252$	0.736068	−	1.27491i	0.0463679	−	0.0803116i
$253$	2.70528	−	1.91872i	0.170079	−	0.120629i
$254$	−10.8541			−0.681047
$255$	3.94427	−	2.86568i	0.247000	−	0.179456i
$256$	0.669131	−	0.743145i	0.0418207	−	0.0464466i
$257$	−17.7831	+	3.77991i	−1.10928	+	0.235784i	−0.725895	−	0.687806i	$-0.758574\pi$
$257$	−17.7831	+	3.77991i	−1.10928	+	0.235784i	−0.383382	+	0.923590i	$0.625241\pi$
$258$	−2.52786	−	1.83660i	−0.157378	−	0.114342i
$259$	1.11803	+	0.812299i	0.0694713	+	0.0504738i
$260$	−10.7596	+	2.28703i	−0.667284	+	0.141835i
$261$	−1.43997	−	0.306074i	−0.0891317	−	0.0189455i
$262$	8.22191	+	3.66063i	0.507951	+	0.226154i
$263$	−10.0729	+	17.4469i	−0.621125	+	1.07582i	0.368152	+	0.929766i	$0.379991\pi$
$263$	−10.0729	+	17.4469i	−0.621125	+	1.07582i	−0.989277	+	0.146054i	$0.953343\pi$
$264$	4.01945	−	0.806532i	0.247380	−	0.0496386i
$265$	−32.0689			−1.96998
$266$	3.64271	−	2.39388i	0.223349	−	0.146778i
$267$	4.56231	+	14.0413i	0.279209	+	0.859316i
$268$	1.55656	+	1.72873i	0.0950819	+	0.105599i
$269$	−14.8639	+	6.61781i	−0.906265	+	0.403495i	−0.806308	−	0.591497i	$-0.798537\pi$
$269$	−14.8639	+	6.61781i	−0.906265	+	0.403495i	−0.0999574	+	0.994992i	$0.531871\pi$
$270$	1.64915	−	15.6907i	0.100364	−	0.954903i
$271$	−13.7962	−	15.3222i	−0.838057	−	0.930756i	0.160357	−	0.987059i	$-0.448735\pi$
$271$	−13.7962	−	15.3222i	−0.838057	−	0.930756i	−0.998414	+	0.0563026i	$0.982069\pi$
$272$	0.924716	−	1.02700i	0.0560691	−	0.0622711i
$273$	3.85410	−	2.80017i	0.233261	−	0.169474i
$274$	3.14590			0.190051
$275$	8.37055	+	6.22874i	0.504763	+	0.375607i
$276$	0.618034	+	1.07047i	0.0372013	+	0.0644345i
$277$	15.9894	−	11.6169i	0.960707	−	0.697995i	0.00739243	−	0.999973i	$-0.497647\pi$
$277$	15.9894	−	11.6169i	0.960707	−	0.697995i	0.953315	+	0.301978i	$0.0976469\pi$
$278$	−1.21885	−	3.75123i	−0.0731016	−	0.224984i
$279$	15.9695	−	3.39442i	0.956067	−	0.203218i
$280$	−2.60735	+	1.16087i	−0.155819	+	0.0693751i
$281$	0.790476	−	7.52088i	0.0471559	−	0.448658i	−0.945313	−	0.326164i	$-0.894244\pi$
$281$	0.790476	−	7.52088i	0.0471559	−	0.448658i	0.992469	−	0.122494i	$-0.0390894\pi$
$282$	−0.827091	−	0.918578i	−0.0492525	−	0.0547005i
$283$	21.6411	+	4.59997i	1.28643	+	0.273440i	0.799852	−	0.600197i	$-0.204911\pi$
$283$	21.6411	+	4.59997i	1.28643	+	0.273440i	0.486580	+	0.873636i	$0.338244\pi$
$284$	10.8262	−	7.86572i	0.642419	−	0.466745i
$285$	8.30495	−	12.9421i	0.491943	−	0.766625i
$286$	−12.4721	−	2.80017i	−0.737493	−	0.165577i
$287$	−0.118034	+	0.204441i	−0.00696733	+	0.0120678i
$288$	−0.153880	−	1.46407i	−0.00906747	−	0.0862712i
$289$	−10.0973	+	11.2142i	−0.593959	+	0.659658i
$290$	1.90977	+	2.12101i	0.112145	+	0.124550i
$291$	1.71016	−	16.2711i	0.100251	−	0.953826i
$292$	8.85410	+	6.43288i	0.518147	+	0.376456i
$293$	−0.927051	+	2.85317i	−0.0541589	+	0.166684i	−0.974477	−	0.224486i	$-0.927930\pi$
$293$	−0.927051	+	2.85317i	−0.0541589	+	0.166684i	0.920318	+	0.391170i	$0.127930\pi$
$294$	−4.96255	+	5.51147i	−0.289422	+	0.321435i
$295$	−10.2841	−	4.57878i	−0.598764	−	0.266587i
$296$	1.38197			0.0803251
$297$	9.34752	−	15.7719i	0.542398	−	0.915180i
$298$	6.39919	+	11.0837i	0.370695	+	0.642062i
$299$	−0.402863	−	3.83299i	−0.0232982	−	0.221667i
$300$	−2.60194	+	2.88975i	−0.150223	+	0.166840i
$301$	1.69147	+	1.87857i	0.0974948	+	0.108279i
$302$	−5.96350	+	2.65512i	−0.343161	+	0.152785i
$303$	−4.00000	−	2.90617i	−0.229794	−	0.166955i
$304$	1.53993	−	4.07782i	0.0883208	−	0.233879i
$305$	−9.57295	−	29.4625i	−0.548145	−	1.68702i
$306$	−0.212657	−	2.02330i	−0.0121568	−	0.115664i
$307$	−15.5172	+	26.8766i	−0.885615	+	1.53393i	−0.0406069	+	0.999175i	$0.512929\pi$
$307$	−15.5172	+	26.8766i	−0.885615	+	1.53393i	−0.845008	+	0.534754i	$0.820404\pi$
$308$	−3.31641	−	0.0378495i	−0.188970	−	0.00215667i
$309$	11.4164	−	19.7738i	0.649457	−	1.12489i
$310$	−28.9160	−	12.8742i	−1.64232	−	0.731207i
$311$	−7.19098	−	22.1316i	−0.407763	−	1.25497i	−0.918566	−	0.395268i	$-0.870652\pi$
$311$	−7.19098	−	22.1316i	−0.407763	−	1.25497i	0.510803	−	0.859698i	$-0.329348\pi$
$312$	1.47214	−	4.53077i	0.0833433	−	0.256504i
$313$	−0.0493516	+	0.469550i	−0.00278952	+	0.0265405i	−0.995828	−	0.0912489i	$-0.970914\pi$
$313$	−0.0493516	+	0.469550i	−0.00278952	+	0.0265405i	0.993039	+	0.117789i	$0.0375808\pi$
$314$	0.562569	−	5.35248i	0.0317476	−	0.302058i
$315$	−1.29837	+	3.99598i	−0.0731551	+	0.225148i
$316$	−1.70820	−	5.25731i	−0.0960940	−	0.295747i
$317$	26.9241	+	11.9874i	1.51221	+	0.673279i	0.984378	−	0.176069i	$-0.0563383\pi$
$317$	26.9241	+	11.9874i	1.51221	+	0.673279i	0.527832	+	0.849349i	$0.323005\pi$
$318$	6.94427	−	12.0278i	0.389415	−	0.674487i
$319$	0.988830	+	3.16579i	0.0553638	+	0.177250i
$320$	−1.42705	+	2.47172i	−0.0797746	+	0.138174i
$321$	2.01792	+	19.1992i	0.112629	+	1.07159i
$322$	−0.309017	−	0.951057i	−0.0172208	−	0.0530003i
$323$	2.12813	−	5.63541i	0.118412	−	0.313563i
$324$	1.95492	+	1.42033i	0.108606	+	0.0789072i
$325$	11.0764	−	4.93152i	0.614407	−	0.273552i
$326$	4.21003	+	4.67572i	0.233172	+	0.258964i
$327$	9.36783	−	10.4040i	0.518042	−	0.575344i
$328$	0.0246758	+	0.234775i	0.00136249	+	0.0129633i
$329$	0.500000	+	0.866025i	0.0275659	+	0.0477455i
$330$	−10.7426	+	4.63677i	−0.591363	+	0.255246i
$331$	−25.7426			−1.41494			−0.707472	−	0.706741i	$-0.750164\pi$
$331$	−25.7426			−1.41494			−0.707472	+	0.706741i	$0.750164\pi$
$332$	4.56773	+	2.03368i	0.250687	+	0.111613i
$333$	1.36131	−	1.51188i	0.0745992	−	0.0828508i
$334$	1.01722	−	3.13068i	0.0556599	−	0.171303i
$335$	−5.37132	−	3.90249i	−0.293467	−	0.213216i
$336$	0.129204	−	1.22930i	0.00704867	−	0.0670636i
$337$	−16.0218	−	17.7941i	−0.872766	−	0.969304i	0.126979	−	0.991905i	$-0.459472\pi$
$337$	−16.0218	−	17.7941i	−0.872766	−	0.969304i	−0.999745	+	0.0226011i	$0.992805\pi$
$338$	−1.24064	+	1.37787i	−0.0674817	+	0.0749460i
$339$	1.78281	+	16.9623i	0.0968289	+	0.921265i
$340$	−1.97214	+	3.41584i	−0.106954	+	0.185250i
$341$	−24.2984	−	27.6134i	−1.31583	−	1.49535i
$342$	−2.94427	−	5.70156i	−0.159208	−	0.308305i
$343$	10.5172	−	7.64121i	0.567877	−	0.412586i
$344$	2.47262	+	0.525572i	0.133315	+	0.0283370i
$345$	−2.36060	−	2.62171i	−0.127091	−	0.141148i
$346$	−0.566169	+	5.38674i	−0.0304374	+	0.289593i
$347$	22.0898	−	9.83503i	1.18584	−	0.527972i	0.283494	−	0.958974i	$-0.408506\pi$
$347$	22.0898	−	9.83503i	1.18584	−	0.527972i	0.902351	+	0.431002i	$0.141840\pi$
$348$	−1.20906	+	0.256993i	−0.0648123	+	0.0137763i
$349$	−7.34346	−	22.6008i	−0.393086	−	1.20980i	−0.930442	−	0.366440i	$-0.880577\pi$
$349$	−7.34346	−	22.6008i	−0.393086	−	1.20980i	0.537356	−	0.843356i	$-0.319423\pi$
$350$	2.54508	−	1.84911i	0.136041	−	0.0988392i
$351$	−10.6525	−	18.4506i	−0.568587	−	0.984822i
$352$	−2.70528	+	1.91872i	−0.144192	+	0.102268i
$353$	14.9443			0.795403			0.397702	−	0.917515i	$-0.369808\pi$
$353$	14.9443			0.795403			0.397702	+	0.917515i	$0.369808\pi$
$354$	3.94427	−	2.86568i	0.209636	−	0.152309i
