LMFDB - Embedded newform 256.2.m.a.5.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, 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:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			5.15
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.369587 - 1.36507i) q^{2} +(-0.111501 + 0.751680i) q^{3} +(-1.72681 + 1.00902i) q^{4} +(-1.56967 - 0.0771129i) q^{5} +(1.06730 - 0.125605i) q^{6} +(1.56830 + 0.838272i) q^{7} +(2.01559 + 1.98429i) q^{8} +(2.31823 + 0.703228i) q^{9} +O(q^{10})$	\(q+(-0.369587 - 1.36507i) q^{2} +(-0.111501 + 0.751680i) q^{3} +(-1.72681 + 1.00902i) q^{4} +(-1.56967 - 0.0771129i) q^{5} +(1.06730 - 0.125605i) q^{6} +(1.56830 + 0.838272i) q^{7} +(2.01559 + 1.98429i) q^{8} +(2.31823 + 0.703228i) q^{9} +(0.474865 + 2.17120i) q^{10} +(1.01106 + 1.68685i) q^{11} +(-0.565920 - 1.41052i) q^{12} +(3.56180 - 3.92984i) q^{13} +(0.564674 - 2.45064i) q^{14} +(0.232984 - 1.17129i) q^{15} +(1.96375 - 3.48478i) q^{16} +(0.925241 + 4.65150i) q^{17} +(0.103164 - 3.42444i) q^{18} +(-0.0523519 - 0.110689i) q^{19} +(2.78833 - 1.45067i) q^{20} +(-0.804979 + 1.08539i) q^{21} +(1.92899 - 2.00360i) q^{22} +(4.59216 + 3.76868i) q^{23} +(-1.71629 + 1.29383i) q^{24} +(-2.51801 - 0.248003i) q^{25} +(-6.68088 - 3.40967i) q^{26} +(-1.76179 + 3.72499i) q^{27} +(-3.55399 + 0.134909i) q^{28} +(-2.65835 + 0.665882i) q^{29} +(-1.68500 + 0.114855i) q^{30} +(5.40378 + 2.23832i) q^{31} +(-5.48273 - 1.39272i) q^{32} +(-1.38071 + 0.571908i) q^{33} +(6.00765 - 2.98215i) q^{34} +(-2.39706 - 1.43674i) q^{35} +(-4.71272 + 1.12480i) q^{36} +(-3.78540 - 10.5795i) q^{37} +(-0.131749 + 0.112373i) q^{38} +(2.55683 + 3.11551i) q^{39} +(-3.01079 - 3.27010i) q^{40} +(-2.43524 + 0.239850i) q^{41} +(1.77914 + 0.697704i) q^{42} +(3.29335 - 0.488522i) q^{43} +(-3.44798 - 1.89269i) q^{44} +(-3.58463 - 1.28260i) q^{45} +(3.44730 - 7.66145i) q^{46} +(-3.50234 + 5.24162i) q^{47} +(2.40048 + 1.86467i) q^{48} +(-2.13214 - 3.19097i) q^{49} +(0.592085 + 3.52891i) q^{50} +(-3.59960 + 0.176837i) q^{51} +(-2.18526 + 10.3800i) q^{52} +(4.13656 + 1.03615i) q^{53} +(5.73600 + 1.02825i) q^{54} +(-1.45695 - 2.72577i) q^{55} +(1.49767 + 4.80156i) q^{56} +(0.0890398 - 0.0270099i) q^{57} +(1.89147 + 3.38272i) q^{58} +(6.69414 + 7.38585i) q^{59} +(0.779538 + 2.25768i) q^{60} +(-2.99455 - 4.03768i) q^{61} +(1.05829 - 8.20378i) q^{62} +(3.04618 + 3.04618i) q^{63} +(0.125194 + 7.99902i) q^{64} +(-5.89388 + 5.89388i) q^{65} +(1.29098 + 1.67339i) q^{66} +(-8.09095 + 6.00066i) q^{67} +(-6.29118 - 7.09867i) q^{68} +(-3.34488 + 3.03162i) q^{69} +(-1.07533 + 3.80315i) q^{70} +(-4.36560 - 14.3915i) q^{71} +(3.27719 + 6.01746i) q^{72} +(-1.04178 + 0.556842i) q^{73} +(-13.0427 + 9.07737i) q^{74} +(0.467180 - 1.86509i) q^{75} +(0.202089 + 0.138314i) q^{76} +(0.171602 + 3.49303i) q^{77} +(3.30791 - 4.64170i) q^{78} +(3.03683 - 2.02914i) q^{79} +(-3.35116 + 5.31852i) q^{80} +(3.43926 + 2.29804i) q^{81} +(1.22744 + 3.23561i) q^{82} +(1.17370 - 3.28026i) q^{83} +(0.294866 - 2.68650i) q^{84} +(-1.09363 - 7.37266i) q^{85} +(-1.88405 - 4.31509i) q^{86} +(-0.204121 - 2.07248i) q^{87} +(-1.30932 + 5.40624i) q^{88} +(8.15638 - 6.69377i) q^{89} +(-0.426001 + 5.36728i) q^{90} +(8.88022 - 3.17739i) q^{91} +(-11.7325 - 1.87422i) q^{92} +(-2.28503 + 3.81234i) q^{93} +(8.44957 + 2.84369i) q^{94} +(0.0736395 + 0.177782i) q^{95} +(1.65821 - 3.96597i) q^{96} +(-4.51959 + 10.9112i) q^{97} +(-3.56787 + 4.08985i) q^{98} +(1.15763 + 4.62152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{64}\right)$	$1$

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 $

$2$	−0.369587	−	1.36507i	−0.261338	−	0.965247i
$2$	−0.369587	−	1.36507i	−0.261338	−	0.965247i
$3$	−0.111501	+	0.751680i	−0.0643752	+	0.433983i	0.932895	+	0.360148i	$0.117274\pi$
$3$	−0.111501	+	0.751680i	−0.0643752	+	0.433983i	−0.997270	+	0.0738348i	$0.976476\pi$
$4$	−1.72681	+	1.00902i	−0.863405	+	0.504511i
$5$	−1.56967	−	0.0771129i	−0.701977	−	0.0344859i	−0.305050	−	0.952336i	$-0.598673\pi$
$5$	−1.56967	−	0.0771129i	−0.701977	−	0.0344859i	−0.396927	+	0.917850i	$0.629923\pi$
$6$	1.06730	−	0.125605i	0.435724	−	0.0512779i
$7$	1.56830	+	0.838272i	0.592760	+	0.316837i	0.740360	−	0.672210i	$-0.234655\pi$
$7$	1.56830	+	0.838272i	0.592760	+	0.316837i	−0.147600	+	0.989047i	$0.547155\pi$
$8$	2.01559	+	1.98429i	0.712618	+	0.701552i
$9$	2.31823	+	0.703228i	0.772744	+	0.234409i
$10$	0.474865	+	2.17120i	0.150166	+	0.686594i
$11$	1.01106	+	1.68685i	0.304846	+	0.508605i	0.971586	−	0.236685i	$-0.0760609\pi$
$11$	1.01106	+	1.68685i	0.304846	+	0.508605i	−0.666740	+	0.745290i	$0.732311\pi$
$12$	−0.565920	−	1.41052i	−0.163367	−	0.407181i
$13$	3.56180	−	3.92984i	0.987864	−	1.08994i	−0.00807972	−	0.999967i	$-0.502572\pi$
$13$	3.56180	−	3.92984i	0.987864	−	1.08994i	0.995944	−	0.0899731i	$-0.0286781\pi$
$14$	0.564674	−	2.45064i	0.150916	−	0.654962i
$15$	0.232984	−	1.17129i	0.0601562	−	0.302426i
$16$	1.96375	−	3.48478i	0.490937	−	0.871195i
$17$	0.925241	+	4.65150i	0.224404	+	1.12815i	0.914547	+	0.404481i	$0.132548\pi$
$17$	0.925241	+	4.65150i	0.224404	+	1.12815i	−0.690143	+	0.723673i	$0.742452\pi$
$18$	0.103164	−	3.42444i	0.0243159	−	0.807149i
$19$	−0.0523519	−	0.110689i	−0.0120103	−	0.0253937i	0.897895	−	0.440210i	$-0.145096\pi$
$19$	−0.0523519	−	0.110689i	−0.0120103	−	0.0253937i	−0.909905	+	0.414816i	$0.863846\pi$
$20$	2.78833	−	1.45067i	0.623489	−	0.324380i
$21$	−0.804979	+	1.08539i	−0.175661	+	0.236851i
$22$	1.92899	−	2.00360i	0.411262	−	0.427170i
$23$	4.59216	+	3.76868i	0.957531	+	0.785825i	0.976836	−	0.213989i	$-0.0686455\pi$
$23$	4.59216	+	3.76868i	0.957531	+	0.785825i	−0.0193055	+	0.999814i	$0.506146\pi$
$24$	−1.71629	+	1.29383i	−0.350336	+	0.264101i
$25$	−2.51801	−	0.248003i	−0.503602	−	0.0496005i
$26$	−6.68088	−	3.40967i	−1.31023	−	0.668691i
$27$	−1.76179	+	3.72499i	−0.339057	+	0.716875i
$28$	−3.55399	+	0.134909i	−0.671640	+	0.0254953i
$29$	−2.65835	+	0.665882i	−0.493643	+	0.123651i	−0.481805	−	0.876279i	$-0.660018\pi$
$29$	−2.65835	+	0.665882i	−0.493643	+	0.123651i	−0.0118388	+	0.999930i	$0.503768\pi$
$30$	−1.68500	+	0.114855i	−0.307637	+	0.0209696i
$31$	5.40378	+	2.23832i	0.970548	+	0.402014i	0.810916	−	0.585162i	$-0.198969\pi$
$31$	5.40378	+	2.23832i	0.970548	+	0.402014i	0.159632	+	0.987177i	$0.448969\pi$
$32$	−5.48273	−	1.39272i	−0.969219	−	0.246200i
$33$	−1.38071	+	0.571908i	−0.240350	+	0.0995564i
$34$	6.00765	−	2.98215i	1.03030	−	0.511434i
$35$	−2.39706	−	1.43674i	−0.405178	−	0.242854i
$36$	−4.71272	+	1.12480i	−0.785453	+	0.187467i
$37$	−3.78540	−	10.5795i	−0.622316	−	1.73926i	−0.672061	−	0.740495i	$-0.734591\pi$
$37$	−3.78540	−	10.5795i	−0.622316	−	1.73926i	0.0497451	−	0.998762i	$-0.484159\pi$
$38$	−0.131749	+	0.112373i	−0.0213725	+	0.0182293i
$39$	2.55683	+	3.11551i	0.409421	+	0.498881i
$40$	−3.01079	−	3.27010i	−0.476048	−	0.517049i
$41$	−2.43524	+	0.239850i	−0.380320	+	0.0374583i	−0.286371	−	0.958119i	$-0.592449\pi$
$41$	−2.43524	+	0.239850i	−0.380320	+	0.0374583i	−0.0939489	+	0.995577i	$0.529949\pi$
$42$	1.77914	+	0.697704i	0.274527	+	0.107658i
$43$	3.29335	−	0.488522i	0.502231	−	0.0744990i	0.109192	−	0.994021i	$-0.465174\pi$
$43$	3.29335	−	0.488522i	0.502231	−	0.0744990i	0.393039	+	0.919522i	$0.371424\pi$
$44$	−3.44798	−	1.89269i	−0.519803	−	0.285334i
$45$	−3.58463	−	1.28260i	−0.534364	−	0.191199i
$46$	3.44730	−	7.66145i	0.508277	−	1.12962i
$47$	−3.50234	+	5.24162i	−0.510868	+	0.764568i	−0.993811	−	0.111084i	$-0.964568\pi$
$47$	−3.50234	+	5.24162i	−0.510868	+	0.764568i	0.482943	+	0.875652i	$0.339568\pi$
$48$	2.40048	+	1.86467i	0.346479	+	0.269142i
$49$	−2.13214	−	3.19097i	−0.304591	−	0.455853i
$50$	0.592085	+	3.52891i	0.0837335	+	0.499063i
$51$	−3.59960	+	0.176837i	−0.504045	+	0.0247622i
$52$	−2.18526	+	10.3800i	−0.303041	+	1.43945i
$53$	4.13656	+	1.03615i	0.568200	+	0.142327i	0.516425	−	0.856332i	$-0.327262\pi$
$53$	4.13656	+	1.03615i	0.568200	+	0.142327i	0.0517742	+	0.998659i	$0.483512\pi$
$54$	5.73600	+	1.02825i	0.780570	+	0.139927i
$55$	−1.45695	−	2.72577i	−0.196455	−	0.367542i
$56$	1.49767	+	4.80156i	0.200134	+	0.641636i
$57$	0.0890398	−	0.0270099i	0.0117936	−	0.00357755i
$58$	1.89147	+	3.38272i	0.248362	+	0.444173i
$59$	6.69414	+	7.38585i	0.871503	+	0.961555i	0.999543	−	0.0302136i	$-0.00961876\pi$
$59$	6.69414	+	7.38585i	0.871503	+	0.961555i	−0.128041	+	0.991769i	$0.540869\pi$
$60$	0.779538	+	2.25768i	0.100638	+	0.291465i
$61$	−2.99455	−	4.03768i	−0.383413	−	0.516972i	0.568772	−	0.822495i	$-0.307419\pi$
$61$	−2.99455	−	4.03768i	−0.383413	−	0.516972i	−0.952185	+	0.305523i	$0.901169\pi$
$62$	1.05829	−	8.20378i	0.134402	−	1.04188i
$63$	3.04618	+	3.04618i	0.383782	+	0.383782i
$64$	0.125194	+	7.99902i	0.0156493	+	0.999878i
$65$	−5.89388	+	5.89388i	−0.731046	+	0.731046i
$66$	1.29098	+	1.67339i	0.158909	+	0.205980i
$67$	−8.09095	+	6.00066i	−0.988467	+	0.733097i	−0.963808	−	0.266599i	$-0.914100\pi$
$67$	−8.09095	+	6.00066i	−0.988467	+	0.733097i	−0.0246597	+	0.999696i	$0.507850\pi$
$68$	−6.29118	−	7.09867i	−0.762917	−	0.860840i
$69$	−3.34488	+	3.03162i	−0.402676	+	0.364964i
$70$	−1.07533	+	3.80315i	−0.128526	+	0.454564i
$71$	−4.36560	−	14.3915i	−0.518102	−	1.70795i	−0.690860	−	0.722988i	$-0.742768\pi$
$71$	−4.36560	−	14.3915i	−0.518102	−	1.70795i	0.172758	−	0.984964i	$-0.444732\pi$
$72$	3.27719	+	6.01746i	0.386221	+	0.709164i
$73$	−1.04178	+	0.556842i	−0.121931	+	0.0651734i	−0.531235	−	0.847225i	$-0.678272\pi$
