LMFDB - Embedded newform 525.2.bg.a.16.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(16,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 10]))

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

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

chi := DirichletCharacter("525.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bg (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$20$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			16.9
Character	$\chi$	$=$	525.16
Dual form			525.2.bg.a.361.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.650196 + 0.289486i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.999309 + 1.10984i) q^{4} +(2.08872 + 0.798271i) q^{5} +(0.219936 - 0.676893i) q^{6} +(0.659935 - 2.56213i) q^{7} +(0.768334 - 2.36469i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.650196 + 0.289486i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.999309 + 1.10984i) q^{4} +(2.08872 + 0.798271i) q^{5} +(0.219936 - 0.676893i) q^{6} +(0.659935 - 2.56213i) q^{7} +(0.768334 - 2.36469i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.58917 + 0.0856230i) q^{10} +(0.346056 - 3.29250i) q^{11} +(-0.156107 - 1.48526i) q^{12} +(3.29380 - 2.39308i) q^{13} +(0.312612 + 1.85692i) q^{14} +(-1.99086 + 1.01808i) q^{15} +(-0.127238 - 1.21059i) q^{16} +(-2.79520 + 0.594138i) q^{17} +(0.355864 + 0.616374i) q^{18} +(-1.33616 - 1.48395i) q^{19} +(-2.97324 + 1.52044i) q^{20} +(1.46245 + 2.20482i) q^{21} +(0.728128 + 2.24095i) q^{22} +(7.33887 - 3.26748i) q^{23} +(1.24319 + 2.15327i) q^{24} +(3.72553 + 3.33473i) q^{25} +(-1.44885 + 2.50948i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.18408 + 3.29278i) q^{28} +(-0.629347 - 1.93693i) q^{29} +(0.999730 - 1.23827i) q^{30} +(-5.61790 + 1.19412i) q^{31} +(2.91956 + 5.05683i) q^{32} +(2.21525 + 2.46028i) q^{33} +(1.64543 - 1.19548i) q^{34} +(3.42369 - 4.82476i) q^{35} +(1.20822 + 0.877824i) q^{36} +(1.01253 + 9.63359i) q^{37} +(1.29835 + 0.578062i) q^{38} +(-0.425573 + 4.04905i) q^{39} +(3.49250 - 4.32584i) q^{40} +(9.60658 - 6.97959i) q^{41} +(-1.58914 - 1.01021i) q^{42} -5.12546 q^{43} +(3.30835 + 3.67429i) q^{44} +(0.575567 - 2.16072i) q^{45} +(-3.82581 + 4.24900i) q^{46} +(1.78014 + 0.378379i) q^{47} +(0.984785 + 0.715488i) q^{48} +(-6.12897 - 3.38167i) q^{49} +(-3.38768 - 1.08974i) q^{50} +(1.42882 - 2.47479i) q^{51} +(-0.635569 + 6.04703i) q^{52} +(3.19621 - 3.54975i) q^{53} +(-0.696175 - 0.147977i) q^{54} +(3.35112 - 6.60087i) q^{55} +(-5.55158 - 3.52911i) q^{56} +1.99686 q^{57} +(0.969912 + 1.07720i) q^{58} +(8.29288 + 3.69223i) q^{59} +(0.859577 - 3.22692i) q^{60} +(-2.22022 + 0.988507i) q^{61} +(3.30705 - 2.40271i) q^{62} +(-2.61707 - 0.388505i) q^{63} +(-1.39259 - 1.01178i) q^{64} +(8.79016 - 2.36914i) q^{65} +(-2.15256 - 0.958382i) q^{66} +(7.46557 - 1.58686i) q^{67} +(2.13387 - 3.69596i) q^{68} +(-2.48246 + 7.64021i) q^{69} +(-0.829370 + 4.12815i) q^{70} +(-2.71494 - 8.35571i) q^{71} +(-2.43205 - 0.516948i) q^{72} +(-0.786915 + 7.48699i) q^{73} +(-3.44713 - 5.97060i) q^{74} +(-4.97105 + 0.537232i) q^{75} +2.98219 q^{76} +(-8.20742 - 3.05947i) q^{77} +(-0.895438 - 2.75587i) q^{78} +(-13.8399 - 2.94176i) q^{79} +(0.700616 - 2.63016i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-4.22567 + 7.31907i) q^{82} +(-0.629429 + 1.93718i) q^{83} +(-3.90845 - 0.580210i) q^{84} +(-6.31268 - 0.990338i) q^{85} +(3.33255 - 1.48375i) q^{86} +(1.86053 + 0.828363i) q^{87} +(-7.51985 - 3.34805i) q^{88} +(-14.8570 + 6.61477i) q^{89} +(0.251267 + 1.57151i) q^{90} +(-3.95769 - 10.0184i) q^{91} +(-3.70741 + 11.4102i) q^{92} +(2.87170 - 4.97394i) q^{93} +(-1.26697 + 0.269303i) q^{94} +(-1.60627 - 4.16619i) q^{95} +(-5.71152 - 1.21402i) q^{96} +(3.93913 + 12.1234i) q^{97} +(4.96398 + 0.424498i) q^{98} -3.31064 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) $ 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.650196	+	0.289486i	−0.459758	+	0.204697i	−0.623528	−	0.781801i	$-0.714301\pi$
$2$	−0.650196	+	0.289486i	−0.459758	+	0.204697i	0.163770	+	0.986499i	$0.447635\pi$
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$3$	−0.669131	+	0.743145i	−0.386323	+	0.429055i
$4$	−0.999309	+	1.10984i	−0.499654	+	0.554922i
$5$	2.08872	+	0.798271i	0.934105	+	0.356998i
$5$	2.08872	+	0.798271i	0.934105	+	0.356998i
$6$	0.219936	−	0.676893i	0.0897885	−	0.276341i
$7$	0.659935	−	2.56213i	0.249432	−	0.968392i
$7$	0.659935	−	2.56213i	0.249432	−	0.968392i
$8$	0.768334	−	2.36469i	0.271647	−	0.836044i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	−1.58917	+	0.0856230i	−0.502539	+	0.0270764i
$11$	0.346056	−	3.29250i	0.104340	−	0.992726i	−0.809629	−	0.586942i	$-0.800332\pi$
$11$	0.346056	−	3.29250i	0.104340	−	0.992726i	0.913969	−	0.405784i	$-0.133002\pi$
$12$	−0.156107	−	1.48526i	−0.0450643	−	0.428758i
$13$	3.29380	−	2.39308i	0.913535	−	0.663722i	−0.0283716	−	0.999597i	$-0.509032\pi$
$13$	3.29380	−	2.39308i	0.913535	−	0.663722i	0.941906	+	0.335876i	$0.109032\pi$
$14$	0.312612	+	1.85692i	0.0835491	+	0.496284i
$15$	−1.99086	+	1.01808i	−0.514038	+	0.262866i
$16$	−0.127238	−	1.21059i	−0.0318096	−	0.302648i
$17$	−2.79520	+	0.594138i	−0.677935	+	0.144100i	−0.533996	−	0.845487i	$-0.679310\pi$
$17$	−2.79520	+	0.594138i	−0.677935	+	0.144100i	−0.143939	+	0.989587i	$0.545977\pi$
$18$	0.355864	+	0.616374i	0.0838779	+	0.145281i
$19$	−1.33616	−	1.48395i	−0.306536	−	0.340443i	0.570119	−	0.821562i	$-0.306897\pi$
$19$	−1.33616	−	1.48395i	−0.306536	−	0.340443i	−0.876655	+	0.481119i	$0.840230\pi$
$20$	−2.97324	+	1.52044i	−0.664836	+	0.339980i
$21$	1.46245	+	2.20482i	0.319132	+	0.481132i
$22$	0.728128	+	2.24095i	0.155237	+	0.477771i
$23$	7.33887	−	3.26748i	1.53026	−	0.681316i	0.542899	−	0.839798i	$-0.317327\pi$
$23$	7.33887	−	3.26748i	1.53026	−	0.681316i	0.987362	+	0.158482i	$0.0506601\pi$
$24$	1.24319	+	2.15327i	0.253765	+	0.439534i
$25$	3.72553	+	3.33473i	0.745105	+	0.666947i
$26$	−1.44885	+	2.50948i	−0.284143	+	0.492149i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	2.18408	+	3.29278i	0.412753	+	0.622277i
$29$	−0.629347	−	1.93693i	−0.116867	−	0.359679i	0.875465	−	0.483281i	$-0.160555\pi$
$29$	−0.629347	−	1.93693i	−0.116867	−	0.359679i	−0.992332	+	0.123603i	$0.960555\pi$
$30$	0.999730	−	1.23827i	0.182525	−	0.226077i
$31$	−5.61790	+	1.19412i	−1.00900	+	0.214471i	−0.682626	−	0.730768i	$-0.739162\pi$
$31$	−5.61790	+	1.19412i	−1.00900	+	0.214471i	−0.326379	+	0.945239i	$0.605829\pi$
$32$	2.91956	+	5.05683i	0.516110	+	0.893929i
$33$	2.21525	+	2.46028i	0.385625	+	0.428280i
$34$	1.64543	−	1.19548i	0.282189	−	0.205022i
$35$	3.42369	−	4.82476i	0.578710	−	0.815534i
$36$	1.20822	+	0.877824i	0.201370	+	0.146304i
$37$	1.01253	+	9.63359i	0.166459	+	1.58375i	0.684899	+	0.728638i	$0.259846\pi$
$37$	1.01253	+	9.63359i	0.166459	+	1.58375i	−0.518440	+	0.855114i	$0.673487\pi$
$38$	1.29835	+	0.578062i	0.210620	+	0.0937740i
$39$	−0.425573	+	4.04905i	−0.0681462	+	0.648367i
$40$	3.49250	−	4.32584i	0.552213	−	0.683975i
$41$	9.60658	−	6.97959i	1.50030	−	1.09003i	0.530032	−	0.847977i	$-0.322180\pi$
$41$	9.60658	−	6.97959i	1.50030	−	1.09003i	0.970263	−	0.242051i	$-0.0778202\pi$
$42$	−1.58914	−	1.01021i	−0.245210	−	0.155879i
$43$	−5.12546			−0.781625			−0.390813	−	0.920470i	$-0.627806\pi$
$43$	−5.12546			−0.781625			−0.390813	+	0.920470i	$0.627806\pi$
$44$	3.30835	+	3.67429i	0.498752	+	0.553920i
$45$	0.575567	−	2.16072i	0.0858005	−	0.322102i
$46$	−3.82581	+	4.24900i	−0.564086	+	0.626480i
$47$	1.78014	+	0.378379i	0.259659	+	0.0551923i	0.335902	−	0.941897i	$-0.390959\pi$
$47$	1.78014	+	0.378379i	0.259659	+	0.0551923i	−0.0762424	+	0.997089i	$0.524292\pi$
$48$	0.984785	+	0.715488i	0.142141	+	0.103272i
$49$	−6.12897	−	3.38167i	−0.875567	−	0.483096i
$50$	−3.38768	−	1.08974i	−0.479090	−	0.154113i
$51$	1.42882	−	2.47479i	0.200075	−	0.346540i
$52$	−0.635569	+	6.04703i	−0.0881375	+	0.838573i
$53$	3.19621	−	3.54975i	0.439033	−	0.487595i	−0.482500	−	0.875896i	$-0.660271\pi$
$53$	3.19621	−	3.54975i	0.439033	−	0.487595i	0.921533	+	0.388301i	$0.126938\pi$
$54$	−0.696175	−	0.147977i	−0.0947374	−	0.0201371i
$55$	3.35112	−	6.60087i	0.451865	−	0.890061i
$56$	−5.55158	−	3.52911i	−0.741861	−	0.471597i
$57$	1.99686			0.264490
$58$	0.969912	+	1.07720i	0.127356	+	0.141443i
$59$	8.29288	+	3.69223i	1.07964	+	0.480687i	0.867951	−	0.496650i	$-0.165437\pi$
$59$	8.29288	+	3.69223i	1.07964	+	0.480687i	0.211690	+	0.977337i	$0.432103\pi$
$60$	0.859577	−	3.22692i	0.110971	−	0.416593i
$61$	−2.22022	+	0.988507i	−0.284270	+	0.126565i	−0.543919	−	0.839138i	$-0.683060\pi$
$61$	−2.22022	+	0.988507i	−0.284270	+	0.126565i	0.259648	+	0.965703i	$0.416393\pi$
$62$	3.30705	−	2.40271i	0.419996	−	0.305145i
$63$	−2.61707	−	0.388505i	−0.329720	−	0.0489470i
$64$	−1.39259	−	1.01178i	−0.174074	−	0.126472i
$65$	8.79016	−	2.36914i	1.09028	−	0.293856i
$66$	−2.15256	−	0.958382i	−0.264962	−	0.117969i
$67$	7.46557	−	1.58686i	0.912065	−	0.193865i	0.272099	−	0.962269i	$-0.412282\pi$
$67$	7.46557	−	1.58686i	0.912065	−	0.193865i	0.639965	+	0.768404i	$0.278949\pi$
$68$	2.13387	−	3.69596i	0.258769	−	0.448201i
$69$	−2.48246	+	7.64021i	−0.298853	+	0.919773i
$70$	−0.829370	+	4.12815i	−0.0991286	+	0.493408i
$71$	−2.71494	−	8.35571i	−0.322204	−	0.991641i	−0.972687	−	0.232120i	$-0.925434\pi$
$71$	−2.71494	−	8.35571i	−0.322204	−	0.991641i	0.650483	−	0.759520i	$-0.274566\pi$
$72$	−2.43205	−	0.516948i	−0.286620	−	0.0609229i
$73$	−0.786915	+	7.48699i	−0.0921014	+	0.876286i	0.846756	+	0.531981i	$0.178552\pi$
$73$	−0.786915	+	7.48699i	−0.0921014	+	0.876286i	−0.938858	+	0.344305i	$0.888114\pi$
$74$	−3.44713	−	5.97060i	−0.400721	−	0.694068i
$75$	−4.97105	+	0.537232i	−0.574008	+	0.0620342i