$355$	−25.5564	+	28.3833i	−1.35639	+	1.50643i
$356$	−7.99228	−	8.87632i	−0.423590	−	0.470444i
$357$	0.178556	−	1.69885i	0.00945018	−	0.0899125i
$358$	−12.5231	+	5.57563i	−0.661865	+	0.294681i
$359$	−18.8936	−	20.9835i	−0.997167	−	1.10747i	−0.994208	−	0.107471i	$-0.965725\pi$
$359$	−18.8936	−	20.9835i	−0.997167	−	1.10747i	−0.00295871	−	0.999996i	$-0.500942\pi$
$360$	1.29837	+	3.99598i	0.0684303	+	0.210607i
$361$	−0.206743	−	18.9989i	−0.0108812	−	0.999941i
$362$	13.7082			0.720487
$363$	−13.5932	−	0.310313i	−0.713458	−	0.0162872i
$364$	−1.92705	+	3.33775i	−0.101005	+	0.174946i
$365$	−28.5356	−	12.7049i	−1.49362	−	0.665002i
$366$	13.1232	+	2.78943i	0.685962	+	0.145806i
$367$	18.9039	−	4.01815i	0.986776	−	0.209746i	0.313864	−	0.949468i	$-0.398376\pi$
$367$	18.9039	−	4.01815i	0.986776	−	0.209746i	0.672912	+	0.739722i	$0.265043\pi$
$368$	−0.809017	−	0.587785i	−0.0421729	−	0.0306404i
$369$	0.281153	+	0.204270i	0.0146362	+	0.0106338i
$370$	−3.85808	+	0.820060i	−0.200572	+	0.0426329i
$371$	−7.51840	+	8.35003i	−0.390336	+	0.433512i
$372$	11.0902	−	8.05748i	0.574999	−	0.417761i
$373$	18.2361			0.944228			0.472114	−	0.881538i	$-0.343491\pi$
$373$	18.2361			0.944228			0.472114	+	0.881538i	$0.343491\pi$
$374$	−3.73860	+	2.65160i	−0.193319	+	0.137111i
$375$	−3.27051	+	5.66469i	−0.168888	+	0.292523i
$376$	0.913545	+	0.406737i	0.0471125	+	0.0209758i
$377$	3.76988	+	0.801313i	0.194159	+	0.0412697i
$378$	−3.69886	−	4.10800i	−0.190249	−	0.211293i
$379$	20.5344	+	14.9191i	1.05478	+	0.766345i	0.973116	−	0.230315i	$-0.0739755\pi$
$379$	20.5344	+	14.9191i	1.05478	+	0.766345i	0.0816672	+	0.996660i	$0.473976\pi$
$380$	−1.87928	+	12.2980i	−0.0964050	+	0.630873i
$381$	−4.14590	+	12.7598i	−0.212401	+	0.653702i
$382$	−12.1996	−	2.59310i	−0.624185	−	0.132675i
$383$	−0.159705	−	1.51949i	−0.00816056	−	0.0776425i	0.989684	−	0.143270i	$-0.0457618\pi$
$383$	−0.159705	−	1.51949i	−0.00816056	−	0.0776425i	−0.997844	+	0.0656275i	$0.979095\pi$
$384$	−0.618034	−	1.07047i	−0.0315389	−	0.0546270i
$385$	9.28099	−	1.86230i	0.473003	−	0.0949114i
$386$	3.11803	+	5.40059i	0.158704	+	0.274883i
$387$	3.01064	−	2.18736i	0.153040	−	0.111190i
$388$	4.09017	+	12.5882i	0.207647	+	0.639072i
$389$	−6.41890	+	1.36438i	−0.325451	+	0.0691768i	−0.367740	−	0.929929i	$-0.619868\pi$
$389$	−6.41890	+	1.36438i	−0.325451	+	0.0691768i	0.0422888	+	0.999105i	$0.486535\pi$
$390$	−1.42125	+	13.5223i	−0.0719676	+	0.684726i
$391$	−1.11803	−	0.812299i	−0.0565414	−	0.0410797i
$392$	1.85410	−	5.70634i	0.0936463	−	0.288214i
$393$	7.44382	−	8.26720i	0.375491	−	0.417025i
$394$	0.802127	+	7.63172i	0.0404106	+	0.384481i
$395$	7.88854	+	13.6634i	0.396916	+	0.687478i
$396$	−0.565744	+	4.84964i	−0.0284297	+	0.243703i
$397$	−15.5623	+	26.9547i	−0.781050	+	1.35282i	0.150281	+	0.988643i	$0.451982\pi$
$397$	−15.5623	+	26.9547i	−0.781050	+	1.35282i	−0.931331	+	0.364175i	$0.881351\pi$
$398$	0.836881	−	0.608030i	0.0419491	−	0.0304778i
$399$	−1.42278	−	5.19664i	−0.0712283	−	0.260158i
$400$	0.972136	−	2.99193i	0.0486068	−	0.149596i
$401$	24.3482	−	10.8405i	1.21589	−	0.541351i	0.304352	−	0.952560i	$-0.401560\pi$
$401$	24.3482	−	10.8405i	1.21589	−	0.541351i	0.911541	+	0.411209i	$0.134893\pi$
$402$	2.62680	−	1.16953i	0.131013	−	0.0583306i
$403$	−41.8086	+	8.88670i	−2.08264	+	0.442678i
$404$	3.91259	+	0.831647i	0.194659	+	0.0413760i
$405$	−6.30043	−	2.80513i	−0.313071	−	0.139388i
$406$	1.00000			0.0496292
$407$	−4.47214	−	1.00406i	−0.221676	−	0.0497693i
$408$	−0.854102	−	1.47935i	−0.0422843	−	0.0732386i
$409$	29.3158	+	13.0522i	1.44957	+	0.645392i	0.972380	−	0.233405i	$-0.0749869\pi$
$409$	29.3158	+	13.0522i	1.44957	+	0.645392i	0.477195	+	0.878797i	$0.341654\pi$
$410$	−0.208204	−	0.640786i	−0.0102825	−	0.0316462i
$411$	1.20163	−	3.69822i	0.0592718	−	0.182420i
$412$	−1.93086	+	18.3709i	−0.0951268	+	0.905071i
$413$	−3.60327	+	1.60428i	−0.177305	+	0.0789415i
$414$	−1.43997	+	0.306074i	−0.0707705	+	0.0150427i
$415$	−13.9587	−	2.96701i	−0.685204	−	0.145645i
$416$	0.402863	+	3.83299i	0.0197520	+	0.187928i
$417$	−4.87539			−0.238749
$418$	−7.94602	+	12.0773i	−0.388652	+	0.590719i
$419$	11.1803			0.546195			0.273098	−	0.961986i	$-0.411952\pi$
$419$	11.1803			0.546195			0.273098	+	0.961986i	$0.411952\pi$
$420$	0.368762	+	3.50854i	0.0179938	+	0.171199i
$421$	9.72697	+	2.06753i	0.474063	+	0.100765i	0.438746	−	0.898611i	$-0.355423\pi$
$421$	9.72697	+	2.06753i	0.474063	+	0.100765i	0.0353168	+	0.999376i	$0.488756\pi$
$422$	−12.0569	+	2.56277i	−0.586920	+	0.124754i
$423$	1.34486	−	0.598772i	0.0653895	−	0.0291133i
$424$	−1.17449	+	11.1745i	−0.0570382	+	0.542682i
$425$	1.34346	−	4.13474i	0.0651673	−	0.200564i
$426$	−5.11146	−	15.7314i	−0.247651	−	0.762191i
$427$	−9.91572	−	4.41476i	−0.479855	−	0.213645i
$428$	−7.80902	−	13.5256i	−0.377463	−	0.653785i
$429$	−8.05573	+	13.5923i	−0.388934	+	0.656243i
$430$	−7.21478			−0.347928
$431$	18.3847	+	8.18542i	0.885562	+	0.394278i	0.798549	−	0.601930i	$-0.205601\pi$
$431$	18.3847	+	8.18542i	0.885562	+	0.394278i	0.0870129	+	0.996207i	$0.472268\pi$
$432$	−5.40707	−	1.14931i	−0.260148	−	0.0552961i
$433$	30.2472	−	6.42925i	1.45359	−	0.308970i	0.587649	−	0.809116i	$-0.300054\pi$
$433$	30.2472	−	6.42925i	1.45359	−	0.308970i	0.865941	+	0.500146i	$0.166720\pi$
$434$	−10.1314	+	4.51078i	−0.486322	+	0.216524i
$435$	3.22286	−	1.43491i	0.154525	−	0.0687987i
$436$	−3.50000	+	10.7719i	−0.167620	+	0.515880i
$437$	−4.21645	−	1.10524i	−0.201700	−	0.0528709i
$438$	10.9443	−	7.95148i	0.522938	−	0.379936i
$439$	20.2984	−	35.1578i	0.968789	−	1.67799i	0.269716	−	0.962940i	$-0.413070\pi$
$439$	20.2984	−	35.1578i	0.968789	−	1.67799i	0.699072	−	0.715051i	$-0.253597\pi$
$440$	6.41385	−	6.96186i	0.305768	−	0.331893i
$441$	−4.41641	−	7.64944i	−0.210305	−	0.364259i
$442$	0.556743	+	5.29706i	0.0264816	+	0.251955i
$443$	−4.30766	+	4.78414i	−0.204663	+	0.227301i	−0.836735	−	0.547609i	$-0.815538\pi$
$443$	−4.30766	+	4.78414i	−0.204663	+	0.227301i	0.632071	+	0.774910i	$0.282205\pi$
$444$	0.527864	−	1.62460i	0.0250513	−	0.0771000i
$445$	27.5795	+	20.0377i	1.30739	+	0.949878i
$446$	−1.35304	+	12.8734i	−0.0640685	+	0.609571i
$447$	15.4740	−	3.28909i	0.731893	−	0.155569i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	−16.0623	+	11.6699i	−0.758027	+	0.550739i	−0.898305	−	0.439373i	$-0.855201\pi$
$449$	−16.0623	+	11.6699i	−0.758027	+	0.550739i	0.140277	+	0.990112i	$0.455201\pi$
$450$	−2.31559	−	4.01073i	−0.109158	−	0.189068i
$451$	0.0907212	−	0.777675i	0.00427190	−	0.0366193i
$452$	−6.89919	−	11.9497i	−0.324510	−	0.562069i
$453$	0.843428	+	8.02468i	0.0396277	+	0.377032i
$454$	−13.9250	−	2.95984i	−0.653531	−	0.138912i
$455$	3.39919	−	10.4616i	0.159356	−	0.490448i
$456$	−4.20557	−	3.36788i	−0.196944	−	0.157715i
$457$	−6.89919	−	5.01255i	−0.322730	−	0.234477i	0.414609	−	0.910000i	$-0.363918\pi$
$457$	−6.89919	−	5.01255i	−0.322730	−	0.234477i	−0.737340	+	0.675522i	$0.763918\pi$