$73$	−1.04178	+	0.556842i	−0.121931	+	0.0651734i	0.409304	+	0.912398i	$0.365772\pi$
$74$	−13.0427	+	9.07737i	−1.51618	+	1.05522i
$75$	0.467180	−	1.86509i	0.0539453	−	0.215362i
$76$	0.202089	+	0.138314i	0.0231812	+	0.0158657i
$77$	0.171602	+	3.49303i	0.0195558	+	0.398068i
$78$	3.30791	−	4.64170i	0.374547	−	0.525569i
$79$	3.03683	−	2.02914i	0.341670	−	0.228296i	−0.372882	−	0.927879i	$-0.621631\pi$
$79$	3.03683	−	2.02914i	0.341670	−	0.228296i	0.714552	+	0.699582i	$0.246631\pi$
$80$	−3.35116	+	5.31852i	−0.374671	+	0.594628i
$81$	3.43926	+	2.29804i	0.382140	+	0.255337i
$82$	1.22744	+	3.23561i	0.135548	+	0.357314i
$83$	1.17370	−	3.28026i	0.128830	−	0.360056i	−0.859758	−	0.510702i	$-0.829385\pi$
$83$	1.17370	−	3.28026i	0.128830	−	0.360056i	0.988588	+	0.150646i	$0.0481355\pi$
$84$	0.294866	−	2.68650i	0.0321725	−	0.293121i
$85$	−1.09363	−	7.37266i	−0.118621	−	0.799677i
$86$	−1.88405	−	4.31509i	−0.203162	−	0.465308i
$87$	−0.204121	−	2.07248i	−0.0218841	−	0.222193i
$88$	−1.30932	+	5.40624i	−0.139574	+	0.576307i
$89$	8.15638	−	6.69377i	0.864575	−	0.709538i	−0.0936344	−	0.995607i	$-0.529848\pi$
$89$	8.15638	−	6.69377i	0.864575	−	0.709538i	0.958209	+	0.286068i	$0.0923485\pi$
$90$	−0.426001	+	5.36728i	−0.0449045	+	0.565761i
$91$	8.88022	−	3.17739i	0.930900	−	0.333081i
$92$	−11.7325	−	1.87422i	−1.22319	−	0.195401i
$93$	−2.28503	+	3.81234i	−0.236947	+	0.395321i
$94$	8.44957	+	2.84369i	0.871507	+	0.293304i
$95$	0.0736395	+	0.177782i	0.00755526	+	0.0182400i
$96$	1.65821	−	3.96597i	0.169240	−	0.404775i
$97$	−4.51959	+	10.9112i	−0.458894	+	1.10787i	0.509951	+	0.860203i	$0.329663\pi$
$97$	−4.51959	+	10.9112i	−0.458894	+	1.10787i	−0.968846	+	0.247666i	$0.920337\pi$
$98$	−3.56787	+	4.08985i	−0.360410	+	0.413137i
$99$	1.15763	+	4.62152i	0.116346	+	0.464480i
$100$	4.59837	−	2.11248i	0.459837	−	0.211248i
$101$	−12.3719	−	5.85146i	−1.23105	−	0.582242i	−0.302391	−	0.953184i	$-0.597785\pi$
$101$	−12.3719	−	5.85146i	−1.23105	−	0.582242i	−0.928656	+	0.370943i	$0.879035\pi$
$102$	1.57176	+	4.84834i	0.155628	+	0.480057i
$103$	0.528012	−	5.36100i	0.0520266	−	0.528235i	−0.933484	−	0.358620i	$-0.883247\pi$
$103$	0.528012	−	5.36100i	0.0520266	−	0.528235i	0.985510	−	0.169615i	$-0.0542525\pi$
$104$	14.9770	−	0.853300i	1.46862	−	0.0836730i
$105$	1.34725	−	1.64163i	0.131478	−	0.160206i
$106$	−0.114400	−	6.02962i	−0.0111115	−	0.585648i
$107$	−10.3994	−	7.71274i	−1.00535	−	0.745618i	−0.0380557	−	0.999276i	$-0.512116\pi$
$107$	−10.3994	−	7.71274i	−1.00535	−	0.745618i	−0.967294	+	0.253657i	$0.918366\pi$
$108$	−0.716321	−	8.21004i	−0.0689280	−	0.790012i
$109$	10.9403	−	5.17439i	1.04789	−	0.495617i	0.175530	−	0.984474i	$-0.443836\pi$
$109$	10.9403	−	5.17439i	1.04789	−	0.495617i	0.872364	+	0.488857i	$0.162586\pi$
$110$	−3.18238	+	2.99624i	−0.303428	+	0.285681i
$111$	8.37447	−	1.66578i	0.794869	−	0.158109i
$112$	6.00093	−	3.81901i	0.567035	−	0.360863i
$113$	−3.19165	−	0.634859i	−0.300245	−	0.0597225i	0.0426687	−	0.999089i	$-0.486414\pi$
$113$	−3.19165	−	0.634859i	−0.300245	−	0.0597225i	−0.342914	+	0.939367i	$0.611414\pi$
$114$	−0.0697783	−	0.111563i	−0.00653534	−	0.0104488i
$115$	−6.91755	−	6.26970i	−0.645065	−	0.584652i
$116$	3.91858	−	3.83219i	0.363831	−	0.355810i
$117$	11.0206	−	6.60551i	1.01886	−	0.610680i
$118$	7.60810	−	11.8677i	0.700382	−	1.09251i
$119$	−2.44817	+	8.07053i	−0.224423	+	0.739824i
$120$	2.79378	−	1.89853i	0.255036	−	0.173311i
$121$	3.36213	−	6.29011i	0.305649	−	0.571828i
$122$	−4.40496	+	5.58003i	−0.398806	+	0.505193i
$123$	0.0912414	−	1.85726i	0.00822696	−	0.167464i
$124$	−11.5898	+	1.58738i	−1.04080	+	0.142551i
$125$	11.7061	+	1.73643i	1.04702	+	0.155311i
$126$	3.03240	−	5.28406i	0.270148	−	0.470742i
$127$			2.85284i			0.253149i	0.991957	+	0.126574i	$0.0403982\pi$
$127$			2.85284i			0.253149i	−0.991957	+	0.126574i	$0.959602\pi$
$128$	10.8729	−	3.12723i	0.961040	−	0.276411i
$129$			2.53002i			0.222755i
$130$	10.2238	+	5.86723i	0.896690	+	0.514590i
$131$	−19.5918	−	2.90617i	−1.71175	−	0.253914i	−0.782309	−	0.622891i	$-0.785958\pi$
$131$	−19.5918	−	2.90617i	−1.71175	−	0.253914i	−0.929438	+	0.368977i	$0.879708\pi$
$132$	1.80715	−	2.38074i	0.157293	−	0.207217i
$133$	0.0106840	−	0.217478i	0.000926420	−	0.0188577i
$134$	11.1816	+	8.82692i	0.965944	+	0.762530i
$135$	3.05267	−	5.71115i	0.262732	−	0.491537i
$136$	−7.36501	+	11.2115i	−0.631545	+	0.961374i
$137$	3.39975	−	11.2075i	0.290460	−	0.957518i	−0.683338	−	0.730102i	$-0.739472\pi$
$137$	3.39975	−	11.2075i	0.290460	−	0.957518i	0.973798	−	0.227416i	$-0.0730277\pi$
$138$	5.37458	+	3.44553i	0.457515	+	0.293303i
$139$	1.96744	−	1.17924i	0.166876	−	0.100021i	−0.428227	−	0.903671i	$-0.640861\pi$
$139$	1.96744	−	1.17924i	0.166876	−	0.100021i	0.595102	+	0.803650i	$0.297111\pi$
$140$	5.58898	+	0.0622964i	0.472355	+	0.00526500i
$141$	−3.54950	−	3.21708i	−0.298922	−	0.270927i
$142$	−18.0318	+	11.2782i	−1.51320	+	0.946449i
$143$	10.2302	+	2.03492i	0.855496	+	0.170169i
$144$	7.00302	−	6.69756i	0.583585	−	0.558130i
$145$	4.22408	−	0.840221i	0.350791	−	0.0697766i
$146$	1.14515	+	1.21629i	0.0947736	+	0.100661i
$147$	2.63632	−	1.24689i	0.217440	−	0.102842i
$148$	17.2116	+	14.4492i	1.41479	+	1.18772i
$149$	−11.0401	−	8.18786i	−0.904436	−	0.670776i	0.0400954	−	0.999196i	$-0.487234\pi$
$149$	−11.0401	−	8.18786i	−0.904436	−	0.670776i	−0.944532	+	0.328420i	$0.893484\pi$
$150$	−2.71863	+	0.0515807i	−0.221975	+	0.00421155i
$151$	9.46081	−	11.5280i	0.769910	−	0.938138i	−0.229471	−	0.973315i	$-0.573700\pi$
$151$	9.46081	−	11.5280i	0.769910	−	0.938138i	0.999381	+	0.0351774i	$0.0111996\pi$
$152$	0.114119	−	0.326984i	0.00925624	−	0.0265219i
$153$	−1.12614	+	11.4339i	−0.0910431	+	0.924376i
$154$	4.70479	−	1.52523i	0.379123	−	0.122906i
$155$	−8.30955	−	3.93012i	−0.667439	−	0.315675i
$156$	−7.55879	−	2.80000i	−0.605187	−	0.224179i
$157$	0.251059	+	1.00228i	0.0200367	+	0.0799910i	0.979225	−	0.202778i	$-0.0649970\pi$
$157$	0.251059	+	1.00228i	0.0200367	+	0.0799910i	−0.959188	+	0.282769i	$0.908747\pi$
$158$	−3.89229	−	3.39552i	−0.309654	−	0.270133i
$159$	−1.24009	+	2.99383i	−0.0983452	+	0.237426i
$160$	8.49867	+	2.60890i	0.671879	+	0.206251i
$161$	4.04268	+	9.75989i	0.318608	+	0.769187i
$162$	1.86587	−	5.54414i	0.146596	−	0.435588i
$163$	−5.79060	+	9.66104i	−0.453555	+	0.756711i	−0.996547	−	0.0830269i	$-0.973541\pi$
$163$	−5.79060	+	9.66104i	−0.453555	+	0.756711i	0.542992	+	0.839738i	$0.317291\pi$
$164$	3.96318	−	2.87138i	0.309472	−	0.224217i
$165$	2.21136	−	0.791235i	0.172154	−	0.0615976i
$166$	−4.91156	−	0.389831i	−0.381211	−	0.0302567i
$167$	5.73174	−	4.70392i	0.443536	−	0.364000i	−0.385958	−	0.922516i	$-0.626129\pi$
$167$	5.73174	−	4.70392i	0.443536	−	0.364000i	0.829494	+	0.558516i	$0.188629\pi$
$168$	−3.77623	+	0.590386i	−0.291343	+	0.0455492i
$169$	−1.48300	−	15.0571i	−0.114077	−	1.15824i
$170$	−9.65997	+	4.21772i	−0.740886	+	0.323484i
$171$	−0.0435243	−	0.293417i	−0.00332839	−	0.0224382i
$172$	−5.19406	+	4.16665i	−0.396043	+	0.317704i
$173$	−4.55388	+	12.7273i	−0.346225	+	0.967635i	0.634616	+	0.772828i	$0.281158\pi$
$173$	−4.55388	+	12.7273i	−0.346225	+	0.967635i	−0.980841	+	0.194808i	$0.937592\pi$
$174$	−2.75363	+	1.04460i	−0.208752	+	0.0791909i
$175$	−3.74110	−	2.49972i	−0.282800	−	0.188961i
$176$	7.86378	−	0.210766i	0.592755	−	0.0158871i
$177$	−6.29820	+	4.20832i	−0.473401	+	0.316317i
$178$	−12.1519	−	8.66007i	−0.910826	−	0.649100i
$179$	0.0318657	+	0.648640i	0.00238175	+	0.0484817i	0.999692	−	0.0248124i	$-0.00789884\pi$
$179$	0.0318657	+	0.648640i	0.00238175	+	0.0484817i	−0.997310	+	0.0732941i	$0.976649\pi$
$180$	7.48414	−	1.40216i	0.557835	−	0.104511i
$181$	−2.92310	+	11.6697i	−0.217272	+	0.867400i	0.759042	+	0.651042i	$0.225668\pi$
$181$	−2.92310	+	11.6697i	−0.217272	+	0.867400i	−0.976314	+	0.216358i	$0.930582\pi$
$182$	−7.61937	−	10.9478i	−0.564785	−	0.811502i
$183$	3.36894	−	1.80074i	0.249039	−	0.133114i
$184$	1.77774	+	16.7083i	0.131056	+	1.23175i
$185$	5.12601	+	16.8982i	0.376872	+	1.24238i
$186$	6.04861	+	1.71022i	0.443506	+	0.125400i
$187$	−6.91092	+	6.26369i	−0.505376	+	0.458047i
$188$	0.758966	−	12.5852i	0.0553533	−	0.917871i
$189$	−5.88557	+	4.36503i	−0.428112	+	0.317510i
$190$	0.215467	−	0.166229i	0.0156316	−	0.0120595i
$191$	−6.88454	+	6.88454i	−0.498148	+	0.498148i	−0.910861	−	0.412713i	$-0.864581\pi$
$191$	−6.88454	+	6.88454i	−0.498148	+	0.498148i	0.412713	+	0.910861i	$0.364581\pi$
$192$	−6.02666	−	0.797794i	−0.434937	−	0.0575758i
$193$	3.64446	+	3.64446i	0.262334	+	0.262334i	0.826002	−	0.563668i	$-0.190610\pi$
$193$	3.64446	+	3.64446i	0.262334	+	0.262334i	−0.563668	+	0.826002i	$0.690610\pi$
$194$	16.5650	+	2.13688i	1.18929	+	0.153419i
$195$	−3.77314	−	5.08748i	−0.270200	−	0.364322i
$196$	6.90156	+	3.35883i	0.492968	+	0.239916i
$197$	−5.91044	−	6.52116i	−0.421101	−	0.464613i	0.493042	−	0.870006i	$-0.335885\pi$
$197$	−5.91044	−	6.52116i	−0.421101	−	0.464613i	−0.914143	+	0.405392i	$0.867135\pi$
$198$	5.88084	−	3.28830i	0.417933	−	0.233689i
$199$	−6.33063	+	1.92038i	−0.448767	+	0.136132i	−0.506575	−	0.862196i	$-0.669089\pi$
$199$	−6.33063	+	1.92038i	−0.448767	+	0.136132i	0.0578085	+	0.998328i	$0.481589\pi$
$200$	−4.58317	−	5.49633i	−0.324079	−	0.388649i
$201$	−3.60842	−	6.75089i	−0.254519	−	0.476171i
$202$	−3.41514	+	19.0510i	−0.240288	+	1.34043i
$203$	−4.72727	−	1.18412i	−0.331789	−	0.0831089i
$204$	6.03740	−	3.93744i	0.422703	−	0.275676i
$205$	3.84101	−	0.188697i	0.268268	−	0.0131791i
$206$	−7.51326	+	1.26058i	−0.523474	+	0.0878291i