$76$	2.98219			0.342081
$77$	−8.20742	−	3.05947i	−0.935322	−	0.348659i
$78$	−0.895438	−	2.75587i	−0.101388	−	0.312041i
$79$	−13.8399	−	2.94176i	−1.55711	−	0.330974i	−0.652692	−	0.757623i	$-0.726360\pi$
$79$	−13.8399	−	2.94176i	−1.55711	−	0.330974i	−0.904417	+	0.426650i	$0.859694\pi$
$80$	0.700616	−	2.63016i	0.0783312	−	0.294061i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	−4.22567	+	7.31907i	−0.466647	+	0.808256i
$83$	−0.629429	+	1.93718i	−0.0690888	+	0.212634i	−0.979640	−	0.200763i	$-0.935658\pi$
$83$	−0.629429	+	1.93718i	−0.0690888	+	0.212634i	0.910551	+	0.413397i	$0.135658\pi$
$84$	−3.90845	−	0.580210i	−0.426447	−	0.0633061i
$85$	−6.31268	−	0.990338i	−0.684706	−	0.107417i
$86$	3.33255	−	1.48375i	0.359358	−	0.159997i
$87$	1.86053	+	0.828363i	0.199470	+	0.0888099i
$88$	−7.51985	−	3.34805i	−0.801619	−	0.356904i
$89$	−14.8570	+	6.61477i	−1.57484	+	0.701164i	−0.993641	−	0.112598i	$-0.964083\pi$
$89$	−14.8570	+	6.61477i	−1.57484	+	0.701164i	−0.581199	+	0.813762i	$0.697416\pi$
$90$	0.251267	+	1.57151i	0.0264859	+	0.165652i
$91$	−3.95769	−	10.0184i	−0.414878	−	1.05021i
$92$	−3.70741	+	11.4102i	−0.386524	+	1.18960i
$93$	2.87170	−	4.97394i	0.297782	−	0.515773i
$94$	−1.26697	+	0.269303i	−0.130678	+	0.0277765i
$95$	−1.60627	−	4.16619i	−0.164800	−	0.427442i
$96$	−5.71152	−	1.21402i	−0.582930	−	0.123906i
$97$	3.93913	+	12.1234i	0.399958	+	1.23094i	0.925032	+	0.379888i	$0.124038\pi$
$97$	3.93913	+	12.1234i	0.399958	+	1.23094i	−0.525074	+	0.851056i	$0.675962\pi$
$98$	4.96398	+	0.424498i	0.501437	+	0.0428808i
$99$	−3.31064			−0.332731
$100$	−7.42399	+	0.802326i	−0.742399	+	0.0802326i
$101$	−2.81416	−	4.87427i	−0.280020	−	0.485008i	0.691370	−	0.722501i	$-0.257008\pi$
$101$	−2.81416	−	4.87427i	−0.280020	−	0.485008i	−0.971389	+	0.237493i	$0.923674\pi$
$102$	−0.212597	+	2.02272i	−0.0210502	+	0.200279i
$103$	14.8451	+	3.15543i	1.46273	+	0.310914i	0.869427	−	0.494062i	$-0.164488\pi$
$103$	14.8451	+	3.15543i	1.46273	+	0.310914i	0.593308	+	0.804976i	$0.297822\pi$
$104$	−3.12816	−	9.62749i	−0.306741	−	0.944053i
$105$	1.29460	+	5.77270i	0.126340	+	0.563357i
$106$	−1.05056	+	3.23329i	−0.102039	+	0.314045i
$107$	4.45850	−	7.72235i	0.431019	−	0.746547i	−0.565942	−	0.824445i	$-0.691487\pi$
$107$	4.45850	−	7.72235i	0.431019	−	0.746547i	0.996961	+	0.0778977i	$0.0248207\pi$
$108$	−1.46081	+	0.310504i	−0.140566	+	0.0298783i
$109$	3.08240	+	1.37238i	0.295241	+	0.131450i	0.549012	−	0.835815i	$-0.315004\pi$
$109$	3.08240	+	1.37238i	0.295241	+	0.131450i	−0.253771	+	0.967264i	$0.581671\pi$
$110$	−0.268027	+	5.26196i	−0.0255553	+	0.501708i
$111$	−7.83667	−	5.69367i	−0.743823	−	0.540419i
$112$	−3.18566	−	0.472912i	−0.301017	−	0.0446859i
$113$	−2.28431	+	1.65965i	−0.214889	+	0.156126i	−0.690023	−	0.723787i	$-0.742400\pi$
$113$	−2.28431	+	1.65965i	−0.214889	+	0.156126i	0.475134	+	0.879914i	$0.342400\pi$
$114$	−1.29835	+	0.578062i	−0.121601	+	0.0541405i
$115$	17.9372	−	0.966441i	1.67265	−	0.0901211i
$116$	2.77860	+	1.23711i	0.257987	+	0.114863i
$117$	−2.72427	−	3.02561i	−0.251859	−	0.279718i
$118$	−6.46084			−0.594768
$119$	−0.322393	+	7.55374i	−0.0295538	+	0.692450i
$120$	0.877787	+	5.48999i	0.0801306	+	0.501165i
$121$	0.0388279	+	0.00825313i	0.00352981	+	0.000750284i
$122$	1.15742	−	1.28545i	0.104788	−	0.116379i
$123$	−1.24121	+	11.8093i	−0.111916	+	1.06481i
$124$	4.28873	−	7.42829i	0.385139	−	0.667081i
$125$	5.11957	+	9.93932i	0.457908	+	0.889000i
$126$	1.81408	−	0.505001i	0.161611	−	0.0449891i
$127$	−15.5006	−	11.2619i	−1.37546	−	0.999328i	−0.997289	−	0.0735910i	$-0.976554\pi$
$127$	−15.5006	−	11.2619i	−1.37546	−	0.999328i	−0.378168	−	0.925737i	$-0.623446\pi$
$128$	−10.2247	−	2.17332i	−0.903743	−	0.192097i
$129$	3.42960	−	3.80896i	0.301960	−	0.335360i
$130$	−5.02949	+	4.08503i	−0.441115	+	0.358281i
$131$	6.04995	+	6.71915i	0.528587	+	0.587055i	0.947013	−	0.321196i	$-0.104085\pi$
$131$	6.04995	+	6.71915i	0.528587	+	0.587055i	−0.418426	+	0.908251i	$0.637418\pi$
$132$	−4.94425			−0.430341
$133$	−4.68386	+	2.44409i	−0.406142	+	0.211930i
$134$	−4.39471	+	3.19294i	−0.379645	+	0.275828i
$135$	1.22060	+	1.87354i	0.105053	+	0.161248i
$136$	−0.742695	+	7.06627i	−0.0636856	+	0.605928i
$137$	15.9166	+	7.08652i	1.35984	+	0.605442i	0.951574	−	0.307419i	$-0.0994653\pi$
$137$	15.9166	+	7.08652i	1.35984	+	0.605442i	0.408271	+	0.912861i	$0.366132\pi$
$138$	−0.597651	−	5.68627i	−0.0508754	−	0.484047i
$139$	−9.13787	−	6.63905i	−0.775064	−	0.563117i	0.128430	−	0.991719i	$-0.459006\pi$
$139$	−9.13787	−	6.63905i	−0.775064	−	0.563117i	−0.903493	+	0.428602i	$0.859006\pi$
$140$	1.93341	+	8.62119i	0.163403	+	0.728624i
$141$	−1.47233	+	1.06971i	−0.123993	+	0.0900861i
$142$	4.18410	+	4.64691i	0.351122	+	0.389960i
$143$	−6.73939	−	11.6730i	−0.563576	−	0.976142i
$144$	−1.19066	+	0.253083i	−0.0992218	+	0.0210902i
$145$	0.231665	−	4.54810i	0.0192387	−	0.377699i
$146$	−1.65573	−	5.09581i	−0.137029	−	0.421732i
$147$	6.61415	−	2.29193i	0.545526	−	0.189036i
$148$	−11.7036	−	8.50318i	−0.962031	−	0.698957i
$149$	−0.250837	+	0.434462i	−0.0205493	+	0.0355925i	−0.876117	−	0.482098i	$-0.839875\pi$
$149$	−0.250837	+	0.434462i	−0.0205493	+	0.0355925i	0.855568	+	0.517691i	$0.173208\pi$
$150$	3.07664	−	1.78836i	0.251206	−	0.146019i
$151$	−1.27370	−	2.20612i	−0.103653	−	0.179532i	0.809534	−	0.587073i	$-0.199720\pi$
$151$	−1.27370	−	2.20612i	−0.103653	−	0.179532i	−0.913187	+	0.407541i	$0.866386\pi$
$152$	−4.53571	+	2.01943i	−0.367894	+	0.163797i
$153$	0.883061	+	2.71778i	0.0713912	+	0.219720i
$154$	6.22210	−	0.386676i	0.501391	−	0.0311592i
$155$	−12.6875	−	1.99042i	−1.01908	−	0.159874i
$156$	−4.06854	−	4.51857i	−0.325744	−	0.361775i
$157$	−2.53252	−	4.38645i	−0.202117	−	0.350076i	0.747094	−	0.664719i	$-0.231449\pi$
$157$	−2.53252	−	4.38645i	−0.202117	−	0.350076i	−0.949210	+	0.314642i	$0.898115\pi$
$158$	9.85023	−	2.09373i	0.783642	−	0.166568i
$159$	0.499297	+	4.75049i	0.0395968	+	0.376738i
$160$	2.06143	+	12.8929i	0.162971	+	1.01927i
$161$	−3.52851	−	20.9594i	−0.278085	−	1.65183i
$162$	0.575800	−	0.418343i	0.0452391	−	0.0328681i
$163$	−1.05300	−	10.0186i	−0.0824773	−	0.784719i	−0.955092	−	0.296310i	$-0.904244\pi$
$163$	−1.05300	−	10.0186i	−0.0824773	−	0.784719i	0.872615	−	0.488409i	$-0.162423\pi$
$164$	−1.85368	+	17.6366i	−0.144748	+	1.37719i
$165$	2.66307	+	6.90721i	0.207319	+	0.537726i
$166$	−0.151535	−	1.44176i	−0.0117614	−	0.111902i
$167$	3.22118	−	9.91377i	0.249262	−	0.767150i	−0.745644	−	0.666345i	$-0.767858\pi$
$167$	3.22118	−	9.91377i	0.249262	−	0.767150i	0.994906	−	0.100806i	$-0.0321420\pi$
$168$	6.33737	−	1.76419i	0.488939	−	0.136110i
$169$	1.10503	−	3.40092i	0.0850021	−	0.261609i
$170$	4.39116	−	1.18352i	0.336787	−	0.0907716i
$171$	−1.33616	+	1.48395i	−0.102179	+	0.113481i
$172$	5.12192	−	5.68847i	0.390543	−	0.433741i
$173$	5.77553	−	2.57143i	0.439106	−	0.195502i	−0.175263	−	0.984522i	$-0.556078\pi$
$173$	5.77553	−	2.57143i	0.439106	−	0.195502i	0.614368	+	0.789019i	$0.289411\pi$
$174$	−1.44951			−0.109887
$175$	11.0026	−	7.34456i	0.831719	−	0.555196i
$176$	−4.02991			−0.303766
$177$	−8.29288	+	3.69223i	−0.623331	+	0.277525i
$178$	7.74508	−	8.60178i	0.580518	−	0.644731i
$179$	−6.45605	+	7.17017i	−0.482548	+	0.535924i	−0.934427	−	0.356156i	$-0.884087\pi$
$179$	−6.45605	+	7.17017i	−0.482548	+	0.535924i	0.451879	+	0.892079i	$0.350754\pi$
$180$	1.82290	+	2.79802i	0.135871	+	0.208552i
$181$	−3.67130	+	11.2991i	−0.272886	+	0.839855i	0.716886	+	0.697191i	$0.245567\pi$
$181$	−3.67130	+	11.2991i	−0.272886	+	0.839855i	−0.989771	+	0.142664i	$0.954433\pi$
$182$	5.47345	+	5.36822i	0.405719	+	0.397919i
$183$	0.751016	−	2.31139i	0.0555167	−	0.170863i
$184$	−2.08786	−	19.8647i	−0.153919	−	1.46444i
$185$	−5.57532	+	20.9302i	−0.409906	+	1.53882i
$186$	−0.427285	+	4.06535i	−0.0313301	+	0.298086i
$187$	0.988904	+	9.40879i	0.0723158	+	0.688039i
$188$	−2.19885	+	1.59756i	−0.160367	+	0.116514i
$189$	2.03988	−	1.68490i	0.148379	−	0.122559i
$190$	2.25044	+	2.24385i	0.163264	+	0.162786i
$191$	−1.59322	−	15.1585i	−0.115281	−	1.09683i	−0.887289	−	0.461214i	$-0.847414\pi$
$191$	−1.59322	−	15.1585i	−0.115281	−	1.09683i	0.772008	−	0.635613i	$-0.219253\pi$
$192$	1.68373	−	0.357887i	0.121512	−	0.0258283i
$193$	−7.67961	−	13.3015i	−0.552790	−	0.957461i	−0.998072	−	0.0620703i	$-0.980230\pi$
$193$	−7.67961	−	13.3015i	−0.552790	−	0.957461i	0.445281	−	0.895391i	$-0.353104\pi$
$194$	−6.07076	−	6.74226i	−0.435855	−	0.484066i
$195$	−4.12115	+	8.11763i	−0.295121	+	0.581315i
$196$	9.87787	−	3.42287i	0.705562	−	0.244491i
$197$	−2.18252	−	6.71711i	−0.155498	−	0.478574i	0.842713	−	0.538363i	$-0.180957\pi$
$197$	−2.18252	−	6.71711i	−0.155498	−	0.478574i	−0.998211	+	0.0597890i	$0.980957\pi$
$198$	2.15256	−	0.958382i	0.152976	−	0.0681092i
$199$	4.49115	+	7.77890i	0.318369	+	0.551432i	0.980148	−	0.198268i	$-0.0635315\pi$
$199$	4.49115	+	7.77890i	0.318369	+	0.551432i	−0.661779	+	0.749699i	$0.730198\pi$
$200$	10.7481	−	6.24752i	0.760002	−	0.441766i
$201$	−3.81618	+	6.60981i	−0.269172	+	0.466220i
$202$	3.24079	+	2.35457i	0.228021	+	0.165667i
$203$	−5.37798	+	0.334217i	−0.377461	+	0.0234575i
$204$	1.31880	+	4.05885i	0.0923346	+	0.284177i
$205$	25.6371	−	6.90977i	1.79057	−	0.482599i
$206$	−10.5657	+	2.24581i	−0.736147	+	0.156473i
$207$	−4.01670	−	6.95712i	−0.279180	−	0.483554i
$208$	−3.31615	−	3.68295i	−0.229933	−	0.255367i
$209$	−5.34830	+	3.88577i	−0.369950	+	0.268784i
$210$	−2.51286	−	3.37861i	−0.173404	−	0.233146i
$211$	15.7073	+	11.4120i	1.08134	+	0.785637i	0.977916	−	0.209001i	$-0.0670211\pi$
$211$	15.7073	+	11.4120i	1.08134	+	0.785637i	0.103421	+	0.994638i	$0.467021\pi$
$212$	0.745671	+	7.09459i	0.0512129	+	0.487258i