$458$	16.5330	+	18.3618i	0.772537	+	0.857989i
$459$	−7.47238	−	1.58830i	−0.348781	−	0.0741357i
$460$	2.60735	+	1.16087i	0.121568	+	0.0541257i
$461$	−5.50000	+	9.52628i	−0.256161	+	0.443683i	−0.965210	−	0.261476i	$-0.915791\pi$
$461$	−5.50000	+	9.52628i	−0.256161	+	0.443683i	0.709050	+	0.705159i	$0.249124\pi$
$462$	−1.31125	+	3.88422i	−0.0610049	+	0.180710i
$463$	2.88854			0.134242			0.0671210	−	0.997745i	$-0.478619\pi$
$463$	2.88854			0.134242			0.0671210	+	0.997745i	$0.478619\pi$
$464$	0.809017	−	0.587785i	0.0375577	−	0.0272872i
$465$	−26.1795	+	29.0753i	−1.21404	+	1.34833i
$466$	−16.4313	+	3.49258i	−0.761165	+	0.161791i
$467$	−12.7082	−	9.23305i	−0.588066	−	0.427255i	0.253557	−	0.967320i	$-0.418399\pi$
$467$	−12.7082	−	9.23305i	−0.588066	−	0.427255i	−0.841623	+	0.540066i	$0.818399\pi$
$468$	4.59017	+	3.33495i	0.212181	+	0.154158i
$469$	−2.27540	+	0.483652i	−0.105068	+	0.0223330i
$470$	−2.79173	−	0.593401i	−0.128773	−	0.0273716i
$471$	−6.07734	−	2.70581i	−0.280029	−	0.124677i
$472$	−1.97214	+	3.41584i	−0.0907749	+	0.157227i
$473$	−7.61973	−	3.49725i	−0.350356	−	0.160804i
$474$	−6.83282			−0.313842
$475$	−0.792158	−	13.6898i	−0.0363467	−	0.628129i
$476$	0.427051	+	1.31433i	0.0195738	+	0.0602421i
$477$	11.0681	+	12.2924i	0.506774	+	0.562829i
$478$	−17.3888	+	7.74200i	−0.795346	+	0.354111i
$479$	4.06496	−	38.6755i	0.185733	−	1.76713i	−0.363628	−	0.931544i	$-0.618462\pi$
$479$	4.06496	−	38.6755i	0.185733	−	1.76713i	0.549361	−	0.835585i	$-0.314871\pi$
$480$	2.36060	+	2.62171i	0.107746	+	0.119664i
$481$	−3.56395	+	3.95817i	−0.162502	+	0.180477i
$482$	−5.16312	+	3.75123i	−0.235174	+	0.170864i
$483$	−1.23607			−0.0562430
$484$	10.1485	−	4.24359i	0.461295	−	0.192891i
$485$	−18.8885	−	32.7159i	−0.857685	−	1.48555i
$486$	−11.0000	+	7.99197i	−0.498970	+	0.362523i
$487$	−1.01722	−	3.13068i	−0.0460947	−	0.141865i	0.925360	−	0.379089i	$-0.123762\pi$
$487$	−1.01722	−	3.13068i	−0.0460947	−	0.141865i	−0.971455	+	0.237224i	$0.923762\pi$
$488$	−10.6169	+	2.25669i	−0.480605	+	0.102156i
$489$	7.10472	−	3.16323i	0.321287	−	0.143046i
$490$	−1.79001	+	17.0308i	−0.0808644	+	0.769373i
$491$	12.1650	+	13.5106i	0.549000	+	0.609726i	0.952233	−	0.305371i	$-0.0987805\pi$
$491$	12.1650	+	13.5106i	0.549000	+	0.609726i	−0.403234	+	0.915097i	$0.632114\pi$
$492$	0.285420	+	0.0606678i	0.0128677	+	0.00273512i
$493$	1.11803	−	0.812299i	0.0503537	−	0.0365841i
$494$	7.70820	+	14.9269i	0.346808	+	0.671592i
$495$	−1.29837	−	13.8746i	−0.0583576	−	0.623617i
$496$	−5.54508	+	9.60437i	−0.248982	+	0.431249i
$497$	1.39880	+	13.3087i	0.0627446	+	0.596975i
$498$	4.13545	−	4.59289i	0.185314	−	0.205812i
$499$	−7.96923	−	8.85073i	−0.356752	−	0.396213i	0.537877	−	0.843023i	$-0.319227\pi$
$499$	−7.96923	−	8.85073i	−0.356752	−	0.396213i	−0.894629	+	0.446810i	$0.852560\pi$
$500$	0.553143	−	5.26281i	0.0247373	−	0.235360i
$501$	−3.29180	−	2.39163i	−0.147067	−	0.106850i
$502$	7.73607	−	23.8092i	0.345278	−	1.06266i
$503$	13.1270	−	14.5790i	0.585305	−	0.650047i	−0.375647	−	0.926763i	$-0.622579\pi$
$503$	13.1270	−	14.5790i	0.585305	−	0.650047i	0.960952	+	0.276716i	$0.0892460\pi$
$504$	1.34486	+	0.598772i	0.0599050	+	0.0266714i
$505$	−11.4164			−0.508023
$506$	2.19098	+	2.48990i	0.0974011	+	0.110689i
$507$	1.14590	+	1.98475i	0.0508911	+	0.0881460i
$508$	−1.13456	−	10.7946i	−0.0503381	−	0.478935i
$509$	9.96238	−	11.0643i	0.441575	−	0.490418i	−0.480737	−	0.876865i	$-0.659631\pi$
$509$	9.96238	−	11.0643i	0.441575	−	0.490418i	0.922312	+	0.386446i	$0.126298\pi$
$510$	3.26227	+	3.62312i	0.144456	+	0.160434i
$511$	−9.99809	+	4.45144i	−0.442289	+	0.196920i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−23.7779	+	3.89878i	−1.04982	+	0.172135i
$514$	−5.61803	−	17.2905i	−0.247801	−	0.762653i
$515$	−5.51088	−	52.4325i	−0.242839	−	2.31045i
$516$	1.56231	−	2.70599i	0.0687767	−	0.119125i
$517$	−2.66078	−	1.97996i	−0.117021	−	0.0870784i
$518$	−0.690983	+	1.19682i	−0.0303601	+	0.0525851i
$519$	6.11623	+	2.72312i	0.268473	+	0.119532i
$520$	−3.39919	−	10.4616i	−0.149064	−	0.458772i
$521$	−5.69098	+	17.5150i	−0.249326	+	0.767348i	0.745568	+	0.666429i	$0.232178\pi$
$521$	−5.69098	+	17.5150i	−0.249326	+	0.767348i	−0.994895	+	0.100919i	$0.967822\pi$
$522$	0.153880	−	1.46407i	0.00673515	−	0.0640807i
$523$	1.09104	−	10.3805i	0.0477077	−	0.453908i	−0.944426	−	0.328724i	$-0.893381\pi$
$523$	1.09104	−	10.3805i	0.0477077	−	0.453908i	0.992134	−	0.125184i	$-0.0399521\pi$
$524$	−2.78115	+	8.55951i	−0.121495	+	0.373924i
$525$	−1.20163	−	3.69822i	−0.0524433	−	0.161404i
$526$	−18.4042	−	8.19407i	−0.802461	−	0.357279i
$527$	−7.66312	+	13.2729i	−0.333811	+	0.578177i
$528$	1.22226	+	3.91313i	0.0531921	+	0.170297i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−3.35211	−	31.8932i	−0.145606	−	1.38535i
$531$	1.79431	+	5.52231i	0.0778664	+	0.239648i
$532$	2.76153	+	3.37253i	0.119728	+	0.146218i
$533$	−0.736068	−	0.534785i	−0.0318826	−	0.0231641i
$534$	−13.4875	+	6.00503i	−0.583662	+	0.259863i
$535$	29.8268	+	33.1260i	1.28953	+	1.43216i
$536$	−1.55656	+	1.72873i	−0.0672330	+	0.0746698i
$537$	1.77116	+	16.8514i	0.0764311	+	0.727194i
$538$	−8.13525	−	14.0907i	−0.350736	−	0.607492i
$539$	−10.1459	+	17.1190i	−0.437015	+	0.737368i
$540$	15.7771			0.678938
$541$	−22.0584	−	9.82102i	−0.948364	−	0.422239i	−0.126528	−	0.991963i	$-0.540383\pi$
$541$	−22.0584	−	9.82102i	−0.948364	−	0.422239i	−0.821836	+	0.569724i	$0.807050\pi$
$542$	13.7962	−	15.3222i	0.592596	−	0.658144i
$543$	5.23607	−	16.1150i	0.224701	−	0.691559i
$544$	1.11803	+	0.812299i	0.0479353	+	0.0348270i
$545$	3.37901	−	32.1492i	0.144741	−	1.37712i
$546$	3.18769	+	3.54029i	0.136421	+	0.151510i
$547$	9.52579	−	10.5795i	0.407293	−	0.452345i	−0.504245	−	0.863561i	$-0.668229\pi$
$547$	9.52579	−	10.5795i	0.407293	−	0.452345i	0.911538	+	0.411216i	$0.134896\pi$
$548$	0.328836	+	3.12866i	0.0140472	+	0.133650i
$549$	−7.98936	+	13.8380i	−0.340977	+	0.590590i
$550$	−5.31966	+	8.97578i	−0.226831	+	0.382729i
$551$	2.35410	−	3.66854i	0.100288	−	0.156285i
$552$	−1.00000	+	0.726543i	−0.0425628	+	0.0309237i
$553$	5.40707	+	1.14931i	0.229932	+	0.0488735i
$554$	13.2247	+	14.6875i	0.561862	+	0.624011i
$555$	−0.509617	+	4.84868i	−0.0216320	+	0.205815i
$556$	3.60327	−	1.60428i	0.152813	−	0.0680366i
$557$	40.9187	−	8.69753i	1.73378	−	0.368526i	0.770586	−	0.637336i	$-0.219964\pi$
$557$	40.9187	−	8.69753i	1.73378	−	0.368526i	0.963193	+	0.268809i	$0.0866302\pi$
$558$	5.04508	+	15.5272i	0.213575	+	0.657318i
$559$	−7.88197	+	5.72658i	−0.333372	+	0.242209i
$560$	−1.42705	−	2.47172i	−0.0603039	−	0.104449i
$561$	1.68912	+	5.40781i	0.0713148	+	0.228318i
$562$	7.56231			0.318997
$563$	19.9443	−	14.4904i	0.840551	−	0.610696i	−0.0819736	−	0.996634i	$-0.526122\pi$
$563$	19.9443	−	14.4904i	0.840551	−	0.610696i	0.922524	+	0.385939i	$0.126122\pi$
$564$	0.827091	−	0.918578i	0.0348268	−	0.0386791i
$565$	26.3517	+	29.2665i	1.10862	+	1.23125i
$566$	−2.31265	+	22.0034i	−0.0972080	+	0.924872i