$207$	7.99543	+	11.9660i	0.555721	+	0.831695i
$208$	−6.70014	−	20.1293i	−0.464571	−	1.39572i
$209$	0.133785	−	0.200223i	0.00925408	−	0.0138497i
$210$	−2.73885	−	1.23236i	−0.188999	−	0.0850408i
$211$	25.7480	+	9.21279i	1.77257	+	0.634235i	1.00000		0.000698483i	$-0.000222334\pi$
$211$	25.7480	+	9.21279i	1.77257	+	0.634235i	0.772567	+	0.634933i	$0.218972\pi$
$212$	−8.18855	+	2.38463i	−0.562392	+	0.163777i
$213$	11.3045	−	1.67687i	0.774575	−	0.114897i
$214$	−6.68490	+	17.0464i	−0.456970	+	1.16527i
$215$	−5.20714	+	0.512858i	−0.355124	+	0.0349766i
$216$	−10.9425	+	4.01215i	−0.744544	+	0.272992i
$217$	6.59841	+	8.04019i	0.447930	+	0.545804i
$218$	−11.1068	−	13.0219i	−0.752247	−	0.881953i
$219$	−0.302408	−	0.845172i	−0.0204348	−	0.0571115i
$220$	5.26624	+	3.23678i	0.355050	+	0.218224i
$221$	21.5751	+	12.9316i	1.45130	+	0.869876i
$222$	−5.36900	−	10.8160i	−0.360344	−	0.725926i
$223$	−19.2358	+	7.96772i	−1.28812	+	0.533558i	−0.918425	−	0.395594i	$-0.870539\pi$
$223$	−19.2358	+	7.96772i	−1.28812	+	0.533558i	−0.369697	+	0.929152i	$0.620539\pi$
$224$	−7.43107	−	6.78021i	−0.496509	−	0.453022i
$225$	−5.66293	−	2.34566i	−0.377529	−	0.156377i
$226$	0.312969	+	4.59145i	0.0208184	+	0.305419i
$227$	−12.4568	+	3.12026i	−0.826786	+	0.207099i	−0.633204	−	0.773985i	$-0.718261\pi$
$227$	−12.4568	+	3.12026i	−0.826786	+	0.207099i	−0.193582	+	0.981084i	$0.562011\pi$
$228$	−0.126501	+	0.136484i	−0.00837775	+	0.00903888i
$229$	1.43591	−	3.03598i	0.0948876	−	0.200623i	−0.850963	−	0.525226i	$-0.823981\pi$
$229$	1.43591	−	3.03598i	0.0948876	−	0.200623i	0.945850	+	0.324603i	$0.105231\pi$
$230$	−6.00192	+	11.7601i	−0.395755	+	0.775439i
$231$	−2.64477	−	0.260487i	−0.174013	−	0.0171388i
$232$	−6.67944	−	3.93279i	−0.438527	−	0.258200i
$233$	22.7087	+	18.6365i	1.48770	+	1.22092i	0.916455	+	0.400138i	$0.131038\pi$
$233$	22.7087	+	18.6365i	1.48770	+	1.22092i	0.571241	+	0.820783i	$0.306462\pi$
$234$	−13.0900	−	12.6026i	−0.855723	−	0.823856i
$235$	5.90170	−	7.95752i	0.384985	−	0.519092i
$236$	−19.0120	−	5.99942i	−1.23758	−	0.390529i
$237$	1.18666	+	2.50897i	0.0770816	+	0.162975i
$238$	11.9216	+	0.359147i	0.772764	+	0.0232801i
$239$	−4.76147	−	23.9375i	−0.307994	−	1.54839i	−0.756129	−	0.654423i	$-0.772912\pi$
$239$	−4.76147	−	23.9375i	−0.307994	−	1.54839i	0.448135	−	0.893966i	$-0.352088\pi$
$240$	−3.62416	−	3.11202i	−0.233939	−	0.200880i
$241$	3.83815	−	19.2957i	0.247237	−	1.24295i	−0.635138	−	0.772399i	$-0.719057\pi$
$241$	3.83815	−	19.2957i	0.247237	−	1.24295i	0.882375	−	0.470547i	$-0.155943\pi$
$242$	−9.82902	−	2.26479i	−0.631833	−	0.145586i
$243$	−10.4126	+	11.4885i	−0.667967	+	0.736989i
$244$	9.24513	+	3.95075i	0.591859	+	0.252921i
$245$	3.10068	+	5.17318i	0.198095	+	0.330502i
$246$	−2.56901	+	0.561870i	−0.163794	+	0.0358235i
$247$	−0.621455	−	0.188516i	−0.0395423	−	0.0119950i
$248$	6.45033	+	15.2342i	0.409596	+	0.967373i
$249$	2.33484	+	1.24800i	0.147964	+	0.0790887i
$250$	−1.95607	−	16.6213i	−0.123713	−	1.05123i
$251$	9.06457	+	0.445314i	0.572151	+	0.0281080i	0.333087	−	0.942896i	$-0.391910\pi$
$251$	9.06457	+	0.445314i	0.572151	+	0.0281080i	0.239063	+	0.971004i	$0.423160\pi$
$252$	−8.33383	−	2.18651i	−0.524982	−	0.137737i
$253$	−1.71427	+	11.5567i	−0.107775	+	0.726561i
$254$	3.89431	−	1.05437i	0.244351	−	0.0661572i
$255$	5.66382			0.354682
$256$	−8.28737	−	13.6865i	−0.517961	−	0.855404i
$257$	−19.1802			−1.19643			−0.598213	−	0.801337i	$-0.704122\pi$
$257$	−19.1802			−1.19643			−0.598213	+	0.801337i	$0.704122\pi$
$258$	3.45364	−	0.935061i	0.215014	−	0.0582144i
$259$	2.93186	−	19.7650i	0.182177	−	1.22814i
$260$	4.23056	−	16.1247i	0.262368	−	1.00001i
$261$	−6.63094	−	0.325757i	−0.410445	−	0.0201639i
$262$	3.27377	+	27.8182i	0.202254	+	1.71862i
$263$	−25.9899	−	13.8919i	−1.60261	−	0.856612i	−0.998202	−	0.0599360i	$-0.980910\pi$
$263$	−25.9899	−	13.8919i	−1.60261	−	0.856612i	−0.604406	−	0.796676i	$-0.706590\pi$
$264$	−3.91777	−	1.58699i	−0.241122	−	0.0976726i
$265$	−6.41312	−	1.94540i	−0.393955	−	0.119505i
$266$	−0.300820	+	0.0657927i	−0.0184445	+	0.00403401i
$267$	4.12213	+	6.87735i	0.252270	+	0.420887i
$268$	7.91675	−	18.5260i	0.483592	−	1.13165i
$269$	6.85690	−	7.56542i	0.418072	−	0.461272i	−0.495106	−	0.868833i	$-0.664871\pi$
$269$	6.85690	−	7.56542i	0.418072	−	0.461272i	0.913178	+	0.407561i	$0.133621\pi$
$270$	−8.92432	−	2.05633i	−0.543117	−	0.125144i
$271$	−3.16392	+	15.9061i	−0.192194	+	0.966226i	0.757449	+	0.652894i	$0.226445\pi$
$271$	−3.16392	+	15.9061i	−0.192194	+	0.966226i	−0.949644	+	0.313332i	$0.898555\pi$
$272$	18.0264	+	5.91012i	1.09301	+	0.358354i
$273$	1.39823	+	7.02937i	0.0846246	+	0.425437i
$274$	−16.5554	−	0.498744i	−1.00015	−	0.0301302i
$275$	−2.12752	−	4.49826i	−0.128294	−	0.271255i
$276$	2.71700	−	8.61008i	0.163544	−	0.518266i
$277$	−3.93187	+	5.30151i	−0.236243	+	0.318537i	−0.905380	−	0.424602i	$-0.860414\pi$
$277$	−3.93187	+	5.30151i	−0.236243	+	0.318537i	0.669137	+	0.743139i	$0.266664\pi$
$278$	−2.33687	−	2.24985i	−0.140156	−	0.134937i
$279$	10.9532	+	8.98904i	0.655749	+	0.538159i
$280$	−1.98058	−	7.65235i	−0.118362	−	0.457316i
$281$	19.9902	+	1.96886i	1.19252	+	0.117453i	0.674735	−	0.738060i	$-0.264258\pi$
$281$	19.9902	+	1.96886i	1.19252	+	0.117453i	0.517782	+	0.855513i	$0.326758\pi$
$282$	−3.07968	+	6.03430i	−0.183392	+	0.359337i
$283$	−3.97866	+	8.41217i	−0.236507	+	0.500052i	−0.986979	−	0.160851i	$-0.948576\pi$
$283$	−3.97866	+	8.41217i	−0.236507	+	0.500052i	0.750472	+	0.660902i	$0.229826\pi$
$284$	22.0599	+	20.4463i	1.30901	+	1.21327i
$285$	−0.141846	+	0.0355305i	−0.00840222	+	0.00210465i
$286$	−1.00316	−	14.7170i	−0.0593184	−	0.870237i
$287$	−4.02023	−	1.66523i	−0.237307	−	0.0982957i
$288$	−11.7308	−	7.08425i	−0.691246	−	0.417443i
$289$	−5.07441	+	2.10189i	−0.298495	+	0.123641i
$290$	−2.70812	−	5.45561i	−0.159026	−	0.320364i
$291$	−7.69783	−	4.61390i	−0.451255	−	0.270472i
$292$	1.23709	−	2.01274i	0.0723951	−	0.117787i
$293$	2.28554	+	6.38766i	0.133523	+	0.373171i	0.989632	−	0.143623i	$-0.0458752\pi$
$293$	2.28554	+	6.38766i	0.133523	+	0.373171i	−0.856110	+	0.516794i	$0.827125\pi$
$294$	−2.67644	−	3.13792i	−0.156093	−	0.183007i
$295$	−9.93804	−	12.1095i	−0.578615	−	0.705044i
$296$	13.3630	−	28.8352i	0.776706	−	1.67601i
$297$	−8.06480	+	0.794313i	−0.467967	+	0.0460907i
$298$	−7.09671	+	18.0965i	−0.411101	+	1.04830i
$299$	31.1666	−	4.62313i	1.80241	−	0.267363i
$300$	1.07518	+	3.69205i	0.0620756	+	0.213160i
$301$	5.57446	+	1.99457i	0.321307	+	0.114965i
$302$	−19.2331	−	8.65402i	−1.10674	−	0.497983i
$303$	5.77790	−	8.64724i	0.331932	−	0.496771i
$304$	−0.488532	−	0.0349303i	−0.0280192	−	0.00200339i
$305$	4.38909	+	6.56874i	0.251319	+	0.376125i
$306$	16.0242	−	2.68857i	0.916045	−	0.153695i
$307$	−5.38992	+	0.264790i	−0.307619	+	0.0151124i	−0.202292	−	0.979325i	$-0.564839\pi$
$307$	−5.38992	+	0.264790i	−0.307619	+	0.0151124i	−0.105327	+	0.994438i	$0.533589\pi$
$308$	−3.82087	−	5.85865i	−0.217714	−	0.333828i
$309$	3.97088	+	0.994654i	0.225896	+	0.0565839i
$310$	−2.29378	+	12.7956i	−0.130278	+	0.726741i
$311$	6.33826	+	11.8580i	0.359410	+	0.672408i	0.995028	−	0.0995953i	$-0.0317548\pi$
$311$	6.33826	+	11.8580i	0.359410	+	0.672408i	−0.635618	+	0.772003i	$0.719255\pi$
$312$	−1.02855	+	11.3531i	−0.0582302	+	0.642742i
$313$	−21.9908	+	6.67083i	−1.24299	+	0.377058i	−0.842227	−	0.539123i	$-0.818756\pi$
$313$	−21.9908	+	6.67083i	−1.24299	+	0.377058i	−0.400765	+	0.916181i	$0.631256\pi$
$314$	1.27540	−	0.713144i	0.0719748	−	0.0402451i
$315$	−4.54659	−	5.01639i	−0.256171	−	0.282641i
$316$	−3.19658	+	6.56817i	−0.179821	+	0.369488i
$317$	6.36645	+	8.58416i	0.357575	+	0.482135i	0.944966	−	0.327169i	$-0.106095\pi$
$317$	6.36645	+	8.58416i	0.357575	+	0.482135i	−0.587390	+	0.809304i	$0.699845\pi$
$318$	4.54510	+	0.586317i	0.254877	+	0.0328790i
$319$	−3.81100	−	3.81100i	−0.213375	−	0.213375i
$320$	0.420314	−	12.5655i	0.0234963	−	0.702431i
$321$	6.95706	−	6.95706i	0.388305	−	0.388305i
$322$	11.8288	−	9.12565i	0.659192	−	0.508553i
$323$	0.466430	−	0.345928i	0.0259529	−	0.0192480i
$324$	−8.25771	−	0.497991i	−0.458762	−	0.0276662i
$325$	−9.94325	+	9.01204i	−0.551552	+	0.499898i
$326$	15.3281	+	4.33396i	0.848944	+	0.240036i
$327$	2.66963	+	8.80058i	0.147631	+	0.486673i
$328$	−5.38437	−	4.34877i	−0.297302	−	0.240121i
$329$	−9.88660	+	5.28450i	−0.545066	+	0.291344i
$330$	−1.89738	−	2.72622i	−0.104447	−	0.150073i
$331$	5.62323	−	22.4492i	0.309081	−	1.23392i	−0.594006	−	0.804461i	$-0.702454\pi$
$331$	5.62323	−	22.4492i	0.309081	−	1.23392i	0.903086	−	0.429459i	$-0.141296\pi$
$332$	1.28311	+	6.84868i	0.0704196	+	0.375870i
$333$	−1.33565	−	27.1877i	−0.0731930	−	1.48988i
$334$	−8.53954	−	6.08570i	−0.467263	−	0.332995i
$335$	13.1628	−	8.79513i	0.719163	−	0.480529i
$336$	2.20156	+	4.93661i	0.120105	+	0.269314i
$337$	7.73840	+	5.17063i	0.421537	+	0.281662i	0.748193	−	0.663481i	$-0.230922\pi$
$337$	7.73840	+	5.17063i	0.421537	+	0.281662i	−0.326656	+	0.945143i	$0.605922\pi$
$338$	−20.0059	+	7.58932i	−1.08818	+	0.412805i
$339$	0.833084	−	2.32831i	0.0452469	−	0.126457i
$340$	9.32766	+	11.6277i	0.505864	+	0.630600i
$341$	1.68784	+	11.3785i	0.0914015	+	0.616179i
$342$	−0.384448	+	0.167857i	−0.0207886	+	0.00907666i
$343$	−1.88903	−	19.1797i	−0.101998	−	1.03560i
$344$	7.60741	+	5.55030i	0.410164	+	0.299252i
$345$	5.48412	−	4.50070i	0.295255	−	0.242310i
$346$	19.0566	+	1.51252i	1.02449	+	0.0813137i
$347$	13.2337	−	4.73510i	0.710424	−	0.254194i	0.0432163	−	0.999066i	$-0.486240\pi$