$213$	8.02615	+	3.57347i	0.549943	+	0.244850i
$214$	−0.663387	+	6.31171i	−0.0453482	+	0.431459i
$215$	−10.7057	−	4.09151i	−0.730120	−	0.279038i
$216$	2.01152	−	1.46146i	0.136867	−	0.0994396i
$217$	−0.647959	+	15.1818i	−0.0439863	+	1.03061i
$218$	−2.40145			−0.162647
$219$	−5.03737	−	5.59457i	−0.340394	−	0.378046i
$220$	3.97714	+	10.3155i	0.268139	+	0.695473i
$221$	−7.78499	+	8.64611i	−0.523675	+	0.581600i
$222$	6.74360	+	1.43340i	0.452601	+	0.0962033i
$223$	22.9750	+	16.6923i	1.53852	+	1.11780i	0.951254	+	0.308408i	$0.0997964\pi$
$223$	22.9750	+	16.6923i	1.53852	+	1.11780i	0.587268	+	0.809393i	$0.300204\pi$
$224$	14.8829	−	4.14310i	0.994408	−	0.276823i
$225$	2.92704	−	4.05369i	0.195136	−	0.270246i
$226$	1.00480	−	1.74037i	0.0668384	−	0.115768i
$227$	−0.389588	+	3.70669i	−0.0258579	+	0.246021i	0.973956	+	0.226736i	$0.0728056\pi$
$227$	−0.389588	+	3.70669i	−0.0258579	+	0.246021i	−0.999814	+	0.0192849i	$0.993861\pi$
$228$	−1.99548	+	2.21620i	−0.132154	+	0.146772i
$229$	−14.9327	−	3.17403i	−0.986777	−	0.209746i	−0.313864	−	0.949468i	$-0.601624\pi$
$229$	−14.9327	−	3.17403i	−0.986777	−	0.209746i	−0.672913	+	0.739722i	$0.734957\pi$
$230$	−11.3829	+	5.82094i	−0.750567	+	0.383821i
$231$	7.76547	−	4.05212i	0.510930	−	0.266610i
$232$	−5.06378			−0.332454
$233$	1.93158	+	2.14523i	0.126542	+	0.140539i	0.803086	−	0.595863i	$-0.203190\pi$
$233$	1.93158	+	2.14523i	0.126542	+	0.140539i	−0.676544	+	0.736402i	$0.736523\pi$
$234$	2.64718	+	1.17860i	0.173051	+	0.0770475i
$235$	3.41616	+	2.21136i	0.222846	+	0.144253i
$236$	−12.3849	+	5.51413i	−0.806191	+	0.358939i
$237$	11.4468	−	8.31662i	0.743552	−	0.540222i
$238$	−1.97708	−	5.00474i	−0.128155	−	0.324409i
$239$	12.2394	+	8.89244i	0.791700	+	0.575204i	0.908468	−	0.417955i	$-0.137253\pi$
$239$	12.2394	+	8.89244i	0.791700	+	0.575204i	−0.116767	+	0.993159i	$0.537253\pi$
$240$	1.48579	+	2.28058i	0.0959073	+	0.147211i
$241$	4.97707	+	2.21594i	0.320602	+	0.142741i	0.560727	−	0.828001i	$-0.310522\pi$
$241$	4.97707	+	2.21594i	0.320602	+	0.142741i	−0.240125	+	0.970742i	$0.577189\pi$
$242$	−0.0276349	+	0.00587398i	−0.00177644	+	0.000377594i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	1.12160	−	3.45193i	0.0718030	−	0.220987i
$245$	−10.1022	−	11.9560i	−0.645408	−	0.763838i
$246$	−2.61160	−	8.03769i	−0.166510	−	0.512465i
$247$	−7.95226	−	1.69031i	−0.505990	−	0.107552i
$248$	−1.49270	+	14.2021i	−0.0947864	+	0.901832i
$249$	−1.01844	−	1.76399i	−0.0645409	−	0.111788i
$250$	−6.20601	−	4.98046i	−0.392503	−	0.314992i
$251$	4.63781			0.292736			0.146368	−	0.989230i	$-0.453242\pi$
$251$	4.63781			0.292736			0.146368	+	0.989230i	$0.453242\pi$
$252$	3.04644	−	2.51631i	0.191908	−	0.158512i
$253$	−8.21850	−	25.2940i	−0.516693	−	1.59022i
$254$	13.3386	+	2.83520i	0.836937	+	0.177896i
$255$	4.95997	−	4.02857i	0.310605	−	0.252279i
$256$	10.6446	−	2.26259i	0.665290	−	0.141412i
$257$	−6.59445	+	11.4219i	−0.411350	+	0.712480i	−0.995038	−	0.0994987i	$-0.968276\pi$
$257$	−6.59445	+	11.4219i	−0.411350	+	0.712480i	0.583687	+	0.811979i	$0.301609\pi$
$258$	−1.12727	+	3.46939i	−0.0701809	+	0.215995i
$259$	25.3507	+	3.76331i	1.57521	+	0.233841i
$260$	−6.15470	+	12.1232i	−0.381698	+	0.751850i
$261$	−1.86053	+	0.828363i	−0.115164	+	0.0512744i
$262$	−5.87875	−	2.61739i	−0.363190	−	0.161703i
$263$	−25.5306	−	11.3670i	−1.57429	−	0.700918i	−0.580713	−	0.814108i	$-0.697226\pi$
$263$	−25.5306	−	11.3670i	−1.57429	−	0.700918i	−0.993573	+	0.113191i	$0.963893\pi$
$264$	7.51985	−	3.34805i	0.462815	−	0.206058i
$265$	9.50965	−	4.86300i	0.584173	−	0.298732i
$266$	2.33789	−	2.94505i	0.143345	−	0.180572i
$267$	5.02555	−	15.4670i	0.307559	−	0.946568i
$268$	−5.69925	+	9.87139i	−0.348137	+	0.602991i
$269$	−2.92505	+	0.621738i	−0.178343	+	0.0379080i	−0.296218	−	0.955120i	$-0.595725\pi$
$269$	−2.92505	+	0.621738i	−0.178343	+	0.0379080i	0.117874	+	0.993029i	$0.462392\pi$
$270$	−1.33599	−	0.864818i	−0.0813058	−	0.0526312i
$271$	7.93895	+	1.68748i	0.482257	+	0.102507i	0.442624	−	0.896707i	$-0.354048\pi$
$271$	7.93895	+	1.68748i	0.482257	+	0.102507i	0.0396331	+	0.999214i	$0.487381\pi$
$272$	1.07492	+	3.30825i	0.0651763	+	0.200592i
$273$	10.0933	+	3.76248i	0.610876	+	0.227716i
$274$	−12.4003			−0.749132
$275$	12.2689	−	11.1123i	0.739840	−	0.670096i
$276$	−5.99871	−	10.3901i	−0.361080	−	0.625409i
$277$	−0.693267	+	6.59599i	−0.0416544	+	0.396315i	0.953753	+	0.300590i	$0.0971836\pi$
$277$	−0.693267	+	6.59599i	−0.0416544	+	0.396315i	−0.995408	+	0.0957248i	$0.969483\pi$
$278$	7.86331	+	1.67140i	0.471610	+	0.100244i
$279$	1.77481	+	5.46231i	0.106255	+	0.327020i
$280$	−8.77852	−	11.8030i	−0.524617	−	0.705364i
$281$	−5.08546	+	15.6514i	−0.303373	+	0.933686i	0.676907	+	0.736069i	$0.263320\pi$
$281$	−5.08546	+	15.6514i	−0.303373	+	0.933686i	−0.980279	+	0.197617i	$0.936680\pi$
$282$	0.647638	−	1.12174i	0.0385663	−	0.0667988i
$283$	22.5493	−	4.79300i	1.34042	−	0.284914i	0.518771	−	0.854913i	$-0.326390\pi$
$283$	22.5493	−	4.79300i	1.34042	−	0.284914i	0.821645	+	0.569999i	$0.193057\pi$
$284$	11.9866	+	5.33678i	0.711274	+	0.316680i
$285$	4.17088	+	1.59403i	0.247062	+	0.0944225i
$286$	7.76108	+	5.63875i	0.458922	+	0.333426i
$287$	−11.5429	−	29.2193i	−0.681354	−	1.72476i
$288$	4.72395	−	3.43215i	0.278361	−	0.202241i
$289$	−8.07014	+	3.59306i	−0.474714	+	0.211356i
$290$	1.16598	+	3.02422i	0.0684688	+	0.177588i
$291$	−11.6452	−	5.18479i	−0.682656	−	0.303938i
$292$	−7.52303	−	8.35517i	−0.440252	−	0.488949i
$293$	24.5101			1.43189			0.715946	−	0.698155i	$-0.245996\pi$
$293$	24.5101			1.43189			0.715946	+	0.698155i	$0.245996\pi$
$294$	−3.63701	+	3.40491i	−0.212115	+	0.198578i
$295$	14.3741	+	14.3320i	0.836894	+	0.834441i
$296$	23.5584	+	5.00749i	1.36930	+	0.291055i
$297$	2.21525	−	2.46028i	0.128542	−	0.142760i
$298$	0.0373224	−	0.355099i	0.00216203	−	0.0205703i
$299$	16.3534	−	28.3249i	0.945742	−	1.63807i
$300$	4.37137	−	6.05396i	0.252381	−	0.349526i
$301$	−3.38247	+	13.1321i	−0.194962	+	0.756920i
$302$	1.46680	+	1.06569i	0.0844047	+	0.0613236i
$303$	5.50533	+	1.17019i	0.316273	+	0.0672259i
$304$	−1.62645	+	1.80636i	−0.0932835	+	0.103602i
$305$	−5.42653	+	0.292377i	−0.310722	+	0.0167414i
$306$	−1.36092	−	1.51146i	−0.0777987	−	0.0864042i
$307$	−12.0578			−0.688175			−0.344087	−	0.938938i	$-0.611812\pi$
$307$	−12.0578			−0.688175			−0.344087	+	0.938938i	$0.611812\pi$
$308$	11.5973	−	6.05161i	0.660817	−	0.344822i
$309$	−12.2783	+	8.92069i	−0.698487	+	0.507480i
$310$	8.82554	−	2.37868i	0.501257	−	0.135100i
$311$	−2.01269	+	19.1495i	−0.114129	+	1.08587i	0.776180	+	0.630511i	$0.217155\pi$
$311$	−2.01269	+	19.1495i	−0.114129	+	1.08587i	−0.890309	+	0.455356i	$0.849512\pi$
$312$	9.24777	+	4.11737i	0.523552	+	0.233100i
$313$	2.37830	+	22.6280i	0.134429	+	1.27901i	0.828862	+	0.559453i	$0.188989\pi$
$313$	2.37830	+	22.6280i	0.134429	+	1.27901i	−0.694432	+	0.719558i	$0.744344\pi$
$314$	2.91644	+	2.11892i	0.164584	+	0.119578i
$315$	−5.15621	−	2.90061i	−0.290519	−	0.163431i
$316$	17.0952	−	12.4204i	0.961681	−	0.698702i
$317$	−0.548454	−	0.609120i	−0.0308043	−	0.0342116i	0.727546	−	0.686059i	$-0.240661\pi$
$317$	−0.548454	−	0.609120i	−0.0308043	−	0.0342116i	−0.758350	+	0.651848i	$0.773994\pi$
$318$	−1.69984	−	2.94421i	−0.0953223	−	0.165103i
$319$	−6.59513	+	1.40184i	−0.369256	+	0.0784879i
$320$	−2.10107	−	3.22499i	−0.117453	−	0.180283i
$321$	2.75550	+	8.48057i	0.153797	+	0.473339i
$322$	8.36167	+	12.6063i	0.465978	+	0.702520i
$323$	4.61650	+	3.35409i	0.256869	+	0.186626i
$324$	0.746722	−	1.29336i	0.0414845	−	0.0718533i
$325$	20.2514	+	2.06845i	1.12335	+	0.114737i
$326$	3.58490	+	6.20924i	0.198549	+	0.343898i
$327$	−3.08240	+	1.37238i	−0.170457	+	0.0758925i
$328$	−9.12349	−	28.0792i	−0.503761	−	1.55042i
$329$	2.14423	−	4.31122i	0.118215	−	0.237685i
$330$	−3.73105	−	3.72012i	−0.205388	−	0.204786i
$331$	−4.07858	−	4.52972i	−0.224179	−	0.248976i	0.620554	−	0.784164i	$-0.286908\pi$
$331$	−4.07858	−	4.52972i	−0.224179	−	0.248976i	−0.844733	+	0.535187i	$0.820241\pi$
$332$	−1.52098	−	2.63441i	−0.0834746	−	0.144582i
$333$	9.47497	−	2.01397i	0.519225	−	0.110365i
$334$	0.775498	+	7.37837i	0.0424334	+	0.403727i
$335$	16.8602	+	2.64505i	0.921174	+	0.144514i
$336$	2.48306	−	2.05097i	0.135462	−	0.111889i
$337$	−9.37456	+	6.81102i	−0.510665	+	0.371020i	−0.813076	−	0.582158i	$-0.802209\pi$
$337$	−9.37456	+	6.81102i	−0.510665	+	0.371020i	0.302411	+	0.953178i	$0.402209\pi$
$338$	0.266035	+	2.53116i	0.0144704	+	0.137677i
$339$	0.295142	−	2.80809i	0.0160299	−	0.152515i
$340$	7.40744	−	6.01644i	0.401725	−	0.326287i
$341$	1.98754	+	18.9102i	0.107631	+	1.02404i
$342$	0.439181	−	1.35166i	0.0237482	−	0.0730894i
$343$	−12.7090	+	13.4715i	−0.686221	+	0.727393i
$344$	−3.93806	+	12.1201i	−0.212326	+	0.653473i
$345$	−11.2841	+	13.9766i	−0.607517	+	0.752475i
$346$	−3.01083	+	3.34387i	−0.161863	+	0.179767i
$347$	−4.83392	+	5.36861i	−0.259499	+	0.288202i	−0.858789	−	0.512329i	$-0.828783\pi$
$347$	−4.83392	+	5.36861i	−0.259499	+	0.288202i	0.599291	+	0.800532i	$0.295449\pi$
$348$	−2.77860	+	1.23711i	−0.148949	+	0.0663163i
$349$	−16.4745			−0.881859			−0.440930	−	0.897542i	$-0.645351\pi$
$349$	−16.4745			−0.881859			−0.440930	+	0.897542i	$0.645351\pi$
$350$	−5.02771	+	7.96050i	−0.268742	+	0.425507i
$351$	4.07136			0.217313
$352$	17.6599	−	7.86271i	0.941277	−	0.419084i
$353$	−15.2537	+	16.9409i	−0.811870	+	0.901673i	−0.996706	−	0.0810963i	$-0.974158\pi$
$353$	−15.2537	+	16.9409i	−0.811870	+	0.901673i	0.184836	+	0.982769i	$0.440825\pi$
$354$	4.32315	−	4.80134i	0.229773	−	0.255188i
$355$	0.999378	−	19.6200i	0.0530415	−	1.04132i
$356$	7.50537	−	23.0992i	0.397784	−	1.22425i
$357$	−5.39780	−	5.29402i	−0.285682	−	0.280189i