$567$	−2.20750	+	0.982842i	−0.0927062	+	0.0412755i
$568$	8.95428	+	9.94474i	0.375713	+	0.417272i
$569$	−4.38197	−	13.4863i	−0.183702	−	0.565375i	0.816222	−	0.577738i	$-0.196065\pi$
$569$	−4.38197	−	13.4863i	−0.183702	−	0.565375i	−0.999924	+	0.0123631i	$0.996065\pi$
$570$	13.7393	+	6.90664i	0.575477	+	0.289287i
$571$	13.5066			0.565233			0.282616	−	0.959233i	$-0.408798\pi$
$571$	13.5066			0.565233			0.282616	+	0.959233i	$0.408798\pi$
$572$	1.48114	−	12.6965i	0.0619294	−	0.530868i
$573$	−7.70820	+	13.3510i	−0.322015	+	0.557746i
$574$	−0.215659	−	0.0960175i	−0.00900143	−	0.00400769i
$575$	−3.07715	−	0.654069i	−0.128326	−	0.0272766i
$576$	1.43997	−	0.306074i	0.0599986	−	0.0127531i
$577$	21.1074	+	15.3354i	0.878712	+	0.638422i	0.932910	−	0.360108i	$-0.117260\pi$
$577$	21.1074	+	15.3354i	0.878712	+	0.638422i	−0.0541983	+	0.998530i	$0.517260\pi$
$578$	−12.2082	−	8.86978i	−0.507794	−	0.368934i
$579$	7.53976	−	1.60263i	0.313342	−	0.0666029i
$580$	−1.90977	+	2.12101i	−0.0792988	+	0.0880702i
$581$	−4.04508	+	2.93893i	−0.167818	+	0.121927i
$582$	16.3607			0.678172
$583$	11.9195	−	35.3082i	0.493655	−	1.46232i
$584$	−5.47214	+	9.47802i	−0.226439	+	0.392203i
$585$	−14.7935	−	6.58649i	−0.611636	−	0.272318i
$586$	−2.93444	−	0.623735i	−0.121221	−	0.0257663i
$587$	−3.89411	−	4.32485i	−0.160727	−	0.178506i	0.657402	−	0.753540i	$-0.271655\pi$
$587$	−3.89411	−	4.32485i	−0.160727	−	0.178506i	−0.818129	+	0.575034i	$0.804989\pi$
$588$	−6.00000	−	4.35926i	−0.247436	−	0.179773i
$589$	−7.30231	+	47.7862i	−0.300886	+	1.96900i
$590$	3.47871	−	10.7064i	0.143216	−	0.440775i
$591$	9.27802	+	1.97210i	0.381647	+	0.0811215i
$592$	0.144455	+	1.37440i	0.00593706	+	0.0564873i
$593$	22.0902	+	38.2613i	0.907135	+	1.57120i	0.818026	+	0.575181i	$0.195068\pi$
$593$	22.0902	+	38.2613i	0.907135	+	1.57120i	0.0891085	+	0.996022i	$0.471598\pi$
$594$	16.6626	+	7.64770i	0.683675	+	0.313789i
$595$	−1.97214	−	3.41584i	−0.0808497	−	0.140036i
$596$	−10.3541	+	7.52270i	−0.424121	+	0.308142i
$597$	−0.395122	−	1.21606i	−0.0161713	−	0.0497700i
$598$	3.76988	−	0.801313i	0.154162	−	0.0327681i
$599$	−0.716449	+	6.81655i	−0.0292733	+	0.278517i	0.970087	+	0.242757i	$0.0780518\pi$
$599$	−0.716449	+	6.81655i	−0.0292733	+	0.278517i	−0.999360	+	0.0357598i	$0.988615\pi$
$600$	−3.14590	−	2.28563i	−0.128431	−	0.0933104i
$601$	−13.0902	+	40.2874i	−0.533959	+	1.64336i	0.211928	+	0.977285i	$0.432026\pi$
$601$	−13.0902	+	40.2874i	−0.533959	+	1.64336i	−0.745887	+	0.666072i	$0.767974\pi$
$602$	−1.69147	+	1.87857i	−0.0689392	+	0.0765648i
$603$	0.357962	+	3.40578i	0.0145773	+	0.138694i
$604$	−3.26393	−	5.65330i	−0.132808	−	0.230029i
$605$	−25.8137	+	17.8691i	−1.04948	+	0.726483i
$606$	2.47214	−	4.28187i	0.100424	−	0.173939i
$607$	11.0451	−	8.02472i	0.448306	−	0.325713i	−0.340620	−	0.940201i	$-0.610637\pi$
$607$	11.0451	−	8.02472i	0.448306	−	0.325713i	0.788927	+	0.614487i	$0.210637\pi$
$608$	4.21645	+	1.10524i	0.171000	+	0.0448235i
$609$	0.381966	−	1.17557i	0.0154780	−	0.0476365i
$610$	28.3005	−	12.6002i	1.14585	−	0.510166i
$611$	−3.52090	+	1.56760i	−0.142440	+	0.0634185i
$612$	1.98998	−	0.422984i	0.0804404	−	0.0170981i
$613$	−38.5342	−	8.19071i	−1.55638	−	0.330820i	−0.652228	−	0.758023i	$-0.726165\pi$
$613$	−38.5342	−	8.19071i	−1.55638	−	0.330820i	−0.904156	+	0.427203i	$0.859499\pi$
$614$	−28.3514	−	12.6228i	−1.14417	−	0.509417i
$615$	−0.832816			−0.0335824
$616$	−0.309017	−	3.30220i	−0.0124506	−	0.133049i
$617$	0.472136	+	0.817763i	0.0190075	+	0.0329219i	0.875373	−	0.483449i	$-0.160616\pi$
$617$	0.472136	+	0.817763i	0.0190075	+	0.0329219i	−0.856365	+	0.516371i	$0.827283\pi$
$618$	20.8588	+	9.28694i	0.839065	+	0.373576i
$619$	−3.83688	−	11.8087i	−0.154217	−	0.474632i	0.843863	−	0.536558i	$-0.180276\pi$
$619$	−3.83688	−	11.8087i	−0.154217	−	0.474632i	−0.998081	+	0.0619260i	$0.980276\pi$
$620$	9.78115	−	30.1033i	0.392821	−	1.20898i
$621$	−0.577819	+	5.49758i	−0.0231871	+	0.220610i
$622$	21.2587	−	9.46497i	0.852395	−	0.379511i
$623$	11.6833	−	2.48335i	0.468080	−	0.0994935i
$624$	4.65983	+	0.990477i	0.186542	+	0.0396508i
$625$	3.22291	+	30.6639i	0.128916	+	1.22656i
$626$	−0.472136			−0.0188703
$627$	11.1626	+	13.9542i	0.445791	+	0.557278i
$628$	5.38197			0.214764
$629$	0.199632	+	1.89937i	0.00795983	+	0.0757328i
$630$	−4.10981	−	0.873567i	−0.163739	−	0.0348037i
$631$	−14.5632	+	3.09550i	−0.579752	+	0.123230i	−0.488448	−	0.872593i	$-0.662437\pi$
$631$	−14.5632	+	3.09550i	−0.579752	+	0.123230i	−0.0913037	+	0.995823i	$0.529103\pi$
$632$	5.04996	−	2.24838i	0.200876	−	0.0894359i
$633$	−1.59260	+	15.1526i	−0.0633003	+	0.602262i
$634$	−9.10739	+	28.0297i	−0.361701	+	1.11320i
$635$	9.57295	+	29.4625i	0.379891	+	1.16918i
$636$	12.6878	+	5.64898i	0.503105	+	0.223997i
$637$	11.5623	+	20.0265i	0.458115	+	0.793479i
$638$	−3.04508	+	1.31433i	−0.120556	+	0.0520347i
$639$	19.7001			0.779323
$640$	−2.60735	−	1.16087i	−0.103065	−	0.0458873i
$641$	10.4405	+	2.21920i	0.412376	+	0.0876531i	0.409428	−	0.912343i	$-0.365728\pi$
$641$	10.4405	+	2.21920i	0.412376	+	0.0876531i	0.00294776	+	0.999996i	$0.499062\pi$
$642$	−18.8831	+	4.01373i	−0.745256	+	0.158409i
$643$	16.8751	−	7.51329i	0.665490	−	0.296295i	−0.0460515	−	0.998939i	$-0.514664\pi$
$643$	16.8751	−	7.51329i	0.665490	−	0.296295i	0.711542	+	0.702644i	$0.247997\pi$
$644$	0.913545	−	0.406737i	0.0359987	−	0.0160277i
$645$	−2.75580	+	8.48148i	−0.108510	+	0.333958i
$646$	5.82699	+	1.52741i	0.229260	+	0.0600950i
$647$	23.3992	−	17.0005i	0.919917	−	0.668359i	−0.0235864	−	0.999722i	$-0.507508\pi$
$647$	23.3992	−	17.0005i	0.919917	−	0.668359i	0.943503	+	0.331363i	$0.107508\pi$
$648$	−1.20820	+	2.09267i	−0.0474627	+	0.0822079i
$649$	8.86372	−	9.62105i	0.347931	−	0.377659i
$650$	6.06231	+	10.5002i	0.237783	+	0.411853i
$651$	1.43290	+	13.6331i	0.0561597	+	0.534324i
$652$	−4.21003	+	4.67572i	−0.164878	+	0.183115i
$653$	−14.1803	+	43.6426i	−0.554920	+	1.70787i	0.141236	+	0.989976i	$0.454892\pi$
$653$	−14.1803	+	43.6426i	−0.554920	+	1.70787i	−0.696156	+	0.717891i	$0.745108\pi$
$654$	11.3262	+	8.22899i	0.442891	+	0.321779i
$655$	2.68501	−	25.5462i	0.104912	−	0.998173i
$656$	−0.230909	+	0.0490813i	−0.00901549	+	0.00191630i
$657$	4.97871	+	15.3229i	0.194238	+	0.597803i
$658$	−0.809017	+	0.587785i	−0.0315388	+	0.0229143i
$659$	7.34346	+	12.7192i	0.286061	+	0.495471i	0.972866	−	0.231370i	$-0.0743208\pi$
$659$	7.34346	+	12.7192i	0.286061	+	0.495471i	−0.686805	+	0.726841i	$0.740987\pi$
$660$	−5.73428	−	10.1991i	−0.223207	−	0.397000i
$661$	−9.21885	−	15.9675i	−0.358572	−	0.621064i	0.629151	−	0.777283i	$-0.283403\pi$
$661$	−9.21885	−	15.9675i	−0.358572	−	0.621064i	−0.987722	+	0.156219i	$0.950069\pi$
$662$	−2.69084	−	25.6016i	−0.104582	−	0.995035i
$663$	6.43972	+	1.36881i	0.250098	+	0.0531600i
$664$	−1.54508	+	4.75528i	−0.0599609	+	0.184541i
$665$	−9.71073	−	7.77649i	−0.376566	−	0.301560i
$666$	1.64590	+	1.19581i	0.0637773	+	0.0463369i