$347$	13.2337	−	4.73510i	0.710424	−	0.254194i	0.667207	+	0.744872i	$0.267490\pi$
$348$	2.44365	+	3.37281i	0.130993	+	0.180802i
$349$	−3.62365	+	6.04570i	−0.193970	+	0.323619i	−0.939313	−	0.343063i	$-0.888536\pi$
$349$	−3.62365	+	6.04570i	−0.193970	+	0.323619i	0.745343	+	0.666681i	$0.232286\pi$
$350$	−2.02962	+	6.03071i	−0.108488	+	0.322355i
$351$	8.36348	+	20.1912i	0.446409	+	1.07773i
$352$	−3.19406	−	10.6567i	−0.170244	−	0.568003i
$353$	−3.17457	+	7.66410i	−0.168965	+	0.407919i	−0.985568	−	0.169282i	$-0.945855\pi$
$353$	−3.17457	+	7.66410i	−0.168965	+	0.407919i	0.816602	+	0.577201i	$0.195855\pi$
$354$	8.07237	+	7.04211i	0.429042	+	0.374284i
$355$	5.74278	+	22.9265i	0.304795	+	1.21681i
$356$	−7.33037	+	19.7888i	−0.388509	+	1.04881i
$357$	−5.79348	−	2.74011i	−0.306624	−	0.145022i
$358$	0.873660	−	0.283228i	0.0461744	−	0.0149691i
$359$	1.66601	−	16.9153i	0.0879286	−	0.892754i	−0.845496	−	0.533981i	$-0.820695\pi$
$359$	1.66601	−	16.9153i	0.0879286	−	0.892754i	0.933425	−	0.358773i	$-0.116805\pi$
$360$	−4.68008	−	9.69813i	−0.246662	−	0.511136i
$361$	12.0440	−	14.6756i	0.633893	−	0.772400i
$362$	17.0102	−	0.322736i	0.894037	−	0.0169626i
$363$	4.35327	+	3.22860i	0.228487	+	0.169458i
$364$	−12.1284	+	14.4471i	−0.635701	+	0.757234i
$365$	1.67819	−	0.793723i	0.0878403	−	0.0415454i
$366$	−3.70324	−	3.93330i	−0.193572	−	0.205597i
$367$	−31.2191	+	6.20986i	−1.62962	+	0.324152i	−0.923400	−	0.383839i	$-0.874602\pi$
$367$	−31.2191	+	6.20986i	−1.62962	+	0.324152i	−0.706222	+	0.707991i	$0.749602\pi$
$368$	22.1509	−	8.60189i	1.15469	−	0.448405i
$369$	−5.81411	−	1.15650i	−0.302670	−	0.0602049i
$370$	21.1726	−	13.2427i	1.10071	−	0.688455i
$371$	5.61877	+	5.09255i	0.291712	+	0.264392i
$372$	0.0990775	−	8.88884i	0.00513693	−	0.460865i
$373$	12.4470	−	7.46044i	0.644481	−	0.386287i	−0.154202	−	0.988039i	$-0.549281\pi$
$373$	12.4470	−	7.46044i	0.644481	−	0.386287i	0.798683	+	0.601753i	$0.205531\pi$
$374$	11.1045	+	7.11888i	0.574202	+	0.368109i
$375$	−2.61048	+	8.60561i	−0.134805	+	0.444392i
$376$	−17.4601	+	3.61529i	−0.900438	+	0.186445i
$377$	−6.85170	+	12.8186i	−0.352880	+	0.660193i
$378$	8.13379	+	6.42093i	0.418357	+	0.330257i
$379$	−1.25305	+	25.5065i	−0.0643650	+	1.31018i	0.721774	+	0.692129i	$0.243327\pi$
$379$	−1.25305	+	25.5065i	−0.0643650	+	1.31018i	−0.786139	+	0.618050i	$0.787923\pi$
$380$	−0.306547	−	0.232691i	−0.0157255	−	0.0119368i
$381$	−2.14442	−	0.318095i	−0.109862	−	0.0162965i
$382$	11.9423	+	6.85342i	0.611021	+	0.350651i
$383$			25.8761i			1.32221i	0.750294	+	0.661104i	$0.229912\pi$
$383$			25.8761i			1.32221i	−0.750294	+	0.661104i	$0.770088\pi$
$384$	1.13834	+	8.52165i	0.0580904	+	0.434868i
$385$		−	5.49613i		−	0.280109i
$386$	3.62798	−	6.32187i	0.184659	−	0.321775i
$387$	7.97829	+	1.18347i	0.405559	+	0.0601590i
$388$	−3.20522	−	23.4020i	−0.162720	−	1.18806i
$389$	−0.333087	+	6.78015i	−0.0168882	+	0.343767i	0.975450	+	0.220219i	$0.0706773\pi$
$389$	−0.333087	+	6.78015i	−0.0168882	+	0.343767i	−0.992339	+	0.123548i	$0.960573\pi$
$390$	−5.55025	+	7.03085i	−0.281048	+	0.356021i
$391$	−13.2812	+	24.8473i	−0.671658	+	1.25658i
$392$	2.03429	−	10.6625i	0.102747	−	0.538536i
$393$	4.36903	−	14.4028i	0.220388	−	0.726523i
$394$	−6.71739	+	10.4783i	−0.338417	+	0.527888i
$395$	−4.92328	+	2.95090i	−0.247717	+	0.148476i
$396$	−6.66222	−	6.81242i	−0.334789	−	0.342337i
$397$	0.357162	+	0.323713i	0.0179254	+	0.0162467i	0.680473	−	0.732774i	$-0.261775\pi$
$397$	0.357162	+	0.323713i	0.0179254	+	0.0162467i	−0.662547	+	0.749020i	$0.730525\pi$
$398$	4.96116	+	7.93199i	0.248681	+	0.397595i
$399$	0.162282	+	0.0322800i	0.00812428	+	0.00161602i
$400$	−5.80898	+	8.28770i	−0.290449	+	0.414385i
$401$	−2.40126	+	0.477639i	−0.119913	+	0.0238522i	−0.254682	−	0.967025i	$-0.581971\pi$
$401$	−2.40126	+	0.477639i	−0.119913	+	0.0238522i	0.134769	+	0.990877i	$0.456971\pi$
$402$	−7.88178	+	7.42078i	−0.393107	+	0.370115i
$403$	28.0434	−	13.2635i	1.39694	−	0.660704i
$404$	27.2681	−	2.37912i	1.35664	−	0.118366i
$405$	−5.22128	−	3.87237i	−0.259448	−	0.192419i
$406$	0.130737	+	6.89067i	0.00648838	+	0.341978i
$407$	14.0188	−	17.0819i	0.694885	−	0.846720i
$408$	−7.60621	−	6.78622i	−0.376564	−	0.335968i
$409$	3.91011	−	39.7000i	0.193342	−	1.96304i	−0.0676877	−	0.997707i	$-0.521562\pi$
$409$	3.91011	−	39.7000i	0.193342	−	1.96304i	0.261030	−	0.965331i	$-0.415938\pi$
$410$	−1.67717	−	5.17349i	−0.0828296	−	0.255501i
$411$	8.04535	+	3.80517i	0.396848	+	0.187695i
$412$	4.49759	+	9.79021i	0.221580	+	0.482329i
$413$	4.30705	+	17.1947i	0.211936	+	0.846096i
$414$	13.3794	−	15.3368i	0.657561	−	0.753762i
$415$	−2.09527	+	5.05842i	−0.102853	+	0.248308i
$416$	−25.0015	+	16.5857i	−1.22580	+	0.813179i
$417$	0.667036	+	1.61037i	0.0326649	+	0.0788601i
$418$	−0.322763	−	0.108625i	−0.0157868	−	0.00531303i
$419$	12.4063	−	20.6987i	0.606087	−	1.01120i	−0.389826	−	0.920888i	$-0.627465\pi$
$419$	12.4063	−	20.6987i	0.606087	−	1.01120i	0.995914	−	0.0903075i	$-0.0287850\pi$
$420$	−0.670005	+	4.19418i	−0.0326929	+	0.204655i
$421$	−22.4235	+	8.02326i	−1.09286	+	0.391030i	−0.820779	−	0.571246i	$-0.806460\pi$
$421$	−22.4235	+	8.02326i	−1.09286	+	0.391030i	−0.272076	+	0.962276i	$0.587710\pi$
$422$	3.05993	−	38.5527i	0.148955	−	1.87672i
$423$	−11.8053	+	9.68834i	−0.573992	+	0.471063i
$424$	6.28157	+	10.2966i	0.305060	+	0.500046i
$425$	−1.17618	−	11.9420i	−0.0570533	−	0.579272i
$426$	−6.46705	−	14.8117i	−0.313330	−	0.717629i
$427$	−1.31167	−	8.84253i	−0.0634759	−	0.427920i
$428$	25.7401	+	2.82519i	1.24420	+	0.136561i
$429$	−2.67030	+	7.46298i	−0.128923	+	0.360316i
$430$	2.62458	+	6.91854i	0.126568	+	0.333642i
$431$	8.55894	+	5.71890i	0.412270	+	0.275470i	0.744361	−	0.667777i	$-0.232754\pi$
$431$	8.55894	+	5.71890i	0.412270	+	0.275470i	−0.332091	+	0.943247i	$0.607754\pi$
$432$	9.52107	+	13.4544i	0.458082	+	0.647326i
$433$	24.4236	−	16.3193i	1.17372	−	0.784257i	0.193296	−	0.981140i	$-0.438082\pi$
$433$	24.4236	−	16.3193i	1.17372	−	0.784257i	0.980427	+	0.196884i	$0.0630821\pi$
$434$	8.53670	−	11.9788i	0.409775	−	0.575002i
$435$	0.160588	+	3.26884i	0.00769959	+	0.156729i
$436$	−13.6708	+	19.9742i	−0.654713	+	0.956592i
$437$	0.176743	−	0.705598i	0.00845476	−	0.0337533i
$438$	−1.04195	+	0.725171i	−0.0497863	+	0.0346500i
$439$	0.291767	−	0.155952i	0.0139253	−	0.00744320i	−0.464419	−	0.885615i	$-0.653737\pi$
$439$	0.291767	−	0.155952i	0.0139253	−	0.00744320i	0.478345	+	0.878172i	$0.341237\pi$
$440$	2.47209	−	8.38504i	0.117852	−	0.399741i
$441$	−2.69881	−	8.89678i	−0.128515	−	0.423656i
$442$	9.67865	−	34.2309i	0.460366	−	1.62820i
$443$	6.96994	−	6.31719i	0.331152	−	0.300139i	−0.489001	−	0.872283i	$-0.662638\pi$
$443$	6.96994	−	6.31719i	0.331152	−	0.300139i	0.820153	+	0.572145i	$0.193888\pi$
$444$	−12.7803	+	11.3265i	−0.606526	+	0.537533i
$445$	−13.3190	+	9.87804i	−0.631381	+	0.468264i
$446$	17.9858	+	23.3133i	0.851650	+	1.10392i
$447$	7.38563	−	7.38563i	0.349328	−	0.349328i
$448$	−6.50901	+	12.6498i	−0.307522	+	0.597646i
$449$	1.59529	+	1.59529i	0.0752866	+	0.0752866i	0.743747	−	0.668461i	$-0.233047\pi$
$449$	1.59529	+	1.59529i	0.0752866	+	0.0752866i	−0.668461	+	0.743747i	$0.733047\pi$
$450$	−1.10904	+	8.59720i	−0.0522805	+	0.405276i
$451$	−2.86676	−	3.86538i	−0.134991	−	0.182014i
$452$	6.15197	−	2.12417i	0.289364	−	0.0999124i
$453$	7.61050	+	8.39689i	0.357572	+	0.394520i
$454$	8.86324	+	15.8511i	0.415972	+	0.743931i
$455$	−14.1840	+	4.30268i	−0.664957	+	0.201713i
$456$	0.233063	+	0.122240i	0.0109142	+	0.00572440i
$457$	−16.4232	−	30.7257i	−0.768246	−	1.43729i	−0.895334	−	0.445395i	$-0.853063\pi$
$457$	−16.4232	−	30.7257i	−0.768246	−	1.43729i	0.127088	−	0.991891i	$-0.459437\pi$
$458$	−4.67500	−	0.838054i	−0.218449	−	0.0391597i
$459$	−18.9569	−	4.74845i	−0.884832	−	0.221639i
$460$	18.2716	+	3.84663i	0.851916	+	0.179350i
$461$	23.2635	−	1.14286i	1.08349	−	0.0532283i	0.500521	−	0.865725i	$-0.333142\pi$
$461$	23.2635	−	1.14286i	1.08349	−	0.0532283i	0.582966	+	0.812496i	$0.301892\pi$
$462$	0.621892	+	3.70656i	0.0289330	+	0.172445i
$463$	−22.6385	−	33.8809i	−1.05210	−	1.57458i	−0.793476	−	0.608602i	$-0.791731\pi$
$463$	−22.6385	−	33.8809i	−1.05210	−	1.57458i	−0.258625	−	0.965978i	$-0.583269\pi$
$464$	−2.89988	+	10.5714i	−0.134624	+	0.490765i
$465$	3.88072	−	5.80791i	0.179964	−	0.269335i
$466$	17.0473	−	37.8867i	0.789699	−	1.75507i
$467$	−13.0423	−	4.66662i	−0.603527	−	0.215945i	0.0173553	−	0.999849i	$-0.494475\pi$
$467$	−13.0423	−	4.66662i	−0.603527	−	0.215945i	−0.620882	+	0.783904i	$0.713225\pi$
$468$	−12.3654	+	22.5265i	−0.571593	+	1.04129i
$469$	−17.7192	+	2.62839i	−0.818197	+	0.121368i
$470$	−13.0437	−	5.11521i	−0.601663	−	0.235947i
$471$	−0.781391	+	0.0769603i	−0.0360046	+	0.00354614i
$472$	−1.16302	+	28.1699i	−0.0535323	+	1.29663i
$473$	4.15384	+	5.06147i	0.190994	+	0.232727i
$474$	2.98634	−	2.54715i	0.137167	−	0.116994i
$475$	0.104372	+	0.291699i	0.00478889	+	0.0133841i
$476$	−3.91582	−	16.4065i	−0.179481	−	0.751992i
$477$	8.86084	+	5.31098i	0.405710	+	0.243173i
$478$	−30.9165	+	15.3467i	−1.41409	+	0.701942i
$479$	−31.6007	+	13.0894i	−1.44387	+	0.598071i	−0.960733	−	0.277473i	$-0.910503\pi$
$479$	−31.6007	+	13.0894i	−1.44387	+	0.598071i	−0.483138	+	0.875544i	$0.660503\pi$
$480$	−2.90867	+	6.09739i	−0.132762	+	0.278306i
$481$	−55.0585	−	22.8060i	−2.51045	−	1.03986i
$482$	−27.7584	+	1.89211i	−1.26436	+	0.0861833i
$483$	−7.78708	+	1.95056i	−0.354324	+	0.0887536i