$358$	2.12203	−	6.53095i	0.112153	−	0.345171i
$359$	1.96953	+	18.7388i	0.103948	+	0.988995i	0.914844	+	0.403806i	$0.132313\pi$
$359$	1.96953	+	18.7388i	0.103948	+	0.988995i	−0.810897	+	0.585189i	$0.801020\pi$
$360$	−4.66721	−	3.02119i	−0.245983	−	0.159231i
$361$	1.56924	−	14.9303i	0.0825916	−	0.785806i
$362$	−0.883865	−	8.40941i	−0.0464549	−	0.441989i
$363$	−0.0321142	+	0.0233323i	−0.00168556	+	0.00122463i
$364$	15.0738	+	5.61905i	0.790083	+	0.294518i
$365$	−7.62030	+	15.0101i	−0.398865	+	0.785663i
$366$	0.180807	+	1.72026i	0.00945093	+	0.0899196i
$367$	−31.0251	+	6.59459i	−1.61950	+	0.344235i	−0.926380	−	0.376590i	$-0.877097\pi$
$367$	−31.0251	+	6.59459i	−1.61950	+	0.344235i	−0.693118	+	0.720825i	$0.743763\pi$
$368$	−4.88937	−	8.46864i	−0.254876	−	0.441458i
$369$	−7.94552	−	8.82439i	−0.413627	−	0.459379i
$370$	−2.43394	−	15.2227i	−0.126534	−	0.791389i
$371$	−6.98561	−	10.5317i	−0.362675	−	0.546778i
$372$	2.65058	+	8.15764i	0.137426	+	0.422954i
$373$	−27.6534	+	12.3121i	−1.43184	+	0.637496i	−0.968574	−	0.248724i	$-0.919989\pi$
$373$	−27.6534	+	12.3121i	−1.43184	+	0.637496i	−0.463265	+	0.886220i	$0.653322\pi$
$374$	−3.36669	−	5.83128i	−0.174088	−	0.301528i
$375$	−10.8120	−	2.84612i	−0.558330	−	0.146973i
$376$	2.26249	−	3.91874i	0.116679	−	0.202094i
$377$	−6.70817	−	4.87377i	−0.345489	−	0.251012i
$378$	−0.838564	+	1.68603i	−0.0431311	+	0.0867201i
$379$	−10.0636	−	30.9727i	−0.516934	−	1.59096i	−0.779735	−	0.626109i	$-0.784646\pi$
$379$	−10.0636	−	30.9727i	−0.516934	−	1.59096i	0.262801	−	0.964850i	$-0.415354\pi$
$380$	6.22898	+	2.38060i	0.319540	+	0.122122i
$381$	18.7411	−	3.98355i	0.960137	−	0.204083i
$382$	5.42406	+	9.39475i	0.277519	+	0.480677i
$383$	15.3471	+	17.0447i	0.784202	+	0.870945i	0.994287	−	0.106738i	$-0.0340406\pi$
$383$	15.3471	+	17.0447i	0.784202	+	0.870945i	−0.210085	+	0.977683i	$0.567374\pi$
$384$	8.45675	−	6.14419i	0.431557	−	0.313544i
$385$	−14.7007	−	12.9421i	−0.749219	−	0.659592i
$386$	8.84384	+	6.42542i	0.450139	+	0.327045i
$387$	0.535756	+	5.09738i	0.0272340	+	0.259114i
$388$	−17.3915	−	7.74320i	−0.882920	−	0.393101i
$389$	1.32974	−	12.6516i	0.0674205	−	0.641463i	−0.907674	−	0.419675i	$-0.862144\pi$
$389$	1.32974	−	12.6516i	0.0674205	−	0.641463i	0.975095	−	0.221788i	$-0.0711894\pi$
$390$	0.329614	−	6.47106i	0.0166907	−	0.327675i
$391$	−18.5723	+	13.4935i	−0.939240	+	0.682398i
$392$	−12.7057	+	11.8949i	−0.641735	+	0.600781i
$393$	−9.04151			−0.456084
$394$	3.36357	+	3.73563i	0.169454	+	0.188198i
$395$	−26.5594	−	17.1925i	−1.33635	−	0.865049i
$396$	3.30835	−	3.67429i	0.166251	−	0.184640i
$397$	3.43648	+	0.730446i	0.172472	+	0.0366600i	0.293338	−	0.956009i	$-0.405234\pi$
$397$	3.43648	+	0.730446i	0.172472	+	0.0366600i	−0.120866	+	0.992669i	$0.538567\pi$
$398$	−5.17201	−	3.75768i	−0.259249	−	0.188356i
$399$	1.31780	−	5.11620i	0.0659723	−	0.256130i
$400$	3.56298	−	4.93440i	0.178149	−	0.246720i
$401$	−8.46096	+	14.6548i	−0.422520	+	0.731827i	−0.996185	−	0.0872633i	$-0.972188\pi$
$401$	−8.46096	+	14.6548i	−0.422520	+	0.731827i	0.573665	+	0.819090i	$0.305521\pi$
$402$	0.567815	−	5.40240i	0.0283201	−	0.269447i
$403$	−15.6466	+	17.3773i	−0.779412	+	0.865625i
$404$	8.22190	+	1.74762i	0.409055	+	0.0869473i
$405$	−2.20905	−	0.346557i	−0.109769	−	0.0172206i
$406$	3.39999	−	1.77416i	0.168739	−	0.0880499i
$407$	32.0690			1.58960
$408$	−4.75430	−	5.28019i	−0.235373	−	0.261408i
$409$	24.3223	+	10.8290i	1.20266	+	0.535459i	0.907526	−	0.419996i	$-0.137969\pi$
$409$	24.3223	+	10.8290i	1.20266	+	0.535459i	0.295135	+	0.955456i	$0.404635\pi$
$410$	−14.6688	+	11.9143i	−0.724443	+	0.588404i
$411$	−15.9166	+	7.08652i	−0.785107	+	0.349552i
$412$	−18.3369	+	13.3225i	−0.903395	+	0.656355i
$413$	14.9327	−	18.8108i	0.734790	−	0.925617i
$414$	4.62563	+	3.36071i	0.227337	+	0.165170i
$415$	−2.86110	+	3.54378i	−0.140446	+	0.173958i
$416$	21.7178	+	9.66941i	1.06480	+	0.474082i
$417$	11.0482	−	2.34837i	0.541033	−	0.115000i
$418$	2.35257	−	4.07477i	0.115068	−	0.199303i
$419$	−3.18156	+	9.79184i	−0.155429	+	0.478363i	−0.998204	−	0.0599038i	$-0.980921\pi$
$419$	−3.18156	+	9.79184i	−0.155429	+	0.478363i	0.842775	+	0.538267i	$0.180921\pi$
$420$	−7.70050	−	4.33190i	−0.375746	−	0.211375i
$421$	9.28500	+	28.5763i	0.452523	+	1.39272i	0.874019	+	0.485892i	$0.161505\pi$
$421$	9.28500	+	28.5763i	0.452523	+	1.39272i	−0.421496	+	0.906830i	$0.638495\pi$
$422$	−13.5165	−	2.87301i	−0.657971	−	0.139856i
$423$	0.190232	−	1.80993i	0.00924939	−	0.0880020i
$424$	−5.93829	−	10.2854i	−0.288389	−	0.499505i
$425$	−12.3949	−	7.10777i	−0.601240	−	0.344778i
$426$	−6.25304			−0.302961
$427$	1.06748	+	6.34084i	0.0516588	+	0.306855i
$428$	4.11519	+	12.6653i	0.198915	+	0.612198i
$429$	13.1842	+	2.80239i	0.636541	+	0.135301i
$430$	8.14521	−	0.438857i	0.392797	−	0.0211636i
$431$	−27.1824	+	5.77779i	−1.30933	+	0.278306i	−0.809143	−	0.587612i	$-0.800068\pi$
$431$	−27.1824	+	5.77779i	−1.30933	+	0.278306i	−0.500185	+	0.865918i	$0.666735\pi$
$432$	0.608631	−	1.05418i	0.0292828	−	0.0507192i
$433$	2.61714	−	8.05473i	0.125772	−	0.387086i	−0.868269	−	0.496093i	$-0.834767\pi$
$433$	2.61714	−	8.05473i	0.125772	−	0.387086i	0.994041	+	0.109008i	$0.0347674\pi$
$434$	−3.97362	−	10.0587i	−0.190740	−	0.482834i
$435$	3.22488	+	3.21543i	0.154621	+	0.154168i
$436$	−4.60340	+	2.04956i	−0.220463	+	0.0981564i
$437$	−14.6547	−	6.52469i	−0.701029	−	0.312118i
$438$	4.89482	+	2.17932i	0.233884	+	0.104132i
$439$	29.7285	−	13.2360i	1.41887	−	0.631720i	0.453177	−	0.891421i	$-0.350291\pi$
$439$	29.7285	−	13.2360i	1.41887	−	0.631720i	0.965689	+	0.259701i	$0.0836239\pi$
$440$	−13.0342	−	12.9960i	−0.621382	−	0.619562i
$441$	−2.72249	+	6.44888i	−0.129643	+	0.307089i
$442$	2.55884	−	7.87531i	0.121712	−	0.374590i
$443$	−2.15945	+	3.74027i	−0.102598	+	0.177706i	−0.912754	−	0.408509i	$-0.866049\pi$
$443$	−2.15945	+	3.74027i	−0.102598	+	0.177706i	0.810156	+	0.586214i	$0.199382\pi$
$444$	14.1503	−	3.00775i	0.671545	−	0.142741i
$445$	−36.3125	+	1.95649i	−1.72138	+	0.0927465i
$446$	−19.7705	−	4.20234i	−0.936158	−	0.198987i
$447$	−0.155026	−	0.477120i	−0.00733246	−	0.0225670i
$448$	−3.51133	+	2.90029i	−0.165895	+	0.137026i
$449$	−10.2226			−0.482436			−0.241218	−	0.970471i	$-0.577547\pi$
$449$	−10.2226			−0.482436			−0.241218	+	0.970471i	$0.577547\pi$
$450$	−0.729665	+	3.48303i	−0.0343967	+	0.164192i
$451$	−19.6559	−	34.0450i	−0.925559	−	1.60312i
$452$	0.440778	−	4.19372i	0.0207325	−	0.197256i
$453$	2.49174	+	0.529636i	0.117072	+	0.0248845i
$454$	−0.819724	−	2.52285i	−0.0384716	−	0.118403i
$455$	−0.269113	−	24.0850i	−0.0126162	−	1.12912i
$456$	1.53425	−	4.72195i	0.0718480	−	0.221125i
$457$	10.8703	−	18.8280i	0.508493	−	0.880736i	−0.491459	−	0.870901i	$-0.663536\pi$
$457$	10.8703	−	18.8280i	0.508493	−	0.880736i	0.999952	−	0.00983472i	$-0.00313054\pi$
$458$	10.6280	−	2.25905i	0.496613	−	0.105558i
$459$	−2.61059	−	1.16231i	−0.121852	−	0.0542519i
$460$	−16.8522	+	20.8733i	−0.785738	+	0.973222i
$461$	−26.2798	−	19.0934i	−1.22397	−	0.889267i	−0.227548	−	0.973767i	$-0.573071\pi$
$461$	−26.2798	−	19.0934i	−1.22397	−	0.889267i	−0.996424	+	0.0844994i	$0.973071\pi$
$462$	−3.87604	+	4.88266i	−0.180330	+	0.227162i
$463$	−33.0277	+	23.9960i	−1.53493	+	1.11519i	−0.581506	+	0.813542i	$0.697536\pi$
$463$	−33.0277	+	23.9960i	−1.53493	+	1.11519i	−0.953420	+	0.301647i	$0.902464\pi$
$464$	−2.26476	+	1.00833i	−0.105139	+	0.0468108i
$465$	9.96874	−	8.09678i	0.462289	−	0.375479i
$466$	−1.87692	−	0.835657i	−0.0869465	−	0.0387111i
$467$	21.0229	+	23.3483i	0.972822	+	1.08043i	0.996737	+	0.0807147i	$0.0257203\pi$
$467$	21.0229	+	23.3483i	0.972822	+	1.08043i	−0.0239149	+	0.999714i	$0.507613\pi$
$468$	6.08034			0.281064
$469$	0.861066	−	20.1749i	0.0397603	−	0.931593i
$470$	−2.86133	−	0.448888i	−0.131983	−	0.0207056i
$471$	4.95435	+	1.05308i	0.228284	+	0.0485233i
$472$	15.1027	−	16.7732i	0.695156	−	0.772049i
$473$	−1.77369	+	16.8756i	−0.0815545	+	0.775940i
$474$	−5.03515	+	8.72113i	−0.231272	+	0.400575i
$475$	−0.0292985	−	9.98425i	−0.00134431	−	0.458109i
$476$	−8.06131	−	7.90633i	−0.369490	−	0.362386i
$477$	−3.86440	−	2.80765i	−0.176939	−	0.128553i
$478$	−10.5322	−	2.23869i	−0.481733	−	0.102396i
$479$	−16.7376	+	18.5890i	−0.764761	+	0.849353i	−0.992228	−	0.124433i	$-0.960289\pi$
$479$	−16.7376	+	18.5890i	−0.764761	+	0.849353i	0.227467	+	0.973786i	$0.426955\pi$
$480$	−10.9607	−	7.09510i	−0.500284	−	0.323845i
$481$	26.3890	+	29.3080i	1.20324	+	1.33633i
$482$	−3.87755			−0.176618
$483$	17.9369	+	11.4024i	0.816158	+	0.518827i
$484$	−0.0479608	+	0.0348455i	−0.00218004	+	0.00158389i
$485$	−1.45001	+	28.4669i	−0.0658415	+	1.29262i
$486$	−0.0743958	+	0.707829i	−0.00337466	+	0.0321078i
$487$	8.07767	+	3.59641i	0.366034	+	0.162969i	0.581508	−	0.813541i	$-0.302463\pi$
$487$	8.07767	+	3.59641i	0.366034	+	0.162969i	−0.215474	+	0.976510i	$0.569130\pi$
$488$	0.631639	+	6.00964i	0.0285929	+	0.272044i
$489$	8.14988	+	5.92124i	0.368550	+	0.267768i
$490$	10.0295	+	4.84926i	0.453087	+	0.219067i
$491$	−7.62055	+	5.53666i	−0.343911	+	0.249866i	−0.746310	−	0.665598i	$-0.768176\pi$
$491$	−7.62055	+	5.53666i	−0.343911	+	0.249866i	0.402399	+	0.915464i	$0.368176\pi$
$492$	−11.8662	−	13.1787i	−0.534969	−	0.594143i
$493$	2.90995	+	5.04019i	0.131058	+	0.226999i
$494$	5.65985	−	1.20304i	0.254648	−	0.0541272i
$495$	−6.91500	−	2.64279i	−0.310806	−	0.118784i
$496$	2.16041	+	6.64905i	0.0970052	+	0.298551i
$497$	−23.2001	+	1.44178i	−1.04067	+	0.0646727i
$498$	1.17283	+	0.852113i	0.0525559	+	0.0381841i
$499$	−6.41082	+	11.1039i	−0.286988	+	0.497078i	−0.973089	−	0.230428i	$-0.925987\pi$
$499$	−6.41082	+	11.1039i	−0.286988	+	0.497078i	0.686101	+	0.727506i	$0.259321\pi$