$667$	−0.669131	−	0.743145i	−0.0259088	−	0.0287747i
$668$	3.21986	+	0.684403i	0.124580	+	0.0264803i
$669$	14.6167	+	6.50779i	0.565115	+	0.251606i
$670$	3.31966	−	5.74982i	0.128250	−	0.222135i
$671$	35.9966	+	0.410822i	1.38963	+	0.0158596i
$672$	1.23607			0.0476824
$673$	−5.47214	+	3.97574i	−0.210935	+	0.153253i	−0.688237	−	0.725486i	$-0.741615\pi$
$673$	−5.47214	+	3.97574i	−0.210935	+	0.153253i	0.477301	+	0.878740i	$0.341615\pi$
$674$	16.0218	−	17.7941i	0.617138	−	0.685402i
$675$	−17.0101	+	3.61560i	−0.654718	+	0.139165i
$676$	−1.50000	−	1.08981i	−0.0576923	−	0.0419159i
$677$	−11.7984	−	8.57202i	−0.453448	−	0.329450i	0.337507	−	0.941323i	$-0.390416\pi$
$677$	−11.7984	−	8.57202i	−0.453448	−	0.329450i	−0.790956	+	0.611873i	$0.790416\pi$
$678$	−16.6830	+	3.54609i	−0.640708	+	0.136187i
$679$	−12.9468	−	2.75193i	−0.496854	−	0.105610i
$680$	−3.60327	−	1.60428i	−0.138179	−	0.0615213i
$681$	−8.79837	+	15.2392i	−0.337154	+	0.583969i
$682$	24.9223	−	27.0517i	0.954322	−	1.03586i
$683$	18.7082			0.715850			0.357925	−	0.933750i	$-0.383484\pi$
$683$	18.7082			0.715850			0.357925	+	0.933750i	$0.383484\pi$
$684$	5.36256	−	3.52412i	0.205043	−	0.134748i
$685$	−2.77458	−	8.53926i	−0.106011	−	0.326269i
$686$	8.69870	+	9.66088i	0.332118	+	0.368854i
$687$	27.9006	−	12.4222i	1.06447	−	0.473935i
$688$	−0.264234	+	2.51402i	−0.0100738	+	0.0958460i
$689$	−28.9767	−	32.1819i	−1.10392	−	1.22603i
$690$	2.36060	−	2.62171i	0.0898666	−	0.0998069i
$691$	−7.57295	+	5.50207i	−0.288089	+	0.209309i	−0.722438	−	0.691436i	$-0.756978\pi$
$691$	−7.57295	+	5.50207i	−0.288089	+	0.209309i	0.434349	+	0.900745i	$0.356978\pi$
$692$	−5.41641			−0.205901
$693$	−3.91704	−	2.91477i	−0.148796	−	0.110723i
$694$	12.0902	+	20.9408i	0.458937	+	0.794901i
$695$	−9.10739	+	6.61691i	−0.345463	+	0.250994i
$696$	−0.381966	−	1.17557i	−0.0144784	−	0.0445599i
$697$	−0.319109	+	0.0678287i	−0.0120871	+	0.00256919i
$698$	21.7094	−	9.66566i	0.821714	−	0.365851i
$699$	−2.17042	+	20.6502i	−0.0820929	+	0.781062i
$700$	2.10502	+	2.33786i	0.0795622	+	0.0883627i
$701$	−18.4758	−	3.92715i	−0.697821	−	0.148326i	−0.154676	−	0.987965i	$-0.549433\pi$
$701$	−18.4758	−	3.92715i	−0.697821	−	0.148326i	−0.543145	+	0.839639i	$0.682767\pi$
$702$	17.2361	−	12.5227i	0.650533	−	0.472640i
$703$	2.76393	+	5.35233i	0.104244	+	0.201867i
$704$	−2.19098	−	2.48990i	−0.0825758	−	0.0938416i
$705$	−1.76393	+	3.05522i	−0.0664335	+	0.115066i
$706$	1.56210	+	14.8624i	0.0587905	+	0.559354i
$707$	−2.67652	+	2.97258i	−0.100661	+	0.111795i
$708$	3.26227	+	3.62312i	0.122604	+	0.136165i
$709$	1.34002	−	12.7494i	0.0503255	−	0.478815i	−0.940113	−	0.340862i	$-0.889281\pi$
$709$	1.34002	−	12.7494i	0.0503255	−	0.478815i	0.990439	−	0.137953i	$-0.0440523\pi$
$710$	−30.8992	−	22.4496i	−1.15963	−	0.842517i
$711$	2.51471	−	7.73948i	0.0943089	−	0.290253i
$712$	7.99228	−	8.87632i	0.299523	−	0.332654i
$713$	10.1314	+	4.51078i	0.379423	+	0.168930i
$714$	1.70820			0.0639279
$715$	3.39919	+	36.3242i	0.127122	+	1.35845i
$716$	−6.85410	−	11.8717i	−0.256150	−	0.443664i
$717$	2.45933	+	23.3990i	0.0918454	+	0.873851i
$718$	18.8936	−	20.9835i	0.705104	−	0.783097i
$719$	−31.7135	−	35.2214i	−1.18271	−	1.31354i	−0.939091	−	0.343668i	$-0.888330\pi$
$719$	−31.7135	−	35.2214i	−1.18271	−	1.31354i	−0.243624	−	0.969870i	$-0.578336\pi$
$720$	−3.83838	+	1.70896i	−0.143048	+	0.0636890i
$721$	−14.9443	−	10.8576i	−0.556554	−	0.404360i
$722$	18.8732	−	2.19153i	0.702387	−	0.0815604i
$723$	2.43769	+	7.50245i	0.0906588	+	0.279019i
$724$	1.43290	+	13.6331i	0.0532532	+	0.506671i
$725$	1.57295	−	2.72443i	0.0584179	−	0.101183i
$726$	−1.11226	−	13.5512i	−0.0412800	−	0.502931i
$727$	11.2533	−	19.4913i	0.417361	−	0.722891i	−0.578312	−	0.815816i	$-0.696288\pi$
$727$	11.2533	−	19.4913i	0.417361	−	0.722891i	0.995673	+	0.0929247i	$0.0296216\pi$
$728$	−3.52090	−	1.56760i	−0.130493	−	0.0580993i
$729$	7.43363	+	22.8784i	0.275320	+	0.847347i
$730$	9.65248	−	29.7073i	0.357254	−	1.09952i
$731$	−0.365162	+	3.47428i	−0.0135060	+	0.128501i
$732$	−1.40240	+	13.3429i	−0.0518341	+	0.493168i
$733$	−3.36475	+	10.3556i	−0.124280	+	0.382494i	−0.993769	−	0.111458i	$-0.964448\pi$
$733$	−3.36475	+	10.3556i	−0.124280	+	0.382494i	0.869489	+	0.493951i	$0.164448\pi$
$734$	5.97214	+	18.3803i	0.220436	+	0.678431i
$735$	19.3372	+	8.60947i	0.713263	+	0.317565i
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	6.29312	−	4.46339i	0.231810	−	0.164411i
$738$	−0.173762	+	0.300965i	−0.00639627	+	0.0110787i
$739$	−2.87162	−	27.3216i	−0.105634	−	1.00504i	−0.911040	−	0.412319i	$-0.864719\pi$
$739$	−2.87162	−	27.3216i	−0.105634	−	1.00504i	0.805405	−	0.592724i	$-0.201948\pi$
$740$	−1.21885	−	3.75123i	−0.0448057	−	0.137898i
$741$	20.4919	−	3.35998i	0.752787	−	0.123432i
$742$	−9.09017	−	6.60440i	−0.333711	−	0.242455i
$743$	−18.9179	+	8.42279i	−0.694030	+	0.309002i	−0.723265	−	0.690571i	$-0.757360\pi$
$743$	−18.9179	+	8.42279i	−0.694030	+	0.309002i	0.0292351	+	0.999573i	$0.490693\pi$
$744$	9.17258	+	10.1872i	0.336283	+	0.373480i
$745$	24.4419	−	27.1455i	0.895482	−	0.994534i
$746$	1.90619	+	18.1362i	0.0697905	+	0.664012i
$747$	3.68034	+	6.37454i	0.134657	+	0.233232i
$748$	−3.02786	−	3.44095i	−0.110710	−	0.125814i
$749$	15.6180			0.570671
$750$	−5.97552	−	2.66047i	−0.218195	−	0.0971467i
$751$	16.5791	−	18.4130i	0.604980	−	0.671899i	−0.360384	−	0.932804i	$-0.617354\pi$
$751$	16.5791	−	18.4130i	0.604980	−	0.671899i	0.965364	+	0.260905i	$0.0840211\pi$
$752$	−0.309017	+	0.951057i	−0.0112687	+	0.0346815i
$753$	−25.0344	−	18.1886i	−0.912306	−	0.662829i
$754$	−0.402863	+	3.83299i	−0.0146714	+	0.139589i
$755$	12.4667	+	13.8457i	0.453710	+	0.503896i
$756$	3.69886	−	4.10800i	0.134526	−	0.149407i
$757$	2.21395	+	21.0643i	0.0804673	+	0.765595i	0.958133	+	0.286323i	$0.0924329\pi$
$757$	2.21395	+	21.0643i	0.0804673	+	0.765595i	−0.877666	+	0.479273i	$0.840900\pi$
$758$	−12.6910	+	21.9814i	−0.460957	+	0.798401i
$759$	3.76393	−	1.62460i	0.136622	−	0.0589692i
$760$	−12.4271	−	0.583495i	−0.450777	−	0.0211656i
$761$	−38.7877	+	28.1809i	−1.40605	+	1.02156i	−0.412173	+	0.911106i	$0.635230\pi$
$761$	−38.7877	+	28.1809i	−1.40605	+	1.02156i	−0.993881	+	0.110452i	$0.964770\pi$
$762$	−13.1232	−	2.78943i	−0.475404	−	0.101050i
$763$	−7.57873	−	8.41704i	−0.274369	−	0.304717i
$764$	1.30369	−	12.4038i	0.0471660	−	0.448754i
$765$	−5.30451	+	2.36172i	−0.191785	+	0.0853881i
$766$	1.49448	−	0.317661i	0.0539976	−	0.0114776i
$767$	−4.69756	−	14.4576i	−0.169619	−	0.522034i
$768$	1.00000	−	0.726543i	0.0360844	−	0.0262168i
$769$	−8.71885	−	15.1015i	−0.314410	−	0.544574i	0.664902	−	0.746930i	$-0.268473\pi$
$769$	−8.71885	−	15.1015i	−0.314410	−	0.544574i	−0.979312	+	0.202357i	$0.935140\pi$
$770$	2.82222	+	9.03548i	0.101706	+	0.325616i
$771$	−22.4721			−0.809314
$772$	−5.04508	+	3.66547i	−0.181577	+	0.131923i
$773$	−2.93211	+	3.25644i	−0.105461	+	0.117126i	−0.793564	−	0.608487i	$-0.791777\pi$