$484$	0.541090	+	14.2543i	0.0245950	+	0.647923i
$485$	7.93565	−	16.7785i	0.360339	−	0.761873i
$486$	19.5309	+	9.96785i	0.885941	+	0.452151i
$487$	18.7051	+	1.84229i	0.847607	+	0.0834820i	0.512489	−	0.858694i	$-0.328724\pi$
$487$	18.7051	+	1.84229i	0.847607	+	0.0834820i	0.335118	+	0.942176i	$0.391224\pi$
$488$	1.97615	−	14.0804i	0.0894561	−	0.637388i
$489$	−6.61635	−	5.42990i	−0.299202	−	0.245548i
$490$	5.91576	−	6.14458i	0.267247	−	0.277584i
$491$	6.14121	−	8.28046i	0.277149	−	0.373692i	−0.642598	−	0.766203i	$-0.722144\pi$
$491$	6.14121	−	8.28046i	0.277149	−	0.373692i	0.919747	+	0.392511i	$0.128394\pi$
$492$	1.71646	+	3.29920i	0.0773840	+	0.148740i
$493$	−5.55696	−	11.7492i	−0.250273	−	0.529158i
$494$	−0.0276554	+	0.918001i	−0.00124428	+	0.0413028i
$495$	−1.46072	−	7.34352i	−0.0656544	−	0.330067i
$496$	18.4117	−	14.4355i	0.826711	−	0.648173i
$497$	5.21740	−	26.2296i	0.234032	−	1.17656i
$498$	0.840673	−	3.64846i	0.0376714	−	0.163491i
$499$	27.5646	−	30.4128i	1.23396	−	1.36147i	0.324385	−	0.945925i	$-0.394843\pi$
$499$	27.5646	−	30.4128i	1.23396	−	1.36147i	0.909575	−	0.415540i	$-0.136407\pi$
$500$	−21.9663	+	8.81320i	−0.982362	+	0.394138i
$501$	2.89675	+	4.83293i	0.129417	+	0.215919i
$502$	−2.74227	−	12.5383i	−0.122393	−	0.559613i
$503$	6.00866	+	1.82271i	0.267913	+	0.0812705i	0.421383	−	0.906883i	$-0.361545\pi$
$503$	6.00866	+	1.82271i	0.267913	+	0.0812705i	−0.153470	+	0.988153i	$0.549045\pi$
$504$	0.0953439	+	12.1843i	0.00424695	+	0.542733i
$505$	18.9685	+	10.1389i	0.844087	+	0.451174i
$506$	16.4092	−	1.93110i	0.729477	−	0.0858480i
$507$	11.4835	+	0.564149i	0.510001	+	0.0250547i
$508$	−2.87858	−	4.92631i	−0.127716	−	0.218570i
$509$	4.62865	−	31.2038i	0.205161	−	1.38309i	−0.604695	−	0.796457i	$-0.706705\pi$
$509$	4.62865	−	31.2038i	0.205161	−	1.38309i	0.809856	−	0.586628i	$-0.199545\pi$
$510$	−2.09327	−	7.73149i	−0.0926918	−	0.342356i
$511$	−2.10060			−0.0929252
$512$	−15.6200	+	16.3712i	−0.690314	+	0.723510i
$513$	0.504548			0.0222763
$514$	7.08874	+	26.1822i	0.312671	+	1.15485i
$515$	−1.24221	+	8.37427i	−0.0547381	+	0.369015i
$516$	−2.55284	−	4.36886i	−0.112383	−	0.192328i
$517$	−12.3829	−	0.608333i	−0.544600	−	0.0267545i
$518$	−28.0641	+	3.30270i	−1.23306	+	0.145112i
$519$	−9.05906	−	4.84217i	−0.397648	−	0.212548i
$520$	−23.5748	+	0.184476i	−1.03382	+	0.00808979i
$521$	−37.4796	−	11.3693i	−1.64201	−	0.498099i	−0.671877	−	0.740663i	$-0.734512\pi$
$521$	−37.4796	−	11.3693i	−1.64201	−	0.498099i	−0.970135	+	0.242564i	$0.922012\pi$
$522$	2.00603	+	9.17206i	0.0878015	+	0.401450i
$523$	11.0551	+	18.4444i	0.483407	+	0.806516i	0.998725	−	0.0504833i	$-0.0160762\pi$
$523$	11.0551	+	18.4444i	0.483407	+	0.806516i	−0.515318	+	0.856999i	$0.672326\pi$
$524$	36.7638	−	14.7502i	1.60603	−	0.644365i
$525$	2.29613	−	2.53338i	0.100211	−	0.110566i
$526$	−9.35783	+	40.6123i	−0.408021	+	1.77078i
$527$	−5.41175	+	27.2067i	−0.235739	+	1.18514i
$528$	−0.718392	+	5.93455i	−0.0312640	+	0.258268i
$529$	2.39783	+	12.0547i	0.104254	+	0.524118i
$530$	−0.285391	+	9.47332i	−0.0123966	+	0.411495i
$531$	10.3246	+	21.8296i	0.448051	+	0.947324i
$532$	0.200991	+	0.386323i	0.00871405	+	0.0167492i
$533$	−7.73124	+	10.4244i	−0.334877	+	0.451530i
$534$	7.86455	−	8.16876i	0.340333	−	0.353497i
$535$	15.7289	+	12.9084i	0.680019	+	0.558077i
$536$	−28.2151	−	3.95993i	−1.21871	−	0.171043i
$537$	−0.491123	−	0.0483714i	−0.0211935	−	0.00208738i
$538$	−12.8615	−	6.56404i	−0.554500	−	0.282996i
$539$	3.22698	−	6.82287i	0.138996	−	0.293882i
$540$	0.491286	+	12.9423i	0.0211416	+	0.556947i
$541$	−15.6792	+	3.92744i	−0.674103	+	0.168854i	−0.564892	−	0.825165i	$-0.691082\pi$
$541$	−15.6792	+	3.92744i	−0.674103	+	0.168854i	−0.109211	+	0.994019i	$0.534832\pi$
$542$	22.8822	−	1.55973i	0.982875	−	0.0669961i
$543$	−8.44593	−	3.49842i	−0.362449	−	0.150131i
$544$	1.40538	−	26.7915i	0.0602553	−	1.14868i
$545$	−17.5717	+	7.27844i	−0.752689	+	0.311774i
$546$	9.07879	−	4.50664i	0.388536	−	0.192866i
$547$	−5.70256	−	3.41798i	−0.243824	−	0.146142i	0.386971	−	0.922092i	$-0.373521\pi$
$547$	−5.70256	−	3.41798i	−0.243824	−	0.146142i	−0.630795	+	0.775949i	$0.717271\pi$
$548$	5.43786	+	22.7836i	0.232294	+	0.973267i
$549$	−4.10265	−	11.4661i	−0.175097	−	0.489363i
$550$	−5.35412	+	4.56670i	−0.228300	+	0.194725i
$551$	0.212875	+	0.259389i	0.00906879	+	0.0110504i
$552$	−12.7575	−	0.526704i	−0.542995	−	0.0224180i
$553$	6.46362	−	0.636611i	0.274861	−	0.0270714i
$554$	8.69009	+	3.40789i	0.369206	+	0.144787i
$555$	−13.2736	+	1.96895i	−0.563432	+	0.0835773i
$556$	−2.20752	+	4.02150i	−0.0936195	+	0.170550i
$557$	−21.5599	−	7.71425i	−0.913522	−	0.326863i	−0.162168	−	0.986763i	$-0.551849\pi$
$557$	−21.5599	−	7.71425i	−0.913522	−	0.326863i	−0.751354	+	0.659900i	$0.770599\pi$
$558$	8.22248	−	18.2740i	0.348085	−	0.773602i
$559$	9.81043	−	14.6823i	0.414937	−	0.620997i
$560$	−9.71397	+	5.53183i	−0.410490	+	0.233762i
$561$	−3.93772	−	5.89321i	−0.166251	−	0.248811i
$562$	−4.70050	−	28.0156i	−0.198279	−	1.18177i
$563$	−3.92225	+	0.192688i	−0.165303	+	0.00812083i	−0.131551	−	0.991309i	$-0.541996\pi$
$563$	−3.92225	+	0.192688i	−0.165303	+	0.00812083i	−0.0337522	+	0.999430i	$0.510746\pi$
$564$	9.37543	+	1.97377i	0.394777	+	0.0831105i
$565$	4.96088	+	1.24264i	0.208706	+	0.0522781i
$566$	12.9536	+	2.32210i	0.544482	+	0.0976053i
$567$	3.46739	+	6.48704i	0.145617	+	0.272430i
$568$	19.7576	−	37.6699i	0.829009	−	1.58059i
$569$	−7.14103	+	2.16621i	−0.299367	+	0.0908121i	−0.436395	−	0.899755i	$-0.643745\pi$
$569$	−7.14103	+	2.16621i	−0.299367	+	0.0908121i	0.137028	+	0.990567i	$0.456245\pi$
$570$	0.100926	+	0.180497i	0.00422732	+	0.00756020i
$571$	26.3383	+	29.0599i	1.10222	+	1.21612i	0.974519	+	0.224305i	$0.0720113\pi$
$571$	26.3383	+	29.0599i	1.10222	+	1.21612i	0.127706	+	0.991812i	$0.459239\pi$
$572$	−19.7190	+	6.80862i	−0.824492	+	0.284683i
$573$	−4.40734	−	5.94261i	−0.184119	−	0.248256i
$574$	−0.787329	+	6.10333i	−0.0328625	+	0.254748i
$575$	−10.6285	−	10.6285i	−0.443237	−	0.443237i
$576$	−5.33490	+	18.6316i	−0.222288	+	0.776317i
$577$	30.0286	−	30.0286i	1.25011	−	1.25011i	0.294435	−	0.955671i	$-0.404868\pi$
$577$	30.0286	−	30.0286i	1.25011	−	1.25011i	0.955671	−	0.294435i	$-0.0951316\pi$
$578$	4.74466	+	6.15008i	0.197352	+	0.255809i
$579$	−3.14583	+	2.33311i	−0.130736	+	0.0969605i
$580$	−6.44638	+	5.71309i	−0.267671	+	0.237223i
$581$	4.59046	−	4.16055i	0.190444	−	0.172609i
$582$	−3.45326	+	12.2133i	−0.143142	+	0.506257i
$583$	2.43447	+	8.02537i	0.100825	+	0.332377i
$584$	−3.20473	−	0.944825i	−0.132613	−	0.0390971i
$585$	−17.8081	+	9.51863i	−0.736275	+	0.393547i
$586$	7.87488	−	5.48072i	0.325308	−	0.226406i
$587$	−6.95761	+	27.7763i	−0.287171	+	1.14645i	0.638957	+	0.769243i	$0.279366\pi$
$587$	−6.95761	+	27.7763i	−0.287171	+	1.14645i	−0.926128	+	0.377209i	$0.876884\pi$
$588$	−3.29429	+	4.81325i	−0.135854	+	0.198495i
$589$	−0.0351413	−	0.715318i	−0.00144797	−	0.0294742i
$590$	−12.8573	+	18.0416i	−0.529328	+	0.742761i
$591$	5.56085	−	3.71564i	0.228743	−	0.152841i
$592$	−44.3008	−	7.58418i	−1.82075	−	0.311708i
$593$	18.3172	+	12.2392i	0.752197	+	0.502602i	0.871584	−	0.490246i	$-0.163093\pi$
$593$	18.3172	+	12.2392i	0.752197	+	0.502602i	−0.119387	+	0.992848i	$0.538093\pi$
$594$	4.06493	+	10.7154i	0.166786	+	0.439659i
$595$	4.46515	−	12.4793i	0.183053	−	0.511600i
$596$	27.3258	+	2.99923i	1.11931	+	0.122853i
$597$	−0.737635	−	4.97273i	−0.0301894	−	0.203520i
$598$	−17.8297	−	40.8359i	−0.729110	−	1.66990i
$599$	−0.910106	−	9.24046i	−0.0371859	−	0.377555i	−0.995709	−	0.0925400i	$-0.970501\pi$
$599$	−0.910106	−	9.24046i	−0.0371859	−	0.377555i	0.958523	−	0.285015i	$-0.0919986\pi$
$600$	4.64251	−	2.83223i	0.189530	−	0.115625i
$601$	−15.4478	+	12.6776i	−0.630127	+	0.517132i	−0.894372	−	0.447324i	$-0.852377\pi$
$601$	−15.4478	+	12.6776i	−0.630127	+	0.517132i	0.264245	+	0.964456i	$0.414877\pi$
$602$	0.662476	−	8.34668i	0.0270005	−	0.340185i
$603$	−22.9765	+	8.22113i	−0.935677	+	0.334790i
$604$	−4.70499	+	29.4529i	−0.191444	+	1.19842i
$605$	−5.76248	+	9.61412i	−0.234278	+	0.390870i
$606$	−13.9395	−	4.69131i	−0.566253	−	0.190571i
$607$	6.67636	+	16.1182i	0.270985	+	0.654216i	0.999526	−	0.0307864i	$-0.00980118\pi$
$607$	6.67636	+	16.1182i	0.270985	+	0.654216i	−0.728541	+	0.685002i	$0.759801\pi$
$608$	0.132873	+	0.679788i	0.00538871	+	0.0275690i
$609$	1.41718	−	3.42136i	0.0574269	−	0.138641i
$610$	7.34461	−	8.41912i	0.297375	−	0.340880i
$611$	8.12409	+	32.4332i	0.328665	+	1.31211i
$612$	−9.59242	−	20.8805i	−0.387751	−	0.844043i
$613$	29.5568	+	13.9793i	1.19379	+	0.564619i	0.917993	−	0.396598i	$-0.129809\pi$
$613$	29.5568	+	13.9793i	1.19379	+	0.564619i	0.275794	+	0.961217i	$0.411059\pi$
$614$	2.35350	+	7.25973i	0.0949796	+	0.292979i
$615$	−0.286438	+	2.90825i	−0.0115503	+	0.117272i
$616$	−6.58530	+	7.38102i	−0.265329	+	0.297390i
$617$	−0.00295367	+	0.00359905i	−0.000118910	+	0.000144892i	−0.773070	−	0.634321i	$-0.781280\pi$
$617$	−0.00295367	+	0.00359905i	−0.000118910	+	0.000144892i	0.772951	+	0.634466i	$0.218780\pi$
$618$	−0.109818	−	5.78813i	−0.00441755	−	0.232833i
$619$	−31.9682	−	23.7092i	−1.28491	−	0.952953i	−0.284925	−	0.958550i	$-0.591969\pi$
$619$	−31.9682	−	23.7092i	−1.28491	−	0.952953i	−0.999984	+	0.00559651i	$0.998219\pi$
$620$	18.3146	−	1.59794i	0.735532	−	0.0641747i
$621$	−22.1287	+	10.4661i	−0.887996	+	0.419991i
$622$	13.8445	−	13.0347i	0.555113	−	0.522645i
$623$	18.4028	−	3.66055i	0.737294	−	0.146657i