$500$	−16.1471	−	4.25052i	−0.722122	−	0.190089i
$501$	5.21198	+	9.02741i	0.232854	+	0.403315i
$502$	−3.01548	+	1.34258i	−0.134588	+	0.0599223i
$503$	0.579636	+	1.78394i	0.0258447	+	0.0795418i	0.963147	−	0.268976i	$-0.0866852\pi$
$503$	0.579636	+	1.78394i	0.0258447	+	0.0795418i	−0.937302	+	0.348518i	$0.886685\pi$
$504$	−2.92948	+	5.89006i	−0.130489	+	0.262364i
$505$	−1.98701	−	12.4275i	−0.0884209	−	0.553015i
$506$	12.6659	+	14.0669i	0.563067	+	0.625349i
$507$	1.78797	+	3.09686i	0.0794066	+	0.137536i
$508$	27.9888	−	5.94920i	1.24180	−	0.263953i
$509$	−1.27306	−	12.1123i	−0.0564273	−	0.536870i	−0.985823	−	0.167786i	$-0.946338\pi$
$509$	−1.27306	−	12.1123i	−0.0564273	−	0.536870i	0.929396	−	0.369084i	$-0.120328\pi$
$510$	−2.05874	+	4.05520i	−0.0911624	+	0.179567i
$511$	18.6633	+	6.95710i	0.825616	+	0.307764i
$512$	10.6474	−	7.73577i	0.470552	−	0.341876i
$513$	−0.208729	−	1.98592i	−0.00921559	−	0.0876805i
$514$	0.981199	−	9.33548i	0.0432788	−	0.411770i
$515$	28.4885	+	18.4413i	1.25535	+	0.812619i
$516$	0.800122	+	7.61265i	0.0352234	+	0.335128i
$517$	1.86184	−	5.73015i	0.0818836	−	0.252012i
$518$	−17.5723	+	4.89177i	−0.772083	+	0.214932i
$519$	−1.95364	+	6.01268i	−0.0857552	+	0.263927i
$520$	1.15149	−	22.6063i	0.0504961	−	0.991351i
$521$	2.23223	−	2.47914i	0.0977956	−	0.108613i	−0.692260	−	0.721648i	$-0.743385\pi$
$521$	2.23223	−	2.47914i	0.0977956	−	0.108613i	0.790056	+	0.613035i	$0.210052\pi$
$522$	0.969912	−	1.07720i	0.0424519	−	0.0471476i
$523$	−21.8609	+	9.73308i	−0.955909	+	0.425598i	−0.824583	−	0.565741i	$-0.808590\pi$
$523$	−21.8609	+	9.73308i	−0.955909	+	0.425598i	−0.131326	+	0.991339i	$0.541923\pi$
$524$	−13.5030			−0.589881
$525$	−1.90412	+	13.0910i	−0.0831025	+	0.571338i
$526$	19.8905			0.867266
$527$	14.9937	−	6.67561i	0.653135	−	0.290794i
$528$	2.69653	−	2.99480i	0.117352	−	0.130332i
$529$	27.7926	−	30.8668i	1.20837	−	1.34204i
$530$	−4.77537	+	5.91481i	−0.207429	+	0.256923i
$531$	2.80516	−	8.63339i	0.121734	−	0.374657i
$532$	1.96805	−	7.64076i	0.0853260	−	0.331269i
$533$	14.9394	−	45.9787i	0.647097	−	1.99156i
$534$	1.20990	+	11.5114i	0.0523575	+	0.498148i
$535$	15.4771	−	12.5707i	0.669133	−	0.543481i
$536$	1.98363	−	18.8730i	0.0856798	−	0.815189i
$537$	−1.00853	−	9.59556i	−0.0435215	−	0.414079i
$538$	1.72187	−	1.25101i	0.0742350	−	0.0539349i
$539$	−13.2551	+	19.0094i	−0.570938	+	0.818792i
$540$	−3.29909	−	0.517564i	−0.141970	−	0.0222724i
$541$	0.906051	+	8.62050i	0.0389542	+	0.370624i	0.996582	+	0.0826143i	$0.0263269\pi$
$541$	0.906051	+	8.62050i	0.0389542	+	0.370624i	−0.957627	+	0.288010i	$0.907006\pi$
$542$	−5.65037	+	1.20102i	−0.242704	+	0.0515884i
$543$	−5.94029	−	10.2889i	−0.254922	−	0.441538i
$544$	−11.1652	−	12.4002i	−0.478704	−	0.531655i
$545$	5.34276	+	5.32711i	0.228859	+	0.228188i
$546$	−7.65182	+	0.475526i	−0.327468	+	0.0203506i
$547$	−12.4188	−	38.2212i	−0.530991	−	1.63422i	−0.752155	−	0.658986i	$-0.770986\pi$
$547$	−12.4188	−	38.2212i	−0.530991	−	1.63422i	0.221164	−	0.975237i	$-0.429014\pi$
$548$	−23.7705	+	10.5833i	−1.01543	+	0.452097i
$549$	1.21517	+	2.10473i	0.0518621	+	0.0898278i
$550$	−4.76030	+	10.7768i	−0.202980	+	0.459525i
$551$	−2.03341	+	3.52197i	−0.0866261	+	0.150041i
$552$	16.1594	+	11.7405i	0.687788	+	0.499707i
$553$	−16.6706	+	33.5182i	−0.708905	+	1.42534i
$554$	−1.45869	−	4.48938i	−0.0619737	−	0.190735i
$555$	−11.8235	−	18.1483i	−0.501881	−	0.770352i
$556$	16.4999	−	3.50715i	0.699750	−	0.148736i
$557$	−12.7895	−	22.1521i	−0.541910	−	0.938615i	−0.998794	−	0.0490894i	$-0.984368\pi$
$557$	−12.7895	−	22.1521i	−0.541910	−	0.938615i	0.456885	−	0.889526i	$-0.348965\pi$
$558$	−2.73523	−	3.03778i	−0.115792	−	0.128600i
$559$	−16.8822	+	12.2657i	−0.714042	+	0.518782i
$560$	−6.27645	−	3.53080i	−0.265228	−	0.149204i
$561$	−7.65380	−	5.56081i	−0.323144	−	0.234778i
$562$	−1.22432	−	11.6487i	−0.0516449	−	0.491369i
$563$	−25.3084	−	11.2680i	−1.06662	−	0.474891i	−0.203078	−	0.979163i	$-0.565094\pi$
$563$	−25.3084	−	11.2680i	−1.06662	−	0.474891i	−0.863545	+	0.504271i	$0.831761\pi$
$564$	0.284101	−	2.70304i	0.0119628	−	0.113818i
$565$	−6.09613	+	1.64304i	−0.256466	+	0.0691234i
$566$	−13.2739	+	9.64408i	−0.557945	+	0.405371i
$567$	−0.112818	+	2.64334i	−0.00473791	+	0.111010i
$568$	−21.8446			−0.916581
$569$	20.5234	+	22.7935i	0.860386	+	0.955555i	0.999397	−	0.0347357i	$-0.0110589\pi$
$569$	20.5234	+	22.7935i	0.860386	+	0.955555i	−0.139011	+	0.990291i	$0.544392\pi$
$570$	−3.17334	+	0.170977i	−0.132917	+	0.00716143i
$571$	−21.5867	+	23.9745i	−0.903375	+	1.00330i	0.0965929	+	0.995324i	$0.469206\pi$
$571$	−21.5867	+	23.9745i	−0.903375	+	1.00330i	−0.999968	+	0.00797592i	$0.997461\pi$
$572$	19.6899	+	4.18522i	0.823276	+	0.174993i
$573$	12.3310	+	8.95900i	0.515135	+	0.374268i
$574$	15.9637	+	15.6568i	0.666312	+	0.653502i
$575$	38.2373	+	12.3001i	1.59461	+	0.512951i
$576$	−0.860671	+	1.49073i	−0.0358613	+	0.0621136i
$577$	−1.40292	+	13.3479i	−0.0584042	+	0.555679i	0.925721	+	0.378206i	$0.123459\pi$
$577$	−1.40292	+	13.3479i	−0.0584042	+	0.555679i	−0.984126	+	0.177473i	$0.943208\pi$
$578$	4.20703	−	4.67238i	0.174989	−	0.194345i
$579$	15.0236	+	3.19336i	0.624359	+	0.132712i
$580$	4.81618	+	4.80207i	0.199981	+	0.199395i
$581$	4.54792	+	2.89109i	0.188680	+	0.119943i
$582$	9.07261			0.376072
$583$	−10.5815	−	11.7519i	−0.438240	−	0.486715i
$584$	17.0998	+	7.61332i	0.707594	+	0.315041i
$585$	−3.27499	−	8.49436i	−0.135404	−	0.351199i
$586$	−15.9363	+	7.09531i	−0.658324	+	0.293105i
$587$	12.8651	−	9.34707i	0.531001	−	0.385795i	−0.289731	−	0.957108i	$-0.593566\pi$
$587$	12.8651	−	9.34707i	0.531001	−	0.385795i	0.820732	+	0.571313i	$0.193566\pi$
$588$	−4.06589	+	9.63104i	−0.167675	+	0.397177i
$589$	9.27843	+	6.74117i	0.382311	+	0.277765i
$590$	−13.4949	−	5.15750i	−0.555576	−	0.212331i
$591$	6.45218	+	2.87269i	0.265407	+	0.118167i
$592$	11.5335	−	2.45152i	0.474025	−	0.100757i
$593$	−3.54341	+	6.13737i	−0.145511	+	0.252032i	−0.929563	−	0.368663i	$-0.879816\pi$
$593$	−3.54341	+	6.13737i	−0.145511	+	0.252032i	0.784053	+	0.620694i	$0.213149\pi$
$594$	−0.728128	+	2.24095i	−0.0298754	+	0.0919472i
$595$	−6.70333	+	15.5203i	−0.274810	+	0.636271i
$596$	−0.231522	−	0.712552i	−0.00948351	−	0.0291873i
$597$	−8.78602	−	1.86753i	−0.359588	−	0.0764327i
$598$	−2.43325	+	23.1508i	−0.0995030	+	0.946708i
$599$	−20.2423	−	35.0607i	−0.827079	−	1.43254i	−0.900320	−	0.435228i	$-0.856668\pi$
$599$	−20.2423	−	35.0607i	−0.827079	−	1.43254i	0.0732416	−	0.997314i	$-0.476666\pi$
$600$	−2.54904	+	12.1678i	−0.104064	+	0.496747i
$601$	17.2115			0.702070			0.351035	−	0.936362i	$-0.385830\pi$
$601$	17.2115			0.702070			0.351035	+	0.936362i	$0.385830\pi$
$602$	−1.60228	−	9.51759i	−0.0653041	−	0.387908i
$603$	−2.35853	−	7.25880i	−0.0960467	−	0.295601i
$604$	3.72128	+	0.790982i	0.151417	+	0.0321846i
$605$	0.0745125	+	0.0482337i	0.00302936	+	0.00196098i
$606$	−3.91830	+	0.832860i	−0.159170	+	0.0338326i
$607$	8.17472	−	14.1590i	0.331802	−	0.574697i	−0.651064	−	0.759023i	$-0.725677\pi$
$607$	8.17472	−	14.1590i	0.331802	−	0.574697i	0.982865	+	0.184326i	$0.0590102\pi$
$608$	3.60311	−	11.0892i	0.146125	−	0.449727i
$609$	3.35020	−	4.22026i	0.135757	−	0.171013i
$610$	3.44367	−	1.76100i	0.139430	−	0.0713010i
$611$	6.76890	−	3.01371i	0.273840	−	0.121922i
$612$	−3.89877	−	1.73584i	−0.157598	−	0.0701673i
$613$	2.81732	+	1.25435i	0.113791	+	0.0506628i	0.462842	−	0.886441i	$-0.346830\pi$
$613$	2.81732	+	1.25435i	0.113791	+	0.0506628i	−0.349052	+	0.937103i	$0.613496\pi$
$614$	7.83993	−	3.49056i	0.316394	−	0.140868i
$615$	−12.0196	+	23.6756i	−0.484677	+	0.954693i
$616$	−13.5407	+	17.0573i	−0.545572	+	0.687258i
$617$	9.18929	−	28.2817i	0.369947	−	1.13858i	−0.576878	−	0.816830i	$-0.695729\pi$
$617$	9.18929	−	28.2817i	0.369947	−	1.13858i	0.946825	−	0.321749i	$-0.104271\pi$
$618$	5.40087	−	9.35458i	0.217255	−	0.376296i
$619$	−20.8049	+	4.42222i	−0.836220	+	0.177744i	−0.606070	−	0.795411i	$-0.707255\pi$
$619$	−20.8049	+	4.42222i	−0.836220	+	0.177744i	−0.230150	+	0.973155i	$0.573922\pi$
$620$	14.8878	−	12.0921i	0.597907	−	0.485630i
$621$	7.85785	+	1.67024i	0.315324	+	0.0670243i
$622$	−4.23486	−	13.0336i	−0.169802	−	0.522598i
$623$	7.14320	+	42.4308i	0.286186	+	1.69996i
$624$	4.95590			0.198395
$625$	2.75909	+	24.8473i	0.110363	+	0.993891i
$626$	−8.09685	−	14.0242i	−0.323615	−	0.560518i
$627$	0.691024	−	6.57465i	0.0275968	−	0.262566i
$628$	7.39904	+	1.57271i	0.295254	+	0.0627581i
$629$	−8.55390	−	26.3262i	−0.341066	−	1.04969i
$630$	4.19223	+	0.393317i	0.167022	+	0.0156701i
$631$	−0.916679	+	2.82125i	−0.0364924	+	0.112312i	−0.967643	−	0.252322i	$-0.918806\pi$
$631$	−0.916679	+	2.82125i	−0.0364924	+	0.112312i	0.931151	+	0.364634i	$0.118806\pi$
$632$	−17.5900	+	30.4668i	−0.699692	+	1.21190i
$633$	−18.9910	+	4.03667i	−0.754826	+	0.160443i
$634$	0.532934	+	0.237278i	0.0211655	+	0.00942350i
$635$	−23.3865	−	35.8966i	−0.928064	−	1.42451i
$636$	−5.77126	−	4.19307i	−0.228845	−	0.166266i
$637$	−28.2802	+	3.52860i	−1.12050	+	0.139808i
$638$	3.88231	−	2.82066i	0.153702	−	0.111671i
$639$	−8.02615	+	3.57347i	−0.317510	+	0.141364i
$640$	−19.6216	−	12.7015i	−0.775613	−	0.502073i
$641$	26.4996	+	11.7984i	1.04667	+	0.466008i	0.856718	−	0.515785i	$-0.172500\pi$
$641$	26.4996	+	11.7984i	1.04667	+	0.466008i	0.189954	+	0.981793i	$0.439166\pi$
$642$	−4.24662	−	4.71635i	−0.167601	−	0.186139i
$643$	−20.9978			−0.828071			−0.414035	−	0.910261i	$-0.635881\pi$
$643$	−20.9978			−0.828071			−0.414035	+	0.910261i	$0.635881\pi$
$644$	26.7878	+	17.0288i	1.05559	+	0.671031i
$645$	10.2041	−	5.21811i	0.401785	−	0.205463i
$646$	−3.97259	−	0.844400i	−0.156299	−	0.0332225i
$647$	−1.78438	+	1.98175i	−0.0701512	+	0.0779107i	−0.777199	−	0.629255i	$-0.783360\pi$