$773$	−2.93211	+	3.25644i	−0.105461	+	0.117126i	0.688103	+	0.725613i	$0.258444\pi$
$774$	2.49008	+	2.76551i	0.0895039	+	0.0994042i
$775$	−3.64685	+	34.6974i	−0.130999	+	1.24637i
$776$	−12.0917	+	5.38359i	−0.434069	+	0.193260i
$777$	1.14301	+	1.26944i	0.0410053	+	0.0455410i
$778$	−2.02786	−	6.24112i	−0.0727024	−	0.223755i
$779$	−0.859927	+	0.565119i	−0.0308101	+	0.0202475i
$780$	−13.5967			−0.486842
$781$	−21.7514	−	38.6875i	−0.778326	−	1.38435i
$782$	0.690983	−	1.19682i	0.0247095	−	0.0427981i
$783$	−5.04996	−	2.24838i	−0.180471	−	0.0803507i
$784$	5.86889	+	1.24747i	0.209603	+	0.0445525i
$785$	−15.0250	+	3.19366i	−0.536266	+	0.113987i
$786$	9.00000	+	6.53888i	0.321019	+	0.233234i
$787$	−9.37132	−	6.80866i	−0.334052	−	0.242703i	0.408096	−	0.912939i	$-0.366193\pi$
$787$	−9.37132	−	6.80866i	−0.334052	−	0.242703i	−0.742148	+	0.670236i	$0.766193\pi$
$788$	−7.50607	+	1.59546i	−0.267393	+	0.0568361i
$789$	−16.6625	+	18.5056i	−0.593200	+	0.658816i
$790$	−12.7639	+	9.27354i	−0.454120	+	0.329938i
$791$	13.7984			0.490614
$792$	−4.88220	−	0.0557196i	−0.173482	−	0.00197991i
$793$	20.9164	−	36.2283i	0.742763	−	1.28650i
$794$	−28.4337	−	12.6595i	−1.00908	−	0.449270i
$795$	−38.7731	−	8.24148i	−1.37514	−	0.292295i
$796$	0.692177	+	0.768740i	0.0245336	+	0.0272473i
$797$	−1.61803	−	1.17557i	−0.0573137	−	0.0416408i	0.558760	−	0.829330i	$-0.311277\pi$
$797$	−1.61803	−	1.17557i	−0.0573137	−	0.0416408i	−0.616073	+	0.787689i	$0.711277\pi$
$798$	5.01945	−	1.95819i	0.177687	−	0.0693191i
$799$	−0.427051	+	1.31433i	−0.0151080	+	0.0464976i
$800$	3.07715	+	0.654069i	0.108794	+	0.0231248i
$801$	−1.83799	−	17.4873i	−0.0649420	−	0.617882i
$802$	13.3262	+	23.0817i	0.470566	+	0.815044i
$803$	24.5944	−	26.6958i	0.867917	−	0.942073i
$804$	1.43769	+	2.49016i	0.0507036	+	0.0878211i
$805$	−2.30902	+	1.67760i	−0.0813822	+	0.0591276i
$806$	−13.2082	−	40.6507i	−0.465239	−	1.43186i
$807$	−19.6720	+	4.18141i	−0.692486	+	0.147192i
$808$	−0.418114	+	3.97809i	−0.0147092	+	0.139949i
$809$	−14.5902	−	10.6004i	−0.512963	−	0.372689i	0.300983	−	0.953629i	$-0.402685\pi$
$809$	−14.5902	−	10.6004i	−0.512963	−	0.372689i	−0.813946	+	0.580940i	$0.802685\pi$
$810$	2.13119	−	6.55913i	0.0748824	−	0.230464i
$811$	−21.5329	+	23.9147i	−0.756121	+	0.839757i	−0.991221	−	0.132214i	$-0.957791\pi$
$811$	−21.5329	+	23.9147i	−0.756121	+	0.839757i	0.235101	+	0.971971i	$0.424458\pi$
$812$	0.104528	+	0.994522i	0.00366823	+	0.0349009i
$813$	−12.7426	−	22.0709i	−0.446904	−	0.774061i
$814$	0.531091	−	4.55259i	0.0186147	−	0.159568i
$815$	8.97871	−	15.5516i	0.314511	−	0.544748i
$816$	1.38197	−	1.00406i	0.0483785	−	0.0351490i
$817$	2.90971	+	10.6276i	0.101798	+	0.371812i
$818$	−9.91641	+	30.5196i	−0.346719	+	1.06709i
$819$	−5.18324	+	2.30773i	−0.181117	+	0.0806385i
$820$	0.615512	−	0.274044i	0.0214946	−	0.00957002i
$821$	−18.2449	+	3.87807i	−0.636751	+	0.135345i	−0.514965	−	0.857211i	$-0.672195\pi$
$821$	−18.2449	+	3.87807i	−0.636751	+	0.135345i	−0.121785	+	0.992556i	$0.538862\pi$
$822$	3.80357	+	0.808474i	0.132665	+	0.0281988i
$823$	−45.2894	−	20.1642i	−1.57869	−	0.702878i	−0.584589	−	0.811330i	$-0.698744\pi$
$823$	−45.2894	−	20.1642i	−1.57869	−	0.702878i	−0.994102	+	0.108451i	$0.965411\pi$
$824$	−18.4721			−0.643507
$825$	8.51973	+	9.68208i	0.296619	+	0.337087i
$826$	−1.97214	−	3.41584i	−0.0686194	−	0.118852i
$827$	3.20342	+	1.42625i	0.111394	+	0.0495957i	0.461677	−	0.887048i	$-0.347248\pi$
$827$	3.20342	+	1.42625i	0.111394	+	0.0495957i	−0.350283	+	0.936644i	$0.613915\pi$
$828$	−0.454915	−	1.40008i	−0.0158094	−	0.0486563i
$829$	−10.5238	+	32.3889i	−0.365507	+	1.12491i	0.584157	+	0.811641i	$0.301425\pi$
$829$	−10.5238	+	32.3889i	−0.365507	+	1.12491i	−0.949663	+	0.313273i	$0.898575\pi$
$830$	1.49167	−	14.1923i	0.0517768	−	0.492623i
$831$	22.3175	−	9.93640i	0.774186	−	0.344690i
$832$	−3.76988	+	0.801313i	−0.130697	+	0.0277805i
$833$	8.11060	+	1.72396i	0.281016	+	0.0597317i
$834$	−0.509617	−	4.84868i	−0.0176466	−	0.167896i
$835$	−9.39512			−0.325132
$836$	−12.8417	−	6.64007i	−0.444140	−	0.229652i
$837$	61.3050			2.11901
$838$	1.16866	+	11.1191i	0.0403708	+	0.384103i
$839$	−34.7307	−	7.38223i	−1.19904	−	0.254863i	−0.435236	−	0.900316i	$-0.643335\pi$
$839$	−34.7307	−	7.38223i	−1.19904	−	0.254863i	−0.763800	+	0.645453i	$0.776668\pi$
$840$	−3.45077	+	0.733484i	−0.119063	+	0.0253076i
$841$	−25.5793	+	11.3886i	−0.882044	+	0.392711i
$842$	−1.03946	+	9.88980i	−0.0358221	+	0.340825i
$843$	2.88854	−	8.89002i	0.0994867	−	0.306189i
$844$	−3.80902	−	11.7229i	−0.131112	−	0.403521i
$845$	4.83430	+	2.15237i	0.166305	+	0.0740437i
$846$	0.736068	+	1.27491i	0.0253065	+	0.0438322i
$847$	−1.39919	+	10.9106i	−0.0480766	+	0.374894i
$848$	−11.2361			−0.385848
$849$	24.9832	+	11.1232i	0.857421	+	0.381749i
$850$	4.25252	+	0.903901i	0.145860	+	0.0310036i
$851$	1.35177	−	0.287327i	0.0463380	−	0.00984944i
$852$	15.1110	−	6.72784i	0.517693	−	0.230492i
$853$	10.8487	−	4.83016i	0.371453	−	0.165381i	−0.212516	−	0.977158i	$-0.568166\pi$
$853$	10.8487	−	4.83016i	0.371453	−	0.165381i	0.583969	+	0.811776i	$0.301499\pi$
$854$	3.35410	−	10.3229i	0.114775	−	0.353241i
$855$	−12.8796	+	13.0205i	−0.440474	+	0.445293i
$856$	12.6353	−	9.18005i	0.431864	−	0.313768i
$857$	1.41641	−	2.45329i	0.0483836	−	0.0838028i	−0.840819	−	0.541316i	$-0.817926\pi$
$857$	1.41641	−	2.45329i	0.0483836	−	0.0838028i	0.889203	+	0.457513i	$0.151260\pi$
$858$	−14.3599	−	6.59082i	−0.490239	−	0.225007i
$859$	16.1180	+	27.9173i	0.549940	+	0.952524i	0.998278	+	0.0586602i	$0.0186828\pi$
$859$	16.1180	+	27.9173i	0.549940	+	0.952524i	−0.448338	+	0.893864i	$0.647984\pi$
$860$	−0.754150	−	7.17526i	−0.0257163	−	0.244674i
$861$	−0.195250	+	0.216847i	−0.00665409	+	0.00739012i
$862$	−6.21885	+	19.1396i	−0.211815	+	0.651899i
$863$	−34.8156	−	25.2950i	−1.18514	−	0.861052i	−0.192395	−	0.981318i	$-0.561625\pi$
$863$	−34.8156	−	25.2950i	−1.18514	−	0.861052i	−0.992742	+	0.120265i	$0.961625\pi$
$864$	0.577819	−	5.49758i	0.0196578	−	0.187032i
$865$	15.1212	−	3.21410i	0.514135	−	0.109283i
$866$	9.55573	+	29.4095i	0.324717	+	0.999376i
$867$	−15.0902	+	10.9637i	−0.512489	+	0.372345i
$868$	−5.54508	−	9.60437i	−0.188212	−	0.325994i
$869$	−17.9755	+	3.60692i	−0.609779	+	0.122356i
$870$	1.76393	+	3.05522i	0.0598029	+	0.103582i
$871$	−0.937156	−	8.91644i	−0.0317543	−	0.302122i
$872$	−11.0787	−	2.35486i	−0.375173	−	0.0797455i
$873$	−6.02129	+	18.5316i	−0.203790	+	0.627200i
$874$	0.658449	−	4.30888i	0.0222724	−	0.145750i
$875$	4.28115	+	3.11044i	0.144729	+	0.105152i
$876$	9.05191	+	10.0532i	0.305836	+	0.339665i
$877$	−18.8157	−	3.99940i	−0.635362	−	0.135050i	−0.121040	−	0.992648i	$-0.538623\pi$
$877$	−18.8157	−	3.99940i	−0.635362	−	0.135050i	−0.514322	+	0.857597i	$0.671956\pi$
$878$	37.0870	+	16.5122i	1.25162	+	0.557259i
$879$	−1.85410	+	3.21140i	−0.0625373	+	0.108318i
$880$	7.59415	+	5.65100i	0.255999	+	0.190495i
$881$	17.7082			0.596605			0.298302	−	0.954471i	$-0.403580\pi$