$624$	15.8779	−	2.79192i	0.635623	−	0.111766i
$625$	−5.83286	−	1.16023i	−0.233315	−	0.0464091i
$626$	17.2336	+	27.5534i	0.688794	+	1.10126i
$627$	0.135586	+	0.122888i	0.00541480	+	0.00490769i
$628$	−1.44486	−	1.47743i	−0.0576562	−	0.0589560i
$629$	45.7081	−	27.3964i	1.82250	−	1.09236i
$630$	−5.16734	+	8.06039i	−0.205872	+	0.321133i
$631$	−11.8515	+	39.0691i	−0.471800	+	1.55532i	0.321758	+	0.946822i	$0.395726\pi$
$631$	−11.8515	+	39.0691i	−0.471800	+	1.55532i	−0.793558	+	0.608495i	$0.791774\pi$
$632$	10.1474	+	1.93603i	0.403642	+	0.0770109i
$633$	−9.79600	+	18.3270i	−0.389356	+	0.728434i
$634$	9.36499	−	11.8632i	0.371931	−	0.471149i
$635$	0.219991	−	4.47801i	0.00873006	−	0.177704i
$636$	−0.879449	−	6.42106i	−0.0348724	−	0.254611i
$637$	−20.1342	−	2.98663i	−0.797747	−	0.118335i
$638$	−3.79377	+	6.61076i	−0.150197	+	0.261723i
$639$		−	36.4328i		−	1.44126i
$640$	−17.3080	+	4.07028i	−0.684160	+	0.160892i
$641$			23.8992i			0.943961i	0.881609	+	0.471981i	$0.156461\pi$
$641$			23.8992i			0.943961i	−0.881609	+	0.471981i	$0.843539\pi$
$642$	−12.0681	−	6.92560i	−0.476289	−	0.273332i
$643$	48.8015	+	7.23901i	1.92454	+	0.285479i	0.996261	−	0.0864001i	$-0.0275363\pi$
$643$	48.8015	+	7.23901i	1.92454	+	0.285479i	0.928281	+	0.371879i	$0.121286\pi$
$644$	−16.8289	−	12.7743i	−0.663151	−	0.503379i
$645$	0.195097	−	3.97129i	0.00768193	−	0.156369i
$646$	−0.644602	−	0.508858i	−0.0253615	−	0.0200207i
$647$	16.6301	−	31.1128i	0.653797	−	1.22317i	−0.308514	−	0.951220i	$-0.599832\pi$
$647$	16.6301	−	31.1128i	0.653797	−	1.22317i	0.962312	−	0.271949i	$-0.0876683\pi$
$648$	2.37215	+	11.4564i	0.0931870	+	0.450049i
$649$	−5.69065	+	18.7596i	−0.223378	+	0.736378i
$650$	15.9769	+	10.2425i	0.626667	+	0.401742i
$651$	−6.77938	+	4.06340i	−0.265705	+	0.159257i
$652$	0.251077	−	22.5256i	0.00983293	−	0.882172i
$653$	2.75900	+	2.50061i	0.107968	+	0.0978564i	0.723758	−	0.690054i	$-0.242413\pi$
$653$	2.75900	+	2.50061i	0.107968	+	0.0978564i	−0.615790	+	0.787910i	$0.711163\pi$
$654$	11.0267	−	6.89680i	0.431178	−	0.269686i
$655$	30.5286	+	6.07251i	1.19285	+	0.237273i
$656$	−3.94637	+	8.95727i	−0.154080	+	0.349723i
$657$	−2.80667	+	0.558281i	−0.109499	+	0.0217806i
$658$	10.8676	+	11.5428i	0.423665	+	0.449984i
$659$	−27.4827	+	12.9983i	−1.07057	+	0.506344i	−0.879826	−	0.475295i	$-0.842341\pi$
$659$	−27.4827	+	12.9983i	−1.07057	+	0.506344i	−0.190747	+	0.981639i	$0.561091\pi$
$660$	−3.02022	+	3.59762i	−0.117562	+	0.140037i
$661$	9.13107	+	6.77206i	0.355157	+	0.263403i	0.758537	−	0.651630i	$-0.225915\pi$
$661$	9.13107	+	6.77206i	0.355157	+	0.263403i	−0.403380	+	0.915033i	$0.632165\pi$
$662$	−32.7229	+	0.620854i	−1.27181	+	0.0241302i
$663$	−12.1261	+	14.7757i	−0.470939	+	0.573841i
$664$	8.87468	−	4.28271i	0.344405	−	0.166201i
$665$	−0.0335407	+	0.340544i	−0.00130065	+	0.0132057i
$666$	−36.6194	+	11.8715i	−1.41897	+	0.460010i
$667$	−14.7171	−	6.96065i	−0.569847	−	0.269518i
$668$	−5.15128	+	13.9062i	−0.199309	+	0.538048i
$669$	−3.84436	−	15.3476i	−0.148632	−	0.593371i
$670$	−16.8707	−	14.7176i	−0.651774	−	0.568590i
$671$	3.78331	−	9.13371i	0.146053	−	0.352603i
$672$	5.92512	−	4.82978i	0.228567	−	0.186313i
$673$	−0.284177	−	0.686065i	−0.0109542	−	0.0264458i	0.918308	−	0.395867i	$-0.129556\pi$
$673$	−0.284177	−	0.686065i	−0.0109542	−	0.0264458i	−0.929262	+	0.369421i	$0.879556\pi$
$674$	4.19824	−	12.4744i	0.161710	−	0.480497i
$675$	5.36002	−	8.94265i	0.206307	−	0.344203i
$676$	17.7539	+	24.5045i	0.682840	+	0.942479i
$677$	−15.8721	+	5.67913i	−0.610014	+	0.218267i	−0.623731	−	0.781639i	$-0.714384\pi$
$677$	−15.8721	+	5.67913i	−0.610014	+	0.218267i	0.0137165	+	0.999906i	$0.495634\pi$
$678$	−3.48620	−	0.276700i	−0.133887	−	0.0106266i
$679$	−16.2346	+	13.3234i	−0.623028	+	0.511306i
$680$	12.4252	−	17.0303i	0.476484	−	0.653083i
$681$	−0.956493	−	9.71143i	−0.0366529	−	0.372143i
$682$	14.9086	−	6.50935i	0.570878	−	0.249256i
$683$	−7.18256	−	48.4209i	−0.274833	−	1.85277i	−0.484228	−	0.874942i	$-0.660899\pi$
$683$	−7.18256	−	48.4209i	−0.274833	−	1.85277i	0.209395	−	0.977831i	$-0.432851\pi$
$684$	0.371223	+	0.462759i	0.0141941	+	0.0176940i
$685$	−6.20072	+	17.3298i	−0.236917	+	0.662139i
$686$	−25.4833	+	9.66721i	−0.972959	+	0.369096i
$687$	2.12198	+	1.41786i	0.0809585	+	0.0540947i
$688$	4.76492	−	12.4359i	0.181661	−	0.474115i
$689$	18.8055	−	12.5654i	0.716432	−	0.478704i
$690$	−8.17062	−	5.82279i	−0.311050	−	0.221670i
$691$	0.512858	+	10.4395i	0.0195100	+	0.397136i	0.988613	+	0.150480i	$0.0480819\pi$
$691$	0.512858	+	10.4395i	0.0195100	+	0.397136i	−0.969103	+	0.246656i	$0.920668\pi$
$692$	−4.97838	−	26.5725i	−0.189250	−	1.01014i
$693$	−2.05858	+	8.21832i	−0.0781991	+	0.312188i
$694$	−11.3547	−	16.3149i	−0.431020	−	0.619304i
$695$	−3.17916	+	1.69929i	−0.120592	+	0.0644579i
$696$	3.70097	−	4.58229i	0.140285	−	0.173691i
$697$	−3.36884	−	11.1056i	−0.127604	−	0.420654i
$698$	9.59203	+	2.71211i	0.363064	+	0.102655i
$699$	−16.5408	+	14.9917i	−0.625629	+	0.567037i
$700$	8.98243	+	0.541696i	0.339504	+	0.0204742i
$701$	−29.5446	+	21.9118i	−1.11589	+	0.827597i	−0.986462	−	0.163992i	$-0.947563\pi$
$701$	−29.5446	+	21.9118i	−1.11589	+	0.827597i	−0.129424	+	0.991589i	$0.541313\pi$
$702$	24.4713	−	18.8791i	0.923610	−	0.712546i
$703$	−0.972857	+	0.972857i	−0.0366920	+	0.0366920i
$704$	−13.3666	+	8.29868i	−0.503772	+	0.312768i
$705$	5.32346	+	5.32346i	0.200493	+	0.200493i
$706$	11.6353	+	1.50095i	0.437900	+	0.0564890i
$707$	−14.4976	−	19.5478i	−0.545240	−	0.735171i
$708$	6.62951	−	13.6220i	0.249152	−	0.511946i
$709$	20.8856	+	23.0437i	0.784374	+	0.865423i	0.993659	−	0.112431i	$-0.0358638\pi$
$709$	20.8856	+	23.0437i	0.784374	+	0.865423i	−0.209286	+	0.977855i	$0.567114\pi$
$710$	29.1737	−	16.3126i	1.09487	−	0.612201i
$711$	8.46701	−	2.56844i	0.317538	−	0.0963241i
$712$	29.7223	+	2.69273i	1.11389	+	0.100914i
$713$	16.3795	+	30.6439i	0.613417	+	1.14762i
$714$	−1.59924	+	8.92120i	−0.0598500	+	0.333867i
$715$	−15.9012	−	3.98304i	−0.594670	−	0.148957i
$716$	−0.709518	−	1.08793i	−0.0265159	−	0.0406577i
$717$	18.5243	−	0.910038i	0.691801	−	0.0339860i
$718$	−23.7062	+	3.97746i	−0.884707	+	0.148437i
$719$	19.5254	+	29.2219i	0.728176	+	1.08979i	0.992124	+	0.125256i	$0.0399751\pi$
$719$	19.5254	+	29.2219i	0.728176	+	1.08979i	−0.263948	+	0.964537i	$0.585025\pi$
$720$	−11.5089	+	9.97292i	−0.428911	+	0.371669i
$721$	5.32205	−	7.96502i	0.198204	−	0.296633i
$722$	−24.4845	−	11.0169i	−0.911218	−	0.410006i
$723$	14.0762	+	5.03656i	0.523501	+	0.187312i
$724$	−6.72731	−	23.1008i	−0.250019	−	0.858534i
$725$	6.85890	−	1.01742i	0.254733	−	0.0377861i
$726$	2.79835	−	7.13575i	0.103856	−	0.264833i
$727$	−18.7995	+	1.85159i	−0.697236	+	0.0686718i	−0.440425	−	0.897790i	$-0.645172\pi$
$727$	−18.7995	+	1.85159i	−0.697236	+	0.0686718i	−0.256812	+	0.966461i	$0.582672\pi$
$728$	24.2037	+	11.2166i	0.897050	+	0.415715i
$729$	0.397563	+	0.484432i	0.0147246	+	0.0179419i
$730$	−1.70372	−	1.99749i	−0.0630575	−	0.0739302i
$731$	5.31950	+	14.8670i	0.196749	+	0.549876i
$732$	−4.00054	+	6.50887i	−0.147864	+	0.240575i
$733$	14.0298	+	8.40915i	0.518203	+	0.310599i	0.749187	−	0.662359i	$-0.230444\pi$
$733$	14.0298	+	8.40915i	0.518203	+	0.310599i	−0.230984	+	0.972958i	$0.574194\pi$
$734$	20.0150	+	40.3210i	0.738768	+	1.48828i
$735$	−4.23430	+	1.75391i	−0.156185	+	0.0646938i
$736$	−19.9288	−	27.0583i	−0.734587	−	0.997381i
$737$	−18.3027	−	7.58122i	−0.674188	−	0.279258i
$738$	0.570124	+	8.36407i	0.0209865	+	0.307886i
$739$	−4.40673	+	1.10383i	−0.162104	+	0.0406050i	−0.323183	−	0.946337i	$-0.604753\pi$
$739$	−4.40673	+	1.10383i	−0.162104	+	0.0406050i	0.161078	+	0.986942i	$0.448503\pi$
$740$	−25.9023	−	24.0077i	−0.952187	−	0.882541i
$741$	0.210997	−	0.446116i	0.00775117	−	0.0163885i
$742$	4.87505	−	9.55213i	0.178969	−	0.350670i
$743$	34.2075	+	3.36915i	1.25495	+	0.123602i	0.703555	−	0.710641i	$-0.251595\pi$
$743$	34.2075	+	3.36915i	1.25495	+	0.123602i	0.551397	+	0.834243i	$0.314095\pi$
$744$	−12.1705	+	3.14995i	−0.446191	+	0.115483i
$745$	16.6978	+	13.7036i	0.611761	+	0.502059i
$746$	−14.7842	−	14.2337i	−0.541289	−	0.521132i
$747$	5.02767	−	6.77903i	0.183953	−	0.248032i
$748$	5.61365	−	17.7895i	0.205255	−	0.650448i
$749$	−9.84400	−	20.8134i	−0.359692	−	0.760505i
$750$	12.7120	+	0.382959i	0.464177	+	0.0139837i
$751$	−7.56038	−	38.0086i	−0.275882	−	1.38695i	−0.831505	−	0.555518i	$-0.812520\pi$
$751$	−7.56038	−	38.0086i	−0.275882	−	1.38695i	0.555623	−	0.831435i	$-0.312480\pi$
$752$	11.3882	+	22.4981i	0.415284	+	0.820421i
$753$	−1.34544	+	6.76400i	−0.0490307	+	0.246494i
$754$	20.0306	+	4.61542i	0.729470	+	0.168084i
$755$	−15.7393	+	17.3656i	−0.572812	+	0.632000i
$756$	5.75885	−	13.4763i	0.209447	−	0.490127i
$757$	18.6736	+	31.1550i	0.678704	+	1.13235i	0.983669	+	0.179986i	$0.0576052\pi$
$757$	18.6736	+	31.1550i	0.678704	+	1.13235i	−0.304965	+	0.952364i	$0.598645\pi$
$758$	35.2811	−	7.71636i	1.28147	−	0.280271i
$759$	−8.49577	−	2.57716i	−0.308377	−	0.0935451i
$760$	−0.204343	+	0.504457i	−0.00741230	+	0.0182986i
$761$	28.5551	+	15.2630i	1.03512	+	0.553284i	0.899247	−	0.437442i	$-0.144115\pi$
$761$	28.5551	+	15.2630i	1.03512	+	0.553284i	0.135875	+	0.990726i	$0.456615\pi$
$762$	0.358330	+	3.04484i	0.0129809	+	0.110303i
$763$	21.4952	+	1.05599i	0.778179	+	0.0382295i
$764$	4.94165	−	18.8350i	0.178783	−	0.681425i
$765$	2.64937	−	17.8606i	0.0957881	−	0.645751i
$766$	35.3226	−	9.56349i	1.27626	−	0.345543i
$767$	52.8683			1.90896
$768$	11.2119	−	4.70339i	0.404574	−	0.169719i