$647$	−1.78438	+	1.98175i	−0.0701512	+	0.0779107i	0.707048	+	0.707166i	$0.250027\pi$
$648$	−0.259898	+	2.47276i	−0.0102097	+	0.0971392i
$649$	15.0264	−	26.0266i	0.589840	−	1.02163i
$650$	−13.7662	+	4.51760i	−0.539954	+	0.177195i
$651$	−10.8487	−	10.6401i	−0.425195	−	0.417020i
$652$	12.1714	+	8.84303i	0.476668	+	0.346320i
$653$	41.9156	+	8.90943i	1.64028	+	0.348653i	0.933444	−	0.358722i	$-0.116787\pi$
$653$	41.9156	+	8.90943i	1.64028	+	0.348653i	0.706839	+	0.707375i	$0.250121\pi$
$654$	1.60688	−	1.78462i	0.0628341	−	0.0697843i
$655$	7.27296	+	18.8639i	0.284178	+	0.737075i
$656$	−9.67177	−	10.7416i	−0.377619	−	0.419388i
$657$	7.52823			0.293704
$658$	−0.146130	+	3.42386i	−0.00569676	+	0.133476i
$659$	−9.22964	+	6.70573i	−0.359536	+	0.261218i	−0.752858	−	0.658182i	$-0.771326\pi$
$659$	−9.22964	+	6.70573i	−0.359536	+	0.261218i	0.393323	+	0.919400i	$0.371326\pi$
$660$	−10.3272	−	3.94685i	−0.401984	−	0.153631i
$661$	2.97766	−	28.3305i	0.115817	−	1.10193i	−0.770048	−	0.637986i	$-0.779768\pi$
$661$	2.97766	−	28.3305i	0.115817	−	1.10193i	0.885865	−	0.463943i	$-0.153566\pi$
$662$	3.96317	+	1.76452i	0.154033	+	0.0685799i
$663$	−1.21614	−	11.5708i	−0.0472308	−	0.449371i
$664$	4.09722	+	2.97681i	0.159003	+	0.115523i
$665$	−11.7343	+	1.36604i	−0.455038	+	0.0529729i
$666$	−5.57757	+	4.05234i	−0.216127	+	0.157025i
$667$	−10.9476	−	12.1585i	−0.423891	−	0.470779i
$668$	7.78379	+	13.4819i	0.301164	+	0.521631i
$669$	−27.7781	+	5.90442i	−1.07396	+	0.228278i
$670$	−11.7282	+	3.16100i	−0.453099	+	0.122120i
$671$	2.48634	+	7.65216i	0.0959840	+	0.295408i
$672$	−6.87971	+	13.8325i	−0.265390	+	0.533599i
$673$	28.5483	+	20.7415i	1.10045	+	0.799527i	0.981134	−	0.193329i	$-0.0619285\pi$
$673$	28.5483	+	20.7415i	1.10045	+	0.799527i	0.119320	+	0.992856i	$0.461928\pi$
$674$	4.12361	−	7.14229i	0.158835	−	0.275111i
$675$	1.05391	+	4.88767i	0.0405648	+	0.188126i
$676$	2.67023	+	4.62498i	0.102701	+	0.177884i
$677$	40.8706	−	18.1967i	1.57078	−	0.699358i	0.577643	−	0.816289i	$-0.303972\pi$
$677$	40.8706	−	18.1967i	1.57078	−	0.699358i	0.993140	+	0.116931i	$0.0373058\pi$
$678$	0.621002	+	1.91125i	0.0238494	+	0.0734010i
$679$	33.6612	−	2.09189i	1.29180	−	0.0802795i
$680$	−7.19208	+	14.1666i	−0.275804	+	0.543265i
$681$	−2.49392	−	2.76978i	−0.0955672	−	0.106138i
$682$	−6.76651	−	11.7199i	−0.259103	−	0.448780i
$683$	6.90388	−	1.46746i	0.264169	−	0.0561510i	−0.0739226	−	0.997264i	$-0.523552\pi$
$683$	6.90388	−	1.46746i	0.264169	−	0.0561510i	0.338092	+	0.941113i	$0.390218\pi$
$684$	−0.311724	−	2.96586i	−0.0119191	−	0.113402i
$685$	27.5884	+	27.5075i	1.05410	+	1.05101i
$686$	4.36352	−	12.4382i	0.166600	−	0.474892i
$687$	12.3507	−	8.97328i	0.471207	−	0.342352i
$688$	0.652155	+	6.20484i	0.0248632	+	0.236557i
$689$	2.03281	−	19.3409i	0.0774441	−	0.736831i
$690$	3.29086	−	12.3541i	0.125281	−	0.470314i
$691$	−0.439513	−	4.18169i	−0.0167199	−	0.159079i	0.982976	−	0.183733i	$-0.0588182\pi$
$691$	−0.439513	−	4.18169i	−0.0167199	−	0.159079i	−0.999696	+	0.0246541i	$0.992152\pi$
$692$	−2.91765	+	8.97960i	−0.110912	+	0.341353i
$693$	−2.18480	+	8.48226i	−0.0829938	+	0.322214i
$694$	1.58886	−	4.89000i	0.0603122	−	0.185622i
$695$	−13.7867	−	21.1616i	−0.522960	−	0.802706i
$696$	3.38833	−	3.76313i	0.128434	−	0.142641i
$697$	−22.7055	+	25.2170i	−0.860031	+	0.955161i
$698$	10.7116	−	4.76913i	0.405442	−	0.180514i
$699$	−2.88670			−0.109185
$700$	−2.84369	+	19.5507i	−0.107481	+	0.738946i
$701$	15.5452			0.587134			0.293567	−	0.955938i	$-0.405158\pi$
$701$	15.5452			0.587134			0.293567	+	0.955938i	$0.405158\pi$
$702$	−2.64718	+	1.17860i	−0.0999113	+	0.0444834i
$703$	12.9429	−	14.3746i	0.488151	−	0.542146i
$704$	−3.81320	+	4.23498i	−0.143715	+	0.159612i
$705$	−3.92922	+	1.05901i	−0.147983	+	0.0398847i
$706$	5.01371	−	15.4306i	0.188693	−	0.580739i
$707$	−14.3457	+	3.99353i	−0.539524	+	0.150192i
$708$	4.18935	−	12.8935i	0.157445	−	0.484567i
$709$	0.342087	+	3.25474i	0.0128473	+	0.122234i	0.999066	−	0.0432137i	$-0.0137596\pi$
$709$	0.342087	+	3.25474i	0.0128473	+	0.122234i	−0.986219	+	0.165448i	$0.947093\pi$
$710$	5.02993	+	13.0462i	0.188770	+	0.489614i
$711$	−1.47898	+	14.0716i	−0.0554661	+	0.527725i
$712$	4.22672	+	40.2145i	0.158403	+	1.50710i
$713$	−37.3273	+	27.1199i	−1.39792	+	1.01565i
$714$	5.04217	+	1.87957i	0.188699	+	0.0703410i
$715$	−4.75852	−	29.7614i	−0.177959	−	1.11301i
$716$	−1.50619	−	14.3304i	−0.0562889	−	0.535553i
$717$	−14.7981	+	3.14544i	−0.552646	+	0.117468i
$718$	−6.70519	−	11.6137i	−0.250235	−	0.433421i
$719$	20.0322	+	22.2480i	0.747073	+	0.829709i	0.990108	−	0.140309i	$-0.0448095\pi$
$719$	20.0322	+	22.2480i	0.747073	+	0.829709i	−0.243034	+	0.970018i	$0.578143\pi$
$720$	−2.68899	−	0.421851i	−0.100213	−	0.0157214i
$721$	17.8814	−	35.9527i	0.665939	−	1.33895i
$722$	3.30180	+	10.1619i	0.122880	+	0.378187i
$723$	−4.97707	+	2.21594i	−0.185099	+	0.0824115i
$724$	−8.87148	−	15.3659i	−0.329706	−	0.571068i
$725$	4.11450	−	9.31479i	0.152809	−	0.345942i
$726$	0.0141261	−	0.0244672i	0.000524270	−	0.000908063i
$727$	24.2299	+	17.6041i	0.898638	+	0.652898i	0.938116	−	0.346322i	$-0.112570\pi$
$727$	24.2299	+	17.6041i	0.898638	+	0.652898i	−0.0394781	+	0.999220i	$0.512570\pi$
$728$	−26.7312	+	1.66122i	−0.990725	+	0.0615691i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	0.609480	−	11.9655i	0.0225579	−	0.442861i
$731$	14.3267	−	3.04523i	0.529891	−	0.112632i
$732$	1.81479	+	3.14330i	0.0670764	+	0.116180i
$733$	11.5543	+	12.8324i	0.426768	+	0.473974i	0.917729	−	0.397208i	$-0.130021\pi$
$733$	11.5543	+	12.8324i	0.426768	+	0.473974i	−0.490960	+	0.871182i	$0.663354\pi$
$734$	18.2634	−	13.2691i	0.674113	−	0.489772i
$735$	15.6447	+	0.492675i	0.577064	+	0.0181726i
$736$	37.9493	+	27.5718i	1.39883	+	1.01631i
$737$	−2.64122	−	25.1295i	−0.0972906	−	0.925658i
$738$	7.72067	+	3.43747i	0.284202	+	0.126535i
$739$	−0.225384	+	2.14438i	−0.00829087	+	0.0788824i	−0.997885	−	0.0650050i	$-0.979294\pi$
$739$	−0.225384	+	2.14438i	−0.00829087	+	0.0788824i	0.989594	+	0.143887i	$0.0459603\pi$
$740$	−17.6578	−	27.1034i	−0.649113	−	0.996342i
$741$	6.57724	−	4.77865i	0.241621	−	0.175548i
$742$	7.59079	+	4.82542i	0.278667	+	0.177147i
$743$	13.2779			0.487120			0.243560	−	0.969886i	$-0.421685\pi$
$743$	13.2779			0.487120			0.243560	+	0.969886i	$0.421685\pi$
$744$	−9.55538	−	10.6123i	−0.350317	−	0.389067i
$745$	−0.870747	+	0.707235i	−0.0319017	+	0.0259111i
$746$	14.4159	−	16.0105i	0.527805	−	0.586187i
$747$	1.99236	+	0.423490i	0.0728968	+	0.0154947i
$748$	−11.4305	−	8.30476i	−0.417941	−	0.303652i
$749$	−16.8433	−	16.5195i	−0.615441	−	0.603609i
$750$	7.85383	−	1.27939i	0.286781	−	0.0467166i
$751$	−16.2894	+	28.2141i	−0.594409	+	1.02955i	0.399221	+	0.916855i	$0.369281\pi$
$751$	−16.2894	+	28.2141i	−0.594409	+	1.02955i	−0.993630	+	0.112692i	$0.964053\pi$
$752$	0.231562	−	2.20316i	0.00844419	−	0.0803411i
$753$	−3.10330	+	3.44656i	−0.113091	+	0.125600i
$754$	5.77251	+	1.22699i	0.210223	+	0.0446842i
$755$	−0.899333	−	5.62474i	−0.0327301	−	0.204705i
$756$	−0.168487	+	3.94769i	−0.00612782	+	0.143576i
$757$	47.9165			1.74155			0.870777	−	0.491678i	$-0.163616\pi$
$757$	47.9165			1.74155			0.870777	+	0.491678i	$0.163616\pi$
$758$	15.5095	+	17.2250i	0.563330	+	0.625641i
$759$	24.2963	+	10.8174i	0.881901	+	0.392647i
$760$	−11.0859	+	0.597298i	−0.402127	+	0.0216663i
$761$	−5.01860	+	2.23442i	−0.181924	+	0.0809978i	−0.495677	−	0.868507i	$-0.665080\pi$
$761$	−5.01860	+	2.23442i	−0.181924	+	0.0809978i	0.313753	+	0.949505i	$0.398413\pi$
$762$	−11.0322	+	8.01537i	−0.399655	+	0.290366i
$763$	5.55038	−	6.99183i	0.200937	−	0.253121i
$764$	18.4157	+	13.3798i	0.666255	+	0.484063i
$765$	−0.325058	+	6.38162i	−0.0117525	+	0.230728i
$766$	−14.9129	−	6.63963i	−0.538823	−	0.239900i
$767$	36.1509	−	7.68410i	1.30533	−	0.277457i
$768$	−5.44123	+	9.42448i	−0.196343	+	0.340077i
$769$	−5.61883	+	17.2930i	−0.202620	+	0.623601i	0.797183	+	0.603738i	$0.206323\pi$
$769$	−5.61883	+	17.2930i	−0.202620	+	0.623601i	−0.999803	+	0.0198625i	$0.993677\pi$
$770$	13.3049	+	4.15927i	0.479476	+	0.149890i
$771$	−4.07559	−	12.5434i	−0.146779	−	0.451739i
$772$	22.4369	+	4.76910i	0.807521	+	0.171644i
$773$	−3.41669	+	32.5076i	−0.122890	+	1.16922i	0.743109	+	0.669171i	$0.233351\pi$
$773$	−3.41669	+	32.5076i	−0.122890	+	1.16922i	−0.865998	+	0.500047i	$0.833316\pi$
$774$	−1.82397	−	3.15920i	−0.0655611	−	0.113555i
$775$	−24.9117	−	14.2855i	−0.894855	−	0.513150i
$776$	31.6946			1.13777
$777$	−19.7596	+	16.3211i	−0.708871	+	0.585515i
$778$	2.79788	+	8.61098i	0.100309	+	0.308719i
$779$	−23.1933	−	4.92989i	−0.830987	−	0.176632i
$780$	−4.89101	−	12.6858i	−0.175126	−	0.454226i
$781$	−28.4507	+	6.04738i	−1.01805	+	0.216392i
$782$	8.16942	−	14.1499i	0.292138	−	0.505998i
$783$	0.629347	−	1.93693i	0.0224910	−	0.0692202i
$784$	−3.31399	+	7.84997i	−0.118357	+	0.280356i
$785$	−1.78815	−	11.1837i	−0.0638218	−	0.399163i
$786$	5.87875	−	2.61739i	0.209688	−	0.0933591i
$787$	−5.38203	−	2.39623i	−0.191849	−	0.0854165i	0.308564	−	0.951204i	$-0.400152\pi$
$787$	−5.38203	−	2.39623i	−0.191849	−	0.0854165i	−0.500412	+	0.865787i	$0.666818\pi$
$788$	9.63596	+	4.29021i	0.343267	+	0.152832i
$789$	25.5306	−	11.3670i	0.908915	−	0.404675i
$790$	22.2458	+	3.48993i	0.791469	+	0.124166i
$791$	2.74473	+	6.94794i	0.0975912	+	0.247040i
$792$	−2.54367	+	7.82862i	−0.0903855	+	0.278178i
$793$	−4.94738	+	8.56912i	−0.175687	+	0.304298i
$794$	−2.44584	+	0.519878i	−0.0867995	+	0.0184498i
$795$	−2.74929	+	10.3210i	−0.0975072	+	0.366049i
$796$	−13.1214	−	2.78904i	−0.465076	−	0.0988551i
$797$	−12.8325	−	39.4943i	−0.454550	−	1.39896i	−0.871663	−	0.490105i	$-0.836958\pi$