$881$	17.7082			0.596605			0.298302	+	0.954471i	$0.403580\pi$
$882$	7.14590	−	5.19180i	0.240615	−	0.174817i
$883$	−20.9844	+	23.3055i	−0.706181	+	0.784293i	−0.984347	−	0.176239i	$-0.943607\pi$
$883$	−20.9844	+	23.3055i	−0.706181	+	0.784293i	0.278166	+	0.960533i	$0.410273\pi$
$884$	−5.20985	+	1.10739i	−0.175226	+	0.0372455i
$885$	−11.2574	−	8.17895i	−0.378412	−	0.274932i
$886$	−5.20820	−	3.78398i	−0.174973	−	0.127125i
$887$	18.1230	−	3.85216i	0.608510	−	0.129343i	0.106657	−	0.994296i	$-0.465985\pi$
$887$	18.1230	−	3.85216i	0.608510	−	0.129343i	0.501853	+	0.864953i	$0.332652\pi$
$888$	1.67088	+	0.355156i	0.0560709	+	0.0119182i
$889$	9.91572	+	4.41476i	0.332562	+	0.148066i
$890$	−17.0451	+	29.5230i	−0.571353	+	0.989612i
$891$	5.43024	−	5.89421i	0.181920	−	0.197464i
$892$	−12.9443			−0.433406
$893$	0.251807	+	4.35162i	0.00842639	+	0.145621i
$894$	4.88854	+	15.0454i	0.163497	+	0.503193i
$895$	26.1795	+	29.0753i	0.875083	+	0.971879i
$896$	−0.913545	+	0.406737i	−0.0305194	+	0.0135881i
$897$	0.497966	−	4.73783i	0.0166266	−	0.158192i
$898$	−13.2850	−	14.7545i	−0.443326	−	0.492363i
$899$	−7.42077	+	8.24160i	−0.247497	+	0.274873i
$900$	3.74671	−	2.72214i	0.124890	−	0.0907382i
$901$	−15.5279			−0.517308
$902$	0.782898	+	0.00893505i	0.0260676	+	0.000297505i
$903$	1.56231	+	2.70599i	0.0519903	+	0.0900498i
$904$	11.1631	−	8.11048i	0.371280	−	0.269751i
$905$	−12.0902	−	37.2097i	−0.401891	−	1.23689i
$906$	−7.89256	+	1.67762i	−0.262213	+	0.0557350i
$907$	11.0135	−	4.90351i	0.365696	−	0.162818i	−0.215658	−	0.976469i	$-0.569190\pi$
$907$	11.0135	−	4.90351i	0.365696	−	0.162818i	0.581354	+	0.813651i	$0.302523\pi$
$908$	1.48807	−	14.1581i	0.0493835	−	0.469852i
$909$	3.94020	+	4.37604i	0.130688	+	0.145144i
$910$	10.7596	+	2.28703i	0.356678	+	0.0758143i
$911$	20.1525	−	14.6416i	0.667681	−	0.485099i	−0.201567	−	0.979475i	$-0.564603\pi$
$911$	20.1525	−	14.6416i	0.667681	−	0.485099i	0.869248	+	0.494376i	$0.164603\pi$
$912$	2.90983	−	4.53457i	0.0963541	−	0.150155i
$913$	8.45492	−	14.2658i	0.279817	−	0.472131i
$914$	4.26393	−	7.38535i	0.141038	−	0.244286i
$915$	−4.00258	−	38.0820i	−0.132321	−	1.25895i
$916$	−16.5330	+	18.3618i	−0.546266	+	0.606690i
$917$	−6.02218	−	6.68830i	−0.198870	−	0.220867i
$918$	0.798526	−	7.59747i	0.0263553	−	0.250754i
$919$	−15.5623	−	11.3067i	−0.513353	−	0.372973i	0.300741	−	0.953706i	$-0.402766\pi$
$919$	−15.5623	−	11.3067i	−0.513353	−	0.372973i	−0.814094	+	0.580733i	$0.802766\pi$
$920$	−0.881966	+	2.71441i	−0.0290776	+	0.0894915i
$921$	−25.6683	+	28.5075i	−0.845799	+	0.939355i
$922$	−10.0490	−	4.47410i	−0.330946	−	0.147347i
$923$	−51.5755			−1.69763
$924$	−4.00000	−	0.898056i	−0.131590	−	0.0295439i
$925$	2.17376	+	3.76507i	0.0714729	+	0.123795i
$926$	0.301935	+	2.87272i	0.00992220	+	0.0944034i
$927$	−18.1960	+	20.2087i	−0.597635	+	0.663741i
$928$	0.669131	+	0.743145i	0.0219653	+	0.0243949i
$929$	−9.73152	+	4.33275i	−0.319281	+	0.142153i	−0.560119	−	0.828412i	$-0.689244\pi$
$929$	−9.73152	+	4.33275i	−0.319281	+	0.142153i	0.240838	+	0.970565i	$0.422578\pi$
$930$	−31.6525	−	22.9969i	−1.03793	−	0.754097i
$931$	25.8088	−	4.23177i	0.845848	−	0.138691i
$932$	−5.19098	−	15.9762i	−0.170036	−	0.523318i
$933$	−3.00665	−	28.6064i	−0.0984333	−	0.936530i
$934$	7.85410	−	13.6037i	0.256994	−	0.445127i
$935$	10.4949	+	7.80949i	0.343218	+	0.255398i
$936$	−2.83688	+	4.91362i	−0.0927264	+	0.160607i
$937$	54.4758	+	24.2542i	1.77965	+	0.792350i	0.981911	+	0.189343i	$0.0606357\pi$
$937$	54.4758	+	24.2542i	1.77965	+	0.792350i	0.797736	+	0.603007i	$0.206031\pi$
$938$	−0.718847	−	2.21238i	−0.0234712	−	0.0722369i
$939$	−0.180340	+	0.555029i	−0.00588517	+	0.0181127i
$940$	0.298335	−	2.83847i	0.00973061	−	0.0925806i
$941$	−2.36783	+	22.5284i	−0.0771890	+	0.734404i	0.885655	+	0.464345i	$0.153710\pi$
$941$	−2.36783	+	22.5284i	−0.0771890	+	0.734404i	−0.962844	+	0.270060i	$0.912957\pi$
$942$	2.05573	−	6.32688i	0.0669792	−	0.206141i
$943$	0.0729490	+	0.224514i	0.00237555	+	0.00731118i
$944$	−3.60327	−	1.60428i	−0.117277	−	0.0522149i
$945$	−7.88854	+	13.6634i	−0.256614	+	0.444469i
$946$	2.68162	−	7.94355i	0.0871869	−	0.258267i
$947$	18.0451	−	31.2550i	0.586386	−	1.01565i	−0.408315	−	0.912841i	$-0.633883\pi$
$947$	18.0451	−	31.2550i	0.586386	−	1.01565i	0.994701	−	0.102810i	$-0.0327833\pi$
$948$	−0.714224	−	6.79538i	−0.0231969	−	0.220704i
$949$	−13.0344	−	40.1159i	−0.423116	−	1.30222i
$950$	13.5320	−	2.21879i	0.439035	−	0.0719870i
$951$	29.4721	+	21.4128i	0.955699	+	0.694356i
$952$	−1.26249	+	0.562096i	−0.0409175	+	0.0182176i
$953$	11.4213	+	12.6847i	0.369973	+	0.410896i	0.899168	−	0.437604i	$-0.144173\pi$
$953$	11.4213	+	12.6847i	0.369973	+	0.410896i	−0.529195	+	0.848500i	$0.677506\pi$
$954$	−11.0681	+	12.2924i	−0.358343	+	0.397980i
$955$	3.72087	+	35.4017i	0.120405	+	1.14557i
$956$	−9.51722	−	16.4843i	−0.307809	−	0.533141i
$957$	0.381966	+	4.08174i	0.0123472	+	0.131944i
$958$	38.8885			1.25643
$959$	−2.87392	−	1.27955i	−0.0928037	−	0.0413189i
$960$	−2.36060	+	2.62171i	−0.0761881	+	0.0846155i
$961$	28.4271	−	87.4895i	0.917002	−	2.82224i
$962$	−4.30902	−	3.13068i	−0.138928	−	0.100937i
$963$	2.40330	−	22.8659i	0.0774454	−	0.736844i
$964$	−4.27037	−	4.74273i	−0.137539	−	0.152753i
$965$	11.9094	−	13.2268i	0.383378	−	0.425785i
$966$	−0.129204	−	1.22930i	−0.00415708	−	0.0395520i
$967$	9.78115	−	16.9415i	0.314541	−	0.544800i	−0.664799	−	0.747022i	$-0.731483\pi$
$967$	9.78115	−	16.9415i	0.314541	−	0.544800i	0.979340	+	0.202222i	$0.0648162\pi$
$968$	5.28115	+	9.64932i	0.169743	+	0.310141i
$969$	4.02129	−	6.26662i	0.129182	−	0.201313i
$970$	30.5623	−	22.2048i	0.981297	−	0.712954i
$971$	−6.24250	−	1.32689i	−0.200332	−	0.0425818i	0.106653	−	0.994296i	$-0.465987\pi$
$971$	−6.24250	−	1.32689i	−0.200332	−	0.0425818i	−0.306984	+	0.951715i	$0.599320\pi$
$972$	−9.09800	−	10.1044i	−0.291818	−	0.324097i
$973$	−0.412289	+	3.92266i	−0.0132174	+	0.125755i
$974$	3.00721	−	1.33889i	0.0963571	−	0.0429009i
$975$	14.6593	−	3.11594i	0.469475	−	0.0997899i
$976$	−3.35410	−	10.3229i	−0.107362	−	0.330427i
$977$	−27.8262	+	20.2169i	−0.890240	+	0.646797i	−0.935941	−	0.352158i	$-0.885448\pi$
$977$	−27.8262	+	20.2169i	−0.890240	+	0.646797i	0.0457004	+	0.998955i	$0.485448\pi$
$978$	3.88854	+	6.73516i	0.124342	+	0.215367i
$979$	−32.3126	+	22.9177i	−1.03271	+	0.732452i
$980$	−17.1246			−0.547026
$981$	−13.4894	+	9.80059i	−0.430682	+	0.312909i
$982$	−12.1650	+	13.5106i	−0.388201	+	0.431141i
$983$	−13.8565	−	15.3892i	−0.441953	−	0.490839i	0.480474	−	0.877009i	$-0.340465\pi$
$983$	−13.8565	−	15.3892i	−0.441953	−	0.490839i	−0.922428	+	0.386170i	$0.873798\pi$
$984$	−0.0305010	+	0.290198i	−0.000972336	+	0.00925116i
$985$	20.0082	−	8.90822i	0.637514	−	0.283840i
$986$	0.924716	+	1.02700i	0.0294489	+	0.0327064i
$987$	0.381966	+	1.17557i	0.0121581	+	0.0374188i
$988$	−14.0394	+	9.22626i	−0.446652	+	0.293526i
$989$	2.52786			0.0803814