$769$	12.9433			0.466748			0.233374	−	0.972387i	$-0.425023\pi$
$769$	12.9433			0.466748			0.233374	+	0.972387i	$0.425023\pi$
$770$	−7.50258	+	2.03130i	−0.270374	+	0.0732029i
$771$	2.13861	−	14.4173i	0.0770202	−	0.519228i
$772$	−9.97063	−	2.61595i	−0.358851	−	0.0941502i
$773$	25.8828	+	1.27154i	0.930941	+	0.0457342i	0.508884	−	0.860835i	$-0.330058\pi$
$773$	25.8828	+	1.27154i	0.930941	+	0.0457342i	0.422057	+	0.906569i	$0.361308\pi$
$774$	−1.33316	−	11.3283i	−0.0479195	−	0.407187i
$775$	−13.0517	−	6.97627i	−0.468830	−	0.250595i
$776$	−30.7607	+	13.0244i	−1.10424	+	0.467549i
$777$	14.5300	+	4.40764i	0.521262	+	0.158123i
$778$	9.37846	−	2.05117i	0.336234	−	0.0735380i
$779$	0.154038	+	0.256997i	0.00551898	+	0.00920786i
$780$	11.6489	+	4.97795i	0.417097	+	0.178239i
$781$	19.8624	−	21.9148i	0.710732	−	0.784172i
$782$	38.8268	+	8.94643i	1.38844	+	0.319924i
$783$	2.20305	−	11.0755i	0.0787306	−	0.395806i
$784$	−15.3068	+	1.16376i	−0.546672	+	0.0415630i
$785$	−0.316791	−	1.59261i	−0.0113067	−	0.0568429i
$786$	−21.2754	−	0.640938i	−0.758870	−	0.0228615i
$787$	18.7761	+	39.6988i	0.669297	+	1.41511i	0.897288	+	0.441446i	$0.145534\pi$
$787$	18.7761	+	39.6988i	0.669297	+	1.41511i	−0.227991	+	0.973663i	$0.573216\pi$
$788$	16.7862	+	5.29705i	0.597983	+	0.188700i
$789$	13.3402	−	17.9872i	0.474923	−	0.640360i
$790$	5.84776	+	5.62999i	0.208054	+	0.200306i
$791$	−4.47327	−	3.67112i	−0.159051	−	0.130530i
$792$	−6.83713	+	11.6122i	−0.242947	+	0.412620i
$793$	−26.5334	−	2.61331i	−0.942229	−	0.0928015i
$794$	0.309887	−	0.607189i	0.0109975	−	0.0215483i
$795$	2.17739	−	4.60370i	0.0772240	−	0.163276i
$796$	8.99410	−	9.70387i	0.318788	−	0.343945i
$797$	−19.5796	+	4.90442i	−0.693544	+	0.173724i	−0.573696	−	0.819069i	$-0.694491\pi$
$797$	−19.5796	+	4.90442i	−0.693544	+	0.173724i	−0.119848	+	0.992792i	$0.538241\pi$
$798$	−0.0159132	−	0.233457i	−0.000563321	−	0.00826427i
$799$	−27.6219	−	11.4414i	−0.977192	−	0.404766i
$800$	13.4602	+	4.86661i	0.475889	+	0.172061i
$801$	23.6156	−	9.78191i	0.834417	−	0.345627i
$802$	1.53948	+	3.10134i	0.0543610	+	0.109512i
$803$	−1.99261	−	1.19433i	−0.0703178	−	0.0421468i
$804$	13.0429	+	8.01653i	0.459986	+	0.282721i
$805$	−5.59305	−	15.6315i	−0.197129	−	0.550939i
$806$	−28.4701	−	33.3791i	−1.00282	−	1.17573i
$807$	4.92222	+	5.99775i	0.173270	+	0.211131i
$808$	−13.3256	−	36.3435i	−0.468793	−	1.27856i
$809$	−5.61495	+	0.553024i	−0.197411	+	0.0194433i	−0.196239	−	0.980556i	$-0.562873\pi$
$809$	−5.61495	+	0.553024i	−0.197411	+	0.0194433i	−0.00117176	+	0.999999i	$0.500373\pi$
$810$	−3.35632	+	8.55857i	−0.117929	+	0.300718i
$811$	47.1620	−	6.99582i	1.65608	−	0.245657i	0.747772	−	0.663955i	$-0.231123\pi$
$811$	47.1620	−	6.99582i	1.65608	−	0.245657i	0.908310	+	0.418298i	$0.137373\pi$
$812$	9.35791	−	2.72517i	0.328398	−	0.0956347i
$813$	−11.6035	−	4.15180i	−0.406953	−	0.145610i
$814$	−28.4991	−	12.8233i	−0.998893	−	0.449456i
$815$	9.83431	−	14.7181i	0.344481	−	0.515552i
$816$	−6.45248	+	12.8911i	−0.225882	+	0.451278i
$817$	−0.226487	−	0.338962i	−0.00792377	−	0.0118588i
$818$	−55.6382	+	9.33505i	−1.94534	+	0.326392i
$819$	22.8208	−	1.12112i	0.797425	−	0.0391750i
$820$	−6.44230	+	4.20151i	−0.224975	+	0.146723i
$821$	−20.6465	−	5.17168i	−0.720567	−	0.180493i	−0.134685	−	0.990889i	$-0.543002\pi$
$821$	−20.6465	−	5.17168i	−0.720567	−	0.180493i	−0.585883	+	0.810396i	$0.699252\pi$
$822$	2.22085	−	12.3888i	0.0774609	−	0.432108i
$823$	12.7199	+	23.7973i	0.443389	+	0.829522i	0.999999	−	0.00125162i	$-0.000398402\pi$
$823$	12.7199	+	23.7973i	0.443389	+	0.829522i	−0.556610	+	0.830774i	$0.687898\pi$
$824$	11.7020	−	9.75784i	0.407659	−	0.339930i
$825$	3.61847	−	1.09765i	0.125979	−	0.0382153i
$826$	21.8801	−	12.2344i	0.761305	−	0.425688i
$827$	11.4926	+	12.6801i	0.399636	+	0.440931i	0.907210	−	0.420677i	$-0.138208\pi$
$827$	11.4926	+	12.6801i	0.399636	+	0.440931i	−0.507574	+	0.861608i	$0.669458\pi$
$828$	−25.8806	−	12.5955i	−0.899412	−	0.437723i
$829$	−8.50980	−	11.4741i	−0.295558	−	0.398513i	0.630321	−	0.776335i	$-0.282923\pi$
$829$	−8.50980	−	11.4741i	−0.295558	−	0.398513i	−0.925879	+	0.377821i	$0.876673\pi$
$830$	7.67946	+	0.990649i	0.266558	+	0.0343859i
$831$	−3.54663	−	3.54663i	−0.123031	−	0.123031i
$832$	31.8808	+	27.9989i	1.10527	+	0.970687i
$833$	12.8700	−	12.8700i	0.445921	−	0.445921i
$834$	1.95173	−	1.50572i	0.0675829	−	0.0521388i
$835$	−9.35967	+	6.94160i	−0.323905	+	0.240224i
$836$	−0.0289915	+	0.480739i	−0.00100269	+	0.0166267i
$837$	−17.8581	+	16.1856i	−0.617265	+	0.559457i
$838$	−32.8403	−	9.28546i	−1.13445	−	0.320761i
$839$	5.15439	+	16.9918i	0.177949	+	0.586621i	0.999856	+	0.0169976i	$0.00541076\pi$
$839$	5.15439	+	16.9918i	0.177949	+	0.586621i	−0.821906	+	0.569623i	$0.807089\pi$
$840$	5.97296	−	0.635514i	0.206087	−	0.0219273i
$841$	−18.9523	+	10.1302i	−0.653527	+	0.349318i
$842$	19.2397	+	27.6443i	0.663045	+	0.952685i
$843$	−3.70889	+	14.8067i	−0.127741	+	0.509970i
$844$	−53.7579	+	10.0716i	−1.85042	+	0.346678i
$845$	1.16672	+	23.7491i	0.0401363	+	0.816993i
$846$	17.5883	+	12.5343i	0.604698	+	0.430938i
$847$	10.5456	−	7.04638i	0.362353	−	0.242116i
$848$	11.7339	−	12.3802i	0.402945	−	0.425139i
$849$	−5.87964	−	3.92865i	−0.201789	−	0.134831i
$850$	−15.8669	+	6.01917i	−0.544230	+	0.206456i
$851$	22.4876	−	62.8487i	0.770865	−	2.15442i
$852$	−17.8288	+	14.3022i	−0.610805	+	0.489984i
$853$	7.48814	+	50.4809i	0.256389	+	1.72843i	0.609441	+	0.792831i	$0.291394\pi$
$853$	7.48814	+	50.4809i	0.256389	+	1.72843i	−0.353052	+	0.935604i	$0.614856\pi$
$854$	−11.5859	+	5.05860i	−0.396460	+	0.173102i
$855$	0.0456925	+	0.463924i	0.00156265	+	0.0158659i
$856$	−5.65666	−	36.1812i	−0.193340	−	1.23665i
$857$	29.5436	−	24.2458i	1.00919	−	0.828221i	0.0240046	−	0.999712i	$-0.492358\pi$
$857$	29.5436	−	24.2458i	1.00919	−	0.828221i	0.985186	+	0.171491i	$0.0548584\pi$
$858$	11.1744	+	0.886909i	0.381486	+	0.0302786i
$859$	−23.8911	+	8.54838i	−0.815154	+	0.291667i	−0.711267	−	0.702922i	$-0.751878\pi$
$859$	−23.8911	+	8.54838i	−0.815154	+	0.291667i	−0.103888	+	0.994589i	$0.533128\pi$
$860$	8.47426	−	6.13973i	0.288970	−	0.209363i
$861$	1.69998	−	2.83625i	0.0579353	−	0.0966592i
$862$	4.64341	−	13.7972i	0.158155	−	0.469933i
$863$	−5.46177	−	13.1859i	−0.185921	−	0.448852i	0.803246	−	0.595647i	$-0.203104\pi$
$863$	−5.46177	−	13.1859i	−0.185921	−	0.448852i	−0.989167	+	0.146795i	$0.953104\pi$
$864$	14.8473	−	17.9695i	0.505115	−	0.611333i
$865$	8.12952	−	19.6264i	0.276412	−	0.667318i
$866$	−31.3036	−	27.3084i	−1.06374	−	0.927978i
$867$	−1.01415	−	4.04870i	−0.0344422	−	0.137501i
$868$	−19.5069	−	7.22594i	−0.662109	−	0.245265i
$869$	6.49328	+	3.07109i	0.220270	+	0.104180i
$870$	4.40283	−	1.42733i	0.149270	−	0.0483912i
$871$	−5.23671	+	53.1693i	−0.177439	+	1.80157i
$872$	32.3187	+	11.2793i	1.09445	+	0.381966i
$873$	−18.1505	+	22.1165i	−0.614302	+	0.748530i
$874$	−1.02851	+	0.0195140i	−0.0347898	+	0.000660070i
$875$	16.9030	+	12.5361i	0.571426	+	0.423798i
$876$	1.37500	+	1.15432i	0.0464569	+	0.0390008i
$877$	13.4741	−	6.37279i	0.454989	−	0.215194i	−0.186301	−	0.982493i	$-0.559650\pi$
$877$	13.4741	−	6.37279i	0.454989	−	0.215194i	0.641289	+	0.767299i	$0.278400\pi$
$878$	−0.320719	−	0.340643i	−0.0108237	−	0.0114961i
$879$	−5.05632	+	1.00576i	−0.170545	+	0.0339236i
$880$	−12.3598	−	0.275565i	−0.416648	−	0.00928931i
$881$	−42.7478	−	8.50307i	−1.44021	−	0.286476i	−0.587654	−	0.809112i	$-0.699949\pi$
$881$	−42.7478	−	8.50307i	−1.44021	−	0.286476i	−0.852556	+	0.522636i	$0.824949\pi$
$882$	−11.1473	+	6.97219i	−0.375347	+	0.234766i
$883$	−29.3555	−	26.6062i	−0.987890	−	0.895371i	0.00662372	−	0.999978i	$-0.497892\pi$
$883$	−29.3555	−	26.6062i	−0.987890	−	0.895371i	−0.994514	+	0.104607i	$0.966642\pi$
$884$	−50.3045	−	0.560708i	−1.69192	−	0.0188587i
$885$	10.2106	−	6.12000i	0.343225	−	0.205721i
$886$	−11.1994	−	7.17968i	−0.376250	−	0.241206i
$887$	2.02148	−	6.66394i	0.0678748	−	0.223753i	−0.916441	−	0.400171i	$-0.868951\pi$
$887$	2.02148	−	6.66394i	0.0678748	−	0.223753i	0.984315	+	0.176417i	$0.0564509\pi$
$888$	20.1849	+	13.2598i	0.677360	+	0.444971i
$889$	−2.39146	+	4.47410i	−0.0802068	+	0.150056i
$890$	18.4067	+	14.5305i	0.616994	+	0.487064i
$891$	−0.399154	+	8.12497i	−0.0133722	+	0.272197i
$892$	25.1769	−	33.1681i	0.842986	−	1.11055i
$893$	0.763542	+	0.113261i	0.0255509	+	0.00379013i
$894$	−12.8115	−	7.35224i	−0.428481	−	0.245896i
$895$		−	1.02061i		−	0.0341151i
$896$	19.6734	+	4.21003i	0.657243	+	0.140647i
$897$			23.9428i			0.799427i
$898$	1.58808	−	2.76728i	0.0529950	−	0.0923454i
$899$	−15.8556	−	2.35196i	−0.528814	−	0.0784422i
$900$	12.1456	−	1.66351i	0.404854	−	0.0554502i
$901$	−0.992356	+	20.1999i	−0.0330602	+	0.672955i
$902$	−4.21698	+	5.34192i	−0.140410	+	0.177866i
$903$	−2.12084	+	3.96781i	−0.0705772	+	0.132041i
$904$	−5.17332	−	7.61278i	−0.172062	−	0.253197i
$905$	5.48818	−	18.0921i	0.182433	−	0.601402i
$906$	8.64957	−	13.4922i	0.287363	−	0.448249i
$907$	−23.0332	+	13.8056i	−0.764805	+	0.458406i	−0.842584	−	0.538564i	$-0.818967\pi$
$907$	−23.0332	+	13.8056i	−0.764805	+	0.458406i	0.0777798	+	0.996971i	$0.475217\pi$
$908$	18.3621	−	17.9573i	0.609368	−	0.595933i
$909$	−24.5659	−	22.2653i	−0.814800	−	0.738492i
$910$	11.1157	+	17.7719i	0.368481	+	0.589133i
$911$	−43.2733	−	8.60759i	−1.43371	−	0.285182i	−0.583707	−	0.811964i	$-0.698398\pi$
$911$	−43.2733	−	8.60759i	−1.43371	−	0.285182i	−0.850000	+	0.526782i	$0.823398\pi$
$912$	0.0807282	−	0.363325i	0.00267318	−	0.0120309i