$797$	−12.8325	−	39.4943i	−0.454550	−	1.39896i	0.417114	−	0.908854i	$-0.363042\pi$
$798$	0.624242	+	3.70801i	0.0220979	+	0.131262i
$799$	−5.20064			−0.183985
$800$	−5.98628	+	28.5753i	−0.211647	+	1.01029i
$801$	8.13151	+	14.0842i	0.287313	+	0.497640i
$802$	1.25892	−	11.9778i	0.0444540	−	0.422952i
$803$	24.3786	+	5.18183i	0.860302	+	0.182863i
$804$	−3.52233	−	10.8406i	−0.124223	−	0.382319i
$805$	9.36124	−	46.5951i	0.329940	−	1.64226i
$806$	5.14286	−	15.8281i	0.181150	−	0.557521i
$807$	1.49520	−	2.58976i	0.0526334	−	0.0911638i
$808$	−13.6884	+	2.90955i	−0.481555	+	0.102358i
$809$	2.71878	+	1.21048i	0.0955873	+	0.0425582i	0.453973	−	0.891015i	$-0.350006\pi$
$809$	2.71878	+	1.21048i	0.0955873	+	0.0425582i	−0.358386	+	0.933574i	$0.616673\pi$
$810$	1.53664	−	0.414158i	0.0539919	−	0.0145520i
$811$	−3.89221	−	2.82786i	−0.136674	−	0.0992996i	0.517347	−	0.855775i	$-0.326919\pi$
$811$	−3.89221	−	2.82786i	−0.136674	−	0.0992996i	−0.654022	+	0.756476i	$0.726919\pi$
$812$	5.00334	−	6.30272i	0.175583	−	0.221182i
$813$	−6.56623	+	4.77065i	−0.230288	+	0.167314i
$814$	−20.8511	+	9.28351i	−0.730831	+	0.325387i
$815$	5.79815	−	21.7667i	0.203101	−	0.762454i
$816$	−3.17777	−	1.41483i	−0.111244	−	0.0495291i
$817$	6.84843	+	7.60595i	0.239596	+	0.266099i
$818$	−18.9491			−0.662540
$819$	−9.54983	+	4.98322i	−0.333698	+	0.174128i
$820$	−17.9506	+	35.3582i	−0.626862	+	1.23476i
$821$	15.0453	+	3.19798i	0.525085	+	0.111610i	0.462825	−	0.886450i	$-0.346836\pi$
$821$	15.0453	+	3.19798i	0.525085	+	0.111610i	0.0622601	+	0.998060i	$0.480169\pi$
$822$	8.29744	−	9.21524i	0.289407	−	0.321419i
$823$	2.13553	−	20.3182i	0.0744400	−	0.708249i	−0.892118	−	0.451802i	$-0.850781\pi$
$823$	2.13553	−	20.3182i	0.0744400	−	0.708249i	0.966558	−	0.256447i	$-0.0825520\pi$
$824$	18.8676	−	32.6797i	0.657285	−	1.13845i
$825$	0.0485746	+	16.5531i	0.00169115	+	0.576305i
$826$	−4.26373	+	16.5535i	−0.148354	+	0.575969i
$827$	5.46895	+	3.97342i	0.190174	+	0.138169i	0.678798	−	0.734325i	$-0.262501\pi$
$827$	5.46895	+	3.97342i	0.190174	+	0.138169i	−0.488624	+	0.872494i	$0.662501\pi$
$828$	11.7352	+	2.49440i	0.407828	+	0.0866865i
$829$	24.8174	−	27.5625i	0.861944	−	0.957286i	−0.137504	−	0.990501i	$-0.543908\pi$
$829$	24.8174	−	27.5625i	0.861944	−	0.957286i	0.999448	+	0.0332152i	$0.0105747\pi$
$830$	0.834400	−	3.13240i	0.0289625	−	0.108727i
$831$	−4.43789	−	4.92878i	−0.153949	−	0.170977i
$832$	−7.00819			−0.242965
$833$	19.1409	+	5.81099i	0.663192	+	0.201339i
$834$	−6.50367	+	4.72520i	−0.225204	+	0.163620i
$835$	14.6420	−	18.1357i	0.506708	−	0.627613i
$836$	1.03201	−	9.81887i	0.0356926	−	0.339593i
$837$	−5.24686	−	2.33605i	−0.181358	−	0.0807458i
$838$	−0.765961	−	7.28763i	−0.0264597	−	0.251747i
$839$	−10.6640	−	7.74788i	−0.368164	−	0.267487i	0.388285	−	0.921539i	$-0.373067\pi$
$839$	−10.6640	−	7.74788i	−0.368164	−	0.267487i	−0.756449	+	0.654053i	$0.773067\pi$
$840$	14.6453	+	1.37403i	0.505311	+	0.0474086i
$841$	20.1059	−	14.6078i	0.693306	−	0.503716i
$842$	−14.3095	−	15.8923i	−0.493138	−	0.547685i
$843$	−8.22844	−	14.2521i	−0.283403	−	0.490868i
$844$	−28.3621	+	6.02854i	−0.976262	+	0.207511i
$845$	5.02295	−	6.22147i	0.172795	−	0.214025i
$846$	0.400262	+	1.23188i	0.0137613	+	0.0423529i
$847$	0.0467694	−	0.0940355i	0.00160702	−	0.00323110i
$848$	−4.70398	−	3.41764i	−0.161535	−	0.117362i
$849$	−11.5265	+	19.9645i	−0.395589	+	0.685181i
$850$	10.1167	+	1.03330i	0.347000	+	0.0354419i
$851$	38.9083	+	67.3912i	1.33376	+	2.31014i
$852$	−11.9866	+	5.33678i	−0.410654	+	0.182835i
$853$	5.39710	+	16.6106i	0.184793	+	0.568734i	0.999945	−	0.0105131i	$-0.00334648\pi$
$853$	5.39710	+	16.6106i	0.184793	+	0.568734i	−0.815152	+	0.579248i	$0.803346\pi$
$854$	−2.52965	−	3.81377i	−0.0865629	−	0.130504i
$855$	−3.97546	+	2.03295i	−0.135958	+	0.0695255i
$856$	−14.8353	−	16.4763i	−0.507061	−	0.563148i
$857$	−2.12446	−	3.67967i	−0.0725702	−	0.125695i	0.827457	−	0.561529i	$-0.189787\pi$
$857$	−2.12446	−	3.67967i	−0.0725702	−	0.125695i	−0.900027	+	0.435834i	$0.856453\pi$
$858$	−9.38358	+	1.99454i	−0.320350	+	0.0680925i
$859$	−2.45414	−	23.3495i	−0.0837341	−	0.796676i	−0.953130	−	0.302561i	$-0.902159\pi$
$859$	−2.45414	−	23.3495i	−0.0837341	−	0.796676i	0.869396	−	0.494116i	$-0.164508\pi$
$860$	15.2392	−	7.79295i	0.519653	−	0.265737i
$861$	29.4379	+	10.9735i	1.00324	+	0.373977i
$862$	16.0013	−	11.6256i	0.545005	−	0.395969i
$863$	−4.48654	−	42.6866i	−0.152724	−	1.45307i	−0.755495	−	0.655155i	$-0.772604\pi$
$863$	−4.48654	−	42.6866i	−0.152724	−	1.45307i	0.602771	−	0.797914i	$-0.294063\pi$
$864$	−0.610354	+	5.80713i	−0.0207647	+	0.197563i
$865$	14.1162	−	0.760568i	0.479965	−	0.0258601i
$866$	0.630076	+	5.99477i	0.0214109	+	0.203711i
$867$	2.72981	−	8.40151i	0.0927094	−	0.285330i
$868$	−16.2019	−	15.8904i	−0.549930	−	0.539357i
$869$	−14.4751	+	44.5498i	−0.491034	+	1.51125i
$870$	−3.02763	−	1.15710i	−0.102646	−	0.0392295i
$871$	20.7926	−	23.0925i	0.704530	−	0.782460i
$872$	5.61356	−	6.23449i	0.190099	−	0.211126i
$873$	11.6452	−	5.18479i	0.394132	−	0.175479i
$874$	11.4172			0.386193
$875$	28.8444	−	6.55767i	0.975117	−	0.221690i
$876$	11.2430			0.379865
$877$	0.820897	−	0.365487i	0.0277197	−	0.0123416i	−0.392830	−	0.919611i	$-0.628504\pi$
$877$	0.820897	−	0.365487i	0.0277197	−	0.0123416i	0.420550	+	0.907270i	$0.361837\pi$
$878$	−15.4977	+	17.2120i	−0.523023	+	0.580876i
$879$	−16.4004	+	18.2145i	−0.553173	+	0.614360i
$880$	−8.41736	−	3.21696i	−0.283749	−	0.108444i
$881$	0.834413	−	2.56806i	0.0281121	−	0.0865201i	−0.936016	−	0.351957i	$-0.885516\pi$
$881$	0.834413	−	2.56806i	0.0281121	−	0.0865201i	0.964128	+	0.265437i	$0.0855163\pi$
$882$	−0.0967042	−	4.98116i	−0.00325620	−	0.167724i
$883$	−4.75605	+	14.6376i	−0.160054	+	0.492595i	−0.998638	−	0.0521771i	$-0.983384\pi$
$883$	−4.75605	+	14.6376i	−0.160054	+	0.492595i	0.838584	+	0.544772i	$0.183384\pi$
$884$	−1.81623	−	17.2803i	−0.0610864	−	0.581198i
$885$	−20.2689	+	1.09207i	−0.681332	+	0.0367096i
$886$	0.321308	−	3.05704i	0.0107945	−	0.102703i
$887$	3.74527	+	35.6339i	0.125754	+	1.19647i	0.857352	+	0.514731i	$0.172108\pi$
$887$	3.74527	+	35.6339i	0.125754	+	1.19647i	−0.731598	+	0.681736i	$0.761225\pi$
$888$	−19.4849	+	14.1566i	−0.653872	+	0.475065i
$889$	−39.0837	+	32.2824i	−1.31082	+	1.08272i
$890$	23.0439	−	11.7841i	0.772433	−	0.395003i
$891$	0.346056	+	3.29250i	0.0115933	+	0.110303i
$892$	−41.4850	+	8.81792i	−1.38902	+	0.295246i
$893$	−1.81705	−	3.14722i	−0.0608051	−	0.105318i
$894$	0.238916	+	0.265344i	0.00799056	+	0.00887442i
$895$	−19.2086	+	9.82282i	−0.642074	+	0.328341i
$896$	−12.3160	+	24.7627i	−0.411447	+	0.827263i
$897$	10.1070	+	31.1060i	0.337462	+	1.03860i
$898$	6.64671	−	2.95931i	0.221804	−	0.0987533i
$899$	5.84854	+	10.1300i	0.195060	+	0.337853i
$900$	1.57395	+	7.29945i	0.0524650	+	0.243315i
$901$	−6.82500	+	11.8212i	−0.227374	+	0.393823i
$902$	22.6357	+	16.4458i	0.753687	+	0.547585i
$903$	−7.49572	−	11.3007i	−0.249442	−	0.376065i
$904$	2.16943	+	6.67683i	0.0721543	+	0.222068i
$905$	−16.6881	+	20.6700i	−0.554730	+	0.687094i
$906$	−1.77344	+	0.376957i	−0.0589187	+	0.0125235i
$907$	−9.56643	−	16.5695i	−0.317648	−	0.550182i	0.662349	−	0.749196i	$-0.269560\pi$
$907$	−9.56643	−	16.5695i	−0.317648	−	0.550182i	−0.979997	+	0.199013i	$0.936226\pi$
$908$	−3.72453	−	4.13651i	−0.123603	−	0.137275i
$909$	−4.55341	+	3.30825i	−0.151027	+	0.109728i
$910$	7.14723	+	15.5820i	0.236928	+	0.516539i
$911$	15.8500	+	11.5157i	0.525133	+	0.381531i	0.818534	−	0.574458i	$-0.194787\pi$
$911$	15.8500	+	11.5157i	0.525133	+	0.381531i	−0.293401	+	0.955989i	$0.594787\pi$
$912$	−0.254077	−	2.41738i	−0.00841333	−	0.0800475i
$913$	6.16036	+	2.74277i	0.203878	+	0.0907724i
$914$	−1.61742	+	15.3887i	−0.0534993	+	0.509012i
$915$	3.41378	−	4.22833i	0.112856	−	0.139784i
$916$	18.4450	−	13.4011i	0.609440	−	0.442784i
$917$	21.2079	−	11.0665i	0.700346	−	0.365449i
$918$	2.03387			0.0671276
$919$	−1.71459	−	1.90424i	−0.0565591	−	0.0628152i	0.714201	−	0.699940i	$-0.246790\pi$
$919$	−1.71459	−	1.90424i	−0.0565591	−	0.0628152i	−0.770760	+	0.637125i	$0.780123\pi$
$920$	11.4964	−	43.1584i	0.379026	−	1.42289i
$921$	8.06824	−	8.96069i	0.265858	−	0.295265i
$922$	22.6143	+	4.80681i	0.744761	+	0.158304i
$923$	−28.9384	−	21.0250i	−0.952518	−	0.692045i
$924$	−3.26288	+	12.6678i	−0.107341	+	0.416739i
$925$	−28.3532	+	39.2667i	−0.932249	+	1.29108i
$926$	14.5279	−	25.1631i	0.477418	−	0.826912i
$927$	1.58641	−	15.0936i	0.0521044	−	0.495740i
$928$	7.95730	−	8.83748i	0.261211	−	0.290104i
$929$	−1.34709	−	0.286334i	−0.0441967	−	0.00939430i	0.185760	−	0.982595i	$-0.440525\pi$
$929$	−1.34709	−	0.286334i	−0.0441967	−	0.00939430i	−0.229957	+	0.973201i	$0.573859\pi$
$930$	−4.13773	+	8.15030i	−0.135682	+	0.267259i
$931$	3.17103	+	13.6136i	0.103926	+	0.446167i
$932$	−4.31112			−0.141215
$933$	−12.8841	−	14.3092i	−0.421806	−	0.468463i
$934$	−20.4280	−	9.09512i	−0.668423	−	0.297601i
$935$	−5.44522	+	20.4418i	−0.178078	+	0.668518i
$936$	−9.24777	+	4.11737i	−0.302273	+	0.134580i
$937$	−32.1910	+	23.3881i	−1.05163	+	0.764057i	−0.972522	−	0.232809i	$-0.925208\pi$
$937$	−32.1910	+	23.3881i	−1.05163	+	0.764057i	−0.0791115	+	0.996866i	$0.525208\pi$
$938$	5.28050	+	13.3669i	0.172414	+	0.436446i
$939$	−18.4073	−	13.3737i	−0.600699	−	0.436433i
$940$	−5.86807	+	1.58158i	−0.191395	+	0.0515853i
$941$	−50.1214	−	22.3155i	−1.63391	−	0.727464i	−0.634928	−	0.772571i	$-0.718970\pi$
$941$	−50.1214	−	22.3155i	−1.63391	−	0.727464i	−0.998982	+	0.0451078i	$0.985637\pi$
$942$	−3.52615	+	0.749506i	−0.114888	+	0.0244202i
$943$	47.6958	−	82.6116i	1.55319	−	2.69020i
$944$	3.41461	−	10.5091i	0.111136	−	0.342042i
$945$	5.60575	−	1.89092i	0.182355	−	0.0615116i