$990$	13.6629	−	2.74155i	0.434235	−	0.0871322i
$991$	−4.04508	+	7.00629i	−0.128496	+	0.222562i	−0.923094	−	0.384574i	$-0.874348\pi$
$991$	−4.04508	+	7.00629i	−0.128496	+	0.222562i	0.794598	+	0.607136i	$0.207682\pi$
$992$	−10.1314	−	4.51078i	−0.321671	−	0.143217i
$993$	−31.1243	−	6.61568i	−0.987701	−	0.209942i
$994$	−13.0895	+	2.78227i	−0.415175	+	0.0882482i
$995$	−2.38854	−	1.73538i	−0.0757219	−	0.0550152i
$996$	5.00000	+	3.63271i	0.158431	+	0.115107i
$997$	15.6841	−	3.33375i	0.496719	−	0.105581i	0.0472613	−	0.998883i	$-0.484951\pi$
$997$	15.6841	−	3.33375i	0.496719	−	0.105581i	0.449458	+	0.893302i	$0.351617\pi$
$998$	7.96923	−	8.85073i	0.252262	−	0.280165i
$999$	6.18034	−	4.49028i	0.195537	−	0.142066i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.n.a.201.1	yes	8
11.4	even	5	inner	418.2.n.a.125.1	✓	8
19.7	even	3	inner	418.2.n.a.311.1	yes	8
209.26	even	15	inner	418.2.n.a.235.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.n.a.125.1	✓	8	11.4	even	5	inner
418.2.n.a.201.1	yes	8	1.1	even	1	trivial
418.2.n.a.235.1	yes	8	209.26	even	15	inner
418.2.n.a.311.1	yes	8	19.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.n (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.104528 + 0.994522i) q^{2} +(1.20906 + 0.256993i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(2.60735 - 1.16087i) q^{5} +(-0.129204 + 1.22930i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.34486 - 0.598772i) q^{9} +O(q^{10})\)	\(q+(0.104528 + 0.994522i) q^{2} +(1.20906 + 0.256993i) q^{3} +(-0.978148 + 0.207912i) q^{4} +(2.60735 - 1.16087i) q^{5} +(-0.129204 + 1.22930i) q^{6} +(0.309017 - 0.951057i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.34486 - 0.598772i) q^{9} +(1.42705 + 2.47172i) q^{10} +(0.309017 + 3.30220i) q^{11} -1.23607 q^{12} +(3.52090 + 1.56760i) q^{13} +(0.978148 + 0.207912i) q^{14} +(3.45077 - 0.733484i) q^{15} +(0.913545 - 0.406737i) q^{16} +(1.26249 - 0.562096i) q^{17} +(0.454915 - 1.40008i) q^{18} +(3.06539 - 3.09893i) q^{19} +(-2.30902 + 1.67760i) q^{20} +(0.618034 - 1.07047i) q^{21} +(-3.25181 + 0.652498i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.129204 - 1.22930i) q^{24} +(2.10502 - 2.33786i) q^{25} +(-1.19098 + 3.66547i) q^{26} +(-4.47214 - 3.24920i) q^{27} +(-0.104528 + 0.994522i) q^{28} +(0.978148 - 0.207912i) q^{29} +(1.09017 + 3.35520i) q^{30} +(-8.97214 + 6.51864i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.475022 + 4.07196i) q^{33} +(0.690983 + 1.19682i) q^{34} +(-0.298335 - 2.83847i) q^{35} +(1.43997 + 0.306074i) q^{36} +(-0.427051 + 1.31433i) q^{37} +(3.40238 + 2.72467i) q^{38} +(3.85410 + 2.80017i) q^{39} +(-1.90977 - 2.12101i) q^{40} +(-0.230909 - 0.0490813i) q^{41} +(1.12920 + 0.502754i) q^{42} +(-1.26393 + 2.18919i) q^{43} +(-0.988830 - 3.16579i) q^{44} -4.20163 q^{45} +(0.809017 - 0.587785i) q^{46} +(-0.669131 + 0.743145i) q^{47} +(1.20906 - 0.256993i) q^{48} +(4.85410 + 3.52671i) q^{49} +(2.54508 + 1.84911i) q^{50} +(1.67088 - 0.355156i) q^{51} +(-3.76988 - 0.801313i) q^{52} +(-10.2647 - 4.57012i) q^{53} +(2.76393 - 4.78727i) q^{54} +(4.63913 + 8.25126i) q^{55} -1.00000 q^{56} +(4.50264 - 2.95900i) q^{57} +(0.309017 + 0.951057i) q^{58} +(-2.63923 - 2.93117i) q^{59} +(-3.22286 + 1.43491i) q^{60} +(1.13456 - 10.7946i) q^{61} +(-7.42077 - 8.24160i) q^{62} +(-0.985051 + 1.09401i) q^{63} +(-0.809017 + 0.587785i) q^{64} +11.0000 q^{65} +(-4.09931 - 0.0467845i) q^{66} +(-1.16312 - 2.01458i) q^{67} +(-1.11803 + 0.812299i) q^{68} +(-0.381966 - 1.17557i) q^{69} +(2.79173 - 0.593401i) q^{70} +(-12.2250 + 5.44294i) q^{71} +(-0.153880 + 1.46407i) q^{72} +(-7.32315 - 8.13318i) q^{73} +(-1.35177 - 0.287327i) q^{74} +(3.14590 - 2.28563i) q^{75} +(-2.35410 + 3.66854i) q^{76} +(3.23607 + 0.726543i) q^{77} +(-2.38197 + 4.12569i) q^{78} +(0.577819 + 5.49758i) q^{79} +(1.90977 - 2.12101i) q^{80} +(-1.61689 - 1.79574i) q^{81} +(0.0246758 - 0.234775i) q^{82} +(-4.04508 - 2.93893i) q^{83} +(-0.381966 + 1.17557i) q^{84} +(2.63923 - 2.93117i) q^{85} +(-2.30932 - 1.02817i) q^{86} +1.23607 q^{87} +(3.04508 - 1.31433i) q^{88} +(5.97214 + 10.3440i) q^{89} +(-0.439190 - 4.17861i) q^{90} +(2.57890 - 2.86416i) q^{91} +(0.669131 + 0.743145i) q^{92} +(-12.5231 + 5.57563i) q^{93} +(-0.809017 - 0.587785i) q^{94} +(4.39511 - 11.6385i) q^{95} +(0.381966 + 1.17557i) q^{96} +(-1.38355 - 13.1636i) q^{97} +(-3.00000 + 5.19615i) q^{98} +(1.56168 - 4.62603i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - q^{2} + 6 q^{3} + q^{4} + 7 q^{5} + 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9}+O(q^{10}) \) 8 * q - q^2 + 6 * q^3 + q^4 + 7 * q^5 + 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9	\( 8 q - q^{2} + 6 q^{3} + q^{4} + 7 q^{5} + 4 q^{6} - 2 q^{7} + 2 q^{8} - 7 q^{9} - 2 q^{10} - 2 q^{11} + 8 q^{12} + 8 q^{13} - q^{14} - 18 q^{15} + q^{16} + 26 q^{18} + 4 q^{19} - 14 q^{20} - 4 q^{21} - 11 q^{22} - 4 q^{23} + 4 q^{24} + 14 q^{25} - 14 q^{26} + q^{28} - q^{29} - 36 q^{30} - 36 q^{31} + 4 q^{32} - 24 q^{33} + 10 q^{34} + 7 q^{35} + 13 q^{36} + 10 q^{37} + 17 q^{38} + 4 q^{39} + 8 q^{40} - 7 q^{41} + 4 q^{42} - 28 q^{43} - 4 q^{44} - 132 q^{45} + 2 q^{46} - q^{47} + 6 q^{48} + 12 q^{49} - 2 q^{50} + 20 q^{51} - 7 q^{52} - 14 q^{53} + 40 q^{54} + 12 q^{55} - 8 q^{56} + 8 q^{57} - 2 q^{58} + 25 q^{59} + 2 q^{60} - 15 q^{61} + 7 q^{62} + 13 q^{63} - 2 q^{64} + 88 q^{65} + 14 q^{66} + 22 q^{67} - 12 q^{69} + 8 q^{70} - 12 q^{71} + 7 q^{72} + 18 q^{73} + 5 q^{74} + 52 q^{75} + 8 q^{76} + 8 q^{77} - 28 q^{78} - 8 q^{80} + 41 q^{81} - 3 q^{82} - 10 q^{83} - 12 q^{84} - 25 q^{85} + 3 q^{86} - 8 q^{87} + 2 q^{88} + 12 q^{89} - 11 q^{90} - 7 q^{91} + q^{92} - 22 q^{93} - 2 q^{94} - 14 q^{95} + 12 q^{96} + 16 q^{97} - 24 q^{98} + 43 q^{99}+O(q^{100}) \) 8 * q - q^2 + 6 * q^3 + q^4 + 7 * q^5 + 4 * q^6 - 2 * q^7 + 2 * q^8 - 7 * q^9 - 2 * q^10 - 2 * q^11 + 8 * q^12 + 8 * q^13 - q^14 - 18 * q^15 + q^16 + 26 * q^18 + 4 * q^19 - 14 * q^20 - 4 * q^21 - 11 * q^22 - 4 * q^23 + 4 * q^24 + 14 * q^25 - 14 * q^26 + q^28 - q^29 - 36 * q^30 - 36 * q^31 + 4 * q^32 - 24 * q^33 + 10 * q^34 + 7 * q^35 + 13 * q^36 + 10 * q^37 + 17 * q^38 + 4 * q^39 + 8 * q^40 - 7 * q^41 + 4 * q^42 - 28 * q^43 - 4 * q^44 - 132 * q^45 + 2 * q^46 - q^47 + 6 * q^48 + 12 * q^49 - 2 * q^50 + 20 * q^51 - 7 * q^52 - 14 * q^53 + 40 * q^54 + 12 * q^55 - 8 * q^56 + 8 * q^57 - 2 * q^58 + 25 * q^59 + 2 * q^60 - 15 * q^61 + 7 * q^62 + 13 * q^63 - 2 * q^64 + 88 * q^65 + 14 * q^66 + 22 * q^67 - 12 * q^69 + 8 * q^70 - 12 * q^71 + 7 * q^72 + 18 * q^73 + 5 * q^74 + 52 * q^75 + 8 * q^76 + 8 * q^77 - 28 * q^78 - 8 * q^80 + 41 * q^81 - 3 * q^82 - 10 * q^83 - 12 * q^84 - 25 * q^85 + 3 * q^86 - 8 * q^87 + 2 * q^88 + 12 * q^89 - 11 * q^90 - 7 * q^91 + q^92 - 22 * q^93 - 2 * q^94 - 14 * q^95 + 12 * q^96 + 16 * q^97 - 24 * q^98 + 43 * q^99

Introduction

L-functions

Modular forms

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