$913$	6.72000	−	1.33669i	0.222400	−	0.0442380i
$914$	−35.8728	+	33.7746i	−1.18657	+	1.11716i
$915$	−5.42698	+	2.56677i	−0.179410	+	0.0848548i
$916$	0.583822	+	6.69142i	0.0192900	+	0.221091i
$917$	−28.2896	−	20.9810i	−0.934206	−	0.692855i
$918$	0.524270	+	27.6324i	0.0173035	+	0.912004i
$919$	0.551217	−	0.671660i	0.0181830	−	0.0221560i	−0.763840	−	0.645406i	$-0.776688\pi$
$919$	0.551217	−	0.671660i	0.0181830	−	0.0221560i	0.782023	+	0.623250i	$0.214188\pi$
$920$	−1.50203	−	26.3635i	−0.0495206	−	0.869180i
$921$	0.401945	−	4.08102i	0.0132445	−	0.134474i
$922$	−10.1580	−	31.3338i	−0.334534	−	1.03192i
$923$	−72.1055	−	34.1034i	−2.37338	−	1.12253i
$924$	4.82986	−	2.21882i	0.158891	−	0.0729939i
$925$	6.90795	+	27.5781i	0.227132	+	0.906761i
$926$	−37.8828	+	43.4250i	−1.24491	+	1.42703i
$927$	4.99406	−	12.0567i	0.164026	−	0.395995i
$928$	15.5024	+	0.0514816i	0.508891	+	0.00168997i
$929$	18.7172	+	45.1874i	0.614092	+	1.48255i	0.858467	+	0.512869i	$0.171417\pi$
$929$	18.7172	+	45.1874i	0.614092	+	1.48255i	−0.244374	+	0.969681i	$0.578583\pi$
$930$	−9.36244	−	3.15091i	−0.307006	−	0.103322i
$931$	−0.241583	+	0.403057i	−0.00791756	+	0.0132097i
$932$	−58.0183	−	9.26821i	−1.90045	−	0.303590i
$933$	−9.62018	+	3.44215i	−0.314950	+	0.112691i
$934$	−1.54997	+	19.5284i	−0.0507164	+	0.638987i
$935$	11.3309	−	9.29900i	0.370559	−	0.304110i
$936$	35.3203	+	8.55413i	1.15448	+	0.279600i
$937$	4.01594	+	40.7745i	0.131195	+	1.33205i	0.805061	+	0.593192i	$0.202132\pi$
$937$	4.01594	+	40.7745i	0.131195	+	1.33205i	−0.673866	+	0.738853i	$0.735368\pi$
$938$	10.1367	+	23.2165i	0.330976	+	0.758044i
$939$	−2.56233	−	17.2738i	−0.0836185	−	0.563710i
$940$	−2.16181	+	19.6961i	−0.0705103	+	0.642415i
$941$	1.13998	−	3.18604i	0.0371624	−	0.103862i	−0.921530	−	0.388308i	$-0.873060\pi$
$941$	1.13998	−	3.18604i	0.0371624	−	0.103862i	0.958692	+	0.284446i	$0.0918097\pi$
$942$	0.393848	+	1.03821i	0.0128323	+	0.0338266i
$943$	−12.0869	−	8.07621i	−0.393604	−	0.262998i
$944$	38.8837	−	8.82365i	1.26556	−	0.287185i
$945$	9.57499	−	6.39780i	0.311474	−	0.208121i
$946$	5.37404	−	7.54092i	0.174725	−	0.245177i
$947$	1.61994	+	32.9747i	0.0526411	+	1.07153i	0.869260	+	0.494356i	$0.164596\pi$
$947$	1.61994	+	32.9747i	0.0526411	+	1.07153i	−0.816618	+	0.577178i	$0.804154\pi$
$948$	−4.58074	−	3.13516i	−0.148776	−	0.101825i
$949$	−1.52230	+	6.07738i	−0.0494161	+	0.197280i
$950$	0.359614	−	0.250282i	0.0116674	−	0.00812023i
$951$	−7.16241	+	3.82839i	−0.232257	+	0.124144i
$952$	−20.9488	+	11.4090i	−0.678953	+	0.369768i
$953$	9.81261	+	32.3478i	0.317862	+	1.04785i	0.959704	+	0.281013i	$0.0906703\pi$
$953$	9.81261	+	32.3478i	0.317862	+	1.04785i	−0.641843	+	0.766836i	$0.721830\pi$
$954$	3.97499	−	14.0585i	0.128695	−	0.455161i
$955$	11.3373	−	10.2756i	0.366868	−	0.332509i
$956$	32.3756	+	36.5311i	1.04710	+	1.18150i
$957$	3.28958	−	2.43972i	0.106337	−	0.0788650i
$958$	29.5471	+	38.2993i	0.954624	+	1.23739i
$959$	14.7267	−	14.7267i	0.475550	−	0.475550i
$960$	9.39834	+	1.71701i	0.303330	+	0.0554161i
$961$	2.27050	+	2.27050i	0.0732419	+	0.0732419i
$962$	−10.7827	+	83.5873i	−0.347650	+	2.69496i
$963$	−18.6844	−	25.1931i	−0.602098	−	0.811835i
$964$	12.8420	+	37.1928i	0.413614	+	1.19790i
$965$	−5.43956	−	6.00163i	−0.175106	−	0.193199i
$966$	5.54065	+	9.90897i	0.178267	+	0.318816i
$967$	−36.8410	+	11.1756i	−1.18473	+	0.359383i	−0.820346	−	0.571868i	$-0.806219\pi$
$967$	−36.8410	+	11.1756i	−1.18473	+	0.359383i	−0.364380	+	0.931250i	$0.618719\pi$
$968$	19.2581	−	6.00683i	0.618978	−	0.193067i
$969$	0.208020	+	0.389178i	0.00668256	+	0.0125022i
$970$	−25.8367	−	4.63156i	−0.829566	−	0.148710i
$971$	−24.6030	−	6.16273i	−0.789548	−	0.197771i	−0.172826	−	0.984952i	$-0.555290\pi$
$971$	−24.6030	−	6.16273i	−0.789548	−	0.197771i	−0.616722	+	0.787181i	$0.711540\pi$
$972$	6.38840	−	30.3450i	0.204908	−	0.973317i
$973$	4.07404	−	0.200145i	0.130608	−	0.00641635i
$974$	−4.39831	−	26.2145i	−0.140931	−	0.839968i
$975$	−5.66548	−	8.47900i	−0.181441	−	0.271545i
$976$	−19.9510	+	2.50635i	−0.638615	+	0.0802262i
$977$	−8.37975	+	12.5412i	−0.268092	+	0.401228i	−0.940951	−	0.338543i	$-0.890066\pi$
$977$	−8.37975	+	12.5412i	−0.268092	+	0.401228i	0.672859	+	0.739771i	$0.265066\pi$
$978$	−4.96685	+	11.0386i	−0.158822	+	0.352975i
$979$	19.5380	+	6.99081i	0.624437	+	0.223427i
$980$	−10.5741	−	5.80444i	−0.337779	−	0.185416i
$981$	29.0010	−	4.30189i	0.925930	−	0.137349i
$982$	−13.5731	−	5.32281i	−0.433135	−	0.169858i
$983$	18.1063	−	1.78331i	0.577500	−	0.0568788i	0.194949	−	0.980813i	$-0.437546\pi$
$983$	18.1063	−	1.78331i	0.577500	−	0.0568788i	0.382551	+	0.923935i	$0.375046\pi$
$984$	3.86925	−	3.56243i	0.123347	−	0.113566i
$985$	8.77456	+	10.6918i	0.279581	+	0.340670i
$986$	−13.9847	+	11.9280i	−0.445363	+	0.379864i
$987$	−2.86988	−	8.02079i	−0.0913494	−	0.255304i
$988$	1.26335	−	0.301530i	0.0401926	−	0.00959294i
$989$	16.9647	+	10.1682i	0.539445	+	0.323331i
$990$	−9.48453	+	4.70805i	−0.301438	+	0.149632i
$991$	11.7999	−	4.88769i	0.374837	−	0.155263i	−0.187308	−	0.982301i	$-0.559976\pi$
$991$	11.7999	−	4.88769i	0.374837	−	0.155263i	0.562145	+	0.827039i	$0.309976\pi$
$992$	−26.5101	−	19.7981i	−0.841698	−	0.628589i
$993$	16.2476	+	6.72998i	0.515602	+	0.213570i
$994$	−37.7335	+	2.57204i	−1.19683	+	0.0815803i
$995$	10.0851	−	2.52618i	0.319719	−	0.0800853i
$996$	−5.29108	+	0.200848i	−0.167654	+	0.00636412i
$997$	25.1918	−	53.2636i	0.797833	−	1.68688i	0.0736344	−	0.997285i	$-0.476540\pi$
$997$	25.1918	−	53.2636i	0.797833	−	1.68688i	0.724199	−	0.689591i	$-0.242210\pi$
$998$	−51.7030	−	26.3873i	−1.63663	−	0.835275i
$999$	46.0776	+	4.53825i	1.45783	+	0.143584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.15	✓	992
256.205	even	64	inner	256.2.m.a.205.15	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.15	✓	992	1.1	even	1	trivial
256.2.m.a.205.15	yes	992	256.205	even	64	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:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.369587 - 1.36507i) q^{2} +(-0.111501 + 0.751680i) q^{3} +(-1.72681 + 1.00902i) q^{4} +(-1.56967 - 0.0771129i) q^{5} +(1.06730 - 0.125605i) q^{6} +(1.56830 + 0.838272i) q^{7} +(2.01559 + 1.98429i) q^{8} +(2.31823 + 0.703228i) q^{9} +O(q^{10})\)	\(q+(-0.369587 - 1.36507i) q^{2} +(-0.111501 + 0.751680i) q^{3} +(-1.72681 + 1.00902i) q^{4} +(-1.56967 - 0.0771129i) q^{5} +(1.06730 - 0.125605i) q^{6} +(1.56830 + 0.838272i) q^{7} +(2.01559 + 1.98429i) q^{8} +(2.31823 + 0.703228i) q^{9} +(0.474865 + 2.17120i) q^{10} +(1.01106 + 1.68685i) q^{11} +(-0.565920 - 1.41052i) q^{12} +(3.56180 - 3.92984i) q^{13} +(0.564674 - 2.45064i) q^{14} +(0.232984 - 1.17129i) q^{15} +(1.96375 - 3.48478i) q^{16} +(0.925241 + 4.65150i) q^{17} +(0.103164 - 3.42444i) q^{18} +(-0.0523519 - 0.110689i) q^{19} +(2.78833 - 1.45067i) q^{20} +(-0.804979 + 1.08539i) q^{21} +(1.92899 - 2.00360i) q^{22} +(4.59216 + 3.76868i) q^{23} +(-1.71629 + 1.29383i) q^{24} +(-2.51801 - 0.248003i) q^{25} +(-6.68088 - 3.40967i) q^{26} +(-1.76179 + 3.72499i) q^{27} +(-3.55399 + 0.134909i) q^{28} +(-2.65835 + 0.665882i) q^{29} +(-1.68500 + 0.114855i) q^{30} +(5.40378 + 2.23832i) q^{31} +(-5.48273 - 1.39272i) q^{32} +(-1.38071 + 0.571908i) q^{33} +(6.00765 - 2.98215i) q^{34} +(-2.39706 - 1.43674i) q^{35} +(-4.71272 + 1.12480i) q^{36} +(-3.78540 - 10.5795i) q^{37} +(-0.131749 + 0.112373i) q^{38} +(2.55683 + 3.11551i) q^{39} +(-3.01079 - 3.27010i) q^{40} +(-2.43524 + 0.239850i) q^{41} +(1.77914 + 0.697704i) q^{42} +(3.29335 - 0.488522i) q^{43} +(-3.44798 - 1.89269i) q^{44} +(-3.58463 - 1.28260i) q^{45} +(3.44730 - 7.66145i) q^{46} +(-3.50234 + 5.24162i) q^{47} +(2.40048 + 1.86467i) q^{48} +(-2.13214 - 3.19097i) q^{49} +(0.592085 + 3.52891i) q^{50} +(-3.59960 + 0.176837i) q^{51} +(-2.18526 + 10.3800i) q^{52} +(4.13656 + 1.03615i) q^{53} +(5.73600 + 1.02825i) q^{54} +(-1.45695 - 2.72577i) q^{55} +(1.49767 + 4.80156i) q^{56} +(0.0890398 - 0.0270099i) q^{57} +(1.89147 + 3.38272i) q^{58} +(6.69414 + 7.38585i) q^{59} +(0.779538 + 2.25768i) q^{60} +(-2.99455 - 4.03768i) q^{61} +(1.05829 - 8.20378i) q^{62} +(3.04618 + 3.04618i) q^{63} +(0.125194 + 7.99902i) q^{64} +(-5.89388 + 5.89388i) q^{65} +(1.29098 + 1.67339i) q^{66} +(-8.09095 + 6.00066i) q^{67} +(-6.29118 - 7.09867i) q^{68} +(-3.34488 + 3.03162i) q^{69} +(-1.07533 + 3.80315i) q^{70} +(-4.36560 - 14.3915i) q^{71} +(3.27719 + 6.01746i) q^{72} +(-1.04178 + 0.556842i) q^{73} +(-13.0427 + 9.07737i) q^{74} +(0.467180 - 1.86509i) q^{75} +(0.202089 + 0.138314i) q^{76} +(0.171602 + 3.49303i) q^{77} +(3.30791 - 4.64170i) q^{78} +(3.03683 - 2.02914i) q^{79} +(-3.35116 + 5.31852i) q^{80} +(3.43926 + 2.29804i) q^{81} +(1.22744 + 3.23561i) q^{82} +(1.17370 - 3.28026i) q^{83} +(0.294866 - 2.68650i) q^{84} +(-1.09363 - 7.37266i) q^{85} +(-1.88405 - 4.31509i) q^{86} +(-0.204121 - 2.07248i) q^{87} +(-1.30932 + 5.40624i) q^{88} +(8.15638 - 6.69377i) q^{89} +(-0.426001 + 5.36728i) q^{90} +(8.88022 - 3.17739i) q^{91} +(-11.7325 - 1.87422i) q^{92} +(-2.28503 + 3.81234i) q^{93} +(8.44957 + 2.84369i) q^{94} +(0.0736395 + 0.177782i) q^{95} +(1.65821 - 3.96597i) q^{96} +(-4.51959 + 10.9112i) q^{97} +(-3.56787 + 4.08985i) q^{98} +(1.15763 + 4.62152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

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Fields

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Database

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