$946$	−3.73199	−	11.4859i	−0.121337	−	0.373438i
$947$	0.0292154	+	0.00620992i	0.000949372	+	0.000201795i	0.208386	−	0.978047i	$-0.433179\pi$
$947$	0.0292154	+	0.00620992i	0.000949372	+	0.000201795i	−0.207437	+	0.978248i	$0.566512\pi$
$948$	−2.20878	+	21.0151i	−0.0717377	+	0.682538i
$949$	15.3251	+	26.5438i	0.497472	+	0.861648i
$950$	2.90935	+	6.48323i	0.0943917	+	0.210344i
$951$	0.819652			0.0265790
$952$	17.6145	+	6.56616i	0.570891	+	0.212810i
$953$	−16.1897	−	49.8268i	−0.524436	−	1.61405i	−0.765428	−	0.643521i	$-0.777473\pi$
$953$	−16.1897	−	49.8268i	−0.524436	−	1.61405i	0.240992	−	0.970527i	$-0.422527\pi$
$954$	3.32539	+	0.706833i	0.107663	+	0.0228846i
$955$	8.77277	−	32.9336i	0.283880	−	1.06571i
$956$	−22.1002	+	4.69753i	−0.714770	+	0.151929i
$957$	3.37123	−	5.83915i	0.108977	−	0.188753i
$958$	5.50147	−	16.9318i	0.177744	−	0.547041i
$959$	28.6604	−	36.1036i	0.925494	−	1.16585i
$960$	3.80253	+	0.596543i	0.122726	+	0.0192534i
$961$	1.81497	−	0.808076i	0.0585473	−	0.0260670i
$962$	−25.6423	−	11.4167i	−0.826741	−	0.368089i
$963$	−8.14608	−	3.62687i	−0.262504	−	0.116874i
$964$	−7.43298	+	3.30938i	−0.239400	+	0.106588i
$965$	−5.42239	−	33.9135i	−0.174553	−	1.09171i
$966$	−14.9633	−	2.22131i	−0.481438	−	0.0714695i
$967$	−0.255280	+	0.785672i	−0.00820926	+	0.0252655i	−0.955077	−	0.296357i	$-0.904228\pi$
$967$	−0.255280	+	0.785672i	−0.00820926	+	0.0252655i	0.946868	+	0.321622i	$0.104228\pi$
$968$	0.0493489	−	0.0854748i	0.00158613	−	0.00274726i
$969$	−5.58161	+	1.18641i	−0.179307	+	0.0381129i
$970$	−7.29798	−	18.9288i	−0.234324	−	0.607768i
$971$	12.0165	+	2.55418i	0.385627	+	0.0819676i	0.396646	−	0.917972i	$-0.370174\pi$
$971$	12.0165	+	2.55418i	0.385627	+	0.0819676i	−0.0110187	+	0.999939i	$0.503507\pi$
$972$	0.461499	+	1.42035i	0.0148026	+	0.0455577i
$973$	−23.0405	+	19.0310i	−0.738644	+	0.610106i
$974$	−6.29317			−0.201646
$975$	−15.0880	+	13.6657i	−0.483203	+	0.437652i
$976$	1.47918	+	2.56201i	0.0473473	+	0.0820080i
$977$	1.61974	−	15.4108i	0.0518202	−	0.493037i	−0.937574	−	0.347785i	$-0.886934\pi$
$977$	1.61974	−	15.4108i	0.0518202	−	0.493037i	0.989395	−	0.145252i	$-0.0463993\pi$
$978$	−7.01313	−	1.49069i	−0.224255	−	0.0476669i
$979$	16.6378	+	51.2058i	0.531745	+	1.63654i
$980$	23.3645	+	0.735783i	0.746352	+	0.0235037i
$981$	1.04266	−	3.20897i	0.0332895	−	0.102455i
$982$	3.35207	−	5.80595i	0.106969	−	0.185275i
$983$	−27.1823	+	5.77777i	−0.866980	+	0.184282i	−0.619869	−	0.784705i	$-0.712814\pi$
$983$	−27.1823	+	5.77777i	−0.866980	+	0.184282i	−0.247110	+	0.968987i	$0.579481\pi$
$984$	26.9717	+	12.0086i	0.859828	+	0.382820i
$985$	0.803394	−	15.7724i	0.0255983	−	0.502551i
$986$	−3.35110	−	2.43472i	−0.106721	−	0.0775372i
$987$	1.76909	+	4.47824i	0.0563109	+	0.142544i
$988$	9.82274	−	7.13664i	0.312503	−	0.227047i
$989$	−37.6151	+	16.7473i	−1.19609	+	0.532534i
$990$	5.26115	−	0.283466i	0.167210	−	0.00900915i
$991$	35.9742	+	16.0167i	1.14276	+	0.508789i	0.888740	−	0.458411i	$-0.151581\pi$
$991$	35.9742	+	16.0167i	1.14276	+	0.508789i	0.254017	+	0.967200i	$0.418248\pi$
$992$	−22.4403	−	24.9224i	−0.712479	−	0.791288i
$993$	6.09535			0.193430
$994$	14.6672	−	7.65353i	0.465216	−	0.242755i
$995$	3.17110	+	19.8331i	0.100530	+	0.628752i
$996$	2.97548	+	0.632459i	0.0942818	+	0.0200402i
$997$	−11.5009	+	12.7730i	−0.364236	+	0.404525i	−0.897208	−	0.441608i	$-0.854408\pi$
$997$	−11.5009	+	12.7730i	−0.364236	+	0.404525i	0.532972	+	0.846133i	$0.321075\pi$
$998$	0.953877	−	9.07553i	0.0301944	−	0.287281i
$999$	−4.84333	+	8.38889i	−0.153236	+	0.265413i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bg.a.16.9	✓	160
7.4	even	3	inner	525.2.bg.a.466.12	yes	160
25.11	even	5	inner	525.2.bg.a.436.12	yes	160
175.11	even	15	inner	525.2.bg.a.361.9	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bg.a.16.9	✓	160	1.1	even	1	trivial
525.2.bg.a.361.9	yes	160	175.11	even	15	inner
525.2.bg.a.436.12	yes	160	25.11	even	5	inner
525.2.bg.a.466.12	yes	160	7.4	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.650196 + 0.289486i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.999309 + 1.10984i) q^{4} +(2.08872 + 0.798271i) q^{5} +(0.219936 - 0.676893i) q^{6} +(0.659935 - 2.56213i) q^{7} +(0.768334 - 2.36469i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.650196 + 0.289486i) q^{2} +(-0.669131 + 0.743145i) q^{3} +(-0.999309 + 1.10984i) q^{4} +(2.08872 + 0.798271i) q^{5} +(0.219936 - 0.676893i) q^{6} +(0.659935 - 2.56213i) q^{7} +(0.768334 - 2.36469i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(-1.58917 + 0.0856230i) q^{10} +(0.346056 - 3.29250i) q^{11} +(-0.156107 - 1.48526i) q^{12} +(3.29380 - 2.39308i) q^{13} +(0.312612 + 1.85692i) q^{14} +(-1.99086 + 1.01808i) q^{15} +(-0.127238 - 1.21059i) q^{16} +(-2.79520 + 0.594138i) q^{17} +(0.355864 + 0.616374i) q^{18} +(-1.33616 - 1.48395i) q^{19} +(-2.97324 + 1.52044i) q^{20} +(1.46245 + 2.20482i) q^{21} +(0.728128 + 2.24095i) q^{22} +(7.33887 - 3.26748i) q^{23} +(1.24319 + 2.15327i) q^{24} +(3.72553 + 3.33473i) q^{25} +(-1.44885 + 2.50948i) q^{26} +(0.809017 + 0.587785i) q^{27} +(2.18408 + 3.29278i) q^{28} +(-0.629347 - 1.93693i) q^{29} +(0.999730 - 1.23827i) q^{30} +(-5.61790 + 1.19412i) q^{31} +(2.91956 + 5.05683i) q^{32} +(2.21525 + 2.46028i) q^{33} +(1.64543 - 1.19548i) q^{34} +(3.42369 - 4.82476i) q^{35} +(1.20822 + 0.877824i) q^{36} +(1.01253 + 9.63359i) q^{37} +(1.29835 + 0.578062i) q^{38} +(-0.425573 + 4.04905i) q^{39} +(3.49250 - 4.32584i) q^{40} +(9.60658 - 6.97959i) q^{41} +(-1.58914 - 1.01021i) q^{42} -5.12546 q^{43} +(3.30835 + 3.67429i) q^{44} +(0.575567 - 2.16072i) q^{45} +(-3.82581 + 4.24900i) q^{46} +(1.78014 + 0.378379i) q^{47} +(0.984785 + 0.715488i) q^{48} +(-6.12897 - 3.38167i) q^{49} +(-3.38768 - 1.08974i) q^{50} +(1.42882 - 2.47479i) q^{51} +(-0.635569 + 6.04703i) q^{52} +(3.19621 - 3.54975i) q^{53} +(-0.696175 - 0.147977i) q^{54} +(3.35112 - 6.60087i) q^{55} +(-5.55158 - 3.52911i) q^{56} +1.99686 q^{57} +(0.969912 + 1.07720i) q^{58} +(8.29288 + 3.69223i) q^{59} +(0.859577 - 3.22692i) q^{60} +(-2.22022 + 0.988507i) q^{61} +(3.30705 - 2.40271i) q^{62} +(-2.61707 - 0.388505i) q^{63} +(-1.39259 - 1.01178i) q^{64} +(8.79016 - 2.36914i) q^{65} +(-2.15256 - 0.958382i) q^{66} +(7.46557 - 1.58686i) q^{67} +(2.13387 - 3.69596i) q^{68} +(-2.48246 + 7.64021i) q^{69} +(-0.829370 + 4.12815i) q^{70} +(-2.71494 - 8.35571i) q^{71} +(-2.43205 - 0.516948i) q^{72} +(-0.786915 + 7.48699i) q^{73} +(-3.44713 - 5.97060i) q^{74} +(-4.97105 + 0.537232i) q^{75} +2.98219 q^{76} +(-8.20742 - 3.05947i) q^{77} +(-0.895438 - 2.75587i) q^{78} +(-13.8399 - 2.94176i) q^{79} +(0.700616 - 2.63016i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(-4.22567 + 7.31907i) q^{82} +(-0.629429 + 1.93718i) q^{83} +(-3.90845 - 0.580210i) q^{84} +(-6.31268 - 0.990338i) q^{85} +(3.33255 - 1.48375i) q^{86} +(1.86053 + 0.828363i) q^{87} +(-7.51985 - 3.34805i) q^{88} +(-14.8570 + 6.61477i) q^{89} +(0.251267 + 1.57151i) q^{90} +(-3.95769 - 10.0184i) q^{91} +(-3.70741 + 11.4102i) q^{92} +(2.87170 - 4.97394i) q^{93} +(-1.26697 + 0.269303i) q^{94} +(-1.60627 - 4.16619i) q^{95} +(-5.71152 - 1.21402i) q^{96} +(3.93913 + 12.1234i) q^{97} +(4.96398 + 0.424498i) q^{98} -3.31064 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9}+O(q^{10}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9	\( 160 q - 2 q^{2} - 20 q^{3} + 20 q^{4} - 4 q^{6} + 4 q^{7} - 6 q^{8} + 20 q^{9} - 2 q^{10} - 6 q^{11} - 20 q^{12} + 28 q^{16} - 6 q^{17} + 8 q^{18} + 4 q^{19} - 8 q^{20} + 7 q^{21} + 32 q^{22} - 2 q^{23} - 18 q^{24} + 4 q^{25} + 56 q^{26} + 40 q^{27} - 43 q^{28} + 26 q^{29} + 12 q^{30} + 3 q^{31} + 54 q^{32} - 4 q^{33} - 76 q^{34} - 37 q^{35} - 40 q^{36} - 18 q^{37} + 19 q^{38} - 22 q^{40} - 30 q^{41} + 16 q^{42} - 164 q^{43} + 6 q^{44} - 5 q^{45} - 10 q^{46} - 11 q^{47} + 56 q^{48} - 136 q^{49} - 86 q^{50} - 4 q^{51} - 19 q^{52} - 34 q^{53} + 2 q^{54} - 48 q^{55} + 33 q^{56} - 72 q^{57} - 24 q^{58} - 24 q^{59} + 11 q^{60} - 16 q^{61} - 128 q^{62} - 7 q^{63} - 162 q^{64} - 36 q^{65} + q^{66} - 6 q^{67} + 16 q^{68} - 24 q^{69} + 32 q^{70} - 68 q^{71} + 3 q^{72} + 34 q^{73} + 4 q^{74} - 9 q^{75} + 420 q^{76} - 40 q^{77} - 8 q^{78} + 14 q^{79} - 76 q^{80} + 20 q^{81} + 54 q^{82} - 38 q^{83} + 54 q^{84} + 42 q^{85} - 30 q^{86} - 12 q^{87} - 30 q^{88} - 33 q^{89} - 26 q^{90} + 5 q^{91} + 2 q^{92} + 2 q^{93} + 46 q^{94} + 4 q^{95} + 11 q^{96} - 58 q^{97} + 166 q^{98} - 8 q^{99}+O(q^{100}) \) 160 * q - 2 * q^2 - 20 * q^3 + 20 * q^4 - 4 * q^6 + 4 * q^7 - 6 * q^8 + 20 * q^9 - 2 * q^10 - 6 * q^11 - 20 * q^12 + 28 * q^16 - 6 * q^17 + 8 * q^18 + 4 * q^19 - 8 * q^20 + 7 * q^21 + 32 * q^22 - 2 * q^23 - 18 * q^24 + 4 * q^25 + 56 * q^26 + 40 * q^27 - 43 * q^28 + 26 * q^29 + 12 * q^30 + 3 * q^31 + 54 * q^32 - 4 * q^33 - 76 * q^34 - 37 * q^35 - 40 * q^36 - 18 * q^37 + 19 * q^38 - 22 * q^40 - 30 * q^41 + 16 * q^42 - 164 * q^43 + 6 * q^44 - 5 * q^45 - 10 * q^46 - 11 * q^47 + 56 * q^48 - 136 * q^49 - 86 * q^50 - 4 * q^51 - 19 * q^52 - 34 * q^53 + 2 * q^54 - 48 * q^55 + 33 * q^56 - 72 * q^57 - 24 * q^58 - 24 * q^59 + 11 * q^60 - 16 * q^61 - 128 * q^62 - 7 * q^63 - 162 * q^64 - 36 * q^65 + q^66 - 6 * q^67 + 16 * q^68 - 24 * q^69 + 32 * q^70 - 68 * q^71 + 3 * q^72 + 34 * q^73 + 4 * q^74 - 9 * q^75 + 420 * q^76 - 40 * q^77 - 8 * q^78 + 14 * q^79 - 76 * q^80 + 20 * q^81 + 54 * q^82 - 38 * q^83 + 54 * q^84 + 42 * q^85 - 30 * q^86 - 12 * q^87 - 30 * q^88 - 33 * q^89 - 26 * q^90 + 5 * q^91 + 2 * q^92 + 2 * q^93 + 46 * q^94 + 4 * q^95 + 11 * q^96 - 58 * q^97 + 166 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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